Finite Group Databasebeta

← #46782823

Subgroups — #46782823

Order 33664.

300 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C2×#22554426C211yesmaximal, characteristic
2#30681799C212yesmaximal
3#30681705C211yesmaximal, characteristic
4#30681704C212yesmaximal
5#342×C263C211yesmaximal, characteristic
6C23×Dic263C2211yescharacteristic
7#22554426—24no—
8C2×Dic263⋊C4C412yescomplemented
9C2×C22⋊Dic263C2212yes—
10C2×C22⋊Dic263C2211yescharacteristic
11C2×C4×Dic263C412yescomplemented
12C263⋊#95—24no—
13C2×C22⋊C4×C263C2212yes—
14C2×C22⋊C4×C263C2211yescharacteristic
15C22×Dic263—22no—
16C22×Dic263—21no—
17C22×Dic263—22no—
18C22×Dic263—21no—
19C22×Dic263C2×C411yescharacteristic
20C22×Dic263C2×C411yescharacteristic
21C22×Dic263C2×C412yes—
22C22×Dic263D414yes—
23Dic263⋊C4—24no—
24C22⋊Dic263—22no—
25C22⋊Dic263—22no—
26C22⋊Dic263—22no—
27C4×Dic263—24no—
28C24×C263C2311yescharacteristic
29C22×C4×C263—22no—
30C22×C4×C263C2×C412yes—
31C22⋊C4×C263—22no—
32C22⋊C4×C263—22no—
33C22⋊C4×C263—22no—
34C2×Dic263—21no—
35C2×Dic263—21no—
36C2×Dic263—21no—
37C2×Dic263—21no—
38C2×Dic263—24no—
39C2×Dic263—24no—
40C2×Dic263—22no—
41C2×Dic263—42no—
42C2×Dic263—44no—
43C2×Dic263—42no—
44C2×Dic263C22⋊C412yes—
45C2×Dic263C22⋊C412yes—
46C23×C263—42no—
47C23×C263C22×C411yescharacteristic
48C23×C263C2×D412yes—
49C23×C263#4111yescharacteristic
50C23×C263#4112yes—
51C23×C263#4111yescharacteristic
52C2×C4×C263—22no—
53C2×C4×C263—42no—
54C2×C4×C263—44no—
55C2×C4×C263—42no—
56C22×C263—22no—
57C22×C263—24no—
58C22×C263—41no—
59C22×C263—42no—
60C22×C263—41no—
61C22×C263C2×C22⋊C411yescharacteristic
62C22×C263#11711yescharacteristic
63C22×C263#11711yescharacteristic
64C22×C263#12312yes—
65C22×C263#12312yes—
66C4×C263—42no—
67C4×C263—82no—
68Dic263—22no—
69Dic263—22no—
70Dic263—42no—
71Dic263—82no—
72C2×C263—22no—
73C2×C263—22no—
74C2×C263—21no—
75C2×C263—21no—
76C2×C263#38111yescharacteristic
77C2×C263#41012yes—
78C263#182011yescharacteristic, complemented, Sylow
79#1820—2631nomaximal, Sylow
80C2×#117—2631no—
81#381—2632no—
82#342—2632no—
83#342—2631no—
84#342D26311yescharacteristic
85C23×C4—2631no—
86#117—5264no—
87C2×C4⋊C4—2632no—
88C2×C22⋊C4—2631no—
89C2×C22⋊C4—2632no—
90C2×C22⋊C4C2×D26312yes—
91C2×C22⋊C4C2×D26311yescharacteristic
92C2×C42—2632no—
93#95—5264no—
94C24C22×D26311yescharacteristic
95C22×C4—22no—
96C22×C4—2631no—
97C22×C4—2631no—
98C22×C4—2634no—
99C22×C4—2632no—
100C22×C4—5261no—
101C22×C4—5262no—
102C22×C4—5261no—
103C22×C4—5262no—
104C22×C4C4×D26312yes—
105C4⋊C4—5264no—
106C22⋊C4—22no—
107C22⋊C4—22no—
108C22⋊C4—22no—
109C22⋊C4—5262no—
110C22⋊C4—5262no—
111C22⋊C4—5262no—
112C42—5264no—
113C23—42no—
114C23C2×C4×D26311yescharacteristic
115C23D4×D26312yes—
116C23#1686237511yescharacteristic
117C23#1686237612yes—
118C23#1686237711yescharacteristic
119C2×C4—22no—
120C2×C4—42no—
121C2×C4—44no—
122C2×C4—42no—
123C2×C4—2632no—
124C2×C4—2632no—
125C2×C4—5261no—
126C2×C4—5261no—
127C2×C4—5261no—
128C2×C4—5261no—
129C2×C4—5264no—
130C2×C4—5264no—
131C2×C4—5262no—
132C2×C4—10522no—
133C2×C4—10524no—
134C2×C4—10522no—
135C22—22no—
136C22—24no—
137C22—41no—
138C22—42no—
139C22—41no—
140C22C22⋊C4×D26311yescharacteristic
141C22#2255442711yescharacteristic
142C22#2255442811yescharacteristic
143C22#2255445212yes—
144C22#2255445512yes—
145C4—42no—
146C4—82no—
147C4—5262no—
148C4—5262no—
149C4—10522no—
150C4—21042no—
151C2—22no—
152C2—22no—
153C2—21no—
154C2—21no—
155C2#3068180011yescharacteristic
156C2#3068191012yes—
subgroupG/H
centerC22C22⋊C4×D263
commutatorC23×C263C22×C4
FrattiniC24C22×D263
Fitting#342×C263C2
socleC22×C263C2×C22⋊C4
prime radical, cosocleC24×C263C23
hypercenter#342D263
hypocenterC263#1820
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
8. C2×Dic263⋊C4C4semidirect
11. C2×C4×Dic263C4semidirect
78. C263#1820semidirect

Maximal subgroups

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

subgroupindex
C2×#225544262
#306817992
#306817052
#306817042
#342×C2632
#1820263