Finite Group Databasebeta

← #13078994

Subgroups — #13078994

Order 1408.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C2×#66997C211yesmaximal, characteristic
2#10623048C211yesmaximal, characteristic
3C11×#419C211yesmaximal, characteristic
4#10622838C211yesmaximal, characteristic
5#10622733C211yesmaximal, characteristic
6M16×Dic11C211yesmaximal, characteristic
7#10622617C211yesmaximal, characteristic
8#10622410C214yesmaximal, complemented
9#10622405C214yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C2×C11×M16C2211yescharacteristic
13C11×#117C2211yescharacteristic
14#66997—22no—
15#66997C2212yes—
16#66997C2212yes—
17#66979C2211yescharacteristic
18C2×Dic11⋊C4—22no—
19C2×C4×Dic11C2211yescharacteristic
20C2×#4318C2211yescharacteristic
21#66943C2212yes—
22#66941C2212yes—
23#66931—22no—
24C4×Dic22—22no—
25C11×#103C2214yes—
26#66899C2214yes—
27#66880C2214yes—
28#66879C2212yes—
29C8×Dic11C2212yes—
30#66874C2214yes—
31C2×Q8×C11—21no—
32C2×Q8×C11—22no—
33C2×Q8×C11—22no—
34C2×Q8×C11C2312yes—
35C22×C4×C11—21no—
36C22×C4×C11C2311yescharacteristic
37C22×Dic11—21no—
38C22×Dic11D412yes—
39C2×Dic22—22no—
40C2×Dic22—21no—
41C2×Dic22—22no—
42C2×Dic22—22no—
43C2×Dic22C2312yes—
44C11×M16—22no—
45C2×C8×C11C2312yes—
46C11×C4⋊C4C2312yes—
47C11×C22⋊C4—21no—
48C42×C11—21no—
49C22⋊Dic11—21no—
50C4⋊Dic11—22no—
51C4⋊Dic11C2312yes—
52Dic11⋊C4—22no—
53Dic11⋊C4—22no—
54Dic11⋊C4—24no—
55Dic11⋊C4—24no—
56C4×Dic11—21no—
57C4×Dic11D412yes—
58C4×Dic11C2311yescharacteristic
59C4×Dic11C2311yescharacteristic
60#4318—22no—
61C2×C11⋊C8C2312yes—
62#3139—111nomaximal, Sylow
63C23×C11C2×D411yescharacteristic
64Q8×C11—22no—
65Q8×C11—22no—
66Q8×C11—42no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—42no—
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11#4112yes—
72C2×C4×C11#4112yes—
73C2×C4×C11C2411yescharacteristic
74C2×Dic11—24no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—42no—
78C2×Dic11C2×D412yes—
79C2×Dic11C2×D412yes—
80Dic22—22no—
81Dic22—22no—
82Dic22—42no—
83Dic22—44no—
84C8×C11—22no—
85C11⋊C8—22no—
86#533—111no—
87C2×C4⋊Q8—111no—
88#491—114no—
89#487—114no—
90#419—111no—
91#419—111no—
92#419—111no—
93#419D1111yescharacteristic
94C4×M16—111no—
95C22×C11—22no—
96C22×C11#12412yes—
97C22×C11C22×D411yescharacteristic
98C4×C11—42no—
99C4×C11—42no—
100C4×C11#12412yes—
101C4×C11C2×#4111yescharacteristic
102C4×C11C2×#4111yescharacteristic
103Dic11—22no—
104Dic11—42no—
105Dic11—42no—
106Dic11#13714yes—
107C22×Q8—111no—
108C22×Q8C2×D1111yescharacteristic
109C2×M16—111no—
110C2×M16C2×D1111yescharacteristic
111C4⋊Q8—112no—
112C4⋊Q8—112no—
113C4⋊Q8—112no—
114C4⋊Q8—222no—
115#125—112no—
116C22⋊Q8—222no—
117C4×Q8—222no—
118#117—111no—
119#117C2×D1111yescharacteristic
120C2×C4⋊C4—222no—
121C2×C42—111no—
122#103—114no—
123#103—114no—
124#103—114no—
125#103C2×D1114yes—
126#97—112no—
127C4×C8—112no—
128C2×C11—22no—
129C2×C11C2×#12411yescharacteristic
130C2×C11C2×#13712yes—
131C2×Q8—21no—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—112no—
135C2×Q8—222no—
136C2×Q8—221no—
137C2×Q8—222no—
138C2×Q8—222no—
139C2×Q8C22×D1112yes—
140C22×C4—21no—
141C22×C4—112no—
142C22×C4—221no—
143C22×C4C22×D1111yescharacteristic
144M16—22no—
145M16—222no—
146C2×C8—112no—
147C2×C8C22×D1112yes—
148C4⋊C4—112no—
149C4⋊C4—224no—
150C4⋊C4—224no—
151C4⋊C4—222no—
152C4⋊C4—222no—
153C4⋊C4—222no—
154C4⋊C4C22×D1112yes—
155C22⋊C4—21no—
156C22⋊C4—221no—
157C42—21no—
158C42—112no—
159C42—111no—
160C42—111no—
161C42—221no—
162C11#313911yescharacteristic, complemented, Sylow
163C23D4×D1111yescharacteristic
164Q8—22no—
165Q8—22no—
166Q8—42no—
167Q8—222no—
168Q8—222no—
169Q8—444no—
170Q8—442no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—112no—
175C2×C4—112no—
176C2×C4—224no—
177C2×C4—222no—
178C2×C4—222no—
179C2×C4—442no—
180C2×C4#433912yes—
181C2×C4D4×D1111yescharacteristic
182C2×C4#434112yes—
183C2×C4C23×D1111yescharacteristic
184C8—22no—
185C8—222no—
186C22—22no—
187C22#6693812yes—
188C22C2×D4×D1111yescharacteristic
189C4—42no—
190C4—42no—
191C4—114no—
192C4—222no—
193C4—442no—
194C4—442no—
195C4#6693812yes—
196C4C2×#433911yescharacteristic
197C4C2×#434111yescharacteristic
198C2—22no—
199C2C2×#6693811yescharacteristic
200C2D11×#13712yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#419C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#419D11
hypocenterC11#3139
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
8. #10622410C2semidirect
9. #10622405C2semidirect
162. C11#3139semidirect

Maximal subgroups

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

subgroupindex
C2×#669972
#106230482
C11×#4192
#106228382
#106227332
M16×Dic112
#106226172
#106224102
#106224052
#313911