Finite Group Databasebeta

← #14580846

Subgroups — #14580846

Order 2624.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C2×#10620308C211yesmaximal, characteristic, complemented
2C22×C4×D41C211yesmaximal, characteristic, complemented
3#13050146C212yesmaximal, complemented
4#13050144C211yesmaximal, characteristic, complemented
5#13050143C211yesmaximal, characteristic, complemented
6#13050135C211yesmaximal, characteristic, complemented
7#13050132C212yesmaximal, complemented
8D4×Dic41C212yesmaximal, complemented
9#13050124C212yesmaximal, complemented
10#13050122C211yesmaximal, characteristic, complemented
11#121×C41C211yesmaximal, characteristic, complemented
12C23×D41C2211yescharacteristic
13C2×D4×C41C2212yes—
14C2×D4×C41C2211yescharacteristic, complemented
15C22×C4×C41C2211yescharacteristic
16C2×C22⋊D41C2212yes—
17C2×C22⋊D41C2212yes—
18C22×Dic41C2211yescharacteristic
19C22×Dic41C2212yescomplemented
20#10620308—24no—
21C2×C4×D41—24no—
22C2×C4×D41C2211yescharacteristic
23C2×C4×D41C2211yescharacteristic
24C2×C4×D41C2211yescharacteristic
25C2×C4×D41C2211yescharacteristic
26C2×Dic82C2211yescharacteristic, complemented
27C4⋊C4×C41C2211yescharacteristic, complemented
28C22⋊C4×C41C2212yescomplemented
29C22⋊Dic41C2212yes—
30C22⋊Dic41C2212yescomplemented
31#10620281C2212yes—
32#10620281C2212yes—
33C4⋊Dic41C2211yescharacteristic, complemented
34C4⋊Dic41C2212yescomplemented
35#10620279C2212yescomplemented
36C4×Dic41C2212yescomplemented
37C23×C41C2312yes—
38C23×C41C2311yescharacteristic
39C22×D41—22no—
40C22×D41—22no—
41C22×D41—22no—
42C22×D41C2311yescharacteristic
43C22×D41C2311yescharacteristic
44D4×C41—24no—
45D4×C41—22no—
46C2×C4×C41—22no—
47C2×C4×C41C2312yes—
48C2×C4×C41C2311yescharacteristic
49C2×C4×C41C2311yescharacteristic
50C22⋊D41—24no—
51C22⋊D41—24no—
52C2×Dic41—22no—
53C2×Dic41—24no—
54C2×Dic41C2312yes—
55C2×Dic41C2312yes—
56C2×Dic41C2311yescharacteristic
57C2×Dic41C2311yescharacteristic
58C4×D41—22no—
59C4×D41—22no—
60C4×D41—22no—
61C4×D41D414yescomplemented
62Dic82—22no—
63C22×C41—21no—
64C22×C41—21no—
65C22×C41—22no—
66C22×C41—22no—
67C22×C41—22no—
68C22×C41#4112yescomplemented
69C22×C41C2411yescharacteristic
70C2×D41—28no—
71C2×D41—21no—
72C2×D41—21no—
73C2×D41—21no—
74C2×D41—21no—
75C2×D41C2×D412yes—
76C2×D41#4112yescomplemented
77C4×C41—21no—
78C4×C41—22no—
79C4×C41C2×D412yes—
80Dic41—22no—
81Dic41—21no—
82Dic41—22no—
83Dic41C2×D412yes—
84C2×C41—22no—
85C2×C41—42no—
86C2×C41C22×D411yescharacteristic
87C2×C41C2×#4111yescharacteristic
88C2×C41C2×#4111yescharacteristic
89D41—22no—
90D41—22no—
91#525—411nomaximal, Sylow
92C41#52511yescharacteristic, complemented, Sylow
93C2×#41—411no—
94C23×C4—411no—
95#123—412no—
96C22⋊Q8—411no—
97C22⋊Q8—411no—
98#121—411no—
