Finite Group Databasebeta

← C11×#24127 #14601320

Subgroups — C11×#24127 #14601320

Order 2816.

1088 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#552C211yesmaximal, characteristic
2C2×C11×#479C211yesmaximal, characteristic, complemented
3C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
4C11×#2536C211yesmaximal, characteristic
5C11×#2036C211yesmaximal, characteristic, complemented
6C11×#2035C211yesmaximal, characteristic, complemented
7C11×#2001C211yesmaximal, characteristic, complemented
8C11×#2001C211yesmaximal, characteristic, complemented
9C11×#1991C211yesmaximal, characteristic, complemented
10C11×#1954C211yesmaximal, characteristic
11C11×#1873C211yesmaximal, characteristic, complemented
12C11×#1872C211yesmaximal, characteristic, complemented
13C11×#1854C211yesmaximal, characteristic, complemented
14C11×#1852C211yesmaximal, characteristic, complemented
15C11×#1805C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C11×#552—24no—
18C11×#552—24no—
19C2×C11×#126—21no—
20C2×C11×#125—21no—
21C2×C11×#125C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117—21no—
31C2×C11×#117C2211yescharacteristic
32C22×C11×C4⋊C4C2211yescharacteristic
33C11×#479—24no—
34C4×C11×Q16—24no—
35C2×C11×#107C2211yescharacteristic
36C2×C11×#107C2211yescharacteristic
37C2×C11×#106C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C2×C4×C8×C11C2211yescharacteristic
50C11×#398—21no—
51C11×#394—21no—
52C11×#388—21no—
53C11×#388—21no—
54C11×#382C2211yescharacteristic
55C11×#380C2211yescharacteristic
56C11×#380C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11D411yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C2×C11×Q16—22no—
70C2×C11×Q16—22no—
71C2×C11×Q16—22no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×#126—28no—
77C11×#125—28no—
78C11×#125—22no—
79C11×#125D414yes—
80C11×#123—28no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—41no—
88C11×C22⋊Q8—41no—
89C4×Q8×C11—22no—
90C4×Q8×C11—22no—
91C4×Q8×C11—22no—
92C4×Q8×C11D414yes—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C11×#117—28no—
96C11×#117—22no—
97C11×#117—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—21no—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4D411yescharacteristic
124C2×C11×C22⋊C4D411yescharacteristic
125C2×C42×C11—21no—
126C2×C42×C11—21no—
127C2×C42×C11—21no—
128C2×C42×C11C2311yescharacteristic
129C11×#107—22no—
130C11×#107—22no—
131C11×#106—22no—
132C11×C4⋊C8—22no—
133C11×#103—22no—
134C11×#103—22no—
135C11×#103—22no—
136C11×#103—22no—
137C11×#103—41no—
138C11×#103—41no—
139C11×C22⋊C8—22no—
140C11×C22⋊C8—22no—
141C11×C22⋊C8—41no—
142C11×C22⋊C8—41no—
143C4×C8×C11—22no—
144C11×#95—21no—
145C11×#95—21no—
146C11×#95—21no—
147C11×#95—21no—
148#24127C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11C2×D411yescharacteristic
150C24×C11C2×D411yescharacteristic
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11C2×D412yes—
162C2×Q8×C11#4112yes—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—41no—
166C22×C4×C11—24no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2411yescharacteristic
194C11×Q16—28no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11#4112yes—
207C11×C4⋊C4—24no—
208C11×C4⋊C4—24no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—24no—
212C11×C4⋊C4—24no—
213C11×C4⋊C4—22no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—42no—
224C11×C4⋊C4—42no—
225C11×C4⋊C4—42no—
226C11×C4⋊C4C2×D412yes—
227C11×C4⋊C4C2×D412yes—
228C11×C4⋊C4C2×D412yes—
229C11×C22⋊C4—24no—
230C11×C22⋊C4—24no—
231C11×C22⋊C4—24no—
232C11×C22⋊C4—22no—
233C11×C22⋊C4—22no—
234C11×C22⋊C4—42no—
235C11×C22⋊C4—42no—
236C11×C22⋊C4—42no—
237C11×C22⋊C4—42no—
238C42×C11—24no—
239C42×C11—24no—
240C42×C11—42no—
241C42×C11C2×D412yes—
242C42×C11C2×D412yes—
243C2×#552C2×C1111yescharacteristic
244C2×#479C2×C1111yescharacteristic, complemented
245C2×C4×Q16C2×C1111yescharacteristic, complemented
246#2536C2×C1111yescharacteristic
247#2036C2×C1111yescharacteristic, complemented
248#2035C2×C1111yescharacteristic, complemented
249#2001C2×C1111yescharacteristic, complemented
250#2001C2×C1111yescharacteristic, complemented
