Finite Group Databasebeta

← C101×#18974 #38801125

Subgroups — C101×#18974 #38801125

Order 25856.

930 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3546C211yesmaximal, characteristic
2C101×#3254C211yesmaximal, characteristic, complemented
3C101×#3248C211yesmaximal, characteristic, complemented
4C101×#3228C211yesmaximal, characteristic, complemented
5C101×#1654C211yesmaximal, characteristic, complemented
6C101×#1652C211yesmaximal, characteristic, complemented
7C101×#1650C211yesmaximal, characteristic, complemented
8C101×#1647C211yesmaximal, characteristic, complemented
9C101×#1642C211yesmaximal, characteristic, complemented
10C101×#1641C211yesmaximal, characteristic, complemented
11C101×#1639C211yesmaximal, characteristic, complemented
12C101×#1639C211yesmaximal, characteristic, complemented
13C101×#1547C211yesmaximal, characteristic, complemented
14C101×#1495C211yesmaximal, characteristic, complemented
15C101×#1480C211yesmaximal, 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#498×C101C2211yescharacteristic, complemented
36#486×C101C2211yescharacteristic
37#486×C101C2211yescharacteristic
38#482×C101—22no—
39#479×C101—21no—
40#478×C101—22no—
41#477×C101—21no—
42#475×C101C2211yescharacteristic, complemented
43#474×C101C2211yescharacteristic
44#474×C101C2211yescharacteristic
45#474×C101C2211yescharacteristic, complemented
46#468×C101—21no—
47#468×C101—21no—
48#467×C101—21no—
49#465×C101—21no—
50#464×C101—21no—
51#462×C101C2211yescharacteristic, complemented
52#461×C101C2211yescharacteristic
53#461×C101C2211yescharacteristic
54#461×C101C2211yescharacteristic, complemented
55#460×C101—21no—
56#431×C101C2211yescharacteristic, complemented
57#423×C101C2211yescharacteristic, complemented
58C2×C4⋊C8×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×Q16×C101—21no—
78C2×SD16×C101—21no—
79C2×SD16×C101—21no—
80C2×SD16×C101—21no—
81C2×M16×C101—21no—
82C22×C8×C101—21no—
83C4⋊Q8×C101D411yescharacteristic
84C4⋊Q8×C101C2311yescharacteristic
85C4⋊Q8×C101C2311yescharacteristic
86C4⋊Q8×C101C2311yescharacteristic
87#127×C101—22no—
88#127×C101—21no—
89#127×C101D411yescharacteristic
90#127×C101C2311yescharacteristic
91#126×C101—22no—
92#126×C101—22no—
93#126×C101—21no—
94#125×C101—21no—
95#125×C101D411yescharacteristic
96#124×C101—22no—
97#124×C101—21no—
98#124×C101—21no—
99#124×C101—21no—
100#124×C101D411yescharacteristic
101#123×C101—22no—
102#123×C101—22no—
103#123×C101—21no—
104#123×C101—22no—
105C22⋊Q8×C101—22no—
106C22⋊Q8×C101—21no—
107C22⋊Q8×C101—21no—
108C22⋊Q8×C101—21no—
109C22⋊Q8×C101—21no—
110C22⋊Q8×C101D411yescharacteristic
111#121×C101—22no—
112#121×C101—22no—
113#121×C101—22no—
114#121×C101—22no—
115#121×C101—22no—
116#121×C101—21no—
117#121×C101—22no—
118#121×C101—21no—
119#121×C101—21no—
120#121×C101—21no—
121#121×C101—21no—
122#121×C101—21no—
123#121×C101D411yescharacteristic
124#121×C101D411yescharacteristic
125#121×C101D411yescharacteristic
126#121×C101D412yes—
127#120×C101—22no—
128#120×C101—22no—
129#120×C101—22no—
130#120×C101—22no—
131C4×Q8×C101—21no—
132C4×Q8×C101—21no—
133C4×Q8×C101—21no—
134C4×Q8×C101C2311yescharacteristic
135C4×D4×C101—22no—
136C4×D4×C101—21no—
137C4×D4×C101—21no—
