Finite Group Databasebeta

← C2×C11×#2923 #14637313

Subgroups — C2×C11×#2923 #14637313

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C11×#41C211yesmaximal, characteristic
2C11×#2923C2116yesmaximal, direct product factor
3C2×C11×#433C214yesmaximal, complemented
4C2×C11×#432C214yesmaximal, complemented
5C2×C11×#424C212yesmaximal, complemented
6C2×C11×#408C212yesmaximal
7C2×C4×C11×M16C211yesmaximal, characteristic, complemented
8C22×C11×#97C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C22×C11×M16C2212yes—
11C23×C8×C11C2212yes—
12C4×C11×#41C418yes—
13C4×C11×#41C2218yes—
14C2×C4×Q8×C11C412yes—
15C2×C4×D4×C11C414yes—
16C2×C4×D4×C11C412yes—
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2212yes—
19C22×C42×C11C2212yes—
20C22×C42×C11C2211yescharacteristic
21C11×#433C22132yescomplemented
22C11×#432C22132yescomplemented
23C11×#424C22116yescomplemented
24C2×C11×C4⋊C8C2218yes—
25C11×#408C22116yes—
26C2×C11×C22⋊C8C2218yes—
27C4×C11×M16C2218yescomplemented
28C2×C11×#97C2212yes—
29C2×C11×#97C2212yes—
30C2×C11×#97C2212yes—
31C2×C11×#97C2218yescomplemented
32C2×C4×C8×C11C2212yes—
33C2×C11×#41—28no—
34C2×C11×#41C2×C414yes—
35C2×C11×#41C2314yes—
36C22×Q8×C11C2×C411yescharacteristic
37C22×D4×C11C2×C412yes—
38C22×D4×C11C2×C411yescharacteristic
39C23×C4×C11C2×C414yes—
40C23×C4×C11C2×C412yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C2×C11×M16—28no—
44C2×C11×M16C2318yes—
45C22×C8×C11—28no—
46C22×C8×C11C2318yes—
47C22×C8×C11C2314yes—
48C22×C8×C11C2314yes—
49C4×Q8×C11C2×C4116yes—
50C4×D4×C11C2×C4132yes—
51C4×D4×C11C2×C4116yes—
52C11×#117C2×C418yes—
53C11×#117C2×C414yes—
54C11×#117C2314yes—
55C11×#117C2318yes—
56C2×C11×C4⋊C4C2×C414yes—
57C2×C11×C4⋊C4C2×C412yes—
58C2×C11×C22⋊C4C2×C414yes—
59C2×C11×C22⋊C4C2×C412yes—
60C2×C42×C11C2×C414yes—
61C2×C42×C11C2×C412yes—
62C2×C42×C11C2×C418yes—
63C2×C42×C11C2×C414yes—
64C2×C42×C11C2314yes—
65C2×C42×C11C2318yes—
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2312yes—
69C11×C4⋊C8C23132yes—
70C11×C22⋊C8C23132yes—
71C11×#97C2318yes—
72C11×#97C2318yes—
73C11×#97C2318yes—
74C4×C8×C11C2318yes—
75C2×#2923C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11C22×C412yes—
77C24×C11C22×C411yescharacteristic
78C11×#41—216no—
79C11×#41—216no—
80C2×Q8×C11—24no—
81C2×Q8×C11C22×C414yes—
82C2×D4×C11—28no—
83C2×D4×C11—24no—
84C2×D4×C11C22×C418yes—
85C2×D4×C11C22×C414yes—
86C22×C4×C11—28no—
87C22×C4×C11—44no—
88C22×C4×C11—48no—
89C22×C4×C11C22×C412yes—
90C22×C4×C11C22×C412yes—
91C22×C4×C11C22×C414yes—
92C22×C4×C11C22×C412yes—
93C22×C4×C11C22×C414yes—
94C22×C4×C11C22×C4116yes—
95C22×C4×C11C22×C418yes—
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C22×C412yes—
98C22×C4×C11#4118yes—
99C22×C4×C11C2414yes—
100C22×C4×C11C2412yes—
101C22×C4×C11C2411yescharacteristic
102C11×M16—216no—
103C2×C8×C11—28no—
104C2×C8×C11—216no—
105C2×C8×C11—28no—
106C2×C8×C11C2418yes—
107C2×C8×C11C2418yes—
108C11×C4⋊C4C22×C4116yes—
109C11×C4⋊C4C22×C418yes—
110C11×C22⋊C4C22×C4116yes—
111C11×C22⋊C4C22×C418yes—
112C42×C11C22×C412yes—
113C42×C11C22×C412yes—
114C42×C11C22×C414yes—
115C42×C11C22×C4116yes—
116C42×C11C22×C418yes—
117C42×C11C2412yes—
118C42×C11C2412yes—
119C42×C11C2414yes—
