Finite Group Databasebeta

← C101×#18962 #38801113

Subgroups — C101×#18962 #38801113

Order 25856.

964 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3546C211yesmaximal, characteristic, complemented
2C101×#3253C211yesmaximal, characteristic, complemented
3C101×#3247C211yesmaximal, characteristic, complemented
4C101×#3207C211yesmaximal, characteristic, complemented
5C101×#1638C211yesmaximal, characteristic, complemented
6C101×#1635C211yesmaximal, characteristic, complemented
7C101×#1631C211yesmaximal, characteristic, complemented
8C101×#1629C211yesmaximal, characteristic, complemented
9C101×#1628C211yesmaximal, characteristic, complemented
10C101×#1625C211yesmaximal, characteristic, complemented
11C101×#1621C211yesmaximal, characteristic, complemented
12C101×#1619C211yesmaximal, 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#532×C101C2211yescharacteristic
31#532×C101C2211yescharacteristic
32#532×C101C2211yescharacteristic, complemented
33#529×C101C2211yescharacteristic
34#493×C101C2211yescharacteristic
35#492×C101C2211yescharacteristic
36#487×C101C2211yescharacteristic, complemented
37#486×C101C2211yescharacteristic, complemented
38#478×C101—21no—
39#477×C101C2211yescharacteristic, complemented
40#476×C101—21no—
41#476×C101C2211yescharacteristic
42#476×C101C2211yescharacteristic
43#476×C101C2211yescharacteristic, complemented
44#469×C101—21no—
45#469×C101—21no—
46#466×C101—21no—
47#465×C101—21no—
48#463×C101—21no—
49#463×C101—22no—
50#460×C101C2211yescharacteristic, complemented
51#459×C101—21no—
52#459×C101C2211yescharacteristic
53#459×C101C2211yescharacteristic
54#459×C101C2211yescharacteristic, complemented
55#449×C101—22no—
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—
75C2×#41×C101—21no—
76C22×D4×C101—21no—
77C22×D4×C101—21no—
78C2×SD16×C101—21no—
79C2×SD16×C101—22no—
80C2×D8×C101—22no—
81C2×D8×C101—21no—
82C2×D8×C101—21no—
83C2×D8×C101—21no—
84C2×M16×C101—21no—
85C22×C8×C101—21no—
86C4⋊Q8×C101D411yescharacteristic
87C4⋊Q8×C101C2311yescharacteristic
88C4⋊Q8×C101C2311yescharacteristic
89#127×C101—22no—
90#127×C101—21no—
91#127×C101D411yescharacteristic
92#127×C101C2311yescharacteristic
93#127×C101C2311yescharacteristic
94#126×C101—22no—
95#126×C101—22no—
96#126×C101—21no—
97#125×C101D411yescharacteristic
98#124×C101—22no—
99#124×C101—21no—
100#124×C101—21no—
101#124×C101—21no—
102#124×C101—21no—
103#124×C101D411yescharacteristic
104#123×C101—22no—
105#123×C101—22no—
106#123×C101—21no—
107#123×C101—22no—
108C22⋊Q8×C101—22no—
109C22⋊Q8×C101—21no—
110C22⋊Q8×C101—21no—
111C22⋊Q8×C101D411yescharacteristic
112#121×C101—22no—
113#121×C101—22no—
114#121×C101—22no—
115#121×C101—22no—
116#121×C101—22no—
117#121×C101—21no—
118#121×C101—22no—
119#121×C101—21no—
120#121×C101—21no—
121#121×C101—21no—
122#121×C101—21no—
123#121×C101—21no—
124#121×C101—21no—
125#121×C101—21no—
126#121×C101D412yes—
127#121×C101D411yescharacteristic
128#121×C101D411yescharacteristic
129#121×C101D411yescharacteristic
130#120×C101—22no—
131#120×C101—22no—
132#120×C101—22no—
133#120×C101—22no—
134C4×Q8×C101—21no—
135C4×Q8×C101C2311yescharacteristic
136C4×D4×C101—22no—
137C4×D4×C101—21no—
138C4×D4×C101—21no—
139C4×D4×C101—21no—
140C4×D4×C101—21no—
141C4×D4×C101—21no—
142C4×D4×C101—21no—
143C4×D4×C101D412yes—
144C4×D4×C101C2311yescharacteristic
145C4×D4×C101C2311yescharacteristic
146C4×D4×C101C2311yescharacteristic
