Finite Group Databasebeta

← C101×#18704 #38800855

Subgroups — C101×#18704 #38800855

Order 25856.

972 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3546C211yesmaximal, characteristic, complemented
2C101×#3251C211yesmaximal, characteristic, complemented
3C101×#3214C211yesmaximal, characteristic, complemented
4C101×#3169C211yesmaximal, characteristic, complemented
5C101×#1650C211yesmaximal, characteristic, complemented
6C101×#1647C211yesmaximal, characteristic, complemented
7C101×#1642C211yesmaximal, characteristic, complemented
8C101×#1639C211yesmaximal, characteristic, complemented
9C101×#1628C211yesmaximal, characteristic, complemented
10C101×#1625C211yesmaximal, characteristic, complemented
11C101×#1621C211yesmaximal, characteristic, complemented
12C101×#1619C211yesmaximal, characteristic, complemented
13C101×#1557C211yesmaximal, characteristic, complemented
14C101×#1494C211yesmaximal, characteristic, complemented
15C101×#1492C211yesmaximal, 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#500×C101C2211yescharacteristic, complemented
35#496×C101—21no—
36#493×C101C2211yescharacteristic
37#489×C101—21no—
38#486×C101C2211yescharacteristic
39#486×C101C2211yescharacteristic, complemented
40#478×C101—21no—
41#475×C101C2211yescharacteristic, complemented
42#474×C101C2211yescharacteristic
43#469×C101—21no—
44#468×C101—21no—
45#466×C101—22no—
46#463×C101—21no—
47#461×C101C2211yescharacteristic
48#461×C101C2211yescharacteristic, complemented
49#460×C101C2211yescharacteristic, complemented
50#459×C101C2211yescharacteristic
51#459×C101C2211yescharacteristic
52#459×C101C2211yescharacteristic, complemented
53#449×C101—21no—
54#449×C101—21no—
55C4×D8×C101—22no—
56#432×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—21no—
80C2×SD16×C101—21no—
81C2×D8×C101—22no—
82C2×D8×C101—21no—
83C2×D8×C101—21no—
84C2×D8×C101—21no—
85C2×M16×C101—21no—
86C22×C8×C101—21no—
87C4⋊Q8×C101D411yescharacteristic
88C4⋊Q8×C101C2311yescharacteristic
89C4⋊Q8×C101C2311yescharacteristic
90#127×C101—22no—
91#127×C101—21no—
92#127×C101D411yescharacteristic
93#127×C101C2311yescharacteristic
94#127×C101C2311yescharacteristic
95#126×C101—22no—
96#126×C101—22no—
97#126×C101—21no—
98#125×C101D411yescharacteristic
99#124×C101—22no—
100#124×C101—21no—
101#124×C101—21no—
102#124×C101—21no—
103#124×C101—21no—
104#124×C101D411yescharacteristic
105#123×C101—22no—
106#123×C101—22no—
107#123×C101—21no—
108#123×C101—22no—
109C22⋊Q8×C101—22no—
110C22⋊Q8×C101—21no—
111C22⋊Q8×C101—21no—
112C22⋊Q8×C101D411yescharacteristic
113#121×C101—22no—
114#121×C101—22no—
115#121×C101—22no—
116#121×C101—22no—
117#121×C101—22no—
118#121×C101—21no—
119#121×C101—22no—
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×C101—21no—
127#121×C101D411yescharacteristic
128#121×C101D411yescharacteristic
129#121×C101D412yes—
130#121×C101D411yescharacteristic
131#120×C101—22no—
132#120×C101—22no—
133#120×C101—22no—
134#120×C101—22no—
135C4×Q8×C101—21no—
136C4×Q8×C101C2311yescharacteristic
137C4×D4×C101—22no—
138C4×D4×C101—21no—
139C4×D4×C101—21no—
140C4×D4×C101—21no—
141C4×D4×C101—21no—
142C4×D4×C101—21no—
143C4×D4×C101—21no—
144C4×D4×C101D412yes—
145C4×D4×C101C2311yescharacteristic
146C4×D4×C101C2311yescharacteristic
147C4×D4×C101C2311yescharacteristic
148#117×C101—21no—
149#117×C101—21no—
150C2×C4⋊C4×C101—21no—
151C2×C22⋊C4×C101—22no—
152C2×C42×C101C2311yescharacteristic
