Finite Group Databasebeta

← C11×#61477 #14638670

Subgroups — C11×#61477 #14638670

Order 2816.

1772 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3515C212yesmaximal, complemented
2C11×#3395C211yesmaximal, characteristic, complemented
3C11×#3380C211yesmaximal, characteristic, complemented
4C11×#3372C212yesmaximal, complemented
5C11×#3338C211yesmaximal, characteristic, complemented
6C11×#3336C212yesmaximal, complemented
7C11×#3331C212yesmaximal, complemented
8C11×#3315C214yesmaximal, complemented
9C11×#3283C211yesmaximal, characteristic, complemented
10C11×#3283C212yesmaximal, complemented
11C11×#3177C212yesmaximal, complemented
12C11×#3170C211yesmaximal, characteristic, complemented
13C11×#3120C214yesmaximal, complemented
14C11×#3116C212yesmaximal, complemented
15C11×#2966C211yesmaximal, characteristic, complemented
16C11×#2951C212yesmaximal, complemented
17C4×C11×#135C211yesmaximal, characteristic, complemented
18C2×C11×#135C2211yescharacteristic
19C2×C11×#135C2212yes—
20C11×#557C2212yes—
21C11×#554C2212yes—
22C11×#554C2212yes—
23C11×#553—22no—
24C11×#552—24no—
25C11×#552—22no—
26C11×#552C2214yes—
27C11×#547C2214yes—
28C11×#547C2212yes—
29C11×#541C2214yes—
30C11×#539—24no—
31C11×#533C2212yes—
32C11×#529—22no—
33C11×#529C2211yescharacteristic
34C2×C11×#125—22no—
35C11×#520C2214yes—
36C4×C11×#41C2212yes—
37C11×#500C2211yescharacteristic
38C11×#499C2212yes—
39C11×#494C2211yescharacteristic
40C11×#494C2212yes—
41C11×#491C2214yes—
42C11×#487C2212yes—
43C11×#485C2214yes—
44C11×#484C2214yes—
45C11×#483C2214yes—
46C11×#479C2214yes—
47C11×#478C2214yes—
48C11×#477C2212yes—
49C11×#476C2212yes—
50C11×#470C2214yes—
51C11×#467C2212yes—
52C11×#467C2212yes—
53C11×#467C2212yes—
54C11×#467C2212yes—
55C11×#462C2214yes—
56C11×#462C2212yes—
57C11×#461C2212yes—
58C11×#461C2214yes—
59C11×#452C2214yes—
60C11×#452C2214yes—
61C11×#452C2214yes—
62C11×#446C2211yescharacteristic
63C8×Q8×C11C2211yescharacteristic
64C11×#441C2214yes—
65C11×#440C2214yes—
66C11×#440C2214yes—
67C4×C11×Q16C2212yes—
68C4×C11×Q16C2212yes—
69C4×C11×Q16C2211yescharacteristic
70C4×C11×Q16C2211yescharacteristic
71C4×C11×Q16C2212yes—
72C4×C11×SD16C2212yes—
73C4×C11×SD16C2212yes—
74C4×C11×D8C2211yescharacteristic
75C4×C11×D8C2211yescharacteristic
76C4×C11×D8C2212yes—
77C11×#436C2211yescharacteristic
78C11×#435C2212yes—
79C8×D4×C11C2212yes—
80C8×D4×C11C2211yescharacteristic
81C11×#433C2212yes—
82C11×#432C2211yescharacteristic
83C11×#427C2211yescharacteristic
84C2×C11×#107C2212yes—
85C11×#417C2214yes—
86C11×#416C2212yes—
87C11×#405C2212yes—
88C2×C4×C8×C11C2211yescharacteristic
89C2×C11×#41C2312yes—
90C2×C11×#41C2314yes—
91C11×#135—24no—
92C11×#135—28no—
93C2×C11×Q16C2312yes—
94C2×C11×Q16C2311yescharacteristic
95C2×C11×Q16C2312yes—
96C2×C11×Q16C2314yes—
97C2×C11×SD16C2312yes—
98C2×C11×SD16C2314yes—
99C2×C11×D8C2311yescharacteristic
100C2×C11×M16C2312yes—
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2312yes—
