Finite Group Databasebeta

← #28400958

Subgroups — #28400958

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×#16813609C211yesmaximal, characteristic
3#20298956C214yesmaximal, complemented
4#20298951C214yesmaximal, complemented
5#20298608C211yesmaximal, characteristic, complemented
6#20298606C211yesmaximal, characteristic, complemented
7#20298603C211yesmaximal, characteristic
8M16×Dic113C211yesmaximal, characteristic, complemented
9#418×C113C211yesmaximal, characteristic
10C22×Dic226C2211yescharacteristic
11C2×#14268631C2211yescharacteristic
12#16813621C2212yescomplemented
13#16813613C2212yescomplemented
14#16813609—22no—
15#16813609C2212yes—
16#16813609C2212yes—
17#16813599—22no—
18C4×Dic226—22no—
19#16813581C2211yescharacteristic
20C2×C22⋊Dic113—22no—
21C2×C4×Dic113C2211yescharacteristic
22#16813547C2214yescomplemented
23#16813545C2214yescomplemented
24#16813543C2214yes—
25#16813532C2212yescomplemented
26C8×Dic113C2212yescomplemented
27C22×D4×C113C2211yescharacteristic
28C2×M16×C113C2211yescharacteristic
29#117×C113C2211yescharacteristic
30#102×C113C2214yes—
31C2×Dic226—22no—
32C2×Dic226—22no—
33C2×Dic226—21no—
34C2×Dic226—22no—
35C2×Dic226C2312yes—
36C22×Dic113—21no—
37C22×Dic113D412yes—
38#14268631—22no—
39C2×#11744751C2312yes—
40C4⋊Dic113—22no—
41C4⋊Dic113C2312yes—
42#14268626—22no—
43#14268626—22no—
44C22⋊Dic113—21no—
45C22⋊Dic113—24no—
46C22⋊Dic113—24no—
47C4×Dic113—21no—
48C4×Dic113D412yes—
49C4×Dic113C2311yescharacteristic
50C4×Dic113C2311yescharacteristic
51C24×C113—21no—
52C2×D4×C113—21no—
53C2×D4×C113—22no—
54C2×D4×C113—22no—
55C2×D4×C113C2312yes—
56C22×C4×C113C2311yescharacteristic
57M16×C113—22no—
58C2×C8×C113C2312yes—
59C4⋊C4×C113C2312yes—
60C22⋊C4×C113—21no—
61C42×C113—21no—
62C23×C113—22no—
63C23×C113—44no—
64C23×C113—42no—
65C23×C113C2×D411yescharacteristic
66D4×C113—22no—
67D4×C113—22no—
68D4×C113—42no—
69C2×C4×C113—22no—
70C2×C4×C113C2×D411yescharacteristic
71C2×C4×C113#4112yes—
72C2×C4×C113#4112yes—
73C2×C4×C113C2411yescharacteristic
74C2×Dic113—22no—
75C2×Dic113—22no—
76C2×Dic113—42no—
77C2×Dic113—42no—
78C2×Dic113C2×D412yes—
79C2×Dic113C2×D412yes—
80Dic226—22no—
81Dic226—22no—
82Dic226—44no—
83Dic226—42no—
84C8×C113—22no—
85#11744751—22no—
86C22×C113—22no—
87C22×C113—42no—
88C22×C113—44no—
89C22×C113—84no—
90C22×C113#12412yes—
91C22×C113C22×D411yescharacteristic
92C4×C113—42no—
93C4×C113#12412yes—
94C4×C113C2×#4111yescharacteristic
95C4×C113C2×#4111yescharacteristic
96Dic113—22no—
97Dic113—22no—
98Dic113—42no—
99Dic113—42no—
100C2×C113—22no—
101C2×C113—82no—
102C2×C113C2×#12411yescharacteristic
103C2×C113#57512yes—
104#3140—1131nomaximal, Sylow
105C113#314011yescharacteristic, complemented, Sylow
106#533—1131no—
107C2×#124—1131no—
108#489—1134no—
109#488—1134no—
110#419—1131no—
111#419—1131no—
112#418—1131no—
113#418D11311yescharacteristic
114C4×M16—1131no—
115C22×Q8—1131no—
116C22×D4C2×D11311yescharacteristic
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#103—1134no—
132#102—1134no—
133#102C2×D11314yes—
134#97—1132no—
135C4×C8—1132no—
136C24—21no—
137C2×Q8—1132no—
138C2×Q8—2262no—
139C2×Q8—2262no—
140C2×Q8—2262no—
141C2×Q8—2261no—
142C2×D4—21no—
143C2×D4—22no—
144C2×D4—22no—
145C2×D4C22×D11312yes—
146C22×C4—1132no—
147C22×C4—2261no—
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—22no—
168C23—44no—
169C23—42no—
170C23D4×D11311yescharacteristic
171Q8—4524no—
172Q8—4522no—
173Q8—2262no—
174Q8—2262no—
175D4—22no—
176D4—22no—
177D4—42no—
178C2×C4—22no—
179C2×C4—1132no—
180C2×C4—1132no—
181C2×C4—4522no—
182C2×C4—4522no—
183C2×C4—2262no—
184C2×C4—2262no—
185C2×C4D4×D11311yescharacteristic
186C2×C4#1426864612yes—
187C2×C4#1426864712yes—
188C2×C4C23×D11311yescharacteristic
189C8—22no—
190C8—2262no—
191C22—22no—
192C22—42no—
193C22—44no—
194C22—84no—
195C22#1681360812yes—
196C22C2×D4×D11311yescharacteristic
197C4—42no—
198C4—4522no—
199C4—4522no—
200C4—2262no—
201C4—2262no—
202C4#1681360812yes—
203C4C2×#1426864611yescharacteristic
204C4C2×#1426864711yescharacteristic
205C2—22no—
206C2—82no—
207C2C2×#1681360811yescharacteristic
208C2#2029939412yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#418×C113C2
socleC22×C113C22×D4
prime radicalC22×D4×C113C22
hypercenter#418D113
hypocenterC113#3140
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #20299151C2semidirect
3. #20298956C2semidirect
4. #20298951C2semidirect
5. #20298608C2semidirect
6. #20298606C2semidirect
8. M16×Dic113C2semidirect
12. #16813621C22semidirect
13. #16813613C22semidirect
22. #16813547C22semidirect
23. #16813545C22semidirect
25. #16813532C22semidirect
26. C8×Dic113C22semidirect
105. C113#3140semidirect

Maximal subgroups

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

subgroupindex
#202991512
C2×#168136092
#202989562
#202989512
#202986082
#202986062
#202986032
M16×Dic1132
#418×C1132
#3140113