Finite Group Databasebeta

← C11×#3321 #13066159

Subgroups — C11×#3321 #13066159

Order 1408.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#555C211yesmaximal, characteristic, complemented
2C11×#548C211yesmaximal, characteristic, complemented
3C11×#489C211yesmaximal, characteristic, complemented
4C11×#485C211yesmaximal, characteristic, complemented
5C11×#482C211yesmaximal, characteristic, complemented
6C11×#475C211yesmaximal, characteristic, complemented
7C11×#469C211yesmaximal, characteristic, complemented
8C11×#465C211yesmaximal, characteristic, complemented
9C11×#463C211yesmaximal, characteristic, complemented
10C11×#449C211yesmaximal, characteristic, complemented
11C11×#448C211yesmaximal, characteristic, complemented
12C11×#440C211yesmaximal, characteristic, complemented
13C11×#435C211yesmaximal, characteristic, complemented
14C11×#419C211yesmaximal, characteristic, complemented
15C11×#416C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C2×C11×D8C2211yescharacteristic
21C2×C11×M16C2211yescharacteristic
22C22×C8×C11C2211yescharacteristic
23C11×C4⋊Q8C2211yescharacteristic
24C11×#124—21no—
25C11×#124—21no—
26C11×#124—21no—
27C11×#124C2211yescharacteristic
28C11×C22⋊Q8—21no—
29C11×C22⋊Q8C2211yescharacteristic
30C11×#121—21no—
31C11×#121—21no—
32C11×#121C2211yescharacteristic
33C11×#121C2211yescharacteristic
34C11×#121C2211yescharacteristic
35C4×Q8×C11C2211yescharacteristic
36C4×D4×C11—21no—
37C4×D4×C11C2211yescharacteristic
38C4×D4×C11C2211yescharacteristic
39C11×#117—21no—
40C11×#117C2211yescharacteristic
41C11×#117C2211yescharacteristic
42C11×#107C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C11×#106C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic
46C11×#103C2211yescharacteristic
47C11×#103C2211yescharacteristic
48C11×#103C2211yescharacteristic
49C11×#103C2211yescharacteristic
50C11×#103C2211yescharacteristic
51C11×#103C2211yescharacteristic
52C11×#102C2211yescharacteristic
53C11×#102C2211yescharacteristic
54C11×#102C2211yescharacteristic
55C11×#102C2211yescharacteristic
56C11×C22⋊C8C2211yescharacteristic
57C11×C22⋊C8C2211yescharacteristic
58C11×#97C2211yescharacteristic
59C11×#41—22no—
60C11×#41—41no—
61C2×Q8×C11—21no—
62C2×Q8×C11—21no—
63C2×Q8×C11—22no—
64C2×Q8×C11—41no—
65C2×Q8×C11C2311yescharacteristic
66C2×Q8×C11C2311yescharacteristic
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11D411yescharacteristic
72C2×D4×C11C2311yescharacteristic
73C2×D4×C11C2311yescharacteristic
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11C2311yescharacteristic
78C22×C4×C11C2311yescharacteristic
79C11×SD16—22no—
80C11×SD16—41no—
81C11×D8—41no—
82C11×M16—41no—
83C2×C8×C11—41no—
84C2×C8×C11C2311yescharacteristic
85C2×C8×C11C2311yescharacteristic
86C2×C8×C11C2311yescharacteristic
87C2×C8×C11C2311yescharacteristic
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4D411yescharacteristic
92C11×C4⋊C4C2311yescharacteristic
93C11×C4⋊C4C2311yescharacteristic
94C11×C4⋊C4C2311yescharacteristic
95C11×C4⋊C4C2311yescharacteristic
96C11×C22⋊C4—21no—
97C11×C22⋊C4—21no—
98C11×C22⋊C4—21no—
99C11×C22⋊C4—21no—
100C11×C22⋊C4—21no—
101C11×C22⋊C4—21no—
102C11×C22⋊C4—21no—
103C11×C22⋊C4—21no—
104C11×C22⋊C4—21no—
105C11×C22⋊C4D411yescharacteristic
106C11×C22⋊C4D411yescharacteristic
107C42×C11—21no—
108C42×C11—21no—
109C42×C11—21no—
110C42×C11C2311yescharacteristic
111#3321C1111yesmaximal, characteristic, direct product factor, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11C2×D411yescharacteristic
115C23×C11C2×D411yescharacteristic
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11—21no—
119Q8×C11—42no—
120Q8×C11—81no—
121Q8×C11#4112yes—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—21no—
125D4×C11—21no—
126D4×C11—41no—
127D4×C11—42no—
128D4×C11—42no—
129D4×C11—81no—
130D4×C11—81no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11C2×D411yescharacteristic
145C2×C4×C11C2×D411yescharacteristic
146C2×C4×C11C2×D411yescharacteristic
147C2×C4×C11C2×D411yescharacteristic
148C2×C4×C11C2411yescharacteristic
149C8×C11—21no—
150C8×C11—21no—
151C8×C11—21no—
152C8×C11—21no—
153#555C2×C1111yescharacteristic, complemented
154#548C2×C1111yescharacteristic, complemented
155#489C2×C1111yescharacteristic, complemented
156#485C2×C1111yescharacteristic, complemented
157#482C2×C1111yescharacteristic, complemented
158#475C2×C1111yescharacteristic, complemented
159#469C2×C1111yescharacteristic, complemented
160#465C2×C1111yescharacteristic, complemented
161#463C2×C1111yescharacteristic, complemented
162#449C2×C1111yescharacteristic, complemented
163#448C2×C1111yescharacteristic, complemented
164#440C2×C1111yescharacteristic, complemented
165#435C2×C1111yescharacteristic, complemented
166#419C2×C1111yescharacteristic, complemented
