Finite Group Databasebeta

← C11×#34128 #14611321

Subgroups — C11×#34128 #14611321

Order 2816.

2446 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C11C211yesmaximal, characteristic
2C11×#2356C216yesmaximal, complemented
3C11×#2351C212yesmaximal, complemented
4C11×#2344C216yesmaximal
5Q8×C11×C22⋊C4C212yesmaximal
6C11×#2295C216yesmaximal, complemented
7C11×#2283C213yesmaximal
8C42×Q8×C11C212yesmaximal, complemented
9C4×C11×#117C213yesmaximal
10C23×Q8×C11C2211yescharacteristic
11C2×C4×Q8×C11C4116yescomplemented
12C2×C4×Q8×C11C2214yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×Q8×C11C2213yes—
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×Q8×C11C2213yes—
17C2×C11×#117C2216yes—
18C22×C11×C4⋊C4C2213yes—
19C22×C42×C11C2213yes—
20C11×#391C22112yes—
21C11×#389C22112yes—
22C11×#387C22124yes—
23C11×#383C2216yes—
24C11×#382C2216yes—
25C11×#381C2216yes—
26C11×#380C2216yes—
27C4×C11×C4⋊C4C2216yes—
28C4×C11×C4⋊C4C2216yes—
29C4×C11×C4⋊C4C2216yes—
30C4×C11×C4⋊C4C22112yes—
31C4×C11×C22⋊C4C2211yescharacteristic
32C4×C11×C22⋊C4C2213yes—
33C4×C11×C22⋊C4C2216yes—
34C11×#376C2216yes—
35C11×#376C2216yes—
36C43×C11C2216yes—
37C22×Q8×C11—28no—
38C22×Q8×C11C2×C418yes—
39C22×Q8×C11C2313yes—
40C22×Q8×C11C2311yescharacteristic
41C23×C4×C11C2313yes—
42C23×C4×C11C2313yes—
43C23×C4×C11C2311yescharacteristic
44C4×Q8×C11—216no—
45C4×Q8×C11C2×C4124yes—
46C4×Q8×C11C2×C4124yes—
47C4×Q8×C11C2×C418yes—
48C4×Q8×C11C2×C418yes—
49C11×#117—224no—
50C2×C11×C4⋊C4C2×C4124yes—
51C2×C11×C4⋊C4C23112yes—
52C2×C11×C4⋊C4C23112yes—
53C2×C11×C4⋊C4C2313yes—
54C2×C11×C4⋊C4C2316yes—
55C2×C11×C4⋊C4C2313yes—
56C2×C11×C22⋊C4C2316yes—
57C2×C11×C22⋊C4C2312yes—
58C2×C42×C11C2×C4124yes—
59C2×C42×C11C23112yes—
60C2×C42×C11C23112yes—
61C2×C42×C11C2312yes—
62C2×C42×C11C2316yes—
63C2×C42×C11C2313yes—
64C2×C42×C11C2313yes—
65C2×C42×C11C2313yes—
66C2×C42×C11C2313yes—
67C11×#95C2312yes—
68C11×#95C2316yes—
69C11×#95C23112yes—
70C11×#95C23112yes—
71C11×#95C23112yes—
72C11×#95C23112yes—
73#34128C1111yesmaximal, characteristic, direct product factor, Sylow
74C24×C11C2411yescharacteristic
75C2×Q8×C11—232no—
76C2×Q8×C11—212no—
77C2×Q8×C11C22×C4112yes—
78C2×Q8×C11C22×C414yes—
79C2×Q8×C11#4118yes—
80C22×C4×C11—212no—
81C22×C4×C11—212no—
82C22×C4×C11—24no—
83C22×C4×C11C22×C414yes—
84C22×C4×C11C22×C4112yes—
85C22×C4×C11C22×C4112yes—
86C22×C4×C11C24112yes—
87C22×C4×C11C2411yescharacteristic
88C22×C4×C11C2413yes—
89C22×C4×C11C2413yes—
90C22×C4×C11C2413yes—
91C22×C4×C11C2414yes—
92C22×C4×C11C2413yes—
93C22×C4×C11C2411yescharacteristic
94C11×C4⋊C4—224no—
95C11×C4⋊C4—224no—
96C11×C4⋊C4C22×C4124yes—
97C11×C4⋊C4C22×C4112yes—
98C11×C4⋊C4C22×C4112yes—
99C11×C22⋊C4—212no—
100C11×C22⋊C4#4118yes—
101C42×C11—224no—
102C42×C11—224no—
103C42×C11—24no—
104C42×C11—212no—
