Finite Group Databasebeta

← C101×#18739 #38800890

Subgroups — C101×#18739 #38800890

Order 25856.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3546C211yesmaximal, characteristic
2C101×#3246C211yesmaximal, characteristic, complemented
3C101×#3233C211yesmaximal, characteristic, complemented
4C101×#3182C211yesmaximal, characteristic, complemented
5C101×#1650C211yesmaximal, characteristic, complemented
6C101×#1647C211yesmaximal, characteristic, complemented
7C101×#1642C211yesmaximal, characteristic, complemented
8C101×#1639C211yesmaximal, characteristic, complemented
9C101×#1638C211yesmaximal, characteristic, complemented
10C101×#1635C211yesmaximal, characteristic, complemented
11C101×#1631C211yesmaximal, characteristic, complemented
12C101×#1629C211yesmaximal, characteristic, complemented
13C101×#1540C211yesmaximal, characteristic, complemented
14C101×#1484C211yesmaximal, characteristic, complemented
15C101×#1483C211yesmaximal, characteristic, complemented
16#560×C101—22no—
17#556×C101C2211yescharacteristic
18#553×C101—21no—
19#550×C101—21no—
20#550×C101C2211yescharacteristic
21#547×C101C2211yescharacteristic
22#546×C101—21no—
23#546×C101—21no—
24D42×C101C2211yescharacteristic
25#542×C101—21no—
26#538×C101—22no—
27#537×C101—21no—
28#535×C101—21no—
29#535×C101—21no—
30#533×C101C2211yescharacteristic, complemented
31#532×C101C2211yescharacteristic
32#532×C101C2211yescharacteristic
33#529×C101C2211yescharacteristic
34#500×C101C2211yescharacteristic, complemented
35#499×C101—21no—
36#492×C101C2211yescharacteristic
37#488×C101—21no—
38#487×C101C2211yescharacteristic, complemented
39#486×C101C2211yescharacteristic
40#485×C101—21no—
41#482×C101—21no—
42#477×C101C2211yescharacteristic, complemented
43#476×C101C2211yescharacteristic
44#476×C101C2211yescharacteristic
45#476×C101C2211yescharacteristic, complemented
46#475×C101—21no—
47#475×C101C2211yescharacteristic, complemented
48#474×C101C2211yescharacteristic
49#468×C101—22no—
50#465×C101—21no—
51#465×C101—21no—
52#461×C101C2211yescharacteristic
53#461×C101C2211yescharacteristic, complemented
54#460×C101—21no—
55#440×C101—22no—
56#431×C101C2211yescharacteristic, complemented
57C2×C4⋊C8×C101C2211yescharacteristic, complemented
58C4×M16×C101C2211yescharacteristic, complemented
59#332×C101C2211yescharacteristic, complemented
60#332×C101C2211yescharacteristic, complemented
61#331×C101C2211yescharacteristic
62#331×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic, complemented
64Q8⋊C8×C101C2211yescharacteristic, complemented
65D4⋊C8×C101C2211yescharacteristic
66D4⋊C8×C101C2211yescharacteristic
67D4⋊C8×C101C2211yescharacteristic
68D4⋊C8×C101C2211yescharacteristic
69D4⋊C8×C101C2211yescharacteristic, complemented
70D4⋊C8×C101C2211yescharacteristic, complemented
71C2×#41×C101—21no—
72C2×#41×C101—21no—
73C2×#41×C101—21no—
74C2×#41×C101—21no—
75C22×D4×C101—21no—
76C22×D4×C101—21no—
77C2×SD16×C101—22no—
78C2×SD16×C101—21no—
79C2×SD16×C101—21no—
80C2×M16×C101—21no—
81C22×C8×C101—21no—
82C4⋊Q8×C101D411yescharacteristic
83C4⋊Q8×C101C2311yescharacteristic
