Finite Group Databasebeta

← #46781817

Subgroups — #46781817

Order 33664.

236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 57 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#30682645C211yesmaximal, characteristic, complemented
2#30682310C211yesmaximal, characteristic, complemented
3#30682135C211yesmaximal, characteristic, complemented
4#30681686C211yesmaximal, characteristic, complemented
5#30681668C211yesmaximal, characteristic, complemented
6D4⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
7#459×C263C211yesmaximal, characteristic
8C2×#16862364—21no—
9C2×#16862364—22no—
10#22554470C2211yescharacteristic
11#22554461—21no—
12#22554449—21no—
13#22554447—22no—
14C4×Dic526C2211yescharacteristic
15D4×Dic263—21no—
16C2×C4⋊Dic263—21no—
17C4⋊(C263⋊C8)C2211yescharacteristic
18#22554391—21no—
19C4×C263⋊C8C2211yescharacteristic
20C2×D8×C263—21no—
21#127×C263C2211yescharacteristic
22C4×D4×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24#102×C263—21no—
25C2×Dic526D411yescharacteristic
26C2×Dic526D412yes—
27C22×Dic263—22no—
28#16862364—44no—
29#16862364—42no—
30C2×C263⋊C8—21no—
31C2×C263⋊C8—21no—
32C4⋊Dic263—22no—
33C4⋊Dic263—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263D411yescharacteristic
36Dic263⋊C4—22no—
37Dic263⋊C4—21no—
38C22⋊Dic263—22no—
39C4×Dic263—21no—
40C2×D4×C263—21no—
41C2×D4×C263—21no—
42C2×D4×C263—21no—
43C2×D4×C263D411yescharacteristic
44C22×C4×C263—21no—
45D8×C263—42no—
46C2×C8×C263—21no—
47C4⋊C4×C263D411yescharacteristic
48C22⋊C4×C263—21no—
49C42×C263C2311yescharacteristic
50Dic526—21no—
51Dic526—21no—
52Dic526—42no—
53C2×Dic263—21no—
54C2×Dic263—21no—
55C2×Dic263—22no—
56C2×Dic263—82no—
57C263⋊C8—22no—
58C263⋊C8—41no—
59C23×C263—21no—
60C23×C263—41no—
61D4×C263—21no—
62D4×C263—42no—
63D4×C263—41no—
64D4×C263—41no—
65D4×C263—41no—
66D4×C263—41no—
67D4×C263SD1612yescomplemented
68C2×C4×C263—21no—
69C2×C4×C263—41no—
70C2×C4×C263—41no—
71C2×C4×C263C2×D411yescharacteristic
72C2×C4×C263C2×D411yescharacteristic
73C2×C4×C263C2×D411yescharacteristic
74C8×C263—41no—
75C22×C263—22no—
76C22×C263—41no—
77C22×C263—41no—
78C22×C263—81no—
79C22×C263—81no—
80C22×C263—81no—
81C22×C263#12011yescharacteristic
82C4×C263—21no—
83C4×C263—41no—
84C4×C263C2×SD1611yescharacteristic
85C4×C263#13511yescharacteristic
86C4×C263AGL(1,ℤ/8)11yescharacteristic
87C4×C263#13711yescharacteristic
88Dic263—41no—
89Dic263—41no—
90Dic263—42no—
91C2×C263—42no—
92C2×C263—161no—
93C2×C263#44811yescharacteristic
94C2×C263#44911yescharacteristic
95C2×C263#45311yescharacteristic
96C263#162211yescharacteristic, complemented, Sylow
97#1622—2631nomaximal, Sylow
98#554—2631no—
99#492—2631no—
100#460—2631no—
101#459D26311yescharacteristic
102#333—2631no—
103Q8⋊C8—2631no—
104D4⋊C8—2631no—
105C2×SD16—5261no—
106C2×SD16—5262no—
107C2×D8—21no—
108C4⋊Q8—2631no—
109#127C2×D26311yescharacteristic
110#125—5261no—
111C22⋊Q8—5262no—
112C22⋊Q8—5261no—
113C4×Q8—2631no—
114C4×D4—5261no—
115C4×D4C2×D26311yescharacteristic
116C2×C4⋊C4—5261no—
117C4⋊C8—2631no—
118C4⋊C8C2×D26311yescharacteristic
119#102—21no—
120#102—5261no—
121C4×C8—2631no—
122C2×Q8—2631no—
123C2×Q8—2632no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4C22⋊D26311yescharacteristic
128C22×C4—21no—
129C22×C4—5262no—
130SD16—10524no—
131SD16—10522no—
132D8—42no—
133C2×C8—21no—
134C2×C8—5261no—
135C2×C8—5261no—
136C4⋊C4—2631no—
137C4⋊C4—5262no—
138C4⋊C4—5262no—
139C4⋊C4—5261no—
140C4⋊C4—5261no—
141C4⋊C4—5261no—
142C4⋊C4C22⋊D26311yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—5262no—
145C42—5261no—
146C42C22×D26311yescharacteristic
147C23—21no—
148C23—41no—
149Q8—5261no—
150Q8—5261no—
151Q8—10522no—
152D4—21no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4#1686236412yescomplemented
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—5261no—
163C2×C4—5261no—
164C2×C4—5262no—
165C2×C4—21042no—
166C2×C4D4×D26311yescharacteristic
167C2×C4D4×D26311yescharacteristic
168C2×C4C2×C22⋊D26311yescharacteristic
169C8—41no—
170C8—5262no—
171C8—10521no—
172C22—22no—
173C22—41no—
174C22—41no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22#2255443811yescharacteristic
179C4—21no—
180C4—41no—
181C4—10521no—
182C4—10521no—
183C4—10522no—
184C4C2×#1686236411yescharacteristic
185C4#2255448911yescharacteristic
186C4#2255449411yescharacteristic
187C4#2255450011yescharacteristic
188C2—42no—
189C2—161no—
190C2#3068207611yescharacteristic
191C2#3068208011yescharacteristic
192C2#3068210411yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting, prime radical#459×C263C2
socleC22×C263#120
hypercenter#459D263
hypocenterC263#1622
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. #30682645C2semidirect
2. #30682310C2semidirect
3. #30682135C2semidirect
4. #30681686C2semidirect
5. #30681668C2semidirect
6. D4⋊(C263⋊C8)C2semidirect
67. D4×C263SD16semidirect
96. C263#1622semidirect
158. D4#16862364semidirect

Maximal subgroups

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

subgroupindex
#306826452
#306823102
#306821352
#306816862
#306816682
D4⋊(C263⋊C8)2
#459×C2632
#1622263