105C42×C11C22×C4112yes—
106C42×C11C22×C4112yes—
107C42×C11C22×C4112yes—
108C42×C11C22×C4112yes—
109C22×C4×Q8C2×C1111yescharacteristic
110#2356C2×C1116yescomplemented
111#2351C2×C1112yescomplemented
112#2344C2×C1116yes—
113Q8×C22⋊C4C2×C1112yes—
114#2295C2×C1116yescomplemented
115#2283C2×C1113yes—
116C42×Q8C2×C1112yescomplemented
117C4×#117C2×C1113yes—
118C23×C11—22no—
119C23×C11—22no—
120C23×C11C23×C412yes—
121C23×C11C2×#4114yes—
122C23×C11C2511yescharacteristic
123Q8×C11—224no—
124Q8×C11#117116yescomplemented
125C2×C4×C11—224no—
126C2×C4×C11—24no—
127C2×C4×C11—26no—
128C2×C4×C11—26no—
129C2×C4×C11—26no—
130C2×C4×C11—24no—
131C2×C4×C11—22no—
132C2×C4×C11—224no—
133C2×C4×C11—28no—
134C2×C4×C11—212no—
135C2×C4×C11—212no—
136C2×C4×C11—212no—
137C2×C4×C11C23×C412yes—
138C2×C4×C11C23×C416yes—
139C2×C4×C11C23×C416yes—
140C2×C4×C11C23×C416yes—
141C2×C4×C11C23×C416yes—
142C2×C4×C11C23×C412yes—
143C2×C4×C11C2×#4118yes—
144C2×C4×C11C2×#41112yes—
145C2×C4×C112−1+414yes—
146C23×Q8C22×C1111yescharacteristic
147C2×C4×Q8C4×C11116yescomplemented
148C2×C4×Q8C22×C1114yes—
149C2×C4×Q8C22×C1111yescharacteristic
150C2×C4×Q8C22×C1113yes—
151C2×C4×Q8C22×C1111yescharacteristic
152C2×C4×Q8C22×C1113yes—
153C2×#117C22×C1116yes—
154C22×C4⋊C4C22×C1113yes—
155C22×C42C22×C1113yes—
156#391C22×C11112yes—
157#389C22×C11112yes—
158#387C22×C11124yes—
159#383C22×C1116yes—
160#382C22×C1116yes—
161#381C22×C1116yes—
162#380C22×C1116yes—
163C4×C4⋊C4C22×C11112yes—
164C4×C4⋊C4C22×C1116yes—
165C4×C4⋊C4C22×C1116yes—
166C4×C4⋊C4C22×C1116yes—
167C4×C22⋊C4C22×C1116yes—
168C4×C22⋊C4C22×C1111yescharacteristic
169C4×C22⋊C4C22×C1113yes—
170#376C22×C1116yes—
171#376C22×C1116yes—
172C43C22×C1116yes—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—28no—
176C22×C11C4×#4114yes—
177C22×C11C24×C411yescharacteristic
178C22×C11C22×#4112yes—
179C22×C11C22×#4112yes—
180C22×C11C2×2−1+412yes—
181C4×C11—26no—
182C4×C11—26no—
183C4×C11—26no—
184C4×C11—22no—
185C4×C11—28no—
186C4×C11—412no—
187C4×C11C2×#117112yes—
188C4×C11#51914yes—
189C22×Q8—28no—
190C22×Q8C2×C4×C1118yes—
191C22×Q8C23×C1113yes—
192C22×Q8C23×C1111yescharacteristic
193C23×C4C23×C1113yes—
194C23×C4C23×C1113yes—
195C23×C4C23×C1111yescharacteristic
196C4×Q8—216no—
197C4×Q8C2×C4×C11124yes—
198C4×Q8C2×C4×C11124yes—
199C4×Q8C2×C4×C1118yes—
200C4×Q8C2×C4×C1118yes—
201#117—224no—
202C2×C4⋊C4C2×C4×C11124yes—
203C2×C4⋊C4C23×C11112yes—
204C2×C4⋊C4C23×C11112yes—
205C2×C4⋊C4C23×C1113yes—
206C2×C4⋊C4C23×C1116yes—
207C2×C4⋊C4C23×C1113yes—
208C2×C22⋊C4C23×C1116yes—
209C2×C22⋊C4C23×C1112yes—
210C2×C42C2×C4×C11124yes—
211C2×C42C23×C11112yes—
212C2×C42C23×C11112yes—
213C2×C42C23×C1112yes—
214C2×C42C23×C1116yes—
215C2×C42C23×C1113yes—
216C2×C42C23×C1113yes—
217C2×C42C23×C1113yes—
218C2×C42C23×C1113yes—
219#95C23×C1112yes—
