Finite Group Databasebeta

← #28267131

Subgroups — #28267131

Order 13568.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288789C211yesmaximal, characteristic, complemented
2#20288781C211yesmaximal, characteristic, complemented
3#20287791C211yesmaximal, characteristic, complemented
4#20287670C211yesmaximal, characteristic, complemented
5#20287369C211yesmaximal, characteristic, complemented
6#20287361C211yesmaximal, characteristic, complemented
7#20287285C211yesmaximal, characteristic, complemented
8#20287259C211yesmaximal, characteristic, complemented
9#20287255C211yesmaximal, characteristic, complemented
10#20286631C211yesmaximal, characteristic, complemented
11#20286627C211yesmaximal, characteristic, complemented
12#20286571C211yesmaximal, characteristic, complemented
13#20286564C211yesmaximal, characteristic, complemented
14#20286556C211yesmaximal, characteristic, complemented
15#20286545C211yesmaximal, characteristic, complemented
16#20286323C211yesmaximal, characteristic, complemented
17#20286247C211yesmaximal, characteristic, complemented
18#20286239C211yesmaximal, characteristic, complemented
19#20285387C211yesmaximal, characteristic, complemented
20#20285281C211yesmaximal, characteristic, complemented
21#20284927C211yesmaximal, characteristic, complemented
22#20284923C211yesmaximal, characteristic, complemented
23#20284903C211yesmaximal, characteristic, complemented
24#20284893C211yesmaximal, characteristic, complemented
25#20284830C211yesmaximal, characteristic, complemented
26#20284822C211yesmaximal, characteristic, complemented
27#20283686C211yesmaximal, characteristic, complemented
28#20283549C211yesmaximal, characteristic, complemented
29#20283542C211yesmaximal, characteristic, complemented
30C4×#13133240C211yesmaximal, characteristic, complemented
31C53×#3178C211yesmaximal, characteristic, complemented
32C2×#13133245C2211yescharacteristic
33C2×#13133244C2211yescharacteristic
34C2×#13133240C2211yescharacteristic
35#16811347C2211yescharacteristic, complemented
36#16811347C2211yescharacteristic, complemented
37#16811344C2211yescharacteristic, complemented
38#16811342C2211yescharacteristic, complemented
39#16811334C2211yescharacteristic, complemented
40#16811329C2211yescharacteristic, complemented
41#16811326—21no—
42#16811326C2211yescharacteristic
43#16811325C2211yescharacteristic
44#16811318—21no—
45#16811315C2211yescharacteristic
46#16811307—21no—
47#16811307C2211yescharacteristic
48#16811305—21no—
49#16811300—21no—
50#16811298—21no—
51#16811298—21no—
52#16811296—21no—
53#16811276C2211yescharacteristic
54#16811275C2211yescharacteristic
55#16811270C2211yescharacteristic
56#16811266C2211yescharacteristic, complemented
57#16811264C2211yescharacteristic
58#16811264C2211yescharacteristic, complemented
59#16811245C2211yescharacteristic
60#16811231C2211yescharacteristic, complemented
61#16811221—21no—
62#16811214—21no—
63#16811212—21no—
64#16811207—21no—
65#16811160C2211yescharacteristic, complemented
66#16811158—21no—
67#16811155C2211yescharacteristic, complemented
68#16811152—21no—
69#16811151C2211yescharacteristic
70#126×D53—21no—
71#126×D53—21no—
72#16811105C2211yescharacteristic
73#16811103C2211yescharacteristic
74#16811097C2211yescharacteristic, complemented
75#16811095C2211yescharacteristic, complemented
76C4×#11719949C2211yescharacteristic, complemented
77C4×#11719949C2211yescharacteristic, complemented
78#16811031C2211yescharacteristic, complemented
79#16811023C2211yescharacteristic, complemented
80#16811016C2211yescharacteristic, complemented
81#16811004C2211yescharacteristic
82#16810979C2211yescharacteristic, complemented
83#16810979C2211yescharacteristic, complemented
84#16810976C2211yescharacteristic, complemented
85#16810972C2211yescharacteristic, complemented
86#16810966C2211yescharacteristic, complemented
87#16810962C2211yescharacteristic, complemented
88#16810962C2211yescharacteristic, complemented
89#16810961C2211yescharacteristic, complemented
90#16810957C2211yescharacteristic, complemented
91#16810956C2211yescharacteristic, complemented
92#16810955C2211yescharacteristic, complemented
93#16810951C2211yescharacteristic, complemented
94#16810950C2211yescharacteristic
95#16810949C2211yescharacteristic, complemented
96#16810945C2211yescharacteristic, complemented
97#16810944C2211yescharacteristic
98#16810932C2211yescharacteristic, complemented
99#16810932C2211yescharacteristic, complemented
100#16810928C2211yescharacteristic, complemented
101#16810927C2211yescharacteristic, complemented
102#16810926C2211yescharacteristic, complemented
103#16810922C2211yescharacteristic, complemented
104#16810922C2211yescharacteristic, complemented
105#16810920C2211yescharacteristic, complemented
106#16810911C2211yescharacteristic, complemented
107#16810910C2211yescharacteristic, complemented
108#16810902C2211yescharacteristic, complemented
109#16810900C2211yescharacteristic, complemented
110#16810878C2211yescharacteristic, complemented
111#16810870C2211yescharacteristic
112#16810863C2211yescharacteristic, complemented
113#16810863C2211yescharacteristic, complemented
114#16810858C2211yescharacteristic
115#16810855C2211yescharacteristic
116#16810853C2211yescharacteristic, complemented
117#16810849C2211yescharacteristic, complemented
118#16810847C2211yescharacteristic, complemented
119#16810843C2211yescharacteristic, complemented
120#16810841C2211yescharacteristic
121#16810841C2211yescharacteristic
122#16810840C2211yescharacteristic
123#16810837C2211yescharacteristic
124#16810835C2211yescharacteristic
125#16810835C2211yescharacteristic
126#16810831C2211yescharacteristic, complemented
127#16810830C2211yescharacteristic, complemented