138C4×D4×C101—21no—
139C4×D4×C101—21no—
140C4×D4×C101D412yes—
141C4×D4×C101C2311yescharacteristic
142C4×D4×C101C2311yescharacteristic
143C4×D4×C101C2311yescharacteristic
144#117×C101—21no—
145#117×C101—21no—
146#117×C101—21no—
147C2×C4⋊C4×C101—21no—
148C2×C22⋊C4×C101—22no—
149C2×C42×C101C2311yescharacteristic
150#107×C101—21no—
151#107×C101—21no—
152#107×C101—21no—
153#107×C101—22no—
154#106×C101—21no—
155#106×C101—22no—
156C4⋊C8×C101—21no—
157C4⋊C8×C101—21no—
158C4⋊C8×C101—21no—
159C4⋊C8×C101C2311yescharacteristic
160C4⋊C8×C101C2311yescharacteristic
161C4⋊C8×C101C2311yescharacteristic
162C4⋊C8×C101C2311yescharacteristic
163#103×C101—21no—
164#103×C101—21no—
165#103×C101—21no—
166#103×C101—21no—
167#103×C101—21no—
168#102×C101—21no—
169#102×C101—21no—
170#102×C101—21no—
171#102×C101—22no—
172#102×C101—22no—
173C22⋊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
220Q16×C101—81no—
221SD16×C101—81no—
222SD16×C101—81no—
223SD16×C101—81no—
224M16×C101—81no—
225C2×C8×C101—21no—
226C2×C8×C101—21no—
227C2×C8×C101—21no—
228C2×C8×C101—21no—
229C2×C8×C101—21no—
230C2×C8×C101—21no—
231C2×C8×C101—81no—
232C4⋊C4×C101—22no—
233C4⋊C4×C101—22no—
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—21no—
244C4⋊C4×C101—41no—
245C4⋊C4×C101—41no—
246C4⋊C4×C101C2×D411yescharacteristic
247C4⋊C4×C101C2×D411yescharacteristic
248C4⋊C4×C101C2×D411yescharacteristic
249C4⋊C4×C101C2×D411yescharacteristic
250C4⋊C4×C101C2×D412yes—
251C22⋊C4×C101—22no—
252C22⋊C4×C101—22no—
253C22⋊C4×C101—22no—
254C22⋊C4×C101—22no—
255C22⋊C4×C101—22no—
256C22⋊C4×C101—21no—
257C22⋊C4×C101—21no—
258C22⋊C4×C101—21no—
259C22⋊C4×C101—21no—
260C22⋊C4×C101—21no—
261C22⋊C4×C101—21no—
262C22⋊C4×C101—22no—
263C22⋊C4×C101—22no—
264C22⋊C4×C101—21no—
265C22⋊C4×C101—21no—
266C22⋊C4×C101—21no—
267C22⋊C4×C101—41no—
268C42×C101—22no—
269C42×C101—21no—
270C42×C101—41no—
271C42×C101C2×D411yescharacteristic
272C42×C101C2×D411yescharacteristic
273C42×C101C2×D411yescharacteristic
274C42×C101C2411yescharacteristic
275C23×C101—21no—
276C23×C101—21no—
277C23×C101—22no—
278C23×C101—21no—
279C23×C101—82no—
280C23×C101—82no—
281C23×C101—82no—
282C23×C101#12011yescharacteristic
283Q8×C101—21no—
284Q8×C101—21no—
285Q8×C101—41no—
286Q8×C101—41no—
287Q8×C101—41no—
288Q8×C101—41no—
289Q8×C101—41no—
290Q8×C101—41no—
291Q8×C101—81no—
292D4×C101—21no—
293D4×C101—21no—
294D4×C101—21no—
295D4×C101—21no—
296D4×C101—21no—
297D4×C101—21no—
298D4×C101—42no—
299D4×C101—41no—
300D4×C101—41no—
301D4×C101—41no—
302D4×C101—41no—
303D4×C101—81no—
304D4×C101—81no—
305D4×C101—81no—
306D4×C101—81no—
307D4×C101—81no—
308D4×C101—82no—
309D4×C101—82no—
310D4×C101—82no—
311D4×C101—82no—
312D4×C101—82no—
313D4×C101—82no—
314C2×C4×C101—21no—
315C2×C4×C101—21no—
316C2×C4×C101—21no—
317C2×C4×C101—21no—
318C2×C4×C101—21no—
319C2×C4×C101—21no—
320C2×C4×C101—21no—
321C2×C4×C101—22no—
322C2×C4×C101—21no—
323C2×C4×C101—21no—
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—41no—
332C2×C4×C101—41no—
333C2×C4×C101—82no—
334C2×C4×C101—82no—
335C2×C4×C101—82no—
336C2×C4×C101#12011yescharacteristic
337C2×C4×C101#12011yescharacteristic
338C2×C4×C101#12011yescharacteristic
339C2×C4×C101C22×D411yescharacteristic
