Finite Group Databasebeta

← #28257128

Subgroups — #28257128

Order 13568.

1822 conjugacy classes of subgroups.

The subgroup lattice has 1726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288099C211yesmaximal, characteristic, complemented
2#542×D53C211yesmaximal, characteristic, complemented
3#20286187C211yesmaximal, characteristic, complemented
4#20286185C211yesmaximal, characteristic, complemented
5#20286182C211yesmaximal, characteristic, complemented
6#20286179C211yesmaximal, characteristic, complemented
7#20286175C211yesmaximal, characteristic, complemented
8#20286173C211yesmaximal, characteristic, complemented
9#20286172C211yesmaximal, characteristic, complemented
10#20286170C211yesmaximal, characteristic, complemented
11#20286147C211yesmaximal, characteristic, complemented
12#20286145C211yesmaximal, characteristic, complemented
13#20286143C211yesmaximal, characteristic, complemented
14#20286141C211yesmaximal, characteristic, complemented
15#20286124C211yesmaximal, characteristic, complemented
16#20286122C211yesmaximal, characteristic, complemented
17#20286120C211yesmaximal, characteristic, complemented
18#20284527C211yesmaximal, characteristic, complemented
19#20284523C211yesmaximal, characteristic, complemented
20#20284518C211yesmaximal, characteristic, complemented
21#20284510C211yesmaximal, characteristic, complemented
22#20284340C211yesmaximal, characteristic, complemented
23#20284338C211yesmaximal, characteristic, complemented
24#20284333C211yesmaximal, characteristic, complemented
25#20284331C211yesmaximal, characteristic, complemented
26#20284204C211yesmaximal, characteristic, complemented
27#20284204C211yesmaximal, characteristic, complemented
28#20284182C211yesmaximal, characteristic, complemented
29#20284174C211yesmaximal, characteristic, complemented
30#20283276C211yesmaximal, characteristic, complemented
31C53×#3257C211yesmaximal, characteristic, complemented
32C2×#13133246C2211yescharacteristic
33C2×#13133246C2211yescharacteristic
34C2×#13133241C2211yescharacteristic
35C2×#13133241C2211yescharacteristic
36C22×#11719912C2211yescharacteristic
37C2×M16×D53C2211yescharacteristic
38#16811247C2211yescharacteristic
39#16811246C2211yescharacteristic
40#16811245C2211yescharacteristic
41#16811244C2211yescharacteristic
42#16811243—21no—
43#16811242C2211yescharacteristic
44#16811241—21no—
45#16811240C2211yescharacteristic
46#16811240C2211yescharacteristic, complemented
47#16811240C2211yescharacteristic, complemented
48#16811239—21no—
49#16811238C2211yescharacteristic
50#16811238C2211yescharacteristic, complemented
51#16811238C2211yescharacteristic, complemented
52#16811237—21no—
53#16811236C2211yescharacteristic, complemented
54#16811235C2211yescharacteristic, complemented
55#16811227C2211yescharacteristic, complemented
56#16811216—21no—
57#16811216—21no—
58#16811205—21no—
59#16811205—21no—
60#16811179C2211yescharacteristic
61#16811171C2211yescharacteristic
62C4⋊Q8×D53C2211yescharacteristic
63#16811154—21no—
64#16811154—21no—
65#16811150—21no—
66#16811150—21no—
67#126×D53—21no—
68#124×D53—21no—
69#124×D53C2211yescharacteristic
70#16811133C2211yescharacteristic
71#16811133C2211yescharacteristic
72#123×D53—21no—
73C22⋊Q8×D53—21no—
74C22⋊Q8×D53C2211yescharacteristic
75#121×D53C2211yescharacteristic
76C4×#11719947C2211yescharacteristic
77C4×#11719947C2211yescharacteristic
78C4×Q8×D53C2211yescharacteristic
79C4×D4×D53C2211yescharacteristic
80#117×D53C2211yescharacteristic
81#16810931C2211yescharacteristic, complemented
82#16810930C2211yescharacteristic, complemented
83#16810927C2211yescharacteristic, complemented
84#16810924C2211yescharacteristic, complemented
85#16810923C2211yescharacteristic, complemented
86#16810920C2211yescharacteristic, complemented
87#16810919C2211yescharacteristic, complemented
88#16810917C2211yescharacteristic, complemented
89#16810917C2211yescharacteristic, complemented
90#16810917C2211yescharacteristic, complemented
91#16810916C2211yescharacteristic, complemented
92#16810915C2211yescharacteristic, complemented
93#16810913C2211yescharacteristic, complemented
94#16810912C2211yescharacteristic, complemented
95#16810911C2211yescharacteristic, complemented
96#16810911C2211yescharacteristic, complemented
97#16810911C2211yescharacteristic, complemented
98#16810909C2211yescharacteristic, complemented
99#16810907C2211yescharacteristic, complemented
100#16810907C2211yescharacteristic, complemented
101#16810907C2211yescharacteristic, complemented
102#16810906C2211yescharacteristic, complemented
103#16810905C2211yescharacteristic, complemented
104#16810903C2211yescharacteristic, complemented
105#16810902C2211yescharacteristic, complemented
106#16810901C2211yescharacteristic, complemented
107#16810901C2211yescharacteristic, complemented
108#16810901C2211yescharacteristic, complemented
109#16810882C2211yescharacteristic, complemented
110#16810881C2211yescharacteristic, complemented
111#16810880C2211yescharacteristic, complemented
112#16810879C2211yescharacteristic, complemented
113#16810875C2211yescharacteristic
114#16810874C2211yescharacteristic
115#16810873C2211yescharacteristic
116#16810870C2211yescharacteristic
117#16810869C2211yescharacteristic
118#16810868C2211yescharacteristic
119#16810868C2211yescharacteristic, complemented
120#16810867C2211yescharacteristic
121#16810867C2211yescharacteristic, complemented
122#16810866C2211yescharacteristic, complemented
123#16810865C2211yescharacteristic, complemented
124#16810864C2211yescharacteristic, complemented
125#16810863C2211yescharacteristic, complemented
126#16810862C2211yescharacteristic, complemented
127#16810858C2211yescharacteristic
