Finite Group Databasebeta

← #45688172

Subgroups — #45688172

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#30659703C212yesmaximal, complemented
3#30659690C212yesmaximal, complemented
4#30659683C212yesmaximal, complemented
5#30659682C212yesmaximal, complemented
6#30659681C212yesmaximal, complemented
7#30659678C212yesmaximal, complemented
8#30659676C211yesmaximal, characteristic, complemented
9#123×C521C211yesmaximal, characteristic, complemented
10C23×D521C2211yescharacteristic
11C2×D2084C2212yes—
12C2×D2084C2212yes—
13C2×D2084C2211yescharacteristic, complemented
14C2×C22⋊D521C2212yes—
15C2×C22⋊D521C2212yes—
16C2×C22⋊D521C2212yescomplemented
17C2×C4×D521C2212yescomplemented
18C4⋊Dic521C2212yescomplemented
19#22552343C2212yescomplemented
20C22⋊Dic521C2211yescharacteristic
21#22552341C2212yes—
22#22552341C2212yes—
23#22552341C2212yes—
24#22552341C2212yescomplemented
25C4×Dic521C2211yescharacteristic, complemented
26C2×D4×C521C2211yescharacteristic
27C22×C4×C521C2211yescharacteristic, complemented
28C4⋊C4×C521C2212yescomplemented
29C22⋊C4×C521C2212yes—
30C22⋊C4×C521C2211yescharacteristic, complemented
31C22×D521—42no—
32C22×D521—41no—
33C22×D521C2312yes—
34C22×D521C2312yes—
35D2084—42no—
36D2084—42no—
37D2084—41no—
38C22⋊D521—42no—
39C22⋊D521—42no—
40C22⋊D521—42no—
41C2×Dic521C2312yes—
42C2×Dic521C2312yes—
43C4×D521—42no—
44C23×C521C2311yescharacteristic
45C23×C521C2311yescharacteristic
46D4×C521—41no—
47C2×C4×C521—41no—
48C2×C4×C521C2312yes—
49C2×C4×C521C2312yes—
50C2×C4×C521C2311yescharacteristic
51C22×C521—21no—
52C22×C521—21no—
53C22×C521—22no—
54C22×C521—22no—
55C22×C521C2411yescharacteristic
56C2×D521—22no—
57C2×D521—22no—
58C2×D521—22no—
59C2×D521—22no—
60C2×D521—22no—
61C2×D521—22no—
62C2×D521—44no—
63C4×C521—22no—
64C4×C521—21no—
65C4×C521—22no—
66Dic521—22no—
67Dic521—22no—
68C2×C521—41no—
69C2×C521—41no—
70C2×C521H(5,𝔽2)11yescharacteristic
71C2×C521H(5,𝔽2)12yes—
72D521—42no—
73D521—42no—
74C521#56011yescharacteristic, complemented, Sylow
75#560—5211nomaximal, Sylow
76#127—5211no—
77#126—5212no—
78#123—5212no—
79#123D52111yescharacteristic, complemented
80#121—5212no—
81#121—5212no—
82#121—5212no—
83#120—5211no—
84#120—5212no—
85C24—5211no—
86C2×D4—5212no—
87C2×D4—5212no—
88C2×D4—5212no—
89C2×D4—5212no—
90C2×D4—5212no—
91C2×D4—5211no—
92C2×D4C2×D52111yescharacteristic
93C22×C4—5212no—
94C22×C4C2×D52111yescharacteristic, complemented
95C4⋊C4—5212no—
96C4⋊C4—5212no—
97C4⋊C4C2×D52112yescomplemented
98C22⋊C4—5211no—
99C22⋊C4—5212no—
100C22⋊C4—5212no—
101C22⋊C4—5212no—
102C22⋊C4—5212no—
103C22⋊C4C2×D52112yes—
104C22⋊C4C2×D52111yescharacteristic, complemented
105C42—5211no—
106C23—5212no—
107C23—5212no—
108C23—20841no—
109C23—20842no—
110C23C22×D52111yescharacteristic
111C23C22×D52111yescharacteristic
112D4—41no—
113D4—20842no—
114D4—20841no—
115D4—20842no—
116D4—20842no—
117D4—20842no—
118D4—20842no—
119C2×C4—41no—
120C2×C4—5212no—
121C2×C4—5212no—
122C2×C4—20842no—
123C2×C4C22×D52111yescharacteristic
124C2×C4C22×D52112yes—
125C2×C4C22×D52112yes—
126C22—21no—
127C22—21no—
128C22—22no—
129C22—22no—
130C22—10422no—
131C22—10422no—
132C22—10422no—
133C22—10422no—
134C22—10422no—
135C22—10422no—
136C22—20844no—
137C22C23×D52111yescharacteristic
138C4—22no—
139C4—21no—
140C4—22no—
141C4—10422no—
142C4—10422no—
143C2—41no—
144C2—41no—
145C2—20842no—
146C2—20842no—
147C2#3065975311yescharacteristic
148C2#3065975412yes—
subgroupG/H
center, FrattiniC22C23×D521
commutator, socle, cosocleC22×C521C24
Fitting#123×C521C2
hypercenter#123D521
hypocenterC521#560
LCSG ▷ C22×C521 ▷ C521
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #30659704C2semidirect
2. #30659703C2semidirect
3. #30659690C2semidirect
4. #30659683C2semidirect
5. #30659682C2semidirect
6. #30659681C2semidirect
7. #30659678C2semidirect
8. #30659676C2semidirect
9. #123×C521C2semidirect
13. C2×D2084C22semidirect
16. C2×C22⋊D521C22semidirect
17. C2×C4×D521C22semidirect
18. C4⋊Dic521C22semidirect
19. #22552343C22semidirect
24. #22552341C22semidirect
25. C4×Dic521C22semidirect
27. C22×C4×C521C22semidirect
28. C4⋊C4×C521C22semidirect
30. C22⋊C4×C521C22semidirect
74. C521#560semidirect
79. #123D521semidirect
94. C22×C4C2×D521semidirect
97. C4⋊C4C2×D521semidirect
104. C22⋊C4C2×D521semidirect

Maximal subgroups

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

subgroupindex
#306597042
#306597032
#306596902
#306596832
#306596822
#306596812
#306596782
#306596762
#123×C5212
#560521