340C2×C4×C101C22×D411yescharacteristic
341C2×C4×C101C22×D411yescharacteristic
342C8×C101—41no—
343C8×C101—41no—
344C8×C101—41no—
345C8×C101—41no—
346C8×C101—41no—
347C8×C101—41no—
348C22×C101—21no—
349C22×C101—21no—
350C22×C101—21no—
351C22×C101—41no—
352C22×C101—41no—
353C22×C101—41no—
354C22×C101—41no—
355C22×C101—42no—
356C22×C101—42no—
357C22×C101—41no—
358C22×C101—41no—
359C22×C101—42no—
360C22×C101—41no—
361C22×C101—41no—
362C22×C101—41no—
363C22×C101—164no—
364C22×C101C2×#12011yescharacteristic
365C4×C101—21no—
366C4×C101—21no—
367C4×C101—21no—
368C4×C101—21no—
369C4×C101—41no—
370C4×C101—41no—
371C4×C101—41no—
372C4×C101—41no—
373C4×C101—42no—
374C4×C101—41no—
375C4×C101—81no—
376C4×C101—81no—
377C4×C101#57611yescharacteristic
378C4×C101#57611yescharacteristic
379C4×C101#57711yescharacteristic
380C4×C101#57711yescharacteristic
381#18974C10111yesmaximal, characteristic, direct product factor, Sylow
382C2×C101—41no—
383C2×C101—81no—
384C2×C101—82no—
385C2×C101—81no—
386C2×C101—81no—
387C2×C101#301211yescharacteristic
388C2×C101#301211yescharacteristic
389C2×C101#302211yescharacteristic
390#3546C2×C10111yescharacteristic
391#3254C2×C10111yescharacteristic, complemented
392#3248C2×C10111yescharacteristic, complemented
393#3228C2×C10111yescharacteristic, complemented
394#1654C2×C10111yescharacteristic, complemented
395#1652C2×C10111yescharacteristic, complemented
396#1650C2×C10111yescharacteristic, complemented
397#1647C2×C10111yescharacteristic, complemented
398#1642C2×C10111yescharacteristic, complemented
399#1641C2×C10111yescharacteristic, complemented
400#1639C2×C10111yescharacteristic, complemented
401#1639C2×C10111yescharacteristic, complemented
402#1547C2×C10111yescharacteristic, complemented
403#1495C2×C10111yescharacteristic, complemented
404#1480C2×C10111yescharacteristic, complemented
405C101#1897411yescharacteristic, direct product factor, Sylow
406#560—22no—
407#556C22×C10111yescharacteristic
408#553—21no—
409#550—21no—
410#550C22×C10111yescharacteristic
411#547C22×C10111yescharacteristic
412#546—21no—
413#546—21no—
414D42C22×C10111yescharacteristic
415#542—21no—
416#538—22no—
417#537—21no—
418#535—21no—
419#535—21no—
420#533C22×C10111yescharacteristic, complemented
421#532C22×C10111yescharacteristic
422#532C22×C10111yescharacteristic
423#529C22×C10111yescharacteristic
424#500C22×C10111yescharacteristic, complemented
425#498C22×C10111yescharacteristic, complemented
426#486C22×C10111yescharacteristic
427#486C22×C10111yescharacteristic
428#482—22no—
429#479—21no—
430#478—22no—
431#477—21no—
432#475C22×C10111yescharacteristic, complemented
433#474C22×C10111yescharacteristic
434#474C22×C10111yescharacteristic
435#474C22×C10111yescharacteristic, complemented
436#468—21no—
437#468—21no—
438#467—21no—
439#465—21no—
440#464—21no—
441#462C22×C10111yescharacteristic, complemented
442#461C22×C10111yescharacteristic
443#461C22×C10111yescharacteristic
444#461C22×C10111yescharacteristic, complemented
445#460—21no—
446#431C22×C10111yescharacteristic, complemented
447#423C22×C10111yescharacteristic, complemented
448C2×C4⋊C8C22×C10111yescharacteristic, complemented
449#332C22×C10111yescharacteristic, complemented
