Finite Group Databasebeta

← C11×#21412 #14598605

Subgroups — C11×#21412 #14598605

Order 2816.

1134 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#542C211yesmaximal, characteristic
2C2×C11×#405C211yesmaximal, characteristic, complemented
3C11×#2314C211yesmaximal, characteristic, complemented
4C11×#1993C211yesmaximal, characteristic, complemented
5C11×#1990C211yesmaximal, characteristic, complemented
6C11×#1959C211yesmaximal, characteristic, complemented
7C11×#1958C211yesmaximal, characteristic, complemented
8C11×#1895C211yesmaximal, characteristic
9C11×#1894C211yesmaximal, characteristic, complemented
10C11×#1893C211yesmaximal, characteristic
11C11×#1892C211yesmaximal, characteristic, complemented
12C11×#1763C211yesmaximal, characteristic, complemented
13C11×#1762C211yesmaximal, characteristic, complemented
14C4×C11×#103C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C11×#542—24no—
19C11×#542C418yescomplemented
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#126—21no—
22C2×C11×#124—21no—
23C2×C11×#124C2211yescharacteristic
24C2×C11×#123—21no—
25C2×C11×C22⋊Q8—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C11×#405—24no—
40C2×C11×#97C2211yescharacteristic
41C2×C11×#97C2211yescharacteristic
42C2×C4×C8×C11C2211yescharacteristic
43C2×C4×C8×C11C2211yescharacteristic
44C11×#388—21no—
45C11×#388—21no—
46C11×#387—21no—
47C11×#387—21no—
48C11×#384C2211yescharacteristic
49C11×#382C2211yescharacteristic
50C11×#380C2211yescharacteristic
51C11×#380C2211yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C22×Q8×C11—21no—
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11—21no—
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C22×C8×C11—22no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×C4⋊Q8—22no—
79C11×C4⋊Q8C2×C414yes—
80C11×#126—28no—
81C11×#124—28no—
82C11×#124—22no—
83C11×#124C2×C414yes—
84C11×#123—28no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—28no—
87C11×C22⋊Q8C2×C414yes—
88C11×#121—22no—
89C11×#121C2×C414yes—
90C4×Q8×C11—22no—
91C4×Q8×C11C2×C414yes—
92C4×D4×C11—22no—
93C4×D4×C11C2×C414yes—
94C11×#117C2×C414yes—
95C11×#117D414yes—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4D411yescharacteristic
102C2×C11×C4⋊C4D411yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4D411yescharacteristic
117C2×C11×C22⋊C4D411yescharacteristic
118C2×C42×C11—21no—
119C2×C42×C11—21no—
120C2×C42×C11—21no—
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C11×#103—22no—
124C11×#103—22no—
125C11×#103—22no—
126C11×#103—22no—
127C11×#102—22no—
128C11×#102—22no—
129C11×#102—22no—
130C11×#102—22no—
131C11×#97—22no—
132C11×#97—22no—
133C4×C8×C11—22no—
134C4×C8×C11—22no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140C11×#95—21no—
141#21412C1111yesmaximal, characteristic, direct product factor, Sylow
142C24×C11—21no—
143C24×C11C2×D411yescharacteristic
144C2×Q8×C11—24no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—81no—
151C2×Q8×C11—81no—
152C2×Q8×C11C22×C412yes—
153C2×D4×C11—24no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—81no—
160C2×D4×C11—81no—
161C2×D4×C11C22×C412yes—
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—24no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—81no—
175C22×C4×C11—81no—
176C22×C4×C11C22×C412yes—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D412yes—