103C22×C8×C11C2311yescharacteristic
104C11×C4⋊Q8C2314yes—
105C11×C4⋊Q8C2312yes—
106C11×C4⋊Q8C2312yes—
107C11×#126—24no—
108C11×#126—24no—
109C11×#126—24no—
110C11×#126D412yes—
111C11×#125—24no—
112C11×#125—24no—
113C11×#125—22no—
114C11×#125—22no—
115C11×#125—24no—
116C11×#125—24no—
117C11×#125—22no—
118C11×#125D411yescharacteristic
119C11×#125C2314yes—
120C11×#124D411yescharacteristic
121C11×#123—24no—
122C11×#123—24no—
123C11×#123—24no—
124C11×#123—24no—
125C11×#123D412yes—
126C11×C22⋊Q8—22no—
127C11×C22⋊Q8—22no—
128C11×C22⋊Q8—24no—
129C11×C22⋊Q8—24no—
130C11×C22⋊Q8D411yescharacteristic
131C11×C22⋊Q8C2314yes—
132C11×C22⋊Q8C2314yes—
133C11×C22⋊Q8C2314yes—
134C11×#121—22no—
135C11×#121—24no—
136C11×#121D411yescharacteristic
137C4×Q8×C11—22no—
138C4×Q8×C11—22no—
139C4×Q8×C11C2312yes—
140C4×Q8×C11C2312yes—
141C4×Q8×C11C2314yes—
142C4×Q8×C11C2314yes—
143C4×Q8×C11C2311yescharacteristic
144C4×D4×C11—22no—
145C4×D4×C11—22no—
146C4×D4×C11—22no—
147C4×D4×C11—24no—
148C4×D4×C11—24no—
149C4×D4×C11C2312yes—
150C4×D4×C11C2312yes—
151C4×D4×C11C2314yes—
152C4×D4×C11C2312yes—
153C4×D4×C11C2311yescharacteristic
154C11×#117—22no—
155C11×#117—24no—
156C11×#117—24no—
157C11×#117—22no—
158C11×#117C2312yes—
159C11×#117C2312yes—
160C2×C11×C4⋊C4—24no—
161C2×C11×C4⋊C4—22no—
162C2×C11×C4⋊C4—24no—
163C2×C11×C4⋊C4—22no—
164C2×C11×C4⋊C4C2314yes—
165C2×C42×C11—22no—
166C2×C42×C11C2311yescharacteristic
167C11×#107C2311yescharacteristic
168C11×#107C2312yes—
169C11×#107C2312yes—
170C11×#107C2311yescharacteristic
171C11×#107C2314yes—
172C11×#106C2314yes—
173C11×#106C2312yes—
174C11×C4⋊C8C2311yescharacteristic
175C11×C4⋊C8C2311yescharacteristic
176C11×C4⋊C8C2312yes—
177C11×C4⋊C8C2312yes—
178C11×#103C2312yes—
179C11×#103C2314yes—
180C11×#103C2314yes—
181C11×#103C2314yes—
182C11×#103C2312yes—
183C11×#103C2314yes—
184C11×#103C2314yes—
185C11×#102C2312yes—
186C11×#102C2312yes—
187C11×#102C2314yes—
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#61477C1111yesmaximal, characteristic, direct product factor, Sylow
199C11×#41—24no—
200C11×#41—28no—
201C11×#41—42no—
202C11×#41—44no—
203C2×Q8×C11—22no—
204C2×Q8×C11C2×D411yescharacteristic
205C2×Q8×C11C2412yes—
206C2×Q8×C11C2414yes—
207C2×D4×C11—22no—
208C2×D4×C11—24no—
209C2×D4×C11C2×D411yescharacteristic
210C2×D4×C11C2×D412yes—
211C2×D4×C11C2412yes—
212C22×C4×C11—24no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—24no—
216C22×C4×C11—22no—
217C22×C4×C11—24no—
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2411yescharacteristic
221C22×C4×C11C2412yes—
222C11×Q16—24no—
223C11×Q16—22no—
224C11×Q16—42no—
225C11×Q16—44no—
226C11×SD16—24no—
227C11×SD16—28no—
228C11×D8#4114yes—
229C11×M16—42no—
230C2×C8×C11—22no—
231C2×C8×C11—24no—
232C2×C8×C11—41no—
233C2×C8×C11C2411yescharacteristic
234C2×C8×C11C2411yescharacteristic
235C2×C8×C11C2411yescharacteristic
236C2×C8×C11C2412yes—
237C2×C8×C11C2412yes—
