Finite Group Databasebeta

← C11×#34328 #14611521

Subgroups — C11×#34328 #14611521

Order 2816.

2036 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#557C211yesmaximal, characteristic
2C11×#2371C214yesmaximal
3C11×#2370C212yesmaximal
4C11×#2365C211yesmaximal, characteristic
5C11×#2365C212yesmaximal
6C11×#2356C212yesmaximal
7C11×#2356C212yesmaximal
8C11×#2355C211yesmaximal, characteristic
9C11×#2355C211yesmaximal, characteristic
10C11×#2336C214yesmaximal
11C11×#2327C212yesmaximal
12C4×C11×C4⋊Q8C211yesmaximal, characteristic
13C4×C11×#125C212yesmaximal
14C11×#2295C212yesmaximal
15C11×#2295C211yesmaximal, characteristic
16C11×#2276C212yesmaximal
17C42×Q8×C11C211yesmaximal, characteristic
18C11×#557C4116yescomplemented
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×C4⋊Q8C2212yes—
21C2×C11×#125C2212yes—
22C2×C11×#125C2214yes—
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×Q8×C11C2212yes—
26C2×C4×Q8×C11C2212yes—
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×Q8×C11C2212yes—
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×Q8×C11C2212yes—
31C11×#391C2211yescharacteristic
32C11×#391C2212yes—
33C11×#391C2211yescharacteristic
34C11×#391C2212yes—
35C11×#391C2212yes—
36C11×#391C2212yes—
37C11×#389C2211yescharacteristic
38C11×#389C2212yes—
39C11×#389C2212yes—
40C11×#389C2211yescharacteristic
41C11×#389C2212yes—
42C11×#389C2214yes—
43C11×#387C2214yes—
44C11×#387C2212yes—
45C11×#387C2214yes—
46C11×#387C2212yes—
47C11×#387C2214yes—
48C11×#387C2214yes—
49C11×#387C2214yes—
50C11×#387C2214yes—
51C11×#387C2214yes—
52C11×#387C2214yes—
53C11×#387C2214yes—
54C11×#387C2214yes—
55C11×#387C2214yes—
56C11×#384C2211yescharacteristic
57C11×#383C2214yes—
58C11×#382C2212yes—
59C11×#382C2212yes—
60C4×C11×C4⋊C4C2211yescharacteristic
61C4×C11×C4⋊C4C2212yes—
62C4×C11×C4⋊C4C2211yescharacteristic
63C4×C11×C4⋊C4C2211yescharacteristic
64C4×C11×C4⋊C4C2212yes—
65C4×C11×C4⋊C4C2212yes—
66C4×C11×C4⋊C4C2214yes—
67C4×C11×C4⋊C4C2214yes—
68C4×C11×C4⋊C4C2212yes—
69C4×C11×C4⋊C4C2212yes—
70C4×C11×C4⋊C4C2214yes—
71C4×C11×C4⋊C4C2211yescharacteristic
72C4×C11×C4⋊C4C2212yes—
73C4×C11×C4⋊C4C2212yes—
74C4×C11×C4⋊C4C2212yes—
75C4×C11×C4⋊C4C2212yes—
76C4×C11×C4⋊C4C2214yes—
77C4×C11×C4⋊C4C2212yes—
78C4×C11×C4⋊C4C2212yes—
79C11×#376C2212yes—
80C11×#376C2214yes—
81C11×#376C2214yes—
82C43×C11C2212yes—
83C43×C11C2211yescharacteristic
84C22×Q8×C11C2311yescharacteristic
85C22×Q8×C11C2311yescharacteristic
86C22×Q8×C11C2312yes—
87C11×C4⋊Q8C2×C418yes—
88C11×C4⋊Q8C2×C4116yes—
89C11×#125C2×C4116yes—
90C11×#125C2×C4132yes—
91C4×Q8×C11—24no—
92C4×Q8×C11—28no—
93C4×Q8×C11—24no—
94C4×Q8×C11—28no—
95C4×Q8×C11C2×C4116yes—
96C4×Q8×C11C2×C418yes—
97C4×Q8×C11C2×C4116yes—
98C4×Q8×C11C2×C418yes—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2312yes—
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C4⋊C4C2312yes—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C4⋊C4C2314yes—