128#16810827C2211yescharacteristic, complemented
129#16810825C2211yescharacteristic, complemented
130#16810788C2211yescharacteristic
131#16810788C2211yescharacteristic, complemented
132#16810784C2211yescharacteristic
133#16810784C2211yescharacteristic, complemented
134#16810783C2211yescharacteristic
135#16810783C2211yescharacteristic
136#16810773C2211yescharacteristic, complemented
137#16810772C2211yescharacteristic, complemented
138#16810771C2211yescharacteristic
139#16810767C2211yescharacteristic
140#16810758C2211yescharacteristic
141#16810756C2211yescharacteristic
142#16810751C2211yescharacteristic, complemented
143C8×Dic106C2211yescharacteristic, complemented
144#16810736C2211yescharacteristic
145#16810736C2211yescharacteristic
146#16810734C2211yescharacteristic
147#16810733C2211yescharacteristic
148#16810728C2211yescharacteristic, complemented
149#16810725C2211yescharacteristic, complemented
150#16810725C2211yescharacteristic, complemented
151#16810724C2211yescharacteristic, complemented
152#16810721C2211yescharacteristic, complemented
153#16810721C2211yescharacteristic, complemented
154Q16×Dic53C2211yescharacteristic, complemented
155C4×#11719925C2211yescharacteristic, complemented
156C4×#11719913C2211yescharacteristic, complemented
157C4×#11719913C2211yescharacteristic, complemented
158C4×#11719924C2211yescharacteristic, complemented
159C4×#11719924C2211yescharacteristic, complemented
160#16810708C2211yescharacteristic, complemented
161#16810708C2211yescharacteristic, complemented
162#16810708C2211yescharacteristic, complemented
163C4×D424C2211yescharacteristic
164C4×D424C2211yescharacteristic
165#16810705C2211yescharacteristic
166C4×#11719922C2211yescharacteristic
167#16810703C2211yescharacteristic
168#16810699C2211yescharacteristic
169#16810696C2211yescharacteristic, complemented
170#16810692C2211yescharacteristic, complemented
171C8×D212C2211yescharacteristic, complemented
172C8×C22⋊D53C2211yescharacteristic
173C8×C22⋊D53C2211yescharacteristic, complemented
174#16810685C2211yescharacteristic, complemented
175#16810684C2211yescharacteristic, complemented
176#16810678C2211yescharacteristic, complemented
177#16810665C2211yescharacteristic, complemented
178#16810662C2211yescharacteristic, complemented
179#16810660C2211yescharacteristic, complemented
180#16810620C2211yescharacteristic
181#16810618C2211yescharacteristic
182#16810618C2211yescharacteristic, complemented
183#16810618C2211yescharacteristic, complemented
184C2×#13133139C2211yescharacteristic, complemented
185#102×D53C2211yescharacteristic, complemented
186#16810577C2211yescharacteristic, complemented
187C4×C8×D53C2211yescharacteristic, complemented
188C53×#542C2211yescharacteristic
189C53×#541C2211yescharacteristic, complemented
190C53×#501C2211yescharacteristic, complemented
191C53×#497C2211yescharacteristic, complemented
192C53×#488C2211yescharacteristic, complemented
193C53×#487C2211yescharacteristic, complemented
194C53×#470C2211yescharacteristic, complemented
195C53×#468C2211yescharacteristic
196C53×#467C2211yescharacteristic, complemented
197C53×#465C2211yescharacteristic
198C53×#441C2211yescharacteristic, complemented
199C53×#440C2211yescharacteristic, complemented
200C4×Q16×C53C2211yescharacteristic, complemented
201C4×SD16×C53C2211yescharacteristic, complemented
202C53×#405C2211yescharacteristic, complemented
203C2×#11719949C2311yescharacteristic
204C2×#11719949C2311yescharacteristic
205C2×#11719949C2311yescharacteristic
206C2×#11719945C2311yescharacteristic
207C22×D212C2311yescharacteristic
208C2×D4×D53C2311yescharacteristic
209#13133245—24no—
210#13133244—24no—
211#13133240—24no—
212C2×#11719925C2311yescharacteristic
213C2×#11719925C2311yescharacteristic
214C2×#11719913C2311yescharacteristic
215C2×#11719913C2311yescharacteristic
216C2×#11719924C2311yescharacteristic
217C2×#11719924C2311yescharacteristic
218C2×#11719924C2311yescharacteristic
219C2×#11719924C2311yescharacteristic
220C2×D424C2311yescharacteristic
221C2×D424C2311yescharacteristic
222C2×#11719922C2311yescharacteristic
223C2×#11719922C2311yescharacteristic
224C2×#11719912C2311yescharacteristic
225C2×C8×D53C2311yescharacteristic
226C2×C8×D53C2311yescharacteristic
227C2×C8×D53C2311yescharacteristic
228#13133216C2311yescharacteristic
229#13133215C2311yescharacteristic
230#13133212—21no—
231#13133212—21no—
232#13133212—21no—
233#13133212—21no—
234#13133212—21no—
235#13133212—21no—
236#13133212—21no—
237#13133212—21no—
238#13133212—21no—
239#13133212D411yescharacteristic
240#13133211—21no—
241#13133211—21no—
242#13133210—21no—
243#13133210—21no—
244#13133210—21no—
245#13133210—21no—
246#13133210—21no—
247#13133210—21no—
248#13133210D411yescharacteristic
249#13133209—21no—
250#13133208—21no—
251#13133208C2311yescharacteristic
252#13133208C2311yescharacteristic
253#13133208C2311yescharacteristic
254#13133207—21no—
255#13133207—21no—
256#13133207D411yescharacteristic
257#13133206—21no—
258#13133206C2311yescharacteristic
259#13133206C2311yescharacteristic
260#13133205—21no—
261#13133204C2311yescharacteristic
262#13133203—21no—
263#13133203D411yescharacteristic
264#13133202—21no—
265#13133202—21no—
266#13133202—21no—
267#13133202—21no—
268#13133202—21no—
269#13133202—21no—
270#13133202—21no—
271#13133202—21no—
272#13133202D411yescharacteristic
273#13133201—21no—
274#13133201—21no—
275#13133199—21no—
276#13133199—21no—
277#13133199—21no—
278#13133199—21no—
279#13133199—21no—
280#13133199D411yescharacteristic
281#13133197—21no—
282#13133197—21no—
283#13133197—21no—
284#13133197C2311yescharacteristic
285#13133197C2311yescharacteristic
286#13133195—21no—
287#13133195—21no—
288#13133195—21no—
289#13133195D411yescharacteristic
290#13133194—21no—
