Finite Group Databasebeta

← #37508301

Subgroups — #37508301

Order 22912.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C179⋊#564C211yesmaximal, characteristic, complemented
2#26038803C212yesmaximal
3#26038181C211yesmaximal, characteristic, complemented
4#26038180C212yesmaximal, complemented
5#490×C179C211yesmaximal, characteristic
6#19153105C2212yes—
7#19153104—22no—
8#19153103—22no—
9#19153103—22no—
10#19153034—22no—
11#19153034—22no—
12#19153024C2212yes—
13#127×C179C2211yescharacteristic
14#125×C179C2211yescharacteristic
15#102×C179—22no—
16#97×C179C2211yescharacteristic
17C2×C179⋊C8—22no—
18C4⋊Dic179—22no—
19C4⋊Dic179D412yes—
20C4⋊Dic179D412yes—
21Dic179⋊C4—22no—
22Dic179⋊C4—22no—
23Dic179⋊C4—22no—
24Dic179⋊C4—22no—
25C4×Dic179—22no—
26C2×D4×C179—21no—
27C2×D4×C179—22no—
28C2×C8×C179—21no—
29C4⋊C4×C179—22no—
30C4⋊C4×C179D412yes—
31C42×C179C2311yescharacteristic
32C2×Dic179—22no—
33C2×Dic179—22no—
34C179⋊C8—42no—
35C23×C179—41no—
36D4×C179—42no—
37D4×C179—44no—
38C2×C4×C179—22no—
39C2×C4×C179C2×D412yes—
40C2×C4×C179C2×D411yescharacteristic
41C8×C179—41no—
42C22×C179—82no—
43C22×C179—81no—
44C22×C179#12011yescharacteristic
45C4×C179—21no—
46C4×C179—22no—
47C4×C179—42no—
48Dic179—42no—
49Dic179—42no—
50C2×C179—161no—
51C2×C179#45412yes—
52C2×C179#45411yescharacteristic
53C179#165811yescharacteristic, complemented, Sylow
54#1658—1791nomaximal, Sylow
55#564—1791no—
56#490—1792no—
57#490D17911yescharacteristic
58#330—1791no—
59#330—1792no—
60#127C2×D17911yescharacteristic
61#125—3582no—
62#125—3582no—
63#125—3582no—
64#125—1792no—
65#125C2×D17911yescharacteristic
66#102—22no—
67#102—3582no—
68#102—3582no—
69#97—1792no—
70#97C2×D17911yescharacteristic
71C2×D4—22no—
72C2×D4—21no—
73C2×C8—21no—
74C2×C8—3582no—
75C4⋊C4—22no—
76C4⋊C4—3582no—
77C4⋊C4—3582no—
78C4⋊C4—3582no—
79C4⋊C4—3582no—
80C4⋊C4—3582no—
81C4⋊C4—1792no—
82C4⋊C4—1792no—
83C4⋊C4C22⋊D17912yes—
84C42—3582no—
85C42C22×D17911yescharacteristic
86C23—41no—
87D4—44no—
88D4—42no—
89C2×C4—22no—
90C2×C4—3582no—
91C2×C4—3582no—
92C2×C4D4×D17912yes—
93C2×C4C2×C22⋊D17911yescharacteristic
94C8—41no—
95C8—7162no—
96C22—82no—
97C22—81no—
98C22#1915308111yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—7162no—
103C4—7162no—
104C2—161no—
105C2#2603861012yes—
106C2#2603861111yescharacteristic
subgroupG/H
centerC22#19153081
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#490×C179C2
socleC22×C179#120
prime radical#127×C179C22
hypercenter#490D179
hypocenterC179#1658
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. C179⋊#564C2semidirect
3. #26038181C2semidirect
4. #26038180C2semidirect
53. C179#1658semidirect

Maximal subgroups

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

subgroupindex
C179⋊#5642
#260388032
#260381812
#260381802
#490×C1792
#1658179