Finite Group Databasebeta

← C11×#61634 #14638827

Subgroups — C11×#61634 #14638827

Order 2816.

2018 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3538C211yesmaximal, characteristic, complemented
2C11×#3486C211yesmaximal, characteristic
3C11×#3312C214yesmaximal, complemented
4C11×#3300C214yesmaximal, complemented
5D4×C11×Q16C214yesmaximal, complemented
6C11×#3270C214yesmaximal, complemented
7C11×#3223C212yesmaximal, complemented
8C11×#3202C212yesmaximal, complemented
9C11×#3190C212yesmaximal, complemented
10C11×#3127C212yesmaximal, complemented
11C11×#3011C212yesmaximal, complemented
12C2×C11×#451C212yesmaximal, complemented
13C11×#2977C211yesmaximal, characteristic, complemented
14C2×C11×2−1+4C2211yescharacteristic
15C23×Q8×C11C2211yescharacteristic
16C2×C11×#137C2212yescomplemented
17C22×C11×Q16C2214yes—
18C22×C11×Q16C2212yescomplemented
19C11×#563—22no—
20C11×#552C2214yes—
21C11×#551—22no—
22D4×Q8×C11—22no—
23D4×Q8×C11C2214yes—
24D4×Q8×C11C2214yes—
25C11×#548—22no—
26C11×#548C2214yes—
27C11×#544—22no—
28C11×#541C2212yes—
29C11×#539—22no—
30C11×#536—22no—
31C11×#536C2211yescharacteristic
32C11×#536C2211yescharacteristic
33C11×#536C2212yes—
34C11×#525—22no—
35C11×#525C2211yescharacteristic
36C11×#525C2211yescharacteristic
37C2×C11×C22⋊Q8C2212yes—
38C11×#519C2211yescharacteristic
39C11×#497C2212yescomplemented
40C11×#494C2212yescomplemented
41C11×#491C2212yescomplemented
42C11×#488C2212yescomplemented
43C11×#485C2214yes—
44C11×#485C2214yescomplemented
45C11×#483C2212yes—
46C11×#480C2212yes—
47C11×#479C2214yescomplemented
48C11×#470C2214yescomplemented
49C11×#467C2214yes—
50C11×#467C2214yescomplemented
51C11×#465C2214yes—
52C11×#464C2214yescomplemented
53C11×#462C2214yescomplemented
54C11×#462C2214yescomplemented
55C11×#452C2214yes—
56C11×#452C2214yescomplemented
57C11×#451C2212yes—
58C11×#451C2214yes—
59C11×#451C2214yes—
60C11×#451C2214yes—
61C11×#451C2214yes—
62C11×#451C2214yescomplemented
63C11×#451C2214yescomplemented
64C11×#448C2212yes—
65C11×#441C2214yescomplemented
66C4×C11×Q16C2214yescomplemented
67C11×#435C2214yes—
68C8×D4×C11C2214yes—
69C11×#433C2212yes—
70C11×#419C2212yescomplemented
71C11×#416C2212yescomplemented
72C2×C11×#103C2214yes—
73C11×#408C2212yes—
74C2×C11×C22⋊C8C2212yes—
75C11×2−1+4—44no—
76C2×C11×#41—22no—
77C2×C11×#41—21no—
78C2×C11×#41C2312yes—
79C2×C11×#41C2311yescharacteristic
80C2×C11×#41C2311yescharacteristic
81C22×Q8×C11—21no—
82C22×Q8×C11—21no—
83C22×Q8×C11—22no—
84C22×Q8×C11—44no—
85C22×Q8×C11C2311yescharacteristic
86C22×Q8×C11C2314yes—
87C22×Q8×C11C2312yes—
88C22×Q8×C11C2312yes—
89C22×Q8×C11C2311yescharacteristic
90C22×Q8×C11C2312yes—
91C23×C4×C11—21no—
92C23×C4×C11C2311yescharacteristic
93C11×#137—44no—
94C2×C11×Q16—48no—
95C2×C11×Q16—44no—
96C2×C11×Q16C2314yes—
97C2×C11×Q16C2314yes—
98C2×C11×Q16C2314yes—
99C2×C11×Q16C2314yes—
100C2×C11×Q16C2314yes—
101C2×C11×SD16C2314yes—