183C22×C4×C11C2411yescharacteristic
184C11×M16—28no—
185C2×C8×C11—28no—
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#4112yes—
195C2×C8×C11#4112yes—
196C2×C8×C11#4112yes—
197C2×C8×C11#4112yes—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—24no—
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—21no—
211C11×C4⋊C4—81no—
212C11×C4⋊C4—81no—
213C11×C4⋊C4C22⋊C414yes—
214C11×C4⋊C4C22⋊C414yes—
215C11×C4⋊C4C22×C412yes—
216C11×C4⋊C4C22×C412yes—
217C11×C22⋊C4—24no—
218C11×C22⋊C4—24no—
219C11×C22⋊C4—24no—
220C11×C22⋊C4—24no—
221C11×C22⋊C4—24no—
222C11×C22⋊C4—81no—
223C11×C22⋊C4—81no—
224C11×C22⋊C4C22⋊C414yes—
225C11×C22⋊C4C22⋊C414yes—
226C42×C11—24no—
227C42×C11—81no—
228C42×C11—81no—
229C42×C11C22×C412yes—
230C42×C11C22×C412yes—
231C42×C11C2×D412yes—
232C42×C11C2×D412yes—
233C2×#542C2×C1111yescharacteristic
234C2×#405C2×C1111yescharacteristic, complemented
235#2314C2×C1111yescharacteristic, complemented
236#1993C2×C1111yescharacteristic, complemented
237#1990C2×C1111yescharacteristic, complemented
238#1959C2×C1111yescharacteristic, complemented
239#1958C2×C1111yescharacteristic, complemented
240#1895C2×C1111yescharacteristic
241#1894C2×C1111yescharacteristic, complemented
242#1893C2×C1111yescharacteristic
243#1892C2×C1111yescharacteristic, complemented
244#1763C2×C1111yescharacteristic, complemented
245#1762C2×C1111yescharacteristic, complemented
246C4×#103C2×C1111yescharacteristic, complemented
247C4×#102C2×C1111yescharacteristic, complemented
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—22no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11C2×C22⋊C412yes—
262C23×C11C22×D411yescharacteristic
263Q8×C11—22no—
264Q8×C11—22no—
265Q8×C11—41no—
266Q8×C11—41no—
267Q8×C11—84no—
268D4×C11—22no—
269D4×C11—22no—
270D4×C11—41no—
271D4×C11—41no—
272D4×C11—84no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
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—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—41no—
308C2×C4×C11—84no—
309C2×C4×C11C2×C22⋊C412yes—
310C2×C4×C11C2×C22⋊C412yes—
311C2×C4×C11C2×C22⋊C412yes—
312C2×C4×C11C2×C22⋊C412yes—
313C2×C4×C11C2×C22⋊C412yes—
314C2×C4×C11C23×C411yescharacteristic
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11C2×#4111yescharacteristic
320C8×C11—22no—
321C8×C11—22no—
322C8×C11—22no—
323C8×C11—22no—
324C22×M16C22×C1111yescharacteristic
325C23×C8C22×C1111yescharacteristic
326#542—24no—
327#542C4×C1118yescomplemented
328C2×C4⋊Q8C22×C1111yescharacteristic
329C2×#126—21no—
330C2×#124—21no—
331C2×#124C22×C1111yescharacteristic
332C2×#123—21no—
333C2×C22⋊Q8—21no—
334C2×C22⋊Q8C22×C1111yescharacteristic
335C2×#121C22×C1111yescharacteristic
336C2×C4×Q8C22×C1111yescharacteristic
337C2×C4×D4C22×C1111yescharacteristic
338C2×#117C22×C1111yescharacteristic
339C2×#103C22×C1111yescharacteristic
340C2×#103C22×C1111yescharacteristic
341C2×#103C22×C1111yescharacteristic
342C2×#103C22×C1111yescharacteristic
343C2×#102C22×C1111yescharacteristic
344C2×#102C22×C1111yescharacteristic
345C2×#102C22×C1111yescharacteristic
346C2×#102C22×C1111yescharacteristic
347#405—24no—
348C2×#97C22×C1111yescharacteristic
349C2×#97C22×C1111yescharacteristic
350C2×C4×C8C22×C1111yescharacteristic
351C2×C4×C8C22×C1111yescharacteristic
352#388—21no—
353#388—21no—
354#387—21no—
355#387—21no—
