Finite Group Databasebeta

← C11×#19214 #14596407

Subgroups — C11×#19214 #14596407

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3209C211yesmaximal, characteristic, complemented
2C11×#3208C211yesmaximal, characteristic
3C2×C11×#486C211yesmaximal, characteristic
4C11×#2960C211yesmaximal, characteristic, complemented
5C11×#1702C214yesmaximal, complemented
6C11×#1682C214yesmaximal, complemented
7C11×#1564C211yesmaximal, characteristic, complemented
8C11×#1549C211yesmaximal, characteristic, complemented
9C11×#1545C211yesmaximal, characteristic
10C11×#533C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#127C2211yescharacteristic
13C11×#494—21no—
14C11×#492—21no—
15C11×#487—21no—
16C11×#486—21no—
17C11×#486—21no—
18C11×#486—21no—
19C11×#486C2212yes—
20C11×#486C2212yes—
21C11×#462C2214yescomplemented
22C11×#460C2214yes—
23C11×#451—22no—
24C11×#450—22no—
25C11×#446—21no—
26C11×#446C2212yescomplemented
27C8×Q8×C11—21no—
28C8×Q8×C11C2212yescomplemented
29C11×#431C2211yescharacteristic
30C11×#431C2211yescharacteristic
31C11×#424—21no—
32C11×#423C2211yescharacteristic
33C2×C11×#102—21no—
34C2×C11×#102—21no—
35C11×#405—21no—
36C2×C4×C8×C11C2211yescharacteristic
37C11×#335C2212yescomplemented
38C11×#334C2212yescomplemented
39C11×#332C2214yescomplemented
40C11×#331C2214yes—
41C22×Q8×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C2×C11×Q16—24no—
46C2×C11×SD16—24no—
47C2×C11×M16—21no—
48C22×C8×C11D411yescharacteristic
49C22×C8×C11D411yescharacteristic
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8C2312yes—
56C11×#127—21no—
57C11×#127—21no—
58C11×#127—21no—
59C11×#127C2312yes—
60C11×#125—21no—
61C11×C22⋊Q8—21no—
62C11×C22⋊Q8D412yes—
63C4×Q8×C11—21no—
64C4×Q8×C11C2312yes—
65C11×#117—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C42×C11C2311yescharacteristic
69C11×C4⋊C8—22no—
70C11×C4⋊C8—22no—
71C11×C4⋊C8—21no—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×C4⋊C8C2312yes—
75C11×#103—24no—
76C11×#102—22no—
77C11×#102—22no—
78C11×#102—22no—
79C11×#102—22no—
80C11×#102—24no—
81C11×C22⋊C8—21no—
82C11×C22⋊C8—21no—
83C11×#97—22no—
84C4×C8×C11—22no—
85C4×C8×C11—21no—
86C4×C8×C11—21no—
87C4×C8×C11D411yescharacteristic
88C4×C8×C11D411yescharacteristic
89C4×C8×C11C2311yescharacteristic
90C4×C8×C11C2311yescharacteristic
91#19214C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—41no—
93C2×Q8×C11—21no—
94C2×Q8×C11—22no—
95C2×Q8×C11—41no—
96C2×Q8×C11—82no—
97C2×Q8×C11C2×D412yes—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C2×D4×C11—41no—
104C2×D4×C11—42no—
105C2×D4×C11—42no—
106C2×D4×C11—82no—
107C2×D4×C11—82no—
108C22×C4×C11—41no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C11×Q16—84no—
113C11×SD16—84no—
114C11×M16—42no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4C2×D412yes—
134C11×C22⋊C4—22no—
135C42×C11—22no—
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139C42×C11C2411yescharacteristic
140#3209C2×C1111yescharacteristic, complemented
141#3208C2×C1111yescharacteristic
