Finite Group Databasebeta

← C101×#18931 #38801082

Subgroups — C101×#18931 #38801082

Order 25856.

986 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3543C211yesmaximal, characteristic
2C101×#3252C211yesmaximal, characteristic, complemented
3C101×#3233C211yesmaximal, characteristic, complemented
4C101×#3208C211yesmaximal, characteristic, complemented
5C101×#1642C211yesmaximal, characteristic, complemented
6C101×#1641C211yesmaximal, characteristic, complemented
7C101×#1640C211yesmaximal, characteristic, complemented
8C101×#1639C211yesmaximal, characteristic, complemented
9C101×#1631C211yesmaximal, characteristic, complemented
10C101×#1631C211yesmaximal, characteristic, complemented
11C101×#1630C211yesmaximal, characteristic, complemented
12C101×#1629C211yesmaximal, 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#533×C101C2211yescharacteristic, complemented
31C2×#127×C101C2211yescharacteristic
32#529×C101C2211yescharacteristic
33#529×C101C2211yescharacteristic
34#499×C101—21no—
35#492×C101C2211yescharacteristic
36#492×C101C2211yescharacteristic, complemented
37#488×C101—21no—
38#486×C101C2211yescharacteristic
39#486×C101C2211yescharacteristic, complemented
40#485×C101—21no—
41#482×C101—21no—
42#479×C101—21no—
43#477×C101C2211yescharacteristic, complemented
44#477×C101C2211yescharacteristic, complemented
45#476×C101C2211yescharacteristic, complemented
46#476×C101C2211yescharacteristic, complemented
47#475×C101C2211yescharacteristic, complemented
48#474×C101C2211yescharacteristic, complemented
49#470×C101—21no—
50#468×C101—21no—
51#464×C101—21no—
52#462×C101C2211yescharacteristic, complemented
53#461×C101C2211yescharacteristic, complemented
54#460×C101—22no—
55#450×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—
73C22×D4×C101—22no—
74C22×D4×C101—21no—
75C22×D4×C101—21no—
76C22×D4×C101—21no—
77C22×D4×C101—21no—
78C22×D4×C101D412yes—
79C2×Q16×C101—21no—
80C2×SD16×C101—22no—
81C2×SD16×C101—22no—
82C2×SD16×C101—21no—
83C2×M16×C101—21no—
84C4⋊Q8×C101C2311yescharacteristic
85C4⋊Q8×C101C2311yescharacteristic
86#127×C101—21no—
87#127×C101—21no—
88#127×C101—21no—
89#127×C101—21no—
90#127×C101D412yes—
91#127×C101C2311yescharacteristic
92#127×C101C2311yescharacteristic
93#126×C101—21no—
94#126×C101—21no—
95#125×C101—21no—
96#125×C101D411yescharacteristic
97#125×C101D411yescharacteristic
98#124×C101—21no—
99#124×C101—21no—
100#124×C101D411yescharacteristic
101#124×C101D411yescharacteristic
102#123×C101—22no—
103#123×C101—22no—
104#123×C101—22no—
105#123×C101—22no—
106#123×C101—21no—
107#123×C101—21no—
108C22⋊Q8×C101—21no—
109C22⋊Q8×C101—21no—
110C22⋊Q8×C101D411yescharacteristic
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—22no—
118#121×C101—22no—
119#121×C101—22no—
120#121×C101—21no—
121#121×C101—21no—
122#121×C101—21no—
123#121×C101—21no—
124#121×C101D411yescharacteristic
125#121×C101D411yescharacteristic
126#120×C101—22no—
127#120×C101—22no—
128#120×C101—22no—
129#120×C101—22no—
130#120×C101—22no—
131#120×C101—22no—
132C4×Q8×C101—21no—
133C4×Q8×C101—21no—
134C4×Q8×C101C2311yescharacteristic
135C4×Q8×C101C2311yescharacteristic
136C4×D4×C101—21no—
137C4×D4×C101—21no—
138C4×D4×C101—21no—
139C4×D4×C101—21no—
140C4×D4×C101—21no—
141C4×D4×C101—21no—
142C4×D4×C101C2311yescharacteristic
143C4×D4×C101C2311yescharacteristic
144#117×C101—21no—
145#117×C101—21no—
146#117×C101—21no—
147C2×C22⋊C4×C101—22no—
