Finite Group Databasebeta

← #46830990

Subgroups — #46830990

Order 34624.

248 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 107 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#31772675C211yesmaximal, characteristic, complemented
2#31772659C213yesmaximal, complemented
3#31772658C213yesmaximal, complemented
4#31772648C213yesmaximal, complemented
5C2×#22575826C213yesmaximal, complemented
6#31772635C211yesmaximal, characteristic, complemented
72−1+4×C541C211yesmaximal, characteristic, complemented
8#22575836C2213yes—
9#22575835—23no—
10C2×Dic1082C2213yes—
11Q8×D541—21no—
12#22575826C2213yes—
13#22575826C2216yes—
14#22575824C2213yes—
15#22575823C2213yes—
16#22575821C2211yescharacteristic
17#22575820C2213yes—
18C2×#16864513C2213yes—
19#41×C541—23no—
20#41×C541C2213yes—
21#41×C541C2211yescharacteristic
22C2×Q8×C541—21no—
23C2×Q8×C541C2213yes—
24Dic1082—23no—
25Dic1082C2313yes—
26D2164C2311yescharacteristic
27C22⋊D541—23no—
28C2×Dic541—23no—
29C4×D541—23no—
30#16864513C2311yescharacteristic
31#16864513C2313yes—
32Q8×C541—23no—
33Q8×C541D411yescharacteristic
34Q8×C541C2313yes—
35D4×C541—23no—
36D4×C541D413yes—
37D4×C541C2311yescharacteristic
38C2×C4×C541—23no—
39C2×C4×C541—23no—
40C2×C4×C541C2313yes—
41C22×C541—21no—
42C22×C541C2×D413yes—
43C2×D541—21no—
44C4×C541—23no—
45C4×C541C2×D413yes—
46C4×C541C2411yescharacteristic
47Dic541—23no—
48C2×C541—23no—
49C2×C541—41no—
50C2×C541C22×D411yescharacteristic
51D541—41no—
52C541#57811yescharacteristic, complemented, Sylow
53#578—5411nomaximal, Sylow
542−1+4—5411no—
552−1+4D54111yescharacteristic, complemented
56#137—5413no—
57#137—5413no—
58#135—5413no—
59C2×Q16—5413no—
60#131—5411no—
61#41—23no—
62#41—5413no—
63#41—10823no—
64#41C2×D54113yes—
65#41C2×D54111yescharacteristic
66C2×Q8—21no—
67C2×Q8—5413no—
68C2×Q8—10821no—
69C2×Q8C2×D54113yes—
70Q16—5413no—
71Q16—5416no—
72SD16—5413no—
73SD16—5413no—
74D8—5411no—
75M16—5413no—
76C2×C8—5413no—
77Q8—23no—
78Q8—5413no—
79Q8—10823no—
80Q8C22⋊D54111yescharacteristic
81Q8C22×D54113yes—
82D4—23no—
83D4—5411no—
84D4—10823no—
85D4C22⋊D54113yes—
86D4C22×D54111yescharacteristic
87C2×C4—23no—
88C2×C4—23no—
89C2×C4—10823no—
90C2×C4—10823no—
91C2×C4C22×D54113yes—
92C8—5411no—
93C8—5413no—
94C22—21no—
95C22—10821no—
96C22C2×C22⋊D54113yes—
97C4—23no—
98C4—10823no—
99C4C2×C22⋊D54113yes—
100C4C23×D54111yescharacteristic
101C2—23no—
102C2—41no—
103C2—21641no—
104C2C22×C22⋊D54111yescharacteristic
subgroupG/H
centerC2C22×C22⋊D541
commutator, cosocleC4×C541C24
FrattiniC4C23×D541
Fitting2−1+4×C541C2
socleC2×C541C22×D4
hypercenter2−1+4D541
hypocenterC541#578
LCSG ▷ C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C2 ◁ #41 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #31772675C2semidirect
2. #31772659C2semidirect
3. #31772658C2semidirect
4. #31772648C2semidirect
5. C2×#22575826C2semidirect
6. #31772635C2semidirect
7. 2−1+4×C541C2semidirect
52. C541#578semidirect
55. 2−1+4D541semidirect

Maximal subgroups

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

subgroupindex
#317726752
#317726592
#317726582
#317726482
C2×#225758262
#317726352
2−1+4×C5412
#578541