Finite Group Databasebeta

← C11×#22841 #14600034

Subgroups — C11×#22841 #14600034

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2290C211yesmaximal, characteristic
2C11×#1955C211yesmaximal, characteristic
3C11×#1954C211yesmaximal, characteristic
4C11×#1924C211yesmaximal, characteristic, complemented
5C11×#1924C211yesmaximal, characteristic, complemented
6C11×#1924C211yesmaximal, characteristic, complemented
7C11×#1923C211yesmaximal, characteristic, complemented
8C11×#1832C211yesmaximal, characteristic, complemented
9C11×#1818C211yesmaximal, characteristic, complemented
10C11×#1817C211yesmaximal, characteristic, complemented
11C11×#1771C211yesmaximal, characteristic, complemented
12C11×#1770C211yesmaximal, characteristic, complemented
13C11×#1768C211yesmaximal, characteristic, complemented
14C11×#1750C211yesmaximal, characteristic, complemented
15C11×#1749C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C11×#97C2211yescharacteristic
32C2×C11×#97C2211yescharacteristic
33C2×C11×#97C2211yescharacteristic
34C2×C11×#97C2211yescharacteristic
35C2×C4×C8×C11C2211yescharacteristic
36C2×C4×C8×C11C2211yescharacteristic
37C11×#388C411yescharacteristic
38C11×#388C411yescharacteristic
39C11×#387C411yescharacteristic
40C11×#387C411yescharacteristic
41C11×#386C411yescharacteristic
42C11×#386C411yescharacteristic
43C11×#385C411yescharacteristic
44C11×#385C411yescharacteristic
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C22⋊C4C2211yescharacteristic
47C4×C11×C22⋊C4C2211yescharacteristic
48C11×#376C2211yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×D4×C11C2×C411yescharacteristic
60C23×C4×C11C2×C411yescharacteristic
61C23×C4×C11C2×C411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C11×#117—41no—
75C11×#117—41no—
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C4⋊C4C2×C411yescharacteristic
80C2×C11×C4⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊C4C2×C411yescharacteristic
83C2×C11×C22⋊C4C2×C411yescharacteristic
84C2×C11×C22⋊C4C2×C411yescharacteristic
85C2×C11×C22⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4C2×C411yescharacteristic
87C2×C11×C22⋊C4C2×C411yescharacteristic
88C2×C11×C22⋊C4C2×C411yescharacteristic
89C2×C42×C11—41no—
90C2×C42×C11—41no—
91C2×C42×C11C2×C411yescharacteristic
92C2×C42×C11C2×C411yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C11×C4⋊C8—22no—
99C11×C4⋊C8—22no—
100C11×C4⋊C8—22no—
101C11×C4⋊C8—22no—
102C11×C22⋊C8—22no—
103C11×C22⋊C8—22no—
104C11×C22⋊C8—22no—
105C11×C22⋊C8—22no—
106C11×C22⋊C8—41no—
107C11×C22⋊C8—41no—
108C11×C22⋊C8—41no—
109C11×C22⋊C8—41no—
110C11×#97—22no—
111C11×#97—41no—
112C11×#97—41no—
113C11×#97—41no—
114C4×C8×C11—22no—
115C4×C8×C11—41no—
116C11×#95C2×C411yescharacteristic
117C11×#95C2×C411yescharacteristic
118C11×#95C2×C411yescharacteristic
119C11×#95C2×C411yescharacteristic
120C11×#95C2×C411yescharacteristic
121C11×#95C2×C411yescharacteristic
122C11×#95C2×C411yescharacteristic
123C11×#95C2×C411yescharacteristic
124C11×#95C2×C411yescharacteristic
125C11×#95C2×C411yescharacteristic
126#22841C1111yesmaximal, characteristic, direct product factor, Sylow
127C24×C11C22×C411yescharacteristic
