Finite Group Databasebeta

← C11×#61484 #14638677

Subgroups — C11×#61484 #14638677

Order 2816.

1750 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3523C212yesmaximal
2C11×#3395C211yesmaximal, characteristic, complemented
3C11×#3383C211yesmaximal, characteristic, complemented
4C11×#3374C212yesmaximal, complemented
5C11×#3342C211yesmaximal, characteristic, complemented
6C11×#3336C212yesmaximal, complemented
7C11×#3328C212yesmaximal, complemented
8C11×#3312C214yesmaximal, complemented
9D4×C11×Q16C211yesmaximal, characteristic, complemented
10D4×C11×Q16C212yesmaximal, complemented
11C11×#3177C212yesmaximal, complemented
12C11×#3170C211yesmaximal, characteristic, complemented
13C11×#3127C214yesmaximal, complemented
14C11×#3113C212yesmaximal, complemented
15C11×#2966C211yesmaximal, characteristic
16C11×#2950C212yesmaximal, complemented
17C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
18C22×C11×Q16C2211yescharacteristic
19C22×C11×Q16C2212yes—
20C11×#557—22no—
21C11×#557C2212yes—
22C11×#557C2212yes—
23C11×#556—22no—
24C11×#556C2212yes—
25C11×#552—24no—
26C11×#552C2214yes—
27D4×Q8×C11C2214yes—
28D4×Q8×C11C2212yes—
29C11×#541—24no—
30C11×#541C2214yes—
31C11×#533—22no—
32C11×#533C2212yes—
33C11×#529—22no—
34C11×#529C2211yescharacteristic
35C11×#519C2214yes—
36C2×C4×Q8×C11C2212yes—
37C11×#500C2211yescharacteristic
38C11×#499C2212yes—
39C11×#494C2211yescharacteristic
40C11×#494C2212yes—
41C11×#491C2214yes—
42C11×#487C2212yes—
43C11×#485C2214yes—
44C11×#485C2214yes—
45C11×#483C2214yes—
46C11×#479C2214yes—
47C11×#479C2214yes—
48C11×#475C2212yes—
49C11×#475C2212yes—
50C11×#470C2214yes—
51C11×#467C2212yes—
52C11×#467C2212yes—
53C11×#467C2212yes—
54C11×#467C2212yes—
55C11×#462C2212yes—
56C11×#462C2214yes—
57C11×#462C2214yes—
58C11×#462C2212yes—
59C11×#451C2214yes—
60C11×#451C2214yes—
61C11×#451C2214yes—
62C11×#446C2211yescharacteristic
63C8×Q8×C11C2211yescharacteristic
64C11×#441C2214yes—
65C11×#441C2214yes—
66C11×#441C2214yes—
67C4×C11×Q16C2212yes—
68C4×C11×Q16C2212yes—
69C4×C11×Q16C2211yescharacteristic
70C4×C11×Q16C2211yescharacteristic
71C4×C11×Q16C2211yescharacteristic
72C4×C11×Q16C2212yes—
73C4×C11×Q16C2211yescharacteristic
74C4×C11×Q16C2212yes—
75C4×C11×Q16C2212yes—
76C4×C11×Q16C2212yes—
77C11×#436C2211yescharacteristic
78C11×#435C2212yes—
79C8×D4×C11C2212yes—
80C8×D4×C11C2211yescharacteristic
81C11×#433C2212yes—
82C11×#432C2211yescharacteristic
83C11×#427C2212yes—
84C2×C11×#107C2211yescharacteristic
85C11×#419C2214yes—
86C2×C11×#103C2212yes—
87C11×#405C2212yes—
88C2×C4×C8×C11C2211yescharacteristic
89C22×Q8×C11C2312yes—
90C22×Q8×C11C2314yes—
91C2×C11×Q16—24no—
92C2×C11×Q16—28no—
93C2×C11×Q16C2312yes—
94C2×C11×Q16C2311yescharacteristic
95C2×C11×Q16C2312yes—
96C2×C11×Q16C2314yes—
97C2×C11×Q16C2312yes—
98C2×C11×Q16C2314yes—
99C2×C11×Q16C2311yescharacteristic
100C2×C11×M16C2312yes—
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2312yes—
