Finite Group Databasebeta

← C11×#25956 #14603149

Subgroups — C11×#25956 #14603149

Order 2816.

986 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#478C211yesmaximal, characteristic, complemented
2C2×C11×#416C211yesmaximal, characteristic
3C11×#2441C211yesmaximal, characteristic, complemented
4C11×#2339C211yesmaximal, characteristic
5C11×#2095C211yesmaximal, characteristic, complemented
6C11×#2068C211yesmaximal, characteristic, complemented
7C11×#2066C211yesmaximal, characteristic, complemented
8C11×#2026C211yesmaximal, characteristic, complemented
9C11×#1862C211yesmaximal, characteristic, complemented
10C11×#1862C211yesmaximal, characteristic, complemented
11C11×#1854C211yesmaximal, characteristic, complemented
12C11×#1850C211yesmaximal, characteristic, complemented
13C11×#1808C211yesmaximal, characteristic, complemented
14C11×#1802C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×#125C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C11×#478—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C11×#416—24no—
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C11×#399—21no—
40C11×#396—21no—
41C11×#391C2211yescharacteristic
42C11×#391C2211yescharacteristic
43C11×#389—21no—
44C11×#389C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#387—21no—
47C11×#386—21no—
48C11×#386—21no—
49C11×#384C2211yescharacteristic
50C11×#381—21no—
51C11×#380C2211yescharacteristic
52C11×#380C2211yescharacteristic
53C4×C11×C22⋊C4C2211yescharacteristic
54C2×C11×#95—21no—
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—41no—
65C2×C11×#41—41no—
66C2×C11×#41Q814yes—
67C22×Q8×C11C2311yescharacteristic
68C22×D4×C11—21no—
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C22×C8×C11—22no—
75C22×C8×C11—22no—
76C22×C8×C11—41no—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C11×#125—22no—
82C11×#125—41no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—41no—
86C4×D4×C11—41no—
87C11×#117—22no—
88C11×#117—41no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4D411yescharacteristic
107C2×C11×C22⋊C4D411yescharacteristic
108C2×C42×C11—21no—
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C11×#107—22no—
112C11×#107—41no—
113C11×#107—41no—
114C11×#106—22no—
115C11×C4⋊C8—22no—
116C11×C4⋊C8—41no—
117C11×#103—22no—
118C11×#103—22no—
119C11×#103—41no—
120C11×#103—41no—
121C11×#102—22no—
122C11×#102—22no—
123C11×#102—22no—
124C11×#102D414yes—
125C11×C22⋊C8—22no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95D411yescharacteristic
135C11×#95D411yescharacteristic
136#25956C1111yesmaximal, characteristic, direct product factor, Sylow
137C24×C11—21no—
138C24×C11C2×D411yescharacteristic
139C11×#41—28no—
140C11×#41—44no—
141C11×#41—44no—
142C11×#41—44no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×Q812yes—
149C2×D4×C11—24no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—42no—
154C2×D4×C11—42no—
155C2×D4×C11C2×D412yes—
156C2×D4×C11C2×Q812yes—
157C2×D4×C11#4112yes—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—24no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—81no—
177C22×C4×C11—81no—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×Q812yes—
184C22×C4×C11#4112yes—
185C22×C4×C11C2411yescharacteristic
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—44no—
198C2×C8×C11C2×D412yes—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—42no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4—42no—
214C11×C4⋊C4—81no—
215C11×C4⋊C4—81no—
216C11×C4⋊C4C2×D412yes—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—41no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—81no—
223C11×C22⋊C4—81no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—21no—
228C42×C11—42no—
229C2×#478C2×C1111yescharacteristic, complemented
230C2×#416C2×C1111yescharacteristic
231#2441C2×C1111yescharacteristic, complemented
232#2339C2×C1111yescharacteristic
233#2095C2×C1111yescharacteristic, complemented
234#2068C2×C1111yescharacteristic, complemented
235#2066C2×C1111yescharacteristic, complemented
236#2026C2×C1111yescharacteristic, complemented
237#1862C2×C1111yescharacteristic, complemented
238#1862C2×C1111yescharacteristic, complemented
239#1854C2×C1111yescharacteristic, complemented
