Finite Group Databasebeta

← #28400946

Subgroups — #28400946

Order 14464.

484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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×#16813618C211yesmaximal, characteristic
3#20298961C214yesmaximal, complemented
4#20298943C214yesmaximal, complemented
5#20298604C211yesmaximal, characteristic, complemented
6#20298603C211yesmaximal, characteristic, complemented
7#20298602C211yesmaximal, characteristic, complemented
8M16×Dic113C211yesmaximal, characteristic, complemented
9#418×C113C211yesmaximal, characteristic, complemented
10C22×D452C2211yescharacteristic
11C22×C22⋊D113—22no—
12C2×#14268631C2211yescharacteristic
13#16813621C2212yescomplemented
14#16813618—22no—
15#16813618C2212yes—
16#16813618C2212yes—
17#16813613C2212yescomplemented
18#16813599—22no—
19C4×Dic226—22no—
20#16813581C2211yescharacteristic
21C2×C4×Dic113C2211yescharacteristic
22#16813544C2214yescomplemented
23#16813543C2214yescomplemented
24#16813542C2214yescomplemented
25#16813532C2212yescomplemented
26C8×Dic113C2212yescomplemented
27C22×D4×C113C2211yescharacteristic
28C2×M16×C113C2211yescharacteristic
29#117×C113C2211yescharacteristic
30#102×C113C2214yescomplemented
31C23×D113—21no—
32C2×Dic226—22no—
33C2×D452—22no—
34C2×D452—22no—
35C2×D452—21no—
36C2×D452C2312yes—
37C2×C22⋊D113—24no—
38C2×C22⋊D113—24no—
39C2×C22⋊D113—48no—
40C22×Dic113D412yes—
41#14268631—22no—
42C2×#11744751C2312yes—
43C4⋊Dic113—22no—
44C4⋊Dic113C2312yes—
45#14268626—22no—
46#14268626—22no—
47C22⋊Dic113—21no—
48C4×Dic113—21no—
49C4×Dic113D412yes—
50C4×Dic113C2311yescharacteristic
51C4×Dic113C2311yescharacteristic
52C24×C113—21no—
53C2×D4×C113—21no—
54C2×D4×C113—22no—
55C2×D4×C113—22no—
56C2×D4×C113C2312yes—
57C22×C4×C113C2311yescharacteristic
58M16×C113—22no—
59C2×C8×C113C2312yes—
60C4⋊C4×C113C2312yes—
61C22⋊C4×C113—21no—
62C42×C113—21no—
63C23×C113—22no—
64C23×C113—44no—
65C23×C113—42no—
66C23×C113C2×D411yescharacteristic
67C22×D113—22no—
68C22×D113—44no—
69C22×D113—42no—
70D4×C113—22no—
71D4×C113—22no—
72D4×C113—42no—
73C2×C4×C113—22no—
74C2×C4×C113C2×D411yescharacteristic
75C2×C4×C113#4112yes—
76C2×C4×C113#4112yes—
77C2×C4×C113C2411yescharacteristic
78C22⋊D113—48no—
79C22⋊D113—48no—
80C2×Dic113—24no—
81C2×Dic113—22no—
82C2×Dic113C2×D412yes—
83C2×Dic113C2×D412yes—
84D452—22no—
85D452—22no—
86D452—42no—
87Dic226—44no—
88C8×C113—22no—
89#11744751—22no—
90C22×C113—22no—
91C22×C113—42no—
92C22×C113—44no—
93C22×C113—84no—
94C22×C113#12412yes—
95C22×C113C22×D411yescharacteristic
96C2×D113—42no—
97C2×D113—44no—
98C2×D113—84no—
99C4×C113—42no—
100C4×C113#12412yes—
101C4×C113C2×#4111yescharacteristic
102C4×C113C2×#4111yescharacteristic
103Dic113—22no—
104Dic113—42no—
105Dic113AGL(1,ℤ/8)14yes—
106C2×C113—22no—
107C2×C113—82no—
108C2×C113C2×#12411yescharacteristic
109C2×C113C2×AGL(1,ℤ/8)12yes—
110D113—82no—
111#3138—1131nomaximal, Sylow
