Finite Group Databasebeta

← #46782047

Subgroups — #46782047

Order 33664.

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

normal subgroups only

This group has 206 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, complemented
2#30682327C211yesmaximal, characteristic
3#30682304C211yesmaximal, characteristic, complemented
4#30682303C211yesmaximal, characteristic, complemented
5#30681679C211yesmaximal, characteristic, complemented
6#30681677C211yesmaximal, characteristic, complemented
7#330×C263C211yesmaximal, characteristic, complemented
8C2×#16862365—21no—
9C2×D2104—21no—
10#22554469—21no—
11#22554467C2211yescharacteristic
12#22554465—21no—
13#22554465—21no—
14#22554462C2211yescharacteristic
15#22554458C2211yescharacteristic
16#22554455—21no—
17#22554450—21no—
18#22554448—21no—
19#22554392—21no—
20#22554392—21no—
21#22554390—21no—
22#22554390—21no—
23#22554381C2211yescharacteristic
24#125×C263C2211yescharacteristic
25#97×C263C2211yescharacteristic
26#97×C263C2211yescharacteristic
27C2×Dic526—21no—
28C2×Dic526D411yescharacteristic
29C2×D1052—21no—
30C2×D1052—21no—
31C2×D1052—21no—
32C2×D1052D411yescharacteristic
33C2×C4×D263—21no—
34#16862365—42no—
35D2104—42no—
36C2×C263⋊C8—21no—
37C4⋊Dic263—21no—
38C4⋊Dic263D411yescharacteristic
39C4⋊Dic263D411yescharacteristic
40Dic263⋊C4—21no—
41Dic263⋊C4—21no—
42Dic263⋊C4—21no—
43(C2×D263)⋊C4—21no—
44(C2×D263)⋊C4—21no—
45(C2×D263)⋊C4—21no—
46(C2×D263)⋊C4—21no—
47(C2×D263)⋊C4—21no—
48C4×Dic263—21no—
49C2×C8×C263—21no—
50C2×C8×C263—21no—
51C4⋊C4×C263—21no—
52C4⋊C4×C263—21no—
53C4⋊C4×C263D411yescharacteristic
54C4⋊C4×C263D411yescharacteristic
55C42×C263C2311yescharacteristic
56C22×D263—21no—
57C22×D263—41no—
58Dic526—41no—
59Dic526—81no—
60D1052—41no—
61D1052—41no—
62D1052—41no—
63D1052—42no—
64D1052—42no—
65C2×Dic263—21no—
66C2×Dic263—21no—
67C2×Dic263—21no—
68C4×D263—81no—
69C263⋊C8—41no—
70C2×C4×C263—21no—
71C2×C4×C263—21no—
72C2×C4×C263C2×D411yescharacteristic
73C2×C4×C263C2×D411yescharacteristic
74C2×C4×C263C2×D411yescharacteristic
75C8×C263—22no—
76C8×C263—41no—
77C22×C263#12011yescharacteristic
78C2×D263—41no—
79C2×D263—41no—
80C2×D263—41no—
81C2×D263—81no—
82C2×D263—81no—
83C2×D263—81no—
84C4×C263—21no—
85C4×C263—21no—
86C4×C263—21no—
87C4×C263—41no—
88C4×C263—41no—
89Dic263—41no—
90Dic263—41no—
91Dic263—41no—
92C2×C263#45311yescharacteristic
93C2×C263#45411yescharacteristic
94C2×C263#45411yescharacteristic
95D263—81no—
96D263—161no—
97C263#165711yescharacteristic, complemented, Sylow
98#1657—2631nomaximal, Sylow
99#563—2631no—
100#496—2631no—
101#490—2631no—
102#490—2631no—
103#330—2631no—
104#330D26311yescharacteristic, complemented
105#329—2631no—
106C2×SD16—5261no—
107C2×D8—5261no—
108C4⋊Q8—5261no—
109#127—2631no—
110#126—5261no—
111#126—5261no—
112#125—2631no—
113#125C2×D26311yescharacteristic
114#124—2631no—
115#123—5261no—
116C22⋊Q8—5261no—
117C22⋊Q8—5261no—
118#102—5261no—
119#102—5261no—
120#102—5261no—
121#102—5261no—
122#97—2631no—
123#97C2×D26311yescharacteristic
124#97C2×D26311yescharacteristic
125C2×Q8—2631no—
126C2×Q8—5261no—
127C2×D4—2631no—
128C2×D4—5261no—
129C2×D4—5261no—
130C2×D4—5261no—
131C22×C4—5261no—
132SD16—10522no—
133D8—10522no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—5261no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—2631no—
140C4⋊C4—2631no—
141C4⋊C4—5261no—
142C4⋊C4—5261no—
143C4⋊C4—5261no—
144C4⋊C4—5261no—
145C4⋊C4D105211yescharacteristic
146C4⋊C4D105211yescharacteristic
147C22⋊C4—5261no—
148C22⋊C4—5261no—
149C22⋊C4—5261no—
150C22⋊C4—5261no—
151C22⋊C4—5261no—
152C42—5261no—
153C42C22×D26311yescharacteristic
154C23—5261no—
155C23—10521no—
156Q8—10521no—
157Q8—21041no—
158D4—10521no—
159D4—10521no—
160D4—10521no—
161D4—10522no—
162D4—10522no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—5261no—
166C2×C4—5261no—
167C2×C4—5261no—
168C2×C4—21041no—
169C2×C4D4×D26311yescharacteristic
170C2×C4D4×D26311yescharacteristic
171C2×C4C2×D105211yescharacteristic
172C8—22no—
173C8—41no—
174C8—10521no—
175C22—10521no—
176C22—10521no—
177C22—10521no—
178C22—21041no—
179C22—21041no—
180C22—21041no—
181C22#2255444011yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—10521no—
188C4—10521no—
189C4—10521no—
190C2—21041no—
191C2—42081no—
192C2#3068210711yescharacteristic
193C2#3068211211yescharacteristic
194C2#3068211311yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#330×C263C2
socleC22×C263#120
prime radical#30682327C2
hypercenter#330D263
hypocenterC263#1657
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #30682692C2semidirect
3. #30682304C2semidirect
4. #30682303C2semidirect
5. #30681679C2semidirect
6. #30681677C2semidirect
7. #330×C263C2semidirect
97. C263#1657semidirect
104. #330D263semidirect

Maximal subgroups

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

subgroupindex
#306826922
#306823272
#306823042
#306823032
#306816792
#306816772
#330×C2632
#1657263