Finite Group Databasebeta

← C101×#18649 #38800800

Subgroups — C101×#18649 #38800800

Order 25856.

868 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3523C211yesmaximal, characteristic
2C101×#3248C211yesmaximal, characteristic
3C101×#3160C211yesmaximal, characteristic, complemented
4C101×#3113C211yesmaximal, characteristic, complemented
5C101×#1653C211yesmaximal, characteristic, complemented
6C101×#1653C211yesmaximal, characteristic, complemented
7C101×#1652C211yesmaximal, characteristic, complemented
8C101×#1651C211yesmaximal, characteristic, complemented
9C101×#1650C211yesmaximal, characteristic, complemented
10C101×#1649C211yesmaximal, characteristic, complemented
11C101×#1648C211yesmaximal, characteristic, complemented
12C101×#1648C211yesmaximal, characteristic, complemented
13C101×#1552C211yesmaximal, characteristic, complemented
14C101×#1494C211yesmaximal, characteristic
15C2×Q8⋊C8×C101C211yesmaximal, characteristic, complemented
16#557×C101—21no—
17#557×C101C2211yescharacteristic
18#557×C101C2211yescharacteristic
19#556×C101—21no—
20#556×C101C2211yescharacteristic
21#552×C101—22no—
22#552×C101—21no—
23D4×Q8×C101—21no—
24D4×Q8×C101C2211yescharacteristic
25#541×C101—22no—
26#541×C101—21no—
27#533×C101—21no—
28#533×C101C2211yescharacteristic
29#533×C101C2211yescharacteristic
30#529×C101—21no—
31#529×C101C2211yescharacteristic
32#519×C101—21no—
33C2×C4×Q8×C101C2211yescharacteristic
34#500×C101C2211yescharacteristic
35#500×C101C2211yescharacteristic
36#499×C101—22no—
37#498×C101C2211yescharacteristic
38#498×C101C2211yescharacteristic
39#483×C101—21no—
40#479×C101—21no—
41#475×C101C2211yescharacteristic
42#475×C101C2211yescharacteristic
43#475×C101C2211yescharacteristic
44#474×C101C2211yescharacteristic
45#467×C101—21no—
46#465×C101—21no—
47#464×C101—21no—
48#462×C101C2211yescharacteristic
49#462×C101C2211yescharacteristic
50#462×C101C2211yescharacteristic
51#461×C101C2211yescharacteristic
52#451×C101—21no—
53#441×C101—21no—
54#441×C101—21no—
55#432×C101C2211yescharacteristic
56#427×C101—22no—
57C2×C4⋊C8×C101C2211yescharacteristic
58C2×C4×C8×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#332×C101C2211yescharacteristic
62#332×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64Q8⋊C8×C101C2211yescharacteristic
65Q8⋊C8×C101C2211yescharacteristic
66Q8⋊C8×C101C2211yescharacteristic
67Q8⋊C8×C101C2211yescharacteristic
68Q8⋊C8×C101C2211yescharacteristic
69D4⋊C8×C101C2211yescharacteristic
70D4⋊C8×C101C2211yescharacteristic
71C22×Q8×C101—21no—
72C22×Q8×C101D411yescharacteristic
73C2×Q16×C101—21no—
74C2×Q16×C101—21no—
75C2×Q16×C101—21no—
76C2×SD16×C101—21no—
77C22×C8×C101—21no—
78C22×C8×C101—21no—
79C4⋊Q8×C101—22no—
80C4⋊Q8×C101—21no—
81C4⋊Q8×C101—21no—
82C4⋊Q8×C101—21no—
83C4⋊Q8×C101C2311yescharacteristic
84C4⋊Q8×C101C2311yescharacteristic
85C4⋊Q8×C101C2311yescharacteristic