147#117×C101—21no—
148#117×C101—21no—
149C2×C4⋊C4×C101—21no—
150C2×C22⋊C4×C101—22no—
151C2×C42×C101C2311yescharacteristic
152#107×C101—21no—
153#106×C101—21no—
154#106×C101—21no—
155#106×C101—21no—
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—22no—
165#102×C101—21no—
166#102×C101—21no—
167#102×C101—21no—
168#102×C101—22no—
169#102×C101—21no—
170#102×C101—21no—
171#102×C101—21no—
172#102×C101—21no—
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—
185#41×C101—82no—
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—21no—
204C2×D4×C101—21no—
205C2×D4×C101—21no—
206C2×D4×C101—41no—
207C2×D4×C101—81no—
208C2×D4×C101—81no—
209C2×D4×C101—81no—
210C2×D4×C101—81no—
211C2×D4×C101C2×D411yescharacteristic
212C2×D4×C101C2×D411yescharacteristic
213C2×D4×C101C2×D411yescharacteristic
214C2×D4×C101C2×D412yes—
215C22×C4×C101—22no—
216C22×C4×C101—22no—
217C22×C4×C101—21no—
218C22×C4×C101—21no—
219C22×C4×C101—21no—
220C22×C4×C101—22no—
221C22×C4×C101—41no—
222C22×C4×C101C2×D411yescharacteristic
223C22×C4×C101C2×D411yescharacteristic
224C22×C4×C101C2×D411yescharacteristic
225SD16×C101—81no—
226SD16×C101—82no—
227D8×C101—81no—
228D8×C101—81no—
229D8×C101—81no—
230D8×C101—82no—
231M16×C101—81no—
232C2×C8×C101—21no—
233C2×C8×C101—21no—
234C2×C8×C101—21no—
235C2×C8×C101—21no—
236C2×C8×C101—21no—
237C2×C8×C101—21no—
238C2×C8×C101—81no—
239C4⋊C4×C101—22no—
240C4⋊C4×C101—22no—
241C4⋊C4×C101—21no—
242C4⋊C4×C101—21no—
243C4⋊C4×C101—21no—
244C4⋊C4×C101—21no—
245C4⋊C4×C101—21no—
246C4⋊C4×C101—21no—
247C4⋊C4×C101—21no—
248C4⋊C4×C101—21no—
249C4⋊C4×C101C2×D412yes—
250C4⋊C4×C101C2×D411yescharacteristic
251C4⋊C4×C101C2×D411yescharacteristic
252C4⋊C4×C101C2×D411yescharacteristic
253C4⋊C4×C101C2×D411yescharacteristic
254C22⋊C4×C101—22no—
255C22⋊C4×C101—22no—
256C22⋊C4×C101—22no—
257C22⋊C4×C101—22no—
258C22⋊C4×C101—22no—
259C22⋊C4×C101—21no—
260C22⋊C4×C101—21no—
261C22⋊C4×C101—21no—
262C22⋊C4×C101—21no—
263C22⋊C4×C101—21no—
264C22⋊C4×C101—21no—
265C22⋊C4×C101—22no—
266C22⋊C4×C101—22no—
267C22⋊C4×C101—21no—
268C22⋊C4×C101—21no—
269C22⋊C4×C101—21no—
270C22⋊C4×C101—41no—
271C22⋊C4×C101—41no—
272C42×C101—22no—
273C42×C101—21no—
274C42×C101C2×D411yescharacteristic
275C42×C101C2×D411yescharacteristic
276C42×C101C2×D411yescharacteristic
277C42×C101C2411yescharacteristic
278C23×C101—21no—
279C23×C101—21no—
280C23×C101—22no—
281C23×C101—21no—
282C23×C101—41no—
283C23×C101—82no—
284C23×C101—82no—
285C23×C101—82no—
286C23×C101#12011yescharacteristic
287Q8×C101—21no—
288Q8×C101—21no—
289Q8×C101—42no—
290Q8×C101—41no—
291Q8×C101—41no—
292Q8×C101—81no—
293D4×C101—21no—
294D4×C101—21no—
295D4×C101—21no—
296D4×C101—21no—
297D4×C101—21no—
298D4×C101—21no—
299D4×C101—42no—
300D4×C101—42no—
301D4×C101—41no—
302D4×C101—41no—
303D4×C101—41no—
304D4×C101—41no—
305D4×C101—41no—
306D4×C101—41no—
307D4×C101—41no—
308D4×C101—41no—
309D4×C101—81no—
310D4×C101—81no—
311D4×C101—81no—
312D4×C101—81no—
313D4×C101—81no—
314D4×C101—82no—
315D4×C101—82no—
316D4×C101—82no—
317D4×C101—82no—
318D4×C101—82no—
319D4×C101—82no—
320D4×C101—82no—
321C2×C4×C101—21no—
322C2×C4×C101—21no—
323C2×C4×C101—21no—
324C2×C4×C101—21no—
325C2×C4×C101—21no—
326C2×C4×C101—21no—
327C2×C4×C101—21no—
328C2×C4×C101—22no—
329C2×C4×C101—21no—
330C2×C4×C101—21no—
331C2×C4×C101—41no—
332C2×C4×C101—41no—
333C2×C4×C101—41no—
334C2×C4×C101—41no—
335C2×C4×C101—41no—
336C2×C4×C101—41no—
337C2×C4×C101—41no—
