Finite Group Databasebeta

← C11×#22660 #14599853

Subgroups — C11×#22660 #14599853

Order 2816.

970 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#435C211yesmaximal, characteristic
2C2×C11×#428C211yesmaximal, characteristic, complemented
3C2×C11×#427C211yesmaximal, characteristic, complemented
4C11×#2354C211yesmaximal, characteristic
5C11×#2352C211yesmaximal, characteristic
6C11×#1949C211yesmaximal, characteristic, complemented
7C11×#1947C211yesmaximal, characteristic, complemented
8C11×#1854C211yesmaximal, characteristic, complemented
9C11×#1854C211yesmaximal, characteristic, complemented
10C11×#1854C211yesmaximal, characteristic, complemented
11C11×#1852C211yesmaximal, characteristic, complemented
12C11×#1847C211yesmaximal, characteristic, complemented
13C11×#1809C211yesmaximal, characteristic, complemented
14C11×#1808C211yesmaximal, characteristic, complemented
15C11×#1776C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C11×#435C418yescomplemented
24C11×#428—24no—
25C11×#427—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#107C2211yescharacteristic
28C2×C11×#107C2211yescharacteristic
29C2×C11×#107C2211yescharacteristic
30C2×C11×#107C2211yescharacteristic
31C2×C11×#107C2211yescharacteristic
32C2×C11×#106C2211yescharacteristic
33C2×C11×#106C2211yescharacteristic
34C2×C11×#106C2211yescharacteristic
35C2×C11×#106C2211yescharacteristic
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×#97C2211yescharacteristic
40C11×#390—21no—
41C11×#388—21no—
42C11×#388—21no—
43C11×#388—21no—
44C11×#387—21no—
45C11×#386—21no—
46C11×#384C2211yescharacteristic
47C11×#382C2211yescharacteristic
48C11×#380C2211yescharacteristic
49C11×#380C2211yescharacteristic
50C11×#380C2211yescharacteristic
51C11×#380C2211yescharacteristic
52C4×C11×C4⋊C4—21no—
53C4×C11×C4⋊C4C2211yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C22⋊C4—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C22×D4×C11D411yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16C2×C414yes—
69C22×C8×C11—22no—
70C22×C8×C11—22no—
71C22×C8×C11C2×C414yescomplemented
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C4×D4×C11C2×C414yes—
77C4×D4×C11Q814yes—
78C11×#117—22no—
79C11×#117—22no—
80C11×#117—22no—
81C11×#117—41no—
82C11×#117—41no—
83C11×#117—41no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—41no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4D411yescharacteristic
106C2×C11×C22⋊C4D411yescharacteristic
107C2×C42×C11—21no—
108C2×C42×C11—21no—
109C2×C42×C11—21no—
110C2×C42×C11—21no—
111C2×C42×C11—21no—
112C2×C42×C11C2311yescharacteristic
113C11×#107—22no—
114C11×#107—22no—
115C11×#107—22no—
116C11×#107—22no—
117C11×#107—22no—
118C11×#107—41no—
119C11×#106—22no—
120C11×#106—22no—
121C11×#106—41no—
122C11×#106D414yescomplemented
123C11×C4⋊C8C2×C414yescomplemented
124C11×C22⋊C8C2×C414yes—
125C11×C22⋊C8C2×C414yescomplemented
126C11×#97C2×C414yescomplemented
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135#22660C1111yesmaximal, characteristic, direct product factor, Sylow
136C24×C11C2×D411yescharacteristic
137C24×C11C2×D411yescharacteristic
138C2×D4×C11—41no—
139C2×D4×C11—41no—
140C2×D4×C11C4⋊C414yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11—81no—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C22×C412yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×Q812yes—
