Finite Group Databasebeta

← #46783904

Subgroups — #46783904

Order 33664.

282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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#30682569C211yesmaximal, characteristic, complemented
2#30681944C212yesmaximal
3#30681839C211yesmaximal, characteristic
4#30681699C212yesmaximal, complemented
5#343×C263C211yesmaximal, characteristic, complemented
6C22×D1052C2211yescharacteristic
7#22554469—22no—
8#22554461—22no—
9#22554449—22no—
10#22554429C2212yes—
11C2×(C2×D263)⋊C4—22no—
12C2×C4×Dic263C2211yescharacteristic
13#22554392—22no—
14#22554392—22no—
15C2×M16×C263C2212yes—
16C2×C4⋊C4×C263C2211yescharacteristic
17C23×D263—21no—
18C2×Dic526—22no—
19C2×D1052—22no—
20C2×D1052—22no—
21C2×D1052—21no—
22C2×D1052Q812yescomplemented
23C22×Dic263—21no—
24C4⋊Dic263—22no—
25C4⋊Dic263D412yes—
26C4⋊Dic263D412yes—
27Dic263⋊C4—24no—
28C22⋊Dic263—22no—
29(C2×D263)⋊C4—44no—
30C4×Dic263—22no—
31C4×Dic263—22no—
32C22×C4×C263D412yes—
33C22×C4×C263C2311yescharacteristic
34M16×C263—22no—
35M16×C263—22no—
36C2×C8×C263—22no—
37C4⋊C4×C263—22no—
38C22×D263—22no—
39C22×D263—42no—
40C22×D263—42no—
41C22×D263—41no—
42C22×D263—41no—
43Dic526—82no—
44D1052—24no—
45D1052—42no—
46C2×Dic263—22no—
47C2×Dic263—22no—
48C2×Dic263—22no—
49C2×Dic263—41no—
50C2×Dic263—41no—
51C23×C263C2×D411yescharacteristic
52C2×C4×C263—22no—
53C2×C4×C263—42no—
54C2×C4×C263C2×D412yes—
55C2×C4×C263C2×Q811yescharacteristic
56C2×C4×C263#4111yescharacteristic
57C2×C4×C263#4112yes—
58C8×C263—42no—
59C22×C263—21no—
60C22×C263—21no—
61C22×C263#12011yescharacteristic
62C22×C263C22⋊Q811yescharacteristic
63C22×C263#12411yescharacteristic
64C2×D263—44no—
65C2×D263—42no—
66C2×D263—82no—
67C2×D263—81no—
68C2×D263—81no—
69C4×C263—42no—
70C4×C263C22⋊Q812yes—
71C4×C263#12412yes—
72Dic263—42no—
73Dic263—42no—
74Dic263—42no—
75C2×C263—21no—
76C2×C263—21no—
77C2×C263#39311yescharacteristic
78C2×C263#45311yescharacteristic
79C2×C263#45411yescharacteristic
80D263—82no—
81C263#202711yescharacteristic, complemented, Sylow
82#2027—2631nomaximal, Sylow
83#544—2631no—
84#418—2632no—
85#390—2631no—
86#343D26311yescharacteristic, complemented
87#339—2632no—
88C22×D4—2631no—
89C2×M16C2×D26312yes—
90C4⋊Q8—5262no—
91#125—5262no—
92C22⋊Q8—5262no—
93#117—2632no—
94C2×C4⋊C4C2×D26311yescharacteristic
95C2×C22⋊C4—5262no—
96C2×C42—2631no—
97#102—5262no—
98#102—5262no—
99C24—5261no—
100C2×Q8—5262no—
101C2×D4—2632no—
102C2×D4—5262no—
103C2×D4—5261no—
104C2×D4—5262no—
105C22×C4—5261no—
106C22×C4D105212yes—
107C22×C4C22×D26311yescharacteristic
108M16—22no—
109M16—22no—
110C2×C8—22no—
111C4⋊C4—22no—
112C4⋊C4—2632no—
113C4⋊C4—2632no—
114C4⋊C4—5262no—
115C4⋊C4—5264no—
116C22⋊C4—5262no—
117C22⋊C4—10524no—
118C42—5262no—
119C42—5262no—
120C23—5262no—
121C23—10522no—
122C23—10522no—
123C23—10521no—
124C23—10521no—
125C23C2×D105211yescharacteristic
126Q8—21042no—
127D4—5264no—
128D4—10522no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—5262no—
132C2×C4—5262no—
133C2×C4—5262no—
134C2×C4—10521no—
135C2×C4—10521no—
136C2×C4D4×D26312yes—
137C2×C4Q8×D26311yescharacteristic
138C2×C4#1686237511yescharacteristic
139C2×C4#1686237612yes—
140C8—42no—
141C22—21no—
142C22—21no—
143C22—10524no—
144C22—10522no—
145C22—21042no—
146C22—21041no—
147C22—21041no—
148C22#2255444011yescharacteristic
149C22#2255445011yescharacteristic
150C22#2255445811yescharacteristic
151C4—42no—
152C4—10522no—
153C4—10522no—
154C4—10522no—
155C4#2255444812yes—
156C4#2255445612yes—
157C2—21no—
158C2—21no—
159C2—21042no—
160C2#3068185111yescharacteristic
161C2#3068210811yescharacteristic
162C2#3068211311yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#343×C263C2
socleC22×C263#120
prime radicalC22×D1052C22
hypercenter#343D263
hypocenterC263#2027
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. #30682569C2semidirect
4. #30681699C2semidirect
5. #343×C263C2semidirect
22. C2×D1052Q8semidirect
81. C263#2027semidirect
86. #343D263semidirect

Maximal subgroups

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

subgroupindex
#306825692
#306819442
#306818392
#306816992
#343×C2632
#2027263