128C24×C11C22×C411yescharacteristic
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—41no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
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#4112yes—
186C2×C8×C11#4112yes—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—41no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4—41no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—41no—
196C11×C22⋊C4—41no—
197C11×C22⋊C4—41no—
198C11×C22⋊C4—41no—
199C11×C22⋊C4—41no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11—21no—
208C42×C11—41no—
209C42×C11—41no—
210C42×C11#4112yes—
211C42×C11#4112yes—
212#2290C2×C1111yescharacteristic
213#1955C2×C1111yescharacteristic
214#1954C2×C1111yescharacteristic
215#1924C2×C1111yescharacteristic, complemented
216#1924C2×C1111yescharacteristic, complemented
217#1924C2×C1111yescharacteristic, complemented
218#1923C2×C1111yescharacteristic, complemented
219#1832C2×C1111yescharacteristic, complemented
220#1818C2×C1111yescharacteristic, complemented
221#1817C2×C1111yescharacteristic, complemented
222#1771C2×C1111yescharacteristic, complemented
223#1770C2×C1111yescharacteristic, complemented
224#1768C2×C1111yescharacteristic, complemented
225#1750C2×C1111yescharacteristic, complemented
226#1749C2×C1111yescharacteristic, complemented
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11#13112yes—
241C23×C11C23×C411yescharacteristic
242D4×C11—44no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—44no—
278C2×C4×C11—44no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11#11712yes—
288C2×C4×C11#11712yes—
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×C4×C11H(5,𝔽2)11yescharacteristic
294C2×C4×C11H(5,𝔽2)11yescharacteristic
295C8×C11—22no—
296C8×C11—22no—
297C8×C11—41no—
298C8×C11—41no—
299C8×C11—41no—
300C8×C11—41no—
301C8×C11—41no—
302C8×C11—41no—
303C2×C4×D4C22×C1111yescharacteristic
304C2×#117C22×C1111yescharacteristic
305C22×C42C22×C1111yescharacteristic
306C2×C4⋊C8C22×C1111yescharacteristic
307C2×C4⋊C8C22×C1111yescharacteristic
308C2×C4⋊C8C22×C1111yescharacteristic
309C2×C4⋊C8C22×C1111yescharacteristic
310C2×C22⋊C8C22×C1111yescharacteristic
311C2×C22⋊C8C22×C1111yescharacteristic
312C2×C22⋊C8C22×C1111yescharacteristic
313C2×C22⋊C8C22×C1111yescharacteristic
314C2×C22⋊C8C22×C1111yescharacteristic
315C2×C22⋊C8C22×C1111yescharacteristic
316C2×C22⋊C8C22×C1111yescharacteristic
317C2×C22⋊C8C22×C1111yescharacteristic
318C2×#97C22×C1111yescharacteristic
319C2×#97C22×C1111yescharacteristic
320C2×#97C22×C1111yescharacteristic
321C2×#97C22×C1111yescharacteristic
322C2×C4×C8C22×C1111yescharacteristic
323C2×C4×C8C22×C1111yescharacteristic
324#388C4×C1111yescharacteristic
325#388C4×C1111yescharacteristic
326#387C4×C1111yescharacteristic
327#387C4×C1111yescharacteristic
328#386C4×C1111yescharacteristic
329#386C4×C1111yescharacteristic
330#385C4×C1111yescharacteristic
331#385C4×C1111yescharacteristic
332C4×C4⋊C4C22×C1111yescharacteristic
333C4×C22⋊C4C22×C1111yescharacteristic
334C4×C22⋊C4C22×C1111yescharacteristic
335#376C22×C1111yescharacteristic
336#336C22×C1111yescharacteristic
337#336C22×C1111yescharacteristic
338#336C22×C1111yescharacteristic