86C4⋊Q8×C101C2311yescharacteristic
87#126×C101—22no—
88#126×C101—22no—
89#126×C101—22no—
90#126×C101—22no—
91#126×C101—21no—
92#125×C101—22no—
93#125×C101—22no—
94#125×C101—22no—
95#125×C101—21no—
96#125×C101—22no—
97#125×C101—22no—
98#125×C101—21no—
99#125×C101—21no—
100#125×C101D411yescharacteristic
101#125×C101D412yes—
102#124×C101—21no—
103#124×C101D411yescharacteristic
104#123×C101—22no—
105#123×C101—21no—
106C22⋊Q8×C101—22no—
107C22⋊Q8×C101—22no—
108C22⋊Q8×C101—21no—
109C22⋊Q8×C101—21no—
110C22⋊Q8×C101—21no—
111C22⋊Q8×C101—21no—
112C22⋊Q8×C101—22no—
113C22⋊Q8×C101—21no—
114C22⋊Q8×C101—21no—
115C22⋊Q8×C101D411yescharacteristic
116#121×C101D411yescharacteristic
117C4×Q8×C101—22no—
118C4×Q8×C101—22no—
119C4×Q8×C101—21no—
120C4×Q8×C101—21no—
121C4×Q8×C101—21no—
122C4×Q8×C101—21no—
123C4×Q8×C101—21no—
124C4×Q8×C101—21no—
125C4×Q8×C101—21no—
126C4×Q8×C101—21no—
127C4×Q8×C101—21no—
128C4×Q8×C101—21no—
129C4×Q8×C101—21no—
130C4×Q8×C101D411yescharacteristic
131C4×Q8×C101D411yescharacteristic
132C4×Q8×C101C2311yescharacteristic
133C4×Q8×C101C2311yescharacteristic
134C4×Q8×C101C2311yescharacteristic
135C4×D4×C101—22no—
136C4×D4×C101—21no—
137C4×D4×C101—21no—
138C4×D4×C101C2311yescharacteristic
139#117×C101—22no—
140#117×C101—22no—
141#117×C101—22no—
142#117×C101—21no—
143#117×C101—21no—
144#117×C101—21no—
145#117×C101D412yes—
146C2×C4⋊C4×C101—21no—
147C2×C4⋊C4×C101D411yescharacteristic
148C2×C42×C101—21no—
149C2×C42×C101C2311yescharacteristic
150#107×C101—22no—
151#107×C101—22no—
152#107×C101—21no—
153#106×C101—22no—
154#106×C101—22no—
155#106×C101—21no—
156#106×C101—21no—
157#106×C101—21no—
158C4⋊C8×C101—21no—
159C4⋊C8×C101C2311yescharacteristic
160C4⋊C8×C101C2311yescharacteristic
161C4⋊C8×C101C2311yescharacteristic
162C4⋊C8×C101C2311yescharacteristic
163#103×C101—21no—
164#103×C101—21no—
165#103×C101—21no—
166#103×C101—21no—
167#103×C101—21no—
168#103×C101—21no—
169#103×C101—21no—
170#102×C101—21no—
171C22⋊C8×C101—21no—
172#97×C101—21no—
173C4×C8×C101—21no—
174C4×C8×C101C2311yescharacteristic
175C4×C8×C101C2311yescharacteristic
176C2×Q8×C101—22no—
177C2×Q8×C101—21no—
178C2×Q8×C101—21no—
179C2×Q8×C101—21no—
180C2×Q8×C101—22no—
181C2×Q8×C101—21no—
182C2×Q8×C101—21no—
183C2×Q8×C101—41no—
184C2×Q8×C101—42no—
185C2×Q8×C101—42no—
186C2×Q8×C101C2×D411yescharacteristic
187C2×Q8×C101C2×D411yescharacteristic
188C2×Q8×C101C2×D411yescharacteristic
189C2×D4×C101—21no—
190C2×D4×C101C2×D411yescharacteristic
191C22×C4×C101—22no—
192C22×C4×C101—21no—
193C22×C4×C101—21no—
194C22×C4×C101—21no—
195C22×C4×C101C2×D411yescharacteristic
196C22×C4×C101C2×D411yescharacteristic
197C22×C4×C101C2×D411yescharacteristic
198Q16×C101—42no—
199Q16×C101—42no—
200Q16×C101—81no—
201SD16×C101—81no—
202C2×C8×C101—24no—
203C2×C8×C101—21no—
204C2×C8×C101—21no—
205C2×C8×C101—21no—
206C2×C8×C101—21no—
