Finite Group Databasebeta

← C2×D11×#382 #14912045

Subgroups — C2×D11×#382 #14912045

Order 2816.

4286 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D11C212yesmaximal
2C22×C42×D11C211yesmaximal, characteristic
3C2×#10622549C211yesmaximal, characteristic, complemented
4C2×#10622590C212yesmaximal, complemented
5C2×#10622263C214yesmaximal, complemented
6D11×#382C2116yesmaximal, direct product factor
7C2×D11×#95C214yesmaximal
8C2×C11×#382C211yesmaximal, characteristic, complemented
9C23×C4×D11C2214yes—
10C23×C4×D11C2212yes—
11C23×C4×D11C2211yescharacteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2212yes—
15C22×Dic11⋊C4C2214yes—
16C22×C4×Dic11C2212yes—
17C22×C4×Dic11C2211yescharacteristic
18C2×C4⋊C4×D11—216no—
19C2×C4⋊C4×D11C22116yes—
20C2×C42×D11C4116yescomplemented
21C2×C42×D11C2218yes—
22C11×#382C2218yescomplemented
23C2×C11×#95C2214yes—
24C2×C11⋊#95C2218yes—
25C2×C11⋊#95C2214yes—
26#10622590C22116yescomplemented
27#10622549C2218yescomplemented
28D11×#95C22132yes—
29#10622263C22132yescomplemented
30C24×D11C2311yescharacteristic
31C23×C4×C11C2314yes—
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C23×Dic11C2314yes—
35C23×Dic11C2312yes—
36C23×Dic11C2311yescharacteristic
37C22×C4×D11—216no—
38C22×C4×D11—216no—
39C22×C4×D11—232no—
40C22×C4×D11C2×C4116yes—
41C22×C4×D11C2×C418yes—
42C22×C4×D11D418yes—
43C22×C4×D11Q818yes—
44C22×C4×D11C23116yes—
45C22×C4×D11C2318yes—
46C22×C4×D11C2314yes—
47C2×C11×C4⋊C4—28no—
48C2×C11×C4⋊C4C2318yes—
49C2×C42×C11C2×C418yescomplemented
50C2×C42×C11C2314yes—
51C2×C4⋊Dic11—28no—
52C2×C4⋊Dic11C2318yes—
53C2×Dic11⋊C4—216no—
54C2×Dic11⋊C4C23116yes—
55C2×C4×Dic11C2×C418yescomplemented
56C2×C4×Dic11C2×C4116yescomplemented
57C2×C4×Dic11C2318yes—
58C2×C4×Dic11C2314yes—
59C4⋊C4×D11—264no—
60C42×D11C2×C4164yescomplemented
61C11×#95C23116yes—
62C11⋊#95C23116yes—
63C11⋊#95C23132yes—
64C22×#382—111nomaximal, Sylow
65C24×C11C2411yescharacteristic
66C23×D11C22×C414yes—
67C23×D11C2×D414yes—
68C23×D11C2×Q814yes—
69C23×D11#41116yes—
70C23×D11C2412yes—
71C22×C4×C11—28no—
72C22×C4×C11—28no—
73C22×C4×C11—216no—
74C22×C4×C11C22×C418yes—
75C22×C4×C11C22×C414yes—
76C22×C4×C11C2×D414yes—
77C22×C4×C11C2×Q814yes—
78C22×C4×C11C2418yes—
79C22×C4×C11C2414yes—
80C22×C4×C11C2412yes—
81C22×Dic11—28no—
82C22×Dic11—28no—
83C22×Dic11—216no—
84C22×Dic11C22×C418yes—
85C22×Dic11C22×C414yes—
86C22×Dic11C2×D414yes—
87C22×Dic11C2×Q814yes—
88C22×Dic11C2418yes—
89C22×Dic11C2414yes—
90C22×Dic11C2412yes—
91C2×C4×D11—264no—
92C2×C4×D11—232no—
93C2×C4×D11—232no—
94C2×C4×D11—264no—
95C2×C4×D11—464no—
96C2×C4×D11C4⋊C4164yes—
97C2×C4×D11C22×C4132yes—
98C2×C4×D11C22×C4116yes—
99C2×C4×D11C2×D4116yes—
100C2×C4×D11C2×Q8116yes—
101C11×C4⋊C4—216no—
102C42×C11C22×C4116yescomplemented
103C4⋊Dic11—216no—
104Dic11⋊C4—232no—
105C4×Dic11C22×C4132yescomplemented
106C4×Dic11C22×C4116yescomplemented
107C23×C4⋊C4—112no—
108C23×C42—111no—
109C2×#382—111no—
110C2×#382—1116no—
