Finite Group Databasebeta

← #28392244

Subgroups — #28392244

Order 14464.

270 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 55 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#20299161C211yesmaximal, characteristic
2#20298570C212yesmaximal, complemented
3#20298391C211yesmaximal, characteristic, complemented
4#20298390C212yesmaximal, complemented
5#353×C113C211yesmaximal, characteristic, complemented
6C2×#14268646C2211yescharacteristic
7C2×D4×D113C411yescharacteristic, complemented
8#16813618C2211yescharacteristic
9#16813610C411yescharacteristic, complemented
10#16813609C411yescharacteristic, complemented
11#16813594—22no—
12#16813590—22no—
13#16813579C411yescharacteristic, complemented
14#16813578—22no—
15#16813537C2212yescomplemented
16#16813536—22no—
17#127×C113C2211yescharacteristic
18#99×C113C2212yescomplemented
19C23×D113—21no—
20#14268646—42no—
21C2×Dic226C2×C411yescharacteristic
22C2×D452C2×C411yescharacteristic
23C2×C22⋊D113—22no—
24C2×C22⋊D113—21no—
25C2×C22⋊D113D412yes—
26D4×D113—42no—
27C22×Dic113D412yes—
28C2×C4×D113C2×C411yescharacteristic
29#14268626—21no—
30#14268626—42no—
31C22⋊Dic113—22no—
32C22⋊Dic113—22no—
33#14268624—21no—
34#14268624—22no—
35C4×Dic113—42no—
36C4×Dic113C2×C411yescharacteristic
37C2×D4×C113—22no—
38C2×D4×C113C2×C411yescharacteristic
39C2×D4×C113C2311yescharacteristic
40C22⋊C4×C113—22no—
41C42×C113C2×C411yescharacteristic
42C23×C113—21no—
43C23×C113C2×D412yes—
44C22×D113—21no—
45C22×D113—42no—
46C22×D113—82no—
47C22×D113C22⋊C411yescharacteristic
48D4×C113—41no—
49D4×C113—41no—
50D4×C113—82no—
51C2×C4×C113—21no—
52C2×C4×C113—42no—
53C2×C4×C113C22×C411yescharacteristic
54C22⋊D113—42no—
55C22⋊D113—42no—
56C22⋊D113—82no—
57C2×Dic113—22no—
58C2×Dic113—22no—
59C2×Dic113—21no—
60C2×Dic113—42no—
61C2×Dic113C22⋊C412yes—
62C2×Dic113C22⋊C411yescharacteristic
63D452—41no—
64C4×D113—22no—
65Dic226—41no—
66C22×C113—22no—
67C22×C113—42no—
68C22×C113—42no—
69C22×C113—41no—
70C22×C113C2×C22⋊C411yescharacteristic
71C2×D113—21no—
72C2×D113—41no—
73C2×D113—42no—
74C2×D113—41no—
75C2×D113—84no—
76C4×C113—21no—
77C4×C113—41no—
78C4×C113—82no—
79Dic113—22no—
80Dic113—41no—
81Dic113—82no—
82Dic113#9912yes—
83C2×C113—21no—
84C2×C113—42no—
85C2×C113—81no—
86C2×C113C2×#9911yescharacteristic
87D113—41no—
88D113—81no—
89#2128—1131nomaximal, Sylow
90C113#212811yescharacteristic, complemented, Sylow
91#535—1131no—
92#410—1132no—
93#353—1131no—
94#353—1132no—
95#353D11311yescharacteristic, complemented
96C2×#41—1131no—
97C22×D4—1131no—
98#127—1131no—
99#127C2×D11311yescharacteristic
100#124—1131no—
101#124—1131no—
102#121—2262no—
103#120—2262no—
104#117—1131no—
105#117—2262no—
106#99—1132no—
107#99—2262no—
108#99C2×D11312yescomplemented
109C24—2261no—
110#41—4522no—
111C2×Q8—1131no—
112C2×D4—22no—
113C2×D4—1132no—
114C2×D4—1131no—
115C2×D4—4522no—
116C2×D4—2261no—
117C2×D4—2262no—
118C2×D4C4×D11311yescharacteristic
119C2×D4C22×D11311yescharacteristic
120C22×C4—1132no—
121C22×C4—1131no—
122C4⋊C4—4522no—
123C4⋊C4—2261no—
124C22⋊C4—22no—
125C22⋊C4—2262no—
126C22⋊C4—2261no—
127C22⋊C4—2262no—
128C22⋊C4—2262no—
129C42—1131no—
130C42—4522no—
131C42C4×D11311yescharacteristic
132C23—21no—
133C23—1131no—
134C23—9042no—
135C23—4522no—
136C23—2261no—
137C23D4×D11312yes—
138Q8—4521no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—9042no—
143D4—4521no—
144D4—4522no—
145D4—4522no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—1131no—
149C2×C4—1132no—
150C2×C4—4522no—
151C2×C4—2262no—
152C2×C4—2262no—
153C2×C4—2262no—
154C2×C4—2261no—
155C2×C4C2×C4×D11311yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—9044no—
161C22—4522no—
162C22—4521no—
163C22—4521no—
164C22—2261no—
165C22C22⋊C4×D11311yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—1132no—
170C4—9042no—
171C4—4521no—
172C4—2262no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—9041no—
177C2—4521no—
178C2#99×D11311yescharacteristic
subgroupG/H
centerC2#99×D113
commutatorC2×C4×C113C22×C4
FrattiniC2×D4C22×D113
Fitting#353×C113C2
socleC2×C113C2×#99
prime radical#20299161C2
cosocleC2×D4×C113C23
hypercenter#353D113
hypocenterC113#2128
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #20298570C2semidirect
3. #20298391C2semidirect
4. #20298390C2semidirect
5. #353×C113C2semidirect
7. C2×D4×D113C4semidirect
9. #16813610C4semidirect
10. #16813609C4semidirect
13. #16813579C4semidirect
15. #16813537C22semidirect
18. #99×C113C22semidirect
90. C113#2128semidirect
95. #353D113semidirect
108. #99C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991612
#202985702
#202983912
#202983902
#353×C1132
#2128113