Finite Group Databasebeta

← C11×#22499 #14599692

Subgroups — C11×#22499 #14599692

Order 2816.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#552C211yesmaximal, characteristic
2C2×C11×#436C211yesmaximal, characteristic
3C11×#2352C211yesmaximal, characteristic
4C11×#1991C211yesmaximal, characteristic, complemented
5C11×#1989C211yesmaximal, characteristic, complemented
6C11×#1894C211yesmaximal, characteristic, complemented
7C11×#1894C211yesmaximal, characteristic, complemented
8C11×#1873C211yesmaximal, characteristic, complemented
9C11×#1872C211yesmaximal, characteristic, complemented
10C11×#1825C211yesmaximal, characteristic, complemented
11C11×#1824C211yesmaximal, characteristic, complemented
12C11×#1805C211yesmaximal, characteristic, complemented
13C4×C11×#103C211yesmaximal, characteristic, complemented
14C11×#1736C211yesmaximal, characteristic, complemented
15C11×#1736C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C11×#552—24no—
19C11×#552C418yescomplemented
20C2×C11×#126—21no—
21C2×C11×#125—21no—
22C2×C11×#125C2211yescharacteristic
23C2×C11×#123—21no—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117—21no—
29C2×C11×#117C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C22×C11×C4⋊C4C2211yescharacteristic
32C22×C11×C4⋊C4C2211yescharacteristic
33C11×#436—24no—
34C2×C11×C4⋊C8C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42C11×#388—21no—
43C11×#387—21no—
44C11×#386—21no—
45C11×#382C2211yescharacteristic
46C11×#380C2211yescharacteristic
47C11×#380C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C22⋊C4—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11D411yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16—41no—
73C2×C11×M16—41no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×#126—28no—
79C11×#125—28no—
80C11×#125—22no—
81C11×#125C2×C414yescomplemented
82C11×#123—28no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8C2×C414yes—
86C11×C22⋊Q8C2×C414yescomplemented
87C4×Q8×C11—22no—
88C4×Q8×C11C2×C414yescomplemented
89C4×D4×C11C2×C414yes—
90C4×D4×C11D414yes—
91C11×#117—22no—
92C11×#117—28no—
93C11×#117—22no—
94C11×#117—41no—
95C11×#117C2×C414yes—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—22no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—41no—
106C2×C11×C4⋊C4C2×C414yescomplemented
107C2×C11×C4⋊C4D411yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4D411yescharacteristic
122C2×C11×C22⋊C4D411yescharacteristic
123C2×C42×C11—21no—
124C2×C42×C11—21no—
125C2×C42×C11—21no—
126C2×C42×C11—21no—
127C2×C42×C11C2311yescharacteristic
128C11×C4⋊C8—22no—
129C11×#103—22no—
130C11×#103—22no—
131C11×#103—41no—
132C11×#103—41no—
133C11×C22⋊C8—22no—
134C11×C22⋊C8—22no—
135C4×C8×C11—22no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140C11×#95—21no—
141#22499C1111yesmaximal, characteristic, direct product factor, Sylow
142C24×C11C2×D411yescharacteristic
143C24×C11C2×D411yescharacteristic
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C22×C412yes—
150C2×D4×C11—41no—
151C2×D4×C11—41no—
152C2×D4×C11C22⋊C414yes—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—24no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
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—81no—
175C22×C4×C11C22×C412yes—
176C22×C4×C11C22×C412yes—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D412yes—
