Finite Group Databasebeta

← #46782081

Subgroups — #46782081

Order 33664.

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

normal subgroups only

This group has 184 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#30682348C211yesmaximal, characteristic, complemented
2#30682308C211yesmaximal, characteristic, complemented
3#30682297C211yesmaximal, characteristic
4#30681680C211yesmaximal, characteristic, complemented
5#30681680C211yesmaximal, characteristic, complemented
6#30681678C211yesmaximal, characteristic
7#563×C263C211yesmaximal, characteristic
8#22554470C2211yescharacteristic
9#22554403—21no—
10#22554401—21no—
11#22554394—21no—
12#22554393—21no—
13#22554393—21no—
14#22554391—21no—
15#22554381C2211yescharacteristic
16#22554381C2211yescharacteristic
17#22554381C2211yescharacteristic
18C4⋊Q8×C263—21no—
19#126×C263—21no—
20#126×C263—21no—
21#125×C263C2211yescharacteristic
22#125×C263C2211yescharacteristic
23#124×C263C2211yescharacteristic
24#123×C263—21no—
25C22⋊Q8×C263—21no—
26C22⋊Q8×C263—21no—
27C2×Dic526—21no—
28C2×C263⋊C8—21no—
29C2×C263⋊C8—21no—
30C2×C263⋊C8—21no—
31C4⋊Dic263—21no—
32C4⋊Dic263—21no—
33C2×Q8×C263—21no—
34C2×Q8×C263D411yescharacteristic
35C2×D4×C263D411yescharacteristic
36C22×C4×C263—21no—
37C4⋊C4×C263—21no—
38C4⋊C4×C263—21no—
39C4⋊C4×C263—21no—
40C4⋊C4×C263—21no—
41C4⋊C4×C263—21no—
42C4⋊C4×C263—21no—
43C4⋊C4×C263D411yescharacteristic
44C4⋊C4×C263D411yescharacteristic
45C4⋊C4×C263D411yescharacteristic
46C4⋊C4×C263D411yescharacteristic
47C22⋊C4×C263—21no—
48C22⋊C4×C263—21no—
49C22⋊C4×C263—21no—
50C22⋊C4×C263—21no—
51C22⋊C4×C263—21no—
52C42×C263—21no—
53C42×C263C2311yescharacteristic
54Dic526—42no—
55C2×Dic263—41no—
56C263⋊C8—22no—
57C263⋊C8—41no—
58C263⋊C8—41no—
59C23×C263—21no—
60Q8×C263—41no—
61Q8×C263—81no—
62D4×C263—41no—
63C2×C4×C263—21no—
64C2×C4×C263—21no—
65C2×C4×C263—21no—
66C2×C4×C263—21no—
67C2×C4×C263—21no—
68C2×C4×C263—81no—
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C2×C4×C263C2×D411yescharacteristic
72C22×C263—41no—
73C22×C263—41no—
74C22×C263—41no—
75C22×C263#12011yescharacteristic
76C4×C263—21no—
77C4×C263—21no—
78C4×C263—21no—
79C4×C263—41no—
80C4×C263—41no—
81C4×C263—41no—
82C4×C263—41no—
83C4×C263—41no—
84Dic263—81no—
85C2×C263—81no—
86C2×C263#45411yescharacteristic
87C2×C263#45511yescharacteristic
88C2×C263#45611yescharacteristic
89C263#166411yescharacteristic, complemented, Sylow
90#1664—2631nomaximal, Sylow
91#563D26311yescharacteristic
92#501—2631no—
93#491—2631no—
94#489—2631no—
95#330—2631no—
96#330—2631no—
97#329—2631no—
98C4⋊Q8—21no—
99C4⋊Q8—2631no—
100#126—21no—
101#126—21no—
102#125C2×D26311yescharacteristic
103#125C2×D26311yescharacteristic
104#124C2×D26311yescharacteristic
105#123—21no—
106C22⋊Q8—21no—
107C22⋊Q8—21no—
108#107—5261no—
109#106—5261no—
110#103—5261no—
111#103—5261no—
112#103—5261no—
113#102—5261no—
114#97—2631no—
115#97—2631no—
116#97—2631no—
117C2×Q8—21no—
118C2×Q8—5261no—
119C2×Q8C22⋊D26311yescharacteristic
120C2×D4C22⋊D26311yescharacteristic
121C22×C4—21no—
122C2×C8—5261no—
123C2×C8—5261no—
124C2×C8—5261no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—5261no—
132C4⋊C4—5261no—
133C4⋊C4C22⋊D26311yescharacteristic
134C4⋊C4C22⋊D26311yescharacteristic
135C4⋊C4C22⋊D26311yescharacteristic
136C4⋊C4C22⋊D26311yescharacteristic
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C22⋊C4—21no—
142C42—21no—
143C42C22×D26311yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—81no—
147Q8—10522no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—81no—
155C2×C4—10521no—
156C2×C4C2×C22⋊D26311yescharacteristic
157C2×C4C2×C22⋊D26311yescharacteristic
158C2×C4C2×C22⋊D26311yescharacteristic
159C8—5262no—
160C8—10521no—
161C8—10521no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#2255443911yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—41no—
172C4—41no—
173C4—41no—
174C4—21041no—
175C2—81no—
176C2#3068211111yescharacteristic
177C2#3068211611yescharacteristic
178C2#3068212111yescharacteristic
subgroupG/H
centerC22#22554439
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#563×C263C2
socleC22×C263#120
prime radicalC2×D4×C263D4
hypercenter#563D263
hypocenterC263#1664
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #30682348C2semidirect
2. #30682308C2semidirect
4. #30681680C2semidirect
5. #30681680C2semidirect
89. C263#1664semidirect

Maximal subgroups

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

subgroupindex
#306823482
#306823082
#306822972
#306816802
#306816782
#563×C2632
#1664263