Finite Group Databasebeta

← C11×#61479 #14638672

Subgroups — C11×#61479 #14638672

Order 2816.

1880 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3517C212yesmaximal, complemented
2C11×#3391C211yesmaximal, characteristic, complemented
3C11×#3383C211yesmaximal, characteristic, complemented
4C11×#3368C212yesmaximal, complemented
5C11×#3339C212yesmaximal, complemented
6C11×#3334C211yesmaximal, characteristic, complemented
7C11×#3332C212yesmaximal, complemented
8C11×#3309C214yesmaximal, complemented
9C11×#3287C211yesmaximal, characteristic, complemented
10C11×#3287C212yesmaximal, complemented
11C11×#3176C212yesmaximal, complemented
12C11×#3169C211yesmaximal, characteristic, complemented
13C11×#3119C214yesmaximal, complemented
14C11×#3115C212yesmaximal, complemented
15C11×#2966C211yesmaximal, characteristic, complemented
16C11×#2951C212yesmaximal, complemented
17C4×C11×#135C211yesmaximal, characteristic, complemented
18C2×C11×#135C2211yescharacteristic
19C2×C11×#135C2212yes—
20C11×#557C2212yes—
21C11×#553—24no—
22C11×#553C2214yes—
23C11×#550—22no—
24C11×#550C2214yes—
25C11×#550C2212yes—
26C11×#550C2212yes—
27C11×#547—22no—
28C11×#547C2212yes—
29C11×#540—24no—
30C11×#540C2214yes—
31C11×#532—22no—
32C11×#532C2212yes—
33C11×#529—22no—
34C11×#529C2211yescharacteristic
35C11×#520C2214yes—
36C4×C11×#41C2212yes—
37C11×#500C2211yescharacteristic
38C11×#499C2212yes—
39C11×#493C2211yescharacteristic
40C11×#493C2212yes—
41C11×#490C2214yes—
42C11×#486C2212yes—
43C11×#482C2214yes—
44C11×#481C2214yes—
45C11×#480C2214yes—
46C11×#479C2214yes—
47C11×#478C2214yes—
48C11×#475C2212yes—
49C11×#474C2212yes—
50C11×#469C2214yes—
51C11×#466C2212yes—
52C11×#466C2212yes—
53C11×#466C2212yes—
54C11×#466C2212yes—
55C11×#460C2212yes—
56C11×#460C2214yes—
57C11×#459C2214yes—
58C11×#459C2212yes—
59C11×#449C2214yes—
60C11×#449C2214yes—
61C11×#449C2214yes—
62C11×#446C2211yescharacteristic
63C8×Q8×C11C2211yescharacteristic
64C11×#442C2214yes—
65C11×#440C2214yes—
66C11×#440C2214yes—
67C4×C11×Q16C2211yescharacteristic
68C4×C11×Q16C2211yescharacteristic
69C4×C11×Q16C2212yes—
70C4×C11×SD16C2212yes—
71C4×C11×SD16C2212yes—
72C4×C11×D8C2212yes—
73C4×C11×D8C2212yes—
74C4×C11×D8C2211yescharacteristic
75C4×C11×D8C2211yescharacteristic
76C4×C11×D8C2212yes—
77C11×#436C2211yescharacteristic
78C11×#435C2212yes—
79C8×D4×C11C2211yescharacteristic
80C8×D4×C11C2212yes—
81C11×#433C2212yes—
82C11×#432C2211yescharacteristic
83C11×#427C2211yescharacteristic
84C2×C11×#107C2212yes—
85C11×#417C2214yes—
86C11×#416C2212yes—
87C11×#405C2212yes—
88C2×C4×C8×C11C2211yescharacteristic
89C2×C11×#41—22no—
90C2×C11×#41—22no—
91C2×C11×#41—22no—
92C2×C11×#41C2312yes—
93C2×C11×#41C2314yes—
94C11×#135—24no—
95C11×#135—28no—
96C2×C11×Q16C2311yescharacteristic
97C2×C11×SD16C2312yes—
98C2×C11×SD16C2314yes—
99C2×C11×D8C2312yes—
100C2×C11×D8C2311yescharacteristic
101C2×C11×D8C2312yes—
102C2×C11×D8C2314yes—
103C2×C11×M16C2312yes—