450#332C22×C10111yescharacteristic, complemented
451#331C22×C10111yescharacteristic
452#331C22×C10111yescharacteristic
453Q8⋊C8C22×C10111yescharacteristic, complemented
454Q8⋊C8C22×C10111yescharacteristic, complemented
455D4⋊C8C22×C10111yescharacteristic
456D4⋊C8C22×C10111yescharacteristic
457D4⋊C8C22×C10111yescharacteristic
458D4⋊C8C22×C10111yescharacteristic
459D4⋊C8C22×C10111yescharacteristic, complemented
460D4⋊C8C22×C10111yescharacteristic, complemented
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C22×D4—21no—
466C22×D4—21no—
467C2×Q16—21no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×M16—21no—
472C22×C8—21no—
473C4⋊Q8D4×C10111yescharacteristic
474C4⋊Q8C23×C10111yescharacteristic
475C4⋊Q8C23×C10111yescharacteristic
476C4⋊Q8C23×C10111yescharacteristic
477#127—22no—
478#127—21no—
479#127D4×C10111yescharacteristic
480#127C23×C10111yescharacteristic
481#126—22no—
482#126—22no—
483#126—21no—
484#125—21no—
485#125D4×C10111yescharacteristic
486#124—22no—
487#124—21no—
488#124—21no—
489#124—21no—
490#124D4×C10111yescharacteristic
491#123—22no—
492#123—22no—
493#123—21no—
494#123—22no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8D4×C10111yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—22no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121D4×C10111yescharacteristic
514#121D4×C10111yescharacteristic
515#121D4×C10111yescharacteristic
516#121D4×C10112yes—
517#120—22no—
518#120—22no—
519#120—22no—
520#120—22no—
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8C23×C10111yescharacteristic
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4D4×C10112yes—
531C4×D4C23×C10111yescharacteristic
532C4×D4C23×C10111yescharacteristic
533C4×D4C23×C10111yescharacteristic
534#117—21no—
535#117—21no—
536#117—21no—
537C2×C4⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C42C23×C10111yescharacteristic
540#107—21no—
541#107—21no—
542#107—21no—
543#107—22no—
544#106—21no—
545#106—22no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549C4⋊C8C23×C10111yescharacteristic
550C4⋊C8C23×C10111yescharacteristic
551C4⋊C8C23×C10111yescharacteristic
552C4⋊C8C23×C10111yescharacteristic
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—22no—
562#102—22no—
563C22⋊C8—21no—
564C4×C8C23×C10111yescharacteristic
565C4×C8C23×C10111yescharacteristic
566C24—22no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573#41—81no—
574#41—81no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C2×D4×C10111yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4C2×D4×C10111yescharacteristic
598C2×D4C2×D4×C10111yescharacteristic
599C2×D4C2×D4×C10111yescharacteristic
600C2×D4C2×D4×C10112yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4C2×D4×C10111yescharacteristic
608C22×C4C2×D4×C10111yescharacteristic
609C22×C4C2×D4×C10111yescharacteristic
610Q16—81no—
611SD16—81no—
612SD16—81no—
613SD16—81no—
614M16—81no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—81no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4C2×D4×C10111yescharacteristic
637C4⋊C4C2×D4×C10111yescharacteristic
638C4⋊C4C2×D4×C10111yescharacteristic
639C4⋊C4C2×D4×C10111yescharacteristic
