Finite Group Databasebeta

← C2×C11×#2931 #14637328

Subgroups — C2×C11×#2931 #14637328

Order 2816.

2894 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#131C212yesmaximal, complemented
2C2×C11×#532C211yesmaximal, characteristic
3C11×#2931C2116yesmaximal, direct product factor
4C2×C11×#436C214yesmaximal, complemented
5C2×C8×D4×C11C214yesmaximal, complemented
6C2×C11×#423C211yesmaximal, characteristic, complemented
7C2×C11×#408C212yesmaximal, complemented
8C22×C4×C8×C11C211yesmaximal, characteristic, complemented
9C22×C11×#41C2212yes—
10C2×C11×#131—216no—
11C2×C11×#131C22116yescomplemented
12C22×C11×M16C2212yes—
13C22×C11×M16C2214yes—
14C23×C8×C11C2211yescharacteristic
15C23×C8×C11C2214yes—
16C23×C8×C11C2211yescharacteristic
17C11×#532C418yes—
18C11×#532C2218yes—
19C2×C11×C4⋊Q8C411yescharacteristic
20C2×C11×#127C411yescharacteristic
21C2×C11×#124C412yes—
22C2×C11×#121C414yes—
23C2×C4×D4×C11C2214yes—
24C22×C42×C11C2211yescharacteristic
25C11×#436C22132yescomplemented
26C8×D4×C11C22132yescomplemented
27C11×#423C2218yescomplemented
28C2×C11×C4⋊C8C2214yes—
29C11×#408C22116yescomplemented
30C2×C11×C22⋊C8C2218yes—
31C2×C4×C8×C11C2212yes—
32C2×C4×C8×C11C2212yes—
33C2×C4×C8×C11C2218yescomplemented
34C2×C11×#41—28no—
35C2×C11×#41—28no—
36C2×C11×#41C2×C418yes—
37C2×C11×#41C2318yes—
38C22×Q8×C11C2×C412yes—
39C22×D4×C11C2×C414yes—
40C22×D4×C11C2×C414yes—
41C22×D4×C11C2×C412yes—
42C23×C4×C11C2×C412yes—
43C23×C4×C11C2314yes—
44C23×C4×C11C2311yescharacteristic
45C11×#131—264no—
46C2×C11×M16—28no—
47C2×C11×M16—216no—
48C2×C11×M16C2318yes—
49C2×C11×M16C23116yes—
50C22×C8×C11—24no—
51C22×C8×C11—216no—
52C22×C8×C11D418yescomplemented
53C22×C8×C11C2312yes—
54C22×C8×C11C2314yes—
55C22×C8×C11C2314yes—
56C22×C8×C11C23116yes—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2314yes—
59C22×C8×C11C2311yescharacteristic
60C11×C4⋊Q8C2×C418yes—
61C11×#127C2×C418yes—
62C11×#124C2×C4116yes—
63C11×#121C2×C4132yes—
64C4×D4×C11C2×C4116yes—
65C4×D4×C11C23116yes—
66C2×C11×C4⋊C4C2×C414yes—
67C2×C11×C22⋊C4C2×C418yes—
68C2×C42×C11C2×C411yescharacteristic
69C2×C42×C11C2×C411yescharacteristic
70C2×C42×C11C2×C414yes—
71C2×C42×C11C2312yes—
72C2×C42×C11C2314yes—
73C11×C4⋊C8C23116yes—
74C11×C22⋊C8C23132yes—
75C4×C8×C11C2318yes—
76C4×C8×C11C2318yes—
77C2×#2931C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11C22×C414yes—
79C24×C11C22×C411yescharacteristic
80C11×#41—232no—
81C11×#41—216no—
82C11×#41—216no—
83C2×Q8×C11—28no—
84C2×Q8×C11C22×C418yes—
85C2×D4×C11—216no—
86C2×D4×C11—28no—
87C2×D4×C11—216no—
88C2×D4×C11C22×C4116yes—
89C2×D4×C11C22×C4116yes—
90C2×D4×C11C22×C418yes—
91C22×C4×C11—28no—
92C22×C4×C11—28no—