183C22×C4×C11C2411yescharacteristic
184C11×M16—44no—
185C11×M16—44no—
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#4112yes—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—24no—
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—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—42no—
215C11×C4⋊C4C22⋊C414yes—
216C11×C4⋊C4C22×C412yes—
217C11×C4⋊C4C22×C412yes—
218C11×C4⋊C4C22×C412yes—
219C11×C4⋊C4#4112yes—
220C11×C22⋊C4—24no—
221C11×C22⋊C4—24no—
222C11×C22⋊C4—24no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—81no—
226C11×C22⋊C4C22⋊C414yes—
227C11×C22⋊C4C22⋊C414yes—
228C42×C11—24no—
229C42×C11—24no—
230C42×C11—42no—
231C42×C11—81no—
232C42×C11C22×C412yes—
233C42×C11C2×D412yes—
234C2×#552C2×C1111yescharacteristic
235C2×#436C2×C1111yescharacteristic
236#2352C2×C1111yescharacteristic
237#1991C2×C1111yescharacteristic, complemented
238#1989C2×C1111yescharacteristic, complemented
239#1894C2×C1111yescharacteristic, complemented
240#1894C2×C1111yescharacteristic, complemented
241#1873C2×C1111yescharacteristic, complemented
242#1872C2×C1111yescharacteristic, complemented
243#1825C2×C1111yescharacteristic, complemented
244#1824C2×C1111yescharacteristic, complemented
245#1805C2×C1111yescharacteristic, complemented
246C4×#103C2×C1111yescharacteristic, complemented
247#1736C2×C1111yescharacteristic, complemented
248#1736C2×C1111yescharacteristic, complemented
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11C2×C22⋊C412yes—
262C23×C11C2×C22⋊C412yes—
263C23×C11C22×D411yescharacteristic
264Q8×C11—22no—
265Q8×C11—22no—
266Q8×C11—41no—
267Q8×C11—41no—
268D4×C11—44no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—48no—
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—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—84no—
311C2×C4×C11C2×C22⋊C412yes—
312C2×C4×C11C2×C22⋊C412yes—
313C2×C4×C11C2×C22⋊C412yes—
314C2×C4×C11C2×C22⋊C412yes—
315C2×C4×C11C23×C411yescharacteristic
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C112−1+411yescharacteristic
321C8×C11—22no—
322C8×C11—41no—
323C8×C11—41no—
324C8×C11—41no—
325C22×M16C22×C1111yescharacteristic
326C22×M16C22×C1111yescharacteristic
327#552—24no—
328#552C4×C1118yescomplemented
329C2×#126—21no—
330C2×#125—21no—
331C2×#125C22×C1111yescharacteristic
332C2×#123—21no—
333C2×C22⋊Q8C22×C1111yescharacteristic
334C2×C22⋊Q8C22×C1111yescharacteristic
335C2×C4×Q8C22×C1111yescharacteristic
336C2×C4×D4C22×C1111yescharacteristic
337C2×#117—21no—
338C2×#117C22×C1111yescharacteristic
339C2×#117C22×C1111yescharacteristic
340C22×C4⋊C4C22×C1111yescharacteristic
341C22×C4⋊C4C22×C1111yescharacteristic
342#436—24no—
343C2×C4⋊C8C22×C1111yescharacteristic
344C2×#103C22×C1111yescharacteristic
345C2×#103C22×C1111yescharacteristic
346C2×#103C22×C1111yescharacteristic
347C2×#103C22×C1111yescharacteristic
348C2×C22⋊C8C22×C1111yescharacteristic
349C2×C22⋊C8C22×C1111yescharacteristic
350C2×C4×C8C22×C1111yescharacteristic
351#388—21no—
352#387—21no—
353#386—21no—
354#382C22×C1111yescharacteristic
355#380C22×C1111yescharacteristic
356#380C22×C1111yescharacteristic
357C4×C4⋊C4C22×C1111yescharacteristic
358C4×C22⋊C4—21no—
359#340C22×C1111yescharacteristic
360#340C22×C1111yescharacteristic
361#340C22×C1111yescharacteristic
362#340C22×C1111yescharacteristic
