Finite Group Databasebeta

← C11×#23138 #14600331

Subgroups — C11×#23138 #14600331

Order 2816.

954 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#468C211yesmaximal, characteristic
2C11×#2362C211yesmaximal, characteristic, complemented
3C11×#2361C211yesmaximal, characteristic
4C11×#1936C211yesmaximal, characteristic, complemented
5C11×#1933C211yesmaximal, characteristic, complemented
6C11×#1921C211yesmaximal, characteristic, complemented
7C11×#1918C211yesmaximal, characteristic, complemented
8C11×#1880C211yesmaximal, characteristic, complemented
9C11×#1877C211yesmaximal, characteristic, complemented
10C11×#1875C211yesmaximal, characteristic
11C11×#1872C211yesmaximal, characteristic, complemented
12C11×#1763C211yesmaximal, characteristic, complemented
13C4×C11×#102C211yesmaximal, characteristic, complemented
14C11×#1753C211yesmaximal, characteristic, complemented
15C11×#1736C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C11×#468C418yescomplemented
26C2×C11×#107C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×#97C2211yescharacteristic
35C2×C4×C8×C11C2211yescharacteristic
36C11×#391C2211yescharacteristic
37C11×#390C2211yescharacteristic
38C11×#389C2211yescharacteristic
39C11×#389C2211yescharacteristic
40C11×#388—21no—
41C11×#388—21no—
42C11×#388—21no—
43C11×#387—21no—
44C11×#386—21no—
45C11×#385—21no—
46C4×C11×C4⋊C4—21no—
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C22⋊C4C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C2×C11×SD16—41no—
67C2×C11×SD16—41no—
68C2×C11×SD16C2×C414yescomplemented
69C2×C11×M16—41no—
70C2×C11×M16—41no—
71C2×C11×M16C2×C414yescomplemented
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8C2×C414yescomplemented
78C11×#121—22no—
79C11×#121C2×C414yes—
80C4×Q8×C11—22no—
81C4×Q8×C11—41no—
82C4×D4×C11—22no—
83C4×D4×C11—41no—
84C4×D4×C11—44no—
85C11×#117—22no—
86C11×#117—41no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
106C2×C11×C22⋊C4D411yescharacteristic
107C2×C11×C22⋊C4D411yescharacteristic
108C2×C42×C11—21no—
109C2×C42×C11—21no—
110C2×C42×C11—21no—
111C2×C42×C11—21no—
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C11×#107C2×C414yescomplemented
115C11×#103—22no—
116C11×#103—41no—
117C11×#103C2×C414yescomplemented
118C11×#102—22no—
119C11×#102—41no—
120C11×#102C2×C414yescomplemented
121C11×C22⋊C8—22no—
122C11×#97—41no—
123C4×C8×C11—41no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95D411yescharacteristic
131C11×#95D411yescharacteristic
132#23138C1111yesmaximal, characteristic, direct product factor, Sylow
133C24×C11—21no—
134C24×C11C2×D411yescharacteristic
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11C22×C412yes—
141C2×D4×C11—24no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11C22×C412yes—
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—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11—42no—
165C22×C4×C11—81no—
166C22×C4×C11—81no—
167C22×C4×C11C22×C412yes—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11#4112yes—
174C22×C4×C11C2411yescharacteristic
175C11×SD16—44no—
176C11×M16—44no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11C22×C412yes—
188C2×C8×C11C22×C412yes—
189C11×C4⋊C4—24no—
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—21no—
198C11×C4⋊C4—42no—
199C11×C4⋊C4—42no—
