Finite Group Databasebeta

← C101×#18594 #38800745

Subgroups — C101×#18594 #38800745

Order 25856.

994 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×#3514C211yesmaximal, characteristic, complemented
2C101×#3251C211yesmaximal, characteristic, complemented
3C101×#3184C211yesmaximal, characteristic, complemented
4C101×#3035C211yesmaximal, characteristic, complemented
5C101×#1652C211yesmaximal, characteristic, complemented
6C101×#1651C211yesmaximal, characteristic, complemented
7C101×#1640C211yesmaximal, characteristic, complemented
8C101×#1639C211yesmaximal, characteristic, complemented
9C101×#1628C211yesmaximal, characteristic, complemented
10C101×#1627C211yesmaximal, characteristic, complemented
11C101×#1620C211yesmaximal, characteristic, complemented
12C101×#1619C211yesmaximal, characteristic, complemented
13C101×#1547C211yesmaximal, characteristic, complemented
14C101×#1489C211yesmaximal, characteristic, complemented
15C101×#1483C211yesmaximal, characteristic, complemented
16C2×#135×C101—21no—
17#559×C101C2211yescharacteristic
18#556×C101C2211yescharacteristic
19#555×C101—21no—
20#551×C101—22no—
21D4×Q8×C101C2211yescharacteristic
22#548×C101—21no—
23#546×C101—21no—
24#546×C101—21no—
25D42×C101C2211yescharacteristic
26#542×C101—21no—
27#538×C101—22no—
28#532×C101C2211yescharacteristic
29#532×C101C2211yescharacteristic, complemented
30#529×C101—21no—
31#529×C101C2211yescharacteristic
32C2×#124×C101—21no—
33#518×C101—21no—
34C4×#41×C101C2211yescharacteristic
35#498×C101C2211yescharacteristic, complemented
36#493×C101C2211yescharacteristic
37#486×C101C2211yescharacteristic
38#486×C101C2211yescharacteristic, complemented
39#478×C101—21no—
40#475×C101C2211yescharacteristic, complemented
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, complemented
49#461×C101C2211yescharacteristic
50#460×C101C2211yescharacteristic, complemented
51#460×C101C2211yescharacteristic, complemented
52#459×C101C2211yescharacteristic
53#459×C101C2211yescharacteristic
54#442×C101—22no—
55#423×C101C2211yescharacteristic, complemented
56C2×C4⋊C8×C101C2211yescharacteristic, complemented
57#416×C101—21no—
58C4×M16×C101C2211yescharacteristic, complemented
59#332×C101C2211yescharacteristic, complemented
60#332×C101C2211yescharacteristic, complemented
61#331×C101C2211yescharacteristic
62#331×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic, complemented
64Q8⋊C8×C101C2211yescharacteristic, complemented
65Q8⋊C8×C101C2211yescharacteristic, complemented
66Q8⋊C8×C101C2211yescharacteristic, complemented
67D4⋊C8×C101C2211yescharacteristic
68D4⋊C8×C101C2211yescharacteristic
69D4⋊C8×C101C2211yescharacteristic
70D4⋊C8×C101C2211yescharacteristic
71C2×#41×C101—21no—
72C2×#41×C101—21no—
73C2×#41×C101D411yescharacteristic
74C22×Q8×C101—21no—
75C22×D4×C101—21no—
76C22×D4×C101—21no—
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×C101C2311yescharacteristic
92#127×C101C2311yescharacteristic
93#126×C101—22no—
94#126×C101—22no—
95#126×C101—21no—
96#125×C101D411yescharacteristic
97#124×C101—22no—
98#124×C101—22no—
99#124×C101—22no—
100#124×C101—21no—
101#124×C101—21no—
102#124×C101—21no—
103#124×C101—21no—
104#124×C101—21no—
105#124×C101D411yescharacteristic
106#123×C101—22no—
107#123×C101—22no—
108#123×C101—22no—
109#123×C101—21no—
110C22⋊Q8×C101—22no—
111C22⋊Q8×C101—21no—
112C22⋊Q8×C101—21no—
113C22⋊Q8×C101—22no—
