Finite Group Databasebeta

← #28400962

Subgroups — #28400962

Order 14464.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299151C211yesmaximal, characteristic, complemented
2C2×#16813611C211yesmaximal, characteristic
3#20298959C214yesmaximal, complemented
4#20298954C214yesmaximal, complemented
5#20298607C211yesmaximal, characteristic, complemented
6#20298604C211yesmaximal, characteristic
7#20298602C211yesmaximal, characteristic
8M16×Dic113C211yesmaximal, characteristic, complemented
9#419×C113C211yesmaximal, characteristic, complemented
10C22×D452C2211yescharacteristic
11C2×#14268631C2211yescharacteristic
12#16813621C2212yescomplemented
13#16813613C2212yescomplemented
14#16813611—22no—
15#16813611C2212yes—
16#16813611C2212yes—
17#16813599—22no—
18C4×Dic226—22no—
19#16813581C2211yescharacteristic
20C2×#14268624—22no—
21C2×C4×Dic113C2211yescharacteristic
22#16813546C2214yescomplemented
23#16813544C2214yes—
24#16813542C2214yes—
25#16813532C2212yescomplemented
26C8×Dic113C2212yescomplemented
27C22×Q8×C113C2211yescharacteristic
28C2×M16×C113C2211yescharacteristic
29#117×C113C2211yescharacteristic
30#103×C113C2214yescomplemented
31C23×D113—21no—
32C2×Dic226—22no—
33C2×D452—22no—
34C2×D452—22no—
35C2×D452—21no—
36C2×D452C2312yes—
37C22×Dic113D412yes—
38#14268631—22no—
39C2×#11744751C2312yes—
40C4⋊Dic113—22no—
41C4⋊Dic113C2312yes—
42#14268626—22no—
43#14268626—22no—
44C22⋊Dic113—21no—
45#14268624—24no—
46#14268624—24no—
47C4×Dic113—21no—
48C4×Dic113D412yes—
49C4×Dic113C2311yescharacteristic
50C4×Dic113C2311yescharacteristic
51C2×Q8×C113—21no—
52C2×Q8×C113—22no—
53C2×Q8×C113—22no—
54C2×Q8×C113C2312yes—
55C22×C4×C113—21no—
56C22×C4×C113C2311yescharacteristic
57M16×C113—22no—
58C2×C8×C113C2312yes—
59C4⋊C4×C113C2312yes—
60C22⋊C4×C113—21no—
61C42×C113—21no—
62C23×C113C2×D411yescharacteristic
63C22×D113—22no—
64C22×D113—44no—
65C22×D113—42no—
66Q8×C113—22no—
67Q8×C113—22no—
68Q8×C113—42no—
69C2×C4×C113—22no—
70C2×C4×C113—22no—
71C2×C4×C113—42no—
72C2×C4×C113C2×D411yescharacteristic
73C2×C4×C113#4112yes—
74C2×C4×C113#4112yes—
75C2×C4×C113C2411yescharacteristic
76C2×Dic113—22no—
77C2×Dic113—42no—
78C2×Dic113C2×D412yes—
79C2×Dic113C2×D412yes—
80D452—22no—
81D452—22no—
82D452—42no—
83Dic226—44no—
84C8×C113—22no—
85#11744751—22no—
86C22×C113—22no—
87C22×C113#12412yes—
88C22×C113C22×D411yescharacteristic
89C2×D113—42no—
90C2×D113—44no—
91C2×D113—84no—
92C4×C113—42no—
93C4×C113—42no—
94C4×C113#12412yes—
95C4×C113C2×#4111yescharacteristic
96C4×C113C2×#4111yescharacteristic
97Dic113—22no—
98Dic113—22no—
99Dic113—42no—
100C2×C113—22no—
101C2×C113C2×#12411yescharacteristic
102C2×C113#57512yes—
103D113—82no—
104#3140—1131nomaximal, Sylow
105C113#314011yescharacteristic, complemented, Sylow
106#533—1131no—
107C2×#124—1131no—
108#489—1134no—
109#488—1134no—
110#419—1131no—
111#419D11311yescharacteristic, complemented
112#418—1131no—
113#418—1131no—
114C4×M16—1131no—
115C22×Q8C2×D11311yescharacteristic
116C22×D4—1131no—
117C2×M16—1131no—
118C2×M16C2×D11311yescharacteristic
119C4⋊Q8—1132no—
120#125—1132no—
121#124—1132no—
122#124—1132no—
123#124—2262no—
124C22⋊Q8—2262no—
125C4×Q8—2262no—
126#117—1131no—
127#117C2×D11311yescharacteristic
128C2×C22⋊C4—2262no—
129C2×C42—1131no—
130#103—1134no—
131#103C2×D11314yescomplemented
132#102—1134no—
133#102—1134no—
134#97—1132no—
135C4×C8—1132no—
136C24—2261no—
137C2×Q8—21no—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8—2262no—
141C2×Q8C22×D11312yes—
142C2×D4—1132no—
143C2×D4—2261no—
144C2×D4—2262no—
145C2×D4—2262no—
146C22×C4—21no—
147C22×C4—1132no—
148C22×C4C22×D11311yescharacteristic
149M16—22no—
150M16—2262no—
151C2×C8—1132no—
152C2×C8C22×D11312yes—
153C4⋊C4—1132no—
154C4⋊C4—2262no—
155C4⋊C4—2262no—
156C4⋊C4—2262no—
157C4⋊C4C22×D11312yes—
158C22⋊C4—21no—
159C22⋊C4—2264no—
160C22⋊C4—2264no—
161C22⋊C4—2261no—
162C42—21no—
163C42—1132no—
164C42—1131no—
165C42—1131no—
166C42—2261no—
167C23—4524no—
168C23—4522no—
169C23—2262no—
170C23D4×D11311yescharacteristic
171Q8—22no—
172Q8—22no—
173Q8—42no—
174Q8—4524no—
175D4—4522no—
176D4—2262no—
177D4—2262no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—1132no—
182C2×C4—1132no—
183C2×C4—4522no—
184C2×C4—2262no—
185C2×C4D4×D11311yescharacteristic
186C2×C4#1426864612yes—
187C2×C4#1426864712yes—
188C2×C4C23×D11311yescharacteristic
189C8—22no—
190C8—2262no—
191C22—22no—
192C22—9044no—
193C22—4522no—
194C22—4524no—
195C22#1681360812yes—
196C22C2×D4×D11311yescharacteristic
197C4—42no—
198C4—42no—
199C4—4522no—
200C4—2262no—
201C4—2262no—
202C4#1681360812yes—
203C4C2×#1426864611yescharacteristic
204C4C2×#1426864711yescharacteristic
205C2—22no—
206C2—9042no—
207C2C2×#1681360811yescharacteristic
208C2#2029939712yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#419×C113C2
socleC22×C113C22×D4
prime radicalC22×D452C22
hypercenter#419D113
hypocenterC113#3140
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. #20299151C2semidirect
3. #20298959C2semidirect
4. #20298954C2semidirect
5. #20298607C2semidirect
8. M16×Dic113C2semidirect
9. #419×C113C2semidirect
12. #16813621C22semidirect
13. #16813613C22semidirect
22. #16813546C22semidirect
25. #16813532C22semidirect
26. C8×Dic113C22semidirect
30. #103×C113C22semidirect
105. C113#3140semidirect
111. #419D113semidirect
131. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991512
C2×#168136112
#202989592
#202989542
#202986072
#202986042
#202986022
M16×Dic1132
#419×C1132
#3140113