Finite Group Databasebeta

← #46783689

Subgroups — #46783689

Order 33664.

260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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
1#30682491C211yesmaximal, characteristic
2M16×Dic263C211yesmaximal, characteristic
3C4×Dic263⋊C4C211yesmaximal, characteristic
4#30681699C211yesmaximal, characteristic
5#30681698C211yesmaximal, characteristic
6#30681697C211yesmaximal, characteristic
7#339×C263C211yesmaximal, characteristic
8C2×#16862360C2211yescharacteristic
9#22554469C411yescharacteristic, complemented
10#22554469C411yescharacteristic, complemented
11#22554461C411yescharacteristic, complemented
12#22554461C411yescharacteristic, complemented
13#22554447—21no—
14#22554447—21no—
15C4×Dic526—21no—
16C4×Dic526—21no—
17#22554429C2211yescharacteristic
18C2×Dic263⋊C4—21no—
19C2×C4×Dic263C2211yescharacteristic
20C2×C4×Dic263C2211yescharacteristic
21#22554380—21no—
22C8×Dic263—21no—
23C263⋊#95—21no—
24C2×M16×C263C2211yescharacteristic
25#117×C263C2211yescharacteristic
26C2×C42×C263C2211yescharacteristic
27C2×Dic526—21no—
28C2×Dic526—21no—
29C22×Dic263—21no—
30C22×Dic263D411yescharacteristic
31C22×Dic263D411yescharacteristic
32#16862360—21no—
33#16862360Q812yescomplemented
34C2×C263⋊C8—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263—21no—
37C4⋊Dic263C2×C411yescharacteristic
38C4⋊Dic263C2×C411yescharacteristic
39Dic263⋊C4—24no—
40Dic263⋊C4—21no—
41Dic263⋊C4—21no—
42Dic263⋊C4—21no—
43Dic263⋊C4—21no—
44C22⋊Dic263—21no—
45C4×Dic263—21no—
46C4×Dic263—21no—
47C4×Dic263—21no—
48C4×Dic263C2×C411yescharacteristic
49C4×Dic263C2×C411yescharacteristic
50C4×Dic263D411yescharacteristic
51C4×Dic263D411yescharacteristic
52C22×C4×C263—21no—
53C22×C4×C263C2311yescharacteristic
54M16×C263—21no—
55M16×C263Q812yescomplemented
56C2×C8×C263—21no—
57C4⋊C4×C263C2×C411yescharacteristic
58C4⋊C4×C263C2×C411yescharacteristic
59C22⋊C4×C263—21no—
60C42×C263—21no—
61C42×C263—21no—
62C42×C263—21no—
63Dic526—42no—
64Dic526—42no—
65C2×Dic263—22no—
66C2×Dic263—22no—
67C2×Dic263—21no—
68C2×Dic263—21no—
69C2×Dic263—41no—
70C2×Dic263—41no—
71C2×Dic263—41no—
72C2×Dic263C22⋊C411yescharacteristic
73C2×Dic263C22⋊C411yescharacteristic
74C2×Dic263C22⋊C411yescharacteristic
75C2×Dic263C22⋊C411yescharacteristic
76C263⋊C8—22no—
77C23×C263C2×D411yescharacteristic
78C2×C4×C263—22no—
79C2×C4×C263—21no—
80C2×C4×C263—21no—
81C2×C4×C263—41no—
82C2×C4×C263—41no—
83C2×C4×C263C22×C411yescharacteristic
84C2×C4×C263C2×D411yescharacteristic
85C2×C4×C263C2×Q811yescharacteristic
86C2×C4×C263C2×Q811yescharacteristic
87C2×C4×C263#4111yescharacteristic
88C2×C4×C263#4111yescharacteristic
89C8×C263—22no—
90C22×C263—21no—
91C22×C263—21no—
92C22×C263C2×C22⋊C411yescharacteristic
93C22×C263#12411yescharacteristic
94C22×C263C4⋊Q811yescharacteristic
95C4×C263—42no—
96C4×C263—41no—
97C4×C263—41no—
98C4×C263C4×Q811yescharacteristic
99C4×C263C4×Q811yescharacteristic
100C4×C263C22⋊Q811yescharacteristic
101C4×C263C22⋊Q811yescharacteristic
102Dic263—21no—
103Dic263—21no—
104Dic263—21no—
105Dic263—42no—
106Dic263—41no—
107Dic263—41no—
108Dic263#10412yes—
109C2×C263—21no—
