Finite Group Databasebeta

← #46783891

Subgroups — #46783891

Order 33664.

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

normal subgroups only

This group has 294 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
1C2×#22554461C211yesmaximal, characteristic, complemented
2C2×#22554391C211yesmaximal, characteristic
3#30681841C211yesmaximal, characteristic
4#30681701C211yesmaximal, characteristic, complemented
5#30681700C211yesmaximal, characteristic, complemented
6#30681692C211yesmaximal, characteristic, complemented
7C2×#102×C263C211yesmaximal, characteristic
8C22×C263⋊C8C2211yescharacteristic
9#22554461—22no—
10#22554461—22no—
11C2×C4⋊Dic263—21no—
12C2×C4⋊Dic263C2211yescharacteristic
13C2×C4⋊Dic263C2211yescharacteristic
14C2×Dic263⋊C4—21no—
15C2×C22⋊Dic263—21no—
16C2×C22⋊Dic263—21no—
17C2×C4×Dic263C2211yescharacteristic
18#22554391—22no—
19C22×D4×C263C2211yescharacteristic
20C22×C8×C263C2211yescharacteristic
21C2×C4⋊C4×C263C2211yescharacteristic
22#102×C263—22no—
23C22×Dic263—21no—
24C22×Dic263—21no—
25C22×Dic263D411yescharacteristic
26C22×Dic263D411yescharacteristic
27C2×C263⋊C8—21no—
28C2×C263⋊C8—21no—
29C2×C263⋊C8—21no—
30C4⋊Dic263—24no—
31C4⋊Dic263—21no—
32C4⋊Dic263—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263D412yes—
35Dic263⋊C4—24no—
36C22⋊Dic263—42no—
37C22⋊Dic263—42no—
38C4×Dic263—21no—
39C4×Dic263—21no—
40C24×C263—21no—
41C2×D4×C263—21no—
42C2×D4×C263—21no—
43C2×D4×C263—21no—
44C2×D4×C263—21no—
45C2×D4×C263—21no—
46C2×D4×C263Q812yes—
47C22×C4×C263—21no—
48C22×C4×C263C2311yescharacteristic
49C2×C8×C263—21no—
50C2×C8×C263—21no—
51C2×C8×C263—21no—
52C4⋊C4×C263—21no—
53C4⋊C4×C263D412yes—
54C2×Dic263—21no—
55C2×Dic263—21no—
56C2×Dic263—22no—
57C2×Dic263—21no—
58C2×Dic263—21no—
59C2×Dic263—21no—
60C2×Dic263—21no—
61C2×Dic263—41no—
62C2×Dic263—41no—
63C2×Dic263—41no—
64C2×Dic263—41no—
65C2×Dic263—41no—
66C263⋊C8—41no—
67C23×C263—22no—
68C23×C263—41no—
69C23×C263—41no—
70C23×C263—41no—
71C23×C263—41no—
72C23×C263—41no—
73C23×C263—41no—
74C23×C263C2×D411yescharacteristic
75D4×C263—22no—
76D4×C263—22no—
77D4×C263—41no—
78D4×C263—41no—
79C2×C4×C263—22no—
80C2×C4×C263—41no—
81C2×C4×C263—41no—
82C2×C4×C263C2×D411yescharacteristic
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263C2×Q811yescharacteristic
85C2×C4×C263#4111yescharacteristic
86C2×C4×C263#4111yescharacteristic
87C2×C4×C263#4111yescharacteristic
88C8×C263—41no—
89C22×C263—42no—
90C22×C263—42no—
91C22×C263—42no—
92C22×C263—81no—
93C22×C263—81no—
94C22×C263—81no—
95C22×C263—81no—
96C22×C263#12011yescharacteristic
97C22×C263C22⋊Q811yescharacteristic
98C22×C263#12411yescharacteristic
99C22×C263#13511yescharacteristic
100C22×C263#13511yescharacteristic
101C22×C263AGL(1,ℤ/8)11yescharacteristic
102C22×C263AGL(1,ℤ/8)11yescharacteristic
103C4×C263—42no—
104C4×C263C22⋊Q811yescharacteristic
105C4×C263C22⋊Q811yescharacteristic
106C4×C263#12411yescharacteristic
107C4×C263#12411yescharacteristic
108Dic263—41no—
109Dic263—41no—
110Dic263—42no—
111Dic263—81no—
112C2×C263—82no—
113C2×C263#39311yescharacteristic
114C2×C263#44911yescharacteristic
115C2×C263#44911yescharacteristic
116C2×C263#47811yescharacteristic
