Finite Group Databasebeta

← #28275813

Subgroups — #28275813

Order 13568.

1664 conjugacy classes of subgroups.

The subgroup lattice has 1648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288613C211yesmaximal, characteristic, complemented
2#20287790C211yesmaximal, characteristic, complemented
3#20287790C211yesmaximal, characteristic, complemented
4#20287781C211yesmaximal, characteristic, complemented
5#20287781C211yesmaximal, characteristic, complemented
6#20287764C211yesmaximal, characteristic, complemented
7#20287742C211yesmaximal, characteristic, complemented
8#20287711C211yesmaximal, characteristic, complemented
9#20287699C211yesmaximal, characteristic, complemented
10#20287557C211yesmaximal, characteristic, complemented
11#20287542C211yesmaximal, characteristic, complemented
12#20287529C211yesmaximal, characteristic, complemented
13#20287483C211yesmaximal, characteristic, complemented
14#20287468C211yesmaximal, characteristic, complemented
15#20287455C211yesmaximal, characteristic, complemented
16#20287411C211yesmaximal, characteristic, complemented
17#20287400C211yesmaximal, characteristic, complemented
18#20285818C211yesmaximal, characteristic, complemented
19#20285803C211yesmaximal, characteristic
20#20285792C211yesmaximal, characteristic, complemented
21#20285781C211yesmaximal, characteristic, complemented
22#20285714C211yesmaximal, characteristic, complemented
23#20285676C211yesmaximal, characteristic, complemented
24#20285010C211yesmaximal, characteristic, complemented
25#20284962C211yesmaximal, characteristic, complemented
26#20284938C211yesmaximal, characteristic, complemented
27#20284893C211yesmaximal, characteristic, complemented
28#20284818C211yesmaximal, characteristic, complemented
29#20284780C211yesmaximal, characteristic, complemented
30#20283810C211yesmaximal, characteristic, complemented
31C53×#3555C211yesmaximal, characteristic, complemented
32#16811358C2211yescharacteristic
33#16811358C2211yescharacteristic
34#16811358C2211yescharacteristic
35#16811358C2211yescharacteristic
36#16811346C2211yescharacteristic
37#16811346C2211yescharacteristic
38#16811346C2211yescharacteristic
39#16811346C2211yescharacteristic
40#16811300—21no—
41#16811300—21no—
42#16811300—21no—
43#16811300—21no—
44#16811247—21no—
45#16811247—21no—
46#16811199C2211yescharacteristic
47#16811192C2211yescharacteristic
48#16811158—21no—
49#16811158—21no—
50C2×#13133205C2211yescharacteristic
51#16811100C2211yescharacteristic
52#16811097C2211yescharacteristic
53C4×#11719945C2211yescharacteristic
54#16811018C2211yescharacteristic, complemented
55#16811015C2211yescharacteristic
56#16811015C2211yescharacteristic
57#16811015C2211yescharacteristic
58#16811015C2211yescharacteristic, complemented
59#16811013C2211yescharacteristic
60#16811005C2211yescharacteristic
61#16811005C2211yescharacteristic
62#16811005C2211yescharacteristic
63#16811005C2211yescharacteristic, complemented
64#16811002C2211yescharacteristic, complemented
65#16810997C2211yescharacteristic
66#16810993C2211yescharacteristic, complemented
67#16810989C2211yescharacteristic
68#16810985C2211yescharacteristic
69#16810985C2211yescharacteristic
70#16810985C2211yescharacteristic
71#16810985C2211yescharacteristic, complemented
72#16810980C2211yescharacteristic
73#16810980C2211yescharacteristic
74#16810980C2211yescharacteristic
75#16810980C2211yescharacteristic, complemented
76#16810975C2211yescharacteristic, complemented
77#16810971C2211yescharacteristic
78#16810961C2211yescharacteristic
79#16810961C2211yescharacteristic
80#16810961C2211yescharacteristic
81#16810944C2211yescharacteristic
82#16810927C2211yescharacteristic, complemented
83#16810927C2211yescharacteristic, complemented
84#16810927C2211yescharacteristic, complemented
85#16810920C2211yescharacteristic
86#16810920C2211yescharacteristic
87#16810920C2211yescharacteristic, complemented
88#16810915C2211yescharacteristic, complemented
89#16810910C2211yescharacteristic
90#16810905C2211yescharacteristic, complemented
91#16810905C2211yescharacteristic, complemented
92#16810900C2211yescharacteristic
93#16810900C2211yescharacteristic, complemented
94#16810845C2211yescharacteristic
95#16810845C2211yescharacteristic
96#16810845C2211yescharacteristic
97#16810845C2211yescharacteristic
98#16810845C2211yescharacteristic
99#16810845C2211yescharacteristic
100#16810845C2211yescharacteristic
101#16810845C2211yescharacteristic
102#16810845C2211yescharacteristic
103#16810845C2211yescharacteristic, complemented
104#16810845C2211yescharacteristic, complemented
105#16810845C2211yescharacteristic, complemented
106#16810842C2211yescharacteristic, complemented
107#16810842C2211yescharacteristic, complemented
108#16810842C2211yescharacteristic, complemented
109#16810838C2211yescharacteristic
110#16810838C2211yescharacteristic
111#16810838C2211yescharacteristic
112#16810838C2211yescharacteristic, complemented
113#16810835C2211yescharacteristic
114#16810835C2211yescharacteristic
115#16810835C2211yescharacteristic, complemented
116#16810833C2211yescharacteristic, complemented
117#16810833C2211yescharacteristic, complemented
118#16810833C2211yescharacteristic, complemented
119#16810830C2211yescharacteristic, complemented
120#16810830C2211yescharacteristic, complemented
121#16810830C2211yescharacteristic, complemented
122#16810828C2211yescharacteristic, complemented