114C22⋊Q8×C101D411yescharacteristic
115#121×C101—22no—
116#121×C101—22no—
117#121×C101—21no—
118#121×C101—21no—
119#121×C101—21no—
120#121×C101—21no—
121#121×C101—21no—
122#121×C101D411yescharacteristic
123#121×C101D412yes—
124#120×C101—22no—
125#120×C101—22no—
126C4×Q8×C101—21no—
127C4×Q8×C101D411yescharacteristic
128C4×Q8×C101C2311yescharacteristic
129C4×Q8×C101C2311yescharacteristic
130C4×D4×C101—22no—
131C4×D4×C101—22no—
132C4×D4×C101—21no—
133C4×D4×C101—21no—
134C4×D4×C101—21no—
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×C101D412yes—
142C4×D4×C101D411yescharacteristic
143C4×D4×C101C2311yescharacteristic
144C4×D4×C101C2311yescharacteristic
145#117×C101—22no—
146#117×C101—21no—
147#117×C101—21no—
148#117×C101—21no—
149#117×C101D411yescharacteristic
150C2×C22⋊C4×C101—22no—
151C2×C22⋊C4×C101—22no—
152C2×C22⋊C4×C101—22no—
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
177C24×C101—22no—
178#41×C101—22no—
179#41×C101—41no—
180#41×C101—42no—
181#41×C101—42no—
182#41×C101—81no—
183#41×C101—81no—
184C2×Q8×C101—22no—
185C2×Q8×C101—21no—
186C2×Q8×C101—21no—
187C2×Q8×C101—81no—
188C2×Q8×C101—81no—
189C2×Q8×C101C2×D411yescharacteristic
190C2×Q8×C101C2×D411yescharacteristic
191C2×D4×C101—22no—
192C2×D4×C101—21no—
193C2×D4×C101—22no—
194C2×D4×C101—21no—
195C2×D4×C101—22no—
196C2×D4×C101—21no—
197C2×D4×C101—21no—
198C2×D4×C101—21no—
199C2×D4×C101—21no—
200C2×D4×C101—21no—
201C2×D4×C101—42no—
202C2×D4×C101—42no—
203C2×D4×C101—41no—
204C2×D4×C101—81no—
205C2×D4×C101—81no—
206C2×D4×C101C2×D411yescharacteristic
207C2×D4×C101C2×D411yescharacteristic
208C2×D4×C101C2×D412yes—
209C22×C4×C101—22no—
210C22×C4×C101—22no—
211C22×C4×C101—21no—
212C22×C4×C101—21no—
213C22×C4×C101—21no—
214C22×C4×C101—21no—
215C22×C4×C101—22no—
216C22×C4×C101—41no—
217C22×C4×C101C2×D411yescharacteristic
218C22×C4×C101C2×D411yescharacteristic
219C22×C4×C101C2×D411yescharacteristic
220Q16×C101—42no—
221SD16×C101—42no—
222SD16×C101—42no—
223SD16×C101—81no—
224D8×C101—44no—
225D8×C101—42no—
226D8×C101—81no—
227M16×C101—42no—
228M16×C101—81no—
229C2×C8×C101—21no—
230C2×C8×C101—21no—
231C2×C8×C101—21no—
232C2×C8×C101—21no—
233C2×C8×C101—21no—
234C2×C8×C101—21no—
235C2×C8×C101—42no—
236C4⋊C4×C101—22no—
237C4⋊C4×C101—22no—
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—21no—
247C4⋊C4×C101C2×D411yescharacteristic
248C4⋊C4×C101C2×D411yescharacteristic
249C4⋊C4×C101C2×D411yescharacteristic
250C4⋊C4×C101C2×D412yes—
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—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—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—44no—
284C23×C101—41no—
285C23×C101—82no—
286C23×C101—82no—
287C23×C101#12011yescharacteristic
288Q8×C101—21no—
289Q8×C101—21no—
290Q8×C101—21no—
291Q8×C101—21no—
292Q8×C101—41no—
293Q8×C101—41no—
294Q8×C101—41no—
295Q8×C101—41no—
296Q8×C101—82no—
297D4×C101—21no—
298D4×C101—21no—
299D4×C101—21no—
300D4×C101—42no—
301D4×C101—42no—
302D4×C101—42no—
303D4×C101—44no—
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—82no—
314D4×C101—82no—
315D4×C101—82no—
316D4×C101AGL(1,ℤ/8)12yes—
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—21no—
326C2×C4×C101—21no—
327C2×C4×C101—22no—
328C2×C4×C101—41no—
329C2×C4×C101—42no—
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—22no—
354C22×C101—21no—
355C22×C101—21no—
356C22×C101—41no—
357C22×C101—41no—
358C22×C101—41no—
359C22×C101—42no—