291#13133193—21no—
292#13133193—21no—
293#13133193C2311yescharacteristic
294#13133193C2311yescharacteristic
295#13133193C2311yescharacteristic
296#13133192—21no—
297#13133192—21no—
298#13133192—21no—
299#13133192—21no—
300#13133192C2311yescharacteristic
301#13133192C2311yescharacteristic
302#13133190—21no—
303#13133190—21no—
304#13133190D411yescharacteristic
305#13133189—21no—
306#13133188—21no—
307#13133188C2311yescharacteristic
308#13133187—21no—
309#13133187—21no—
310#13133187—21no—
311#13133185—21no—
312Q8×Dic53—21no—
313Q8×Dic53C2311yescharacteristic
314Q8×Dic53C2311yescharacteristic
315Q8×Dic53C2311yescharacteristic
316C4×Dic106C2311yescharacteristic
317C4×Dic106C2311yescharacteristic
318C4×Dic106C2311yescharacteristic
319#13133182—21no—
320C4×D212—21no—
321C4×D212—21no—
322C4×D212—21no—
323C4×D212—21no—
324C4×D212C2311yescharacteristic
325C4×D212C2311yescharacteristic
326C4×D212C2311yescharacteristic
327C4×D212C2311yescharacteristic
328C4×D212C2311yescharacteristic
329C4×D212C2311yescharacteristic
330C4×D212C2311yescharacteristic
331D4×Dic53—21no—
332D4×Dic53C2311yescharacteristic
333#13133179—21no—
334#13133179—21no—
335#13133179—21no—
336#13133179—21no—
337#13133179—21no—
338#13133179—21no—
339#13133179C2311yescharacteristic
340#13133179C2311yescharacteristic
341#13133179C2311yescharacteristic
342#13133179C2311yescharacteristic
343C4×C22⋊D53—21no—
344C4×C22⋊D53—21no—
345C4×C22⋊D53C2311yescharacteristic
346C4×C22⋊D53C2311yescharacteristic
347#13133177—21no—
348#13133177—21no—
349#13133177—21no—
350#13133176—21no—
351#13133176C2311yescharacteristic
352#13133175—21no—
353#13133175—21no—
354#13133175—21no—
355#13133175—21no—
356#13133175—21no—
357#13133175C2311yescharacteristic
358#13133175C2311yescharacteristic
359#13133175C2311yescharacteristic
360#13133174—21no—
361#13133174—21no—
362#13133174C2311yescharacteristic
363#13133173—21no—
364#13133173—21no—
365C2×C4⋊Dic53C2311yescharacteristic
366C4⋊C4×D53—21no—
367C4⋊C4×D53—21no—
368C4⋊C4×D53—21no—
369C4⋊C4×D53—21no—
370C4⋊C4×D53—21no—
371C4⋊C4×D53—21no—
372C4⋊C4×D53C2311yescharacteristic
373C2×#11719921—21no—
374C22⋊C4×D53—21no—
375C22⋊C4×D53—21no—
376C22⋊C4×D53—21no—
377C22⋊C4×D53—21no—
378C22⋊C4×D53—21no—
379C22⋊C4×D53—21no—
380C22⋊C4×D53—21no—
381C42×D53—21no—
382C42×D53—21no—
383C42×D53C2311yescharacteristic
384#13133151C2311yescharacteristic
385#13133151C2311yescharacteristic
386#13133150C2311yescharacteristic
387#13133150C2311yescharacteristic
388#13133150C2311yescharacteristic
389#13133150C2311yescharacteristic
390#13133149C2311yescharacteristic
391#13133149C2311yescharacteristic
392#13133148C2311yescharacteristic
393#13133148C2311yescharacteristic
394#13133148C2311yescharacteristic
395#13133148C2311yescharacteristic
396C4⋊#88322C2311yescharacteristic
397C4⋊#88322C2311yescharacteristic
398#13133146C2311yescharacteristic
399#13133146C2311yescharacteristic
400#13133146C2311yescharacteristic
401#13133146C2311yescharacteristic
402#13133142C2311yescharacteristic
403#13133142C2311yescharacteristic
404#13133141C2311yescharacteristic
405#13133141C2311yescharacteristic
406#13133141C2311yescharacteristic
407#13133141C2311yescharacteristic
408#13133141C2311yescharacteristic
409#13133141C2311yescharacteristic
410#13133140C2311yescharacteristic
411#13133140C2311yescharacteristic
412#13133139C2311yescharacteristic
413#13133139C2311yescharacteristic
414#13133139C2311yescharacteristic
415#13133139C2311yescharacteristic
416#13133139C2311yescharacteristic
417#13133139C2311yescharacteristic
418#13133138C2311yescharacteristic
419#13133138C2311yescharacteristic
420#13133137C2311yescharacteristic
421#13133137C2311yescharacteristic
422#13133137C2311yescharacteristic
423#13133137C2311yescharacteristic
424#13133137C2311yescharacteristic
425#13133137C2311yescharacteristic
426C22⋊#88322C2311yescharacteristic
427C22⋊#88322C2311yescharacteristic
428#13133129C2311yescharacteristic
429#13133129C2311yescharacteristic
430#13133129C2311yescharacteristic
431#13133129C2311yescharacteristic
432#13133128C2311yescharacteristic
433#13133127C2311yescharacteristic
434C4×#88322C2311yescharacteristic
435C8×Dic53C2311yescharacteristic
436C8×Dic53C2311yescharacteristic
437C8×Dic53C2311yescharacteristic
438C2×Q16×C53C2311yescharacteristic
439C2×Q16×C53C2311yescharacteristic
440C2×SD16×C53C2311yescharacteristic
441C2×SD16×C53C2311yescharacteristic
442C2×M16×C53C2311yescharacteristic
443C22×C8×C53C2311yescharacteristic
444C4⋊Q8×C53C2311yescharacteristic
445C4⋊Q8×C53C2311yescharacteristic
446#126×C53—21no—
447#126×C53—21no—
448#126×C53—21no—
449#125×C53—21no—
450#125×C53—21no—
451#125×C53C2311yescharacteristic
452#124×C53—21no—
453#124×C53C2311yescharacteristic
454#123×C53—21no—
455C22⋊Q8×C53—21no—
456C22⋊Q8×C53C2311yescharacteristic
457C22⋊Q8×C53C2311yescharacteristic
458C22⋊Q8×C53C2311yescharacteristic
459#121×C53C2311yescharacteristic
460C4×Q8×C53C2311yescharacteristic
461C4×Q8×C53C2311yescharacteristic
462C4×Q8×C53C2311yescharacteristic
463C4×D4×C53C2311yescharacteristic
464#117×C53C2311yescharacteristic
465#107×C53C2311yescharacteristic
466#107×C53C2311yescharacteristic
467#106×C53C2311yescharacteristic
468#106×C53C2311yescharacteristic
469#103×C53C2311yescharacteristic
470#103×C53C2311yescharacteristic
471#103×C53C2311yescharacteristic
472#103×C53C2311yescharacteristic
473#103×C53C2311yescharacteristic
474#103×C53C2311yescharacteristic
475#102×C53C2311yescharacteristic
476#102×C53C2311yescharacteristic
477#97×C53C2311yescharacteristic
478#97×C53C2311yescharacteristic
479C4×C8×C53C2311yescharacteristic
480C4×C8×C53C2311yescharacteristic
481C23×D53—21no—
482C23×D53—21no—
483C2×Q8×C53—21no—
484C2×Q8×C53C2411yescharacteristic
485C2×Q8×C53C2411yescharacteristic
