Finite Group Databasebeta

← #46781901

Subgroups — #46781901

Order 33664.

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

normal subgroups only

This group has 234 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#30682593C211yesmaximal, characteristic
2#30682289C211yesmaximal, characteristic, complemented
3#30682229C211yesmaximal, characteristic, complemented
4#30682228C211yesmaximal, characteristic, complemented
5#30681685C211yesmaximal, characteristic, complemented
6#30681667C211yesmaximal, characteristic, complemented
7D4⋊C8×C263C211yesmaximal, characteristic, complemented
8C2×#16862376—21no—
9#22554470C2211yescharacteristic
10#22554470C2211yescharacteristic
11#22554452—22no—
12#22554449—21no—
13#22554441—21no—
14C4×D1052C2211yescharacteristic
15C4⋊C4×D263—21no—
16#22554402—21no—
17#22554401—21no—
18C4⋊(C263⋊C8)C2211yescharacteristic
19#22554395—22no—
20#22554392—21no—
21#22554391—21no—
22C4×D4×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25#16862376—42no—
26#16862376—42no—
27C2×Dic526—21no—
28C2×Dic526—21no—
29C2×D1052D411yescharacteristic
30C2×C22⋊D263—22no—
31C2×C4×D263—22no—
32C2×C4×D263—21no—
33C2×C263⋊C8—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263—21no—
37C4⋊Dic263D412yes—
38C4⋊Dic263D411yescharacteristic
39Dic263⋊C4—22no—
40C22⋊Dic263—22no—
41(C2×D263)⋊C4—21no—
42C2×D4×C263D411yescharacteristic
43C22×C4×C263—21no—
44C2×C8×C263—21no—
45C2×C8×C263—21no—
46C4⋊C4×C263D411yescharacteristic
47C22⋊C4×C263—21no—
48C42×C263C2311yescharacteristic
49C22×D263—21no—
50Dic526—41no—
51Dic526—41no—
52Dic526—42no—
53D1052—21no—
54D1052SD1612yes—
55C22⋊D263—44no—
56C2×Dic263—21no—
57C2×Dic263—22no—
58C2×Dic263—41no—
59C4×D263—44no—
60C4×D263—41no—
61C4×D263—41no—
62C263⋊C8—41no—
63C23×C263—21no—
64D4×C263—21no—
65D4×C263—21no—
66C2×C4×C263—21no—
67C2×C4×C263—41no—
68C2×C4×C263—41no—
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C2×C4×C263C2×D411yescharacteristic
72C8×C263—41no—
73C8×C263—41no—
74C22×C263—41no—
75C22×C263—41no—
76C22×C263—41no—
77C22×C263#12011yescharacteristic
78C2×D263—22no—
79C2×D263—41no—
80C2×D263—41no—
81C4×C263—21no—
82C4×C263—41no—
83C4×C263C2×SD1611yescharacteristic
84C4×C263#13511yescharacteristic
85C4×C263AGL(1,ℤ/8)11yescharacteristic
86C4×C263#13711yescharacteristic
87Dic263—42no—
88Dic263—41no—
89Dic263—81no—
90C2×C263—81no—
91C2×C263#45011yescharacteristic
92C2×C263#45211yescharacteristic
93C2×C263#45411yescharacteristic
94D263—42no—
95C263#163511yescharacteristic, complemented, Sylow
96#1635—2631nomaximal, Sylow
97#547—2631no—
98#487—2631no—
99#476—2631no—
100#476—2631no—
101#332—2631no—
102D4⋊C8—2631no—
103D4⋊C8D26311yescharacteristic, complemented
104C2×#41—5261no—
105C4⋊Q8—2631no—
106C4⋊Q8—2631no—
107#123—5262no—
108C22⋊Q8—5261no—
109#121—5261no—
110C4×D4—2631no—
111C4×D4C2×D26311yescharacteristic
112C2×C4⋊C4—5261no—
113#106—5261no—
114#106—5261no—
115C4⋊C8—2631no—
116C4⋊C8C2×D26311yescharacteristic
117#103—5262no—
118#102—5261no—
119#102—5261no—
120C4×C8C2×D26311yescharacteristic
121#41—10522no—
122#41—10522no—
123C2×Q8—5261no—
124C2×Q8—5261no—
125C2×D4—2631no—
126C2×D4—5262no—
127C2×D4D105211yescharacteristic
128C22×C4—21no—
129C22×C4—5262no—
130C22×C4—5261no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—5261no—
134C4⋊C4—2632no—
135C4⋊C4—2631no—
136C4⋊C4—5262no—
137C4⋊C4—5261no—
138C4⋊C4—5261no—
139C4⋊C4—5261no—
140C4⋊C4D105211yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—5262no—
143C22⋊C4—5261no—
144C42C22×D26311yescharacteristic
145C23—21no—
146C23—5261no—
147Q8—10522no—
148Q8—10521no—
149Q8—10521no—
150D4—21no—
151D4—21no—
152D4—2632no—
153D4—5261no—
154D4—10524no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—5261no—
159C2×C4—5262no—
160C2×C4—10524no—
161C2×C4—10521no—
162C2×C4—10521no—
163C2×C4—10521no—
164C2×C4D4×D26311yescharacteristic
165C2×C4D4×D26311yescharacteristic
166C2×C4C2×D105211yescharacteristic
167C8—41no—
168C8—41no—
169C8—10521no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—5262no—
174C22—10521no—
175C22—10521no—
176C22#2255444011yescharacteristic
177C4—21no—
178C4—41no—
179C4—10522no—
180C4—10521no—
181C4—21041no—
182C4SD16×D26311yescharacteristic
183C4#2255449211yescharacteristic
184C4#2255449411yescharacteristic
185C4#2255450311yescharacteristic
186C2—81no—
187C2—10522no—
188C2#3068209011yescharacteristic
189C2#3068210211yescharacteristic
190C2#3068211211yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingD4⋊C8×C263C2
socleC22×C263#120
prime radical#30682593C2
hypercenterD4⋊C8D263
hypocenterC263#1635
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #30682289C2semidirect
3. #30682229C2semidirect
4. #30682228C2semidirect
5. #30681685C2semidirect
6. #30681667C2semidirect
7. D4⋊C8×C263C2semidirect
95. C263#1635semidirect
103. D4⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
#306825932
#306822892
#306822292
#306822282
#306816852
#306816672
D4⋊C8×C2632
#1635263