Finite Group Databasebeta

← C2×C11×#2932 #14637329

Subgroups — C2×C11×#2932 #14637329

Order 2816.

2806 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
1C22×C11×#131C212yesmaximal, complemented
2C2×C11×#532C211yesmaximal, characteristic
3C11×#2932C2116yesmaximal, direct product factor
4C2×C11×#435C218yesmaximal, complemented
5C2×C11×#423C211yesmaximal, characteristic, complemented
6C2×C11×#408C212yesmaximal, complemented
7C22×C11×#97C211yesmaximal, characteristic, complemented
8C22×C11×#41C2212yes—
9C2×C11×#131—216no—
10C2×C11×#131C22116yescomplemented
11C22×C11×M16C2212yes—
12C22×C11×M16C2214yes—
13C23×C8×C11C2214yes—
14C23×C8×C11C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C11×#532C418yes—
17C11×#532C2218yes—
18C2×C11×C4⋊Q8C411yescharacteristic
19C2×C11×#127C411yescharacteristic
20C2×C11×#124C412yes—
21C2×C11×#121C414yes—
22C2×C4×D4×C11C2214yes—
23C22×C42×C11C2211yescharacteristic
24C11×#435C22164yescomplemented
25C11×#423C2218yescomplemented
26C2×C11×C4⋊C8C2214yes—
27C11×#408C22116yescomplemented
28C2×C11×C22⋊C8C2218yes—
29C2×C11×#97C2214yes—
30C2×C11×#97C2218yescomplemented
31C2×C11×#41—28no—
32C2×C11×#41—28no—
33C2×C11×#41C2×C418yes—
34C2×C11×#41C2318yes—
35C22×Q8×C11C2×C412yes—
36C22×D4×C11C2×C414yes—
37C22×D4×C11C2×C412yes—
38C22×D4×C11C2×C414yes—
39C23×C4×C11C2×C412yes—
40C23×C4×C11C2314yes—
41C23×C4×C11C2311yescharacteristic
42C11×#131—264no—
43C2×C11×M16—28no—
44C2×C11×M16—216no—
45C2×C11×M16C2318yes—
46C2×C11×M16C23116yes—
47C22×C8×C11—24no—
48C22×C8×C11—216no—
49C22×C8×C11D418yescomplemented
50C22×C8×C11C2314yes—
51C22×C8×C11C23116yes—
52C22×C8×C11C2312yes—
53C22×C8×C11C2314yes—
54C22×C8×C11C2312yes—
55C22×C8×C11C2314yes—
56C11×C4⋊Q8C2×C418yes—
57C11×#127C2×C418yes—
58C11×#124C2×C4116yes—
59C11×#121C2×C4132yes—
60C4×D4×C11C2×C4116yes—
61C4×D4×C11C23116yes—
62C2×C11×C4⋊C4C2×C414yes—
63C2×C11×C22⋊C4C2×C418yes—
64C2×C42×C11C2×C411yescharacteristic
65C2×C42×C11C2×C411yescharacteristic
66C2×C42×C11C2×C414yes—
67C2×C42×C11C2314yes—
68C2×C42×C11C2312yes—
69C11×C4⋊C8C23116yes—
70C11×C22⋊C8C23132yes—
71C11×#97C23116yes—
72C2×#2932C1111yesmaximal, characteristic, direct product factor, Sylow
73C24×C11C22×C414yes—
74C24×C11C22×C411yescharacteristic
75C11×#41—232no—
76C11×#41—216no—
77C11×#41—216no—
78C2×Q8×C11—28no—
79C2×Q8×C11C22×C418yes—
80C2×D4×C11—216no—
81C2×D4×C11—28no—
82C2×D4×C11—48no—
83C2×D4×C11C22×C4116yes—
84C2×D4×C11C22×C418yes—
85C2×D4×C11C22×C4116yes—
86C22×C4×C11—28no—
87C22×C4×C11—28no—
88C22×C4×C11—44no—
89C22×C4×C11C22×C412yes—
90C22×C4×C11C22×C412yes—
91C22×C4×C11C22×C414yes—
92C22×C4×C11C22×C418yes—
93C22×C4×C11C22×C418yes—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C22×C412yes—
96C22×C4×C11C2×D414yes—
97C22×C4×C11#4114yes—
98C22×C4×C11C2418yes—
99C22×C4×C11C2412yes—
100C22×C4×C11C2411yescharacteristic
101C11×M16—232no—
102C11×M16—216no—
103C2×C8×C11—232no—
104C2×C8×C11—28no—
105C2×C8×C11—24no—
106C2×C8×C11—28no—
107C2×C8×C11C2×D418yes—
108C2×C8×C11C2×D4116yescomplemented
109C2×C8×C11C2414yes—
110C2×C8×C11C2418yes—
111C2×C8×C11C2414yes—
112C11×C4⋊C4C22×C4116yes—
113C11×C22⋊C4C22×C4132yes—
114C42×C11C22×C414yes—
115C42×C11C22×C414yes—
116C42×C11C22×C414yes—
117C42×C11C2414yes—
118C22×#131C2×C1112yescomplemented