128#16810857C2211yescharacteristic
129#16810856C2211yescharacteristic
130#16810853C2211yescharacteristic
131#16810852C2211yescharacteristic
132#16810851C2211yescharacteristic
133#16810851C2211yescharacteristic, complemented
134#16810850C2211yescharacteristic
135#16810850C2211yescharacteristic, complemented
136#16810849C2211yescharacteristic, complemented
137#16810848C2211yescharacteristic, complemented
138#16810848C2211yescharacteristic, complemented
139#16810846C2211yescharacteristic, complemented
140#16810846C2211yescharacteristic, complemented
141#16810844C2211yescharacteristic, complemented
142#16810844C2211yescharacteristic, complemented
143#16810844C2211yescharacteristic, complemented
144#16810844C2211yescharacteristic, complemented
145#16810843C2211yescharacteristic, complemented
146#16810843C2211yescharacteristic, complemented
147#16810842C2211yescharacteristic, complemented
148#16810842C2211yescharacteristic, complemented
149#16810840C2211yescharacteristic, complemented
150#16810840C2211yescharacteristic, complemented
151#16810838C2211yescharacteristic, complemented
152#16810838C2211yescharacteristic, complemented
153#16810837C2211yescharacteristic, complemented
154#16810837C2211yescharacteristic, complemented
155#16810836C2211yescharacteristic, complemented
156#16810836C2211yescharacteristic, complemented
157#16810836C2211yescharacteristic, complemented
158#16810836C2211yescharacteristic, complemented
159#16810834C2211yescharacteristic, complemented
160#16810833C2211yescharacteristic, complemented
161#16810829C2211yescharacteristic, complemented
162#16810828C2211yescharacteristic, complemented
163#16810820C2211yescharacteristic, complemented
164#16810815C2211yescharacteristic, complemented
165#16810664C2211yescharacteristic
166#16810664C2211yescharacteristic
167#16810662C2211yescharacteristic
168#16810662C2211yescharacteristic
169#16810651C2211yescharacteristic, complemented
170#16810650C2211yescharacteristic, complemented
171#16810649C2211yescharacteristic, complemented
172#16810648C2211yescharacteristic, complemented
173#16810648C2211yescharacteristic, complemented
174#16810648C2211yescharacteristic, complemented
175#16810648C2211yescharacteristic, complemented
176#16810645C2211yescharacteristic
177#16810645C2211yescharacteristic
178#16810645C2211yescharacteristic
179#16810645C2211yescharacteristic
180#16810630C2211yescharacteristic
181#16810630C2211yescharacteristic
182#16810626C2211yescharacteristic
183#16810626C2211yescharacteristic
184#16810621C2211yescharacteristic
185#16810621C2211yescharacteristic
186#16810621C2211yescharacteristic
187#16810621C2211yescharacteristic
188C53×#542C2211yescharacteristic
189C53×#540C2211yescharacteristic, complemented
190C53×#479C2211yescharacteristic, complemented
191C53×#478C2211yescharacteristic, complemented
192C53×#476C2211yescharacteristic, complemented
193C53×#474C2211yescharacteristic, complemented
194C53×#469C2211yescharacteristic
195C53×#468C2211yescharacteristic, complemented
196C53×#466C2211yescharacteristic
197C53×#465C2211yescharacteristic, complemented
198C53×#463C2211yescharacteristic, complemented
199C53×#463C2211yescharacteristic, complemented
200C53×#460C2211yescharacteristic, complemented
201C53×#459C2211yescharacteristic, complemented
202C53×#424C2211yescharacteristic, complemented
203C2×#11719947C2311yescharacteristic
204C2×#11719947C2311yescharacteristic
205C2×Q8×D53—21no—
206C2×Q8×D53C2311yescharacteristic
207C2×D4×D53—21no—
208C2×D4×D53C2311yescharacteristic
209C22×C4×D53—21no—
210C22×C4×D53C2311yescharacteristic
211#13133246—42no—
212#13133246—42no—
213#13133241—42no—
214#13133241—42no—
215C2×Dic212C2311yescharacteristic
216C2×Dic212C2311yescharacteristic
217C2×#11719925C2311yescharacteristic
218C2×#11719925C2311yescharacteristic
219C2×#11719913C2311yescharacteristic
220C2×#11719913C2311yescharacteristic
221C2×#11719923C2311yescharacteristic
222C2×#11719923C2311yescharacteristic
223C2×#11719923C2311yescharacteristic
224C2×#11719923C2311yescharacteristic
225C2×#11719922C2311yescharacteristic
226C2×#11719922C2311yescharacteristic
227C2×#11719917C2311yescharacteristic
228C2×#11719912—42no—
229C2×#11719912C2311yescharacteristic
230C2×#11719912C2311yescharacteristic
231C2×#11719912C2311yescharacteristic
232C2×#11719912C2311yescharacteristic
233C2×#11719912C2311yescharacteristic
234C2×#11719912C2311yescharacteristic
235M16×D53—42no—
236C22×#88322C2311yescharacteristic
237C2×C8×D53C2311yescharacteristic
238C2×C8×D53C2311yescharacteristic
239#13133217C2311yescharacteristic
240#13133217C2311yescharacteristic
241#13133216—21no—
242#13133216C2311yescharacteristic
243#13133216C2311yescharacteristic
244#13133216C2311yescharacteristic
245#13133216C2311yescharacteristic
246#13133215—21no—
247#13133212—21no—
248#13133212—21no—
249#13133212—21no—
250#13133212—21no—
251#13133212—21no—
252#13133211—21no—
253#13133210—21no—
254#13133210—21no—
255#13133210—21no—
256#13133210—21no—
257#13133210—21no—
258#13133210—21no—
259#13133210—21no—
260#13133210—21no—
261#13133210—21no—
262#13133209C2311yescharacteristic
263#13133208—21no—
264#13133208—21no—
265#13133207—21no—
266#13133207—21no—
267#13133206—21no—
268#13133206C2311yescharacteristic
269#13133205—21no—
270#13133205C2311yescharacteristic
271#13133204—21no—
272#13133204—21no—
273#13133204—21no—
274#13133204C2311yescharacteristic
275#13133204C2311yescharacteristic
276#13133204C2311yescharacteristic
277#13133203—21no—
278#13133203—21no—
279#13133203—21no—
280#13133203—21no—
281#13133203—21no—
282#13133203—21no—
283#13133203—21no—
284#13133203—21no—
285#13133202—21no—
286#13133202—21no—
287#13133201—21no—
288#13133200—21no—