207C2×C8×C101—21no—
208C2×C8×C101—21no—
209C2×C8×C101—81no—
210C4⋊C4×C101—22no—
211C4⋊C4×C101—22no—
212C4⋊C4×C101—22no—
213C4⋊C4×C101—22no—
214C4⋊C4×C101—22no—
215C4⋊C4×C101—22no—
216C4⋊C4×C101—22no—
217C4⋊C4×C101—22no—
218C4⋊C4×C101—21no—
219C4⋊C4×C101—21no—
220C4⋊C4×C101—21no—
221C4⋊C4×C101—22no—
222C4⋊C4×C101—21no—
223C4⋊C4×C101—21no—
224C4⋊C4×C101—21no—
225C4⋊C4×C101—22no—
226C4⋊C4×C101—21no—
227C4⋊C4×C101—21no—
228C4⋊C4×C101—21no—
229C4⋊C4×C101—21no—
230C4⋊C4×C101—21no—
231C4⋊C4×C101—21no—
232C4⋊C4×C101—21no—
233C4⋊C4×C101—21no—
234C4⋊C4×C101—21no—
235C4⋊C4×C101—41no—
236C4⋊C4×C101—41no—
237C4⋊C4×C101C2×D411yescharacteristic
238C4⋊C4×C101C2×D411yescharacteristic
239C4⋊C4×C101C2×D411yescharacteristic
240C4⋊C4×C101C2×D411yescharacteristic
241C4⋊C4×C101C2×D412yes—
242C4⋊C4×C101C2×D412yes—
243C22⋊C4×C101—22no—
244C22⋊C4×C101—22no—
245C22⋊C4×C101—22no—
246C22⋊C4×C101—21no—
247C22⋊C4×C101—22no—
248C22⋊C4×C101—21no—
249C22⋊C4×C101—21no—
250C22⋊C4×C101—21no—
251C22⋊C4×C101—21no—
252C22⋊C4×C101—41no—
253C42×C101—22no—
254C42×C101—22no—
255C42×C101—22no—
256C42×C101—21no—
257C42×C101—21no—
258C42×C101—22no—
259C42×C101—21no—
260C42×C101—21no—
261C42×C101—21no—
262C42×C101—41no—
263C42×C101C2×D411yescharacteristic
264C42×C101C2×D411yescharacteristic
265C42×C101C2×D411yescharacteristic
266C42×C101C2411yescharacteristic
267C23×C101—21no—
268C23×C101#12011yescharacteristic
269Q8×C101—21no—
270Q8×C101—21no—
271Q8×C101—21no—
272Q8×C101—21no—
273Q8×C101—21no—
274Q8×C101—42no—
275Q8×C101—44no—
276Q8×C101—41no—
277Q8×C101—41no—
278Q8×C101—41no—
279Q8×C101—41no—
280Q8×C101—41no—
281Q8×C101—41no—
282Q8×C101—41no—
283Q8×C101—41no—
284Q8×C101#13512yes—
285D4×C101—21no—
286D4×C101—21no—
287D4×C101—42no—
288C2×C4×C101—21no—
289C2×C4×C101—22no—
290C2×C4×C101—21no—
291C2×C4×C101—21no—
292C2×C4×C101—21no—
293C2×C4×C101—21no—
294C2×C4×C101—21no—
295C2×C4×C101—21no—
296C2×C4×C101—22no—
297C2×C4×C101—21no—
298C2×C4×C101—21no—
299C2×C4×C101—21no—
300C2×C4×C101—21no—
301C2×C4×C101—22no—
302C2×C4×C101—42no—
303C2×C4×C101—44no—
304C2×C4×C101—42no—
305C2×C4×C101—41no—
306C2×C4×C101—41no—
307C2×C4×C101—41no—
308C2×C4×C101—41no—
309C2×C4×C101#12011yescharacteristic
310C2×C4×C101#12011yescharacteristic
311C2×C4×C101#12011yescharacteristic
312C2×C4×C101C22×D411yescharacteristic
313C2×C4×C101C22×D411yescharacteristic
314C2×C4×C101C22×D411yescharacteristic
315C8×C101—22no—
316C8×C101—22no—
317C8×C101—41no—
318C8×C101—41no—
319C8×C101—41no—
320C8×C101—41no—
321C22×C101—21no—
322C22×C101—21no—
323C22×C101—41no—
324C22×C101—41no—
325C22×C101—41no—
326C22×C101#45612yes—
327C22×C101C2×#12011yescharacteristic
328C4×C101—21no—
329C4×C101—22no—
330C4×C101—21no—
331C4×C101—21no—
332C4×C101—21no—
333C4×C101—41no—
334C4×C101—42no—
335C4×C101—41no—
336C4×C101—41no—
337C4×C101—42no—
338C4×C101—41no—
339C4×C101—41no—