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2312yes—
106C22×C8×C11C2311yescharacteristic
107C11×C4⋊Q8—22no—
108C11×C4⋊Q8C2312yes—
109C11×#127—22no—
110C11×#127—24no—
111C11×#127C2314yes—
112C11×#127C2312yes—
113C11×#126—24no—
114C11×#126D412yes—
115C11×#125—24no—
116C11×#125D411yescharacteristic
117C11×#125C2314yes—
118C11×#124—22no—
119C11×#124D411yescharacteristic
120C11×#123—24no—
121C11×#123—24no—
122C11×#123—24no—
123C11×#123—24no—
124C11×#123D412yes—
125C11×C22⋊Q8—22no—
126C11×C22⋊Q8D411yescharacteristic
127C11×#121—24no—
128C11×#121—22no—
129C11×#121—22no—
130C11×#121—24no—
131C11×#121—24no—
132C11×#121—24no—
133C11×#121—24no—
134C11×#121—24no—
135C11×#121—24no—
136C11×#121D411yescharacteristic
137C11×#121C2314yes—
138C11×#121C2314yes—
139C11×#121C2314yes—
140C4×Q8×C11—22no—
141C4×Q8×C11C2312yes—
142C4×Q8×C11C2312yes—
143C4×Q8×C11C2314yes—
144C4×Q8×C11C2311yescharacteristic
145C4×D4×C11—22no—
146C4×D4×C11—22no—
147C4×D4×C11—22no—
148C4×D4×C11—24no—
149C4×D4×C11—24no—
150C4×D4×C11—24no—
151C4×D4×C11—24no—
152C4×D4×C11—22no—
153C4×D4×C11C2312yes—
154C4×D4×C11C2312yes—
155C4×D4×C11C2314yes—
156C4×D4×C11C2314yes—
157C4×D4×C11C2311yescharacteristic
158C4×D4×C11C2312yes—
159C11×#117—24no—
160C11×#117—22no—
161C11×#117C2312yes—
162C11×#117C2312yes—
163C2×C11×C4⋊C4—24no—
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×#103C2312yes—
180C11×#103C2314yes—
181C11×#102C2312yes—
182C11×#102C2314yes—
183C11×#102C2314yes—
184C11×#102C2314yes—
185C11×#102C2312yes—
186C11×#102C2314yes—
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#61479C1111yesmaximal, characteristic, direct product factor, Sylow
199C11×#41—24no—
200C11×#41—28no—
201C11×#41—42no—
202C11×#41—44no—
203C11×#41—84no—
204C11×#41—84no—
205C11×#41—84no—
206C2×Q8×C11—22no—
207C2×Q8×C11C2×D411yescharacteristic
208C2×Q8×C11C2412yes—
209C2×D4×C11—22no—
210C2×D4×C11—24no—
211C2×D4×C11—24no—
212C2×D4×C11—24no—
213C2×D4×C11—24no—
214C2×D4×C11—22no—
215C2×D4×C11—22no—
216C2×D4×C11—24no—
217C2×D4×C11—24no—
218C2×D4×C11C2×D411yescharacteristic
219C2×D4×C11C2×D412yes—
220C2×D4×C11C2412yes—
221C2×D4×C11C2414yes—
222C22×C4×C11—24no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—24no—
226C22×C4×C11—22no—
227C22×C4×C11—24no—
228C22×C4×C11—24no—
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2411yescharacteristic
232C22×C4×C11C2412yes—
233C11×Q16#4114yescomplemented
234C11×SD16—24no—
235C11×SD16—28no—
236C11×D8—24no—
237C11×D8—22no—
238C11×D8—42no—
239C11×D8—44no—
240C11×M16—42no—
241C2×C8×C11—22no—
242C2×C8×C11—24no—
243C2×C8×C11—41no—
244C2×C8×C11C2411yescharacteristic
245C2×C8×C11C2411yescharacteristic
246C2×C8×C11C2411yescharacteristic
247C2×C8×C11C2412yes—
248C2×C8×C11C2412yes—
249C2×C8×C11C2411yescharacteristic
250C11×C4⋊C4—22no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—22no—
254C11×C4⋊C4—22no—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—24no—