84C4⋊Q8×C101C2311yescharacteristic
85C4⋊Q8×C101C2311yescharacteristic
86#127×C101—22no—
87#127×C101—21no—
88#127×C101D411yescharacteristic
89#127×C101C2311yescharacteristic
90#126×C101—22no—
91#126×C101—22no—
92#126×C101—21no—
93#125×C101—21no—
94#125×C101D411yescharacteristic
95#124×C101—22no—
96#124×C101—21no—
97#124×C101—21no—
98#124×C101—21no—
99#124×C101D411yescharacteristic
100#123×C101—22no—
101#123×C101—22no—
102#123×C101—21no—
103#123×C101—22no—
104C22⋊Q8×C101—22no—
105C22⋊Q8×C101—21no—
106C22⋊Q8×C101—21no—
107C22⋊Q8×C101—21no—
108C22⋊Q8×C101—21no—
109C22⋊Q8×C101D411yescharacteristic
110#121×C101—22no—
111#121×C101—22no—
112#121×C101—22no—
113#121×C101—22no—
114#121×C101—22no—
115#121×C101—21no—
116#121×C101—22no—
117#121×C101—21no—
118#121×C101—21no—
119#121×C101—21no—
120#121×C101—21no—
121#121×C101—21no—
122#121×C101D411yescharacteristic
123#121×C101D411yescharacteristic
124#121×C101D412yes—
125#121×C101D411yescharacteristic
126#120×C101—22no—
127#120×C101—22no—
128#120×C101—22no—
129#120×C101—22no—
130C4×Q8×C101—21no—
131C4×Q8×C101—21no—
132C4×Q8×C101—21no—
133C4×Q8×C101C2311yescharacteristic
134C4×D4×C101—22no—
135C4×D4×C101—21no—
136C4×D4×C101—21no—
137C4×D4×C101—21no—
138C4×D4×C101—21no—
139C4×D4×C101D412yes—
140C4×D4×C101C2311yescharacteristic
141C4×D4×C101C2311yescharacteristic
142C4×D4×C101C2311yescharacteristic
143#117×C101—21no—
144#117×C101—21no—
145#117×C101—21no—
146C2×C4⋊C4×C101—21no—
147C2×C22⋊C4×C101—22no—
148C2×C42×C101C2311yescharacteristic
149#107×C101—22no—
150#107×C101—21no—
151#107×C101—21no—
152#106×C101—21no—
153#106×C101—21no—
154#106×C101—21no—
155#106×C101—21no—
156C4⋊C8×C101—21no—
157C4⋊C8×C101C2311yescharacteristic
158C4⋊C8×C101C2311yescharacteristic
159C4⋊C8×C101C2311yescharacteristic
160C4⋊C8×C101C2311yescharacteristic
161#103×C101—21no—
162#103×C101—21no—
163#103×C101—22no—
164#103×C101—21no—
165#103×C101—21no—
166#102×C101—22no—
167#102×C101—21no—
168#102×C101—21no—
169#102×C101—21no—
170#102×C101—21no—
171C22⋊C8×C101—21no—
172#97×C101—21no—
173C4×C8×C101—21no—
174C4×C8×C101C2311yescharacteristic
175C4×C8×C101C2311yescharacteristic
176C24×C101—22no—
177#41×C101—81no—
178#41×C101—81no—
179#41×C101—81no—
180#41×C101—81no—
181#41×C101—81no—
182#41×C101—81no—
183#41×C101—81no—
184#41×C101—81no—
185C2×Q8×C101—21no—
186C2×Q8×C101—21no—
187C2×Q8×C101—21no—
188C2×Q8×C101—21no—
189C2×Q8×C101C2×D411yescharacteristic
190C2×D4×C101—22no—
191C2×D4×C101—22no—
192C2×D4×C101—22no—
193C2×D4×C101—22no—
194C2×D4×C101—22no—
195C2×D4×C101—21no—
196C2×D4×C101—21no—
197C2×D4×C101—22no—
198C2×D4×C101—21no—
199C2×D4×C101—21no—
200C2×D4×C101—21no—
201C2×D4×C101—21no—
202C2×D4×C101—21no—
203C2×D4×C101—81no—
204C2×D4×C101—81no—
205C2×D4×C101—81no—
206C2×D4×C101—81no—
207C2×D4×C101C2×D411yescharacteristic
208C2×D4×C101C2×D411yescharacteristic
209C2×D4×C101C2×D411yescharacteristic
210C2×D4×C101C2×D412yes—
211C22×C4×C101—22no—
212C22×C4×C101—22no—
213C22×C4×C101—21no—
214C22×C4×C101—21no—
215C22×C4×C101—21no—
216C22×C4×C101—22no—
