Finite Group Databasebeta

← C101×#18930 #38801081

Subgroups — C101×#18930 #38801081

Order 25856.

1020 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3543C211yesmaximal, characteristic, complemented
2C101×#3251C211yesmaximal, characteristic, complemented
3C101×#3212C211yesmaximal, characteristic, complemented
4C101×#3205C211yesmaximal, characteristic, complemented
5C101×#1642C211yesmaximal, characteristic, complemented
6C101×#1641C211yesmaximal, characteristic, complemented
7C101×#1640C211yesmaximal, characteristic, complemented
8C101×#1639C211yesmaximal, characteristic, complemented
9C101×#1621C211yesmaximal, characteristic, complemented
10C101×#1621C211yesmaximal, characteristic, complemented
11C101×#1620C211yesmaximal, characteristic, complemented
12C101×#1619C211yesmaximal, characteristic, complemented
13C101×#1545C211yesmaximal, characteristic, complemented
14C101×#1495C211yesmaximal, characteristic, complemented
15C101×#1482C211yesmaximal, characteristic, complemented
16#560×C101—22no—
17#559×C101C2211yescharacteristic
18#550×C101C2211yescharacteristic
19#550×C101C2211yescharacteristic
20#546×C101—21no—
21#546×C101—21no—
22D42×C101—21no—
23D42×C101—21no—
24D42×C101C2211yescharacteristic
25#540×C101—21no—
26#540×C101—21no—
27#535×C101—21no—
28#535×C101—21no—
29#534×C101—22no—
30#532×C101C2211yescharacteristic, complemented
31C2×#127×C101C2211yescharacteristic
32#529×C101C2211yescharacteristic
33#529×C101C2211yescharacteristic
34#495×C101—21no—
35#493×C101C2211yescharacteristic
36#493×C101C2211yescharacteristic, complemented
37#488×C101—21no—
38#486×C101C2211yescharacteristic
39#486×C101C2211yescharacteristic, complemented
40#478×C101—21no—
41#475×C101C2211yescharacteristic, complemented
42#474×C101C2211yescharacteristic, complemented
43#469×C101—21no—
44#468×C101—21no—
45#463×C101—21no—
46#462×C101C2211yescharacteristic, complemented
47#461×C101C2211yescharacteristic, complemented
48#460×C101C2211yescharacteristic, complemented
49#460×C101C2211yescharacteristic, complemented
50#459×C101—22no—
51#459×C101C2211yescharacteristic, complemented
52#459×C101C2211yescharacteristic, complemented
53#452×C101—21no—
54#449×C101—21no—
55#447×C101—22no—
56#431×C101C2211yescharacteristic, complemented
57#431×C101C2211yescharacteristic, complemented
58#423×C101C2211yescharacteristic, complemented
59#331×C101C2211yescharacteristic
60#331×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic, complemented
62#331×C101C2211yescharacteristic, complemented
63Q8⋊C8×C101C2211yescharacteristic, complemented
64Q8⋊C8×C101C2211yescharacteristic, complemented
65Q8⋊C8×C101C2211yescharacteristic, complemented
66Q8⋊C8×C101C2211yescharacteristic, complemented
67D4⋊C8×C101C2211yescharacteristic, complemented
68D4⋊C8×C101C2211yescharacteristic, complemented
69D4⋊C8×C101C2211yescharacteristic, complemented
70D4⋊C8×C101C2211yescharacteristic, complemented
71C2×#41×C101—21no—
72C2×#41×C101—21no—
73C2×#41×C101—21no—
74C22×D4×C101—22no—
75C22×D4×C101—21no—
76C22×D4×C101—21no—
77C22×D4×C101—21no—
78C22×D4×C101—21no—
79C22×D4×C101D412yes—
80C2×Q16×C101—21no—
81C2×SD16×C101—21no—
82C2×SD16×C101—21no—
83C2×SD16×C101—21no—
84C2×D8×C101—22no—
85C2×D8×C101—22no—
86C2×D8×C101—21no—
87C2×D8×C101—21no—
88C2×M16×C101—21no—
89C4⋊Q8×C101C2311yescharacteristic