240#1850C2×C1111yescharacteristic, complemented
241#1808C2×C1111yescharacteristic, complemented
242#1802C2×C1111yescharacteristic, complemented
243#1788C2×C1111yescharacteristic
244C23×C11—22no—
245C23×C11—21no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11C22⋊Q812yes—
258C23×C11C22×D411yescharacteristic
259Q8×C11—22no—
260Q8×C11—22no—
261Q8×C11—41no—
262Q8×C11—41no—
263D4×C11—22no—
264D4×C11—22no—
265D4×C11—22no—
266D4×C11—48no—
267D4×C11C22⋊Q814yes—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—22no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—48no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—84no—
308C2×C4×C11—84no—
309C2×C4×C11C22⋊Q812yes—
310C2×C4×C11#13512yes—
311C2×C4×C11C22×D411yescharacteristic
312C2×C4×C11C22×Q811yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11H(5,𝔽2)11yescharacteristic
316C2×C4×C11H(5,𝔽2)11yescharacteristic
317C8×C11—22no—
318C8×C11—41no—
319C8×C11—41no—
320C8×C11—41no—
321C22×#41C22×C1111yescharacteristic
322C23×C8C22×C1111yescharacteristic
323C2×#125C22×C1111yescharacteristic
324C2×C4×D4C22×C1111yescharacteristic
325C2×C4×D4C22×C1111yescharacteristic
326C2×#117C22×C1111yescharacteristic
327#478—24no—
328C2×#107C22×C1111yescharacteristic
329C2×#107C22×C1111yescharacteristic
330C2×#107C22×C1111yescharacteristic
331C2×#106C22×C1111yescharacteristic
332C2×C4⋊C8C22×C1111yescharacteristic
333C2×C4⋊C8C22×C1111yescharacteristic
334#416—24no—
335C2×#103C22×C1111yescharacteristic
336C2×#103C22×C1111yescharacteristic
337C2×#103C22×C1111yescharacteristic
338C2×#103C22×C1111yescharacteristic
339C2×#102C22×C1111yescharacteristic
340C2×#102C22×C1111yescharacteristic
341C2×#102C22×C1111yescharacteristic
342C2×#102C22×C1111yescharacteristic
343C2×C22⋊C8C22×C1111yescharacteristic
344#399—21no—
345#396—21no—
346#391C22×C1111yescharacteristic
347#391C22×C1111yescharacteristic
348#389—21no—
349#389C22×C1111yescharacteristic
350#389C22×C1111yescharacteristic
351#387—21no—
352#386—21no—
353#386—21no—
354#384C22×C1111yescharacteristic
355#381—21no—
356#380C22×C1111yescharacteristic
357#380C22×C1111yescharacteristic
358C4×C22⋊C4C22×C1111yescharacteristic
359C2×#95—21no—
360#340C22×C1111yescharacteristic
361#340C22×C1111yescharacteristic
362#340C22×C1111yescharacteristic
363#340C22×C1111yescharacteristic
364#336C22×C1111yescharacteristic
365#336C22×C1111yescharacteristic
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—22no—
369C22×C11—24no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—42no—
380C22×C11C2×C22⋊Q811yescharacteristic
381C22×C11D4211yescharacteristic
382C22×C11#54611yescharacteristic
383C22×C11C2×#13511yescharacteristic
384C22×C11#57511yescharacteristic
385C22×C11#57611yescharacteristic
386C22×C11#57811yescharacteristic
387C4×C11—22no—
388C4×C11—22no—
389C4×C11—42no—
390C4×C11—41no—
391C4×C11—41no—
392C4×C11—42no—
393C4×C11—41no—
394C4×C11—81no—
395C4×C11—81no—
396C4×C11—81no—
397C4×C11—81no—
398C4×C11—81no—
399C4×C11C2×C22⋊Q811yescharacteristic
400C4×C11#54311yescharacteristic
401C4×C11#54611yescharacteristic
402C4×C11#55111yescharacteristic
403C2×#41—22no—
404C2×#41—22no—
405C2×#41—22no—
406C2×#41—41no—
407C2×#41—41no—
408C2×#41Q8×C1114yes—
409C22×Q8C23×C1111yescharacteristic
410C22×D4—21no—
411C22×D4C23×C1111yescharacteristic
412C23×C4—21no—
413C23×C4—21no—
414C23×C4—21no—
415C23×C4C23×C1111yescharacteristic
416C22×C8—22no—
417C22×C8—22no—
418C22×C8—41no—
419C22×C8C23×C1111yescharacteristic
420C22×C8C23×C1111yescharacteristic
421C22×C8C23×C1111yescharacteristic
422C22×C8C23×C1111yescharacteristic
423#125—22no—
424#125—41no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—41no—
428C4×D4—41no—
429#117—22no—
430#117—41no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4C23×C1111yescharacteristic
438C2×C4⋊C4C23×C1111yescharacteristic
439C2×C4⋊C4C23×C1111yescharacteristic
440C2×C4⋊C4C23×C1111yescharacteristic
441C2×C4⋊C4C23×C1111yescharacteristic
442C2×C4⋊C4C23×C1111yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4D4×C1111yescharacteristic
449C2×C22⋊C4D4×C1111yescharacteristic
450C2×C42—21no—
451C2×C42C23×C1111yescharacteristic
452C2×C42C23×C1111yescharacteristic
453#107—22no—
454#107—41no—
455#107—41no—
456#106—22no—
