Finite Group Databasebeta

← #45690381

Subgroups — #45690381

Order 33472.

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

normal subgroups only

This group has 152 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#30660419C211yesmaximal, characteristic
2#30660404C211yesmaximal, characteristic, complemented
3#30660362C211yesmaximal, characteristic, complemented
4#30660300C211yesmaximal, characteristic, complemented
5#30660299C211yesmaximal, characteristic, complemented
6#30660289C211yesmaximal, characteristic, complemented
7#137×C523C211yesmaximal, characteristic, complemented
8#22552642—21no—
9#22552641—21no—
10#22552641C2211yescharacteristic
11C2×D2092—21no—
12C2×D2092C2211yescharacteristic
13D4×D523—22no—
14D4×D523—21no—
15#22552631—21no—
16#22552628—21no—
17#22552625C2211yescharacteristic, complemented
18(C2×D523)⋊C4—22no—
19C4×Dic523C2211yescharacteristic, complemented
20#41×C523C2211yescharacteristic
21C2×Q8×C523C2211yescharacteristic, complemented
22Q16×C523—21no—
23SD16×C523—21no—
24M16×C523C2211yescharacteristic, complemented
25C22×D523—22no—
26C22×D523D412yes—
27Dic1046D411yescharacteristic
28D2092—22no—
29D2092—21no—
30D2092—21no—
31D2092D411yescharacteristic
32C22⋊D523—22no—
33C22⋊D523—21no—
34C2×Dic523—21no—
35C4×D523—22no—
36C4×D523—21no—
37C523⋊C8—21no—
38Q8×C523—21no—
39Q8×C523—21no—
40Q8×C523D411yescharacteristic
41D4×C523—21no—
42D4×C523D411yescharacteristic
43C2×C4×C523—21no—
44C2×C4×C523—21no—
45C2×C4×C523C2311yescharacteristic
46C8×C523—21no—
47C22×C523—21no—
48C22×C523C2×D411yescharacteristic
49C2×D523—22no—
50C2×D523—21no—
51C2×D523—42no—
52C2×D523—82no—
53C4×C523—21no—
54C4×C523—41no—
55C4×C523C2×D411yescharacteristic
56C4×C523C2×D411yescharacteristic
57Dic523—21no—
58Dic523—41no—
59C2×C523—21no—
60C2×C523—41no—
61C2×C523#12011yescharacteristic
62D523—42no—
63D523—41no—
64C523#45511yescharacteristic, complemented, Sylow
65#455—5231nomaximal, Sylow
66H(5,𝔽2)—5231no—
67#137—5231no—
68#137D52311yescharacteristic, complemented
69#124—5231no—
70#104—5231no—
71#104—5231no—
72#100—5231no—
73#41—5231no—
74#41—10461no—
75#41—10461no—
76#41C2×D52311yescharacteristic
77C2×Q8C2×D52311yescharacteristic, complemented
78C2×D4—5231no—
79C2×D4—10461no—
80C2×D4—10462no—
81C2×D4—10461no—
82Q16—21no—
83Q16—10461no—
84SD16—21no—
85SD16—10461no—
86M16—5231no—
87M16C2×D52311yescharacteristic, complemented
88C22⋊C4—10462no—
89C42—5231no—
90C23—5232no—
91C23—10462no—
92Q8—21no—
93Q8—21no—
94Q8—5231no—
95Q8C22⋊D52311yescharacteristic
96D4—21no—
97D4—5231no—
98D4—10462no—
99D4—10462no—
100D4—10461no—
101D4—10461no—
102D4—10461no—
103D4C22⋊D52311yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—10462no—
107C2×C4—10461no—
108C2×C4—10461no—
109C2×C4C22×D52311yescharacteristic
110C8—21no—
111C8—10461no—
112C22—21no—
113C22—10461no—
114C22—10462no—
115C22—20922no—
116C22—41842no—
117C22D4×D52311yescharacteristic
118C4—21no—
119C4—41no—
120C4—10461no—
121C4—20921no—
122C4D4×D52311yescharacteristic
123C4C2×C22⋊D52311yescharacteristic
124C2—21no—
125C2—41no—
126C2—20922no—
127C2—20921no—
128C2#3066034111yescharacteristic
subgroupG/H
centerC2#30660341
commutator, cosocleC2×C4×C523C23
FrattiniC2×C4C22×D523
Fitting#137×C523C2
socleC2×C523#120
prime radical#30660419C2
hypercenter#137D523
hypocenterC523#455
LCSG ▷ C2×C4×C523 ▷ C2×C523 ▷ C523
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #30660404C2semidirect
3. #30660362C2semidirect
4. #30660300C2semidirect
5. #30660299C2semidirect
6. #30660289C2semidirect
7. #137×C523C2semidirect
17. #22552625C22semidirect
19. C4×Dic523C22semidirect
21. C2×Q8×C523C22semidirect
24. M16×C523C22semidirect
64. C523#455semidirect
68. #137D523semidirect
77. C2×Q8C2×D523semidirect
87. M16C2×D523semidirect

Maximal subgroups

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

subgroupindex
#306604192
#306604042
#306603622
#306603002
#306602992
#306602892
#137×C5232
#455523