Finite Group Databasebeta

← C11×#24030 #14601223

Subgroups — C11×#24030 #14601223

Order 2816.

1280 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3489C211yesmaximal, characteristic
2C11×#3092C211yesmaximal, characteristic, complemented
3C2×C11×#417C211yesmaximal, characteristic, complemented
4C11×#2502C211yesmaximal, characteristic, complemented
5C11×#2039C212yesmaximal, complemented
6C11×#2038C212yesmaximal, complemented
7C11×#1901C211yesmaximal, characteristic, complemented
8C11×#1871C211yesmaximal, characteristic, complemented
9C11×#1859C212yesmaximal, complemented
10C11×#1793C212yesmaximal, complemented
11C11×#1789C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2211yescharacteristic
13C22×C11×#41C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15D4×Q8×C11—21no—
16C11×#548—21no—
17C11×#547—21no—
18C11×#547—22no—
19C11×#546—21no—
20C11×#546—22no—
21C11×#537—21no—
22C11×#537C2211yescharacteristic
23C11×#536—21no—
24C11×#536C2211yescharacteristic
25C11×#525—21no—
26C11×#525C2211yescharacteristic
27C2×C11×C22⋊Q8—21no—
28C2×C11×C22⋊Q8C2211yescharacteristic
29C11×#520C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C11×#484—21no—
32C11×#483—21no—
33C11×#481—21no—
34C11×#480—21no—
35C11×#428C2212yescomplemented
36C2×C11×#104C2212yes—
37C2×C11×#104C2212yes—
38C2×C11×#104C2212yescomplemented
39C11×#417—21no—
40C11×#417—21no—
41C11×#417C2212yes—
42C11×#417C2212yes—
43C11×#417C2212yescomplemented
44C2×C11×#103—21no—
45C2×C11×#102—21no—
46C2×C11×#101C2212yescomplemented
47C11×#407C2211yescharacteristic
48C11×#398—22no—
49C11×#391C2212yescomplemented
50C11×#385—22no—
51C11×#384C2212yescomplemented
52C4×C11×C22⋊C4C2211yescharacteristic
53C11×#343C2212yescomplemented
54C11×#339C2212yescomplemented
55C11×2−1+4—24no—
56C11×2−1+4—42no—
57C2×C11×#41—21no—
58C2×C11×#41—21no—
59C2×C11×#41—21no—
60C2×C11×#41—22no—
61C2×C11×#41—21no—
62C2×C11×#41—24no—
63C2×C11×#41—42no—
64C2×C11×#41D411yescharacteristic
65C2×C11×#41D411yescharacteristic
66C2×C11×#41C2311yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C2×C11×#41C2311yescharacteristic
69C22×Q8×C11—21no—
70C22×Q8×C11—21no—
71C22×Q8×C11D411yescharacteristic
72C22×Q8×C11C2311yescharacteristic
73C22×D4×C11—21no—
74C22×D4×C11D411yescharacteristic
75C23×C4×C11—21no—
76C23×C4×C11—21no—
77C23×C4×C11C2311yescharacteristic
78C2×C11×M16—21no—
79C2×C11×M16—42no—
80C2×C11×M16C2312yes—
81C2×C11×M16C2312yes—
82C22×C8×C11—21no—
83C11×C4⋊Q8—22no—
84C11×C4⋊Q8—21no—
85C11×#124—22no—
86C11×#124—21no—
87C11×#123—22no—
88C11×#123—22no—
89C11×#123—22no—
90C11×#123—21no—
91C11×#123—22no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8—21no—
96C11×C22⋊Q8—21no—
97C11×C22⋊Q8—21no—
98C11×C22⋊Q8—21no—
99C11×C22⋊Q8—21no—
100C11×C22⋊Q8—21no—
101C11×C22⋊Q8—21no—
102C11×C22⋊Q8—21no—
103C11×C22⋊Q8D411yescharacteristic
104C11×C22⋊Q8D411yescharacteristic
105C11×#121—22no—
106C11×#121—22no—
107C11×#121—22no—
108C11×#121—21no—
109C11×#121—21no—
110C11×#121—22no—
111C11×#121D411yescharacteristic
112C11×#121D411yescharacteristic
113C11×#120—22no—
114C11×#120—21no—
115C4×Q8×C11—21no—
116C4×D4×C11—22no—
117C4×D4×C11—22no—
118C4×D4×C11—21no—