93C22×C4×C11—28no—
94C22×C4×C11C22×C412yes—
95C22×C4×C11C22×C418yes—
96C22×C4×C11C22×C414yes—
97C22×C4×C11C22×C418yes—
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C22×C412yes—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C2×D414yes—
102C22×C4×C11#4114yes—
103C22×C4×C11C2418yes—
104C22×C4×C11C2411yescharacteristic
105C22×C4×C11C2412yes—
106C11×M16—232no—
107C11×M16—216no—
108C2×C8×C11—232no—
109C2×C8×C11—28no—
110C2×C8×C11—24no—
111C2×C8×C11—28no—
112C2×C8×C11C2×D414yes—
113C2×C8×C11C2×D414yes—
114C2×C8×C11C2×D4116yescomplemented
115C2×C8×C11C2414yes—
116C2×C8×C11C2418yes—
117C2×C8×C11C2412yes—
118C2×C8×C11C2412yes—
119C11×C4⋊C4C22×C4116yes—
120C11×C22⋊C4C22×C4132yes—
121C42×C11C22×C414yes—
122C42×C11C22×C414yes—
123C42×C11C22×C414yes—
124C42×C11C2414yes—
125C22×#131C2×C1112yescomplemented
126C2×#532C2×C1111yescharacteristic
127#2931C2×C11116yesdirect product factor
128C2×#436C2×C1114yescomplemented
129C2×C8×D4C2×C1114yescomplemented
130C2×#423C2×C1111yescharacteristic, complemented
131C2×#408C2×C1112yescomplemented
132C22×C4×C8C2×C1111yescharacteristic, complemented
133C23×C11—24no—
134C23×C11—28no—
135C23×C11—216no—
136C23×C11C4×D414yes—
137C23×C11C23×C418yes—
138C23×C11C23×C412yes—
139C23×C11C23×C411yescharacteristic
140Q8×C11—216no—
141D4×C11—232no—
142D4×C11—216no—
143D4×C11—232no—
144C2×C4×C11—28no—
145C2×C4×C11—24no—
146C2×C4×C11—216no—
147C2×C4×C11—216no—
148C2×C4×C11—28no—
149C2×C4×C11—28no—
150C2×C4×C11C4×D414yes—
151C2×C4×C11C4×D418yes—
152C2×C4×C11#13118yescomplemented
153C2×C4×C11C23×C414yes—
154C2×C4×C11C23×C418yes—
155C2×C4×C11C23×C411yescharacteristic
156C2×C4×C11C23×C412yes—
157C2×C4×C11C23×C414yes—
158C2×C4×C11C22×D412yes—
159C2×C4×C11C22×D414yes—
160C2×C4×C11C2×#4112yes—
161C2×C4×C11C2×#4114yes—
162C2×C4×C11C2511yescharacteristic
163C8×C11—28no—
164C8×C11—24no—
165C8×C11C22×D414yes—
166C8×C11C22×D414yes—
167C22×#41C22×C1112yes—
168C2×#131—216no—
169C2×#131C22×C11116yescomplemented
170C22×M16C22×C1112yes—
171C22×M16C22×C1114yes—
172C23×C8C22×C1111yescharacteristic
173C23×C8C22×C1114yes—
174C23×C8C22×C1111yescharacteristic
175#532C4×C1118yes—
176#532C22×C1118yes—
177C2×C4⋊Q8C4×C1111yescharacteristic
178C2×#127C4×C1111yescharacteristic
179C2×#124C4×C1112yes—
180C2×#121C4×C1114yes—
181C2×C4×D4C22×C1114yes—
182C22×C42C22×C1111yescharacteristic
183#436C22×C11132yescomplemented
184C8×D4C22×C11132yescomplemented
185#423C22×C1118yescomplemented
186C2×C4⋊C8C22×C1114yes—
187#408C22×C11116yescomplemented
188C2×C22⋊C8C22×C1118yes—
189C2×C4×C8C22×C1112yes—
190C2×C4×C8C22×C1112yes—
191C2×C4×C8C22×C1118yescomplemented
192C22×C11—28no—
193C22×C11—24no—