167C22×C4×C11C2×Q812yes—
168C22×C4×C11C2411yescharacteristic
169C11×M16—28no—
170C2×C8×C11—28no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11C22×C412yes—
178C2×C8×C11C22×C412yes—
179C2×C8×C11C22×C412yes—
180C2×C8×C11C22×C412yes—
181C2×C8×C11C2×D412yes—
182C2×C8×C11#4112yes—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—42no—
198C11×C4⋊C4—42no—
199C11×C4⋊C4—81no—
200C11×C4⋊C4C4⋊C414yes—
201C11×C4⋊C4C2×D412yes—
202C11×C4⋊C4C2×D412yes—
203C11×C22⋊C4—42no—
204C11×C22⋊C4—42no—
205C11×C22⋊C4—42no—
206C11×C22⋊C4—42no—
207C11×C22⋊C4—81no—
208C11×C22⋊C4—81no—
209C11×C22⋊C4—81no—
210C11×C22⋊C4C4⋊C414yes—
211C11×C22⋊C4C4⋊C414yes—
212C42×C11—42no—
213C42×C11—42no—
214C42×C11—42no—
215C42×C11—42no—
216C42×C11—81no—
217C42×C11C22×C412yes—
218C42×C11C2×Q812yes—
219C2×#435C2×C1111yescharacteristic
220C2×#428C2×C1111yescharacteristic, complemented
221C2×#427C2×C1111yescharacteristic, complemented
222#2354C2×C1111yescharacteristic
223#2352C2×C1111yescharacteristic
224#1949C2×C1111yescharacteristic, complemented
225#1947C2×C1111yescharacteristic, complemented
226#1854C2×C1111yescharacteristic, complemented
227#1854C2×C1111yescharacteristic, complemented
228#1854C2×C1111yescharacteristic, complemented
229#1852C2×C1111yescharacteristic, complemented
230#1847C2×C1111yescharacteristic, complemented
231#1809C2×C1111yescharacteristic, complemented
232#1808C2×C1111yescharacteristic, complemented
233#1776C2×C1111yescharacteristic, complemented
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11C2×C4⋊C412yes—
247C23×C11C2×C4⋊C412yes—
248C23×C11C22×D411yescharacteristic
249D4×C11—44no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—84no—
291C2×C4×C11C2×C4⋊C412yes—
292C2×C4×C11C2×C4⋊C412yes—
293C2×C4×C11C2×C4⋊C412yes—
294C2×C4×C11C2×C4⋊C412yes—
295C2×C4×C11C23×C411yescharacteristic
296C2×C4×C11C22×D411yescharacteristic
297C2×C4×C11C22×Q811yescharacteristic
298C2×C4×C11C2×#4111yescharacteristic
299C2×C4×C11H(5,𝔽2)11yescharacteristic
300C2×C4×C112−1+411yescharacteristic
301C8×C11—22no—
302C8×C11—22no—
303C8×C11—22no—
304C8×C11C4×D414yes—
305C22×M16C22×C1111yescharacteristic
306C23×C8C22×C1111yescharacteristic
307C2×C4×D4C22×C1111yescharacteristic
308C2×#117C22×C1111yescharacteristic
309C2×#117C22×C1111yescharacteristic
310C2×#117C22×C1111yescharacteristic
311C22×C4⋊C4C22×C1111yescharacteristic
312#435C4×C1118yescomplemented
313#428—24no—
314#427—24no—
315C2×#107C22×C1111yescharacteristic
316C2×#107C22×C1111yescharacteristic
317C2×#107C22×C1111yescharacteristic
318C2×#107C22×C1111yescharacteristic
319C2×#107C22×C1111yescharacteristic
320C2×#107C22×C1111yescharacteristic
321C2×#106C22×C1111yescharacteristic
322C2×#106C22×C1111yescharacteristic
323C2×#106C22×C1111yescharacteristic
324C2×#106C22×C1111yescharacteristic
325C2×C4⋊C8C22×C1111yescharacteristic
326C2×C22⋊C8C22×C1111yescharacteristic
327C2×C22⋊C8C22×C1111yescharacteristic
328C2×#97C22×C1111yescharacteristic
329#390—21no—
330#388—21no—
331#388—21no—
332#388—21no—
333#387—21no—
334#386—21no—
335#384C22×C1111yescharacteristic
336#382C22×C1111yescharacteristic
337#380C22×C1111yescharacteristic
338#380C22×C1111yescharacteristic
