Finite Group Databasebeta

← C11×#61478 #14638671

Subgroups — C11×#61478 #14638671

Order 2816.

1768 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×#3518C212yesmaximal, complemented
2C11×#3393C211yesmaximal, characteristic, complemented
3Q8×C11×Q16C211yesmaximal, characteristic, complemented
4C11×#3369C212yesmaximal, complemented
5C11×#3342C212yesmaximal, complemented
6C11×#3341C211yesmaximal, characteristic, complemented
7C11×#3329C212yesmaximal, complemented
8C11×#3313C214yesmaximal, complemented
9D4×C11×Q16C211yesmaximal, characteristic, complemented
10C11×#3285C212yesmaximal, complemented
11C11×#3175C212yesmaximal, complemented
12C11×#3170C211yesmaximal, characteristic, complemented
13C11×#3121C214yesmaximal, complemented
14C11×#3116C212yesmaximal, complemented
15C11×#2966C211yesmaximal, characteristic, complemented
16C11×#2950C212yesmaximal, complemented
17C4×C11×#135C211yesmaximal, characteristic, complemented
18C2×C11×#135C2211yescharacteristic
19C22×C11×Q16C2212yes—
20Q82×C11C2212yes—
21C11×#556—24no—
22C11×#556—22no—
23C11×#556C2212yes—
24C11×#556C2214yes—
25C11×#555—22no—
26C11×#555C2212yes—
27D4×Q8×C11C2212yes—
28C11×#548C2214yes—
29C11×#542—24no—
30C11×#542C2214yes—
31C11×#533—22no—
32C11×#533C2212yes—
33C11×#529—22no—
34C11×#529C2211yescharacteristic
35C11×#519C2214yes—
36C4×C11×#41C2212yes—
37C11×#500C2211yescharacteristic
38C11×#500C2212yes—
39C11×#495C2212yes—
40C11×#494C2211yescharacteristic
41C11×#489C2214yes—
42C11×#487C2212yes—
43C11×#485C2214yes—
44C11×#485C2214yes—
45C11×#482C2214yes—
46C11×#477C2214yes—
47C11×#477C2212yes—
48C11×#476C2212yes—
49C11×#475C2214yes—
50C11×#468C2214yes—
51C11×#467C2212yes—
52C11×#467C2212yes—
53C11×#467C2212yes—
54C11×#466C2212yes—
55C11×#464C2214yes—
56C11×#464C2214yes—
57C11×#462C2212yes—
58C11×#461C2212yes—
59C11×#452C2214yes—
60C11×#451C2214yes—
61C11×#448C2214yes—
62C11×#446C2211yescharacteristic
63C8×Q8×C11C2211yescharacteristic
64C11×#441C2214yes—
65C11×#441C2214yes—
66C11×#440C2214yes—
67C4×C11×Q16C2212yes—
68C4×C11×Q16C2212yes—
69C4×C11×Q16C2211yescharacteristic
70C4×C11×Q16C2211yescharacteristic
71C4×C11×Q16C2212yes—
72C4×C11×Q16C2212yes—
73C4×C11×SD16C2212yes—
74C4×C11×SD16C2212yes—
75C4×C11×D8C2211yescharacteristic
76C4×C11×D8C2211yescharacteristic
77C11×#436C2211yescharacteristic
78C11×#435C2212yes—
79C8×D4×C11C2212yes—
80C8×D4×C11C2211yescharacteristic
81C11×#433C2212yes—
82C11×#432C2211yescharacteristic
83C11×#427C2211yescharacteristic
84C11×#427C2212yes—
85C11×#419C2214yes—
86C11×#416C2212yes—
87C11×#405C2212yes—
88C2×C4×C8×C11C2211yescharacteristic
89C2×C11×#41C2312yes—
90C22×Q8×C11C2314yes—
91C11×#135—24no—
92C2×C11×Q16—28no—
93C2×C11×Q16C2312yes—
94C2×C11×Q16C2314yes—
95C2×C11×Q16C2312yes—
96C2×C11×Q16C2311yescharacteristic
97C2×C11×SD16C2312yes—
98C2×C11×SD16C2314yes—
99C2×C11×D8C2311yescharacteristic
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⋊Q8C2312yes—
108C11×C4⋊Q8C2314yes—
109C11×C4⋊Q8C2312yes—
110C11×#126—24no—
111C11×#126—24no—
112C11×#126—24no—
113C11×#126—24no—
114C11×#126D412yes—
115C11×#125—22no—
116C11×#125D411yescharacteristic
117C11×#124—24no—
118C11×#124—24no—
119C11×#124—24no—
