Finite Group Databasebeta

← C11×#33776 #14610969

Subgroups — C11×#33776 #14610969

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3170C211yesmaximal, characteristic, complemented
2C11×#3147C211yesmaximal, characteristic
3C11×#2248C211yesmaximal, characteristic, complemented
4C11×#2247C211yesmaximal, characteristic, complemented
5C11×#2241C211yesmaximal, characteristic, complemented
6C11×#2240C211yesmaximal, characteristic, complemented
7C11×#2211C214yesmaximal, complemented
8C11×#2189C214yesmaximal, complemented
9C11×#2162C211yesmaximal, characteristic, complemented
10C2×C11×#135—21no—
11C2×C11×#135C2212yes—
12C11×#533—21no—
13C11×#532—21no—
14C2×C11×Q32C2214yes—
15C2×C11×SD32C2214yes—
16C11×#500C2211yescharacteristic
17C11×#495—21no—
18C11×#495C2212yes—
19C11×#494C2211yescharacteristic
20C11×#494C2211yescharacteristic
21C11×#493C2211yescharacteristic
22C11×#492—21no—
23C11×#487—21no—
24C11×#467—21no—
25C11×#467C2212yes—
26C4×C11×Q16—21no—
27C4×C11×Q16C2212yes—
28C2×C4×C8×C11C2211yescharacteristic
29C11×C4⋊C16C2212yes—
30C11×#358C2214yes—
31C11×#357C2214yes—
32C11×C22⋊C16C2212yes—
33C4×C11×C16C2211yescharacteristic
34C4×C11×C16C2211yescharacteristic
35C2×C11×#41—22no—
36C11×#135—44no—
37C11×#135—44no—
38C2×C11×Q16—21no—
39C2×C11×Q16—21no—
40C2×C11×Q16C2312yes—
41C2×C11×Q16C2312yes—
42C2×C11×SD16—22no—
43C2×C11×SD16—22no—
44C2×C11×D8—21no—
45C2×C11×D8C2312yes—
46C22×C8×C11D411yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×#127—21no—
52C11×#125—41no—
53C11×#124—22no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—41no—
56C11×#121—41no—
57C11×#121—41no—
58C4×Q8×C11—22no—
59C4×Q8×C11—41no—
60C4×D4×C11—41no—
61C4×D4×C11—41no—
62C11×#117—41no—
63C2×C42×C11D411yescharacteristic
64C11×Q32—44no—
65C11×SD32—44no—
66C2×C11×C16C2312yes—
67C2×C11×C16C2312yes—
68C11×#107—21no—
69C11×#107C2312yes—
70C11×#103—22no—
71C11×#103—22no—
72C4×C8×C11D411yescharacteristic
73C4×C8×C11D411yescharacteristic
74C4×C8×C11C2311yescharacteristic
75C4×C8×C11C2311yescharacteristic
76#33776C1111yesmaximal, characteristic, direct product factor, Sylow
77C11×#41—44no—
78C11×#41—44no—
79C2×Q8×C11—22no—
80C2×Q8×C11—22no—
81C2×Q8×C11—41no—
82C2×D4×C11—22no—
83C2×D4×C11—42no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C22×C4×C11—42no—
87C22×C4×C11D811yescharacteristic
88C22×C4×C11D811yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C11×Q16—24no—
91C11×Q16—24no—
92C11×Q16—42no—
93C11×Q16—42no—
94C11×SD16—44no—
95C11×SD16—44no—
96C11×D8—24no—
97C11×D8—42no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2411yescharacteristic
104C11×C4⋊C4—22no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—42no—
110C11×C4⋊C4—42no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—42no—
114C11×C22⋊C4—42no—
115C42×C11—42no—
116C42×C11D811yescharacteristic
117C42×C11D811yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C11×C16—22no—
121C11×C16—22no—
122#3170C2×C1111yescharacteristic, complemented
123#3147C2×C1111yescharacteristic
124#2248C2×C1111yescharacteristic, complemented
125#2247C2×C1111yescharacteristic, complemented
126#2241C2×C1111yescharacteristic, complemented
127#2240C2×C1111yescharacteristic, complemented
128#2211C2×C1114yescomplemented
129#2189C2×C1114yescomplemented
130#2162C2×C1111yescharacteristic, complemented
131C23×C11—42no—
132C23×C11C2×D811yescharacteristic
133Q8×C11—42no—
134Q8×C11—42no—
135Q8×C11—42no—
136Q8×C11—42no—
137Q8×C11—82no—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—84no—
141D4×C11—82no—
142D4×C11—82no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—84no—
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C2×D811yescharacteristic
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11C2×D811yescharacteristic
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C8×C11—21no—
158C8×C11—21no—
159C8×C11AGL(1,ℤ/8)12yes—
160C8×C11H(5,𝔽2)12yes—
161C2×#135—21no—
162C2×#135C22×C1112yes—
163#533—21no—
164#532—21no—
165C2×Q32C22×C1114yes—
166C2×SD32C22×C1114yes—
167#500C22×C1111yescharacteristic
168#495—21no—
169#495C22×C1112yes—
170#494C22×C1111yescharacteristic
171#494C22×C1111yescharacteristic
172#493C22×C1111yescharacteristic
173#492—21no—