360C22×C101—42no—
361C22×C101—41no—
362C22×C101—42no—
363C22×C101—41no—
364C22×C101—81no—
365C22×C101—81no—
366C22×C101—81no—
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—42no—
377C4×C101—41no—
378C4×C101—41no—
379C4×C101—41no—
380C4×C101—81no—
381C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
382C4×C101#57511yescharacteristic
383C4×C101#57611yescharacteristic
384C4×C101#57711yescharacteristic
385#18594C10111yesmaximal, characteristic, direct product factor, Sylow
386C2×C101—41no—
387C2×C101—42no—
388C2×C101—82no—
389C2×C101—81no—
390C2×C101—161no—
391C2×C101#300611yescharacteristic
392C2×C101#301211yescharacteristic
393C2×C101#301811yescharacteristic
394#3514C2×C10111yescharacteristic, complemented
395#3251C2×C10111yescharacteristic, complemented
396#3184C2×C10111yescharacteristic, complemented
397#3035C2×C10111yescharacteristic, complemented
398#1652C2×C10111yescharacteristic, complemented
399#1651C2×C10111yescharacteristic, complemented
400#1640C2×C10111yescharacteristic, complemented
401#1639C2×C10111yescharacteristic, complemented
402#1628C2×C10111yescharacteristic, complemented
403#1627C2×C10111yescharacteristic, complemented
404#1620C2×C10111yescharacteristic, complemented
405#1619C2×C10111yescharacteristic, complemented
406#1547C2×C10111yescharacteristic, complemented
407#1489C2×C10111yescharacteristic, complemented
408#1483C2×C10111yescharacteristic, complemented
409C101#1859411yescharacteristic, direct product factor, Sylow
410C2×#135—21no—
411#559C22×C10111yescharacteristic
412#556C22×C10111yescharacteristic
413#555—21no—
414#551—22no—
415D4×Q8C22×C10111yescharacteristic
416#548—21no—
417#546—21no—
418#546—21no—
419D42C22×C10111yescharacteristic
420#542—21no—
421#538—22no—
422#532C22×C10111yescharacteristic
423#532C22×C10111yescharacteristic, complemented
424#529—21no—
425#529C22×C10111yescharacteristic
426C2×#124—21no—
427#518—21no—
428C4×#41C22×C10111yescharacteristic
429#498C22×C10111yescharacteristic, complemented
430#493C22×C10111yescharacteristic
431#486C22×C10111yescharacteristic
432#486C22×C10111yescharacteristic, complemented
433#478—21no—
434#475C22×C10111yescharacteristic, complemented
435#474C22×C10111yescharacteristic
436#469—22no—
437#469—21no—
438#468—21no—
439#464—21no—
440#463—21no—
441#463—21no—
442#462C22×C10111yescharacteristic, complemented
443#461C22×C10111yescharacteristic
444#460C22×C10111yescharacteristic, complemented
445#460C22×C10111yescharacteristic, complemented
446#459C22×C10111yescharacteristic
447#459C22×C10111yescharacteristic
448#442—22no—
449#423C22×C10111yescharacteristic, complemented
450C2×C4⋊C8C22×C10111yescharacteristic, complemented
451#416—21no—
452C4×M16C22×C10111yescharacteristic, complemented
453#332C22×C10111yescharacteristic, complemented
454#332C22×C10111yescharacteristic, complemented
455#331C22×C10111yescharacteristic
456#331C22×C10111yescharacteristic
457Q8⋊C8C22×C10111yescharacteristic, complemented
458Q8⋊C8C22×C10111yescharacteristic, complemented
459Q8⋊C8C22×C10111yescharacteristic, complemented
460Q8⋊C8C22×C10111yescharacteristic, complemented
461D4⋊C8C22×C10111yescharacteristic
462D4⋊C8C22×C10111yescharacteristic
463D4⋊C8C22×C10111yescharacteristic
464D4⋊C8C22×C10111yescharacteristic
465C2×#41—21no—
466C2×#41—21no—
467C2×#41D4×C10111yescharacteristic
468C22×Q8—21no—
469C22×D4—21no—
470C22×D4—21no—
471#135—44no—
