Finite Group Databasebeta

← C11×#34237 #14611430

Subgroups — C11×#34237 #14611430

Order 2816.

2186 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#529C211yesmaximal, characteristic
2C11×#2370C212yesmaximal, complemented
3C11×#2367C212yesmaximal, complemented
4C11×#2363C212yesmaximal
5C11×#2362C212yesmaximal, complemented
6C11×#2357C212yesmaximal, complemented
7C11×#2353C212yesmaximal, complemented
8C11×#2346C212yesmaximal, complemented
9C11×#2343C212yesmaximal, complemented
10C11×#2335C214yesmaximal, complemented
11C11×#2320C211yesmaximal, characteristic, complemented
12C11×#2319C211yesmaximal, characteristic, complemented
13C4×C11×#126C214yesmaximal, complemented
14C11×#2283C211yesmaximal, characteristic, complemented
15C11×#2276C211yesmaximal, characteristic, complemented
16C11×#2275C211yesmaximal, characteristic, complemented
17C4×C11×#117C211yesmaximal, characteristic, complemented
18C11×#529C4116yescomplemented
19C2×C11×#126C2212yes—
20C2×C11×#125C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C11×#123C2212yes—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×C4×Q8×C11C2212yes—
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11C2212yes—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2212yes—
30C2×C11×#117C2212yes—
31C2×C11×#117C2212yes—
32C22×C42×C11C2211yescharacteristic
33C11×#391C2212yes—
34C11×#390C2212yes—
35C11×#390C2214yes—
36C11×#389C2212yes—
37C11×#389C2212yes—
38C11×#389C2214yes—
39C11×#388C2214yes—
40C11×#388C2214yes—
41C11×#388C2214yes—
42C11×#388C2214yes—
43C11×#388C2214yes—
44C11×#388C2214yes—
45C11×#387C2214yes—
46C11×#387C2214yes—
47C11×#387C2214yes—
48C11×#387C2214yes—
49C11×#386C2214yes—
50C11×#385C2214yes—
51C11×#383C2212yes—
52C11×#383C2212yes—
53C11×#382C2211yescharacteristic
54C11×#382C2211yescharacteristic
55C11×#382C2212yes—
56C11×#381C2211yescharacteristic
57C11×#381C2211yescharacteristic
58C11×#381C2212yes—
59C11×#380C2212yes—
60C11×#380C2212yes—
61C4×C11×C4⋊C4C2211yescharacteristic
62C4×C11×C4⋊C4C2211yescharacteristic
63C4×C11×C4⋊C4C2212yes—
64C4×C11×C4⋊C4C2212yes—
65C4×C11×C4⋊C4C2214yes—
66C4×C11×C4⋊C4C2212yes—
67C4×C11×C4⋊C4C2212yes—
68C4×C11×C4⋊C4C2212yes—
69C4×C11×C4⋊C4C2214yes—
70C4×C11×C4⋊C4C2214yes—
71C4×C11×C22⋊C4C2212yes—
72C4×C11×C22⋊C4C2212yes—
73C4×C11×C22⋊C4C2214yes—
74C4×C11×C22⋊C4C2212yes—
75C4×C11×C22⋊C4C2212yes—
76C4×C11×C22⋊C4C2214yes—
77C4×C11×C22⋊C4C2214yes—
78C11×#376C2212yes—
79C11×#376C2211yescharacteristic
80C11×#376C2211yescharacteristic
81C11×#376C2212yes—
82C2×C11×#95C2212yes—
83C43×C11C2212yes—
84C22×Q8×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2312yes—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2314yes—
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2312yes—
92C11×#126C2×C4116yescomplemented
93C11×#125C2×C418yescomplemented
94C11×#124C2×C418yes—
95C11×#123C2×C4116yescomplemented
96C11×C22⋊Q8C2×C418yescomplemented