153#107×C101—22no—
154#107×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—21no—
164#102×C101—22no—
165#102×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—
185#41×C101—81no—
186#41×C101—81no—
187C2×Q8×C101—21no—
188C2×Q8×C101—21no—
189C2×Q8×C101—21no—
190C2×Q8×C101C2×D411yescharacteristic
191C2×D4×C101—22no—
192C2×D4×C101—22no—
193C2×D4×C101—22no—
194C2×D4×C101—22no—
195C2×D4×C101—22no—
196C2×D4×C101—21no—
197C2×D4×C101—21no—
198C2×D4×C101—22no—
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—21no—
207C2×D4×C101—41no—
208C2×D4×C101—81no—
209C2×D4×C101—81no—
210C2×D4×C101—81no—
211C2×D4×C101—81no—
212C2×D4×C101C2×D411yescharacteristic
213C2×D4×C101C2×D411yescharacteristic
214C2×D4×C101C2×D411yescharacteristic
215C2×D4×C101C2×D412yes—
216C22×C4×C101—22no—
217C22×C4×C101—22no—
218C22×C4×C101—21no—
219C22×C4×C101—21no—
220C22×C4×C101—21no—
221C22×C4×C101—22no—
222C22×C4×C101—41no—
223C22×C4×C101C2×D411yescharacteristic
224C22×C4×C101C2×D411yescharacteristic
225C22×C4×C101C2×D411yescharacteristic
226SD16×C101—81no—
227SD16×C101—81no—
228SD16×C101—81no—
229D8×C101—44no—
230D8×C101—81no—
231D8×C101—81no—
232D8×C101—81no—
233M16×C101—81no—
234C2×C8×C101—21no—
235C2×C8×C101—21no—
236C2×C8×C101—21no—
237C2×C8×C101—21no—
238C2×C8×C101—21no—
239C2×C8×C101—21no—
240C2×C8×C101—42no—
241C4⋊C4×C101—22no—
242C4⋊C4×C101—22no—
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×C101—21no—
250C4⋊C4×C101—21no—
251C4⋊C4×C101C2×D411yescharacteristic
252C4⋊C4×C101C2×D411yescharacteristic
253C4⋊C4×C101C2×D411yescharacteristic
254C4⋊C4×C101C2×D411yescharacteristic
255C4⋊C4×C101C2×D412yes—
256C22⋊C4×C101—22no—
257C22⋊C4×C101—22no—
258C22⋊C4×C101—22no—
259C22⋊C4×C101—22no—
260C22⋊C4×C101—22no—
261C22⋊C4×C101—21no—
262C22⋊C4×C101—21no—
263C22⋊C4×C101—21no—
264C22⋊C4×C101—21no—
265C22⋊C4×C101—21no—
266C22⋊C4×C101—21no—
267C22⋊C4×C101—22no—
268C22⋊C4×C101—22no—
269C22⋊C4×C101—21no—
270C22⋊C4×C101—21no—
271C22⋊C4×C101—21no—
272C22⋊C4×C101—41no—
273C22⋊C4×C101—41no—
274C42×C101—22no—
275C42×C101—21no—
276C42×C101C2×D411yescharacteristic
277C42×C101C2×D411yescharacteristic
278C42×C101C2×D411yescharacteristic
279C42×C101C2411yescharacteristic
280C23×C101—21no—
281C23×C101—21no—
282C23×C101—22no—
283C23×C101—21no—
284C23×C101—41no—
285C23×C101—82no—
286C23×C101—82no—
287C23×C101—82no—
288C23×C101#12011yescharacteristic
289Q8×C101—21no—
290Q8×C101—21no—
291Q8×C101—41no—
292Q8×C101—41no—
293Q8×C101—41no—
294Q8×C101—41no—
295Q8×C101—81no—
296D4×C101—21no—
297D4×C101—21no—
298D4×C101—21no—
299D4×C101—21no—
300D4×C101—21no—
301D4×C101—21no—
302D4×C101—42no—
303D4×C101—42no—
304D4×C101—41no—
305D4×C101—41no—
306D4×C101—41no—
307D4×C101—41no—
308D4×C101—41no—
309D4×C101—41no—
310D4×C101—41no—
311D4×C101—41no—
312D4×C101—81no—
313D4×C101—81no—
314D4×C101—81no—
315D4×C101—82no—
316D4×C101—81no—
317D4×C101—81no—
318D4×C101—82no—
319D4×C101—82no—
320D4×C101—82no—
321D4×C101—82no—
322D4×C101—82no—
323D4×C101—82no—
324C2×C4×C101—21no—
325C2×C4×C101—21no—
326C2×C4×C101—21no—
327C2×C4×C101—21no—
328C2×C4×C101—21no—
329C2×C4×C101—21no—
330C2×C4×C101—21no—
331C2×C4×C101—22no—
332C2×C4×C101—21no—
333C2×C4×C101—21no—
334C2×C4×C101—41no—
335C2×C4×C101—41no—
336C2×C4×C101—41no—
337C2×C4×C101—41no—
338C2×C4×C101—41no—
339C2×C4×C101—41no—
340C2×C4×C101—41no—
341C2×C4×C101—41no—
342C2×C4×C101—82no—
343C2×C4×C101—82no—
344C2×C4×C101—82no—