120C11×#124—24no—
121C11×#124D411yescharacteristic
122C11×#124C2314yes—
123C11×#123—24no—
124C11×#123D412yes—
125C11×C22⋊Q8—22no—
126C11×C22⋊Q8—22no—
127C11×C22⋊Q8—24no—
128C11×C22⋊Q8—24no—
129C11×C22⋊Q8—24no—
130C11×C22⋊Q8D411yescharacteristic
131C11×C22⋊Q8C2314yes—
132C11×C22⋊Q8C2314yes—
133C11×#121—22no—
134C11×#121—24no—
135C11×#121D411yescharacteristic
136C11×#121C2314yes—
137C4×Q8×C11—22no—
138C4×Q8×C11—24no—
139C4×Q8×C11—24no—
140C4×Q8×C11—24no—
141C4×Q8×C11—22no—
142C4×Q8×C11C2312yes—
143C4×Q8×C11C2312yes—
144C4×Q8×C11C2314yes—
145C4×Q8×C11C2314yes—
146C4×Q8×C11C2314yes—
147C4×Q8×C11C2311yescharacteristic
148C4×D4×C11—22no—
149C4×D4×C11—22no—
150C4×D4×C11—22no—
151C4×D4×C11—24no—
152C4×D4×C11C2312yes—
153C4×D4×C11C2312yes—
154C4×D4×C11C2312yes—
155C4×D4×C11C2311yescharacteristic
156C11×#117—22no—
157C11×#117—22no—
158C11×#117—22no—
159C11×#117—24no—
160C11×#117—24no—
161C11×#117—22no—
162C11×#117C2312yes—
163C11×#117C2314yes—
164C11×#117C2312yes—
165C2×C42×C11—22no—
166C2×C42×C11C2311yescharacteristic
167C11×#107C2311yescharacteristic
168C11×#107C2312yes—
169C11×#107C2312yes—
170C11×#107C2314yes—
171C11×#107C2311yescharacteristic
172C11×#106C2312yes—
173C11×#106C2314yes—
174C11×C4⋊C8C2311yescharacteristic
175C11×C4⋊C8C2311yescharacteristic
176C11×C4⋊C8C2312yes—
177C11×C4⋊C8C2312yes—
178C11×#103C2314yes—
179C11×#103C2314yes—
180C11×#103C2312yes—
181C11×#103C2312yes—
182C11×#103C2314yes—
183C11×#103C2314yes—
184C11×#103C2314yes—
185C11×#102C2312yes—
186C11×#102C2314yes—
187C11×#102C2312yes—
188C11×C22⋊C8C2312yes—
189C11×C22⋊C8C2312yes—
190C11×C22⋊C8C2312yes—
191C11×#97C2312yes—
192C11×#97C2312yes—
193C4×C8×C11C2311yescharacteristic
194C4×C8×C11C2312yes—
195C4×C8×C11C2311yescharacteristic
196C4×C8×C11C2311yescharacteristic
197C4×C8×C11C2311yescharacteristic
198#61478C1111yesmaximal, characteristic, direct product factor, Sylow
199C11×#41—24no—
200C11×#41—42no—
201C2×Q8×C11—24no—
202C2×Q8×C11—22no—
203C2×Q8×C11—24no—
204C2×Q8×C11—28no—
205C2×Q8×C11—44no—
206C2×Q8×C11C2×D411yescharacteristic
207C2×Q8×C11C2414yes—
208C2×Q8×C11C2412yes—
209C2×D4×C11—22no—
210C2×D4×C11—24no—
211C2×D4×C11C2×D411yescharacteristic
212C2×D4×C11C2×D412yes—
213C2×D4×C11C2412yes—
214C22×C4×C11—24no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2411yescharacteristic
221C22×C4×C11C2412yes—
222C11×Q16—24no—
223C11×Q16—28no—
224C11×Q16—42no—
225C11×Q16#4114yes—
226C11×SD16—24no—
227C11×SD16—44no—
228C11×D8—22no—
229C11×M16—42no—
230C2×C8×C11—24no—
231C2×C8×C11—22no—
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—22no—
240C11×C4⋊C4—22no—
241C11×C4⋊C4—22no—
242C11×C4⋊C4—22no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4—24no—
247C11×C4⋊C4—22no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—24no—
250C11×C4⋊C4C2×D411yescharacteristic
251C11×C4⋊C4C2×D411yescharacteristic
252C11×C4⋊C4C2×D412yes—
253C11×C4⋊C4C2×D412yes—
254C11×C4⋊C4C2×D412yes—
255C11×C4⋊C4C2×D412yes—
256C11×C4⋊C4C2412yes—
257C11×C4⋊C4C2412yes—
258C11×C4⋊C4C2414yes—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—22no—
262C11×C22⋊C4—24no—
263C11×C22⋊C4—22no—
264C11×C22⋊C4—22no—
265C11×C22⋊C4—24no—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—24no—
