Finite Group Databasebeta

← #28265485

Subgroups — #28265485

Order 13568.

1932 conjugacy classes of subgroups.

The subgroup lattice has 1784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288605C211yesmaximal, characteristic, complemented
2#20288559C211yesmaximal, characteristic, complemented
3#20287804C211yesmaximal, characteristic, complemented
4#20287798C211yesmaximal, characteristic, complemented
5#20287795C211yesmaximal, characteristic, complemented
6#20287790C211yesmaximal, characteristic, complemented
7#20287788C211yesmaximal, characteristic, complemented
8#20287783C211yesmaximal, characteristic, complemented
9#20287778C211yesmaximal, characteristic, complemented
10#20287776C211yesmaximal, characteristic, complemented
11#20287757C211yesmaximal, characteristic, complemented
12#20287754C211yesmaximal, characteristic, complemented
13#20287730C211yesmaximal, characteristic, complemented
14#20287727C211yesmaximal, characteristic, complemented
15#20287726C211yesmaximal, characteristic, complemented
16#20287716C211yesmaximal, characteristic, complemented
17#20287714C211yesmaximal, characteristic, complemented
18#20285199C211yesmaximal, characteristic, complemented
19#20285184C211yesmaximal, characteristic, complemented
20#20285180C211yesmaximal, characteristic, complemented
21#20284260C211yesmaximal, characteristic, complemented
22#20284255C211yesmaximal, characteristic, complemented
23#20284231C211yesmaximal, characteristic, complemented
24#20284213C211yesmaximal, characteristic, complemented
25#20284165C211yesmaximal, characteristic, complemented
26#463×D53C211yesmaximal, characteristic, complemented
27#20283660C211yesmaximal, characteristic, complemented
28#20283555C211yesmaximal, characteristic, complemented
29#20283540C211yesmaximal, characteristic, complemented
30#20283520C211yesmaximal, characteristic, complemented
31C53×#3397C211yesmaximal, characteristic, complemented
32C2×#13133246C2211yescharacteristic
33C2×#13133246C2211yescharacteristic
34C2×#13133244C2211yescharacteristic
35C2×#13133241C2211yescharacteristic
36C2×#13133241C2211yescharacteristic
37C2×#13133238C2211yescharacteristic
38C2×#13133238C2211yescharacteristic
39C2×SD16×D53C2211yescharacteristic
40C2×D8×D53C2211yescharacteristic
41#16811359C2211yescharacteristic, complemented
42#16811359C2211yescharacteristic, complemented
43#16811358C2211yescharacteristic, complemented
44#16811358C2211yescharacteristic, complemented
45#16811356C2211yescharacteristic, complemented
46#16811356C2211yescharacteristic, complemented
47#16811356C2211yescharacteristic, complemented
48#16811355C2211yescharacteristic, complemented
49#16811347C2211yescharacteristic, complemented
50#16811346C2211yescharacteristic, complemented
51#16811345C2211yescharacteristic, complemented
52#16811343C2211yescharacteristic, complemented
53#16811342C2211yescharacteristic, complemented
54#16811337—21no—
55#16811316—21no—
56#16811316—21no—
57#16811300—21no—
58#16811298—21no—
59#16811298—21no—
60#16811297—21no—
61#16811293C2211yescharacteristic, complemented
62#16811272—21no—
63#16811243—21no—
64#16811239—21no—
65#16811205—21no—
66#16811205—21no—
67#16811198C2211yescharacteristic
68#16811191C2211yescharacteristic
69#16811186C2211yescharacteristic
70#16811186C2211yescharacteristic
71#16811177C2211yescharacteristic
72#16811171C2211yescharacteristic
73#16811156—21no—
74#16811151—21no—
75#124×D53C2211yescharacteristic
76#16811133—21no—
77#16811130—21no—
78#16811102C2211yescharacteristic
79#16811102C2211yescharacteristic
80#16811099C2211yescharacteristic
81#16811095C2211yescharacteristic
82C4×#11719949C2211yescharacteristic
83C4×D4×D53C2211yescharacteristic
84#16811018C2211yescharacteristic, complemented
85#16811017C2211yescharacteristic, complemented
86#16811015C2211yescharacteristic, complemented
87#16811014C2211yescharacteristic, complemented
88#16811012C2211yescharacteristic
89#16811011C2211yescharacteristic
90#16811010C2211yescharacteristic, complemented
91#16811010C2211yescharacteristic, complemented
92#16811009C2211yescharacteristic
93#16811009C2211yescharacteristic, complemented
94#16811007C2211yescharacteristic, complemented
95#16811006C2211yescharacteristic, complemented
96#16811006C2211yescharacteristic, complemented
97#16811005C2211yescharacteristic
98#16811004C2211yescharacteristic
99#16811004C2211yescharacteristic, complemented
100#16811004C2211yescharacteristic, complemented
101#16811004C2211yescharacteristic, complemented
102#16810999C2211yescharacteristic
103#16810998C2211yescharacteristic
104#16810994C2211yescharacteristic, complemented
105#16810848C2211yescharacteristic, complemented
106#16810848C2211yescharacteristic, complemented
107#16810846C2211yescharacteristic, complemented
108#16810846C2211yescharacteristic, complemented
109#16810845C2211yescharacteristic, complemented
110#16810844C2211yescharacteristic, complemented
111#16810843C2211yescharacteristic, complemented
112#16810843C2211yescharacteristic, complemented
113#16810843C2211yescharacteristic, complemented
114#16810842C2211yescharacteristic, complemented
115#16810841C2211yescharacteristic
116#16810840C2211yescharacteristic
117#16810840C2211yescharacteristic, complemented
118#16810840C2211yescharacteristic, complemented
119#16810839C2211yescharacteristic
120#16810839C2211yescharacteristic
121#16810838C2211yescharacteristic
122#16810838C2211yescharacteristic
123#16810838C2211yescharacteristic, complemented
124#16810837C2211yescharacteristic
125#16810837C2211yescharacteristic
126#16810837C2211yescharacteristic, complemented
127#16810837C2211yescharacteristic, complemented
128#16810836C2211yescharacteristic
129#16810836C2211yescharacteristic
130#16810835C2211yescharacteristic
131#16810833C2211yescharacteristic, complemented
132#16810832C2211yescharacteristic, complemented
133#16810830C2211yescharacteristic, complemented
