Finite Group Databasebeta

← #46781685

Subgroups — #46781685

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#30682089C211yesmaximal, characteristic
3#30681852C211yesmaximal, characteristic
4#30681676C211yesmaximal, characteristic, complemented
5#30681675C211yesmaximal, characteristic, complemented
6#30681663C211yesmaximal, characteristic, complemented
7#450×C263C211yesmaximal, characteristic
8C2×#16862364—21no—
9#22554469—21no—
10#22554468—21no—
11#22554460—21no—
12#22554460—21no—
13#22554449C2211yescharacteristic
14#22554447—21no—
15#22554426—21no—
16C2×Dic263⋊C4C2211yescharacteristic
17C2×C22⋊Dic263—21no—
18C2×C22⋊Dic263—21no—
19#22554391—21no—
20C22⋊(C263⋊C8)C2211yescharacteristic
21C263⋊#95C2211yescharacteristic
22C22×D4×C263C2211yescharacteristic
23C2×SD16×C263—21no—
24C22⋊Q8×C263C2211yescharacteristic
25#102×C263—21no—
26C22⋊C8×C263C2211yescharacteristic
27C2×Dic526—21no—
28C2×Dic526D411yescharacteristic
29C22×Dic263—21no—
30C22×Dic263D411yescharacteristic
31C22×Dic263D411yescharacteristic
32#16862364—42no—
33C2×C263⋊C8—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263D411yescharacteristic
36Dic263⋊C4—21no—
37Dic263⋊C4—21no—
38Dic263⋊C4—21no—
39Dic263⋊C4—21no—
40Dic263⋊C4—21no—
41Dic263⋊C4—21no—
42Dic263⋊C4—21no—
43C22⋊Dic263—21no—
44C22⋊Dic263—42no—
45C22⋊Dic263—42no—
46C4×Dic263—21no—
47C4×Dic263—21no—
48C24×C263—21no—
49C2×Q8×C263D411yescharacteristic
50C2×D4×C263—21no—
51C2×D4×C263—21no—
52C2×D4×C263—42no—
53C22×C4×C263C2311yescharacteristic
54SD16×C263—42no—
55C2×C8×C263—21no—
56C4⋊C4×C263—21no—
57C4⋊C4×C263D411yescharacteristic
58C22⋊C4×C263—21no—
59Dic526—41no—
60Dic526—81no—
61C2×Dic263—21no—
62C2×Dic263—21no—
63C2×Dic263—21no—
64C2×Dic263—21no—
65C2×Dic263—21no—
66C2×Dic263—41no—
67C2×Dic263—41no—
68C2×Dic263—41no—
69C2×Dic263—41no—
70C2×Dic263SD1612yescomplemented
71C263⋊C8—41no—
72C23×C263—22no—
73C23×C263—41no—
74C23×C263—41no—
75C23×C263—41no—
76C23×C263—41no—
77C23×C263—41no—
78C23×C263—41no—
79C23×C263C2×D411yescharacteristic
80Q8×C263—41no—
81D4×C263—22no—
82D4×C263—22no—
83D4×C263—41no—
84D4×C263—41no—
85C2×C4×C263—21no—
86C2×C4×C263—21no—
87C2×C4×C263—41no—
88C2×C4×C263C2×D411yescharacteristic
89C2×C4×C263C2×D411yescharacteristic
90C8×C263—41no—
91C22×C263—21no—
92C22×C263—21no—
93C22×C263—42no—
94C22×C263—42no—
95C22×C263—42no—
96C22×C263—81no—
97C22×C263—81no—
98C22×C263—81no—
99C22×C263—81no—
100C22×C263#12011yescharacteristic
101C22×C263C2×SD1611yescharacteristic
102C22×C263#13711yescharacteristic
103C4×C263—21no—
104C4×C263—21no—
105C4×C263—41no—
106C4×C263—41no—
107Dic263—22no—
108Dic263—41no—
109Dic263—41no—
110Dic263—41no—
111Dic263—81no—
112C2×C263—21no—
113C2×C263—21no—
114C2×C263—82no—
115C2×C263#44811yescharacteristic
116C2×C263#45411yescharacteristic
117C2×C263B(4,𝔽2)11yescharacteristic
118C263#159911yescharacteristic, complemented, Sylow
119#1599—2631nomaximal, Sylow
120#544—2631no—
121#450—2631no—
122#450D26311yescharacteristic
123#394—2631no—
124#328—2631no—
125#328—2631no—
126#324—2631no—
127C22×D4C2×D26311yescharacteristic
128C2×SD16—21no—
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—21no—
142#102—5261no—
143C22⋊C8—2631no—
144C22⋊C8C2×D26311yescharacteristic
145#95—2631no—
146C24—21no—
147C2×Q8—2631no—
148C2×Q8—5261no—
149C2×Q8C22⋊D26311yescharacteristic
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—42no—
153C22×C4—2631no—
154C22×C4—2631no—
155C22×C4—5261no—
156C22×C4C22×D26311yescharacteristic
157SD16—42no—
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⋊C4C22⋊D26311yescharacteristic
172C22⋊C4—21no—
173C22⋊C4—5261no—
174C22⋊C4—10522no—
175C22⋊C4—10522no—
176C42—5261no—
177C42—5261no—
178C23—22no—
179C23—41no—
180C23—41no—
181C23—41no—
182C23—41no—
183C23—41no—
184C23—41no—
185C23D4×D26311yescharacteristic
186Q8—41no—
187Q8—10521no—
188Q8—21041no—
189D4—22no—
190D4—22no—
191D4—41no—
192D4—41no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—2632no—
197C2×C4—5261no—
198C2×C4—5261no—
199C2×C4—5261no—
200C2×C4—5261no—
201C2×C4—5261no—
202C2×C4—10521no—
203C2×C4—10521no—
204C2×C4—10521no—
205C2×C4—10521no—
206C2×C4D4×D26311yescharacteristic
207C2×C4C2×C22⋊D26311yescharacteristic
208C8—41no—
209C8—10521no—
210C22—21no—
211C22—21no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—81no—
216C22—81no—
217C22—81no—
218C22—81no—
219C22#2255443811yescharacteristic
220C22SD16×D26311yescharacteristic
221C22#2255449911yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—41no—
226C4—5262no—
227C4—10521no—
228C4—10521no—
229C4—10521no—
230C4—21041no—
231C2—21no—
232C2—21no—
233C2—82no—
234C2#3068207511yescharacteristic
235C2#3068210911yescharacteristic
236C2#3068212411yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#450×C263C2
socleC22×C263#120
prime radicalC22×D4×C263C22
hypercenter#450D263
hypocenterC263#1599
LCSG ▷ C22×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #30682567C2semidirect
4. #30681676C2semidirect
5. #30681675C2semidirect
6. #30681663C2semidirect
70. C2×Dic263SD16semidirect
118. C263#1599semidirect

Maximal subgroups

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

subgroupindex
#306825672
#306820892
#306818522
#306816762
#306816752
#306816632
#450×C2632
#1599263