Finite Group Databasebeta

← #46781832

Subgroups — #46781832

Order 33664.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#30682653C211yesmaximal, characteristic, complemented
2#30682311C211yesmaximal, characteristic, complemented
3#30682134C211yesmaximal, characteristic, complemented
4#30682133C211yesmaximal, characteristic, complemented
5#30681686C211yesmaximal, characteristic, complemented
6#30681667C211yesmaximal, characteristic, complemented
7D4⋊C8×C263C211yesmaximal, characteristic, complemented
8C2×#16862365—22no—
9C2×D2104—21no—
10C2×#16862361—21no—
11#22554470C2211yescharacteristic
12#22554467C2211yescharacteristic
13#22554456—22no—
14#22554444—21no—
15#22554441—21no—
16C4×D1052C2211yescharacteristic
17#22554429—21no—
18#22554428—21no—
19C4⋊(C263⋊C8)C2211yescharacteristic
20#22554392—21no—
21#22554390—21no—
22C4×D4×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25C2×Dic526D412yes—
26C2×D1052—21no—
27C2×D1052—21no—
28C2×D1052—21no—
29C2×D1052D411yescharacteristic
30C2×C22⋊D263—22no—
31C2×C4×D263—21no—
32#16862365—44no—
33D2104—42no—
34#16862361—42no—
35C2×C263⋊C8—21no—
36C4⋊Dic263—21no—
37C4⋊Dic263—21no—
38C4⋊Dic263D411yescharacteristic
39C22⋊Dic263—22no—
40(C2×D263)⋊C4—22no—
41(C2×D263)⋊C4—21no—
42C4×Dic263—22no—
43C2×D4×C263D411yescharacteristic
44C22×C4×C263—21no—
45C2×C8×C263—21no—
46C2×C8×C263—21no—
47C4⋊C4×C263D411yescharacteristic
48C22⋊C4×C263—21no—
49C42×C263C2311yescharacteristic
50C22×D263—21no—
51C22×D263—41no—
52Dic526—42no—
53D1052—21no—
54D1052—21no—
55D1052—42no—
56D1052—41no—
57D1052—41no—
58D1052—41no—
59D1052—41no—
60C22⋊D263—82no—
61C2×Dic263—21no—
62C2×Dic263—22no—
63C4×D263—41no—
64C4×D263—41no—
65C263⋊C8—41no—
66C23×C263—21no—
67D4×C263—21no—
68D4×C263—21no—
69C2×C4×C263—21no—
70C2×C4×C263—41no—
71C2×C4×C263—41no—
72C2×C4×C263C2×D411yescharacteristic
73C2×C4×C263C2×D411yescharacteristic
74C2×C4×C263C2×D411yescharacteristic
75C8×C263—22no—
76C8×C263—41no—
77C22×C263—41no—
78C22×C263—41no—
79C22×C263—41no—
80C22×C263#12011yescharacteristic
81C2×D263—41no—
82C2×D263—41no—
83C2×D263—41no—
84C2×D263—81no—
85C2×D263—81no—
86C2×D263—81no—
87C4×C263—21no—
88C4×C263—41no—
89C4×C263#13511yescharacteristic
90C4×C263#13511yescharacteristic
91C4×C263AGL(1,ℤ/8)11yescharacteristic
92C4×C263AGL(1,ℤ/8)11yescharacteristic
93Dic263—41no—
94Dic263—42no—
95C2×C263—81no—
96C2×C263#44911yescharacteristic
97C2×C263#44911yescharacteristic
98C2×C263#45311yescharacteristic
99D263—81no—
100D263—161no—
101C263#162411yescharacteristic, complemented, Sylow
102#1624—2631nomaximal, Sylow
103#555—2631no—
104#492—2631no—
105#459—2631no—
106#459—2631no—
107#333—2631no—
108D4⋊C8—2631no—
109D4⋊C8D26311yescharacteristic, complemented
110C2×SD16—5262no—
111C2×D8—5261no—
112C2×D8—5261no—
113C4⋊Q8—2631no—
114#127—2631no—
115#124—5262no—
116#121—5261no—
117#121—5261no—
118C4×D4—2631no—
119C4×D4C2×D26311yescharacteristic
120#117—5261no—
121#117—5261no—
122C4⋊C8—2631no—
123C4⋊C8C2×D26311yescharacteristic
124#102—5261no—
125#102—5261no—
126C4×C8C2×D26311yescharacteristic
127C2×Q8—2632no—
128C2×D4—2631no—
129C2×D4—5262no—
130C2×D4—5261no—
131C2×D4—5261no—
132C2×D4—5261no—
133C2×D4D105211yescharacteristic
134C22×C4—21no—
135C22×C4—5261no—
136SD16—10524no—
137D8—10522no—
138D8—10522no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—5261no—
142C4⋊C4—2631no—
143C4⋊C4—5261no—
144C4⋊C4—5261no—
145C4⋊C4D105211yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—5262no—
148C22⋊C4—5262no—
149C22⋊C4—5261no—
150C42—5262no—
151C42C22×D26311yescharacteristic
152C23—21no—
153C23—5261no—
154C23—10521no—
155Q8—10522no—
156D4—21no—
157D4—21no—
158D4—5261no—
159D4—5261no—
160D4—10522no—
161D4—10521no—
162D4—10521no—
163D4—10521no—
164D4—10521no—
165D4—21042no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—5261no—
170C2×C4—5262no—
171C2×C4—10521no—
172C2×C4—10521no—
173C2×C4D4×D26311yescharacteristic
174C2×C4D4×D26311yescharacteristic
175C2×C4C2×D105211yescharacteristic
176C8—22no—
177C8—41no—
178C8—10521no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—10521no—
183C22—10521no—
184C22—10521no—
185C22—21041no—
186C22—21041no—
187C22—21041no—
188C22#2255444011yescharacteristic
189C4—21no—
190C4—41no—
191C4—10521no—
192C4—10522no—
193C4#2255449111yescharacteristic
194C4#2255449211yescharacteristic
195C4#2255449411yescharacteristic
196C4#2255449811yescharacteristic
197C2—81no—
198C2—21041no—
199C2—42081no—
200C2#3068208411yescharacteristic
201C2#3068208511yescharacteristic
202C2#3068210711yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingD4⋊C8×C263C2
socleC22×C263#120
hypercenterD4⋊C8D263
hypocenterC263#1624
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
1. #30682653C2semidirect
2. #30682311C2semidirect
3. #30682134C2semidirect
4. #30682133C2semidirect
5. #30681686C2semidirect
6. #30681667C2semidirect
7. D4⋊C8×C263C2semidirect
101. C263#1624semidirect
109. D4⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
#306826532
#306823112
#306821342
#306821332
#306816862
#306816672
D4⋊C8×C2632
#1624263