102C2×C11×M16C2312yes—
103C22×C8×C11C2314yes—
104C22×C8×C11C2312yes—
105C11×C4⋊Q8—22no—
106C11×C4⋊Q8—21no—
107C11×C4⋊Q8—24no—
108C11×C4⋊Q8—24no—
109C11×C4⋊Q8C2312yes—
110C11×C4⋊Q8C2312yes—
111C11×#126—24no—
112C11×#126—24no—
113C11×#125—24no—
114C11×#125—24no—
115C11×#125C2312yes—
116C11×#124—21no—
117C11×#124—22no—
118C11×#124—24no—
119C11×#124C2312yes—
120C11×#123—22no—
121C11×#123—22no—
122C11×#123—22no—
123C11×#123—24no—
124C11×#123—21no—
125C11×#123—22no—
126C11×#123D412yes—
127C11×C22⋊Q8—22no—
128C11×C22⋊Q8—22no—
129C11×C22⋊Q8—24no—
130C11×C22⋊Q8—22no—
131C11×C22⋊Q8—24no—
132C11×C22⋊Q8—24no—
133C11×C22⋊Q8—24no—
134C11×C22⋊Q8—24no—
135C11×C22⋊Q8D412yes—
136C11×C22⋊Q8C2314yes—
137C11×C22⋊Q8C2314yes—
138C11×C22⋊Q8C2312yes—
139C11×C22⋊Q8C2314yes—
140C11×C22⋊Q8C2314yes—
141C11×#121—24no—
142C11×#121D412yes—
143C11×#121C2312yes—
144C11×#120—21no—
145C11×#120D412yes—
146C4×Q8×C11—22no—
147C4×Q8×C11C2314yes—
148C4×Q8×C11C2314yes—
149C4×D4×C11—24no—
150C4×D4×C11—24no—
151C4×D4×C11—22no—
152C4×D4×C11—24no—
153C4×D4×C11C2314yes—
154C11×#117—22no—
155C11×#117—24no—
156C11×#117C2311yescharacteristic
157C11×#117C2312yes—
158C11×#117C2311yescharacteristic
159C2×C11×C4⋊C4—22no—
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C22⋊C4—22no—
162C11×#107C2314yes—
163C11×#106C2314yes—
164C11×C4⋊C8C2314yes—
165C11×#103C2314yes—
166C11×#103C2314yes—
167C11×#103C2314yes—
168C11×#103C2314yes—
169C11×#103C2314yes—
170C11×#103C2314yes—
171C11×#103C2314yes—
172C11×#102C2314yes—
173C11×C22⋊C8C2314yes—
174C11×C22⋊C8C2312yes—
175C11×C22⋊C8C2312yes—
176C11×C22⋊C8C2314yes—
177C11×#97C2312yes—
178C4×C8×C11C2312yes—
179#61634C1111yesmaximal, characteristic, direct product factor, Sylow
180C24×C11C2×D411yescharacteristic
181C11×#41—24no—
182C11×#41—42no—
183C11×#41—42no—
184C11×#41—42no—
185C11×#41—48no—
186C11×#41—44no—
187C2×Q8×C11—24no—
188C2×Q8×C11—21no—
189C2×Q8×C11—24no—
190C2×Q8×C11—21no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11—28no—
195C2×Q8×C11—24no—
196C2×Q8×C11—44no—
197C2×Q8×C11—42no—
198C2×Q8×C11—42no—
199C2×Q8×C11—44no—
200C2×Q8×C11—44no—
201C2×Q8×C11—42no—
202C2×Q8×C11—42no—
203C2×Q8×C11—48no—
204C2×Q8×C11—44no—
205C2×Q8×C11C2×D411yescharacteristic
206C2×Q8×C11C2412yes—
207C2×Q8×C11C2411yescharacteristic
208C2×Q8×C11C2414yes—
209C2×Q8×C11C2412yes—
210C2×D4×C11—22no—
211C2×D4×C11—21no—
212C2×D4×C11—22no—
213C2×D4×C11C2×D414yes—
214C2×D4×C11C2×D412yes—
215C2×D4×C11C2×D411yescharacteristic
216C2×D4×C11C2411yescharacteristic
217C22×C4×C11—21no—
218C22×C4×C11—22no—
219C22×C4×C11—24no—
220C22×C4×C11—22no—
221C22×C4×C11—21no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—21no—
226C22×C4×C11—42no—
227C22×C4×C11—44no—
228C22×C4×C11C2×D412yes—
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2411yescharacteristic
231C22×C4×C11C2412yes—
232C22×C4×C11C2412yes—
233C11×Q16—28no—
234C11×Q16—28no—
