Finite Group Databasebeta

← C101×#18606 #38800757

Subgroups — C101×#18606 #38800757

Order 25856.

984 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3517C211yesmaximal, characteristic, complemented
2C101×#3251C211yesmaximal, characteristic, complemented
3C101×#3184C211yesmaximal, characteristic, complemented
4C101×#3035C211yesmaximal, characteristic, complemented
5C101×#1654C211yesmaximal, characteristic, complemented
6C101×#1653C211yesmaximal, characteristic, complemented
7C101×#1642C211yesmaximal, characteristic, complemented
8C101×#1641C211yesmaximal, characteristic, complemented
9C101×#1626C211yesmaximal, characteristic, complemented
10C101×#1625C211yesmaximal, characteristic, complemented
11C101×#1621C211yesmaximal, characteristic, complemented
12C101×#1621C211yesmaximal, characteristic, complemented
13C101×#1547C211yesmaximal, characteristic, complemented
14C101×#1489C211yesmaximal, characteristic, complemented
15C101×#1483C211yesmaximal, characteristic, complemented
16C2×#135×C101—21no—
17#557×C101C2211yescharacteristic
18#553×C101—22no—
19#553×C101—21no—
20#550×C101—21no—
21#550×C101—21no—
22#550×C101C2211yescharacteristic
23#550×C101C2211yescharacteristic
24#547×C101—21no—
25#547×C101C2211yescharacteristic
26#540×C101—22no—
27#540×C101—21no—
28#532×C101—21no—
29#532×C101C2211yescharacteristic
30#532×C101C2211yescharacteristic
31#529×C101—21no—
32#529×C101C2211yescharacteristic
33#520×C101—21no—
34C4×#41×C101C2211yescharacteristic
35#498×C101C2211yescharacteristic
36#493×C101C2211yescharacteristic
37#486×C101C2211yescharacteristic
38#486×C101C2211yescharacteristic
39#478×C101—21no—
40#475×C101C2211yescharacteristic
41#474×C101C2211yescharacteristic
42#469×C101—22no—
43#469×C101—21no—
44#468×C101—21no—
45#464×C101—21no—
46#463×C101—21no—
47#463×C101—21no—
48#462×C101C2211yescharacteristic
49#461×C101C2211yescharacteristic
50#460×C101C2211yescharacteristic
51#460×C101C2211yescharacteristic
52#459×C101C2211yescharacteristic
53#459×C101C2211yescharacteristic
54#442×C101—22no—
55#423×C101C2211yescharacteristic
56C2×C4⋊C8×C101C2211yescharacteristic
57#416×C101—21no—
58C4×M16×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62#331×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64Q8⋊C8×C101C2211yescharacteristic
65Q8⋊C8×C101C2211yescharacteristic
66Q8⋊C8×C101C2211yescharacteristic
67D4⋊C8×C101C2211yescharacteristic
68D4⋊C8×C101C2211yescharacteristic
69D4⋊C8×C101C2211yescharacteristic
70D4⋊C8×C101C2211yescharacteristic
71C2×#41×C101—21no—
72C2×#41×C101—21no—
73C2×#41×C101—21no—
74C2×#41×C101—21no—
75C2×#41×C101—21no—
76C2×#41×C101D411yescharacteristic
77#135×C101—44no—
78C2×Q16×C101—21no—
79C2×SD16×C101—21no—
80C2×SD16×C101—21no—
81C2×SD16×C101—21no—
82C2×D8×C101—22no—
83C2×D8×C101—21no—
84C2×D8×C101—21no—
85C2×M16×C101—21no—
86C2×M16×C101—21no—
87C22×C8×C101—21no—
88C4⋊Q8×C101—21no—
89C4⋊Q8×C101C2311yescharacteristic
90C4⋊Q8×C101C2311yescharacteristic
91#127×C101—22no—
92#127×C101—21no—
93#127×C101—21no—
94#127×C101C2311yescharacteristic
95#127×C101C2311yescharacteristic
96#126×C101—22no—
97#126×C101—21no—
98#125×C101—22no—
99#125×C101—21no—
100#125×C101D411yescharacteristic
101#124×C101—21no—
102#124×C101—21no—
103#124×C101D411yescharacteristic
104#123×C101—22no—
105#123×C101—22no—
106#123×C101—22no—
107#123×C101—21no—
108#123×C101—22no—