97C11×#121C2×C418yes—
98C4×Q8×C11—28no—
99C4×Q8×C11C2×C418yescomplemented
100C4×D4×C11—28no—
101C4×D4×C11C2×C418yes—
102C4×D4×C11C2×C4116yescomplemented
103C11×#117—28no—
104C11×#117C2×C4116yescomplemented
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C4⋊C4C2312yes—
108C2×C11×C4⋊C4C2312yes—
109C2×C11×C4⋊C4C2314yes—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C4⋊C4C2312yes—
112C2×C11×C4⋊C4C2312yes—
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2312yes—
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C4⋊C4C2312yes—
118C2×C11×C22⋊C4C2314yes—
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2312yes—
121C2×C11×C22⋊C4C2312yes—
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2312yes—
125C2×C11×C22⋊C4C2312yes—
126C2×C11×C22⋊C4C2312yes—
127C2×C11×C22⋊C4C2312yes—
128C2×C11×C22⋊C4C2312yes—
129C2×C42×C11C2×C418yescomplemented
130C2×C42×C11C2314yes—
131C2×C42×C11C2312yes—
132C2×C42×C11C2314yes—
133C2×C42×C11C2312yes—
134C2×C42×C11C2312yes—
135C2×C42×C11C2314yes—
136C2×C42×C11C2312yes—
137C2×C42×C11C2314yes—
138C2×C42×C11C2314yes—
139C2×C42×C11C2311yescharacteristic
140C2×C42×C11C2311yescharacteristic
141C2×C42×C11C2311yescharacteristic
142C2×C42×C11C2311yescharacteristic
143C2×C42×C11C2312yes—
144C11×#95C2311yescharacteristic
145C11×#95C2312yes—
146C11×#95C2314yes—
147C11×#95C2311yescharacteristic
148C11×#95C2312yes—
149C11×#95C2311yescharacteristic
150C11×#95C2312yes—
151C11×#95C2314yes—
152C11×#95C2312yes—
153C11×#95C2311yescharacteristic
154C11×#95C2314yes—
155C11×#95C2312yes—
156C11×#95C2312yes—
157C11×#95C2312yes—
158C11×#95C2314yes—
159C11×#95C2314yes—
160C11×#95C2312yes—
161C11×#95C2314yes—
162C11×#95C2314yes—
163#34237C1111yesmaximal, characteristic, direct product factor, Sylow
164C24×C11C2411yescharacteristic
165C24×C11C2412yes—
166C2×Q8×C11—24no—
167C2×Q8×C11C22×C414yes—
168C2×D4×C11—24no—
169C2×D4×C11—42no—
170C2×D4×C11—42no—
171C2×D4×C11C22×C414yes—
172C2×D4×C11C22×C418yes—
173C22×C4×C11—24no—
174C22×C4×C11—28no—
175C22×C4×C11—41no—
176C22×C4×C11—41no—
177C22×C4×C11—42no—
178C22×C4×C11—44no—
179C22×C4×C11—44no—
180C22×C4×C11—44no—
181C22×C4×C11C22×C414yes—
182C22×C4×C11C22×C414yes—
183C22×C4×C11C22×C414yes—
184C22×C4×C11C22×C418yes—
185C22×C4×C11C2412yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2412yes—
188C22×C4×C11C2414yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2411yescharacteristic
191C22×C4×C11C2411yescharacteristic
192C22×C4×C11C2411yescharacteristic
193C22×C4×C11C2411yescharacteristic
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2411yescharacteristic
198C22×C4×C11C2414yes—
199C22×C4×C11C2411yescharacteristic
200C11×C4⋊C4—24no—
201C11×C4⋊C4—28no—
202C11×C4⋊C4—44no—
203C11×C4⋊C4—42no—
204C11×C4⋊C4—42no—
205C11×C4⋊C4—44no—
206C11×C4⋊C4C22×C418yes—
207C11×C4⋊C4C22×C418yes—
208C11×C4⋊C4C22×C414yes—
209C11×C4⋊C4C22×C418yes—
210C11×C4⋊C4C22×C414yes—