134#16810829C2211yescharacteristic, complemented
135#16810826C2211yescharacteristic, complemented
136#16810824C2211yescharacteristic, complemented
137#16810822C2211yescharacteristic, complemented
138#16810822C2211yescharacteristic, complemented
139#16810821C2211yescharacteristic, complemented
140#16810820C2211yescharacteristic, complemented
141#16810818C2211yescharacteristic, complemented
142#16810817C2211yescharacteristic
143#16810816C2211yescharacteristic
144#16810816C2211yescharacteristic, complemented
145#16810815C2211yescharacteristic
146#16810815C2211yescharacteristic, complemented
147#16810754C2211yescharacteristic, complemented
148#16810752C2211yescharacteristic, complemented
149#16810752C2211yescharacteristic, complemented
150#16810751C2211yescharacteristic, complemented
151#16810751C2211yescharacteristic, complemented
152C8×Dic106C2211yescharacteristic, complemented
153#16810747C2211yescharacteristic, complemented
154#16810736C2211yescharacteristic, complemented
155#16810735C2211yescharacteristic, complemented
156#16810733C2211yescharacteristic, complemented
157#16810733C2211yescharacteristic, complemented
158#16810731C2211yescharacteristic, complemented
159#16810727C2211yescharacteristic, complemented
160#16810723C2211yescharacteristic, complemented
161#16810722C2211yescharacteristic, complemented
162#16810721C2211yescharacteristic, complemented
163#16810720C2211yescharacteristic, complemented
164#16810717C2211yescharacteristic, complemented
165C4×#11719925C2211yescharacteristic, complemented
166#16810714C2211yescharacteristic, complemented
167C4×#11719913C2211yescharacteristic, complemented
168SD16×Dic53C2211yescharacteristic, complemented
169SD16×Dic53C2211yescharacteristic, complemented
170C4×#11719923C2211yescharacteristic, complemented
171#16810708C2211yescharacteristic, complemented
172#16810705C2211yescharacteristic, complemented
173#16810703C2211yescharacteristic, complemented
174#16810703C2211yescharacteristic, complemented
175#16810664C2211yescharacteristic
176#16810648C2211yescharacteristic
177#16810648C2211yescharacteristic
178C4⋊C8×D53C2211yescharacteristic
179#16810626C2211yescharacteristic
180#16810623C2211yescharacteristic
181#16810616C2211yescharacteristic
182#16810616C2211yescharacteristic
183#103×D53C2211yescharacteristic
184#102×D53C2211yescharacteristic
185#16810580C2211yescharacteristic
186#16810577C2211yescharacteristic
187#16810575C2211yescharacteristic
188C53×#556C2211yescharacteristic, complemented
189C53×#550C2211yescharacteristic, complemented
190C53×#496C2211yescharacteristic
191C53×#496C2211yescharacteristic, complemented
192C53×#492C2211yescharacteristic, complemented
193C53×#463C2211yescharacteristic
194C53×#463C2211yescharacteristic, complemented
195C53×#461C2211yescharacteristic, complemented
196C53×#460C2211yescharacteristic, complemented
197C53×#460C2211yescharacteristic, complemented
198C53×#459C2211yescharacteristic
199C53×#446C2211yescharacteristic, complemented
200C53×#440C2211yescharacteristic, complemented
201C53×#440C2211yescharacteristic, complemented
202C4×D8×C53C2211yescharacteristic, complemented
203C2×#11719949C2311yescharacteristic
204C2×#11719947—21no—
205C2×#11719947C2311yescharacteristic
206C2×#11719947C2311yescharacteristic
207C2×Q8×D53C2311yescharacteristic
208C2×D4×D53C2311yescharacteristic
209C2×D4×D53C2311yescharacteristic
210C22×C4×D53—21no—
211#13133246—24no—
212#13133246—42no—
213#13133244—24no—
214#13133241—24no—
215#13133241—42no—
216#13133238—42no—
217#13133238—42no—
218C2×Dic212C2311yescharacteristic
219C2×Dic212C2311yescharacteristic
220C2×#11719925C2311yescharacteristic
221C2×#11719925C2311yescharacteristic
222C2×#11719925C2311yescharacteristic
223C2×#11719925C2311yescharacteristic
224C2×#11719913C2311yescharacteristic
225C2×#11719913C2311yescharacteristic
226C2×#11719913C2311yescharacteristic
227C2×#11719913C2311yescharacteristic
228C2×#11719913C2311yescharacteristic
229C2×#11719923C2311yescharacteristic
230C2×#11719923C2311yescharacteristic
231C2×#11719923C2311yescharacteristic
232C2×#11719923C2311yescharacteristic
233C2×#11719923C2311yescharacteristic
234C2×#11719924C2311yescharacteristic
235C2×#11719924C2311yescharacteristic
236SD16×D53—42no—
237C2×D424C2311yescharacteristic
238C2×D424C2311yescharacteristic
239C2×#11719922C2311yescharacteristic
240C2×#11719922C2311yescharacteristic
241C2×#11719922C2311yescharacteristic
242C2×#11719922C2311yescharacteristic
243C2×#11719922C2311yescharacteristic
244C2×#11719922C2311yescharacteristic
245C2×#11719922C2311yescharacteristic
246D8×D53—42no—
247C2×#11719912C2311yescharacteristic
248C2×#11719912C2311yescharacteristic
249C2×C8×D53C2311yescharacteristic
250C2×C8×D53C2311yescharacteristic
251#13133217C2311yescharacteristic
252#13133216D411yescharacteristic
253#13133215D411yescharacteristic
254#13133215C2311yescharacteristic
255#13133214C2311yescharacteristic
256#13133213C2311yescharacteristic
257#13133213C2311yescharacteristic
258#13133213C2311yescharacteristic
259#13133212—21no—
260#13133212—21no—
261#13133212—21no—
262#13133212—21no—
263#13133212—21no—
264#13133211—21no—
265#13133210—21no—
266#13133210—21no—
267#13133210—21no—
268#13133210—21no—
269#13133207D411yescharacteristic
270#13133207D411yescharacteristic
271#13133206—21no—
272#13133206C2311yescharacteristic
273#13133206C2311yescharacteristic
274#13133206C2311yescharacteristic
275#13133205—21no—
276#13133205C2311yescharacteristic
277#13133205C2311yescharacteristic
278#13133205C2311yescharacteristic
279#13133205C2311yescharacteristic
280#13133204—21no—
281#13133204—21no—
282#13133204C2311yescharacteristic
283#13133204C2311yescharacteristic
284#13133204C2311yescharacteristic
285#13133204C2311yescharacteristic
286#13133204C2311yescharacteristic
287#13133203—21no—
288#13133203—21no—
289#13133203—21no—
290#13133203—21no—
291#13133203—21no—