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C4⋊C4C2312yes—
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2312yes—
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C4⋊C4C2314yes—
117C2×C11×C4⋊C4C2312yes—
118C2×C11×C4⋊C4C2312yes—
119C2×C11×C4⋊C4C2314yes—
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2312yes—
123C2×C42×C11C2311yescharacteristic
124C2×C42×C11C2312yes—
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2312yes—
127C2×C42×C11C2311yescharacteristic
128C2×C42×C11C2312yes—
129C2×C42×C11C2314yes—
130C2×C42×C11C2314yes—
131C2×C42×C11C2312yes—
132C2×C42×C11C2312yes—
133C2×C42×C11C2311yescharacteristic
134C2×C42×C11C2314yes—
135C2×C42×C11C2314yes—
136C2×C42×C11C2312yes—
137C2×C42×C11C2311yescharacteristic
138C2×C42×C11C2314yes—
139C2×C42×C11C2312yes—
140C2×C42×C11C2311yescharacteristic
141C11×#95C2312yes—
142C11×#95C2312yes—
143C11×#95C2312yes—
144C11×#95C2314yes—
145C11×#95C2312yes—
146C11×#95C2312yes—
147C11×#95C2312yes—
148C11×#95C2314yes—
149C11×#95C2314yes—
150C11×#95C2314yes—
151C11×#95C2314yes—
152C11×#95C2312yes—
153C11×#95C2312yes—
154C11×#95C2314yes—
155C11×#95C2314yes—
156C11×#95C2312yes—
157C11×#95C2314yes—
158C11×#95C2314yes—
159C11×#95C2312yes—
160C11×#95C2314yes—
161#34328C1111yesmaximal, characteristic, direct product factor, Sylow
162C2×Q8×C11—22no—
163C2×Q8×C11—24no—
164C2×Q8×C11—22no—
165C2×Q8×C11—24no—
166C2×Q8×C11—22no—
167C2×Q8×C11—22no—
168C2×Q8×C11C22×C414yes—
169C2×Q8×C11C22×C414yes—
170C2×Q8×C11C22×C418yes—
171C22×C4×C11C2412yes—
172C22×C4×C11C2412yes—
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2412yes—
175C22×C4×C11C2414yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2412yes—
178C22×C4×C11C2411yescharacteristic
179C22×C4×C11C2412yes—
180C22×C4×C11C2414yes—
181C22×C4×C11C2412yes—
182C22×C4×C11C2411yescharacteristic
183C22×C4×C11C2412yes—
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C22×C4×C11C2411yescharacteristic
188C11×C4⋊C4—24no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—28no—
191C11×C4⋊C4—28no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—24no—
194C11×C4⋊C4—24no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—42no—
199C11×C4⋊C4—42no—
200C11×C4⋊C4C22×C414yes—
201C11×C4⋊C4C22×C418yes—
202C11×C4⋊C4C22×C4116yes—
203C11×C4⋊C4C22×C418yes—
204C11×C4⋊C4C22×C414yes—
205C11×C4⋊C4C22×C4116yes—
206C11×C4⋊C4C22×C418yes—
207C11×C4⋊C4C22×C4116yes—
208C11×C4⋊C4C22×C418yes—
209C11×C4⋊C4#4114yes—
210C42×C11—24no—
211C42×C11—22no—
212C42×C11—28no—
213C42×C11—28no—
214C42×C11—24no—
215C42×C11—24no—
216C42×C11—22no—
217C42×C11—22no—
218C42×C11—24no—
219C42×C11—22no—
220C42×C11—24no—
221C42×C11—42no—
222C42×C11—44no—
223C42×C11—41no—
224C42×C11—44no—
225C42×C11C22×C4116yes—
226C42×C11C22×C418yes—
227C42×C11C22×C418yes—
228C42×C11C22×C414yes—
229C42×C11#4114yes—
230C2×#557C2×C1111yescharacteristic
231#2371C2×C1114yes—
232#2370C2×C1112yes—