340C4×C101—41no—
341C4×C101—81no—
342C4×C101—81no—
343C4×C101C2×#13511yescharacteristic
344C4×C101#57511yescharacteristic
345C4×C101#57711yescharacteristic
346C4×C101#57811yescharacteristic
347#18649C10111yesmaximal, characteristic, direct product factor, Sylow
348C2×C101—22no—
349C2×C101—81no—
350C2×C101#300211yescharacteristic
351C2×C101#301311yescharacteristic
352C2×C101C2×#45611yescharacteristic
353#3523C2×C10111yescharacteristic
354#3248C2×C10111yescharacteristic
355#3160C2×C10111yescharacteristic, complemented
356#3113C2×C10111yescharacteristic, complemented
357#1653C2×C10111yescharacteristic, complemented
358#1653C2×C10111yescharacteristic, complemented
359#1652C2×C10111yescharacteristic, complemented
360#1651C2×C10111yescharacteristic, complemented
361#1650C2×C10111yescharacteristic, complemented
362#1649C2×C10111yescharacteristic, complemented
363#1648C2×C10111yescharacteristic, complemented
364#1648C2×C10111yescharacteristic, complemented
365#1552C2×C10111yescharacteristic, complemented
366#1494C2×C10111yescharacteristic
367C2×Q8⋊C8C2×C10111yescharacteristic, complemented
368C101#1864911yescharacteristic, direct product factor, Sylow
369#557—21no—
370#557C22×C10111yescharacteristic
371#557C22×C10111yescharacteristic
372#556—21no—
373#556C22×C10111yescharacteristic
374#552—22no—
375#552—21no—
376D4×Q8—21no—
377D4×Q8C22×C10111yescharacteristic
378#541—22no—
379#541—21no—
380#533—21no—
381#533C22×C10111yescharacteristic
382#533C22×C10111yescharacteristic
383#529—21no—
384#529C22×C10111yescharacteristic
385#519—21no—
386C2×C4×Q8C22×C10111yescharacteristic
387#500C22×C10111yescharacteristic
388#500C22×C10111yescharacteristic
389#499—22no—
390#498C22×C10111yescharacteristic
391#498C22×C10111yescharacteristic
392#483—21no—
393#479—21no—
394#475C22×C10111yescharacteristic
395#475C22×C10111yescharacteristic
396#475C22×C10111yescharacteristic
397#474C22×C10111yescharacteristic
398#467—21no—
399#465—21no—
400#464—21no—
401#462C22×C10111yescharacteristic
402#462C22×C10111yescharacteristic
403#462C22×C10111yescharacteristic
404#461C22×C10111yescharacteristic
405#451—21no—
406#441—21no—
407#441—21no—
408#432C22×C10111yescharacteristic
409#427—22no—
410C2×C4⋊C8C22×C10111yescharacteristic
411C2×C4×C8C22×C10111yescharacteristic
412#332C22×C10111yescharacteristic
413#332C22×C10111yescharacteristic
414#332C22×C10111yescharacteristic
415#332C22×C10111yescharacteristic
416Q8⋊C8C22×C10111yescharacteristic
417Q8⋊C8C22×C10111yescharacteristic
418Q8⋊C8C22×C10111yescharacteristic
419Q8⋊C8C22×C10111yescharacteristic
420Q8⋊C8C22×C10111yescharacteristic
421Q8⋊C8C22×C10111yescharacteristic
422D4⋊C8C22×C10111yescharacteristic
423D4⋊C8C22×C10111yescharacteristic
424C22×Q8—21no—
425C22×Q8D4×C10111yescharacteristic
426C2×Q16—21no—
427C2×Q16—21no—
428C2×Q16—21no—
429C2×SD16—21no—
430C22×C8—21no—