472C2×Q16—21no—
473C2×SD16—21no—
474C2×SD16—21no—
475C2×SD16—21no—
476C2×D8—21no—
477C2×D8—22no—
478C2×D8—21no—
479C2×M16—21no—
480C2×M16—21no—
481C22×C8—21no—
482C4⋊Q8—21no—
483C4⋊Q8C23×C10111yescharacteristic
484C4⋊Q8C23×C10111yescharacteristic
485#127C23×C10111yescharacteristic
486#127C23×C10111yescharacteristic
487#126—22no—
488#126—22no—
489#126—21no—
490#125D4×C10111yescharacteristic
491#124—22no—
492#124—22no—
493#124—22no—
494#124—21no—
495#124—21no—
496#124—21no—
497#124—21no—
498#124—21no—
499#124D4×C10111yescharacteristic
500#123—22no—
501#123—22no—
502#123—22no—
503#123—21no—
504C22⋊Q8—22no—
505C22⋊Q8—21no—
506C22⋊Q8—21no—
507C22⋊Q8—22no—
508C22⋊Q8D4×C10111yescharacteristic
509#121—22no—
510#121—22no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121D4×C10111yescharacteristic
517#121D4×C10112yes—
518#120—22no—
519#120—22no—
520C4×Q8—21no—
521C4×Q8D4×C10111yescharacteristic
522C4×Q8C23×C10111yescharacteristic
523C4×Q8C23×C10111yescharacteristic
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4D4×C10111yescharacteristic
536C4×D4D4×C10112yes—
537C4×D4C23×C10111yescharacteristic
538C4×D4C23×C10111yescharacteristic
539#117—22no—
540#117—21no—
541#117—21no—
542#117—21no—
543#117D4×C10111yescharacteristic
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C42—21no—
548C2×C42C23×C10111yescharacteristic
549#107—21no—
550#106—22no—
551#106—21no—
552C4⋊C8—21no—
553C4⋊C8—21no—
554C4⋊C8C23×C10111yescharacteristic
555C4⋊C8C23×C10111yescharacteristic
556C4⋊C8C23×C10111yescharacteristic
557C4⋊C8C23×C10111yescharacteristic
558#103—21no—
559#103—21no—
560#103—21no—
561#102—22no—
562#102—21no—
563#102—21no—
564#102—21no—
565#102—22no—
566#102—21no—
567#102—21no—
568#97—21no—
569C4×C8C23×C10111yescharacteristic
570C4×C8C23×C10111yescharacteristic
571C24—22no—
572#41—22no—
573#41—41no—
574#41—42no—
575#41—42no—
576#41—81no—
577#41—81no—
578C2×Q8—22no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—81no—
582C2×Q8—81no—
583C2×Q8C2×D4×C10111yescharacteristic
584C2×Q8C2×D4×C10111yescharacteristic
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—41no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4C2×D4×C10111yescharacteristic
601C2×D4C2×D4×C10111yescharacteristic
602C2×D4C2×D4×C10112yes—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—41no—
611C22×C4C2×D4×C10111yescharacteristic
612C22×C4C2×D4×C10111yescharacteristic
613C22×C4C2×D4×C10111yescharacteristic
614Q16—42no—
615SD16—42no—
616SD16—42no—
617SD16—81no—
618D8—44no—
619D8—42no—
620D8—81no—
621M16—42no—
622M16—81no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—42no—
630C4⋊C4—22no—
631C4⋊C4—22no—
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—21no—
641C4⋊C4C2×D4×C10111yescharacteristic
642C4⋊C4C2×D4×C10111yescharacteristic
643C4⋊C4C2×D4×C10111yescharacteristic
644C4⋊C4C2×D4×C10112yes—
645C4⋊C4C2×D4×C10111yescharacteristic
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—41no—
664C22⋊C4—41no—
665C42—22no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42C2×D4×C10111yescharacteristic
671C42C2×D4×C10111yescharacteristic
672C42C2×D4×C10111yescharacteristic
673C42C24×C10111yescharacteristic
674C23—21no—
675C23—21no—
676C23—22no—
677C23—44no—
678C23—41no—
679C23—82no—
680C23—82no—
681C23#120×C10111yescharacteristic
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—21no—
686Q8—41no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690Q8—82no—