148C2×C42×C101C2311yescharacteristic
149#107×C101—21no—
150#107×C101—21no—
151#107×C101—21no—
152#106×C101—21no—
153#106×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#103×C101—21no—
165#103×C101—21no—
166#102×C101—22no—
167#102×C101—22no—
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—
182C2×Q8×C101—21no—
183C2×Q8×C101—21no—
184C2×Q8×C101C2×D411yescharacteristic
185C2×Q8×C101C2×D411yescharacteristic
186C2×D4×C101—21no—
187C2×D4×C101—21no—
188C2×D4×C101—22no—
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—21no—
198C2×D4×C101—21no—
199C2×D4×C101—21no—
200C2×D4×C101—21no—
201C2×D4×C101—81no—
202C2×D4×C101—81no—
203C2×D4×C101—81no—
204C2×D4×C101—81no—
205C2×D4×C101—81no—
206C2×D4×C101—81no—
207C2×D4×C101—81no—
208C2×D4×C101—81no—
209C2×D4×C101—82no—
210C2×D4×C101—84no—
211C2×D4×C101C2×D411yescharacteristic
212C2×D4×C101C2×D411yescharacteristic
213C2×D4×C101C2×D412yes—
214C2×D4×C101C2×D412yes—
215C22×C4×C101—22no—
216C22×C4×C101—22no—
217C22×C4×C101—22no—
218C22×C4×C101—21no—
219C22×C4×C101—21no—
220C22×C4×C101C2×D411yescharacteristic
221C22×C4×C101C2×D411yescharacteristic
222C22×C4×C101C2×D411yescharacteristic
223Q16×C101—81no—
224SD16×C101—81no—
225SD16×C101—82no—
226SD16×C101—82no—
227M16×C101—81no—
228C2×C8×C101—21no—
229C2×C8×C101—21no—
230C2×C8×C101—21no—
231C2×C8×C101—21no—
232C2×C8×C101—21no—
233C2×C8×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—21no—
244C4⋊C4×C101—21no—
245C4⋊C4×C101—21no—
246C4⋊C4×C101—41no—
247C4⋊C4×C101—41no—
248C4⋊C4×C101C2×D411yescharacteristic
249C4⋊C4×C101C2×D411yescharacteristic
250C4⋊C4×C101C2×D411yescharacteristic
251C4⋊C4×C101C2×D411yescharacteristic
252C22⋊C4×C101—22no—
253C22⋊C4×C101—22no—
254C22⋊C4×C101—22no—
255C22⋊C4×C101—22no—
256C22⋊C4×C101—22no—
257C22⋊C4×C101—22no—
258C22⋊C4×C101—21no—
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—21no—
266C22⋊C4×C101—21no—
267C22⋊C4×C101—21no—
268C22⋊C4×C101—41no—
269C42×C101—21no—
270C42×C101—21no—
271C42×C101—41no—
272C42×C101C2×D411yescharacteristic
273C42×C101C2×D411yescharacteristic
274C42×C101C2×D411yescharacteristic
275C42×C101C2411yescharacteristic
276C23×C101—21no—
277C23×C101—21no—
278C23×C101—22no—
279C23×C101—22no—
280C23×C101—44no—
281C23×C101—82no—
282C23×C101—82no—
283C23×C101—82no—
284C23×C101—82no—
285C23×C101—82no—
286C23×C101#12011yescharacteristic
287Q8×C101—21no—
288Q8×C101—21no—
289Q8×C101—21no—
290Q8×C101—21no—
291Q8×C101—42no—
292Q8×C101—41no—
293Q8×C101—41no—
294D4×C101—21no—
295D4×C101—21no—
296D4×C101—21no—
297D4×C101—21no—
298D4×C101—42no—
299D4×C101—42no—
300D4×C101—42no—
301D4×C101—42no—
302D4×C101—41no—
303D4×C101—41no—
304D4×C101—41no—
305D4×C101—41no—
306D4×C101—41no—
307D4×C101—41no—
308D4×C101—41no—
309D4×C101—41no—
310D4×C101—82no—
311D4×C101—82no—
312D4×C101—82no—
313D4×C101—82no—
314D4×C101—82no—
315D4×C101—82no—
316D4×C101—82no—
317D4×C101—82no—
318D4×C101—82no—
319C2×C4×C101—21no—
320C2×C4×C101—21no—
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—21no—
329C2×C4×C101—41no—
330C2×C4×C101—41no—
331C2×C4×C101—41no—
332C2×C4×C101—41no—
333C2×C4×C101—41no—
334C2×C4×C101—41no—
335C2×C4×C101—41no—
336C2×C4×C101—82no—
337C2×C4×C101—82no—
338C2×C4×C101—82no—
339C2×C4×C101#12011yescharacteristic
340C2×C4×C101#12011yescharacteristic
341C2×C4×C101#12011yescharacteristic
342C2×C4×C101C22×D411yescharacteristic
343C2×C4×C101C22×D411yescharacteristic
344C2×C4×C101C22×D411yescharacteristic