339#336C22×C1111yescharacteristic
340#336C22×C1111yescharacteristic
341#336C22×C1111yescharacteristic
342#336C22×C1111yescharacteristic
343#336C22×C1111yescharacteristic
344#336C22×C1111yescharacteristic
345#336C22×C1111yescharacteristic
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11C2×#11711yescharacteristic
361C22×C11C4×#4111yescharacteristic
362C22×C11#51811yescharacteristic
363C22×C11C2×#13111yescharacteristic
364C22×C11#56811yescharacteristic
365C22×C11#56811yescharacteristic
366C22×C11#56811yescharacteristic
367C4×C11—22no—
368C4×C11—22no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11#55311yescharacteristic
380C4×C11#55311yescharacteristic
381C4×C11#55911yescharacteristic
382C4×C11#55911yescharacteristic
383C22×D4C2×C4×C1111yescharacteristic
384C23×C4C2×C4×C1111yescharacteristic
385C23×C4C2×C4×C1111yescharacteristic
386C23×C4C23×C1111yescharacteristic
387C23×C4C23×C1111yescharacteristic
388C22×C8C23×C1111yescharacteristic
389C22×C8C23×C1111yescharacteristic
390C22×C8C23×C1111yescharacteristic
391C22×C8C23×C1111yescharacteristic
392C22×C8C23×C1111yescharacteristic
393C22×C8C23×C1111yescharacteristic
394C22×C8C23×C1111yescharacteristic
395C22×C8C23×C1111yescharacteristic
396C4×D4—22no—
397C4×D4—22no—
398#117—41no—
399#117—41no—
400C2×C4⋊C4C2×C4×C1111yescharacteristic
401C2×C4⋊C4C2×C4×C1111yescharacteristic
402C2×C4⋊C4C2×C4×C1111yescharacteristic
403C2×C4⋊C4C2×C4×C1111yescharacteristic
404C2×C4⋊C4C2×C4×C1111yescharacteristic
405C2×C22⋊C4C2×C4×C1111yescharacteristic
406C2×C22⋊C4C2×C4×C1111yescharacteristic
407C2×C22⋊C4C2×C4×C1111yescharacteristic
408C2×C22⋊C4C2×C4×C1111yescharacteristic
409C2×C22⋊C4C2×C4×C1111yescharacteristic
410C2×C22⋊C4C2×C4×C1111yescharacteristic
411C2×C22⋊C4C2×C4×C1111yescharacteristic
412C2×C22⋊C4C2×C4×C1111yescharacteristic
413C2×C42—41no—
414C2×C42—41no—
415C2×C42C2×C4×C1111yescharacteristic
416C2×C42C2×C4×C1111yescharacteristic
417C2×C42C23×C1111yescharacteristic
418C2×C42C23×C1111yescharacteristic
419C2×C42C23×C1111yescharacteristic
420C2×C42C23×C1111yescharacteristic
421C2×C42C23×C1111yescharacteristic
422C4⋊C8—22no—
423C4⋊C8—22no—
424C4⋊C8—22no—
425C4⋊C8—22no—
426C22⋊C8—22no—
427C22⋊C8—22no—
428C22⋊C8—22no—
429C22⋊C8—22no—
430C22⋊C8—41no—
431C22⋊C8—41no—
432C22⋊C8—41no—
433C22⋊C8—41no—
434#97—22no—
435#97—41no—
436#97—41no—
437#97—41no—
438C4×C8—22no—
439C4×C8—41no—
440#95C2×C4×C1111yescharacteristic
441#95C2×C4×C1111yescharacteristic
442#95C2×C4×C1111yescharacteristic
443#95C2×C4×C1111yescharacteristic
444#95C2×C4×C1111yescharacteristic
445#95C2×C4×C1111yescharacteristic
446#95C2×C4×C1111yescharacteristic
447#95C2×C4×C1111yescharacteristic
448#95C2×C4×C1111yescharacteristic
449#95C2×C4×C1111yescharacteristic
450C2×C11—42no—
451C2×C11—81no—
452C2×C11#235711yescharacteristic
453C2×C11#292311yescharacteristic
454C2×C11#292411yescharacteristic
455C2×C11#296711yescharacteristic
456C2×C11#296811yescharacteristic
457C2×C11#297611yescharacteristic
458C2×C11#297811yescharacteristic
459C24C22×C4×C1111yescharacteristic
460C24C22×C4×C1111yescharacteristic
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—41no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4C22×C4×C1111yescharacteristic
