Finite Group Databasebeta

← #46781271

Subgroups — #46781271

Order 33664.

242 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 63 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#30682474C211yesmaximal, characteristic
2#30681992C211yesmaximal, characteristic, complemented
3#30681789C211yesmaximal, characteristic, complemented
4#30681675C211yesmaximal, characteristic, complemented
5#30681673C211yesmaximal, characteristic
6#30681671C211yesmaximal, characteristic
7#328×C263C211yesmaximal, characteristic, complemented
8#22554465—21no—
9#22554461C411yescharacteristic, complemented
10#22554459C411yescharacteristic, complemented
11#22554454—21no—
12#22554444C2211yescharacteristic
13Q8×Dic263C411yescharacteristic, complemented
14#22554432C411yescharacteristic, complemented
15(C22⋊D263)⋊C4—21no—
16#22554428—21no—
17C2×Dic263⋊C4—21no—
18C2×C4×Dic263—21no—
19C2×C4×Dic263C2211yescharacteristic
20Dic263⋊C8—21no—
21C22⋊(C263⋊C8)C2211yescharacteristic
22#22554380—21no—
23C263⋊#95C2211yescharacteristic
24C22⋊Q8×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic
26#95×C263C2211yescharacteristic
27C2×D1052C2×C411yescharacteristic
28C2×C22⋊D263—21no—
29C22×Dic263—21no—
30C22×Dic263D411yescharacteristic
31C22×Dic263D411yescharacteristic
32C2×C4×D263—21no—
33C2×C263⋊C8—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263C2×C411yescharacteristic
37Dic263⋊C4—24no—
38Dic263⋊C4—21no—
39(C2×D263)⋊C4—21no—
40(C2×D263)⋊C4—21no—
41(C2×D263)⋊C4—21no—
42(C2×D263)⋊C4—21no—
43C4×Dic263—21no—
44C4×Dic263—42no—
45C4×Dic263C2×C411yescharacteristic
46C4×Dic263C2×C411yescharacteristic
47C4×Dic263D411yescharacteristic
48C4×Dic263D411yescharacteristic
49C2×Q8×C263C2×C411yescharacteristic
50C22×C4×C263—21no—
51C22×C4×C263C2311yescharacteristic
52C2×C8×C263—21no—
53C4⋊C4×C263—21no—
54C4⋊C4×C263C2×C411yescharacteristic
55C22⋊C4×C263—21no—
56C22×D263—21no—
57D1052—41no—
58C22⋊D263—41no—
59C22⋊D263—41no—
60C2×Dic263—21no—
61C2×Dic263—21no—
62C2×Dic263—22no—
63C2×Dic263—22no—
64C2×Dic263—21no—
65C2×Dic263—41no—
66C2×Dic263—41no—
67C2×Dic263C22⋊C411yescharacteristic
68C2×Dic263C22⋊C411yescharacteristic
69C2×Dic263C22⋊C411yescharacteristic
70C2×Dic263C22⋊C411yescharacteristic
71C4×D263—42no—
72C263⋊C8—41no—
73C23×C263C2×D411yescharacteristic
74Q8×C263—41no—
75C2×C4×C263—22no—
76C2×C4×C263—21no—
77C2×C4×C263—21no—
78C2×C4×C263—41no—
79C2×C4×C263—41no—
80C2×C4×C263—41no—
81C2×C4×C263C22×C411yescharacteristic
82C2×C4×C263C2×D411yescharacteristic
83C8×C263—41no—
84C22×C263—21no—
85C22×C263—21no—
86C22×C263C2×C22⋊C411yescharacteristic
87C22×C263AGL(1,ℤ/8)11yescharacteristic
88C22×C263#13711yescharacteristic
89C2×D263—41no—
90C2×D263—41no—
91C2×D263—41no—
92C4×C263—21no—
93C4×C263—21no—
94C4×C263—42no—
95C4×C263—41no—
96C4×C263—41no—
97Dic263—21no—
98Dic263—21no—
99Dic263—21no—
100Dic263—42no—
101Dic263—41no—
102Dic263#10412yes—
