Finite Group Databasebeta

← #37508141

Subgroups — #37508141

Order 22912.

206 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 57 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#26039169C211yesmaximal, characteristic
2#26038818C211yesmaximal, characteristic
3#26038735C212yesmaximal
4#26038169C212yesmaximal
5#333×C179C211yesmaximal, characteristic
6C2×#15668249—22no—
7#19153113C2211yescharacteristic
8#19153112—22no—
9#19153111—22no—
10C4×Dic358C2212yes—
11#19153078—22no—
12#19153047—22no—
13#19153038—22no—
14C4×C179⋊C8C2211yescharacteristic
15C4⋊Q8×C179C2211yescharacteristic
16C4⋊C8×C179C2212yes—
17C2×Dic358—22no—
18C2×Dic358—21no—
19C2×Dic358D412yes—
20#15668249—44no—
21C2×C179⋊C8—21no—
22C4⋊Dic179—22no—
23C4⋊Dic179D412yes—
24Dic179⋊C4—24no—
25Dic179⋊C4—22no—
26C4×Dic179—22no—
27C4×Dic179—22no—
28C2×Q8×C179D412yes—
29C2×C8×C179—22no—
30C4⋊C4×C179—22no—
31C42×C179C2311yescharacteristic
32Dic358—22no—
33Dic358—42no—
34Dic358—82no—
35Dic358Q1614yescomplemented
36C2×Dic179—22no—
37C2×Dic179—22no—
38C2×Dic179—41no—
39C179⋊C8—22no—
40Q8×C179—42no—
41C2×C4×C179—22no—
42C2×C4×C179C2×D412yes—
43C2×C4×C179C2×D411yescharacteristic
44C8×C179—42no—
45C22×C179#12011yescharacteristic
46C4×C179—21no—
47C4×C179—42no—
48C4×C179C2×Q1612yes—
49C4×C179#13712yes—
50Dic179—24no—
51Dic179—42no—
52Dic179—81no—
53C2×C179#45112yes—
54C2×C179#45311yescharacteristic
55C179#163311yescharacteristic, complemented, Sylow
56#1633—1791nomaximal, Sylow
57Q82—1791no—
58#494—1791no—
59#477—1792no—
60#333D17911yescharacteristic
61Q8⋊C8—1792no—
62C2×Q16—3582no—
63C4⋊Q8—3582no—
64C4⋊Q8—3582no—
65C4⋊Q8—1791no—
66C4⋊Q8C2×D17911yescharacteristic
67C4×Q8—3582no—
68C4×Q8—1792no—
69#107—3582no—
70C4⋊C8C2×D17912yes—
71#103—3582no—
72C4×C8—1791no—
73C2×Q8—3582no—
74C2×Q8—3581no—
75C2×Q8—1792no—
76C2×Q8D71612yes—
77Q16—7164no—
78C2×C8—22no—
79C2×C8—3581no—
80C4⋊C4—22no—
81C4⋊C4—3584no—
82C4⋊C4—3582no—
83C4⋊C4—3582no—
84C4⋊C4—1792no—
85C42—3582no—
86C42—3582no—
87C42C22×D17911yescharacteristic
88Q8—42no—
89Q8—3582no—
90Q8—14322no—
91Q8—1794no—
92Q8—7162no—
93C2×C4—22no—
94C2×C4—3582no—
95C2×C4—3582no—
96C2×C4—7161no—
97C2×C4D4×D17912yes—
98C2×C4C2×D71611yescharacteristic
99C8—42no—
100C8—3582no—
101C22#1915308311yescharacteristic
102C4—21no—
103C4—42no—
104C4—3584no—
105C4—14321no—
106C4—7162no—
107C4Q16×D17912yes—
108C4#1915314212yes—
109C2#2603859612yes—
110C2#2603860911yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#333×C179C2
socle, prime radicalC22×C179#120
hypercenter#333D179
hypocenterC179#1633
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
35. Dic358Q16semidirect
55. C179#1633semidirect

Maximal subgroups

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

subgroupindex
#260391692
#260388182
#260387352
#260381692
#333×C1792
#1633179