486C2×Q8×C53C2411yescharacteristic
487C2×D4×C53—21no—
488C2×D4×C53C2411yescharacteristic
489C22×C4×C53—21no—
490C22×C4×C53C2411yescharacteristic
491C2×C22⋊D53—21no—
492C2×C22⋊D53—21no—
493C2×C22⋊D53—21no—
494C2×C22⋊D53C2×D411yescharacteristic
495C2×C22⋊D53C2×D411yescharacteristic
496C22×Dic53—21no—
497C22×Dic53—21no—
498#11719949—22no—
499#11719949—22no—
500#11719949—22no—
501#11719949—41no—
502#11719949—41no—
503#11719949—41no—
504D4×D53—22no—
505D4×D53—41no—
506#11719945—22no—
507#11719945—41no—
508C2×D212—22no—
509C2×D212—21no—
510C2×D212—21no—
511C2×D212—21no—
512C2×D212—21no—
513C2×D212—21no—
514C2×D212—21no—
515C2×D212—41no—
516C2×D212C2×D411yescharacteristic
517C2×D212C2411yescharacteristic
518C2×D212C2411yescharacteristic
519C2×D212C2411yescharacteristic
520C2×C4×D53—21no—
521C2×C4×D53—21no—
522C2×C4×D53—21no—
523C2×C4×D53—21no—
524C2×C4×D53—21no—
525C2×C4×D53—21no—
526C2×C4×D53—21no—
527C2×C4×D53—21no—
528C2×C4×D53—21no—
529C2×C4×D53—21no—
530C2×C4×D53—21no—
531C2×C4×D53—21no—
532C2×C4×D53—21no—
533C2×C4×D53—21no—
534C2×C4×D53—21no—
535C2×C4×D53C2×D411yescharacteristic
536C2×C4×D53C2×D411yescharacteristic
537C2×C4×D53C2411yescharacteristic
538C2×C4×D53C2411yescharacteristic
539C2×Dic106—21no—
540C2×Dic106C2×D411yescharacteristic
541C2×Dic106C2411yescharacteristic
542Q16×C53—22no—
543Q16×C53—41no—
544SD16×C53—22no—
545SD16×C53—41no—
546M16×C53—22no—
547C2×C8×C53—41no—
548C2×C8×C53C2411yescharacteristic
549C2×C8×C53C2411yescharacteristic
550C2×C8×C53C2411yescharacteristic
551C2×C8×C53C2411yescharacteristic
552C4⋊C4×C53—21no—
553C4⋊C4×C53—21no—
554C4⋊C4×C53—21no—
555C4⋊C4×C53—21no—
556C4⋊C4×C53—21no—
557C4⋊C4×C53—21no—
558C4⋊C4×C53—21no—
559C4⋊C4×C53—21no—
560C4⋊C4×C53—21no—
561C4⋊C4×C53—21no—
562C4⋊C4×C53—21no—
563C4⋊C4×C53C2×D411yescharacteristic
564C4⋊C4×C53C2×D411yescharacteristic
565C4⋊C4×C53C2411yescharacteristic
566C4⋊C4×C53C2411yescharacteristic
567C4⋊C4×C53C2411yescharacteristic
568C4⋊C4×C53C2411yescharacteristic
569C22⋊C4×C53—21no—
570C22⋊C4×C53—21no—
571C22⋊C4×C53—21no—
572C22⋊C4×C53—21no—
573C22⋊C4×C53—21no—
574C22⋊C4×C53—21no—
575C22⋊C4×C53—21no—
576C22⋊C4×C53C2×D411yescharacteristic
577C22⋊C4×C53C2×D411yescharacteristic
578C42×C53—21no—
579C42×C53—21no—
580C42×C53—21no—
581C42×C53C2411yescharacteristic
582C42×C53C2411yescharacteristic
583C22⋊Dic53—21no—
584C22⋊Dic53—21no—
585C22⋊Dic53—21no—
586C22⋊Dic53—21no—
587C22⋊Dic53—21no—
588C22⋊Dic53C2×D411yescharacteristic
589C22⋊Dic53C2×D411yescharacteristic
590#11719925—41no—
591#11719925—41no—
592#11719924—22no—
593#11719924—22no—
594#11719924—22no—
595#11719924—41no—
596#11719922—22no—
597#11719922—41no—
598#11719921—21no—
599#11719921—21no—
600#11719921—21no—
601#11719921—21no—
602#11719921—21no—
603#11719921—21no—
604#11719921—21no—
605#11719921—21no—
606#11719921—21no—
607#11719921—21no—
608#11719921—21no—
609#11719921—21no—
610#11719921—21no—
611#11719921—21no—
612#11719921—21no—
613#11719921—21no—
614#11719921—21no—
615#11719921—21no—
616#11719921—21no—
617#11719921—21no—
618#11719921—21no—
619#11719921—21no—
620#11719921—21no—
621#11719921—21no—
622#11719921C2×D411yescharacteristic
623#11719921C2×D411yescharacteristic
624#11719921C2×D411yescharacteristic
625#11719921C2×D411yescharacteristic
626#11719921C2×D411yescharacteristic
627#11719921C2×D411yescharacteristic
628C4⋊Dic53—21no—
629C4⋊Dic53—21no—
630C4⋊Dic53—21no—
631C4⋊Dic53—21no—
632C4⋊Dic53—21no—
633C4⋊Dic53—21no—
634C4⋊Dic53—21no—
635C4⋊Dic53—21no—
636C4⋊Dic53—21no—
637C4⋊Dic53C2×D411yescharacteristic
638C4⋊Dic53C2×D411yescharacteristic
639C4⋊Dic53C2411yescharacteristic
640C4⋊Dic53C2411yescharacteristic
641C4⋊Dic53C2411yescharacteristic
642C4⋊Dic53C2411yescharacteristic
643#11719919—21no—
644#11719919—21no—
645#11719919—21no—
646#11719919—21no—
647#11719919—21no—
648#11719919—21no—
649#11719919—21no—
650#11719919—21no—
651#11719919—21no—
652#11719919—21no—
653#11719919—21no—
654#11719919—21no—
655#11719919C2×D411yescharacteristic
656#11719919C2×D411yescharacteristic
657#11719919C2×D411yescharacteristic
658#11719919C2×D411yescharacteristic
659#11719919C2×D411yescharacteristic
660#11719919C2×D411yescharacteristic
661C4×Dic53—21no—
662C4×Dic53—21no—
663C4×Dic53—21no—
664C4×Dic53—21no—
665C4×Dic53—21no—
666C4×Dic53—21no—
667C4×Dic53—21no—
668C4×Dic53—21no—
669C4×Dic53—21no—
670C4×Dic53C2×D411yescharacteristic
671C4×Dic53C2×D411yescharacteristic
672C4×Dic53C2411yescharacteristic
673C4×Dic53C2411yescharacteristic
674C2×#88322C2411yescharacteristic
675C2×#88322C2411yescharacteristic
676C2×#88322C2411yescharacteristic
677C2×#88322C2411yescharacteristic
678D424—22no—
679D424#4114yes—
680#11719913—22no—
681#11719913—22no—
682#11719912—22no—
683C8×D53—22no—
684C8×D53—41no—
685C8×D53—41no—
686C23×C53—21no—
687C23×C53C22×D411yescharacteristic
688C22×D53—21no—
689C22×D53—21no—
690C22×D53—21no—
691C22×D53—42no—
692C22×D53—42no—
693C22×D53—81no—
694C22×D53—81no—
695C22×D53—81no—
696C22×D53—81no—
697C22×D53C22×D411yescharacteristic
698C22×D53C22×D411yescharacteristic
699Q8×C53—21no—
700Q8×C53—21no—
701Q8×C53—21no—
702Q8×C53—21no—
703Q8×C53—21no—
704Q8×C53—21no—
705Q8×C53—81no—
706D4×C53—21no—
707D4×C53—21no—
708D4×C53—81no—
709C2×C4×C53—21no—
710C2×C4×C53—21no—
711C2×C4×C53—21no—
712C2×C4×C53—21no—
713C2×C4×C53—21no—
714C2×C4×C53—21no—
715C2×C4×C53—21no—
716C2×C4×C53—21no—
717C2×C4×C53—21no—
718C2×C4×C53—81no—
719C2×C4×C53C22×D411yescharacteristic
720C2×C4×C53C22×D411yescharacteristic
721C2×C4×C53C22×D411yescharacteristic
722C2×C4×C53C22×D411yescharacteristic
723C2×C4×C53C22×D411yescharacteristic
724C2×C4×C53C2511yescharacteristic
725C22⋊D53—41no—
726C22⋊D53—41no—
727C22⋊D53—42no—
728C22⋊D53—42no—
729C22⋊D53—81no—
730C2×Dic53—21no—