257C11×C4⋊C4C2×D412yes—
258C11×C4⋊C4C2×D412yes—
259C11×C4⋊C4C2×D411yescharacteristic
260C11×C4⋊C4C2×D412yes—
261C11×C4⋊C4C2×D411yescharacteristic
262C11×C4⋊C4C2×D412yes—
263C11×C4⋊C4C2412yes—
264C11×C4⋊C4C2412yes—
265C11×C4⋊C4C2414yes—
266C11×C22⋊C4—22no—
267C11×C22⋊C4—24no—
268C11×C22⋊C4—22no—
269C11×C22⋊C4—22no—
270C11×C22⋊C4—24no—
271C11×C22⋊C4—24no—
272C11×C22⋊C4—24no—
273C11×C22⋊C4—24no—
274C11×C22⋊C4C2×D412yes—
275C11×C22⋊C4C2×D412yes—
276C11×C22⋊C4C2×D412yes—
277C11×C22⋊C4C2×D412yes—
278C11×C22⋊C4C2×D412yes—
279C42×C11—22no—
280C42×C11—22no—
281C42×C11—22no—
282C42×C11—24no—
283C42×C11C2×D411yescharacteristic
284C42×C11C2×D411yescharacteristic
285C42×C11C2411yescharacteristic
286C42×C11C2411yescharacteristic
287C42×C11C2412yes—
288#3517C2×C1112yescomplemented
289#3391C2×C1111yescharacteristic, complemented
290#3383C2×C1111yescharacteristic, complemented
291#3368C2×C1112yescomplemented
292#3339C2×C1112yescomplemented
293#3334C2×C1111yescharacteristic, complemented
294#3332C2×C1112yescomplemented
295#3309C2×C1114yescomplemented
296#3287C2×C1111yescharacteristic, complemented
297#3287C2×C1112yescomplemented
298#3176C2×C1112yescomplemented
299#3169C2×C1111yescharacteristic, complemented
300#3119C2×C1114yescomplemented
301#3115C2×C1112yescomplemented
302#2966C2×C1111yescharacteristic, complemented
303#2951C2×C1112yescomplemented
304C4×#135C2×C1111yescharacteristic, complemented
305C23×C11—22no—
306C23×C11—24no—
307C23×C11C22×D411yescharacteristic
308C23×C11C22×D412yes—
309Q8×C11—22no—
310Q8×C11—22no—
311Q8×C11—44no—
312Q8×C11C2×#4114yes—
313D4×C11—22no—
314D4×C11—22no—
315D4×C11—24no—
316D4×C11—24no—
317D4×C11—22no—
318D4×C11—42no—
319D4×C11—44no—
320D4×C11—48no—
321D4×C11—44no—
322D4×C11—82no—
323D4×C11—84no—
324D4×C11—84no—
325D4×C11—84no—
326D4×C11—84no—
327D4×C11—84no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—21no—
331C2×C4×C11—22no—
332C2×C4×C11—21no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—24no—
337C2×C4×C11—41no—
338C2×C4×C11—44no—
339C2×C4×C11—48no—
340C2×C4×C11—44no—
341C2×C4×C11—82no—
342C2×C4×C11—84no—
343C2×C4×C11—84no—
344C2×C4×C11—84no—
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C22×D412yes—
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C22×D412yes—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C2511yescharacteristic
354C8×C11—21no—
355C8×C11—22no—
356C8×C11—21no—
357C8×C11—21no—
358C8×C11—22no—
359C8×C11C2×#4112yes—
360C2×#135C22×C1111yescharacteristic
361C2×#135C22×C1112yes—
362#557C22×C1112yes—
363#553—24no—
364#553C22×C1114yes—
365#550—22no—
366#550C22×C1112yes—
367#550C22×C1114yes—
368#550C22×C1112yes—
369#547—22no—
370#547C22×C1112yes—
371#540—24no—
372#540C22×C1114yes—
373#532—22no—
374#532C22×C1112yes—
375#529—22no—
376#529C22×C1111yescharacteristic
377#520C22×C1114yes—
378C4×#41C22×C1112yes—
379#500C22×C1111yescharacteristic
380#499C22×C1112yes—
381#493C22×C1111yescharacteristic
