Finite Group Databasebeta

← #45688171

Subgroups — #45688171

Order 33344.

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#30659704C211yesmaximal, characteristic, complemented
2#30659701C212yesmaximal, complemented
3#30659690C212yesmaximal, complemented
4#30659689C211yesmaximal, characteristic, complemented
5#30659681C212yesmaximal, complemented
6#30659680C212yesmaximal, complemented
7#30659679C212yesmaximal, complemented
8#30659677C212yesmaximal, complemented
9#120×C521C211yesmaximal, characteristic, complemented
10C2×D2084C2211yescharacteristic, complemented
11C2×C22⋊D521C2212yes—
12C2×C22⋊D521C2212yes—
13C2×C22⋊D521C2212yes—
14C2×C22⋊D521C2212yescomplemented
15C22×Dic521C2211yescharacteristic, complemented
16C2×C4×D521C2212yescomplemented
17C4⋊Dic521C2212yescomplemented
18#22552343C2212yescomplemented
19#22552343C2212yescomplemented
20C22⋊Dic521C2212yes—
21C22⋊Dic521C2212yes—
22C22⋊Dic521C2212yes—
23C22⋊Dic521C2211yescharacteristic, complemented
24#22552341C2212yescomplemented
25C4×Dic521C2211yescharacteristic, complemented
26C24×C521C2211yescharacteristic
27C2×D4×C521C2212yes—
28C2×D4×C521C2211yescharacteristic
29C22⋊C4×C521C2212yes—
30C22⋊C4×C521C2211yescharacteristic
31C22×D521C2312yes—
32D2084—41no—
33C22⋊D521—42no—
34C22⋊D521—42no—
35C22⋊D521—42no—
36C22⋊D521—42no—
37C2×Dic521—41no—
38C2×Dic521C2312yes—
39C2×Dic521C2312yes—
40C2×Dic521C2312yes—
41C4×D521—42no—
42C23×C521—42no—
43C23×C521—41no—
44C23×C521C2312yes—
45C23×C521C2311yescharacteristic
46C23×C521C2311yescharacteristic
47D4×C521—42no—
48D4×C521—41no—
49C2×C4×C521C2311yescharacteristic
50C2×C4×C521C2312yes—
51C22×C521—22no—
52C22×C521—21no—
53C22×C521—21no—
54C22×C521—22no—
55C22×C521—22no—
56C22×C521—22no—
57C22×C521—22no—
58C22×C521—44no—
59C22×C521C2411yescharacteristic
60C2×D521—22no—
61C2×D521—22no—
62C2×D521—22no—
63C4×C521—22no—
64C4×C521—21no—
65Dic521—22no—
66Dic521—22no—
67Dic521—22no—
68C2×C521—41no—
69C2×C521—42no—
70C2×C521—41no—
71C2×C521H(5,𝔽2)12yes—
72C2×C521H(5,𝔽2)11yescharacteristic
73D521—42no—
74C521#56011yescharacteristic, complemented, Sylow
75#560—5211nomaximal, Sylow
76#127—5211no—
77#126—5212no—
78#123—5211no—
79#123—5212no—
80#121—5212no—
81#121—5212no—
82#121—5212no—
83#120—5212no—
84#120D52111yescharacteristic, complemented
85C24C2×D52111yescharacteristic
86C2×D4—5212no—
87C2×D4—5212no—
88C2×D4—5212no—
89C2×D4—5212no—
90C2×D4—5211no—
91C2×D4C2×D52112yes—
92C2×D4C2×D52111yescharacteristic
93C22×C4—5211no—
94C22×C4—5212no—
95C4⋊C4—5212no—
96C4⋊C4—5212no—
97C4⋊C4—5212no—
98C22⋊C4—5212no—
99C22⋊C4—5212no—
100C22⋊C4—5212no—
101C22⋊C4—5211no—
102C22⋊C4—5212no—
103C22⋊C4C2×D52112yes—
104C22⋊C4C2×D52111yescharacteristic
105C42—5211no—
106C23—42no—
107C23—41no—
108C23—5212no—
109C23C22×D52112yes—
110C23C22×D52111yescharacteristic
111C23C22×D52111yescharacteristic
112D4—42no—
113D4—41no—
114D4—20841no—
115D4—20842no—
116D4—20842no—
117D4—20842no—
118D4—20842no—
119C2×C4—5212no—
120C2×C4—5212no—
121C2×C4—5212no—
122C2×C4—20842no—
123C2×C4—20841no—
124C2×C4C22×D52111yescharacteristic
125C2×C4C22×D52112yes—
126C22—21no—
127C22—22no—
128C22—22no—
129C22—21no—
130C22—22no—
131C22—22no—
132C22—22no—
133C22—44no—
134C22—10422no—
135C22—10422no—
136C22—10422no—
137C22C23×D52111yescharacteristic
138C4—22no—
139C4—21no—
140C4—10422no—
141C4—10422no—
142C4—10422no—
143C2—42no—
144C2—41no—
145C2—41no—
146C2—20842no—
147C2#3065975312yes—
148C2#3065975311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D521
commutator, socle, cosocleC22×C521C24
Fitting#120×C521C2
hypercenter#120D521
hypocenterC521#560
LCSG ▷ C22×C521 ▷ C521
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #30659704C2semidirect
2. #30659701C2semidirect
3. #30659690C2semidirect
4. #30659689C2semidirect
5. #30659681C2semidirect
6. #30659680C2semidirect
7. #30659679C2semidirect
8. #30659677C2semidirect
9. #120×C521C2semidirect
10. C2×D2084C22semidirect
14. C2×C22⋊D521C22semidirect
15. C22×Dic521C22semidirect
16. C2×C4×D521C22semidirect
17. C4⋊Dic521C22semidirect
18. #22552343C22semidirect
19. #22552343C22semidirect
23. C22⋊Dic521C22semidirect
24. #22552341C22semidirect
25. C4×Dic521C22semidirect
74. C521#560semidirect
84. #120D521semidirect

Maximal subgroups

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

subgroupindex
#306597042
#306597012
#306596902
#306596892
#306596812
#306596802
#306596792
#306596772
#120×C5212
#560521