Finite Group Databasebeta

← #44537285

Subgroups — #44537285

Order 31424.

346 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C22×C22⋊D491C211yesmaximal, characteristic, complemented
2C2×D4×D491C211yesmaximal, characteristic, complemented
3#30628321C211yesmaximal, characteristic, complemented
4#30628319C212yesmaximal, complemented
5#30628318C211yesmaximal, characteristic, complemented
6#30628310C212yesmaximal, complemented
7#30628308C212yesmaximal, complemented
8#30628306C211yesmaximal, characteristic, complemented
9#30628305C212yesmaximal, complemented
10C22⋊C4×D491C211yesmaximal, characteristic, complemented
11#120×C491C211yesmaximal, characteristic, complemented
12C23×D491C2211yescharacteristic
13C23×D491C2211yescharacteristic, complemented
14C2×D1964C2211yescharacteristic, complemented
15C2×C22⋊D491—24no—
16C2×C22⋊D491C2211yescharacteristic
17C2×C22⋊D491C2212yes—
18C2×C22⋊D491C2211yescharacteristic, complemented
19C2×C22⋊D491C2212yescomplemented
20C2×C22⋊D491C2212yescomplemented
21D4×D491—24no—
22C22×Dic491C2211yescharacteristic, complemented
23C2×C4×D491C2211yescharacteristic, complemented
24C2×C4×D491C2212yescomplemented
25C4⋊Dic491C2212yescomplemented
26Dic491⋊C4C2212yescomplemented
27C22⋊Dic491C2211yescharacteristic, complemented
28C22⋊Dic491C2212yescomplemented
29C22⋊Dic491C2212yescomplemented
30(C2×D491)⋊C4C2212yescomplemented
31(C2×D491)⋊C4C2212yescomplemented
32C24×C491C2211yescharacteristic, complemented
33C2×D4×C491C2211yescharacteristic
34C2×D4×C491C2212yescomplemented
35C22⋊C4×C491C2211yescharacteristic, complemented
36C22⋊C4×C491C2212yescomplemented
37C22×D491—22no—
38C22×D491—42no—
39C22×D491—42no—
40C22×D491D414yescomplemented
41C22×D491C2311yescharacteristic
42C22×D491C2311yescharacteristic
43C22×D491C2311yescharacteristic
44D1964—22no—
45C22⋊D491—22no—
46C22⋊D491—22no—
47C22⋊D491—24no—
48C22⋊D491—24no—
49C22⋊D491—42no—
50C2×Dic491—22no—
51C2×Dic491C2312yes—
52C2×Dic491C2312yes—
53C2×Dic491C2311yescharacteristic
54C4×D491—22no—
55C4×D491—42no—
56C23×C491—22no—
57C23×C491—42no—
58C23×C491C2311yescharacteristic
59C23×C491C2312yes—
60C23×C491C2311yescharacteristic
61D4×C491—22no—
62D4×C491—42no—
63C2×C4×C491C2311yescharacteristic
64C2×C4×C491C2312yes—
65C22×C491—22no—
66C22×C491—21no—
67C22×C491—22no—
68C22×C491—22no—
69C22×C491—22no—
70C22×C491—22no—
71C22×C491—44no—
72C22×C491C2×D412yes—
73C22×C491C2411yescharacteristic
74C2×D491—22no—
75C2×D491—22no—
76C2×D491—21no—
77C2×D491—22no—
78C2×D491—44no—
79C2×D491—44no—
80C2×D491C2×D412yes—
81C2×D491C2×D412yes—
82C4×C491—21no—
83C4×C491—22no—
84Dic491—21no—
85Dic491—22no—
86Dic491—22no—
87C2×C491—22no—
88C2×C491—41no—
89C2×C491—42no—
90C2×C491C22×D411yescharacteristic
91C2×C491H(5,𝔽2)12yes—
92D491—22no—
93D491—22no—
94D491—41no—
95C491#53411yescharacteristic, complemented, Sylow
96#534—4911nomaximal, Sylow
97C22×D4—4911no—
98C22×D4—4911no—
99#123—4911no—
100#123—4912no—
101#123—4911no—
102#121—4912no—
103#121—4912no—
104#120—4911no—
