Finite Group Databasebeta

← #13069558

Subgroups — #13069558

Order 1408.

260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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#10623048C211yesmaximal, characteristic
2M16×Dic11C211yesmaximal, characteristic
3C4×Dic11⋊C4C211yesmaximal, characteristic
4C11×#339C211yesmaximal, characteristic
5#10622193C211yesmaximal, characteristic
6#10622170C211yesmaximal, characteristic
7#10622161C211yesmaximal, characteristic
8C2×C11×M16C2211yescharacteristic
9C11×#117C2211yescharacteristic
10C2×C42×C11C2211yescharacteristic
11#66979C2211yescharacteristic
12C2×Dic11⋊C4—21no—
13C2×C4×Dic11C2211yescharacteristic
14C2×C4×Dic11C2211yescharacteristic
15C2×#4318C2211yescharacteristic
16#66943C411yescharacteristic, complemented
17#66943C411yescharacteristic, complemented
18#66941C411yescharacteristic, complemented
19#66941C411yescharacteristic, complemented
20#66931—21no—
21#66931—21no—
22C4×Dic22—21no—
23C4×Dic22—21no—
24C11⋊#95—21no—
25#66879—21no—
26C8×Dic11—21no—
27C22×C4×C11—21no—
28C22×C4×C11C2311yescharacteristic
29C22×Dic11—21no—
30C22×Dic11D411yescharacteristic
31C22×Dic11D411yescharacteristic
32C2×Dic22—21no—
33C2×Dic22—21no—
34C11×M16—21no—
35C11×M16Q812yescomplemented
36C2×C8×C11—21no—
37C11×C4⋊C4C2×C411yescharacteristic
38C11×C4⋊C4C2×C411yescharacteristic
39C11×C22⋊C4—21no—
40C42×C11—21no—
41C42×C11—21no—
42C42×C11—21no—
43C22⋊Dic11—21no—
44C4⋊Dic11—21no—
45C4⋊Dic11—21no—
46C4⋊Dic11C2×C411yescharacteristic
47C4⋊Dic11C2×C411yescharacteristic
48Dic11⋊C4—24no—
49Dic11⋊C4—21no—
50Dic11⋊C4—21no—
51Dic11⋊C4—21no—
52Dic11⋊C4—21no—
53C4×Dic11—21no—
54C4×Dic11—21no—
55C4×Dic11—21no—
56C4×Dic11C2×C411yescharacteristic
57C4×Dic11C2×C411yescharacteristic
58C4×Dic11D411yescharacteristic
59C4×Dic11D411yescharacteristic
60#4318—21no—
61#4318Q812yescomplemented
62C2×C11⋊C8—21no—
63#1986—111nomaximal, Sylow
64C23×C11C2×D411yescharacteristic
65C2×C4×C11—22no—
66C2×C4×C11—21no—
67C2×C4×C11—21no—
68C2×C4×C11—41no—
69C2×C4×C11—41no—
70C2×C4×C11C22×C411yescharacteristic
71C2×C4×C11C2×D411yescharacteristic
72C2×C4×C11C2×Q811yescharacteristic
73C2×C4×C11C2×Q811yescharacteristic
74C2×C4×C11#4111yescharacteristic
75C2×C4×C11#4111yescharacteristic
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—21no—
79C2×Dic11—21no—
80C2×Dic11—41no—
81C2×Dic11—41no—
82C2×Dic11—41no—
83C2×Dic11C22⋊C411yescharacteristic
84C2×Dic11C22⋊C411yescharacteristic
85C2×Dic11C22⋊C411yescharacteristic
86C2×Dic11C22⋊C411yescharacteristic
87Dic22—42no—
88Dic22—42no—
89C8×C11—22no—
90C11⋊C8—22no—
91#533—111no—
92C4×M16—111no—
93C4×C4⋊C4—111no—
94#339—111no—
95#339—111no—
96#339—111no—
97#339D1111yescharacteristic
98C22×C11—21no—
99C22×C11—21no—
100C22×C11C2×C22⋊C411yescharacteristic
101C22×C11#12411yescharacteristic
102C22×C11C4⋊Q811yescharacteristic
103C4×C11—42no—
104C4×C11—41no—
105C4×C11—41no—
106C4×C11C4×Q811yescharacteristic
107C4×C11C4×Q811yescharacteristic
108C4×C11C22⋊Q811yescharacteristic