289#13133200—21no—
290#13133200—21no—
291#13133199—21no—
292#13133199—21no—
293#13133199—21no—
294#13133199—21no—
295#13133198—21no—
296#13133198—21no—
297#13133198—21no—
298#13133198—21no—
299#13133198—21no—
300#13133197—21no—
301#13133197C2311yescharacteristic
302#13133197C2311yescharacteristic
303#13133197C2311yescharacteristic
304#13133196—21no—
305#13133196—21no—
306#13133196—21no—
307#13133196C2311yescharacteristic
308#13133196C2311yescharacteristic
309#13133196C2311yescharacteristic
310#13133195—21no—
311#13133195—21no—
312#13133195—21no—
313#13133195—21no—
314#13133195—21no—
315#13133194—21no—
316#13133194—21no—
317#13133194—21no—
318#13133194—21no—
319#13133194—21no—
320#13133193—21no—
321#13133193C2311yescharacteristic
322#13133192C2311yescharacteristic
323#13133191C2311yescharacteristic
324#13133190—21no—
325#13133189—21no—
326#13133189—21no—
327#13133189—21no—
328#13133188—21no—
329#13133188—21no—
330#13133188C2311yescharacteristic
331#13133188C2311yescharacteristic
332#13133188C2311yescharacteristic
333#13133185—21no—
334#13133185—21no—
335Q8×Dic53C2311yescharacteristic
336C4×Dic106—21no—
337C4×Dic106C2311yescharacteristic
338C4×Dic106C2311yescharacteristic
339C4×Dic106C2311yescharacteristic
340#13133182—21no—
341#13133182—21no—
342#13133182—21no—
343#13133182C2311yescharacteristic
344#13133182C2311yescharacteristic
345#13133182C2311yescharacteristic
346C4×D212C2311yescharacteristic
347D4×Dic53—21no—
348D4×Dic53—21no—
349D4×Dic53—21no—
350D4×Dic53—21no—
351D4×Dic53C2311yescharacteristic
352D4×Dic53C2311yescharacteristic
353D4×Dic53C2311yescharacteristic
354#13133179C2311yescharacteristic
355C4×C22⋊D53—21no—
356C4×C22⋊D53—21no—
357C4×C22⋊D53—21no—
358#13133177—21no—
359#13133177—21no—
360#13133177—21no—
361#13133177—21no—
362#13133177—21no—
363#13133176C2311yescharacteristic
364#13133175D411yescharacteristic
365#13133175D411yescharacteristic
366#13133175C2311yescharacteristic
367#13133175C2311yescharacteristic
368#13133174C2311yescharacteristic
369#13133174C2311yescharacteristic
370#13133173—21no—
371#13133173—21no—
372#13133173D411yescharacteristic
373#13133173D411yescharacteristic
374C4⋊C4×D53—21no—
375C4⋊C4×D53—21no—
376C4⋊C4×D53—21no—
377C4⋊C4×D53D411yescharacteristic
378C4⋊C4×D53D411yescharacteristic
379C4⋊C4×D53C2311yescharacteristic
380C4⋊C4×D53C2311yescharacteristic
381C22⋊C4×D53—21no—
382C22⋊C4×D53—21no—
383C22⋊C4×D53—21no—
384C22⋊C4×D53—21no—
385C22⋊C4×D53—21no—
386C22⋊C4×D53D411yescharacteristic
387C22⋊C4×D53D411yescharacteristic
388C2×C4×Dic53—21no—
389C2×C4×Dic53—21no—
390C42×D53—21no—
391C42×D53C2311yescharacteristic
392C42×D53C2311yescharacteristic
393#13133151C2311yescharacteristic
394#13133151C2311yescharacteristic
395#13133150C2311yescharacteristic
396#13133150C2311yescharacteristic
397#13133150C2311yescharacteristic
398#13133150C2311yescharacteristic
399#13133149C2311yescharacteristic
400#13133149C2311yescharacteristic
401#13133148C2311yescharacteristic
402#13133148C2311yescharacteristic
403#13133148C2311yescharacteristic
404#13133148C2311yescharacteristic
405C4⋊#88322C2311yescharacteristic
406C4⋊#88322C2311yescharacteristic
407C4⋊#88322C2311yescharacteristic
408C4⋊#88322C2311yescharacteristic
409#13133146C2311yescharacteristic
410#13133146C2311yescharacteristic
411#13133146C2311yescharacteristic
412#13133146C2311yescharacteristic
413#13133146C2311yescharacteristic
414#13133146C2311yescharacteristic
415#13133146C2311yescharacteristic
416#13133146C2311yescharacteristic
417#13133142C2311yescharacteristic
418#13133142C2311yescharacteristic
419#13133142C2311yescharacteristic
420#13133142C2311yescharacteristic
421#13133142C2311yescharacteristic
422#13133142C2311yescharacteristic
423#13133141C2311yescharacteristic
424#13133141C2311yescharacteristic
425#13133140C2311yescharacteristic
426#13133140C2311yescharacteristic
427#13133140C2311yescharacteristic
428#13133140C2311yescharacteristic
429#13133140C2311yescharacteristic
430#13133140C2311yescharacteristic
431#13133139C2311yescharacteristic
432#13133139C2311yescharacteristic
433#13133138C2311yescharacteristic
434#13133138C2311yescharacteristic
435#13133138C2311yescharacteristic
436#13133138C2311yescharacteristic
437#13133138C2311yescharacteristic
438#13133138C2311yescharacteristic
439#13133137C2311yescharacteristic
440#13133137C2311yescharacteristic
441C2×SD16×C53C2311yescharacteristic
442C2×SD16×C53C2311yescharacteristic
443C2×D8×C53C2311yescharacteristic
444C2×D8×C53C2311yescharacteristic
445C2×M16×C53C2311yescharacteristic
446C22×C8×C53C2311yescharacteristic
447C4⋊Q8×C53C2311yescharacteristic
448#127×C53C2311yescharacteristic
449#126×C53—21no—
450#125×C53C2311yescharacteristic
451#124×C53—21no—
452#124×C53C2311yescharacteristic
453#123×C53—21no—
454#123×C53—21no—
455#123×C53—21no—
456C22⋊Q8×C53—21no—
457C22⋊Q8×C53C2311yescharacteristic
458#121×C53—21no—
459#121×C53—21no—
460#121×C53C2311yescharacteristic
461#121×C53C2311yescharacteristic
462#121×C53C2311yescharacteristic
463C4×Q8×C53C2311yescharacteristic
464C4×D4×C53C2311yescharacteristic
465C4×D4×C53C2311yescharacteristic
466C4×D4×C53C2311yescharacteristic
467#117×C53C2311yescharacteristic
468#107×C53C2311yescharacteristic
469#107×C53C2311yescharacteristic
470#106×C53C2311yescharacteristic
471#106×C53C2311yescharacteristic
472C4⋊C8×C53C2311yescharacteristic
473C4⋊C8×C53C2311yescharacteristic
474C4⋊C8×C53C2311yescharacteristic
475C4⋊C8×C53C2311yescharacteristic
476#103×C53C2311yescharacteristic
477#103×C53C2311yescharacteristic
478#102×C53C2311yescharacteristic
479#102×C53C2311yescharacteristic
480#102×C53C2311yescharacteristic
481#102×C53C2311yescharacteristic
482#102×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484C23×D53—21no—
