Finite Group Databasebeta

← C11×#3345 #13066183

Subgroups — C11×#3345 #13066183

Order 1408.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#553C211yesmaximal, characteristic, complemented
2C11×#547C211yesmaximal, characteristic, complemented
3C11×#501C211yesmaximal, characteristic, complemented
4C11×#482C211yesmaximal, characteristic, complemented
5C11×#481C211yesmaximal, characteristic, complemented
6C11×#481C211yesmaximal, characteristic, complemented
7C11×#480C211yesmaximal, characteristic, complemented
8C11×#478C211yesmaximal, characteristic, complemented
9C11×#476C211yesmaximal, characteristic, complemented
10C11×#469C211yesmaximal, characteristic, complemented
11C11×#466C211yesmaximal, characteristic, complemented
12C11×#442C211yesmaximal, characteristic, complemented
13C11×#435C211yesmaximal, characteristic, complemented
14C11×#428C211yesmaximal, characteristic, complemented
15C2×C11×#106C211yesmaximal, characteristic, complemented
16C2×C11×#41—21no—
17C2×C11×D8C2211yescharacteristic
18C2×C11×M16C2211yescharacteristic
19C22×C8×C11C2211yescharacteristic
20C11×C4⋊Q8C2211yescharacteristic
21C11×#126—21no—
22C11×#125C2211yescharacteristic
23C11×#123—21no—
24C11×#123—21no—
25C11×#123—21no—
26C11×C22⋊Q8—21no—
27C11×#121—21no—
28C11×#121C2211yescharacteristic
29C11×#121C2211yescharacteristic
30C11×#121C2211yescharacteristic
31C11×#121C2211yescharacteristic
32C4×D4×C11—21no—
33C4×D4×C11C2211yescharacteristic
34C4×D4×C11C2211yescharacteristic
35C4×D4×C11C2211yescharacteristic
36C11×#117C2211yescharacteristic
37C2×C11×C4⋊C4C2211yescharacteristic
38C2×C11×C4⋊C4C2211yescharacteristic
39C2×C11×C4⋊C4C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#107C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C11×#106C2211yescharacteristic
45C11×#106C2211yescharacteristic
46C11×#106C2211yescharacteristic
47C11×#106C2211yescharacteristic
48C11×#106C2211yescharacteristic
49C11×C4⋊C8C2211yescharacteristic
50C11×#102C2211yescharacteristic
51C11×#102C2211yescharacteristic
52C11×#102C2211yescharacteristic
53C11×#102C2211yescharacteristic
54C11×#102C2211yescharacteristic
55C11×#102C2211yescharacteristic
56C11×C22⋊C8C2211yescharacteristic
57C11×C22⋊C8C2211yescharacteristic
58C11×#97C2211yescharacteristic
59C11×#41—44no—
60C2×Q8×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11D411yescharacteristic
66C2×D4×C11C2311yescharacteristic
67C2×D4×C11C2311yescharacteristic
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C11×D8—22no—
76C11×M16—22no—
77C2×C8×C11—22no—
78C2×C8×C11C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4D411yescharacteristic
89C11×C4⋊C4C2311yescharacteristic
90C11×C4⋊C4C2311yescharacteristic
91C11×C4⋊C4C2311yescharacteristic
92C11×C4⋊C4C2311yescharacteristic
93C11×C4⋊C4C2311yescharacteristic
94C11×C4⋊C4C2311yescharacteristic
95C11×C22⋊C4—21no—
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⋊C4D411yescharacteristic
103C11×C22⋊C4D411yescharacteristic
104C42×C11—21no—
105C42×C11C2311yescharacteristic
106#3345C1111yesmaximal, characteristic, direct product factor, Sylow
107C23×C11—21no—
108C23×C11—21no—
109C23×C11C2×D411yescharacteristic
110C23×C11C2×D411yescharacteristic
111Q8×C11—42no—
112D4×C11—22no—
113D4×C11—21no—
114D4×C11—21no—
115D4×C11—21no—
116D4×C11—21no—
117D4×C11—42no—
118D4×C11—42no—
119D4×C11—42no—
120D4×C11—81no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—81no—
135C2×C4×C11—81no—
136C2×C4×C11C2×D411yescharacteristic
137C2×C4×C11C2×D411yescharacteristic
138C2×C4×C11C2×D411yescharacteristic
139C2×C4×C11C2×D411yescharacteristic
140C2×C4×C11C2411yescharacteristic
141C8×C11—21no—
142C8×C11—21no—
143C8×C11—21no—
144C8×C11#4112yescomplemented
145#553C2×C1111yescharacteristic, complemented
146#547C2×C1111yescharacteristic, complemented
147#501C2×C1111yescharacteristic, complemented
148#482C2×C1111yescharacteristic, complemented
149#481C2×C1111yescharacteristic, complemented
150#481C2×C1111yescharacteristic, complemented
151#480C2×C1111yescharacteristic, complemented
152#478C2×C1111yescharacteristic, complemented
153#476C2×C1111yescharacteristic, complemented
154#469C2×C1111yescharacteristic, complemented
155#466C2×C1111yescharacteristic, complemented
156#442C2×C1111yescharacteristic, complemented
157#435C2×C1111yescharacteristic, complemented
158#428C2×C1111yescharacteristic, complemented
159C2×#106C2×C1111yescharacteristic, complemented
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11AGL(1,ℤ/8)12yes—
172C22×C11C22×D411yescharacteristic
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11C2×#4111yescharacteristic