382#493C22×C1112yes—
383#490C22×C1114yes—
384#486C22×C1112yes—
385#482C22×C1114yes—
386#481C22×C1114yes—
387#480C22×C1114yes—
388#479C22×C1114yes—
389#478C22×C1114yes—
390#475C22×C1112yes—
391#474C22×C1112yes—
392#469C22×C1114yes—
393#466C22×C1112yes—
394#466C22×C1112yes—
395#466C22×C1112yes—
396#466C22×C1112yes—
397#460C22×C1112yes—
398#460C22×C1114yes—
399#459C22×C1112yes—
400#459C22×C1114yes—
401#449C22×C1114yes—
402#449C22×C1114yes—
403#449C22×C1114yes—
404#446C22×C1111yescharacteristic
405C8×Q8C22×C1111yescharacteristic
406#442C22×C1114yes—
407#440C22×C1114yes—
408#440C22×C1114yes—
409C4×Q16C22×C1111yescharacteristic
410C4×Q16C22×C1112yes—
411C4×Q16C22×C1111yescharacteristic
412C4×SD16C22×C1112yes—
413C4×SD16C22×C1112yes—
414C4×D8C22×C1111yescharacteristic
415C4×D8C22×C1112yes—
416C4×D8C22×C1112yes—
417C4×D8C22×C1112yes—
418C4×D8C22×C1111yescharacteristic
419#436C22×C1111yescharacteristic
420#435C22×C1112yes—
421C8×D4C22×C1111yescharacteristic
422C8×D4C22×C1112yes—
423#433C22×C1112yes—
424#432C22×C1111yescharacteristic
425#427C22×C1111yescharacteristic
426C2×#107C22×C1112yes—
427#417C22×C1114yes—
428#416C22×C1112yes—
429#405C22×C1112yes—
430C2×C4×C8C22×C1111yescharacteristic
431C22×C11—21no—
432C22×C11—22no—
433C22×C11—21no—
434C22×C11—22no—
435C22×C11—21no—
436C22×C11—22no—
437C22×C11—42no—
438C22×C11—44no—
439C22×C11—42no—
440C22×C11—44no—
441C22×C11—42no—
442C22×C11—44no—
443C22×C11C23×D411yescharacteristic
444C4×C11—21no—
445C4×C11—21no—
446C4×C11—22no—
447C4×C11—21no—
448C4×C11—22no—
449C4×C11—24no—
450C4×C11—21no—
451C4×C11—22no—
452C4×C11—42no—
453C4×C11—42no—
454C4×C11—44no—
455C4×C11#57612yes—
456C4×C11C22×#4111yescharacteristic
457C4×C11#58511yescharacteristic
458C2×#41—22no—
459C2×#41—22no—
460C2×#41—22no—
461C2×#41C23×C1112yes—
462C2×#41C23×C1114yes—
463#135—24no—
464#135—28no—
465C2×Q16C23×C1111yescharacteristic
466C2×SD16C23×C1112yes—
467C2×SD16C23×C1114yes—
468C2×D8C23×C1111yescharacteristic
469C2×D8C23×C1112yes—
470C2×D8C23×C1112yes—
471C2×D8C23×C1114yes—
472C2×M16C23×C1112yes—
473C22×C8C23×C1111yescharacteristic
474C22×C8C23×C1112yes—
475C22×C8C23×C1111yescharacteristic
476C4⋊Q8—22no—
477C4⋊Q8C23×C1112yes—
478#127—22no—
479#127—24no—
480#127C23×C1112yes—
481#127C23×C1114yes—
482#126—24no—
483#126D4×C1112yes—
484#125—24no—
485#125D4×C1111yescharacteristic
486#125C23×C1114yes—
487#124—22no—
488#124D4×C1111yescharacteristic
489#123—24no—
490#123—24no—
491#123—24no—
492#123—24no—
493#123D4×C1112yes—
494C22⋊Q8—22no—
495C22⋊Q8D4×C1111yescharacteristic
496#121—24no—
497#121—22no—
498#121—22no—
499#121—24no—
500#121—24no—
501#121—24no—
502#121—24no—
503#121—24no—
504#121—24no—
505#121D4×C1111yescharacteristic
506#121C23×C1114yes—
507#121C23×C1114yes—
508#121C23×C1114yes—
509C4×Q8—22no—
510C4×Q8C23×C1112yes—
511C4×Q8C23×C1112yes—
512C4×Q8C23×C1114yes—
513C4×Q8C23×C1111yescharacteristic
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—22no—