345C2×C4×C101—82no—
346C2×C4×C101#12011yescharacteristic
347C2×C4×C101#12011yescharacteristic
348C2×C4×C101#12011yescharacteristic
349C2×C4×C101C22×D411yescharacteristic
350C2×C4×C101C22×D411yescharacteristic
351C2×C4×C101C22×D411yescharacteristic
352C8×C101—22no—
353C8×C101—41no—
354C8×C101—41no—
355C8×C101—41no—
356C8×C101—41no—
357C8×C101—41no—
358C22×C101—21no—
359C22×C101—21no—
360C22×C101—21no—
361C22×C101—41no—
362C22×C101—41no—
363C22×C101—42no—
364C22×C101—41no—
365C22×C101—41no—
366C22×C101—41no—
367C22×C101—42no—
368C22×C101—41no—
369C22×C101—42no—
370C22×C101—41no—
371C22×C101—41no—
372C22×C101—41no—
373C22×C101—81no—
374C22×C101—81no—
375C22×C101—81no—
376C22×C101—164no—
377C22×C101C2×#12011yescharacteristic
378C4×C101—21no—
379C4×C101—21no—
380C4×C101—21no—
381C4×C101—21no—
382C4×C101—41no—
383C4×C101—42no—
384C4×C101—41no—
385C4×C101—41no—
386C4×C101—41no—
387C4×C101—41no—
388C4×C101—81no—
389C4×C101#57611yescharacteristic
390C4×C101#57611yescharacteristic
391C4×C101#57611yescharacteristic
392C4×C101#57711yescharacteristic
393#18704C10111yesmaximal, characteristic, direct product factor, Sylow
394C2×C101—41no—
395C2×C101—81no—
396C2×C101—82no—
397C2×C101—81no—
398C2×C101—81no—
399C2×C101—161no—
400C2×C101#300811yescharacteristic
401C2×C101#301211yescharacteristic
402C2×C101#301811yescharacteristic
403#3546C2×C10111yescharacteristic, complemented
404#3251C2×C10111yescharacteristic, complemented
405#3214C2×C10111yescharacteristic, complemented
406#3169C2×C10111yescharacteristic, complemented
407#1650C2×C10111yescharacteristic, complemented
408#1647C2×C10111yescharacteristic, complemented
409#1642C2×C10111yescharacteristic, complemented
410#1639C2×C10111yescharacteristic, complemented
411#1628C2×C10111yescharacteristic, complemented
412#1625C2×C10111yescharacteristic, complemented
413#1621C2×C10111yescharacteristic, complemented
414#1619C2×C10111yescharacteristic, complemented
415#1557C2×C10111yescharacteristic, complemented
416#1494C2×C10111yescharacteristic, complemented
417#1492C2×C10111yescharacteristic, complemented
418C101#1870411yescharacteristic, direct product factor, Sylow
419#560—22no—
420#556C22×C10111yescharacteristic
421#553—21no—
422#550—21no—
423#550C22×C10111yescharacteristic
424#547C22×C10111yescharacteristic
425#546—21no—
426#546—21no—
427D42C22×C10111yescharacteristic
428#542—21no—
429#538—22no—
430#537—21no—
431#535—21no—
432#535—21no—
433#532C22×C10111yescharacteristic
434#532C22×C10111yescharacteristic
435#532C22×C10111yescharacteristic, complemented
436#529C22×C10111yescharacteristic
437#500C22×C10111yescharacteristic, complemented
438#496—21no—
439#493C22×C10111yescharacteristic
440#489—21no—
441#486C22×C10111yescharacteristic
442#486C22×C10111yescharacteristic, complemented
443#478—21no—
444#475C22×C10111yescharacteristic, complemented
445#474C22×C10111yescharacteristic
446#469—21no—
447#468—21no—
448#466—22no—
449#463—21no—
450#461C22×C10111yescharacteristic
451#461C22×C10111yescharacteristic, complemented
452#460C22×C10111yescharacteristic, complemented
453#459C22×C10111yescharacteristic
454#459C22×C10111yescharacteristic
455#459C22×C10111yescharacteristic, complemented
456#449—21no—
457#449—21no—
458C4×D8—22no—
459#432C22×C10111yescharacteristic, complemented
460#423C22×C10111yescharacteristic, complemented
461C2×C4×C8C22×C10111yescharacteristic, complemented