235C11×Q16—44no—
236C11×Q16—44no—
237C11×Q16—44no—
238C11×SD16—44no—
239C11×M16—42no—
240C2×C8×C11—44no—
241C2×C8×C11—42no—
242C2×C8×C11C2414yes—
243C2×C8×C11C2414yes—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4—22no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—24no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—22no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—24no—
255C11×C4⋊C4C2×D412yes—
256C11×C4⋊C4C2×D414yes—
257C11×C4⋊C4C2414yes—
258C11×C4⋊C4C2412yes—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—21no—
262C11×C22⋊C4—22no—
263C11×C22⋊C4—22no—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—24no—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—22no—
268C11×C22⋊C4C2×D412yes—
269C11×C22⋊C4C2×D414yes—
270C11×C22⋊C4C2×D414yes—
271C42×C11—22no—
272C42×C11—24no—
273C42×C11—24no—
274C42×C11—21no—
275C42×C11C2412yes—
276#3538C2×C1111yescharacteristic, complemented
277#3486C2×C1111yescharacteristic
278#3312C2×C1114yescomplemented
279#3300C2×C1114yescomplemented
280D4×Q16C2×C1114yescomplemented
281#3270C2×C1114yescomplemented
282#3223C2×C1112yescomplemented
283#3202C2×C1112yescomplemented
284#3190C2×C1112yescomplemented
285#3127C2×C1112yescomplemented
286#3011C2×C1112yescomplemented
287C2×#451C2×C1112yescomplemented
288#2977C2×C1111yescharacteristic, complemented
289C23×C11—24no—
290C23×C11—21no—
291C23×C11—41no—
292C23×C11C22×D411yescharacteristic
293C23×C11C22×D412yes—
294C23×C11C22×D412yes—
295Q8×C11—24no—
296Q8×C11—22no—
297Q8×C11—24no—
298Q8×C11—24no—
299Q8×C11—24no—
300Q8×C11—22no—
301Q8×C11—41no—
302Q8×C11—48no—
303Q8×C11—44no—
304Q8×C11—42no—
305Q8×C11—82no—
306Q8×C11—82no—
307Q8×C11H(5,𝔽2)14yes—
308D4×C11—28no—
309D4×C11—22no—
310D4×C11—41no—
311D4×C11—42no—
312D4×C11—44no—
313D4×C11—42no—
314D4×C11—44no—
315C2×C4×C11—24no—
316C2×C4×C11—22no—
317C2×C4×C11—24no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—24no—
323C2×C4×C11—24no—
324C2×C4×C11—22no—
325C2×C4×C11—21no—
326C2×C4×C11—42no—
327C2×C4×C11—41no—
328C2×C4×C11—44no—
329C2×C4×C11—48no—
330C2×C4×C11—44no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—44no—
334C2×C4×C11—82no—
335C2×C4×C11—82no—
336C2×C4×C11C22×D414yes—
337C2×C4×C11C22×D412yes—
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C22×D412yes—
340C2×C4×C11C2511yescharacteristic
341C8×C11—24no—
342C8×C11—24no—
343C2×2−1+4C22×C1111yescharacteristic
344C23×Q8C22×C1111yescharacteristic
345C2×#137C22×C1112yescomplemented
346C22×Q16C22×C1114yes—
347C22×Q16C22×C1112yescomplemented
348#563—22no—
349#552C22×C1114yes—
350#551—22no—
351D4×Q8—22no—
352D4×Q8C22×C1114yes—
353D4×Q8C22×C1114yes—
354#548—22no—
355#548C22×C1114yes—
356#544—22no—
357#541C22×C1112yes—
358#539—22no—
359#536—22no—
360#536C22×C1111yescharacteristic
361#536C22×C1111yescharacteristic
362#536C22×C1112yes—
363#525—22no—
364#525C22×C1111yescharacteristic
365#525C22×C1111yescharacteristic
