Finite Group Databasebeta

← #46781835

Subgroups — #46781835

Order 33664.

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

normal subgroups only

This group has 256 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, complemented
2#30682284C211yesmaximal, characteristic, complemented
3#30682130C211yesmaximal, characteristic, complemented
4#30681683C211yesmaximal, characteristic, complemented
5D4⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7#459×C263C211yesmaximal, characteristic, complemented
8C2×#16862376—21no—
9C2×#16862361—21no—
10#22554470C2211yescharacteristic
11#22554452—22no—
12#22554449—21no—
13#22554441—21no—
14C4×D1052C2211yescharacteristic
15C4⋊C4×D263—21no—
16C4⋊(C263⋊C8)C2211yescharacteristic
17#22554391—21no—
18#22554391—22no—
19C4×C263⋊C8C2211yescharacteristic
20C2×D8×C263—21no—
21#127×C263C2211yescharacteristic
22C4×D4×C263C2211yescharacteristic
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#16862361—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×D4×C263—21no—
42C2×D4×C263—21no—
43C2×D4×C263—21no—
44C2×D4×C263D411yescharacteristic
45C22×C4×C263—21no—
46D8×C263—42no—
47C2×C8×C263—21no—
48C4⋊C4×C263D411yescharacteristic
49C22⋊C4×C263—21no—
50C42×C263C2311yescharacteristic
51C22×D263—21no—
52Dic526—41no—
53Dic526—41no—
54D1052—21no—
55D1052D812yescomplemented
56C22⋊D263—44no—
57C2×Dic263—21no—
58C2×Dic263—22no—
59C4×D263—44no—
60C4×D263—41no—
61C4×D263—41no—
62C263⋊C8—41no—
63C263⋊C8—41no—
64C23×C263—21no—
65C23×C263—41no—
66D4×C263—21no—
67D4×C263—21no—
68D4×C263—42no—
69D4×C263—41no—
70D4×C263—41no—
71D4×C263—41no—
72D4×C263—41no—
73C2×C4×C263—21no—
74C2×C4×C263—41no—
75C2×C4×C263—41no—
76C2×C4×C263C2×D411yescharacteristic
77C2×C4×C263C2×D411yescharacteristic
78C2×C4×C263C2×D411yescharacteristic
79C8×C263—41no—
80C22×C263—41no—
81C22×C263—41no—
82C22×C263—41no—
83C22×C263—81no—
84C22×C263—81no—
85C22×C263—81no—
86C22×C263#12011yescharacteristic
87C2×D263—22no—
88C2×D263—41no—
89C2×D263—41no—
90C4×C263—21no—
91C4×C263—41no—
92C4×C263C2×D811yescharacteristic
93C4×C263#13511yescharacteristic
94C4×C263AGL(1,ℤ/8)11yescharacteristic
95C4×C263AGL(1,ℤ/8)11yescharacteristic
96Dic263—42no—
97Dic263—41no—
98C2×C263—81no—
99C2×C263—161no—
100C2×C263#44711yescharacteristic
101C2×C263#44911yescharacteristic
102C2×C263#45411yescharacteristic
103D263—42no—
104C263#162511yescharacteristic, complemented, Sylow
105#1625—2631nomaximal, Sylow
106#547—2631no—
107#486—2631no—
108#459—2631no—
109#459D26311yescharacteristic, complemented
110#332—2631no—
111D4⋊C8—2631no—
112D4⋊C8—2631no—
113C2×#41—5261no—
114C2×D8—21no—
115C2×D8—5261no—
116C4⋊Q8—2631no—
117#127C2×D26311yescharacteristic
118#123—5262no—
119C22⋊Q8—5261no—
120#121—5261no—
121C4×D4—2631no—
122C4×D4C2×D26311yescharacteristic
123C2×C4⋊C4—5261no—
124C4⋊C8—2631no—
125C4⋊C8C2×D26311yescharacteristic
126#102—21no—
127#102—5261no—
128#102—5262no—
129C4×C8—2631no—
130#41—10522no—
131#41—10522no—
132C2×Q8—5261no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—2631no—
137C2×D4—5262no—
138C2×D4C22⋊D26311yescharacteristic
139C22×C4—21no—
140C22×C4—5262no—
141C22×C4—5261no—
142D8—42no—
143D8—10522no—
144C2×C8—21no—
145C2×C8—5261no—
146C2×C8—5261no—
147C4⋊C4—2631no—
148C4⋊C4—2632no—
149C4⋊C4—5262no—
150C4⋊C4—5261no—
151C4⋊C4C22⋊D26311yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—5262no—
154C22⋊C4—5261no—
155C42C22×D26311yescharacteristic
156C23—21no—
157C23—41no—
158C23—5261no—
159Q8—10521no—
160Q8—10521no—
161D4—21no—
162D4—21no—
163D4—42no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168D4—2632no—
169D4—5261no—
170D4—10524no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—5261no—
175C2×C4—5262no—
176C2×C4—10524no—
177C2×C4—10521no—
178C2×C4—10521no—
179C2×C4D4×D26311yescharacteristic
180C2×C4D4×D26311yescharacteristic
181C2×C4C2×C22⋊D26311yescharacteristic
182C8—41no—
183C8—10521no—
184C8—10521no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—5262no—
192C22—10521no—
193C22—10521no—
194C22#2255443811yescharacteristic
195C4—21no—
196C4—41no—
197C4—10522no—
198C4—10521no—
199C4D8×D26311yescharacteristic
200C4#2255449011yescharacteristic
201C4#2255449411yescharacteristic
202C4#2255449611yescharacteristic
203C2—81no—
204C2—161no—
205C2—10522no—
206C2#3068207011yescharacteristic
207C2#3068208111yescharacteristic
208C2#3068210911yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#459×C263C2
socleC22×C263#120
hypercenter#459D263
hypocenterC263#1625
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #30682593C2semidirect
2. #30682284C2semidirect
3. #30682130C2semidirect
4. #30681683C2semidirect
5. D4⋊(C263⋊C8)C2semidirect
6. #30681665C2semidirect
7. #459×C263C2semidirect
55. D1052D8semidirect
104. C263#1625semidirect
109. #459D263semidirect

Maximal subgroups

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

subgroupindex
#306825932
#306822842
#306821302
#306816832
D4⋊(C263⋊C8)2
#306816652
#459×C2632
#1625263