731C2×Dic53—21no—
732C2×Dic53—21no—
733C2×Dic53—21no—
734C2×Dic53—21no—
735C2×Dic53—81no—
736C2×Dic53—81no—
737C2×Dic53C22×D411yescharacteristic
738C2×Dic53C22×D411yescharacteristic
739C2×Dic53C22×D411yescharacteristic
740C2×Dic53C22×D411yescharacteristic
741C2×Dic53C22×D411yescharacteristic
742C2×Dic53C22×D411yescharacteristic
743D212—21no—
744D212—21no—
745D212—21no—
746D212—21no—
747D212—41no—
748D212—42no—
749D212—42no—
750D212—42no—
751D212—42no—
752D212—81no—
753D212—81no—
754D212C2×#4112yes—
755D212C2×#4112yes—
756C4×D53—21no—
757C4×D53—21no—
758C4×D53—21no—
759C4×D53—21no—
760C4×D53—41no—
761C4×D53—41no—
762C4×D53—42no—
763C4×D53—42no—
764C4×D53—42no—
765C4×D53—42no—
766C4×D53—81no—
767C4×D53—81no—
768C4×D53—81no—
769C4×D53—81no—
770C4×D53—81no—
771C4×D53—81no—
772C4×D53—81no—
773C4×D53—81no—
774C4×D53—81no—
775C4×D53—81no—
776C4×D53—81no—
777Dic106—21no—
778Dic106—21no—
779Dic106—41no—
780Dic106—81no—
781C8×C53—21no—
782C8×C53—21no—
783C8×C53—21no—
784C8×C53C2×#4112yes—
785#88322—21no—
786#88322—21no—
787#88322—21no—
788#88322—21no—
789#61501—531nomaximal, Sylow
790C22×C53—21no—
791C22×C53—21no—
792C22×C53—21no—
793C22×C53—41no—
794C22×C53—41no—
795C22×C53—41no—
796C22×C53C23×D411yescharacteristic
797C2×D53—21no—
798C2×D53—21no—
799C2×D53—21no—
800C2×D53—21no—
801C2×D53—21no—
802C2×D53—21no—
803C2×D53—22no—
804C2×D53—22no—
805C2×D53—41no—
806C2×D53—41no—
807C2×D53—41no—
808C2×D53—41no—
809C2×D53—41no—
810C2×D53—41no—
811C2×D53—41no—
812C2×D53—162no—
813C2×D53—162no—
814C4×C53—21no—
815C4×C53—21no—
816C4×C53—21no—
817C4×C53—21no—
818C4×C53—21no—
819C4×C53—41no—
820C4×C53—41no—
821C4×C53—41no—
822C4×C53—41no—
823C4×C53—41no—
824C4×C53—41no—
825C4×C53—41no—
826C4×C53C22×#4111yescharacteristic
827C4×C53#58511yescharacteristic
828Dic53—21no—
829Dic53—21no—
830Dic53—21no—
831Dic53—21no—
832Dic53—21no—
833Dic53—21no—
834Dic53—41no—
835Dic53—41no—
836Dic53—41no—
837Dic53—41no—
838Dic53—41no—
839#3521—531no—
840#3521—531no—
841#3402—531no—
842#3389—531no—
843#3360—531no—
844#3360—531no—
845#3352—531no—
846#3350—531no—
847#3350—531no—
848#3302—531no—
849#3302—531no—
850#3297—531no—
851#3297—531no—
852#3296—531no—
853#3296—531no—
854#3273—531no—
855#3267—531no—
856#3267—531no—
857#3178—531no—
858#3178D5311yescharacteristic, complemented
859#3168—531no—
860#3120—531no—
861#3120—531no—
862#3118—531no—
863#3118—531no—
864#3111—531no—
865#3111—531no—
866#2966—531no—
867#2946—531no—
868#2946—531no—
869C4×#135—531no—
870C2×C53—41no—
871C2×C53—81no—
872C2×C53D4×#4111yescharacteristic
873C2×C53#358411yescharacteristic
874C2×C53#358411yescharacteristic
875D53—41no—
876D53—41no—
877D53—42no—
878D53—42no—
879D53—81no—
880C2×AGL(1,ℤ/8)—531no—
881C2×AGL(1,ℤ/8)—531no—
882C2×#135—531no—
883#556—531no—
884#556—531no—
885#556—531no—
886#556—531no—
887#554—531no—
888#554—531no—
889#553—531no—
890#553—531no—
891#553—1061no—
892#553—1061no—
893#552—531no—
894#552—531no—
895#552—1061no—
896#552—1061no—
897#551—1061no—
898#551—1061no—
899#551—1061no—
900#551—1061no—
901#547—531no—
902#547—531no—
903#546—531no—
904#546—531no—
905#546—531no—
906#546—531no—
907#542—531no—
908#542C2×D5311yescharacteristic
909#541—531no—
910#541C2×D5311yescharacteristic, complemented
911#539—1061no—
912#539—1061no—
913#538—1061no—
914#538—1061no—
915#529—531no—
916#529—531no—
917#529—531no—
918#529—1061no—
919#529—1061no—
920C2×#126—1061no—
921C2×#126—1061no—
922#520—531no—
923#520—531no—
924#518—531no—
925#518—531no—
926C4×#41—531no—
927C4×#41—531no—
928#501—531no—
929#501C2×D5311yescharacteristic, complemented
930#499—531no—
931#497—531no—
932#497C2×D5311yescharacteristic, complemented
933#495—531no—
934#488—531no—
935#488—531no—
936#488—531no—
937#488C2×D5311yescharacteristic, complemented
938#487—531no—
939#487C2×D5311yescharacteristic, complemented
940#485—531no—
941#485—531no—
942#485—531no—
943#485—531no—
944#484—531no—
945#484—531no—
946#483—531no—
947#483—531no—
948#482—531no—
949#482—531no—
950#482—531no—
951#482—531no—
952#479—531no—
953#479—531no—
954#479—531no—
955#479—531no—
956#478—531no—
957#478—531no—
958#478—531no—
959#478—531no—
960#476—531no—
961#476—531no—
962#474—531no—
963#474—531no—
964#470—531no—
965#470C2×D5311yescharacteristic, complemented
966#468—531no—
967#468C2×D5311yescharacteristic
968#467—531no—
969#467—531no—
970#467C2×D5311yescharacteristic, complemented
971#466—531no—
972#465—531no—
973#465—531no—
974#465—531no—
975#465C2×D5311yescharacteristic
976#464—531no—
977#464—531no—
978#463—531no—
979#463—531no—
980#463—531no—
981#463—531no—
982#463—531no—
983#463—531no—
984#462—531no—
985#462—531no—
986#461—531no—
987#461—531no—
988#452—531no—
989#452—531no—
990#452—531no—
991#452—531no—
992#452—531no—
993#452—531no—
994#450—531no—
995#450—531no—
996#449—531no—
997#449—531no—
998#447—531no—
999#447—531no—
1000#446—531no—
1001C8×Q8—531no—
1002#442—531no—
1003#442—531no—
1004#442—531no—
1005#442—531no—
1006#441—531no—
1007#441C2×D5311yescharacteristic, complemented
1008#440—531no—
1009#440—531no—
1010#440—531no—
1011#440—531no—
1012#440—531no—
1013#440C2×D5311yescharacteristic, complemented
1014C4×Q16—531no—
1015C4×Q16—531no—
1016C4×Q16C2×D5311yescharacteristic, complemented
1017C4×SD16—531no—
1018C4×SD16—531no—
1019C4×SD16—531no—
1020C4×SD16—531no—
1021C4×SD16—531no—
1022C4×SD16—531no—
1023C4×SD16—531no—
1024C4×SD16C2×D5311yescharacteristic, complemented
1025C4×D8—531no—
1026C4×D8—531no—
1027C4×D8—531no—
1028C4×D8—531no—
1029C4×D8—531no—
1030#436—531no—
1031#435—531no—
1032#435—531no—
1033C8×D4—531no—
1034C8×D4—531no—
1035C8×D4—531no—
1036#433—531no—
1037#433—531no—
1038#432—531no—
1039#428—531no—
1040#428—531no—
1041#427—531no—
1042#416—531no—
1043#416—531no—
1044#416—531no—