142C2×#486C2×C1111yescharacteristic
143#2960C2×C1111yescharacteristic, complemented
144#1702C2×C1114yescomplemented
145#1682C2×C1114yescomplemented
146#1564C2×C1111yescharacteristic, complemented
147#1549C2×C1111yescharacteristic, complemented
148#1545C2×C1111yescharacteristic
149C23×C11—42no—
150C23×C11—82no—
151C23×C11—82no—
152C23×C11—82no—
153C23×C11#12111yescharacteristic
154Q8×C11—24no—
155Q8×C11—42no—
156Q8×C11—44no—
157Q8×C11—82no—
158D4×C11—42no—
159D4×C11—42no—
160D4×C11—44no—
161D4×C11—82no—
162D4×C11—82no—
163D4×C11—82no—
164D4×C11—82no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—42no—
170C2×C4×C11—82no—
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#13512yes—
175C2×C4×C11#13712yes—
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C8×C11—21no—
180C8×C11—21no—
181C8×C11—21no—
182C8×C11—21no—
183C8×C11—42no—
184C8×C11—42no—
185C8×C11—42no—
186#533C22×C1111yescharacteristic
187C2×C4⋊Q8C22×C1111yescharacteristic
188C2×#127C22×C1111yescharacteristic
189#494—21no—
190#492—21no—
191#487—21no—
192#486—21no—
193#486—21no—
194#486—21no—
195#486C22×C1112yes—
196#486C22×C1112yes—
197#462C22×C1114yescomplemented
198#460C22×C1114yes—
199#451—22no—
200#450—22no—
201#446—21no—
202#446C22×C1112yescomplemented
203C8×Q8—21no—
204C8×Q8C22×C1112yescomplemented
205#431C22×C1111yescharacteristic
206#431C22×C1111yescharacteristic
207#424—21no—
208#423C22×C1111yescharacteristic
209C2×#102—21no—
210C2×#102—21no—
211#405—21no—
212C2×C4×C8C22×C1111yescharacteristic
213#335C22×C1112yescomplemented
214#334C22×C1112yescomplemented
215#332C22×C1114yescomplemented
216#331C22×C1114yes—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11—164no—
223C22×C11#46412yes—
224C22×C11C2×#12111yescharacteristic
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—42no—
228C4×C11—42no—
229C4×C11—82no—
230C4×C11#46412yes—
231C4×C11#47112yes—
232C4×C11C2×#13511yescharacteristic
233C4×C11C2×#13711yescharacteristic
234C4×C11#57612yes—
235C22×Q8—21no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4—21no—
239C2×Q16—24no—
240C2×SD16—24no—
241C2×M16—21no—
242C22×C8D4×C1111yescharacteristic
243C22×C8D4×C1111yescharacteristic
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8D4×C1111yescharacteristic
248C4⋊Q8D4×C1111yescharacteristic
249C4⋊Q8C23×C1112yes—
250#127—21no—
251#127—21no—
252#127—21no—
253#127C23×C1112yes—
254#125—21no—
255C22⋊Q8—21no—
256C22⋊Q8D4×C1112yes—
257C4×Q8—21no—
258C4×Q8C23×C1112yes—
259#117—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C42C23×C1111yescharacteristic
263C4⋊C8—22no—
264C4⋊C8—22no—
265C4⋊C8—21no—
266C4⋊C8C23×C1112yes—
267C4⋊C8C23×C1112yes—
268C4⋊C8C23×C1112yes—
269#103—24no—
270#102—22no—
271#102—22no—
272#102—22no—
273#102—22no—
274#102—24no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277#97—22no—
278C4×C8—22no—
279C4×C8—21no—
280C4×C8—21no—
281C4×C8D4×C1111yescharacteristic
282C4×C8D4×C1111yescharacteristic
283C4×C8C23×C1111yescharacteristic
284C4×C8C23×C1111yescharacteristic