238C2×C8×C11C2411yescharacteristic
239C11×C4⋊C4—24no—
240C11×C4⋊C4—22no—
241C11×C4⋊C4—22no—
242C11×C4⋊C4—24no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4—24no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—22no—
250C11×C4⋊C4—22no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—22no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4C2×D412yes—
255C11×C4⋊C4C2×D411yescharacteristic
256C11×C4⋊C4C2×D412yes—
257C11×C4⋊C4C2×D411yescharacteristic
258C11×C4⋊C4C2×D412yes—
259C11×C4⋊C4C2×D412yes—
260C11×C4⋊C4C2412yes—
261C11×C4⋊C4C2412yes—
262C11×C4⋊C4C2414yes—
263C11×C22⋊C4—24no—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—22no—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—22no—
268C11×C22⋊C4—22no—
269C11×C22⋊C4—24no—
270C11×C22⋊C4C2×D412yes—
271C11×C22⋊C4C2×D412yes—
272C11×C22⋊C4C2×D412yes—
273C11×C22⋊C4C2×D412yes—
274C11×C22⋊C4C2×D412yes—
275C42×C11—22no—
276C42×C11—22no—
277C42×C11—22no—
278C42×C11—24no—
279C42×C11—24no—
280C42×C11C2×D411yescharacteristic
281C42×C11C2×D411yescharacteristic
282C42×C11C2411yescharacteristic
283C42×C11C2411yescharacteristic
284C42×C11C2412yes—
285#3515C2×C1112yescomplemented
286#3395C2×C1111yescharacteristic, complemented
287#3380C2×C1111yescharacteristic, complemented
288#3372C2×C1112yescomplemented
289#3338C2×C1111yescharacteristic, complemented
290#3336C2×C1112yescomplemented
291#3331C2×C1112yescomplemented
292#3315C2×C1114yescomplemented
293#3283C2×C1111yescharacteristic, complemented
294#3283C2×C1112yescomplemented
295#3177C2×C1112yescomplemented
296#3170C2×C1111yescharacteristic, complemented
297#3120C2×C1114yescomplemented
298#3116C2×C1112yescomplemented
299#2966C2×C1111yescharacteristic, complemented
300#2951C2×C1112yescomplemented
301C4×#135C2×C1111yescharacteristic, complemented
302C23×C11—22no—
303C23×C11C22×D411yescharacteristic
304C23×C11C22×D412yes—
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—24no—
308Q8×C11—24no—
309Q8×C11—22no—
310Q8×C11—82no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—42no—
314D4×C11—44no—
315D4×C11—48no—
316D4×C11C2×#4114yes—
317C2×C4×C11—22no—
318C2×C4×C11—21no—
319C2×C4×C11—22no—
320C2×C4×C11—21no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—24no—
326C2×C4×C11—24no—
327C2×C4×C11—41no—
328C2×C4×C11—44no—
329C2×C4×C11—48no—
330C2×C4×C11—44no—
331C2×C4×C11—82no—
332C2×C4×C11—84no—
333C2×C4×C11—84no—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C22×D412yes—
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2511yescharacteristic
343C8×C11—21no—
344C8×C11—22no—
345C8×C11—21no—
346C8×C11—21no—
347C8×C11—22no—
348C8×C11C2×#4112yes—
349C2×#135C22×C1111yescharacteristic
350C2×#135C22×C1112yes—
351#557C22×C1112yes—
352#554C22×C1112yes—
353#554C22×C1112yes—
354#553—22no—
355#552—24no—
356#552—22no—
357#552C22×C1114yes—
358#547C22×C1112yes—
359#547C22×C1114yes—
360#541C22×C1114yes—
361#539—24no—
