Finite Group Databasebeta

← #46781113

Subgroups — #46781113

Order 33664.

214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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×#22554463C211yesmaximal, characteristic
2#30681992C211yesmaximal, characteristic, complemented
3#30681988C211yesmaximal, characteristic, complemented
4#30681663C211yesmaximal, characteristic, complemented
5#30681663C211yesmaximal, characteristic, complemented
6#30681662C211yesmaximal, characteristic
7#323×C263C211yesmaximal, characteristic
8#22554463—21no—
9#22554463—21no—
10#22554463—21no—
11#22554463—21no—
12C2×C4⋊Dic263C411yescharacteristic
13C2×Dic263⋊C4C411yescharacteristic
14C2×Dic263⋊C4C2211yescharacteristic
15C2×C22⋊Dic263C411yescharacteristic
16C2×C22⋊Dic263C411yescharacteristic
17C2×C4×Dic263C2211yescharacteristic
18Dic263⋊C8—21no—
19Dic263⋊C8—21no—
20C22⋊(C263⋊C8)C2211yescharacteristic
21C22⋊(C263⋊C8)C2211yescharacteristic
22#22554380—21no—
23C8×Dic263—21no—
24C2×C22⋊C4×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic
26C22⋊C8×C263C2211yescharacteristic
27C22×Dic263C2×C411yescharacteristic
28C22×Dic263C2×C411yescharacteristic
29C22×Dic263C2×C411yescharacteristic
30C22×Dic263C2×C411yescharacteristic
31C2×C263⋊C8—21no—
32C2×C263⋊C8—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263—21no—
35Dic263⋊C4—21no—
36Dic263⋊C4—21no—
37Dic263⋊C4—21no—
38Dic263⋊C4—21no—
39C22⋊Dic263—21no—
40C22⋊Dic263—21no—
41C22⋊Dic263—21no—
42C22⋊Dic263—21no—
43C4×Dic263D411yescharacteristic
44C4×Dic263D411yescharacteristic
45C4×Dic263D411yescharacteristic
46C4×Dic263D411yescharacteristic
47C24×C263C2×C411yescharacteristic
48C22×C4×C263C2×C411yescharacteristic
49C22×C4×C263C2311yescharacteristic
50C2×C8×C263—21no—
51C2×C8×C263—21no—
52C22⋊C4×C263—21no—
53C22⋊C4×C263—21no—
54C2×Dic263—21no—
55C2×Dic263—21no—
56C2×Dic263—21no—
57C2×Dic263—21no—
58C2×Dic263—21no—
59C2×Dic263—21no—
60C2×Dic263—41no—
61C2×Dic263—41no—
62C2×Dic263C22⋊C411yescharacteristic
63C2×Dic263C22⋊C411yescharacteristic
64C2×Dic263C22⋊C411yescharacteristic
65C2×Dic263C22⋊C411yescharacteristic
66C263⋊C8—41no—
67C263⋊C8—41no—
68C23×C263—21no—
69C23×C263—21no—
70C23×C263—21no—
71C23×C263—41no—
72C23×C263—41no—
73C23×C263C22×C411yescharacteristic
74C2×C4×C263—21no—
75C2×C4×C263—41no—
76C2×C4×C263—41no—
77C2×C4×C263C2×D411yescharacteristic
78C2×C4×C263C2×D411yescharacteristic
79C8×C263—41no—
80C8×C263—41no—
81C22×C263—21no—
82C22×C263—21no—
83C22×C263—41no—
84C22×C263—41no—
85C22×C263—41no—
86C22×C263—81no—
87C22×C263—81no—
88C22×C263C2×C22⋊C411yescharacteristic
89C22×C263#13111yescharacteristic
90C22×C263#13111yescharacteristic
91C4×C263—21no—
92C4×C263—21no—
93C4×C263—41no—
94Dic263—21no—
95Dic263—21no—
96Dic263—21no—
97Dic263—21no—
98Dic263—41no—
99Dic263—41no—
100C2×C263—21no—
101C2×C263—21no—
102C2×C263—81no—
103C2×C263#40811yescharacteristic
104C2×C263#41011yescharacteristic
105C2×C263#41311yescharacteristic
106C263#147311yescharacteristic, complemented, Sylow
107#1473—2631nomaximal, Sylow
108C2×#126—2631no—
109#432—2631no—
110#431—2631no—
111#324—2631no—
112#324—2631no—
113#323—2631no—
114#323D26311yescharacteristic
115#126—5261no—
116#126—5261no—
117#126—5261no—
118#126—5261no—
119C2×C4⋊C4—2631no—
120C2×C4⋊C4—2631no—
121C2×C4⋊C4—2631no—
122C2×C22⋊C4—2631no—
123C2×C22⋊C4—2631no—
124C2×C22⋊C4C2×D26311yescharacteristic
125C2×C42—2631no—
126C4⋊C8—5261no—
127C4⋊C8—5261no—
128C22⋊C8—2631no—
129C22⋊C8—2631no—
130C22⋊C8C2×D26311yescharacteristic
131C22⋊C8C2×D26311yescharacteristic
132#97—5261no—
133C4×C8—5261no—
134C24C4×D26311yescharacteristic
135C22×C4—2631no—
136C22×C4—2631no—
137C22×C4—2631no—
138C22×C4—2631no—
139C22×C4C4×D26311yescharacteristic
140C22×C4C22×D26311yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—5261no—
144C2×C8—5261no—
145C4⋊C4—5261no—
146C4⋊C4—5261no—
147C4⋊C4—5261no—
148C4⋊C4—5261no—
149C4⋊C4—5261no—
150C4⋊C4—5261no—
151C22⋊C4—21no—
152C22⋊C4—21no—
153C22⋊C4—5261no—
154C22⋊C4—5261no—
155C22⋊C4—5261no—
156C22⋊C4—5261no—
157C42—2631no—
158C42—2631no—
159C42—2631no—
160C42—2631no—
161C23—21no—
162C23—21no—
163C23—21no—
164C23—41no—
165C23—41no—
166C23C2×C4×D26311yescharacteristic
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—2631no—
171C2×C4—2631no—
172C2×C4—2631no—
173C2×C4—2631no—
174C2×C4—5261no—
175C2×C4—5261no—
176C2×C4—5261no—
177C2×C4—5261no—
178C2×C4—5261no—
179C2×C4—5261no—
180C2×C4—10521no—
181C2×C4—10521no—
182C2×C4D4×D26311yescharacteristic
183C2×C4D4×D26311yescharacteristic
184C8—41no—
185C8—41no—
186C8—10521no—
187C8—10521no—
188C22—21no—
189C22—21no—
190C22—41no—
191C22—41no—
192C22—41no—
193C22—81no—
194C22—81no—
195C22C22⋊C4×D26311yescharacteristic
196C22#2255447611yescharacteristic
197C22#2255447811yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—5261no—
202C4—5261no—
203C4—5261no—
204C4—5261no—
205C4—10521no—
206C4—10521no—
207C2—21no—
208C2—21no—
209C2—81no—
210C2#3068190311yescharacteristic
211C2#3068191011yescharacteristic
212C2#3068191911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC23×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#323×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC24×C263C2×C4
cosocleC22×C4×C263C23
hypercenter#323D263
hypocenterC263#1473
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #30681992C2semidirect
3. #30681988C2semidirect
4. #30681663C2semidirect
5. #30681663C2semidirect
106. C263#1473semidirect

Maximal subgroups

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

subgroupindex
C2×#225544632
#306819922
#306819882
#306816632
#306816622
#323×C2632
#1473263