Finite Group Databasebeta

← #99×Dic263 #46782537

Subgroups — #99×Dic263 #46782537

Order 33664.

412 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 119 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×D4×Dic263C211yesmaximal, characteristic
2C2×#22554385C211yesmaximal, characteristic
3C22⋊C4×Dic263C212yesmaximal, complemented
4#30681704C212yesmaximal, complemented
5C2×#99×C263C211yesmaximal, characteristic
6C23×Dic263C411yescharacteristic, complemented
7C23×Dic263C2211yescharacteristic
8D4×Dic263—22no—
9D4×Dic263—22no—
10C2×C4⋊Dic263C411yescharacteristic, complemented
11C2×C22⋊Dic263C411yescharacteristic, complemented
12C2×C22⋊Dic263C2211yescharacteristic
13C2×C22⋊Dic263C2212yes—
14C2×C4×Dic263—22no—
15C2×C4×Dic263C411yescharacteristic, complemented
16#22554385C414yescomplemented
17C263⋊#95—22no—
18C22×D4×C263C2211yescharacteristic
19C2×C22⋊C4×C263C2212yes—
20#99×C263C414yescomplemented
21C22×Dic263—21no—
22C22×Dic263—21no—
23C22×Dic263—22no—
24C22×Dic263—42no—
25C22×Dic263—42no—
26C22×Dic263C2×C411yescharacteristic
27C22×Dic263C2×C411yescharacteristic
28C22×Dic263C2×C411yescharacteristic
29C22×Dic263C2×C411yescharacteristic
30C22×Dic263D412yes—
31C22×Dic263D412yes—
32C4⋊Dic263—22no—
33C22⋊Dic263—22no—
34C22⋊Dic263—22no—
35C22⋊Dic263—22no—
36C22⋊Dic263C2×C414yescomplemented
37C4×Dic263—21no—
38C4×Dic263—21no—
39C4×Dic263—44no—
40C24×C263C2×C411yescharacteristic
41C24×C263C2311yescharacteristic
42C2×D4×C263—22no—
43C2×D4×C263—22no—
44C2×D4×C263C2×C412yes—
45C2×D4×C263C2×C412yes—
46C22×C4×C263—22no—
47C22×C4×C263C2×C411yescharacteristic
48C22⋊C4×C263—22no—
49C22⋊C4×C263C2×C414yescomplemented
50C2×Dic263—24no—
51C2×Dic263—22no—
52C2×Dic263—21no—
53C2×Dic263—21no—
54C2×Dic263—24no—
55C2×Dic263—41no—
56C2×Dic263—42no—
57C2×Dic263—42no—
58C2×Dic263—42no—
59C2×Dic263—42no—
60C2×Dic263—42no—
61C2×Dic263—41no—
62C2×Dic263—41no—
63C2×Dic263C22⋊C411yescharacteristic
64C2×Dic263C22⋊C412yes—
65C2×Dic263C22⋊C411yescharacteristic
66C23×C263—21no—
67C23×C263—21no—
68C23×C263—41no—
69C23×C263—41no—
70C23×C263—41no—
71C23×C263—41no—
72C23×C263C4212yescomplemented
73C23×C263C22×C411yescharacteristic
74C23×C263C22×C411yescharacteristic
75C23×C263C22×C411yescharacteristic
76C23×C263C2×D412yes—
77C23×C263#4112yes—
78D4×C263—24no—
79D4×C263—24no—
80C2×C4×C263—21no—
81C2×C4×C263—21no—
82C2×C4×C263—24no—
83C2×C4×C263—42no—
84C2×C4×C263—42no—
85C2×C4×C263C4212yescomplemented
86C22×C263—22no—
87C22×C263—21no—
88C22×C263—22no—
89C22×C263—21no—
90C22×C263—22no—
91C22×C263—41no—
92C22×C263—41no—
93C22×C263—42no—
94C22×C263—42no—
95C22×C263—42no—
96C22×C263—41no—
97C22×C263—41no—
98C22×C263C2×C4211yescharacteristic
99C22×C263C2×C22⋊C411yescharacteristic
100C22×C263#11711yescharacteristic
101C22×C263C4×D412yes—
102C22×C263C4×D412yes—
103C4×C263—22no—
104C4×C263—44no—
105Dic263—21no—
106Dic263—22no—
107Dic263—44no—
108Dic263—41no—
109Dic263—41no—
110Dic263#9912yesdirect product factor
111C2×C263—22no—
112C2×C263—22no—
113C2×C263—21no—
114C2×C263—21no—
115C2×C263—42no—
116C2×C263C4×C22⋊C411yescharacteristic
117C2×C263C2×#9911yescharacteristic
118C2×C263#41011yescharacteristic
119C263C4×#9911yescharacteristic, complemented, Sylow
120C4×#99—2631nomaximal, Sylow