119C2×#532C2×C1111yescharacteristic
120#2932C2×C11116yesdirect product factor
121C2×#435C2×C1118yescomplemented
122C2×#423C2×C1111yescharacteristic, complemented
123C2×#408C2×C1112yescomplemented
124C22×#97C2×C1111yescharacteristic, complemented
125C23×C11—24no—
126C23×C11—28no—
127C23×C11—216no—
128C23×C11C4×D414yes—
129C23×C11C23×C418yes—
130C23×C11C23×C412yes—
131C23×C11C23×C411yescharacteristic
132Q8×C11—216no—
133D4×C11—232no—
134D4×C11—216no—
135D4×C11—416no—
136C2×C4×C11—28no—
137C2×C4×C11—24no—
138C2×C4×C11—24no—
139C2×C4×C11—216no—
140C2×C4×C11—28no—
141C2×C4×C11—28no—
142C2×C4×C11—48no—
143C2×C4×C11C4×D414yes—
144C2×C4×C11C4×D418yes—
145C2×C4×C11C23×C414yes—
146C2×C4×C11C23×C414yes—
147C2×C4×C11C23×C418yes—
148C2×C4×C11C23×C411yescharacteristic
149C2×C4×C11C23×C412yes—
150C2×C4×C11C22×D412yes—
151C2×C4×C11C22×D414yes—
152C2×C4×C11C2×#4112yes—
153C2×C4×C11C2×#4114yes—
154C2×C4×C11C2511yescharacteristic
155C8×C11—28no—
156C8×C11—24no—
157C8×C11C22×D418yes—
158C22×#41C22×C1112yes—
159C2×#131—216no—
160C2×#131C22×C11116yescomplemented
161C22×M16C22×C1112yes—
162C22×M16C22×C1114yes—
163C23×C8C22×C1111yescharacteristic
164C23×C8C22×C1114yes—
165C23×C8C22×C1111yescharacteristic
166#532C4×C1118yes—
167#532C22×C1118yes—
168C2×C4⋊Q8C4×C1111yescharacteristic
169C2×#127C4×C1111yescharacteristic
170C2×#124C4×C1112yes—
171C2×#121C4×C1114yes—
172C2×C4×D4C22×C1114yes—
173C22×C42C22×C1111yescharacteristic
174#435C22×C11164yescomplemented
175#423C22×C1118yescomplemented
176C2×C4⋊C8C22×C1114yes—
177#408C22×C11116yescomplemented
178C2×C22⋊C8C22×C1118yes—
179C2×#97C22×C1114yes—
180C2×#97C22×C1118yescomplemented
181C22×C11—28no—
182C22×C11—24no—
183C22×C11—28no—
184C22×C11—216no—
185C22×C11—416no—
186C22×C11C2×C4×D414yes—
187C22×C11C2×C4×D412yes—
188C22×C11#56814yes—
189C22×C11C24×C411yescharacteristic
190C4×C11—28no—
191C4×C11—24no—
192C4×C11—24no—
193C4×C11C2×C4×D412yes—
194C4×C11C2×C4×D414yes—
195C4×C11C23×D411yescharacteristic
196C4×C11C22×#4111yescharacteristic
197C2×#41—28no—
198C2×#41—28no—
199C2×#41C2×C4×C1118yes—
200C2×#41C23×C1118yes—
201C22×Q8C2×C4×C1112yes—
202C22×D4C2×C4×C1114yes—
203C22×D4C2×C4×C1112yes—
204C22×D4C2×C4×C1114yes—
205C23×C4C2×C4×C1112yes—
206C23×C4C23×C1114yes—
207C23×C4C23×C1111yescharacteristic
208#131—264no—
209C2×M16—28no—
210C2×M16—216no—
211C2×M16C23×C1118yes—
212C2×M16C23×C11116yes—
213C22×C8—24no—
214C22×C8—216no—
215C22×C8D4×C1118yescomplemented
216C22×C8C23×C1114yes—
217C22×C8C23×C11116yes—
218C22×C8C23×C1112yes—
219C22×C8C23×C1114yes—
220C22×C8C23×C1112yes—
221C22×C8C23×C1114yes—
222C4⋊Q8C2×C4×C1118yes—
223#127C2×C4×C1118yes—
224#124C2×C4×C11116yes—
225#121C2×C4×C11132yes—
226C4×D4C2×C4×C11116yes—
227C4×D4C23×C11116yes—
228C2×C4⋊C4C2×C4×C1114yes—
229C2×C22⋊C4C2×C4×C1118yes—
230C2×C42C2×C4×C1111yescharacteristic
231C2×C42C2×C4×C1111yescharacteristic
232C2×C42C2×C4×C1114yes—
233C2×C42C23×C1112yes—
234C2×C42C23×C1114yes—
235C4⋊C8C23×C11116yes—
236C22⋊C8C23×C11132yes—
237#97C23×C11116yes—
238C2×C11—24no—
239C2×C11—48no—
240C2×C11#293214yesdirect product factor
241C2×C11C22×C4×D411yescharacteristic
242C2×C11C2×#56812yes—
243C24C22×C4×C1114yes—
244C24C22×C4×C1111yescharacteristic
245#41—232no—
246#41—216no—
247#41—216no—
248C2×Q8—28no—