268C11×C22⋊C4C2×D412yes—
269C11×C22⋊C4C2×D412yes—
270C11×C22⋊C4C2×D412yes—
271C11×C22⋊C4C2×D412yes—
272C11×C22⋊C4C2×D412yes—
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#3518C2×C1112yescomplemented
286#3393C2×C1111yescharacteristic, complemented
287Q8×Q16C2×C1111yescharacteristic, complemented
288#3369C2×C1112yescomplemented
289#3342C2×C1112yescomplemented
290#3341C2×C1111yescharacteristic, complemented
291#3329C2×C1112yescomplemented
292#3313C2×C1114yescomplemented
293D4×Q16C2×C1111yescharacteristic, complemented
294#3285C2×C1112yescomplemented
295#3175C2×C1112yescomplemented
296#3170C2×C1111yescharacteristic, complemented
297#3121C2×C1114yescomplemented
298#3116C2×C1112yescomplemented
299#2966C2×C1111yescharacteristic, complemented
300#2950C2×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—48no—
310Q8×C11—82no—
311Q8×C11—84no—
312Q8×C11C2×#4114yes—
313D4×C11—22no—
314D4×C11—22no—
315D4×C11—22no—
316D4×C11—42no—
317D4×C11—44no—
318D4×C11—84no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—24no—
327C2×C4×C11—24no—
328C2×C4×C11—22no—
329C2×C4×C11—41no—
330C2×C4×C11—44no—
331C2×C4×C11—48no—
332C2×C4×C11—44no—
333C2×C4×C11—82no—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C22×D412yes—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D411yescharacteristic
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
350C22×Q16C22×C1112yes—
351Q82C22×C1112yes—
352#556—24no—
353#556—22no—
354#556C22×C1112yes—
355#556C22×C1114yes—
356#555—22no—
357#555C22×C1112yes—
358D4×Q8C22×C1112yes—
359#548C22×C1114yes—
360#542—24no—
361#542C22×C1114yes—
362#533—22no—
363#533C22×C1112yes—
364#529—22no—
365#529C22×C1111yescharacteristic
366#519C22×C1114yes—
367C4×#41C22×C1112yes—
368#500C22×C1111yescharacteristic
369#500C22×C1112yes—
370#495C22×C1112yes—
371#494C22×C1111yescharacteristic
372#489C22×C1114yes—
373#487C22×C1112yes—
374#485C22×C1114yes—
375#485C22×C1114yes—
376#482C22×C1114yes—
377#477C22×C1112yes—
378#477C22×C1114yes—
379#476C22×C1112yes—
380#475C22×C1114yes—
381#468C22×C1114yes—
382#467C22×C1112yes—
383#467C22×C1112yes—
384#467C22×C1112yes—
385#466C22×C1112yes—
386#464C22×C1114yes—
387#464C22×C1114yes—
388#462C22×C1112yes—
389#461C22×C1112yes—
390#452C22×C1114yes—
391#451C22×C1114yes—
392#448C22×C1114yes—
393#446C22×C1111yescharacteristic
394C8×Q8C22×C1111yescharacteristic
395#441C22×C1114yes—
396#441C22×C1114yes—
397#440C22×C1114yes—
398C4×Q16C22×C1112yes—
399C4×Q16C22×C1112yes—
400C4×Q16C22×C1111yescharacteristic
401C4×Q16C22×C1112yes—
402C4×Q16C22×C1112yes—
403C4×Q16C22×C1111yescharacteristic
404C4×SD16C22×C1112yes—
405C4×SD16C22×C1112yes—
406C4×D8C22×C1111yescharacteristic
407C4×D8C22×C1111yescharacteristic
408#436C22×C1111yescharacteristic
409#435C22×C1112yes—
410C8×D4C22×C1111yescharacteristic
411C8×D4C22×C1112yes—
412#433C22×C1112yes—
413#432C22×C1111yescharacteristic
414#427C22×C1112yes—
415#427C22×C1111yescharacteristic
416#419C22×C1114yes—
417#416C22×C1112yes—
418#405C22×C1112yes—
419C2×C4×C8C22×C1111yescharacteristic
420C22×C11—21no—
421C22×C11—22no—
422C22×C11—22no—
423C22×C11—21no—
424C22×C11—21no—
425C22×C11—22no—