121C2×C4×D4—2631no—
122C2×#99—2631no—
123C2×#99D26311yescharacteristic
124C4×C22⋊C4—2632no—
125#342—2632no—
126C22×D4C2×D26311yescharacteristic
127C23×C4—2631no—
128C23×C4—2631no—
129C4×D4—5262no—
130C4×D4—5262no—
131C2×C4⋊C4—2631no—
132C2×C22⋊C4—2632no—
133C2×C22⋊C4—2631no—
134C2×C22⋊C4—2631no—
135C2×C22⋊C4C2×D26312yes—
136C2×C42—2631no—
137C2×C42—5262no—
138#99—2634no—
139#99Dic26314yesdirect product factor
140#95—5262no—
141C24C4×D26311yescharacteristic
142C24C22×D26311yescharacteristic
143C2×D4—22no—
144C2×D4—22no—
145C2×D4C4×D26312yes—
146C2×D4C2×Dic26312yes—
147C22×C4—22no—
148C22×C4—2631no—
149C22×C4—2632no—
150C22×C4—2631no—
151C22×C4—2632no—
152C22×C4—2631no—
153C22×C4—2631no—
154C22×C4—5261no—
155C22×C4—5261no—
156C22×C4—5262no—
157C22×C4—10522no—
158C22×C4—10522no—
159C22×C4C4×D26311yescharacteristic
160C4⋊C4—5262no—
161C22⋊C4—22no—
162C22⋊C4—2634no—
163C22⋊C4—5262no—
164C22⋊C4—5262no—
165C22⋊C4—5262no—
166C22⋊C4C2×Dic26314yescomplemented
167C42—5261no—
168C42—5261no—
169C42—10524no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23C4×Dic26312yescomplemented
177C23C2×C4×D26311yescharacteristic
178C23C2×C4×D26311yescharacteristic
179C23C22×Dic26311yescharacteristic
180C23D4×D26312yes—
181C23#1686237512yes—
182D4—24no—
183D4—24no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—24no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—2631no—
190C2×C4—2631no—
191C2×C4—2632no—
192C2×C4—5264no—
193C2×C4—5262no—
194C2×C4—5261no—
195C2×C4—5261no—
196C2×C4—5264no—
197C2×C4—10522no—
198C2×C4—10522no—
199C2×C4—10521no—
200C2×C4—10522no—
201C2×C4—10522no—
202C2×C4—10522no—
203C2×C4—10521no—
204C2×C4—10521no—
205C2×C4C4×Dic26312yescomplemented
206C22—22no—
207C22—21no—
208C22—22no—
209C22—21no—
210C22—22no—
211C22—41no—
212C22—41no—
213C22—42no—
214C22—42no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22C2×C4×Dic26311yescharacteristic
219C22C22⋊C4×D26311yescharacteristic
220C22#2255442611yescharacteristic
221C22(C22⋊D263)⋊C412yes—
222C22D4×Dic26312yes—
223C4—22no—
224C4—44no—
225C4—2632no—
226C4—5261no—
227C4—5262no—
228C4—10524no—
229C4—10521no—
230C4—10521no—
231C2—22no—
232C2—22no—
233C2—21no—
234C2—21no—
235C2—42no—
236C2C22⋊C4×Dic26311yescharacteristic
237C2#99×D26311yescharacteristic
238C2#3068191011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC22×C263C2×C42
FrattiniC24C22×D263
FittingC2×#99×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC22×D4×C263C22
cosocleC24×C263C23
hypercenterC2×#99D263
hypocenterC263C4×#99
LCSG ▷ C22×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. C22⋊C4×Dic263C2semidirect
4. #30681704C2semidirect
6. C23×Dic263C4semidirect
10. C2×C4⋊Dic263C4semidirect
11. C2×C22⋊Dic263C4semidirect
15. C2×C4×Dic263C4semidirect
16. #22554385C4semidirect
20. #99×C263C4semidirect
36. C22⋊Dic263C2×C4semidirect
49. C22⋊C4×C263C2×C4semidirect
72. C23×C263C42semidirect
85. C2×C4×C263C42semidirect
110. Dic263#99direct (N × H)
119. C263C4×#99semidirect
139. #99Dic263direct (N × H)
166. C22⋊C4C2×Dic263semidirect
176. C23C4×Dic263semidirect
205. C2×C4C4×Dic263semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic2632
C2×#225543852
C22⋊C4×Dic2632
#306817042
C2×#99×C2632
C4×#99263