Finite Group Databasebeta

← C101×#18754 #38800905

Subgroups — C101×#18754 #38800905

Order 25856.

1042 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×#3481C211yesmaximal, characteristic, complemented
2C101×#3207C211yesmaximal, characteristic, complemented
3C101×#3115C211yesmaximal, characteristic, complemented
4C101×#3035C211yesmaximal, characteristic, complemented
5C101×#1644C211yesmaximal, characteristic, complemented
6C101×#1643C211yesmaximal, characteristic, complemented
7C101×#1640C211yesmaximal, characteristic, complemented
8C101×#1639C211yesmaximal, characteristic, complemented
9C101×#1622C211yesmaximal, characteristic, complemented
10C101×#1622C211yesmaximal, characteristic, complemented
11C101×#1620C211yesmaximal, characteristic, complemented
12C101×#1619C211yesmaximal, characteristic, complemented
13C101×#1551C211yesmaximal, characteristic, complemented
14C101×#1488C211yesmaximal, characteristic, complemented
15C101×#1477C211yesmaximal, characteristic, complemented
16C2×#135×C101—21no—
17#559×C101C2211yescharacteristic
18#554×C101C2211yescharacteristic
19#554×C101C2211yescharacteristic
20#553×C101—21no—
21#553×C101—21no—
22#551×C101—22no—
23#546×C101—21no—
24#546×C101—21no—
25D42×C101C2211yescharacteristic
26#532×C101C2211yescharacteristic
27#532×C101C2211yescharacteristic, complemented
28#529×C101—21no—
29#529×C101—21no—
30#525×C101—22no—
31C4×#41×C101C2211yescharacteristic
32C4×#41×C101C2211yescharacteristic
33C2×C4×D4×C101—21no—
34C2×C4×D4×C101—21no—
35#493×C101C2211yescharacteristic
36#492×C101C2211yescharacteristic, complemented
37#487×C101C2211yescharacteristic, complemented
38#486×C101C2211yescharacteristic
39#482×C101—21no—
40#475×C101C2211yescharacteristic, complemented
41#474×C101C2211yescharacteristic
42#464×C101—21no—
43#463×C101—22no—
44#463×C101—21no—
45#462×C101C2211yescharacteristic, complemented
46#461×C101C2211yescharacteristic
47#460×C101C2211yescharacteristic, complemented
48#460×C101C2211yescharacteristic, complemented
49#459×C101C2211yescharacteristic
50#459×C101C2211yescharacteristic
51#449×C101—22no—
52#449×C101—21no—
53#442×C101—21no—
54#440×C101—21no—
55#432×C101C2211yescharacteristic, complemented
56#431×C101C2211yescharacteristic, complemented
57C2×C4⋊C8×C101C2211yescharacteristic, complemented
58#416×C101—21no—
59#333×C101C2211yescharacteristic, complemented
60#333×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×C101D411yescharacteristic
73C2×#41×C101D411yescharacteristic
74C2×#41×C101D412yes—
75C22×D4×C101—21no—
76C22×D4×C101—21no—
77C23×C4×C101—22no—
78#135×C101—44no—
79C2×Q16×C101—21no—
80C2×SD16×C101—21no—
81C2×SD16×C101—21no—
82C2×SD16×C101—21no—
83C2×SD16×C101—22no—
84C2×D8×C101—21no—
85C2×D8×C101—21no—
86C2×D8×C101—22no—
87C22×C8×C101—21no—
88C4⋊Q8×C101C2311yescharacteristic
89C4⋊Q8×C101C2311yescharacteristic
90#127×C101C2311yescharacteristic
91#127×C101C2311yescharacteristic
92#126×C101—22no—
93#126×C101—22no—
94#125×C101—21no—
95#125×C101—21no—
96#124×C101—21no—
97#124×C101—21no—
98#124×C101—21no—
99#124×C101D412yes—
100#123×C101—22no—
101#123×C101—22no—
102#123×C101—22no—
103#123×C101—22no—
104C22⋊Q8×C101—22no—
105C22⋊Q8×C101—22no—
106C22⋊Q8×C101—21no—
107C22⋊Q8×C101—21no—
108#121×C101—22no—
109#121×C101—22no—
110#121×C101—21no—
111#121×C101—21no—
112#121×C101—21no—
113#121×C101—21no—
