Finite Group Databasebeta

← #46782046

Subgroups — #46782046

Order 33664.

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

normal subgroups only

This group has 206 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#30682688C211yesmaximal, characteristic, complemented
2#30682328C211yesmaximal, characteristic
3#30682303C212yesmaximal, complemented
4#30681679C212yesmaximal, complemented
5#329×C263C211yesmaximal, characteristic, complemented
6C2×#16862363—21no—
7C2×#16862361—21no—
8#22554468—21no—
9#22554467C2211yescharacteristic
10#22554463—22no—
11#22554462C2212yes—
12#22554451—21no—
13#22554447—22no—
14#22554392—22no—
15#22554392—22no—
16#22554381C2211yescharacteristic
17#124×C263C2211yescharacteristic
18#97×C263C2212yes—
19C2×Dic526—21no—
20C2×D1052—22no—
21C2×D1052—21no—
22C22×Dic263—21no—
23#16862363—42no—
24#16862361—42no—
25C2×C263⋊C8—21no—
26C4⋊Dic263D412yes—
27C4⋊Dic263D412yes—
28Dic263⋊C4—22no—
29Dic263⋊C4—22no—
30Dic263⋊C4—22no—
31C22⋊Dic263—22no—
32C22⋊Dic263—21no—
33C4×Dic263—21no—
34C2×Q8×C263D411yescharacteristic
35C2×D4×C263D411yescharacteristic
36C2×C8×C263—22no—
37C22⋊C4×C263—22no—
38C42×C263C2311yescharacteristic
39C22×D263—41no—
40Dic526—81no—
41D1052—41no—
42D1052—41no—
43D1052—44no—
44C2×Dic263—22no—
45C2×Dic263—22no—
46C2×Dic263—81no—
47C263⋊C8—22no—
48C23×C263—21no—
49Q8×C263—41no—
50D4×C263—41no—
51C2×C4×C263—21no—
52C2×C4×C263C2×D412yes—
53C2×C4×C263C2×D411yescharacteristic
54C8×C263—42no—
55C22×C263—41no—
56C22×C263—42no—
57C22×C263#12011yescharacteristic
58C2×D263—81no—
59C2×D263—82no—
60C4×C263—21no—
61C4×C263—22no—
62C4×C263—41no—
63Dic263—42no—
64Dic263—42no—
65C2×C263—81no—
66C2×C263#45311yescharacteristic
67C2×C263#45412yes—
68D263—161no—
69C263#165711yescharacteristic, complemented, Sylow
70#1657—2631nomaximal, Sylow
71#563—2631no—
72#496—2631no—
73#490—2632no—
74#330—2632no—
75#329D26311yescharacteristic, complemented
76C2×SD16—5261no—
77C2×D8—5261no—
78C4⋊Q8—5261no—
79#127—2631no—
80#126—5262no—
81#125—2632no—
82#124C2×D26311yescharacteristic
83#123—5261no—
84C22⋊Q8—5262no—
85#102—5262no—
86#102—5262no—
87#97—2631no—
88#97C2×D26312yes—
89C2×Q8—5261no—
90C2×Q8D105211yescharacteristic
91C2×D4—5262no—
92C2×D4—5261no—
93C2×D4D105211yescharacteristic
94C22×C4—5261no—
95SD16—10522no—
96D8—10522no—
97C2×C8—22no—
98C2×C8—5261no—
99C4⋊C4—2632no—
100C4⋊C4—2632no—
101C4⋊C4—5262no—
102C4⋊C4—5262no—
103C4⋊C4—5262no—
104C22⋊C4—22no—
105C22⋊C4—5262no—
106C22⋊C4—5261no—
107C42—5261no—
108C42C22×D26311yescharacteristic
109C23—21no—
110C23—10521no—
111Q8—41no—
112Q8—21041no—
113D4—41no—
114D4—10521no—
115D4—10521no—
116D4—10524no—
117C2×C4—21no—
118C2×C4—5262no—
119C2×C4—5262no—
120C2×C4—21041no—
121C2×C4D4×D26312yes—
122C2×C4C2×D105211yescharacteristic
123C8—42no—
124C8—5262no—
125C22—42no—
126C22—41no—
127C22—21042no—
128C22—21041no—
129C22#2255444011yescharacteristic
130C4—22no—
131C4—21no—
132C4—41no—
133C4—10522no—
134C4—10522no—
135C2—81no—
136C2—42081no—
137C2#3068210811yescharacteristic
138C2#3068211212yes—
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#329×C263C2
socleC22×C263#120
prime radical#30682328C2
hypercenter#329D263
hypocenterC263#1657
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #30682688C2semidirect
3. #30682303C2semidirect
4. #30681679C2semidirect
5. #329×C263C2semidirect
69. C263#1657semidirect
75. #329D263semidirect

Maximal subgroups

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

subgroupindex
#306826882
#306823282
#306823032
#306816792
#329×C2632
#1657263