356#384C22×C1111yescharacteristic
357#382C22×C1111yescharacteristic
358#380C22×C1111yescharacteristic
359#380C22×C1111yescharacteristic
360C4×C4⋊C4C22×C1111yescharacteristic
361C4×C4⋊C4C22×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
370C22×C11—22no—
371C22×C11—22no—
372C22×C11—22no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—81no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11—81no—
384C22×C11C22×C22⋊C411yescharacteristic
385C22×C11#53211yescharacteristic
386C22×C11#53211yescharacteristic
387C22×C11#57611yescharacteristic
388C22×C11#57711yescharacteristic
389C22×C11#57711yescharacteristic
390C22×C11#57811yescharacteristic
391C4×C11—22no—
392C4×C11—22no—
393C4×C11—22no—
394C4×C11—22no—
395C4×C11—22no—
396C4×C11—42no—
397C4×C11—42no—
398C4×C11—42no—
399C4×C11—81no—
400C4×C11—81no—
401C4×C11—81no—
402C4×C11—81no—
403C4×C11C4×#4111yescharacteristic
404C4×C11C4×#4111yescharacteristic
405C4×C11#52511yescharacteristic
406C4×C11#52511yescharacteristic
407C22×Q8—21no—
408C22×Q8C23×C1111yescharacteristic
409C22×D4—21no—
410C22×D4C23×C1111yescharacteristic
411C23×C4—21no—
412C23×C4C23×C1111yescharacteristic
413C2×M16—22no—
414C2×M16—22no—
415C2×M16—22no—
416C22×C8—22no—
417C22×C8—22no—
418C22×C8—22no—
419C22×C8C23×C1111yescharacteristic
420C22×C8C23×C1111yescharacteristic
421C22×C8C23×C1111yescharacteristic
422C22×C8C23×C1111yescharacteristic
423C4⋊Q8—22no—
424C4⋊Q8C2×C4×C1114yes—
425#126—28no—
426#124—28no—
427#124—22no—
428#124C2×C4×C1114yes—
429#123—28no—
430C22⋊Q8—22no—
431C22⋊Q8—28no—
432C22⋊Q8C2×C4×C1114yes—
433#121—22no—
434#121C2×C4×C1114yes—
435C4×Q8—22no—
436C4×Q8C2×C4×C1114yes—
437C4×D4—22no—
438C4×D4C2×C4×C1114yes—
439#117C2×C4×C1114yes—
440#117D4×C1114yes—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4D4×C1111yescharacteristic
447C2×C4⋊C4D4×C1111yescharacteristic
448C2×C4⋊C4C23×C1111yescharacteristic
449C2×C4⋊C4C23×C1111yescharacteristic
450C2×C4⋊C4C23×C1111yescharacteristic
451C2×C4⋊C4C23×C1111yescharacteristic
452C2×C4⋊C4C23×C1111yescharacteristic
453C2×C4⋊C4C23×C1111yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4D4×C1111yescharacteristic
462C2×C22⋊C4D4×C1111yescharacteristic
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42C23×C1111yescharacteristic
467C2×C42C23×C1111yescharacteristic
468#103—22no—
469#103—22no—
470#103—22no—
471#103—22no—
472#102—22no—
473#102—22no—
474#102—22no—
475#102—22no—
476#97—22no—
477#97—22no—
478C4×C8—22no—
479C4×C8—22no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486C2×C11—42no—
487C2×C11—82no—
488C2×C11#229711yescharacteristic
489C2×C11#289711yescharacteristic
490C2×C11#289811yescharacteristic
491C2×C11#317311yescharacteristic
492C2×C11#317511yescharacteristic
493C2×C11#317811yescharacteristic
494C2×C11#317911yescharacteristic
495C24—21no—
496C24C2×D4×C1111yescharacteristic
497C2×Q8—24no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—81no—
504C2×Q8—81no—
505C2×Q8C22×C4×C1112yes—
506C2×D4—24no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4C22×C4×C1112yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—24no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4C22×C4×C1112yes—
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C2×D4×C1111yescharacteristic
532C22×C4C2×D4×C1111yescharacteristic
533C22×C4C2×D4×C1111yescharacteristic