292#13133203—21no—
293#13133202—21no—
294#13133202—21no—
295#13133202—21no—
296#13133202—21no—
297#13133202—21no—
298#13133202—21no—
299#13133201—21no—
300#13133200—21no—
301#13133200—21no—
302#13133200—21no—
303#13133199—21no—
304#13133199—21no—
305#13133199—21no—
306#13133199—21no—
307#13133198—21no—
308#13133198—21no—
309#13133198—21no—
310#13133198—21no—
311#13133197—21no—
312#13133197D411yescharacteristic
313#13133196—21no—
314#13133195—21no—
315#13133195—21no—
316#13133195—21no—
317#13133195D411yescharacteristic
318#13133195D411yescharacteristic
319#13133194—21no—
320#13133193—21no—
321#13133193D411yescharacteristic
322#13133190—21no—
323#13133190—21no—
324#13133189—21no—
325#13133189—21no—
326#13133189—21no—
327#13133189—21no—
328#13133189—21no—
329#13133189—21no—
330#13133188—21no—
331#13133188—21no—
332#13133188—21no—
333#13133187—21no—
334#13133187—21no—
335#13133185—21no—
336#13133185—21no—
337#13133185—21no—
338#13133185—21no—
339Q8×Dic53C2311yescharacteristic
340Q8×Dic53C2311yescharacteristic
341C4×Dic106—21no—
342C4×Dic106C2311yescharacteristic
343C4×Dic106C2311yescharacteristic
344C4×Dic106C2311yescharacteristic
345C4×Dic106C2311yescharacteristic
346C4×Dic106C2311yescharacteristic
347C4×Dic106C2311yescharacteristic
348#13133182—21no—
349#13133182C2311yescharacteristic
350#13133182C2311yescharacteristic
351#13133182C2311yescharacteristic
352C4×D212—21no—
353C4×D212—21no—
354C4×D212C2311yescharacteristic
355C4×D212C2311yescharacteristic
356C4×D212C2311yescharacteristic
357D4×Dic53—21no—
358D4×Dic53—21no—
359D4×Dic53—21no—
360D4×Dic53—21no—
361D4×Dic53C2311yescharacteristic
362D4×Dic53C2311yescharacteristic
363D4×Dic53C2311yescharacteristic
364D4×Dic53C2311yescharacteristic
365#13133179—21no—
366#13133179—21no—
367#13133179C2311yescharacteristic
368#13133179C2311yescharacteristic
369#13133179C2311yescharacteristic
370C4×C22⋊D53—21no—
371C4×C22⋊D53—21no—
372C4×C22⋊D53—21no—
373C4×C22⋊D53—21no—
374C4×C22⋊D53—21no—
375C4×C22⋊D53—21no—
376C4×C22⋊D53—21no—
377#13133177—21no—
378#13133177—21no—
379#13133177—21no—
380#13133177—21no—
381#13133177—21no—
382#13133176—21no—
383#13133175—21no—
384#13133175—21no—
385#13133175—21no—
386#13133175—21no—
387#13133175C2311yescharacteristic
388#13133174—21no—
389#13133174—21no—
390#13133174C2311yescharacteristic
391#13133174C2311yescharacteristic
392#13133173—21no—
393#13133173—21no—
394#13133173—21no—
395C2×#11719919—21no—
396C2×#11719919—21no—
397C4⋊C4×D53C2311yescharacteristic
398C2×#11719921—21no—
399C22⋊C4×D53—21no—
400C22⋊C4×D53—21no—
401C22⋊C4×D53—21no—
402C22⋊C4×D53—21no—
403C42×D53—21no—
404C42×D53C2311yescharacteristic
405#13133150C2311yescharacteristic
406#13133149C2311yescharacteristic
407#13133148C2311yescharacteristic
408C4⋊#88322C2311yescharacteristic
409C4⋊#88322C2311yescharacteristic
410C4⋊#88322C2311yescharacteristic
411#13133146C2311yescharacteristic
412#13133146C2311yescharacteristic
413#13133146C2311yescharacteristic
414#13133146C2311yescharacteristic
415#13133146C2311yescharacteristic
416#13133146C2311yescharacteristic
417#13133142C2311yescharacteristic
418#13133142C2311yescharacteristic
419#13133142C2311yescharacteristic
420#13133141C2311yescharacteristic
421#13133141C2311yescharacteristic
422#13133140C2311yescharacteristic
423#13133140C2311yescharacteristic
424#13133140C2311yescharacteristic
425#13133139C2311yescharacteristic
426#13133139C2311yescharacteristic
427#13133139C2311yescharacteristic
428#13133138C2311yescharacteristic
429#13133138C2311yescharacteristic
430#13133138C2311yescharacteristic
431#13133138C2311yescharacteristic
432#13133137C2311yescharacteristic
433#13133137C2311yescharacteristic
434#13133137C2311yescharacteristic
435#13133128C2311yescharacteristic
436#13133128C2311yescharacteristic
437#13133127C2311yescharacteristic
438#13133127C2311yescharacteristic
439C4×#88322C2311yescharacteristic
440C8×Dic53C2311yescharacteristic
441C8×Dic53C2311yescharacteristic
442C8×Dic53C2311yescharacteristic
443C8×Dic53C2311yescharacteristic
444C2×#41×C53—21no—
445C2×SD16×C53C2311yescharacteristic
446C2×SD16×C53C2311yescharacteristic
447C2×SD16×C53C2311yescharacteristic
448C2×SD16×C53C2311yescharacteristic
449C2×SD16×C53C2311yescharacteristic
450C2×SD16×C53C2311yescharacteristic
451C2×D8×C53C2311yescharacteristic
452C2×D8×C53C2311yescharacteristic
453C2×D8×C53C2311yescharacteristic
454C4⋊Q8×C53C2311yescharacteristic
455#127×C53C2311yescharacteristic
456#127×C53C2311yescharacteristic
457#127×C53C2311yescharacteristic
458#126×C53—21no—
459#126×C53—21no—
460#124×C53C2311yescharacteristic
461#124×C53C2311yescharacteristic
462C22⋊Q8×C53—21no—
463#121×C53—21no—
464#121×C53—21no—
465#121×C53—21no—
466C4×Q8×C53C2311yescharacteristic
467C4×Q8×C53C2311yescharacteristic
468C4×Q8×C53C2311yescharacteristic
469C4×D4×C53C2311yescharacteristic
470C4×D4×C53C2311yescharacteristic
471C4×D4×C53C2311yescharacteristic
472C4×D4×C53C2311yescharacteristic
473#117×C53—21no—
474#107×C53C2311yescharacteristic
475C4⋊C8×C53C2311yescharacteristic
476C4⋊C8×C53C2311yescharacteristic
477C4⋊C8×C53C2311yescharacteristic
478#103×C53C2311yescharacteristic
479#103×C53C2311yescharacteristic
480#102×C53C2311yescharacteristic
481#102×C53C2311yescharacteristic
482#102×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484#97×C53C2311yescharacteristic
485#97×C53C2311yescharacteristic
486C4×C8×C53C2311yescharacteristic
487C23×D53—21no—
488C23×D53—21no—
489#41×C53—82no—
490C2×Q8×C53C2×D411yescharacteristic
491C2×Q8×C53C2411yescharacteristic
492C2×Q8×C53C2411yescharacteristic
493C2×D4×C53—21no—
494C2×D4×C53—21no—
495C2×D4×C53—21no—
496C2×D4×C53—21no—
497C2×D4×C53—21no—
498C2×D4×C53—21no—
499C2×D4×C53C2411yescharacteristic
500C2×D4×C53C2411yescharacteristic
501C2×D4×C53C2411yescharacteristic
502C2×D4×C53C2411yescharacteristic
503C22×C4×C53—21no—
504C22×C4×C53—21no—
505C22×C4×C53—21no—
506C22×C4×C53—21no—