200C11×C4⋊C4—42no—
201C11×C4⋊C4—42no—
202C11×C4⋊C4C22×C412yes—
203C11×C4⋊C4C22×C412yes—
204C11×C4⋊C4#4112yes—
205C11×C4⋊C4#4112yes—
206C11×C22⋊C4—24no—
207C11×C22⋊C4—24no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—41no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—81no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—42no—
219C42×C11—42no—
220C42×C11—42no—
221C42×C11—42no—
222C2×#468C2×C1111yescharacteristic
223#2362C2×C1111yescharacteristic, complemented
224#2361C2×C1111yescharacteristic
225#1936C2×C1111yescharacteristic, complemented
226#1933C2×C1111yescharacteristic, complemented
227#1921C2×C1111yescharacteristic, complemented
228#1918C2×C1111yescharacteristic, complemented
229#1880C2×C1111yescharacteristic, complemented
230#1877C2×C1111yescharacteristic, complemented
231#1875C2×C1111yescharacteristic
232#1872C2×C1111yescharacteristic, complemented
233#1763C2×C1111yescharacteristic, complemented
234C4×#102C2×C1111yescharacteristic, complemented
235#1753C2×C1111yescharacteristic, complemented
236#1736C2×C1111yescharacteristic, complemented
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—22no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11C4×D412yes—
251C23×C11C22×D411yescharacteristic
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—41no—
255Q8×C11—41no—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—48no—
259D4×C11—41no—
260D4×C11—41no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
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—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—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—84no—
300C2×C4×C11—84no—
301C2×C4×C11C4×D412yes—
302C2×C4×C11AGL(1,ℤ/8)12yes—
303C2×C4×C11C23×C411yescharacteristic
304C2×C4×C11C2×#4111yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11H(5,𝔽2)11yescharacteristic
308C2×C4×C11H(5,𝔽2)11yescharacteristic
309C8×C11—22no—
310C8×C11—22no—
311C8×C11—41no—
312C8×C11—41no—
313C22×SD16C22×C1111yescharacteristic
314C22×M16C22×C1111yescharacteristic
315C2×C22⋊Q8C22×C1111yescharacteristic
316C2×#121C22×C1111yescharacteristic
317C2×C4×Q8C22×C1111yescharacteristic
318C2×C4×D4—21no—
319C2×C4×D4C22×C1111yescharacteristic
320C2×#117C22×C1111yescharacteristic
321C22×C4⋊C4C22×C1111yescharacteristic
322#468C4×C1118yescomplemented
323C2×#107C22×C1111yescharacteristic
324C2×#103C22×C1111yescharacteristic
325C2×#103C22×C1111yescharacteristic
326C2×#103C22×C1111yescharacteristic
327C2×#102C22×C1111yescharacteristic
328C2×#102C22×C1111yescharacteristic
329C2×#102C22×C1111yescharacteristic
330C2×C22⋊C8C22×C1111yescharacteristic
331C2×#97C22×C1111yescharacteristic
332C2×C4×C8C22×C1111yescharacteristic
333#391C22×C1111yescharacteristic
334#390C22×C1111yescharacteristic
335#389C22×C1111yescharacteristic
336#389C22×C1111yescharacteristic
337#388—21no—
338#388—21no—
339#388—21no—
340#387—21no—
341#386—21no—
342#385—21no—
343C4×C4⋊C4—21no—
344C4×C4⋊C4C22×C1111yescharacteristic
345C4×C4⋊C4C22×C1111yescharacteristic
346C4×C22⋊C4C22×C1111yescharacteristic
347#340C22×C1111yescharacteristic
348#340C22×C1111yescharacteristic
349#340C22×C1111yescharacteristic
350#340C22×C1111yescharacteristic
351#340C22×C1111yescharacteristic
352#340C22×C1111yescharacteristic
353#340C22×C1111yescharacteristic