109C4×C11C22⋊Q811yescharacteristic
110Dic11—21no—
111Dic11—21no—
112Dic11—21no—
113Dic11—42no—
114Dic11—41no—
115Dic11—41no—
116Dic11#10412yes—
117C2×M16—111no—
118C2×M16C2×D1111yescharacteristic
119C4⋊Q8—111no—
120C4⋊Q8—111no—
121#125—111no—
122#125—111no—
123C22⋊Q8—221no—
124C22⋊Q8—221no—
125C4×Q8—221no—
126C4×Q8—221no—
127#117—111no—
128#117C2×D1111yescharacteristic
129C2×C4⋊C4—221no—
130C2×C42—111no—
131C2×C42—111no—
132C2×C42C2×D1111yescharacteristic
133#97—221no—
134C4×C8—221no—
135#95—221no—
136C2×C11—21no—
137C2×C11—21no—
138C2×C11#39111yescharacteristic
139C2×C11C2×#10411yescharacteristic
140C2×C11#42111yescharacteristic
141C2×Q8—221no—
142C2×Q8—221no—
143C22×C4—21no—
144C22×C4—111no—
145C22×C4—111no—
146C22×C4—221no—
147C22×C4C22×D1111yescharacteristic
148M16—21no—
149M16—112no—
150M16—221no—
151M16Dic2212yescomplemented
152C2×C8—21no—
153C2×C8—221no—
154C4⋊C4—111no—
155C4⋊C4—111no—
156C4⋊C4—221no—
157C4⋊C4—221no—
158C4⋊C4—221no—
159C4⋊C4—221no—
160C4⋊C4—221no—
161C4⋊C4—221no—
162C4⋊C4—224no—
163C4⋊C4C4×D1111yescharacteristic
164C4⋊C4C4×D1111yescharacteristic
165C22⋊C4—21no—
166C22⋊C4—221no—
167C42—21no—
168C42—21no—
169C42—21no—
170C42—111no—
171C42—111no—
172C42—111no—
173C42—111no—
174C42—221no—
175C42—221no—
176C42—221no—
177C11#198611yescharacteristic, complemented, Sylow
178C23D4×D1111yescharacteristic
179Q8—442no—
180Q8—442no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—111no—
187C2×C4—111no—
188C2×C4—111no—
189C2×C4—111no—
190C2×C4—222no—
191C2×C4—222no—
192C2×C4—221no—
193C2×C4—221no—
194C2×C4—441no—
195C2×C4—441no—
196C2×C4—441no—
197C2×C4C2×Dic2211yescharacteristic
198C2×C4C2×C4×D1111yescharacteristic
199C2×C4#433911yescharacteristic
200C2×C4D4×D1111yescharacteristic
201C2×C4#434111yescharacteristic
202C2×C4Q8×D1111yescharacteristic
203C8—22no—
204C8—222no—
205C22—21no—
206C22—21no—
207C22C22⋊C4×D1111yescharacteristic
208C22#6693811yescharacteristic
209C22#6694111yescharacteristic
210C4—42no—
211C4—41no—
212C4—41no—
213C4—112no—
214C4—221no—
215C4—221no—
216C4—221no—
217C4—442no—
218C4—441no—
219C4—441no—
220C4C4×Dic2211yescharacteristic
221C4#6693111yescharacteristic
222C4#6694011yescharacteristic
223C4#6694911yescharacteristic
224C2—21no—
225C2—21no—
226C2#1062225911yescharacteristic
227C2D11×#10411yescharacteristic
228C2#1062243411yescharacteristic
subgroupG/H
centerC2×C4D4×D11
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC11×#339C2
socleC22×C11C2×C22⋊C4
prime radicalC23×C11C2×D4
cosocleC22×C4×C11C23
hypercenter#339D11
hypocenterC11#1986
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
16. #66943C4semidirect
17. #66943C4semidirect
18. #66941C4semidirect
19. #66941C4semidirect
35. C11×M16Q8semidirect
61. #4318Q8semidirect
151. M16Dic22semidirect
177. C11#1986semidirect

Maximal subgroups

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

subgroupindex
#106230482
M16×Dic112
C4×Dic11⋊C42
C11×#3392
#106221932
#106221702
#106221612
#198611