Finite Group Databasebeta

← #46783562

Subgroups — #46783562

Order 33664.

344 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 99 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×#22554457C211yesmaximal, characteristic
2C2×#22554395C211yesmaximal, characteristic, complemented
3C2×#22554393C211yesmaximal, characteristic, complemented
4C2×#22554391C211yesmaximal, characteristic
5C2×#22554380C211yesmaximal, characteristic, complemented
6#30681807C211yesmaximal, characteristic, complemented
7C2×#102×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9C22×C263⋊C8C2211yescharacteristic
10#22554457—22no—
11#22554457C414yescomplemented
12C2×C4⋊Dic263C2211yescharacteristic
13C2×Dic263⋊C4—22no—
14C2×C22⋊Dic263—22no—
15C2×C4×Dic263C2211yescharacteristic
16#22554395—22no—
17#22554393—22no—
18#22554391—22no—
19#22554380—22no—
20C22×D4×C263C2211yescharacteristic
21C22×C8×C263C2211yescharacteristic
22C2×C4⋊C4×C263C2211yescharacteristic
23#102×C263—22no—
24C2×Dic526—21no—
25C2×Dic526—21no—
26C2×Dic526—21no—
27C2×Dic526—21no—
28C2×Dic526—21no—
29C2×Dic526C2×C412yes—
30C22×Dic263—21no—
31C22×Dic263—21no—
32C22×Dic263D412yes—
33C2×C263⋊C8—21no—
34C2×C263⋊C8—21no—
35C2×C263⋊C8D412yes—
36C4⋊Dic263—21no—
37C4⋊Dic263—21no—
38Dic263⋊C4—44no—
39C22⋊Dic263—28no—
40C4×Dic263C2×C412yes—
41C4×Dic263D412yes—
42C24×C263—21no—
43C2×D4×C263—21no—
44C2×D4×C263—21no—
45C2×D4×C263—21no—
46C2×D4×C263—21no—
47C2×D4×C263—21no—
48C2×D4×C263C2×C412yes—
49C22×C4×C263—21no—
50C22×C4×C263C2311yescharacteristic
51C2×C8×C263—21no—
52C2×C8×C263—21no—
53C2×C8×C263D412yes—
54C4⋊C4×C263—21no—
55C4⋊C4×C263—21no—
56Dic526—22no—
57Dic526—22no—
58Dic526—41no—
59Dic526—41no—
60C2×Dic263—22no—
61C2×Dic263—22no—
62C2×Dic263—22no—
63C2×Dic263—41no—
64C2×Dic263—41no—
65C2×Dic263—41no—
66C2×Dic263—42no—
67C2×Dic263C22⋊C414yes—
68C263⋊C8—22no—
69C23×C263—22no—
70C23×C263—41no—
71C23×C263—41no—
72C23×C263—42no—
73C23×C263—42no—
74C23×C263C2×D411yescharacteristic
75D4×C263—22no—
76D4×C263—22no—
77D4×C263—41no—
78D4×C263—41no—
79C2×C4×C263—41no—
80C2×C4×C263—42no—
81C2×C4×C263C22×C411yescharacteristic
82C2×C4×C263C2×D411yescharacteristic
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263C2×D411yescharacteristic
85C2×C4×C263#4111yescharacteristic
86C2×C4×C263#4111yescharacteristic
87C8×C263—22no—
88C22×C263—42no—
89C22×C263—44no—
90C22×C263—82no—
91C22×C263—81no—
92C22×C263—81no—
93C22×C263C2×C22⋊C411yescharacteristic
94C22×C263#12411yescharacteristic
95C22×C263#12711yescharacteristic
96C22×C263AGL(1,ℤ/8)12yes—
97C22×C263#13712yes—
98C4×C263—81no—
99C4×C263C4×D411yescharacteristic
100C4×C263C4×D411yescharacteristic
101C4×C263#12111yescharacteristic
102C4×C263#12111yescharacteristic
103Dic263—24no—
104Dic263—42no—
105Dic263—81no—
106C2×C263—82no—
107C2×C263#39011yescharacteristic
108C2×C263#41712yes—
109C2×C263#48912yes—
110C2×C263#49611yescharacteristic
111C2×C263#49711yescharacteristic