120C2×C4×#41C2×C1111yescharacteristic
121#2923C2×C11116yesdirect product factor
122C2×#433C2×C1114yescomplemented
123C2×#432C2×C1114yescomplemented
124C2×#424C2×C1112yescomplemented
125C2×#408C2×C1112yes—
126C2×C4×M16C2×C1111yescharacteristic, complemented
127C22×#97C2×C1111yescharacteristic, complemented
128C23×C11—24no—
129C23×C11—24no—
130C23×C11—28no—
131C23×C11#11714yes—
132C23×C11C23×C414yes—
133C23×C11C23×C412yes—
134C23×C11C23×C411yescharacteristic
135Q8×C11—28no—
136D4×C11—216no—
137D4×C11—28no—
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—24no—
141C2×C4×C11—28no—
142C2×C4×C11—28no—
143C2×C4×C11—28no—
144C2×C4×C11—48no—
145C2×C4×C11—416no—
146C2×C4×C11#11714yes—
147C2×C4×C11#11718yes—
148C2×C4×C11C23×C414yes—
149C2×C4×C11C23×C414yes—
150C2×C4×C11C23×C414yes—
151C2×C4×C11C23×C418yes—
152C2×C4×C11C23×C411yescharacteristic
153C2×C4×C11C23×C412yes—
154C2×C4×C11C2×#4114yes—
155C2×C4×C11C2×#4118yes—
156C2×C4×C11C2511yescharacteristic
157C8×C11—28no—
158C8×C11—28no—
159C22×#41C22×C1111yescharacteristic
160C22×M16C22×C1112yes—
161C23×C8C22×C1112yes—
162C4×#41C4×C1118yes—
163C4×#41C22×C1118yes—
164C2×C4×Q8C4×C1112yes—
165C2×C4×D4C4×C1114yes—
166C2×C4×D4C4×C1112yes—
167C2×#117C22×C1111yescharacteristic
168C2×#117C22×C1112yes—
169C22×C42C22×C1111yescharacteristic
170C22×C42C22×C1112yes—
171#433C22×C11132yescomplemented
172#432C22×C11132yescomplemented
173#424C22×C11116yescomplemented
174C2×C4⋊C8C22×C1118yes—
175#408C22×C11116yes—
176C2×C22⋊C8C22×C1118yes—
177C4×M16C22×C1118yescomplemented
178C2×#97C22×C1112yes—
179C2×#97C22×C1112yes—
180C2×#97C22×C1112yes—
181C2×#97C22×C1118yescomplemented
182C2×C4×C8C22×C1112yes—
183C22×C11—28no—
184C22×C11—24no—
185C22×C11—24no—
186C22×C11—28no—
187C22×C11—48no—
188C22×C11C2×#11714yes—
189C22×C11C2×#11712yes—
190C22×C11#56814yes—
191C22×C11C24×C411yescharacteristic
192C4×C11—24no—
193C4×C11—24no—
194C4×C11—24no—
195C4×C11—28no—
196C4×C11C2×#11712yes—
197C4×C11C2×#11714yes—
198C4×C11C22×#4112yes—
199C2×#41—28no—
200C2×#41C2×C4×C1114yes—
201C2×#41C23×C1114yes—
202C22×Q8C2×C4×C1111yescharacteristic
203C22×D4C2×C4×C1112yes—
204C22×D4C2×C4×C1111yescharacteristic
205C23×C4C2×C4×C1114yes—
206C23×C4C2×C4×C1112yes—
207C23×C4C23×C1112yes—
208C23×C4C23×C1111yescharacteristic
209C2×M16—28no—
210C2×M16C23×C1118yes—
211C22×C8—28no—
212C22×C8C23×C1114yes—
213C22×C8C23×C1118yes—
214C22×C8C23×C1114yes—
215C4×Q8C2×C4×C11116yes—
216C4×D4C2×C4×C11132yes—
217C4×D4C2×C4×C11116yes—
218#117C2×C4×C1118yes—
219#117C2×C4×C1114yes—
220#117C23×C1114yes—
221#117C23×C1118yes—
222C2×C4⋊C4C2×C4×C1114yes—
223C2×C4⋊C4C2×C4×C1112yes—
224C2×C22⋊C4C2×C4×C1114yes—
225C2×C22⋊C4C2×C4×C1112yes—
226C2×C42C2×C4×C1114yes—
227C2×C42C2×C4×C1112yes—
228C2×C42C2×C4×C1118yes—
229C2×C42C2×C4×C1114yes—
230C2×C42C23×C1111yescharacteristic
231C2×C42C23×C1112yes—
232C2×C42C23×C1114yes—
233C2×C42C23×C1118yes—
234C2×C42C23×C1111yescharacteristic
235C4⋊C8C23×C11132yes—
236C22⋊C8C23×C11132yes—
237#97C23×C1118yes—
238#97C23×C1118yes—
239#97C23×C1118yes—
240C4×C8C23×C1118yes—
241C2×C11—24no—
242C2×C11—44no—
243C2×C11#292314yesdirect product factor
244C2×C11C22×#11711yescharacteristic
245C2×C11C2×#56812yes—
