Finite Group Databasebeta

← #28407051

Subgroups — #28407051

Order 14464.

512 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 162 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#20299547C218yesmaximal, complemented
2#20299541C212yesmaximal
3#20299540C212yesmaximal
4C4×C22⋊#90673C212yesmaximal
5C2×C4⋊C4×D113C211yesmaximal, characteristic
6C2×C4⋊#90673C2214yes—
7C2×C22⋊#90673C2214yes—
8C2×C4×#90673C2214yes—
9(C2×#90673)⋊C4C2214yes—
10(C2×#90673)⋊C4C2214yes—
11(C2×#90673)⋊C4C2218yes—
12C22×C4×D113C2211yescharacteristic
13C22×C4×D113C2211yescharacteristic
14C22×C4×D113C2211yescharacteristic
15C2×C4⋊Dic113C411yescharacteristic, complemented
16C2×#14268626C411yescharacteristic, complemented
17C2×#14268626C411yescharacteristic, complemented
18C4⋊C4×D113C414yescomplemented
19C4⋊C4×D113C2214yes—
20C2×C4⋊C4×C113C411yescharacteristic, complemented
21C22×#90673C2318yes—
22C4⋊#90673—44no—
23C22⋊#90673—28no—
24C4×#90673—44no—
25C23×D113C2311yescharacteristic
26C22×Dic113C2×C411yescharacteristic
27C22×Dic113C2×C411yescharacteristic
28C22×Dic113C2×C411yescharacteristic
29C2×C4×D113—24no—
30C2×C4×D113—42no—
31C2×C4×D113—42no—
32C2×C4×D113C2×C412yes—
33C2×C4×D113C2×C412yes—
34C2×C4×D113C2×C412yes—
35C2×C4×D113C2312yes—
36C2×C4×D113C2312yes—
37C2×C4×D113C2312yes—
38C4⋊Dic113C2×C414yes—
39#14268626C2×C414yes—
40#14268626C2×C414yes—
41C22×C4×C113C2×C411yescharacteristic
42C22×C4×C113C2×C411yescharacteristic
43C22×C4×C113C2×C411yescharacteristic
44C4⋊C4×C113C2×C414yes—
45C23×C113C22×C411yescharacteristic
46C22×D113—22no—
47C22×D113—22no—
48C22×D113C22×C411yescharacteristic
49C22×D113#4114yes—
50C22×D113C2411yescharacteristic
51C2×#90673—28no—
52C2×#90673—28no—
53C2×#90673—28no—
54C2×C4×C113—22no—
55C2×C4×C113—41no—
56C2×C4×C113—41no—
57C2×C4×C113C22×C412yes—
58C2×C4×C113C22×C412yes—
59C2×C4×C113C22×C412yes—
60C2×Dic113—22no—
61C2×Dic113—41no—
62C2×Dic113—41no—
63C2×Dic113C22×C412yes—
64C2×Dic113C22×C412yes—
65C2×Dic113C22×C412yes—
66C4×D113—24no—
67C4×D113—24no—
68C4×D113—24no—
69C4×D113—24no—
70C4×D113—42no—
71C4×D113—42no—
72C22×C113—21no—
73C22×C113—21no—
74C22×C113#11712yes—
75C22×C113C23×C411yescharacteristic
76C2×D113—21no—
77C2×D113—21no—
78C2×D113—28no—
79C2×D113#11712yes—
80C2×D113C2×#4112yes—
81C2×D113H(5,𝔽2)12yes—
82C2×D1132−1+412yes—
83#90673—48no—
84C4×C113—22no—
85C4×C113—22no—
86C4×C113—22no—
87Dic113—22no—
88Dic113—22no—
89Dic113—22no—
90C2×C113—22no—
91C2×C113C2×#11711yescharacteristic
92C2×C113#51811yescharacteristic
93C2×C113#51911yescharacteristic
94D113—22no—
95D113#53914yes—
96#2313—1131nomaximal, Sylow
97C113#231311yescharacteristic, complemented, Sylow
98C22×C4⋊C4—1131no—
99#387—1138no—
100#381—1132no—
101#380—1132no—
102C4×C22⋊C4—1132no—
103C23×C4—1131no—
104C23×C4—1131no—
105C23×C4—1131no—
106C2×C4⋊C4—1131no—
107C2×C4⋊C4—1131no—
108C2×C4⋊C4—1131no—
109C2×C4⋊C4—1134no—
110C2×C4⋊C4—1134no—
111C2×C4⋊C4—1134no—
112C2×C4⋊C4#9067311yescharacteristic, complemented
113C2×C22⋊C4—1134no—
114C2×C42—1134no—
115#95—1134no—
116#95—1134no—
117#95—1138no—
118C24—1131no—
119C22×C4—1131no—
120C22×C4—1131no—
121C22×C4—1131no—
122C22×C4—1132no—
123C22×C4—1132no—
124C22×C4—1132no—
125C22×C4—1132no—
126C22×C4—1132no—
127C22×C4—1132no—
128C22×C4—1138no—
129C22×C4—4522no—
130C22×C4—4522no—
131C22×C4—2264no—
132C22×C4C2×#9067311yescharacteristic
133C22×C4C2×#9067311yescharacteristic
134C22×C4C2×#9067311yescharacteristic
135C4⋊C4—1134no—
136C4⋊C4—1134no—
137C4⋊C4—1134no—
138C4⋊C4—4524no—
139C4⋊C4C2×#9067314yes—
140C22⋊C4—2268no—
141C42—4524no—
142C23—1131no—
143C23—1134no—
144C23—1131no—
145C23—2262no—
146C23—2262no—
147C23C22×#9067311yescharacteristic
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—1132no—
152C2×C4—1132no—
153C2×C4—1132no—
154C2×C4—4522no—
155C2×C4—4522no—
156C2×C4—4521no—
157C2×C4—4521no—
158C2×C4—2264no—
159C2×C4—2264no—
160C2×C4—2264no—
161C2×C4—2264no—
162C2×C4—2268no—
163C2×C4—2268no—
164C2×C4—2268no—
165C2×C4—2262no—
166C2×C4C22×#9067312yes—
167C2×C4C22×#9067312yes—
168C2×C4C22×#9067312yes—
169C22—21no—
170C22—21no—
171C22—1132no—
172C22—1132no—
173C22—1132no—
174C22—1132no—
175C22—2268no—
176C22—2261no—
177C22—2261no—
178C22#1681370112yes—
179C22C23×#9067311yescharacteristic
180C4—22no—
181C4—22no—
182C4—22no—
183C4—4528no—
184C4—2262no—
185C4—2262no—
186C4—2262no—
187C2—22no—
188C2—1134no—
189C2—2262no—
190C2C2×#1681370111yescharacteristic
191C2#2029966511yescharacteristic
192C2#2029966611yescharacteristic
subgroupG/H
center, FrattiniC22C23×#90673
commutator, socleC22×C113C23×C4
FittingC2×C4⋊C4×C113C4
prime radicalC23×D113C23
cosocleC22×D113C24
hypercenterC2×C4⋊C4#90673
hypocenterC113#2313
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #20299547C2semidirect
15. C2×C4⋊Dic113C4semidirect
16. C2×#14268626C4semidirect
17. C2×#14268626C4semidirect
18. C4⋊C4×D113C4semidirect
20. C2×C4⋊C4×C113C4semidirect
97. C113#2313semidirect
112. C2×C4⋊C4#90673semidirect

Maximal subgroups

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

subgroupindex
#202995472
#202995412
#202995402
C4×C22⋊#906732
C2×C4⋊C4×D1132
#2313113