251#1991C2×C1111yescharacteristic, complemented
252#1954C2×C1111yescharacteristic
253#1873C2×C1111yescharacteristic, complemented
254#1872C2×C1111yescharacteristic, complemented
255#1854C2×C1111yescharacteristic, complemented
256#1852C2×C1111yescharacteristic, complemented
257#1805C2×C1111yescharacteristic, complemented
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11#13512yes—
272C23×C11C22×D411yescharacteristic
273Q8×C11—22no—
274Q8×C11—22no—
275Q8×C11—22no—
276Q8×C11—22no—
277Q8×C11—41no—
278Q8×C11—41no—
279Q8×C11—41no—
280Q8×C11—41no—
281D4×C11—44no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—21no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—48no—
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—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11#12012yes—
326C2×C4×C11#12012yes—
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C2×C4×C11C2×#4111yescharacteristic
331C2×C4×C11H(5,𝔽2)11yescharacteristic
332C2×C4×C112−1+411yescharacteristic
333C8×C11—22no—
334C8×C11—41no—
335C8×C11—41no—
336C8×C11—41no—
337C22×Q16C22×C1111yescharacteristic
338#552—24no—
339#552—24no—
340C2×#126—21no—
341C2×#125—21no—
342C2×#125C22×C1111yescharacteristic
343C2×#123—21no—
344C2×C22⋊Q8C22×C1111yescharacteristic
345C2×C22⋊Q8C22×C1111yescharacteristic
346C2×C22⋊Q8C22×C1111yescharacteristic
347C2×C22⋊Q8C22×C1111yescharacteristic
348C2×C4×Q8C22×C1111yescharacteristic
349C2×C4×Q8C22×C1111yescharacteristic
350C2×C4×D4C22×C1111yescharacteristic
351C2×#117—21no—
352C2×#117C22×C1111yescharacteristic
353C22×C4⋊C4C22×C1111yescharacteristic
354#479—24no—
355C4×Q16—24no—
356C2×#107C22×C1111yescharacteristic
357C2×#107C22×C1111yescharacteristic
358C2×#106C22×C1111yescharacteristic
359C2×C4⋊C8C22×C1111yescharacteristic
360C2×#103C22×C1111yescharacteristic
361C2×#103C22×C1111yescharacteristic
362C2×#103C22×C1111yescharacteristic
363C2×#103C22×C1111yescharacteristic
364C2×#103C22×C1111yescharacteristic
365C2×#103C22×C1111yescharacteristic
366C2×C22⋊C8C22×C1111yescharacteristic
367C2×C22⋊C8C22×C1111yescharacteristic
368C2×C22⋊C8C22×C1111yescharacteristic
369C2×C22⋊C8C22×C1111yescharacteristic
370C2×C4×C8C22×C1111yescharacteristic
371#398—21no—
372#394—21no—
373#388—21no—
374#388—21no—
375#382C22×C1111yescharacteristic
376#380C22×C1111yescharacteristic
377#380C22×C1111yescharacteristic
378#340C22×C1111yescharacteristic
379#340C22×C1111yescharacteristic
380#340C22×C1111yescharacteristic
381#340C22×C1111yescharacteristic
382#340C22×C1111yescharacteristic
383#340C22×C1111yescharacteristic
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11C2×#12011yescharacteristic
399C22×C11#54611yescharacteristic
400C22×C11#54711yescharacteristic
401C22×C11C2×#13511yescharacteristic
402C22×C11#57511yescharacteristic
403C22×C11#57811yescharacteristic
404C22×C11#57811yescharacteristic
405C4×C11—22no—
406C4×C11—22no—
407C4×C11—41no—
408C4×C11—41no—
409C4×C11—42no—
410C4×C11—42no—
411C4×C11—42no—
412C4×C11—42no—
413C4×C11—42no—
414C4×C11—81no—
415C4×C11—81no—
416C4×C11—81no—
417C4×C11#52511yescharacteristic
418C4×C11#53711yescharacteristic
419C4×C11#54811yescharacteristic
420C4×C11#55011yescharacteristic
421C22×Q8C23×C1111yescharacteristic
422C22×Q8C23×C1111yescharacteristic
423C22×D4D4×C1111yescharacteristic
424C23×C4—21no—
425C23×C4C23×C1111yescharacteristic
426C23×C4C23×C1111yescharacteristic
427C2×Q16—22no—
428C2×Q16—22no—
429C2×Q16—22no—
430C22×C8C23×C1111yescharacteristic
431C22×C8C23×C1111yescharacteristic
432C22×C8C23×C1111yescharacteristic
433C22×C8C23×C1111yescharacteristic
434#126—28no—
435#125—28no—
436#125—22no—
437#125D4×C1114yes—
438#123—28no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443C22⋊Q8—22no—
444C22⋊Q8—22no—
445C22⋊Q8—41no—
446C22⋊Q8—41no—
447C4×Q8—22no—
448C4×Q8—22no—
449C4×Q8—22no—
450C4×Q8D4×C1114yes—
451C4×D4—22no—
452C4×D4—22no—
453#117—28no—
454#117—22no—
455#117—22no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4D4×C1111yescharacteristic
468C2×C4⋊C4C23×C1111yescharacteristic
469C2×C4⋊C4C23×C1111yescharacteristic
470C2×C4⋊C4C23×C1111yescharacteristic
471C2×C4⋊C4C23×C1111yescharacteristic
