Finite Group Databasebeta

← #46780865

Subgroups — #46780865

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
2C2×#22554385C211yesmaximal, characteristic
3#386×C263C211yesmaximal, characteristic
4C2×#16862360—21no—
5C2×C22⋊Dic263—21no—
6#22554387—21no—
7#22554387C412yescomplemented
8#22554385—21no—
9#22554385C412yescomplemented
10C22×D4×C263C2211yescharacteristic
11C23×C4×C263C411yescharacteristic, complemented
12C2×C22⋊C4×C263—21no—
13C2×C22⋊C4×C263C411yescharacteristic, complemented
14#95×C263—21no—
15C22×Dic263—41no—
16#16862360—22no—
17#16862360—41no—
18C2×C263⋊C8—41no—
19C22⋊Dic263—22no—
20C22⋊Dic263—41no—
21C24×C263C2×C411yescharacteristic
22C24×C263D411yescharacteristic
23C2×D4×C263—41no—
24C2×D4×C263—41no—
25C2×D4×C263C2×C411yescharacteristic
26C2×D4×C263C2×C411yescharacteristic
27C2×D4×C263D411yescharacteristic
28C2×D4×C263Q811yescharacteristic
29C22×C4×C263—21no—
30C22×C4×C263—21no—
31C22×C4×C263—42no—
32C22×C4×C263—41no—
33C22×C4×C263D411yescharacteristic
34C22⋊C4×C263—42no—
35C22⋊C4×C263—41no—
36C2×Dic263—42no—
37C2×Dic263—81no—
38C2×Dic263—81no—
39C263⋊C8—42no—
40C23×C263—21no—
41C23×C263—21no—
42C23×C263—21no—
43C23×C263—21no—
44C23×C263—41no—
45C23×C263—41no—
46C23×C263—41no—
47C23×C263—41no—
48C23×C263C4211yescharacteristic
49C23×C263C22⋊C411yescharacteristic
50C23×C263C22⋊C411yescharacteristic
51C23×C263C4⋊C411yescharacteristic
52C23×C263C4⋊C411yescharacteristic
53D4×C263—41no—
54D4×C263—41no—
55D4×C263—41no—
56D4×C263—41no—
57C2×C4×C263—21no—
58C2×C4×C263—21no—
59C2×C4×C263—22no—
60C2×C4×C263—41no—
61C2×C4×C263—42no—
62C2×C4×C263—41no—
63C2×C4×C263—42no—
64C2×C4×C263—41no—
65C2×C4×C263—41no—
66C2×C4×C263—41no—
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—42no—
91C4×C263—81no—
92Dic263—82no—
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×#99—2631no—
106#386D26311yescharacteristic
107C22×D4C2×D26311yescharacteristic
108C23×C4Dic26311yescharacteristic, complemented
109C2×M16—5261no—
110C2×C22⋊C4—21no—
111C2×C22⋊C4—5261no—
112C2×C22⋊C4Dic26311yescharacteristic, complemented
113#100—2632no—
114#100—5261no—
115#99—2632no—
116#99—5261no—
117#95—21no—
118C24C2×Dic26311yescharacteristic
119C24C22⋊D26311yescharacteristic
120C2×D4—41no—
121C2×D4—41no—
122C2×D4C4×D26311yescharacteristic
123C2×D4C4×D26311yescharacteristic
124C2×D4D105211yescharacteristic
125C2×D4Dic52611yescharacteristic
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—42no—
129C22×C4—41no—
130C22×C4—10521no—
131C22×C4C22⋊D26311yescharacteristic
132M16—5262no—
133M16—10521no—
134C2×C8—10521no—
135C22⋊C4—42no—
136C22⋊C4—41no—
137C22⋊C4—5262no—
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
151C23C4⋊Dic26311yescharacteristic
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—10522no—
167C2×C4—21041no—
168C2×C4—21041no—
169C2×C4(C2×D263)⋊C411yescharacteristic
170C2×C4Dic263⋊C411yescharacteristic
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#2255438511yescharacteristic
190C22#2255438511yescharacteristic
191C4—21no—
192C4—21no—
193C4—42no—
194C4—81no—
195C4—21042no—
196C2—21no—
197C2—21no—
198C2—41no—
199C2—41no—
200C2—41no—
201C2—41no—
202C2#3068170511yescharacteristic
203C2#3068172511yescharacteristic
204C2#3068172811yescharacteristic
subgroupG/H
centerC22#22554385
commutatorC23×C263C42
FrattiniC22×D4C2×D263
Fitting#386×C263C2
socleC22×C263#99
prime radical, cosocleC22×D4×C263C22
hypercenter#386D263
hypocenterC263#1390
LCSG ▷ C23×C263 ▷ C22×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #386

Complements

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

NH ≅ G/Ntype
7. #22554387C4semidirect
9. #22554385C4semidirect
11. C23×C4×C263C4semidirect
13. C2×C22⋊C4×C263C4semidirect
102. C263#1390semidirect
108. C23×C4Dic263semidirect
112. C2×C22⋊C4Dic263semidirect

Maximal subgroups

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

subgroupindex
C2×#225543872
C2×#225543852
#386×C2632
#1390263