119C4×D4×C11—22no—
120C4×D4×C11—21no—
121C4×D4×C11—21no—
122C11×#117—21no—
123C11×#117C2311yescharacteristic
124C2×C11×C4⋊C4—22no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—24no—
132C2×C11×C4⋊C4D412yes—
133C2×C11×C4⋊C4C2312yes—
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C22⋊C4—22no—
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4D412yes—
138C2×C42×C11C2312yes—
139C11×#107—22no—
140C11×#106—22no—
141C11×#104—24no—
142C11×#104—42no—
143C11×#104—42no—
144C11×#103—22no—
145C11×#103—22no—
146C11×#103—22no—
147C11×#102—22no—
148C11×#102—22no—
149C11×#102—22no—
150C11×#101—42no—
151C11×C22⋊C8—21no—
152C11×C22⋊C8—21no—
153C11×#95—21no—
154C11×#95—24no—
155#24030C1111yesmaximal, characteristic, direct product factor, Sylow
156C24×C11—21no—
157C24×C11C2×D411yescharacteristic
158C11×#41—22no—
159C11×#41—22no—
160C11×#41—22no—
161C11×#41—22no—
162C11×#41—22no—
163C11×#41—22no—
164C11×#41—22no—
165C11×#41—44no—
166C11×#41—41no—
167C11×#41—41no—
168C11×#41—44no—
169C11×#41—44no—
170C11×#41—48no—
171C11×#41—42no—
172C11×#41—42no—
173C11×#41#4114yes—
174C2×Q8×C11—22no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—22no—
179C2×Q8×C11—22no—
180C2×Q8×C11—22no—
181C2×Q8×C11—41no—
182C2×Q8×C11—44no—
183C2×Q8×C11—42no—
184C2×Q8×C11—42no—
185C2×Q8×C11C2×D411yescharacteristic
186C2×Q8×C11C2×D411yescharacteristic
187C2×Q8×C11C2×D411yescharacteristic
188C2×D4×C11—21no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—22no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—41no—
200C2×D4×C11—44no—
201C2×D4×C11C2×D411yescharacteristic
202C2×D4×C11C2×D411yescharacteristic
203C2×D4×C11C2×D411yescharacteristic
204C22×C4×C11—21no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—21no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—22no—
217C22×C4×C11—44no—
218C22×C4×C11—41no—
219C22×C4×C11—41no—
220C22×C4×C11—82no—
221C22×C4×C11C2×D412yes—
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D412yes—
228C22×C4×C11C2411yescharacteristic
229C11×M16—22no—
230C11×M16—22no—
231C11×M16—22no—
232C11×M16—22no—
233C11×M16—42no—
234C2×C8×C11—22no—
235C2×C8×C11—22no—
236C2×C8×C11—42no—
237C11×C4⋊C4—22no—
238C11×C4⋊C4—22no—
239C11×C4⋊C4—22no—
240C11×C4⋊C4—22no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—22no—
243C11×C4⋊C4—22no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—22no—
248C11×C4⋊C4—22no—
249C11×C4⋊C4—41no—
250C11×C4⋊C4—41no—
251C11×C4⋊C4—84no—
252C11×C4⋊C4C2×D411yescharacteristic
253C11×C4⋊C4C2×D411yescharacteristic
254C11×C22⋊C4—24no—
255C11×C22⋊C4—22no—
256C11×C22⋊C4—22no—
257C11×C22⋊C4—22no—
258C11×C22⋊C4—22no—
259C11×C22⋊C4—22no—
260C11×C22⋊C4—21no—
261C11×C22⋊C4—22no—
262C11×C22⋊C4—22no—
263C11×C22⋊C4—21no—
264C11×C22⋊C4—21no—
265C11×C22⋊C4—21no—
266C11×C22⋊C4—21no—
267C42×C11—22no—
268C42×C11—21no—
269C42×C11—22no—
270C42×C11—22no—
271#3489C2×C1111yescharacteristic
272#3092C2×C1111yescharacteristic, complemented
273C2×#417C2×C1111yescharacteristic, complemented
274#2502C2×C1111yescharacteristic, complemented
275#2039C2×C1112yescomplemented
276#2038C2×C1112yescomplemented
277#1901C2×C1111yescharacteristic, complemented