90#127×C101—21no—
91#127×C101—21no—
92#127×C101—21no—
93#127×C101—21no—
94#127×C101D412yes—
95#127×C101C2311yescharacteristic
96#127×C101C2311yescharacteristic
97#127×C101C2311yescharacteristic
98#126×C101—21no—
99#126×C101—21no—
100#125×C101D411yescharacteristic
101#125×C101D411yescharacteristic
102#124×C101—21no—
103#124×C101—21no—
104#124×C101—21no—
105#124×C101D411yescharacteristic
106#124×C101D411yescharacteristic
107#123×C101—22no—
108#123×C101—22no—
109#123×C101—22no—
110#123×C101—22no—
111#123×C101—21no—
112#123×C101—21no—
113C22⋊Q8×C101D411yescharacteristic
114C22⋊Q8×C101D411yescharacteristic
115#121×C101—22no—
116#121×C101—22no—
117#121×C101—22no—
118#121×C101—22no—
119#121×C101—22no—
120#121×C101—22no—
121#121×C101—22no—
122#121×C101—22no—
123#121×C101—21no—
124#121×C101—21no—
125#121×C101—21no—
126#121×C101—21no—
127#121×C101—21no—
128#121×C101—21no—
129#121×C101D411yescharacteristic
130#121×C101D411yescharacteristic
131#120×C101—22no—
132#120×C101—22no—
133#120×C101—22no—
134#120×C101—22no—
135#120×C101—22no—
136#120×C101—22no—
137C4×Q8×C101C2311yescharacteristic
138C4×Q8×C101C2311yescharacteristic
139C4×D4×C101—21no—
140C4×D4×C101—21no—
141C4×D4×C101—21no—
142C4×D4×C101—21no—
143C4×D4×C101—21no—
144C4×D4×C101—21no—
145C4×D4×C101—21no—
146C4×D4×C101—21no—
147C4×D4×C101C2311yescharacteristic
148C4×D4×C101C2311yescharacteristic
149#117×C101—21no—
150#117×C101—21no—
151C2×C22⋊C4×C101—22no—
152C2×C42×C101C2311yescharacteristic
153#107×C101—21no—
154#106×C101—21no—
155C4⋊C8×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—21no—
164#102×C101—22no—
165#102×C101—22no—
166#102×C101—21no—
167#102×C101—21no—
168#102×C101—21no—
169#102×C101—21no—
170#102×C101—21no—
171C22⋊C8×C101—21no—
172C22⋊C8×C101—21no—
173C4×C8×C101—21no—
174C4×C8×C101C2311yescharacteristic
175C4×C8×C101C2311yescharacteristic
176C24×C101—22no—
177C24×C101—22no—
178#41×C101—81no—
179#41×C101—81no—
180#41×C101—81no—
181#41×C101—81no—
182#41×C101—81no—
183#41×C101—81no—
184C2×Q8×C101—21no—
185C2×Q8×C101C2×D411yescharacteristic
186C2×Q8×C101C2×D411yescharacteristic
187C2×D4×C101—21no—
188C2×D4×C101—21no—
189C2×D4×C101—22no—
190C2×D4×C101—22no—
191C2×D4×C101—22no—
192C2×D4×C101—22no—
193C2×D4×C101—22no—
194C2×D4×C101—22no—
195C2×D4×C101—22no—
196C2×D4×C101—22no—
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—21no—
204C2×D4×C101—21no—
205C2×D4×C101—41no—
206C2×D4×C101—81no—
207C2×D4×C101—81no—
208C2×D4×C101—81no—
209C2×D4×C101—81no—
210C2×D4×C101—81no—
211C2×D4×C101—81no—
212C2×D4×C101—81no—
213C2×D4×C101—81no—
214C2×D4×C101—82no—
215C2×D4×C101—84no—
216C2×D4×C101C2×D411yescharacteristic
217C2×D4×C101C2×D411yescharacteristic
218C2×D4×C101C2×D412yes—
219C2×D4×C101C2×D412yes—
220C22×C4×C101—22no—
221C22×C4×C101—22no—
222C22×C4×C101—22no—
223C22×C4×C101—21no—
224C22×C4×C101—21no—
225C22×C4×C101—41no—
226C22×C4×C101C2×D411yescharacteristic
227C22×C4×C101C2×D411yescharacteristic
228C22×C4×C101C2×D411yescharacteristic
229Q16×C101—81no—
230SD16×C101—81no—
231SD16×C101—81no—
232SD16×C101—81no—
233D8×C101—81no—
234D8×C101—81no—
235D8×C101—82no—
236D8×C101—82no—
237M16×C101—81no—
238C2×C8×C101—21no—
239C2×C8×C101—21no—
240C2×C8×C101—21no—
241C2×C8×C101—21no—
242C2×C8×C101—21no—
243C2×C8×C101—21no—
244C4⋊C4×C101—21no—
245C4⋊C4×C101—21no—
246C4⋊C4×C101—21no—