114#121×C101—21no—
115#121×C101—21no—
116#120×C101—22no—
117#120×C101—22no—
118C4×Q8×C101D411yescharacteristic
119C4×Q8×C101D411yescharacteristic
120C4×Q8×C101C2311yescharacteristic
121C4×Q8×C101C2311yescharacteristic
122C4×D4×C101—22no—
123C4×D4×C101—22no—
124C4×D4×C101—22no—
125C4×D4×C101—22no—
126C4×D4×C101—21no—
127C4×D4×C101—21no—
128C4×D4×C101—21no—
129C4×D4×C101—21no—
130C4×D4×C101—21no—
131C4×D4×C101—21no—
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×C101D411yescharacteristic
139C4×D4×C101D411yescharacteristic
140C4×D4×C101C2311yescharacteristic
141C4×D4×C101C2311yescharacteristic
142#117×C101—22no—
143#117×C101—21no—
144#117×C101—21no—
145#117×C101D411yescharacteristic
146#117×C101D411yescharacteristic
147C2×C4⋊C4×C101—21no—
148C2×C4⋊C4×C101—21no—
149C2×C22⋊C4×C101—22no—
150C2×C22⋊C4×C101—22no—
151C2×C42×C101—21no—
152C2×C42×C101—21no—
153C2×C42×C101C2311yescharacteristic
154#107×C101—21no—
155#106×C101—21no—
156C4⋊C8×C101—21no—
157C4⋊C8×C101—21no—
158C4⋊C8×C101C2311yescharacteristic
159C4⋊C8×C101C2311yescharacteristic
160C4⋊C8×C101C2311yescharacteristic
161C4⋊C8×C101C2311yescharacteristic
162#103×C101—21no—
163#103×C101—22no—
164#103×C101—21no—
165#103×C101—21no—
166#102×C101—21no—
167#102×C101—22no—
168#102×C101—21no—
169#102×C101—21no—
170#102×C101—21no—
171#102×C101—21no—
172C22⋊C8×C101—21no—
173C22⋊C8×C101—21no—
174#97×C101—21no—
175C4×C8×C101C2311yescharacteristic
176C4×C8×C101C2311yescharacteristic
177C24×C101—22no—
178#41×C101—22no—
179#41×C101—22no—
180#41×C101—41no—
181#41×C101—41no—
182#41×C101—42no—
183#41×C101—42no—
184#41×C101—82no—
185C2×Q8×C101—21no—
186C2×Q8×C101C2×D411yescharacteristic
187C2×Q8×C101C2×D411yescharacteristic
188C2×Q8×C101C2×D412yes—
189C2×D4×C101—22no—
190C2×D4×C101—22no—
191C2×D4×C101—21no—
192C2×D4×C101—21no—
193C2×D4×C101—22no—
194C2×D4×C101—21no—
195C2×D4×C101—21no—
196C2×D4×C101—21no—
197C2×D4×C101—21no—
198C2×D4×C101—21no—
199C2×D4×C101—42no—
200C2×D4×C101—42no—
201C2×D4×C101—42no—
202C2×D4×C101—42no—
203C2×D4×C101—41no—
204C2×D4×C101C2×D411yescharacteristic
205C2×D4×C101C2×D411yescharacteristic
206C2×D4×C101C2×D412yes—
207C22×C4×C101—22no—
208C22×C4×C101—22no—
209C22×C4×C101—22no—
210C22×C4×C101—21no—
211C22×C4×C101—21no—
212C22×C4×C101—21no—
213C22×C4×C101—21no—
214C22×C4×C101—22no—
215C22×C4×C101—21no—
216C22×C4×C101—21no—
217C22×C4×C101—41no—
218C22×C4×C101—84no—
219C22×C4×C101C2×D411yescharacteristic
220C22×C4×C101C2×D411yescharacteristic
221C22×C4×C101C2×D411yescharacteristic
222Q16×C101—42no—
223SD16×C101—42no—
224SD16×C101—42no—
225SD16×C101—42no—
226SD16×C101—82no—
227D8×C101—42no—
228D8×C101—42no—
229D8×C101—82no—
230C2×C8×C101—21no—
231C2×C8×C101—21no—
232C2×C8×C101—21no—
233C2×C8×C101—21no—
234C2×C8×C101—21no—
235C2×C8×C101—21no—
236C2×C8×C101—42no—
237C4⋊C4×C101—22no—
238C4⋊C4×C101—22no—
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×D411yescharacteristic
250C4⋊C4×C101C2×D411yescharacteristic
251C4⋊C4×C101C2×D411yescharacteristic
252C4⋊C4×C101C2×D411yescharacteristic
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—22no—
264C22⋊C4×C101—22no—
265C22⋊C4×C101—21no—
266C22⋊C4×C101—21no—
267C22⋊C4×C101—41no—
268C22⋊C4×C101—41no—
269C42×C101—21no—
270C42×C101—21no—
271C42×C101—21no—
272C42×C101—21no—
273C42×C101—21no—
274C42×C101—21no—
275C42×C101C2×D411yescharacteristic