339#380C22×C1111yescharacteristic
340#380C22×C1111yescharacteristic
341C4×C4⋊C4—21no—
342C4×C4⋊C4C22×C1111yescharacteristic
343C4×C4⋊C4C22×C1111yescharacteristic
344C4×C22⋊C4—21no—
345#340C22×C1111yescharacteristic
346#340C22×C1111yescharacteristic
347#340C22×C1111yescharacteristic
348#340C22×C1111yescharacteristic
349#340C22×C1111yescharacteristic
350#340C22×C1111yescharacteristic
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11C22×C4⋊C411yescharacteristic
366C22×C11D4211yescharacteristic
367C22×C11#54711yescharacteristic
368C22×C11#57511yescharacteristic
369C22×C11#57511yescharacteristic
370C22×C11#57611yescharacteristic
371C22×C11#57811yescharacteristic
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—22no—
375C4×C11—22no—
376C4×C11—42no—
377C4×C11—42no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11C2×C4×D411yescharacteristic
385C4×C11#52011yescharacteristic
386C4×C11D4×Q811yescharacteristic
387C4×C11#55411yescharacteristic
388C22×D4D4×C1111yescharacteristic
389C23×C4—21no—
390C23×C4C23×C1111yescharacteristic
391C23×C4C23×C1111yescharacteristic
392C2×M16—22no—
393C2×M16—22no—
394C2×M16C2×C4×C1114yes—
395C22×C8—22no—
396C22×C8—22no—
397C22×C8C2×C4×C1114yescomplemented
398C22×C8C23×C1111yescharacteristic
399C22×C8C23×C1111yescharacteristic
400C22×C8C23×C1111yescharacteristic
401C22×C8C23×C1111yescharacteristic
402C4×D4C2×C4×C1114yes—
403C4×D4Q8×C1114yes—
404#117—22no—
405#117—22no—
406#117—22no—
407#117—41no—
408#117—41no—
409#117—41no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—41no—
415C2×C4⋊C4D4×C1111yescharacteristic
416C2×C4⋊C4C23×C1111yescharacteristic
417C2×C4⋊C4C23×C1111yescharacteristic
418C2×C4⋊C4C23×C1111yescharacteristic
419C2×C4⋊C4C23×C1111yescharacteristic
420C2×C4⋊C4C23×C1111yescharacteristic
421C2×C4⋊C4C23×C1111yescharacteristic
422C2×C4⋊C4C23×C1111yescharacteristic
423C2×C4⋊C4C23×C1111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4D4×C1111yescharacteristic
432C2×C22⋊C4D4×C1111yescharacteristic
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42C23×C1111yescharacteristic
439#107—22no—
440#107—22no—
441#107—22no—
442#107—22no—
443#107—22no—
444#107—41no—
445#106—22no—
446#106—22no—
447#106—41no—
448#106D4×C1114yescomplemented
449C4⋊C8C2×C4×C1114yescomplemented
450C22⋊C8C2×C4×C1114yes—
451C22⋊C8C2×C4×C1114yescomplemented
452#97C2×C4×C1114yescomplemented
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461C2×C11—42no—
462C2×C11—42no—
463C2×C11D4×C4⋊C411yescharacteristic
464C2×C11#291111yescharacteristic
465C2×C11#291311yescharacteristic
466C2×C11#326811yescharacteristic
467C2×C11#326911yescharacteristic
468C2×C11#334711yescharacteristic
469C2×C11#334911yescharacteristic
470C24C2×D4×C1111yescharacteristic
471C24C2×D4×C1111yescharacteristic
472C2×D4—41no—
473C2×D4—41no—
474C2×D4C11×C4⋊C414yes—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—81no—
494C22×C4C22×C4×C1112yes—
495C22×C4C22×C4×C1112yes—
496C22×C4C2×D4×C1111yescharacteristic
497C22×C4C2×D4×C1111yescharacteristic
498C22×C4C2×D4×C1111yescharacteristic
499C22×C4C2×D4×C1111yescharacteristic
500C22×C4C2×Q8×C1112yes—
501C22×C4C2×Q8×C1112yes—
502C22×C4C24×C1111yescharacteristic
503M16—28no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—28no—
511C2×C8C22×C4×C1112yes—