112C263#195911yescharacteristic, complemented, Sylow
113#1959—2631nomaximal, Sylow
114C2×#124—2631no—
115C2×#103—2631no—
116C2×#103—2631no—
117C2×#102—2631no—
118C2×#102D26311yescharacteristic
119C2×#97—2631no—
120#384—2631no—
121C22×Q8—2631no—
122C22×D4C2×D26311yescharacteristic
123C22×C8—2631no—
124C22×C8C2×D26311yescharacteristic
125#124—2634no—
126#124—5262no—
127C2×C4⋊C4—2631no—
128C2×C4⋊C4—5262no—
129C2×C4⋊C4C2×D26311yescharacteristic
130C2×C22⋊C4—5262no—
131C2×C42—2631no—
132#103—5262no—
133#103—5262no—
134#102—22no—
135#102—5262no—
136#97—5262no—
137C24—21no—
138C2×Q8—2632no—
139C2×Q8—5261no—
140C2×Q8—5261no—
141C2×Q8—5261no—
142C2×Q8—5261no—
143C2×Q8—5261no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4C4×D26312yes—
150C22×C4—21no—
151C22×C4—2632no—
152C22×C4—5261no—
153C22×C4—5261no—
154C22×C4C22×D26311yescharacteristic
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—2632no—
158C2×C8—5261no—
159C2×C8—5261no—
160C2×C8C22⋊D26312yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—5261no—
164C4⋊C4—5261no—
165C4⋊C4—10524no—
166C22⋊C4—5268no—
167C42—2632no—
168C42—2632no—
169C23—22no—
170C23—41no—
171C23—41no—
172C23—42no—
173C23—42no—
174C23D4×D26311yescharacteristic
175Q8—5262no—
176Q8—5262no—
177Q8—10521no—
178Q8—10521no—
179D4—22no—
180D4—22no—
181D4—41no—
182D4—41no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—2634no—
186C2×C4—5262no—
187C2×C4—5262no—
188C2×C4—5262no—
189C2×C4—10521no—
190C2×C4—10521no—
191C2×C4—10521no—
192C2×C4—10522no—
193C2×C4C2×C4×D26311yescharacteristic
194C2×C4D4×D26311yescharacteristic
195C2×C4D4×D26311yescharacteristic
196C2×C4C2×C22⋊D26311yescharacteristic
197C2×C4#1686237511yescharacteristic
198C2×C4#1686237611yescharacteristic
199C8—22no—
200C8—5262no—
201C22—44no—
202C22—42no—
203C22—82no—
204C22—81no—
205C22—81no—
206C22C22⋊C4×D26311yescharacteristic
207C22#2255445611yescharacteristic
208C22#2255446611yescharacteristic
209C22#2255449412yes—
210C22#2255449912yes—
211C4—81no—
212C4—5264no—
213C4—10522no—
214C4—21041no—
215C4(C22⋊D263)⋊C411yescharacteristic
216C4C4×C22⋊D26311yescharacteristic
217C4#2255444211yescharacteristic
218C4#2255444311yescharacteristic
219C2—82no—
220C2#3068183811yescharacteristic
221C2#3068193612yes—
222C2#3068229612yes—
223C2#3068232611yescharacteristic
224C2#3068232911yescharacteristic
subgroupG/H
centerC23D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#102×C263C2
socleC23×C263C2×D4
prime radicalC22×D4×C263C22
cosocleC22×C4×C263C23
hypercenterC2×#102D263
hypocenterC263#1959
LCSG ▷ C2×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
2. C2×#22554395C2semidirect
3. C2×#22554393C2semidirect
5. C2×#22554380C2semidirect
6. #30681807C2semidirect
11. #22554457C4semidirect
112. C263#1959semidirect

Maximal subgroups

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

subgroupindex
C2×#225544572
C2×#225543952
C2×#225543932
C2×#225543912
C2×#225543802
#306818072
C2×#102×C2632
#1959263