233#2365C2×C1112yes—
234#2365C2×C1111yescharacteristic
235#2356C2×C1112yes—
236#2356C2×C1112yes—
237#2355C2×C1111yescharacteristic
238#2355C2×C1111yescharacteristic
239#2336C2×C1114yes—
240#2327C2×C1112yes—
241C4×C4⋊Q8C2×C1111yescharacteristic
242C4×#125C2×C1112yes—
243#2295C2×C1111yescharacteristic
244#2295C2×C1112yes—
245#2276C2×C1112yes—
246C42×Q8C2×C1111yescharacteristic
247C23×C11C2511yescharacteristic
248Q8×C11—28no—
249Q8×C11—216no—
250Q8×C11—28no—
251C2×C4×C11—21no—
252C2×C4×C11—24no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—24no—
273C2×C4×C11—22no—
274C2×C4×C11—21no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—21no—
279C2×C4×C11—24no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—24no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11C23×C414yes—
287C2×C4×C11C23×C414yes—
288C2×C4×C11C23×C412yes—
289C2×C4×C11C23×C414yes—
290C2×C4×C11C23×C418yes—
291C2×C4×C11C23×C414yes—
292C2×C4×C11C23×C412yes—
293C2×C4×C11C23×C412yes—
294C2×C4×C11C2×#4112yes—
295C2×C4×C11C2×#4114yes—
296C2×C4×C11C2×#4112yes—
297C2×C4×C11C2×#4112yes—
298C2×C4×C11C2×#4112yes—
299C2×C4×C112−1+412yes—
300C2×C4×C112−1+412yes—
301C2×C4×C112−1+412yes—
302#557C4×C11116yescomplemented
303C2×C4⋊Q8C22×C1111yescharacteristic
304C2×C4⋊Q8C22×C1112yes—
305C2×#125C22×C1112yes—
306C2×#125C22×C1114yes—
307C2×C4×Q8C22×C1112yes—
308C2×C4×Q8C22×C1111yescharacteristic
309C2×C4×Q8C22×C1111yescharacteristic
310C2×C4×Q8C22×C1112yes—
311C2×C4×Q8C22×C1111yescharacteristic
312C2×C4×Q8C22×C1111yescharacteristic
313C2×C4×Q8C22×C1112yes—
314C2×C4×Q8C22×C1112yes—
315#391C22×C1112yes—
316#391C22×C1112yes—
317#391C22×C1112yes—
318#391C22×C1112yes—
319#391C22×C1111yescharacteristic
320#391C22×C1111yescharacteristic
321#389C22×C1111yescharacteristic
322#389C22×C1112yes—
323#389C22×C1112yes—
324#389C22×C1114yes—
325#389C22×C1112yes—
326#389C22×C1111yescharacteristic
327#387C22×C1114yes—
328#387C22×C1114yes—
329#387C22×C1114yes—
330#387C22×C1114yes—
331#387C22×C1114yes—
332#387C22×C1112yes—
333#387C22×C1114yes—
334#387C22×C1114yes—
335#387C22×C1114yes—
336#387C22×C1114yes—
337#387C22×C1114yes—
338#387C22×C1114yes—
339#387C22×C1112yes—
340#384C22×C1111yescharacteristic
341#383C22×C1114yes—
342#382C22×C1112yes—
343#382C22×C1112yes—
344C4×C4⋊C4C22×C1114yes—
345C4×C4⋊C4C22×C1112yes—
346C4×C4⋊C4C22×C1112yes—
347C4×C4⋊C4C22×C1114yes—
348C4×C4⋊C4C22×C1112yes—
349C4×C4⋊C4C22×C1112yes—
350C4×C4⋊C4C22×C1112yes—
351C4×C4⋊C4C22×C1114yes—
352C4×C4⋊C4C22×C1112yes—
353C4×C4⋊C4C22×C1111yescharacteristic
354C4×C4⋊C4C22×C1112yes—
355C4×C4⋊C4C22×C1111yescharacteristic
356C4×C4⋊C4C22×C1112yes—
357C4×C4⋊C4C22×C1111yescharacteristic
358C4×C4⋊C4C22×C1112yes—
359C4×C4⋊C4C22×C1112yes—
360C4×C4⋊C4C22×C1114yes—
361C4×C4⋊C4C22×C1112yes—
362C4×C4⋊C4C22×C1111yescharacteristic
363#376C22×C1112yes—
364#376C22×C1114yes—
365#376C22×C1114yes—
366C43C22×C1112yes—
367C43C22×C1111yescharacteristic
