Finite Group Databasebeta

← #37508295

Subgroups — #37508295

Order 22912.

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

normal subgroups only

This group has 230 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
1#26039187C211yesmaximal, characteristic, complemented
2#26038828C212yesmaximal, complemented
3#26038805C211yesmaximal, characteristic, complemented
4#26038178C212yesmaximal, complemented
5#330×C179C211yesmaximal, characteristic, complemented
6C2×#15668248—22no—
7C2×D1432—22no—
8#19153110C2211yescharacteristic
9#19153101C2212yes—
10#19153098—22no—
11#19153091—22no—
12#19153088—22no—
13#19153033—22no—
14#19153024C2211yescharacteristic
15#125×C179C2211yescharacteristic
16#97×C179C2212yes—
17C2×Dic358D412yes—
18C2×D716—22no—
19C2×D716—21no—
20C2×D716—22no—
21C2×D716D412yes—
22C2×C4×D179—22no—
23#15668248—44no—
24D1432—44no—
25C2×C179⋊C8—21no—
26Dic179⋊C4—22no—
27(C2×D179)⋊C4—22no—
28(C2×D179)⋊C4—22no—
29(C2×D179)⋊C4—22no—
30C2×C8×C179—22no—
31C4⋊C4×C179—22no—
32C4⋊C4×C179D412yes—
33C42×C179C2311yescharacteristic
34C22×D179—22no—
35C22×D179—41no—
36Dic358—42no—
37D716—42no—
38D716—42no—
39D716—42no—
40D716—42no—
41D716—82no—
42C2×Dic179—22no—
43C4×D179—82no—
44C179⋊C8—41no—
45C2×C4×C179—22no—
46C2×C4×C179C2×D412yes—
47C2×C4×C179C2×D411yescharacteristic
48C8×C179—24no—
49C22×C179#12011yescharacteristic
50C2×D179—42no—
51C2×D179—42no—
52C2×D179—42no—
53C2×D179—82no—
54C2×D179—81no—
55C4×C179—22no—
56C4×C179—21no—
57C4×C179—42no—
58Dic179—42no—
59C2×C179#45312yes—
60C2×C179#45411yescharacteristic
61D179—82no—
62D179—161no—
63C179#165611yescharacteristic, complemented, Sylow
64#1656—1791nomaximal, Sylow
65#562—1791no—
66#496—1792no—
67#490—1791no—
68#330D17911yescharacteristic, complemented
69#329—1792no—
70C2×SD16—3582no—
71C2×D8—3582no—
72#127—1791no—
73#125C2×D17911yescharacteristic
74#124—1792no—
75#123—3582no—
76C22⋊Q8—3582no—
77#121—3582no—
78#102—3582no—
79#97—1791no—
80#97C2×D17912yes—
81C2×Q8—1792no—
82C2×D4—3582no—
83C2×D4—3582no—
84C2×D4—3581no—
85C2×D4—1792no—
86C22×C4—3582no—
87SD16—7164no—
88D8—7164no—
89C2×C8—22no—
90C2×C8—3581no—
91C4⋊C4—22no—
92C4⋊C4—3582no—
93C4⋊C4D71612yes—
94C22⋊C4—3582no—
95C22⋊C4—3582no—
96C22⋊C4—3582no—
97C42C22×D17911yescharacteristic
98C23—3582no—
99C23—7161no—
100Q8—7162no—
101D4—14322no—
102D4—7162no—
103D4—7162no—
104D4—7162no—
105D4—7162no—
106C2×C4—22no—
107C2×C4—3582no—
108C2×C4—14322no—
109C2×C4D4×D17912yes—
110C2×C4C2×D71611yescharacteristic
111C8—24no—
112C8—7161no—
113C22—14322no—
114C22—14321no—
115C22—7162no—
116C22—7162no—
117C22—7162no—
118C22#1915308311yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—7162no—
123C2—28641no—
124C2—14322no—
125C2#2603860812yes—
126C2#2603861411yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#330×C179C2
socleC22×C179#120
hypercenter#330D179
hypocenterC179#1656
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #26039187C2semidirect
2. #26038828C2semidirect
3. #26038805C2semidirect
4. #26038178C2semidirect
5. #330×C179C2semidirect
63. C179#1656semidirect
68. #330D179semidirect

Maximal subgroups

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

subgroupindex
#260391872
#260388282
#260388052
#260381782
#330×C1792
#1656179