472C2×C4⋊C4C23×C1111yescharacteristic
473C2×C4⋊C4C23×C1111yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4D4×C1111yescharacteristic
482C2×C22⋊C4D4×C1111yescharacteristic
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—21no—
486C2×C42C23×C1111yescharacteristic
487#107—22no—
488#107—22no—
489#106—22no—
490C4⋊C8—22no—
491#103—22no—
492#103—22no—
493#103—22no—
494#103—22no—
495#103—41no—
496#103—41no—
497C22⋊C8—22no—
498C22⋊C8—22no—
499C22⋊C8—41no—
500C22⋊C8—41no—
501C4×C8—22no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506C2×C11—42no—
507C2×C11—81no—
508C2×C11#240711yescharacteristic
509C2×C11#300211yescharacteristic
510C2×C11#301111yescharacteristic
511C2×C11#330011yescharacteristic
512C2×C11#332711yescharacteristic
513C2×C11#333611yescharacteristic
514C2×C11#335211yescharacteristic
515C24C2×D4×C1111yescharacteristic
516C24C2×D4×C1111yescharacteristic
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8C2×D4×C1112yes—
528C2×Q8C11×#4112yes—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—41no—
532C22×C4—24no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4C2×D4×C1111yescharacteristic
556C22×C4C2×D4×C1111yescharacteristic
557C22×C4C2×D4×C1111yescharacteristic
558C22×C4C2×D4×C1111yescharacteristic
559C22×C4C24×C1111yescharacteristic
560Q16—28no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8C11×#4112yes—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—22no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4C2×D4×C1112yes—
593C4⋊C4C2×D4×C1112yes—
594C4⋊C4C2×D4×C1112yes—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C42—24no—
605C42—24no—
606C42—42no—
607C42C2×D4×C1112yes—
608C42C2×D4×C1112yes—
609C11#2412711yescharacteristic, direct product factor, Sylow
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23C11×#13512yes—
624C23C22×D4×C1111yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633D4—44no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—48no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4C11×#12012yes—
678C2×C4C11×#12012yes—
679C2×C4C22×D4×C1111yescharacteristic
680C2×C4C22×D4×C1111yescharacteristic
681C2×C4C2×C11×#4111yescharacteristic
682C2×C4C2×C11×#4111yescharacteristic
683C2×C4C11×H(5,𝔽2)11yescharacteristic
684C2×C4C11×2−1+411yescharacteristic
685C8—22no—
686C8—41no—
687C8—41no—
688C8—41no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22C2×C11×#12011yescharacteristic
704C22C11×#54611yescharacteristic
705C22C11×#54711yescharacteristic
706C22C2×C11×#13511yescharacteristic
707C22C11×#57511yescharacteristic
708C22C11×#57811yescharacteristic
709C22C11×#57811yescharacteristic
710C4—22no—
711C4—22no—
712C4—41no—
713C4—41no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4C11×#52511yescharacteristic
723C4C11×#53711yescharacteristic
724C4C11×#54811yescharacteristic
725C4C11×#55011yescharacteristic
726C2—42no—
727C2—81no—
728C2C11×#240711yescharacteristic
729C2C11×#300211yescharacteristic
730C2C11×#301111yescharacteristic
731C2C11×#330011yescharacteristic
732C2C11×#332711yescharacteristic
733C2C11×#333611yescharacteristic
734C2C11×#335211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×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×#479C2semidirect
3. C2×C4×C11×Q16C2semidirect
5. C11×#2036C2semidirect
6. C11×#2035C2semidirect
7. C11×#2001C2semidirect
8. C11×#2001C2semidirect
9. C11×#1991C2semidirect
11. C11×#1873C2semidirect
12. C11×#1872C2semidirect
13. C11×#1854C2semidirect
14. C11×#1852C2semidirect
15. C11×#1805C2semidirect
148. #24127C11direct (N × H)
244. C2×#479C2×C11semidirect
245. C2×C4×Q16C2×C11semidirect
247. #2036C2×C11semidirect
248. #2035C2×C11semidirect
249. #2001C2×C11semidirect
250. #2001C2×C11semidirect
251. #1991C2×C11semidirect
253. #1873C2×C11semidirect
254. #1872C2×C11semidirect
255. #1854C2×C11semidirect
256. #1852C2×C11semidirect
257. #1805C2×C11semidirect
609. C11#24127direct (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×#4792
C2×C4×C11×Q162
C11×#25362
C11×#20362
C11×#20352
C11×#20012
C11×#19912
C11×#19542
C11×#18732
C11×#18722
C11×#18542
C11×#18522
C11×#18052
#2412711