Finite Group Databasebeta

← C11×#23142 #14600335

Subgroups — C11×#23142 #14600335

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#468C211yesmaximal, characteristic
2C11×#2363C211yesmaximal, characteristic
3C11×#2360C211yesmaximal, characteristic, complemented
4C11×#1935C211yesmaximal, characteristic, complemented
5C11×#1934C211yesmaximal, characteristic, complemented
6C11×#1921C211yesmaximal, characteristic, complemented
7C11×#1918C211yesmaximal, characteristic, complemented
8C11×#1880C211yesmaximal, characteristic, complemented
9C11×#1877C211yesmaximal, characteristic, complemented
10C11×#1874C211yesmaximal, characteristic
11C11×#1873C211yesmaximal, characteristic, complemented
12C11×#1762C211yesmaximal, characteristic, complemented
13C4×C11×#103C211yesmaximal, 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×C11C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#468C418yescomplemented
25C2×C11×#107C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×#97C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35C11×#391C2211yescharacteristic
36C11×#390—21no—
37C11×#390C2211yescharacteristic
38C11×#389—21no—
39C11×#389C2211yescharacteristic
40C11×#389C2211yescharacteristic
41C11×#388—21no—
42C11×#387—21no—
43C11×#386—21no—
44C11×#385—21no—
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C22⋊C4—21no—
48C4×C11×C22⋊C4—21no—
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—
84C11×#117—22no—
85C11×#117—41no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—41no—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
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⋊C4D411yescharacteristic
106C2×C11×C22⋊C4D411yescharacteristic
107C2×C42×C11—21no—
108C2×C42×C11—21no—
109C2×C42×C11—21no—
110C2×C42×C11—21no—
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C11×#107C2×C414yescomplemented
114C11×#103—22no—
115C11×#103—41no—
116C11×#103C2×C414yescomplemented
117C11×#102—22no—
118C11×#102—41no—
119C11×#102C2×C414yescomplemented
120C11×C22⋊C8—22no—
121C11×#97—41no—
122C4×C8×C11—41no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95D411yescharacteristic
130C11×#95D411yescharacteristic
131#23142C1111yesmaximal, characteristic, direct product factor, Sylow
132C24×C11—21no—
133C24×C11C2×D411yescharacteristic
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C22×C412yes—
140C2×D4×C11—24no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—81no—
147C2×D4×C11—81no—
148C2×D4×C11C22×C412yes—
149C22×C4×C11—21no—
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—42no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11—81no—
165C22×C4×C11—81no—
166C22×C4×C11C22×C412yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11#4112yes—
173C22×C4×C11C2411yescharacteristic
174C11×SD16—44no—
175C11×M16—44no—
176C2×C8×C11—21no—
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×C11C22×C412yes—
187C2×C8×C11C22×C412yes—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—21no—
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—42no—
198C11×C4⋊C4—42no—
199C11×C4⋊C4—81no—
200C11×C4⋊C4—81no—
201C11×C4⋊C4C22×C412yes—
202C11×C4⋊C4C22×C412yes—
203C11×C4⋊C4#4112yes—
204C11×C4⋊C4#4112yes—
205C11×C22⋊C4—24no—
206C11×C22⋊C4—24no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—41no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—81no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—42no—
218C42×C11—42no—
219C42×C11—81no—
220C42×C11—81no—
221C2×#468C2×C1111yescharacteristic
222#2363C2×C1111yescharacteristic
223#2360C2×C1111yescharacteristic, complemented
224#1935C2×C1111yescharacteristic, complemented
225#1934C2×C1111yescharacteristic, complemented
226#1921C2×C1111yescharacteristic, complemented
227#1918C2×C1111yescharacteristic, complemented
228#1880C2×C1111yescharacteristic, complemented
229#1877C2×C1111yescharacteristic, complemented
230#1874C2×C1111yescharacteristic
231#1873C2×C1111yescharacteristic, complemented
232#1762C2×C1111yescharacteristic, complemented
233C4×#103C2×C1111yescharacteristic, complemented
234#1753C2×C1111yescharacteristic, complemented
235#1736C2×C1111yescharacteristic, complemented
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—22no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11C4×D412yes—
250C23×C11C22×D411yescharacteristic
251Q8×C11—22no—
252Q8×C11—22no—
253Q8×C11—41no—
254Q8×C11—41no—