366C2×C22⋊Q8C22×C1112yes—
367#519C22×C1111yescharacteristic
368#497C22×C1112yescomplemented
369#494C22×C1112yescomplemented
370#491C22×C1112yescomplemented
371#488C22×C1112yescomplemented
372#485C22×C1114yes—
373#485C22×C1114yescomplemented
374#483C22×C1112yes—
375#480C22×C1112yes—
376#479C22×C1114yescomplemented
377#470C22×C1114yescomplemented
378#467C22×C1114yes—
379#467C22×C1114yescomplemented
380#465C22×C1114yes—
381#464C22×C1114yescomplemented
382#462C22×C1114yescomplemented
383#462C22×C1114yescomplemented
384#452C22×C1114yes—
385#452C22×C1114yescomplemented
386#451C22×C1114yes—
387#451C22×C1112yes—
388#451C22×C1114yes—
389#451C22×C1114yes—
390#451C22×C1114yes—
391#451C22×C1114yescomplemented
392#451C22×C1114yescomplemented
393#448C22×C1112yes—
394#441C22×C1114yescomplemented
395C4×Q16C22×C1114yescomplemented
396#435C22×C1114yes—
397C8×D4C22×C1114yes—
398#433C22×C1112yes—
399#419C22×C1112yescomplemented
400#416C22×C1112yescomplemented
401C2×#103C22×C1114yes—
402#408C22×C1112yes—
403C2×C22⋊C8C22×C1112yes—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—21no—
407C22×C11—22no—
408C22×C11—24no—
409C22×C11—22no—
410C22×C11—44no—
411C22×C11—41no—
412C22×C11—42no—
413C22×C11#57814yes—
414C22×C11C23×D411yescharacteristic
415C4×C11—24no—
416C4×C11—21no—
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—24no—
420C4×C11—41no—
421C4×C11—42no—
422C4×C11—44no—
423C4×C11—44no—
424C4×C11—42no—
425C4×C11C2×H(5,𝔽2)12yes—
4262−1+4—44no—
427C2×#41—22no—
428C2×#41—21no—
429C2×#41C23×C1112yes—
430C2×#41C23×C1111yescharacteristic
431C2×#41C23×C1111yescharacteristic
432C22×Q8—21no—
433C22×Q8—21no—
434C22×Q8—22no—
435C22×Q8—44no—
436C22×Q8C23×C1111yescharacteristic
437C22×Q8C23×C1114yes—
438C22×Q8C23×C1112yes—
439C22×Q8C23×C1112yes—
440C22×Q8C23×C1111yescharacteristic
441C22×Q8C23×C1112yes—
442C23×C4—21no—
443C23×C4C23×C1111yescharacteristic
444#137—44no—
445C2×Q16—48no—
446C2×Q16—44no—
447C2×Q16C23×C1114yes—
448C2×Q16C23×C1114yes—
449C2×Q16C23×C1114yes—
450C2×Q16C23×C1114yes—
451C2×Q16C23×C1114yes—
452C2×SD16C23×C1114yes—
453C2×M16C23×C1112yes—
454C22×C8C23×C1114yes—
455C22×C8C23×C1112yes—
456C4⋊Q8—22no—
457C4⋊Q8—21no—
458C4⋊Q8—24no—
459C4⋊Q8—24no—
460C4⋊Q8C23×C1112yes—
461C4⋊Q8C23×C1112yes—
462#126—24no—
463#126—24no—
464#125—24no—
465#125—24no—
466#125C23×C1112yes—
467#124—21no—
468#124—22no—
469#124—24no—
470#124C23×C1112yes—
471#123—22no—
472#123—22no—
473#123—22no—
474#123—24no—
475#123—21no—
476#123—22no—
477#123D4×C1112yes—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8—24no—
481C22⋊Q8—22no—
482C22⋊Q8—24no—
483C22⋊Q8—24no—
484C22⋊Q8—24no—
485C22⋊Q8—24no—
486C22⋊Q8D4×C1112yes—
487C22⋊Q8C23×C1114yes—
488C22⋊Q8C23×C1114yes—
489C22⋊Q8C23×C1112yes—
490C22⋊Q8C23×C1114yes—
491C22⋊Q8C23×C1114yes—
492#121—24no—
493#121D4×C1112yes—
494#121C23×C1112yes—
495#120—21no—
496#120D4×C1112yes—
497C4×Q8—22no—