640C4⋊C4C2×D4×C10112yes—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—41no—
658C42—22no—
659C42—21no—
660C42—41no—
661C42C2×D4×C10111yescharacteristic
662C42C2×D4×C10111yescharacteristic
663C42C2×D4×C10111yescharacteristic
664C42C24×C10111yescharacteristic
665C23—21no—
666C23—21no—
667C23—22no—
668C23—21no—
669C23—82no—
670C23—82no—
671C23—82no—
672C23#120×C10111yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—81no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—82no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4#120×C10111yescharacteristic
727C2×C4#120×C10111yescharacteristic
728C2×C4#120×C10111yescharacteristic
729C2×C4C22×D4×C10111yescharacteristic
730C2×C4C22×D4×C10111yescharacteristic
731C2×C4C22×D4×C10111yescharacteristic
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—164no—
754C22C2×#120×C10111yescharacteristic
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—41no—
765C4—81no—
766C4—81no—
767C4#576×C10111yescharacteristic
768C4#576×C10111yescharacteristic
769C4#577×C10111yescharacteristic
770C4#577×C10111yescharacteristic
771C2—41no—
772C2—81no—
773C2—81no—
774C2—82no—
775C2—81no—
776C2C101×#301211yescharacteristic
777C2C101×#301211yescharacteristic
778C2C101×#302211yescharacteristic
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×#3254C2semidirect
3. C101×#3248C2semidirect
4. C101×#3228C2semidirect
5. C101×#1654C2semidirect
6. C101×#1652C2semidirect
7. C101×#1650C2semidirect
8. C101×#1647C2semidirect
9. C101×#1642C2semidirect
10. C101×#1641C2semidirect
11. C101×#1639C2semidirect
12. C101×#1639C2semidirect
13. C101×#1547C2semidirect
14. C101×#1495C2semidirect
15. C101×#1480C2semidirect
30. #533×C101C22semidirect
34. #500×C101C22semidirect
35. #498×C101C22semidirect
42. #475×C101C22semidirect
45. #474×C101C22semidirect
51. #462×C101C22semidirect
54. #461×C101C22semidirect
56. #431×C101C22semidirect
57. #423×C101C22semidirect
58. C2×C4⋊C8×C101C22semidirect
59. #332×C101C22semidirect
60. #332×C101C22semidirect
63. Q8⋊C8×C101C22semidirect
64. Q8⋊C8×C101C22semidirect
69. D4⋊C8×C101C22semidirect
70. D4⋊C8×C101C22semidirect
381. #18974C101direct (N × H)
391. #3254C2×C101semidirect
392. #3248C2×C101semidirect
393. #3228C2×C101semidirect
394. #1654C2×C101semidirect
395. #1652C2×C101semidirect
396. #1650C2×C101semidirect
397. #1647C2×C101semidirect
398. #1642C2×C101semidirect
399. #1641C2×C101semidirect
400. #1639C2×C101semidirect
401. #1639C2×C101semidirect
402. #1547C2×C101semidirect
403. #1495C2×C101semidirect
404. #1480C2×C101semidirect
405. C101#18974direct (N × H)
420. #533C22×C101semidirect
424. #500C22×C101semidirect
425. #498C22×C101semidirect
432. #475C22×C101semidirect
435. #474C22×C101semidirect
441. #462C22×C101semidirect
444. #461C22×C101semidirect
446. #431C22×C101semidirect
447. #423C22×C101semidirect
448. C2×C4⋊C8C22×C101semidirect
449. #332C22×C101semidirect
450. #332C22×C101semidirect
453. Q8⋊C8C22×C101semidirect
454. Q8⋊C8C22×C101semidirect
459. D4⋊C8C22×C101semidirect
460. 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×#32542
C101×#32482
C101×#32282
C101×#16542
C101×#16522
C101×#16502
C101×#16472
C101×#16422
C101×#16412
C101×#16392
C101×#15472
C101×#14952
C101×#14802
#18974101