255D4×C11—22no—
256D4×C11—22no—
257D4×C11—41no—
258D4×C11—41no—
259D4×C11—84no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
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—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
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—41no—
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—84no—
299C2×C4×C11—84no—
300C2×C4×C11C4×D412yes—
301C2×C4×C11#13712yes—
302C2×C4×C11C23×C411yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C2×C4×C11C2×#4111yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C2×C4×C11H(5,𝔽2)11yescharacteristic
307C2×C4×C11H(5,𝔽2)11yescharacteristic
308C8×C11—22no—
309C8×C11—22no—
310C8×C11—41no—
311C8×C11—41no—
312C22×SD16C22×C1111yescharacteristic
313C22×M16C22×C1111yescharacteristic
314C2×C22⋊Q8C22×C1111yescharacteristic
315C2×#121C22×C1111yescharacteristic
316C2×C4×Q8C22×C1111yescharacteristic
317C2×C4×D4C22×C1111yescharacteristic
318C2×#117C22×C1111yescharacteristic
319C22×C4⋊C4C22×C1111yescharacteristic
320#468C4×C1118yescomplemented
321C2×#107C22×C1111yescharacteristic
322C2×#103C22×C1111yescharacteristic
323C2×#103C22×C1111yescharacteristic
324C2×#103C22×C1111yescharacteristic
325C2×#102C22×C1111yescharacteristic
326C2×#102C22×C1111yescharacteristic
327C2×#102C22×C1111yescharacteristic
328C2×C22⋊C8C22×C1111yescharacteristic
329C2×#97C22×C1111yescharacteristic
330C2×C4×C8C22×C1111yescharacteristic
331#391C22×C1111yescharacteristic
332#390—21no—
333#390C22×C1111yescharacteristic
334#389—21no—
335#389C22×C1111yescharacteristic
336#389C22×C1111yescharacteristic
337#388—21no—
338#387—21no—
339#386—21no—
340#385—21no—
341C4×C4⋊C4C22×C1111yescharacteristic
342C4×C4⋊C4C22×C1111yescharacteristic
343C4×C22⋊C4—21no—
344C4×C22⋊C4—21no—
345C4×C22⋊C4C22×C1111yescharacteristic
346#340C22×C1111yescharacteristic
347#340C22×C1111yescharacteristic
348#340C22×C1111yescharacteristic
349#340C22×C1111yescharacteristic
350#340C22×C1111yescharacteristic
351#340C22×C1111yescharacteristic
352#340C22×C1111yescharacteristic
353#340C22×C1111yescharacteristic
354#336C22×C1111yescharacteristic
355#336C22×C1111yescharacteristic
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11C2×C4×D411yescharacteristic
371C22×C11#54611yescharacteristic
372C22×C11#54611yescharacteristic
373C22×C11C2×#13711yescharacteristic
374C22×C11#57511yescharacteristic
375C22×C11#57611yescharacteristic
376C22×C11#57711yescharacteristic
377C4×C11—22no—
378C4×C11—22no—
379C4×C11—41no—
380C4×C11—42no—
381C4×C11—42no—
382C4×C11—42no—
383C4×C11—41no—
384C4×C11—42no—
385C4×C11—41no—
386C4×C11—42no—
387C4×C11—81no—
388C4×C11—81no—
389C4×C11C4×#4111yescharacteristic
390C4×C11#51811yescharacteristic
391C4×C11#55311yescharacteristic
392C4×C11#55311yescharacteristic
393C22×Q8C23×C1111yescharacteristic
394C22×D4—21no—
395C22×D4C23×C1111yescharacteristic
396C23×C4—21no—
397C23×C4—21no—
398C23×C4C23×C1111yescharacteristic
399C2×SD16—41no—
400C2×SD16—41no—
401C2×SD16C2×C4×C1114yescomplemented
402C2×M16—41no—
403C2×M16—41no—
404C2×M16C2×C4×C1114yescomplemented
405C22×C8C23×C1111yescharacteristic
406C22×C8C23×C1111yescharacteristic
407C22×C8C23×C1111yescharacteristic
408C22×C8C23×C1111yescharacteristic
409C22⋊Q8—22no—
410C22⋊Q8C2×C4×C1114yescomplemented
411#121—22no—
412#121C2×C4×C1114yes—
413C4×Q8—22no—
414C4×Q8—41no—
415C4×D4—22no—
416C4×D4—41no—
417#117—22no—
418#117—41no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—41no—
426C2×C4⋊C4C23×C1111yescharacteristic
427C2×C4⋊C4C23×C1111yescharacteristic
428C2×C4⋊C4C23×C1111yescharacteristic
429C2×C4⋊C4C23×C1111yescharacteristic
430C2×C4⋊C4C23×C1111yescharacteristic
431C2×C4⋊C4C23×C1111yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4D4×C1111yescharacteristic
439C2×C22⋊C4D4×C1111yescharacteristic
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42C23×C1111yescharacteristic
445C2×C42C23×C1111yescharacteristic
446#107C2×C4×C1114yescomplemented
447#103—22no—
448#103—41no—
449#103C2×C4×C1114yescomplemented
450#102—22no—
451#102—41no—
452#102C2×C4×C1114yescomplemented
453C22⋊C8—22no—
454#97—41no—
455C4×C8—41no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95D4×C1111yescharacteristic
463#95D4×C1111yescharacteristic
464C2×C11—42no—
465C2×C11—82no—
466C2×C11#236411yescharacteristic
467C2×C11C4×#13711yescharacteristic
468C2×C11#294611yescharacteristic