534C22×C4C2×D4×C1111yescharacteristic
535C22×C4C2×D4×C1112yes—
536C22×C4C24×C1111yescharacteristic
537M16—28no—
538C2×C8—28no—
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×C8C11×#4112yes—
548C2×C8C11×#4112yes—
549C2×C8C11×#4112yes—
550C2×C8C11×#4112yes—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—81no—
565C4⋊C4—81no—
566C4⋊C4C11×C22⋊C414yes—
567C4⋊C4C11×C22⋊C414yes—
568C4⋊C4C22×C4×C1112yes—
569C4⋊C4C22×C4×C1112yes—
570C22⋊C4—24no—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C22⋊C4C11×C22⋊C414yes—
578C22⋊C4C11×C22⋊C414yes—
579C42—24no—
580C42—81no—
581C42—81no—
582C42C22×C4×C1112yes—
583C42C22×C4×C1112yes—
584C42C2×D4×C1112yes—
585C42C2×D4×C1112yes—
586C11#2141211yescharacteristic, direct product factor, Sylow
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—22no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C2×C11×C22⋊C412yes—
601C23C22×D4×C1111yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606Q8—84no—
607D4—22no—
608D4—22no—
609D4—41no—
610D4—41no—
611D4—84no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
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—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—84no—
648C2×C4C2×C11×C22⋊C412yes—
649C2×C4C2×C11×C22⋊C412yes—
650C2×C4C2×C11×C22⋊C412yes—
651C2×C4C2×C11×C22⋊C412yes—
652C2×C4C2×C11×C22⋊C412yes—
653C2×C4C23×C4×C1111yescharacteristic
654C2×C4C22×D4×C1111yescharacteristic
655C2×C4C2×C11×#4111yescharacteristic
656C2×C4C2×C11×#4111yescharacteristic
657C2×C4C2×C11×#4111yescharacteristic
658C2×C4C2×C11×#4111yescharacteristic
659C8—22no—
660C8—22no—
661C8—22no—
662C8—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C22×C11×C22⋊C411yescharacteristic
678C22C11×#53211yescharacteristic
679C22C11×#53211yescharacteristic
680C22C11×#57611yescharacteristic
681C22C11×#57711yescharacteristic
682C22C11×#57711yescharacteristic
683C22C11×#57811yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4C4×C11×#4111yescharacteristic
697C4C4×C11×#4111yescharacteristic
698C4C11×#52511yescharacteristic
699C4C11×#52511yescharacteristic
700C2—42no—
701C2—82no—
702C2C11×#229711yescharacteristic
703C2C11×#289711yescharacteristic
704C2C11×#289811yescharacteristic
705C2C11×#317311yescharacteristic
706C2C11×#317511yescharacteristic
707C2C11×#317811yescharacteristic
708C2C11×#317911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#405C2semidirect
3. C11×#2314C2semidirect
4. C11×#1993C2semidirect
5. C11×#1990C2semidirect
6. C11×#1959C2semidirect
7. C11×#1958C2semidirect
9. C11×#1894C2semidirect
11. C11×#1892C2semidirect
12. C11×#1763C2semidirect
13. C11×#1762C2semidirect
14. C4×C11×#103C2semidirect
15. C4×C11×#102C2semidirect
19. C11×#542C4semidirect
141. #21412C11direct (N × H)
234. C2×#405C2×C11semidirect
235. #2314C2×C11semidirect
236. #1993C2×C11semidirect
237. #1990C2×C11semidirect
238. #1959C2×C11semidirect
239. #1958C2×C11semidirect
241. #1894C2×C11semidirect
243. #1892C2×C11semidirect
244. #1763C2×C11semidirect
245. #1762C2×C11semidirect
246. C4×#103C2×C11semidirect
247. C4×#102C2×C11semidirect
327. #542C4×C11semidirect
586. C11#21412direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5422
C2×C11×#4052
C11×#23142
C11×#19932
C11×#19902
C11×#19592
C11×#19582
C11×#18952
C11×#18942
C11×#18932
C11×#18922
C11×#17632
C11×#17622
C4×C11×#1032
C4×C11×#1022
#2141211