431C22×C8—21no—
432C4⋊Q8—22no—
433C4⋊Q8—21no—
434C4⋊Q8—21no—
435C4⋊Q8—21no—
436C4⋊Q8C23×C10111yescharacteristic
437C4⋊Q8C23×C10111yescharacteristic
438C4⋊Q8C23×C10111yescharacteristic
439C4⋊Q8C23×C10111yescharacteristic
440#126—22no—
441#126—22no—
442#126—22no—
443#126—22no—
444#126—21no—
445#125—22no—
446#125—22no—
447#125—22no—
448#125—21no—
449#125—22no—
450#125—22no—
451#125—21no—
452#125—21no—
453#125D4×C10111yescharacteristic
454#125D4×C10112yes—
455#124—21no—
456#124D4×C10111yescharacteristic
457#123—22no—
458#123—21no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—21no—
462C22⋊Q8—21no—
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465C22⋊Q8—22no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8D4×C10111yescharacteristic
469#121D4×C10111yescharacteristic
470C4×Q8—22no—
471C4×Q8—22no—
472C4×Q8—21no—
473C4×Q8—21no—
474C4×Q8—21no—
475C4×Q8—21no—
476C4×Q8—21no—
477C4×Q8—21no—
478C4×Q8—21no—
479C4×Q8—21no—
480C4×Q8—21no—
481C4×Q8—21no—
482C4×Q8—21no—
483C4×Q8D4×C10111yescharacteristic
484C4×Q8D4×C10111yescharacteristic
485C4×Q8C23×C10111yescharacteristic
486C4×Q8C23×C10111yescharacteristic
487C4×Q8C23×C10111yescharacteristic
488C4×D4—22no—
489C4×D4—21no—
490C4×D4—21no—
491C4×D4C23×C10111yescharacteristic
492#117—22no—
493#117—22no—
494#117—22no—
495#117—21no—
496#117—21no—
497#117—21no—
498#117D4×C10112yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4D4×C10111yescharacteristic
501C2×C42—21no—
502C2×C42C23×C10111yescharacteristic
503#107—22no—
504#107—22no—
505#107—21no—
506#106—22no—
507#106—22no—
508#106—21no—
509#106—21no—
510#106—21no—
511C4⋊C8—21no—
512C4⋊C8C23×C10111yescharacteristic
513C4⋊C8C23×C10111yescharacteristic
514C4⋊C8C23×C10111yescharacteristic
515C4⋊C8C23×C10111yescharacteristic
516#103—21no—
517#103—21no—
518#103—21no—
519#103—21no—
520#103—21no—
521#103—21no—
522#103—21no—
523#102—21no—
524C22⋊C8—21no—
525#97—21no—
526C4×C8—21no—
527C4×C8C23×C10111yescharacteristic
528C4×C8C23×C10111yescharacteristic
529C2×Q8—22no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—22no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—41no—
537C2×Q8—42no—
538C2×Q8—42no—
539C2×Q8C2×D4×C10111yescharacteristic
540C2×Q8C2×D4×C10111yescharacteristic
541C2×Q8C2×D4×C10111yescharacteristic
542C2×D4—21no—
543C2×D4C2×D4×C10111yescharacteristic
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4C2×D4×C10111yescharacteristic
549C22×C4C2×D4×C10111yescharacteristic
550C22×C4C2×D4×C10111yescharacteristic
551Q16—42no—
552Q16—42no—
553Q16—81no—
554SD16—81no—
555C2×C8—24no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—81no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—22no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—41no—
589C4⋊C4—41no—
590C4⋊C4C2×D4×C10111yescharacteristic
591C4⋊C4C2×D4×C10111yescharacteristic
592C4⋊C4C2×D4×C10111yescharacteristic