363#340C22×C1111yescharacteristic
364#340C22×C1111yescharacteristic
365#340C22×C1111yescharacteristic
366#340C22×C1111yescharacteristic
367#340C22×C1111yescharacteristic
368#340C22×C1111yescharacteristic
369#340C22×C1111yescharacteristic
370#340C22×C1111yescharacteristic
371C22×C11—22no—
372C22×C11—22no—
373C22×C11—22no—
374C22×C11—22no—
375C22×C11—22no—
376C22×C11—22no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11C22×C22⋊C411yescharacteristic
386C22×C11#54611yescharacteristic
387C22×C11#54711yescharacteristic
388C22×C11#57511yescharacteristic
389C22×C11#57511yescharacteristic
390C22×C11#57711yescharacteristic
391C22×C11#57811yescharacteristic
392C4×C11—22no—
393C4×C11—22no—
394C4×C11—22no—
395C4×C11—22no—
396C4×C11—42no—
397C4×C11—42no—
398C4×C11—42no—
399C4×C11—42no—
400C4×C11—42no—
401C4×C11—81no—
402C4×C11—81no—
403C4×C11—81no—
404C4×C11C4×#4111yescharacteristic
405C4×C11#52011yescharacteristic
406C4×C11#54611yescharacteristic
407C4×C11#54711yescharacteristic
408C22×Q8C23×C1111yescharacteristic
409C22×D4D4×C1111yescharacteristic
410C23×C4—21no—
411C23×C4—21no—
412C23×C4C23×C1111yescharacteristic
413C23×C4C23×C1111yescharacteristic
414C2×M16—22no—
415C2×M16—22no—
416C2×M16—22no—
417C2×M16—22no—
418C2×M16—41no—
419C2×M16—41no—
420C22×C8C23×C1111yescharacteristic
421C22×C8C23×C1111yescharacteristic
422C22×C8C23×C1111yescharacteristic
423C22×C8C23×C1111yescharacteristic
424#126—28no—
425#125—28no—
426#125—22no—
427#125C2×C4×C1114yescomplemented
428#123—28no—
429C22⋊Q8—22no—
430C22⋊Q8—22no—
431C22⋊Q8C2×C4×C1114yes—
432C22⋊Q8C2×C4×C1114yescomplemented
433C4×Q8—22no—
434C4×Q8C2×C4×C1114yescomplemented
435C4×D4C2×C4×C1114yes—
436C4×D4D4×C1114yes—
437#117—22no—
438#117—28no—
439#117—22no—
440#117—41no—
441#117C2×C4×C1114yes—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—41no—
452C2×C4⋊C4C2×C4×C1114yescomplemented
453C2×C4⋊C4D4×C1111yescharacteristic
454C2×C4⋊C4C23×C1111yescharacteristic
455C2×C4⋊C4C23×C1111yescharacteristic
456C2×C4⋊C4C23×C1111yescharacteristic
457C2×C4⋊C4C23×C1111yescharacteristic
458C2×C4⋊C4C23×C1111yescharacteristic
459C2×C4⋊C4C23×C1111yescharacteristic
460C2×C4⋊C4C23×C1111yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4D4×C1111yescharacteristic
468C2×C22⋊C4D4×C1111yescharacteristic
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42C23×C1111yescharacteristic
474C4⋊C8—22no—
475#103—22no—
476#103—22no—
477#103—41no—
478#103—41no—
479C22⋊C8—22no—
480C22⋊C8—22no—
481C4×C8—22no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487C2×C11—42no—
488C2×C11—42no—
489C2×C11#233911yescharacteristic
490C2×C11#289611yescharacteristic
491C2×C11#289811yescharacteristic
492C2×C11#332311yescharacteristic
493C2×C11#332711yescharacteristic
494C2×C11#335111yescharacteristic
495C2×C11#335211yescharacteristic
496C24C2×D4×C1111yescharacteristic
497C24C2×D4×C1111yescharacteristic
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8C22×C4×C1112yes—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4C11×C22⋊C414yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—81no—
529C22×C4C22×C4×C1112yes—
530C22×C4C22×C4×C1112yes—
531C22×C4C2×D4×C1111yescharacteristic
532C22×C4C2×D4×C1111yescharacteristic
533C22×C4C2×D4×C1111yescharacteristic
534C22×C4C2×D4×C1111yescharacteristic
535C22×C4C2×D4×C1112yes—
536C22×C4C2×D4×C1112yes—