211C11×C4⋊C4C22×C418yes—
212C11×C4⋊C4#4118yes—
213C11×C22⋊C4—28no—
214C11×C22⋊C4—28no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—44no—
217C11×C22⋊C4—44no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4C22×C418yes—
220C11×C22⋊C4C22×C418yes—
221C11×C22⋊C4C22×C418yes—
222C11×C22⋊C4C22×C418yes—
223C11×C22⋊C4C22×C418yes—
224C42×C11—28no—
225C42×C11—24no—
226C42×C11—28no—
227C42×C11—24no—
228C42×C11—42no—
229C42×C11—44no—
230C42×C11—44no—
231C42×C11—44no—
232C42×C11—42no—
233C42×C11C22×C414yes—
234C42×C11C22×C414yes—
235C42×C11C22×C414yes—
236C42×C11C22×C414yes—
237C42×C11C22×C418yes—
238C2×#529C2×C1111yescharacteristic
239#2370C2×C1112yescomplemented
240#2367C2×C1112yescomplemented
241#2363C2×C1112yes—
242#2362C2×C1112yescomplemented
243#2357C2×C1112yescomplemented
244#2353C2×C1112yescomplemented
245#2346C2×C1112yescomplemented
246#2343C2×C1112yescomplemented
247#2335C2×C1114yescomplemented
248#2320C2×C1111yescharacteristic, complemented
249#2319C2×C1111yescharacteristic, complemented
250C4×#126C2×C1114yescomplemented
251#2283C2×C1111yescharacteristic, complemented
252#2276C2×C1111yescharacteristic, complemented
253#2275C2×C1111yescharacteristic, complemented
254C4×#117C2×C1111yescharacteristic, complemented
255C23×C11—22no—
256C23×C11—24no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—24no—
260C23×C11—22no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11C23×C414yes—
264C23×C11C23×C412yes—
265C23×C11C2511yescharacteristic
266Q8×C11—28no—
267D4×C11—28no—
268D4×C11—48no—
269C2×C4×C11—22no—
270C2×C4×C11—24no—
271C2×C4×C11—21no—
272C2×C4×C11—22no—
273C2×C4×C11—21no—
274C2×C4×C11—24no—
275C2×C4×C11—24no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—28no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—24no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—24no—
291C2×C4×C11—24no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—44no—
299C2×C4×C11—48no—
300C2×C4×C11—44no—
301C2×C4×C11—88no—
302C2×C4×C11C23×C412yes—
303C2×C4×C11C23×C412yes—
304C2×C4×C11C23×C412yes—
305C2×C4×C11C23×C412yes—
306C2×C4×C11C23×C412yes—
307C2×C4×C11C23×C414yes—
308C2×C4×C11C23×C414yes—
309C2×C4×C11C23×C414yes—
310C2×C4×C11C23×C412yes—
311C2×C4×C11C2×#4118yes—
312C2×C4×C11C2×#4114yes—
313#529C4×C11116yescomplemented
314C2×#126C22×C1112yes—
315C2×#125C22×C1111yescharacteristic
316C2×#124C22×C1111yescharacteristic
317C2×#123C22×C1112yes—
318C2×C22⋊Q8C22×C1111yescharacteristic
319C2×#121C22×C1111yescharacteristic
320C2×C4×Q8C22×C1112yes—
321C2×C4×Q8C22×C1111yescharacteristic
322C2×C4×D4C22×C1112yes—
323C2×C4×D4C22×C1111yescharacteristic
324C2×C4×D4C22×C1112yes—
325C2×#117C22×C1112yes—
326C2×#117C22×C1112yes—
327C22×C42C22×C1111yescharacteristic
328#391C22×C1112yes—
329#390C22×C1112yes—
330#390C22×C1114yes—
331#389C22×C1112yes—
332#389C22×C1112yes—
333#389C22×C1114yes—
334#388C22×C1114yes—
335#388C22×C1114yes—