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—22no—
119#121×C101—21no—
120#121×C101—21no—
121#121×C101—21no—
122#121×C101—21no—
123#121×C101—21no—
124#121×C101D411yescharacteristic
125#121×C101D412yes—
126C4×Q8×C101—21no—
127C4×Q8×C101—21no—
128C4×Q8×C101D411yescharacteristic
129C4×Q8×C101C2311yescharacteristic
130C4×Q8×C101C2311yescharacteristic
131C4×D4×C101—22no—
132C4×D4×C101—22no—
133C4×D4×C101—22no—
134C4×D4×C101—22no—
135C4×D4×C101—21no—
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×C101—21no—
143C4×D4×C101D412yes—
144C4×D4×C101D411yescharacteristic
145C4×D4×C101C2311yescharacteristic
146C4×D4×C101C2311yescharacteristic
147#117×C101—22no—
148#117×C101—21no—
149#117×C101—21no—
150#117×C101D411yescharacteristic
151C2×C4⋊C4×C101—22no—
152C2×C4⋊C4×C101—21no—
153C2×C42×C101—21no—
154C2×C42×C101C2311yescharacteristic
155#107×C101—21no—
156#106×C101—22no—
157#106×C101—21no—
158C4⋊C8×C101—21no—
159C4⋊C8×C101—21no—
160C4⋊C8×C101C2311yescharacteristic
161C4⋊C8×C101C2311yescharacteristic
162C4⋊C8×C101C2311yescharacteristic
163C4⋊C8×C101C2311yescharacteristic
164#103×C101—21no—
165#103×C101—21no—
166#103×C101—21no—
167#102×C101—22no—
168#102×C101—21no—
169#102×C101—21no—
170#102×C101—21no—
171#102×C101—22no—
172#102×C101—21no—
173#102×C101—21no—
174#97×C101—21no—
175C4×C8×C101C2311yescharacteristic
176C4×C8×C101C2311yescharacteristic
177#41×C101—22no—
178#41×C101—41no—
179#41×C101—42no—
180#41×C101—42no—
181#41×C101—42no—
182#41×C101—42no—
183#41×C101—81no—
184#41×C101—81no—
185#41×C101—81no—
186#41×C101—81no—
187#41×C101—81no—
188#41×C101—81no—
189C2×Q8×C101—21no—
190C2×Q8×C101—21no—
191C2×Q8×C101C2×D411yescharacteristic
192C2×Q8×C101C2×D411yescharacteristic
193C2×D4×C101—22no—
194C2×D4×C101—21no—
195C2×D4×C101—22no—
196C2×D4×C101—22no—
197C2×D4×C101—22no—
198C2×D4×C101—22no—
199C2×D4×C101—21no—
200C2×D4×C101—22no—
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×C101C2×D411yescharacteristic
208C2×D4×C101C2×D411yescharacteristic
209C2×D4×C101C2×D412yes—
210C22×C4×C101—22no—
211C22×C4×C101—22no—
212C22×C4×C101—22no—
213C22×C4×C101—21no—
214C22×C4×C101—21no—
215C22×C4×C101—21no—
216C22×C4×C101—21no—
217C22×C4×C101—22no—
218C22×C4×C101—41no—
219C22×C4×C101C2×D411yescharacteristic
220C22×C4×C101C2×D411yescharacteristic
221C22×C4×C101C2×D411yescharacteristic
222Q16×C101—42no—
223SD16×C101—42no—
224SD16×C101—42no—
225SD16×C101—81no—
226D8×C101—44no—
227D8×C101—42no—
228D8×C101—81no—
229M16×C101—42no—
230M16×C101—81no—
231C2×C8×C101—21no—
232C2×C8×C101—21no—
233C2×C8×C101—21no—
234C2×C8×C101—21no—
235C2×C8×C101—21no—
236C2×C8×C101—21no—
237C2×C8×C101—42no—
238C4⋊C4×C101—22no—
239C4⋊C4×C101—22no—
240C4⋊C4×C101—22no—
241C4⋊C4×C101—22no—
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×C101—21no—
250C4⋊C4×C101—21no—
251C4⋊C4×C101C2×D411yescharacteristic
252C4⋊C4×C101C2×D411yescharacteristic
253C4⋊C4×C101C2×D412yes—
254C4⋊C4×C101C2×D411yescharacteristic
255C4⋊C4×C101C2×D411yescharacteristic
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—22no—
264C22⋊C4×C101—21no—
265C22⋊C4×C101—21no—
266C22⋊C4×C101—22no—
267C22⋊C4×C101—21no—
268C22⋊C4×C101—21no—
269C22⋊C4×C101—41no—
270C22⋊C4×C101—41no—
271C42×C101—22no—
272C42×C101—21no—
273C42×C101—21no—
274C42×C101—21no—
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—41no—
284C23×C101#12011yescharacteristic
285Q8×C101—21no—