345C8×C101—41no—
346C8×C101—41no—
347C8×C101—41no—
348C8×C101—41no—
349C8×C101—41no—
350C8×C101—41no—
351C22×C101—21no—
352C22×C101—21no—
353C22×C101—21no—
354C22×C101—41no—
355C22×C101—42no—
356C22×C101—41no—
357C22×C101—42no—
358C22×C101—41no—
359C22×C101—42no—
360C22×C101—41no—
361C22×C101—42no—
362C22×C101—42no—
363C22×C101—41no—
364C22×C101—41no—
365C22×C101—42no—
366C22×C101—164no—
367C22×C101—164no—
368C22×C101C2×#12011yescharacteristic
369C4×C101—21no—
370C4×C101—21no—
371C4×C101—21no—
372C4×C101—21no—
373C4×C101—41no—
374C4×C101—41no—
375C4×C101—41no—
376C4×C101—41no—
377C4×C101—41no—
378C4×C101—41no—
379C4×C101—81no—
380C4×C101—81no—
381C4×C101#57611yescharacteristic
382C4×C101#57711yescharacteristic
383C4×C101#57711yescharacteristic
384C4×C101#57711yescharacteristic
385#18931C10111yesmaximal, characteristic, direct product factor, Sylow
386C2×C101—41no—
387C2×C101—82no—
388C2×C101—81no—
389C2×C101—81no—
390C2×C101—82no—
391C2×C101#300911yescharacteristic
392C2×C101#301211yescharacteristic
393C2×C101#301911yescharacteristic
394#3543C2×C10111yescharacteristic
395#3252C2×C10111yescharacteristic, complemented
396#3233C2×C10111yescharacteristic, complemented
397#3208C2×C10111yescharacteristic, complemented
398#1642C2×C10111yescharacteristic, complemented
399#1641C2×C10111yescharacteristic, complemented
400#1640C2×C10111yescharacteristic, complemented
401#1639C2×C10111yescharacteristic, complemented
402#1631C2×C10111yescharacteristic, complemented
403#1631C2×C10111yescharacteristic, complemented
404#1630C2×C10111yescharacteristic, complemented
405#1629C2×C10111yescharacteristic, complemented
406#1545C2×C10111yescharacteristic, complemented
407#1495C2×C10111yescharacteristic, complemented
408#1482C2×C10111yescharacteristic, complemented
409C101#1893111yescharacteristic, direct product factor, Sylow
410#560—22no—
411#559C22×C10111yescharacteristic
412#550C22×C10111yescharacteristic
413#550C22×C10111yescharacteristic
414#546—21no—
415#546—21no—
416D42—21no—
417D42—21no—
418D42C22×C10111yescharacteristic
419#540—21no—
420#540—21no—
421#535—21no—
422#535—21no—
423#534—22no—
424#533C22×C10111yescharacteristic, complemented
425C2×#127C22×C10111yescharacteristic
426#529C22×C10111yescharacteristic
427#529C22×C10111yescharacteristic
428#499—21no—
429#492C22×C10111yescharacteristic
430#492C22×C10111yescharacteristic, complemented
431#488—21no—
432#486C22×C10111yescharacteristic
433#486C22×C10111yescharacteristic, complemented
434#485—21no—
435#482—21no—
436#479—21no—
437#477C22×C10111yescharacteristic, complemented
438#477C22×C10111yescharacteristic, complemented
439#476C22×C10111yescharacteristic, complemented
440#476C22×C10111yescharacteristic, complemented
441#475C22×C10111yescharacteristic, complemented
442#474C22×C10111yescharacteristic, complemented
443#470—21no—
444#468—21no—
445#464—21no—
446#462C22×C10111yescharacteristic, complemented
447#461C22×C10111yescharacteristic, complemented
448#460—22no—
449#450—22no—
450#431C22×C10111yescharacteristic, complemented
451#431C22×C10111yescharacteristic, complemented
452#423C22×C10111yescharacteristic, complemented
453#331C22×C10111yescharacteristic
454#331C22×C10111yescharacteristic
455#331C22×C10111yescharacteristic, complemented
456#331C22×C10111yescharacteristic, complemented
457Q8⋊C8C22×C10111yescharacteristic, complemented
458Q8⋊C8C22×C10111yescharacteristic, complemented