246C24C22×C4×C1112yes—
247C24C22×C4×C1111yescharacteristic
248#41—216no—
249#41—216no—
250C2×Q8—24no—
251C2×Q8C22×C4×C1114yes—
252C2×D4—28no—
253C2×D4—24no—
254C2×D4C22×C4×C1118yes—
255C2×D4C22×C4×C1114yes—
256C22×C4—28no—
257C22×C4—44no—
258C22×C4—48no—
259C22×C4C22×C4×C1112yes—
260C22×C4C22×C4×C1112yes—
261C22×C4C22×C4×C1114yes—
262C22×C4C22×C4×C1112yes—
263C22×C4C22×C4×C1114yes—
264C22×C4C22×C4×C11116yes—
265C22×C4C22×C4×C1118yes—
266C22×C4C22×C4×C1111yescharacteristic
267C22×C4C22×C4×C1112yes—
268C22×C4C11×#4118yes—
269C22×C4C24×C1114yes—
270C22×C4C24×C1111yescharacteristic
271C22×C4C24×C1112yes—
272M16—216no—
273C2×C8—28no—
274C2×C8—216no—
275C2×C8—28no—
276C2×C8C24×C1118yes—
277C2×C8C24×C1118yes—
278C4⋊C4C22×C4×C11116yes—
279C4⋊C4C22×C4×C1118yes—
280C22⋊C4C22×C4×C11116yes—
281C22⋊C4C22×C4×C1118yes—
282C42C22×C4×C1112yes—
283C42C22×C4×C1112yes—
284C42C22×C4×C1114yes—
285C42C22×C4×C11116yes—
286C42C22×C4×C1118yes—
287C42C24×C1112yes—
288C42C24×C1112yes—
289C42C24×C1114yes—
290C11C2×#292311yescharacteristic, direct product factor, Sylow
291C23—24no—
292C23—24no—
293C23—28no—
294C23C11×#11714yes—
295C23C23×C4×C1114yes—
296C23C23×C4×C1112yes—
297C23C23×C4×C1111yescharacteristic
298Q8—28no—
299D4—216no—
300D4—28no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—28no—
305C2×C4—28no—
306C2×C4—28no—
307C2×C4—48no—
308C2×C4—416no—
309C2×C4C11×#11714yes—
310C2×C4C11×#11718yes—
311C2×C4C23×C4×C1114yes—
312C2×C4C23×C4×C1114yes—
313C2×C4C23×C4×C1114yes—
314C2×C4C23×C4×C1118yes—
315C2×C4C23×C4×C1111yescharacteristic
316C2×C4C23×C4×C1112yes—
317C2×C4C2×C11×#4114yes—
318C2×C4C2×C11×#4118yes—
319C2×C4C25×C1111yescharacteristic
320C8—28no—
321C8—28no—
322C22—28no—
323C22—24no—
324C22—24no—
325C22—28no—
326C22—48no—
327C22C2×C11×#11714yes—
328C22C2×C11×#11712yes—
329C22C11×#56814yes—
330C22C24×C4×C1111yescharacteristic
331C4—24no—
332C4—24no—
333C4—24no—
334C4—28no—
335C4C2×C11×#11712yes—
336C4C2×C11×#11714yes—
337C4C22×C11×#4112yes—
338C2—24no—
339C2—44no—
340C2C11×#292314yesdirect product factor
341C2C22×C11×#11711yescharacteristic
342C2C2×C11×#56812yes—
subgroupG/H
centerC22×C4×C11C24
commutatorC22C24×C4×C11
Frattini, cosocleC2×C4C25×C11
socleC23×C11C23×C4
prime radicalC22×C11×#41C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2923C2direct (N × H)
3. C2×C11×#433C2semidirect
4. C2×C11×#432C2semidirect
5. C2×C11×#424C2semidirect
7. C2×C4×C11×M16C2semidirect
8. C22×C11×#97C2semidirect
21. C11×#433C22semidirect
22. C11×#432C22semidirect
23. C11×#424C22semidirect
27. C4×C11×M16C22semidirect
31. C2×C11×#97C22semidirect
75. C2×#2923C11direct (N × H)
121. #2923C2×C11direct (N × H)
122. C2×#433C2×C11semidirect
123. C2×#432C2×C11semidirect
124. C2×#424C2×C11semidirect
126. C2×C4×M16C2×C11semidirect
127. C22×#97C2×C11semidirect
171. #433C22×C11semidirect
172. #432C22×C11semidirect
173. #424C22×C11semidirect
177. C4×M16C22×C11semidirect
181. C2×#97C22×C11semidirect
243. C2×C11#2923direct (N × H)
290. C11C2×#2923direct (N × H)
340. C2C11×#2923direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C11×#412
C11×#29232
C2×C11×#4332
C2×C11×#4322
C2×C11×#4242
C2×C11×#4082
C2×C4×C11×M162
C22×C11×#972
C2×#292311