485C23×D53C2×D411yescharacteristic
486C2×Q8×C53—21no—
487C2×Q8×C53C2411yescharacteristic
488C2×D4×C53—21no—
489C2×D4×C53—21no—
490C2×D4×C53—21no—
491C2×D4×C53—21no—
492C2×D4×C53—21no—
493C2×D4×C53C2411yescharacteristic
494C2×D4×C53C2411yescharacteristic
495C2×D4×C53C2411yescharacteristic
496C22×C4×C53—21no—
497C22×C4×C53—21no—
498C22×C4×C53—21no—
499C22×C4×C53C2411yescharacteristic
500C2×C22⋊D53—21no—
501C2×C22⋊D53—21no—
502C2×C22⋊D53—21no—
503C2×C22⋊D53—21no—
504C2×C22⋊D53—21no—
505C2×C22⋊D53—21no—
506C2×C22⋊D53—21no—
507C22×Dic53—21no—
508C22×Dic53—21no—
509C22×Dic53—21no—
510C22×Dic53—21no—
511C22×Dic53—21no—
512C22×Dic53C2×D411yescharacteristic
513Q8×D53—22no—
514Q8×D53—22no—
515Q8×D53—82no—
516#11719947—22no—
517#11719947—22no—
518#11719947—22no—
519#11719947—22no—
520D4×D53—22no—
521D4×D53—22no—
522D4×D53—82no—
523C2×D212—21no—
524C2×D212C2411yescharacteristic
525C2×C4×D53—22no—
526C2×C4×D53—22no—
527C2×C4×D53—21no—
528C2×C4×D53—21no—
529C2×C4×D53—21no—
530C2×C4×D53—21no—
531C2×C4×D53—21no—
532C2×C4×D53—82no—
533C2×C4×D53C2×D411yescharacteristic
534C2×C4×D53C2×D411yescharacteristic
535C2×C4×D53C2×D411yescharacteristic
536C2×C4×D53C2×D411yescharacteristic
537C2×C4×D53C2×D411yescharacteristic
538C2×C4×D53C2×D411yescharacteristic
539C2×C4×D53C2411yescharacteristic
540C2×C4×D53C2411yescharacteristic
541C2×Dic106—21no—
542C2×Dic106—21no—
543C2×Dic106—21no—
544C2×Dic106—21no—
545C2×Dic106—21no—
546C2×Dic106—21no—
547C2×Dic106C2411yescharacteristic
548C2×Dic106C2411yescharacteristic
549C2×Dic106C2411yescharacteristic
550SD16×C53—41no—
551SD16×C53—41no—
552D8×C53—41no—
553D8×C53—41no—
554M16×C53—41no—
555C2×C8×C53—41no—
556C2×C8×C53C2411yescharacteristic
557C2×C8×C53C2411yescharacteristic
558C2×C8×C53C2411yescharacteristic
559C2×C8×C53C2411yescharacteristic
560C4⋊C4×C53—21no—
561C4⋊C4×C53—21no—
562C4⋊C4×C53—21no—
563C4⋊C4×C53—21no—
564C4⋊C4×C53—21no—
565C4⋊C4×C53C2×D411yescharacteristic
566C4⋊C4×C53C2×D411yescharacteristic
567C4⋊C4×C53C2411yescharacteristic
568C4⋊C4×C53C2411yescharacteristic
569C4⋊C4×C53C2411yescharacteristic
570C4⋊C4×C53C2411yescharacteristic
571C22⋊C4×C53—21no—
572C22⋊C4×C53—21no—
573C22⋊C4×C53—21no—
574C22⋊C4×C53—21no—
575C22⋊C4×C53—21no—
576C22⋊C4×C53—21no—
577C22⋊C4×C53—21no—
578C22⋊C4×C53—21no—
579C22⋊C4×C53—21no—
580C22⋊C4×C53C2×D411yescharacteristic
581C22⋊C4×C53C2×D411yescharacteristic
582C42×C53—21no—
583C42×C53C2411yescharacteristic
584C42×C53C2411yescharacteristic
585C22⋊Dic53—21no—
586C22⋊Dic53—21no—
587C22⋊Dic53—21no—
588C22⋊Dic53—21no—
589C22⋊Dic53—21no—
590C22⋊Dic53—21no—
591C22⋊Dic53—21no—
592C22⋊Dic53—21no—
593C22⋊Dic53—21no—
594C22⋊Dic53—21no—
595C22⋊Dic53—21no—
596C22⋊Dic53—21no—
597C22⋊Dic53—21no—
598C22⋊Dic53—21no—
599C22⋊Dic53—21no—
600C22⋊Dic53C2×D411yescharacteristic
601C22⋊Dic53C2×D411yescharacteristic
602#11719925—41no—
603#11719925—41no—
604#11719923—41no—
605#11719923—41no—
606#11719923—41no—
607#11719923—41no—
608#11719922—41no—
609#11719922—41no—
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#11719921—21no—
623#11719921—21no—
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⋊Dic53C2×D411yescharacteristic
636C4⋊Dic53C2×D411yescharacteristic
637C4⋊Dic53C2411yescharacteristic
638C4⋊Dic53C2411yescharacteristic
639C4⋊Dic53C2411yescharacteristic
640C4⋊Dic53C2411yescharacteristic
641#11719919—21no—
642#11719919—21no—
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#11719919—21no—
656#11719919—21no—
657#11719919—21no—
658#11719919—21no—
659#11719919C2×D411yescharacteristic
660#11719919C2×D411yescharacteristic
661#11719919C2×D411yescharacteristic
662#11719919C2×D411yescharacteristic
663C4×Dic53—21no—
664C4×Dic53—21no—
665C4×Dic53—21no—
666C4×Dic53—21no—
667C4×Dic53—21no—
668C4×Dic53—21no—
669C4×Dic53—21no—
670C4×Dic53—21no—
671C4×Dic53—21no—
672C4×Dic53C2×D411yescharacteristic
673C4×Dic53C2×D411yescharacteristic
674C4×Dic53C2×D411yescharacteristic
675C4×Dic53C2×D411yescharacteristic
676C4×Dic53C2411yescharacteristic
677C4×Dic53C2411yescharacteristic
678#11719917—41no—
679C2×#88322—41no—
680C2×#88322C2411yescharacteristic
681C2×#88322C2411yescharacteristic
682C2×#88322C2411yescharacteristic
683C2×#88322C2411yescharacteristic
684Dic212—41no—
685Dic212—41no—
686#11719913—41no—
687#11719913—41no—
688#11719912—22no—
689#11719912—22no—
690#11719912—22no—
691#11719912—22no—
692#11719912—41no—
693#11719912—41no—
694C8×D53—41no—
695C8×D53—41no—
696C23×C53—21no—
697C23×C53—21no—
698C23×C53—21no—
699C23×C53C22×D411yescharacteristic
700C22×D53—22no—
701C22×D53—21no—
702C22×D53—41no—
703C22×D53—41no—
704C22×D53—42no—
705C22×D53—42no—
706C22×D53—42no—
707C22×D53C22×D411yescharacteristic
708C22×D53C22×D411yescharacteristic
709Q8×C53—21no—
710Q8×C53—21no—
711Q8×C53—81no—
712D4×C53—21no—
713D4×C53—21no—
714D4×C53—21no—
715D4×C53—21no—
716D4×C53—21no—
717D4×C53—21no—
718D4×C53—81no—
719D4×C53—81no—
720D4×C53—81no—
721D4×C53—81no—
722D4×C53—81no—
723C2×C4×C53—21no—
724C2×C4×C53—21no—
725C2×C4×C53—21no—
726C2×C4×C53—21no—
727C2×C4×C53—21no—
728C2×C4×C53—21no—
729C2×C4×C53—21no—
730C2×C4×C53—81no—
731C2×C4×C53—81no—
732C2×C4×C53—81no—
733C2×C4×C53C22×D411yescharacteristic
734C2×C4×C53C22×D411yescharacteristic
735C2×C4×C53C22×D411yescharacteristic
736C2×C4×C53C22×D411yescharacteristic
737C2×C4×C53C22×D411yescharacteristic
738C2×C4×C53C2511yescharacteristic
739C22⋊D53—42no—
740C22⋊D53—42no—
741C22⋊D53—42no—
742C22⋊D53—81no—
743C22⋊D53—81no—
744C22⋊D53—81no—
745C22⋊D53—81no—
746C2×Dic53—22no—
747C2×Dic53—21no—
748C2×Dic53—21no—
749C2×Dic53—21no—
750C2×Dic53—21no—
751C2×Dic53—21no—
752C2×Dic53—21no—
753C2×Dic53—21no—
754C2×Dic53—42no—
755C2×Dic53—42no—