512C2×C8C22×C4×C1112yes—
513C2×C8C22×C4×C1112yes—
514C2×C8C22×C4×C1112yes—
515C2×C8C2×D4×C1112yes—
516C2×C8C11×#4112yes—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—81no—
534C4⋊C4C11×C4⋊C414yes—
535C4⋊C4C2×D4×C1112yes—
536C4⋊C4C2×D4×C1112yes—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—81no—
542C22⋊C4—81no—
543C22⋊C4—81no—
544C22⋊C4C11×C4⋊C414yes—
545C22⋊C4C11×C4⋊C414yes—
546C42—42no—
547C42—42no—
548C42—42no—
549C42—42no—
550C42—81no—
551C42C22×C4×C1112yes—
552C42C2×Q8×C1112yes—
553C11#2266011yescharacteristic, direct product factor, Sylow
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23C2×C11×C4⋊C412yes—
567C23C2×C11×C4⋊C412yes—
568C23C22×D4×C1111yescharacteristic
569D4—44no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—84no—
611C2×C4C2×C11×C4⋊C412yes—
612C2×C4C2×C11×C4⋊C412yes—
613C2×C4C2×C11×C4⋊C412yes—
614C2×C4C2×C11×C4⋊C412yes—
615C2×C4C23×C4×C1111yescharacteristic
616C2×C4C22×D4×C1111yescharacteristic
617C2×C4C22×Q8×C1111yescharacteristic
618C2×C4C2×C11×#4111yescharacteristic
619C2×C4C11×H(5,𝔽2)11yescharacteristic
620C2×C4C11×2−1+411yescharacteristic
621C8—22no—
622C8—22no—
623C8—22no—
624C8C4×D4×C1114yes—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22C22×C11×C4⋊C411yescharacteristic
640C22D42×C1111yescharacteristic
641C22C11×#54711yescharacteristic
642C22C11×#57511yescharacteristic
643C22C11×#57511yescharacteristic
644C22C11×#57611yescharacteristic
645C22C11×#57811yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—42no—
651C4—42no—
652C4—81no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4C2×C4×D4×C1111yescharacteristic
659C4C11×#52011yescharacteristic
660C4D4×Q8×C1111yescharacteristic
661C4C11×#55411yescharacteristic
662C2—42no—
663C2—42no—
664C2D4×C11×C4⋊C411yescharacteristic
665C2C11×#291111yescharacteristic
666C2C11×#291311yescharacteristic
667C2C11×#326811yescharacteristic
668C2C11×#326911yescharacteristic
669C2C11×#334711yescharacteristic
670C2C11×#334911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#428C2semidirect
3. C2×C11×#427C2semidirect
6. C11×#1949C2semidirect
7. C11×#1947C2semidirect
8. C11×#1854C2semidirect
9. C11×#1854C2semidirect
10. C11×#1854C2semidirect
11. C11×#1852C2semidirect
12. C11×#1847C2semidirect
13. C11×#1809C2semidirect
14. C11×#1808C2semidirect
15. C11×#1776C2semidirect
23. C11×#435C4semidirect
71. C22×C8×C11C2×C4semidirect
122. C11×#106D4semidirect
123. C11×C4⋊C8C2×C4semidirect
125. C11×C22⋊C8C2×C4semidirect
126. C11×#97C2×C4semidirect
135. #22660C11direct (N × H)
220. C2×#428C2×C11semidirect
221. C2×#427C2×C11semidirect
224. #1949C2×C11semidirect
225. #1947C2×C11semidirect
226. #1854C2×C11semidirect
227. #1854C2×C11semidirect
228. #1854C2×C11semidirect
229. #1852C2×C11semidirect
230. #1847C2×C11semidirect
231. #1809C2×C11semidirect
232. #1808C2×C11semidirect
233. #1776C2×C11semidirect
312. #435C4×C11semidirect
397. C22×C8C2×C4×C11semidirect
448. #106D4×C11semidirect
449. C4⋊C8C2×C4×C11semidirect
451. C22⋊C8C2×C4×C11semidirect
452. #97C2×C4×C11semidirect
553. C11#22660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4352
C2×C11×#4282
C2×C11×#4272
C11×#23542
C11×#23522
C11×#19492
C11×#19472
C11×#18542
C11×#18522
C11×#18472
C11×#18092
C11×#18082
C11×#17762
#2266011