286Q8×C101—21no—
287Q8×C101—21no—
288Q8×C101—41no—
289Q8×C101—41no—
290Q8×C101—41no—
291Q8×C101—41no—
292Q8×C101AGL(1,ℤ/8)12yes—
293D4×C101—21no—
294D4×C101—21no—
295D4×C101—21no—
296D4×C101—21no—
297D4×C101—42no—
298D4×C101—42no—
299D4×C101—44no—
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—82no—
311D4×C101—82no—
312D4×C101—82no—
313D4×C101—82no—
314D4×C101—82no—
315D4×C101—82no—
316C2×C4×C101—21no—
317C2×C4×C101—21no—
318C2×C4×C101—21no—
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—22no—
326C2×C4×C101—21no—
327C2×C4×C101—41no—
328C2×C4×C101—42no—
329C2×C4×C101—44no—
330C2×C4×C101—41no—
331C2×C4×C101—41no—
332C2×C4×C101—41no—
333C2×C4×C101—41no—
334C2×C4×C101—41no—
335C2×C4×C101—81no—
336C2×C4×C101—82no—
337C2×C4×C101—82no—
338C2×C4×C101—82no—
339C2×C4×C101—82no—
340C2×C4×C101#12011yescharacteristic
341C2×C4×C101#12011yescharacteristic
342C2×C4×C101#12011yescharacteristic
343C2×C4×C101C22×D411yescharacteristic
344C2×C4×C101C22×D411yescharacteristic
345C2×C4×C101C22×D411yescharacteristic
346C8×C101—22no—
347C8×C101—41no—
348C8×C101—41no—
349C8×C101—41no—
350C8×C101—41no—
351C8×C101—41no—
352C22×C101—21no—
353C22×C101—21no—
354C22×C101—21no—
355C22×C101—41no—
356C22×C101—42no—
357C22×C101—41no—
358C22×C101—41no—
359C22×C101—41no—
360C22×C101—42no—
361C22×C101—41no—
362C22×C101—42no—
363C22×C101—41no—
364C22×C101—81no—
365C22×C101—81no—
366C22×C101—81no—
367C22×C101C2×#12011yescharacteristic
368C4×C101—21no—
369C4×C101—22no—
370C4×C101—21no—
371C4×C101—21no—
372C4×C101—21no—
373C4×C101—41no—
374C4×C101—41no—
375C4×C101—41no—
376C4×C101—42no—
377C4×C101—41no—
378C4×C101—41no—
379C4×C101—81no—
380C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
381C4×C101#57511yescharacteristic
382C4×C101#57611yescharacteristic
383C4×C101#57711yescharacteristic
384#18606C10111yesmaximal, characteristic, direct product factor, Sylow
385C2×C101—41no—
386C2×C101—81no—
387C2×C101—81no—
388C2×C101—82no—
389C2×C101—161no—
390C2×C101#300611yescharacteristic
391C2×C101#301211yescharacteristic
392C2×C101#301811yescharacteristic
393#3517C2×C10111yescharacteristic, complemented
394#3251C2×C10111yescharacteristic, complemented
395#3184C2×C10111yescharacteristic, complemented
396#3035C2×C10111yescharacteristic, complemented
397#1654C2×C10111yescharacteristic, complemented
398#1653C2×C10111yescharacteristic, complemented
399#1642C2×C10111yescharacteristic, complemented
400#1641C2×C10111yescharacteristic, complemented
401#1626C2×C10111yescharacteristic, complemented
402#1625C2×C10111yescharacteristic, complemented
403#1621C2×C10111yescharacteristic, complemented
404#1621C2×C10111yescharacteristic, complemented
405#1547C2×C10111yescharacteristic, complemented
406#1489C2×C10111yescharacteristic, complemented
407#1483C2×C10111yescharacteristic, complemented
408C101#1860611yescharacteristic, direct product factor, Sylow
409C2×#135—21no—
410#557C22×C10111yescharacteristic
411#553—22no—
412#553—21no—
413#550—21no—
414#550—21no—
415#550C22×C10111yescharacteristic
416#550C22×C10111yescharacteristic
417#547—21no—
418#547C22×C10111yescharacteristic
419#540—22no—
420#540—21no—
421#532—21no—
422#532C22×C10111yescharacteristic
423#532C22×C10111yescharacteristic
424#529—21no—
425#529C22×C10111yescharacteristic
426#520—21no—
427C4×#41C22×C10111yescharacteristic
428#498C22×C10111yescharacteristic