247C4⋊C4×C101—21no—
248C4⋊C4×C101—21no—
249C4⋊C4×C101—21no—
250C4⋊C4×C101—21no—
251C4⋊C4×C101—21no—
252C4⋊C4×C101—21no—
253C4⋊C4×C101—21no—
254C4⋊C4×C101C2×D411yescharacteristic
255C4⋊C4×C101C2×D411yescharacteristic
256C4⋊C4×C101C2×D411yescharacteristic
257C4⋊C4×C101C2×D411yescharacteristic
258C22⋊C4×C101—22no—
259C22⋊C4×C101—22no—
260C22⋊C4×C101—22no—
261C22⋊C4×C101—22no—
262C22⋊C4×C101—22no—
263C22⋊C4×C101—22no—
264C22⋊C4×C101—21no—
265C22⋊C4×C101—21no—
266C22⋊C4×C101—21no—
267C22⋊C4×C101—21no—
268C22⋊C4×C101—21no—
269C22⋊C4×C101—21no—
270C22⋊C4×C101—21no—
271C22⋊C4×C101—21no—
272C22⋊C4×C101—21no—
273C22⋊C4×C101—21no—
274C22⋊C4×C101—41no—
275C22⋊C4×C101—41no—
276C42×C101—21no—
277C42×C101—21no—
278C42×C101C2×D411yescharacteristic
279C42×C101C2×D411yescharacteristic
280C42×C101C2×D411yescharacteristic
281C42×C101C2411yescharacteristic
282C23×C101—21no—
283C23×C101—21no—
284C23×C101—22no—
285C23×C101—22no—
286C23×C101—44no—
287C23×C101—41no—
288C23×C101—82no—
289C23×C101—82no—
290C23×C101—82no—
291C23×C101—82no—
292C23×C101—82no—
293C23×C101#12011yescharacteristic
294Q8×C101—21no—
295Q8×C101—21no—
296Q8×C101—21no—
297Q8×C101—21no—
298Q8×C101—41no—
299Q8×C101—41no—
300D4×C101—21no—
301D4×C101—21no—
302D4×C101—21no—
303D4×C101—21no—
304D4×C101—42no—
305D4×C101—42no—
306D4×C101—42no—
307D4×C101—42no—
308D4×C101—42no—
309D4×C101—41no—
310D4×C101—41no—
311D4×C101—41no—
312D4×C101—41no—
313D4×C101—41no—
314D4×C101—41no—
315D4×C101—41no—
316D4×C101—41no—
317D4×C101—41no—
318D4×C101—41no—
319D4×C101—41no—
320D4×C101—41no—
321D4×C101—82no—
322D4×C101—82no—
323D4×C101—82no—
324D4×C101—82no—
325D4×C101—82no—
326D4×C101—82no—
327D4×C101—82no—
328D4×C101—82no—
329D4×C101—82no—
330D4×C101—82no—
331C2×C4×C101—21no—
332C2×C4×C101—21no—
333C2×C4×C101—21no—
334C2×C4×C101—21no—
335C2×C4×C101—21no—
336C2×C4×C101—21no—
337C2×C4×C101—21no—
338C2×C4×C101—21no—
339C2×C4×C101—21no—
340C2×C4×C101—21no—
341C2×C4×C101—41no—
342C2×C4×C101—41no—
343C2×C4×C101—41no—
344C2×C4×C101—41no—
345C2×C4×C101—41no—
346C2×C4×C101—41no—
347C2×C4×C101—82no—
348C2×C4×C101—82no—
349C2×C4×C101—82no—
350C2×C4×C101—82no—
351C2×C4×C101#12011yescharacteristic
352C2×C4×C101#12011yescharacteristic
353C2×C4×C101#12011yescharacteristic
354C2×C4×C101C22×D411yescharacteristic
355C2×C4×C101C22×D411yescharacteristic
356C2×C4×C101C22×D411yescharacteristic
357C8×C101—41no—
358C8×C101—41no—
359C8×C101—41no—
360C8×C101—41no—
361C8×C101—41no—
362C8×C101—41no—
363C22×C101—21no—
364C22×C101—21no—
365C22×C101—21no—
366C22×C101—41no—
367C22×C101—42no—
368C22×C101—41no—
369C22×C101—42no—
370C22×C101—41no—
371C22×C101—42no—
372C22×C101—41no—
373C22×C101—42no—
374C22×C101—42no—
375C22×C101—41no—
376C22×C101—41no—
377C22×C101—42no—
378C22×C101—81no—
379C22×C101—81no—
380C22×C101—81no—
381C22×C101—164no—
382C22×C101—164no—
383C22×C101C2×#12011yescharacteristic
384C4×C101—21no—
385C4×C101—21no—
386C4×C101—21no—
387C4×C101—21no—
388C4×C101—41no—
389C4×C101—41no—
390C4×C101—41no—
391C4×C101—41no—
392C4×C101—41no—
393C4×C101—41no—
394C4×C101—81no—
395C4×C101#57611yescharacteristic
396C4×C101#57611yescharacteristic
397C4×C101#57611yescharacteristic
398C4×C101#57711yescharacteristic
399#18930C10111yesmaximal, characteristic, direct product factor, Sylow
400C2×C101—41no—
401C2×C101—82no—
402C2×C101—81no—