483C22×C4C22×C4×C1111yescharacteristic
484C22×C4C22×C4×C1111yescharacteristic
485C22×C4C22×C4×C1111yescharacteristic
486C22×C4C22×C4×C1111yescharacteristic
487C22×C4C22×C4×C1111yescharacteristic
488C22×C4C22×C4×C1111yescharacteristic
489C22×C4C22×C4×C1111yescharacteristic
490C22×C4C22×C4×C1111yescharacteristic
491C22×C4C22×C4×C1111yescharacteristic
492C22×C4C22×C4×C1111yescharacteristic
493C22×C4C22×C4×C1111yescharacteristic
494C22×C4C24×C1111yescharacteristic
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8C11×#4112yes—
518C2×C8C11×#4112yes—
519C4⋊C4—22no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—41no—
541C42—41no—
542C42C11×#4112yes—
543C42C11×#4112yes—
544C11#2284111yescharacteristic, direct product factor, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23C11×#13112yes—
559C23C23×C4×C1111yescharacteristic
560D4—44no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—44no—
596C2×C4—44no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4C11×#11712yes—
606C2×C4C11×#11712yes—
607C2×C4C2×C11×#4111yescharacteristic
608C2×C4C2×C11×#4111yescharacteristic
609C2×C4C2×C11×#4111yescharacteristic
610C2×C4C2×C11×#4111yescharacteristic
611C2×C4C11×H(5,𝔽2)11yescharacteristic
612C2×C4C11×H(5,𝔽2)11yescharacteristic
613C8—22no—
614C8—22no—
615C8—41no—
616C8—41no—
617C8—41no—
618C8—41no—
619C8—41no—
620C8—41no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×C11×#11711yescharacteristic
636C22C4×C11×#4111yescharacteristic
637C22C11×#51811yescharacteristic
638C22C2×C11×#13111yescharacteristic
639C22C11×#56811yescharacteristic
640C22C11×#56811yescharacteristic
641C22C11×#56811yescharacteristic
642C4—22no—
643C4—22no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4C11×#55311yescharacteristic
655C4C11×#55311yescharacteristic
656C4C11×#55911yescharacteristic
657C4C11×#55911yescharacteristic
658C2—42no—
659C2—81no—
660C2C11×#235711yescharacteristic
661C2C11×#292311yescharacteristic
662C2C11×#292411yescharacteristic
663C2C11×#296711yescharacteristic
664C2C11×#296811yescharacteristic
665C2C11×#297611yescharacteristic
666C2C11×#297811yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC22×D4×C11C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1924C2semidirect
5. C11×#1924C2semidirect
6. C11×#1924C2semidirect
7. C11×#1923C2semidirect
8. C11×#1832C2semidirect
9. C11×#1818C2semidirect
10. C11×#1817C2semidirect
11. C11×#1771C2semidirect
12. C11×#1770C2semidirect
13. C11×#1768C2semidirect
14. C11×#1750C2semidirect
15. C11×#1749C2semidirect
126. #22841C11direct (N × H)
215. #1924C2×C11semidirect
216. #1924C2×C11semidirect
217. #1924C2×C11semidirect
218. #1923C2×C11semidirect
219. #1832C2×C11semidirect
220. #1818C2×C11semidirect
221. #1817C2×C11semidirect
222. #1771C2×C11semidirect
223. #1770C2×C11semidirect
224. #1768C2×C11semidirect
225. #1750C2×C11semidirect
226. #1749C2×C11semidirect
544. C11#22841direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#22902
C11×#19552
C11×#19542
C11×#19242
C11×#19232
C11×#18322
C11×#18182
C11×#18172
C11×#17712
C11×#17702
C11×#17682
C11×#17502
C11×#17492
#2284111