Finite Group Databasebeta

← #28392236

Subgroups — #28392236

Order 14464.

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

normal subgroups only

This group has 258 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#20299146C211yesmaximal, characteristic
2#20298570C212yesmaximal, complemented
3#20298392C212yesmaximal, complemented
4#20298391C211yesmaximal, characteristic, complemented
5#353×C113C211yesmaximal, characteristic, complemented
6C2×#14268646C411yescharacteristic, complemented
7C2×#14268646C2211yescharacteristic
8#16813622C411yescharacteristic, complemented
9#16813609C411yescharacteristic, complemented
10#16813609C2211yescharacteristic
11#16813593—22no—
12D4×Dic113—22no—
13#16813578—22no—
14C42×D113C411yescharacteristic, complemented
15#16813537C2212yes—
16#16813536—22no—
17#127×C113C2211yescharacteristic
18#99×C113C2212yes—
19#14268646—41no—
20#14268646—41no—
21#14268646—41no—
22#14268646—41no—
23C2×Dic226C2×C411yescharacteristic
24C2×Dic226C2×C411yescharacteristic
25C2×C22⋊D113—21no—
26C2×C22⋊D113D412yes—
27C22×Dic113—21no—
28C22×Dic113D412yes—
29C2×C4×D113—21no—
30C2×C4×D113C2×C411yescharacteristic
31C4⋊Dic113—22no—
32#14268626—42no—
33C22⋊Dic113—22no—
34C22⋊Dic113—22no—
35C22⋊Dic113—22no—
36C4×Dic113—21no—
37C4×Dic113—42no—
38C4×Dic113C2×C411yescharacteristic
39C2×D4×C113—22no—
40C2×D4×C113C2×C411yescharacteristic
41C2×D4×C113C2311yescharacteristic
42C22⋊C4×C113—22no—
43C42×C113C2×C411yescharacteristic
44C23×C113—21no—
45C23×C113C2×D412yes—
46C22×D113C22⋊C411yescharacteristic
47D4×C113—41no—
48D4×C113—41no—
49D4×C113—44no—
50C2×C4×C113—21no—
51C2×C4×C113—42no—
52C2×C4×C113C22×C411yescharacteristic
53C22⋊D113—42no—
54C22⋊D113—42no—
55C2×Dic113—22no—
56C2×Dic113—22no—
57C2×Dic113—21no—
58C2×Dic113—21no—
59C2×Dic113—41no—
60C2×Dic113—41no—
61C2×Dic113—42no—
62C2×Dic113C22⋊C412yes—
63C2×Dic113C22⋊C411yescharacteristic
64C4×D113—21no—
65C4×D113—21no—
66C4×D113—42no—
67Dic226—41no—
68Dic226—41no—
69C22×C113—22no—
70C22×C113—42no—
71C22×C113—42no—
72C22×C113—41no—
73C22×C113C2×C22⋊C411yescharacteristic
74C2×D113—21no—
75C2×D113—41no—
76C4×C113—22no—
77C4×C113—21no—
78C4×C113—82no—
79Dic113—22no—
80Dic113—41no—
81Dic113—41no—
82Dic113—82no—
83Dic113#9911yescharacteristic
84Dic113#9911yescharacteristic
85C2×C113—21no—
86C2×C113—42no—
87C2×C113—81no—
88C2×C113C2×#9911yescharacteristic
89D113—41no—
90#2126—1131nomaximal, Sylow
91C113#212611yescharacteristic, complemented, Sylow
92#532—1131no—
93#410—1132no—
94#354—1132no—
95#353—1131no—
96#353D11311yescharacteristic, complemented
97C2×#41—1131no—
98C2×#41—1131no—
99C4⋊Q8—1131no—
100#127C2×D11311yescharacteristic
101#124—1131no—
102#124—1131no—
103#121—2262no—
104C4×D4—2262no—
105#117—2262no—
106C2×C42—1131no—
107#99—1132no—
108#99—2262no—
109#99C2×D11312yes—
110#41—4521no—
111#41—4521no—
112#41—4521no—
113#41—4521no—
114C2×Q8—1131no—
115C2×Q8—1131no—
116C2×D4—22no—
117C2×D4—1132no—
118C2×D4—2261no—
119C2×D4C4×D11311yescharacteristic
120C2×D4C22×D11311yescharacteristic
121C22×C4—1132no—
122C22×C4—1131no—
123C22×C4—2261no—
124C22×C4—2261no—
125C4⋊C4—4522no—
126C4⋊C4—2262no—
127C22⋊C4—22no—
128C22⋊C4—2262no—
129C22⋊C4—2262no—
130C22⋊C4—2262no—
131C42—1131no—
132C42—4522no—
133C42—2261no—
134C42C4×D11311yescharacteristic
135C23—21no—
136C23—1131no—
137C23D4×D11312yes—
138Q8—4521no—
139Q8—4521no—
140D4—41no—
141D4—41no—
142D4—44no—
143D4—4522no—
144D4—4522no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—1131no—
148C2×C4—1132no—
149C2×C4—4522no—
150C2×C4—4521no—
151C2×C4—4521no—
152C2×C4—4522no—
153C2×C4—2261no—
154C2×C4—2261no—
155C2×C4—2262no—
156C2×C4—2262no—
157C2×C4—2261no—
158C2×C4—2261no—
159C2×C4C2×C4×D11311yescharacteristic
160C22—22no—
161C22—42no—
162C22—42no—
163C22—41no—
164C22—4521no—
165C22—2261no—
166C22C22⋊C4×D11311yescharacteristic
167C4—22no—
168C4—21no—
169C4—82no—
170C4—1131no—
171C4—1131no—
172C4—9042no—
173C4—4521no—
174C4—4521no—
175C4—2262no—
176C2—21no—
177C2—42no—
178C2—81no—
179C2—4521no—
180C2#99×D11311yescharacteristic
subgroupG/H
centerC2#99×D113
commutatorC2×C4×C113C22×C4
FrattiniC2×D4C22×D113
Fitting#353×C113C2
socleC2×C113C2×#99
prime radical#20299146C2
cosocleC2×D4×C113C23
hypercenter#353D113
hypocenterC113#2126
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. #20298392C2semidirect
4. #20298391C2semidirect
5. #353×C113C2semidirect
6. C2×#14268646C4semidirect
8. #16813622C4semidirect
9. #16813609C4semidirect
14. C42×D113C4semidirect
91. C113#2126semidirect
96. #353D113semidirect

Maximal subgroups

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

subgroupindex
#202991462
#202985702
#202983922
#202983912
#353×C1132
#2126113