459Q8⋊C8C22×C10111yescharacteristic, complemented
460Q8⋊C8C22×C10111yescharacteristic, complemented
461D4⋊C8C22×C10111yescharacteristic, complemented
462D4⋊C8C22×C10111yescharacteristic, complemented
463D4⋊C8C22×C10111yescharacteristic, complemented
464D4⋊C8C22×C10111yescharacteristic, complemented
465C2×#41—21no—
466C2×#41—21no—
467C22×D4—22no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4D4×C10112yes—
473C2×Q16—21no—
474C2×SD16—22no—
475C2×SD16—22no—
476C2×SD16—21no—
477C2×M16—21no—
478C4⋊Q8C23×C10111yescharacteristic
479C4⋊Q8C23×C10111yescharacteristic
480#127—21no—
481#127—21no—
482#127—21no—
483#127—21no—
484#127D4×C10112yes—
485#127C23×C10111yescharacteristic
486#127C23×C10111yescharacteristic
487#126—21no—
488#126—21no—
489#125—21no—
490#125D4×C10111yescharacteristic
491#125D4×C10111yescharacteristic
492#124—21no—
493#124—21no—
494#124D4×C10111yescharacteristic
495#124D4×C10111yescharacteristic
496#123—22no—
497#123—22no—
498#123—22no—
499#123—22no—
500#123—21no—
501#123—21no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8D4×C10111yescharacteristic
505C22⋊Q8D4×C10111yescharacteristic
506#121—22no—
507#121—22no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121D4×C10111yescharacteristic
519#121D4×C10111yescharacteristic
520#120—22no—
521#120—22no—
522#120—22no—
523#120—22no—
524#120—22no—
525#120—22no—
526C4×Q8—21no—
527C4×Q8—21no—
528C4×Q8C23×C10111yescharacteristic
529C4×Q8C23×C10111yescharacteristic
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4C23×C10111yescharacteristic
537C4×D4C23×C10111yescharacteristic
538#117—21no—
539#117—21no—
540#117—21no—
541C2×C22⋊C4—22no—
542C2×C42C23×C10111yescharacteristic
543#107—21no—
544#107—21no—
545#107—21no—
546#106—21no—
547#106—21no—
548#106—21no—
549C4⋊C8—21no—
550C4⋊C8—21no—
551C4⋊C8C23×C10111yescharacteristic
552C4⋊C8C23×C10111yescharacteristic
553C4⋊C8C23×C10111yescharacteristic
554C4⋊C8C23×C10111yescharacteristic
555#103—21no—
556#103—21no—
557#103—21no—
558#103—21no—
559#103—21no—
560#102—22no—
561#102—22no—
562#102—21no—
563#102—21no—
564#102—21no—
565C22⋊C8—21no—
566C22⋊C8—21no—
567C4×C8—21no—
568C4×C8C23×C10111yescharacteristic
569C4×C8C23×C10111yescharacteristic
570C24—22no—
571C24—22no—
572#41—81no—
573#41—81no—
574#41—81no—
575#41—81no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8C2×D4×C10111yescharacteristic
579C2×Q8C2×D4×C10111yescharacteristic
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4—81no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—82no—
604C2×D4—84no—
605C2×D4C2×D4×C10111yescharacteristic
606C2×D4C2×D4×C10111yescharacteristic
607C2×D4C2×D4×C10112yes—
608C2×D4C2×D4×C10112yes—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4C2×D4×C10111yescharacteristic
615C22×C4C2×D4×C10111yescharacteristic
616C22×C4C2×D4×C10111yescharacteristic
617Q16—81no—
618SD16—81no—
619SD16—82no—
620SD16—82no—
621M16—81no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4C2×D4×C10111yescharacteristic
643C4⋊C4C2×D4×C10111yescharacteristic
644C4⋊C4C2×D4×C10111yescharacteristic
645C4⋊C4C2×D4×C10111yescharacteristic
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—41no—
663C42—21no—
664C42—21no—
665C42—41no—
666C42C2×D4×C10111yescharacteristic
667C42C2×D4×C10111yescharacteristic
668C42C2×D4×C10111yescharacteristic
669C42C24×C10111yescharacteristic
670C23—21no—
671C23—21no—
672C23—22no—
673C23—22no—