756C2×Dic53—81no—
757C2×Dic53—81no—
758C2×Dic53—81no—
759C2×Dic53C22×D411yescharacteristic
760C2×Dic53C22×D411yescharacteristic
761C2×Dic53C22×D411yescharacteristic
762C2×Dic53C22×D411yescharacteristic
763C2×Dic53C22×D411yescharacteristic
764C2×Dic53C22×D411yescharacteristic
765D212—21no—
766D212—21no—
767D212—81no—
768C4×D53—22no—
769C4×D53—21no—
770C4×D53—21no—
771C4×D53—22no—
772C4×D53—41no—
773C4×D53—41no—
774C4×D53—41no—
775C4×D53—41no—
776C4×D53—42no—
777C4×D53—42no—
778C4×D53—42no—
779C4×D53—81no—
780C4×D53—81no—
781C4×D53H(5,𝔽2)12yes—
782C4×D532−1+412yes—
783Dic106—21no—
784Dic106—21no—
785Dic106—21no—
786Dic106—21no—
787Dic106—21no—
788Dic106—21no—
789Dic106—42no—
790Dic106—81no—
791Dic106—81no—
792Dic106—81no—
793Dic106—81no—
794Dic106—81no—
795C8×C53—21no—
796C8×C53—21no—
797C8×C53—21no—
798C8×C53—21no—
799#88322—21no—
800#88322—21no—
801#88322—21no—
802#88322—21no—
803#60919—531nomaximal, Sylow
804C22×C53—21no—
805C22×C53—21no—
806C22×C53—21no—
807C22×C53—41no—
808C22×C53—41no—
809C22×C53—41no—
810C22×C53—41no—
811C22×C53—41no—
812C22×C53—41no—
813C22×C53—41no—
814C22×C53—41no—
815C22×C53—41no—
816C22×C53C23×D411yescharacteristic
817C2×D53—21no—
818C2×D53—21no—
819C2×D53—21no—
820C2×D53—21no—
821C2×D53—21no—
822C2×D53—41no—
823C2×D53—41no—
824C2×D53—41no—
825C2×D53—82no—
826C2×D53—84no—
827C2×D53#53712yes—
828C4×C53—21no—
829C4×C53—21no—
830C4×C53—21no—
831C4×C53—21no—
832C4×C53—21no—
833C4×C53—41no—
834C4×C53—41no—
835C4×C53—41no—
836C4×C53—41no—
837C4×C53—41no—
838C4×C53C2×H(5,𝔽2)11yescharacteristic
839C4×C53C2×2−1+411yescharacteristic
840Dic53—21no—
841Dic53—21no—
842Dic53—21no—
843Dic53—21no—
844Dic53—21no—
845Dic53—41no—
846Dic53—41no—
847Dic53—41no—
848Dic53—41no—
849Dic53—41no—
850Dic53—41no—
851Dic53—41no—
852Dic53#53712yes—
853#3455—531no—
854C2×#542—531no—
855#3263—531no—
856#3263—531no—
857#3263—531no—
858#3263—531no—
859#3262—531no—
860#3262—531no—
861#3262—531no—
862#3262—531no—
863#3258—531no—
864#3258—531no—
865#3258—531no—
866#3258—531no—
867#3257—531no—
868#3257—531no—
869#3257—531no—
870#3257D5311yescharacteristic, complemented
871#3079—531no—
872#3079—531no—
873#3078—531no—
874#3077—531no—
875#3056—531no—
876#3056—531no—
877#3055—531no—
878#3055—531no—
879#3040—531no—
880#3040—531no—
881#3037—531no—
882#3036—531no—
883#2905—531no—
884C2×C53—41no—
885C2×C53—81no—
886C2×C53—81no—
887C2×C53—81no—
888C2×C53C2×#53711yescharacteristic
889C2×C53#358511yescharacteristic
890C2×C53#358611yescharacteristic
891D53—22no—
892D53—41no—
893D53—81no—
894C2×#137—531no—
895C2×#137—531no—
896C2×AGL(1,ℤ/8)—531no—
897C2×AGL(1,ℤ/8)—531no—
898C22×M16—531no—
899C22×M16—531no—
900#542—531no—
901#542—531no—
902#542—531no—
903#542—531no—
904#542—531no—
905#542—531no—
906#542—531no—
907#542—531no—
908#542—531no—
909#542—531no—
910#542—531no—
911#542—1061no—
912#542—1061no—
913#542—1061no—
914#542—1061no—
915#542C2×D5311yescharacteristic
916#541—531no—
917#541—531no—
918#540—531no—
919#540C2×D5311yescharacteristic, complemented
920#539—1061no—
921#539—1061no—
922#538—1061no—
923#538—1061no—
924#533—531no—
925#532—531no—
926C2×C4⋊Q8—531no—
927#529—1061no—
928#529—1061no—
929#529—1061no—
930#529—1061no—
931C2×#126—1061no—
932C2×#124—531no—
933C2×#124—1061no—
934#525—531no—
935#525—531no—
936C2×#123—1061no—
937C2×C22⋊Q8—531no—
938C2×C22⋊Q8—1061no—
939C2×#121—531no—
940C4×#41—531no—
941C4×#41—531no—
942C2×C4×Q8—531no—
943C2×C4×D4—531no—
944C2×#117—531no—
945#479—531no—
946#479—531no—
947#479—531no—
948#479C2×D5311yescharacteristic, complemented
949#478—531no—
950#478—531no—
951#478—531no—
952#478C2×D5311yescharacteristic, complemented
953#477—531no—
954#477—531no—
955#477—531no—
956#477—531no—
957#477—531no—
958#477—531no—
959#476—531no—
960#476—531no—
961#476—531no—
962#476—531no—
963#476—531no—
964#476C2×D5311yescharacteristic, complemented
965#475—531no—
966#475—531no—
967#475—531no—
968#475—531no—
969#475—531no—
970#475—531no—
971#474—531no—
972#474—531no—
973#474—531no—
974#474—531no—
975#474—531no—
976#474C2×D5311yescharacteristic, complemented
977#470—531no—
978#470—531no—
979#470—531no—
980#470—531no—
981#469—531no—
982#469—531no—
983#469—531no—
984#469C2×D5311yescharacteristic
985#468—531no—
986#468—531no—
987#468—531no—
988#468—531no—
989#468—531no—
990#468—531no—
991#468—531no—
992#468C2×D5311yescharacteristic, complemented
993#467—531no—
994#467—531no—
995#467—531no—
996#467—531no—
997#466—531no—
998#466—531no—
999#466—531no—
1000#466C2×D5311yescharacteristic
1001#465—531no—
1002#465—531no—
1003#465—531no—
1004#465—531no—
1005#465—531no—
1006#465—531no—
1007#465—531no—
1008#465C2×D5311yescharacteristic, complemented
1009#464—531no—
1010#464—531no—
1011#464—531no—
1012#464—531no—
1013#464—531no—
1014#464—531no—
1015#464—531no—
1016#464—531no—
1017#464—531no—
1018#464—531no—
1019#464—531no—
1020#464—531no—
1021#463—531no—
1022#463—531no—
1023#463—531no—
1024#463—531no—
1025#463—531no—
1026#463—531no—
1027#463—531no—
1028#463—531no—
1029#463—531no—
1030#463—531no—
1031#463C2×D5311yescharacteristic, complemented
1032#463C2×D5311yescharacteristic, complemented
1033#462—531no—
1034#462—531no—
1035#461—531no—
1036#461—531no—
1037#460—531no—
1038#460C2×D5311yescharacteristic, complemented
1039#459—531no—
1040#459C2×D5311yescharacteristic, complemented
1041#428—531no—
1042#428—531no—
1043#428—531no—
1044#428—531no—
1045#424—531no—
1046#424—531no—
1047#424—531no—
1048#424—531no—
1049#424—531no—
1050#424—531no—
1051#424—531no—
1052#424C2×D5311yescharacteristic, complemented
1053#423—531no—
1054#423—531no—
1055#423—531no—
1056#423—531no—
1057#419—531no—
1058#419—531no—
1059#418—531no—
1060#418—531no—
1061#417—531no—
1062#417—531no—