112C113#313811yescharacteristic, complemented, Sylow
113#533—1131no—
114C2×#127—1131no—
115#490—1134no—
116#486—1134no—
117#418—1131no—
118#418—1131no—
119#418—1131no—
120#418D11311yescharacteristic, complemented
121C4×M16—1131no—
122C22×D4—1131no—
123C22×D4—2262no—
124C22×D4C2×D11311yescharacteristic
125C2×M16—1131no—
126C2×M16C2×D11311yescharacteristic
127C4⋊Q8—1132no—
128#127—1132no—
129#127—1132no—
130#127—2262no—
131#125—1132no—
132C22⋊Q8—2262no—
133C4×Q8—2262no—
134#117—1131no—
135#117C2×D11311yescharacteristic
136C2×C42—1131no—
137#102—1134no—
138#102—1134no—
139#102—1134no—
140#102C2×D11314yescomplemented
141#97—1132no—
142C4×C8—1132no—
143C24—21no—
144C24—2261no—
145C2×Q8—2262no—
146C2×D4—21no—
147C2×D4—22no—
148C2×D4—22no—
149C2×D4—1132no—
150C2×D4—4528no—
151C2×D4—2264no—
152C2×D4—2264no—
153C2×D4—2261no—
154C2×D4—2262no—
155C2×D4—2262no—
156C2×D4C22×D11312yes—
157C22×C4—1132no—
158C22×C4C22×D11311yescharacteristic
159M16—22no—
160M16—2262no—
161C2×C8—1132no—
162C2×C8C22×D11312yes—
163C4⋊C4—1132no—
164C4⋊C4—2262no—
165C4⋊C4—2262no—
166C4⋊C4—2262no—
167C4⋊C4C22×D11312yes—
168C22⋊C4—21no—
169C22⋊C4—2261no—
170C42—21no—
171C42—1132no—
172C42—1131no—
173C42—1131no—
174C42—2261no—
175C23—22no—
176C23—44no—
177C23—42no—
178C23—4524no—
179C23—4522no—
180C23—2262no—
181C23D4×D11311yescharacteristic
182Q8—4524no—
183D4—22no—
184D4—22no—
185D4—42no—
186D4—4528no—
187D4—4528no—
188D4—4522no—
189D4—2262no—
190D4—2262no—
191C2×C4—22no—
192C2×C4—1132no—
193C2×C4—1132no—
194C2×C4—2264no—
195C2×C4—2262no—
196C2×C4D4×D11311yescharacteristic
197C2×C4#1426864612yes—
198C2×C4#1426864712yes—
199C2×C4C23×D11311yescharacteristic
200C8—22no—
201C8—2262no—
202C22—22no—
203C22—42no—
204C22—44no—
205C22—84no—
206C22—9044no—
207C22—4522no—
208C22—4524no—
209C22#1681360812yes—
210C22C2×D4×D11311yescharacteristic
211C4—42no—
212C4—1134no—
213C4—4522no—
214C4—2262no—
215C4#1681360812yes—
216C4C2×#1426864611yescharacteristic
217C4C2×#1426864711yescharacteristic
218C2—22no—
219C2—82no—
220C2—9042no—
221C2C2×#1681360811yescharacteristic
222C2AGL(1,ℤ/8)×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#418×C113C2
socleC22×C113C22×D4
prime radicalC2×#16813618C2
hypercenter#418D113
hypocenterC113#3138
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. #20298961C2semidirect
4. #20298943C2semidirect
5. #20298604C2semidirect
6. #20298603C2semidirect
7. #20298602C2semidirect
8. M16×Dic113C2semidirect
9. #418×C113C2semidirect
13. #16813621C22semidirect
17. #16813613C22semidirect
22. #16813544C22semidirect
23. #16813543C22semidirect
24. #16813542C22semidirect
25. #16813532C22semidirect
26. C8×Dic113C22semidirect
30. #102×C113C22semidirect
112. C113#3138semidirect
120. #418D113semidirect
140. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991512
C2×#168136182
#202989612
#202989432
#202986042
#202986032
#202986022
M16×Dic1132
#418×C1132
#3138113