Finite Group Databasebeta

← #28406100

Subgroups — #28406100

Order 14464.

198 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 58 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#20299618C211yesmaximal, characteristic
2#20299615C211yesmaximal, characteristic
3#20299458C212yesmaximal, complemented
4#20299457C212yesmaximal, complemented
5#20299150C211yesmaximal, characteristic
6#16813689C2212yes—
7#16813689C2212yes—
8C22⋊#11744753—21no—
9C22⋊#11744753—21no—
10#16813677—21no—
11C4×#11744753—21no—
12#16813621C2211yescharacteristic
13#16813620C2211yescharacteristic
14#16813612—21no—
15#16813601C411yescharacteristic
16#16813599—21no—
17Q8×Dic113C411yescharacteristic
18#16813587—21no—
19#16813587C411yescharacteristic
20#16813578—21no—
21C2×C4×Dic113C2211yescharacteristic
22C22⋊Q8×C113C411yescharacteristic
23C2×#11744753—22no—
24C2×#11744753—22no—
25C2×Dic226—21no—
26C2×Dic226C2×C411yescharacteristic
27C22×Dic113D411yescharacteristic
28C22×Dic113D411yescharacteristic
29C4⋊Dic113—21no—
30C4⋊Dic113C2×C411yescharacteristic
31#14268626—21no—
32#14268626—21no—
33#14268626—21no—
34#14268626—21no—
35#14268626—21no—
36C22⋊Dic113—21no—
37C4×Dic113—21no—
38C4×Dic113—21no—
39C4×Dic113C2×C411yescharacteristic
40C4×Dic113D411yescharacteristic
41C4×Dic113D411yescharacteristic
42C4×Dic113C2311yescharacteristic
43C2×Q8×C113C2×C411yescharacteristic
44C22×C4×C113C2×C411yescharacteristic
45C4⋊C4×C113—21no—
46C4⋊C4×C113C2×C411yescharacteristic
47C22⋊C4×C113—21no—
48C23×C113C22⋊C411yescharacteristic
49Q8×C113—41no—
50C2×C4×C113—21no—
51C2×C4×C113—21no—
52C2×C4×C113—41no—
53C2×C4×C113C22⋊C411yescharacteristic
54C2×C4×C113C22×C411yescharacteristic
55C2×Dic113—22no—
56C2×Dic113—22no—
57C2×Dic113—21no—
58C2×Dic113—21no—
59C2×Dic113C22⋊C411yescharacteristic
60C2×Dic113C22⋊C411yescharacteristic
61C2×Dic113C2×D411yescharacteristic
62C2×Dic113C2×D411yescharacteristic
63Dic226—42no—
64Dic226—41no—
65#11744753—42no—
66#11744753—42no—
67C22×C113—21no—
68C22×C113—21no—
69C22×C113—21no—
70C22×C113C2×C22⋊C411yescharacteristic
71C4×C113—21no—
72C4×C113—21no—
73C4×C113—41no—
74C4×C113—41no—
75Dic113—21no—
76Dic113—21no—
77Dic113—41no—
78Dic113—41no—
79Dic113#13512yes—
80Dic113#13712yes—
81C2×C113—41no—
82C2×C113#41311yescharacteristic
83C2×C113#41611yescharacteristic
84C2×C113#41911yescharacteristic
85#1554—1131nomaximal, Sylow
86C113#155411yescharacteristic, complemented, Sylow
87#533—1131no—
88#432—1131no—
89#431—1131no—
90#333—1132no—
91#332—1132no—
92C4⋊Q8—1131no—
93C4⋊Q8—1131no—
94#125—2261no—
95C22⋊Q8—1131no—
96C22⋊Q8—2261no—
97C22⋊Q8#9067311yescharacteristic
98C4×Q8—1131no—
99C4×Q8—1131no—
100C4×Q8—2261no—
101#117—2261no—
102C2×C42—1131no—
103C4⋊C8—1132no—
104C4⋊C8—1132no—
105C22⋊C8—2261no—
106C22⋊C8—2261no—
107#97—2261no—
108C4×C8—2261no—
109C2×Q8—1131no—
110C2×Q8—2261no—
111C2×Q8C2×#9067311yescharacteristic
112C22×C4—1131no—
113C22×C4—1131no—
114C22×C4C2×#9067311yescharacteristic
115C2×C8—2262no—
116C2×C8—2262no—
117C4⋊C4—21no—
118C4⋊C4—1131no—
119C4⋊C4—2261no—
120C4⋊C4—2261no—
121C4⋊C4—2261no—
122C4⋊C4—2261no—
123C4⋊C4—2261no—
124C4⋊C4—2261no—
125C4⋊C4C2×#9067311yescharacteristic
126C22⋊C4—21no—
127C22⋊C4—2261no—
128C42—1131no—
129C42—1131no—
130C42—1131no—
131C42—1131no—
132C42—2261no—
133C42—2261no—
134C23C22⋊#9067311yescharacteristic
135Q8—41no—
136Q8—4521no—
137Q8—4522no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—1131no—
142C2×C4—1131no—
143C2×C4—1131no—
144C2×C4—1131no—
145C2×C4—2262no—
146C2×C4—2262no—
147C2×C4—2261no—
148C2×C4—2261no—
149C2×C4C22⋊#9067311yescharacteristic
150C2×C4C22×#9067311yescharacteristic
151C8—4522no—
152C8—4522no—
153C22—21no—
154C22—21no—
155C22—21no—
156C22C2×C22⋊#9067311yescharacteristic
157C4—21no—
158C4—21no—
159C4—41no—
160C4—41no—
161C4—1132no—
162C4—1132no—
163C4—4521no—
164C4—4521no—
165C4—2261no—
166C4—2261no—
167C2—41no—
168C2#2029958511yescharacteristic
169C2#2029958811yescharacteristic
170C2#2029959111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC22⋊Q8×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC23×C113C22⋊C4
cosocleC4×Dic113C23
hypercenterC22⋊Q8#90673
hypocenterC113#1554
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #20299458C2semidirect
4. #20299457C2semidirect
86. C113#1554semidirect

Maximal subgroups

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

subgroupindex
#202996182
#202996152
#202994582
#202994572
#202991502
#1554113