507C2×C22⋊D53—21no—
508C2×C22⋊D53—21no—
509C2×C22⋊D53—21no—
510C2×C22⋊D53—21no—
511C2×C22⋊D53—21no—
512C2×C22⋊D53—21no—
513C2×C22⋊D53—21no—
514C2×C22⋊D53—21no—
515C2×C22⋊D53—21no—
516C2×C22⋊D53—21no—
517C22×Dic53—21no—
518C22×Dic53—21no—
519C22×Dic53—21no—
520C22×Dic53—21no—
521C22×Dic53—21no—
522C22×Dic53—21no—
523#11719949—22no—
524#11719949—22no—
525Q8×D53—22no—
526Q8×D53—22no—
527#11719947—22no—
528#11719947—22no—
529#11719947—22no—
530#11719947—22no—
531#11719947—82no—
532D4×D53—22no—
533D4×D53—22no—
534D4×D53—22no—
535D4×D53—22no—
536C2×D212—21no—
537C2×D212—21no—
538C2×D212—21no—
539C2×D212C2411yescharacteristic
540C2×D212C2411yescharacteristic
541C2×D212C2411yescharacteristic
542C2×C4×D53—21no—
543C2×C4×D53—21no—
544C2×C4×D53—21no—
545C2×C4×D53—21no—
546C2×C4×D53—21no—
547C2×C4×D53—21no—
548C2×C4×D53—21no—
549C2×C4×D53—21no—
550C2×C4×D53—21no—
551C2×C4×D53—82no—
552C2×C4×D53C2×D411yescharacteristic
553C2×C4×D53C2×D411yescharacteristic
554C2×C4×D53C2411yescharacteristic
555C2×Dic106—21no—
556C2×Dic106C2×D411yescharacteristic
557C2×Dic106C2×D411yescharacteristic
558C2×Dic106C2×D411yescharacteristic
559C2×Dic106C2411yescharacteristic
560C2×Dic106C2411yescharacteristic
561C2×Dic106C2411yescharacteristic
562SD16×C53—22no—
563SD16×C53—22no—
564SD16×C53—41no—
565SD16×C53—41no—
566SD16×C53—41no—
567SD16×C53—41no—
568D8×C53—22no—
569D8×C53—41no—
570D8×C53—41no—
571C2×C8×C53C2411yescharacteristic
572C2×C8×C53C2411yescharacteristic
573C2×C8×C53C2411yescharacteristic
574C2×C8×C53C2411yescharacteristic
575C4⋊C4×C53—21no—
576C4⋊C4×C53—21no—
577C4⋊C4×C53—21no—
578C4⋊C4×C53—21no—
579C4⋊C4×C53C2×D411yescharacteristic
580C4⋊C4×C53C2×D411yescharacteristic
581C4⋊C4×C53C2×D411yescharacteristic
582C4⋊C4×C53C2411yescharacteristic
583C4⋊C4×C53C2411yescharacteristic
584C22⋊C4×C53—21no—
585C22⋊C4×C53—21no—
586C22⋊C4×C53—21no—
587C22⋊C4×C53—21no—
588C22⋊C4×C53—21no—
589C22⋊C4×C53—21no—
590C22⋊C4×C53—21no—
591C22⋊C4×C53—21no—
592C42×C53—21no—
593C42×C53—21no—
594C42×C53C2411yescharacteristic
595C42×C53C2411yescharacteristic
596C42×C53C2411yescharacteristic
597C22⋊Dic53—21no—
598C22⋊Dic53—21no—
599C22⋊Dic53—21no—
600C22⋊Dic53—21no—
601C22⋊Dic53—21no—
602C22⋊Dic53—21no—
603C22⋊Dic53—21no—
604C22⋊Dic53—21no—
605C22⋊Dic53—21no—
606C22⋊Dic53—21no—
607C22⋊Dic53—21no—
608C22⋊Dic53—21no—
609C22⋊Dic53—21no—
610C22⋊Dic53—21no—
611#11719925—22no—
612#11719925—41no—
613#11719925—41no—
614#11719925—41no—
615#11719924—22no—
616#11719924—41no—
617#11719923—22no—
618#11719923—22no—
619#11719923—41no—
620#11719923—41no—
621#11719923—41no—
622#11719922—22no—
623#11719922—22no—
624#11719922—41no—
625#11719922—41no—
626#11719922—41no—
627#11719922—41no—
628#11719922—41no—
629#11719921—21no—
630#11719921—21no—
631#11719921—21no—
632#11719921—21no—
633#11719921—21no—
634#11719921—21no—
635#11719921—21no—
636#11719921—21no—
637#11719921—21no—
638#11719921—21no—
639#11719921—21no—
640#11719921—21no—
641#11719921—21no—
642#11719921—21no—
643#11719921—21no—
644#11719921—21no—
645#11719921—21no—
646#11719921—21no—
647#11719921—21no—
648#11719921—21no—
649#11719921—21no—
650#11719921C2×D411yescharacteristic
651#11719921C2×D411yescharacteristic
652#11719921C2×D411yescharacteristic
653#11719921C2×D411yescharacteristic
654C4⋊Dic53—21no—
655C4⋊Dic53—21no—
656C4⋊Dic53—21no—
657C4⋊Dic53—21no—
658C4⋊Dic53C2×D411yescharacteristic
659C4⋊Dic53C2×D411yescharacteristic
660C4⋊Dic53C2×D411yescharacteristic
661C4⋊Dic53C2411yescharacteristic
662C4⋊Dic53C2411yescharacteristic
663#11719919—21no—
664#11719919—21no—
665#11719919—21no—
666#11719919—21no—
667#11719919—21no—
668#11719919—21no—
669#11719919—21no—
670#11719919—21no—
671#11719919—21no—
672#11719919C2×D411yescharacteristic
673#11719919C2×D411yescharacteristic
674#11719919C2×D411yescharacteristic
675#11719919C2×D411yescharacteristic
676#11719919C2×D411yescharacteristic
677#11719919C2×D411yescharacteristic
678#11719919C2×D411yescharacteristic
679#11719919C2×D411yescharacteristic
680#11719919C2×D411yescharacteristic
681#11719919C2×D411yescharacteristic
682C4×Dic53—21no—
683C4×Dic53—21no—
684C4×Dic53—21no—
685C4×Dic53—21no—
686C4×Dic53—21no—
687C4×Dic53—21no—
688C4×Dic53—21no—
689C4×Dic53—21no—
690C4×Dic53—21no—
691C4×Dic53C2×D411yescharacteristic
692C4×Dic53C2×D411yescharacteristic
693C4×Dic53C2411yescharacteristic
694C4×Dic53C2411yescharacteristic
695C4×Dic53C2411yescharacteristic
696C2×#88322C2411yescharacteristic
697C2×#88322C2411yescharacteristic
698C2×#88322C2411yescharacteristic
699C2×#88322C2411yescharacteristic
700Dic212—22no—
701Dic212—41no—
702D424—22no—
703D424—41no—
704#11719913—22no—
705#11719913—41no—
706#11719913—41no—
707#11719913—41no—
708#11719913—41no—
709#11719912—22no—
710#11719912#4114yescomplemented
711C8×D53—22no—
712C8×D53—22no—
713C23×C53—21no—
714C23×C53—21no—
715C23×C53—21no—
716C23×C53—21no—
717C22×D53—21no—
718C22×D53—21no—
719C22×D53—21no—
720C22×D53—42no—
721C22×D53—42no—
722C22×D53—81no—
723C22×D53—81no—
724C22×D53—81no—
725C22×D53—81no—
726C22×D53C22×D411yescharacteristic
727Q8×C53—21no—
728Q8×C53—21no—
729Q8×C53—21no—
730Q8×C53—21no—
731Q8×C53—41no—
732D4×C53—21no—
733D4×C53—21no—
734D4×C53—21no—
735D4×C53—21no—
736D4×C53—21no—
737D4×C53—21no—
738D4×C53—21no—
739D4×C53—21no—
740D4×C53—42no—
741D4×C53—81no—
742D4×C53—81no—
743D4×C53—81no—
744D4×C53—81no—
745D4×C53—81no—
746C2×C4×C53—21no—
747C2×C4×C53—21no—
748C2×C4×C53—21no—
749C2×C4×C53—21no—
750C2×C4×C53—42no—
751C2×C4×C53—81no—
752C2×C4×C53—81no—
753C2×C4×C53—81no—
754C2×C4×C53C22×D411yescharacteristic
755C2×C4×C53C22×D411yescharacteristic
756C2×C4×C53C22×D411yescharacteristic
757C2×C4×C53C22×D411yescharacteristic
758C2×C4×C53C22×D411yescharacteristic
759C2×C4×C53C22×D411yescharacteristic
760C2×C4×C53C2511yescharacteristic
761C22⋊D53—42no—
762C22⋊D53—42no—
763C22⋊D53—42no—
764C22⋊D53—42no—
765C22⋊D53—81no—
766C22⋊D53—81no—
767C22⋊D53—81no—
768C22⋊D53—81no—
