Finite Group Databasebeta

← #46830356

Subgroups — #46830356

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#31772659C211yesmaximal, characteristic, complemented
3#31772626C211yesmaximal, characteristic, complemented
4#31772555C211yesmaximal, characteristic, complemented
5#31772554C211yesmaximal, characteristic, complemented
6#31772546C211yesmaximal, characteristic, complemented
7#137×C541C211yesmaximal, characteristic, complemented
8#22575836—21no—
9#22575836C2211yescharacteristic
10#22575835—21no—
11#22575835—22no—
12C2×Dic1082—21no—
13C2×Dic1082C2211yescharacteristic
14Q8×D541—21no—
15#22575826—21no—
16#22575823—21no—
17#22575820C2211yescharacteristic
18#22575815—22no—
19C4×Dic541C2211yescharacteristic
20#41×C541C2211yescharacteristic
21C2×Q8×C541C2211yescharacteristic
22Q16×C541—21no—
23SD16×C541—21no—
24M16×C541C2211yescharacteristic
25Dic1082—22no—
26Dic1082—21no—
27Dic1082—21no—
28Dic1082D411yescharacteristic
29D2164D411yescharacteristic
30C22⋊D541—22no—
31C22⋊D541—21no—
32C2×Dic541—22no—
33C2×Dic541—21no—
34C2×Dic541D412yes—
35C4×D541—22no—
36C4×D541—21no—
37#16864513—21no—
38Q8×C541—21no—
39Q8×C541—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—21no—
51C4×C541—41no—
52C4×C541C2×D411yescharacteristic
53C4×C541C2×D411yescharacteristic
54Dic541—22no—
55Dic541—21no—
56Dic541—22no—
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#137D54111yescharacteristic, complemented
66C4⋊Q8—5411no—
67#104—5411no—
68#104—5411no—
69#101—5411no—
70#41—5411no—
71#41—10821no—
72#41—10822no—
73#41—10821no—
74#41C2×D54111yescharacteristic
75C2×Q8—5411no—
76C2×Q8—10821no—
77C2×Q8—10821no—
78C2×Q8C2×D54111yescharacteristic
79Q16—21no—
80Q16—10821no—
81SD16—21no—
82SD16—10821no—
83M16—5411no—
84M16C2×D54111yescharacteristic
85C4⋊C4—10822no—
86C42—5411no—
87Q8—21no—
88Q8—21no—
89Q8—5411no—
90Q8—10822no—
91Q8—10821no—
92Q8—10821no—
93Q8C22⋊D54111yescharacteristic
94D4—21no—
95D4—5411no—
96D4—10822no—
97D4—10821no—
98D4C22⋊D54111yescharacteristic
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—21no—
113C4—41no—
114C4—10822no—
115C4—10822no—
116C4—10821no—
117C4D4×D54111yescharacteristic
118C4C2×C22⋊D54111yescharacteristic
119C2—21no—
120C2—41no—
121C2—21641no—
122C2#3177259611yescharacteristic
subgroupG/H
centerC2#31772596
commutator, cosocleC2×C4×C541C23
FrattiniC2×C4C22×D541
Fitting#137×C541C2
socleC2×C541#120
prime radical#31772675C2
hypercenter#137D541
hypocenterC541#456
LCSG ▷ C2×C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #31772659C2semidirect
3. #31772626C2semidirect
4. #31772555C2semidirect
5. #31772554C2semidirect
6. #31772546C2semidirect
7. #137×C541C2semidirect
61. C541#456semidirect
65. #137D541semidirect

Maximal subgroups

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

subgroupindex
#317726752
#317726592
#317726262
#317725552
#317725542
#317725462
#137×C5412
#456541