167#416C2×C1111yescharacteristic, complemented
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11C22×D411yescharacteristic
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—22no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11C2×#4111yescharacteristic
192C4×C11H(5,𝔽2)11yescharacteristic
193C2×#41C22×C1111yescharacteristic
194C22×Q8C22×C1111yescharacteristic
195C2×SD16C22×C1111yescharacteristic
196C2×SD16C22×C1111yescharacteristic
197C2×D8C22×C1111yescharacteristic
198C2×M16C22×C1111yescharacteristic
199C22×C8C22×C1111yescharacteristic
200C4⋊Q8C22×C1111yescharacteristic
201#124—21no—
202#124—21no—
203#124—21no—
204#124C22×C1111yescharacteristic
205C22⋊Q8—21no—
206C22⋊Q8C22×C1111yescharacteristic
207#121—21no—
208#121—21no—
209#121C22×C1111yescharacteristic
210#121C22×C1111yescharacteristic
211#121C22×C1111yescharacteristic
212C4×Q8C22×C1111yescharacteristic
213C4×D4—21no—
214C4×D4C22×C1111yescharacteristic
215C4×D4C22×C1111yescharacteristic
216#117—21no—
217#117C22×C1111yescharacteristic
218#117C22×C1111yescharacteristic
219#107C22×C1111yescharacteristic
220#106C22×C1111yescharacteristic
221#106C22×C1111yescharacteristic
222C4⋊C8C22×C1111yescharacteristic
223#103C22×C1111yescharacteristic
224#103C22×C1111yescharacteristic
225#103C22×C1111yescharacteristic
226#103C22×C1111yescharacteristic
227#103C22×C1111yescharacteristic
228#103C22×C1111yescharacteristic
229#102C22×C1111yescharacteristic
230#102C22×C1111yescharacteristic
231#102C22×C1111yescharacteristic
232#102C22×C1111yescharacteristic
233C22⋊C8C22×C1111yescharacteristic
234C22⋊C8C22×C1111yescharacteristic
235#97C22×C1111yescharacteristic
236C2×C11—41no—
237C2×C11—41no—
238C2×C11—81no—
239C2×C11—81no—
240C2×C11#54611yescharacteristic
241C2×C11#57511yescharacteristic
242C2×C11#57711yescharacteristic
243#41—22no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C23×C1111yescharacteristic
250C2×Q8C23×C1111yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4D4×C1111yescharacteristic
256C2×D4C23×C1111yescharacteristic
257C2×D4C23×C1111yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4C23×C1111yescharacteristic
262C22×C4C23×C1111yescharacteristic
263SD16—22no—
264SD16—41no—
265D8—41no—
266M16—41no—
267C2×C8—41no—
268C2×C8C23×C1111yescharacteristic
269C2×C8C23×C1111yescharacteristic
270C2×C8C23×C1111yescharacteristic
271C2×C8C23×C1111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4D4×C1111yescharacteristic
276C4⋊C4C23×C1111yescharacteristic
277C4⋊C4C23×C1111yescharacteristic
278C4⋊C4C23×C1111yescharacteristic
279C4⋊C4C23×C1111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4D4×C1111yescharacteristic
290C22⋊C4D4×C1111yescharacteristic
291C42—21no—
292C42—21no—
293C42—21no—
294C42C23×C1111yescharacteristic
295C11#332111yescharacteristic, direct product factor, Sylow
296C23—21no—
297C23—21no—
298C23C2×D4×C1111yescharacteristic
299C23C2×D4×C1111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8—81no—
305Q8C11×#4112yes—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—21no—
310D4—41no—
311D4—42no—
312D4—42no—
313D4—81no—
314D4—81no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4C2×D4×C1111yescharacteristic
329C2×C4C2×D4×C1111yescharacteristic
330C2×C4C2×D4×C1111yescharacteristic
331C2×C4C2×D4×C1111yescharacteristic
332C2×C4C24×C1111yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22C22×D4×C1111yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4C2×C11×#4111yescharacteristic
361C4C11×H(5,𝔽2)11yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—81no—
366C2C11×#54611yescharacteristic
367C2C11×#57511yescharacteristic
368C2C11×#57711yescharacteristic
subgroupG/H
center, socleC22×C11C22×D4
commutator, Frattini, cosocleC2×C4C24×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#555C2semidirect
2. C11×#548C2semidirect
3. C11×#489C2semidirect
4. C11×#485C2semidirect
5. C11×#482C2semidirect
6. C11×#475C2semidirect
7. C11×#469C2semidirect
8. C11×#465C2semidirect
9. C11×#463C2semidirect
10. C11×#449C2semidirect
11. C11×#448C2semidirect
12. C11×#440C2semidirect
13. C11×#435C2semidirect
14. C11×#419C2semidirect
15. C11×#416C2semidirect
111. #3321C11direct (N × H)
153. #555C2×C11semidirect
154. #548C2×C11semidirect
155. #489C2×C11semidirect
156. #485C2×C11semidirect
157. #482C2×C11semidirect
158. #475C2×C11semidirect
159. #469C2×C11semidirect
160. #465C2×C11semidirect
161. #463C2×C11semidirect
162. #449C2×C11semidirect
163. #448C2×C11semidirect
164. #440C2×C11semidirect
165. #435C2×C11semidirect
166. #419C2×C11semidirect
167. #416C2×C11semidirect
295. C11#3321direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5552
C11×#5482
C11×#4892
C11×#4852
C11×#4822
C11×#4752
C11×#4692
C11×#4652
C11×#4632
C11×#4492
C11×#4482
C11×#4402
C11×#4352
C11×#4192
C11×#4162
#332111