220#95C23×C1116yes—
221#95C23×C11112yes—
222#95C23×C11112yes—
223#95C23×C11112yes—
224#95C23×C11112yes—
225C2×C11—24no—
226C2×C11C22×#11711yescharacteristic
227C2×C11C2×C4×#4111yescharacteristic
228C2×C11C2×#51911yescharacteristic
229C2×C11#348214yes—
230C24C24×C1111yescharacteristic
231C2×Q8—232no—
232C2×Q8—212no—
233C2×Q8C22×C4×C11112yes—
234C2×Q8C22×C4×C1114yes—
235C2×Q8C11×#4118yes—
236C22×C4—212no—
237C22×C4—212no—
238C22×C4—24no—
239C22×C4C22×C4×C1114yes—
240C22×C4C22×C4×C11112yes—
241C22×C4C22×C4×C11112yes—
242C22×C4C24×C11112yes—
243C22×C4C24×C1111yescharacteristic
244C22×C4C24×C1113yes—
245C22×C4C24×C1113yes—
246C22×C4C24×C1113yes—
247C22×C4C24×C1114yes—
248C22×C4C24×C1113yes—
249C22×C4C24×C1111yescharacteristic
250C4⋊C4—224no—
251C4⋊C4—224no—
252C4⋊C4C22×C4×C11124yes—
253C4⋊C4C22×C4×C11112yes—
254C4⋊C4C22×C4×C11112yes—
255C22⋊C4—212no—
256C22⋊C4C11×#4118yes—
257C42—224no—
258C42—224no—
259C42—24no—
260C42—212no—
261C42C22×C4×C11112yes—
262C42C22×C4×C11112yes—
263C42C22×C4×C11112yes—
264C42C22×C4×C11112yes—
265C11#3412811yescharacteristic, direct product factor, Sylow
266C23—22no—
267C23—22no—
268C23C23×C4×C1112yes—
269C23C2×C11×#4114yes—
270C23C25×C1111yescharacteristic
271Q8—224no—
272Q8C11×#117116yescomplemented
273C2×C4—224no—
274C2×C4—24no—
275C2×C4—26no—
276C2×C4—26no—
277C2×C4—26no—
278C2×C4—24no—
279C2×C4—22no—
280C2×C4—224no—
281C2×C4—28no—
282C2×C4—212no—
283C2×C4—212no—
284C2×C4—212no—
285C2×C4C23×C4×C1112yes—
286C2×C4C23×C4×C1116yes—
287C2×C4C23×C4×C1116yes—
288C2×C4C23×C4×C1116yes—
289C2×C4C23×C4×C1116yes—
290C2×C4C23×C4×C1112yes—
291C2×C4C2×C11×#4118yes—
292C2×C4C2×C11×#41112yes—
293C2×C4C11×2−1+414yes—
294C22—22no—
295C22—22no—
296C22—28no—
297C22C4×C11×#4114yes—
298C22C24×C4×C1111yescharacteristic
299C22C22×C11×#4112yes—
300C22C22×C11×#4112yes—
301C22C2×C11×2−1+412yes—
302C4—26no—
303C4—26no—
304C4—26no—
305C4—22no—
306C4—28no—
307C4—412no—
308C4C2×C11×#117112yes—
309C4C11×#51914yes—
310C2—24no—
311C2C22×C11×#11711yescharacteristic
312C2C2×C4×C11×#4111yescharacteristic
313C2C2×C11×#51911yescharacteristic
314C2C11×#348214yes—
subgroupG/H
centerC22×C4×C11C24
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC24×C11C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2356C2semidirect
3. C11×#2351C2semidirect
6. C11×#2295C2semidirect
8. C42×Q8×C11C2semidirect
11. C2×C4×Q8×C11C4semidirect
73. #34128C11direct (N × H)
110. #2356C2×C11semidirect
111. #2351C2×C11semidirect
114. #2295C2×C11semidirect
116. C42×Q8C2×C11semidirect
124. Q8×C11#117semidirect
147. C2×C4×Q8C4×C11semidirect
265. C11#34128direct (N × H)
272. Q8C11×#117semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C112
C11×#23562
C11×#23512
C11×#23442
Q8×C11×C22⋊C42
C11×#22952
C11×#22832
C42×Q8×C112
C4×C11×#1172
#3412811