Finite Group Databasebeta

← #46782037

Subgroups — #46782037

Order 33664.

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

normal subgroups only

This group has 262 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#30682680C211yesmaximal, characteristic, complemented
2#30682328C211yesmaximal, characteristic, complemented
3#30682327C212yesmaximal, complemented
4#30681677C212yesmaximal, complemented
5#329×C263C211yesmaximal, characteristic, complemented
6C2×#16862365—22no—
7C2×#16862363—21no—
8C2×D2104—22no—
9C2×#16862361—21no—
10#22554467C2211yescharacteristic, complemented
11#22554459—21no—
12#22554458C2212yes—
13#22554456—22no—
14#22554440—22no—
15#22554438—21no—
16#22554381C2211yescharacteristic, complemented
17#124×C263C2211yescharacteristic
18#97×C263C2212yescomplemented
19C23×D263—21no—
20C2×Dic526D412yes—
21C2×D1052—21no—
22C2×D1052—21no—
23C2×D1052—22no—
24C2×D1052D412yes—
25C2×C22⋊D263—22no—
26#16862365—44no—
27#16862363—42no—
28D2104—44no—
29#16862361—42no—
30C2×C263⋊C8—21no—
31C22⋊Dic263—21no—
32(C2×D263)⋊C4—22no—
33(C2×D263)⋊C4—22no—
34(C2×D263)⋊C4—22no—
35C4×Dic263—21no—
36C2×Q8×C263D411yescharacteristic
37C2×D4×C263D411yescharacteristic
38C2×C8×C263—22no—
39C22⋊C4×C263—22no—
40C42×C263C2311yescharacteristic
41C22×D263—22no—
42C22×D263—41no—
43C22×D263—82no—
44C22×D263—81no—
45Dic526—42no—
46D1052—42no—
47D1052—41no—
48D1052—42no—
49D1052—41no—
50D1052—42no—
51D1052—81no—
52C22⋊D263—82no—
53C2×Dic263—22no—
54C263⋊C8—22no—
55C23×C263—21no—
56Q8×C263—41no—
57D4×C263—41no—
58C2×C4×C263—21no—
59C2×C4×C263C2×D412yes—
60C2×C4×C263C2×D411yescharacteristic
61C8×C263—24no—
62C22×C263—41no—
63C22×C263—42no—
64C22×C263#12011yescharacteristic
65C2×D263—42no—
66C2×D263—42no—
67C2×D263—42no—
68C2×D263—84no—
69C2×D263—82no—
70C2×D263—81no—
71C4×C263—22no—
72C4×C263—21no—
73C4×C263—41no—
74Dic263—42no—
75C2×C263—81no—
76C2×C263#45312yes—
77C2×C263#45311yescharacteristic
78D263—82no—
79D263—161no—
80C263#165511yescharacteristic, complemented, Sylow
81#1655—2631nomaximal, Sylow
82H(3,𝔽4)—2631no—
83#496—2631no—
84#496—2632no—
85#329—2632no—
86#329D26311yescharacteristic, complemented
87C2×SD16—5262no—
88C2×SD16—5261no—
89C2×D8—5262no—
90C2×D8—5261no—
91#127—2631no—
92#124—2632no—
93#124—5262no—
94#124—5261no—
95#124C2×D26311yescharacteristic
96#120—5262no—
97#120—5261no—
98#97—2631no—
99#97C2×D26312yescomplemented
100C24—5261no—
101C2×Q8—2632no—
102C2×Q8D105211yescharacteristic
103C2×D4—2632no—
104C2×D4—5261no—
105C2×D4—5262no—
106C2×D4—5262no—
107C2×D4—5261no—
108C2×D4D105211yescharacteristic
109SD16—10524no—
110SD16—10522no—
111D8—10524no—
112D8—10522no—
113C2×C8—22no—
114C2×C8—5261no—
115C22⋊C4—22no—
116C22⋊C4—5262no—
117C22⋊C4—5261no—
118C22⋊C4—5262no—
119C22⋊C4—5262no—
120C42—5261no—
121C42C22×D26311yescharacteristic
122C23—21no—
123C23—5262no—
124C23—10521no—
125C23—21042no—
126C23—21041no—
127Q8—41no—
128Q8—10522no—
129D4—41no—
130D4—10522no—
131D4—10522no—
132D4—10521no—
133D4—10522no—
134D4—10521no—
135D4—21041no—
136D4—21042no—
137C2×C4—21no—
138C2×C4—5262no—
139C2×C4D4×D26312yes—
140C2×C4C2×D105211yescharacteristic
141C8—24no—
142C8—5262no—
143C22—42no—
144C22—41no—
145C22—10522no—
146C22—10522no—
147C22—10522no—
148C22—21044no—
149C22—21042no—
150C22—21041no—
151C22#2255444011yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—10522no—
156C2—81no—
157C2—21042no—
158C2—42081no—
159C2#3068210712yes—
160C2#3068210811yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#329×C263C2
socleC22×C263#120
hypercenter#329D263
hypocenterC263#1655
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. #30682680C2semidirect
2. #30682328C2semidirect
3. #30682327C2semidirect
4. #30681677C2semidirect
5. #329×C263C2semidirect
10. #22554467C22semidirect
16. #22554381C22semidirect
18. #97×C263C22semidirect
80. C263#1655semidirect
86. #329D263semidirect
99. #97C2×D263semidirect

Maximal subgroups

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

subgroupindex
#306826802
#306823282
#306823272
#306816772
#329×C2632
#1655263