123#16810825C2211yescharacteristic
124#16810825C2211yescharacteristic
125#16810825C2211yescharacteristic, complemented
126#16810823C2211yescharacteristic
127#16810823C2211yescharacteristic
128#16810823C2211yescharacteristic
129#16810818C2211yescharacteristic
130#16810783C2211yescharacteristic
131#16810783C2211yescharacteristic
132#16810783C2211yescharacteristic
133#16810778C2211yescharacteristic
134#16810778C2211yescharacteristic
135#16810778C2211yescharacteristic
136#16810773C2211yescharacteristic
137#16810773C2211yescharacteristic
138#16810773C2211yescharacteristic
139#16810766C2211yescharacteristic
140#16810761C2211yescharacteristic
141#16810756C2211yescharacteristic
142#16810754C2211yescharacteristic, complemented
143#16810754C2211yescharacteristic, complemented
144#16810754C2211yescharacteristic, complemented
145#16810754C2211yescharacteristic, complemented
146#16810754C2211yescharacteristic, complemented
147#16810754C2211yescharacteristic, complemented
148Q8×#88322C2211yescharacteristic, complemented
149Q8×#88322C2211yescharacteristic, complemented
150#16810733C2211yescharacteristic
151#16810733C2211yescharacteristic, complemented
152#16810728C2211yescharacteristic, complemented
153#16810728C2211yescharacteristic, complemented
154#16810728C2211yescharacteristic, complemented
155#16810728C2211yescharacteristic, complemented
156#16810723C2211yescharacteristic, complemented
157#16810723C2211yescharacteristic, complemented
158#16810721C2211yescharacteristic
159#16810721C2211yescharacteristic
160#16810721C2211yescharacteristic
161#16810721C2211yescharacteristic, complemented
162C4×#11719925C2211yescharacteristic, complemented
163C4×#11719925C2211yescharacteristic, complemented
164C4×#11719925C2211yescharacteristic, complemented
165C4×#11719925C2211yescharacteristic, complemented
166C4×#11719925C2211yescharacteristic, complemented
167C4×#11719924C2211yescharacteristic
168C4×#11719924C2211yescharacteristic
169C4×#11719924C2211yescharacteristic
170C4×#11719924C2211yescharacteristic, complemented
171C4×#11719924C2211yescharacteristic, complemented
172C4×#11719923C2211yescharacteristic, complemented
173C4×#11719922C2211yescharacteristic
174#16810684C2211yescharacteristic
175#16810684C2211yescharacteristic
176#16810684C2211yescharacteristic
177#16810684C2211yescharacteristic
178#16810680C2211yescharacteristic
179#16810676C2211yescharacteristic
180C53×#563—21no—
181C53×#563—21no—
182Q82×C53C2211yescharacteristic, complemented
183C53×#557C2211yescharacteristic, complemented
184C53×#557C2211yescharacteristic, complemented
185C53×#557C2211yescharacteristic, complemented
186C53×#556—21no—
187C53×#556C2211yescharacteristic, complemented
188C53×#556C2211yescharacteristic, complemented
189C53×#556C2211yescharacteristic, complemented
190C53×#554C2211yescharacteristic, complemented
191C53×#552—21no—
192C53×#544—21no—
193C53×#542C2211yescharacteristic
194C53×#542C2211yescharacteristic
195C53×#541—21no—
196C53×#541—21no—
197C53×#541—21no—
198C53×#541C2211yescharacteristic
199C53×#541C2211yescharacteristic
200C53×#533C2211yescharacteristic
201C53×#533C2211yescharacteristic
202C53×#529C2211yescharacteristic
203C2×#11719945C2311yescharacteristic
204C22×Dic106C2311yescharacteristic
205C22×D212C2311yescharacteristic
206C2×#11719925C2311yescharacteristic
207C2×#11719925C2311yescharacteristic
208C2×#11719925C2311yescharacteristic
209C2×#11719925C2311yescharacteristic
210C2×#11719925C2311yescharacteristic
211C2×#11719925C2311yescharacteristic
212C2×#11719925C2311yescharacteristic
213C2×#11719925C2311yescharacteristic
214C2×#11719925C2311yescharacteristic
215C2×#11719923C2311yescharacteristic
216C2×#11719923C2311yescharacteristic
217C2×#11719923C2311yescharacteristic
218C2×#11719924C2311yescharacteristic
219C2×#11719924C2311yescharacteristic
220C2×#11719924C2311yescharacteristic
221C2×#11719924C2311yescharacteristic
222C2×#11719924C2311yescharacteristic
223C2×#11719924C2311yescharacteristic
224C2×#11719924C2311yescharacteristic
225C2×#11719924C2311yescharacteristic
226C2×#11719924C2311yescharacteristic
227C2×#11719922C2311yescharacteristic
228C2×#11719922C2311yescharacteristic
229C2×#11719922C2311yescharacteristic
230#13133217C2311yescharacteristic
231#13133217C2311yescharacteristic
232#13133214C2311yescharacteristic
233#13133214C2311yescharacteristic
234#13133212—21no—
235#13133212—21no—
236#13133212—21no—
237#13133212—21no—
238#13133212—21no—
239#13133212—21no—
240#13133212—21no—
241#13133212—21no—
242#13133206—21no—
243#13133206—21no—
244#13133206—21no—
245#13133206—21no—
246#13133205—21no—
247#13133205—21no—
248#13133205C2311yescharacteristic
249#13133205C2311yescharacteristic
250#13133205C2311yescharacteristic
251#13133205C2311yescharacteristic
252#13133205C2311yescharacteristic
253#13133205C2311yescharacteristic
254#13133205C2311yescharacteristic
255#13133205C2311yescharacteristic
256#13133202—21no—
257#13133202—21no—
258#13133202—21no—
259#13133202—21no—
260#13133202—21no—
261#13133202—21no—
262#13133202—21no—
263#13133202—21no—
264#13133201—21no—
265#13133201—21no—
266#13133197—21no—
267#13133197—21no—
268#13133193—21no—
269#13133193—21no—
270#13133193—21no—
271#13133193—21no—
272#13133192—21no—
273#13133192—21no—
274#13133187—21no—
275#13133187—21no—
276C4×Dic106C2311yescharacteristic
277C4×Dic106C2311yescharacteristic
