Finite Group Databasebeta

← #28390653

Subgroups — #28390653

Order 14464.

316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C2×C4⋊C4×D113C211yesmaximal, characteristic
2#20298561C212yesmaximal
3#20298367C211yesmaximal, characteristic, complemented
4#20298366C212yesmaximal, complemented
5#343×C113C211yesmaximal, characteristic, complemented
6C22×C4×D113C412yes—
7C22×C4×D113C2211yescharacteristic
8C2×#14268631C2212yes—
9C2×C4⋊Dic113C2211yescharacteristic
10C2×#14268626C412yes—
11C4⋊C4×D113—22no—
12C4⋊C4×D113—22no—
13#16813534—22no—
14#16813534—22no—
15C2×M16×C113C2212yes—
16C2×C4⋊C4×C113C2211yescharacteristic
17C23×D113C2×C411yescharacteristic
18C22×Dic113C2×C411yescharacteristic
19C22×Dic113C2×C412yes—
20C2×C4×D113—21no—
21C2×C4×D113—22no—
22C2×C4×D113—21no—
23C2×C4×D113—22no—
24C2×C4×D113—22no—
25C2×C4×D113—44no—
26C2×C4×D113D412yes—
27C2×C4×D113D412yes—
28#14268631—22no—
29#14268631—22no—
30C2×#11744751—22no—
31C4⋊Dic113—22no—
32#14268626—24no—
33C22×C4×C113C2×C412yes—
34C22×C4×C113C2311yescharacteristic
35M16×C113—22no—
36M16×C113—22no—
37C2×C8×C113—22no—
38C4⋊C4×C113—22no—
39C23×C113C22×C411yescharacteristic
40C22×D113—21no—
41C22×D113—21no—
42C22×D113—22no—
43C22×D113—22no—
44C22×D113C22⋊C411yescharacteristic
45C22×D113C22⋊C411yescharacteristic
46C2×C4×C113—22no—
47C2×C4×C113—42no—
48C2×C4×C113C2×D412yes—
49C2×C4×C113#4111yescharacteristic
50C2×C4×C113#4112yes—
51C2×C4×C113#4111yescharacteristic
52C2×Dic113—21no—
53C2×Dic113—21no—
54C2×Dic113—22no—
55C2×Dic113—42no—
56C2×Dic113C22⋊C412yes—
57C4×D113—22no—
58C4×D113—22no—
59C4×D113—22no—
60C4×D113—22no—
61C4×D113—44no—
62C4×D113—44no—
63C8×C113—42no—
64#11744751—42no—
65C22×C113—21no—
66C22×C113—21no—
67C22×C113C2×C22⋊C411yescharacteristic
68C22×C113#11711yescharacteristic
69C22×C113#11711yescharacteristic
70C2×D113—24no—
71C2×D113—24no—
72C2×D113—21no—
73C2×D113—21no—
74C2×D113—21no—
75C2×D113—21no—
76C2×D113#10012yes—
77C2×D113#10112yes—
78C4×C113—42no—
79C4×C113#12312yes—
80C4×C113#12312yes—
81Dic113—22no—
82Dic113—42no—
83C2×C113—21no—
84C2×C113—21no—
85C2×C113#38111yescharacteristic
86C2×C113C2×#10011yescharacteristic
87C2×C113C2×#10111yescharacteristic
88D113—22no—
89D113—22no—
90#1821—1131nomaximal, Sylow
91C113#182111yescharacteristic, complemented, Sylow
92C22×C4⋊C4—1131no—
93#407—1132no—
94#343—1132no—
95#343—1131no—
96#343D11311yescharacteristic, complemented
97C23×C4—1131no—
98C23×C4—1132no—
99C2×M16—1132no—
100C2×M16C2×D11312yes—
101C2×C4⋊C4—1132no—
102C2×C4⋊C4—1131no—
103C2×C4⋊C4—2262no—
104C2×C4⋊C4—2262no—
105C2×C4⋊C4C2×D11311yescharacteristic
106C22⋊C8—2262no—
107C22⋊C8—2262no—
108C24—1131no—
109C22×C4—1131no—
110C22×C4—1132no—
111C22×C4—1132no—
112C22×C4—1132no—
113C22×C4—4524no—
114C22×C4—2262no—
115C22×C4—2262no—
116C22×C4—2261no—
117C22×C4—2262no—
118C22×C4—2261no—
119C22×C4C4×D11312yes—
120C22×C4C22×D11311yescharacteristic
121M16—22no—
122M16—22no—
123M16—2262no—
124M16—2262no—
125C2×C8—22no—
126C2×C8—2262no—
127C4⋊C4—22no—
128C4⋊C4—2264no—
129C4⋊C4—2262no—
130C23—1131no—
131C23—1131no—
132C23—2262no—
133C23—2262no—
134C23—2261no—
135C23—2261no—
136C23C2×C4×D11311yescharacteristic
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—1132no—
140C2×C4—4524no—
141C2×C4—4524no—
142C2×C4—4522no—
143C2×C4—2262no—
144C2×C4—2261no—
145C2×C4—2261no—
146C2×C4—2262no—
147C2×C4—2262no—
148C2×C4—2262no—
149C2×C4—2262no—
150C2×C4D4×D11312yes—
151C2×C4#1426864611yescharacteristic
152C2×C4#1426864712yes—
153C2×C4#1426864811yescharacteristic
154C8—42no—
155C8—4522no—
156C22—21no—
157C22—21no—
158C22—1132no—
159C22—1132no—
160C22—2264no—
161C22—2264no—
162C22—2261no—
163C22—2261no—
164C22—2261no—
165C22—2261no—
166C22C22⋊C4×D11311yescharacteristic
167C22#1681357911yescharacteristic
168C22#1681358011yescharacteristic
169C4—42no—
170C4—4522no—
171C4—2262no—
172C4#1681360412yes—
173C4#1681360712yes—
174C2—21no—
175C2—21no—
176C2—2262no—
177C2—2262no—
178C2#2029846011yescharacteristic
179C2#100×D11311yescharacteristic
180C2#101×D11311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC23×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#343×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC23×D113C2×C4
cosocleC22×C4×C113C23
hypercenter#343D113
hypocenterC113#1821
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. #20298367C2semidirect
4. #20298366C2semidirect
5. #343×C113C2semidirect
91. C113#1821semidirect
96. #343D113semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D1132
#202985612
#202983672
#202983662
#343×C1132
#1821113