Finite Group Databasebeta

← C11×#33794 #14610987

Subgroups — C11×#33794 #14610987

Order 2816.

504 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3169C211yesmaximal, characteristic
2C11×#3160C211yesmaximal, characteristic, complemented
3C11×#2254C211yesmaximal, characteristic, complemented
4C11×#2252C211yesmaximal, characteristic, complemented
5C11×#2240C211yesmaximal, characteristic, complemented
6C11×#2240C211yesmaximal, characteristic, complemented
7C11×#2234C214yesmaximal, complemented
8C11×#2228C214yesmaximal, complemented
9C11×#2162C211yesmaximal, characteristic, complemented
10C11×#533—21no—
11C11×#532—21no—
12C11×#500C2211yescharacteristic
13C11×#500C2211yescharacteristic
14C11×#500C2211yescharacteristic
15C11×#499—21no—
16C11×#499C2212yes—
17C11×#498—21no—
18C11×#493C2211yescharacteristic
19C11×#486—21no—
20C11×#466—21no—
21C11×#466C2212yes—
22C4×C11×D8—21no—
23C4×C11×D8C2212yes—
24C11×#427—21no—
25C11×#427C2212yes—
26C2×C4×C8×C11C2211yescharacteristic
27C11×#367C2214yes—
28C11×#366C2214yes—
29C11×C4⋊C16C2212yes—
30C11×#357C2214yes—
31C11×#357C2214yes—
32C11×C22⋊C16C2212yes—
33C4×C11×C16C2211yescharacteristic
34C4×C11×C16C2211yescharacteristic
35C2×C11×#41—41no—
36C2×C11×D8—21no—
37C2×C11×D8C2312yes—
38C22×C8×C11D411yescharacteristic
39C22×C8×C11C2311yescharacteristic
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×#127—21no—
44C11×#125—22no—
45C11×#124—41no—
46C11×C22⋊Q8—41no—
47C11×C22⋊Q8—41no—
48C11×#121—22no—
49C11×#121—41no—
50C4×Q8×C11—41no—
51C4×Q8×C11—41no—
52C4×D4×C11—22no—
53C4×D4×C11—41no—
54C11×#117—22no—
55C2×C42×C11D411yescharacteristic
56C2×C11×C16C2312yes—
57C2×C11×C16C2312yes—
58C11×#107—21no—
59C11×#107—21no—
60C11×#107—21no—
61C11×#107C2312yes—
62C11×#107C2312yes—
63C11×#107C2312yes—
64C11×#106—22no—
65C11×#106—22no—
66C11×#102—22no—
67C11×#102—22no—
68C4×C8×C11D411yescharacteristic
69C4×C8×C11D411yescharacteristic
70C4×C8×C11C2311yescharacteristic
71C4×C8×C11C2311yescharacteristic
72#33794C1111yesmaximal, characteristic, direct product factor, Sylow
73C11×#41—84no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×D4×C11—22no—
78C2×D4×C11—42no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C22×C4×C11—42no—
82C22×C4×C11D811yescharacteristic
83C22×C4×C11D811yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C11×D8—24no—
86C11×D8—42no—
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11C2411yescharacteristic
93C11×C4⋊C4—22no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—42no—
98C11×C4⋊C4—42no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—42no—
104C42×C11—42no—
105C42×C11D811yescharacteristic
106C42×C11D811yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C11×C16—22no—
110C11×C16—22no—
111#3169C2×C1111yescharacteristic
112#3160C2×C1111yescharacteristic, complemented
113#2254C2×C1111yescharacteristic, complemented
114#2252C2×C1111yescharacteristic, complemented
115#2240C2×C1111yescharacteristic, complemented
116#2240C2×C1111yescharacteristic, complemented
117#2234C2×C1114yescomplemented
118#2228C2×C1114yescomplemented
119#2162C2×C1111yescharacteristic, complemented
120C23×C11—42no—
121C23×C11C2×D811yescharacteristic
122Q8×C11—82no—
123Q8×C11—82no—
124Q8×C11—82no—
125D4×C11—42no—
126D4×C11—42no—
127D4×C11—84no—
128D4×C11—82no—
129D4×C11—82no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—84no—
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C22×D411yescharacteristic
144C8×C11—21no—
145C8×C11—21no—
146C8×C11#13712yes—
147C8×C112−1+412yes—
148#533—21no—
149#532—21no—
150#500C22×C1111yescharacteristic
151#500C22×C1111yescharacteristic
152#500C22×C1111yescharacteristic
153#499—21no—
154#499C22×C1112yes—
155#498—21no—
156#493C22×C1111yescharacteristic
157#486—21no—
158#466—21no—
159#466C22×C1112yes—
160C4×D8—21no—
161C4×D8C22×C1112yes—
162#427—21no—
163#427C22×C1112yes—