362#533C22×C1112yes—
363#529—22no—
364#529C22×C1111yescharacteristic
365C2×#125—22no—
366#520C22×C1114yes—
367C4×#41C22×C1112yes—
368#500C22×C1111yescharacteristic
369#499C22×C1112yes—
370#494C22×C1111yescharacteristic
371#494C22×C1112yes—
372#491C22×C1114yes—
373#487C22×C1112yes—
374#485C22×C1114yes—
375#484C22×C1114yes—
376#483C22×C1114yes—
377#479C22×C1114yes—
378#478C22×C1114yes—
379#477C22×C1112yes—
380#476C22×C1112yes—
381#470C22×C1114yes—
382#467C22×C1112yes—
383#467C22×C1112yes—
384#467C22×C1112yes—
385#467C22×C1112yes—
386#462C22×C1112yes—
387#462C22×C1114yes—
388#461C22×C1112yes—
389#461C22×C1114yes—
390#452C22×C1114yes—
391#452C22×C1114yes—
392#452C22×C1114yes—
393#446C22×C1111yescharacteristic
394C8×Q8C22×C1111yescharacteristic
395#441C22×C1114yes—
396#440C22×C1114yes—
397#440C22×C1114yes—
398C4×Q16C22×C1112yes—
399C4×Q16C22×C1111yescharacteristic
400C4×Q16C22×C1112yes—
401C4×Q16C22×C1112yes—
402C4×Q16C22×C1111yescharacteristic
403C4×SD16C22×C1112yes—
404C4×SD16C22×C1112yes—
405C4×D8C22×C1111yescharacteristic
406C4×D8C22×C1112yes—
407C4×D8C22×C1111yescharacteristic
408#436C22×C1111yescharacteristic
409#435C22×C1112yes—
410C8×D4C22×C1112yes—
411C8×D4C22×C1111yescharacteristic
412#433C22×C1112yes—
413#432C22×C1111yescharacteristic
414#427C22×C1111yescharacteristic
415C2×#107C22×C1112yes—
416#417C22×C1114yes—
417#416C22×C1112yes—
418#405C22×C1112yes—
419C2×C4×C8C22×C1111yescharacteristic
420C22×C11—21no—
421C22×C11—22no—
422C22×C11—21no—
423C22×C11—22no—
424C22×C11—24no—
425C22×C11—21no—
426C22×C11—22no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11C23×D411yescharacteristic
430C4×C11—21no—
431C4×C11—21no—
432C4×C11—22no—
433C4×C11—21no—
434C4×C11—22no—
435C4×C11—21no—
436C4×C11—22no—
437C4×C11—42no—
438C4×C11—44no—
439C4×C11—42no—
440C4×C11—44no—
441C4×C11—42no—
442C4×C11#57812yes—
443C4×C11C22×#4111yescharacteristic
444C4×C11#58511yescharacteristic
445C2×#41C23×C1112yes—
446C2×#41C23×C1114yes—
447#135—24no—
448#135—28no—
449C2×Q16C23×C1111yescharacteristic
450C2×Q16C23×C1112yes—
451C2×Q16C23×C1112yes—
452C2×Q16C23×C1114yes—
453C2×SD16C23×C1112yes—
454C2×SD16C23×C1114yes—
455C2×D8C23×C1111yescharacteristic
456C2×M16C23×C1112yes—
457C22×C8C23×C1111yescharacteristic
458C22×C8C23×C1112yes—
459C22×C8C23×C1111yescharacteristic
460C4⋊Q8C23×C1112yes—
461C4⋊Q8C23×C1114yes—
462C4⋊Q8C23×C1112yes—
463#126—24no—
464#126—24no—
465#126—24no—
466#126D4×C1112yes—
467#125—24no—
468#125—24no—
469#125—22no—
470#125—22no—
471#125—24no—
472#125—24no—
473#125—22no—
474#125D4×C1111yescharacteristic
475#125C23×C1114yes—
476#124D4×C1111yescharacteristic
477#123—24no—
478#123—24no—
479#123—24no—
480#123—24no—
481#123D4×C1112yes—
482C22⋊Q8—22no—
483C22⋊Q8—22no—
484C22⋊Q8—24no—
485C22⋊Q8—24no—
486C22⋊Q8D4×C1111yescharacteristic
487C22⋊Q8C23×C1114yes—
488C22⋊Q8C23×C1114yes—
489C22⋊Q8C23×C1114yes—
490#121—22no—
491#121—24no—
492#121D4×C1111yescharacteristic