354#340C22×C1111yescharacteristic
355#336C22×C1111yescharacteristic
356#336C22×C1111yescharacteristic
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11C2×C4×D411yescharacteristic
372C22×C11#54611yescharacteristic
373C22×C11#54611yescharacteristic
374C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C11#57511yescharacteristic
376C22×C11#57711yescharacteristic
377C22×C11#57811yescharacteristic
378C4×C11—22no—
379C4×C11—22no—
380C4×C11—41no—
381C4×C11—42no—
382C4×C11—42no—
383C4×C11—42no—
384C4×C11—42no—
385C4×C11—42no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11—81no—
389C4×C11—81no—
390C4×C11C4×#4111yescharacteristic
391C4×C11#51811yescharacteristic
392C4×C11#55311yescharacteristic
393C4×C11#55311yescharacteristic
394C22×Q8C23×C1111yescharacteristic
395C22×D4—21no—
396C22×D4C23×C1111yescharacteristic
397C23×C4—21no—
398C23×C4—21no—
399C23×C4C23×C1111yescharacteristic
400C2×SD16—41no—
401C2×SD16—41no—
402C2×SD16C2×C4×C1114yescomplemented
403C2×M16—41no—
404C2×M16—41no—
405C2×M16C2×C4×C1114yescomplemented
406C22×C8C23×C1111yescharacteristic
407C22×C8C23×C1111yescharacteristic
408C22×C8C23×C1111yescharacteristic
409C22×C8C23×C1111yescharacteristic
410C22⋊Q8—22no—
411C22⋊Q8C2×C4×C1114yescomplemented
412#121—22no—
413#121C2×C4×C1114yes—
414C4×Q8—22no—
415C4×Q8—41no—
416C4×D4—22no—
417C4×D4—41no—
418C4×D4—44no—
419#117—22no—
420#117—41no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4C23×C1111yescharacteristic
429C2×C4⋊C4C23×C1111yescharacteristic
430C2×C4⋊C4C23×C1111yescharacteristic
431C2×C4⋊C4C23×C1111yescharacteristic
432C2×C4⋊C4C23×C1111yescharacteristic
433C2×C4⋊C4C23×C1111yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4D4×C1111yescharacteristic
441C2×C22⋊C4D4×C1111yescharacteristic
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42C23×C1111yescharacteristic
447C2×C42C23×C1111yescharacteristic
448#107C2×C4×C1114yescomplemented
449#103—22no—
450#103—41no—
451#103C2×C4×C1114yescomplemented
452#102—22no—
453#102—41no—
454#102C2×C4×C1114yescomplemented
455C22⋊C8—22no—
456#97—41no—
457C4×C8—41no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95D4×C1111yescharacteristic
465#95D4×C1111yescharacteristic
466C2×C11—42no—
467C2×C11—82no—
468C2×C11#236411yescharacteristic
469C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
470C2×C11#294711yescharacteristic
471C2×C11#331011yescharacteristic
472C2×C11#331311yescharacteristic
473C2×C11#332611yescharacteristic
474C2×C11#333011yescharacteristic
475C24—21no—
476C24C2×D4×C1111yescharacteristic
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8C22×C4×C1112yes—
483C2×D4—24no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4C22×C4×C1112yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—81no—
508C22×C4—81no—
509C22×C4C22×C4×C1112yes—
510C22×C4C2×D4×C1111yescharacteristic
511C22×C4C2×D4×C1111yescharacteristic
512C22×C4C2×D4×C1111yescharacteristic
513C22×C4C2×D4×C1111yescharacteristic
514C22×C4C2×D4×C1111yescharacteristic
515C22×C4C11×#4112yes—
516C22×C4C24×C1111yescharacteristic
517SD16—44no—
518M16—44no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8C22×C4×C1112yes—
530C2×C8C22×C4×C1112yes—
531C4⋊C4—24no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4C22×C4×C1112yes—
545C4⋊C4C22×C4×C1112yes—
546C4⋊C4C11×#4112yes—