498C4×Q8C23×C1114yes—
499C4×Q8C23×C1114yes—
500C4×D4—24no—
501C4×D4—24no—
502C4×D4—22no—
503C4×D4—24no—
504C4×D4C23×C1114yes—
505#117—22no—
506#117—24no—
507#117C23×C1111yescharacteristic
508#117C23×C1112yes—
509#117C23×C1111yescharacteristic
510C2×C4⋊C4—22no—
511C2×C4⋊C4C23×C1112yes—
512C2×C22⋊C4—22no—
513#107C23×C1114yes—
514#106C23×C1114yes—
515C4⋊C8C23×C1114yes—
516#103C23×C1114yes—
517#103C23×C1114yes—
518#103C23×C1114yes—
519#103C23×C1114yes—
520#103C23×C1114yes—
521#103C23×C1114yes—
522#103C23×C1114yes—
523#102C23×C1114yes—
524C22⋊C8C23×C1114yes—
525C22⋊C8C23×C1112yes—
526C22⋊C8C23×C1112yes—
527C22⋊C8C23×C1114yes—
528#97C23×C1112yes—
529C4×C8C23×C1112yes—
530C2×C11—24no—
531C2×C11—42no—
532C2×C11—41no—
533C2×C11—81no—
534C2×C11#348411yescharacteristic
535C2×C11C2×#57812yes—
536C24C2×D4×C1111yescharacteristic
537#41—24no—
538#41—42no—
539#41—42no—
540#41—42no—
541#41—48no—
542#41—44no—
543C2×Q8—24no—
544C2×Q8—21no—
545C2×Q8—24no—
546C2×Q8—21no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—28no—
551C2×Q8—24no—
552C2×Q8—44no—
553C2×Q8—42no—
554C2×Q8—42no—
555C2×Q8—44no—
556C2×Q8—44no—
557C2×Q8—42no—
558C2×Q8—42no—
559C2×Q8—48no—
560C2×Q8—44no—
561C2×Q8C2×D4×C1111yescharacteristic
562C2×Q8C24×C1112yes—
563C2×Q8C24×C1111yescharacteristic
564C2×Q8C24×C1114yes—
565C2×Q8C24×C1112yes—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4C2×D4×C1114yes—
570C2×D4C2×D4×C1112yes—
571C2×D4C2×D4×C1111yescharacteristic
572C2×D4C24×C1111yescharacteristic
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—42no—
583C22×C4—44no—
584C22×C4C2×D4×C1112yes—
585C22×C4C2×D4×C1111yescharacteristic
586C22×C4C24×C1111yescharacteristic
587C22×C4C24×C1112yes—
588C22×C4C24×C1112yes—
589Q16—28no—
590Q16—28no—
591Q16—44no—
592Q16—44no—
593Q16—44no—
594SD16—44no—
595M16—42no—
596C2×C8—42no—
597C2×C8—44no—
598C2×C8C24×C1114yes—
599C2×C8C24×C1114yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—22no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—22no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4C2×D4×C1112yes—
612C4⋊C4C2×D4×C1114yes—
613C4⋊C4C24×C1114yes—
614C4⋊C4C24×C1112yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—21no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—22no—
624C22⋊C4C2×D4×C1112yes—
625C22⋊C4C2×D4×C1114yes—
626C22⋊C4C2×D4×C1114yes—
627C42—22no—
628C42—24no—
629C42—24no—
630C42—21no—
631C42C24×C1112yes—
632C11#6163411yescharacteristic, direct product factor, Sylow
633C23—24no—
634C23—21no—
635C23—41no—
636C23C22×D4×C1111yescharacteristic
637C23C22×D4×C1112yes—
638C23C22×D4×C1112yes—
639Q8—24no—
640Q8—22no—
641Q8—24no—
642Q8—24no—
643Q8—24no—
644Q8—22no—
645Q8—41no—
646Q8—48no—
647Q8—44no—
648Q8—42no—
649Q8—82no—
650Q8—82no—
651Q8C11×H(5,𝔽2)14yes—
652D4—28no—
653D4—22no—
654D4—41no—
655D4—42no—
656D4—44no—
657D4—42no—
658D4—44no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—44no—