517C4×D4—24no—
518C4×D4—24no—
519C4×D4—24no—
520C4×D4—24no—
521C4×D4—22no—
522C4×D4C23×C1112yes—
523C4×D4C23×C1112yes—
524C4×D4C23×C1114yes—
525C4×D4C23×C1114yes—
526C4×D4C23×C1111yescharacteristic
527C4×D4C23×C1112yes—
528#117—24no—
529#117—22no—
530#117C23×C1112yes—
531#117C23×C1112yes—
532C2×C4⋊C4—24no—
533C2×C4⋊C4C23×C1114yes—
534C2×C42—22no—
535C2×C42C23×C1111yescharacteristic
536#107C23×C1111yescharacteristic
537#107C23×C1112yes—
538#107C23×C1114yes—
539#107C23×C1111yescharacteristic
540#107C23×C1112yes—
541#106C23×C1112yes—
542#106C23×C1114yes—
543C4⋊C8C23×C1111yescharacteristic
544C4⋊C8C23×C1111yescharacteristic
545C4⋊C8C23×C1112yes—
546C4⋊C8C23×C1112yes—
547#103C23×C1112yes—
548#103C23×C1112yes—
549#103C23×C1114yes—
550#102C23×C1112yes—
551#102C23×C1112yes—
552#102C23×C1114yes—
553#102C23×C1114yes—
554#102C23×C1114yes—
555#102C23×C1114yes—
556#102C23×C1114yes—
557C22⋊C8C23×C1112yes—
558C22⋊C8C23×C1112yes—
559C22⋊C8C23×C1112yes—
560#97C23×C1112yes—
561#97C23×C1112yes—
562C4×C8C23×C1111yescharacteristic
563C4×C8C23×C1111yescharacteristic
564C4×C8C23×C1111yescharacteristic
565C4×C8C23×C1111yescharacteristic
566C4×C8C23×C1112yes—
567C2×C11—41no—
568C2×C11—42no—
569C2×C11—82no—
570C2×C11—84no—
571C2×C11D4×#4111yescharacteristic
572C2×C11C2×#57611yescharacteristic
573C2×C11#358411yescharacteristic
574#41—24no—
575#41—28no—
576#41—42no—
577#41—44no—
578#41—84no—
579#41—84no—
580#41—84no—
581C2×Q8—22no—
582C2×Q8C2×D4×C1111yescharacteristic
583C2×Q8C24×C1112yes—
584C2×D4—22no—
585C2×D4—24no—
586C2×D4—24no—
587C2×D4—24no—
588C2×D4—24no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4C2×D4×C1111yescharacteristic
594C2×D4C2×D4×C1112yes—
595C2×D4C24×C1112yes—
596C2×D4C24×C1114yes—
597C22×C4—24no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—24no—
601C22×C4—22no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4C2×D4×C1111yescharacteristic
605C22×C4C2×D4×C1111yescharacteristic
606C22×C4C24×C1111yescharacteristic
607C22×C4C24×C1112yes—
608Q16C11×#4114yescomplemented
609SD16—24no—
610SD16—28no—
611D8—22no—
612D8—24no—
613D8—42no—
614D8—44no—
615M16—42no—
616C2×C8—22no—
617C2×C8—24no—
618C2×C8—41no—
619C2×C8C24×C1111yescharacteristic
620C2×C8C24×C1111yescharacteristic
621C2×C8C24×C1111yescharacteristic
622C2×C8C24×C1112yes—
623C2×C8C24×C1112yes—
624C2×C8C24×C1111yescharacteristic
625C4⋊C4—22no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4C2×D4×C1112yes—
633C4⋊C4C2×D4×C1112yes—
634C4⋊C4C2×D4×C1111yescharacteristic
635C4⋊C4C2×D4×C1112yes—
636C4⋊C4C2×D4×C1111yescharacteristic
637C4⋊C4C2×D4×C1112yes—
638C4⋊C4C24×C1112yes—
639C4⋊C4C24×C1112yes—
640C4⋊C4C24×C1114yes—
641C22⋊C4—22no—
642C22⋊C4—24no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4C2×D4×C1112yes—
650C22⋊C4C2×D4×C1112yes—
651C22⋊C4C2×D4×C1112yes—
652C22⋊C4C2×D4×C1112yes—
653C22⋊C4C2×D4×C1112yes—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—24no—
