Finite Group Databasebeta

← #14664491

Subgroups — #14664491

Order 2816.

402 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071884C211yesmaximal, characteristic
2#13068693C211yesmaximal, characteristic
3#13066641C212yesmaximal
4#13066638C212yesmaximal
5C11×#1464C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C2×C4×Dic22C411yescharacteristic, complemented
8C11×#432—21no—
9#10622824—21no—
10C4×C22⋊Dic11—21no—
11#10622599C411yescharacteristic, complemented
12#10622597—21no—
13#10622592C411yescharacteristic, complemented
14#10622562C2211yescharacteristic
15#10622561—21no—
16#10622560C2211yescharacteristic
17C4×C4⋊Dic11C411yescharacteristic, complemented
18C4×Dic11⋊C4—21no—
19C11×#324—21no—
20C11×#323C2212yes—
21#10622164—21no—
22#10622164C2212yes—
23C23×C4×C11D411yescharacteristic
24C22×Dic22C2×C411yescharacteristic
25C11×#117—41no—
26C11×#117—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C22⋊C4D411yescharacteristic
30C2×C11×C22⋊C4C2311yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—22no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11—21no—
42C2×C4×Dic11—21no—
43C4×Dic22—41no—
44C4×Dic22—41no—
45C11×C4⋊C8—41no—
46C11×C22⋊C8—22no—
47C11×#97—41no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—41no—
53C11⋊#95—41no—
54C11⋊#95C2×C411yescharacteristic
55C11⋊#95C2×C411yescharacteristic
56#11810—111nomaximal, Sylow
57C24×C11C2×D411yescharacteristic
58C22×C4×C11—22no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—41no—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—42no—
73C2×Dic22—41no—
74C2×Dic22—42no—
75C2×C8×C11—42no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C22⋊C4—41no—
79C11×C22⋊C4—41no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—21no—
84C22⋊Dic11—42no—
85C22⋊Dic11—42no—
86C22⋊Dic11—42no—
87C22⋊Dic11—42no—
88C4⋊Dic11—41no—
89C4⋊Dic11—42no—
90Dic11⋊C4—42no—
91Dic11⋊C4—42no—
92Dic11⋊C4—42no—
93C4×Dic11—42no—
94C4×Dic11—41no—
95C4×Dic11—41no—
96#2396—111no—
97#1820—111no—
98#1464D1111yescharacteristic
99#1352—112no—
100#1351—112no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11C2×C22⋊C411yescharacteristic
106C23×C11#13712yes—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11#9911yescharacteristic
123C2×C4×C11#9911yescharacteristic
124C2×Dic11—22no—
125C2×Dic11—22no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—82no—
137C2×Dic11—82no—
138C2×Dic11—82no—
139Dic22—42no—
140Dic22—42no—
141C8×C11—82no—
142C2×C4×Q8—111no—
143C2×#117C2×D1111yescharacteristic
144#432—21no—
145#400—111no—
146#399—111no—
147#398—221no—
148#396—221no—
149#395—111no—
150#393—111no—
151#381—221no—
152C4×C4⋊C4—111no—
153C4×C4⋊C4—221no—
154C4×C22⋊C4—221no—
155#342—112no—
156#342—221no—
157#324—21no—
158#323C2×D1112yes—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—22no—
162C22×C11—42no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—81no—
166C22×C11C2×#9911yescharacteristic
167C22×C11#41911yescharacteristic
168C22×C11#42111yescharacteristic
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176Dic11—42no—
177Dic11—42no—
178Dic11—81no—
179Dic11—81no—
180Dic11—162no—
181C22×Q8—111no—
182C23×C4D4411yescharacteristic
183C4×Q8—441no—
184C4×Q8—441no—
185#117—41no—
186#117—41no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—221no—
191C2×C4⋊C4—221no—
192C2×C4⋊C4C4×D1111yescharacteristic
193C2×C4⋊C4C22⋊D1111yescharacteristic
194C2×C22⋊C4—221no—
195C2×C22⋊C4—221no—
196C2×C22⋊C4—222no—
197C2×C22⋊C4D4411yescharacteristic
198C2×C22⋊C4C22×D1111yescharacteristic
199C2×C42—221no—
200C2×C42—221no—
201C2×C42C4×D1111yescharacteristic
202C2×C42C22⋊D1111yescharacteristic
203C4⋊C8—41no—
204C22⋊C8—22no—
205#97—41no—
206#95—111no—
207#95—111no—
208#95—221no—
209#95—221no—
210#95—221no—
211#95—221no—
212#95—441no—
213#95—441no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11—42no—
217C2×C11#151111yescharacteristic
218C2×C11#212011yescharacteristic
219C2×C11#212611yescharacteristic
220C24C2×D4411yescharacteristic
221C2×Q8—441no—
222C2×Q8—442no—
223C22×C4—22no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—41no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4—221no—
231C22×C4—442no—
232C22×C4(C2×D11)⋊C411yescharacteristic
233C22×C4(C2×D11)⋊C411yescharacteristic
234C22×C4(C2×D11)⋊C411yescharacteristic
235C22×C4(C2×D11)⋊C411yescharacteristic
236C22×C4C2×C4×D1111yescharacteristic
237C22×C4C2×C22⋊D1111yescharacteristic
238C2×C8—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—441no—
242C4⋊C4—442no—
243C4⋊C4—442no—
244C4⋊C4—442no—
245C4⋊C4—442no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—442no—
249C22⋊C4—442no—
250C22⋊C4—442no—
251C22⋊C4—442no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—442no—
257C42—441no—
258C42—441no—
259C11#1181011yescharacteristic, complemented, Sylow
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23#6696212yes—
265C23C2×(C2×D11)⋊C411yescharacteristic
266Q8—442no—
267Q8—442no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—222no—
284C2×C4—222no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—882no—
296C2×C4—882no—
297C2×C4—882no—
298C2×C4#6687011yescharacteristic
299C2×C4#6687011yescharacteristic
300C8—82no—
301C22—21no—
302C22—21no—
303C22—22no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22C2×#6687011yescharacteristic
309C22#1062273311yescharacteristic
310C22#1062275211yescharacteristic
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—442no—
319C4—442no—
320C4—881no—
321C4—881no—
322C4—1762no—
323C2—21no—
324C2—21no—
325C2—42no—
326C2#1306715011yescharacteristic
327C2#1307025811yescharacteristic
328C2#1307027911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1464C2
socleC22×C11C2×#99
prime radicalC24×C11C2×D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1464D11
hypocenterC11#11810
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
7. C2×C4×Dic22C4semidirect
11. #10622599C4semidirect
13. #10622592C4semidirect
17. C4×C4⋊Dic11C4semidirect
259. C11#11810semidirect

Maximal subgroups

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

subgroupindex
#130718842
#130686932
#130666412
#130666382
C11×#14642
#1181011