673C2×C4—48no—
674C2×C4—44no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—44no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4C22×D4×C1114yes—
681C2×C4C22×D4×C1112yes—
682C2×C4C22×D4×C1111yescharacteristic
683C2×C4C22×D4×C1112yes—
684C2×C4C25×C1111yescharacteristic
685C8—24no—
686C8—24no—
687C22—22no—
688C22—22no—
689C22—21no—
690C22—22no—
691C22—24no—
692C22—22no—
693C22—44no—
694C22—41no—
695C22—42no—
696C22C11×#57814yes—
697C22C23×D4×C1111yescharacteristic
698C4—24no—
699C4—21no—
700C4—22no—
701C4—22no—
702C4—24no—
703C4—41no—
704C4—42no—
705C4—44no—
706C4—44no—
707C4—42no—
708C4C2×C11×H(5,𝔽2)12yes—
709C2—24no—
710C2—41no—
711C2—42no—
712C2—81no—
713C2C11×#348411yescharacteristic
714C2C2×C11×#57812yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3486C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#525 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3538C2semidirect
3. C11×#3312C2semidirect
4. C11×#3300C2semidirect
5. D4×C11×Q16C2semidirect
6. C11×#3270C2semidirect
7. C11×#3223C2semidirect
8. C11×#3202C2semidirect
9. C11×#3190C2semidirect
10. C11×#3127C2semidirect
11. C11×#3011C2semidirect
12. C2×C11×#451C2semidirect
13. C11×#2977C2semidirect
16. C2×C11×#137C22semidirect
18. C22×C11×Q16C22semidirect
39. C11×#497C22semidirect
40. C11×#494C22semidirect
41. C11×#491C22semidirect
42. C11×#488C22semidirect
44. C11×#485C22semidirect
47. C11×#479C22semidirect
48. C11×#470C22semidirect
50. C11×#467C22semidirect
52. C11×#464C22semidirect
53. C11×#462C22semidirect
54. C11×#462C22semidirect
56. C11×#452C22semidirect
62. C11×#451C22semidirect
63. C11×#451C22semidirect
65. C11×#441C22semidirect
66. C4×C11×Q16C22semidirect
70. C11×#419C22semidirect
71. C11×#416C22semidirect
179. #61634C11direct (N × H)
276. #3538C2×C11semidirect
278. #3312C2×C11semidirect
279. #3300C2×C11semidirect
280. D4×Q16C2×C11semidirect
281. #3270C2×C11semidirect
282. #3223C2×C11semidirect
283. #3202C2×C11semidirect
284. #3190C2×C11semidirect
285. #3127C2×C11semidirect
286. #3011C2×C11semidirect
287. C2×#451C2×C11semidirect
288. #2977C2×C11semidirect
345. C2×#137C22×C11semidirect
347. C22×Q16C22×C11semidirect
368. #497C22×C11semidirect
369. #494C22×C11semidirect
370. #491C22×C11semidirect
371. #488C22×C11semidirect
373. #485C22×C11semidirect
376. #479C22×C11semidirect
377. #470C22×C11semidirect
379. #467C22×C11semidirect
381. #464C22×C11semidirect
382. #462C22×C11semidirect
383. #462C22×C11semidirect
385. #452C22×C11semidirect
391. #451C22×C11semidirect
392. #451C22×C11semidirect
394. #441C22×C11semidirect
395. C4×Q16C22×C11semidirect
399. #419C22×C11semidirect
400. #416C22×C11semidirect
632. C11#61634direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35382
C11×#34862
C11×#33122
C11×#33002
D4×C11×Q162
C11×#32702
C11×#32232
C11×#32022
C11×#31902
C11×#31272
C11×#30112
C2×C11×#4512
C11×#29772
#6163411