462#332C22×C10111yescharacteristic, complemented
463#332C22×C10111yescharacteristic, complemented
464#331C22×C10111yescharacteristic
465#331C22×C10111yescharacteristic
466Q8⋊C8C22×C10111yescharacteristic, complemented
467Q8⋊C8C22×C10111yescharacteristic, complemented
468D4⋊C8C22×C10111yescharacteristic
469D4⋊C8C22×C10111yescharacteristic
470D4⋊C8C22×C10111yescharacteristic
471D4⋊C8C22×C10111yescharacteristic
472D4⋊C8C22×C10111yescharacteristic, complemented
473D4⋊C8C22×C10111yescharacteristic, complemented
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C22×D4—21no—
480C22×D4—21no—
481C2×SD16—21no—
482C2×SD16—21no—
483C2×SD16—21no—
484C2×D8—22no—
485C2×D8—21no—
486C2×D8—21no—
487C2×D8—21no—
488C2×M16—21no—
489C22×C8—21no—
490C4⋊Q8D4×C10111yescharacteristic
491C4⋊Q8C23×C10111yescharacteristic
492C4⋊Q8C23×C10111yescharacteristic
493#127—22no—
494#127—21no—
495#127D4×C10111yescharacteristic
496#127C23×C10111yescharacteristic
497#127C23×C10111yescharacteristic
498#126—22no—
499#126—22no—
500#126—21no—
501#125D4×C10111yescharacteristic
502#124—22no—
503#124—21no—
504#124—21no—
505#124—21no—
506#124—21no—
507#124D4×C10111yescharacteristic
508#123—22no—
509#123—22no—
510#123—21no—
511#123—22no—
512C22⋊Q8—22no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515C22⋊Q8D4×C10111yescharacteristic
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—21no—
522#121—22no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121D4×C10111yescharacteristic
531#121D4×C10111yescharacteristic
532#121D4×C10111yescharacteristic
533#121D4×C10112yes—
534#120—22no—
535#120—22no—
536#120—22no—
537#120—22no—
538C4×Q8—21no—
539C4×Q8C23×C10111yescharacteristic
540C4×D4—22no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4D4×C10112yes—
548C4×D4C23×C10111yescharacteristic
549C4×D4C23×C10111yescharacteristic
550C4×D4C23×C10111yescharacteristic
551#117—21no—
552#117—21no—
553C2×C4⋊C4—21no—
554C2×C22⋊C4—22no—
555C2×C42C23×C10111yescharacteristic
556#107—22no—
557#107—21no—
558#106—21no—
559C4⋊C8—21no—
560C4⋊C8C23×C10111yescharacteristic
561C4⋊C8C23×C10111yescharacteristic
562C4⋊C8C23×C10111yescharacteristic
563C4⋊C8C23×C10111yescharacteristic
564#103—21no—
565#103—21no—
566#103—21no—
567#102—22no—
568#102—21no—
569#102—22no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574C22⋊C8—21no—
575#97—21no—
576C4×C8—21no—
577C4×C8C23×C10111yescharacteristic
578C4×C8C23×C10111yescharacteristic
579C24—22no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—81no—
586#41—81no—
587#41—81no—
588#41—81no—
589#41—81no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8C2×D4×C10111yescharacteristic
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C2×D4×C10111yescharacteristic
616C2×D4C2×D4×C10111yescharacteristic
617C2×D4C2×D4×C10111yescharacteristic
618C2×D4C2×D4×C10112yes—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—41no—
626C22×C4C2×D4×C10111yescharacteristic
627C22×C4C2×D4×C10111yescharacteristic
628C22×C4C2×D4×C10111yescharacteristic
629SD16—81no—
630SD16—81no—
631SD16—81no—
632D8—44no—
633D8—81no—
634D8—81no—
635D8—81no—
636M16—81no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—42no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4C2×D4×C10111yescharacteristic
655C4⋊C4C2×D4×C10111yescharacteristic
656C4⋊C4C2×D4×C10111yescharacteristic
657C4⋊C4C2×D4×C10111yescharacteristic
658C4⋊C4C2×D4×C10112yes—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C42—22no—