99#121D4111yescharacteristic, complemented
100#120—412no—
101C4×D4—412no—
102C4×D4—412no—
103#117—411no—
104C24—411no—
105#41—824no—
106C2×Q8—411no—
107C2×D4—412no—
108C2×D4—412no—
109C2×D4C2×D4112yes—
110C2×D4C2×D4111yescharacteristic, complemented
111C22×C4—411no—
112C22×C4—411no—
113C22×C4—412no—
114C22×C4—411no—
115C22×C4—411no—
116C22×C4—411no—
117C22×C4—824no—
118C22×C4C2×D4111yescharacteristic
119C4⋊C4—411no—
120C4⋊C4—412no—
121C4⋊C4—412no—
122C4⋊C4C2×D4111yescharacteristic, complemented
123C22⋊C4—412no—
124C22⋊C4—412no—
125C22⋊C4—412no—
126C22⋊C4—412no—
127C22⋊C4C2×D4112yescomplemented
128C42—412no—
129C23—411no—
130C23—411no—
131C23—822no—
132C23—822no—
133C23—822no—
134C23C22×D4112yes—
135C23C22×D4111yescharacteristic
136Q8—822no—
137D4—24no—
138D4—22no—
139D4—824no—
140D4—824no—
141C2×C4—22no—
142C2×C4—411no—
143C2×C4—414no—
144C2×C4—412no—
145C2×C4—411no—
146C2×C4—412no—
147C2×C4—822no—
148C2×C4—822no—
149C2×C4—822no—
150C2×C4—824no—
151C2×C4—822no—
152C2×C4C22×D4112yes—
153C2×C4C22×D4111yescharacteristic
154C2×C4C22×D4111yescharacteristic
155C22—21no—
156C22—21no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—412no—
161C22—412no—
162C22—828no—
163C22—821no—
164C22—821no—
165C22—821no—
166C22—821no—
167C22#1062030812yescomplemented
168C22C23×D4111yescharacteristic
169C4—21no—
170C4—22no—
171C4—412no—
172C4—821no—
173C4—822no—
174C4—822no—
175C4D4×D4112yes—
176C2—22no—
177C2—42no—
178C2—822no—
179C2—822no—
180C2C2×D4×D4111yescharacteristic
181C2#41×D4111yescharacteristic
182C2C2×#1062030811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D41
commutator, socle, cosocleC22×C41C24
Fitting#121×C41C2
hypercenter#121D41
hypocenterC41#525
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#10620308C2semidirect
2. C22×C4×D41C2semidirect
3. #13050146C2semidirect
4. #13050144C2semidirect
5. #13050143C2semidirect
6. #13050135C2semidirect
7. #13050132C2semidirect
8. D4×Dic41C2semidirect
9. #13050124C2semidirect
10. #13050122C2semidirect
11. #121×C41C2semidirect
14. C2×D4×C41C22semidirect
19. C22×Dic41C22semidirect
26. C2×Dic82C22semidirect
27. C4⋊C4×C41C22semidirect
28. C22⋊C4×C41C22semidirect
30. C22⋊Dic41C22semidirect
33. C4⋊Dic41C22semidirect
34. C4⋊Dic41C22semidirect
35. #10620279C22semidirect
36. C4×Dic41C22semidirect
61. C4×D41D4semidirect
68. C22×C41#41semidirect
76. C2×D41#41semidirect
92. C41#525semidirect
99. #121D41semidirect
110. C2×D4C2×D41semidirect
122. C4⋊C4C2×D41semidirect
127. C22⋊C4C2×D41semidirect
167. C22#10620308semidirect

Maximal subgroups

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

subgroupindex
C2×#106203082
C22×C4×D412
#130501462
#130501442
#130501432
#130501352
#130501322
D4×Dic412
#130501242
#130501222
#121×C412
#52541