338C2×C4×C101—41no—
339C2×C4×C101—82no—
340C2×C4×C101—82no—
341C2×C4×C101—82no—
342C2×C4×C101—82no—
343C2×C4×C101#12011yescharacteristic
344C2×C4×C101#12011yescharacteristic
345C2×C4×C101#12011yescharacteristic
346C2×C4×C101C22×D411yescharacteristic
347C2×C4×C101C22×D411yescharacteristic
348C2×C4×C101C22×D411yescharacteristic
349C8×C101—41no—
350C8×C101—41no—
351C8×C101—41no—
352C8×C101—41no—
353C8×C101—41no—
354C8×C101—41no—
355C22×C101—21no—
356C22×C101—21no—
357C22×C101—21no—
358C22×C101—41no—
359C22×C101—41no—
360C22×C101—41no—
361C22×C101—41no—
362C22×C101—42no—
363C22×C101—42no—
364C22×C101—41no—
365C22×C101—41no—
366C22×C101—42no—
367C22×C101—41no—
368C22×C101—41no—
369C22×C101—41no—
370C22×C101—81no—
371C22×C101—81no—
372C22×C101—81no—
373C22×C101—164no—
374C22×C101C2×#12011yescharacteristic
375C4×C101—21no—
376C4×C101—21no—
377C4×C101—21no—
378C4×C101—21no—
379C4×C101—41no—
380C4×C101—41no—
381C4×C101—41no—
382C4×C101—41no—
383C4×C101—42no—
384C4×C101—41no—
385C4×C101—81no—
386C4×C101#57611yescharacteristic
387C4×C101#57611yescharacteristic
388C4×C101#57711yescharacteristic
389C4×C101#57711yescharacteristic
390#18962C10111yesmaximal, characteristic, direct product factor, Sylow
391C2×C101—41no—
392C2×C101—81no—
393C2×C101—82no—
394C2×C101—81no—
395C2×C101—81no—
396C2×C101—161no—
397C2×C101#301211yescharacteristic
398C2×C101#301211yescharacteristic
399C2×C101#302111yescharacteristic
400#3546C2×C10111yescharacteristic, complemented
401#3253C2×C10111yescharacteristic, complemented
402#3247C2×C10111yescharacteristic, complemented
403#3207C2×C10111yescharacteristic, complemented
404#1638C2×C10111yescharacteristic, complemented
405#1635C2×C10111yescharacteristic, complemented
406#1631C2×C10111yescharacteristic, complemented
407#1629C2×C10111yescharacteristic, complemented
408#1628C2×C10111yescharacteristic, complemented
409#1625C2×C10111yescharacteristic, complemented
410#1621C2×C10111yescharacteristic, complemented
411#1619C2×C10111yescharacteristic, complemented
412#1547C2×C10111yescharacteristic, complemented
413#1495C2×C10111yescharacteristic, complemented
414#1480C2×C10111yescharacteristic, complemented
415C101#1896211yescharacteristic, direct product factor, Sylow
416#560—22no—
417#556C22×C10111yescharacteristic
418#553—21no—
419#550—21no—
420#550C22×C10111yescharacteristic
421#547C22×C10111yescharacteristic
422#546—21no—
423#546—21no—
424D42C22×C10111yescharacteristic
425#542—21no—
426#538—22no—
427#537—21no—
428#535—21no—
429#535—21no—
430#532C22×C10111yescharacteristic
431#532C22×C10111yescharacteristic
432#532C22×C10111yescharacteristic, complemented
433#529C22×C10111yescharacteristic
434#493C22×C10111yescharacteristic
435#492C22×C10111yescharacteristic
436#487C22×C10111yescharacteristic, complemented
437#486C22×C10111yescharacteristic, complemented
438#478—21no—
439#477C22×C10111yescharacteristic, complemented
440#476—21no—
441#476C22×C10111yescharacteristic
442#476C22×C10111yescharacteristic
443#476C22×C10111yescharacteristic, complemented
444#469—21no—
445#469—21no—
446#466—21no—
447#465—21no—
448#463—21no—
449#463—22no—
450#460C22×C10111yescharacteristic, complemented
451#459—21no—
452#459C22×C10111yescharacteristic
453#459C22×C10111yescharacteristic
454#459C22×C10111yescharacteristic, complemented
455#449—22no—
456#431C22×C10111yescharacteristic, complemented
457#423C22×C10111yescharacteristic, complemented