278C4×Dic106C2311yescharacteristic
279C4×Dic106C2311yescharacteristic
280C4×Dic106C2311yescharacteristic
281C4×Dic106C2311yescharacteristic
282#13133182—21no—
283#13133182—21no—
284C4×D212C2311yescharacteristic
285C4×D212C2311yescharacteristic
286C4×D212C2311yescharacteristic
287C4×D212C2311yescharacteristic
288C4×D212C2311yescharacteristic
289C4×D212C2311yescharacteristic
290#13133179—21no—
291#13133179—21no—
292#13133179—21no—
293#13133179—21no—
294#13133179—21no—
295#13133179—21no—
296C4×C22⋊D53—21no—
297C4×C22⋊D53—21no—
298#13133176C2311yescharacteristic
299#13133175—21no—
300#13133175—21no—
301#13133175—21no—
302#13133175—21no—
303#13133174—21no—
304#13133173—21no—
305#13133173—21no—
306C2×#11719921—21no—
307C2×#11719921—21no—
308C22⋊C4×D53—21no—
309C22⋊C4×D53—21no—
310C42×D53—21no—
311#13133150C2311yescharacteristic
312#13133150C2311yescharacteristic
313#13133150C2311yescharacteristic
314#13133150C2311yescharacteristic
315#13133148C2311yescharacteristic
316#13133148C2311yescharacteristic
317#13133148C2311yescharacteristic
318#13133148C2311yescharacteristic
319C4⋊#88322C2311yescharacteristic
320C4⋊#88322C2311yescharacteristic
321C4⋊#88322C2311yescharacteristic
322C4⋊#88322C2311yescharacteristic
323C4⋊#88322C2311yescharacteristic
324C4⋊#88322C2311yescharacteristic
325C4⋊#88322C2311yescharacteristic
326C4⋊#88322C2311yescharacteristic
327C4⋊#88322C2311yescharacteristic
328C4⋊#88322C2311yescharacteristic
329C4⋊#88322C2311yescharacteristic
330C4⋊#88322C2311yescharacteristic
331#13133141C2311yescharacteristic
332#13133141C2311yescharacteristic
333#13133141C2311yescharacteristic
334#13133141C2311yescharacteristic
335#13133141C2311yescharacteristic
336#13133141C2311yescharacteristic
337#13133140C2311yescharacteristic
338#13133140C2311yescharacteristic
339#13133140C2311yescharacteristic
340#13133140C2311yescharacteristic
341#13133140C2311yescharacteristic
342#13133140C2311yescharacteristic
343#13133140C2311yescharacteristic
344#13133140C2311yescharacteristic
345#13133140C2311yescharacteristic
346#13133140C2311yescharacteristic
347#13133140C2311yescharacteristic
348#13133140C2311yescharacteristic
349#13133138C2311yescharacteristic
350#13133138C2311yescharacteristic
351#13133137C2311yescharacteristic
352#13133137C2311yescharacteristic
353#13133137C2311yescharacteristic
354#13133137C2311yescharacteristic
355#13133137C2311yescharacteristic
356#13133137C2311yescharacteristic
357#13133137C2311yescharacteristic
358#13133137C2311yescharacteristic
359#13133137C2311yescharacteristic
360#13133137C2311yescharacteristic
361#13133137C2311yescharacteristic
362#13133137C2311yescharacteristic
363C22⋊#88322C2311yescharacteristic
364C22⋊#88322C2311yescharacteristic
365C22⋊#88322C2311yescharacteristic
366C22⋊#88322C2311yescharacteristic
367#13133128C2311yescharacteristic
368#13133128C2311yescharacteristic
369#13133128C2311yescharacteristic
370#13133128C2311yescharacteristic
371#13133128C2311yescharacteristic
372#13133128C2311yescharacteristic
373C4×#88322C2311yescharacteristic
374C4×#88322C2311yescharacteristic
375C4×#88322C2311yescharacteristic
376C4×#88322C2311yescharacteristic
377C4×#88322C2311yescharacteristic
378C4×#88322C2311yescharacteristic
379C4⋊Q8×C53—21no—
380C4⋊Q8×C53—21no—
381C4⋊Q8×C53—21no—
382C4⋊Q8×C53—21no—
383C4⋊Q8×C53—21no—
384C4⋊Q8×C53D411yescharacteristic
385C4⋊Q8×C53D411yescharacteristic
386C4⋊Q8×C53C2311yescharacteristic
387C4⋊Q8×C53C2311yescharacteristic
388C4⋊Q8×C53C2311yescharacteristic
389C4⋊Q8×C53C2311yescharacteristic
390C4⋊Q8×C53C2311yescharacteristic
391C4⋊Q8×C53C2311yescharacteristic
392#126×C53—21no—
393#126×C53—21no—
394#126×C53—21no—
395#126×C53—21no—
396#126×C53—21no—
397#126×C53—21no—
398#126×C53—21no—
399#126×C53—21no—
400#126×C53—21no—
401#126×C53—21no—
402#126×C53—21no—
403#126×C53—21no—
404#126×C53—21no—
405#125×C53—21no—
406#125×C53—21no—
407#125×C53—21no—
408#125×C53—21no—
409#125×C53—21no—
410#125×C53—21no—
411#125×C53—21no—
412#125×C53—21no—
413#125×C53—21no—
414#125×C53—21no—
415#125×C53—21no—
416#125×C53—21no—
417#125×C53D411yescharacteristic
418#125×C53D411yescharacteristic
419#125×C53C2311yescharacteristic
420#125×C53C2311yescharacteristic
421#125×C53C2311yescharacteristic
422#124×C53—21no—
423#124×C53—21no—
424#124×C53C2311yescharacteristic
425#124×C53C2311yescharacteristic
426#124×C53C2311yescharacteristic
427#123×C53—21no—
428#123×C53—21no—
429#123×C53—21no—
430C22⋊Q8×C53—21no—
431C22⋊Q8×C53—21no—
432C22⋊Q8×C53—21no—
433C22⋊Q8×C53—21no—
434C22⋊Q8×C53—21no—
435C22⋊Q8×C53—21no—
436C22⋊Q8×C53—21no—
437C22⋊Q8×C53—21no—
438C22⋊Q8×C53—21no—
439C22⋊Q8×C53D411yescharacteristic
440C22⋊Q8×C53D411yescharacteristic
441C22⋊Q8×C53D411yescharacteristic
442C22⋊Q8×C53D411yescharacteristic
443C22⋊Q8×C53C2311yescharacteristic
444C22⋊Q8×C53C2311yescharacteristic
445C22⋊Q8×C53C2311yescharacteristic
446#121×C53C2311yescharacteristic
447C4×Q8×C53—21no—
448C4×Q8×C53—21no—
449C4×Q8×C53—21no—
450C4×Q8×C53—21no—
451C4×Q8×C53—21no—
452C4×Q8×C53C2311yescharacteristic
453C4×Q8×C53C2311yescharacteristic
454C4×Q8×C53C2311yescharacteristic
455C4×Q8×C53C2311yescharacteristic
456C4×Q8×C53C2311yescharacteristic
457C4×Q8×C53C2311yescharacteristic
458C4×Q8×C53C2311yescharacteristic
459C4×Q8×C53C2311yescharacteristic
460C4×Q8×C53C2311yescharacteristic
461C4×Q8×C53C2311yescharacteristic
462C4×Q8×C53C2311yescharacteristic
