Finite Group Databasebeta

← #13067039

Subgroups — #13067039

Order 1408.

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

normal subgroups only

This group has 312 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
1C4×D4×D11C211yesmaximal, characteristic
2#10622450C211yesmaximal, characteristic, complemented
3#10622298C211yesmaximal, characteristic, complemented
4C11×D4⋊C8C211yesmaximal, characteristic, complemented
5D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6#10622121C211yesmaximal, characteristic, complemented
7#10622097C211yesmaximal, characteristic, complemented
8C2×D4×D11C411yescharacteristic
9C22×C4×D11—21no—
10C4×D4×C11C2211yescharacteristic
11D4×Dic11C411yescharacteristic
12C4×C22⋊D11—21no—
13C2×#4313—21no—
14#66946C411yescharacteristic
15C4⋊C4×D11C411yescharacteristic
16(C22⋊D11)⋊C4—21no—
17C22⋊C4×D11—21no—
18C4×D44C2211yescharacteristic
19C42×D11C2211yescharacteristic
20C11×C4⋊C8C2211yescharacteristic, complemented
21C4×C8×C11C2211yescharacteristic, complemented
22(C2×D11)⋊C8—21no—
23Dic11⋊C8—21no—
24Dic11⋊C8—21no—
25C4⋊(C11⋊C8)C2211yescharacteristic, complemented
26C4×C11⋊C8C2211yescharacteristic, complemented
27C23×D11—21no—
28C2×D4×C11C2×C411yescharacteristic
29C22×C4×C11—21no—
30C2×C22⋊D11—21no—
31C22×Dic11—21no—
32D4×D11—22no—
33D4×D11—22no—
34C2×D44C2×C411yescharacteristic
35C2×C4×D11—21no—
36C2×C4×D11—21no—
37C2×C4×D11—21no—
38C2×C4×D11—42no—
39C2×C4×D11—42no—
40C2×C4×D11C2×C411yescharacteristic
41C2×C4×D11D411yescharacteristic
42C2×C4×D11D411yescharacteristic
43C2×C8×C11—21no—
44C2×C8×C11—21no—
45C11×C4⋊C4C2×C411yescharacteristic
46C11×C22⋊C4—21no—
47C42×C11C2311yescharacteristic
48C22⋊Dic11—21no—
49(C2×D11)⋊C4—21no—
50(C2×D11)⋊C4—21no—
51C4⋊Dic11C2×C411yescharacteristic
52Dic11⋊C4—21no—
53C4×Dic11C2×C411yescharacteristic
54C4×Dic11D411yescharacteristic
55C4×Dic11D411yescharacteristic
56C2×C11⋊C8—21no—
57C2×C11⋊C8—21no—
58#4313—42no—
59#1486—111nomaximal, Sylow
60C23×C11—21no—
61C22×D11—24no—
62C22×D11—21no—
63C22×D11—42no—
64C22×D11—42no—
65C22×D11C22⋊C411yescharacteristic
66D4×C11—21no—
67D4×C11M1612yescomplemented
68C2×C4×C11—21no—
69C2×C4×C11—41no—
70C2×C4×C11—41no—
71C2×C4×C11C22×C411yescharacteristic
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2×D411yescharacteristic
74C22⋊D11—24no—
75C2×Dic11—21no—
76C2×Dic11—42no—
77C2×Dic11C22⋊C411yescharacteristic
78C2×Dic11C22⋊C411yescharacteristic
79C2×Dic11C22⋊C411yescharacteristic
80D44—21no—
81D44M1612yescomplemented
82C4×D11—21no—
83C4×D11—21no—
84C4×D11—41no—
85C4×D11—42no—
86C4×D11—41no—
87C4×D11—41no—
88C4×D11—42no—
89C4×D11D812yes—
90C4×D11SD1612yes—
91C8×C11—41no—
92C8×C11—41no—
93C11⋊C8—41no—
94C11⋊C8—41no—
95C2×C4×D4—111no—
96#431—111no—
97#423—111no—
98D4⋊C8—111no—
99D4⋊C8—111no—
100D4⋊C8—111no—
101D4⋊C8D1111yescharacteristic, complemented
102C22×C11—22no—
103C22×C11—41no—
104C22×C11—41no—
105C22×C11C2×C22⋊C411yescharacteristic
106C2×D11—21no—
107C2×D11—21no—
108C2×D11—22no—
109C2×D11—48no—
110C2×D11—41no—
111C2×D11—41no—
112C2×D11#10212yes—
113C4×C11—21no—
114C4×C11—41no—
115C4×C11C2×M1611yescharacteristic
116C4×C11C2×M1611yescharacteristic
117C4×C11C2×D811yescharacteristic
118C4×C11C2×SD1611yescharacteristic
