Finite Group Databasebeta

← #46782040

Subgroups — #46782040

Order 33664.

230 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 49 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#30682328C212yesmaximal, complemented
2#30682304C211yesmaximal, characteristic, complemented
3#30681680C211yesmaximal, characteristic, complemented
4#30681678C212yesmaximal, complemented
5#562×C263C211yesmaximal, characteristic, complemented
6C2×#16862363—22no—
7C2×#16862361—22no—
8#22554467C2211yescharacteristic
9#22554390—22no—
10#22554381C2211yescharacteristic
11#22554381C2212yes—
12#125×C263C2211yescharacteristic
13#124×C263C2212yes—
14#123×C263—22no—
15C22⋊Q8×C263—22no—
16#121×C263—22no—
17C2×D1052—21no—
18C2×D1052—22no—
19#16862363—44no—
20#16862361—44no—
21C2×C263⋊C8—22no—
22C2×C263⋊C8—21no—
23C2×Q8×C263D412yes—
24C2×D4×C263—22no—
25C2×D4×C263D412yes—
26C22×C4×C263—22no—
27C4⋊C4×C263—22no—
28C4⋊C4×C263—22no—
29C4⋊C4×C263D412yes—
30C22⋊C4×C263—22no—
31C22⋊C4×C263—22no—
32C22⋊C4×C263—22no—
33C42×C263C2311yescharacteristic
34C22×D263—41no—
35D1052—42no—
36D1052—42no—
37D1052—42no—
38C263⋊C8—24no—
39C263⋊C8—41no—
40C23×C263—22no—
41Q8×C263—42no—
42D4×C263—42no—
43D4×C263—82no—
44C2×C4×C263—22no—
45C2×C4×C263—22no—
46C2×C4×C263—82no—
47C2×C4×C263C2×D411yescharacteristic
48C2×C4×C263C2×D412yes—
49C22×C263—42no—
50C22×C263—42no—
51C22×C263—42no—
52C22×C263#12011yescharacteristic
53C2×D263—82no—
54C2×D263—81no—
55C4×C263—22no—
56C4×C263—21no—
57C4×C263—42no—
58C4×C263—42no—
59C2×C263—82no—
60C2×C263#45312yes—
61C2×C263#45411yescharacteristic
62D263—161no—
63C263#165611yescharacteristic, complemented, Sylow
64#1656—2631nomaximal, Sylow
65#562D26311yescharacteristic, complemented
66#496—2632no—
67#490—2631no—
68#330—2631no—
69#329—2632no—
70C2×SD16—5262no—
71C2×D8—5262no—
72#127—2631no—
73#125C2×D26311yescharacteristic
74#124C2×D26312yes—
75#123—22no—
76C22⋊Q8—22no—
77#121—22no—
78#102—5262no—
79#97—2631no—
80#97—2632no—
81C2×Q8C22⋊D26312yes—
82C2×D4—22no—
83C2×D4—5261no—
84C2×D4—5262no—
85C2×D4C22⋊D26312yes—
86C22×C4—22no—
87SD16—10524no—
88D8—10524no—
89C2×C8—5262no—
90C2×C8—5261no—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4C22⋊D26312yes—
94C22⋊C4—22no—
95C22⋊C4—22no—
96C22⋊C4—22no—
97C42C22×D26311yescharacteristic
98C23—22no—
99C23—10521no—
100Q8—42no—
101D4—42no—
102D4—82no—
103D4—10522no—
104D4—10522no—
105D4—10522no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—82no—
109C2×C4C2×C22⋊D26311yescharacteristic
110C2×C4C2×C22⋊D26312yes—
111C8—5264no—
112C8—10521no—
113C22—42no—
114C22—42no—
115C22—42no—
116C22—21042no—
117C22—21041no—
118C22#2255443911yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C2—82no—
124C2—42081no—
125C2#3068210612yes—
126C2#3068211111yescharacteristic
subgroupG/H
centerC22#22554439
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#562×C263C2
socleC22×C263#120
hypercenter#562D263
hypocenterC263#1656
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #30682328C2semidirect
2. #30682304C2semidirect
3. #30681680C2semidirect
4. #30681678C2semidirect
5. #562×C263C2semidirect
63. C263#1656semidirect
65. #562D263semidirect

Maximal subgroups

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

subgroupindex
#306823282
#306823042
#306816802
#306816782
#562×C2632
#1656263