Finite Group Databasebeta

← #46780864

Subgroups — #46780864

Order 33664.

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

normal subgroups only

This group has 234 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
1C2×#22554387C211yesmaximal, characteristic
2#30681818C211yesmaximal, characteristic
3C2×#99×C263C211yesmaximal, characteristic
4C23×Dic263C411yescharacteristic, complemented
5C2×#16862360—21no—
6C2×C22⋊Dic263—21no—
7C2×C22⋊Dic263C411yescharacteristic, complemented
8#22554387—21no—
9#22554387C412yescomplemented
10C263⋊#95—21no—
11C22×D4×C263C2211yescharacteristic
12C2×C22⋊C4×C263—21no—
13#99×C263—21no—
14#99×C263C412yescomplemented
15C22×Dic263—21no—
16C22×Dic263—21no—
17C22×Dic263—41no—
18C22×Dic263—42no—
19#16862360—22no—
20#16862360—41no—
21C2×C263⋊C8—41no—
22C22⋊Dic263—41no—
23C22⋊Dic263—42no—
24C24×C263C2×C411yescharacteristic
25C24×C263D411yescharacteristic
26C2×D4×C263—41no—
27C2×D4×C263—41no—
28C2×D4×C263C2×C411yescharacteristic
29C2×D4×C263C2×C411yescharacteristic
30C2×D4×C263D411yescharacteristic
31C2×D4×C263Q811yescharacteristic
32C22×C4×C263—41no—
33C22×C4×C263D411yescharacteristic
34C22⋊C4×C263—22no—
35C22⋊C4×C263—41no—
36C2×Dic263—22no—
37C2×Dic263—41no—
38C2×Dic263—42no—
39C2×Dic263—41no—
40C2×Dic263—42no—
41C2×Dic263—41no—
42C2×Dic263—41no—
43C2×Dic263—41no—
44C263⋊C8—42no—
45C23×C263—21no—
46C23×C263—21no—
47C23×C263—21no—
48C23×C263—21no—
49C23×C263—41no—
50C23×C263—41no—
51C23×C263—41no—
52C23×C263—41no—
53C23×C263C4211yescharacteristic
54C23×C263C22⋊C411yescharacteristic
55C23×C263C22⋊C411yescharacteristic
56C23×C263C4⋊C411yescharacteristic
57C23×C263C4⋊C411yescharacteristic
58D4×C263—41no—
59D4×C263—41no—
60D4×C263—41no—
61D4×C263—41no—
62C2×C4×C263—21no—
63C2×C4×C263—21no—
64C2×C4×C263—42no—
65C2×C4×C263—81no—
66C2×C4×C263—81no—
67C2×C4×C263C22⋊C411yescharacteristic
68C2×C4×C263C4⋊C411yescharacteristic
69C22×C263—21no—
70C22×C263—21no—
71C22×C263—21no—
72C22×C263—21no—
73C22×C263—21no—
74C22×C263—21no—
75C22×C263—41no—
76C22×C263—41no—
77C22×C263—41no—
78C22×C263—41no—
79C22×C263—42no—
80C22×C263—41no—
81C22×C263—41no—
82C22×C263—41no—
83C22×C263—41no—
84C22×C263—81no—
85C22×C263#9511yescharacteristic
86C22×C263#9911yescharacteristic
87C22×C263#9911yescharacteristic
88C4×C263—21no—
89C4×C263—21no—
90C4×C263—82no—
91Dic263—42no—
92Dic263—81no—
93C2×C263—21no—
94C2×C263—21no—
95C2×C263—41no—
96C2×C263—41no—
97C2×C263—41no—
98C2×C263—41no—
99C2×C263#34211yescharacteristic
100C2×C263AΣL(1,𝔽16)11yescharacteristic
101C2×C263#35211yescharacteristic
102C263#139011yescharacteristic, complemented, Sylow
103#1390—2631nomaximal, Sylow
104C2×#100—2631no—
105C2×#99D26311yescharacteristic
106#386—2631no—
107C22×D4C2×D26311yescharacteristic
108C23×C4—2631no—
109C2×M16—5261no—
110C2×C22⋊C4—21no—
111C2×C22⋊C4—2631no—
112C2×C22⋊C4—5261no—
113#100—2632no—
114#100—5261no—
115#99—21no—
116#99Dic26312yescomplemented
117#95—5261no—
118C24C4×D26311yescharacteristic
119C24C22⋊D26311yescharacteristic
120C2×D4—41no—
121C2×D4—41no—
122C2×D4C4×D26311yescharacteristic
123C2×D4C2×Dic26311yescharacteristic
124C2×D4C22⋊D26311yescharacteristic
125C2×D4Dic52611yescharacteristic
126C22×C4—41no—
127C22×C4—5261no—
128C22×C4—5261no—
129C22×C4—10522no—
130C22×C4—10521no—
131C22×C4D105211yescharacteristic
132M16—5262no—
133M16—10521no—
134C2×C8—10521no—
135C22⋊C4—22no—
136C22⋊C4—41no—
137C22⋊C4—10522no—
138C22⋊C4—10521no—
139C23—21no—
140C23—21no—
141C23—21no—
142C23—21no—
143C23—41no—
144C23—41no—
145C23—41no—
146C23—41no—
147C23C4×Dic26311yescharacteristic
148C23(C2×D263)⋊C411yescharacteristic
149C23C22⋊Dic26311yescharacteristic
150C23Dic263⋊C411yescharacteristic
151C23Dic263⋊C411yescharacteristic
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—42no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—5262no—
162C2×C4—10521no—
163C2×C4—10522no—
164C2×C4—10521no—
165C2×C4—10522no—
166C2×C4—10521no—
167C2×C4—10521no—
168C2×C4—10521no—
169C2×C4(C2×D263)⋊C411yescharacteristic
170C2×C4C4⋊Dic26311yescharacteristic
171C8—10522no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22—81no—
188C22C263⋊#9511yescharacteristic
189C22#2255438411yescharacteristic
190C22#2255438411yescharacteristic
191C4—21no—
192C4—21no—
193C4—82no—
194C4—10522no—
195C4—21041no—
196C2—21no—
197C2—21no—
198C2—41no—
199C2—41no—
200C2—41no—
201C2—41no—
202C2#3068170411yescharacteristic
203C2#3068172411yescharacteristic
204C2#3068172711yescharacteristic
subgroupG/H
centerC22#22554384
commutatorC23×C263C42
FrattiniC22×D4C2×D263
FittingC2×#99×C263C2
socleC22×C263#99
prime radical, cosocleC22×D4×C263C22
hypercenterC2×#99D263
hypocenterC263#1390
LCSG ▷ C23×C263 ▷ C22×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
4. C23×Dic263C4semidirect
7. C2×C22⋊Dic263C4semidirect
9. #22554387C4semidirect
14. #99×C263C4semidirect
102. C263#1390semidirect
116. #99Dic263semidirect

Maximal subgroups

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

subgroupindex
C2×#225543872
#306818182
C2×#99×C2632
#1390263