184C4×C112−1+411yescharacteristic
185C2×#41—21no—
186C2×D8C22×C1111yescharacteristic
187C2×M16C22×C1111yescharacteristic
188C22×C8C22×C1111yescharacteristic
189C4⋊Q8C22×C1111yescharacteristic
190#126—21no—
191#125C22×C1111yescharacteristic
192#123—21no—
193#123—21no—
194#123—21no—
195C22⋊Q8—21no—
196#121—21no—
197#121C22×C1111yescharacteristic
198#121C22×C1111yescharacteristic
199#121C22×C1111yescharacteristic
200#121C22×C1111yescharacteristic
201C4×D4—21no—
202C4×D4C22×C1111yescharacteristic
203C4×D4C22×C1111yescharacteristic
204C4×D4C22×C1111yescharacteristic
205#117C22×C1111yescharacteristic
206C2×C4⋊C4C22×C1111yescharacteristic
207C2×C4⋊C4C22×C1111yescharacteristic
208C2×C4⋊C4C22×C1111yescharacteristic
209#107C22×C1111yescharacteristic
210#107C22×C1111yescharacteristic
211#107C22×C1111yescharacteristic
212#106C22×C1111yescharacteristic
213#106C22×C1111yescharacteristic
214#106C22×C1111yescharacteristic
215#106C22×C1111yescharacteristic
216#106C22×C1111yescharacteristic
217#106C22×C1111yescharacteristic
218C4⋊C8C22×C1111yescharacteristic
219#102C22×C1111yescharacteristic
220#102C22×C1111yescharacteristic
221#102C22×C1111yescharacteristic
222#102C22×C1111yescharacteristic
223#102C22×C1111yescharacteristic
224#102C22×C1111yescharacteristic
225C22⋊C8C22×C1111yescharacteristic
226C22⋊C8C22×C1111yescharacteristic
227#97C22×C1111yescharacteristic
228C2×C11—22no—
229C2×C11—41no—
230C2×C11—81no—
231C2×C11—81no—
232C2×C11#54711yescharacteristic
233C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
234C2×C11#57711yescharacteristic
235#41—44no—
236C2×Q8—21no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4D4×C1111yescharacteristic
242C2×D4C23×C1111yescharacteristic
243C2×D4C23×C1111yescharacteristic
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4C23×C1111yescharacteristic
250C22×C4C23×C1111yescharacteristic
251D8—22no—
252M16—22no—
253C2×C8—22no—
254C2×C8C23×C1111yescharacteristic
255C2×C8C23×C1111yescharacteristic
256C2×C8C23×C1111yescharacteristic
257C2×C8C23×C1111yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4D4×C1111yescharacteristic
265C4⋊C4C23×C1111yescharacteristic
266C4⋊C4C23×C1111yescharacteristic
267C4⋊C4C23×C1111yescharacteristic
268C4⋊C4C23×C1111yescharacteristic
269C4⋊C4C23×C1111yescharacteristic
270C4⋊C4C23×C1111yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4D4×C1111yescharacteristic
279C22⋊C4D4×C1111yescharacteristic
280C42—21no—
281C42C23×C1111yescharacteristic
282C11#334511yescharacteristic, direct product factor, Sylow
283C23—21no—
284C23—21no—
285C23C2×D4×C1111yescharacteristic
286C23C2×D4×C1111yescharacteristic
287Q8—42no—
288D4—22no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—21no—
293D4—42no—
294D4—42no—
295D4—42no—
296D4—81no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4C2×D4×C1111yescharacteristic
313C2×C4C2×D4×C1111yescharacteristic
314C2×C4C2×D4×C1111yescharacteristic
315C2×C4C2×D4×C1111yescharacteristic
316C2×C4C24×C1111yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8C11×#4112yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22C11×AGL(1,ℤ/8)12yes—
333C22C22×D4×C1111yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4C2×C11×#4111yescharacteristic
345C4C11×2−1+411yescharacteristic
346C2—22no—
347C2—41no—
348C2—81no—
349C2—81no—
350C2C11×#54711yescharacteristic
351C2C2×C11×AGL(1,ℤ/8)11yescharacteristic
352C2C11×#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×#553C2semidirect
2. C11×#547C2semidirect
3. C11×#501C2semidirect
4. C11×#482C2semidirect
5. C11×#481C2semidirect
6. C11×#481C2semidirect
7. C11×#480C2semidirect
8. C11×#478C2semidirect
9. C11×#476C2semidirect
10. C11×#469C2semidirect
11. C11×#466C2semidirect
12. C11×#442C2semidirect
13. C11×#435C2semidirect
14. C11×#428C2semidirect
15. C2×C11×#106C2semidirect
106. #3345C11direct (N × H)
144. C8×C11#41semidirect
145. #553C2×C11semidirect
146. #547C2×C11semidirect
147. #501C2×C11semidirect
148. #482C2×C11semidirect
149. #481C2×C11semidirect
150. #481C2×C11semidirect
151. #480C2×C11semidirect
152. #478C2×C11semidirect
153. #476C2×C11semidirect
154. #469C2×C11semidirect
155. #466C2×C11semidirect
156. #442C2×C11semidirect
157. #435C2×C11semidirect
158. #428C2×C11semidirect
159. C2×#106C2×C11semidirect
282. C11#3345direct (N × H)
320. C8C11×#41semidirect

Maximal subgroups

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

subgroupindex
C11×#5532
C11×#5472
C11×#5012
C11×#4822
C11×#4812
C11×#4802
C11×#4782
C11×#4762
C11×#4692
C11×#4662
C11×#4422
C11×#4352
C11×#4282
C2×C11×#1062
#334511