119Dic11—21no—
120Dic11—21no—
121Dic11—41no—
122Dic11#10212yes—
123C22×D4—111no—
124C23×C4—221no—
125C2×M16—221no—
126C4×D4—111no—
127C4×D4—111no—
128C4×D4—111no—
129C4×D4—221no—
130C4×D4—221no—
131C4×D4C2×D1111yescharacteristic
132C2×C4⋊C4—111no—
133C2×C22⋊C4—221no—
134C2×C42—111no—
135C4⋊C8—111no—
136C4⋊C8—221no—
137C4⋊C8—221no—
138C4⋊C8C2×D1111yescharacteristic, complemented
139C22⋊C8—221no—
140C4×C8—111no—
141C4×C8C2×D1111yescharacteristic, complemented
142C2×C11—42no—
143C2×C11#40711yescharacteristic
144C2×C11C2×#10211yescharacteristic
145C2×C11#42111yescharacteristic
146D11—22no—
147D11—42no—
148C24—221no—
149C2×D4—111no—
150C2×D4—221no—
151C2×D4—222no—
152C2×D4—222no—
153C2×D4C4×D1111yescharacteristic
154C22×C4—21no—
155C22×C4—111no—
156C22×C4—111no—
157C22×C4—111no—
158C22×C4—221no—
159C22×C4—221no—
160C22×C4—221no—
161C22×C4—221no—
162C22×C4—442no—
163C22×C4—442no—
164M16—442no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—221no—
168C2×C8—221no—
169C4⋊C4—111no—
170C4⋊C4—221no—
171C4⋊C4C4×D1111yescharacteristic
172C22⋊C4—21no—
173C22⋊C4—221no—
174C22⋊C4—221no—
175C22⋊C4—221no—
176C42—111no—
177C42—111no—
178C42—111no—
179C42C22×D1111yescharacteristic
180C11#148611yescharacteristic, complemented, Sylow
181C23—21no—
182C23—111no—
183C23—224no—
184C23—221no—
185C23—442no—
186C23—442no—
187D4—21no—
188D4—112no—
189D4—224no—
190D4—221no—
191D4#431312yescomplemented
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—111no—
196C2×C4—112no—
197C2×C4—112no—
198C2×C4—111no—
199C2×C4—111no—
200C2×C4—221no—
201C2×C4—221no—
202C2×C4—221no—
203C2×C4—441no—
204C2×C4—442no—
205C2×C4—442no—
206C2×C4—442no—
207C2×C4—441no—
208C2×C4—441no—
209C2×C4C2×C4×D1111yescharacteristic
210C2×C4D4×D1111yescharacteristic
211C2×C4D4×D1111yescharacteristic
212C8—41no—
213C8—41no—
214C8—441no—
215C8—441no—
216C22—22no—
217C22—41no—
218C22—41no—
219C22—112no—
220C22—221no—
221C22—221no—
222C22—222no—
223C22—448no—
224C22—441no—
225C22—441no—
226C22C22⋊C4×D1111yescharacteristic
227C4—21no—
228C4—41no—
229C4—112no—
230C4—221no—
231C4—221no—
232C4—441no—
233C4C2×#431311yescharacteristic
234C4M16×D1111yescharacteristic
235C4D8×D1111yescharacteristic
236C4SD16×D1111yescharacteristic
237C2—42no—
238C2—222no—
239C2—442no—
240C2#1062233911yescharacteristic
241C2D11×#10211yescharacteristic
242C2#1062243411yescharacteristic
subgroupG/H
centerC2×C4D4×D11
commutatorC2×C4×C11C22×C4
FrattiniC42C22×D11
FittingC11×D4⋊C8C2
socleC22×C11C2×C22⋊C4
prime radicalC2×D4×D11C4
cosocleC42×C11C23
hypercenterD4⋊C8D11
hypocenterC11#1486
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10622450C2semidirect
3. #10622298C2semidirect
4. C11×D4⋊C8C2semidirect
5. D4⋊(C11⋊C8)C2semidirect
6. #10622121C2semidirect
7. #10622097C2semidirect
20. C11×C4⋊C8C22semidirect
21. C4×C8×C11C22semidirect
25. C4⋊(C11⋊C8)C22semidirect
26. C4×C11⋊C8C22semidirect
67. D4×C11M16semidirect
81. D44M16semidirect
101. D4⋊C8D11semidirect
138. C4⋊C8C2×D11semidirect
141. C4×C8C2×D11semidirect
180. C11#1486semidirect
191. D4#4313semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D112
#106224502
#106222982
C11×D4⋊C82
D4⋊(C11⋊C8)2
#106221212
#106220972
#148611