1045#416—531no—
1046C2×#102—531no—
1047C2×#102—531no—
1048#405—531no—
1049#405C2×D5311yescharacteristic, complemented
1050C2×C4×C8—531no—
1051C53#6150111yescharacteristic, complemented, Sylow
1052C2×#41—531no—
1053C2×#41—531no—
1054C2×#41—531no—
1055C2×#41—531no—
1056C22×D4—531no—
1057C22×D4—531no—
1058AGL(1,ℤ/8)—1064no—
1059AGL(1,ℤ/8)—1064no—
1060#135—1064no—
1061C2×Q16—531no—
1062C2×Q16—531no—
1063C2×Q16C22×D5311yescharacteristic
1064C2×Q16C22×D5311yescharacteristic
1065C2×SD16—531no—
1066C2×SD16—531no—
1067C2×SD16—531no—
1068C2×SD16—531no—
1069C2×SD16—531no—
1070C2×SD16—531no—
1071C2×SD16C22×D5311yescharacteristic
1072C2×SD16C22×D5311yescharacteristic
1073C2×D8—531no—
1074C2×D8—531no—
1075C2×D8—531no—
1076C2×D8—531no—
1077C2×M16—531no—
1078C2×M16C22×D5311yescharacteristic
1079C22×C8—531no—
1080C22×C8—531no—
1081C22×C8—531no—
1082C22×C8C22×D5311yescharacteristic
1083C4⋊Q8—531no—
1084C4⋊Q8—531no—
1085C4⋊Q8C22×D5311yescharacteristic
1086C4⋊Q8C22×D5311yescharacteristic
1087#126—21no—
1088#126—21no—
1089#126—21no—
1090#126—531no—
1091#126—531no—
1092#126—1061no—
1093#126—1061no—
1094#126—1061no—
1095#126—1061no—
1096#126—1061no—
1097#126—1061no—
1098#126—1061no—
1099#126—1061no—
1100#126—1061no—
1101#126—1061no—
1102#126—1061no—
1103#126—1061no—
1104#126—1061no—
1105#126—1061no—
1106#126—1061no—
1107#126—1061no—
1108#126—1061no—
1109#125—21no—
1110#125—21no—
1111#125—531no—
1112#125—531no—
1113#125—531no—
1114#125—531no—
1115#125—1061no—
1116#125—1061no—
1117#125—1061no—
1118#125—1061no—
1119#125C22×D5311yescharacteristic
1120#124—21no—
1121#124—531no—
1122#124—531no—
1123#124—531no—
1124#124—531no—
1125#124—1061no—
1126#124—1061no—
1127#124—1061no—
1128#124C22×D5311yescharacteristic
1129#123—21no—
1130#123—531no—
1131#123—531no—
1132#123—1061no—
1133#123—1061no—
1134#123—1061no—
1135#123—1061no—
1136#123—1061no—
1137#123—1061no—
1138#123—1061no—
1139#123—1061no—
1140#123—1061no—
1141#123—1061no—
1142#123—1061no—
1143#123—1061no—
1144#123—1061no—
1145#123—1061no—
1146#123—1061no—
1147C22⋊Q8—21no—
1148C22⋊Q8—531no—
1149C22⋊Q8—531no—
1150C22⋊Q8—531no—
1151C22⋊Q8—531no—
1152C22⋊Q8—531no—
1153C22⋊Q8—531no—
1154C22⋊Q8—1061no—
1155C22⋊Q8—1061no—
1156C22⋊Q8—1061no—
1157C22⋊Q8—1061no—
1158C22⋊Q8—1061no—
1159C22⋊Q8—1061no—
1160C22⋊Q8—1061no—
1161C22⋊Q8—1061no—
1162C22⋊Q8—1061no—
1163C22⋊Q8C22×D5311yescharacteristic
1164C22⋊Q8C22×D5311yescharacteristic
1165C22⋊Q8C22×D5311yescharacteristic
1166#121—531no—
1167#121—531no—
1168#121—531no—
1169#121—531no—
1170#121—1061no—
1171#121—1061no—
1172#121—1061no—
1173#121—1061no—
1174#121—1061no—
1175#121—1061no—
1176#121—1061no—
1177#121—1061no—
1178#121C22×D5311yescharacteristic
1179#120—1061no—
1180#120—1061no—
1181#120—1061no—
1182#120—1061no—
1183C4×Q8—531no—
1184C4×Q8—531no—
1185C4×Q8—531no—
1186C4×Q8—531no—
1187C4×Q8—531no—
1188C4×Q8—531no—
1189C4×Q8—1061no—
1190C4×Q8—1061no—
1191C4×Q8C22×D5311yescharacteristic
1192C4×Q8C22×D5311yescharacteristic
1193C4×Q8C22×D5311yescharacteristic
1194C4×D4—531no—
1195C4×D4—531no—
1196C4×D4—531no—
1197C4×D4—531no—
1198C4×D4—531no—
1199C4×D4—531no—
1200C4×D4—531no—
1201C4×D4—531no—
1202C4×D4—531no—
1203C4×D4—531no—
1204C4×D4—531no—
1205C4×D4—531no—
1206C4×D4—531no—
1207C4×D4—531no—
1208C4×D4—1061no—
1209C4×D4—1061no—
1210C4×D4—1061no—
1211C4×D4—1061no—
1212C4×D4—1061no—
1213C4×D4—1061no—
1214C4×D4—1061no—
1215C4×D4—1061no—
1216C4×D4—1061no—
1217C4×D4—1061no—
1218C4×D4—1061no—
1219C4×D4—1061no—
1220C4×D4—1061no—
1221C4×D4—1061no—
1222C4×D4—1061no—
1223C4×D4—1061no—
1224C4×D4C22×D5311yescharacteristic
1225#117—531no—
1226#117—531no—
1227#117—531no—
1228#117—531no—
1229#117—531no—
1230#117—1061no—
1231#117—1061no—
1232#117—1061no—
1233#117—1061no—
1234#117—1061no—
1235#117—1061no—
1236#117—1061no—
1237#117—1061no—
1238#117—1061no—
1239#117—1061no—
1240#117C22×D5311yescharacteristic
1241C2×C4⋊C4—531no—
1242C2×C4⋊C4—531no—
1243C2×C4⋊C4—1061no—
1244C2×C4⋊C4—1061no—
1245C2×C4⋊C4—1061no—
1246C2×C4⋊C4—1061no—
1247C2×C4⋊C4—1061no—
1248C2×C4⋊C4—1061no—
1249C2×C22⋊C4—1061no—
1250C2×C22⋊C4—1061no—
1251C2×C22⋊C4—1061no—
1252C2×C22⋊C4—1061no—
1253C2×C22⋊C4—1061no—
1254C2×C22⋊C4—1061no—
1255C2×C22⋊C4—1061no—
1256C2×C22⋊C4—1061no—
1257C2×C42—531no—
1258C2×C42—1061no—
1259C2×C42—1061no—
1260#107—531no—
1261#107—531no—
1262#107—531no—
1263#107—531no—
1264#107—531no—
1265#107—531no—
1266#107C22×D5311yescharacteristic
1267#107C22×D5311yescharacteristic
1268#106—531no—
1269#106—531no—
1270#106—531no—
1271#106—531no—
1272#106—531no—
1273#106—531no—
1274#106C22×D5311yescharacteristic
1275#106C22×D5311yescharacteristic
1276C4⋊C8—531no—
1277C4⋊C8—531no—
1278C4⋊C8—531no—
1279C4⋊C8—531no—
1280C4⋊C8—531no—
1281C4⋊C8—531no—
1282#103—531no—
1283#103—531no—
1284#103—531no—
1285#103—531no—
1286#103—531no—
1287#103—531no—
1288#103—531no—
1289#103—531no—
1290#103—531no—
1291#103—531no—
1292#103C22×D5311yescharacteristic
1293#103C22×D5311yescharacteristic
1294#103C22×D5311yescharacteristic
1295#103C22×D5311yescharacteristic
1296#103C22×D5311yescharacteristic
1297#103C22×D5311yescharacteristic
1298#102—531no—
1299#102—531no—
1300#102—531no—
1301#102—531no—
1302#102—531no—
1303#102—531no—
1304#102—531no—
1305#102—531no—
1306#102—531no—
1307#102—531no—
1308#102—531no—
1309#102—531no—
1310#102—531no—
1311#102—531no—
1312#102C22×D5311yescharacteristic
1313#102C22×D5311yescharacteristic
1314C22⋊C8—531no—
1315C22⋊C8—531no—
1316C22⋊C8—531no—
1317C22⋊C8—531no—
1318C22⋊C8—531no—
1319C22⋊C8—531no—
1320#97—531no—
1321#97—531no—
1322#97C22×D5311yescharacteristic
1323#97C22×D5311yescharacteristic
1324C4×C8—531no—
1325C4×C8—531no—
1326C4×C8—531no—
1327C4×C8—531no—
1328C4×C8C22×D5311yescharacteristic
1329C4×C8C22×D5311yescharacteristic
1330C24—1061no—
