Finite Group Databasebeta

← #46782057

Subgroups — #46782057

Order 33664.

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

normal subgroups only

This group has 196 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#30682344C211yesmaximal, characteristic, complemented
3#30682330C211yesmaximal, characteristic
4#30681680C211yesmaximal, characteristic, complemented
5#30681679C211yesmaximal, characteristic, complemented
6#30681677C211yesmaximal, characteristic
7#501×C263C211yesmaximal, characteristic, complemented
8C2×#16862366—21no—
9C2×#16862363—21no—
10#22554469—21no—
11#22554465—21no—
12#22554465—21no—
13#22554462C2211yescharacteristic
14#22554458C2211yescharacteristic
15#22554455—21no—
16#22554450—21no—
17#22554448—21no—
18#22554403—21no—
19#22554401—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—
31#16862366—42no—
32#16862363—42no—
33C2×C263⋊C8—21no—
34C2×C263⋊C8—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263D411yescharacteristic
37C4⋊Dic263D411yescharacteristic
38Dic263⋊C4—21no—
39Dic263⋊C4—21no—
40Dic263⋊C4—21no—
41(C2×D263)⋊C4—21no—
42(C2×D263)⋊C4—21no—
43(C2×D263)⋊C4—21no—
44(C2×D263)⋊C4—21no—
45(C2×D263)⋊C4—21no—
46C4×Dic263—21no—
47C2×Q8×C263—21no—
48C2×C8×C263—21no—
49C4⋊C4×C263—21no—
50C4⋊C4×C263—21no—
51C4⋊C4×C263—21no—
52C4⋊C4×C263—21no—
53C4⋊C4×C263D411yescharacteristic
54C4⋊C4×C263D411yescharacteristic
55C42×C263C2311yescharacteristic
56C22×D263—21no—
57Dic526—41no—
58Dic526—81no—
59D1052—41no—
60C2×Dic263—21no—
61C2×Dic263—21no—
62C2×Dic263—21no—
63C4×D263—81no—
64C263⋊C8—22no—
65C263⋊C8—22no—
66Q8×C263—41no—
67Q8×C263—41no—
68C2×C4×C263—21no—
69C2×C4×C263—21no—
70C2×C4×C263—41no—
71C2×C4×C263C2×D411yescharacteristic
72C2×C4×C263C2×D411yescharacteristic
73C2×C4×C263C2×D411yescharacteristic
74C8×C263—22no—
75C22×C263#12011yescharacteristic
76C2×D263—41no—
77C2×D263—41no—
78C2×D263—41no—
79C4×C263—21no—
80C4×C263—21no—
81C4×C263—21no—
82C4×C263—41no—
83C4×C263—41no—
84C4×C263—81no—
85Dic263—41no—
86Dic263—41no—
87Dic263—41no—
88C2×C263#45311yescharacteristic
89C2×C263#45611yescharacteristic
90C2×C263#45611yescharacteristic
91D263—81no—
92C263#166011yescharacteristic, complemented, Sylow
93#1660—2631nomaximal, Sylow
94#563—2631no—
95#501—2631no—
96#501D26311yescharacteristic, complemented
97#497—2631no—
98#330—2631no—
99#330—2631no—
100#329—2631no—
101C2×Q16—5261no—
102C2×SD16—5261no—
103C4⋊Q8—5261no—
104C4⋊Q8C2×D26311yescharacteristic
105#126—5261no—
106#126—5261no—
107#125—2631no—
108#125C2×D26311yescharacteristic
109#124—2631no—
110#123—5261no—
111C22⋊Q8—5261no—
112C22⋊Q8—5261no—
113#107—21no—
114#107—5261no—
115#106—21no—
116#106—5261no—
117#97—2631no—
118#97—2631no—
119#97C2×D26311yescharacteristic
120C2×Q8—21no—
121C2×Q8—2631no—
122C2×Q8—5261no—
123C2×D4—2631no—
124C22×C4—5261no—
125Q16—10522no—
126SD16—10522no—
127C2×C8—21no—
128C2×C8—5261no—
129C2×C8—5261no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—2631no—
135C4⋊C4—2631no—
136C4⋊C4—5261no—
137C4⋊C4—5261no—
138C4⋊C4—5261no—
139C4⋊C4—5261no—
140C4⋊C4C22⋊D26311yescharacteristic
141C4⋊C4C22⋊D26311yescharacteristic
142C22⋊C4—5261no—
143C22⋊C4—5261no—
144C22⋊C4—5261no—
145C22⋊C4—5261no—
146C22⋊C4—5261no—
147C42—5261no—
148C42C22×D26311yescharacteristic
149C23—5261no—
150Q8—41no—
151Q8—41no—
152Q8—10521no—
153Q8—21041no—
154D4—10521no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—5261no—
159C2×C4—5261no—
160C2×C4—5261no—
161C2×C4—21041no—
162C2×C4D4×D26311yescharacteristic
163C2×C4D4×D26311yescharacteristic
164C2×C4C2×C22⋊D26311yescharacteristic
165C8—22no—
166C8—5262no—
167C8—5262no—
168C22—10521no—
169C22—10521no—
170C22—10521no—
171C22#2255443811yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—10521no—
179C4—10521no—
180C4—10521no—
181C2—21041no—
182C2#3068210411yescharacteristic
183C2#3068211911yescharacteristic
184C2#3068212011yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#501×C263C2
socleC22×C263#120
prime radicalC2×D1052D4
hypercenter#501D263
hypocenterC263#1660
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. #30682344C2semidirect
4. #30681680C2semidirect
5. #30681679C2semidirect
7. #501×C263C2semidirect
92. C263#1660semidirect
96. #501D263semidirect

Maximal subgroups

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

subgroupindex
#306826922
#306823442
#306823302
#306816802
#306816792
#306816772
#501×C2632
#1660263