463C4×Q8×C53C2311yescharacteristic
464C4×Q8×C53C2311yescharacteristic
465C4×D4×C53—21no—
466C4×D4×C53C2311yescharacteristic
467C4×D4×C53C2311yescharacteristic
468C4×D4×C53C2311yescharacteristic
469#117×C53—21no—
470#117×C53—21no—
471#117×C53—21no—
472#117×C53—21no—
473#117×C53—21no—
474#117×C53C2311yescharacteristic
475#117×C53C2311yescharacteristic
476C2×C4⋊C4×C53—21no—
477C2×C42×C53C2311yescharacteristic
478C23×D53—21no—
479C2×Q8×C53—21no—
480C2×Q8×C53—21no—
481C2×Q8×C53—21no—
482C2×Q8×C53C2×D411yescharacteristic
483C2×Q8×C53C2×D411yescharacteristic
484C2×Q8×C53C2×D411yescharacteristic
485C2×Q8×C53C2×D411yescharacteristic
486C2×Q8×C53C2411yescharacteristic
487C2×Q8×C53C2411yescharacteristic
488C2×Q8×C53C2411yescharacteristic
489C2×D4×C53—21no—
490C2×D4×C53C2411yescharacteristic
491C22×C4×C53—21no—
492C22×C4×C53—21no—
493C22×C4×C53—21no—
494C22×C4×C53C2×D411yescharacteristic
495C22×C4×C53C2×D411yescharacteristic
496C22×C4×C53C2411yescharacteristic
497C2×C22⋊D53—21no—
498C22×Dic53—21no—
499#11719945—41no—
500#11719945—41no—
501C2×D212—21no—
502C2×D212—21no—
503C2×D212—21no—
504C2×D212—21no—
505C2×D212—21no—
506C2×D212—41no—
507C2×D212—41no—
508C2×D212C2411yescharacteristic
509C2×D212C2411yescharacteristic
510C2×D212C2411yescharacteristic
511C2×C4×D53—21no—
512C2×C4×D53—21no—
513C2×C4×D53—21no—
514C2×C4×D53—21no—
515C2×C4×D53—21no—
516C2×C4×D53—21no—
517C2×C4×D53—21no—
518C2×Dic106—21no—
519C2×Dic106—41no—
520C2×Dic106—41no—
521C2×Dic106C2411yescharacteristic
522C2×Dic106C2411yescharacteristic
523C2×Dic106C2411yescharacteristic
524C4⋊C4×C53—21no—
525C4⋊C4×C53—21no—
526C4⋊C4×C53—21no—
527C4⋊C4×C53—21no—
528C4⋊C4×C53—21no—
529C4⋊C4×C53—21no—
530C4⋊C4×C53—21no—
531C4⋊C4×C53—21no—
532C4⋊C4×C53—21no—
533C4⋊C4×C53—21no—
534C4⋊C4×C53—21no—
535C4⋊C4×C53—21no—
536C4⋊C4×C53—21no—
537C4⋊C4×C53—21no—
538C4⋊C4×C53—21no—
539C4⋊C4×C53—21no—
540C4⋊C4×C53—21no—
541C4⋊C4×C53—21no—
542C4⋊C4×C53—21no—
543C4⋊C4×C53—21no—
544C4⋊C4×C53—21no—
545C4⋊C4×C53—21no—
546C4⋊C4×C53—21no—
547C4⋊C4×C53—21no—
548C4⋊C4×C53—21no—
549C4⋊C4×C53—21no—
550C4⋊C4×C53—21no—
551C4⋊C4×C53C2×D411yescharacteristic
552C4⋊C4×C53C2×D411yescharacteristic
553C4⋊C4×C53C2×D411yescharacteristic
554C4⋊C4×C53C2×D411yescharacteristic
555C4⋊C4×C53C2×D411yescharacteristic
556C4⋊C4×C53C2×D411yescharacteristic
557C4⋊C4×C53C2×D411yescharacteristic
558C4⋊C4×C53C2×D411yescharacteristic
559C4⋊C4×C53C2×D411yescharacteristic
560C4⋊C4×C53C2×D411yescharacteristic
561C4⋊C4×C53C2×D411yescharacteristic
562C4⋊C4×C53C2×D411yescharacteristic
563C4⋊C4×C53C2×D411yescharacteristic
564C4⋊C4×C53C2×D411yescharacteristic
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×C53—21no—
581C22⋊C4×C53—21no—
582C22⋊C4×C53—21no—
583C22⋊C4×C53—21no—
584C22⋊C4×C53C2×D411yescharacteristic
585C22⋊C4×C53C2×D411yescharacteristic
586C22⋊C4×C53C2×D411yescharacteristic
587C22⋊C4×C53C2×D411yescharacteristic
588C42×C53—21no—
589C42×C53—21no—
590C42×C53—21no—
591C42×C53—21no—
592C42×C53—21no—
593C42×C53—21no—
594C42×C53—21no—
595C42×C53—21no—
596C42×C53—21no—
597C42×C53C2×D411yescharacteristic
598C42×C53C2×D411yescharacteristic
599C42×C53C2411yescharacteristic
600C42×C53C2411yescharacteristic
601C42×C53C2411yescharacteristic
602C42×C53C2411yescharacteristic
603C42×C53C2411yescharacteristic
604C42×C53C2411yescharacteristic
605C22⋊Dic53—21no—
606#11719925—41no—
607#11719925—41no—
608#11719925—41no—
609#11719925—41no—
610#11719925—41no—
611#11719925—41no—
612#11719925—41no—
613#11719925—41no—
614#11719925—41no—
615#11719924—41no—
616#11719924—41no—
617#11719924—41no—
618#11719924—41no—
619#11719924—41no—
620#11719924—41no—
621#11719924—41no—
622#11719924—41no—
623#11719924—41no—
624#11719923—41no—
625#11719923—41no—
626#11719923—41no—
627#11719922—41no—
628#11719922—41no—
629#11719922—41no—
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#11719921—21no—
651#11719921—21no—
652C4⋊Dic53—21no—
653C4⋊Dic53—21no—
654C4⋊Dic53—21no—
655C4⋊Dic53—21no—
656C4⋊Dic53C2411yescharacteristic
657C4⋊Dic53C2411yescharacteristic
658#11719919—21no—
659#11719919—21no—
660#11719919—21no—
661#11719919—21no—
662#11719919—21no—
663#11719919—21no—
664C4×Dic53—21no—
665C4×Dic53—21no—
666C4×Dic53—21no—
667C4×Dic53—21no—
668C4×Dic53—21no—
669C4×Dic53—21no—
670C4×Dic53—21no—
671C2×#88322C2411yescharacteristic
672C2×#88322C2411yescharacteristic
673C2×#88322C2411yescharacteristic
674C2×#88322C2411yescharacteristic
675C2×#88322C2411yescharacteristic
676C2×#88322C2411yescharacteristic
677C2×#88322C2411yescharacteristic
678C2×#88322C2411yescharacteristic
679C23×C53—21no—
680C23×C53C22×D411yescharacteristic
681C22×D53—21no—
682C22×D53—21no—
683C22×D53—21no—
684C22×D53—42no—
685C22×D53—81no—
686C22×D53—81no—
687Q8×C53—21no—
688Q8×C53—21no—
689Q8×C53—21no—
690Q8×C53—21no—
691Q8×C53—21no—
692Q8×C53—21no—
693Q8×C53—41no—
694Q8×C53—41no—
695Q8×C53—41no—
696Q8×C53—41no—
697Q8×C53—81no—
698Q8×C53—81no—
699Q8×C53—81no—
700D4×C53—21no—
701D4×C53—21no—
702D4×C53—81no—
703C2×C4×C53—21no—
704C2×C4×C53—21no—
705C2×C4×C53—21no—
706C2×C4×C53—21no—
707C2×C4×C53—21no—
708C2×C4×C53—21no—
709C2×C4×C53—21no—
710C2×C4×C53—21no—
711C2×C4×C53—21no—
712C2×C4×C53—41no—
713C2×C4×C53—41no—
714C2×C4×C53—42no—
715C2×C4×C53—81no—
716C2×C4×C53—81no—
717C2×C4×C53C22×D411yescharacteristic
718C2×C4×C53C22×D411yescharacteristic
719C2×C4×C53C22×D411yescharacteristic
720C2×C4×C53C22×D411yescharacteristic