769C22⋊D53—81no—
770C22⋊D53—81no—
771C2×Dic53—21no—
772C2×Dic53—21no—
773C2×Dic53—21no—
774C2×Dic53—21no—
775C2×Dic53—21no—
776C2×Dic53—42no—
777C2×Dic53—42no—
778C2×Dic53—81no—
779C2×Dic53—81no—
780C2×Dic53—81no—
781C2×Dic53—81no—
782C2×Dic53C22×D411yescharacteristic
783C2×Dic53C22×D411yescharacteristic
784C2×Dic53C22×D411yescharacteristic
785C2×Dic53C22×D411yescharacteristic
786C2×Dic53C22×D411yescharacteristic
787C2×Dic53C22×D411yescharacteristic
788C2×Dic53C22×D411yescharacteristic
789D212—21no—
790D212—21no—
791D212—21no—
792D212—21no—
793D212—21no—
794D212—21no—
795D212—42no—
796D212—81no—
797D212—81no—
798C4×D53—41no—
799C4×D53—41no—
800C4×D53—42no—
801C4×D53—42no—
802C4×D53—42no—
803C4×D53—81no—
804C4×D53—81no—
805C4×D53—81no—
806C4×D53—81no—
807C4×D53—81no—
808C4×D53—81no—
809C4×D53C2×#4112yes—
810C4×D53H(5,𝔽2)12yes—
811Dic106—21no—
812Dic106—21no—
813Dic106—21no—
814Dic106—21no—
815Dic106—21no—
816Dic106—21no—
817Dic106—41no—
818Dic106—41no—
819Dic106—41no—
820Dic106—42no—
821C8×C53—21no—
822C8×C53—21no—
823C8×C53—21no—
824C8×C53C2×#4112yes—
825#88322—21no—
826#88322—21no—
827#88322—21no—
828#88322C2×#4112yes—
829#61424—531nomaximal, Sylow
830C22×C53—41no—
831C22×C53—41no—
832C22×C53—41no—
833C22×C53—41no—
834C22×C53—41no—
835C22×C53—41no—
836C22×C53—41no—
837C22×C53—41no—
838C22×C53—41no—
839C22×C53—41no—
840C22×C53—41no—
841C22×C53—41no—
842C22×C53C23×D411yescharacteristic
843C2×D53—21no—
844C2×D53—21no—
845C2×D53—41no—
846C2×D53—41no—
847C2×D53—41no—
848C2×D53—41no—
849C2×D53—41no—
850C2×D53—41no—
851C2×D53—41no—
852C2×D53—41no—
853C2×D53—41no—
854C2×D53—84no—
855C2×D53—162no—
856C2×D53#55012yes—
857C4×C53—21no—
858C4×C53—21no—
859C4×C53—21no—
860C4×C53—21no—
861C4×C53—21no—
862C4×C53—21no—
863C4×C53—41no—
864C4×C53—41no—
865C4×C53—41no—
866C4×C53—41no—
867C4×C53C22×#4111yescharacteristic
868C4×C53C2×H(5,𝔽2)11yescharacteristic
869Dic53—21no—
870Dic53—21no—
871Dic53—21no—
872Dic53—21no—
873Dic53—21no—
874Dic53—21no—
875Dic53—41no—
876Dic53—41no—
877Dic53—41no—
878Dic53—41no—
879Dic53—41no—
880Dic53#55012yes—
881#3510—531no—
882#3506—531no—
883#3403—531no—
884#3403—531no—
885#3402—531no—
886#3402—531no—
887#3401—531no—
888#3401—531no—
889#3401—531no—
890#3401—531no—
891#3399—531no—
892#3399—531no—
893#3397—531no—
894#3397D5311yescharacteristic, complemented
895#3396—531no—
896#3396—531no—
897#3394—531no—
898#3394—531no—
899#3155—531no—
900#3154—531no—
901#3153—531no—
902#3046—531no—
903#3045—531no—
904#3043—531no—
905#3041—531no—
906#3035—531no—
907C2×#463—531no—
908#2962—531no—
909#2947—531no—
910#2946—531no—
911C4×AGL(1,ℤ/8)—531no—
912C2×C53—81no—
913C2×C53—81no—
914C2×C53—81no—
915C2×C53—81no—
916C2×C53C2×#55011yescharacteristic
917C2×C53#358411yescharacteristic
918C2×C53#358511yescharacteristic
919D53—22no—
920D53—81no—
921D53—81no—
922D53—81no—
923C2×#137—531no—
924C2×#137—531no—
925C2×AGL(1,ℤ/8)—531no—
926C2×AGL(1,ℤ/8)—531no—
927C2×AGL(1,ℤ/8)—531no—
928C2×#135—531no—
929C2×#135—531no—
930C22×SD16—531no—
931C22×D8—531no—
932#559—531no—
933#559—531no—
934#559—531no—
935#559—531no—
936#559—531no—
937#559—531no—
938#559—531no—
939#559—531no—
940#556—531no—
941#556—531no—
942#556—531no—
943#556—531no—
944#556—531no—
945#556C2×D5311yescharacteristic, complemented
946#555—1061no—
947#553—1061no—
948#553—1061no—
949#551—1061no—
950#551—1061no—
951#551—1061no—
952#551—1061no—
953#550—531no—
954#550C2×D5311yescharacteristic, complemented
955#547—1061no—
956#542—1061no—
957#542—1061no—
958#538—1061no—
959#538—1061no—
960#536—531no—
961#535—531no—
962#535—531no—
963#535—531no—
964#533—531no—
965#532—531no—
966#529—1061no—
967#529—1061no—
968C2×#124—531no—
969#525—1061no—
970#525—1061no—
971#520—531no—
972#520—531no—
973#519—531no—
974#518—531no—
975C4×#41—531no—
976C2×C4×D4—531no—
977#497—531no—
978#497—531no—
979#497—531no—
980#497—531no—
981#496—531no—
982#496—531no—
983#496—531no—
984#496—531no—
985#496—531no—
986#496—531no—
987#496C2×D5311yescharacteristic
988#496C2×D5311yescharacteristic, complemented
989#495—531no—
990#495—531no—
991#495—531no—
992#495—531no—
993#495—531no—
994#495—531no—
995#495—531no—
996#495—531no—
997#493—531no—
998#493—531no—
999#492—531no—
1000#492C2×D5311yescharacteristic, complemented
1001#464—531no—
1002#464—531no—
1003#464—531no—
1004#464—531no—
1005#464—531no—
1006#464—531no—
1007#464—531no—
1008#464—531no—
1009#464—531no—
1010#464—531no—
1011#463—531no—
1012#463—531no—
1013#463—531no—
1014#463—531no—
1015#463—531no—
1016#463—531no—
1017#463—531no—
1018#463—531no—
1019#463—531no—
1020#463—531no—
1021#463—531no—
1022#463—531no—
1023#463—531no—
1024#463—531no—
1025#463—531no—
1026#463—531no—
1027#463C2×D5311yescharacteristic
1028#463C2×D5311yescharacteristic, complemented
1029#462—531no—
1030#462—531no—
1031#462—531no—
1032#461—531no—
1033#461—531no—
1034#461C2×D5311yescharacteristic, complemented
1035#460—531no—
1036#460—531no—
1037#460—531no—
1038#460—531no—
1039#460—531no—
1040#460C2×D5311yescharacteristic, complemented
1041#460C2×D5311yescharacteristic, complemented
1042#459—531no—
1043#459—531no—
1044#459—531no—
1045#459—531no—
1046#459—531no—
1047#459—531no—
1048#459C2×D5311yescharacteristic
1049#446—531no—
1050#446—531no—
1051#446—531no—
1052#446—531no—
1053#446—531no—
1054#446C2×D5311yescharacteristic, complemented
1055C8×Q8—531no—
1056C8×Q8—531no—
1057#442—531no—
1058#442—531no—
1059#442—531no—
1060#442—531no—
1061#441—531no—
1062#441—531no—
1063#440—531no—
1064#440—531no—
1065#440—531no—
1066#440—531no—
1067#440C2×D5311yescharacteristic, complemented
1068#440C2×D5311yescharacteristic, complemented
1069C4×Q16—531no—
1070C4×Q16—531no—
1071C4×SD16—531no—
1072C4×SD16—531no—
1073C4×SD16—531no—
1074C4×SD16—531no—
1075C4×SD16—531no—
1076C4×SD16—531no—
1077C4×D8—531no—
1078C4×D8—531no—
1079C4×D8—531no—
1080C4×D8C2×D5311yescharacteristic, complemented
1081#428—531no—
1082#424—531no—
