Finite Group Databasebeta

← #46783814

Subgroups — #46783814

Order 33664.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#30682449C212yesmaximal, complemented
3#30681954C212yesmaximal, complemented
4#30681695C211yesmaximal, characteristic, complemented
5#407×C263C211yesmaximal, characteristic, complemented
6C2×#16862376C2212yes—
7#22554503—22no—
8#22554498—22no—
9#22554492—22no—
10#22554453—22no—
11#22554449—22no—
12#22554444—22no—
13#22554439—22no—
14C4×C22⋊D263—24no—
15#22554429C2212yes—
16#22554396—24no—
17C23×C4×C263C2211yescharacteristic
18C2×M16×C263C2211yescharacteristic
19C2×M16×C263C2211yescharacteristic
20C22⋊C8×C263—22no—
21#16862376—22no—
22#16862376—22no—
23#16862376—22no—
24#16862376—22no—
25C2×Dic526D412yescomplemented
26C2×D1052D412yescomplemented
27C2×C22⋊D263—24no—
28C2×C22⋊D263—22no—
29C2×C4×D263—22no—
30Dic1052—22no—
31#16862365—24no—
32D2104—22no—
33C4⋊Dic263—22no—
34Dic263⋊C4—24no—
35C22⋊Dic263—24no—
36C22⋊Dic263—22no—
37(C2×D263)⋊C4—24no—
38C4×Dic263D414yescomplemented
39C24×C263D411yescharacteristic
40C22×C4×C263—22no—
41C22×C4×C263—22no—
42C22×C4×C263—21no—
43C22×C4×C263—21no—
44C22×C4×C263D411yescharacteristic
45C22×C4×C263C2311yescharacteristic
46M16×C263—22no—
47M16×C263—22no—
48C2×C8×C263—21no—
49C2×C8×C263D412yescomplemented
50C22×D263—22no—
51Dic526—22no—
52Dic526—22no—
53D1052—22no—
54D1052—22no—
55C22⋊D263—48no—
56C22⋊D263—42no—
57C22⋊D263—42no—
58C2×Dic263—24no—
59C2×Dic263—22no—
60C4×D263—42no—
61C4×D263—42no—
62C23×C263—22no—
63C23×C263—21no—
64C23×C263—42no—
65C23×C263C2×D411yescharacteristic
66C2×C4×C263—22no—
67C2×C4×C263—21no—
68C2×C4×C263—41no—
69C2×C4×C263—42no—
70C2×C4×C263—41no—
71C2×C4×C263C2×D412yes—
72C2×C4×C263C2×D412yes—
73C2×C4×C263C2×D411yescharacteristic
74C2×C4×C263#4111yescharacteristic
75C8×C263—22no—
76C8×C263—41no—
77C22×C263—22no—
78C22×C263—24no—
79C22×C263—41no—
80C22×C263—42no—
81C22×C263—41no—
82C22×C263—41no—
83C22×C263#12012yes—
84C22×C263#12111yescharacteristic
85C2×D263—44no—
86C2×D263—42no—
87C4×C263—41no—
88C4×C263#12011yescharacteristic
89C4×C263#12112yes—
90C4×C263#12711yescharacteristic
91Dic263—44no—
92Dic263—42no—
93C2×C263—22no—
94C2×C263—21no—
95C2×C263—42no—
96C2×C263#39211yescharacteristic
97D263—82no—
98C263#201011yescharacteristic, complemented, Sylow
99#2010—2631nomaximal, Sylow
100#575—2631no—
101#525—2632no—
102#421—2632no—
103#407D26311yescharacteristic, complemented
104H(3,ℤ/4)—2631no—
105C2×#41—2632no—
106C23×C4C2×D26311yescharacteristic
107#137—5262no—
108AGL(1,ℤ/8)—5262no—
109#135—5262no—
110C2×M16C2×D26311yescharacteristic
111C2×M16C2×D26311yescharacteristic
112#123—5262no—
113C22⋊Q8—5262no—
114#121—5262no—
115#120—5262no—
116C4×D4—5264no—
117#117—2632no—
118#104—5264no—
119C22⋊C8—22no—
120C24D105211yescharacteristic
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—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—5262no—
134C22×C4D105211yescharacteristic
135C22×C4C22×D26311yescharacteristic
136Q16—5262no—
137SD16—5264no—
138D8—5262no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D26312yescomplemented
143C4⋊C4—5264no—
144C4⋊C4—5262no—
145C22⋊C4—5264no—
146C22⋊C4—5264no—
147C22⋊C4—5262no—
148C42—2634no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—5262no—
153C23C2×D105211yescharacteristic
154Q8—5262no—
155Q8—5262no—
156D4—5262no—
157D4—5262no—
158D4—10528no—
159D4—10522no—
160D4—10522no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—5264no—
167C2×C4—5262no—
168C2×C4—10522no—
169C2×C4—10522no—
170C2×C4D4×D26312yes—
171C2×C4D4×D26312yes—
172C2×C4C2×C22⋊D26311yescharacteristic
173C2×C4#1686237611yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—10524no—
183C22—10522no—
184C22#2255444012yes—
185C22#2255444411yescharacteristic
186C4—41no—
187C4—10524no—
188C4—10522no—
189C4#2255443811yescharacteristic
190C4#2255444312yes—
191C4#2255446611yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—21042no—
196C2#3068184711yescharacteristic
subgroupG/H
centerC4#22554466
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#407×C263C2
socleC2×C263#392
hypercenter#407D263
hypocenterC263#2010
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #30682738C2semidirect
2. #30682449C2semidirect
3. #30681954C2semidirect
4. #30681695C2semidirect
5. #407×C263C2semidirect
25. C2×Dic526D4semidirect
26. C2×D1052D4semidirect
38. C4×Dic263D4semidirect
49. C2×C8×C263D4semidirect
98. C263#2010semidirect
103. #407D263semidirect
142. C2×C8C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
#306827382
#306824492
#306819542
#306816952
#407×C2632
#2010263