721C2×C4×C53C22×D411yescharacteristic
722C2×C4×C53C22×D411yescharacteristic
723C2×C4×C53C22×D411yescharacteristic
724C2×C4×C53C22×D411yescharacteristic
725C2×C4×C53C22×D411yescharacteristic
726C2×C4×C53C22×D411yescharacteristic
727C2×C4×C53C22×D411yescharacteristic
728C2×C4×C53C22×D411yescharacteristic
729C2×C4×C53C22×D411yescharacteristic
730C2×C4×C53C2511yescharacteristic
731C22⋊D53—42no—
732C2×Dic53—21no—
733C2×Dic53—21no—
734C2×Dic53—21no—
735C2×Dic53—21no—
736C2×Dic53—21no—
737C2×Dic53—42no—
738D212—21no—
739D212—21no—
740D212—21no—
741D212—21no—
742D212—21no—
743D212—21no—
744D212—42no—
745D212—81no—
746D212—81no—
747D212—81no—
748D212—81no—
749C4×D53—42no—
750C4×D53—81no—
751C4×D53—81no—
752C4×D53—81no—
753C4×D53—81no—
754C4×D53—81no—
755C4×D53—81no—
756Dic106—21no—
757Dic106—21no—
758Dic106—21no—
759Dic106—21no—
760Dic106—21no—
761Dic106—21no—
762Dic106—42no—
763#88322—21no—
764#88322—21no—
765#88322—21no—
766#88322—21no—
767#88322—21no—
768#88322—21no—
769#88322—21no—
770#88322—21no—
771#61925—531nomaximal, Sylow
772C22×C53—21no—
773C22×C53—21no—
774C22×C53—21no—
775C22×C53—41no—
776C22×C53—41no—
777C22×C53—41no—
778C22×C53C23×D411yescharacteristic
779C2×D53—41no—
780C2×D53—41no—
781C2×D53—41no—
782C2×D53—41no—
783C2×D53—41no—
784C2×D53—41no—
785C2×D53—41no—
786C2×D53—41no—
787C2×D53—41no—
788C2×D53—162no—
789C4×C53—21no—
790C4×C53—21no—
791C4×C53—21no—
792C4×C53—21no—
793C4×C53—21no—
794C4×C53—21no—
795C4×C53—21no—
796C4×C53—21no—
797C4×C53—21no—
798C4×C53—21no—
799C4×C53—21no—
800C4×C53—21no—
801C4×C53—21no—
802C4×C53—41no—
803C4×C53—41no—
804C4×C53—41no—
805C4×C53—41no—
806C4×C53—41no—
807C4×C53—41no—
808C4×C53—41no—
809C4×C53#58511yescharacteristic
810C4×C53#58511yescharacteristic
811Dic53—41no—
812Dic53—41no—
813Dic53—41no—
814Dic53—41no—
815Dic53—41no—
816#3555D5311yescharacteristic, complemented
817#3510—531no—
818#3402—531no—
819#3402—531no—
820#3401—531no—
821#3401—531no—
822#3400—531no—
823#3398—531no—
824#3394—531no—
825#3393—531no—
826#3377—531no—
827#3376—531no—
828#3375—531no—
829#3371—531no—
830#3370—531no—
831#3369—531no—
832#3365—531no—
833#3364—531no—
834#3225—531no—
835#3224—531no—
836#3223—531no—
837#3222—531no—
838#3215—531no—
839#3211—531no—
840#3127—531no—
841#3123—531no—
842#3121—531no—
843#3118—531no—
844#3111—531no—
845#3107—531no—
846#2985—531no—
847C2×C53—41no—
848C2×C53—81no—
849C2×C53#348711yescharacteristic
850C2×C53#358411yescharacteristic
851C2×C53#358611yescharacteristic
852D53—81no—
853D53—81no—
854D53—81no—
855#563—21no—
856#563—21no—
857#559—531no—
858#559—531no—
859#559—531no—
860#559—531no—
861Q82C2×D5311yescharacteristic, complemented
862#557C2×D5311yescharacteristic, complemented
863#557C2×D5311yescharacteristic, complemented
864#557C2×D5311yescharacteristic, complemented
865#556—21no—
866#556—531no—
867#556—531no—
868#556—531no—
869#556—531no—
870#556C2×D5311yescharacteristic, complemented
871#556C2×D5311yescharacteristic, complemented
872#556C2×D5311yescharacteristic, complemented
873#554C2×D5311yescharacteristic, complemented
874#552—21no—
875#551—1061no—
876#551—1061no—
877#551—1061no—
878#551—1061no—
879#544—21no—
880#542—1061no—
881#542—1061no—
882#542C2×D5311yescharacteristic
883#542C2×D5311yescharacteristic
884#541—21no—
885#541—21no—
886#541—21no—
887#541C2×D5311yescharacteristic
888#541C2×D5311yescharacteristic
889#536—531no—
890#535—531no—
891#533C2×D5311yescharacteristic
892#533C2×D5311yescharacteristic
893#529—1061no—
894#529—1061no—
895#529C2×D5311yescharacteristic
896C2×#124—531no—
897#519—531no—
898#518—531no—
899C4×#41—531no—
900#497—531no—
901#497—531no—
902#497—531no—
903#497—531no—
904#497—531no—
905#496—531no—
906#495—531no—
907#495—531no—
908#495—531no—
909#495—531no—
910#494—531no—
911#492—531no—
912#491—531no—
913#490—531no—
914#489—531no—
915#489—531no—
916#489—531no—
917#489—531no—
918#488—531no—
919#488—531no—
920#488—531no—
921#488—531no—
922#487—531no—
923#486—531no—
924#485—531no—
925#485—531no—
926#485—531no—
927#482—531no—
928#479—531no—
929#479—531no—
930#479—531no—
931#478—531no—
932#478—531no—
933#478—531no—
934#477—531no—
935#476—531no—
936#475—531no—
937#475—531no—
938#474—531no—
939#474—531no—
940#464—531no—
941#464—531no—
942#464—531no—
943#464—531no—
944#464—531no—
945#464—531no—
946#464—531no—
947#464—531no—
948#464—531no—
949#464—531no—
950#464—531no—
951#464—531no—
952#464—531no—
953#464—531no—
954#464—531no—
955#463—531no—
956#463—531no—
957#463—531no—
958#463—531no—
959#463—531no—
960#463—531no—
961#463—531no—
962#462—531no—
963#462—531no—
964#462—531no—
965#462—531no—
966#462—531no—
967#462—531no—
968#461—531no—
969#461—531no—
970#461—531no—
971#461—531no—
972#460—531no—
973#460—531no—
974#460—531no—
975#459—531no—
976#452—531no—
977#452—531no—
978#452—531no—
979#451—531no—
980#451—531no—
981#451—531no—
982#450—531no—
983#450—531no—
984#450—531no—
985#449—531no—
986#448—531no—
987#447—531no—
988#446—531no—
989#446—531no—
990#446—531no—
991#446—531no—
992#446—531no—
993#446—531no—
994C8×Q8—531no—
995C8×Q8—531no—
996#442—531no—
997#442—531no—
998#441—531no—
999#441—531no—
1000#441—531no—
1001#441—531no—
1002#440—531no—
1003#440—531no—
1004#440—531no—
1005#440—531no—
1006#440—531no—
1007#440—531no—
1008C4×Q16—531no—
1009C4×Q16—531no—
1010C4×Q16—531no—
1011C4×Q16—531no—
1012C4×Q16—531no—
1013C4×SD16—531no—
