Finite Group Databasebeta

← #45690371

Subgroups — #45690371

Order 33472.

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

normal subgroups only

This group has 168 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, complemented
2#30660399C211yesmaximal, characteristic, complemented
3#30660369C211yesmaximal, characteristic, complemented
4#30660300C211yesmaximal, characteristic, complemented
5#30660299C211yesmaximal, characteristic, complemented
6#30660289C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C523C211yesmaximal, characteristic, complemented
8#22552642—21no—
9#22552641—21no—
10#22552641C2211yescharacteristic
11C2×D2092—21no—
12C2×D2092C2211yescharacteristic
13C2×C22⋊D523—22no—
14D4×D523—22no—
15D4×D523—21no—
16#22552629—21no—
17#22552626—21no—
18#22552625C2211yescharacteristic, complemented
19C4×Dic523C2211yescharacteristic, complemented
20#41×C523C2211yescharacteristic
21C2×D4×C523C2211yescharacteristic, complemented
22SD16×C523—21no—
23D8×C523—21no—
24M16×C523C2211yescharacteristic, complemented
25C22×D523—22no—
26C22×D523D412yes—
27Dic1046D411yescharacteristic, complemented
28D2092—22no—
29D2092—21no—
30D2092—21no—
31D2092D411yescharacteristic, complemented
32C22⋊D523—22no—
33C22⋊D523—21no—
34C22⋊D523—44no—
35C2×Dic523—21no—
36C4×D523—22no—
37C4×D523—21no—
38C523⋊C8—21no—
39C23×C523—21no—
40Q8×C523D411yescharacteristic, complemented
41D4×C523—21no—
42D4×C523—21no—
43D4×C523—21no—
44D4×C523D411yescharacteristic, complemented
45C2×C4×C523—21no—
46C2×C4×C523C2311yescharacteristic
47C8×C523—21no—
48C22×C523—21no—
49C22×C523—42no—
50C22×C523—41no—
51C22×C523C2×D411yescharacteristic
52C2×D523—22no—
53C2×D523—21no—
54C2×D523—42no—
55C2×D523—82no—
56C4×C523—21no—
57C4×C523C2×D411yescharacteristic
58C4×C523C2×D411yescharacteristic
59Dic523—22no—
60Dic523—21no—
61C2×C523—21no—
62C2×C523—41no—
63C2×C523—81no—
64C2×C523#12011yescharacteristic
65D523—42no—
66D523—41no—
67C523#45311yescharacteristic, complemented, Sylow
68#453—5231nomaximal, Sylow
69H(5,𝔽2)—5231no—
70AGL(1,ℤ/8)—5231no—
71AGL(1,ℤ/8)D52311yescharacteristic, complemented
72#127—5231no—
73#104—5231no—
74#104—5231no—
75#100—5231no—
76#41—5231no—
77#41—10461no—
78#41—10461no—
79#41C2×D52311yescharacteristic
80C2×D4—5231no—
81C2×D4—10461no—
82C2×D4—10462no—
83C2×D4—10461no—
84C2×D4—10462no—
85C2×D4C2×D52311yescharacteristic, complemented
86SD16—21no—
87SD16—10461no—
88D8—21no—
89D8—10461no—
90M16—5231no—
91M16C2×D52311yescharacteristic, complemented
92C42—5231no—
93C23—21no—
94C23—5232no—
95C23—10462no—
96Q8—5231no—
97Q8C22⋊D52311yescharacteristic, complemented
98D4—21no—
99D4—21no—
100D4—21no—
101D4—5231no—
102D4—10462no—
103D4—10462no—
104D4—10461no—
105D4—10461no—
106D4—10461no—
107D4—20924no—
108D4C22⋊D52311yescharacteristic, complemented
109C2×C4—21no—
110C2×C4—10462no—
111C2×C4—10461no—
112C2×C4—10461no—
113C2×C4C22×D52311yescharacteristic
114C8—21no—
115C8—10461no—
116C22—21no—
117C22—42no—
118C22—41no—
119C22—10461no—
120C22—10462no—
121C22—20922no—
122C22—41842no—
123C22D4×D52311yescharacteristic
124C4—21no—
125C4—10462no—
126C4—10461no—
127C4D4×D52311yescharacteristic
128C4C2×C22⋊D52311yescharacteristic
129C2—21no—
130C2—41no—
131C2—81no—
132C2—20922no—
133C2—20921no—
134C2#3066034111yescharacteristic
subgroupG/H
centerC2#30660341
commutator, cosocleC2×C4×C523C23
FrattiniC2×C4C22×D523
FittingAGL(1,ℤ/8)×C523C2
socleC2×C523#120
hypercenterAGL(1,ℤ/8)D523
hypocenterC523#453
LCSG ▷ C2×C4×C523 ▷ C2×C523 ▷ C523
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #30660419C2semidirect
2. #30660399C2semidirect
3. #30660369C2semidirect
4. #30660300C2semidirect
5. #30660299C2semidirect
6. #30660289C2semidirect
7. AGL(1,ℤ/8)×C523C2semidirect
18. #22552625C22semidirect
19. C4×Dic523C22semidirect
21. C2×D4×C523C22semidirect
24. M16×C523C22semidirect
27. Dic1046D4semidirect
31. D2092D4semidirect
40. Q8×C523D4semidirect
44. D4×C523D4semidirect
67. C523#453semidirect
71. AGL(1,ℤ/8)D523semidirect
85. C2×D4C2×D523semidirect
91. M16C2×D523semidirect
97. Q8C22⋊D523semidirect
108. D4C22⋊D523semidirect

Maximal subgroups

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

subgroupindex
#306604192
#306603992
#306603692
#306603002
#306602992
#306602892
AGL(1,ℤ/8)×C5232
#453523