691D4—21no—
692D4—21no—
693D4—21no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—44no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—82no—
707D4—81no—
708D4—82no—
709D4—82no—
710D4AGL(1,ℤ/8)×C10112yes—
711C2×C4—21no—
712C2×C4—21no—
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—22no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—82no—
730C2×C4—81no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4#120×C10111yescharacteristic
735C2×C4#120×C10111yescharacteristic
736C2×C4#120×C10111yescharacteristic
737C2×C4C22×D4×C10111yescharacteristic
738C2×C4C22×D4×C10111yescharacteristic
739C2×C4C22×D4×C10111yescharacteristic
740C8—22no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C22—21no—
747C22—22no—
748C22—21no—
749C22—21no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—42no—
757C22—41no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—164no—
762C22C2×#120×C10111yescharacteristic
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—81no—
775C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
776C4#575×C10111yescharacteristic
777C4#576×C10111yescharacteristic
778C4#577×C10111yescharacteristic
779C2—41no—
780C2—42no—
781C2—81no—
782C2—82no—
783C2—161no—
784C2C101×#300611yescharacteristic
785C2C101×#301211yescharacteristic
786C2C101×#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×#3514C2semidirect
2. C101×#3251C2semidirect
3. C101×#3184C2semidirect
4. C101×#3035C2semidirect
5. C101×#1652C2semidirect
6. C101×#1651C2semidirect
7. C101×#1640C2semidirect
8. C101×#1639C2semidirect
9. C101×#1628C2semidirect
10. C101×#1627C2semidirect
11. C101×#1620C2semidirect
12. C101×#1619C2semidirect
13. C101×#1547C2semidirect
14. C101×#1489C2semidirect
15. C101×#1483C2semidirect
29. #532×C101C22semidirect
35. #498×C101C22semidirect
38. #486×C101C22semidirect
40. #475×C101C22semidirect
48. #462×C101C22semidirect
50. #460×C101C22semidirect
51. #460×C101C22semidirect
55. #423×C101C22semidirect
56. C2×C4⋊C8×C101C22semidirect
58. C4×M16×C101C22semidirect
59. #332×C101C22semidirect
60. #332×C101C22semidirect
63. Q8⋊C8×C101C22semidirect
64. Q8⋊C8×C101C22semidirect
65. Q8⋊C8×C101C22semidirect
66. Q8⋊C8×C101C22semidirect
385. #18594C101direct (N × H)
394. #3514C2×C101semidirect
395. #3251C2×C101semidirect
396. #3184C2×C101semidirect
397. #3035C2×C101semidirect
398. #1652C2×C101semidirect
399. #1651C2×C101semidirect
400. #1640C2×C101semidirect
401. #1639C2×C101semidirect
402. #1628C2×C101semidirect
403. #1627C2×C101semidirect
404. #1620C2×C101semidirect
405. #1619C2×C101semidirect
406. #1547C2×C101semidirect
407. #1489C2×C101semidirect
408. #1483C2×C101semidirect
409. C101#18594direct (N × H)
423. #532C22×C101semidirect
429. #498C22×C101semidirect
432. #486C22×C101semidirect
434. #475C22×C101semidirect
442. #462C22×C101semidirect
444. #460C22×C101semidirect
445. #460C22×C101semidirect
449. #423C22×C101semidirect
450. C2×C4⋊C8C22×C101semidirect
452. C4×M16C22×C101semidirect
453. #332C22×C101semidirect
454. #332C22×C101semidirect
457. Q8⋊C8C22×C101semidirect
458. Q8⋊C8C22×C101semidirect
459. Q8⋊C8C22×C101semidirect
460. Q8⋊C8C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35142
C101×#32512
C101×#31842
C101×#30352
C101×#16522
C101×#16512
C101×#16402
C101×#16392
C101×#16282
C101×#16272
C101×#16202
C101×#16192
C101×#15472
C101×#14892
C101×#14832
#18594101