Finite Group Databasebeta

← #28405982

Subgroups — #28405982

Order 14464.

274 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 60 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#20299570C211yesmaximal, characteristic
2#20299541C211yesmaximal, characteristic
3#20299451C214yesmaximal, complemented
4C2×#16813602C211yesmaximal, characteristic
5C2×#14268656—21no—
6C2×C22⋊#90673—21no—
7#16813679—21no—
8#16813679C2212yes—
9(C2×#90673)⋊C4—21no—
10(C2×#90673)⋊C4C2212yes—
11C22×Dic226C411yescharacteristic, complemented
12C22×C4×D113C2211yescharacteristic
13#16813602—21no—
14#16813602—21no—
15#16813602C412yescomplemented
16#16813602C2212yes—
17C2×C4⋊Dic113—21no—
18C2×#14268624—21no—
19C2×C4⋊C4×C113C411yescharacteristic, complemented
20C22×#90673—22no—
21#14268656—42no—
22C2×#11744753—22no—
23C22⋊#90673—42no—
24C23×D113D411yescharacteristic
25C2×Dic226—21no—
26C2×Dic226—42no—
27C2×Dic226C2×C412yes—
28C22×Dic113—21no—
29C22×Dic113D411yescharacteristic
30C2×C4×D113—42no—
31C2×C4×D113C2×C411yescharacteristic
32C2×C4×D113D411yescharacteristic
33C2×C4×D113D411yescharacteristic
34C2×C4×D113C2311yescharacteristic
35C4⋊Dic113—22no—
36C4⋊Dic113—22no—
37#14268624—22no—
38#14268624—22no—
39C22×C4×C113—21no—
40C22×C4×C113C2×C411yescharacteristic
41C4⋊C4×C113—21no—
42C4⋊C4×C113C2×C412yes—
43C23×C113C22⋊C411yescharacteristic
44C22×D113—22no—
45C22×D113—22no—
46C22×D113—41no—
47C22×D113C22⋊C411yescharacteristic
48C22×D113C2×D411yescharacteristic
49C2×#90673—42no—
50C2×#90673—42no—
51C2×#90673—42no—
52C2×C4×C113—22no—
53C2×C4×C113—22no—
54C2×C4×C113—42no—
55C2×C4×C113C22⋊C411yescharacteristic
56C2×C4×C113C22×C411yescharacteristic
57C2×Dic113—22no—
58C2×Dic113—22no—
59C2×Dic113—42no—
60C2×Dic113C22⋊C411yescharacteristic
61C2×Dic113C2×D411yescharacteristic
62C4×D113—41no—
63C4×D113—41no—
64C4×D113—41no—
65C4×D113—41no—
66Dic226—42no—
67Dic226—42no—
68#11744753—42no—
69C22×C113—21no—
70C22×C113—21no—
71C22×C113#9912yes—
72C22×C113C2×C22⋊C411yescharacteristic
73C2×D113—21no—
74C2×D113—21no—
75C2×D113—21no—
76C2×D113—21no—
77C2×D113—21no—
78C2×D113—44no—
79C2×D113#13712yes—
80#90673—82no—
81C4×C113—21no—
82C4×C113—21no—
83C4×C113—42no—
84Dic113—21no—
85Dic113—21no—
86Dic113—42no—
87C2×C113—22no—
88C2×C113C2×#9911yescharacteristic
89C2×C113#41911yescharacteristic
90C2×C113#42111yescharacteristic
91D113—22no—
92D113—41no—
93#1511—1131nomaximal, Sylow
94C113#151111yescharacteristic, complemented, Sylow
95C2×C22⋊Q8—1131no—
96#407—1131no—
97#381—1131no—
98#328—1134no—
99C22×Q8—1131no—
100C23×C4—1131no—
101C2×M16—2261no—
102C22⋊Q8—1132no—
103C22⋊Q8—1132no—
104C22⋊Q8—2261no—
105C22⋊Q8—2261no—
106C2×C4⋊C4—2261no—
107C2×C4⋊C4#9067311yescharacteristic, complemented
108C2×C22⋊C4—2261no—
109C2×C22⋊C4—2261no—
110C22⋊C8—1132no—
111C22⋊C8—2261no—
112#95—1132no—
113#95—2261no—
114C24—1131no—
115C2×Q8—1132no—
116C2×Q8—4522no—
117C2×Q8—2261no—
118C22×C4—21no—
119C22×C4—1131no—
120C22×C4—1131no—
121C22×C4—1131no—
122C22×C4—1131no—
123C22×C4—1131no—
124C22×C4—4522no—
125C22×C4—2262no—
126C22×C4—2261no—
127C22×C4C2×#9067311yescharacteristic
128M16—4522no—
129C2×C8—2262no—
130C4⋊C4—21no—
131C4⋊C4—2262no—
132C4⋊C4—2262no—
133C4⋊C4C2×#9067312yes—
134C22⋊C4—4522no—
135C22⋊C4—2262no—
136C22⋊C4—2262no—
137C23—1131no—
138C23—1131no—
139C23—4521no—
140C23—2262no—
141C23—2262no—
142C23C22⋊#9067311yescharacteristic
143Q8—4522no—
144Q8—4522no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—42no—
148C2×C4—1131no—
149C2×C4—1131no—
150C2×C4—4521no—
151C2×C4—4521no—
152C2×C4—4521no—
153C2×C4—4521no—
154C2×C4—4522no—
155C2×C4—4522no—
156C2×C4—4522no—
157C2×C4—4522no—
158C2×C4—2262no—
159C2×C4—2262no—
160C2×C4C22⋊#9067311yescharacteristic
161C2×C4C22×#9067311yescharacteristic
162C8—4522no—
163C22—21no—
164C22—21no—
165C22—1132no—
166C22—4524no—
167C22—2261no—
168C22—2261no—
169C22—2261no—
170C22—2261no—
171C22—2261no—
172C22#1681368112yes—
173C22C2×C22⋊#9067311yescharacteristic
174C4—21no—
175C4—21no—
176C4—42no—
177C4—9042no—
178C4—4522no—
179C4—2261no—
180C4—2261no—
181C2—22no—
182C2—4521no—
183C2—2262no—
184C2C2×#1681368111yescharacteristic
185C2#2029959111yescharacteristic
186C2#2029959611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC2×C4⋊C4×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC23×D113D4
cosocleC2×C4×D113C23
hypercenterC2×C4⋊C4#90673
hypocenterC113#1511
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #20299451C2semidirect
11. C22×Dic226C4semidirect
15. #16813602C4semidirect
19. C2×C4⋊C4×C113C4semidirect
94. C113#1511semidirect
107. C2×C4⋊C4#90673semidirect

Maximal subgroups

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

subgroupindex
#202995702
#202995412
#202994512
C2×#168136022
#1511113