217C22×C4×C101C2×D411yescharacteristic
218C22×C4×C101C2×D411yescharacteristic
219C22×C4×C101C2×D411yescharacteristic
220SD16×C101—44no—
221SD16×C101—81no—
222SD16×C101—81no—
223M16×C101—42no—
224C2×C8×C101—21no—
225C2×C8×C101—21no—
226C2×C8×C101—21no—
227C2×C8×C101—21no—
228C2×C8×C101—21no—
229C2×C8×C101—21no—
230C2×C8×C101—81no—
231C4⋊C4×C101—22no—
232C4⋊C4×C101—22no—
233C4⋊C4×C101—21no—
234C4⋊C4×C101—21no—
235C4⋊C4×C101—21no—
236C4⋊C4×C101—21no—
237C4⋊C4×C101—21no—
238C4⋊C4×C101—21no—
239C4⋊C4×C101—21no—
240C4⋊C4×C101—21no—
241C4⋊C4×C101—21no—
242C4⋊C4×C101—21no—
243C4⋊C4×C101—41no—
244C4⋊C4×C101—41no—
245C4⋊C4×C101C2×D411yescharacteristic
246C4⋊C4×C101C2×D411yescharacteristic
247C4⋊C4×C101C2×D412yes—
248C4⋊C4×C101C2×D411yescharacteristic
249C4⋊C4×C101C2×D411yescharacteristic
250C22⋊C4×C101—22no—
251C22⋊C4×C101—22no—
252C22⋊C4×C101—22no—
253C22⋊C4×C101—22no—
254C22⋊C4×C101—22no—
255C22⋊C4×C101—21no—
256C22⋊C4×C101—21no—
257C22⋊C4×C101—21no—
258C22⋊C4×C101—21no—
259C22⋊C4×C101—21no—
260C22⋊C4×C101—21no—
261C22⋊C4×C101—22no—
262C22⋊C4×C101—22no—
263C22⋊C4×C101—21no—
264C22⋊C4×C101—21no—
265C22⋊C4×C101—21no—
266C22⋊C4×C101—41no—
267C42×C101—22no—
268C42×C101—21no—
269C42×C101—41no—
270C42×C101C2×D411yescharacteristic
271C42×C101C2×D411yescharacteristic
272C42×C101C2×D411yescharacteristic
273C42×C101C2411yescharacteristic
274C23×C101—21no—
275C23×C101—21no—
276C23×C101—22no—
277C23×C101—21no—
278C23×C101—82no—
279C23×C101—82no—
280C23×C101—82no—
281C23×C101#12011yescharacteristic
282Q8×C101—21no—
283Q8×C101—21no—
284Q8×C101—42no—
285Q8×C101—41no—
286Q8×C101—41no—
287Q8×C101—41no—
288Q8×C101—41no—
289Q8×C101—81no—
290D4×C101—21no—
291D4×C101—21no—
292D4×C101—21no—
293D4×C101—21no—
294D4×C101—21no—
295D4×C101—21no—
296D4×C101—42no—
297D4×C101—41no—
298D4×C101—41no—
299D4×C101—41no—
300D4×C101—41no—
301D4×C101—81no—
302D4×C101—81no—
303D4×C101—81no—
304D4×C101—81no—
305D4×C101—81no—
306D4×C101—82no—
307D4×C101—82no—
308D4×C101—82no—
309D4×C101—82no—
310D4×C101—82no—
311D4×C101—82no—
312C2×C4×C101—21no—
313C2×C4×C101—21no—
314C2×C4×C101—21no—
315C2×C4×C101—21no—
316C2×C4×C101—21no—
317C2×C4×C101—21no—
318C2×C4×C101—21no—
319C2×C4×C101—22no—
320C2×C4×C101—21no—
321C2×C4×C101—21no—
322C2×C4×C101—41no—
323C2×C4×C101—41no—
324C2×C4×C101—41no—
325C2×C4×C101—41no—
326C2×C4×C101—41no—
327C2×C4×C101—41no—
328C2×C4×C101—41no—
329C2×C4×C101—41no—
330C2×C4×C101—41no—
331C2×C4×C101—82no—
332C2×C4×C101—82no—
333C2×C4×C101—82no—
334C2×C4×C101#12011yescharacteristic
335C2×C4×C101#12011yescharacteristic
336C2×C4×C101#12011yescharacteristic
337C2×C4×C101C22×D411yescharacteristic
338C2×C4×C101C22×D411yescharacteristic
339C2×C4×C101C22×D411yescharacteristic
340C8×C101—22no—
341C8×C101—41no—
342C8×C101—41no—
343C8×C101—41no—
344C8×C101—41no—
345C8×C101—41no—
346C22×C101—21no—
347C22×C101—21no—
348C22×C101—21no—
349C22×C101—41no—
350C22×C101—41no—
351C22×C101—42no—
352C22×C101—41no—
353C22×C101—41no—
354C22×C101—41no—
355C22×C101—42no—
356C22×C101—41no—
357C22×C101—42no—
358C22×C101—41no—
359C22×C101—41no—
360C22×C101—41no—