1083#424—531no—
1084C2×C4⋊C8—531no—
1085#418—531no—
1086#417—531no—
1087#416—531no—
1088#416—531no—
1089C2×#103—531no—
1090C2×#102—531no—
1091#405—531no—
1092#405—531no—
1093C4×M16—531no—
1094C53#6142411yescharacteristic, complemented, Sylow
1095C2×#41—21no—
1096C2×#41—531no—
1097C2×#41—531no—
1098C2×#41—531no—
1099C2×#41—1061no—
1100C22×Q8—531no—
1101C22×D4—531no—
1102C22×D4—531no—
1103C23×C4—1061no—
1104#137—1064no—
1105#137—2122no—
1106AGL(1,ℤ/8)—1064no—
1107AGL(1,ℤ/8)—1064no—
1108AGL(1,ℤ/8)—2122no—
1109#135—2122no—
1110#135—2122no—
1111C2×Q16—531no—
1112C2×Q16—531no—
1113C2×Q16—531no—
1114C2×Q16—531no—
1115C2×Q16—531no—
1116C2×Q16—531no—
1117C2×SD16—531no—
1118C2×SD16—531no—
1119C2×SD16—531no—
1120C2×SD16—531no—
1121C2×SD16—531no—
1122C2×SD16—531no—
1123C2×SD16—531no—
1124C2×SD16—531no—
1125C2×SD16—531no—
1126C2×SD16—531no—
1127C2×SD16—531no—
1128C2×SD16—531no—
1129C2×SD16—2122no—
1130C2×SD16C22×D5311yescharacteristic
1131C2×SD16C22×D5311yescharacteristic
1132C2×SD16C22×D5311yescharacteristic
1133C2×SD16C22×D5311yescharacteristic
1134C2×SD16C22×D5311yescharacteristic
1135C2×SD16C22×D5311yescharacteristic
1136C2×D8—531no—
1137C2×D8—531no—
1138C2×D8—531no—
1139C2×D8—531no—
1140C2×D8—531no—
1141C2×D8—531no—
1142C2×D8—531no—
1143C2×D8—531no—
1144C2×D8—531no—
1145C2×D8—2122no—
1146C2×D8C22×D5311yescharacteristic
1147C2×D8C22×D5311yescharacteristic
1148C2×D8C22×D5311yescharacteristic
1149C2×M16—531no—
1150C2×M16—531no—
1151C22×C8—531no—
1152C22×C8—531no—
1153C4⋊Q8—531no—
1154C4⋊Q8—531no—
1155C4⋊Q8—531no—
1156C4⋊Q8—531no—
1157C4⋊Q8C22×D5311yescharacteristic
1158#127—531no—
1159#127—531no—
1160#127—531no—
1161#127—531no—
1162#127C22×D5311yescharacteristic
1163#127C22×D5311yescharacteristic
1164#127C22×D5311yescharacteristic
1165#126—21no—
1166#126—21no—
1167#126—1061no—
1168#126—1061no—
1169#126—1061no—
1170#126—1061no—
1171#126—1061no—
1172#126—1061no—
1173#126—1061no—
1174#126—1061no—
1175#126—1061no—
1176#126—1061no—
1177#125—531no—
1178#125—531no—
1179#124—531no—
1180#124—531no—
1181#124—531no—
1182#124—531no—
1183#124—531no—
1184#124—531no—
1185#124—531no—
1186#124—531no—
1187#124—531no—
1188#124—531no—
1189#124—531no—
1190#124—531no—
1191#124—1061no—
1192#124—1061no—
1193#124—1061no—
1194#124—1061no—
1195#124—1061no—
1196#124—1061no—
1197#124—1061no—
1198#124—1061no—
1199#124—1061no—
1200#124—1061no—
1201#124C22×D5311yescharacteristic
1202#124C22×D5311yescharacteristic
1203#123—1061no—
1204#123—1061no—
1205#123—1061no—
1206#123—1061no—
1207#123—1061no—
1208#123—1061no—
1209#123—1061no—
1210#123—1061no—
1211#123—1061no—
1212#123—1061no—
1213#123—1061no—
1214#123—1061no—
1215#123—1061no—
1216#123—1061no—
1217#123—1061no—
1218#123—1061no—
1219#123—1061no—
1220#123—1061no—
1221C22⋊Q8—21no—
1222C22⋊Q8—531no—
1223C22⋊Q8—531no—
1224C22⋊Q8—531no—
1225C22⋊Q8—531no—
1226C22⋊Q8—1061no—
1227C22⋊Q8—1061no—
1228C22⋊Q8—1061no—
1229C22⋊Q8—1061no—
1230C22⋊Q8—1061no—
1231C22⋊Q8—1061no—
1232C22⋊Q8—1061no—
1233#121—21no—
1234#121—21no—
1235#121—21no—
1236#121—1061no—
1237#121—1061no—
1238#121—1061no—
1239#121—1061no—
1240#121—1061no—
1241#121—1061no—
1242#121—1061no—
1243#121—1061no—
1244#121—1061no—
1245#121—1061no—
1246#121—1061no—
1247#120—1061no—
1248#120—1061no—
1249#120—1061no—
1250#120—1061no—
1251#120—1061no—
1252#120—1061no—
1253C4×Q8—531no—
1254C4×Q8—531no—
1255C4×Q8—531no—
1256C4×Q8—531no—
1257C4×Q8—531no—
1258C4×Q8—531no—
1259C4×Q8—531no—
1260C4×Q8—531no—
1261C4×Q8—531no—
1262C4×Q8—531no—
1263C4×Q8—531no—
1264C4×Q8—1061no—
1265C4×Q8—1061no—
1266C4×Q8C22×D5311yescharacteristic
1267C4×Q8C22×D5311yescharacteristic
1268C4×Q8C22×D5311yescharacteristic
1269C4×D4—531no—
1270C4×D4—531no—
1271C4×D4—531no—
1272C4×D4—531no—
1273C4×D4—531no—
1274C4×D4—531no—
1275C4×D4—531no—
1276C4×D4—531no—
1277C4×D4—531no—
1278C4×D4—531no—
1279C4×D4—1061no—
1280C4×D4—1061no—
1281C4×D4—1061no—
1282C4×D4—1061no—
1283C4×D4—1061no—
1284C4×D4—1061no—
1285C4×D4—1061no—
1286C4×D4—1061no—
1287C4×D4—1061no—
1288C4×D4—1061no—
1289C4×D4—1061no—
1290C4×D4—1061no—
1291C4×D4—1061no—
1292C4×D4—1061no—
1293C4×D4—1061no—
1294C4×D4—1061no—
1295C4×D4—1061no—
1296C4×D4—1061no—
1297C4×D4—1061no—
1298C4×D4—1061no—
1299C4×D4C22×D5311yescharacteristic
1300C4×D4C22×D5311yescharacteristic
1301C4×D4C22×D5311yescharacteristic
1302C4×D4C22×D5311yescharacteristic
1303#117—21no—
1304#117—531no—
1305#117—531no—
1306#117—531no—
1307#117—1061no—
1308#117—1061no—
1309#117—1061no—
1310#117—1061no—
1311#117—1061no—
1312#117—1061no—
1313#117—1061no—
1314#117—1061no—
1315#117—1061no—
1316#117—1061no—
1317C2×C4⋊C4—531no—
1318C2×C4⋊C4—1061no—
1319C2×C4⋊C4—1061no—
1320C2×C22⋊C4—1061no—
1321C2×C22⋊C4—1061no—
1322C2×C22⋊C4—1061no—
1323C2×C22⋊C4—1061no—
1324C2×C22⋊C4—1061no—
1325C2×C42—531no—
1326C2×C42—1061no—
1327#107—531no—
1328#107C22×D5311yescharacteristic
1329#106—531no—
1330#106—531no—
1331C4⋊C8—531no—
1332C4⋊C8—531no—
1333C4⋊C8—531no—
1334C4⋊C8—531no—
1335C4⋊C8—531no—
1336C4⋊C8—531no—
1337C4⋊C8—531no—
1338C4⋊C8—531no—
1339C4⋊C8—531no—
1340C4⋊C8C22×D5311yescharacteristic
1341C4⋊C8C22×D5311yescharacteristic
1342C4⋊C8C22×D5311yescharacteristic
1343#103—531no—
1344#103—531no—
1345#103—531no—
1346#103—531no—
1347#103—531no—
1348#103—531no—
1349#103—531no—
1350#103—531no—
1351#103C22×D5311yescharacteristic
1352#103C22×D5311yescharacteristic
1353#102—531no—
1354#102—531no—
1355#102—531no—
1356#102—531no—
1357#102—531no—
1358#102—531no—
1359#102—531no—
1360#102—531no—
1361#102—531no—
1362#102—531no—
1363#102C22×D5311yescharacteristic
1364#102C22×D5311yescharacteristic
1365#102C22×D5311yescharacteristic
1366#102C22×D5311yescharacteristic
1367#97—531no—
1368#97—531no—
1369#97—531no—
1370#97—531no—
1371#97C22×D5311yescharacteristic
1372#97C22×D5311yescharacteristic
1373C4×C8—531no—
1374C4×C8—531no—
1375C4×C8—531no—
1376C4×C8—531no—
1377C4×C8—531no—
1378C4×C8C22×D5311yescharacteristic
1379C24—1061no—