403C2×C101—81no—
404C2×C101—82no—
405C2×C101—161no—
406C2×C101#300811yescharacteristic
407C2×C101#301211yescharacteristic
408C2×C101#301911yescharacteristic
409#3543C2×C10111yescharacteristic, complemented
410#3251C2×C10111yescharacteristic, complemented
411#3212C2×C10111yescharacteristic, complemented
412#3205C2×C10111yescharacteristic, complemented
413#1642C2×C10111yescharacteristic, complemented
414#1641C2×C10111yescharacteristic, complemented
415#1640C2×C10111yescharacteristic, complemented
416#1639C2×C10111yescharacteristic, complemented
417#1621C2×C10111yescharacteristic, complemented
418#1621C2×C10111yescharacteristic, complemented
419#1620C2×C10111yescharacteristic, complemented
420#1619C2×C10111yescharacteristic, complemented
421#1545C2×C10111yescharacteristic, complemented
422#1495C2×C10111yescharacteristic, complemented
423#1482C2×C10111yescharacteristic, complemented
424C101#1893011yescharacteristic, direct product factor, Sylow
425#560—22no—
426#559C22×C10111yescharacteristic
427#550C22×C10111yescharacteristic
428#550C22×C10111yescharacteristic
429#546—21no—
430#546—21no—
431D42—21no—
432D42—21no—
433D42C22×C10111yescharacteristic
434#540—21no—
435#540—21no—
436#535—21no—
437#535—21no—
438#534—22no—
439#532C22×C10111yescharacteristic, complemented
440C2×#127C22×C10111yescharacteristic
441#529C22×C10111yescharacteristic
442#529C22×C10111yescharacteristic
443#495—21no—
444#493C22×C10111yescharacteristic
445#493C22×C10111yescharacteristic, complemented
446#488—21no—
447#486C22×C10111yescharacteristic
448#486C22×C10111yescharacteristic, complemented
449#478—21no—
450#475C22×C10111yescharacteristic, complemented
451#474C22×C10111yescharacteristic, complemented
452#469—21no—
453#468—21no—
454#463—21no—
455#462C22×C10111yescharacteristic, complemented
456#461C22×C10111yescharacteristic, complemented
457#460C22×C10111yescharacteristic, complemented
458#460C22×C10111yescharacteristic, complemented
459#459—22no—
460#459C22×C10111yescharacteristic, complemented
461#459C22×C10111yescharacteristic, complemented
462#452—21no—
463#449—21no—
464#447—22no—
465#431C22×C10111yescharacteristic, complemented
466#431C22×C10111yescharacteristic, complemented
467#423C22×C10111yescharacteristic, complemented
468#331C22×C10111yescharacteristic
469#331C22×C10111yescharacteristic
470#331C22×C10111yescharacteristic, complemented
471#331C22×C10111yescharacteristic, complemented
472Q8⋊C8C22×C10111yescharacteristic, complemented
473Q8⋊C8C22×C10111yescharacteristic, complemented
474Q8⋊C8C22×C10111yescharacteristic, complemented
475Q8⋊C8C22×C10111yescharacteristic, complemented
476D4⋊C8C22×C10111yescharacteristic, complemented
477D4⋊C8C22×C10111yescharacteristic, complemented
478D4⋊C8C22×C10111yescharacteristic, complemented
479D4⋊C8C22×C10111yescharacteristic, complemented
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C22×D4—22no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4D4×C10112yes—
489C2×Q16—21no—
490C2×SD16—21no—
491C2×SD16—21no—
492C2×SD16—21no—
493C2×D8—22no—
494C2×D8—22no—
495C2×D8—21no—
496C2×D8—21no—
497C2×M16—21no—
498C4⋊Q8C23×C10111yescharacteristic
499#127—21no—
500#127—21no—
501#127—21no—
502#127—21no—
503#127D4×C10112yes—
504#127C23×C10111yescharacteristic
505#127C23×C10111yescharacteristic