361C22×C101—164no—
362C22×C101C2×#12011yescharacteristic
363C4×C101—21no—
364C4×C101—21no—
365C4×C101—21no—
366C4×C101—21no—
367C4×C101—41no—
368C4×C101—41no—
369C4×C101—41no—
370C4×C101—41no—
371C4×C101—42no—
372C4×C101—41no—
373C4×C101—81no—
374C4×C101—81no—
375C4×C101#57611yescharacteristic
376C4×C101#57711yescharacteristic
377C4×C101#57711yescharacteristic
378C4×C101#57711yescharacteristic
379#18739C10111yesmaximal, characteristic, direct product factor, Sylow
380C2×C101—41no—
381C2×C101—81no—
382C2×C101—82no—
383C2×C101—81no—
384C2×C101—81no—
385C2×C101#300911yescharacteristic
386C2×C101#301211yescharacteristic
387C2×C101#301811yescharacteristic
388#3546C2×C10111yescharacteristic
389#3246C2×C10111yescharacteristic, complemented
390#3233C2×C10111yescharacteristic, complemented
391#3182C2×C10111yescharacteristic, complemented
392#1650C2×C10111yescharacteristic, complemented
393#1647C2×C10111yescharacteristic, complemented
394#1642C2×C10111yescharacteristic, complemented
395#1639C2×C10111yescharacteristic, complemented
396#1638C2×C10111yescharacteristic, complemented
397#1635C2×C10111yescharacteristic, complemented
398#1631C2×C10111yescharacteristic, complemented
399#1629C2×C10111yescharacteristic, complemented
400#1540C2×C10111yescharacteristic, complemented
401#1484C2×C10111yescharacteristic, complemented
402#1483C2×C10111yescharacteristic, complemented
403C101#1873911yescharacteristic, direct product factor, Sylow
404#560—22no—
405#556C22×C10111yescharacteristic
406#553—21no—
407#550—21no—
408#550C22×C10111yescharacteristic
409#547C22×C10111yescharacteristic
410#546—21no—
411#546—21no—
412D42C22×C10111yescharacteristic
413#542—21no—
414#538—22no—
415#537—21no—
416#535—21no—
417#535—21no—
418#533C22×C10111yescharacteristic, complemented
419#532C22×C10111yescharacteristic
420#532C22×C10111yescharacteristic
421#529C22×C10111yescharacteristic
422#500C22×C10111yescharacteristic, complemented
423#499—21no—
424#492C22×C10111yescharacteristic
425#488—21no—
426#487C22×C10111yescharacteristic, complemented
427#486C22×C10111yescharacteristic
428#485—21no—
429#482—21no—
430#477C22×C10111yescharacteristic, complemented
431#476C22×C10111yescharacteristic
432#476C22×C10111yescharacteristic
433#476C22×C10111yescharacteristic, complemented
434#475—21no—
435#475C22×C10111yescharacteristic, complemented
436#474C22×C10111yescharacteristic
437#468—22no—
438#465—21no—
439#465—21no—
440#461C22×C10111yescharacteristic
441#461C22×C10111yescharacteristic, complemented
442#460—21no—
443#440—22no—
444#431C22×C10111yescharacteristic, complemented
445C2×C4⋊C8C22×C10111yescharacteristic, complemented
446C4×M16C22×C10111yescharacteristic, complemented
447#332C22×C10111yescharacteristic, complemented
448#332C22×C10111yescharacteristic, complemented
449#331C22×C10111yescharacteristic
450#331C22×C10111yescharacteristic
451Q8⋊C8C22×C10111yescharacteristic, complemented
452Q8⋊C8C22×C10111yescharacteristic, complemented
453D4⋊C8C22×C10111yescharacteristic
454D4⋊C8C22×C10111yescharacteristic
455D4⋊C8C22×C10111yescharacteristic
