Finite Group Databasebeta

← #324×D263 #46781055

Subgroups — #324×D263 #46781055

Order 33664.

328 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4⋊C4×D263C211yesmaximal, characteristic
2C22⋊C8×D263C212yesmaximal
3#30681664C211yesmaximal, characteristic, complemented
4#30681663C212yesmaximal, complemented
5#324×C263C211yesmaximal, characteristic, complemented
6C22×C4×D263C411yescharacteristic
7C22×C4×D263C411yescharacteristic
8C22×C4×D263C2211yescharacteristic
9C2×C8×D263—22no—
10C2×C4⋊Dic263C411yescharacteristic
11C2×Dic263⋊C4C411yescharacteristic
12C2×Dic263⋊C4C2211yescharacteristic
13C4⋊C4×D263—22no—
14C4⋊C4×D263—22no—
15C22⋊(C263⋊C8)C2212yes—
16(C2×D263)⋊C8—22no—
17C2×C4⋊C4×C263C2211yescharacteristic
18C22⋊C8×C263C2212yes—
19C23×D263C2×C411yescharacteristic
20C22×Dic263C2×C411yescharacteristic
21C22×Dic263C2×C411yescharacteristic
22C22×Dic263C2×C411yescharacteristic
23C2×C4×D263—21no—
24C2×C4×D263—21no—
25C2×C4×D263—22no—
26C2×C4×D263—21no—
27C2×C4×D263—21no—
28C2×C4×D263—42no—
29C2×C4×D263—42no—
30C2×C4×D263C814yescomplemented
31C2×C4×D263D412yes—
32C2×C4×D263D412yes—
33C2×C263⋊C8—22no—
34C8×D263—44no—
35C4⋊Dic263—22no—
36Dic263⋊C4—22no—
37Dic263⋊C4—22no—
38C22×C4×C263C2×C411yescharacteristic
39C22×C4×C263C2×C411yescharacteristic
40C22×C4×C263C2311yescharacteristic
41C2×C8×C263—22no—
42C4⋊C4×C263—22no—
43C22×D263—22no—
44C22×D263—22no—
45C22×D263C22⋊C411yescharacteristic
46C22×D263C22⋊C411yescharacteristic
47C22×D263C2×C812yes—
48C22×D263M1612yes—
49C2×Dic263—21no—
50C2×Dic263—21no—
51C2×Dic263—21no—
52C2×Dic263—41no—
53C2×Dic263—41no—
54C2×Dic263C22⋊C412yes—
55C2×Dic263C2×C812yescomplemented
56C4×D263—24no—
57C4×D263—24no—
58C4×D263—24no—
59C4×D263—42no—
60C4×D263—42no—
61C4×D263—42no—
62C263⋊C8—42no—
63C23×C263C22×C411yescharacteristic
64C2×C4×C263—21no—
65C2×C4×C263—21no—
66C2×C4×C263—21no—
67C2×C4×C263—41no—
68C2×C4×C263—41no—
69C2×C4×C263C2×C812yescomplemented
70C2×C4×C263C2×D412yes—
71C8×C263—42no—
72C22×C263—21no—
73C22×C263—21no—
74C22×C263C2×C22⋊C411yescharacteristic
75C22×C263C22×C811yescharacteristic
76C22×C263C2×M1611yescharacteristic
77C2×D263—21no—
78C2×D263—21no—
79C2×D263—24no—
80C2×D263—24no—
81C2×D263C22⋊C812yes—
82C2×D263C22⋊C812yes—
83C2×D263#9912yes—
84C2×D263#10112yes—
85C4×C263—22no—
86C4×C263—22no—
87C4×C263—41no—
88Dic263—22no—
89Dic263—22no—
90Dic263—41no—
91C2×C263—21no—
92C2×C263—21no—
93C2×C263C2×C22⋊C811yescharacteristic
94C2×C263C2×#9911yescharacteristic
95C2×C263C2×#10111yescharacteristic
96D263—22no—
97D263#32414yesdirect product factor
98C263C2×#32411yescharacteristic, complemented, Sylow
99C2×#324—2631nomaximal, Sylow
100C22×C4⋊C4—2631no—
101C2×C22⋊C8—2632no—
102#324—2631no—
103#324—2632no—
104#324D26311yescharacteristic, direct product factor
105C23×C4—2631no—
106C23×C4—2631no—
107C23×C4—2631no—
108C22×C8—5262no—
109C2×C4⋊C4—2631no—
110C2×C4⋊C4—2631no—
111C2×C4⋊C4—2631no—
112C2×C4⋊C4—5262no—
113C2×C4⋊C4—5262no—
114C2×C4⋊C4C2×D26311yescharacteristic
115C22⋊C8—2632no—
116C22⋊C8—5262no—
117C22⋊C8C2×D26312yes—
118C24—2631no—
119C22×C4—2631no—
120C22×C4—2631no—
121C22×C4—2634no—
122C22×C4—2632no—
123C22×C4—2632no—
124C22×C4—2631no—
125C22×C4—5261no—
126C22×C4—5261no—
127C22×C4—5262no—
128C22×C4—5261no—
129C22×C4—5261no—
130C22×C4—10522no—
131C22×C4—10522no—
132C22×C4C4×D26311yescharacteristic
133C22×C4C4×D26311yescharacteristic
134C22×C4C22×D26311yescharacteristic
135C2×C8—22no—
136C2×C8—5262no—
137C2×C8—10524no—
138C4⋊C4—22no—
139C4⋊C4—5262no—
140C4⋊C4—5262no—
141C4⋊C4—5262no—
142C23—2631no—
143C23—2631no—
144C23—2632no—
145C23—2632no—
146C23—5262no—
147C23—5262no—
148C23C2×C4×D26311yescharacteristic
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—2632no—
155C2×C4—2632no—
156C2×C4—5264no—
157C2×C4—5264no—
158C2×C4—5264no—
159C2×C4—5261no—
160C2×C4—5261no—
161C2×C4—5261no—
162C2×C4—10522no—
163C2×C4—10522no—
164C2×C4—10522no—
165C2×C4—10521no—
166C2×C4—10521no—
167C2×C4C8×D26312yescomplemented
168C2×C4D4×D26312yes—
169C8—42no—
170C8—10522no—
171C22—21no—
172C22—21no—
173C22—2632no—
174C22—2632no—
175C22—2632no—
176C22—2632no—
177C22—5264no—
178C22—5264no—
179C22—5261no—
180C22—5261no—
181C22C22⋊C4×D26311yescharacteristic
182C22C2×C8×D26311yescharacteristic
183C22M16×D26311yescharacteristic
184C4—22no—
185C4—22no—
186C4—41no—
187C4—5262no—
188C4—5262no—
189C4—10521no—
190C2—21no—
191C2—21no—
192C2—2634no—
193C2—5262no—
194C2C22⋊C8×D26311yescharacteristic
195C2#99×D26311yescharacteristic
196C2#101×D26311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC22×C263C22×C8
FrattiniC22×C4C22×D263
Fitting#324×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC23×D263C2×C4
cosocleC22×C4×C263C23
hypercenter#324D263
hypocenterC263C2×#324
LCSG ▷ C22×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
3. #30681664C2semidirect
4. #30681663C2semidirect
5. #324×C263C2semidirect
30. C2×C4×D263C8semidirect
55. C2×Dic263C2×C8semidirect
69. C2×C4×C263C2×C8semidirect
97. D263#324direct (N × H)
98. C263C2×#324semidirect
104. #324D263direct (N × H)
167. C2×C4C8×D263semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D2632
C22⋊C8×D2632
#306816642
#306816632
#324×C2632
C2×#324263