336#388C22×C1114yes—
337#388C22×C1114yes—
338#388C22×C1114yes—
339#388C22×C1114yes—
340#387C22×C1114yes—
341#387C22×C1114yes—
342#387C22×C1114yes—
343#387C22×C1114yes—
344#386C22×C1114yes—
345#385C22×C1114yes—
346#383C22×C1112yes—
347#383C22×C1112yes—
348#382C22×C1112yes—
349#382C22×C1111yescharacteristic
350#382C22×C1111yescharacteristic
351#381C22×C1112yes—
352#381C22×C1111yescharacteristic
353#381C22×C1111yescharacteristic
354#380C22×C1112yes—
355#380C22×C1112yes—
356C4×C4⋊C4C22×C1114yes—
357C4×C4⋊C4C22×C1114yes—
358C4×C4⋊C4C22×C1114yes—
359C4×C4⋊C4C22×C1111yescharacteristic
360C4×C4⋊C4C22×C1112yes—
361C4×C4⋊C4C22×C1112yes—
362C4×C4⋊C4C22×C1112yes—
363C4×C4⋊C4C22×C1112yes—
364C4×C4⋊C4C22×C1112yes—
365C4×C4⋊C4C22×C1111yescharacteristic
366C4×C22⋊C4C22×C1114yes—
367C4×C22⋊C4C22×C1114yes—
368C4×C22⋊C4C22×C1114yes—
369C4×C22⋊C4C22×C1112yes—
370C4×C22⋊C4C22×C1112yes—
371C4×C22⋊C4C22×C1112yes—
372C4×C22⋊C4C22×C1112yes—
373#376C22×C1111yescharacteristic
374#376C22×C1111yescharacteristic
375#376C22×C1112yes—
376#376C22×C1112yes—
377C2×#95C22×C1112yes—
378C43C22×C1112yes—
379C22×C11—22no—
380C22×C11—24no—
381C22×C11—22no—
382C22×C11—22no—
383C22×C11—24no—
384C22×C11—24no—
385C22×C11—44no—
386C22×C11—42no—
387C22×C11—42no—
388C22×C11—44no—
389C22×C11C24×C411yescharacteristic
390C22×C11C22×#4112yes—
391C22×C11#58511yescharacteristic
392C22×C11#58512yes—
393C22×C11#58511yescharacteristic
394C4×C11—22no—
395C4×C11—24no—
396C4×C11—22no—
397C4×C11—22no—
398C4×C11—22no—
399C4×C11—24no—
400C4×C11—22no—
401C4×C11—24no—
402C4×C11—28no—
403C4×C11—42no—
404C4×C11—42no—
405C4×C11—42no—
406C4×C11—42no—
407C4×C11—44no—
408C4×C11C4×#4114yes—
409C22×Q8C23×C1111yescharacteristic
410C22×D4C23×C1111yescharacteristic
411C22×D4C23×C1112yes—
412C23×C4C23×C1111yescharacteristic
413C23×C4C23×C1114yes—
414C23×C4C23×C1112yes—
415C23×C4C23×C1111yescharacteristic
416C23×C4C23×C1111yescharacteristic
417#126C2×C4×C11116yescomplemented
418#125C2×C4×C1118yescomplemented
419#124C2×C4×C1118yes—
420#123C2×C4×C11116yescomplemented
421C22⋊Q8C2×C4×C1118yescomplemented
422#121C2×C4×C1118yes—
423C4×Q8—28no—
424C4×Q8C2×C4×C1118yescomplemented
425C4×D4—28no—
426C4×D4C2×C4×C1118yes—
427C4×D4C2×C4×C11116yescomplemented
428#117—28no—
429#117C2×C4×C11116yescomplemented
430C2×C4⋊C4C23×C1112yes—
431C2×C4⋊C4C23×C1114yes—
432C2×C4⋊C4C23×C1112yes—
433C2×C4⋊C4C23×C1112yes—
434C2×C4⋊C4C23×C1114yes—
435C2×C4⋊C4C23×C1114yes—
436C2×C4⋊C4C23×C1112yes—
437C2×C4⋊C4C23×C1112yes—
438C2×C4⋊C4C23×C1111yescharacteristic
439C2×C4⋊C4C23×C1112yes—
440C2×C4⋊C4C23×C1111yescharacteristic
441C2×C4⋊C4C23×C1112yes—
442C2×C4⋊C4C23×C1112yes—
443C2×C22⋊C4C23×C1114yes—
444C2×C22⋊C4C23×C1114yes—
445C2×C22⋊C4C23×C1112yes—
446C2×C22⋊C4C23×C1112yes—
447C2×C22⋊C4C23×C1114yes—
448C2×C22⋊C4C23×C1114yes—
449C2×C22⋊C4C23×C1112yes—
450C2×C22⋊C4C23×C1112yes—
451C2×C22⋊C4C23×C1112yes—
452C2×C22⋊C4C23×C1112yes—
