Finite Group Databasebeta

← #49148508

Subgroups — #49148508

Order 36928.

346 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 111 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⋊D577C211yesmaximal, characteristic, complemented
2#32914647C212yesmaximal, complemented
3#32914645C212yesmaximal, complemented
4#32914636C214yesmaximal, complemented
5#32914633C212yesmaximal, complemented
6#32914632C212yesmaximal, complemented
7C2×C22⋊Dic577C211yesmaximal, characteristic, complemented
8C22×D4×C577C211yesmaximal, characteristic, complemented
9C23×D577C2211yescharacteristic, complemented
10C2×C22⋊D577—24no—
11C2×C22⋊D577C2212yes—
12C2×C22⋊D577C2212yescomplemented
13C2×C22⋊D577C2214yescomplemented
14C22×Dic577C2211yescharacteristic, complemented
15C22×Dic577C2212yescomplemented
16#22604397C2214yescomplemented
17C22⋊Dic577C2212yescomplemented
18C22⋊Dic577C2212yescomplemented
19C22⋊Dic577C2214yescomplemented
20#22604395C2214yescomplemented
21C24×C577C2211yescharacteristic
22C24×C577C2211yescharacteristic, complemented
23C2×D4×C577—24no—
24C2×D4×C577C2212yes—
25C2×D4×C577C2212yescomplemented
26C22×C4×C577C2211yescharacteristic, complemented
27C22×D577—22no—
28C22×D577—42no—
29C22×D577C2312yes—
30C22⋊D577—24no—
31C22⋊D577—24no—
32C22⋊D577—44no—
33C2×Dic577—22no—
34C2×Dic577—42no—
35C2×Dic577C2314yes—
36C2×Dic577C2312yes—
37C23×C577—22no—
38C23×C577—42no—
39C23×C577—42no—
40C23×C577D414yescomplemented
41C23×C577C2312yes—
42C23×C577C2311yescharacteristic
43C23×C577C2311yescharacteristic
44C23×C577C2311yescharacteristic
45D4×C577—24no—
46D4×C577—24no—
47C2×C4×C577—22no—
48C2×C4×C577C2312yes—
49C22×C577—22no—
50C22×C577—22no—
51C22×C577—22no—
52C22×C577—22no—
53C22×C577—24no—
54C22×C577—44no—
55C22×C577—44no—
56C22×C577C2×D412yes—
57C22×C577C2×D412yes—
58C22×C577C2×D412yes—
59C22×C577C2411yescharacteristic
60C2×D577—22no—
61C2×D577—24no—
62C2×D577—44no—
63C4×C577—22no—
64Dic577—22no—
65Dic577—24no—
66C2×C577—22no—
67C2×C577—22no—
68C2×C577—22no—
69C2×C577—42no—
70C2×C577C22×D411yescharacteristic
71C2×C577H(5,𝔽2)12yes—
72D577—42no—
73C577#53411yescharacteristic, complemented, Sylow
74#534—5771nomaximal, Sylow
75C22×D4—5771no—
76C22×D4D57711yescharacteristic, complemented
77#123—5772no—
78#123—5772no—
79#121—5774no—
80#120—5772no—
81#120—5772no—
82C2×C22⋊C4—5771no—
83C24—5771no—
84C24C2×D57711yescharacteristic
85C24C2×D57711yescharacteristic, complemented
86C2×D4—24no—
87C2×D4—5774no—
88C2×D4—5772no—
89C2×D4—5772no—
90C2×D4—11544no—
91C2×D4C2×D57712yes—
92C2×D4C2×D57712yescomplemented
93C22×C4—5772no—
94C22×C4—5771no—
95C22×C4C2×D57711yescharacteristic, complemented
96C4⋊C4—5774no—
97C22⋊C4—5772no—
98C22⋊C4—5772no—
99C22⋊C4—5774no—
100C22⋊C4—5774no—
101C23—22no—
102C23—42no—
103C23—42no—
104C23—23082no—
105C23—5772no—
106C23—11542no—
107C23C22⋊D57714yescomplemented
108C23C22×D57712yes—
109C23C22×D57711yescharacteristic
110C23C22×D57711yescharacteristic
111C23C22×D57711yescharacteristic
112D4—24no—
113D4—24no—
114D4—23084no—
115D4—11544no—
116D4—11544no—
117C2×C4—22no—
118C2×C4—23082no—
119C2×C4—5774no—
120C2×C4—5772no—
121C2×C4—11542no—
122C2×C4C22×D57712yes—
123C22—22no—
124C22—22no—
125C22—22no—
126C22—22no—
127C22—24no—
128C22—44no—
129C22—44no—
130C22—23084no—
131C22—11542no—
132C22—11544no—
133C22C2×C22⋊D57712yes—
134C22C2×C22⋊D57712yes—
135C22C2×C22⋊D57712yes—
136C22C23×D57711yescharacteristic
137C4—22no—
138C4—11542no—
139C4—11544no—
140C2—22no—
141C2—22no—
142C2—22no—
143C2—42no—
144C2—23082no—
145C2C22×C22⋊D57711yescharacteristic
146C2#3291470912yes—
subgroupG/H
center, FrattiniC22C23×D577
commutator, socle, cosocleC22×C577C24
FittingC22×D4×C577C2
hypercenterC22×D4D577
hypocenterC577#534
LCSG ▷ C22×C577 ▷ C577
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D577C2semidirect
2. #32914647C2semidirect
3. #32914645C2semidirect
4. #32914636C2semidirect
5. #32914633C2semidirect
6. #32914632C2semidirect
7. C2×C22⋊Dic577C2semidirect
8. C22×D4×C577C2semidirect
9. C23×D577C22semidirect
12. C2×C22⋊D577C22semidirect
13. C2×C22⋊D577C22semidirect
14. C22×Dic577C22semidirect
15. C22×Dic577C22semidirect
16. #22604397C22semidirect
17. C22⋊Dic577C22semidirect
18. C22⋊Dic577C22semidirect
19. C22⋊Dic577C22semidirect
20. #22604395C22semidirect
22. C24×C577C22semidirect
25. C2×D4×C577C22semidirect
26. C22×C4×C577C22semidirect
40. C23×C577D4semidirect
73. C577#534semidirect
76. C22×D4D577semidirect
85. C24C2×D577semidirect
92. C2×D4C2×D577semidirect
95. C22×C4C2×D577semidirect
107. C23C22⋊D577semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D5772
#329146472
#329146452
#329146362
#329146332
#329146322
C2×C22⋊Dic5772
C22×D4×C5772
#534577