174#487—21no—
175#467—21no—
176#467C22×C1112yes—
177C4×Q16—21no—
178C4×Q16C22×C1112yes—
179C2×C4×C8C22×C1111yescharacteristic
180C4⋊C16C22×C1112yes—
181#358C22×C1114yes—
182#357C22×C1114yes—
183C22⋊C16C22×C1112yes—
184C4×C16C22×C1111yescharacteristic
185C4×C16C22×C1111yescharacteristic
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—82no—
190C22×C11—82no—
191C22×C11—82no—
192C22×C11C22×D811yescharacteristic
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—82no—
197C4×C11—82no—
198C4×C11—82no—
199C4×C11#50812yes—
200C4×C11#51012yes—
201C4×C11#53511yescharacteristic
202C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
203C2×#41—22no—
204#135—44no—
205#135—44no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16C23×C1112yes—
209C2×Q16C23×C1112yes—
210C2×SD16—22no—
211C2×SD16—22no—
212C2×D8—21no—
213C2×D8C23×C1112yes—
214C22×C8D4×C1111yescharacteristic
215C22×C8C23×C1111yescharacteristic
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219#127—21no—
220#125—41no—
221#124—22no—
222C22⋊Q8—22no—
223C22⋊Q8—41no—
224#121—41no—
225#121—41no—
226C4×Q8—22no—
227C4×Q8—41no—
228C4×D4—41no—
229C4×D4—41no—
230#117—41no—
231C2×C42D4×C1111yescharacteristic
232Q32—44no—
233SD32—44no—
234C2×C16C23×C1112yes—
235C2×C16C23×C1112yes—
236#107—21no—
237#107C23×C1112yes—
238#103—22no—
239#103—22no—
240C4×C8D4×C1111yescharacteristic
241C4×C8D4×C1111yescharacteristic
242C4×C8C23×C1111yescharacteristic
243C4×C8C23×C1111yescharacteristic
244C2×C11—41no—
245C2×C11—162no—
246C2×C11#320511yescharacteristic
247C2×C11C2×#50811yescharacteristic
248C2×C11C2×#51011yescharacteristic
249#41—44no—
250#41—44no—
251C2×Q8—22no—
252C2×Q8—22no—
253C2×Q8—41no—
254C2×D4—22no—
255C2×D4—42no—
256C2×D4—41no—
257C2×D4—41no—
258C22×C4—42no—
259C22×C4C11×D811yescharacteristic
260C22×C4C11×D811yescharacteristic
261C22×C4C2×D4×C1111yescharacteristic
262Q16—24no—
263Q16—24no—
264Q16—42no—
265Q16—42no—
266SD16—44no—
267SD16—44no—
268D8—24no—
269D8—42no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8C2×D4×C1111yescharacteristic
273C2×C8C2×D4×C1111yescharacteristic
274C2×C8C2×D4×C1111yescharacteristic
275C2×C8C24×C1111yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—41no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C42—42no—
288C42C11×D811yescharacteristic
289C42C11×D811yescharacteristic
290C42C2×D4×C1111yescharacteristic
291C42C2×D4×C1111yescharacteristic
292C16—22no—
293C16—22no—
294C11#3377611yescharacteristic, direct product factor, Sylow
295C23—42no—
296C23C2×C11×D811yescharacteristic
297Q8—42no—
298Q8—42no—
299Q8—42no—
300Q8—42no—
301Q8—82no—
302D4—42no—
303D4—42no—
304D4—84no—
305D4—82no—
306D4—82no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—84no—
315C2×C4C2×C11×D811yescharacteristic
316C2×C4C2×C11×D811yescharacteristic
317C2×C4C2×C11×D811yescharacteristic
318C2×C4C2×C11×D811yescharacteristic
319C2×C4C2×C11×D811yescharacteristic
320C2×C4C22×D4×C1111yescharacteristic
321C8—21no—
322C8—21no—
323C8C11×AGL(1,ℤ/8)12yes—
324C8C11×H(5,𝔽2)12yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—82no—
329C22—82no—
330C22—82no—
331C22C22×C11×D811yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—82no—
336C4—82no—
337C4—82no—
338C4C11×#50812yes—
339C4C11×#51012yes—
340C4C11×#53511yescharacteristic
341C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
342C2—41no—
343C2—162no—
344C2C11×#320511yescharacteristic
345C2C2×C11×#50811yescharacteristic
346C2C2×C11×#51011yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
prime radicalC11×#3147C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3170C2semidirect
3. C11×#2248C2semidirect
4. C11×#2247C2semidirect
5. C11×#2241C2semidirect
6. C11×#2240C2semidirect
7. C11×#2211C2semidirect
8. C11×#2189C2semidirect
9. C11×#2162C2semidirect
76. #33776C11direct (N × H)
122. #3170C2×C11semidirect
124. #2248C2×C11semidirect
125. #2247C2×C11semidirect
126. #2241C2×C11semidirect
127. #2240C2×C11semidirect
128. #2211C2×C11semidirect
129. #2189C2×C11semidirect
130. #2162C2×C11semidirect
294. C11#33776direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31702
C11×#31472
C11×#22482
C11×#22472
C11×#22412
C11×#22402
C11×#22112
C11×#21892
C11×#21622
#3377611