Finite Group Databasebeta

← #13068898

Subgroups — #13068898

Order 1408.

374 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 83 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#10623017C211yesmaximal, characteristic
2#10622571C211yesmaximal, characteristic
3C2×#66870C211yesmaximal, characteristic
4#10622563C211yesmaximal, characteristic, complemented
5#10622559C211yesmaximal, characteristic, complemented
6C11×#342C211yesmaximal, characteristic, complemented
7#10622165C211yesmaximal, characteristic, complemented
8C22×C22⋊D11C2211yescharacteristic
9C23×Dic11C2211yescharacteristic
10C2×C11×C22⋊C4C2211yescharacteristic
11C2×C11×C22⋊C4C2211yescharacteristic
12C2×C11×C22⋊C4C2211yescharacteristic
13C2×C22⋊Dic11C2211yescharacteristic
14C2×C22⋊Dic11C2211yescharacteristic
15C4×C22⋊D11—21no—
16C4×C22⋊D11—21no—
17C2×(C2×D11)⋊C4—21no—
18C2×C4⋊Dic11—21no—
19C2×Dic11⋊C4—21no—
20(C22⋊D11)⋊C4—21no—
21(C22⋊D11)⋊C4—21no—
22C22⋊C4×D11—21no—
23#66930—21no—
24C11⋊#95—21no—
25C11⋊#95—21no—
26C11⋊#95—21no—
27#66870C414yescomplemented
28C24×C11C2311yescharacteristic
29C23×D11D411yescharacteristic
30C22×C4×C11—21no—
31C22×C4×C11—21no—
32C22×C4×C11D411yescharacteristic
33C22×C4×C11D411yescharacteristic
34C2×C22⋊D11—21no—
35C2×C22⋊D11—21no—
36C2×C22⋊D11—21no—
37C2×C22⋊D11—21no—
38C2×C22⋊D11C2×C412yes—
39C2×C22⋊D11Q812yes—
40C22×Dic11—21no—
41C22×Dic11—21no—
42C22×Dic11—21no—
43C22×Dic11—21no—
44C22×Dic11—42no—
45C22×Dic11D411yescharacteristic
46C22×Dic11D411yescharacteristic
47C22×Dic11D411yescharacteristic
48C2×C4×D11—21no—
49C2×C4×D11—21no—
50C11×C22⋊C4—21no—
51C11×C22⋊C4—21no—
52C11×C22⋊C4—21no—
53C11×C22⋊C4—21no—
54C11×C22⋊C4—21no—
55C11×C22⋊C4C2×C412yescomplemented
56C22⋊Dic11—21no—
57C22⋊Dic11—21no—
58C22⋊Dic11—21no—
59C22⋊Dic11C2×C412yescomplemented
60(C2×D11)⋊C4—21no—
61(C2×D11)⋊C4—21no—
62(C2×D11)⋊C4—42no—
63C4⋊Dic11—42no—
64Dic11⋊C4—21no—
65Dic11⋊C4—21no—
66Dic11⋊C4—42no—
67C4×Dic11—21no—
68C4×Dic11—21no—
69#1867—111nomaximal, Sylow
70C23×C11—41no—
71C23×C11—41no—
72C23×C11C22×C411yescharacteristic
73C23×C11C2×D411yescharacteristic
74C23×C11C2×D411yescharacteristic
75C23×C11C2×D411yescharacteristic
76C23×C11C2×Q811yescharacteristic
77C23×C11#4111yescharacteristic
78C23×C11#4111yescharacteristic
79C22×D11—21no—
80C22×D11—21no—
81C22×D11—41no—
82C22×D11—41no—
83C22×D11C4⋊C412yescomplemented
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11—41no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
94C22⋊D11—22no—
95C22⋊D11—22no—
96C22⋊D11—22no—
97C22⋊D11—22no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—21no—
105C2×Dic11—21no—
106C2×Dic11—41no—
107C2×Dic11—41no—
108C2×Dic11—41no—
109C2×Dic11—41no—
110C2×Dic11—41no—
111C2×Dic11—41no—
112C2×Dic11—41no—
113C2×Dic11—41no—
114C2×Dic11C4⋊C412yescomplemented
115C4×D11—81no—
116C4×D11—81no—
117#518—111no—
118C2×#99—111no—
119#386—111no—
120#385—111no—
121#385—111no—
122#342—111no—
123#342D1111yescharacteristic, complemented
124C22×C11—21no—
125C22×C11—21no—
126C22×C11—21no—
127C22×C11—21no—
128C22×C11—21no—
129C22×C11—21no—
130C22×C11—41no—
131C22×C11—41no—
132C22×C11—41no—
133C22×C11—41no—
134C22×C11C2×C4⋊C411yescharacteristic
135C22×C11C4×D411yescharacteristic
136C22×C11C4×D411yescharacteristic
137C22×C11#12011yescharacteristic
138C22×C11C22⋊Q811yescharacteristic
139C22×C11C22⋊Q811yescharacteristic
140C22×C11#12311yescharacteristic
141C2×D11—22no—
142C2×D11—41no—
143C2×D11—41no—
144C2×D11—42no—
145C2×D11—81no—
146C4×C11—42no—
147C4×C11—41no—
148C4×C11—41no—
149C4×C11—81no—
150Dic11—22no—
151Dic11—42no—