429#493C22×C10111yescharacteristic
430#486C22×C10111yescharacteristic
431#486C22×C10111yescharacteristic
432#478—21no—
433#475C22×C10111yescharacteristic
434#474C22×C10111yescharacteristic
435#469—22no—
436#469—21no—
437#468—21no—
438#464—21no—
439#463—21no—
440#463—21no—
441#462C22×C10111yescharacteristic
442#461C22×C10111yescharacteristic
443#460C22×C10111yescharacteristic
444#460C22×C10111yescharacteristic
445#459C22×C10111yescharacteristic
446#459C22×C10111yescharacteristic
447#442—22no—
448#423C22×C10111yescharacteristic
449C2×C4⋊C8C22×C10111yescharacteristic
450#416—21no—
451C4×M16C22×C10111yescharacteristic
452#332C22×C10111yescharacteristic
453#332C22×C10111yescharacteristic
454#331C22×C10111yescharacteristic
455#331C22×C10111yescharacteristic
456Q8⋊C8C22×C10111yescharacteristic
457Q8⋊C8C22×C10111yescharacteristic
458Q8⋊C8C22×C10111yescharacteristic
459Q8⋊C8C22×C10111yescharacteristic
460D4⋊C8C22×C10111yescharacteristic
461D4⋊C8C22×C10111yescharacteristic
462D4⋊C8C22×C10111yescharacteristic
463D4⋊C8C22×C10111yescharacteristic
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41D4×C10111yescharacteristic
470#135—44no—
471C2×Q16—21no—
472C2×SD16—21no—
473C2×SD16—21no—
474C2×SD16—21no—
475C2×D8—21no—
476C2×D8—22no—
477C2×D8—21no—
478C2×M16—21no—
479C2×M16—21no—
480C22×C8—21no—
481C4⋊Q8—21no—
482C4⋊Q8C23×C10111yescharacteristic
483C4⋊Q8C23×C10111yescharacteristic
484#127—22no—
485#127—21no—
486#127—21no—
487#127C23×C10111yescharacteristic
488#127C23×C10111yescharacteristic
489#126—22no—
490#126—21no—
491#125—22no—
492#125—21no—
493#125D4×C10111yescharacteristic
494#124—21no—
495#124—21no—
496#124D4×C10111yescharacteristic
497#123—22no—
498#123—22no—
499#123—22no—
500#123—21no—
501#123—22no—
502C22⋊Q8—21no—
503C22⋊Q8D4×C10111yescharacteristic
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509#121—21no—
510#121—22no—
511#121—22no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121D4×C10111yescharacteristic
518#121D4×C10112yes—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8D4×C10111yescharacteristic
522C4×Q8C23×C10111yescharacteristic
523C4×Q8C23×C10111yescharacteristic
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4D4×C10111yescharacteristic
537C4×D4D4×C10112yes—
538C4×D4C23×C10111yescharacteristic
539C4×D4C23×C10111yescharacteristic
540#117—22no—
541#117—21no—
542#117—21no—
543#117D4×C10111yescharacteristic
544C2×C4⋊C4—22no—
545C2×C4⋊C4—21no—
546C2×C42—21no—
547C2×C42C23×C10111yescharacteristic
548#107—21no—
549#106—22no—
550#106—21no—
551C4⋊C8—21no—
552C4⋊C8—21no—
553C4⋊C8C23×C10111yescharacteristic
554C4⋊C8C23×C10111yescharacteristic
555C4⋊C8C23×C10111yescharacteristic
556C4⋊C8C23×C10111yescharacteristic
557#103—21no—
558#103—21no—
559#103—21no—
560#102—22no—
561#102—21no—
562#102—21no—
563#102—21no—
564#102—22no—
565#102—21no—
566#102—21no—
567#97—21no—
568C4×C8C23×C10111yescharacteristic
569C4×C8C23×C10111yescharacteristic
570#41—22no—
571#41—41no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576#41—81no—
577#41—81no—
578#41—81no—
579#41—81no—
580#41—81no—
581#41—81no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8C2×D4×C10111yescharacteristic
585C2×Q8C2×D4×C10111yescharacteristic
586C2×D4—22no—
587C2×D4—21no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—22no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—41no—