506#127C23×C10111yescharacteristic
507#126—21no—
508#126—21no—
509#125D4×C10111yescharacteristic
510#125D4×C10111yescharacteristic
511#124—21no—
512#124—21no—
513#124—21no—
514#124D4×C10111yescharacteristic
515#124D4×C10111yescharacteristic
516#123—22no—
517#123—22no—
518#123—22no—
519#123—22no—
520#123—21no—
521#123—21no—
522C22⋊Q8D4×C10111yescharacteristic
523C22⋊Q8D4×C10111yescharacteristic
524#121—22no—
525#121—22no—
526#121—22no—
527#121—22no—
528#121—22no—
529#121—22no—
530#121—22no—
531#121—22no—
532#121—21no—
533#121—21no—
534#121—21no—
535#121—21no—
536#121—21no—
537#121—21no—
538#121D4×C10111yescharacteristic
539#121D4×C10111yescharacteristic
540#120—22no—
541#120—22no—
542#120—22no—
543#120—22no—
544#120—22no—
545#120—22no—
546C4×Q8C23×C10111yescharacteristic
547C4×Q8C23×C10111yescharacteristic
548C4×D4—21no—
549C4×D4—21no—
550C4×D4—21no—
551C4×D4—21no—
552C4×D4—21no—
553C4×D4—21no—
554C4×D4—21no—
555C4×D4—21no—
556C4×D4C23×C10111yescharacteristic
557C4×D4C23×C10111yescharacteristic
558#117—21no—
559#117—21no—
560C2×C22⋊C4—22no—
561C2×C42C23×C10111yescharacteristic
562#107—21no—
563#106—21no—
564C4⋊C8—21no—
565C4⋊C8—21no—
566C4⋊C8C23×C10111yescharacteristic
567C4⋊C8C23×C10111yescharacteristic
568C4⋊C8C23×C10111yescharacteristic
569C4⋊C8C23×C10111yescharacteristic
570#103—21no—
571#103—21no—
572#103—21no—
573#102—22no—
574#102—22no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C4×C8—21no—
583C4×C8C23×C10111yescharacteristic
584C4×C8C23×C10111yescharacteristic
585C24—22no—
586C24—22no—
587#41—81no—
588#41—81no—
589#41—81no—
590#41—81no—
591#41—81no—
592#41—81no—
593C2×Q8—21no—
594C2×Q8C2×D4×C10111yescharacteristic
595C2×Q8C2×D4×C10111yescharacteristic
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—41no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4—81no—
623C2×D4—82no—
624C2×D4—84no—
625C2×D4C2×D4×C10111yescharacteristic
626C2×D4C2×D4×C10111yescharacteristic
627C2×D4C2×D4×C10112yes—
628C2×D4C2×D4×C10112yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—41no—
635C22×C4C2×D4×C10111yescharacteristic
636C22×C4C2×D4×C10111yescharacteristic
637C22×C4C2×D4×C10111yescharacteristic
638Q16—81no—
639SD16—81no—
640SD16—81no—
641SD16—81no—
642D8—81no—
643D8—81no—
644D8—82no—
645D8—82no—
646M16—81no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4C2×D4×C10111yescharacteristic
664C4⋊C4C2×D4×C10111yescharacteristic
665C4⋊C4C2×D4×C10111yescharacteristic
666C4⋊C4C2×D4×C10111yescharacteristic
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C42—21no—
686C42—21no—
687C42C2×D4×C10111yescharacteristic
688C42C2×D4×C10111yescharacteristic
689C42C2×D4×C10111yescharacteristic
690C42C24×C10111yescharacteristic
691C23—21no—
692C23—21no—
693C23—22no—
694C23—22no—
695C23—44no—
696C23—41no—
697C23—82no—
698C23—82no—
699C23—82no—
700C23—82no—
701C23—82no—
702C23#120×C10111yescharacteristic
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—21no—
707Q8—41no—
708Q8—41no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—82no—
731D4—82no—
732D4—82no—
733D4—82no—
734D4—82no—
735D4—82no—
736D4—82no—
737D4—82no—
738D4—82no—
739D4—82no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—82no—
757C2×C4—82no—
758C2×C4—82no—
759C2×C4—82no—
760C2×C4#120×C10111yescharacteristic
761C2×C4#120×C10111yescharacteristic
762C2×C4#120×C10111yescharacteristic