658C42C2×D4×C1111yescharacteristic
659C42C2×D4×C1111yescharacteristic
660C42C24×C1111yescharacteristic
661C42C24×C1111yescharacteristic
662C42C24×C1112yes—
663C11#6147911yescharacteristic, direct product factor, Sylow
664C23—22no—
665C23—24no—
666C23C22×D4×C1111yescharacteristic
667C23C22×D4×C1112yes—
668Q8—22no—
669Q8—22no—
670Q8—44no—
671Q8C2×C11×#4114yes—
672D4—22no—
673D4—22no—
674D4—24no—
675D4—24no—
676D4—22no—
677D4—42no—
678D4—44no—
679D4—48no—
680D4—44no—
681D4—82no—
682D4—84no—
683D4—84no—
684D4—84no—
685D4—84no—
686D4—84no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—41no—
697C2×C4—44no—
698C2×C4—48no—
699C2×C4—44no—
700C2×C4—82no—
701C2×C4—84no—
702C2×C4—84no—
703C2×C4—84no—
704C2×C4C22×D4×C1111yescharacteristic
705C2×C4C22×D4×C1111yescharacteristic
706C2×C4C22×D4×C1112yes—
707C2×C4C22×D4×C1111yescharacteristic
708C2×C4C22×D4×C1111yescharacteristic
709C2×C4C22×D4×C1112yes—
710C2×C4C22×D4×C1112yes—
711C2×C4C22×D4×C1111yescharacteristic
712C2×C4C25×C1111yescharacteristic
713C8—21no—
714C8—22no—
715C8—21no—
716C8—21no—
717C8—22no—
718C8C2×C11×#4112yes—
719C22—21no—
720C22—22no—
721C22—21no—
722C22—22no—
723C22—21no—
724C22—22no—
725C22—42no—
726C22—44no—
727C22—42no—
728C22—44no—
729C22—42no—
730C22—44no—
731C22C23×D4×C1111yescharacteristic
732C4—21no—
733C4—22no—
734C4—24no—
735C4—21no—
736C4—22no—
737C4—21no—
738C4—21no—
739C4—22no—
740C4—42no—
741C4—44no—
742C4—42no—
743C4C11×#57612yes—
744C4C22×C11×#4111yescharacteristic
745C4C11×#58511yescharacteristic
746C2—41no—
747C2—42no—
748C2—82no—
749C2—84no—
750C2D4×C11×#4111yescharacteristic
751C2C2×C11×#57611yescharacteristic
752C2C11×#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×#3517C2semidirect
2. C11×#3391C2semidirect
3. C11×#3383C2semidirect
4. C11×#3368C2semidirect
5. C11×#3339C2semidirect
6. C11×#3334C2semidirect
7. C11×#3332C2semidirect
8. C11×#3309C2semidirect
9. C11×#3287C2semidirect
10. C11×#3287C2semidirect
11. C11×#3176C2semidirect
12. C11×#3169C2semidirect
13. C11×#3119C2semidirect
14. C11×#3115C2semidirect
15. C11×#2966C2semidirect
16. C11×#2951C2semidirect
17. C4×C11×#135C2semidirect
198. #61479C11direct (N × H)
233. C11×Q16#41semidirect
288. #3517C2×C11semidirect
289. #3391C2×C11semidirect
290. #3383C2×C11semidirect
291. #3368C2×C11semidirect
292. #3339C2×C11semidirect
293. #3334C2×C11semidirect
294. #3332C2×C11semidirect
295. #3309C2×C11semidirect
296. #3287C2×C11semidirect
297. #3287C2×C11semidirect
298. #3176C2×C11semidirect
299. #3169C2×C11semidirect
300. #3119C2×C11semidirect
301. #3115C2×C11semidirect
302. #2966C2×C11semidirect
303. #2951C2×C11semidirect
304. C4×#135C2×C11semidirect
608. Q16C11×#41semidirect
663. C11#61479direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35172
C11×#33912
C11×#33832
C11×#33682
C11×#33392
C11×#33342
C11×#33322
C11×#33092
C11×#32872
C11×#31762
C11×#31692
C11×#31192
C11×#31152
C11×#29662
C11×#29512
C4×C11×#1352
#6147911