600C2×D4C2×D4×C10111yescharacteristic
601C2×D4C2×D4×C10111yescharacteristic
602C2×D4C2×D4×C10112yes—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—41no—
612C22×C4C2×D4×C10111yescharacteristic
613C22×C4C2×D4×C10111yescharacteristic
614C22×C4C2×D4×C10111yescharacteristic
615Q16—42no—
616SD16—42no—
617SD16—42no—
618SD16—81no—
619D8—44no—
620D8—42no—
621D8—81no—
622M16—42no—
623M16—81no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—42no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4C2×D4×C10111yescharacteristic
645C4⋊C4C2×D4×C10111yescharacteristic
646C4⋊C4C2×D4×C10112yes—
647C4⋊C4C2×D4×C10111yescharacteristic
648C4⋊C4C2×D4×C10111yescharacteristic
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—22no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—22no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—41no—
663C22⋊C4—41no—
664C42—22no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42C2×D4×C10111yescharacteristic
670C42C2×D4×C10111yescharacteristic
671C42C2×D4×C10111yescharacteristic
672C42C24×C10111yescharacteristic
673C23—21no—
674C23—21no—
675C23—22no—
676C23—41no—
677C23#120×C10111yescharacteristic
678Q8—21no—
679Q8—21no—
680Q8—21no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8AGL(1,ℤ/8)×C10112yes—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—21no—
690D4—42no—
691D4—42no—
692D4—44no—
693D4—42no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—82no—
703D4—81no—
704D4—82no—
705D4—82no—
706D4—82no—
707D4—82no—
708D4—82no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—82no—
729C2×C4—81no—
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—22no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—42no—
754C22—41no—
755C22—42no—
756C22—41no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22C2×#120×C10111yescharacteristic
761C4—21no—
762C4—22no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—81no—
773C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
774C4#575×C10111yescharacteristic
775C4#576×C10111yescharacteristic
776C4#577×C10111yescharacteristic
777C2—41no—
778C2—81no—
779C2—81no—
780C2—82no—
781C2—161no—
782C2C101×#300611yescharacteristic
783C2C101×#301211yescharacteristic
784C2C101×#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×#3517C2semidirect
2. C101×#3251C2semidirect
3. C101×#3184C2semidirect
4. C101×#3035C2semidirect
5. C101×#1654C2semidirect
6. C101×#1653C2semidirect
7. C101×#1642C2semidirect
8. C101×#1641C2semidirect
9. C101×#1626C2semidirect
10. C101×#1625C2semidirect
11. C101×#1621C2semidirect
12. C101×#1621C2semidirect
13. C101×#1547C2semidirect
14. C101×#1489C2semidirect
15. C101×#1483C2semidirect
384. #18606C101direct (N × H)
393. #3517C2×C101semidirect
394. #3251C2×C101semidirect
395. #3184C2×C101semidirect
396. #3035C2×C101semidirect
397. #1654C2×C101semidirect
398. #1653C2×C101semidirect
399. #1642C2×C101semidirect
400. #1641C2×C101semidirect
401. #1626C2×C101semidirect
402. #1625C2×C101semidirect
403. #1621C2×C101semidirect
404. #1621C2×C101semidirect
405. #1547C2×C101semidirect
406. #1489C2×C101semidirect
407. #1483C2×C101semidirect
408. C101#18606direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#35172
C101×#32512
C101×#31842
C101×#30352
C101×#16542
C101×#16532
C101×#16422
C101×#16412
C101×#16262
C101×#16252
C101×#16212
C101×#15472
C101×#14892
C101×#14832
#18606101