547C4⋊C4C11×#4112yes—
548C22⋊C4—24no—
549C22⋊C4—24no—
550C22⋊C4—22no—
551C22⋊C4—41no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—81no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—42no—
561C42—42no—
562C42—42no—
563C42—42no—
564C11#2313811yescharacteristic, direct product factor, Sylow
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—22no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23C4×D4×C1112yes—
579C23C22×D4×C1111yescharacteristic
580Q8—22no—
581Q8—22no—
582Q8—41no—
583Q8—41no—
584D4—22no—
585D4—22no—
586D4—48no—
587D4—41no—
588D4—41no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—84no—
628C2×C4—84no—
629C2×C4C4×D4×C1112yes—
630C2×C4C11×AGL(1,ℤ/8)12yes—
631C2×C4C23×C4×C1111yescharacteristic
632C2×C4C2×C11×#4111yescharacteristic
633C2×C4C2×C11×#4111yescharacteristic
634C2×C4C2×C11×#4111yescharacteristic
635C2×C4C11×H(5,𝔽2)11yescharacteristic
636C2×C4C11×H(5,𝔽2)11yescharacteristic
637C8—22no—
638C8—22no—
639C8—41no—
640C8—41no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22C2×C4×D4×C1111yescharacteristic
656C22C11×#54611yescharacteristic
657C22C11×#54611yescharacteristic
658C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
659C22C11×#57511yescharacteristic
660C22C11×#57711yescharacteristic
661C22C11×#57811yescharacteristic
662C4—22no—
663C4—22no—
664C4—42no—
665C4—42no—
666C4—42no—
667C4—41no—
668C4—41no—
669C4—41no—
670C4—42no—
671C4—42no—
672C4—81no—
673C4—81no—
674C4C4×C11×#4111yescharacteristic
675C4C11×#51811yescharacteristic
676C4C11×#55311yescharacteristic
677C4C11×#55311yescharacteristic
678C2—42no—
679C2—82no—
680C2C11×#236411yescharacteristic
681C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
682C2C11×#294711yescharacteristic
683C2C11×#331011yescharacteristic
684C2C11×#331311yescharacteristic
685C2C11×#332611yescharacteristic
686C2C11×#333011yescharacteristic
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 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2362C2semidirect
4. C11×#1936C2semidirect
5. C11×#1933C2semidirect
6. C11×#1921C2semidirect
7. C11×#1918C2semidirect
8. C11×#1880C2semidirect
9. C11×#1877C2semidirect
11. C11×#1872C2semidirect
12. C11×#1763C2semidirect
13. C4×C11×#102C2semidirect
14. C11×#1753C2semidirect
15. C11×#1736C2semidirect
25. C11×#468C4semidirect
68. C2×C11×SD16C2×C4semidirect
71. C2×C11×M16C2×C4semidirect
77. C11×C22⋊Q8C2×C4semidirect
114. C11×#107C2×C4semidirect
117. C11×#103C2×C4semidirect
120. C11×#102C2×C4semidirect
132. #23138C11direct (N × H)
223. #2362C2×C11semidirect
225. #1936C2×C11semidirect
226. #1933C2×C11semidirect
227. #1921C2×C11semidirect
228. #1918C2×C11semidirect
229. #1880C2×C11semidirect
230. #1877C2×C11semidirect
232. #1872C2×C11semidirect
233. #1763C2×C11semidirect
234. C4×#102C2×C11semidirect
235. #1753C2×C11semidirect
236. #1736C2×C11semidirect
322. #468C4×C11semidirect
402. C2×SD16C2×C4×C11semidirect
405. C2×M16C2×C4×C11semidirect
411. C22⋊Q8C2×C4×C11semidirect
448. #107C2×C4×C11semidirect
451. #103C2×C4×C11semidirect
454. #102C2×C4×C11semidirect
564. C11#23138direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4682
C11×#23622
C11×#23612
C11×#19362
C11×#19332
C11×#19212
C11×#19182
C11×#18802
C11×#18772
C11×#18752
C11×#18722
C11×#17632
C4×C11×#1022
C11×#17532
C11×#17362
#2313811