Finite Group Databasebeta

← #46781688

Subgroups — #46781688

Order 33664.

266 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 51 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#30682567C211yesmaximal, characteristic, complemented
2#30682091C211yesmaximal, characteristic
3#30682088C211yesmaximal, characteristic
4#30681856C211yesmaximal, characteristic
5#30681674C211yesmaximal, characteristic, complemented
6#30681663C211yesmaximal, characteristic, complemented
7#328×C263C211yesmaximal, characteristic, complemented
8C22×D1052C2211yescharacteristic
9C2×#16862365—21no—
10C2×#16862363—21no—
11#22554469—21no—
12#22554468—21no—
13#22554460—21no—
14#22554460—21no—
15#22554449C2211yescharacteristic
16#22554447—21no—
17#22554426—21no—
18C2×Dic263⋊C4C2211yescharacteristic
19C2×(C2×D263)⋊C4—21no—
20C2×(C2×D263)⋊C4—21no—
21#22554392—21no—
22#22554390—21no—
23C22⋊(C263⋊C8)C2211yescharacteristic
24C22⋊Q8×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic
26#95×C263C2211yescharacteristic
27C23×D263—21no—
28C2×Dic526—21no—
29C2×Dic526D411yescharacteristic
30C2×D1052—21no—
31C2×D1052—21no—
32C2×D1052—42no—
33C22×Dic263D411yescharacteristic
34C22×Dic263D411yescharacteristic
35#16862365—42no—
36#16862363—42no—
37C2×C263⋊C8—21no—
38C4⋊Dic263—21no—
39C4⋊Dic263D411yescharacteristic
40Dic263⋊C4—21no—
41Dic263⋊C4—21no—
42Dic263⋊C4—21no—
43Dic263⋊C4—21no—
44Dic263⋊C4—21no—
45Dic263⋊C4—21no—
46Dic263⋊C4—21no—
47C22⋊Dic263—21no—
48(C2×D263)⋊C4—42no—
49(C2×D263)⋊C4—42no—
50C4×Dic263—21no—
51C4×Dic263—21no—
52C2×Q8×C263D411yescharacteristic
53C22×C4×C263—21no—
54C22×C4×C263C2311yescharacteristic
55C2×C8×C263—21no—
56C4⋊C4×C263—21no—
57C4⋊C4×C263D411yescharacteristic
58C22⋊C4×C263—21no—
59C22×D263—22no—
60C22×D263—41no—
61C22×D263—41no—
62C22×D263—41no—
63C22×D263—41no—
64C22×D263—41no—
65C22×D263—41no—
66Dic526—41no—
67Dic526—81no—
68D1052—22no—
69D1052—22no—
70D1052—41no—
71D1052—41no—
72C2×Dic263—21no—
73C2×Dic263—21no—
74C2×Dic263—21no—
75C2×Dic263—21no—
76C2×Dic263—21no—
77C2×Dic263—41no—
78C2×Dic263SD1612yescomplemented
79C263⋊C8—41no—
80C23×C263C2×D411yescharacteristic
81Q8×C263—41no—
82C2×C4×C263—21no—
83C2×C4×C263—21no—
84C2×C4×C263—41no—
85C2×C4×C263—41no—
86C2×C4×C263—41no—
87C2×C4×C263—41no—
88C2×C4×C263C2×D411yescharacteristic
89C2×C4×C263C2×D411yescharacteristic
90C8×C263—41no—
91C22×C263—21no—
92C22×C263—21no—
93C22×C263#12011yescharacteristic
94C22×C263C2×SD1611yescharacteristic
95C22×C263#13711yescharacteristic
96C2×D263—42no—
97C2×D263—42no—
98C2×D263—42no—
99C2×D263—81no—
100C2×D263—81no—
101C2×D263—81no—
102C2×D263—81no—
103C4×C263—21no—
104C4×C263—21no—
105C4×C263—41no—
106C4×C263—41no—
107C4×C263—81no—
108Dic263—22no—
109Dic263—41no—
110Dic263—41no—
111Dic263—41no—
112C2×C263—21no—
113C2×C263—21no—
114C2×C263#44811yescharacteristic
115C2×C263#45411yescharacteristic