103C22×C8×C11C2311yescharacteristic
104C11×C4⋊Q8—22no—
105C11×C4⋊Q8—22no—
106C11×C4⋊Q8—24no—
107C11×C4⋊Q8C2314yes—
108C11×C4⋊Q8C2312yes—
109C11×C4⋊Q8C2312yes—
110C11×#126—24no—
111C11×#126—24no—
112C11×#126—24no—
113C11×#126—24no—
114C11×#126D412yes—
115C11×#125—22no—
116C11×#125—24no—
117C11×#125—24no—
118C11×#125—24no—
119C11×#125—24no—
120C11×#125—24no—
121C11×#125—22no—
122C11×#125D411yescharacteristic
123C11×#125C2314yes—
124C11×#124—22no—
125C11×#124D411yescharacteristic
126C11×#123—24no—
127C11×#123D412yes—
128C11×C22⋊Q8—22no—
129C11×C22⋊Q8—24no—
130C11×C22⋊Q8—24no—
131C11×C22⋊Q8—24no—
132C11×C22⋊Q8D411yescharacteristic
133C11×C22⋊Q8C2314yes—
134C11×C22⋊Q8C2314yes—
135C11×C22⋊Q8C2314yes—
136C11×#121D411yescharacteristic
137C4×Q8×C11—22no—
138C4×Q8×C11—24no—
139C4×Q8×C11—24no—
140C4×Q8×C11—22no—
141C4×Q8×C11—22no—
142C4×Q8×C11—22no—
143C4×Q8×C11—22no—
144C4×Q8×C11—22no—
145C4×Q8×C11C2312yes—
146C4×Q8×C11C2312yes—
147C4×Q8×C11C2312yes—
148C4×Q8×C11C2312yes—
149C4×Q8×C11C2314yes—
150C4×Q8×C11C2314yes—
151C4×Q8×C11C2314yes—
152C4×Q8×C11C2311yescharacteristic
153C4×D4×C11—24no—
154C4×D4×C11—22no—
155C4×D4×C11C2312yes—
156C4×D4×C11C2311yescharacteristic
157C11×#117—22no—
158C11×#117—24no—
159C11×#117—24no—
160C11×#117—24no—
161C11×#117C2314yes—
162C11×#117C2312yes—
163C2×C11×C4⋊C4—22no—
164C2×C11×C4⋊C4C2312yes—
165C2×C42×C11—22no—
166C2×C42×C11C2311yescharacteristic
167C11×#107C2311yescharacteristic
168C11×#107C2312yes—
169C11×#107C2312yes—
170C11×#107C2311yescharacteristic
171C11×#107C2312yes—
172C11×#106C2314yes—
173C11×#106C2314yes—
174C11×C4⋊C8C2311yescharacteristic
175C11×C4⋊C8C2311yescharacteristic
176C11×C4⋊C8C2312yes—
177C11×C4⋊C8C2312yes—
178C11×#103C2312yes—
179C11×#103C2314yes—
180C11×#103C2314yes—
181C11×#103C2314yes—
182C11×#103C2312yes—
183C11×#103C2312yes—
184C11×#103C2312yes—
185C11×#103C2314yes—
186C11×#103C2314yes—
187C11×#103C2314yes—
188C11×C22⋊C8C2312yes—
189C11×C22⋊C8C2312yes—
190C11×C22⋊C8C2312yes—
191C11×#97C2312yes—
192C11×#97C2312yes—
193C4×C8×C11C2312yes—
194C4×C8×C11C2311yescharacteristic
195C4×C8×C11C2311yescharacteristic
196C4×C8×C11C2311yescharacteristic
197C4×C8×C11C2311yescharacteristic
198#61484C1111yesmaximal, characteristic, direct product factor, Sylow
199C2×Q8×C11—22no—
200C2×Q8×C11—24no—
201C2×Q8×C11—22no—
202C2×Q8×C11—24no—
203C2×Q8×C11—28no—
204C2×Q8×C11—42no—
205C2×Q8×C11—44no—
206C2×Q8×C11C2×D411yescharacteristic
207C2×Q8×C11C2412yes—
208C2×Q8×C11C2414yes—
209C2×Q8×C11C2412yes—
210C2×D4×C11C2×D412yes—
211C2×D4×C11C2×D411yescharacteristic
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—24no—
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2411yescharacteristic
218C22×C4×C11C2412yes—
219C11×Q16—22no—
220C11×Q16—24no—
221C11×Q16—24no—
222C11×Q16—28no—
223C11×Q16—42no—
224C11×Q16—44no—
225C11×Q16#4114yes—
226C11×M16—42no—
227C2×C8×C11—22no—
228C2×C8×C11—24no—
229C2×C8×C11—41no—
