Finite Group Databasebeta

← #13079639

Subgroups — #13079639

Order 1408.

386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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
1D11×C4⋊Q8C211yesmaximal, characteristic, complemented
2#10623211C211yesmaximal, characteristic
3C11×#497C211yesmaximal, characteristic, complemented
4#10622799C212yesmaximal, complemented
5#10622795C212yesmaximal, complemented
6#10622783C212yesmaximal
7#10622775C212yesmaximal, complemented
8#10622695C211yesmaximal, characteristic, complemented
9#10622673C211yesmaximal, characteristic, complemented
10#10622318C211yesmaximal, characteristic, complemented
11#10622316C211yesmaximal, characteristic, complemented
12C2×Q8×D11C2212yes—
13C2×C11×Q16C2212yes—
14C2×C11×SD16C2212yes—
15C11×C4⋊Q8C2211yescharacteristic
16C11×#124C2211yescharacteristic
17#66999C2211yescharacteristic
18Q8×Dic11C2211yescharacteristic
19#66997C2212yes—
20C2×#4326C2212yes—
21#66991C2211yescharacteristic
22D4×Dic11C2211yescharacteristic
23C2×#4324C2212yes—
24C4⋊C4×D11—21no—
25C4⋊C4×D11—21no—
26#66941—21no—
27#66941—21no—
28#66936—21no—
29(C22⋊D11)⋊C4—21no—
30#66932—21no—
31#66930—21no—
32C42×D11C2211yescharacteristic
33#66923C2211yescharacteristic
34#66922C2211yescharacteristic
35C11×#97C2211yescharacteristic
36#66899C2212yes—
37#66899C2212yes—
38(C2×D11)⋊C8C2212yes—
39#66880C2212yes—
40#66880C2212yes—
41Dic11⋊C8C2212yes—
42#66867C2211yescharacteristic
43C2×Q8×C11C2312yes—
44C2×Q8×C11C2311yescharacteristic
45C2×D4×C11C2311yescharacteristic
46C2×C22⋊D11—21no—
47C22×Dic11—21no—
48Q8×D11—42no—
49Q8×D11—42no—
50C2×C4×D11—22no—
51C2×C4×D11D411yescharacteristic
52C2×C4×D11D411yescharacteristic
53C2×C4×D11C2311yescharacteristic
54C2×Dic22—22no—
55C2×Dic22C2312yes—
56C11×Q16—42no—
57C11×SD16—42no—
58C2×C8×C11C2312yes—
59C11×C4⋊C4—21no—
60C11×C4⋊C4—21no—
61C11×C22⋊C4—21no—
62C11×C22⋊C4—21no—
63C42×C11C2311yescharacteristic
64C22⋊Dic11—21no—
65C22⋊Dic11—21no—
66#4326—42no—
67#4324—42no—
68(C2×D11)⋊C4—21no—
69C4⋊Dic11—21no—
70C4⋊Dic11—21no—
71C4⋊Dic11—21no—
72C4⋊Dic11C2311yescharacteristic
73C4⋊Dic11C2311yescharacteristic
74Dic11⋊C4—21no—
75Dic11⋊C4—22no—
76Dic11⋊C4—22no—
77Dic11⋊C4—21no—
78Dic11⋊C4—21no—
79C4×Dic11—21no—
80C4×Dic11D411yescharacteristic
81C4×Dic11D411yescharacteristic
82C4×Dic11C2311yescharacteristic
83C2×C11⋊C8C2312yes—
84#3218—111nomaximal, Sylow
85C23×C11—21no—
86C22×D11C2×D411yescharacteristic
87Q8×C11—22no—
88Q8×C11—22no—
89Q8×C11—22no—
90D4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11C2411yescharacteristic
96C22⋊D11—42no—
97C2×Dic11—21no—
98C2×Dic11—21no—
99C2×Dic11—22no—
100C2×Dic11—42no—
101C2×Dic11C2×D411yescharacteristic
102C2×Dic11C2×D411yescharacteristic
103C2×Dic11C2×D411yescharacteristic
104C4×D11—22no—
105C4×D11—22no—
106C4×D11—22no—
107C4×D11—44no—
108Dic22—22no—
109Dic22—22no—
110Dic22—44no—
111C8×C11—22no—
112C11⋊C8—22no—
113C2×C4⋊Q8—111no—
114#529—111no—
115#497—111no—
116#497D1111yescharacteristic, complemented
117#491—111no—
118#491—111no—
119#462—112no—
120#461—112no—
121#451—112no—
122#448—112no—
123#432—111no—
124C22×C11—41no—
125C22×C11—41no—
126C22×C11—41no—
127C22×C11C22×D411yescharacteristic
128C2×D11—21no—
129C2×D11—21no—
130C2×D11#13712yes—
