Finite Group Databasebeta

← #46830359

Subgroups — #46830359

Order 34624.

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

normal subgroups only

This group has 142 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#31772675C211yesmaximal, characteristic
2#31772661C211yesmaximal, characteristic, complemented
3#31772658C211yesmaximal, characteristic, complemented
4#31772628C211yesmaximal, characteristic, complemented
5#31772556C211yesmaximal, characteristic, complemented
6#31772546C211yesmaximal, characteristic, complemented
7#104×C541C211yesmaximal, characteristic, complemented
8#22575836—21no—
9#22575836C2211yescharacteristic
10#22575835—21no—
11#22575835—22no—
12C2×Dic1082—21no—
13C2×Dic1082C2211yescharacteristic
14C2×Dic1082C2211yescharacteristic
15Q8×D541—21no—
16Dic2164—21no—
17#22575826—21no—
18#22575825—21no—
19#22575824—21no—
20#22575820C2211yescharacteristic
21C4⋊Dic541—22no—
22#41×C541C2211yescharacteristic
23M16×C541C2211yescharacteristic
24C42×C541C2211yescharacteristic
25Dic1082—22no—
26Dic1082—21no—
27Dic1082—21no—
28Dic1082—21no—
29Dic1082—21no—
30Dic1082D411yescharacteristic
31D2164D411yescharacteristic
32C22⋊D541—22no—
33C22⋊D541—21no—
34C2×Dic541—22no—
35C2×Dic541—21no—
36C2×Dic541D412yes—
37C4×D541—22no—
38C4×D541—21no—
39#16864513—21no—
40Q8×C541D411yescharacteristic
41D4×C541—21no—
42D4×C541D411yescharacteristic
43C2×C4×C541—21no—
44C2×C4×C541—21no—
45C2×C4×C541C2311yescharacteristic
46C8×C541—21no—
47C22×C541—21no—
48C22×C541C2×D411yescharacteristic
49C2×D541—21no—
50C4×C541—22no—
51C4×C541—21no—
52C4×C541C2×D411yescharacteristic
53C4×C541C2×D411yescharacteristic
54Dic541—21no—
55Dic541—22no—
56Dic541—41no—
57C2×C541—21no—
58C2×C541—41no—
59C2×C541#12011yescharacteristic
60D541—41no—
61C541#45611yescharacteristic, complemented, Sylow
62#456—5411nomaximal, Sylow
632−1+4—5411no—
64#137—5411no—
65#137—5411no—
66C4⋊Q8—5411no—
67#104—5411no—
68#104D54111yescharacteristic, complemented
69#101—5411no—
70#41—5411no—
71#41—10821no—
72#41—10822no—
73#41—10821no—
74#41C2×D54111yescharacteristic
75C2×Q8—5411no—
76C2×Q8—5411no—
77C2×Q8—10821no—
78C2×Q8—10821no—
79Q16—10821no—
80Q16—10821no—
81SD16—10821no—
82SD16—10821no—
83M16—5411no—
84M16C2×D54111yescharacteristic
85C4⋊C4—10822no—
86C42C2×D54111yescharacteristic
87Q8—5411no—
88Q8—10822no—
89Q8—10821no—
90Q8—10821no—
91Q8—10821no—
92Q8—10821no—
93Q8D216411yescharacteristic
94D4—21no—
95D4—5411no—
96D4—10822no—
97D4—10821no—
98D4D216411yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—5412no—
102C2×C4—10822no—
103C2×C4—10822no—
104C2×C4—10821no—
105C2×C4—10821no—
106C2×C4C22×D54111yescharacteristic
107C8—21no—
108C8—10821no—
109C22—21no—
110C22—10821no—
111C22D4×D54111yescharacteristic
112C4—22no—
113C4—21no—
114C4—10822no—
115C4—10821no—
116C4—21641no—
117C4D4×D54111yescharacteristic
118C4C2×D216411yescharacteristic
119C2—21no—
120C2—41no—
121C2—21641no—
122C2#3177259811yescharacteristic
subgroupG/H
centerC2#31772598
commutator, cosocleC2×C4×C541C23
FrattiniC2×C4C22×D541
Fitting#104×C541C2
socleC2×C541#120
prime radical#31772675C2
hypercenter#104D541
hypocenterC541#456
LCSG ▷ C2×C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #31772661C2semidirect
3. #31772658C2semidirect
4. #31772628C2semidirect
5. #31772556C2semidirect
6. #31772546C2semidirect
7. #104×C541C2semidirect
61. C541#456semidirect
68. #104D541semidirect

Maximal subgroups

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

subgroupindex
#317726752
#317726612
#317726582
#317726282
#317725562
#317725462
#104×C5412
#456541