Finite Group Databasebeta

← #28392242

Subgroups — #28392242

Order 14464.

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

normal subgroups only

This group has 286 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#20299166C211yesmaximal, characteristic
2#99×D113C212yesmaximal, complemented
3#20298393C211yesmaximal, characteristic, complemented
4#20298390C212yesmaximal, complemented
5#354×C113C211yesmaximal, characteristic, complemented
6C2×#14268648C411yescharacteristic, complemented
7C2×D4×D113C2211yescharacteristic
8#16813619C411yescharacteristic, complemented
9#16813618C2211yescharacteristic
10#16813611C411yescharacteristic, complemented
11#16813595—22no—
12#16813592—22no—
13#16813579C411yescharacteristic, complemented
14C22⋊C4×D113—22no—
15#16813537C2212yes—
16#16813536—22no—
17#124×C113C2211yescharacteristic
18#99×C113C2212yes—
19C23×D113D412yes—
20#14268648—42no—
21C2×D452—21no—
22C2×D452—22no—
23C2×D452C2×C411yescharacteristic
24C2×D452C2×C411yescharacteristic, complemented
25C2×C22⋊D113—22no—
26C2×C22⋊D113D412yes—
27D4×D113—42no—
28C2×C4×D113—21no—
29C2×C4×D113—42no—
30C2×C4×D113C2×C411yescharacteristic
31#14268626—21no—
32C22⋊Dic113—22no—
33#14268624—21no—
34#14268624—22no—
35#14268624—42no—
36C4×Dic113C2×C411yescharacteristic, complemented
37C2×Q8×C113C2×C411yescharacteristic, complemented
38C2×D4×C113C2311yescharacteristic
39C22⋊C4×C113—22no—
40C22⋊C4×C113—22no—
41C42×C113C2×C411yescharacteristic, complemented
42C23×C113C2×D412yes—
43C22×D113—22no—
44C22×D113—22no—
45C22×D113—21no—
46C22×D113—82no—
47C22×D113C22⋊C412yes—
48C22×D113C22⋊C411yescharacteristic
49Q8×C113—41no—
50D4×C113—41no—
51C2×C4×C113—21no—
52C2×C4×C113—21no—
53C2×C4×C113—42no—
54C2×C4×C113C22×C411yescharacteristic
55C22⋊D113—42no—
56C22⋊D113—82no—
57C2×Dic113—21no—
58C2×Dic113—42no—
59C2×Dic113C22⋊C411yescharacteristic
60D452—41no—
61D452—41no—
62D452—42no—
63D452—82no—
64C4×D113—22no—
65C4×D113—42no—
66C4×D113—84no—
67C22×C113—22no—
68C22×C113—42no—
69C22×C113C2×C22⋊C411yescharacteristic
70C2×D113—22no—
71C2×D113—41no—
72C2×D113—44no—
73C2×D113—42no—
74C2×D113—42no—
75C2×D113—41no—
76C2×D113—82no—
77C2×D113#9912yes—
78C4×C113—21no—
79C4×C113—41no—
80C4×C113—41no—
81C4×C113—82no—
82Dic113—21no—
83Dic113—41no—
84Dic113—82no—
85C2×C113—21no—
86C2×C113—42no—
87C2×C113C2×#9911yescharacteristic
88D113—22no—
89D113—42no—
90D113—81no—
91#2127—1131nomaximal, Sylow
92C113#212711yescharacteristic, complemented, Sylow
93#535—1131no—
94C2×#99—1132no—
95#354—1131no—
96#354D11311yescharacteristic, complemented
97#353—1132no—
98C2×#41—1131no—
99C22×D4—1131no—
100#127—1131no—
101#127—1131no—
102#124—1131no—
103#124C2×D11311yescharacteristic
104#121—2262no—
105#120—2262no—
106#117—1131no—
107C2×C22⋊C4—2262no—
108#99—1132no—
109#99—2262no—
110#99C2×D11312yes—
111C24—1132no—
112#41—4522no—
113C2×Q8C4×D11311yescharacteristic, complemented
114C2×D4—1132no—
115C2×D4—1131no—
116C2×D4—1131no—
117C2×D4—4522no—
118C2×D4—2262no—
119C2×D4—2261no—
120C2×D4—2262no—
121C2×D4C22×D11311yescharacteristic
122C22×C4—1131no—
123C22×C4—4522no—
124C22×C4—2261no—
125C4⋊C4—2261no—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C22⋊C4—4522no—
129C22⋊C4—2261no—
130C22⋊C4—2262no—
131C22⋊C4—2262no—
132C42—1131no—
133C42C4×D11311yescharacteristic, complemented
134C23—1131no—
135C23—1132no—
136C23—9042no—
137C23—2262no—
138C23—2262no—
139C23—2261no—
140C23D4×D11312yes—
141Q8—41no—
142D4—41no—
143D4—9042no—
144D4—9042no—
145D4—4521no—
146D4—4521no—
147D4—4522no—
148D4—4522no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—1131no—
153C2×C4—9044no—
154C2×C4—4522no—
155C2×C4—4522no—
156C2×C4—2262no—
157C2×C4—2261no—
158C2×C4C2×C4×D11311yescharacteristic
159C22—22no—
160C22—42no—
161C22—1132no—
162C22—9042no—
163C22—4522no—
164C22—4522no—
165C22—4521no—
166C22—4524no—
167C22—4521no—
168C22—2262no—
169C22C22⋊C4×D11311yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—9042no—
175C4—4521no—
176C4—2261no—
177C2—21no—
178C2—42no—
179C2—9041no—
180C2—4522no—
181C2—2262no—
182C2#99×D11311yescharacteristic
subgroupG/H
centerC2#99×D113
commutatorC2×C4×C113C22×C4
FrattiniC2×D4C22×D113
Fitting#354×C113C2
socleC2×C113C2×#99
prime radical#20299166C2
cosocleC2×D4×C113C23
hypercenter#354D113
hypocenterC113#2127
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #99×D113C2semidirect
3. #20298393C2semidirect
4. #20298390C2semidirect
5. #354×C113C2semidirect
6. C2×#14268648C4semidirect
8. #16813619C4semidirect
10. #16813611C4semidirect
13. #16813579C4semidirect
24. C2×D452C2×C4semidirect
36. C4×Dic113C2×C4semidirect
37. C2×Q8×C113C2×C4semidirect
41. C42×C113C2×C4semidirect
92. C113#2127semidirect
96. #354D113semidirect
113. C2×Q8C4×D113semidirect
133. C42C4×D113semidirect

Maximal subgroups

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

subgroupindex
#202991662
#99×D1132
#202983932
#202983902
#354×C1132
#2127113