117C2×C263#47811yescharacteristic
118C2×C263#48811yescharacteristic
119C2×C263#49011yescharacteristic
120C263#202511yescharacteristic, complemented, Sylow
121#2025—2631nomaximal, Sylow
122C2×#125—2631no—
123C2×#102—2631no—
124C2×#102D26311yescharacteristic
125#390—2631no—
126#340—2631no—
127#340—2631no—
128#336—2631no—
129C22×D4C2×D26311yescharacteristic
130C22×C8—2631no—
131C22×C8C2×D26311yescharacteristic
132#125—5262no—
133#125—5262no—
134C2×C4⋊C4—2631no—
135C2×C4⋊C4—2631no—
136C2×C4⋊C4—5261no—
137C2×C4⋊C4—5261no—
138C2×C4⋊C4C2×D26311yescharacteristic
139C2×C22⋊C4—5261no—
140C2×C22⋊C4—5261no—
141C2×C42—2631no—
142#102—22no—
143#102—5262no—
144C24—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4Dic52612yes—
151C22×C4—21no—
152C22×C4—2631no—
153C22×C4—2631no—
154C22×C4—5261no—
155C22×C4—5261no—
156C22×C4C22×D26311yescharacteristic
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—5261no—
161C2×C8—5261no—
162C2×C8—5261no—
163C4⋊C4—21no—
164C4⋊C4—2632no—
165C4⋊C4—5264no—
166C4⋊C4—5264no—
167C4⋊C4—5261no—
168C4⋊C4—5261no—
169C4⋊C4—5261no—
170C4⋊C4C22⋊D26312yes—
171C22⋊C4—10522no—
172C22⋊C4—10522no—
173C42—5261no—
174C42—5261no—
175C23—22no—
176C23—41no—
177C23—41no—
178C23—41no—
179C23—41no—
180C23—41no—
181C23—41no—
182C23D4×D26311yescharacteristic
183D4—22no—
184D4—22no—
185D4—41no—
186D4—41no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—5261no—
191C2×C4—5261no—
192C2×C4—5262no—
193C2×C4—5261no—
194C2×C4—5261no—
195C2×C4—5261no—
196C2×C4—5261no—
197C2×C4—10521no—
198C2×C4—10521no—
199C2×C4—10521no—
200C2×C4—10521no—
201C2×C4—10521no—
202C2×C4D4×D26311yescharacteristic
203C2×C4C2×C22⋊D26311yescharacteristic
204C2×C4C2×Dic52611yescharacteristic
205C2×C4#1686237511yescharacteristic
206C2×C4#1686237511yescharacteristic
207C2×C4#1686237611yescharacteristic
208C8—41no—
209C8—10521no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—81no—
214C22—81no—
215C22—81no—
216C22—81no—
217C22#2255443811yescharacteristic
218C22#2255444711yescharacteristic
219C22#2255445611yescharacteristic
220C22#2255448911yescharacteristic
221C22#2255449111yescharacteristic
222C22#2255449411yescharacteristic
223C22#2255449711yescharacteristic
224C4—42no—
225C4—10521no—
226C4—10521no—
227C4—10522no—
228C4—21041no—
229C4#2255444711yescharacteristic
230C4#2255444911yescharacteristic
231C4#2255445611yescharacteristic
232C4#2255445711yescharacteristic
233C2—82no—
234C2#3068185011yescharacteristic
235C2#3068208011yescharacteristic
236C2#3068208211yescharacteristic
237C2#3068223611yescharacteristic
238C2#3068224011yescharacteristic
239C2#3068229111yescharacteristic
240C2#3068230111yescharacteristic
subgroupG/H
centerC23D4×D263
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#102×C263C2
socleC23×C263C2×D4
prime radicalC22×D4×C263C22
hypercenterC2×#102D263
hypocenterC263#2025
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#22554461C2semidirect
4. #30681701C2semidirect
5. #30681700C2semidirect
6. #30681692C2semidirect
120. C263#2025semidirect

Maximal subgroups

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

subgroupindex
C2×#225544612
C2×#225543912
#306818412
#306817012
#306817002
#306816922
C2×#102×C2632
#2025263