493C4×Q8—22no—
494C4×Q8—22no—
495C4×Q8C23×C1112yes—
496C4×Q8C23×C1112yes—
497C4×Q8C23×C1114yes—
498C4×Q8C23×C1114yes—
499C4×Q8C23×C1111yescharacteristic
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—22no—
503C4×D4—24no—
504C4×D4—24no—
505C4×D4C23×C1112yes—
506C4×D4C23×C1112yes—
507C4×D4C23×C1114yes—
508C4×D4C23×C1112yes—
509C4×D4C23×C1111yescharacteristic
510#117—22no—
511#117—24no—
512#117—24no—
513#117—22no—
514#117C23×C1112yes—
515#117C23×C1112yes—
516C2×C4⋊C4—24no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—24no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4C23×C1114yes—
521C2×C42—22no—
522C2×C42C23×C1111yescharacteristic
523#107C23×C1111yescharacteristic
524#107C23×C1112yes—
525#107C23×C1114yes—
526#107C23×C1111yescharacteristic
527#107C23×C1112yes—
528#106C23×C1112yes—
529#106C23×C1114yes—
530C4⋊C8C23×C1111yescharacteristic
531C4⋊C8C23×C1111yescharacteristic
532C4⋊C8C23×C1112yes—
533C4⋊C8C23×C1112yes—
534#103C23×C1112yes—
535#103C23×C1112yes—
536#103C23×C1114yes—
537#103C23×C1114yes—
538#103C23×C1114yes—
539#103C23×C1114yes—
540#103C23×C1114yes—
541#102C23×C1112yes—
542#102C23×C1112yes—
543#102C23×C1114yes—
544C22⋊C8C23×C1112yes—
545C22⋊C8C23×C1112yes—
546C22⋊C8C23×C1112yes—
547#97C23×C1112yes—
548#97C23×C1112yes—
549C4×C8C23×C1111yescharacteristic
550C4×C8C23×C1111yescharacteristic
551C4×C8C23×C1111yescharacteristic
552C4×C8C23×C1111yescharacteristic
553C4×C8C23×C1112yes—
554C2×C11—41no—
555C2×C11—42no—
556C2×C11—44no—
557C2×C11D4×#4111yescharacteristic
558C2×C11C2×#57811yescharacteristic
559C2×C11#358411yescharacteristic
560#41—24no—
561#41—28no—
562#41—42no—
563#41—44no—
564C2×Q8—22no—
565C2×Q8C2×D4×C1111yescharacteristic
566C2×Q8C24×C1112yes—
567C2×Q8C24×C1114yes—
568C2×D4—22no—
569C2×D4—24no—
570C2×D4C2×D4×C1111yescharacteristic
571C2×D4C2×D4×C1112yes—
572C2×D4C24×C1112yes—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4C2×D4×C1111yescharacteristic
580C22×C4C2×D4×C1111yescharacteristic
581C22×C4C24×C1111yescharacteristic
582C22×C4C24×C1112yes—
583Q16—22no—
584Q16—24no—
585Q16—42no—
586Q16—44no—
587SD16—24no—
588SD16—28no—
589D8C11×#4114yes—
590M16—42no—
591C2×C8—22no—
592C2×C8—24no—
593C2×C8—41no—
594C2×C8C24×C1111yescharacteristic
595C2×C8C24×C1111yescharacteristic
596C2×C8C24×C1111yescharacteristic
597C2×C8C24×C1112yes—
598C2×C8C24×C1112yes—
599C2×C8C24×C1111yescharacteristic
600C4⋊C4—24no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—24no—
615C4⋊C4C2×D4×C1112yes—
616C4⋊C4C2×D4×C1111yescharacteristic
617C4⋊C4C2×D4×C1112yes—
618C4⋊C4C2×D4×C1111yescharacteristic
619C4⋊C4C2×D4×C1112yes—
620C4⋊C4C2×D4×C1112yes—
621C4⋊C4C24×C1112yes—
622C4⋊C4C24×C1112yes—
623C4⋊C4C24×C1114yes—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—22no—
627C22⋊C4—24no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—24no—
631C22⋊C4C2×D4×C1112yes—
632C22⋊C4C2×D4×C1112yes—
633C22⋊C4C2×D4×C1112yes—