230C2×C8×C11C2411yescharacteristic
231C2×C8×C11C2411yescharacteristic
232C2×C8×C11C2411yescharacteristic
233C2×C8×C11C2412yes—
234C2×C8×C11C2412yes—
235C2×C8×C11C2411yescharacteristic
236C11×C4⋊C4—22no—
237C11×C4⋊C4—22no—
238C11×C4⋊C4—22no—
239C11×C4⋊C4—22no—
240C11×C4⋊C4—22no—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—24no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—22no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4—22no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—22no—
249C11×C4⋊C4—24no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4C2×D412yes—
255C11×C4⋊C4C2×D412yes—
256C11×C4⋊C4C2×D411yescharacteristic
257C11×C4⋊C4C2×D412yes—
258C11×C4⋊C4C2×D411yescharacteristic
259C11×C4⋊C4C2×D412yes—
260C11×C4⋊C4C2412yes—
261C11×C4⋊C4C2412yes—
262C11×C4⋊C4C2414yes—
263C11×C22⋊C4—24no—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—24no—
266C11×C22⋊C4—24no—
267C11×C22⋊C4C2×D412yes—
268C11×C22⋊C4C2×D412yes—
269C11×C22⋊C4C2×D412yes—
270C11×C22⋊C4C2×D412yes—
271C11×C22⋊C4C2×D412yes—
272C42×C11—22no—
273C42×C11—22no—
274C42×C11—22no—
275C42×C11—22no—
276C42×C11—24no—
277C42×C11—24no—
278C42×C11—24no—
279C42×C11—24no—
280C42×C11C2×D411yescharacteristic
281C42×C11C2×D411yescharacteristic
282C42×C11C2411yescharacteristic
283C42×C11C2411yescharacteristic
284C42×C11C2412yes—
285#3523C2×C1112yes—
286#3395C2×C1111yescharacteristic, complemented
287#3383C2×C1111yescharacteristic, complemented
288#3374C2×C1112yescomplemented
289#3342C2×C1111yescharacteristic, complemented
290#3336C2×C1112yescomplemented
291#3328C2×C1112yescomplemented
292#3312C2×C1114yescomplemented
293D4×Q16C2×C1111yescharacteristic, complemented
294D4×Q16C2×C1112yescomplemented
295#3177C2×C1112yescomplemented
296#3170C2×C1111yescharacteristic, complemented
297#3127C2×C1114yescomplemented
298#3113C2×C1112yescomplemented
299#2966C2×C1111yescharacteristic
300#2950C2×C1112yescomplemented
301C2×C4×Q16C2×C1111yescharacteristic, complemented
302C23×C11C22×D412yes—
303C23×C11C22×D411yescharacteristic
304Q8×C11—22no—
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—24no—
308Q8×C11—24no—
309Q8×C11—22no—
310Q8×C11—44no—
311Q8×C11—48no—
312Q8×C11—44no—
313Q8×C11C2×#4114yes—
314D4×C11—24no—
315D4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—21no—
320C2×C4×C11—22no—
321C2×C4×C11—21no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—24no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—24no—
328C2×C4×C11—44no—
329C2×C4×C11—48no—
330C2×C4×C11—44no—
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C22×D412yes—
334C2×C4×C11C22×D412yes—
335C2×C4×C11C22×D412yes—
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C2511yescharacteristic
340C8×C11—21no—
341C8×C11—22no—
342C8×C11—21no—
343C8×C11—21no—
344C8×C11—22no—
345C8×C11C2×#4112yes—
346C22×Q16C22×C1111yescharacteristic
347C22×Q16C22×C1112yes—
348#557—22no—
349#557C22×C1112yes—