110C2×C263—21no—
111C2×C263#39111yescharacteristic
112C2×C263C2×#10411yescharacteristic
113C2×C263#42111yescharacteristic
114C263#198611yescharacteristic, complemented, Sylow
115#1986—2631nomaximal, Sylow
116#533—2631no—
117C4×M16—2631no—
118C4×C4⋊C4—2631no—
119#339—2631no—
120#339—2631no—
121#339—2631no—
122#339D26311yescharacteristic
123C2×M16—2631no—
124C2×M16C2×D26311yescharacteristic
125C4⋊Q8—2631no—
126C4⋊Q8—2631no—
127#125—2631no—
128#125—2631no—
129C22⋊Q8—5261no—
130C22⋊Q8—5261no—
131C4×Q8—5261no—
132C4×Q8—5261no—
133#117—2631no—
134#117C2×D26311yescharacteristic
135C2×C4⋊C4—5261no—
136C2×C42—2631no—
137C2×C42—2631no—
138C2×C42C2×D26311yescharacteristic
139#97—5261no—
140C4×C8—5261no—
141#95—5261no—
142C2×Q8—5261no—
143C2×Q8—5261no—
144C22×C4—21no—
145C22×C4—2631no—
146C22×C4—2631no—
147C22×C4—5261no—
148C22×C4C22×D26311yescharacteristic
149M16—21no—
150M16—2632no—
151M16—5261no—
152M16Dic52612yescomplemented
153C2×C8—21no—
154C2×C8—5261no—
155C4⋊C4—2631no—
156C4⋊C4—2631no—
157C4⋊C4—5261no—
158C4⋊C4—5261no—
159C4⋊C4—5261no—
160C4⋊C4—5261no—
161C4⋊C4—5261no—
162C4⋊C4—5261no—
163C4⋊C4—5264no—
164C4⋊C4C4×D26311yescharacteristic
165C4⋊C4C4×D26311yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—5261no—
168C42—21no—
169C42—21no—
170C42—21no—
171C42—2631no—
172C42—2631no—
173C42—2631no—
174C42—2631no—
175C42—5261no—
176C42—5261no—
177C42—5261no—
178C23D4×D26311yescharacteristic
179Q8—10522no—
180Q8—10522no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—2631no—
187C2×C4—2631no—
188C2×C4—2631no—
189C2×C4—2631no—
190C2×C4—5262no—
191C2×C4—5262no—
192C2×C4—5261no—
193C2×C4—5261no—
194C2×C4—10521no—
195C2×C4—10521no—
196C2×C4—10521no—
197C2×C4C2×C4×D26311yescharacteristic
198C2×C4D4×D26311yescharacteristic
199C2×C4Q8×D26311yescharacteristic
200C2×C4C2×Dic52611yescharacteristic
201C2×C4#1686237511yescharacteristic
202C2×C4#1686237611yescharacteristic
203C8—22no—
204C8—5262no—
205C22—21no—
206C22—21no—
207C22C22⋊C4×D26311yescharacteristic
208C22#2255445611yescharacteristic
209C22#2255446911yescharacteristic
210C4—42no—
211C4—41no—
212C4—41no—
213C4—2632no—
214C4—5261no—
215C4—5261no—
216C4—5261no—
217C4—10522no—
218C4—10521no—
219C4—10521no—
220C4#2255443511yescharacteristic
221C4C4×Dic52611yescharacteristic
222C4#2255444711yescharacteristic
223C4#2255444811yescharacteristic
224C2—21no—
225C2—21no—
226C2#3068184211yescharacteristic
227C2#104×D26311yescharacteristic
228C2#3068195311yescharacteristic
subgroupG/H
centerC2×C4D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#339×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC23×C263C2×D4
cosocleC22×C4×C263C23
hypercenter#339D263
hypocenterC263#1986
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
9. #22554469C4semidirect
10. #22554469C4semidirect
11. #22554461C4semidirect
12. #22554461C4semidirect
33. #16862360Q8semidirect
55. M16×C263Q8semidirect
114. C263#1986semidirect
152. M16Dic526semidirect

Maximal subgroups

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

subgroupindex
#306824912
M16×Dic2632
C4×Dic263⋊C42
#306816992
#306816982
#306816972
#339×C2632
#1986263