1063#417—531no—
1064#417—531no—
1065C53#6091911yescharacteristic, complemented, Sylow
1066C2×#41—531no—
1067C2×#41—531no—
1068C22×Q8—531no—
1069C22×Q8—1061no—
1070C22×D4—531no—
1071C22×D4—1061no—
1072C23×C4—531no—
1073C23×C4—1061no—
1074#137—2122no—
1075#137—2122no—
1076AGL(1,ℤ/8)—2122no—
1077AGL(1,ℤ/8)—2122no—
1078C2×Q16—531no—
1079C2×Q16—531no—
1080C2×Q16—531no—
1081C2×Q16—531no—
1082C2×SD16—531no—
1083C2×SD16—531no—
1084C2×SD16—531no—
1085C2×SD16—531no—
1086C2×SD16—531no—
1087C2×SD16—531no—
1088C2×SD16C22×D5311yescharacteristic
1089C2×SD16C22×D5311yescharacteristic
1090C2×D8—531no—
1091C2×D8—531no—
1092C2×D8C22×D5311yescharacteristic
1093C2×D8C22×D5311yescharacteristic
1094C2×M16—531no—
1095C2×M16—531no—
1096C2×M16—531no—
1097C2×M16—531no—
1098C2×M16—531no—
1099C2×M16—531no—
1100C2×M16—531no—
1101C2×M16—2122no—
1102C2×M16—2122no—
1103C2×M16C22×D5311yescharacteristic
1104C22×C8—531no—
1105C22×C8—531no—
1106C22×C8—531no—
1107C22×C8C22×D5311yescharacteristic
1108C4⋊Q8—531no—
1109C4⋊Q8—531no—
1110C4⋊Q8—531no—
1111C4⋊Q8—531no—
1112C4⋊Q8—531no—
1113C4⋊Q8—531no—
1114C4⋊Q8—1061no—
1115C4⋊Q8—1061no—
1116C4⋊Q8C22×D5311yescharacteristic
1117#127C22×D5311yescharacteristic
1118#126—21no—
1119#126—1061no—
1120#126—1061no—
1121#126—1061no—
1122#126—1061no—
1123#126—1061no—
1124#126—1061no—
1125#126—1061no—
1126#126—1061no—
1127#126—1061no—
1128#126—1061no—
1129#126—1061no—
1130#126—1061no—
1131#126—1061no—
1132#126—1061no—
1133#126—1061no—
1134#125—531no—
1135#125—1061no—
1136#125—1061no—
1137#125—1061no—
1138#125—1061no—
1139#125C22×D5311yescharacteristic
1140#124—21no—
1141#124—531no—
1142#124—531no—
1143#124—531no—
1144#124—531no—
1145#124—531no—
1146#124—1061no—
1147#124—1061no—
1148#124—1061no—
1149#124—1061no—
1150#124—1061no—
1151#124—1061no—
1152#124—1061no—
1153#124—1061no—
1154#124—1061no—
1155#124—1061no—
1156#124—1061no—
1157#124—1061no—
1158#124—1061no—
1159#124C22×D5311yescharacteristic
1160#123—21no—
1161#123—21no—
1162#123—21no—
1163#123—1061no—
1164#123—1061no—
1165#123—1061no—
1166#123—1061no—
1167#123—1061no—
1168#123—1061no—
1169#123—1061no—
1170#123—1061no—
1171#123—1061no—
1172#123—1061no—
1173#123—1061no—
1174#123—1061no—
1175#123—1061no—
1176#123—1061no—
1177#123—1061no—
1178C22⋊Q8—21no—
1179C22⋊Q8—531no—
1180C22⋊Q8—531no—
1181C22⋊Q8—531no—
1182C22⋊Q8—531no—
1183C22⋊Q8—531no—
1184C22⋊Q8—531no—
1185C22⋊Q8—531no—
1186C22⋊Q8—1061no—
1187C22⋊Q8—1061no—
1188C22⋊Q8—1061no—
1189C22⋊Q8—1061no—
1190C22⋊Q8—1061no—
1191C22⋊Q8—1061no—
1192C22⋊Q8—1061no—
1193C22⋊Q8—1061no—
1194C22⋊Q8—1061no—
1195C22⋊Q8—1061no—
1196C22⋊Q8—1061no—
1197C22⋊Q8—1061no—
1198C22⋊Q8—1061no—
1199C22⋊Q8—1061no—
1200C22⋊Q8—1061no—
1201C22⋊Q8C22×D5311yescharacteristic
1202#121—21no—
1203#121—21no—
1204#121—531no—
1205#121—531no—
1206#121—531no—
1207#121—531no—
1208#121—531no—
1209#121—1061no—
1210#121—1061no—
1211#121—1061no—
1212#121—1061no—
1213#121—1061no—
1214#121—1061no—
1215#121C22×D5311yescharacteristic
1216#121C22×D5311yescharacteristic
1217#121C22×D5311yescharacteristic
1218#120—1061no—
1219#120—1061no—
1220C4×Q8—531no—
1221C4×Q8—531no—
1222C4×Q8—531no—
1223C4×Q8—531no—
1224C4×Q8—531no—
1225C4×Q8—531no—
1226C4×Q8—531no—
1227C4×Q8—1061no—
1228C4×Q8—1061no—
1229C4×Q8—1061no—
1230C4×Q8—1061no—
1231C4×Q8C22×D5311yescharacteristic
1232C4×D4—531no—
1233C4×D4—531no—
1234C4×D4—531no—
1235C4×D4—531no—
1236C4×D4—531no—
1237C4×D4—1061no—
1238C4×D4—1061no—
1239C4×D4—1061no—
1240C4×D4—1061no—
1241C4×D4—1061no—
1242C4×D4—1061no—
1243C4×D4—1061no—
1244C4×D4—1061no—
1245C4×D4—1061no—
1246C4×D4—1061no—
1247C4×D4—1061no—
1248C4×D4—1061no—
1249C4×D4C22×D5311yescharacteristic
1250C4×D4C22×D5311yescharacteristic
1251C4×D4C22×D5311yescharacteristic
1252#117—531no—
1253#117—531no—
1254#117—531no—
1255#117—531no—
1256#117—531no—
1257#117—531no—
1258#117—531no—
1259#117—531no—
1260#117—531no—
1261#117—1061no—
1262#117—1061no—
1263#117C22×D5311yescharacteristic
1264C2×C4⋊C4—531no—
1265C2×C4⋊C4—531no—
1266C2×C4⋊C4—531no—
1267C2×C4⋊C4—531no—
1268C2×C4⋊C4—1061no—
1269C2×C4⋊C4—1061no—
1270C2×C4⋊C4—1061no—
1271C2×C22⋊C4—531no—
1272C2×C22⋊C4—531no—
1273C2×C22⋊C4—1061no—
1274C2×C22⋊C4—1061no—
1275C2×C22⋊C4—1061no—
1276C2×C22⋊C4—1061no—
1277C2×C22⋊C4—1061no—
1278C2×C42—531no—
1279C2×C42—531no—
1280C2×C42—1061no—
1281C2×C42—1061no—
1282C2×C42—1061no—
1283#107—531no—
1284#107—531no—
1285#107—531no—
1286#107—531no—
1287#107—531no—
1288#107—531no—
1289#107C22×D5311yescharacteristic
1290#107C22×D5311yescharacteristic
1291#106—531no—
1292#106—531no—
1293#106—531no—
1294#106—531no—
1295#106—531no—
1296#106—531no—
1297#106C22×D5311yescharacteristic
1298#106C22×D5311yescharacteristic
1299C4⋊C8—531no—
1300C4⋊C8—531no—
1301C4⋊C8—531no—
1302C4⋊C8—531no—
1303C4⋊C8—531no—
1304C4⋊C8—531no—
1305C4⋊C8—531no—
1306C4⋊C8—531no—
1307C4⋊C8—531no—
1308C4⋊C8—531no—
1309C4⋊C8—531no—
1310C4⋊C8—531no—
1311C4⋊C8C22×D5311yescharacteristic
1312C4⋊C8C22×D5311yescharacteristic
1313C4⋊C8C22×D5311yescharacteristic
1314C4⋊C8C22×D5311yescharacteristic
1315#103—531no—
1316#103—531no—
1317#103—531no—
1318#103—531no—
1319#103—531no—
1320#103—531no—
1321#103—531no—
1322#103—531no—
1323#103—531no—
1324#103—531no—
1325#103—531no—
1326#103—531no—
1327#103—531no—
1328#103—531no—
1329#103C22×D5311yescharacteristic
1330#103C22×D5311yescharacteristic
1331#102—531no—
1332#102—531no—
1333#102—531no—
1334#102—531no—
1335#102—531no—
1336#102—531no—
1337#102—531no—
1338#102—531no—
1339#102—531no—
1340#102—531no—
1341#102C22×D5311yescharacteristic
1342#102C22×D5311yescharacteristic
1343#102C22×D5311yescharacteristic
1344#102C22×D5311yescharacteristic
1345#102C22×D5311yescharacteristic
1346#102C22×D5311yescharacteristic