350#557C22×C1112yes—
351#556—22no—
352#556C22×C1112yes—
353#552—24no—
354#552C22×C1114yes—
355D4×Q8C22×C1112yes—
356D4×Q8C22×C1114yes—
357#541—24no—
358#541C22×C1114yes—
359#533—22no—
360#533C22×C1112yes—
361#529—22no—
362#529C22×C1111yescharacteristic
363#519C22×C1114yes—
364C2×C4×Q8C22×C1112yes—
365#500C22×C1111yescharacteristic
366#499C22×C1112yes—
367#494C22×C1111yescharacteristic
368#494C22×C1112yes—
369#491C22×C1114yes—
370#487C22×C1112yes—
371#485C22×C1114yes—
372#485C22×C1114yes—
373#483C22×C1114yes—
374#479C22×C1114yes—
375#479C22×C1114yes—
376#475C22×C1112yes—
377#475C22×C1112yes—
378#470C22×C1114yes—
379#467C22×C1112yes—
380#467C22×C1112yes—
381#467C22×C1112yes—
382#467C22×C1112yes—
383#462C22×C1112yes—
384#462C22×C1112yes—
385#462C22×C1114yes—
386#462C22×C1114yes—
387#451C22×C1114yes—
388#451C22×C1114yes—
389#451C22×C1114yes—
390#446C22×C1111yescharacteristic
391C8×Q8C22×C1111yescharacteristic
392#441C22×C1114yes—
393#441C22×C1114yes—
394#441C22×C1114yes—
395C4×Q16C22×C1112yes—
396C4×Q16C22×C1112yes—
397C4×Q16C22×C1111yescharacteristic
398C4×Q16C22×C1112yes—
399C4×Q16C22×C1112yes—
400C4×Q16C22×C1111yescharacteristic
401C4×Q16C22×C1112yes—
402C4×Q16C22×C1112yes—
403C4×Q16C22×C1111yescharacteristic
404C4×Q16C22×C1111yescharacteristic
405#436C22×C1111yescharacteristic
406#435C22×C1112yes—
407C8×D4C22×C1112yes—
408C8×D4C22×C1111yescharacteristic
409#433C22×C1112yes—
410#432C22×C1111yescharacteristic
411#427C22×C1112yes—
412C2×#107C22×C1111yescharacteristic
413#419C22×C1114yes—
414C2×#103C22×C1112yes—
415#405C22×C1112yes—
416C2×C4×C8C22×C1111yescharacteristic
417C22×C11—21no—
418C22×C11—21no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—22no—
422C22×C11#57812yes—
423C22×C11C23×D411yescharacteristic
424C4×C11—21no—
425C4×C11—22no—
426C4×C11—24no—
427C4×C11—21no—
428C4×C11—21no—
429C4×C11—21no—
430C4×C11—22no—
431C4×C11—22no—
432C4×C11—42no—
433C4×C11—44no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—44no—
437C4×C11#57812yes—
438C4×C11C22×#4111yescharacteristic
439C4×C11#58511yescharacteristic
440C22×Q8C23×C1112yes—
441C22×Q8C23×C1114yes—
442C2×Q16—24no—
443C2×Q16—28no—
444C2×Q16C23×C1112yes—
445C2×Q16C23×C1111yescharacteristic
446C2×Q16C23×C1112yes—
447C2×Q16C23×C1114yes—
448C2×Q16C23×C1112yes—
449C2×Q16C23×C1114yes—
450C2×Q16C23×C1111yescharacteristic
451C2×M16C23×C1112yes—
452C22×C8C23×C1111yescharacteristic
453C22×C8C23×C1112yes—
454C22×C8C23×C1111yescharacteristic
455C4⋊Q8—22no—
456C4⋊Q8—22no—
457C4⋊Q8—24no—
458C4⋊Q8C23×C1112yes—
459C4⋊Q8C23×C1114yes—
460C4⋊Q8C23×C1112yes—
461#126—24no—
462#126—24no—
463#126—24no—
464#126—24no—
465#126D4×C1112yes—
466#125—22no—
467#125—24no—
468#125—24no—
469#125—24no—
470#125—24no—
471#125—24no—
472#125—22no—
473#125D4×C1111yescharacteristic
474#125C23×C1114yes—
475#124—22no—
476#124D4×C1111yescharacteristic
477#123—24no—
478#123D4×C1112yes—
479C22⋊Q8—22no—
480C22⋊Q8—24no—