678C42—21no—
679C42C2×D4×C10111yescharacteristic
680C42C2×D4×C10111yescharacteristic
681C42C2×D4×C10111yescharacteristic
682C42C24×C10111yescharacteristic
683C23—21no—
684C23—21no—
685C23—22no—
686C23—21no—
687C23—41no—
688C23—82no—
689C23—82no—
690C23—82no—
691C23#120×C10111yescharacteristic
692Q8—21no—
693Q8—21no—
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—81no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—42no—
706D4—42no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—81no—
716D4—81no—
717D4—82no—
718D4—81no—
719D4—81no—
720D4—81no—
721D4—82no—
722D4—82no—
723D4—82no—
724D4—82no—
725D4—82no—
726D4—82no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—82no—
746C2×C4—82no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4#120×C10111yescharacteristic
750C2×C4#120×C10111yescharacteristic
751C2×C4#120×C10111yescharacteristic
752C2×C4C22×D4×C10111yescharacteristic
753C2×C4C22×D4×C10111yescharacteristic
754C2×C4C22×D4×C10111yescharacteristic
755C8—22no—
756C8—41no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—164no—
780C22C2×#120×C10111yescharacteristic
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—41no—
786C4—42no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4#576×C10111yescharacteristic
793C4#576×C10111yescharacteristic
794C4#576×C10111yescharacteristic
795C4#577×C10111yescharacteristic
796C2—41no—
797C2—81no—
798C2—81no—
799C2—82no—
800C2—81no—
801C2—161no—
802C2C101×#300811yescharacteristic
803C2C101×#301211yescharacteristic
804C2C101×#301811yescharacteristic
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×#3251C2semidirect
3. C101×#3214C2semidirect
4. C101×#3169C2semidirect
5. C101×#1650C2semidirect
6. C101×#1647C2semidirect
7. C101×#1642C2semidirect
8. C101×#1639C2semidirect
9. C101×#1628C2semidirect
10. C101×#1625C2semidirect
11. C101×#1621C2semidirect
12. C101×#1619C2semidirect
13. C101×#1557C2semidirect
14. C101×#1494C2semidirect
15. C101×#1492C2semidirect
32. #532×C101C22semidirect
34. #500×C101C22semidirect
39. #486×C101C22semidirect
41. #475×C101C22semidirect
48. #461×C101C22semidirect
49. #460×C101C22semidirect
52. #459×C101C22semidirect
56. #432×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
393. #18704C101direct (N × H)
403. #3546C2×C101semidirect
404. #3251C2×C101semidirect
405. #3214C2×C101semidirect
406. #3169C2×C101semidirect
407. #1650C2×C101semidirect
408. #1647C2×C101semidirect
409. #1642C2×C101semidirect
410. #1639C2×C101semidirect
411. #1628C2×C101semidirect
412. #1625C2×C101semidirect
413. #1621C2×C101semidirect
414. #1619C2×C101semidirect
415. #1557C2×C101semidirect
416. #1494C2×C101semidirect
417. #1492C2×C101semidirect
418. C101#18704direct (N × H)
435. #532C22×C101semidirect
437. #500C22×C101semidirect
442. #486C22×C101semidirect
444. #475C22×C101semidirect
451. #461C22×C101semidirect
452. #460C22×C101semidirect
455. #459C22×C101semidirect
459. #432C22×C101semidirect
460. #423C22×C101semidirect
461. C2×C4×C8C22×C101semidirect
462. #332C22×C101semidirect
463. #332C22×C101semidirect
466. Q8⋊C8C22×C101semidirect
467. Q8⋊C8C22×C101semidirect
472. D4⋊C8C22×C101semidirect
473. 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×#32512
C101×#32142
C101×#31692
C101×#16502
C101×#16472
C101×#16422
C101×#16392
C101×#16282
C101×#16252
C101×#16212
C101×#16192
C101×#15572
C101×#14942
C101×#14922
#18704101