116C2×C263B(4,𝔽2)11yescharacteristic
117D263—82no—
118C263#159911yescharacteristic, complemented, Sylow
119#1599—2631nomaximal, Sylow
120#544—2631no—
121#450—2631no—
122#450—2631no—
123#394—2631no—
124#328—2631no—
125#328D26311yescharacteristic, complemented
126#324—2631no—
127C22×D4—2631no—
128C2×SD16—5261no—
129C2×SD16—5261no—
130C4⋊Q8—5261no—
131C4⋊Q8—5261no—
132#125—5261no—
133#125—5261no—
134C22⋊Q8—2631no—
135C22⋊Q8—5261no—
136C22⋊Q8C2×D26311yescharacteristic
137#117—5261no—
138C2×C4⋊C4—2631no—
139C2×C22⋊C4—5261no—
140C2×C22⋊C4—5261no—
141#102—5261no—
142#102—5261no—
143C22⋊C8—2631no—
144C22⋊C8C2×D26311yescharacteristic
145#95C2×D26311yescharacteristic
146C24—5261no—
147C2×Q8—2631no—
148C2×Q8—5261no—
149C2×Q8D105211yescharacteristic
150C2×D4—5261no—
151C2×D4—5261no—
152C2×D4—10522no—
153C22×C4—21no—
154C22×C4—2631no—
155C22×C4—2631no—
156C22×C4C22×D26311yescharacteristic
157SD16—10522no—
158SD16—10522no—
159C2×C8—21no—
160C2×C8—5261no—
161C4⋊C4—21no—
162C4⋊C4—2631no—
163C4⋊C4—5261no—
164C4⋊C4—5261no—
165C4⋊C4—5261no—
166C4⋊C4—5261no—
167C4⋊C4—5261no—
168C4⋊C4—5261no—
169C4⋊C4—5261no—
170C4⋊C4—5261no—
171C4⋊C4D105211yescharacteristic
172C22⋊C4—21no—
173C22⋊C4—5261no—
174C22⋊C4—10522no—
175C22⋊C4—10522no—
176C42—5261no—
177C42—5261no—
178C23—5262no—
179C23—10521no—
180C23—10521no—
181C23—10521no—
182C23—10521no—
183C23—10521no—
184C23—10521no—
185C23D4×D26311yescharacteristic
186Q8—41no—
187Q8—10521no—
188Q8—21041no—
189D4—5262no—
190D4—5262no—
191D4—10521no—
192D4—10521no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—2632no—
200C2×C4—5261no—
201C2×C4—5261no—
202C2×C4—5261no—
203C2×C4—5261no—
204C2×C4—5261no—
205C2×C4—10521no—
206C2×C4D4×D26311yescharacteristic
207C2×C4C2×D105211yescharacteristic
208C8—41no—
209C8—10521no—
210C22—21no—
211C22—21no—
212C22—10522no—
213C22—10522no—
214C22—10522no—
215C22—21041no—
216C22—21041no—
217C22—21041no—
218C22—21041no—
219C22#2255444011yescharacteristic
220C22SD16×D26311yescharacteristic
221C22#2255450211yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—41no—
226C4—81no—
227C4—5262no—
228C4—10521no—
229C4—10521no—
230C4—10521no—
231C2—21no—
232C2—21no—
233C2—21042no—
234C2#3068207811yescharacteristic
235C2#3068211211yescharacteristic
236C2#3068212611yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#328×C263C2
socleC22×C263#120
prime radicalC22×D1052C22
hypercenter#328D263
hypocenterC263#1599
LCSG ▷ C22×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
1. #30682567C2semidirect
5. #30681674C2semidirect
6. #30681663C2semidirect
7. #328×C263C2semidirect
78. C2×Dic263SD16semidirect
118. C263#1599semidirect
125. #328D263semidirect

Maximal subgroups

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

subgroupindex
#306825672
#306820912
#306820882
#306818562
#306816742
#306816632
#328×C2632
#1599263