276C42×C101C2×D411yescharacteristic
277C42×C101C2×D411yescharacteristic
278C42×C101C2411yescharacteristic
279C23×C101—21no—
280C23×C101—21no—
281C23×C101—22no—
282C23×C101—44no—
283C23×C101—44no—
284C23×C101—41no—
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—42no—
297D4×C101—42no—
298D4×C101—42no—
299D4×C101—42no—
300D4×C101—44no—
301D4×C101—44no—
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#13512yescomplemented
313D4×C101AGL(1,ℤ/8)12yes—
314C2×C4×C101—21no—
315C2×C4×C101—21no—
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—22no—
325C2×C4×C101—41no—
326C2×C4×C101—42no—
327C2×C4×C101—42no—
328C2×C4×C101—42no—
329C2×C4×C101—42no—
330C2×C4×C101—44no—
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—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—41no—
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—22no—
356C22×C101—21no—
357C22×C101—41no—
358C22×C101—41no—
359C22×C101—41no—
360C22×C101—41no—
361C22×C101—42no—
362C22×C101—42no—
363C22×C101—42no—
364C22×C101—88no—
365C22×C101—81no—
366C22×C101—81no—
367C22×C101—81no—
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—42no—
380C4×C101—81no—
381C4×C101C2×#13511yescharacteristic
382C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
383C4×C101#57511yescharacteristic
384C4×C101#57511yescharacteristic
385#18754C10111yesmaximal, characteristic, direct product factor, Sylow
386C2×C101—41no—
387C2×C101—42no—
388C2×C101—42no—
389C2×C101—82no—
390C2×C101—161no—
391C2×C101#300211yescharacteristic
392C2×C101#300611yescharacteristic
393C2×C101#301911yescharacteristic
394#3481C2×C10111yescharacteristic, complemented
395#3207C2×C10111yescharacteristic, complemented
396#3115C2×C10111yescharacteristic, complemented
397#3035C2×C10111yescharacteristic, complemented
398#1644C2×C10111yescharacteristic, complemented
399#1643C2×C10111yescharacteristic, complemented
400#1640C2×C10111yescharacteristic, complemented
401#1639C2×C10111yescharacteristic, complemented
402#1622C2×C10111yescharacteristic, complemented
403#1622C2×C10111yescharacteristic, complemented
404#1620C2×C10111yescharacteristic, complemented
405#1619C2×C10111yescharacteristic, complemented
406#1551C2×C10111yescharacteristic, complemented
407#1488C2×C10111yescharacteristic, complemented
408#1477C2×C10111yescharacteristic, complemented
409C101#1875411yescharacteristic, direct product factor, Sylow
410C2×#135—21no—
411#559C22×C10111yescharacteristic
412#554C22×C10111yescharacteristic
413#554C22×C10111yescharacteristic
414#553—21no—
415#553—21no—
416#551—22no—
417#546—21no—
418#546—21no—
419D42C22×C10111yescharacteristic
420#532C22×C10111yescharacteristic
421#532C22×C10111yescharacteristic, complemented
422#529—21no—
423#529—21no—
424#525—22no—
425C4×#41C22×C10111yescharacteristic
426C4×#41C22×C10111yescharacteristic
427C2×C4×D4—21no—
428C2×C4×D4—21no—
429#493C22×C10111yescharacteristic
430#492C22×C10111yescharacteristic, complemented
431#487C22×C10111yescharacteristic, complemented
432#486C22×C10111yescharacteristic
433#482—21no—
434#475C22×C10111yescharacteristic, complemented
435#474C22×C10111yescharacteristic
436#464—21no—
437#463—22no—
438#463—21no—
439#462C22×C10111yescharacteristic, complemented
440#461C22×C10111yescharacteristic
441#460C22×C10111yescharacteristic, complemented