457C4⋊C8—22no—
458C4⋊C8—41no—
459#103—22no—
460#103—22no—
461#103—41no—
462#103—41no—
463#102—22no—
464#102—22no—
465#102—22no—
466#102D4×C1114yes—
467C22⋊C8—22no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95D4×C1111yescharacteristic
477#95D4×C1111yescharacteristic
478C2×C11—42no—
479C2×C11—44no—
480C2×C11#243711yescharacteristic
481C2×C11#307611yescharacteristic
482C2×C11#308311yescharacteristic
483C2×C11#326811yescharacteristic
484C2×C11#328311yescharacteristic
485C2×C11#329711yescharacteristic
486C2×C11#331511yescharacteristic
487C24—21no—
488C24C2×D4×C1111yescharacteristic
489#41—28no—
490#41—44no—
491#41—44no—
492#41—44no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8C2×Q8×C1112yes—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4C2×D4×C1112yes—
506C2×D4C2×Q8×C1112yes—
507C2×D4C11×#4112yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—24no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4C2×D4×C1111yescharacteristic
529C22×C4C2×D4×C1111yescharacteristic
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C2×D4×C1111yescharacteristic
532C22×C4C2×D4×C1111yescharacteristic
533C22×C4C2×Q8×C1112yes—
534C22×C4C11×#4112yes—
535C22×C4C24×C1111yescharacteristic
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—44no—
548C2×C8C2×D4×C1112yes—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—81no—
565C4⋊C4—81no—
566C4⋊C4C2×D4×C1112yes—
567C22⋊C4—22no—
568C22⋊C4—41no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—42no—
579C11#2595611yescharacteristic, direct product factor, Sylow
580C23—22no—
581C23—21no—
582C23—22no—
583C23—22no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C11×C22⋊Q812yes—
594C23C22×D4×C1111yescharacteristic
595Q8—22no—
596Q8—22no—
597Q8—41no—
598Q8—41no—
599D4—22no—
600D4—22no—
601D4—22no—
602D4—48no—
603D4C11×C22⋊Q814yes—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—48no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—84no—
644C2×C4—84no—
645C2×C4C11×C22⋊Q812yes—
646C2×C4C11×#13512yes—
647C2×C4C22×D4×C1111yescharacteristic
648C2×C4C22×Q8×C1111yescharacteristic
649C2×C4C2×C11×#4111yescharacteristic
650C2×C4C2×C11×#4111yescharacteristic
651C2×C4C11×H(5,𝔽2)11yescharacteristic
652C2×C4C11×H(5,𝔽2)11yescharacteristic
653C8—22no—
654C8—41no—
655C8—41no—
656C8—41no—
657C22—22no—
658C22—24no—
659C22—22no—
660C22—22no—
661C22—42no—
662C22—41no—
663C22—41no—
664C22—42no—
665C22—42no—
666C22—41no—
667C22—41no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22C2×C11×C22⋊Q811yescharacteristic
672C22D42×C1111yescharacteristic
673C22C11×#54611yescharacteristic
674C22C2×C11×#13511yescharacteristic
675C22C11×#57511yescharacteristic
676C22C11×#57611yescharacteristic
677C22C11×#57811yescharacteristic
678C4—22no—
679C4—22no—
680C4—42no—
681C4—41no—
682C4—41no—
683C4—42no—
684C4—41no—
685C4—81no—
686C4—81no—
687C4—81no—
688C4—81no—
689C4—81no—
690C4C2×C11×C22⋊Q811yescharacteristic
691C4C11×#54311yescharacteristic
692C4C11×#54611yescharacteristic
693C4C11×#55111yescharacteristic
694C2—42no—
695C2—44no—
696C2C11×#243711yescharacteristic
697C2C11×#307611yescharacteristic
698C2C11×#308311yescharacteristic
699C2C11×#326811yescharacteristic
700C2C11×#328311yescharacteristic
701C2C11×#329711yescharacteristic
702C2C11×#331511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#478C2semidirect
3. C11×#2441C2semidirect
5. C11×#2095C2semidirect
6. C11×#2068C2semidirect
7. C11×#2066C2semidirect
8. C11×#2026C2semidirect
9. C11×#1862C2semidirect
10. C11×#1862C2semidirect
11. C11×#1854C2semidirect
12. C11×#1850C2semidirect
13. C11×#1808C2semidirect
14. C11×#1802C2semidirect
136. #25956C11direct (N × H)
229. C2×#478C2×C11semidirect
231. #2441C2×C11semidirect
233. #2095C2×C11semidirect
234. #2068C2×C11semidirect
235. #2066C2×C11semidirect
236. #2026C2×C11semidirect
237. #1862C2×C11semidirect
238. #1862C2×C11semidirect
239. #1854C2×C11semidirect
240. #1850C2×C11semidirect
241. #1808C2×C11semidirect
242. #1802C2×C11semidirect
579. C11#25956direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4782
C2×C11×#4162
C11×#24412
C11×#23392
C11×#20952
C11×#20682
C11×#20662
C11×#20262
C11×#18622
C11×#18542
C11×#18502
C11×#18082
C11×#18022
C11×#17882
#2595611