Finite Group Databasebeta

← #46783815

Subgroups — #46783815

Order 33664.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#30682738C211yesmaximal, characteristic, complemented
2#30682450C212yesmaximal, complemented
3#30681956C212yesmaximal, complemented
4#30681901C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C263C211yesmaximal, characteristic, complemented
6C2×#16862376C2212yes—
7C22×C4×D263C2211yescharacteristic
8#22554503—22no—
9#22554498—22no—
10#22554492—22no—
11C2×#16862360C2211yescharacteristic
12#22554454—22no—
13#22554450—22no—
14#22554445—22no—
15#22554440—22no—
16C4×D1052—24no—
17#22554398—24no—
18(C2×D263)⋊C8—22no—
19C2×M16×C263C2211yescharacteristic
20#117×C263C2212yes—
21C23×D263D411yescharacteristic
22#16862376—22no—
23#16862376—22no—
24#16862376—22no—
25#16862376—22no—
26C2×Dic526D412yescomplemented
27C2×D1052—24no—
28C2×D1052D412yescomplemented
29C2×C22⋊D263—22no—
30C22×Dic263D411yescharacteristic
31C2×C4×D263—21no—
32C2×C4×D263—22no—
33C2×C4×D263—22no—
34C2×C4×D263—22no—
35C2×C4×D263—21no—
36Dic1052—22no—
37#16862365—24no—
38D2104—22no—
39#16862360—22no—
40C2×C263⋊C8—21no—
41C4⋊Dic263—24no—
42(C2×D263)⋊C4—24no—
43(C2×D263)⋊C4—24no—
44C22×C4×C263C2311yescharacteristic
45M16×C263—22no—
46C2×C8×C263D412yescomplemented
47C4⋊C4×C263—22no—
48C22⋊C4×C263—22no—
49C42×C263D414yescomplemented
50C22×D263—22no—
51C22×D263—21no—
52C22×D263—22no—
53C22×D263—42no—
54Dic526—22no—
55Dic526—22no—
56D1052—22no—
57D1052—22no—
58D1052—48no—
59C22⋊D263—42no—
60C22⋊D263—42no—
61C2×Dic263—22no—
62C2×Dic263—22no—
63C2×Dic263—21no—
64C4×D263—41no—
65C4×D263—42no—
66C4×D263—42no—
67C4×D263—41no—
68C4×D263—42no—
69C263⋊C8—41no—
70C23×C263C2×D411yescharacteristic
71C2×C4×C263—24no—
72C2×C4×C263C2×D412yes—
73C2×C4×C263C2×D411yescharacteristic
74C2×C4×C263C2×D412yes—
75C2×C4×C263#4111yescharacteristic
76C8×C263—22no—
77C22×C263—41no—
78C22×C263#12012yes—
79C22×C263#12111yescharacteristic
80C2×D263—24no—
81C2×D263—22no—
82C2×D263—42no—
83C2×D263—41no—
84C2×D263—41no—
85C2×D263—44no—
86C2×D263—42no—
87C4×C263—44no—
88C4×C263#12011yescharacteristic
89C4×C263#12112yes—
90C4×C263#12711yescharacteristic
91Dic263—41no—
92Dic263—42no—
93C2×C263—22no—
94C2×C263—21no—
95C2×C263#39211yescharacteristic
96D263—42no—
97D263—82no—
98C263#201011yescharacteristic, complemented, Sylow
99#2010—2631nomaximal, Sylow
100#575—2631no—
101#525—2632no—
102#421—2632no—
103#407—2631no—
104H(3,ℤ/4)D26311yescharacteristic, complemented
105C2×#41—2632no—
106C23×C4—2631no—
107#137—5262no—
108AGL(1,ℤ/8)—5262no—
109#135—5262no—
110C2×M16—2631no—
111C2×M16C2×D26311yescharacteristic
112#123—5262no—
113C22⋊Q8—5262no—
114#121—5262no—
115#120—5262no—
116C4×D4—5264no—
117#117C2×D26312yes—
118#104—5264no—
119C22⋊C8—5262no—
120C24—2631no—
121#41—5262no—
122#41—5262no—
123#41—5262no—
124#41—5262no—
125C2×Q8—2632no—
126C2×D4—2632no—
127C2×D4—5264no—
128C2×D4—5262no—
129C22×C4—2631no—
130C22×C4—5262no—
131C22×C4—5261no—
132C22×C4—5262no—
133C22×C4—5262no—
134C22×C4—5261no—
135C22×C4C22×D26311yescharacteristic
136Q16—5262no—
137SD16—5264no—
138D8—5262no—
139M16—22no—
140M16—5262no—
141C2×C8—5261no—
142C2×C8D105212yescomplemented
143C4⋊C4—22no—
144C4⋊C4—5264no—
145C22⋊C4—22no—
146C22⋊C4—5264no—
147C22⋊C4—5264no—
148C42D105214yescomplemented
149C23—5262no—
150C23—5261no—
151C23—5262no—
152C23—10522no—
153C23D4×D26311yescharacteristic
154Q8—5262no—
155Q8—5262no—
156D4—5262no—
157D4—5262no—
158D4—10528no—
159D4—10522no—
160D4—10522no—
161C2×C4—24no—
162C2×C4—5262no—
163C2×C4—5262no—
164C2×C4—5261no—
165C2×C4—10521no—
166C2×C4—10522no—
167C2×C4—10522no—
168C2×C4—10521no—
169C2×C4—10522no—
170C2×C4D4×D26312yes—
171C2×C4C2×D105211yescharacteristic
172C2×C4C2×D105212yes—
173C2×C4#1686237711yescharacteristic
174C8—22no—
175C8—10521no—
176C22—41no—
177C22—5264no—
178C22—5262no—
179C22—10522no—
180C22—10521no—
181C22—10524no—
182C22—10521no—
183C22—10522no—
184C22#2255444012yes—
185C22#2255444511yescharacteristic
186C4—44no—
187C4—10521no—
188C4—10522no—
189C4#2255444011yescharacteristic
190C4#2255444512yes—
191C4#2255446711yescharacteristic
192C2—22no—
193C2—21no—
194C2—10522no—
195C2—21042no—
196C2#3068184811yescharacteristic
subgroupG/H
centerC4#22554467
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingH(3,ℤ/4)×C263C2
socleC2×C263#392
hypercenterH(3,ℤ/4)D263
hypocenterC263#2010
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #30682738C2semidirect
2. #30682450C2semidirect
3. #30681956C2semidirect
4. #30681901C2semidirect
5. H(3,ℤ/4)×C263C2semidirect
26. C2×Dic526D4semidirect
28. C2×D1052D4semidirect
46. C2×C8×C263D4semidirect
49. C42×C263D4semidirect
98. C263#2010semidirect
104. H(3,ℤ/4)D263semidirect
142. C2×C8D1052semidirect
148. C42D1052semidirect

Maximal subgroups

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

subgroupindex
#306827382
#306824502
#306819562
#306819012
H(3,ℤ/4)×C2632
#2010263