1331C24—1061no—
1332#41—1062no—
1333#41—1062no—
1334#41—1062no—
1335#41—1062no—
1336#41—2121no—
1337#41—2121no—
1338#41—2121no—
1339#41—2121no—
1340C2×Q8—21no—
1341C2×Q8—531no—
1342C2×Q8—531no—
1343C2×Q8—1061no—
1344C2×Q8C23×D5311yescharacteristic
1345C2×Q8C23×D5311yescharacteristic
1346C2×Q8C23×D5311yescharacteristic
1347C2×D4—21no—
1348C2×D4—531no—
1349C2×D4—531no—
1350C2×D4—531no—
1351C2×D4—531no—
1352C2×D4—531no—
1353C2×D4—531no—
1354C2×D4—1062no—
1355C2×D4—1061no—
1356C2×D4—1061no—
1357C2×D4—1061no—
1358C2×D4—1061no—
1359C2×D4—1061no—
1360C2×D4—1061no—
1361C2×D4—1062no—
1362C2×D4—1061no—
1363C2×D4—1061no—
1364C2×D4—1061no—
1365C2×D4—2121no—
1366C2×D4—2121no—
1367C2×D4C23×D5311yescharacteristic
1368C22×C4—21no—
1369C22×C4—531no—
1370C22×C4—531no—
1371C22×C4—531no—
1372C22×C4—531no—
1373C22×C4—1061no—
1374C22×C4—1061no—
1375C22×C4—1061no—
1376C22×C4—1061no—
1377C22×C4—1061no—
1378C22×C4—1061no—
1379C22×C4—1061no—
1380C22×C4—1061no—
1381C22×C4—1061no—
1382C22×C4—1061no—
1383C22×C4—1061no—
1384C22×C4—1061no—
1385C22×C4—1061no—
1386C22×C4—1061no—
1387C22×C4—1061no—
1388C22×C4—1061no—
1389C22×C4—1061no—
1390C22×C4C23×D5311yescharacteristic
1391Q16—22no—
1392Q16—41no—
1393Q16—2121no—
1394Q16—2121no—
1395SD16—22no—
1396SD16—41no—
1397SD16—1062no—
1398SD16—1062no—
1399SD16—1062no—
1400SD16—1062no—
1401SD16—1062no—
1402SD16—2121no—
1403D8—534no—
1404D8—1062no—
1405D8—1062no—
1406D8—2121no—
1407M16—22no—
1408M16—1062no—
1409C2×C8—41no—
1410C2×C8—531no—
1411C2×C8—531no—
1412C2×C8—531no—
1413C2×C8—531no—
1414C2×C8—1062no—
1415C2×C8—2121no—
1416C2×C8—2121no—
1417C2×C8C23×D5311yescharacteristic
1418C2×C8C23×D5311yescharacteristic
1419C2×C8C23×D5311yescharacteristic
1420C2×C8C23×D5311yescharacteristic
1421C4⋊C4—21no—
1422C4⋊C4—21no—
1423C4⋊C4—21no—
1424C4⋊C4—21no—
1425C4⋊C4—21no—
1426C4⋊C4—21no—
1427C4⋊C4—21no—
1428C4⋊C4—21no—
1429C4⋊C4—21no—
1430C4⋊C4—21no—
1431C4⋊C4—21no—
1432C4⋊C4—531no—
1433C4⋊C4—531no—
1434C4⋊C4—531no—
1435C4⋊C4—531no—
1436C4⋊C4—531no—
1437C4⋊C4—531no—
1438C4⋊C4—531no—
1439C4⋊C4—531no—
1440C4⋊C4—531no—
1441C4⋊C4—531no—
1442C4⋊C4—531no—
1443C4⋊C4—531no—
1444C4⋊C4—1061no—
1445C4⋊C4—1061no—
1446C4⋊C4—1061no—
1447C4⋊C4—1061no—
1448C4⋊C4—1061no—
1449C4⋊C4—1061no—
1450C4⋊C4—1061no—
1451C4⋊C4—1061no—
1452C4⋊C4—1061no—
1453C4⋊C4—1061no—
1454C4⋊C4—1061no—
1455C4⋊C4—1061no—
1456C4⋊C4—1061no—
1457C4⋊C4—1061no—
1458C4⋊C4—1061no—
1459C4⋊C4—1061no—
1460C4⋊C4—1061no—
1461C4⋊C4—1061no—
1462C4⋊C4—1061no—
1463C4⋊C4—1061no—
1464C4⋊C4—1061no—
1465C4⋊C4D4×D5311yescharacteristic
1466C4⋊C4D4×D5311yescharacteristic
1467C4⋊C4C23×D5311yescharacteristic
1468C4⋊C4C23×D5311yescharacteristic
1469C4⋊C4C23×D5311yescharacteristic
1470C4⋊C4C23×D5311yescharacteristic
1471C22⋊C4—21no—
1472C22⋊C4—21no—
1473C22⋊C4—21no—
1474C22⋊C4—21no—
1475C22⋊C4—21no—
1476C22⋊C4—21no—
1477C22⋊C4—21no—
1478C22⋊C4—531no—
1479C22⋊C4—531no—
1480C22⋊C4—531no—
1481C22⋊C4—531no—
1482C22⋊C4—531no—
1483C22⋊C4—531no—
1484C22⋊C4—531no—
1485C22⋊C4—531no—
1486C22⋊C4—1061no—
1487C22⋊C4—1061no—
1488C22⋊C4—1061no—
1489C22⋊C4—1061no—
1490C22⋊C4—1061no—
1491C22⋊C4—1061no—
1492C22⋊C4—1061no—
1493C22⋊C4—1061no—
1494C22⋊C4—1061no—
1495C22⋊C4—1061no—
1496C22⋊C4—1061no—
1497C22⋊C4—1061no—
1498C22⋊C4—1061no—
1499C22⋊C4—1061no—
1500C22⋊C4—1061no—
1501C22⋊C4—1061no—
1502C22⋊C4—1061no—
1503C22⋊C4—1061no—
1504C22⋊C4—1061no—
1505C22⋊C4—1061no—
1506C22⋊C4—1061no—
1507C22⋊C4—1061no—
1508C22⋊C4—1061no—
1509C22⋊C4—1061no—
1510C22⋊C4—1061no—
1511C22⋊C4—1061no—
1512C22⋊C4—1061no—
1513C22⋊C4—1061no—
1514C22⋊C4—1061no—
1515C22⋊C4D4×D5311yescharacteristic
1516C22⋊C4D4×D5311yescharacteristic
1517C42—21no—
1518C42—21no—
1519C42—21no—
1520C42—531no—
1521C42—531no—
1522C42—531no—
1523C42—531no—
1524C42—1061no—
1525C42—1061no—
1526C42—1061no—
1527C42—1061no—
1528C42—1061no—
1529C42—1061no—
1530C42—1061no—
1531C42—1061no—
1532C42—1061no—
1533C42C23×D5311yescharacteristic
1534C42C23×D5311yescharacteristic
1535C23—21no—
1536C23—531no—
1537C23—531no—
1538C23—1061no—
1539C23—1061no—
1540C23—1061no—
1541C23—4241no—
1542C23—4241no—
1543C23—4241no—
1544C23—4241no—
1545C23—2122no—
1546C23—2122no—
1547C23C2×D4×D5311yescharacteristic
1548Q8—21no—
1549Q8—21no—
1550Q8—21no—
1551Q8—21no—
1552Q8—21no—
1553Q8—21no—
1554Q8—81no—
1555Q8—1061no—
1556Q8—1061no—
1557Q8—4241no—
1558Q8—2121no—
1559D4—21no—
1560D4—21no—
1561D4—81no—
1562D4—532no—
1563D4—532no—
1564D4—1061no—
1565D4—1061no—
1566D4—1061no—
1567D4—1061no—
1568D4—4241no—
1569D4—4241no—
1570D4—4241no—
1571D4—2121no—
1572D4—2122no—
1573D4—2122no—
1574D4—2122no—
1575D4—2122no—
1576D4—2121no—
1577D4—2121no—
1578D4—2122no—
1579D4—2122no—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—81no—
1590C2×C4—531no—
1591C2×C4—531no—
1592C2×C4—531no—
1593C2×C4—531no—
1594C2×C4—531no—
1595C2×C4—531no—
1596C2×C4—1061no—
1597C2×C4—1061no—
1598C2×C4—1061no—
1599C2×C4—1061no—
1600C2×C4—1061no—
1601C2×C4—1061no—
1602C2×C4—1061no—
1603C2×C4—1061no—
1604C2×C4—1061no—
1605C2×C4—4241no—
1606C2×C4—4241no—
1607C2×C4—4241no—
1608C2×C4—4241no—
1609C2×C4—4241no—
1610C2×C4—4241no—
1611C2×C4—4241no—
1612C2×C4—4241no—
1613C2×C4—4241no—
1614C2×C4—4241no—
1615C2×C4—4241no—
1616C2×C4—4241no—
1617C2×C4—4241no—
1618C2×C4—2121no—
1619C2×C4—2121no—
1620C2×C4—2122no—
1621C2×C4—2122no—
1622C2×C4—2122no—
1623C2×C4—2122no—
1624C2×C4C2×D4×D5311yescharacteristic
1625C2×C4C2×D4×D5311yescharacteristic
1626C2×C4C2×D4×D5311yescharacteristic
1627C2×C4C2×D4×D5311yescharacteristic
1628C2×C4C2×D4×D5311yescharacteristic
1629C2×C4C24×D5311yescharacteristic
1630C8—21no—
1631C8—21no—
1632C8—21no—
1633C8—1061no—
1634C8—1061no—
1635C8—1061no—
1636C8—1061no—
1637C8#41×D5312yes—
1638C22—21no—
1639C22—21no—
1640C22—21no—
1641C22—41no—
1642C22—41no—