458C2×C4⋊C8C22×C10111yescharacteristic, complemented
459#332C22×C10111yescharacteristic, complemented
460#332C22×C10111yescharacteristic, complemented
461#331C22×C10111yescharacteristic
462#331C22×C10111yescharacteristic
463Q8⋊C8C22×C10111yescharacteristic, complemented
464Q8⋊C8C22×C10111yescharacteristic, complemented
465D4⋊C8C22×C10111yescharacteristic
466D4⋊C8C22×C10111yescharacteristic
467D4⋊C8C22×C10111yescharacteristic
468D4⋊C8C22×C10111yescharacteristic
469D4⋊C8C22×C10111yescharacteristic, complemented
470D4⋊C8C22×C10111yescharacteristic, complemented
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C22×D4—21no—
477C22×D4—21no—
478C2×SD16—21no—
479C2×SD16—22no—
480C2×D8—22no—
481C2×D8—21no—
482C2×D8—21no—
483C2×D8—21no—
484C2×M16—21no—
485C22×C8—21no—
486C4⋊Q8D4×C10111yescharacteristic
487C4⋊Q8C23×C10111yescharacteristic
488C4⋊Q8C23×C10111yescharacteristic
489#127—22no—
490#127—21no—
491#127D4×C10111yescharacteristic
492#127C23×C10111yescharacteristic
493#127C23×C10111yescharacteristic
494#126—22no—
495#126—22no—
496#126—21no—
497#125D4×C10111yescharacteristic
498#124—22no—
499#124—21no—
500#124—21no—
501#124—21no—
502#124—21no—
503#124D4×C10111yescharacteristic
504#123—22no—
505#123—22no—
506#123—21no—
507#123—22no—
508C22⋊Q8—22no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8D4×C10111yescharacteristic
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—21no—
518#121—22no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121D4×C10111yescharacteristic
527#121D4×C10111yescharacteristic
528#121D4×C10111yescharacteristic
529#121D4×C10112yes—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534C4×Q8—21no—
535C4×Q8C23×C10111yescharacteristic
536C4×D4—22no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4D4×C10112yes—
544C4×D4C23×C10111yescharacteristic
545C4×D4C23×C10111yescharacteristic
546C4×D4C23×C10111yescharacteristic
547#117—21no—
548#117—21no—
549C2×C4⋊C4—21no—
550C2×C22⋊C4—22no—
551C2×C42C23×C10111yescharacteristic
552#107—21no—
553#106—21no—
554#106—21no—
555#106—21no—
556C4⋊C8—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559C4⋊C8C23×C10111yescharacteristic
560C4⋊C8C23×C10111yescharacteristic
561C4⋊C8C23×C10111yescharacteristic
562C4⋊C8C23×C10111yescharacteristic
563#103—21no—
564#103—22no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—22no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573C22⋊C8—21no—
574C4×C8C23×C10111yescharacteristic
575C4×C8C23×C10111yescharacteristic
576C24—22no—
577#41—81no—
578#41—81no—
579#41—81no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—82no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8C2×D4×C10111yescharacteristic
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—41no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4C2×D4×C10111yescharacteristic
612C2×D4C2×D4×C10111yescharacteristic
613C2×D4C2×D4×C10111yescharacteristic
614C2×D4C2×D4×C10112yes—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—41no—
622C22×C4C2×D4×C10111yescharacteristic
623C22×C4C2×D4×C10111yescharacteristic
624C22×C4C2×D4×C10111yescharacteristic
625SD16—81no—
626SD16—82no—
627D8—81no—
628D8—81no—
629D8—81no—
630D8—82no—
631M16—81no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—81no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4C2×D4×C10112yes—
650C4⋊C4C2×D4×C10111yescharacteristic