1014C4×SD16—531no—
1015C4×SD16—531no—
1016C4×SD16—531no—
1017C4×SD16—531no—
1018C4×SD16—531no—
1019C4×D8—531no—
1020#433—531no—
1021#433—531no—
1022#433—531no—
1023#433—531no—
1024#432—531no—
1025#431—531no—
1026C53#6192511yescharacteristic, complemented, Sylow
1027C2×#41—531no—
1028C22×Q8—531no—
1029C22×D4—531no—
1030C2×Q16—531no—
1031C2×Q16—531no—
1032C2×Q16—531no—
1033C2×Q16—531no—
1034C2×Q16—531no—
1035C2×Q16—531no—
1036C2×Q16—531no—
1037C2×Q16—531no—
1038C2×Q16—531no—
1039C2×SD16—531no—
1040C2×SD16—531no—
1041C2×SD16—531no—
1042C2×SD16—531no—
1043C2×SD16—531no—
1044C2×SD16—531no—
1045C2×SD16—531no—
1046C2×SD16—531no—
1047C2×SD16—531no—
1048C2×SD16—531no—
1049C2×SD16—531no—
1050C2×SD16—531no—
1051C2×D8—531no—
1052C2×D8—531no—
1053C2×D8—531no—
1054C4⋊Q8—21no—
1055C4⋊Q8—21no—
1056C4⋊Q8—21no—
1057C4⋊Q8—21no—
1058C4⋊Q8—21no—
1059C4⋊Q8—531no—
1060C4⋊Q8—531no—
1061C4⋊Q8C22⋊D5311yescharacteristic
1062C4⋊Q8C22⋊D5311yescharacteristic
1063C4⋊Q8C22×D5311yescharacteristic
1064C4⋊Q8C22×D5311yescharacteristic
1065C4⋊Q8C22×D5311yescharacteristic
1066C4⋊Q8C22×D5311yescharacteristic
1067C4⋊Q8C22×D5311yescharacteristic
1068C4⋊Q8C22×D5311yescharacteristic
1069#127—531no—
1070#127—531no—
1071#126—21no—
1072#126—21no—
1073#126—21no—
1074#126—21no—
1075#126—21no—
1076#126—21no—
1077#126—21no—
1078#126—21no—
1079#126—21no—
1080#126—21no—
1081#126—21no—
1082#126—21no—
1083#126—21no—
1084#126—1061no—
1085#126—1061no—
1086#126—1061no—
1087#126—1061no—
1088#126—1061no—
1089#126—1061no—
1090#126—1061no—
1091#126—1061no—
1092#125—21no—
1093#125—21no—
1094#125—21no—
1095#125—21no—
1096#125—21no—
1097#125—21no—
1098#125—21no—
1099#125—21no—
1100#125—21no—
1101#125—21no—
1102#125—21no—
1103#125—21no—
1104#125C22⋊D5311yescharacteristic
1105#125C22⋊D5311yescharacteristic
1106#125C22×D5311yescharacteristic
1107#125C22×D5311yescharacteristic
1108#125C22×D5311yescharacteristic
1109#124—21no—
1110#124—21no—
1111#124—531no—
1112#124—531no—
1113#124—531no—
1114#124—531no—
1115#124—531no—
1116#124—531no—
1117#124—531no—
1118#124—531no—
1119#124—1061no—
1120#124—1061no—
1121#124—1061no—
1122#124—1061no—
1123#124—1061no—
1124#124—1061no—
1125#124C22×D5311yescharacteristic
1126#124C22×D5311yescharacteristic
1127#124C22×D5311yescharacteristic
1128#123—21no—
1129#123—21no—
1130#123—21no—
1131#123—1061no—
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—
1141C22⋊Q8—21no—
1142C22⋊Q8—21no—
1143C22⋊Q8—21no—
1144C22⋊Q8—21no—
1145C22⋊Q8—21no—
1146C22⋊Q8—21no—
1147C22⋊Q8—21no—
1148C22⋊Q8—21no—
1149C22⋊Q8—21no—
1150C22⋊Q8—1061no—
1151C22⋊Q8—1061no—
1152C22⋊Q8—1061no—
1153C22⋊Q8—1061no—
1154C22⋊Q8—1061no—
1155C22⋊Q8—1061no—
1156C22⋊Q8C22⋊D5311yescharacteristic
1157C22⋊Q8C22⋊D5311yescharacteristic
1158C22⋊Q8C22⋊D5311yescharacteristic
1159C22⋊Q8C22⋊D5311yescharacteristic
1160C22⋊Q8C22×D5311yescharacteristic
1161C22⋊Q8C22×D5311yescharacteristic
1162C22⋊Q8C22×D5311yescharacteristic
1163#121—1061no—
1164#121—1061no—
1165#121C22×D5311yescharacteristic
1166#120—1061no—
1167#120—1061no—
1168C4×Q8—21no—
1169C4×Q8—21no—
1170C4×Q8—21no—
1171C4×Q8—21no—
1172C4×Q8—21no—
1173C4×Q8—531no—
1174C4×Q8—531no—
1175C4×Q8—531no—
1176C4×Q8—531no—
1177C4×Q8—531no—
1178C4×Q8—531no—
1179C4×Q8—1061no—
1180C4×Q8—1061no—
1181C4×Q8C22×D5311yescharacteristic
1182C4×Q8C22×D5311yescharacteristic
1183C4×Q8C22×D5311yescharacteristic
1184C4×Q8C22×D5311yescharacteristic
1185C4×Q8C22×D5311yescharacteristic
1186C4×Q8C22×D5311yescharacteristic
1187C4×Q8C22×D5311yescharacteristic
1188C4×Q8C22×D5311yescharacteristic
1189C4×Q8C22×D5311yescharacteristic
1190C4×Q8C22×D5311yescharacteristic
1191C4×Q8C22×D5311yescharacteristic
1192C4×Q8C22×D5311yescharacteristic
1193C4×Q8C22×D5311yescharacteristic
1194C4×D4—21no—
1195C4×D4—531no—
1196C4×D4—531no—
1197C4×D4—531no—
1198C4×D4—531no—
1199C4×D4—531no—
1200C4×D4—531no—
1201C4×D4—1061no—
1202C4×D4—1061no—
1203C4×D4—1061no—
1204C4×D4—1061no—
1205C4×D4—1061no—
1206C4×D4—1061no—
1207C4×D4—1061no—
1208C4×D4—1061no—
1209C4×D4C22×D5311yescharacteristic
1210C4×D4C22×D5311yescharacteristic
1211C4×D4C22×D5311yescharacteristic
1212#117—21no—
1213#117—21no—
1214#117—21no—
1215#117—21no—
1216#117—21no—
1217#117—531no—
1218#117—1061no—
1219#117—1061no—
1220#117—1061no—
1221#117—1061no—
1222#117—1061no—
1223#117—1061no—
1224#117—1061no—
1225#117C22×D5311yescharacteristic
1226#117C22×D5311yescharacteristic
1227C2×C4⋊C4—21no—
1228C2×C22⋊C4—1061no—
1229C2×C22⋊C4—1061no—
1230C2×C22⋊C4—1061no—
1231C2×C22⋊C4—1061no—
1232C2×C42—1061no—
1233C2×C42C22×D5311yescharacteristic
1234#107—531no—
1235#107—531no—
1236#107—531no—
1237#107—531no—
1238#106—531no—
1239#106—531no—
1240#106—531no—
1241#106—531no—
1242C4⋊C8—531no—
1243C4⋊C8—531no—
1244C4⋊C8—531no—
1245C4⋊C8—531no—
1246C4⋊C8—531no—
1247C4⋊C8—531no—
1248C4⋊C8—531no—
1249C4⋊C8—531no—
1250C4⋊C8—531no—
1251C4⋊C8—531no—
1252C4⋊C8—531no—
1253C4⋊C8—531no—
1254#103—531no—
1255#103—531no—
1256#103—531no—
1257#103—531no—
1258#103—531no—
1259#103—531no—
1260#103—531no—
1261#103—531no—
1262#103—531no—
1263#103—531no—
1264#103—531no—
1265#103—531no—
1266#103—531no—
1267#103—531no—
1268#103—531no—
1269#103—531no—
1270#103—531no—
1271#103—531no—
1272#102—531no—
1273#102—531no—
1274#102—531no—
1275#102—531no—
1276#102—531no—
1277#102—531no—
1278#102—531no—
1279#102—531no—
1280#102—531no—
1281#102—531no—
1282#102—531no—
1283#102—531no—
1284#102—531no—
