Finite Group Databasebeta

← #44537464

Subgroups — #44537464

Order 31424.

252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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#30628333C211yesmaximal, characteristic, complemented
2#30628330C212yesmaximal, complemented
3#30628319C212yesmaximal, complemented
4#30628318C211yesmaximal, characteristic, complemented
5#30628310C212yesmaximal, complemented
6#30628309C212yesmaximal, complemented
7#30628308C212yesmaximal, complemented
8#30628306C212yesmaximal, complemented
9#120×C491C211yesmaximal, characteristic, complemented
10C2×D1964C2211yescharacteristic, complemented
11C2×C22⋊D491C2212yes—
12C2×C22⋊D491C2212yes—
13C2×C22⋊D491C2212yes—
14C2×C22⋊D491C2212yescomplemented
15C22×Dic491C2211yescharacteristic, complemented
16C2×C4×D491C2212yescomplemented
17C4⋊Dic491C2212yescomplemented
18Dic491⋊C4C2212yescomplemented
19Dic491⋊C4C2212yescomplemented
20C22⋊Dic491C2212yes—
21C22⋊Dic491C2212yes—
22C22⋊Dic491C2212yes—
23C22⋊Dic491C2211yescharacteristic, complemented
24(C2×D491)⋊C4C2212yescomplemented
25C4×Dic491C2211yescharacteristic, complemented
26C24×C491C2211yescharacteristic
27C2×D4×C491C2212yes—
28C2×D4×C491C2211yescharacteristic
29C22⋊C4×C491C2212yes—
30C22⋊C4×C491C2211yescharacteristic
31C22×D491C2312yes—
32D1964—41no—
33C22⋊D491—42no—
34C22⋊D491—42no—
35C22⋊D491—42no—
36C22⋊D491—42no—
37C2×Dic491—41no—
38C2×Dic491C2312yes—
39C2×Dic491C2312yes—
40C2×Dic491C2312yes—
41C4×D491—42no—
42C23×C491—42no—
43C23×C491—41no—
44C23×C491C2311yescharacteristic
45C23×C491C2312yes—
46C23×C491C2311yescharacteristic
47D4×C491—42no—
48D4×C491—41no—
49C2×C4×C491C2311yescharacteristic
50C2×C4×C491C2312yes—
51C22×C491—22no—
52C22×C491—21no—
53C22×C491—21no—
54C22×C491—22no—
55C22×C491—22no—
56C22×C491—22no—
57C22×C491—22no—
58C22×C491—44no—
59C22×C491C2411yescharacteristic
60C2×D491—22no—
61C2×D491—22no—
62C2×D491—22no—
63C4×C491—22no—
64C4×C491—21no—
65Dic491—22no—
66Dic491—22no—
67Dic491—22no—
68C2×C491—41no—
69C2×C491—42no—
70C2×C491—41no—
71C2×C491H(5,𝔽2)12yes—
72C2×C491H(5,𝔽2)11yescharacteristic
73D491—42no—
74C491#56011yescharacteristic, complemented, Sylow
75#560—4911nomaximal, Sylow
76#127—4911no—
77#126—4912no—
78#123—4911no—
79#123—4912no—
80#121—4912no—
81#121—4912no—
82#121—4912no—
83#120—4912no—
84#120D49111yescharacteristic, complemented
85C24C2×D49111yescharacteristic
86C2×D4—4912no—
87C2×D4—4912no—
88C2×D4—4912no—
89C2×D4—4912no—
90C2×D4—4911no—
91C2×D4C2×D49112yes—
92C2×D4C2×D49111yescharacteristic
93C22×C4—4911no—
94C22×C4—4912no—
95C4⋊C4—4912no—
96C4⋊C4—4912no—
97C4⋊C4—4912no—
98C22⋊C4—4912no—
99C22⋊C4—4912no—
100C22⋊C4—4912no—
101C22⋊C4—4911no—
102C22⋊C4—4912no—
103C22⋊C4C2×D49112yes—
104C22⋊C4C2×D49111yescharacteristic
105C42—4911no—
106C23—42no—
107C23—41no—
108C23—4912no—
109C23C22×D49112yes—
110C23C22×D49111yescharacteristic
111C23C22×D49111yescharacteristic
112D4—42no—
113D4—41no—
114D4—19641no—
115D4—19642no—
116D4—19642no—
117D4—19642no—
118D4—19642no—
119C2×C4—19642no—
120C2×C4—19641no—
121C2×C4—4912no—
122C2×C4—4912no—
123C2×C4—4912no—
124C2×C4C22×D49111yescharacteristic
125C2×C4C22×D49112yes—
126C22—21no—
127C22—22no—
128C22—22no—
129C22—21no—
130C22—22no—
131C22—22no—
132C22—22no—
133C22—44no—
134C22—9822no—
135C22—9822no—
136C22—9822no—
137C22C23×D49111yescharacteristic
138C4—22no—
139C4—21no—
140C4—9822no—
141C4—9822no—
142C4—9822no—
143C2—42no—
144C2—41no—
145C2—41no—
146C2—19642no—
147C2#3062838212yes—
148C2#3062838211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D491
commutator, socle, cosocleC22×C491C24
Fitting#120×C491C2
hypercenter#120D491
hypocenterC491#560
LCSG ▷ C22×C491 ▷ C491
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #30628333C2semidirect
2. #30628330C2semidirect
3. #30628319C2semidirect
4. #30628318C2semidirect
5. #30628310C2semidirect
6. #30628309C2semidirect
7. #30628308C2semidirect
8. #30628306C2semidirect
9. #120×C491C2semidirect
10. C2×D1964C22semidirect
14. C2×C22⋊D491C22semidirect
15. C22×Dic491C22semidirect
16. C2×C4×D491C22semidirect
17. C4⋊Dic491C22semidirect
18. Dic491⋊C4C22semidirect
19. Dic491⋊C4C22semidirect
23. C22⋊Dic491C22semidirect
24. (C2×D491)⋊C4C22semidirect
25. C4×Dic491C22semidirect
74. C491#560semidirect
84. #120D491semidirect

Maximal subgroups

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

subgroupindex
#306283332
#306283302
#306283192
#306283182
#306283102
#306283092
#306283082
#306283062
#120×C4912
#560491