Finite Group Databasebeta

← #44537283

Subgroups — #44537283

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
1C2×D4×D491C212yesmaximal, complemented
2#30628322C212yesmaximal, complemented
3#30628319C212yesmaximal, complemented
4#30628311C211yesmaximal, characteristic, complemented
5#30628309C212yesmaximal, complemented
6#30628307C212yesmaximal, complemented
7#30628305C212yesmaximal, complemented
8C2×(C2×D491)⋊C4C211yesmaximal, characteristic, complemented
9#121×C491C211yesmaximal, characteristic, complemented
10C23×D491C2211yescharacteristic
11C23×D491C2212yescomplemented
12C2×D1964C2212yes—
13C2×D1964C2211yescharacteristic, complemented
14C2×C22⋊D491C2212yes—
15C2×C22⋊D491C2212yescomplemented
16C2×C22⋊D491C2212yescomplemented
17D4×D491—28no—
18C22×Dic491C2211yescharacteristic, complemented
19C2×C4×D491C2212yescomplemented
20C4⋊Dic491C2211yescharacteristic, complemented
21Dic491⋊C4C2212yescomplemented
22C22⋊Dic491C2212yescomplemented
23(C2×D491)⋊C4C2212yescomplemented
24(C2×D491)⋊C4C2212yescomplemented
25(C2×D491)⋊C4C2212yescomplemented
26(C2×D491)⋊C4C2212yescomplemented
27C2×D4×C491C2212yescomplemented
28C2×D4×C491C2211yescharacteristic, complemented
29C22×C4×C491C2211yescharacteristic, complemented
30C4⋊C4×C491C2211yescharacteristic, complemented
31C22⋊C4×C491C2212yescomplemented
32C22×D491—24no—
33C22×D491—41no—
34C22×D491—41no—
35C22×D491—42no—
36C22×D491—42no—
37C22×D491D414yescomplemented
38C22×D491C2312yes—
39C22×D491C2312yes—
40D1964—24no—
41D1964—41no—
42C22⋊D491—24no—
43C22⋊D491—24no—
44C22⋊D491—42no—
45C2×Dic491—41no—
46C2×Dic491C2312yes—
47C2×Dic491C2312yes—
48C4×D491—24no—
49C23×C491C2312yes—
50C23×C491C2311yescharacteristic
51D4×C491—24no—
52D4×C491—41no—
53C2×C4×C491—41no—
54C2×C4×C491C2311yescharacteristic
55C2×C4×C491C2311yescharacteristic
56C2×C4×C491C2312yes—
57C22×C491—21no—
58C22×C491—21no—
59C22×C491—22no—
60C22×C491—22no—
61C22×C491—22no—
62C22×C491C2×D412yes—
63C22×C491C2411yescharacteristic
64C2×D491—22no—
65C2×D491—22no—
66C2×D491—22no—
67C2×D491—22no—
68C2×D491—22no—
69C2×D491—44no—
70C2×D491—48no—
71C2×D491C2×D414yes—
72C4×C491—22no—
73C4×C491—21no—
74C4×C491—21no—
75Dic491—22no—
76Dic491—22no—
77C2×C491—22no—
78C2×C491—42no—
79C2×C491C22×D411yescharacteristic
80C2×C491H(5,𝔽2)11yescharacteristic
81C2×C491H(5,𝔽2)11yescharacteristic
82D491—24no—
83D491—42no—
84C491#53411yescharacteristic, complemented, Sylow
85#534—4911nomaximal, Sylow
86C22×D4—4912no—
87#123—4912no—
88#123—4912no—
89#121—4912no—
90#121—4911no—
91#121D49111yescharacteristic, complemented
92#120—4912no—
93#120—4912no—
94C2×C22⋊C4—4911no—
95C24—4912no—
96C24—4911no—
97C2×D4—9828no—
98C2×D4—4912no—
99C2×D4—4912no—
100C2×D4—4912no—
101C2×D4—4911no—
102C2×D4—4912no—
103C2×D4C2×D49112yescomplemented
104C2×D4C2×D49111yescharacteristic, complemented
105C22×C4—4911no—
106C22×C4—4912no—
107C22×C4C2×D49111yescharacteristic, complemented
108C4⋊C4—4912no—
109C4⋊C4—4911no—
110C4⋊C4C2×D49111yescharacteristic, complemented
111C22⋊C4—4912no—
112C22⋊C4—4912no—
113C22⋊C4—4912no—
114C22⋊C4—4912no—
115C22⋊C4—4912no—
116C22⋊C4C2×D49112yescomplemented
117C23—19641no—
118C23—19641no—
119C23—19642no—
120C23—19642no—
121C23—9824no—
122C23—4914no—
123C23—4912no—
124C23—4912no—
125C23C22×D49112yes—
126C23C22×D49111yescharacteristic
127D4—24no—
128D4—41no—
129D4—19641no—
130D4—19642no—
131D4—9824no—
132D4—9824no—
133D4—9824no—
134C2×C4—41no—
135C2×C4—19641no—
136C2×C4—9824no—
137C2×C4—4912no—
138C2×C4—4912no—
139C2×C4C22×D49111yescharacteristic
140C2×C4C22×D49111yescharacteristic
141C2×C4C22×D49112yes—
142C22—21no—
143C22—21no—
144C22—22no—
145C22—22no—
146C22—22no—
147C22—19644no—
148C22—19648no—
149C22—9822no—
150C22—9822no—
151C22—9822no—
152C22—9822no—
153C22—9822no—
154C22—4914no—
155C22D4×D49112yes—
156C22C23×D49111yescharacteristic
157C4—22no—
158C4—21no—
159C4—21no—
160C4—9822no—
161C4—9822no—
162C2—22no—
163C2—42no—
164C2—19642no—
165C2—9824no—
166C2C2×D4×D49111yescharacteristic
167C2#3062838211yescharacteristic
168C2#3062838311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D491
commutator, socle, cosocleC22×C491C24
Fitting#121×C491C2
hypercenter#121D491
hypocenterC491#534
LCSG ▷ C22×C491 ▷ C491
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D491C2semidirect
2. #30628322C2semidirect
3. #30628319C2semidirect
4. #30628311C2semidirect
5. #30628309C2semidirect
6. #30628307C2semidirect
7. #30628305C2semidirect
8. C2×(C2×D491)⋊C4C2semidirect
9. #121×C491C2semidirect
11. C23×D491C22semidirect
13. C2×D1964C22semidirect
15. C2×C22⋊D491C22semidirect
16. C2×C22⋊D491C22semidirect
18. C22×Dic491C22semidirect
19. C2×C4×D491C22semidirect
20. C4⋊Dic491C22semidirect
21. Dic491⋊C4C22semidirect
22. C22⋊Dic491C22semidirect
23. (C2×D491)⋊C4C22semidirect
24. (C2×D491)⋊C4C22semidirect
25. (C2×D491)⋊C4C22semidirect
26. (C2×D491)⋊C4C22semidirect
27. C2×D4×C491C22semidirect
28. C2×D4×C491C22semidirect
29. C22×C4×C491C22semidirect
30. C4⋊C4×C491C22semidirect
31. C22⋊C4×C491C22semidirect
37. C22×D491D4semidirect
84. C491#534semidirect
91. #121D491semidirect
103. C2×D4C2×D491semidirect
104. C2×D4C2×D491semidirect
107. C22×C4C2×D491semidirect
110. C4⋊C4C2×D491semidirect
116. C22⋊C4C2×D491semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D4912
#306283222
#306283192
#306283112
#306283092
#306283072
#306283052
C2×(C2×D491)⋊C42
#121×C4912
#534491