456D4⋊C8C22×C10111yescharacteristic
457D4⋊C8C22×C10111yescharacteristic, complemented
458D4⋊C8C22×C10111yescharacteristic, complemented
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C22×D4—21no—
464C22×D4—21no—
465C2×SD16—22no—
466C2×SD16—21no—
467C2×SD16—21no—
468C2×M16—21no—
469C22×C8—21no—
470C4⋊Q8D4×C10111yescharacteristic
471C4⋊Q8C23×C10111yescharacteristic
472C4⋊Q8C23×C10111yescharacteristic
473C4⋊Q8C23×C10111yescharacteristic
474#127—22no—
475#127—21no—
476#127D4×C10111yescharacteristic
477#127C23×C10111yescharacteristic
478#126—22no—
479#126—22no—
480#126—21no—
481#125—21no—
482#125D4×C10111yescharacteristic
483#124—22no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124D4×C10111yescharacteristic
488#123—22no—
489#123—22no—
490#123—21no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C10111yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—21no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C10111yescharacteristic
511#121D4×C10111yescharacteristic
512#121D4×C10111yescharacteristic
513#121D4×C10112yes—
514#120—22no—
515#120—22no—
516#120—22no—
517#120—22no—
518C4×Q8—21no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8C23×C10111yescharacteristic
522C4×D4—22no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4D4×C10112yes—
528C4×D4C23×C10111yescharacteristic
529C4×D4C23×C10111yescharacteristic
530C4×D4C23×C10111yescharacteristic
531#117—21no—
532#117—21no—
533#117—21no—
534C2×C4⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C42C23×C10111yescharacteristic
537#107—22no—
538#107—21no—
539#107—21no—
540#106—21no—
541#106—21no—
542#106—21no—
543#106—21no—
544C4⋊C8—21no—
545C4⋊C8C23×C10111yescharacteristic
546C4⋊C8C23×C10111yescharacteristic
547C4⋊C8C23×C10111yescharacteristic
548C4⋊C8C23×C10111yescharacteristic
549#103—21no—
550#103—21no—
551#103—22no—
552#103—21no—
553#103—21no—
554#102—22no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559C22⋊C8—21no—
560#97—21no—
561C4×C8—21no—
562C4×C8C23×C10111yescharacteristic
563C4×C8C23×C10111yescharacteristic
564C24—22no—
565#41—81no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C10111yescharacteristic
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4C2×D4×C10111yescharacteristic
596C2×D4C2×D4×C10111yescharacteristic
597C2×D4C2×D4×C10111yescharacteristic
598C2×D4C2×D4×C10112yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4C2×D4×C10111yescharacteristic
606C22×C4C2×D4×C10111yescharacteristic
607C22×C4C2×D4×C10111yescharacteristic
608SD16—44no—
609SD16—81no—
610SD16—81no—
611M16—42no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—81no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4C2×D4×C10111yescharacteristic
634C4⋊C4C2×D4×C10111yescharacteristic
635C4⋊C4C2×D4×C10112yes—
636C4⋊C4C2×D4×C10111yescharacteristic
637C4⋊C4C2×D4×C10111yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C42—22no—
656C42—21no—
657C42—41no—
658C42C2×D4×C10111yescharacteristic
659C42C2×D4×C10111yescharacteristic
660C42C2×D4×C10111yescharacteristic
661C42C24×C10111yescharacteristic