111C2×#382—114no—
112C2×#382—112no—
113C2×#382D1111yescharacteristic, direct product factor
114C22×#95—114no—
115C23×C11C23×C412yes—
116C23×C11C22×D412yes—
117C23×C11C22×Q812yes—
118C23×C11C2×#4118yes—
119C23×C11C2511yescharacteristic
120C22×D11C2×C4⋊C4116yes—
121C22×D11#117132yes—
122C22×D11#124132yes—
123C22×D11#125132yes—
124C22×D11C23×C414yes—
125C22×D11C22×D414yes—
126C22×D11C22×Q814yes—
127C22×D11C2×#41116yes—
128C2×C4×C11—216no—
129C2×C4×C11—28no—
130C2×C4×C11—28no—
131C2×C4×C11—216no—
132C2×C4×C11—416no—
133C2×C4×C11C2×C4⋊C4116yes—
134C2×C4×C11C23×C418yes—
135C2×C4×C11C23×C414yes—
136C2×C4×C11C22×D414yes—
137C2×C4×C11C22×Q814yes—
138C2×Dic11—216no—
139C2×Dic11—28no—
140C2×Dic11—28no—
141C2×Dic11—216no—
142C2×Dic11—416no—
143C2×Dic11C2×C4⋊C4116yes—
144C2×Dic11C23×C418yes—
145C2×Dic11C23×C414yes—
146C2×Dic11C22×D414yes—
147C2×Dic11C22×Q814yes—
148C4×D11—264no—
149C4×D11—464no—
150C4×D11C2×C4⋊C4164yes—
151C24×C4—111no—
152C24×C4—112no—
153C24×C4—114no—
154C22×C4⋊C4—114no—
155C22×C4⋊C4—112no—
156C22×C4⋊C4—1116no—
157C22×C4⋊C4—2216no—
158C22×C4⋊C4C2×D1112yes—
159C22×C42—112no—
160C22×C42—111no—
161C22×C42—118no—
162C22×C42—1116no—
163C22×C42C2×D1111yescharacteristic
164#382—1116no—
165#382—118no—
166#382—1132no—
167#382C2×D1118yesdirect product factor
168C2×#95—118no—
169C2×#95—114no—
170C2×#95—1132no—
171C2×#95C2×D1114yes—
172C22×C11C22×C4⋊C414yes—
173C22×C11C2×#11718yes—
174C22×C11C2×#12418yes—
175C22×C11C2×#12518yes—
176C22×C11C24×C411yescharacteristic
177C22×C11C23×D411yescharacteristic
178C22×C11C23×Q811yescharacteristic
179C22×C11C22×#4114yes—
180C2×D11#382164yesdirect product factor
181C2×D11C22×C4⋊C418yes—
182C2×D11C2×#117116yes—
183C2×D11C2×#124116yes—
184C2×D11C2×#125116yes—
185C4×C11—28no—
186C4×C11—48no—
187C4×C11C22×C4⋊C418yes—
188Dic11—28no—
189Dic11—48no—
190Dic11C22×C4⋊C418yes—
191C25—111no—
192C23×C4—111no—
193C23×C4—118no—
194C23×C4—118no—
195C23×C4—118no—
196C23×C4—114no—
197C23×C4—112no—
198C23×C4—1116no—
199C23×C4—118no—
200C23×C4—114no—
201C23×C4—1116no—
202C23×C4—2216no—
203C23×C4—2216no—
204C23×C4—2232no—
205C23×C4C22×D1114yes—
206C23×C4C22×D1112yes—
207C23×C4C22×D1111yescharacteristic
208C2×C4⋊C4—28no—
209C2×C4⋊C4—1116no—
210C2×C4⋊C4—118no—
211C2×C4⋊C4—2264no—
212C2×C4⋊C4—2216no—
213C2×C4⋊C4—228no—
214C2×C4⋊C4C22×D1118yes—
215C2×C42—1116no—
216C2×C42—118no—
217C2×C42—118no—
218C2×C42—114no—
219C2×C42—1164no—
220C2×C42C4×D1118yescomplemented
221C2×C42C22×D1114yes—
222#95—1132no—
223#95—1116no—
224#95C22×D11116yes—
225C2×C11C2×#38218yescomplemented
226C2×C11C23×C4⋊C411yescharacteristic
227C2×C11C22×#11712yes—
228C2×C11C22×#12412yes—
229C2×C11C22×#12512yes—
230D11C2×#382116yesdirect product factor
231C24—114no—
232C24—114no—
233C24—114no—
234C24—1116no—
235C24—112no—
236C24C23×D1111yescharacteristic
237C22×C4—28no—
238C22×C4—28no—
239C22×C4—216no—
240C22×C4—114no—
241C22×C4—114no—
242C22×C4—114no—
243C22×C4—112no—
244C22×C4—1164no—