105#120—4912no—
106#120D49111yescharacteristic, complemented
107C2×C22⋊C4—4911no—
108C24—4911no—
109C24—4911no—
110C24C2×D49111yescharacteristic, complemented
111C2×D4—9824no—
112C2×D4—9824no—
113C2×D4—4912no—
114C2×D4—4912no—
115C2×D4—4911no—
116C2×D4—4911no—
117C2×D4—4912no—
118C2×D4—4911no—
119C2×D4C2×D49111yescharacteristic
120C2×D4C2×D49112yescomplemented
121C22×C4—4912no—
122C22×C4—4911no—
123C22×C4—4911no—
124C4⋊C4—4912no—
125C4⋊C4—4912no—
126C22⋊C4—4911no—
127C22⋊C4—4912no—
128C22⋊C4—4912no—
129C22⋊C4—4912no—
130C22⋊C4—4912no—
131C22⋊C4C2×D49111yescharacteristic, complemented
132C22⋊C4C2×D49112yescomplemented
133C23—22no—
134C23—42no—
135C23—19642no—
136C23—19642no—
137C23—9822no—
138C23—4914no—
139C23—4911no—
140C23—4911no—
141C23—4911no—
142C23C22×D49111yescharacteristic
143C23C22×D49112yes—
144C23C22×D49111yescharacteristic
145D4—22no—
146D4—42no—
147D4—19642no—
148D4—9822no—
149D4—9822no—
150D4—9824no—
151D4—9824no—
152D4—9822no—
153C2×C4—19642no—
154C2×C4—9822no—
155C2×C4—9822no—
156C2×C4—4912no—
157C2×C4—4911no—
158C2×C4—4912no—
159C2×C4C22×D49112yes—
160C2×C4C22×D49111yescharacteristic
161C22—22no—
162C22—21no—
163C22—22no—
164C22—22no—
165C22—22no—
166C22—22no—
167C22—44no—
168C22—19644no—
169C22—19644no—
170C22—9821no—
171C22—9822no—
172C22—9822no—
173C22—9822no—
174C22—4912no—
175C22—4912no—
176C22D4×D49112yes—
177C22C23×D49111yescharacteristic
178C4—21no—
179C4—22no—
180C4—9821no—
181C4—9822no—
182C4—9822no—
183C2—22no—
184C2—42no—
185C2—41no—
186C2—19641no—
187C2—9822no—
188C2—9822no—
189C2C2×D4×D49111yescharacteristic
190C2#3062838212yes—
subgroupG/H
center, FrattiniC22C23×D491
commutator, socle, cosocleC22×C491C24
Fitting#120×C491C2
hypercenter#120D491
hypocenterC491#534
LCSG ▷ C22×C491 ▷ C491
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D491C2semidirect
2. C2×D4×D491C2semidirect
3. #30628321C2semidirect
4. #30628319C2semidirect
5. #30628318C2semidirect
6. #30628310C2semidirect
7. #30628308C2semidirect
8. #30628306C2semidirect
9. #30628305C2semidirect
10. C22⋊C4×D491C2semidirect
11. #120×C491C2semidirect
13. C23×D491C22semidirect
14. C2×D1964C22semidirect
18. C2×C22⋊D491C22semidirect
19. C2×C22⋊D491C22semidirect
20. C2×C22⋊D491C22semidirect
22. C22×Dic491C22semidirect
23. C2×C4×D491C22semidirect
24. C2×C4×D491C22semidirect
25. C4⋊Dic491C22semidirect
26. Dic491⋊C4C22semidirect
27. C22⋊Dic491C22semidirect
28. C22⋊Dic491C22semidirect
29. C22⋊Dic491C22semidirect
30. (C2×D491)⋊C4C22semidirect
31. (C2×D491)⋊C4C22semidirect
32. C24×C491C22semidirect
34. C2×D4×C491C22semidirect
35. C22⋊C4×C491C22semidirect
36. C22⋊C4×C491C22semidirect
40. C22×D491D4semidirect
95. C491#534semidirect
106. #120D491semidirect
110. C24C2×D491semidirect
120. C2×D4C2×D491semidirect
131. C22⋊C4C2×D491semidirect
132. C22⋊C4C2×D491semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D4912
C2×D4×D4912
#306283212
#306283192
#306283182
#306283102
#306283082
#306283062
#306283052
C22⋊C4×D4912
#120×C4912
#534491