442#460C22×C10111yescharacteristic, complemented
443#459C22×C10111yescharacteristic
444#459C22×C10111yescharacteristic
445#449—21no—
446#449—22no—
447#442—21no—
448#440—21no—
449#432C22×C10111yescharacteristic, complemented
450#431C22×C10111yescharacteristic, complemented
451C2×C4⋊C8C22×C10111yescharacteristic, complemented
452#416—21no—
453#333C22×C10111yescharacteristic, complemented
454#333C22×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×#41D4×C10111yescharacteristic
467C2×#41D4×C10111yescharacteristic
468C2×#41D4×C10112yes—
469C22×D4—21no—
470C22×D4—21no—
471C23×C4—22no—
472#135—44no—
473C2×Q16—21no—
474C2×SD16—21no—
475C2×SD16—21no—
476C2×SD16—21no—
477C2×SD16—22no—
478C2×D8—21no—
479C2×D8—21no—
480C2×D8—22no—
481C22×C8—21no—
482C4⋊Q8C23×C10111yescharacteristic
483C4⋊Q8C23×C10111yescharacteristic
484#127C23×C10111yescharacteristic
485#127C23×C10111yescharacteristic
486#126—22no—
487#126—22no—
488#125—21no—
489#125—21no—
490#124—21no—
491#124—21no—
492#124—21no—
493#124D4×C10112yes—
494#123—22no—
495#123—22no—
496#123—22no—
497#123—22no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#120—22no—
511#120—22no—
512C4×Q8D4×C10111yescharacteristic
513C4×Q8D4×C10111yescharacteristic
514C4×Q8C23×C10111yescharacteristic
515C4×Q8C23×C10111yescharacteristic
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4D4×C10111yescharacteristic
533C4×D4D4×C10111yescharacteristic
534C4×D4C23×C10111yescharacteristic
535C4×D4C23×C10111yescharacteristic
536#117—22no—
537#117—21no—
538#117—21no—
539#117D4×C10111yescharacteristic
540#117D4×C10111yescharacteristic
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C42—21no—
546C2×C42—21no—
547C2×C42C23×C10111yescharacteristic
548#107—21no—
549#106—21no—
550C4⋊C8—21no—
551C4⋊C8—21no—
552C4⋊C8C23×C10111yescharacteristic
553C4⋊C8C23×C10111yescharacteristic
554C4⋊C8C23×C10111yescharacteristic
555C4⋊C8C23×C10111yescharacteristic
556#103—21no—
557#103—22no—
558#103—21no—
559#103—21no—
560#102—21no—
561#102—22no—
562#102—21no—
563#102—21no—
564#102—21no—
565#102—21no—
566C22⋊C8—21no—
567C22⋊C8—21no—
568#97—21no—
569C4×C8C23×C10111yescharacteristic
570C4×C8C23×C10111yescharacteristic
571C24—22no—
572#41—22no—
573#41—22no—
574#41—41no—
575#41—41no—
576#41—42no—
577#41—42no—
578#41—82no—
579C2×Q8—21no—
580C2×Q8C2×D4×C10111yescharacteristic
581C2×Q8C2×D4×C10111yescharacteristic
582C2×Q8C2×D4×C10112yes—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—41no—
598C2×D4C2×D4×C10111yescharacteristic
599C2×D4C2×D4×C10111yescharacteristic
600C2×D4C2×D4×C10112yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—41no—
612C22×C4—84no—
613C22×C4C2×D4×C10111yescharacteristic
614C22×C4C2×D4×C10111yescharacteristic
615C22×C4C2×D4×C10111yescharacteristic
616Q16—42no—
617SD16—42no—
618SD16—42no—
619SD16—42no—
620SD16—82no—
621D8—42no—
622D8—42no—
623D8—82no—
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⋊C4C2×D4×C10111yescharacteristic
644C4⋊C4C2×D4×C10111yescharacteristic
645C4⋊C4C2×D4×C10111yescharacteristic
646C4⋊C4C2×D4×C10111yescharacteristic
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—22no—
658C22⋊C4—22no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—41no—
662C22⋊C4—41no—
663C42—21no—
664C42—21no—
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—44no—
677C23—44no—
678C23—41no—
679C23—82no—
680C23#120×C10111yescharacteristic
