Finite Group Databasebeta

← #49148507

Subgroups — #49148507

Order 36928.

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×D577C212yesmaximal, complemented
2#32914649C212yesmaximal, complemented
3#32914646C212yesmaximal, complemented
4#32914638C211yesmaximal, characteristic, complemented
5#32914636C212yesmaximal, complemented
6#32914634C212yesmaximal, complemented
7#32914632C212yesmaximal, complemented
8C2×#22604395C211yesmaximal, characteristic, complemented
9#121×C577C211yesmaximal, characteristic, complemented
10C23×D577C2211yescharacteristic
11C23×D577C2212yescomplemented
12C2×D2308C2212yes—
13C2×D2308C2211yescharacteristic, complemented
14C2×C22⋊D577C2212yes—
15C2×C22⋊D577C2212yescomplemented
16C2×C22⋊D577C2212yescomplemented
17D4×D577—28no—
18C22×Dic577C2211yescharacteristic, complemented
19C2×C4×D577C2212yescomplemented
20C4⋊Dic577C2211yescharacteristic, complemented
21#22604397C2212yescomplemented
22C22⋊Dic577C2212yescomplemented
23#22604395C2212yescomplemented
24#22604395C2212yescomplemented
25#22604395C2212yescomplemented
26#22604395C2212yescomplemented
27C2×D4×C577C2212yescomplemented
28C2×D4×C577C2211yescharacteristic, complemented
29C22×C4×C577C2211yescharacteristic, complemented
30C4⋊C4×C577C2211yescharacteristic, complemented
31C22⋊C4×C577C2212yescomplemented
32C22×D577—24no—
33C22×D577—41no—
34C22×D577—41no—
35C22×D577—42no—
36C22×D577—42no—
37C22×D577D414yescomplemented
38C22×D577C2312yes—
39C22×D577C2312yes—
40D2308—24no—
41D2308—41no—
42C22⋊D577—24no—
43C22⋊D577—24no—
44C22⋊D577—42no—
45C2×Dic577—41no—
46C2×Dic577C2312yes—
47C2×Dic577C2312yes—
48C4×D577—24no—
49C23×C577C2312yes—
50C23×C577C2311yescharacteristic
51D4×C577—24no—
52D4×C577—41no—
53C2×C4×C577—41no—
54C2×C4×C577C2311yescharacteristic
55C2×C4×C577C2312yes—
56C2×C4×C577C2311yescharacteristic
57C22×C577—21no—
58C22×C577—21no—
59C22×C577—22no—
60C22×C577—22no—
61C22×C577—22no—
62C22×C577C2×D412yes—
63C22×C577C2411yescharacteristic
64C2×D577—22no—
65C2×D577—22no—
66C2×D577—22no—
67C2×D577—22no—
68C2×D577—22no—
69C2×D577—44no—
70C2×D577—48no—
71C2×D577C2×D414yes—
72C4×C577—22no—
73C4×C577—21no—
74C4×C577—21no—
75Dic577—22no—
76Dic577—22no—
77C2×C577—22no—
78C2×C577—42no—
79C2×C577C22×D411yescharacteristic
80C2×C577H(5,𝔽2)11yescharacteristic
81C2×C577H(5,𝔽2)11yescharacteristic
82D577—24no—
83D577—42no—
84C577#53411yescharacteristic, complemented, Sylow
85#534—5771nomaximal, Sylow
86C22×D4—5772no—
87#123—5772no—
88#123—5772no—
89#121—5772no—
90#121—5771no—
91#121D57711yescharacteristic, complemented
92#120—5772no—
93#120—5772no—
94C2×C22⋊C4—5771no—
95C24—5771no—
96C24—5772no—
97C2×D4—5772no—
98C2×D4—5772no—
99C2×D4—5772no—
100C2×D4—5771no—
101C2×D4—5772no—
102C2×D4—11548no—
103C2×D4C2×D57712yescomplemented
104C2×D4C2×D57711yescharacteristic, complemented
105C22×C4—5771no—
106C22×C4—5772no—
107C22×C4C2×D57711yescharacteristic, complemented
108C4⋊C4—5772no—
109C4⋊C4—5771no—
110C4⋊C4C2×D57711yescharacteristic, complemented
111C22⋊C4—5772no—
112C22⋊C4—5772no—
113C22⋊C4—5772no—
114C22⋊C4—5772no—
115C22⋊C4—5772no—
116C22⋊C4C2×D57712yescomplemented
117C23—23081no—
118C23—23081no—
119C23—23082no—
120C23—23082no—
121C23—5774no—
122C23—5772no—
123C23—5772no—
124C23—11544no—
125C23C22×D57712yes—
126C23C22×D57711yescharacteristic
127D4—24no—
128D4—41no—
129D4—23081no—
130D4—23082no—
131D4—11544no—
132D4—11544no—
133D4—11544no—
134C2×C4—41no—
135C2×C4—23081no—
136C2×C4—5772no—
137C2×C4—5772no—
138C2×C4—11544no—
139C2×C4C22×D57711yescharacteristic
140C2×C4C22×D57711yescharacteristic
141C2×C4C22×D57712yes—
142C22—21no—
143C22—21no—
144C22—22no—
145C22—22no—
146C22—22no—
147C22—23084no—
148C22—23088no—
149C22—5774no—
150C22—11542no—
151C22—11542no—
152C22—11542no—
153C22—11542no—
154C22—11542no—
155C22D4×D57712yes—
156C22C23×D57711yescharacteristic
157C4—22no—
158C4—21no—
159C4—21no—
160C4—11542no—
161C4—11542no—
162C2—22no—
163C2—42no—
164C2—23082no—
165C2—11544no—
166C2C2×D4×D57711yescharacteristic
167C2#3291470911yescharacteristic
168C2#3291471011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D577
commutator, socle, cosocleC22×C577C24
Fitting#121×C577C2
hypercenter#121D577
hypocenterC577#534
LCSG ▷ C22×C577 ▷ C577
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D577C2semidirect
2. #32914649C2semidirect
3. #32914646C2semidirect
4. #32914638C2semidirect
5. #32914636C2semidirect
6. #32914634C2semidirect
7. #32914632C2semidirect
8. C2×#22604395C2semidirect
9. #121×C577C2semidirect
11. C23×D577C22semidirect
13. C2×D2308C22semidirect
15. C2×C22⋊D577C22semidirect
16. C2×C22⋊D577C22semidirect
18. C22×Dic577C22semidirect
19. C2×C4×D577C22semidirect
20. C4⋊Dic577C22semidirect
21. #22604397C22semidirect
22. C22⋊Dic577C22semidirect
23. #22604395C22semidirect
24. #22604395C22semidirect
25. #22604395C22semidirect
26. #22604395C22semidirect
27. C2×D4×C577C22semidirect
28. C2×D4×C577C22semidirect
29. C22×C4×C577C22semidirect
30. C4⋊C4×C577C22semidirect
31. C22⋊C4×C577C22semidirect
37. C22×D577D4semidirect
84. C577#534semidirect
91. #121D577semidirect
103. C2×D4C2×D577semidirect
104. C2×D4C2×D577semidirect
107. C22×C4C2×D577semidirect
110. C4⋊C4C2×D577semidirect
116. C22⋊C4C2×D577semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D5772
#329146492
#329146462
#329146382
#329146362
#329146342
#329146322
C2×#226043952
#121×C5772
#534577