1347C24—531no—
1348C24—1061no—
1349#41—1062no—
1350#41—1062no—
1351#41—1062no—
1352#41—1062no—
1353C2×Q8—21no—
1354C2×Q8—531no—
1355C2×Q8—531no—
1356C2×Q8—531no—
1357C2×Q8—1061no—
1358C2×Q8—1061no—
1359C2×Q8—1061no—
1360C2×Q8—1061no—
1361C2×Q8—1061no—
1362C2×Q8—1062no—
1363C2×Q8—1062no—
1364C2×Q8—1061no—
1365C2×Q8—4242no—
1366C2×Q8C23×D5311yescharacteristic
1367C2×D4—21no—
1368C2×D4—21no—
1369C2×D4—21no—
1370C2×D4—21no—
1371C2×D4—21no—
1372C2×D4—531no—
1373C2×D4—1061no—
1374C2×D4—1062no—
1375C2×D4—1062no—
1376C2×D4—1061no—
1377C2×D4—1061no—
1378C2×D4—1061no—
1379C2×D4—1061no—
1380C2×D4—1061no—
1381C2×D4—1061no—
1382C2×D4—1061no—
1383C2×D4—4242no—
1384C2×D4C23×D5311yescharacteristic
1385C2×D4C23×D5311yescharacteristic
1386C2×D4C23×D5311yescharacteristic
1387C22×C4—21no—
1388C22×C4—21no—
1389C22×C4—21no—
1390C22×C4—531no—
1391C22×C4—531no—
1392C22×C4—531no—
1393C22×C4—531no—
1394C22×C4—531no—
1395C22×C4—531no—
1396C22×C4—531no—
1397C22×C4—531no—
1398C22×C4—531no—
1399C22×C4—1062no—
1400C22×C4—1062no—
1401C22×C4—1061no—
1402C22×C4—1061no—
1403C22×C4—1061no—
1404C22×C4—1061no—
1405C22×C4—1061no—
1406C22×C4—1061no—
1407C22×C4—1061no—
1408C22×C4—1061no—
1409C22×C4—1061no—
1410C22×C4—1061no—
1411C22×C4—4242no—
1412C22×C4C23×D5311yescharacteristic
1413Q16—2121no—
1414Q16—2121no—
1415Q16—2121no—
1416Q16—2121no—
1417SD16—41no—
1418SD16—41no—
1419SD16—2121no—
1420SD16—2121no—
1421SD16—2121no—
1422SD16—2121no—
1423SD16—2121no—
1424SD16—2121no—
1425D8—41no—
1426D8—41no—
1427D8—2121no—
1428D8—2121no—
1429M16—41no—
1430M16—1062no—
1431M16—1062no—
1432M16—1062no—
1433M16—1062no—
1434M16—2121no—
1435M16—2121no—
1436M16—2121no—
1437C2×C8—41no—
1438C2×C8—531no—
1439C2×C8—531no—
1440C2×C8—531no—
1441C2×C8—531no—
1442C2×C8—2121no—
1443C2×C8—2121no—
1444C2×C8—2121no—
1445C2×C8C23×D5311yescharacteristic
1446C2×C8C23×D5311yescharacteristic
1447C2×C8C23×D5311yescharacteristic
1448C2×C8C23×D5311yescharacteristic
1449C4⋊C4—21no—
1450C4⋊C4—21no—
1451C4⋊C4—21no—
1452C4⋊C4—21no—
1453C4⋊C4—21no—
1454C4⋊C4—531no—
1455C4⋊C4—531no—
1456C4⋊C4—531no—
1457C4⋊C4—531no—
1458C4⋊C4—531no—
1459C4⋊C4—531no—
1460C4⋊C4—531no—
1461C4⋊C4—531no—
1462C4⋊C4—531no—
1463C4⋊C4—531no—
1464C4⋊C4—1061no—
1465C4⋊C4—1061no—
1466C4⋊C4—1061no—
1467C4⋊C4—1061no—
1468C4⋊C4—1061no—
1469C4⋊C4—1061no—
1470C4⋊C4—1061no—
1471C4⋊C4—1061no—
1472C4⋊C4—1061no—
1473C4⋊C4—1061no—
1474C4⋊C4—1061no—
1475C4⋊C4—1061no—
1476C4⋊C4—1061no—
1477C4⋊C4—1061no—
1478C4⋊C4—1061no—
1479C4⋊C4—1061no—
1480C4⋊C4—1061no—
1481C4⋊C4—1061no—
1482C4⋊C4—1061no—
1483C4⋊C4—1061no—
1484C4⋊C4—1061no—
1485C4⋊C4—1061no—
1486C4⋊C4—1061no—
1487C4⋊C4—1061no—
1488C4⋊C4—1061no—
1489C4⋊C4D4×D5311yescharacteristic
1490C4⋊C4D4×D5311yescharacteristic
1491C4⋊C4C23×D5311yescharacteristic
1492C4⋊C4C23×D5311yescharacteristic
1493C4⋊C4C23×D5311yescharacteristic
1494C4⋊C4C23×D5311yescharacteristic
1495C22⋊C4—21no—
1496C22⋊C4—21no—
1497C22⋊C4—21no—
1498C22⋊C4—21no—
1499C22⋊C4—21no—
1500C22⋊C4—21no—
1501C22⋊C4—21no—
1502C22⋊C4—21no—
1503C22⋊C4—21no—
1504C22⋊C4—531no—
1505C22⋊C4—531no—
1506C22⋊C4—531no—
1507C22⋊C4—531no—
1508C22⋊C4—531no—
1509C22⋊C4—531no—
1510C22⋊C4—1061no—
1511C22⋊C4—1061no—
1512C22⋊C4—1061no—
1513C22⋊C4—1061no—
1514C22⋊C4—1061no—
1515C22⋊C4—1061no—
1516C22⋊C4—1061no—
1517C22⋊C4—1061no—
1518C22⋊C4—1061no—
1519C22⋊C4—1061no—
1520C22⋊C4—1061no—
1521C22⋊C4—1061no—
1522C22⋊C4—1061no—
1523C22⋊C4—1061no—
1524C22⋊C4—1061no—
1525C22⋊C4—1061no—
1526C22⋊C4—1061no—
1527C22⋊C4—1061no—
1528C22⋊C4—1061no—
1529C22⋊C4—1061no—
1530C22⋊C4—1061no—
1531C22⋊C4—1061no—
1532C22⋊C4—1061no—
1533C22⋊C4—1061no—
1534C22⋊C4—1061no—
1535C22⋊C4—1061no—
1536C22⋊C4—1061no—
1537C22⋊C4—1061no—
1538C22⋊C4—1061no—
1539C22⋊C4D4×D5311yescharacteristic
1540C22⋊C4D4×D5311yescharacteristic
1541C42—21no—
1542C42—531no—
1543C42—531no—
1544C42—531no—
1545C42—531no—
1546C42—531no—
1547C42—531no—
1548C42—1061no—
1549C42—1061no—
1550C42—1061no—
1551C42—1061no—
1552C42—1061no—
1553C42—1061no—
1554C42—1061no—
1555C42—1061no—
1556C42—1061no—
1557C42C23×D5311yescharacteristic
1558C42C23×D5311yescharacteristic
1559C23—21no—
1560C23—21no—
1561C23—21no—
1562C23—531no—
1563C23—531no—
1564C23—1062no—
1565C23—1061no—
1566C23—2121no—
1567C23—2121no—
1568C23—2122no—
1569C23—2122no—
1570C23—2122no—
1571C23C2×D4×D5311yescharacteristic
1572Q8—21no—
1573Q8—21no—
1574Q8—81no—
1575Q8—1061no—
1576Q8—1061no—
1577Q8—1061no—
1578Q8—1061no—
1579Q8—1061no—
1580Q8—1061no—
1581Q8—4241no—
1582Q8—4241no—
1583Q8—4241no—
1584Q8—4241no—
1585Q8—4241no—
1586Q8—2122no—
1587D4—21no—
1588D4—21no—
1589D4—21no—
1590D4—21no—
1591D4—21no—
1592D4—21no—
1593D4—81no—
1594D4—81no—
1595D4—81no—
1596D4—81no—
1597D4—81no—
1598D4—1061no—
1599D4—1061no—
1600D4—4241no—
1601D4—4241no—
1602D4—4241no—
1603D4—4241no—
1604D4—4241no—
1605D4—2122no—
1606D4—2122no—
1607D4—2122no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—81no—
1616C2×C4—81no—
1617C2×C4—81no—
1618C2×C4—531no—
1619C2×C4—532no—
1620C2×C4—532no—
1621C2×C4—531no—
1622C2×C4—531no—
1623C2×C4—531no—
1624C2×C4—531no—
1625C2×C4—531no—
1626C2×C4—1062no—
1627C2×C4—1062no—
1628C2×C4—1062no—
1629C2×C4—1061no—
1630C2×C4—1061no—
1631C2×C4—1061no—
1632C2×C4—1061no—
1633C2×C4—1061no—
1634C2×C4—1061no—
1635C2×C4—1061no—
1636C2×C4—1061no—
1637C2×C4—1061no—
1638C2×C4—4241no—
1639C2×C4—4241no—
1640C2×C4—4241no—
1641C2×C4—4241no—
1642C2×C4—4241no—
1643C2×C4—2121no—
1644C2×C4—2121no—
1645C2×C4—2121no—
1646C2×C4—2121no—
1647C2×C4—2122no—
1648C2×C4—2122no—
1649C2×C4—2122no—
1650C2×C4—2122no—
1651C2×C4—2122no—
1652C2×C4C2×D4×D5311yescharacteristic
1653C2×C4C2×D4×D5311yescharacteristic
1654C2×C4C2×D4×D5311yescharacteristic
1655C2×C4C2×D4×D5311yescharacteristic
1656C2×C4C2×D4×D5311yescharacteristic