245C22×C4—1116no—
246C22×C4—1116no—
247C22×C4—1116no—
248C22×C4—118no—
249C22×C4—114no—
250C22×C4—1132no—
251C22×C4—118no—
252C22×C4—2264no—
253C22×C4—2232no—
254C22×C4—2232no—
255C22×C4—2264no—
256C22×C4—228no—
257C22×C4—228no—
258C22×C4—2216no—
259C22×C4—4464no—
260C22×C4C2×C4×D1118yes—
261C22×C4C2×C4×D1114yes—
262C22×C4D4×D1114yes—
263C22×C4Q8×D1114yes—
264C22×C4C23×D1118yes—
265C22×C4C23×D1114yes—
266C22×C4C23×D1112yes—
267C4⋊C4—216no—
268C4⋊C4—2232no—
269C4⋊C4—2216no—
270C42—1132no—
271C42—1116no—
272C42C2×C4×D11116yescomplemented
273C11C22×#38211yescharacteristic, complemented, Sylow
274C23—1116no—
275C23—1132no—
276C23—114no—
277C23—114no—
278C23—114no—
279C23—1116no—
280C23—1132no—
281C23—1132no—
282C23C22×C4×D1112yes—
283C23C2×D4×D1112yes—
284C23C2×Q8×D1112yes—
285C23#41×D1118yes—
286C23C24×D1111yescharacteristic
287C2×C4—216no—
288C2×C4—28no—
289C2×C4—28no—
290C2×C4—216no—
291C2×C4—416no—
292C2×C4—1116no—
293C2×C4—114no—
294C2×C4—114no—
295C2×C4—114no—
296C2×C4—1164no—
297C2×C4—118no—
298C2×C4—2264no—
299C2×C4—2216no—
300C2×C4—228no—
301C2×C4—228no—
302C2×C4—2216no—
303C2×C4—4464no—
304C2×C4—4416no—
305C2×C4C4⋊C4×D11116yes—
306C2×C4C22×C4×D1118yes—
307C2×C4C22×C4×D1114yes—
308C2×C4C2×D4×D1114yes—
309C2×C4C2×Q8×D1114yes—
310C22—1116no—
311C22—1116no—
312C22—1164no—
313C22—118no—
314C22—1116no—
315C22C2×C4⋊C4×D1114yes—
316C22D11×#11718yes—
317C22D11×#12418yes—
318C22D11×#12518yes—
319C22C23×C4×D1111yescharacteristic
320C22C22×D4×D1111yescharacteristic
321C22C22×Q8×D1111yescharacteristic
322C22C2×#41×D1114yes—
323C4—28no—
324C4—48no—
325C4—118no—
326C4—228no—
327C4—448no—
328C4C2×C4⋊C4×D1118yes—
329C2—1116no—
330C2D11×#38218yesdirect product factor
331C2C22×C4⋊C4×D1111yescharacteristic
332C2C2×D11×#11712yes—
333C2C2×D11×#12412yes—
334C2C2×D11×#12512yes—
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#382C2
socleC24×C11C24
prime radicalC24×D11C23
cosocleC23×C11C25
hypercenterC2×#382D11
hypocenterC11C22×#382
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
3. C2×#10622549C2semidirect
4. C2×#10622590C2semidirect
5. C2×#10622263C2semidirect
6. D11×#382C2direct (N × H)
8. C2×C11×#382C2semidirect
20. C2×C42×D11C4semidirect
22. C11×#382C22semidirect
26. #10622590C22semidirect
27. #10622549C22semidirect
29. #10622263C22semidirect
49. C2×C42×C11C2×C4semidirect
55. C2×C4×Dic11C2×C4semidirect
56. C2×C4×Dic11C2×C4semidirect
60. C42×D11C2×C4semidirect
102. C42×C11C22×C4semidirect
105. C4×Dic11C22×C4semidirect
106. C4×Dic11C22×C4semidirect
113. C2×#382D11direct (N × H)
167. #382C2×D11direct (N × H)
180. C2×D11#382direct (N × H)
220. C2×C42C4×D11semidirect
225. C2×C11C2×#382semidirect
230. D11C2×#382direct (N × H)
272. C42C2×C4×D11semidirect
273. C11C22×#382semidirect
330. C2D11×#382direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D112
C22×C42×D112
C2×#106225492
C2×#106225902
C2×#106222632
D11×#3822
C2×D11×#952
C2×C11×#3822
C22×#38211