285C2×C11—22no—
286C2×C11—162no—
287C2×C11C2×#46411yescharacteristic
288C2×C11#305811yescharacteristic
289C2×C11C2×#47111yescharacteristic
290C24—41no—
291C2×Q8—21no—
292C2×Q8—22no—
293C2×Q8—41no—
294C2×Q8—82no—
295C2×Q8C2×D4×C1112yes—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—42no—
303C2×D4—42no—
304C2×D4—82no—
305C2×D4—82no—
306C22×C4—41no—
307C22×C4C2×D4×C1111yescharacteristic
308C22×C4C2×D4×C1111yescharacteristic
309C22×C4C11×#4111yescharacteristic
310Q16—84no—
311SD16—84no—
312M16—42no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8C2×D4×C1111yescharacteristic
319C2×C8C2×D4×C1111yescharacteristic
320C2×C8C2×D4×C1111yescharacteristic
321C2×C8C2×D4×C1111yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4C2×D4×C1112yes—
332C22⋊C4—22no—
333C42—22no—
334C42C2×D4×C1111yescharacteristic
335C42C2×D4×C1111yescharacteristic
336C42C11×#4111yescharacteristic
337C42C24×C1111yescharacteristic
338C11#1921411yescharacteristic, direct product factor, Sylow
339C23—42no—
340C23—82no—
341C23—82no—
342C23—82no—
343C23C11×#12111yescharacteristic
344Q8—24no—
345Q8—42no—
346Q8—44no—
347Q8—82no—
348D4—42no—
349D4—42no—
350D4—44no—
351D4—82no—
352D4—82no—
353D4—82no—
354D4—82no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—42no—
360C2×C4—82no—
361C2×C4C11×#12111yescharacteristic
362C2×C4C11×#12111yescharacteristic
363C2×C4C11×#12111yescharacteristic
364C2×C4C11×#13512yes—
365C2×C4C11×#13712yes—
366C2×C4C22×D4×C1111yescharacteristic
367C2×C4C22×D4×C1111yescharacteristic
368C2×C4C2×C11×#4111yescharacteristic
369C8—21no—
370C8—21no—
371C8—21no—
372C8—21no—
373C8—42no—
374C8—42no—
375C8—42no—
376C22—21no—
377C22—21no—
378C22—82no—
379C22—82no—
380C22—82no—
381C22—164no—
382C22C11×#46412yes—
383C22C2×C11×#12111yescharacteristic
384C4—21no—
385C4—21no—
386C4—42no—
387C4—42no—
388C4—82no—
389C4C11×#46412yes—
390C4C11×#47112yes—
391C4C2×C11×#13511yescharacteristic
392C4C2×C11×#13711yescharacteristic
393C4C11×#57612yes—
394C2—22no—
395C2—162no—
396C2C2×C11×#46411yescharacteristic
397C2C11×#305811yescharacteristic
398C2C2×C11×#47111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3209C2semidirect
4. C11×#2960C2semidirect
5. C11×#1702C2semidirect
6. C11×#1682C2semidirect
7. C11×#1564C2semidirect
8. C11×#1549C2semidirect
21. C11×#462C22semidirect
26. C11×#446C22semidirect
28. C8×Q8×C11C22semidirect
37. C11×#335C22semidirect
38. C11×#334C22semidirect
39. C11×#332C22semidirect
91. #19214C11direct (N × H)
140. #3209C2×C11semidirect
143. #2960C2×C11semidirect
144. #1702C2×C11semidirect
145. #1682C2×C11semidirect
146. #1564C2×C11semidirect
147. #1549C2×C11semidirect
197. #462C22×C11semidirect
202. #446C22×C11semidirect
204. C8×Q8C22×C11semidirect
213. #335C22×C11semidirect
214. #334C22×C11semidirect
215. #332C22×C11semidirect
338. C11#19214direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32092
C11×#32082
C2×C11×#4862
C11×#29602
C11×#17022
C11×#16822
C11×#15642
C11×#15492
C11×#15452
#1921411