1380C24—1061no—
1381#41—82no—
1382#41—1062no—
1383#41—1062no—
1384#41—1062no—
1385#41—1062no—
1386#41—1062no—
1387#41—1062no—
1388#41—4242no—
1389C2×Q8—531no—
1390C2×Q8—531no—
1391C2×Q8—531no—
1392C2×Q8—531no—
1393C2×Q8—531no—
1394C2×Q8—531no—
1395C2×Q8—1061no—
1396C2×Q8—1062no—
1397C2×Q8—1062no—
1398C2×Q8D4×D5311yescharacteristic
1399C2×Q8C23×D5311yescharacteristic
1400C2×Q8C23×D5311yescharacteristic
1401C2×D4—21no—
1402C2×D4—21no—
1403C2×D4—21no—
1404C2×D4—21no—
1405C2×D4—21no—
1406C2×D4—21no—
1407C2×D4—531no—
1408C2×D4—531no—
1409C2×D4—531no—
1410C2×D4—1061no—
1411C2×D4—1062no—
1412C2×D4—1062no—
1413C2×D4—1062no—
1414C2×D4—1062no—
1415C2×D4—1061no—
1416C2×D4—1061no—
1417C2×D4—1061no—
1418C2×D4—1061no—
1419C2×D4—1061no—
1420C2×D4—1061no—
1421C2×D4—1061no—
1422C2×D4—1061no—
1423C2×D4—1061no—
1424C2×D4—1061no—
1425C2×D4—1061no—
1426C2×D4—1061no—
1427C2×D4C23×D5311yescharacteristic
1428C2×D4C23×D5311yescharacteristic
1429C2×D4C23×D5311yescharacteristic
1430C2×D4C23×D5311yescharacteristic
1431C22×C4—21no—
1432C22×C4—21no—
1433C22×C4—21no—
1434C22×C4—21no—
1435C22×C4—531no—
1436C22×C4—531no—
1437C22×C4—531no—
1438C22×C4—1061no—
1439C22×C4—1061no—
1440C22×C4—1061no—
1441C22×C4—1061no—
1442C22×C4—1061no—
1443C22×C4—1061no—
1444C22×C4—1061no—
1445C22×C4—1061no—
1446C22×C4—1061no—
1447C22×C4—1061no—
1448C22×C4—1061no—
1449C22×C4—1061no—
1450C22×C4—1061no—
1451C22×C4—1061no—
1452C22×C4—1061no—
1453C22×C4—4242no—
1454Q16—1062no—
1455Q16—1062no—
1456Q16—2121no—
1457Q16—2121no—
1458Q16—2121no—
1459Q16—2121no—
1460SD16—22no—
1461SD16—22no—
1462SD16—41no—
1463SD16—41no—
1464SD16—41no—
1465SD16—41no—
1466SD16—1062no—
1467SD16—1062no—
1468SD16—1062no—
1469SD16—1062no—
1470SD16—2121no—
1471SD16—2121no—
1472SD16—2121no—
1473SD16—2121no—
1474SD16—2121no—
1475SD16—2121no—
1476SD16—2121no—
1477SD16—2121no—
1478D8—22no—
1479D8—41no—
1480D8—41no—
1481D8—1062no—
1482D8—1062no—
1483D8—1062no—
1484D8—2121no—
1485D8—2121no—
1486D8—2121no—
1487D8—2121no—
1488D8—2121no—
1489D8—2121no—
1490M16—534no—
1491M16—1062no—
1492C2×C8—531no—
1493C2×C8—531no—
1494C2×C8—531no—
1495C2×C8—531no—
1496C2×C8—1062no—
1497C2×C8—1062no—
1498C2×C8C23×D5311yescharacteristic
1499C2×C8C23×D5311yescharacteristic
1500C2×C8C23×D5311yescharacteristic
1501C2×C8C23×D5311yescharacteristic
1502C4⋊C4—21no—
1503C4⋊C4—21no—
1504C4⋊C4—21no—
1505C4⋊C4—21no—
1506C4⋊C4—531no—
1507C4⋊C4—531no—
1508C4⋊C4—531no—
1509C4⋊C4—531no—
1510C4⋊C4—531no—
1511C4⋊C4—531no—
1512C4⋊C4—531no—
1513C4⋊C4—531no—
1514C4⋊C4—531no—
1515C4⋊C4—531no—
1516C4⋊C4—531no—
1517C4⋊C4—531no—
1518C4⋊C4—531no—
1519C4⋊C4—531no—
1520C4⋊C4—531no—
1521C4⋊C4—1061no—
1522C4⋊C4—1061no—
1523C4⋊C4—1061no—
1524C4⋊C4—1061no—
1525C4⋊C4—1061no—
1526C4⋊C4—1061no—
1527C4⋊C4—1061no—
1528C4⋊C4—1061no—
1529C4⋊C4—1061no—
1530C4⋊C4—1061no—
1531C4⋊C4—1061no—
1532C4⋊C4—1061no—
1533C4⋊C4—1061no—
1534C4⋊C4D4×D5311yescharacteristic
1535C4⋊C4D4×D5311yescharacteristic
1536C4⋊C4D4×D5311yescharacteristic
1537C4⋊C4C23×D5311yescharacteristic
1538C4⋊C4C23×D5311yescharacteristic
1539C22⋊C4—21no—
1540C22⋊C4—21no—
1541C22⋊C4—21no—
1542C22⋊C4—21no—
1543C22⋊C4—21no—
1544C22⋊C4—21no—
1545C22⋊C4—21no—
1546C22⋊C4—21no—
1547C22⋊C4—531no—
1548C22⋊C4—531no—
1549C22⋊C4—531no—
1550C22⋊C4—531no—
1551C22⋊C4—1061no—
1552C22⋊C4—1061no—
1553C22⋊C4—1061no—
1554C22⋊C4—1061no—
1555C22⋊C4—1061no—
1556C22⋊C4—1061no—
1557C22⋊C4—1061no—
1558C22⋊C4—1061no—
1559C22⋊C4—1061no—
1560C22⋊C4—1061no—
1561C22⋊C4—1061no—
1562C22⋊C4—1061no—
1563C22⋊C4—1061no—
1564C22⋊C4—1061no—
1565C22⋊C4—1061no—
1566C22⋊C4—1061no—
1567C22⋊C4—1061no—
1568C22⋊C4—1061no—
1569C22⋊C4—1061no—
1570C22⋊C4—1061no—
1571C22⋊C4—1061no—
1572C22⋊C4—1061no—
1573C22⋊C4—1061no—
1574C22⋊C4—1061no—
1575C22⋊C4—1061no—
1576C22⋊C4—1061no—
1577C22⋊C4—1061no—
1578C22⋊C4—1061no—
1579C22⋊C4—1061no—
1580C22⋊C4—1061no—
1581C22⋊C4—1061no—
1582C22⋊C4—1061no—
1583C22⋊C4—1061no—
1584C22⋊C4—1061no—
1585C22⋊C4—1061no—
1586C42—21no—
1587C42—21no—
1588C42—531no—
1589C42—531no—
1590C42—531no—
1591C42—531no—
1592C42—531no—
1593C42—1061no—
1594C42—1061no—
1595C42—1061no—
1596C42—1061no—
1597C42—1061no—
1598C42—1061no—
1599C42—1061no—
1600C42—1061no—
1601C42—1061no—
1602C42C23×D5311yescharacteristic
1603C42C23×D5311yescharacteristic
1604C42C23×D5311yescharacteristic
1605C23—21no—
1606C23—21no—
1607C23—21no—
1608C23—21no—
1609C23—531no—
1610C23—1061no—
1611C23—1061no—
1612C23—1061no—
1613C23—4241no—
1614C23—4241no—
1615C23—4241no—
1616C23—4241no—
1617C23—2122no—
1618C23—2122no—
1619Q8—21no—
1620Q8—21no—
1621Q8—21no—
1622Q8—21no—
1623Q8—41no—
1624Q8—1061no—
1625Q8—1061no—
1626Q8—1061no—
1627Q8—1061no—
1628Q8—1061no—
1629Q8—1061no—
1630Q8—2121no—
1631Q8—2121no—
1632Q8—2121no—
1633Q8—2122no—
1634D4—21no—
1635D4—21no—
1636D4—21no—
1637D4—21no—
1638D4—21no—
1639D4—21no—
1640D4—21no—
1641D4—21no—
1642D4—42no—
1643D4—81no—
1644D4—81no—
1645D4—81no—
1646D4—81no—
1647D4—81no—
1648D4—1061no—
1649D4—1061no—
1650D4—1061no—
1651D4—1061no—
1652D4—1061no—
1653D4—1061no—
1654D4—4241no—
1655D4—4241no—
1656D4—4241no—
1657D4—4241no—
1658D4—4241no—
1659D4—4241no—
1660D4—4241no—
1661D4—4241no—
1662D4—2122no—
1663D4—2122no—
1664D4—2122no—
1665D4—2122no—
1666D4—2122no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—21no—
1671C2×C4—42no—
1672C2×C4—81no—
1673C2×C4—81no—
1674C2×C4—81no—
1675C2×C4—531no—
1676C2×C4—532no—
1677C2×C4—532no—
1678C2×C4—531no—
1679C2×C4—531no—
1680C2×C4—531no—
1681C2×C4—531no—
1682C2×C4—531no—
1683C2×C4—531no—
1684C2×C4—1061no—
1685C2×C4—1061no—
1686C2×C4—1061no—
1687C2×C4—1061no—
1688C2×C4—1061no—
1689C2×C4—4241no—
1690C2×C4—4241no—
1691C2×C4—4241no—
1692C2×C4—4241no—
1693C2×C4—4241no—
1694C2×C4—4241no—
1695C2×C4—4241no—
1696C2×C4—4241no—
1697C2×C4—4241no—
1698C2×C4—4241no—
1699C2×C4—2121no—
1700C2×C4—2121no—
1701C2×C4—2122no—
1702C2×C4—2122no—
1703C2×C4—2122no—
1704C2×C4—2122no—
1705C2×C4—2122no—
1706C2×C4C2×D4×D5311yescharacteristic
