Finite Group Databasebeta

← #46781948

Subgroups — #46781948

Order 33664.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#30682608C211yesmaximal, characteristic
2#30682284C211yesmaximal, characteristic, complemented
3#30682224C211yesmaximal, characteristic, complemented
4#30682144C211yesmaximal, characteristic, complemented
5#30681668C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7#331×C263C211yesmaximal, characteristic, complemented
8C2×#16862375—21no—
9C2×#16862365—21no—
10#22554470C2211yescharacteristic
11#22554466—21no—
12#22554442—22no—
13#22554441—21no—
14C4×Dic526C2211yescharacteristic
15C4×D1052C2211yescharacteristic
16D4×Dic263—21no—
17#22554402—21no—
18#22554395—21no—
19#22554395—21no—
20#22554391—22no—
21C4×C263⋊C8C2211yescharacteristic
22#127×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4⋊C8×C263C2211yescharacteristic
25#16862375—42no—
26#16862375—42no—
27C2×Dic526—21no—
28C2×Dic526D411yescharacteristic
29C2×D1052D411yescharacteristic
30C2×C22⋊D263—22no—
31C2×C22⋊D263—22no—
32C22×Dic263—22no—
33C2×C4×D263—21no—
34#16862365—42no—
35C2×C263⋊C8—21no—
36C4⋊Dic263—21no—
37C4⋊Dic263—21no—
38C4⋊Dic263D411yescharacteristic
39C4⋊Dic263D411yescharacteristic
40Dic263⋊C4—21no—
41C22⋊Dic263—22no—
42(C2×D263)⋊C4—21no—
43C4×Dic263—21no—
44C2×D4×C263—21no—
45C2×D4×C263—21no—
46C2×D4×C263D412yes—
47C2×C8×C263—21no—
48C2×C8×C263—21no—
49C42×C263C2311yescharacteristic
50C22×D263—21no—
51Dic526—21no—
52Dic526—41no—
53Dic526—41no—
54Dic526SD1612yescomplemented
55D1052—21no—
56D1052—21no—
57C22⋊D263—44no—
58C22⋊D263—82no—
59C2×Dic263—21no—
60C2×Dic263—21no—
61C2×Dic263—21no—
62C2×Dic263—44no—
63C2×Dic263—41no—
64C4×D263—41no—
65C4×D263—41no—
66C263⋊C8—41no—
67C23×C263—22no—
68D4×C263—42no—
69D4×C263—41no—
70D4×C263—41no—
71D4×C263—41no—
72D4×C263—41no—
73C2×C4×C263C2×D411yescharacteristic
74C2×C4×C263C2×D411yescharacteristic
75C2×C4×C263C2×D411yescharacteristic
76C8×C263—41no—
77C8×C263—41no—
78C22×C263—42no—
79C22×C263—42no—
80C22×C263—42no—
81C22×C263#12011yescharacteristic
82C2×D263—41no—
83C2×D263—41no—
84C2×D263—41no—
85C4×C263—21no—
86C4×C263C2×SD1611yescharacteristic
87C4×C263#13511yescharacteristic
88C4×C263AGL(1,ℤ/8)11yescharacteristic
89C4×C263AGL(1,ℤ/8)11yescharacteristic
90Dic263—22no—
91Dic263—41no—
92Dic263—41no—
93Dic263—81no—
94C2×C263—82no—
95C2×C263#44911yescharacteristic
96C2×C263#45011yescharacteristic
97C2×C263#45511yescharacteristic
98D263—81no—
99C263#164211yescharacteristic, complemented, Sylow
100#1642—2631nomaximal, Sylow
101#550—2631no—
102#486—2631no—
103#475—2631no—
104#461—2631no—
105#331D26311yescharacteristic, complemented
106Q8⋊C8—2631no—
107D4⋊C8—2631no—
108C2×#41—5261no—
109C2×SD16—5261no—
110C4⋊Q8—2631no—
111#127—5261no—
112#127C2×D26311yescharacteristic
113#121—5261no—
114#121—5262no—
115C4×Q8—2631no—
116C4×D4—2631no—
117C4×D4—5261no—
118#106—5261no—
119C4⋊C8C2×D26311yescharacteristic
120C4⋊C8C2×D26311yescharacteristic
121#103—5261no—
122#103—5261no—
123#102—5262no—
124C4×C8—2631no—
125#41—10522no—
126#41—10522no—
127C2×Q8—2631no—
128C2×Q8—5261no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—2631no—
132C2×D4—5262no—
133C2×D4—5262no—
134C2×D4D105212yes—
135C22×C4—5262no—
136C22×C4—5261no—
137SD16—10522no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—5261no—
141C4⋊C4—2631no—
142C4⋊C4—2631no—
143C4⋊C4—5261no—
144C4⋊C4—5261no—
145C4⋊C4—5261no—
146C22⋊C4—5262no—
147C22⋊C4—5261no—
148C42—5261no—
149C42C22×D26311yescharacteristic
150C23—22no—
151C23—5261no—
152Q8—2632no—
153Q8—5261no—
154Q8—10521no—
155Q8—10521no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—5261no—
162D4—5261no—
163D4—10524no—
164D4—21042no—
165C2×C4—5261no—
166C2×C4—5261no—
167C2×C4—5261no—
168C2×C4—10524no—
169C2×C4—10521no—
170C2×C4—10521no—
171C2×C4—10521no—
172C2×C4D4×D26311yescharacteristic
173C2×C4D4×D26311yescharacteristic
174C2×C4C2×D105211yescharacteristic
175C8—41no—
176C8—41no—
177C8—10521no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—10521no—
182C22—10521no—
183C22—10521no—
184C22#2255444011yescharacteristic
185C4—21no—
186C4—5262no—
187C4—10521no—
188C4—10521no—
189C4—21041no—
190C4SD16×D26311yescharacteristic
191C4#2255449111yescharacteristic
192C4#2255449411yescharacteristic
193C4#2255449411yescharacteristic
194C2—82no—
195C2—21041no—
196C2#3068208411yescharacteristic
197C2#3068209011yescharacteristic
198C2#3068211811yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#331×C263C2
socleC22×C263#120
prime radical#30682608C2
hypercenter#331D263
hypocenterC263#1642
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #30682284C2semidirect
3. #30682224C2semidirect
4. #30682144C2semidirect
5. #30681668C2semidirect
6. #30681665C2semidirect
7. #331×C263C2semidirect
54. Dic526SD16semidirect
99. C263#1642semidirect
105. #331D263semidirect

Maximal subgroups

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

subgroupindex
#306826082
#306822842
#306822242
#306821442
#306816682
#306816652
#331×C2632
#1642263