Finite Group Databasebeta

← #45690394

Subgroups — #45690394

Order 33472.

160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 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#30660418C211yesmaximal, characteristic
2#30660356C212yesmaximal, complemented
3#30660288C211yesmaximal, characteristic, complemented
4#30660287C212yesmaximal, complemented
5#123×C523C211yesmaximal, characteristic, complemented
6#22552641—21no—
7#22552640—22no—
8C2×C22⋊D523—21no—
9C2×C22⋊D523C2212yes—
10D4×D523—22no—
11Dic523⋊C4—22no—
12C22⋊Dic523C2212yescomplemented
13(C2×D523)⋊C4—22no—
14C2×D4×C523C2211yescharacteristic
15C22×C4×C523C2211yescharacteristic, complemented
16C4⋊C4×C523—21no—
17C22⋊C4×C523—21no—
18C22⋊C4×C523C2211yescharacteristic, complemented
19C22×D523—21no—
20C22×D523D412yes—
21Dic1046—21no—
22D2092—21no—
23C22⋊D523—22no—
24C22⋊D523—22no—
25C22⋊D523—22no—
26C2×Dic523—21no—
27C2×Dic523—22no—
28C2×Dic523D412yes—
29C4×D523—22no—
30C23×C523D411yescharacteristic
31C23×C523C2311yescharacteristic
32D4×C523—22no—
33C2×C4×C523—21no—
34C2×C4×C523—21no—
35C2×C4×C523—22no—
36C2×C4×C523D411yescharacteristic
37C22×C523—21no—
38C22×C523—41no—
39C22×C523—41no—
40C22×C523C2×D412yes—
41C22×C523C2×D411yescharacteristic
42C2×D523—22no—
43C2×D523—42no—
44C2×D523—81no—
45C4×C523—21no—
46C4×C523—41no—
47C4×C523—41no—
48Dic523—22no—
49Dic523—42no—
50C2×C523—22no—
51C2×C523—21no—
52C2×C523—41no—
53C2×C523#12011yescharacteristic
54D523—42no—
55C523#45811yescharacteristic, complemented, Sylow
56#458—5231nomaximal, Sylow
57H(5,𝔽2)—5231no—
58#123—5232no—
59#123D52311yescharacteristic, complemented
60#99—5231no—
61#99—5232no—
62#41—10462no—
63#41—10461no—
64C2×D4—5232no—
65C2×D4—10462no—
66C2×D4—10461no—
67C2×D4C2×D52311yescharacteristic
68C22×C4C2×D52311yescharacteristic, complemented
69C4⋊C4—21no—
70C4⋊C4—10462no—
71C22⋊C4—21no—
72C22⋊C4—5232no—
73C22⋊C4—10462no—
74C22⋊C4C2×D52311yescharacteristic, complemented
75C23—5232no—
76C23—10461no—
77C23C22⋊D52311yescharacteristic
78C23C22×D52311yescharacteristic
79Q8—10461no—
80D4—22no—
81D4—10461no—
82D4—10462no—
83D4—10462no—
84D4—10462no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—5232no—
89C2×C4—10462no—
90C2×C4—10461no—
91C2×C4—10462no—
92C2×C4C22⋊D52311yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—10462no—
97C22—20922no—
98C22—41841no—
99C22D4×D52312yes—
100C22C2×C22⋊D52311yescharacteristic
101C4—21no—
102C4—41no—
103C4—41no—
104C4—10462no—
105C4—20922no—
106C2—21no—
107C2—22no—
108C2—41no—
109C2—20922no—
110C2#3066034111yescharacteristic
subgroupG/H
centerC2#30660341
commutator, cosocleC23×C523C23
FrattiniC23C22×D523
Fitting#123×C523C2
socleC2×C523#120
prime radical#30660418C2
hypercenter#123D523
hypocenterC523#458
LCSG ▷ C23×C523 ▷ C2×C523 ▷ C523
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #30660356C2semidirect
3. #30660288C2semidirect
4. #30660287C2semidirect
5. #123×C523C2semidirect
12. C22⋊Dic523C22semidirect
15. C22×C4×C523C22semidirect
18. C22⋊C4×C523C22semidirect
55. C523#458semidirect
59. #123D523semidirect
68. C22×C4C2×D523semidirect
74. C22⋊C4C2×D523semidirect

Maximal subgroups

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

subgroupindex
#306604182
#306603562
#306602882
#306602872
#123×C5232
#458523