453C2×C22⋊C4C23×C1112yes—
454C2×C42C2×C4×C1118yescomplemented
455C2×C42C23×C1114yes—
456C2×C42C23×C1112yes—
457C2×C42C23×C1114yes—
458C2×C42C23×C1112yes—
459C2×C42C23×C1112yes—
460C2×C42C23×C1114yes—
461C2×C42C23×C1112yes—
462C2×C42C23×C1114yes—
463C2×C42C23×C1114yes—
464C2×C42C23×C1111yescharacteristic
465C2×C42C23×C1112yes—
466C2×C42C23×C1111yescharacteristic
467C2×C42C23×C1111yescharacteristic
468C2×C42C23×C1111yescharacteristic
469#95C23×C1111yescharacteristic
470#95C23×C1112yes—
471#95C23×C1114yes—
472#95C23×C1111yescharacteristic
473#95C23×C1112yes—
474#95C23×C1111yescharacteristic
475#95C23×C1112yes—
476#95C23×C1114yes—
477#95C23×C1112yes—
478#95C23×C1111yescharacteristic
479#95C23×C1114yes—
480#95C23×C1112yes—
481#95C23×C1112yes—
482#95C23×C1112yes—
483#95C23×C1114yes—
484#95C23×C1114yes—
485#95C23×C1112yes—
486#95C23×C1114yes—
487#95C23×C1114yes—
488C2×C11—42no—
489C2×C11—44no—
490C2×C11C2×C4×#4111yescharacteristic
491C2×C11#342811yescharacteristic
492C2×C11#342811yescharacteristic
493C2×C11#352112yes—
494C2×C11#352412yes—
495C24C24×C1111yescharacteristic
496C24C24×C1112yes—
497C2×Q8—24no—
498C2×Q8C22×C4×C1114yes—
499C2×D4—24no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4C22×C4×C1114yes—
503C2×D4C22×C4×C1118yes—
504C22×C4—24no—
505C22×C4—28no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—42no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4C22×C4×C1114yes—
513C22×C4C22×C4×C1114yes—
514C22×C4C22×C4×C1114yes—
515C22×C4C22×C4×C1118yes—
516C22×C4C24×C1112yes—
517C22×C4C24×C1112yes—
518C22×C4C24×C1112yes—
519C22×C4C24×C1114yes—
520C22×C4C24×C1112yes—
521C22×C4C24×C1111yescharacteristic
522C22×C4C24×C1111yescharacteristic
523C22×C4C24×C1111yescharacteristic
524C22×C4C24×C1111yescharacteristic
525C22×C4C24×C1112yes—
526C22×C4C24×C1112yes—
527C22×C4C24×C1112yes—
528C22×C4C24×C1111yescharacteristic
529C22×C4C24×C1114yes—
530C22×C4C24×C1111yescharacteristic
531C4⋊C4—24no—
532C4⋊C4—28no—
533C4⋊C4—44no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—44no—
537C4⋊C4C22×C4×C1118yes—
538C4⋊C4C22×C4×C1118yes—
539C4⋊C4C22×C4×C1114yes—
540C4⋊C4C22×C4×C1118yes—
541C4⋊C4C22×C4×C1114yes—
542C4⋊C4C22×C4×C1118yes—
543C4⋊C4C11×#4118yes—
544C22⋊C4—28no—
545C22⋊C4—28no—
546C22⋊C4—42no—
547C22⋊C4—44no—
548C22⋊C4—44no—
549C22⋊C4—42no—
550C22⋊C4C22×C4×C1118yes—
551C22⋊C4C22×C4×C1118yes—
552C22⋊C4C22×C4×C1118yes—
553C22⋊C4C22×C4×C1118yes—
554C22⋊C4C22×C4×C1118yes—
555C42—28no—
556C42—24no—
557C42—28no—
558C42—24no—
559C42—42no—
560C42—44no—
561C42—44no—
562C42—44no—
563C42—42no—
564C42C22×C4×C1114yes—
565C42C22×C4×C1114yes—
566C42C22×C4×C1114yes—
567C42C22×C4×C1114yes—
568C42C22×C4×C1118yes—
569C11#3423711yescharacteristic, direct product factor, Sylow
570C23—22no—
571C23—24no—
572C23—22no—
573C23—22no—
574C23—24no—
575C23—22no—
576C23—21no—
577C23—21no—
578C23C23×C4×C1114yes—
579C23C23×C4×C1112yes—