634C22⋊C4C2×D4×C1112yes—
635C22⋊C4C2×D4×C1112yes—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—24no—
640C42—24no—
641C42C2×D4×C1111yescharacteristic
642C42C2×D4×C1111yescharacteristic
643C42C24×C1111yescharacteristic
644C42C24×C1111yescharacteristic
645C42C24×C1112yes—
646C11#6147711yescharacteristic, direct product factor, Sylow
647C23—22no—
648C23C22×D4×C1111yescharacteristic
649C23C22×D4×C1112yes—
650Q8—22no—
651Q8—22no—
652Q8—24no—
653Q8—24no—
654Q8—22no—
655Q8—82no—
656D4—22no—
657D4—22no—
658D4—42no—
659D4—44no—
660D4—48no—
661D4C2×C11×#4114yes—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—41no—
673C2×C4—44no—
674C2×C4—48no—
675C2×C4—44no—
676C2×C4—82no—
677C2×C4—84no—
678C2×C4—84no—
679C2×C4C22×D4×C1111yescharacteristic
680C2×C4C22×D4×C1111yescharacteristic
681C2×C4C22×D4×C1111yescharacteristic
682C2×C4C22×D4×C1112yes—
683C2×C4C22×D4×C1111yescharacteristic
684C2×C4C22×D4×C1112yes—
685C2×C4C22×D4×C1112yes—
686C2×C4C22×D4×C1111yescharacteristic
687C2×C4C25×C1111yescharacteristic
688C8—21no—
689C8—22no—
690C8—21no—
691C8—21no—
692C8—22no—
693C8C2×C11×#4112yes—
694C22—21no—
695C22—22no—
696C22—24no—
697C22—21no—
698C22—22no—
699C22—21no—
700C22—22no—
701C22—42no—
702C22—42no—
703C22C23×D4×C1111yescharacteristic
704C4—21no—
705C4—22no—
706C4—21no—
707C4—22no—
708C4—21no—
709C4—21no—
710C4—22no—
711C4—42no—
712C4—44no—
713C4—42no—
714C4—42no—
715C4—44no—
716C4C11×#57812yes—
717C4C22×C11×#4111yescharacteristic
718C4C11×#58511yescharacteristic
719C2—41no—
720C2—42no—
721C2—44no—
722C2D4×C11×#4111yescharacteristic
723C2C2×C11×#57811yescharacteristic
724C2C11×#358411yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
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
1. C11×#3515C2semidirect
2. C11×#3395C2semidirect
3. C11×#3380C2semidirect
4. C11×#3372C2semidirect
5. C11×#3338C2semidirect
6. C11×#3336C2semidirect
7. C11×#3331C2semidirect
8. C11×#3315C2semidirect
9. C11×#3283C2semidirect
10. C11×#3283C2semidirect
11. C11×#3177C2semidirect
12. C11×#3170C2semidirect
13. C11×#3120C2semidirect
14. C11×#3116C2semidirect
15. C11×#2966C2semidirect
16. C11×#2951C2semidirect
17. C4×C11×#135C2semidirect
198. #61477C11direct (N × H)
285. #3515C2×C11semidirect
286. #3395C2×C11semidirect
287. #3380C2×C11semidirect
288. #3372C2×C11semidirect
289. #3338C2×C11semidirect
290. #3336C2×C11semidirect
291. #3331C2×C11semidirect
292. #3315C2×C11semidirect
293. #3283C2×C11semidirect
294. #3283C2×C11semidirect
295. #3177C2×C11semidirect
296. #3170C2×C11semidirect
297. #3120C2×C11semidirect
298. #3116C2×C11semidirect
299. #2966C2×C11semidirect
300. #2951C2×C11semidirect
301. C4×#135C2×C11semidirect
646. C11#61477direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35152
C11×#33952
C11×#33802
C11×#33722
C11×#33382
C11×#33362
C11×#33312
C11×#33152
C11×#32832
C11×#31772
C11×#31702
C11×#31202
C11×#31162
C11×#29662
C11×#29512
C4×C11×#1352
#6147711