368C22×C11C24×C411yescharacteristic
369C22×C11C22×#4111yescharacteristic
370C22×C11C22×#4111yescharacteristic
371C22×C11C2×2−1+411yescharacteristic
372C22×C11C2×2−1+411yescharacteristic
373C22×C11C2×2−1+411yescharacteristic
374C22×C11#58511yescharacteristic
375C4×C11—28no—
376C4×C11—24no—
377C4×C11—24no—
378C4×C11—24no—
379C4×C11—22no—
380C4×C11—24no—
381C4×C11—22no—
382C4×C11—22no—
383C4×C11—24no—
384C4×C11—22no—
385C4×C11—44no—
386C4×C11—42no—
387C4×C11—41no—
388C4×C11—42no—
389C4×C11—42no—
390C4×C11C4×#4114yes—
391C4×C11#51914yes—
392C22×Q8C23×C1112yes—
393C22×Q8C23×C1111yescharacteristic
394C22×Q8C23×C1111yescharacteristic
395C4⋊Q8C2×C4×C1118yes—
396C4⋊Q8C2×C4×C11116yes—
397#125C2×C4×C11116yes—
398#125C2×C4×C11132yes—
399C4×Q8—24no—
400C4×Q8—28no—
401C4×Q8—28no—
402C4×Q8—24no—
403C4×Q8C2×C4×C11116yes—
404C4×Q8C2×C4×C1118yes—
405C4×Q8C2×C4×C11116yes—
406C4×Q8C2×C4×C1118yes—
407C2×C4⋊C4C23×C1111yescharacteristic
408C2×C4⋊C4C23×C1112yes—
409C2×C4⋊C4C23×C1112yes—
410C2×C4⋊C4C23×C1114yes—
411C2×C4⋊C4C23×C1112yes—
412C2×C4⋊C4C23×C1114yes—
413C2×C4⋊C4C23×C1111yescharacteristic
414C2×C4⋊C4C23×C1112yes—
415C2×C4⋊C4C23×C1112yes—
416C2×C4⋊C4C23×C1111yescharacteristic
417C2×C4⋊C4C23×C1112yes—
418C2×C4⋊C4C23×C1112yes—
419C2×C4⋊C4C23×C1111yescharacteristic
420C2×C4⋊C4C23×C1112yes—
421C2×C4⋊C4C23×C1114yes—
422C2×C4⋊C4C23×C1111yescharacteristic
423C2×C4⋊C4C23×C1112yes—
424C2×C4⋊C4C23×C1112yes—
425C2×C4⋊C4C23×C1114yes—
426C2×C4⋊C4C23×C1114yes—
427C2×C4⋊C4C23×C1112yes—
428C2×C4⋊C4C23×C1111yescharacteristic
429C2×C42C23×C1112yes—
430C2×C42C23×C1111yescharacteristic
431C2×C42C23×C1112yes—
432C2×C42C23×C1114yes—
433C2×C42C23×C1114yes—
434C2×C42C23×C1112yes—
435C2×C42C23×C1111yescharacteristic
436C2×C42C23×C1112yes—
437C2×C42C23×C1111yescharacteristic
438C2×C42C23×C1112yes—
439C2×C42C23×C1111yescharacteristic
440C2×C42C23×C1112yes—
441C2×C42C23×C1111yescharacteristic
442C2×C42C23×C1114yes—
443C2×C42C23×C1114yes—
444C2×C42C23×C1112yes—
445C2×C42C23×C1114yes—
446C2×C42C23×C1111yescharacteristic
447C2×C42C23×C1112yes—
448C2×C42C23×C1111yescharacteristic
449#95C23×C1112yes—
450#95C23×C1112yes—
451#95C23×C1112yes—
452#95C23×C1114yes—
453#95C23×C1112yes—
454#95C23×C1112yes—
455#95C23×C1112yes—
456#95C23×C1114yes—
457#95C23×C1114yes—
458#95C23×C1114yes—
459#95C23×C1114yes—
460#95C23×C1112yes—
461#95C23×C1112yes—
462#95C23×C1114yes—
463#95C23×C1114yes—
464#95C23×C1112yes—
465#95C23×C1114yes—
466#95C23×C1114yes—
467#95C23×C1112yes—
468#95C23×C1114yes—
469C2×C11C2×C4×#4111yescharacteristic
470C2×C11C2×#51911yescharacteristic
471C2×C11C4×2−1+411yescharacteristic
472C2×C11#350711yescharacteristic
473C2×C11#350911yescharacteristic
474C2×C11#351511yescharacteristic
475C2×C11#352311yescharacteristic
476C2×Q8—22no—
477C2×Q8—24no—
478C2×Q8—24no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8C22×C4×C1114yes—
483C2×Q8C22×C4×C1114yes—
484C2×Q8C22×C4×C1118yes—
485C22×C4C24×C1112yes—
