Finite Group Databasebeta

← #46782079

Subgroups — #46782079

Order 33664.

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

normal subgroups only

This group has 184 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#30682692C211yesmaximal, characteristic
2#30682306C211yesmaximal, characteristic, complemented
3#30682300C211yesmaximal, characteristic
4#30681680C211yesmaximal, characteristic, complemented
5#30681679C211yesmaximal, characteristic, complemented
6#30681677C211yesmaximal, characteristic
7#501×C263C211yesmaximal, characteristic, complemented
8#22554469—21no—
9#22554465—21no—
10#22554465—21no—
11#22554462C2211yescharacteristic
12#22554458C2211yescharacteristic
13#22554455—21no—
14#22554450—21no—
15#22554448—21no—
16#22554394—21no—
17#22554394—21no—
18#22554393—21no—
19#22554390—21no—
20#22554381C2211yescharacteristic
21#22554381C2211yescharacteristic
22C4⋊Q8×C263C2211yescharacteristic
23#125×C263C2211yescharacteristic
24#107×C263—21no—
25#106×C263—21no—
26#97×C263C2211yescharacteristic
27C2×Dic526—21no—
28C2×Dic526D411yescharacteristic
29C2×D1052D411yescharacteristic
30C2×C4×D263—21no—
31C2×C263⋊C8—21no—
32C2×C263⋊C8—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263D411yescharacteristic
35C4⋊Dic263D411yescharacteristic
36Dic263⋊C4—21no—
37Dic263⋊C4—21no—
38Dic263⋊C4—21no—
39(C2×D263)⋊C4—21no—
40(C2×D263)⋊C4—21no—
41(C2×D263)⋊C4—21no—
42(C2×D263)⋊C4—21no—
43(C2×D263)⋊C4—21no—
44C4×Dic263—21no—
45C2×Q8×C263—21no—
46C2×C8×C263—21no—
47C4⋊C4×C263—21no—
48C4⋊C4×C263—21no—
49C4⋊C4×C263—21no—
50C4⋊C4×C263—21no—
51C4⋊C4×C263D411yescharacteristic
52C4⋊C4×C263D411yescharacteristic
53C42×C263C2311yescharacteristic
54C22×D263—21no—
55Dic526—41no—
56Dic526—81no—
57D1052—41no—
58C2×Dic263—21no—
59C2×Dic263—21no—
60C2×Dic263—21no—
61C4×D263—81no—
62C263⋊C8—41no—
63C263⋊C8—41no—
64Q8×C263—42no—
65C2×C4×C263—21no—
66C2×C4×C263—21no—
67C2×C4×C263—41no—
68C2×C4×C263C2×D411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C8×C263—22no—
72C22×C263#12011yescharacteristic
73C2×D263—41no—
74C2×D263—41no—
75C2×D263—41no—
76C4×C263—21no—
77C4×C263—21no—
78C4×C263—21no—
79C4×C263—41no—
80C4×C263—41no—
81C4×C263—81no—
82Dic263—41no—
83Dic263—41no—
84Dic263—41no—
85C2×C263#45411yescharacteristic
86C2×C263#45511yescharacteristic
87C2×C263#45611yescharacteristic
88D263—81no—
89C263#166411yescharacteristic, complemented, Sylow
90#1664—2631nomaximal, Sylow
91#563—2631no—
92#501D26311yescharacteristic, complemented
93#491—2631no—
94#489—2631no—
95#330—2631no—
96#330—2631no—
97#329—2631no—
98C4⋊Q8—5261no—
99C4⋊Q8C2×D26311yescharacteristic
100#126—5261no—
101#126—5261no—
102#125—2631no—
103#125C2×D26311yescharacteristic
104#124—2631no—
105#123—5261no—
106C22⋊Q8—5261no—
107C22⋊Q8—5261no—
108#107—21no—
109#106—21no—
110#103—5261no—
111#103—5261no—
112#103—5261no—
113#102—5261no—
114#97—2631no—
115#97—2631no—
116#97C2×D26311yescharacteristic
117C2×Q8—21no—
118C2×Q8—2631no—
119C2×Q8—5261no—
120C2×D4—2631no—
121C22×C4—5261no—
122C2×C8—21no—
123C2×C8—5261no—
124C2×C8—5261no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—2631no—
130C4⋊C4—2631no—
131C4⋊C4—5261no—
132C4⋊C4—5261no—
133C4⋊C4—5261no—
134C4⋊C4—5261no—
135C4⋊C4C22⋊D26311yescharacteristic
136C4⋊C4C22⋊D26311yescharacteristic
137C22⋊C4—5261no—
138C22⋊C4—5261no—
139C22⋊C4—5261no—
140C22⋊C4—5261no—
141C22⋊C4—5261no—
142C42—5261no—
143C42C22×D26311yescharacteristic
144C23—5261no—
145Q8—42no—
146Q8—10521no—
147Q8—21041no—
148D4—10521no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—5261no—
153C2×C4—5261no—
154C2×C4—5261no—
155C2×C4—21041no—
156C2×C4D4×D26311yescharacteristic
157C2×C4D4×D26311yescharacteristic
158C2×C4C2×C22⋊D26311yescharacteristic
159C8—22no—
160C8—10521no—
161C8—10521no—
162C22—10521no—
163C22—10521no—
164C22—10521no—
165C22#2255443811yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—10521no—
173C4—10521no—
174C4—10521no—
175C2—21041no—
176C2#3068210911yescharacteristic
177C2#3068211411yescharacteristic
178C2#3068212011yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#501×C263C2
socleC22×C263#120
prime radicalC2×D1052D4
hypercenter#501D263
hypocenterC263#1664
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #30682306C2semidirect
4. #30681680C2semidirect
5. #30681679C2semidirect
7. #501×C263C2semidirect
89. C263#1664semidirect
92. #501D263semidirect

Maximal subgroups

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

subgroupindex
#306826922
#306823062
#306823002
#306816802
#306816792
#306816772
#501×C2632
#1664263