194C22×C11—28no—
195C22×C11—216no—
196C22×C11—416no—
197C22×C11C2×C4×D414yes—
198C22×C11C2×C4×D412yes—
199C22×C11C2×#13114yes—
200C22×C11C24×C411yescharacteristic
201C4×C11—28no—
202C4×C11—24no—
203C4×C11C2×C4×D412yes—
204C4×C11C2×C4×D414yes—
205C4×C11C2×#13118yescomplemented
206C4×C11C23×D411yescharacteristic
207C4×C11C22×#4111yescharacteristic
208C2×#41—28no—
209C2×#41—28no—
210C2×#41C2×C4×C1118yes—
211C2×#41C23×C1118yes—
212C22×Q8C2×C4×C1112yes—
213C22×D4C2×C4×C1114yes—
214C22×D4C2×C4×C1114yes—
215C22×D4C2×C4×C1112yes—
216C23×C4C2×C4×C1112yes—
217C23×C4C23×C1114yes—
218C23×C4C23×C1111yescharacteristic
219#131—264no—
220C2×M16—28no—
221C2×M16—216no—
222C2×M16C23×C1118yes—
223C2×M16C23×C11116yes—
224C22×C8—24no—
225C22×C8—216no—
226C22×C8D4×C1118yescomplemented
227C22×C8C23×C1114yes—
228C22×C8C23×C11116yes—
229C22×C8C23×C1112yes—
230C22×C8C23×C1114yes—
231C22×C8C23×C1111yescharacteristic
232C22×C8C23×C1111yescharacteristic
233C22×C8C23×C1114yes—
234C4⋊Q8C2×C4×C1118yes—
235#127C2×C4×C1118yes—
236#124C2×C4×C11116yes—
237#121C2×C4×C11132yes—
238C4×D4C2×C4×C11116yes—
239C4×D4C23×C11116yes—
240C2×C4⋊C4C2×C4×C1114yes—
241C2×C22⋊C4C2×C4×C1118yes—
242C2×C42C2×C4×C1111yescharacteristic
243C2×C42C2×C4×C1111yescharacteristic
244C2×C42C2×C4×C1114yes—
245C2×C42C23×C1112yes—
246C2×C42C23×C1114yes—
247C4⋊C8C23×C11116yes—
248C22⋊C8C23×C11132yes—
249C4×C8C23×C1118yes—
250C4×C8C23×C1118yes—
251C2×C11—24no—
252C2×C11—48no—
253C2×C11#293114yesdirect product factor
254C2×C11C22×C4×D411yescharacteristic
255C2×C11C22×#13112yes—
256C24C22×C4×C1114yes—
257C24C22×C4×C1111yescharacteristic
258#41—232no—
259#41—216no—
260#41—216no—
261C2×Q8—28no—
262C2×Q8C22×C4×C1118yes—
263C2×D4—216no—
264C2×D4—28no—
265C2×D4—216no—
266C2×D4C22×C4×C11116yes—
267C2×D4C22×C4×C11116yes—
268C2×D4C22×C4×C1118yes—
269C22×C4—28no—
270C22×C4—28no—
271C22×C4—28no—
272C22×C4C22×C4×C1112yes—
273C22×C4C22×C4×C1118yes—
274C22×C4C22×C4×C1114yes—
275C22×C4C22×C4×C1118yes—
276C22×C4C22×C4×C1111yescharacteristic
277C22×C4C22×C4×C1112yes—
278C22×C4C22×C4×C1112yes—
279C22×C4C2×D4×C1114yes—
280C22×C4C11×#4114yes—
281C22×C4C24×C1118yes—
282C22×C4C24×C1111yescharacteristic
283C22×C4C24×C1112yes—
284M16—216no—
285M16—232no—
286C2×C8—28no—
287C2×C8—24no—
288C2×C8—28no—
289C2×C8—232no—
290C2×C8C2×D4×C1114yes—
291C2×C8C2×D4×C1114yes—
292C2×C8C2×D4×C11116yescomplemented
293C2×C8C24×C1114yes—
294C2×C8C24×C1118yes—
295C2×C8C24×C1112yes—
296C2×C8C24×C1112yes—
297C4⋊C4C22×C4×C11116yes—
298C22⋊C4C22×C4×C11132yes—
299C42C22×C4×C1114yes—
300C42C22×C4×C1114yes—
301C42C22×C4×C1114yes—
302C42C24×C1114yes—
303C11C2×#293111yescharacteristic, direct product factor, Sylow
