Finite Group Databasebeta

← #28389550

Subgroups — #28389550

Order 14464.

238 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 53 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#20299229C211yesmaximal, characteristic
2#20298756C212yesmaximal
3#20298518C211yesmaximal, characteristic
4#20298336C212yesmaximal
5#324×C113C211yesmaximal, characteristic
6C22×Dic226C2211yescharacteristic
7C2×Dic452—22no—
8#16813621—22no—
9#16813613—22no—
10#16813601—21no—
11#16813601C2212yes—
12#16813581—21no—
13C2×#14268626—21no—
14#16813547—22no—
15#16813529—21no—
16#16813529C2211yescharacteristic
17C2×C4⋊C4×C113C2211yescharacteristic
18C22⋊C8×C113C2212yes—
19C2×Dic226—22no—
20C2×Dic226—21no—
21C2×Dic226—42no—
22C2×Dic226D412yes—
23C22×Dic113—21no—
24C22×Dic113—21no—
25Dic452—44no—
26C4⋊Dic113—21no—
27C4⋊Dic113—21no—
28C4⋊Dic113—21no—
29C4⋊Dic113D412yes—
30#14268626—22no—
31#14268626—22no—
32#14268626—42no—
33C22⋊Dic113—22no—
34C4×Dic113—22no—
35C22×C4×C113D411yescharacteristic
36C22×C4×C113D411yescharacteristic
37C22×C4×C113C2311yescharacteristic
38C2×C8×C113—22no—
39C4⋊C4×C113—22no—
40C23×C113C2×D411yescharacteristic
41C2×C4×C113—21no—
42C2×C4×C113—21no—
43C2×C4×C113—21no—
44C2×C4×C113—41no—
45C2×C4×C113—41no—
46C2×C4×C113Q1612yescomplemented
47C2×C4×C113C2×D412yes—
48C2×Dic113—22no—
49C2×Dic113—22no—
50C2×Dic113—22no—
51C2×Dic113—22no—
52C2×Dic113—41no—
53C2×Dic113—41no—
54C2×Dic113—41no—
55C2×Dic113—41no—
56Dic226—24no—
57Dic226—42no—
58Dic226—42no—
59Dic226—81no—
60C8×C113—42no—
61C22×C113—21no—
62C22×C113—21no—
63C22×C113#12011yescharacteristic
64C22×C113C2×Q1611yescharacteristic
65C22×C113#13711yescharacteristic
66C4×C113—22no—
67C4×C113—22no—
68C4×C113—41no—
69Dic113—42no—
70Dic113—42no—
71Dic113—42no—
72Dic113—42no—
73C2×C113—21no—
74C2×C113—21no—
75C2×C113#45111yescharacteristic
76C2×C113#45611yescharacteristic
77C2×C113B(4,𝔽2)11yescharacteristic
78#1605—1131nomaximal, Sylow
79C113#160511yescharacteristic, complemented, Sylow
80#544—1131no—
81#451—1132no—
82#395—1131no—
83#328—1132no—
84#324D11311yescharacteristic
85C22×Q8—1131no—
86C2×Q16—2262no—
87C4⋊Q8—2262no—
88#125—2262no—
89C22⋊Q8—1132no—
90C22⋊Q8—2261no—
91#117—2261no—
92C2×C4⋊C4—2261no—
93C2×C4⋊C4C2×D11311yescharacteristic
94#103—2262no—
95C22⋊C8C2×D11312yes—
96#95—1131no—
97#95—2261no—
98C2×Q8—1132no—
99C2×Q8—4522no—
100C2×Q8—2261no—
101C2×Q8—2262no—
102C22×C4—2261no—
103C22×C4—2261no—
104C22×C4D45211yescharacteristic
105C22×C4D45211yescharacteristic
106C22×C4C22×D11311yescharacteristic
107Q16—4524no—
108C2×C8—22no—
109C4⋊C4—22no—
110C4⋊C4—1132no—
111C4⋊C4—4522no—
112C4⋊C4—2261no—
113C4⋊C4—2261no—
114C4⋊C4—2261no—
115C4⋊C4—2262no—
116C4⋊C4—2262no—
117C22⋊C4—2262no—
118C42—2262no—
119C23C2×D45211yescharacteristic
120Q8—9041no—
121Q8—4522no—
122Q8—4522no—
123Q8—2264no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—4521no—
130C2×C4—4521no—
131C2×C4—4521no—
132C2×C4—4521no—
133C2×C4—2262no—
134C2×C4—2262no—
135C2×C4—2262no—
136C2×C4—2262no—
137C2×C4Dic45212yescomplemented
138C2×C4D4×D11312yes—
139C8—42no—
140C22—21no—
141C22—21no—
142C22#1681359211yescharacteristic
143C22C2×Dic45211yescharacteristic
144C22#1681365511yescharacteristic
145C4—22no—
146C4—22no—
147C4—41no—
148C4—4522no—
149C4—4522no—
150C4—4522no—
151C4—4522no—
152C2—21no—
153C2—21no—
154C2#2029875611yescharacteristic
155C2#2029878311yescharacteristic
156C2#2029878611yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#324×C113C2
socleC22×C113#120
prime radicalC23×C113C2×D4
hypercenter#324D113
hypocenterC113#1605
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
46. C2×C4×C113Q16semidirect
79. C113#1605semidirect
137. C2×C4Dic452semidirect

Maximal subgroups

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

subgroupindex
#202992292
#202987562
#202985182
#202983362
#324×C1132
#1605113