481C22⋊Q8—24no—
482C22⋊Q8—24no—
483C22⋊Q8D4×C1111yescharacteristic
484C22⋊Q8C23×C1114yes—
485C22⋊Q8C23×C1114yes—
486C22⋊Q8C23×C1114yes—
487#121D4×C1111yescharacteristic
488C4×Q8—22no—
489C4×Q8—24no—
490C4×Q8—24no—
491C4×Q8—22no—
492C4×Q8—22no—
493C4×Q8—22no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×Q8C23×C1112yes—
497C4×Q8C23×C1112yes—
498C4×Q8C23×C1112yes—
499C4×Q8C23×C1112yes—
500C4×Q8C23×C1114yes—
501C4×Q8C23×C1114yes—
502C4×Q8C23×C1114yes—
503C4×Q8C23×C1111yescharacteristic
504C4×D4—24no—
505C4×D4—22no—
506C4×D4C23×C1112yes—
507C4×D4C23×C1111yescharacteristic
508#117—22no—
509#117—24no—
510#117—24no—
511#117—24no—
512#117C23×C1114yes—
513#117C23×C1112yes—
514C2×C4⋊C4—22no—
515C2×C4⋊C4C23×C1112yes—
516C2×C42—22no—
517C2×C42C23×C1111yescharacteristic
518#107C23×C1111yescharacteristic
519#107C23×C1111yescharacteristic
520#107C23×C1112yes—
521#107C23×C1112yes—
522#107C23×C1112yes—
523#106C23×C1114yes—
524#106C23×C1114yes—
525C4⋊C8C23×C1111yescharacteristic
526C4⋊C8C23×C1111yescharacteristic
527C4⋊C8C23×C1112yes—
528C4⋊C8C23×C1112yes—
529#103C23×C1112yes—
530#103C23×C1112yes—
531#103C23×C1112yes—
532#103C23×C1112yes—
533#103C23×C1114yes—
534#103C23×C1114yes—
535#103C23×C1114yes—
536#103C23×C1114yes—
537#103C23×C1114yes—
538#103C23×C1114yes—
539C22⋊C8C23×C1112yes—
540C22⋊C8C23×C1112yes—
541C22⋊C8C23×C1112yes—
542#97C23×C1112yes—
543#97C23×C1112yes—
544C4×C8C23×C1111yescharacteristic
545C4×C8C23×C1111yescharacteristic
546C4×C8C23×C1111yescharacteristic
547C4×C8C23×C1111yescharacteristic
548C4×C8C23×C1112yes—
549C2×C11—22no—
550C2×C11—42no—
551C2×C11D4×#4111yescharacteristic
552C2×C11C2×#57811yescharacteristic
553C2×C11C2×#57811yescharacteristic
554C2×Q8—22no—
555C2×Q8—24no—
556C2×Q8—22no—
557C2×Q8—24no—
558C2×Q8—28no—
559C2×Q8—42no—
560C2×Q8—44no—
561C2×Q8C2×D4×C1111yescharacteristic
562C2×Q8C24×C1112yes—
563C2×Q8C24×C1114yes—
564C2×Q8C24×C1112yes—
565C2×D4C2×D4×C1112yes—
566C2×D4C2×D4×C1111yescharacteristic
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4C2×D4×C1111yescharacteristic
571C22×C4C2×D4×C1111yescharacteristic
572C22×C4C24×C1111yescharacteristic
573C22×C4C24×C1112yes—
574Q16—24no—
575Q16—28no—
576Q16—22no—
577Q16—24no—
578Q16—42no—
579Q16—44no—
580Q16C11×#4114yes—
581M16—42no—
582C2×C8—22no—
583C2×C8—24no—
584C2×C8—41no—
585C2×C8C24×C1111yescharacteristic
586C2×C8C24×C1111yescharacteristic
587C2×C8C24×C1111yescharacteristic
588C2×C8C24×C1112yes—
589C2×C8C24×C1112yes—
590C2×C8C24×C1111yescharacteristic
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—22no—
600C4⋊C4—24no—
601C4⋊C4—22no—
602C4⋊C4—24no—
603C4⋊C4—22no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4C2×D4×C1112yes—
610C4⋊C4C2×D4×C1112yes—
611C4⋊C4C2×D4×C1111yescharacteristic
612C4⋊C4C2×D4×C1112yes—
613C4⋊C4C2×D4×C1111yescharacteristic
614C4⋊C4C2×D4×C1112yes—
615C4⋊C4C24×C1112yes—
616C4⋊C4C24×C1112yes—