1643C22—41no—
1644C22—8482no—
1645C22—8482no—
1646C22—1061no—
1647C22—1061no—
1648C22—1062no—
1649C22—1062no—
1650C22—1061no—
1651C22—1061no—
1652C22—1061no—
1653C22—1061no—
1654C22—2121no—
1655C22—2121no—
1656C22—2121no—
1657C22—2121no—
1658C22—2121no—
1659C22—2121no—
1660C22—2121no—
1661C22C22×D4×D5311yescharacteristic
1662C4—21no—
1663C4—21no—
1664C4—21no—
1665C4—21no—
1666C4—21no—
1667C4—41no—
1668C4—41no—
1669C4—41no—
1670C4—41no—
1671C4—41no—
1672C4—41no—
1673C4—41no—
1674C4—1061no—
1675C4—1061no—
1676C4—1061no—
1677C4—1061no—
1678C4—1061no—
1679C4—1061no—
1680C4—2121no—
1681C4—2121no—
1682C4—2121no—
1683C4—2121no—
1684C4—2121no—
1685C4C2×#41×D5311yescharacteristic
1686C4#1681145911yescharacteristic
1687C2—41no—
1688C2—81no—
1689C2—4241no—
1690C2—2121no—
1691C2—2122no—
1692C2—2122no—
1693C2—2121no—
1694C2#2028820111yescharacteristic
1695C2#2028948511yescharacteristic
1696C2#2028948711yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3178C2
socleC22×C53C23×D4
hypercenter#3178D53
hypocenterC53#61501
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #3178

Complements

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

NH ≅ G/Ntype
1. #20288789C2semidirect
2. #20288781C2semidirect
3. #20287791C2semidirect
4. #20287670C2semidirect
5. #20287369C2semidirect
6. #20287361C2semidirect
7. #20287285C2semidirect
8. #20287259C2semidirect
9. #20287255C2semidirect
10. #20286631C2semidirect
11. #20286627C2semidirect
12. #20286571C2semidirect
13. #20286564C2semidirect
14. #20286556C2semidirect
15. #20286545C2semidirect
16. #20286323C2semidirect
17. #20286247C2semidirect
18. #20286239C2semidirect
19. #20285387C2semidirect
20. #20285281C2semidirect
21. #20284927C2semidirect
22. #20284923C2semidirect
23. #20284903C2semidirect
24. #20284893C2semidirect
25. #20284830C2semidirect
26. #20284822C2semidirect
27. #20283686C2semidirect
28. #20283549C2semidirect
29. #20283542C2semidirect
30. C4×#13133240C2semidirect
31. C53×#3178C2semidirect
35. #16811347C22semidirect
36. #16811347C22semidirect
37. #16811344C22semidirect
38. #16811342C22semidirect
39. #16811334C22semidirect
40. #16811329C22semidirect
56. #16811266C22semidirect
58. #16811264C22semidirect
60. #16811231C22semidirect
65. #16811160C22semidirect
67. #16811155C22semidirect
74. #16811097C22semidirect
75. #16811095C22semidirect
76. C4×#11719949C22semidirect
77. C4×#11719949C22semidirect
78. #16811031C22semidirect
79. #16811023C22semidirect
80. #16811016C22semidirect
82. #16810979C22semidirect
83. #16810979C22semidirect
84. #16810976C22semidirect
85. #16810972C22semidirect
86. #16810966C22semidirect
87. #16810962C22semidirect
88. #16810962C22semidirect
89. #16810961C22semidirect
90. #16810957C22semidirect
91. #16810956C22semidirect
92. #16810955C22semidirect
93. #16810951C22semidirect
95. #16810949C22semidirect
96. #16810945C22semidirect
98. #16810932C22semidirect
99. #16810932C22semidirect
100. #16810928C22semidirect
101. #16810927C22semidirect
102. #16810926C22semidirect
103. #16810922C22semidirect
104. #16810922C22semidirect
105. #16810920C22semidirect
106. #16810911C22semidirect
107. #16810910C22semidirect
108. #16810902C22semidirect
109. #16810900C22semidirect
110. #16810878C22semidirect
112. #16810863C22semidirect
113. #16810863C22semidirect
116. #16810853C22semidirect
117. #16810849C22semidirect
118. #16810847C22semidirect
119. #16810843C22semidirect
126. #16810831C22semidirect
127. #16810830C22semidirect
128. #16810827C22semidirect
129. #16810825C22semidirect
131. #16810788C22semidirect
133. #16810784C22semidirect
136. #16810773C22semidirect
137. #16810772C22semidirect
142. #16810751C22semidirect
143. C8×Dic106C22semidirect
148. #16810728C22semidirect
149. #16810725C22semidirect
150. #16810725C22semidirect
151. #16810724C22semidirect
152. #16810721C22semidirect
153. #16810721C22semidirect
154. Q16×Dic53C22semidirect
155. C4×#11719925C22semidirect
156. C4×#11719913C22semidirect
157. C4×#11719913C22semidirect
158. C4×#11719924C22semidirect
159. C4×#11719924C22semidirect
160. #16810708C22semidirect
161. #16810708C22semidirect
162. #16810708C22semidirect
169. #16810696C22semidirect
170. #16810692C22semidirect
171. C8×D212C22semidirect
173. C8×C22⋊D53C22semidirect
174. #16810685C22semidirect
175. #16810684C22semidirect
176. #16810678C22semidirect
177. #16810665C22semidirect
178. #16810662C22semidirect
179. #16810660C22semidirect
182. #16810618C22semidirect
183. #16810618C22semidirect
184. C2×#13133139C22semidirect
185. #102×D53C22semidirect
186. #16810577C22semidirect
187. C4×C8×D53C22semidirect
189. C53×#541C22semidirect
190. C53×#501C22semidirect
191. C53×#497C22semidirect
192. C53×#488C22semidirect
193. C53×#487C22semidirect
194. C53×#470C22semidirect
196. C53×#467C22semidirect
198. C53×#441C22semidirect
199. C53×#440C22semidirect
200. C4×Q16×C53C22semidirect
201. C4×SD16×C53C22semidirect
202. C53×#405C22semidirect
858. #3178D53semidirect
910. #541C2×D53semidirect
929. #501C2×D53semidirect
932. #497C2×D53semidirect
937. #488C2×D53semidirect
939. #487C2×D53semidirect
965. #470C2×D53semidirect
970. #467C2×D53semidirect
1007. #441C2×D53semidirect
1013. #440C2×D53semidirect
1016. C4×Q16C2×D53semidirect
1024. C4×SD16C2×D53semidirect
1049. #405C2×D53semidirect
1051. C53#61501semidirect

Maximal subgroups

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

subgroupindex
#202887892
#202887812
#202877912
#202876702
#202873692
#202873612
#202872852
#202872592
#202872552
#202866312
#202866272
#202865712
#202865642
#202865562
#202865452
#202863232
#202862472
#202862392
#202853872
#202852812
#202849272
#202849232
#202849032
#202848932
#202848302
#202848222
#202836862
#202835492
#202835422
C4×#131332402
C53×#31782
#6150153