Finite Group Databasebeta

← #46783607

Subgroups — #46783607

Order 33664.

312 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C22×#16862366C211yesmaximal, characteristic
2C2×#22554403C211yesmaximal, characteristic
3C2×#22554394C211yesmaximal, characteristic
4C2×#22554393C211yesmaximal, characteristic
5C2×C4×C263⋊C8C211yesmaximal, characteristic
6#30681844C211yesmaximal, characteristic
7#391×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9C2×#16862366—22no—
10C2×#16862366—22no—
11C2×#16862366C414yescomplemented
12C22×C263⋊C8C2211yescharacteristic
13C22×C263⋊C8C2211yescharacteristic
14C2×C4⋊Dic263C2211yescharacteristic
15#22554403—22no—
16#22554394—22no—
17#22554393—22no—
18C4×C263⋊C8—22no—
19C263⋊#95—22no—
20C22×Q8×C263C2211yescharacteristic
21C2×C4⋊C4×C263C2211yescharacteristic
22C2×C42×C263C2211yescharacteristic
23#95×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—
32#16862366—28no—
33C2×C263⋊C8—21no—
34C2×C263⋊C8—21no—
35C2×C263⋊C8C2×C412yes—
36C2×C263⋊C8D412yes—
37C2×C263⋊C8D412yes—
38C2×C263⋊C8D412yes—
39C4⋊Dic263—21no—
40C4⋊Dic263—21no—
41C2×Q8×C263—21no—
42C2×Q8×C263—21no—
43C2×Q8×C263—21no—
44C2×Q8×C263—21no—
45C2×Q8×C263—21no—
46C2×Q8×C263C2×C412yes—
47C22×C4×C263—21no—
48C22×C4×C263—21no—
49C22×C4×C263D412yes—
50C22×C4×C263C2311yescharacteristic
51C4⋊C4×C263—21no—
52C4⋊C4×C263—21no—
53C42×C263—21no—
54C42×C263—21no—
55Dic526—22no—
56Dic526—22no—
57Dic526—41no—
58Dic526—41no—
59C2×Dic263—22no—
60C2×Dic263—41no—
61C2×Dic263—41no—
62C2×Dic263—41no—
63C2×Dic263—42no—
64C263⋊C8—22no—
65C263⋊C8C22⋊C414yes—
66C23×C263C2×D411yescharacteristic
67Q8×C263—22no—
68Q8×C263—22no—
69Q8×C263—41no—
70Q8×C263—41no—
71C2×C4×C263—22no—
72C2×C4×C263—22no—
73C2×C4×C263—22no—
74C2×C4×C263—41no—
75C2×C4×C263—41no—
76C2×C4×C263—41no—
77C2×C4×C263—42no—
78C2×C4×C263Q1614yescomplemented
79C2×C4×C263C22×C411yescharacteristic
80C2×C4×C263C2×D411yescharacteristic
81C2×C4×C263C2×D411yescharacteristic
82C2×C4×C263C2×D411yescharacteristic
83C2×C4×C263#4111yescharacteristic
84C2×C4×C263#4111yescharacteristic
85C22×C263C4×D411yescharacteristic
86C22×C263#12111yescharacteristic
87C22×C263#12711yescharacteristic
88C22×C263C2×Q1612yes—
89C22×C263#13512yes—
90C4×C263—24no—
91C4×C263—42no—
92C4×C263—81no—
93C4×C263C2×C22⋊C411yescharacteristic
94C4×C263C4×D411yescharacteristic
95C4×C263#12111yescharacteristic
96C4×C263#12411yescharacteristic
97Dic263—42no—
98Dic263—81no—
99C2×C263#39011yescharacteristic
100C2×C263C4×Q1612yes—
101C2×C263#46712yes—
102C2×C263#49411yescharacteristic
103C2×C263#49511yescharacteristic
104C263#196911yescharacteristic, complemented, Sylow
105#1969—2631nomaximal, Sylow
106C22×Q16—2631no—
107C2×#107—2631no—
108C2×#103—2631no—
109C2×#103—2631no—
110C2×C4×C8—2631no—
111#391—2631no—
112#391D26311yescharacteristic
113C22×Q8—2631no—
114C22×Q8C2×D26311yescharacteristic
115C2×Q16—2634no—
116C2×Q16—5262no—
117C2×Q16—5262no—
118C22×C8—2631no—
119C22×C8—2631no—
120C2×C4⋊C4—2631no—
121C2×C4⋊C4C2×D26311yescharacteristic
122C2×C42C2×D26311yescharacteristic
123#107—5262no—
124#103—5262no—
125#103—5262no—
126C4×C8—5262no—
127#95—22no—
128#95—5262no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—2632no—
135C2×Q8—5261no—
136C2×Q8—5261no—
137C2×Q8—5261no—
138C2×Q8—5261no—
139C2×Q8—5261no—
140C2×Q8C4×D26312yes—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—5261no—
144C22×C4—5261no—
145C22×C4C22⋊D26312yes—
146C22×C4C22×D26311yescharacteristic
147Q16—5268no—
148C2×C8—2632no—
149C2×C8—2632no—
150C2×C8—2632no—
151C2×C8—2632no—
152C2×C8—5261no—
153C2×C8—5261no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—5261no—
157C4⋊C4—5261no—
158C42—21no—
159C42—21no—
160C23C2×C22⋊D26311yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165Q8—5262no—
166Q8—5262no—
167Q8—10521no—
168Q8—10521no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—42no—
176C2×C4—5262no—
177C2×C4—10521no—
178C2×C4—10521no—
179C2×C4—10521no—
180C2×C4—10522no—
181C2×C4#1686236614yescomplemented
182C2×C4C2×C4×D26311yescharacteristic
183C2×C4D4×D26311yescharacteristic
184C2×C4D4×D26311yescharacteristic
185C2×C4D4×D26311yescharacteristic
186C2×C4#1686237511yescharacteristic
187C2×C4#1686237611yescharacteristic
188C8—2634no—
189C8—5262no—
190C22C4×C22⋊D26311yescharacteristic
191C22#2255444211yescharacteristic
192C22#2255446611yescharacteristic
193C22C2×#1686236612yes—
194C22#2255449012yes—
195C4—24no—
196C4—42no—
197C4—81no—
198C4—10522no—
199C4—21041no—
200C4C22⋊C4×D26311yescharacteristic
201C4(C22⋊D263)⋊C411yescharacteristic
202C4#2255444311yescharacteristic
203C4#2255445611yescharacteristic
204C2#3068183811yescharacteristic
205C2C4×#1686236612yes—
206C2#3068217712yes—
207C2#3068231711yescharacteristic
208C2#3068232011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#391×C263C2
socle, prime radicalC23×C263C2×D4
cosocleC22×C4×C263C23
hypercenter#391D263
hypocenterC263#1969
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
11. C2×#16862366C4semidirect
78. C2×C4×C263Q16semidirect
104. C263#1969semidirect
181. C2×C4#16862366semidirect

Maximal subgroups

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

subgroupindex
C22×#168623662
C2×#225544032
C2×#225543942
C2×#225543932
C2×C4×C263⋊C82
#306818442
#391×C2632
#1969263