164C2×C4×C8C22×C1111yescharacteristic
165#367C22×C1114yes—
166#366C22×C1114yes—
167C4⋊C16C22×C1112yes—
168#357C22×C1114yes—
169#357C22×C1114yes—
170C22⋊C16C22×C1112yes—
171C4×C16C22×C1111yescharacteristic
172C4×C16C22×C1111yescharacteristic
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—82no—
177C22×C11—82no—
178C22×C11—82no—
179C22×C11C22×D811yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—82no—
184C4×C11—82no—
185C4×C11—82no—
186C4×C11#50812yes—
187C4×C11#50912yes—
188C4×C11#53611yescharacteristic
189C4×C11C2×#13711yescharacteristic
190C2×#41—41no—
191C2×D8—21no—
192C2×D8C23×C1112yes—
193C22×C8D4×C1111yescharacteristic
194C22×C8C23×C1111yescharacteristic
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198#127—21no—
199#125—22no—
200#124—41no—
201C22⋊Q8—41no—
202C22⋊Q8—41no—
203#121—22no—
204#121—41no—
205C4×Q8—41no—
206C4×Q8—41no—
207C4×D4—22no—
208C4×D4—41no—
209#117—22no—
210C2×C42D4×C1111yescharacteristic
211C2×C16C23×C1112yes—
212C2×C16C23×C1112yes—
213#107—21no—
214#107—21no—
215#107—21no—
216#107C23×C1112yes—
217#107C23×C1112yes—
218#107C23×C1112yes—
219#106—22no—
220#106—22no—
221#102—22no—
222#102—22no—
223C4×C8D4×C1111yescharacteristic
224C4×C8D4×C1111yescharacteristic
225C4×C8C23×C1111yescharacteristic
226C4×C8C23×C1111yescharacteristic
227C2×C11—41no—
228C2×C11—162no—
229C2×C11#322611yescharacteristic
230C2×C11C2×#50811yescharacteristic
231C2×C11C2×#50911yescharacteristic
232#41—84no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×D4—22no—
237C2×D4—42no—
238C2×D4—41no—
239C2×D4—41no—
240C22×C4—42no—
241C22×C4C11×D811yescharacteristic
242C22×C4C11×D811yescharacteristic
243C22×C4C2×D4×C1111yescharacteristic
244D8—24no—
245D8—42no—
246C2×C8—22no—
247C2×C8—22no—
248C2×C8C2×D4×C1111yescharacteristic
249C2×C8C2×D4×C1111yescharacteristic
250C2×C8C2×D4×C1111yescharacteristic
251C2×C8C24×C1111yescharacteristic
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C42—42no—
264C42C11×D811yescharacteristic
265C42C11×D811yescharacteristic
266C42C2×D4×C1111yescharacteristic
267C42C2×D4×C1111yescharacteristic
268C16—22no—
269C16—22no—
270C11#3379411yescharacteristic, direct product factor, Sylow
271C23—42no—
272C23C2×C11×D811yescharacteristic
273Q8—82no—
274Q8—82no—
275Q8—82no—
276D4—42no—
277D4—42no—
278D4—84no—
279D4—82no—
280D4—82no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—84no—
289C2×C4C2×C11×D811yescharacteristic
290C2×C4C2×C11×D811yescharacteristic
291C2×C4C2×C11×D811yescharacteristic
292C2×C4C2×C11×D811yescharacteristic
293C2×C4C2×C11×D811yescharacteristic
294C2×C4C22×D4×C1111yescharacteristic
295C8—21no—
296C8—21no—
297C8C11×#13712yes—
298C8C11×2−1+412yes—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—82no—
303C22—82no—
304C22—82no—
305C22C22×C11×D811yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—82no—
310C4—82no—
311C4—82no—
312C4C11×#50812yes—
313C4C11×#50912yes—
314C4C11×#53611yescharacteristic
315C4C2×C11×#13711yescharacteristic
316C2—41no—
317C2—162no—
318C2C11×#322611yescharacteristic
319C2C2×C11×#50811yescharacteristic
320C2C2×C11×#50911yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
prime radicalC11×#3169C2
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
2. C11×#3160C2semidirect
3. C11×#2254C2semidirect
4. C11×#2252C2semidirect
5. C11×#2240C2semidirect
6. C11×#2240C2semidirect
7. C11×#2234C2semidirect
8. C11×#2228C2semidirect
9. C11×#2162C2semidirect
72. #33794C11direct (N × H)
112. #3160C2×C11semidirect
113. #2254C2×C11semidirect
114. #2252C2×C11semidirect
115. #2240C2×C11semidirect
116. #2240C2×C11semidirect
117. #2234C2×C11semidirect
118. #2228C2×C11semidirect
119. #2162C2×C11semidirect
270. C11#33794direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31692
C11×#31602
C11×#22542
C11×#22522
C11×#22402
C11×#22342
C11×#22282
C11×#21622
#3379411