152Dic11—41no—
153Dic11—42no—
154Dic11—41no—
155C22×D4—111no—
156C23×C4—111no—
157C4×D4—221no—
158C4×D4—221no—
159C4×D4—221no—
160C4×D4—221no—
161#117—221no—
162C2×C4⋊C4—221no—
163C2×C4⋊C4—221no—
164C2×C22⋊C4—111no—
165C2×C22⋊C4—111no—
166C2×C22⋊C4—221no—
167C2×C22⋊C4—221no—
168C2×C22⋊C4C2×D1111yescharacteristic
169C2×C22⋊C4C2×D1111yescharacteristic
170C2×C22⋊C4C2×D1111yescharacteristic
171#99—114no—
172#95—221no—
173#95—221no—
174#95—221no—
175C2×C11—21no—
176C2×C11—21no—
177C2×C11—21no—
178C2×C11—21no—
179C2×C11—21no—
180C2×C11—21no—
181C2×C11#38511yescharacteristic
182C2×C11B(4,𝔽2)11yescharacteristic
183C2×C11#45811yescharacteristic
184D11—42no—
185C24—111no—
186C24C22×D1111yescharacteristic
187C2×D4—112no—
188C2×D4—112no—
189C2×D4—221no—
190C2×D4—221no—
191C2×D4—221no—
192C2×D4—221no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—111no—
196C22×C4—111no—
197C22×C4—111no—
198C22×C4—221no—
199C22×C4—221no—
200C22×C4—221no—
201C22×C4—221no—
202C22×C4—221no—
203C22×C4—221no—
204C22×C4—442no—
205C22×C4D4411yescharacteristic
206C22×C4D4411yescharacteristic
207C4⋊C4—221no—
208C4⋊C4—221no—
209C4⋊C4—442no—
210C4⋊C4—442no—
211C22⋊C4—21no—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—112no—
217C22⋊C4—221no—
218C22⋊C4—221no—
219C22⋊C4—221no—
220C22⋊C4—221no—
221C22⋊C4—221no—
222C22⋊C4—442no—
223C22⋊C4C4×D1112yescomplemented
224C42—221no—
225C42—221no—
226C11#186711yescharacteristic, complemented, Sylow
227C23—41no—
228C23—41no—
229C23—112no—
230C23—221no—
231C23—221no—
232C23—441no—
233C23—441no—
234C23C2×C4×D1111yescharacteristic
235C23C2×D4411yescharacteristic
236C23#433911yescharacteristic
237C23D4×D1111yescharacteristic
238C23D4×D1111yescharacteristic
239C23#434111yescharacteristic
240C23Q8×D1111yescharacteristic
241D4—222no—
242D4—222no—
243D4—222no—
244D4—222no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—112no—
256C2×C4—221no—
257C2×C4—221no—
258C2×C4—222no—
259C2×C4—222no—
260C2×C4—222no—
261C2×C4—222no—
262C2×C4—221no—
263C2×C4—221no—
264C2×C4—441no—
265C2×C4—441no—
266C2×C4—441no—
267C2×C4—441no—
268C2×C4—441no—
269C2×C4—441no—
270C2×C4—441no—
271C2×C4—441no—
272C2×C4—881no—
273C2×C4—881no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—222no—
285C22—442no—
286C22—441no—
287C22—441no—
288C22—881no—
289C22C4×D4411yescharacteristic
290C22(C22⋊D11)⋊C411yescharacteristic
291C22#6693511yescharacteristic
292C22#6693611yescharacteristic
293C22C4⋊C4×D1111yescharacteristic
294C22#6694911yescharacteristic
295C22#6695011yescharacteristic
296C4—42no—
297C4—41no—
298C4—41no—
299C4—81no—
300C4—222no—
301C4—442no—
302C4—442no—
303C4—441no—
304C4—441no—
305C2—21no—
306C2—21no—
307C2—21no—
308C2—21no—
309C2—21no—
310C2—21no—
311C2—442no—
312C2#1062228111yescharacteristic
313C2#1062235411yescharacteristic
314C2#1062235511yescharacteristic
subgroupG/H
centerC22#66935
commutatorC23×C11C22×C4
FrattiniC24C22×D11
FittingC11×#342C2
socleC22×C11#120
prime radicalC22×C22⋊D11C22
cosocleC24×C11C23
hypercenter#342D11
hypocenterC11#1867
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
4. #10622563C2semidirect
5. #10622559C2semidirect
6. C11×#342C2semidirect
7. #10622165C2semidirect
27. #66870C4semidirect
55. C11×C22⋊C4C2×C4semidirect
59. C22⋊Dic11C2×C4semidirect
83. C22×D11C4⋊C4semidirect
114. C2×Dic11C4⋊C4semidirect
123. #342D11semidirect
223. C22⋊C4C4×D11semidirect
226. C11#1867semidirect

Maximal subgroups

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

subgroupindex
#106230172
#106225712
C2×#668702
#106225632
#106225592
C11×#3422
#106221652
#186711