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—42no—
686Q8—41no—
687Q8—41no—
688D4—21no—
689D4—21no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—42no—
694D4—44no—
695D4—44no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—82no—
705D4—82no—
706D4#135×C10112yescomplemented
707D4AGL(1,ℤ/8)×C10112yes—
708C2×C4—21no—
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—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
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—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—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C22—21no—
747C22—22no—
748C22—21no—
749C22—22no—
750C22—21no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—88no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22C2×#120×C10111yescharacteristic
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—42no—
774C4—81no—
775C4C2×#135×C10111yescharacteristic
776C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
777C4#575×C10111yescharacteristic
778C4#575×C10111yescharacteristic
779C2—41no—
780C2—42no—
781C2—42no—
782C2—82no—
783C2—161no—
784C2C101×#300211yescharacteristic
785C2C101×#300611yescharacteristic
786C2C101×#301911yescharacteristic
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×#3481C2semidirect
2. C101×#3207C2semidirect
3. C101×#3115C2semidirect
4. C101×#3035C2semidirect
5. C101×#1644C2semidirect
6. C101×#1643C2semidirect
7. C101×#1640C2semidirect
8. C101×#1639C2semidirect
9. C101×#1622C2semidirect
10. C101×#1622C2semidirect
11. C101×#1620C2semidirect
12. C101×#1619C2semidirect
13. C101×#1551C2semidirect
14. C101×#1488C2semidirect
15. C101×#1477C2semidirect
27. #532×C101C22semidirect
36. #492×C101C22semidirect
37. #487×C101C22semidirect
40. #475×C101C22semidirect
45. #462×C101C22semidirect
47. #460×C101C22semidirect
48. #460×C101C22semidirect
55. #432×C101C22semidirect
56. #431×C101C22semidirect
57. C2×C4⋊C8×C101C22semidirect
59. #333×C101C22semidirect
60. #333×C101C22semidirect
63. Q8⋊C8×C101C22semidirect
64. Q8⋊C8×C101C22semidirect
65. Q8⋊C8×C101C22semidirect
66. Q8⋊C8×C101C22semidirect
312. D4×C101#135semidirect
385. #18754C101direct (N × H)
394. #3481C2×C101semidirect
395. #3207C2×C101semidirect
396. #3115C2×C101semidirect
397. #3035C2×C101semidirect
398. #1644C2×C101semidirect
399. #1643C2×C101semidirect
400. #1640C2×C101semidirect
401. #1639C2×C101semidirect
402. #1622C2×C101semidirect
403. #1622C2×C101semidirect
404. #1620C2×C101semidirect
405. #1619C2×C101semidirect
406. #1551C2×C101semidirect
407. #1488C2×C101semidirect
408. #1477C2×C101semidirect
409. C101#18754direct (N × H)
421. #532C22×C101semidirect
430. #492C22×C101semidirect
431. #487C22×C101semidirect
434. #475C22×C101semidirect
439. #462C22×C101semidirect
441. #460C22×C101semidirect
442. #460C22×C101semidirect
449. #432C22×C101semidirect
450. #431C22×C101semidirect
451. C2×C4⋊C8C22×C101semidirect
453. #333C22×C101semidirect
454. #333C22×C101semidirect
457. Q8⋊C8C22×C101semidirect
458. Q8⋊C8C22×C101semidirect
459. Q8⋊C8C22×C101semidirect
460. Q8⋊C8C22×C101semidirect
706. D4#135×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#34812
C101×#32072
C101×#31152
C101×#30352
C101×#16442
C101×#16432
C101×#16402
C101×#16392
C101×#16222
C101×#16202
C101×#16192
C101×#15512
C101×#14882
C101×#14772
#18754101