Finite Group Databasebeta

← #46781849

Subgroups — #46781849

Order 33664.

250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic526C211yesmaximal, characteristic, complemented
2#30682284C211yesmaximal, characteristic, complemented
3#30682135C211yesmaximal, characteristic, complemented
4#30681683C211yesmaximal, characteristic, complemented
5#30681668C211yesmaximal, characteristic, complemented
6D4⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
7#459×C263C211yesmaximal, characteristic
8C22×Dic526—21no—
9C2×#16862364—21no—
10#22554470C2211yescharacteristic
11#22554469—21no—
12#22554449—21no—
13#22554447—22no—
14C4×Dic526C2211yescharacteristic
15D4×Dic263—21no—
16C4⋊(C263⋊C8)C2211yescharacteristic
17#22554391—21no—
18#22554391—22no—
19C4×C263⋊C8C2211yescharacteristic
20C2×D8×C263—21no—
21#127×C263C2211yescharacteristic
22C4×D4×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24#102×C263—21no—
25C2×Dic526—22no—
26C2×Dic526—21no—
27C2×Dic526—42no—
28C2×Dic526—42no—
29C2×Dic526D411yescharacteristic
30C22×Dic263—22no—
31#16862364—42no—
32C2×C263⋊C8—21no—
33C2×C263⋊C8—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263D411yescharacteristic
36C4⋊Dic263D412yes—
37Dic263⋊C4—22no—
38Dic263⋊C4—21no—
39C22⋊Dic263—22no—
40C4×Dic263—21no—
41C2×D4×C263—21no—
42C2×D4×C263—21no—
43C2×D4×C263—21no—
44C2×D4×C263D411yescharacteristic
45C22×C4×C263—21no—
46D8×C263—42no—
47C2×C8×C263—21no—
48C4⋊C4×C263D411yescharacteristic
49C22⋊C4×C263—21no—
50C42×C263C2311yescharacteristic
51Dic526—21no—
52Dic526—44no—
53Dic526—41no—
54Dic526—41no—
55Dic526D812yescomplemented
56C2×Dic263—21no—
57C2×Dic263—21no—
58C2×Dic263—22no—
59C2×Dic263—44no—
60C263⋊C8—41no—
61C263⋊C8—41no—
62C23×C263—21no—
63C23×C263—41no—
64D4×C263—21no—
65D4×C263—42no—
66D4×C263—41no—
67D4×C263—41no—
68D4×C263—41no—
69D4×C263—41no—
70D4×C263SD1612yescomplemented
71C2×C4×C263—21no—
72C2×C4×C263—41no—
73C2×C4×C263—41no—
74C2×C4×C263C2×D411yescharacteristic
75C2×C4×C263C2×D411yescharacteristic
76C2×C4×C263C2×D411yescharacteristic
77C8×C263—41no—
78C22×C263—22no—
79C22×C263—41no—
80C22×C263—41no—
81C22×C263—81no—
82C22×C263—81no—
83C22×C263—81no—
84C22×C263#12011yescharacteristic
85C4×C263—21no—
86C4×C263—41no—
87C4×C263C2×D811yescharacteristic
88C4×C263C2×SD1611yescharacteristic
89C4×C263AGL(1,ℤ/8)11yescharacteristic
90C4×C263#13711yescharacteristic
91Dic263—22no—
92Dic263—42no—
93Dic263—41no—
94C2×C263—42no—
95C2×C263—161no—
96C2×C263#44711yescharacteristic
97C2×C263#44811yescharacteristic
98C2×C263#45411yescharacteristic
99C263#162711yescharacteristic, complemented, Sylow
100#1627—2631nomaximal, Sylow
101D4×Q8—2631no—
102#486—2631no—
103#460—2631no—
104#459D26311yescharacteristic
105#332—2631no—
106Q8⋊C8—2631no—
107D4⋊C8—2631no—
108C22×Q8—5261no—
109C2×SD16—5261no—
110C2×D8—21no—
111C4⋊Q8—2631no—
112C4⋊Q8—5261no—
113#127C2×D26311yescharacteristic
114C22⋊Q8—5262no—
115C22⋊Q8—5261no—
116C4×Q8—2631no—
117C4×D4—5261no—
118C4×D4C2×D26311yescharacteristic
119C4⋊C8—2631no—
120C4⋊C8C2×D26311yescharacteristic
121#102—21no—
122#102—5261no—
123#102—5262no—
124C4×C8—2631no—
125C2×Q8—2631no—
126C2×Q8—5262no—
127C2×Q8—5261no—
128C2×Q8—10522no—
129C2×Q8—10522no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4C22⋊D26311yescharacteristic
134C22×C4—21no—
135C22×C4—5262no—
136SD16—10522no—
137D8—42no—
138C2×C8—21no—
139C2×C8—5261no—
140C2×C8—5261no—
141C4⋊C4—2631no—
142C4⋊C4—2632no—
143C4⋊C4—5262no—
144C4⋊C4—5261no—
145C4⋊C4—5261no—
146C4⋊C4C22⋊D26311yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—5262no—
149C42—5261no—
150C42C22×D26311yescharacteristic
151C23—21no—
152C23—41no—
153Q8—2632no—
154Q8—5261no—
155Q8—10524no—
156Q8—10521no—
157Q8—10521no—
158D4—21no—
159D4—42no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—41no—
164D4#1686236412yescomplemented
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—5261no—
169C2×C4—5261no—
170C2×C4—5262no—
171C2×C4—10524no—
172C2×C4D4×D26311yescharacteristic
173C2×C4D4×D26311yescharacteristic
174C2×C4C2×C22⋊D26311yescharacteristic
175C8—41no—
176C8—10521no—
177C8—10521no—
178C22—22no—
179C22—41no—
180C22—41no—
181C22—81no—
182C22—81no—
183C22—81no—
184C22#2255443811yescharacteristic
185C4—21no—
186C4—41no—
187C4—5262no—
188C4—10522no—
189C4—10521no—
190C4D8×D26311yescharacteristic
191C4C2×#1686236411yescharacteristic
192C4#2255449411yescharacteristic
193C4#2255450011yescharacteristic
194C2—42no—
195C2—161no—
196C2#3068207011yescharacteristic
197C2#3068207611yescharacteristic
198C2#3068210911yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting, prime radical#459×C263C2
socleC22×C263#120
hypercenter#459D263
hypocenterC263#1627
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. D4×Dic526C2semidirect
2. #30682284C2semidirect
3. #30682135C2semidirect
4. #30681683C2semidirect
5. #30681668C2semidirect
6. D4⋊(C263⋊C8)C2semidirect
55. Dic526D8semidirect
70. D4×C263SD16semidirect
99. C263#1627semidirect
164. D4#16862364semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5262
#306822842
#306821352
#306816832
#306816682
D4⋊(C263⋊C8)2
#459×C2632
#1627263