537C22×C4C24×C1111yescharacteristic
538M16—44no—
539M16—44no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8C11×#4112yes—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—42no—
569C4⋊C4C11×C22⋊C414yes—
570C4⋊C4C22×C4×C1112yes—
571C4⋊C4C22×C4×C1112yes—
572C4⋊C4C22×C4×C1112yes—
573C4⋊C4C11×#4112yes—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—81no—
580C22⋊C4C11×C22⋊C414yes—
581C22⋊C4C11×C22⋊C414yes—
582C42—24no—
583C42—24no—
584C42—42no—
585C42—81no—
586C42C22×C4×C1112yes—
587C42C2×D4×C1112yes—
588C11#2249911yescharacteristic, direct product factor, Sylow
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23C2×C11×C22⋊C412yes—
602C23C2×C11×C22⋊C412yes—
603C23C22×D4×C1111yescharacteristic
604Q8—22no—
605Q8—22no—
606Q8—41no—
607Q8—41no—
608D4—44no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—48no—
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—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—84no—
651C2×C4C2×C11×C22⋊C412yes—
652C2×C4C2×C11×C22⋊C412yes—
653C2×C4C2×C11×C22⋊C412yes—
654C2×C4C2×C11×C22⋊C412yes—
655C2×C4C23×C4×C1111yescharacteristic
656C2×C4C22×D4×C1111yescharacteristic
657C2×C4C2×C11×#4111yescharacteristic
658C2×C4C2×C11×#4111yescharacteristic
659C2×C4C11×H(5,𝔽2)11yescharacteristic
660C2×C4C11×2−1+411yescharacteristic
661C8—22no—
662C8—41no—
663C8—41no—
664C8—41no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22C22×C11×C22⋊C411yescharacteristic
680C22C11×#54611yescharacteristic
681C22C11×#54711yescharacteristic
682C22C11×#57511yescharacteristic
683C22C11×#57511yescharacteristic
684C22C11×#57711yescharacteristic
685C22C11×#57811yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4C4×C11×#4111yescharacteristic
699C4C11×#52011yescharacteristic
700C4C11×#54611yescharacteristic
701C4C11×#54711yescharacteristic
702C2—42no—
703C2—42no—
704C2C11×#233911yescharacteristic
705C2C11×#289611yescharacteristic
706C2C11×#289811yescharacteristic
707C2C11×#332311yescharacteristic
708C2C11×#332711yescharacteristic
709C2C11×#335111yescharacteristic
710C2C11×#335211yescharacteristic
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
4. C11×#1991C2semidirect
5. C11×#1989C2semidirect
6. C11×#1894C2semidirect
7. C11×#1894C2semidirect
8. C11×#1873C2semidirect
9. C11×#1872C2semidirect
10. C11×#1825C2semidirect
11. C11×#1824C2semidirect
12. C11×#1805C2semidirect
13. C4×C11×#103C2semidirect
14. C11×#1736C2semidirect
15. C11×#1736C2semidirect
19. C11×#552C4semidirect
81. C11×#125C2×C4semidirect
86. C11×C22⋊Q8C2×C4semidirect
88. C4×Q8×C11C2×C4semidirect
106. C2×C11×C4⋊C4C2×C4semidirect
141. #22499C11direct (N × H)
237. #1991C2×C11semidirect
238. #1989C2×C11semidirect
239. #1894C2×C11semidirect
240. #1894C2×C11semidirect
241. #1873C2×C11semidirect
242. #1872C2×C11semidirect
243. #1825C2×C11semidirect
244. #1824C2×C11semidirect
245. #1805C2×C11semidirect
246. C4×#103C2×C11semidirect
247. #1736C2×C11semidirect
248. #1736C2×C11semidirect
328. #552C4×C11semidirect
427. #125C2×C4×C11semidirect
432. C22⋊Q8C2×C4×C11semidirect
434. C4×Q8C2×C4×C11semidirect
452. C2×C4⋊C4C2×C4×C11semidirect
588. C11#22499direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5522
C2×C11×#4362
C11×#23522
C11×#19912
C11×#19892
C11×#18942
C11×#18732
C11×#18722
C11×#18252
C11×#18242
C11×#18052
C4×C11×#1032
C11×#17362
#2249911