304C23—24no—
305C23—28no—
306C23—216no—
307C23C4×D4×C1114yes—
308C23C23×C4×C1118yes—
309C23C23×C4×C1112yes—
310C23C23×C4×C1111yescharacteristic
311Q8—216no—
312D4—232no—
313D4—216no—
314D4—232no—
315C2×C4—28no—
316C2×C4—24no—
317C2×C4—216no—
318C2×C4—216no—
319C2×C4—28no—
320C2×C4—28no—
321C2×C4C4×D4×C1114yes—
322C2×C4C4×D4×C1118yes—
323C2×C4C11×#13118yescomplemented
324C2×C4C23×C4×C1114yes—
325C2×C4C23×C4×C1118yes—
326C2×C4C23×C4×C1111yescharacteristic
327C2×C4C23×C4×C1112yes—
328C2×C4C23×C4×C1114yes—
329C2×C4C22×D4×C1112yes—
330C2×C4C22×D4×C1114yes—
331C2×C4C2×C11×#4112yes—
332C2×C4C2×C11×#4114yes—
333C2×C4C25×C1111yescharacteristic
334C8—28no—
335C8—24no—
336C8C22×D4×C1114yes—
337C8C22×D4×C1114yes—
338C22—28no—
339C22—24no—
340C22—28no—
341C22—216no—
342C22—416no—
343C22C2×C4×D4×C1114yes—
344C22C2×C4×D4×C1112yes—
345C22C2×C11×#13114yes—
346C22C24×C4×C1111yescharacteristic
347C4—28no—
348C4—24no—
349C4C2×C4×D4×C1112yes—
350C4C2×C4×D4×C1114yes—
351C4C2×C11×#13118yescomplemented
352C4C23×D4×C1111yescharacteristic
353C4C22×C11×#4111yescharacteristic
354C2—24no—
355C2—48no—
356C2C11×#293114yesdirect product factor
357C2C22×C4×D4×C1111yescharacteristic
358C2C22×C11×#13112yes—
subgroupG/H
centerC22×C8×C11C23
commutatorC22C24×C4×C11
Frattini, cosocleC2×C4C25×C11
socleC23×C11C23×C4
prime radicalC2×C11×#532C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#131C2semidirect
3. C11×#2931C2direct (N × H)
4. C2×C11×#436C2semidirect
5. C2×C8×D4×C11C2semidirect
6. C2×C11×#423C2semidirect
7. C2×C11×#408C2semidirect
8. C22×C4×C8×C11C2semidirect
11. C2×C11×#131C22semidirect
25. C11×#436C22semidirect
26. C8×D4×C11C22semidirect
27. C11×#423C22semidirect
29. C11×#408C22semidirect
33. C2×C4×C8×C11C22semidirect
52. C22×C8×C11D4semidirect
77. C2×#2931C11direct (N × H)
114. C2×C8×C11C2×D4semidirect
125. C22×#131C2×C11semidirect
127. #2931C2×C11direct (N × H)
128. C2×#436C2×C11semidirect
129. C2×C8×D4C2×C11semidirect
130. C2×#423C2×C11semidirect
131. C2×#408C2×C11semidirect
132. C22×C4×C8C2×C11semidirect
152. C2×C4×C11#131semidirect
169. C2×#131C22×C11semidirect
183. #436C22×C11semidirect
184. C8×D4C22×C11semidirect
185. #423C22×C11semidirect
187. #408C22×C11semidirect
191. C2×C4×C8C22×C11semidirect
205. C4×C11C2×#131semidirect
226. C22×C8D4×C11semidirect
253. C2×C11#2931direct (N × H)
292. C2×C8C2×D4×C11semidirect
303. C11C2×#2931direct (N × H)
323. C2×C4C11×#131semidirect
351. C4C2×C11×#131semidirect
356. C2C11×#2931direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1312
C2×C11×#5322
C11×#29312
C2×C11×#4362
C2×C8×D4×C112
C2×C11×#4232
C2×C11×#4082
C22×C4×C8×C112
C2×#293111