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23#120×C10111yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—42no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—81no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—82no—
694D4—81no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#120×C10111yescharacteristic
723C2×C4#120×C10111yescharacteristic
724C2×C4#120×C10111yescharacteristic
725C2×C4C22×D4×C10111yescharacteristic
726C2×C4C22×D4×C10111yescharacteristic
727C2×C4C22×D4×C10111yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—164no—
750C22C2×#120×C10111yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—42no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4#576×C10111yescharacteristic
764C4#577×C10111yescharacteristic
765C4#577×C10111yescharacteristic
766C4#577×C10111yescharacteristic
767C2—41no—
768C2—81no—
769C2—81no—
770C2—82no—
771C2—81no—
772C2C101×#300911yescharacteristic
773C2C101×#301211yescharacteristic
774C2C101×#301811yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3546C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#3246C2semidirect
3. C101×#3233C2semidirect
4. C101×#3182C2semidirect
5. C101×#1650C2semidirect
6. C101×#1647C2semidirect
7. C101×#1642C2semidirect
8. C101×#1639C2semidirect
9. C101×#1638C2semidirect
10. C101×#1635C2semidirect
11. C101×#1631C2semidirect
12. C101×#1629C2semidirect
13. C101×#1540C2semidirect
14. C101×#1484C2semidirect
15. C101×#1483C2semidirect
30. #533×C101C22semidirect
34. #500×C101C22semidirect
38. #487×C101C22semidirect
42. #477×C101C22semidirect
45. #476×C101C22semidirect
47. #475×C101C22semidirect
53. #461×C101C22semidirect
56. #431×C101C22semidirect
57. C2×C4⋊C8×C101C22semidirect
58. C4×M16×C101C22semidirect
59. #332×C101C22semidirect
60. #332×C101C22semidirect
63. Q8⋊C8×C101C22semidirect
64. Q8⋊C8×C101C22semidirect
69. D4⋊C8×C101C22semidirect
70. D4⋊C8×C101C22semidirect
379. #18739C101direct (N × H)
389. #3246C2×C101semidirect
390. #3233C2×C101semidirect
391. #3182C2×C101semidirect
392. #1650C2×C101semidirect
393. #1647C2×C101semidirect
394. #1642C2×C101semidirect
395. #1639C2×C101semidirect
396. #1638C2×C101semidirect
397. #1635C2×C101semidirect
398. #1631C2×C101semidirect
399. #1629C2×C101semidirect
400. #1540C2×C101semidirect
401. #1484C2×C101semidirect
402. #1483C2×C101semidirect
403. C101#18739direct (N × H)
418. #533C22×C101semidirect
422. #500C22×C101semidirect
426. #487C22×C101semidirect
430. #477C22×C101semidirect
433. #476C22×C101semidirect
435. #475C22×C101semidirect
441. #461C22×C101semidirect
444. #431C22×C101semidirect
445. C2×C4⋊C8C22×C101semidirect
446. C4×M16C22×C101semidirect
447. #332C22×C101semidirect
448. #332C22×C101semidirect
451. Q8⋊C8C22×C101semidirect
452. Q8⋊C8C22×C101semidirect
457. D4⋊C8C22×C101semidirect
458. D4⋊C8C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35462
C101×#32462
C101×#32332
C101×#31822
C101×#16502
C101×#16472
C101×#16422
C101×#16392
C101×#16382
C101×#16352
C101×#16312
C101×#16292
C101×#15402
C101×#14842
C101×#14832
#18739101