426C22×C11—42no—
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—24no—
436C4×C11—21no—
437C4×C11—22no—
438C4×C11—42no—
439C4×C11—44no—
440C4×C11—44no—
441C4×C11—42no—
442C4×C11#57812yes—
443C4×C11C22×#4111yescharacteristic
444C4×C11#58511yescharacteristic
445C2×#41C23×C1112yes—
446C22×Q8C23×C1114yes—
447#135—24no—
448C2×Q16—28no—
449C2×Q16C23×C1112yes—
450C2×Q16C23×C1114yes—
451C2×Q16C23×C1112yes—
452C2×Q16C23×C1111yescharacteristic
453C2×SD16C23×C1112yes—
454C2×SD16C23×C1114yes—
455C2×D8C23×C1111yescharacteristic
456C2×M16C23×C1112yes—
457C22×C8C23×C1112yes—
458C22×C8C23×C1111yescharacteristic
459C22×C8C23×C1111yescharacteristic
460C4⋊Q8—22no—
461C4⋊Q8—22no—
462C4⋊Q8—24no—
463C4⋊Q8C23×C1112yes—
464C4⋊Q8C23×C1112yes—
465C4⋊Q8C23×C1114yes—
466#126—24no—
467#126—24no—
468#126—24no—
469#126—24no—
470#126D4×C1112yes—
471#125—22no—
472#125D4×C1111yescharacteristic
473#124—24no—
474#124—24no—
475#124—24no—
476#124—24no—
477#124D4×C1111yescharacteristic
478#124C23×C1114yes—
479#123—24no—
480#123D4×C1112yes—
481C22⋊Q8—22no—
482C22⋊Q8—22no—
483C22⋊Q8—24no—
484C22⋊Q8—24no—
485C22⋊Q8—24no—
486C22⋊Q8D4×C1111yescharacteristic
487C22⋊Q8C23×C1114yes—
488C22⋊Q8C23×C1114yes—
489#121—22no—
490#121—24no—
491#121D4×C1111yescharacteristic
492#121C23×C1114yes—
493C4×Q8—22no—
494C4×Q8—24no—
495C4×Q8—24no—
496C4×Q8—24no—
497C4×Q8—22no—
498C4×Q8C23×C1112yes—
499C4×Q8C23×C1112yes—
500C4×Q8C23×C1114yes—
501C4×Q8C23×C1114yes—
502C4×Q8C23×C1114yes—
503C4×Q8C23×C1111yescharacteristic
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—24no—
508C4×D4C23×C1112yes—
509C4×D4C23×C1112yes—
510C4×D4C23×C1112yes—
511C4×D4C23×C1111yescharacteristic
512#117—22no—
513#117—22no—
514#117—22no—
515#117—24no—
516#117—24no—
517#117—22no—
518#117C23×C1112yes—
519#117C23×C1114yes—
520#117C23×C1112yes—
521C2×C42—22no—
522C2×C42C23×C1111yescharacteristic
523#107C23×C1111yescharacteristic
524#107C23×C1111yescharacteristic
525#107C23×C1112yes—
526#107C23×C1112yes—
527#107C23×C1114yes—
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—82no—
557C2×C11D4×#4111yescharacteristic
558C2×C11C2×#57811yescharacteristic
559C2×C11#358411yescharacteristic
560#41—24no—
561#41—42no—
562C2×Q8—24no—
563C2×Q8—22no—
564C2×Q8—24no—
565C2×Q8—28no—
566C2×Q8—44no—
567C2×Q8C2×D4×C1111yescharacteristic
568C2×Q8C24×C1114yes—
569C2×Q8C24×C1112yes—
570C2×D4—22no—
571C2×D4—24no—
572C2×D4C2×D4×C1111yescharacteristic
573C2×D4C2×D4×C1112yes—
574C2×D4C24×C1112yes—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4C2×D4×C1111yescharacteristic
580C22×C4C2×D4×C1111yescharacteristic
581C22×C4C24×C1111yescharacteristic
582C22×C4C24×C1112yes—
583Q16—28no—
584Q16—24no—
585Q16—42no—
586Q16C11×#4114yes—
587SD16—24no—
588SD16—44no—
589D8—22no—
590M16—42no—
591C2×C8—24no—
592C2×C8—22no—
593C2×C8—41no—
594C2×C8C24×C1111yescharacteristic
595C2×C8C24×C1111yescharacteristic
596C2×C8C24×C1111yescharacteristic
597C2×C8C24×C1112yes—
598C2×C8C24×C1112yes—
599C2×C8C24×C1111yescharacteristic
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—22no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4C2×D4×C1111yescharacteristic
612C4⋊C4C2×D4×C1111yescharacteristic