1285#102—531no—
1286C22⋊C8—531no—
1287C22⋊C8—531no—
1288C22⋊C8—531no—
1289C22⋊C8—531no—
1290#97—531no—
1291#97—531no—
1292#97—531no—
1293#97—531no—
1294#97—531no—
1295#97—531no—
1296C4×C8—531no—
1297C4×C8—531no—
1298C4×C8—531no—
1299C4×C8—531no—
1300C4×C8—531no—
1301C4×C8—531no—
1302C24—1061no—
1303#41—2121no—
1304#41—2121no—
1305C2×Q8—21no—
1306C2×Q8—21no—
1307C2×Q8—21no—
1308C2×Q8—531no—
1309C2×Q8—531no—
1310C2×Q8—531no—
1311C2×Q8—1061no—
1312C2×Q8—2121no—
1313C2×Q8—2121no—
1314C2×Q8C2×C22⋊D5311yescharacteristic
1315C2×Q8C2×C22⋊D5311yescharacteristic
1316C2×Q8C2×C22⋊D5311yescharacteristic
1317C2×Q8C2×C22⋊D5311yescharacteristic
1318C2×Q8C23×D5311yescharacteristic
1319C2×Q8C23×D5311yescharacteristic
1320C2×Q8C23×D5311yescharacteristic
1321C2×D4—21no—
1322C2×D4—531no—
1323C2×D4—531no—
1324C2×D4—531no—
1325C2×D4—1061no—
1326C2×D4—1061no—
1327C2×D4—1061no—
1328C2×D4—1061no—
1329C2×D4—1061no—
1330C2×D4—1061no—
1331C2×D4—2121no—
1332C2×D4—2121no—
1333C2×D4C23×D5311yescharacteristic
1334C22×C4—21no—
1335C22×C4—21no—
1336C22×C4—21no—
1337C22×C4—1061no—
1338C22×C4—1061no—
1339C22×C4—1061no—
1340C22×C4—1061no—
1341C22×C4—1061no—
1342C22×C4—1061no—
1343C22×C4—1061no—
1344C22×C4—1061no—
1345C22×C4C2×C22⋊D5311yescharacteristic
1346C22×C4C2×C22⋊D5311yescharacteristic
1347C22×C4C23×D5311yescharacteristic
1348Q16—2121no—
1349Q16—2121no—
1350Q16—2121no—
1351Q16—2121no—
1352Q16—2121no—
1353Q16—2121no—
1354Q16—2121no—
1355Q16—2121no—
1356Q16—2121no—
1357SD16—2121no—
1358SD16—2121no—
1359SD16—2121no—
1360SD16—2121no—
1361SD16—2121no—
1362SD16—2121no—
1363SD16—2121no—
1364SD16—2121no—
1365SD16—2121no—
1366SD16—2121no—
1367SD16—2121no—
1368SD16—2121no—
1369D8—2121no—
1370D8—2121no—
1371D8—2121no—
1372C2×C8—531no—
1373C2×C8—531no—
1374C2×C8—531no—
1375C2×C8—531no—
1376C2×C8—531no—
1377C2×C8—531no—
1378C2×C8—531no—
1379C2×C8—531no—
1380C4⋊C4—21no—
1381C4⋊C4—21no—
1382C4⋊C4—21no—
1383C4⋊C4—21no—
1384C4⋊C4—21no—
1385C4⋊C4—21no—
1386C4⋊C4—21no—
1387C4⋊C4—21no—
1388C4⋊C4—21no—
1389C4⋊C4—21no—
1390C4⋊C4—21no—
1391C4⋊C4—21no—
1392C4⋊C4—21no—
1393C4⋊C4—21no—
1394C4⋊C4—21no—
1395C4⋊C4—21no—
1396C4⋊C4—21no—
1397C4⋊C4—21no—
1398C4⋊C4—21no—
1399C4⋊C4—21no—
1400C4⋊C4—21no—
1401C4⋊C4—21no—
1402C4⋊C4—21no—
1403C4⋊C4—21no—
1404C4⋊C4—21no—
1405C4⋊C4—21no—
1406C4⋊C4—21no—
1407C4⋊C4—531no—
1408C4⋊C4—531no—
1409C4⋊C4—1061no—
1410C4⋊C4—1061no—
1411C4⋊C4—1061no—
1412C4⋊C4—1061no—
1413C4⋊C4—1061no—
1414C4⋊C4—1061no—
1415C4⋊C4—1061no—
1416C4⋊C4—1061no—
1417C4⋊C4—1061no—
1418C4⋊C4—1061no—
1419C4⋊C4C2×C22⋊D5311yescharacteristic
1420C4⋊C4C2×C22⋊D5311yescharacteristic
1421C4⋊C4C2×C22⋊D5311yescharacteristic
1422C4⋊C4C2×C22⋊D5311yescharacteristic
1423C4⋊C4C2×C22⋊D5311yescharacteristic
1424C4⋊C4C2×C22⋊D5311yescharacteristic
1425C4⋊C4C2×C22⋊D5311yescharacteristic
1426C4⋊C4C2×C22⋊D5311yescharacteristic
1427C4⋊C4C2×C22⋊D5311yescharacteristic
1428C4⋊C4C2×C22⋊D5311yescharacteristic
1429C4⋊C4C2×C22⋊D5311yescharacteristic
1430C4⋊C4C2×C22⋊D5311yescharacteristic
1431C4⋊C4C2×C22⋊D5311yescharacteristic
1432C4⋊C4C2×C22⋊D5311yescharacteristic
1433C4⋊C4C2×C22⋊D5311yescharacteristic
1434C4⋊C4C2×C22⋊D5311yescharacteristic
1435C4⋊C4C23×D5311yescharacteristic
1436C4⋊C4C23×D5311yescharacteristic
1437C4⋊C4C23×D5311yescharacteristic
1438C4⋊C4C23×D5311yescharacteristic
1439C22⋊C4—21no—
1440C22⋊C4—21no—
1441C22⋊C4—21no—
1442C22⋊C4—21no—
1443C22⋊C4—21no—
1444C22⋊C4—21no—
1445C22⋊C4—21no—
1446C22⋊C4—21no—
1447C22⋊C4—21no—
1448C22⋊C4—21no—
1449C22⋊C4—21no—
1450C22⋊C4—21no—
1451C22⋊C4—21no—
1452C22⋊C4—1061no—
1453C22⋊C4—1061no—
1454C22⋊C4—1061no—
1455C22⋊C4—1061no—
1456C22⋊C4—1061no—
1457C22⋊C4—1061no—
1458C22⋊C4—1061no—
1459C22⋊C4—1061no—
1460C22⋊C4—1061no—
1461C22⋊C4—1061no—
1462C22⋊C4—1061no—
1463C22⋊C4—1061no—
1464C22⋊C4—1061no—
1465C22⋊C4—1061no—
1466C22⋊C4—1061no—
1467C22⋊C4—1061no—
1468C22⋊C4—1061no—
1469C22⋊C4—1061no—
1470C22⋊C4—1061no—
1471C22⋊C4—1061no—
1472C22⋊C4—1061no—
1473C22⋊C4—1061no—
1474C22⋊C4—1061no—
1475C22⋊C4C2×C22⋊D5311yescharacteristic
1476C22⋊C4C2×C22⋊D5311yescharacteristic
1477C22⋊C4C2×C22⋊D5311yescharacteristic
1478C22⋊C4C2×C22⋊D5311yescharacteristic
1479C42—21no—
1480C42—21no—
1481C42—21no—
1482C42—21no—
1483C42—21no—
1484C42—21no—
1485C42—21no—
1486C42—21no—
1487C42—21no—
1488C42—1061no—
1489C42—1061no—
1490C42—1061no—
1491C42—1061no—
1492C42—1061no—
1493C42—1061no—
1494C42—1061no—
1495C42C2×C22⋊D5311yescharacteristic
1496C42C2×C22⋊D5311yescharacteristic
1497C42C23×D5311yescharacteristic
1498C42C23×D5311yescharacteristic
1499C42C23×D5311yescharacteristic
1500C42C23×D5311yescharacteristic
1501C42C23×D5311yescharacteristic
1502C42C23×D5311yescharacteristic
1503C23—21no—
1504C23—1061no—
1505C23—1061no—
1506C23—1061no—
1507C23—4241no—
1508C23—4241no—
1509C23—2122no—
1510C23C22×C22⋊D5311yescharacteristic
1511Q8—21no—
1512Q8—21no—
1513Q8—21no—
1514Q8—21no—
1515Q8—21no—
1516Q8—21no—
1517Q8—41no—
1518Q8—41no—
1519Q8—41no—
1520Q8—41no—
1521Q8—81no—
1522Q8—81no—
1523Q8—81no—
1524Q8—1061no—
1525Q8—1061no—
1526Q8—1061no—
1527Q8—1061no—
1528Q8—1061no—
1529Q8—1061no—
1530Q8—2122no—
1531D4—21no—
1532D4—21no—
1533D4—81no—
1534D4—1061no—
1535D4—1061no—
1536D4—1061no—
1537D4—1061no—
1538D4—1061no—
1539D4—1061no—
1540D4—4241no—
1541D4—4241no—
1542D4—4241no—
1543D4—4241no—
1544D4—2122no—
1545D4—2122no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—41no—
1556C2×C4—41no—
1557C2×C4—42no—