617C4⋊C4C24×C1114yes—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4C2×D4×C1112yes—
623C22⋊C4C2×D4×C1112yes—
624C22⋊C4C2×D4×C1112yes—
625C22⋊C4C2×D4×C1112yes—
626C22⋊C4C2×D4×C1112yes—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—24no—
632C42—24no—
633C42—24no—
634C42—24no—
635C42C2×D4×C1111yescharacteristic
636C42C2×D4×C1111yescharacteristic
637C42C24×C1111yescharacteristic
638C42C24×C1111yescharacteristic
639C42C24×C1112yes—
640C11#6148411yescharacteristic, direct product factor, Sylow
641C23C22×D4×C1112yes—
642C23C22×D4×C1111yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—22no—
646Q8—24no—
647Q8—24no—
648Q8—22no—
649Q8—44no—
650Q8—48no—
651Q8—44no—
652Q8C2×C11×#4114yes—
653D4—24no—
654D4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—44no—
668C2×C4—48no—
669C2×C4—44no—
670C2×C4C22×D4×C1111yescharacteristic
671C2×C4C22×D4×C1111yescharacteristic
672C2×C4C22×D4×C1112yes—
673C2×C4C22×D4×C1112yes—
674C2×C4C22×D4×C1112yes—
675C2×C4C22×D4×C1111yescharacteristic
676C2×C4C22×D4×C1111yescharacteristic
677C2×C4C22×D4×C1111yescharacteristic
678C2×C4C25×C1111yescharacteristic
679C8—21no—
680C8—22no—
681C8—21no—
682C8—21no—
683C8—22no—
684C8C2×C11×#4112yes—
685C22—21no—
686C22—21no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22C11×#57812yes—
691C22C23×D4×C1111yescharacteristic
692C4—21no—
693C4—22no—
694C4—24no—
695C4—21no—
696C4—21no—
697C4—21no—
698C4—22no—
699C4—22no—
700C4—42no—
701C4—44no—
702C4—42no—
703C4—42no—
704C4—44no—
705C4C11×#57812yes—
706C4C22×C11×#4111yescharacteristic
707C4C11×#58511yescharacteristic
708C2—22no—
709C2—42no—
710C2D4×C11×#4111yescharacteristic
711C2C2×C11×#57811yescharacteristic
712C2C2×C11×#57811yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#121D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#529 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C11×#3395C2semidirect
3. C11×#3383C2semidirect
4. C11×#3374C2semidirect
5. C11×#3342C2semidirect
6. C11×#3336C2semidirect
7. C11×#3328C2semidirect
8. C11×#3312C2semidirect
9. D4×C11×Q16C2semidirect
10. D4×C11×Q16C2semidirect
11. C11×#3177C2semidirect
12. C11×#3170C2semidirect
13. C11×#3127C2semidirect
14. C11×#3113C2semidirect
16. C11×#2950C2semidirect
17. C2×C4×C11×Q16C2semidirect
198. #61484C11direct (N × H)
286. #3395C2×C11semidirect
287. #3383C2×C11semidirect
288. #3374C2×C11semidirect
289. #3342C2×C11semidirect
290. #3336C2×C11semidirect
291. #3328C2×C11semidirect
292. #3312C2×C11semidirect
293. D4×Q16C2×C11semidirect
294. D4×Q16C2×C11semidirect
295. #3177C2×C11semidirect
296. #3170C2×C11semidirect
297. #3127C2×C11semidirect
298. #3113C2×C11semidirect
300. #2950C2×C11semidirect
301. C2×C4×Q16C2×C11semidirect
640. C11#61484direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35232
C11×#33952
C11×#33832
C11×#33742
C11×#33422
C11×#33362
C11×#33282
C11×#33122
D4×C11×Q162
C11×#31772
C11×#31702
C11×#31272
C11×#31132
C11×#29662
C11×#29502
C2×C4×C11×Q162
#6148411