469C2×C11#331911yescharacteristic
470C2×C11#332011yescharacteristic
471C2×C11#332311yescharacteristic
472C2×C11#333311yescharacteristic
473C24—21no—
474C24C2×D4×C1111yescharacteristic
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8C22×C4×C1112yes—
481C2×D4—24no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—81no—
488C2×D4—81no—
489C2×D4C22×C4×C1112yes—
490C22×C4—21no—
491C22×C4—21no—
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—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4C22×C4×C1112yes—
508C22×C4C2×D4×C1111yescharacteristic
509C22×C4C2×D4×C1111yescharacteristic
510C22×C4C2×D4×C1111yescharacteristic
511C22×C4C2×D4×C1111yescharacteristic
512C22×C4C2×D4×C1111yescharacteristic
513C22×C4C11×#4112yes—
514C22×C4C24×C1111yescharacteristic
515SD16—44no—
516M16—44no—
517C2×C8—21no—
518C2×C8—21no—
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×C8C22×C4×C1112yes—
528C2×C8C22×C4×C1112yes—
529C4⋊C4—24no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—81no—
541C4⋊C4—81no—
542C4⋊C4C22×C4×C1112yes—
543C4⋊C4C22×C4×C1112yes—
544C4⋊C4C11×#4112yes—
545C4⋊C4C11×#4112yes—
546C22⋊C4—24no—
547C22⋊C4—24no—
548C22⋊C4—22no—
549C22⋊C4—41no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—81no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—42no—
559C42—42no—
560C42—81no—
561C42—81no—
562C11#2314211yescharacteristic, direct product factor, Sylow
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—22no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23C4×D4×C1112yes—
577C23C22×D4×C1111yescharacteristic
578Q8—22no—
579Q8—22no—
580Q8—41no—
581Q8—41no—
582D4—22no—
583D4—22no—
584D4—41no—
585D4—41no—
586D4—84no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—41no—
610C2×C4—41no—
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—84no—
626C2×C4—84no—
627C2×C4C4×D4×C1112yes—
628C2×C4C11×#13712yes—
629C2×C4C23×C4×C1111yescharacteristic
630C2×C4C2×C11×#4111yescharacteristic
631C2×C4C2×C11×#4111yescharacteristic
632C2×C4C2×C11×#4111yescharacteristic
633C2×C4C11×H(5,𝔽2)11yescharacteristic
634C2×C4C11×H(5,𝔽2)11yescharacteristic
635C8—22no—
636C8—22no—
637C8—41no—
638C8—41no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22C2×C4×D4×C1111yescharacteristic
654C22C11×#54611yescharacteristic
655C22C11×#54611yescharacteristic
656C22C2×C11×#13711yescharacteristic
657C22C11×#57511yescharacteristic
658C22C11×#57611yescharacteristic
659C22C11×#57711yescharacteristic
660C4—22no—
661C4—22no—
662C4—42no—
663C4—42no—
664C4—41no—
665C4—42no—
666C4—41no—
667C4—42no—
668C4—41no—
669C4—42no—
670C4—81no—
671C4—81no—
672C4C4×C11×#4111yescharacteristic
673C4C11×#51811yescharacteristic
674C4C11×#55311yescharacteristic
675C4C11×#55311yescharacteristic
676C2—42no—
677C2—82no—
678C2C11×#236411yescharacteristic
679C2C4×C11×#13711yescharacteristic
680C2C11×#294611yescharacteristic
681C2C11×#331911yescharacteristic
682C2C11×#332011yescharacteristic
683C2C11×#332311yescharacteristic
684C2C11×#333311yescharacteristic
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
3. C11×#2360C2semidirect
4. C11×#1935C2semidirect
5. C11×#1934C2semidirect
6. C11×#1921C2semidirect
7. C11×#1918C2semidirect
8. C11×#1880C2semidirect
9. C11×#1877C2semidirect
11. C11×#1873C2semidirect
12. C11×#1762C2semidirect
13. C4×C11×#103C2semidirect
14. C11×#1753C2semidirect
15. C11×#1736C2semidirect
24. C11×#468C4semidirect
68. C2×C11×SD16C2×C4semidirect
71. C2×C11×M16C2×C4semidirect
77. C11×C22⋊Q8C2×C4semidirect
113. C11×#107C2×C4semidirect
116. C11×#103C2×C4semidirect
119. C11×#102C2×C4semidirect
131. #23142C11direct (N × H)
223. #2360C2×C11semidirect
224. #1935C2×C11semidirect
225. #1934C2×C11semidirect
226. #1921C2×C11semidirect
227. #1918C2×C11semidirect
228. #1880C2×C11semidirect
229. #1877C2×C11semidirect
231. #1873C2×C11semidirect
232. #1762C2×C11semidirect
233. C4×#103C2×C11semidirect
234. #1753C2×C11semidirect
235. #1736C2×C11semidirect
320. #468C4×C11semidirect
401. C2×SD16C2×C4×C11semidirect
404. C2×M16C2×C4×C11semidirect
410. C22⋊Q8C2×C4×C11semidirect
446. #107C2×C4×C11semidirect
449. #103C2×C4×C11semidirect
452. #102C2×C4×C11semidirect
562. C11#23142direct (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×#23632
C11×#23602
C11×#19352
C11×#19342
C11×#19212
C11×#19182
C11×#18802
C11×#18772
C11×#18742
C11×#18732
C11×#17622
C4×C11×#1032
C11×#17532
C11×#17362
#2314211