486C22×C4C24×C1112yes—
487C22×C4C24×C1111yescharacteristic
488C22×C4C24×C1112yes—
489C22×C4C24×C1114yes—
490C22×C4C24×C1112yes—
491C22×C4C24×C1112yes—
492C22×C4C24×C1111yescharacteristic
493C22×C4C24×C1112yes—
494C22×C4C24×C1114yes—
495C22×C4C24×C1112yes—
496C22×C4C24×C1111yescharacteristic
497C22×C4C24×C1112yes—
498C22×C4C24×C1111yescharacteristic
499C22×C4C24×C1111yescharacteristic
500C22×C4C24×C1111yescharacteristic
501C22×C4C24×C1111yescharacteristic
502C4⋊C4—24no—
503C4⋊C4—24no—
504C4⋊C4—28no—
505C4⋊C4—28no—
506C4⋊C4—22no—
507C4⋊C4—24no—
508C4⋊C4—24no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—24no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4C22×C4×C1114yes—
515C4⋊C4C22×C4×C1118yes—
516C4⋊C4C22×C4×C11116yes—
517C4⋊C4C22×C4×C1118yes—
518C4⋊C4C22×C4×C1114yes—
519C4⋊C4C22×C4×C11116yes—
520C4⋊C4C22×C4×C1118yes—
521C4⋊C4C22×C4×C11116yes—
522C4⋊C4C22×C4×C1118yes—
523C4⋊C4C11×#4114yes—
524C42—24no—
525C42—22no—
526C42—28no—
527C42—28no—
528C42—24no—
529C42—24no—
530C42—22no—
531C42—22no—
532C42—24no—
533C42—22no—
534C42—24no—
535C42—42no—
536C42—44no—
537C42—41no—
538C42—44no—
539C42C22×C4×C11116yes—
540C42C22×C4×C1118yes—
541C42C22×C4×C1118yes—
542C42C22×C4×C1114yes—
543C42C11×#4114yes—
544C11#3432811yescharacteristic, direct product factor, Sylow
545C23C25×C1111yescharacteristic
546Q8—28no—
547Q8—216no—
548Q8—28no—
549C2×C4—21no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4C23×C4×C1114yes—
585C2×C4C23×C4×C1114yes—
586C2×C4C23×C4×C1112yes—
587C2×C4C23×C4×C1114yes—
588C2×C4C23×C4×C1118yes—
589C2×C4C23×C4×C1114yes—
590C2×C4C23×C4×C1112yes—
591C2×C4C23×C4×C1112yes—
592C2×C4C2×C11×#4112yes—
593C2×C4C2×C11×#4114yes—
594C2×C4C2×C11×#4112yes—
595C2×C4C2×C11×#4112yes—
596C2×C4C2×C11×#4112yes—
597C2×C4C11×2−1+412yes—
598C2×C4C11×2−1+412yes—
599C2×C4C11×2−1+412yes—
600C22C24×C4×C1111yescharacteristic
601C22C22×C11×#4111yescharacteristic
602C22C22×C11×#4111yescharacteristic
603C22C2×C11×2−1+411yescharacteristic
604C22C2×C11×2−1+411yescharacteristic
605C22C2×C11×2−1+411yescharacteristic
606C22C11×#58511yescharacteristic
607C4—28no—
608C4—24no—
609C4—24no—
610C4—24no—
611C4—22no—
612C4—24no—
613C4—22no—
614C4—22no—
615C4—24no—
616C4—22no—
617C4—44no—
618C4—42no—
619C4—41no—
620C4—42no—
621C4—42no—
622C4C4×C11×#4114yes—
623C4C11×#51914yes—
624C2C2×C4×C11×#4111yescharacteristic
625C2C2×C11×#51911yescharacteristic
626C2C4×C11×2−1+411yescharacteristic
627C2C11×#350711yescharacteristic
628C2C11×#350911yescharacteristic
629C2C11×#351511yescharacteristic
630C2C11×#352311yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
18. C11×#557C4semidirect
161. #34328C11direct (N × H)
302. #557C4×C11semidirect
544. C11#34328direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5572
C11×#23712
C11×#23702
C11×#23652
C11×#23562
C11×#23552
C11×#23362
C11×#23272
C4×C11×C4⋊Q82
C4×C11×#1252
C11×#22952
C11×#22762
C42×Q8×C112
#3432811