103C2×C263—21no—
104C2×C263—21no—
105C2×C263#41011yescharacteristic
106C2×C263#41711yescharacteristic
107C2×C263C2×#10411yescharacteristic
108D263—81no—
109C263#150911yescharacteristic, complemented, Sylow
110#1509—2631nomaximal, Sylow
111#529—2631no—
112#432—2631no—
113C4×C4⋊C4—2631no—
114#328—2631no—
115#328D26311yescharacteristic, complemented
116#327—2631no—
117#327—2631no—
118#126—5261no—
119#125—2631no—
120#124—2631no—
121#123—5261no—
122C22⋊Q8C2×D26311yescharacteristic
123#121—2631no—
124C4×Q8—2631no—
125C4×D4—2631no—
126C4×D4—5261no—
127#117—5261no—
128C2×C4⋊C4—5261no—
129C2×C42—2631no—
130C2×C42—5261no—
131C4⋊C8—5261no—
132C22⋊C8—2631no—
133C22⋊C8C2×D26311yescharacteristic
134#97—5261no—
135#95—2631no—
136#95C2×D26311yescharacteristic
137C2×Q8C4×D26311yescharacteristic
138C2×D4—2631no—
139C2×D4—5261no—
140C22×C4—21no—
141C22×C4—2631no—
142C22×C4—2631no—
143C22×C4—5261no—
144C22×C4—5261no—
145C22×C4C22×D26311yescharacteristic
146C2×C8—21no—
147C2×C8—5261no—
148C4⋊C4—21no—
149C4⋊C4—2631no—
150C4⋊C4—5261no—
151C4⋊C4—5261no—
152C4⋊C4—5261no—
153C4⋊C4—5264no—
154C4⋊C4C4×D26311yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—5261no—
157C22⋊C4—5261no—
158C22⋊C4—5261no—
159C22⋊C4—5261no—
160C42—2631no—
161C42—2631no—
162C42—2631no—
163C42—2631no—
164C42—5261no—
165C42—10522no—
166C23—5261no—
167C23D4×D26311yescharacteristic
168Q8—41no—
169D4—10521no—
170D4—10521no—
171D4—10521no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—2631no—
179C2×C4—2631no—
180C2×C4—2631no—
181C2×C4—2631no—
182C2×C4—5262no—
183C2×C4—5261no—
184C2×C4—5261no—
185C2×C4—5262no—
186C2×C4—5261no—
187C2×C4—10522no—
188C2×C4—10521no—
189C2×C4—10521no—
190C2×C4C2×C4×D26311yescharacteristic
191C2×C4D4×D26311yescharacteristic
192C8—41no—
193C8—10521no—
194C22—21no—
195C22—21no—
196C22—10521no—
197C22—10521no—
198C22—10521no—
199C22C22⋊C4×D26311yescharacteristic
200C22#2255449711yescharacteristic
201C22#2255450211yescharacteristic
202C4—21no—
203C4—21no—
204C4—42no—
205C4—41no—
206C4—41no—
207C4—2632no—
208C4—5261no—
209C4—5261no—
210C4—5261no—
211C4—10522no—
212C4—10521no—
213C2—21no—
214C2—21no—
215C2—21041no—
216C2#3068191011yescharacteristic
217C2#3068193811yescharacteristic
218C2#104×D26311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#328×C263C2
socleC22×C263C2×C22⋊C4
prime radical#22554444C22
cosocleC22×C4×C263C23
hypercenter#328D263
hypocenterC263#1509
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #30681992C2semidirect
3. #30681789C2semidirect
4. #30681675C2semidirect
7. #328×C263C2semidirect
9. #22554461C4semidirect
10. #22554459C4semidirect
13. Q8×Dic263C4semidirect
14. #22554432C4semidirect
109. C263#1509semidirect
115. #328D263semidirect

Maximal subgroups

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

subgroupindex
#306824742
#306819922
#306817892
#306816752
#306816732
#306816712
#328×C2632
#1509263