580C23C25×C1111yescharacteristic
581Q8—28no—
582D4—28no—
583D4—48no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—22no—
592C2×C4—24no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—28no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—44no—
614C2×C4—48no—
615C2×C4—44no—
616C2×C4—88no—
617C2×C4C23×C4×C1112yes—
618C2×C4C23×C4×C1112yes—
619C2×C4C23×C4×C1112yes—
620C2×C4C23×C4×C1112yes—
621C2×C4C23×C4×C1112yes—
622C2×C4C23×C4×C1114yes—
623C2×C4C23×C4×C1114yes—
624C2×C4C23×C4×C1114yes—
625C2×C4C23×C4×C1112yes—
626C2×C4C2×C11×#4118yes—
627C2×C4C2×C11×#4114yes—
628C22—22no—
629C22—24no—
630C22—22no—
631C22—22no—
632C22—24no—
633C22—24no—
634C22—44no—
635C22—42no—
636C22—42no—
637C22—44no—
638C22C24×C4×C1111yescharacteristic
639C22C22×C11×#4112yes—
640C22C11×#58511yescharacteristic
641C22C11×#58512yes—
642C22C11×#58511yescharacteristic
643C4—22no—
644C4—24no—
645C4—22no—
646C4—22no—
647C4—22no—
648C4—24no—
649C4—22no—
650C4—24no—
651C4—28no—
652C4—42no—
653C4—42no—
654C4—42no—
655C4—42no—
656C4—44no—
657C4C4×C11×#4114yes—
658C2—42no—
659C2—44no—
660C2C2×C4×C11×#4111yescharacteristic
661C2C11×#342811yescharacteristic
662C2C11×#342811yescharacteristic
663C2C11×#352112yes—
664C2C11×#352412yes—
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2370C2semidirect
3. C11×#2367C2semidirect
5. C11×#2362C2semidirect
6. C11×#2357C2semidirect
7. C11×#2353C2semidirect
8. C11×#2346C2semidirect
9. C11×#2343C2semidirect
10. C11×#2335C2semidirect
11. C11×#2320C2semidirect
12. C11×#2319C2semidirect
13. C4×C11×#126C2semidirect
14. C11×#2283C2semidirect
15. C11×#2276C2semidirect
16. C11×#2275C2semidirect
17. C4×C11×#117C2semidirect
18. C11×#529C4semidirect
92. C11×#126C2×C4semidirect
93. C11×#125C2×C4semidirect
95. C11×#123C2×C4semidirect
96. C11×C22⋊Q8C2×C4semidirect
99. C4×Q8×C11C2×C4semidirect
102. C4×D4×C11C2×C4semidirect
104. C11×#117C2×C4semidirect
129. C2×C42×C11C2×C4semidirect
163. #34237C11direct (N × H)
239. #2370C2×C11semidirect
240. #2367C2×C11semidirect
242. #2362C2×C11semidirect
243. #2357C2×C11semidirect
244. #2353C2×C11semidirect
245. #2346C2×C11semidirect
246. #2343C2×C11semidirect
247. #2335C2×C11semidirect
248. #2320C2×C11semidirect
249. #2319C2×C11semidirect
250. C4×#126C2×C11semidirect
251. #2283C2×C11semidirect
252. #2276C2×C11semidirect
253. #2275C2×C11semidirect
254. C4×#117C2×C11semidirect
313. #529C4×C11semidirect
417. #126C2×C4×C11semidirect
418. #125C2×C4×C11semidirect
420. #123C2×C4×C11semidirect
421. C22⋊Q8C2×C4×C11semidirect
424. C4×Q8C2×C4×C11semidirect
427. C4×D4C2×C4×C11semidirect
429. #117C2×C4×C11semidirect
454. C2×C42C2×C4×C11semidirect
569. C11#34237direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5292
C11×#23702
C11×#23672
C11×#23632
C11×#23622
C11×#23572
C11×#23532
C11×#23462
C11×#23432
C11×#23352
C11×#23202
C11×#23192
C4×C11×#1262
C11×#22832
C11×#22762
C11×#22752
C4×C11×#1172
#3423711