278#1871C2×C1111yescharacteristic, complemented
279#1859C2×C1112yescomplemented
280#1793C2×C1112yescomplemented
281#1789C2×C1111yescharacteristic, complemented
282C23×C11—21no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—41no—
288C23×C11—42no—
289C23×C11—42no—
290C23×C11—81no—
291C23×C11#12011yescharacteristic
292C23×C11#12011yescharacteristic
293C23×C11C22×D411yescharacteristic
294Q8×C11—21no—
295Q8×C11—21no—
296Q8×C11—21no—
297Q8×C11—22no—
298Q8×C11—42no—
299Q8×C11—44no—
300Q8×C11—41no—
301Q8×C11—41no—
302Q8×C11—42no—
303Q8×C11#12312yes—
304D4×C11—24no—
305D4×C11—21no—
306D4×C11—21no—
307D4×C11—21no—
308D4×C11—22no—
309D4×C11—42no—
310D4×C11—42no—
311D4×C11—42no—
312D4×C11—44no—
313D4×C11—42no—
314D4×C11—42no—
315D4×C11—42no—
316D4×C11—81no—
317D4×C11—82no—
318D4×C11#12312yes—
319C2×C4×C11—21no—
320C2×C4×C11—22no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—24no—
328C2×C4×C11—24no—
329C2×C4×C11—21no—
330C2×C4×C11—22no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—22no—
334C2×C4×C11—21no—
335C2×C4×C11—24no—
336C2×C4×C11—42no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11—44no—
340C2×C4×C11—42no—
341C2×C4×C11—44no—
342C2×C4×C11—42no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—42no—
346C2×C4×C11—42no—
347C2×C4×C11—44no—
348C2×C4×C11—42no—
349C2×C4×C11—82no—
350C2×C4×C11—82no—
351C2×C4×C11—82no—
352C2×C4×C11#12011yescharacteristic
353C2×C4×C11#12011yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C2×#4112yes—
357C2×C4×C11H(5,𝔽2)12yes—
358C8×C11—42no—
359C8×C11—42no—
360C2×2−1+4C22×C1111yescharacteristic
361C22×#41C22×C1111yescharacteristic
362C22×M16C22×C1111yescharacteristic
363D4×Q8—21no—
364#548—21no—
365#547—21no—
366#547—22no—
367#546—21no—
368#546—22no—
369#537—21no—
370#537C22×C1111yescharacteristic
371#536—21no—
372#536C22×C1111yescharacteristic
373#525—21no—
374#525C22×C1111yescharacteristic
375C2×C22⋊Q8—21no—
376C2×C22⋊Q8C22×C1111yescharacteristic
377#520C22×C1111yescharacteristic
378C22×C4⋊C4C22×C1111yescharacteristic
379#484—21no—
380#483—21no—
381#481—21no—
382#480—21no—
383#428C22×C1112yescomplemented
384C2×#104C22×C1112yes—
385C2×#104C22×C1112yes—
386C2×#104C22×C1112yescomplemented
387#417—21no—
388#417—21no—
389#417C22×C1112yes—
390#417C22×C1112yes—
391#417C22×C1112yescomplemented
392C2×#103—21no—
393C2×#102—21no—
394C2×#101C22×C1112yescomplemented
395#407C22×C1111yescharacteristic
396#398—22no—
397#391C22×C1112yescomplemented
398#385—22no—
399#384C22×C1112yescomplemented
400C4×C22⋊C4C22×C1111yescharacteristic
401#343C22×C1112yescomplemented
402#339C22×C1112yescomplemented
403C22×C11—21no—
404C22×C11—21no—
405C22×C11—21no—
406C22×C11—21no—
407C22×C11—21no—
408C22×C11—22no—
409C22×C11—21no—
410C22×C11—21no—
411C22×C11—44no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—84no—
421C22×C11#45612yes—
422C22×C11C2×#12011yescharacteristic
423C22×C11#54612yes—
424C4×C11—21no—
425C4×C11—21no—
426C4×C11—22no—
427C4×C11—44no—
428C4×C11—42no—
429C4×C11—41no—
430C4×C11—41no—
431C4×C11—41no—
432C4×C11—42no—
433C4×C11—41no—
434C4×C11—82no—
435C4×C11C2×#12311yescharacteristic
436C4×C11#53411yescharacteristic
437C4×C11#54612yes—
4382−1+4—24no—