249C2×Q8C22×C4×C1118yes—
250C2×D4—216no—
251C2×D4—28no—
252C2×D4—48no—
253C2×D4C22×C4×C11116yes—
254C2×D4C22×C4×C1118yes—
255C2×D4C22×C4×C11116yes—
256C22×C4—28no—
257C22×C4—28no—
258C22×C4—44no—
259C22×C4C22×C4×C1112yes—
260C22×C4C22×C4×C1112yes—
261C22×C4C22×C4×C1114yes—
262C22×C4C22×C4×C1118yes—
263C22×C4C22×C4×C1118yes—
264C22×C4C22×C4×C1111yescharacteristic
265C22×C4C22×C4×C1112yes—
266C22×C4C2×D4×C1114yes—
267C22×C4C11×#4114yes—
268C22×C4C24×C1118yes—
269C22×C4C24×C1111yescharacteristic
270C22×C4C24×C1112yes—
271M16—216no—
272M16—232no—
273C2×C8—28no—
274C2×C8—24no—
275C2×C8—28no—
276C2×C8—232no—
277C2×C8C2×D4×C1118yes—
278C2×C8C2×D4×C11116yescomplemented
279C2×C8C24×C1114yes—
280C2×C8C24×C1118yes—
281C2×C8C24×C1114yes—
282C4⋊C4C22×C4×C11116yes—
283C22⋊C4C22×C4×C11132yes—
284C42C22×C4×C1114yes—
285C42C22×C4×C1114yes—
286C42C22×C4×C1114yes—
287C42C24×C1114yes—
288C11C2×#293211yescharacteristic, direct product factor, Sylow
289C23—24no—
290C23—28no—
291C23—216no—
292C23C4×D4×C1114yes—
293C23C23×C4×C1118yes—
294C23C23×C4×C1112yes—
295C23C23×C4×C1111yescharacteristic
296Q8—216no—
297D4—232no—
298D4—216no—
299D4—416no—
300C2×C4—28no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—216no—
304C2×C4—28no—
305C2×C4—28no—
306C2×C4—48no—
307C2×C4C4×D4×C1114yes—
308C2×C4C4×D4×C1118yes—
309C2×C4C23×C4×C1114yes—
310C2×C4C23×C4×C1114yes—
311C2×C4C23×C4×C1118yes—
312C2×C4C23×C4×C1111yescharacteristic
313C2×C4C23×C4×C1112yes—
314C2×C4C22×D4×C1112yes—
315C2×C4C22×D4×C1114yes—
316C2×C4C2×C11×#4112yes—
317C2×C4C2×C11×#4114yes—
318C2×C4C25×C1111yescharacteristic
319C8—28no—
320C8—24no—
321C8C22×D4×C1118yes—
322C22—28no—
323C22—24no—
324C22—28no—
325C22—216no—
326C22—416no—
327C22C2×C4×D4×C1114yes—
328C22C2×C4×D4×C1112yes—
329C22C11×#56814yes—
330C22C24×C4×C1111yescharacteristic
331C4—28no—
332C4—24no—
333C4—24no—
334C4C2×C4×D4×C1112yes—
335C4C2×C4×D4×C1114yes—
336C4C23×D4×C1111yescharacteristic
337C4C22×C11×#4111yescharacteristic
338C2—24no—
339C2—48no—
340C2C11×#293214yesdirect product factor
341C2C22×C4×D4×C1111yescharacteristic
342C2C2×C11×#56812yes—
subgroupG/H
centerC22×C4×C11C24
commutatorC22C24×C4×C11
Frattini, cosocleC2×C4C25×C11
socleC23×C11C23×C4
prime radicalC2×C11×#532C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#131C2semidirect
3. C11×#2932C2direct (N × H)
4. C2×C11×#435C2semidirect
5. C2×C11×#423C2semidirect
6. C2×C11×#408C2semidirect
7. C22×C11×#97C2semidirect
10. C2×C11×#131C22semidirect
24. C11×#435C22semidirect
25. C11×#423C22semidirect
27. C11×#408C22semidirect
30. C2×C11×#97C22semidirect
49. C22×C8×C11D4semidirect
72. C2×#2932C11direct (N × H)
108. C2×C8×C11C2×D4semidirect
118. C22×#131C2×C11semidirect
120. #2932C2×C11direct (N × H)
121. C2×#435C2×C11semidirect
122. C2×#423C2×C11semidirect
123. C2×#408C2×C11semidirect
124. C22×#97C2×C11semidirect
160. C2×#131C22×C11semidirect
174. #435C22×C11semidirect
175. #423C22×C11semidirect
177. #408C22×C11semidirect
180. C2×#97C22×C11semidirect
215. C22×C8D4×C11semidirect
240. C2×C11#2932direct (N × H)
278. C2×C8C2×D4×C11semidirect
288. C11C2×#2932direct (N × H)
340. C2C11×#2932direct (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×#29322
C2×C11×#4352
C2×C11×#4232
C2×C11×#4082
C22×C11×#972
C2×#293211