Finite Group Databasebeta

← #28401469

Subgroups — #28401469

Order 14464.

378 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299169C212yesmaximal
2#20298940C214yesmaximal, complemented
3#20298856C212yesmaximal, complemented
4#20298839C212yesmaximal, complemented
5#20298756C214yesmaximal, complemented
6#408×C113C211yesmaximal, characteristic
7C22×Dic226C2212yes—
8C2×Dic452C2212yes—
9C2×Dic452C2212yes—
10#16813620—22no—
11#16813609—22no—
12#16813603—22no—
13#16813603—22no—
14#16813601C2214yes—
15#16813601C2214yes—
16#16813581C2212yes—
17#16813556C2212yes—
18#16813554C2212yes—
19#16813547C2214yes—
20#16813547C2214yes—
21C2×#41×C113C2211yescharacteristic
22C2×M16×C113C2211yescharacteristic
23C22×C8×C113C2211yescharacteristic
24C22⋊C8×C113C2214yes—
25C2×Dic226—22no—
26C2×Dic226—42no—
27C2×Dic226—42no—
28C2×Dic226C2314yes—
29C22×Dic113—22no—
30Dic452—42no—
31Dic452—42no—
32C4⋊Dic113C2314yes—
33#14268626—24no—
34#14268626—24no—
35C22⋊Dic113—22no—
36C22⋊Dic113—24no—
37C22⋊Dic113—24no—
38C4×Dic113—22no—
39#41×C113—41no—
40#41×C113—41no—
41C2×Q8×C113D411yescharacteristic
42C2×D4×C113D411yescharacteristic
43C2×D4×C113D412yes—
44C22×C4×C113C2312yes—
45C22×C4×C113C2311yescharacteristic
46M16×C113—41no—
47C2×C8×C113—41no—
48C2×C8×C113C2312yes—
49C2×C8×C113C2312yes—
50C23×C113C2×D411yescharacteristic
51C23×C113C2×D412yes—
52Q8×C113—41no—
53D4×C113—42no—
54D4×C113—41no—
55C2×C4×C113—21no—
56C2×C4×C113—21no—
57C2×C4×C113—22no—
58C2×C4×C113—22no—
59C2×C4×C113C2×D412yes—
60C2×C4×C113C2×D411yescharacteristic
61C2×C4×C113C2411yescharacteristic
62C2×Dic113—24no—
63C2×Dic113—24no—
64C2×Dic113—44no—
65Dic226—24no—
66Dic226—24no—
67Dic226—44no—
68C8×C113—22no—
69C8×C113—22no—
70C22×C113—22no—
71C22×C113—21no—
72C22×C113—22no—
73C22×C113—24no—
74C22×C113C22×D411yescharacteristic
75C4×C113—22no—
76C4×C113—21no—
77C4×C113H(5,𝔽2)11yescharacteristic
78C4×C113H(5,𝔽2)11yescharacteristic
79Dic113—44no—
80Dic113—44no—
81C2×C113—42no—
82C2×C113—41no—
83C2×C113#53411yescharacteristic
84C2×C113#57812yes—
85#3202—1131nomaximal, Sylow
86C113#320211yescharacteristic, complemented, Sylow
87#536—1132no—
88#485—1134no—
89#470—1132no—
90#467—1132no—
91#451—1134no—
92#408D11311yescharacteristic
93C2×#41C2×D11311yescharacteristic
94C22×Q8—1132no—
95C2×Q16—1132no—
96C2×Q16—1132no—
97C2×M16C2×D11311yescharacteristic
98C22×C8C2×D11311yescharacteristic
99C4⋊Q8—2262no—
100#124—2262no—
101#123—2262no—
102#123—2262no—
103C22⋊Q8—1134no—
104C22⋊Q8—1134no—
105#117—1132no—
106#107—1132no—
107#106—1132no—
108#103—1134no—
109#103—1134no—
110C22⋊C8C2×D11314yes—
111#41—41no—
112#41—41no—
113C2×Q8—1134no—
114C2×Q8—4522no—
115C2×Q8—4522no—
116C2×Q8—2262no—
117C2×Q8D45211yescharacteristic
118C2×D4D45211yescharacteristic
119C2×D4D45212yes—
120C22×C4—2262no—
121C22×C4C22×D11312yes—
122C22×C4C22×D11311yescharacteristic
123Q16—4522no—
124Q16—4522no—
125M16—41no—
126C2×C8—41no—
127C2×C8C22×D11312yes—
128C2×C8C22×D11312yes—
129C4⋊C4—1134no—
130C4⋊C4—2264no—
131C4⋊C4—2264no—
132C22⋊C4—2262no—
133C22⋊C4—2264no—
134C22⋊C4—2264no—
135C42—2262no—
136C23C2×D45211yescharacteristic
137C23C2×D45212yes—
138Q8—41no—
139Q8—4524no—
140Q8—2264no—
141Q8—2264no—
142D4—42no—
143D4—41no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—4524no—
149C2×C4—2264no—
150C2×C4—2264no—
151C2×C4C2×D45212yes—
152C2×C4C2×D45211yescharacteristic
153C2×C4C23×D11311yescharacteristic
154C8—22no—
155C8—22no—
156C22—22no—
157C22—24no—
158C22—22no—
159C22—21no—
160C22C22×D45211yescharacteristic
161C4—22no—
162C4—21no—
163C4—4524no—
164C4—4524no—
165C4#1681366711yescharacteristic
166C4#1681366711yescharacteristic
167C2—42no—
168C2—41no—
169C2#2029916011yescharacteristic
170C2#2029941512yes—
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#408×C113C2
socleC22×C113C22×D4
prime radicalC2×#41×C113C22
hypercenter#408D113
hypocenterC113#3202
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #20298940C2semidirect
3. #20298856C2semidirect
4. #20298839C2semidirect
5. #20298756C2semidirect
86. C113#3202semidirect

Maximal subgroups

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

subgroupindex
#202991692
#202989402
#202988562
#202988392
#202987562
#408×C1132
#3202113