1657C2×C4C24×D5311yescharacteristic
1658C8—21no—
1659C8—21no—
1660C8—21no—
1661C8—21no—
1662C8—1061no—
1663C8—1061no—
1664C8—1061no—
1665C8—1061no—
1666C22—21no—
1667C22—21no—
1668C22—21no—
1669C22—41no—
1670C22—41no—
1671C22—41no—
1672C22—41no—
1673C22—41no—
1674C22—41no—
1675C22—41no—
1676C22—41no—
1677C22—41no—
1678C22—532no—
1679C22—1061no—
1680C22—1061no—
1681C22—1061no—
1682C22—1061no—
1683C22—1061no—
1684C22—4242no—
1685C22—4244no—
1686C22—2121no—
1687C22—2121no—
1688C22—2121no—
1689C22C22×D4×D5311yescharacteristic
1690C4—21no—
1691C4—21no—
1692C4—21no—
1693C4—21no—
1694C4—21no—
1695C4—41no—
1696C4—41no—
1697C4—41no—
1698C4—41no—
1699C4—41no—
1700C4—532no—
1701C4—1061no—
1702C4—1061no—
1703C4—1061no—
1704C4—1061no—
1705C4—1061no—
1706C4—2121no—
1707C4—2121no—
1708C4—2121no—
1709C4—2121no—
1710C4—2121no—
1711C4—2121no—
1712C4—2121no—
1713C4H(5,𝔽2)×D5311yescharacteristic
1714C42−1+4×D5311yescharacteristic
1715C2—41no—
1716C2—81no—
1717C2—81no—
1718C2—81no—
1719C2—1062no—
1720C2—4241no—
1721C2—2121no—
1722C2#537×D5311yescharacteristic
1723C2#2028949011yescharacteristic
1724C2#2028949711yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3257C2
socleC22×C53C23×D4
hypercenter#3257D53
hypocenterC53#60919
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #3257

Complements

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

NH ≅ G/Ntype
1. #20288099C2semidirect
2. #542×D53C2semidirect
3. #20286187C2semidirect
4. #20286185C2semidirect
5. #20286182C2semidirect
6. #20286179C2semidirect
7. #20286175C2semidirect
8. #20286173C2semidirect
9. #20286172C2semidirect
10. #20286170C2semidirect
11. #20286147C2semidirect
12. #20286145C2semidirect
13. #20286143C2semidirect
14. #20286141C2semidirect
15. #20286124C2semidirect
16. #20286122C2semidirect
17. #20286120C2semidirect
18. #20284527C2semidirect
19. #20284523C2semidirect
20. #20284518C2semidirect
21. #20284510C2semidirect
22. #20284340C2semidirect
23. #20284338C2semidirect
24. #20284333C2semidirect
25. #20284331C2semidirect
26. #20284204C2semidirect
27. #20284204C2semidirect
28. #20284182C2semidirect
29. #20284174C2semidirect
30. #20283276C2semidirect
31. C53×#3257C2semidirect
46. #16811240C22semidirect
47. #16811240C22semidirect
50. #16811238C22semidirect
51. #16811238C22semidirect
53. #16811236C22semidirect
54. #16811235C22semidirect
55. #16811227C22semidirect
81. #16810931C22semidirect
82. #16810930C22semidirect
83. #16810927C22semidirect
84. #16810924C22semidirect
85. #16810923C22semidirect
86. #16810920C22semidirect
87. #16810919C22semidirect
88. #16810917C22semidirect
89. #16810917C22semidirect
90. #16810917C22semidirect
91. #16810916C22semidirect
92. #16810915C22semidirect
93. #16810913C22semidirect
94. #16810912C22semidirect
95. #16810911C22semidirect
96. #16810911C22semidirect
97. #16810911C22semidirect
98. #16810909C22semidirect
99. #16810907C22semidirect
100. #16810907C22semidirect
101. #16810907C22semidirect
102. #16810906C22semidirect
103. #16810905C22semidirect
104. #16810903C22semidirect
105. #16810902C22semidirect
106. #16810901C22semidirect
107. #16810901C22semidirect
108. #16810901C22semidirect
109. #16810882C22semidirect
110. #16810881C22semidirect
111. #16810880C22semidirect
112. #16810879C22semidirect
119. #16810868C22semidirect
121. #16810867C22semidirect
122. #16810866C22semidirect
123. #16810865C22semidirect
124. #16810864C22semidirect
125. #16810863C22semidirect
126. #16810862C22semidirect
133. #16810851C22semidirect
135. #16810850C22semidirect
136. #16810849C22semidirect
137. #16810848C22semidirect
138. #16810848C22semidirect
139. #16810846C22semidirect
140. #16810846C22semidirect
141. #16810844C22semidirect
142. #16810844C22semidirect
143. #16810844C22semidirect
144. #16810844C22semidirect
145. #16810843C22semidirect
146. #16810843C22semidirect
147. #16810842C22semidirect
148. #16810842C22semidirect
149. #16810840C22semidirect
150. #16810840C22semidirect
151. #16810838C22semidirect
152. #16810838C22semidirect
153. #16810837C22semidirect
154. #16810837C22semidirect
155. #16810836C22semidirect
156. #16810836C22semidirect
157. #16810836C22semidirect
158. #16810836C22semidirect
159. #16810834C22semidirect
160. #16810833C22semidirect
161. #16810829C22semidirect
162. #16810828C22semidirect
163. #16810820C22semidirect
164. #16810815C22semidirect
169. #16810651C22semidirect
170. #16810650C22semidirect
171. #16810649C22semidirect
172. #16810648C22semidirect
173. #16810648C22semidirect
174. #16810648C22semidirect
175. #16810648C22semidirect
189. C53×#540C22semidirect
190. C53×#479C22semidirect
191. C53×#478C22semidirect
192. C53×#476C22semidirect
193. C53×#474C22semidirect
195. C53×#468C22semidirect
197. C53×#465C22semidirect
198. C53×#463C22semidirect
199. C53×#463C22semidirect
200. C53×#460C22semidirect
201. C53×#459C22semidirect
202. C53×#424C22semidirect
870. #3257D53semidirect
919. #540C2×D53semidirect
948. #479C2×D53semidirect
952. #478C2×D53semidirect
964. #476C2×D53semidirect
976. #474C2×D53semidirect
992. #468C2×D53semidirect
1008. #465C2×D53semidirect
1031. #463C2×D53semidirect
1032. #463C2×D53semidirect
1038. #460C2×D53semidirect
1040. #459C2×D53semidirect
1052. #424C2×D53semidirect
1065. C53#60919semidirect

Maximal subgroups

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

subgroupindex
#202880992
#542×D532
#202861872
#202861852
#202861822
#202861792
#202861752
#202861732
#202861722
#202861702
#202861472
#202861452
#202861432
#202861412
#202861242
#202861222
#202861202
#202845272
#202845232
#202845182
#202845102
#202843402
#202843382
#202843332
#202843312
#202842042
#202841822
#202841742
#202832762
C53×#32572
#6091953