4392−1+4—42no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—22no—
444C2×#41—21no—
445C2×#41—24no—
446C2×#41—42no—
447C2×#41D4×C1111yescharacteristic
448C2×#41D4×C1111yescharacteristic
449C2×#41C23×C1111yescharacteristic
450C2×#41C23×C1111yescharacteristic
451C2×#41C23×C1111yescharacteristic
452C22×Q8—21no—
453C22×Q8—21no—
454C22×Q8D4×C1111yescharacteristic
455C22×Q8C23×C1111yescharacteristic
456C22×D4—21no—
457C22×D4D4×C1111yescharacteristic
458C23×C4—21no—
459C23×C4—21no—
460C23×C4C23×C1111yescharacteristic
461C2×M16—21no—
462C2×M16—42no—
463C2×M16C23×C1112yes—
464C2×M16C23×C1112yes—
465C22×C8—21no—
466C4⋊Q8—22no—
467C4⋊Q8—21no—
468#124—22no—
469#124—21no—
470#123—22no—
471#123—22no—
472#123—22no—
473#123—21no—
474#123—22no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8—21no—
486C22⋊Q8D4×C1111yescharacteristic
487C22⋊Q8D4×C1111yescharacteristic
488#121—22no—
489#121—22no—
490#121—22no—
491#121—21no—
492#121—21no—
493#121—22no—
494#121D4×C1111yescharacteristic
495#121D4×C1111yescharacteristic
496#120—22no—
497#120—21no—
498C4×Q8—21no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—21no—
502C4×D4—22no—
503C4×D4—21no—
504C4×D4—21no—
505#117—21no—
506#117C23×C1111yescharacteristic
507C2×C4⋊C4—22no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—24no—
515C2×C4⋊C4D4×C1112yes—
516C2×C4⋊C4C23×C1112yes—
517C2×C4⋊C4C23×C1111yescharacteristic
518C2×C22⋊C4—22no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4D4×C1112yes—
521C2×C42C23×C1112yes—
522#107—22no—
523#106—22no—
524#104—24no—
525#104—42no—
526#104—42no—
527#103—22no—
528#103—22no—
529#103—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#101—42no—
534C22⋊C8—21no—
535C22⋊C8—21no—
536#95—21no—
537#95—24no—
538C2×C11—22no—
539C2×C11—22no—
540C2×C11—41no—
541C2×C11—42no—
542C2×C11—81no—
543C2×C11—81no—
544C2×C11#240511yescharacteristic
545C2×C11C2×#45611yescharacteristic
546C2×C11#302111yescharacteristic
547C24—21no—
548C24C2×D4×C1111yescharacteristic
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—44no—
557#41—41no—
558#41—41no—
559#41—44no—
560#41—44no—
561#41—48no—
562#41—42no—
563#41—42no—
564#41C11×#4114yes—
565C2×Q8—22no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—41no—
573C2×Q8—44no—
574C2×Q8—42no—
575C2×Q8—42no—
576C2×Q8C2×D4×C1111yescharacteristic
577C2×Q8C2×D4×C1111yescharacteristic
578C2×Q8C2×D4×C1111yescharacteristic
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—41no—
591C2×D4—44no—
592C2×D4C2×D4×C1111yescharacteristic
593C2×D4C2×D4×C1111yescharacteristic
594C2×D4C2×D4×C1111yescharacteristic
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—44no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—82no—
612C22×C4C2×D4×C1112yes—
613C22×C4C2×D4×C1111yescharacteristic
614C22×C4C2×D4×C1111yescharacteristic
615C22×C4C2×D4×C1111yescharacteristic
616C22×C4C2×D4×C1111yescharacteristic
617C22×C4C2×D4×C1111yescharacteristic
618C22×C4C2×D4×C1112yes—
619C22×C4C24×C1111yescharacteristic
620M16—22no—
621M16—22no—
622M16—22no—
623M16—22no—
624M16—42no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—42no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—21no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4—84no—