1558C2×C4—81no—
1559C2×C4—81no—
1560C2×C4—1061no—
1561C2×C4—1061no—
1562C2×C4—1061no—
1563C2×C4—1061no—
1564C2×C4—1061no—
1565C2×C4—4241no—
1566C2×C4—4241no—
1567C2×C4—4241no—
1568C2×C4—4241no—
1569C2×C4—4241no—
1570C2×C4—4241no—
1571C2×C4—2122no—
1572C2×C4—2122no—
1573C2×C4C22×C22⋊D5311yescharacteristic
1574C2×C4C22×C22⋊D5311yescharacteristic
1575C2×C4C22×C22⋊D5311yescharacteristic
1576C2×C4C22×C22⋊D5311yescharacteristic
1577C2×C4C22×C22⋊D5311yescharacteristic
1578C2×C4C22×C22⋊D5311yescharacteristic
1579C2×C4C22×C22⋊D5311yescharacteristic
1580C2×C4C22×C22⋊D5311yescharacteristic
1581C2×C4C22×C22⋊D5311yescharacteristic
1582C2×C4C22×C22⋊D5311yescharacteristic
1583C2×C4C22×C22⋊D5311yescharacteristic
1584C2×C4C22×C22⋊D5311yescharacteristic
1585C2×C4C22×C22⋊D5311yescharacteristic
1586C2×C4C24×D5311yescharacteristic
1587C8—1061no—
1588C8—1061no—
1589C8—1061no—
1590C8—1061no—
1591C8—1061no—
1592C8—1061no—
1593C8—1061no—
1594C8—1061no—
1595C22—21no—
1596C22—21no—
1597C22—21no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—8482no—
1602C22—2121no—
1603C22—2121no—
1604C22—2121no—
1605C22—2121no—
1606C22—2121no—
1607C22—2121no—
1608C22—2121no—
1609C22—2121no—
1610C22—2121no—
1611C22C23×C22⋊D5311yescharacteristic
1612C4—21no—
1613C4—21no—
1614C4—21no—
1615C4—21no—
1616C4—21no—
1617C4—21no—
1618C4—21no—
1619C4—21no—
1620C4—21no—
1621C4—21no—
1622C4—21no—
1623C4—21no—
1624C4—21no—
1625C4—41no—
1626C4—41no—
1627C4—41no—
1628C4—41no—
1629C4—41no—
1630C4—41no—
1631C4—41no—
1632C4—2121no—
1633C4—2121no—
1634C4—2121no—
1635C4—2121no—
1636C4—2121no—
1637C4#1681146011yescharacteristic
1638C4#1681146011yescharacteristic
1639C2—41no—
1640C2—81no—
1641C2—4241no—
1642C2—4241no—
1643C2—4241no—
1644C2#2028837011yescharacteristic
1645C2#2028948611yescharacteristic
1646C2#2028950211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3555C2
socleC22×C53C23×D4
prime radical#20285803C2
hypercenter#3555D53
hypocenterC53#61925
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #533 ◁ #3555

Complements

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

NH ≅ G/Ntype
1. #20288613C2semidirect
2. #20287790C2semidirect
3. #20287790C2semidirect
4. #20287781C2semidirect
5. #20287781C2semidirect
6. #20287764C2semidirect
7. #20287742C2semidirect
8. #20287711C2semidirect
9. #20287699C2semidirect
10. #20287557C2semidirect
11. #20287542C2semidirect
12. #20287529C2semidirect
13. #20287483C2semidirect
14. #20287468C2semidirect
15. #20287455C2semidirect
16. #20287411C2semidirect
17. #20287400C2semidirect
18. #20285818C2semidirect
20. #20285792C2semidirect
21. #20285781C2semidirect
22. #20285714C2semidirect
23. #20285676C2semidirect
24. #20285010C2semidirect
25. #20284962C2semidirect
26. #20284938C2semidirect
27. #20284893C2semidirect
28. #20284818C2semidirect
29. #20284780C2semidirect
30. #20283810C2semidirect
31. C53×#3555C2semidirect
54. #16811018C22semidirect
58. #16811015C22semidirect
63. #16811005C22semidirect
64. #16811002C22semidirect
66. #16810993C22semidirect
71. #16810985C22semidirect
75. #16810980C22semidirect
76. #16810975C22semidirect
82. #16810927C22semidirect
83. #16810927C22semidirect
84. #16810927C22semidirect
87. #16810920C22semidirect
88. #16810915C22semidirect
90. #16810905C22semidirect
91. #16810905C22semidirect
93. #16810900C22semidirect
103. #16810845C22semidirect
104. #16810845C22semidirect
105. #16810845C22semidirect
106. #16810842C22semidirect
107. #16810842C22semidirect
108. #16810842C22semidirect
112. #16810838C22semidirect
115. #16810835C22semidirect
116. #16810833C22semidirect
117. #16810833C22semidirect
118. #16810833C22semidirect
119. #16810830C22semidirect
120. #16810830C22semidirect
121. #16810830C22semidirect
122. #16810828C22semidirect
125. #16810825C22semidirect
142. #16810754C22semidirect
143. #16810754C22semidirect
144. #16810754C22semidirect
145. #16810754C22semidirect
146. #16810754C22semidirect
147. #16810754C22semidirect
148. Q8×#88322C22semidirect
149. Q8×#88322C22semidirect
151. #16810733C22semidirect
152. #16810728C22semidirect
153. #16810728C22semidirect
154. #16810728C22semidirect
155. #16810728C22semidirect
156. #16810723C22semidirect
157. #16810723C22semidirect
161. #16810721C22semidirect
162. C4×#11719925C22semidirect
163. C4×#11719925C22semidirect
164. C4×#11719925C22semidirect
165. C4×#11719925C22semidirect
166. C4×#11719925C22semidirect
170. C4×#11719924C22semidirect
171. C4×#11719924C22semidirect
172. C4×#11719923C22semidirect
182. Q82×C53C22semidirect
183. C53×#557C22semidirect
184. C53×#557C22semidirect
185. C53×#557C22semidirect
187. C53×#556C22semidirect
188. C53×#556C22semidirect
189. C53×#556C22semidirect
190. C53×#554C22semidirect
816. #3555D53semidirect
861. Q82C2×D53semidirect
862. #557C2×D53semidirect
863. #557C2×D53semidirect
864. #557C2×D53semidirect
870. #556C2×D53semidirect
871. #556C2×D53semidirect
872. #556C2×D53semidirect
873. #554C2×D53semidirect
1026. C53#61925semidirect

Maximal subgroups

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

subgroupindex
#202886132
#202877902
#202877812
#202877642
#202877422
#202877112
#202876992
#202875572
#202875422
#202875292
#202874832
#202874682
#202874552
#202874112
#202874002
#202858182
#202858032
#202857922
#202857812
#202857142
#202856762
#202850102
#202849622
#202849382
#202848932
#202848182
#202847802
#202838102
C53×#35552
#6192553