674C23—44no—
675C23—82no—
676C23—82no—
677C23—82no—
678C23—82no—
679C23—82no—
680C23#120×C10111yescharacteristic
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—42no—
686Q8—41no—
687Q8—41no—
688D4—21no—
689D4—21no—
690D4—21no—
691D4—21no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—82no—
705D4—82no—
706D4—82no—
707D4—82no—
708D4—82no—
709D4—82no—
710D4—82no—
711D4—82no—
712D4—82no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4#120×C10111yescharacteristic
734C2×C4#120×C10111yescharacteristic
735C2×C4#120×C10111yescharacteristic
736C2×C4C22×D4×C10111yescharacteristic
737C2×C4C22×D4×C10111yescharacteristic
738C2×C4C22×D4×C10111yescharacteristic
739C8—41no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—42no—
752C22—41no—
753C22—42no—
754C22—41no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—164no—
761C22—164no—
762C22C2×#120×C10111yescharacteristic
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—81no—
774C4—81no—
775C4#576×C10111yescharacteristic
776C4#577×C10111yescharacteristic
777C4#577×C10111yescharacteristic
778C4#577×C10111yescharacteristic
779C2—41no—
780C2—81no—
781C2—81no—
782C2—82no—
783C2—82no—
784C2C101×#300911yescharacteristic
785C2C101×#301211yescharacteristic
786C2C101×#301911yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3543C2
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×#3252C2semidirect
3. C101×#3233C2semidirect
4. C101×#3208C2semidirect
5. C101×#1642C2semidirect
6. C101×#1641C2semidirect
7. C101×#1640C2semidirect
8. C101×#1639C2semidirect
9. C101×#1631C2semidirect
10. C101×#1631C2semidirect
11. C101×#1630C2semidirect
12. C101×#1629C2semidirect
13. C101×#1545C2semidirect
14. C101×#1495C2semidirect
15. C101×#1482C2semidirect
30. #533×C101C22semidirect
36. #492×C101C22semidirect
39. #486×C101C22semidirect
43. #477×C101C22semidirect
44. #477×C101C22semidirect
45. #476×C101C22semidirect
46. #476×C101C22semidirect
47. #475×C101C22semidirect
48. #474×C101C22semidirect
52. #462×C101C22semidirect
53. #461×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
385. #18931C101direct (N × H)
395. #3252C2×C101semidirect
396. #3233C2×C101semidirect
397. #3208C2×C101semidirect
398. #1642C2×C101semidirect
399. #1641C2×C101semidirect
400. #1640C2×C101semidirect
401. #1639C2×C101semidirect
402. #1631C2×C101semidirect
403. #1631C2×C101semidirect
404. #1630C2×C101semidirect
405. #1629C2×C101semidirect
406. #1545C2×C101semidirect
407. #1495C2×C101semidirect
408. #1482C2×C101semidirect
409. C101#18931direct (N × H)
424. #533C22×C101semidirect
430. #492C22×C101semidirect
433. #486C22×C101semidirect
437. #477C22×C101semidirect
438. #477C22×C101semidirect
439. #476C22×C101semidirect
440. #476C22×C101semidirect
441. #475C22×C101semidirect
442. #474C22×C101semidirect
446. #462C22×C101semidirect
447. #461C22×C101semidirect
450. #431C22×C101semidirect
451. #431C22×C101semidirect
452. #423C22×C101semidirect
455. #331C22×C101semidirect
456. #331C22×C101semidirect
457. Q8⋊C8C22×C101semidirect
458. Q8⋊C8C22×C101semidirect
459. Q8⋊C8C22×C101semidirect
460. Q8⋊C8C22×C101semidirect
461. D4⋊C8C22×C101semidirect
462. D4⋊C8C22×C101semidirect
463. D4⋊C8C22×C101semidirect
464. 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×#32522
C101×#32332
C101×#32082
C101×#16422
C101×#16412
C101×#16402
C101×#16392
C101×#16312
C101×#16302
C101×#16292
C101×#15452
C101×#14952
C101×#14822
#18931101