Finite Group Databasebeta

← #46781065

Subgroups — #46781065

Order 33664.

332 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 113 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×C22⋊(C263⋊C8)C212yesmaximal, complemented
2#30681664C212yesmaximal, complemented
3#30681662C212yesmaximal, complemented
4C2×C4×D4×C263C211yesmaximal, characteristic
5C22×C263⋊C8—22no—
6C22⋊(C263⋊C8)—22no—
7C22⋊(C263⋊C8)C2214yes—
8C22×D4×C263C411yescharacteristic
9C23×C4×C263C411yescharacteristic
10C23×C4×C263C2211yescharacteristic
11C4×D4×C263—22no—
12C4×D4×C263—22no—
13C2×C4⋊C4×C263C2211yescharacteristic
14C2×C22⋊C4×C263C411yescharacteristic
15C2×C22⋊C4×C263C2211yescharacteristic
16C2×C42×C263C411yescharacteristic
17C2×C263⋊C8—24no—
18C2×C263⋊C8—44no—
19C24×C263C2×C411yescharacteristic
20C24×C263C2×C411yescharacteristic
21C2×D4×C263—22no—
22C2×D4×C263—22no—
23C2×D4×C263C814yescomplemented
24C22×C4×C263—21no—
25C22×C4×C263—21no—
26C22×C4×C263—42no—
27C22×C4×C263—42no—
28C22×C4×C263C2×C411yescharacteristic
29C22×C4×C263C2×C411yescharacteristic
30C22×C4×C263C2×C411yescharacteristic
31C22×C4×C263C2×C411yescharacteristic
32C22×C4×C263D412yes—
33C22×C4×C263D412yes—
34C22×C4×C263C2311yescharacteristic
35C4⋊C4×C263—22no—
36C22⋊C4×C263—22no—
37C22⋊C4×C263—22no—
38C42×C263—21no—
39C42×C263—21no—
40C263⋊C8—44no—
41C23×C263—21no—
42C23×C263—21no—
43C23×C263—41no—
44C23×C263—41no—
45C23×C263—41no—
46C23×C263—41no—
47C23×C263C22⋊C412yes—
48C23×C263C2×C812yes—
49C23×C263C2×C812yescomplemented
50C23×C263M1612yes—
51C23×C263C22×C411yescharacteristic
52D4×C263—28no—
53C2×C4×C263—21no—
54C2×C4×C263—21no—
55C2×C4×C263—22no—
56C2×C4×C263—24no—
57C2×C4×C263—21no—
58C2×C4×C263—21no—
59C2×C4×C263—42no—
60C2×C4×C263—41no—
61C2×C4×C263—42no—
62C2×C4×C263—42no—
63C2×C4×C263—41no—
64C2×C4×C263—41no—
65C2×C4×C263C22⋊C411yescharacteristic
66C2×C4×C263C22⋊C411yescharacteristic
67C2×C4×C263C2×C812yescomplemented
68C2×C4×C263C2×D412yes—
69C22×C263—21no—
70C22×C263—22no—
71C22×C263—21no—
72C22×C263—22no—
73C22×C263—22no—
74C22×C263—42no—
75C22×C263—42no—
76C22×C263—42no—
77C22×C263—42no—
78C22×C263—41no—
79C22×C263—41no—
80C22×C263C22⋊C814yes—
81C22×C263C2×C22⋊C411yescharacteristic
82C22×C263C22×C811yescharacteristic
83C22×C263C2×M1611yescharacteristic
84C4×C263—22no—
85C4×C263—21no—
86C4×C263—22no—
87C4×C263—41no—
88C4×C263—41no—
89C4×C263#9912yes—
90C2×C263—21no—
91C2×C263—21no—
92C2×C263—24no—
93C2×C263—42no—
94C2×C263C2×C22⋊C811yescharacteristic
95C2×C263C2×#9911yescharacteristic
96C2×C263#41311yescharacteristic
97C263#145911yescharacteristic, complemented, Sylow
98#1459—2631nomaximal, Sylow
99C2×C4×D4D26311yescharacteristic
100C2×C22⋊C8—2632no—
101#324—2632no—
102#323—2632no—
103C22×D4Dic26311yescharacteristic
104C23×C4Dic26311yescharacteristic
105C23×C4C2×D26311yescharacteristic
106C22×C8—5262no—
107C4×D4—22no—
108C4×D4—22no—
109C2×C4⋊C4C2×D26311yescharacteristic
110C2×C22⋊C4Dic26311yescharacteristic
111C2×C22⋊C4C2×D26311yescharacteristic
112C2×C42Dic26311yescharacteristic
113C22⋊C8—2634no—
114C22⋊C8—5262no—
115C24C2×Dic26311yescharacteristic
116C24C2×Dic26311yescharacteristic
117C2×D4—22no—
118C2×D4—22no—
119C2×D4C263⋊C814yescomplemented
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—42no—
123C22×C4—42no—
124C22×C4C2×Dic26311yescharacteristic
125C22×C4C2×Dic26311yescharacteristic
126C22×C4C2×Dic26311yescharacteristic
127C22×C4C2×Dic26311yescharacteristic
128C22×C4C22⋊D26312yes—
129C22×C4C22⋊D26312yes—
130C22×C4C22×D26311yescharacteristic
131C2×C8—5264no—
132C2×C8—10524no—
133C4⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C42—21no—
137C42—21no—
138C23—21no—
139C23—21no—
140C23—41no—
141C23—41no—
142C23—41no—
143C23—41no—
144C23C22⋊Dic26312yes—
145C23C2×C263⋊C812yes—
146C23C2×C263⋊C812yescomplemented
147C23#1686236012yes—
148C23C22×Dic26311yescharacteristic
149D4—28no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—24no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4C22⋊Dic26311yescharacteristic
163C2×C4C22⋊Dic26311yescharacteristic
164C2×C4C2×C263⋊C812yescomplemented
165C2×C4C2×C22⋊D26312yes—
166C8—10524no—
167C22—21no—
168C22—22no—
169C22—21no—
170C22—22no—
171C22—22no—
172C22—42no—
173C22—42no—
174C22—42no—
175C22—42no—
176C22—41no—
177C22—41no—
178C22C22⋊(C263⋊C8)14yes—
179C22C2×C22⋊Dic26311yescharacteristic
180C22C22×C263⋊C811yescharacteristic
181C22C2×#1686236011yescharacteristic
182C4—22no—
183C4—22no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4#2255438512yes—
188C2—21no—
189C2—21no—
190C2—24no—
191C2—42no—
192C2C2×C22⋊(C263⋊C8)11yescharacteristic
193C2C2×#2255438511yescharacteristic
194C2#3068192211yescharacteristic
subgroupG/H
centerC2×C4C22⋊Dic263
commutatorC22×C263C22×C8
FrattiniC22×C4C22×D263
FittingC2×C4×D4×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC22×D4×C263C4
cosocleC22×C4×C263C23
hypercenterC2×C4×D4D263
hypocenterC263#1459
LCSG ▷ C22×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊(C263⋊C8)C2semidirect
2. #30681664C2semidirect
3. #30681662C2semidirect
23. C2×D4×C263C8semidirect
49. C23×C263C2×C8semidirect
67. C2×C4×C263C2×C8semidirect
97. C263#1459semidirect
119. C2×D4C263⋊C8semidirect
146. C23C2×C263⋊C8semidirect
164. C2×C4C2×C263⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊(C263⋊C8)2
#306816642
#306816622
C2×C4×D4×C2632
#1459263