593C4⋊C4C2×D4×C10111yescharacteristic
594C4⋊C4C2×D4×C10112yes—
595C4⋊C4C2×D4×C10112yes—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—21no—
600C22⋊C4—22no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—41no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—21no—
610C42—21no—
611C42—22no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—41no—
616C42C2×D4×C10111yescharacteristic
617C42C2×D4×C10111yescharacteristic
618C42C2×D4×C10111yescharacteristic
619C42C24×C10111yescharacteristic
620C23—21no—
621C23#120×C10111yescharacteristic
622Q8—21no—
623Q8—21no—
624Q8—21no—
625Q8—21no—
626Q8—21no—
627Q8—42no—
628Q8—44no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8#135×C10112yes—
638D4—21no—
639D4—21no—
640D4—42no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—42no—
656C2×C4—44no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4#120×C10111yescharacteristic
663C2×C4#120×C10111yescharacteristic
664C2×C4#120×C10111yescharacteristic
665C2×C4C22×D4×C10111yescharacteristic
666C2×C4C22×D4×C10111yescharacteristic
667C2×C4C22×D4×C10111yescharacteristic
668C8—22no—
669C8—22no—
670C8—41no—
671C8—41no—
672C8—41no—
673C8—41no—
674C22—21no—
675C22—21no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22#456×C10112yes—
680C22C2×#120×C10111yescharacteristic
681C4—21no—
682C4—22no—
683C4—21no—
684C4—21no—
685C4—21no—
686C4—41no—
687C4—42no—
688C4—41no—
689C4—41no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—41no—
694C4—81no—
695C4—81no—
696C4C2×#135×C10111yescharacteristic
697C4#575×C10111yescharacteristic
698C4#577×C10111yescharacteristic
699C4#578×C10111yescharacteristic
700C2—22no—
701C2—81no—
702C2C101×#300211yescharacteristic
703C2C101×#301311yescharacteristic
704C2C2×#456×C10111yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC42C24×C101
prime radical#121×C101D4
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
3. C101×#3160C2semidirect
4. C101×#3113C2semidirect
5. C101×#1653C2semidirect
6. C101×#1653C2semidirect
7. C101×#1652C2semidirect
8. C101×#1651C2semidirect
9. C101×#1650C2semidirect
10. C101×#1649C2semidirect
11. C101×#1648C2semidirect
12. C101×#1648C2semidirect
13. C101×#1552C2semidirect
15. C2×Q8⋊C8×C101C2semidirect
347. #18649C101direct (N × H)
355. #3160C2×C101semidirect
356. #3113C2×C101semidirect
357. #1653C2×C101semidirect
358. #1653C2×C101semidirect
359. #1652C2×C101semidirect
360. #1651C2×C101semidirect
361. #1650C2×C101semidirect
362. #1649C2×C101semidirect
363. #1648C2×C101semidirect
364. #1648C2×C101semidirect
365. #1552C2×C101semidirect
367. C2×Q8⋊C8C2×C101semidirect
368. C101#18649direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#35232
C101×#32482
C101×#31602
C101×#31132
C101×#16532
C101×#16522
C101×#16512
C101×#16502
C101×#16492
C101×#16482
C101×#15522
C101×#14942
C2×Q8⋊C8×C1012
#18649101