131C4×C11—21no—
132C4×C11—21no—
133C4×C11—41no—
134C4×C11—42no—
135C4×C11H(5,𝔽2)12yes—
136Dic11—21no—
137Dic11—21no—
138Dic11—42no—
139Dic11—41no—
140Dic11—41no—
141Dic11#13712yes—
142C22×Q8—112no—
143C2×Q16—112no—
144C2×Q16C2×D1112yes—
145C2×SD16—112no—
146C2×SD16C2×D1112yes—
147C4⋊Q8—112no—
148C4⋊Q8—111no—
149C4⋊Q8—221no—
150C4⋊Q8—221no—
151C4⋊Q8C2×D1111yescharacteristic
152#126—221no—
153#125—111no—
154#124C2×D1111yescharacteristic
155#123—221no—
156C22⋊Q8—111no—
157#121—111no—
158C4×Q8—111no—
159C4×D4—111no—
160C4×D4—221no—
161#117—221no—
162C2×C4⋊C4—221no—
163C2×C4⋊C4—221no—
164C2×C42—111no—
165C4⋊C8—112no—
166#103—112no—
167#103—112no—
168#103—112no—
169#103—112no—
170C22⋊C8—112no—
171#97—111no—
172#97C2×D1111yescharacteristic
173C2×C11—81no—
174C2×C11#53511yescharacteristic
175C2×C11C2×#13711yescharacteristic
176C2×C11C2×#13711yescharacteristic
177D11—22no—
178C2×Q8—112no—
179C2×Q8—222no—
180C2×Q8—442no—
181C2×Q8—442no—
182C2×Q8C22×D1112yes—
183C2×Q8C22×D1111yescharacteristic
184C2×D4—221no—
185C2×D4C22×D1111yescharacteristic
186C22×C4—111no—
187C22×C4—111no—
188C22×C4—111no—
189C22×C4—222no—
190C22×C4—221no—
191Q16—42no—
192Q16—442no—
193SD16—42no—
194SD16—442no—
195C2×C8—112no—
196C2×C8C22×D1112yes—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—111no—
200C4⋊C4—111no—
201C4⋊C4—222no—
202C4⋊C4—222no—
203C4⋊C4—221no—
204C4⋊C4—221no—
205C4⋊C4—221no—
206C4⋊C4—221no—
207C4⋊C4—221no—
208C4⋊C4—221no—
209C22⋊C4—21no—
210C22⋊C4—21no—
211C22⋊C4—221no—
212C22⋊C4—221no—
213C22⋊C4—221no—
214C42—111no—
215C42—111no—
216C42—111no—
217C42—221no—
218C42C22×D1111yescharacteristic
219C11#321811yescharacteristic, complemented, Sylow
220C23—21no—
221C23—111no—
222Q8—22no—
223Q8—22no—
224Q8—22no—
225Q8—222no—
226Q8—222no—
227Q8—444no—
228D4—22no—
229D4—442no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—111no—
233C2×C4—111no—
234C2×C4—111no—
235C2×C4—222no—
236C2×C4—222no—
237C2×C4—222no—
238C2×C4—221no—
239C2×C4—221no—
240C2×C4—222no—
241C2×C4—444no—
242C2×C4—442no—
243C2×C4D4×D1111yescharacteristic
244C2×C4D4×D1111yescharacteristic
245C2×C4C23×D1111yescharacteristic
246C8—22no—
247C8—222no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—112no—
252C22—221no—
253C22—221no—
254C22C2×D4×D1111yescharacteristic
255C4—21no—
256C4—21no—
257C4—42no—
258C4—41no—
259C4—112no—
260C4—221no—
261C4—221no—
262C4—442no—
263C4—441no—
264C4—441no—
265C4#6703712yes—
266C2—81no—
267C2—222no—
268C2#1062324611yescharacteristic
269C2D11×#13711yescharacteristic
270C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#497C2
socleC22×C11C22×D4
prime radical#66991C22
hypercenter#497D11
hypocenterC11#3218
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. D11×C4⋊Q8C2semidirect
3. C11×#497C2semidirect
4. #10622799C2semidirect
5. #10622795C2semidirect
7. #10622775C2semidirect
8. #10622695C2semidirect
9. #10622673C2semidirect
10. #10622318C2semidirect
11. #10622316C2semidirect
116. #497D11semidirect
219. C11#3218semidirect

Maximal subgroups

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

subgroupindex
D11×C4⋊Q82
#106232112
C11×#4972
#106227992
#106227952
#106227832
#106227752
#106226952
#106226732
#106223182
#106223162
#321811