Finite Group Databasebeta

← #46781981

Subgroups — #46781981

Order 33664.

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

normal subgroups only

This group has 240 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#30682341C211yesmaximal, characteristic, complemented
3#30682140C211yesmaximal, characteristic, complemented
4#30681683C211yesmaximal, characteristic, complemented
5D4⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7#474×C263C211yesmaximal, characteristic, complemented
8C2×#16862376—21no—
9C2×#16862363—21no—
10#22554470C2211yescharacteristic
11#22554452—22no—
12#22554449—21no—
13#22554441—21no—
14C4×D1052C2211yescharacteristic
15C4⋊C4×D263—21no—
16#22554403—22no—
17C4⋊(C263⋊C8)C2211yescharacteristic
18#22554394—21no—
19C4×C263⋊C8C2211yescharacteristic
20C4⋊Q8×C263C2211yescharacteristic
21C4×D4×C263C2211yescharacteristic
22#107×C263—21no—
23C4⋊C8×C263C2211yescharacteristic
24#102×C263—21no—
25#16862376—42no—
26#16862376—42no—
27C2×Dic526—21no—
28C2×D1052D411yescharacteristic
29C2×C22⋊D263—22no—
30C2×C4×D263—22no—
31C2×C4×D263—21no—
32#16862363—42no—
33C2×C263⋊C8—21no—
34C2×C263⋊C8—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263D411yescharacteristic
37C4⋊Dic263D412yes—
38Dic263⋊C4—22no—
39C22⋊Dic263—22no—
40(C2×D263)⋊C4—21no—
41C2×Q8×C263—21no—
42C2×D4×C263D411yescharacteristic
43C22×C4×C263—21no—
44C2×C8×C263—21no—
45C4⋊C4×C263—21no—
46C4⋊C4×C263—21no—
47C4⋊C4×C263D411yescharacteristic
48C22⋊C4×C263—21no—
49C42×C263C2311yescharacteristic
50C22×D263—21no—
51Dic526—41no—
52Dic526—41no—
53D1052—21no—
54D1052D812yes—
55C22⋊D263—44no—
56C2×Dic263—21no—
57C2×Dic263—22no—
58C4×D263—44no—
59C4×D263—41no—
60C4×D263—41no—
61C263⋊C8—22no—
62C263⋊C8—41no—
63C23×C263—21no—
64Q8×C263—41no—
65Q8×C263—41no—
66D4×C263—21no—
67D4×C263—21no—
68C2×C4×C263—21no—
69C2×C4×C263—41no—
70C2×C4×C263—41no—
71C2×C4×C263—41no—
72C2×C4×C263C2×D411yescharacteristic
73C2×C4×C263C2×D411yescharacteristic
74C2×C4×C263C2×D411yescharacteristic
75C8×C263—41no—
76C22×C263—41no—
77C22×C263—41no—
78C22×C263—41no—
79C22×C263#12011yescharacteristic
80C2×D263—22no—
81C2×D263—41no—
82C2×D263—41no—
83C4×C263—21no—
84C4×C263—41no—
85C4×C263—81no—
86C4×C263C2×D811yescharacteristic
87C4×C263#13511yescharacteristic
88C4×C263AGL(1,ℤ/8)11yescharacteristic
89C4×C263#13711yescharacteristic
90Dic263—42no—
91Dic263—41no—
92C2×C263—81no—
93C2×C263#44711yescharacteristic
94C2×C263#45211yescharacteristic
95C2×C263#45611yescharacteristic
96D263—42no—
97C263#164711yescharacteristic, complemented, Sylow
98#1647—2631nomaximal, Sylow
99#547—2631no—
100#500—2631no—
101#474D26311yescharacteristic, complemented
102#461—2631no—
103#332—2631no—
104D4⋊C8—2631no—
105D4⋊C8—2631no—
106C2×#41—5261no—
107C2×SD16—5261no—
108C4⋊Q8—2631no—
109C4⋊Q8C2×D26311yescharacteristic
110#123—5262no—
111C22⋊Q8—5261no—
112#121—5261no—
113C4×D4—2631no—
114C4×D4C2×D26311yescharacteristic
115C2×C4⋊C4—5261no—
116#107—21no—
117#107—5262no—
118C4⋊C8—2631no—
119C4⋊C8C2×D26311yescharacteristic
120#103—5261no—
121#102—21no—
122C4×C8—2631no—
123#41—10522no—
124#41—10522no—
125C2×Q8—21no—
126C2×Q8—5261no—
127C2×D4—2631no—
128C2×D4—5262no—
129C2×D4C22⋊D26311yescharacteristic
130C22×C4—21no—
131C22×C4—5262no—
132C22×C4—5261no—
133SD16—10522no—
134C2×C8—21no—
135C2×C8—5261no—
136C2×C8—5261no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—2631no—
140C4⋊C4—2632no—
141C4⋊C4—5262no—
142C4⋊C4—5261no—
143C4⋊C4C22⋊D26311yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—5262no—
146C22⋊C4—5261no—
147C42C22×D26311yescharacteristic
148C23—21no—
149C23—5261no—
150Q8—41no—
151Q8—41no—
152Q8—10521no—
153Q8—10521no—
154D4—21no—
155D4—21no—
156D4—2632no—
157D4—5261no—
158D4—10524no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—5261no—
164C2×C4—5262no—
165C2×C4—10524no—
166C2×C4—10521no—
167C2×C4—10521no—
168C2×C4D4×D26311yescharacteristic
169C2×C4D4×D26311yescharacteristic
170C2×C4C2×C22⋊D26311yescharacteristic
171C8—41no—
172C8—5262no—
173C8—10521no—
174C22—41no—
175C22—41no—
176C22—41no—
177C22—5262no—
178C22—10521no—
179C22—10521no—
180C22#2255443811yescharacteristic
181C4—21no—
182C4—41no—
183C4—81no—
184C4—10522no—
185C4—10521no—
186C4D8×D26311yescharacteristic
187C4#2255449011yescharacteristic
188C4#2255449411yescharacteristic
189C4#2255450111yescharacteristic
190C2—81no—
191C2—10522no—
192C2#3068207011yescharacteristic
193C2#3068209811yescharacteristic
194C2#3068211911yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#474×C263C2
socleC22×C263#120
prime radical#30682593C2
hypercenter#474D263
hypocenterC263#1647
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #30682341C2semidirect
3. #30682140C2semidirect
4. #30681683C2semidirect
5. D4⋊(C263⋊C8)C2semidirect
6. #30681665C2semidirect
7. #474×C263C2semidirect
97. C263#1647semidirect
101. #474D263semidirect

Maximal subgroups

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

subgroupindex
#306825932
#306823412
#306821402
#306816832
D4⋊(C263⋊C8)2
#306816652
#474×C2632
#1647263