613C4⋊C4C2×D4×C1112yes—
614C4⋊C4C2×D4×C1112yes—
615C4⋊C4C2×D4×C1112yes—
616C4⋊C4C2×D4×C1112yes—
617C4⋊C4C24×C1112yes—
618C4⋊C4C24×C1112yes—
619C4⋊C4C24×C1114yes—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—22no—
623C22⋊C4—24no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4C2×D4×C1112yes—
630C22⋊C4C2×D4×C1112yes—
631C22⋊C4C2×D4×C1112yes—
632C22⋊C4C2×D4×C1112yes—
633C22⋊C4C2×D4×C1112yes—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—24no—
638C42—24no—
639C42—24no—
640C42—24no—
641C42C2×D4×C1111yescharacteristic
642C42C2×D4×C1111yescharacteristic
643C42C24×C1111yescharacteristic
644C42C24×C1111yescharacteristic
645C42C24×C1112yes—
646C11#6147811yescharacteristic, direct product factor, Sylow
647C23—22no—
648C23C22×D4×C1111yescharacteristic
649C23C22×D4×C1112yes—
650Q8—22no—
651Q8—22no—
652Q8—24no—
653Q8—24no—
654Q8—48no—
655Q8—82no—
656Q8—84no—
657Q8C2×C11×#4114yes—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—42no—
662D4—44no—
663D4—84no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—44no—
676C2×C4—48no—
677C2×C4—44no—
678C2×C4—82no—
679C2×C4C22×D4×C1111yescharacteristic
680C2×C4C22×D4×C1111yescharacteristic
681C2×C4C22×D4×C1111yescharacteristic
682C2×C4C22×D4×C1112yes—
683C2×C4C22×D4×C1112yes—
684C2×C4C22×D4×C1112yes—
685C2×C4C22×D4×C1111yescharacteristic
686C2×C4C22×D4×C1111yescharacteristic
687C2×C4C25×C1111yescharacteristic
688C8—21no—
689C8—22no—
690C8—21no—
691C8—21no—
692C8—22no—
693C8C2×C11×#4112yes—
694C22—22no—
695C22—21no—
696C22—21no—
697C22—22no—
698C22—21no—
699C22—22no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22C23×D4×C1111yescharacteristic
704C4—21no—
705C4—22no—
706C4—24no—
707C4—21no—
708C4—22no—
709C4—21no—
710C4—21no—
711C4—22no—
712C4—44no—
713C4—42no—
714C4—42no—
715C4—44no—
716C4C11×#57812yes—
717C4C22×C11×#4111yescharacteristic
718C4C11×#58511yescharacteristic
719C2—42no—
720C2—41no—
721C2—82no—
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×#3518C2semidirect
2. C11×#3393C2semidirect
3. Q8×C11×Q16C2semidirect
4. C11×#3369C2semidirect
5. C11×#3342C2semidirect
6. C11×#3341C2semidirect
7. C11×#3329C2semidirect
8. C11×#3313C2semidirect
9. D4×C11×Q16C2semidirect
10. C11×#3285C2semidirect
11. C11×#3175C2semidirect
12. C11×#3170C2semidirect
13. C11×#3121C2semidirect
14. C11×#3116C2semidirect
15. C11×#2966C2semidirect
16. C11×#2950C2semidirect
17. C4×C11×#135C2semidirect
198. #61478C11direct (N × H)
285. #3518C2×C11semidirect
286. #3393C2×C11semidirect
287. Q8×Q16C2×C11semidirect
288. #3369C2×C11semidirect
289. #3342C2×C11semidirect
290. #3341C2×C11semidirect
291. #3329C2×C11semidirect
292. #3313C2×C11semidirect
293. D4×Q16C2×C11semidirect
294. #3285C2×C11semidirect
295. #3175C2×C11semidirect
296. #3170C2×C11semidirect
297. #3121C2×C11semidirect
298. #3116C2×C11semidirect
299. #2966C2×C11semidirect
300. #2950C2×C11semidirect
301. C4×#135C2×C11semidirect
646. C11#61478direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35182
C11×#33932
Q8×C11×Q162
C11×#33692
C11×#33422
C11×#33412
C11×#33292
C11×#33132
D4×C11×Q162
C11×#32852
C11×#31752
C11×#31702
C11×#31212
C11×#31162
C11×#29662
C11×#29502
C4×C11×#1352
#6147811