643C4⋊C4C2×D4×C1111yescharacteristic
644C4⋊C4C2×D4×C1111yescharacteristic
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—24no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C42—22no—
659C42—21no—
660C42—22no—
661C42—22no—
662C11#2403011yescharacteristic, direct product factor, Sylow
663C23—21no—
664C23—22no—
665C23—22no—
666C23—21no—
667C23—21no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23C11×#12011yescharacteristic
673C23C11×#12011yescharacteristic
674C23C22×D4×C1111yescharacteristic
675Q8—21no—
676Q8—21no—
677Q8—21no—
678Q8—22no—
679Q8—42no—
680Q8—44no—
681Q8—41no—
682Q8—41no—
683Q8—42no—
684Q8C11×#12312yes—
685D4—24no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—22no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—44no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—81no—
698D4—82no—
699D4C11×#12312yes—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—24no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4C11×#12011yescharacteristic
734C2×C4C11×#12011yescharacteristic
735C2×C4C22×D4×C1111yescharacteristic
736C2×C4C22×D4×C1111yescharacteristic
737C2×C4C2×C11×#4112yes—
738C2×C4C11×H(5,𝔽2)12yes—
739C8—42no—
740C8—42no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—22no—
747C22—21no—
748C22—21no—
749C22—44no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—84no—
759C22C11×#45612yes—
760C22C2×C11×#12011yescharacteristic
761C22C11×#54612yes—
762C4—21no—
763C4—21no—
764C4—22no—
765C4—44no—
766C4—42no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—41no—
772C4—82no—
773C4C2×C11×#12311yescharacteristic
774C4C11×#53411yescharacteristic
775C4C11×#54612yes—
776C2—22no—
777C2—22no—
778C2—41no—
779C2—42no—
780C2—81no—
781C2—81no—
782C2C11×#240511yescharacteristic
783C2C2×C11×#45611yescharacteristic
784C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3489C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3092C2semidirect
3. C2×C11×#417C2semidirect
4. C11×#2502C2semidirect
5. C11×#2039C2semidirect
6. C11×#2038C2semidirect
7. C11×#1901C2semidirect
8. C11×#1871C2semidirect
9. C11×#1859C2semidirect
10. C11×#1793C2semidirect
11. C11×#1789C2semidirect
35. C11×#428C22semidirect
38. C2×C11×#104C22semidirect
43. C11×#417C22semidirect
46. C2×C11×#101C22semidirect
49. C11×#391C22semidirect
51. C11×#384C22semidirect
53. C11×#343C22semidirect
54. C11×#339C22semidirect
155. #24030C11direct (N × H)
272. #3092C2×C11semidirect
273. C2×#417C2×C11semidirect
274. #2502C2×C11semidirect
275. #2039C2×C11semidirect
276. #2038C2×C11semidirect
277. #1901C2×C11semidirect
278. #1871C2×C11semidirect
279. #1859C2×C11semidirect
280. #1793C2×C11semidirect
281. #1789C2×C11semidirect
383. #428C22×C11semidirect
386. C2×#104C22×C11semidirect
391. #417C22×C11semidirect
394. C2×#101C22×C11semidirect
397. #391C22×C11semidirect
399. #384C22×C11semidirect
401. #343C22×C11semidirect
402. #339C22×C11semidirect
662. C11#24030direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34892
C11×#30922
C2×C11×#4172
C11×#25022
C11×#20392
C11×#20382
C11×#19012
C11×#18712
C11×#18592
C11×#17932
C11×#17892
#2403011