Finite Group Databasebeta

← #46781859

Subgroups — #46781859

Order 33664.

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

normal subgroups only

This group has 216 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#30682658C211yesmaximal, characteristic, complemented
2#30682285C211yesmaximal, characteristic, complemented
3#30682139C211yesmaximal, characteristic, complemented
4#30682133C211yesmaximal, characteristic
5#30681683C211yesmaximal, characteristic, complemented
6#30681670C211yesmaximal, characteristic, complemented
7D4⋊C8×C263C211yesmaximal, characteristic, complemented
8C2×#16862365—21no—
9C2×#16862361—21no—
10#22554470C2211yescharacteristic
11#22554467C2211yescharacteristic
12#22554463—22no—
13#22554457—21no—
14#22554449—21no—
15C4×Dic526C2211yescharacteristic
16#22554435—21no—
17#22554429—21no—
18C4⋊(C263⋊C8)C2211yescharacteristic
19#22554392—21no—
20#22554392—22no—
21#22554390—21no—
22C4×D4×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25C2×Dic526—21no—
26C2×Dic526D411yescharacteristic
27C2×D1052—21no—
28C2×D1052—21no—
29C2×D1052—21no—
30#16862365—42no—
31#16862361—42no—
32C2×C263⋊C8—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263D411yescharacteristic
35C4⋊Dic263D412yes—
36Dic263⋊C4—22no—
37Dic263⋊C4—21no—
38C22⋊Dic263—22no—
39C22⋊Dic263—22no—
40C4×Dic263—22no—
41C4×Dic263—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—41no—
50Dic526—21no—
51Dic526—21no—
52Dic526—41no—
53Dic526—41no—
54D1052—42no—
55D1052—41no—
56D1052—41no—
57D1052—41no—
58D1052—41no—
59C2×Dic263—21no—
60C2×Dic263—21no—
61C2×Dic263—22no—
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—81no—
79C2×D263—81no—
80C2×D263—81no—
81C4×C263—21no—
82C4×C263—41no—
83C4×C263#13511yescharacteristic
84C4×C263#13511yescharacteristic
85C4×C263AGL(1,ℤ/8)11yescharacteristic
86C4×C263AGL(1,ℤ/8)11yescharacteristic
87Dic263—41no—
88Dic263—42no—
89Dic263—41no—
90C2×C263—81no—
91C2×C263#44911yescharacteristic
92C2×C263#44911yescharacteristic
93C2×C263#45411yescharacteristic
94D263—161no—
95C263#162811yescharacteristic, complemented, Sylow
96#1628—2631nomaximal, Sylow
97#556—2631no—
98#486—2631no—
99#460—2631no—
100#459—2631no—
101#332—2631no—
102Q8⋊C8—2631no—
103D4⋊C8D26311yescharacteristic, complemented
104C2×SD16—5261no—
105C2×D8—5261no—
106C4⋊Q8—2631no—
107#127—2631no—
108#126—5262no—
109#124—5261no—
110C22⋊Q8—5261no—
111C4×Q8—2631no—
112C4×Q8—5261no—
113C4×D4C2×D26311yescharacteristic
114#117—5261no—
115C4⋊C8—2631no—
116C4⋊C8C2×D26311yescharacteristic
117#102—5261no—
118#102—5262no—
119#102—5261no—
120C4×C8C2×D26311yescharacteristic
121C2×Q8—2631no—
122C2×Q8—5261no—
123C2×D4—5261no—
124C2×D4—5261no—
125C2×D4—5261no—
126C2×D4D105211yescharacteristic
127C22×C4—21no—
128SD16—10522no—
129D8—10522no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—5261no—
133C4⋊C4—2631no—
134C4⋊C4—2632no—
135C4⋊C4—5262no—
136C4⋊C4—5261no—
137C4⋊C4—5261no—
138C4⋊C4D105211yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—5262no—
141C22⋊C4—5262no—
142C42—5262no—
143C42—5261no—
144C42C22×D26311yescharacteristic
145C23—21no—
146C23—10521no—
147Q8—5261no—
148Q8—5261no—
149Q8—10521no—
150Q8—10521no—
151D4—21no—
152D4—21no—
153D4—10522no—
154D4—10521no—
155D4—10521no—
156D4—10521no—
157D4—10521no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—5261no—
162C2×C4—5262no—
163C2×C4—5261no—
164C2×C4D4×D26311yescharacteristic
165C2×C4D4×D26311yescharacteristic
166C2×C4C2×D105211yescharacteristic
167C8—41no—
168C8—41no—
169C8—10521no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—21041no—
174C22—21041no—
175C22—21041no—
176C22#2255444011yescharacteristic
177C4—21no—
178C4—41no—
179C4—10521no—
180C4—10521no—
181C4—10522no—
182C4#2255449111yescharacteristic
183C4#2255449211yescharacteristic
184C4#2255449411yescharacteristic
185C4#2255449811yescharacteristic
186C2—81no—
187C2—42081no—
188C2#3068208411yescharacteristic
189C2#3068208511yescharacteristic
190C2#3068211211yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingD4⋊C8×C263C2
socleC22×C263#120
prime radical#30682133C2
hypercenterD4⋊C8D263
hypocenterC263#1628
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. #30682658C2semidirect
2. #30682285C2semidirect
3. #30682139C2semidirect
5. #30681683C2semidirect
6. #30681670C2semidirect
7. D4⋊C8×C263C2semidirect
95. C263#1628semidirect
103. D4⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
#306826582
#306822852
#306821392
#306821332
#306816832
#306816702
D4⋊C8×C2632
#1628263