763C2×C4C22×D4×C10111yescharacteristic
764C2×C4C22×D4×C10111yescharacteristic
765C2×C4C22×D4×C10111yescharacteristic
766C8—41no—
767C8—41no—
768C8—41no—
769C8—41no—
770C8—41no—
771C8—41no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—41no—
785C22—41no—
786C22—42no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—164no—
791C22—164no—
792C22C2×#120×C10111yescharacteristic
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4#576×C10111yescharacteristic
805C4#576×C10111yescharacteristic
806C4#576×C10111yescharacteristic
807C4#577×C10111yescharacteristic
808C2—41no—
809C2—81no—
810C2—81no—
811C2—82no—
812C2—82no—
813C2—161no—
814C2C101×#300811yescharacteristic
815C2C101×#301211yescharacteristic
816C2C101×#301911yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC42C24×C101
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
1. C101×#3543C2semidirect
2. C101×#3251C2semidirect
3. C101×#3212C2semidirect
4. C101×#3205C2semidirect
5. C101×#1642C2semidirect
6. C101×#1641C2semidirect
7. C101×#1640C2semidirect
8. C101×#1639C2semidirect
9. C101×#1621C2semidirect
10. C101×#1621C2semidirect
11. C101×#1620C2semidirect
12. C101×#1619C2semidirect
13. C101×#1545C2semidirect
14. C101×#1495C2semidirect
15. C101×#1482C2semidirect
30. #532×C101C22semidirect
36. #493×C101C22semidirect
39. #486×C101C22semidirect
41. #475×C101C22semidirect
42. #474×C101C22semidirect
46. #462×C101C22semidirect
47. #461×C101C22semidirect
48. #460×C101C22semidirect
49. #460×C101C22semidirect
51. #459×C101C22semidirect
52. #459×C101C22semidirect
56. #431×C101C22semidirect
57. #431×C101C22semidirect
58. #423×C101C22semidirect
61. #331×C101C22semidirect
62. #331×C101C22semidirect
63. Q8⋊C8×C101C22semidirect
64. Q8⋊C8×C101C22semidirect
65. Q8⋊C8×C101C22semidirect
66. Q8⋊C8×C101C22semidirect
67. D4⋊C8×C101C22semidirect
68. D4⋊C8×C101C22semidirect
69. D4⋊C8×C101C22semidirect
70. D4⋊C8×C101C22semidirect
399. #18930C101direct (N × H)
409. #3543C2×C101semidirect
410. #3251C2×C101semidirect
411. #3212C2×C101semidirect
412. #3205C2×C101semidirect
413. #1642C2×C101semidirect
414. #1641C2×C101semidirect
415. #1640C2×C101semidirect
416. #1639C2×C101semidirect
417. #1621C2×C101semidirect
418. #1621C2×C101semidirect
419. #1620C2×C101semidirect
420. #1619C2×C101semidirect
421. #1545C2×C101semidirect
422. #1495C2×C101semidirect
423. #1482C2×C101semidirect
424. C101#18930direct (N × H)
439. #532C22×C101semidirect
445. #493C22×C101semidirect
448. #486C22×C101semidirect
450. #475C22×C101semidirect
451. #474C22×C101semidirect
455. #462C22×C101semidirect
456. #461C22×C101semidirect
457. #460C22×C101semidirect
458. #460C22×C101semidirect
460. #459C22×C101semidirect
461. #459C22×C101semidirect
465. #431C22×C101semidirect
466. #431C22×C101semidirect
467. #423C22×C101semidirect
470. #331C22×C101semidirect
471. #331C22×C101semidirect
472. Q8⋊C8C22×C101semidirect
473. Q8⋊C8C22×C101semidirect
474. Q8⋊C8C22×C101semidirect
475. Q8⋊C8C22×C101semidirect
476. D4⋊C8C22×C101semidirect
477. D4⋊C8C22×C101semidirect
478. D4⋊C8C22×C101semidirect
479. D4⋊C8C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35432
C101×#32512
C101×#32122
C101×#32052
C101×#16422
C101×#16412
C101×#16402
C101×#16392
C101×#16212
C101×#16202
C101×#16192
C101×#15452
C101×#14952
C101×#14822
#18930101