651C4⋊C4C2×D4×C10111yescharacteristic
652C4⋊C4C2×D4×C10111yescharacteristic
653C4⋊C4C2×D4×C10111yescharacteristic
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C42—22no—
673C42—21no—
674C42C2×D4×C10111yescharacteristic
675C42C2×D4×C10111yescharacteristic
676C42C2×D4×C10111yescharacteristic
677C42C24×C10111yescharacteristic
678C23—21no—
679C23—21no—
680C23—22no—
681C23—21no—
682C23—41no—
683C23—82no—
684C23—82no—
685C23—82no—
686C23#120×C10111yescharacteristic
687Q8—21no—
688Q8—21no—
689Q8—42no—
690Q8—41no—
691Q8—41no—
692Q8—81no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—81no—
710D4—81no—
711D4—81no—
712D4—81no—
713D4—82no—
714D4—81no—
715D4—82no—
716D4—82no—
717D4—82no—
718D4—82no—
719D4—82no—
720D4—82no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—82no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4#120×C10111yescharacteristic
744C2×C4#120×C10111yescharacteristic
745C2×C4#120×C10111yescharacteristic
746C2×C4C22×D4×C10111yescharacteristic
747C2×C4C22×D4×C10111yescharacteristic
748C2×C4C22×D4×C10111yescharacteristic
749C8—41no—
750C8—41no—
751C8—41no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—164no—
774C22C2×#120×C10111yescharacteristic
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—41no—
785C4—81no—
786C4#576×C10111yescharacteristic
787C4#576×C10111yescharacteristic
788C4#577×C10111yescharacteristic
789C4#577×C10111yescharacteristic
790C2—41no—
791C2—81no—
792C2—81no—
793C2—82no—
794C2—81no—
795C2—161no—
796C2C101×#301211yescharacteristic
797C2C101×#301211yescharacteristic
798C2C101×#302111yescharacteristic
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×#3546C2semidirect
2. C101×#3253C2semidirect
3. C101×#3247C2semidirect
4. C101×#3207C2semidirect
5. C101×#1638C2semidirect
6. C101×#1635C2semidirect
7. C101×#1631C2semidirect
8. C101×#1629C2semidirect
9. C101×#1628C2semidirect
10. C101×#1625C2semidirect
11. C101×#1621C2semidirect
12. C101×#1619C2semidirect
13. C101×#1547C2semidirect
14. C101×#1495C2semidirect
15. C101×#1480C2semidirect
32. #532×C101C22semidirect
36. #487×C101C22semidirect
37. #486×C101C22semidirect
39. #477×C101C22semidirect
43. #476×C101C22semidirect
50. #460×C101C22semidirect
54. #459×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
390. #18962C101direct (N × H)
400. #3546C2×C101semidirect
401. #3253C2×C101semidirect
402. #3247C2×C101semidirect
403. #3207C2×C101semidirect
404. #1638C2×C101semidirect
405. #1635C2×C101semidirect
406. #1631C2×C101semidirect
407. #1629C2×C101semidirect
408. #1628C2×C101semidirect
409. #1625C2×C101semidirect
410. #1621C2×C101semidirect
411. #1619C2×C101semidirect
412. #1547C2×C101semidirect
413. #1495C2×C101semidirect
414. #1480C2×C101semidirect
415. C101#18962direct (N × H)
432. #532C22×C101semidirect
436. #487C22×C101semidirect
437. #486C22×C101semidirect
439. #477C22×C101semidirect
443. #476C22×C101semidirect
450. #460C22×C101semidirect
454. #459C22×C101semidirect
456. #431C22×C101semidirect
457. #423C22×C101semidirect
458. C2×C4⋊C8C22×C101semidirect
459. #332C22×C101semidirect
460. #332C22×C101semidirect
463. Q8⋊C8C22×C101semidirect
464. Q8⋊C8C22×C101semidirect
469. D4⋊C8C22×C101semidirect
470. 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×#32532
C101×#32472
C101×#32072
C101×#16382
C101×#16352
C101×#16312
C101×#16292
C101×#16282
C101×#16252
C101×#16212
C101×#16192
C101×#15472
C101×#14952
C101×#14802
#18962101