Finite Group Databasebeta

← #46783791

Subgroups — #46783791

Order 33664.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×#22554498C212yesmaximal, complemented
2#30682519C211yesmaximal, characteristic, complemented
3C2×#22554396C212yesmaximal, complemented
4#30681839C211yesmaximal, characteristic, complemented
5#343×C263C211yesmaximal, characteristic, complemented
6C2×#16862376C2212yes—
7C22×D1052C2211yescharacteristic
8#22554498—24no—
9#22554498—24no—
10C2×#16862365—22no—
11C2×D2104—22no—
12#22554450—22no—
13#22554445—22no—
14#22554444—22no—
15C2×(C2×D263)⋊C4—22no—
16C2×C4×Dic263C2211yescharacteristic
17#22554396—24no—
18C2×M16×C263C2212yes—
19C2×C4⋊C4×C263C2211yescharacteristic
20C23×D263—21no—
21#16862376—22no—
22#16862376—22no—
23#16862376—22no—
24#16862376—22no—
25C2×Dic526D412yes—
26C2×D1052—22no—
27C2×D1052—22no—
28C2×D1052—22no—
29C2×D1052—21no—
30C2×D1052D412yes—
31C2×D1052D412yescomplemented
32C2×C22⋊D263—22no—
33C22×Dic263—21no—
34C2×C4×D263—22no—
35#16862365—28no—
36D2104—28no—
37C4⋊Dic263—22no—
38(C2×D263)⋊C4—24no—
39(C2×D263)⋊C4—44no—
40C4×Dic263—22no—
41C22×C4×C263D412yes—
42C22×C4×C263C2311yescharacteristic
43M16×C263—22no—
44M16×C263D414yescomplemented
45C2×C8×C263—22no—
46C4⋊C4×C263—22no—
47C22×D263—22no—
48C22×D263—22no—
49C22×D263—42no—
50C22×D263—42no—
51C22×D263—41no—
52C22×D263—41no—
53Dic526—22no—
54Dic526—22no—
55D1052—22no—
56D1052—24no—
57D1052—22no—
58D1052—42no—
59D1052—82no—
60C22⋊D263—42no—
61C22⋊D263—42no—
62C2×Dic263—22no—
63C2×Dic263—22no—
64C2×Dic263—41no—
65C2×Dic263—41no—
66C4×D263—42no—
67C4×D263—42no—
68C23×C263C2×D411yescharacteristic
69C2×C4×C263—22no—
70C2×C4×C263—42no—
71C2×C4×C263C2×D411yescharacteristic
72C2×C4×C263C2×D412yes—
73C2×C4×C263C2×D412yes—
74C2×C4×C263#4111yescharacteristic
75C8×C263—24no—
76C22×C263—21no—
77C22×C263—21no—
78C22×C263#12011yescharacteristic
79C22×C263#12111yescharacteristic
80C22×C263#12711yescharacteristic
81C2×D263—44no—
82C2×D263—42no—
83C2×D263—42no—
84C2×D263—42no—
85C2×D263—42no—
86C2×D263—82no—
87C2×D263—81no—
88C2×D263—81no—
89C4×C263—42no—
90C4×C263#12012yes—
91C4×C263#12112yes—
92Dic263—42no—
93Dic263—42no—
94C2×C263—21no—
95C2×C263—21no—
96C2×C263#39211yescharacteristic
97C2×C263#45311yescharacteristic
98C2×C263#45411yescharacteristic
99D263—82no—
100D263—82no—
101C263#200611yescharacteristic, complemented, Sylow
102#2006—2631nomaximal, Sylow
103C2×AGL(1,ℤ/8)—2632no—
104#537—2631no—
105C2×#104—2632no—
106#390—2631no—
107#343D26311yescharacteristic, complemented
108C2×#41—2632no—
109C22×D4—2631no—
110AGL(1,ℤ/8)—5264no—
111AGL(1,ℤ/8)—5264no—
112C2×SD16—5262no—
113C2×D8—5262no—
114C2×M16C2×D26312yes—
115C22⋊Q8—5262no—
116#121—5262no—
117#121—5262no—
118C2×C4⋊C4C2×D26311yescharacteristic
119C2×C22⋊C4—5262no—
120C2×C42—2631no—
121#104—5264no—
122C24—5261no—
123#41—5262no—
124#41—5262no—
125#41—5262no—
126#41—5262no—
127C2×Q8—2632no—
128C2×D4—2632no—
129C2×D4—2632no—
130C2×D4—5262no—
131C2×D4—5262no—
132C2×D4—5262no—
133C2×D4—5262no—
134C2×D4—5261no—
135C22×C4—5261no—
136C22×C4—5262no—
137C22×C4D105212yes—
138C22×C4C22×D26311yescharacteristic
139SD16—5268no—
140D8—5268no—
141M16—22no—
142M16D105214yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—5262no—
146C22⋊C4—5264no—
147C22⋊C4—10524no—
148C42—5262no—
149C23—5262no—
150C23—5262no—
151C23—10522no—
152C23—10522no—
153C23—10521no—
154C23—10521no—
155C23C2×D105211yescharacteristic
156Q8—5262no—
157Q8—5262no—
158D4—5262no—
159D4—5264no—
160D4—5262no—
161D4—10522no—
162D4—10522no—
163D4—10522no—
164D4—21042no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—5262no—
168C2×C4—5262no—
169C2×C4—10521no—
170C2×C4—10521no—
171C2×C4—10522no—
172C2×C4—10522no—
173C2×C4D4×D26311yescharacteristic
174C2×C4D4×D26312yes—
175C2×C4C2×D105212yes—
176C2×C4#1686237711yescharacteristic
177C8—24no—
178C22—21no—
179C22—21no—
180C22—10524no—
181C22—10522no—
182C22—10522no—
183C22—10522no—
184C22—10522no—
185C22—21042no—
186C22—21041no—
187C22—21041no—
188C22#2255444011yescharacteristic
189C22#2255444511yescharacteristic
190C22#2255446711yescharacteristic
191C4—42no—
192C4—10522no—
193C4—10522no—
194C4#2255444012yes—
195C4#2255444512yes—
196C2—21no—
197C2—21no—
198C2—21042no—
199C2—21042no—
200C2#3068184811yescharacteristic
201C2#3068210811yescharacteristic
202C2#3068211311yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#343×C263C2
socleC22×C263#120
hypercenter#343D263
hypocenterC263#2006
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#22554498C2semidirect
2. #30682519C2semidirect
3. C2×#22554396C2semidirect
4. #30681839C2semidirect
5. #343×C263C2semidirect
31. C2×D1052D4semidirect
44. M16×C263D4semidirect
101. C263#2006semidirect
107. #343D263semidirect
142. M16D1052semidirect

Maximal subgroups

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

subgroupindex
C2×#225544982
#306825192
C2×#225543962
#306818392
#343×C2632
#2006263