1707C2×C4C2×D4×D5311yescharacteristic
1708C2×C4C2×D4×D5311yescharacteristic
1709C2×C4C2×D4×D5311yescharacteristic
1710C2×C4C2×D4×D5311yescharacteristic
1711C2×C4C2×D4×D5311yescharacteristic
1712C2×C4C24×D5311yescharacteristic
1713C8—21no—
1714C8—21no—
1715C8—21no—
1716C8—532no—
1717C8—1061no—
1718C8—1061no—
1719C8—1061no—
1720C8#41×D5312yes—
1721C22—41no—
1722C22—41no—
1723C22—41no—
1724C22—41no—
1725C22—41no—
1726C22—41no—
1727C22—41no—
1728C22—41no—
1729C22—41no—
1730C22—41no—
1731C22—41no—
1732C22—41no—
1733C22—532no—
1734C22—8482no—
1735C22—1061no—
1736C22—1061no—
1737C22—4244no—
1738C22—2121no—
1739C22—2121no—
1740C22—2121no—
1741C22—2121no—
1742C22—2121no—
1743C22—2121no—
1744C22—2121no—
1745C22—2121no—
1746C22—2121no—
1747C22C22×D4×D5311yescharacteristic
1748C4—21no—
1749C4—21no—
1750C4—21no—
1751C4—21no—
1752C4—21no—
1753C4—21no—
1754C4—41no—
1755C4—41no—
1756C4—41no—
1757C4—41no—
1758C4—532no—
1759C4—1061no—
1760C4—1061no—
1761C4—1061no—
1762C4—1061no—
1763C4—1061no—
1764C4—1061no—
1765C4—2121no—
1766C4—2121no—
1767C4—2121no—
1768C4—2121no—
1769C4—2121no—
1770C4C2×#41×D5311yescharacteristic
1771C4H(5,𝔽2)×D5311yescharacteristic
1772C2—81no—
1773C2—81no—
1774C2—81no—
1775C2—81no—
1776C2—1062no—
1777C2—4241no—
1778C2—4241no—
1779C2—4241no—
1780C2#550×D5311yescharacteristic
1781C2#2028948711yescharacteristic
1782C2#2028949111yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3397C2
socleC22×C53C23×D4
hypercenter#3397D53
hypocenterC53#61424
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3397

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20288605C2semidirect
2. #20288559C2semidirect
3. #20287804C2semidirect
4. #20287798C2semidirect
5. #20287795C2semidirect
6. #20287790C2semidirect
7. #20287788C2semidirect
8. #20287783C2semidirect
9. #20287778C2semidirect
10. #20287776C2semidirect
11. #20287757C2semidirect
12. #20287754C2semidirect
13. #20287730C2semidirect
14. #20287727C2semidirect
15. #20287726C2semidirect
16. #20287716C2semidirect
17. #20287714C2semidirect
18. #20285199C2semidirect
19. #20285184C2semidirect
20. #20285180C2semidirect
21. #20284260C2semidirect
22. #20284255C2semidirect
23. #20284231C2semidirect
24. #20284213C2semidirect
25. #20284165C2semidirect
26. #463×D53C2semidirect
27. #20283660C2semidirect
28. #20283555C2semidirect
29. #20283540C2semidirect
30. #20283520C2semidirect
31. C53×#3397C2semidirect
41. #16811359C22semidirect
42. #16811359C22semidirect
43. #16811358C22semidirect
44. #16811358C22semidirect
45. #16811356C22semidirect
46. #16811356C22semidirect
47. #16811356C22semidirect
48. #16811355C22semidirect
49. #16811347C22semidirect
50. #16811346C22semidirect
51. #16811345C22semidirect
52. #16811343C22semidirect
53. #16811342C22semidirect
61. #16811293C22semidirect
84. #16811018C22semidirect
85. #16811017C22semidirect
86. #16811015C22semidirect
87. #16811014C22semidirect
90. #16811010C22semidirect
91. #16811010C22semidirect
93. #16811009C22semidirect
94. #16811007C22semidirect
95. #16811006C22semidirect
96. #16811006C22semidirect
99. #16811004C22semidirect
100. #16811004C22semidirect
101. #16811004C22semidirect
104. #16810994C22semidirect
105. #16810848C22semidirect
106. #16810848C22semidirect
107. #16810846C22semidirect
108. #16810846C22semidirect
109. #16810845C22semidirect
110. #16810844C22semidirect
111. #16810843C22semidirect
112. #16810843C22semidirect
113. #16810843C22semidirect
114. #16810842C22semidirect
117. #16810840C22semidirect
118. #16810840C22semidirect
123. #16810838C22semidirect
126. #16810837C22semidirect
127. #16810837C22semidirect
131. #16810833C22semidirect
132. #16810832C22semidirect
133. #16810830C22semidirect
134. #16810829C22semidirect
135. #16810826C22semidirect
136. #16810824C22semidirect
137. #16810822C22semidirect
138. #16810822C22semidirect
139. #16810821C22semidirect
140. #16810820C22semidirect
141. #16810818C22semidirect
144. #16810816C22semidirect
146. #16810815C22semidirect
147. #16810754C22semidirect
148. #16810752C22semidirect
149. #16810752C22semidirect
150. #16810751C22semidirect
151. #16810751C22semidirect
152. C8×Dic106C22semidirect
153. #16810747C22semidirect
154. #16810736C22semidirect
155. #16810735C22semidirect
156. #16810733C22semidirect
157. #16810733C22semidirect
158. #16810731C22semidirect
159. #16810727C22semidirect
160. #16810723C22semidirect
161. #16810722C22semidirect
162. #16810721C22semidirect
163. #16810720C22semidirect
164. #16810717C22semidirect
165. C4×#11719925C22semidirect
166. #16810714C22semidirect
167. C4×#11719913C22semidirect
168. SD16×Dic53C22semidirect
169. SD16×Dic53C22semidirect
170. C4×#11719923C22semidirect
171. #16810708C22semidirect
172. #16810705C22semidirect
173. #16810703C22semidirect
174. #16810703C22semidirect
188. C53×#556C22semidirect
189. C53×#550C22semidirect
191. C53×#496C22semidirect
192. C53×#492C22semidirect
194. C53×#463C22semidirect
195. C53×#461C22semidirect
196. C53×#460C22semidirect
197. C53×#460C22semidirect
199. C53×#446C22semidirect
200. C53×#440C22semidirect
201. C53×#440C22semidirect
202. C4×D8×C53C22semidirect
710. #11719912#41semidirect
894. #3397D53semidirect
945. #556C2×D53semidirect
954. #550C2×D53semidirect
988. #496C2×D53semidirect
1000. #492C2×D53semidirect
1028. #463C2×D53semidirect
1034. #461C2×D53semidirect
1040. #460C2×D53semidirect
1041. #460C2×D53semidirect
1054. #446C2×D53semidirect
1067. #440C2×D53semidirect
1068. #440C2×D53semidirect
1080. C4×D8C2×D53semidirect
1094. C53#61424semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202886052
#202885592
#202878042
#202877982
#202877952
#202877902
#202877882
#202877832
#202877782
#202877762
#202877572
#202877542
#202877302
#202877272
#202877262
#202877162
#202877142
#202851992
#202851842
#202851802
#202842602
#202842552
#202842312
#202842132
#202841652
#463×D532
#202836602
#202835552
#202835402
#202835202
C53×#33972
#6142453