Finite Group Databasebeta

← #46781852

Subgroups — #46781852

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
1Q8×D1052C211yesmaximal, characteristic, complemented
2#30682285C211yesmaximal, characteristic, complemented
3#30682138C211yesmaximal, characteristic, complemented
4#30682134C211yesmaximal, characteristic
5#30681683C211yesmaximal, characteristic, complemented
6#30681667C211yesmaximal, characteristic, complemented
7Q8⋊C8×C263C211yesmaximal, characteristic, complemented
8C2×Q8×D263—21no—
9C2×#16862363—21no—
10C2×D2104—21no—
11#22554470—21no—
12#22554470C2211yescharacteristic
13#22554467C2211yescharacteristic
14#22554450—22no—
15#22554450—21no—
16C4×D1052—21no—
17C4×D1052C2211yescharacteristic
18C4⋊(C263⋊C8)C2211yescharacteristic
19#22554392—21no—
20#22554392—22no—
21#22554390—21no—
22C4×Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25C2×Dic526—22no—
26C2×Dic526—21no—
27Q8×D263—42no—
28Q8×D263—42no—
29C2×D1052—21no—
30C2×D1052—21no—
31C2×D1052—21no—
32C2×D1052D411yescharacteristic
33C2×C4×D263—22no—
34C2×C4×D263—21no—
35#16862363—42no—
36D2104—42no—
37C2×C263⋊C8—21no—
38C4⋊Dic263—22no—
39C4⋊Dic263—21no—
40C4⋊Dic263D411yescharacteristic
41C4⋊Dic263D412yes—
42(C2×D263)⋊C4—22no—
43(C2×D263)⋊C4—21no—
44C2×Q8×C263D411yescharacteristic
45C2×C8×C263—21no—
46C2×C8×C263—21no—
47C4⋊C4×C263—21no—
48C4⋊C4×C263D411yescharacteristic
49C42×C263—21no—
50C42×C263C2311yescharacteristic
51C22×D263—21no—
52C22×D263—41no—
53Dic526—44no—
54Dic526—41no—
55Dic526—41no—
56D1052—21no—
57D1052—42no—
58D1052—41no—
59D1052—41no—
60D1052—41no—
61D1052—41no—
62D1052SD1612yescomplemented
63C2×Dic263—22no—
64C2×Dic263—21no—
65C4×D263—44no—
66C4×D263—41no—
67C4×D263—41no—
68C263⋊C8—41no—
69Q8×C263—21no—
70Q8×C263D812yescomplemented
71C2×C4×C263—21no—
72C2×C4×C263—21no—
73C2×C4×C263C2×D411yescharacteristic
74C2×C4×C263C2×D411yescharacteristic
75C2×C4×C263C2×D411yescharacteristic
76C8×C263—41no—
77C8×C263—41no—
78C22×C263#12011yescharacteristic
79C2×D263—22no—
80C2×D263—41no—
81C2×D263—41no—
82C2×D263—81no—
83C2×D263—81no—
84C2×D263—81no—
85C4×C263—22no—
86C4×C263—21no—
87C4×C263—41no—
88C4×C263C2×D811yescharacteristic
89C4×C263C2×SD1611yescharacteristic
90C4×C263AGL(1,ℤ/8)11yescharacteristic
91C4×C263#13711yescharacteristic
92Dic263—42no—
93Dic263—41no—
94C2×C263#44711yescharacteristic
95C2×C263#44811yescharacteristic
96C2×C263#45411yescharacteristic
97D263—42no—
98D263—161no—
99C263#162711yescharacteristic, complemented, Sylow
100#1627—2631nomaximal, Sylow
101D4×Q8—2631no—
102#486—2631no—
103#460—2631no—
104#459—2631no—
105#332—2631no—
106Q8⋊C8D26311yescharacteristic, complemented
107D4⋊C8—2631no—
108C22×Q8—5261no—
109C2×SD16—5261no—
110C2×D8—5261no—
111C4⋊Q8—2631no—
112C4⋊Q8—5261no—
113#127—2631no—
114C22⋊Q8—5262no—
115C22⋊Q8—5261no—
116C4×Q8C2×D26311yescharacteristic
117C4×D4—2631no—
118C4×D4—5261no—
119C4⋊C8—2631no—
120C4⋊C8C2×D26311yescharacteristic
121#102—5261no—
122#102—5262no—
123#102—5261no—
124C4×C8C2×D26311yescharacteristic
125C2×Q8—5262no—
126C2×Q8—5261no—
127C2×Q8—10522no—
128C2×Q8—10522no—
129C2×Q8D105211yescharacteristic
130C2×D4—2631no—
131C2×D4—5261no—
132C2×D4—5261no—
133C2×D4—5261no—
134C22×C4—5262no—
135C22×C4—5261no—
136SD16—10522no—
137D8—10522no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—5261no—
141C4⋊C4—21no—
142C4⋊C4—2631no—
143C4⋊C4—2632no—
144C4⋊C4—5262no—
145C4⋊C4—5261no—
146C4⋊C4D105211yescharacteristic
147C22⋊C4—5262no—
148C22⋊C4—5261no—
149C42—21no—
150C42C22×D26311yescharacteristic
151C23—5261no—
152C23—10521no—
153Q8—21no—
154Q8—10524no—
155Q8—10521no—
156Q8—10521no—
157Q8D210412yescomplemented
158D4—2632no—
159D4—5261no—
160D4—10522no—
161D4—10521no—
162D4—10521no—
163D4—10521no—
164D4—10521no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—5262no—
168C2×C4—5261no—
169C2×C4—10524no—
170C2×C4—10521no—
171C2×C4—10521no—
172C2×C4D4×D26311yescharacteristic
173C2×C4D4×D26311yescharacteristic
174C2×C4C2×D105211yescharacteristic
175C8—41no—
176C8—41no—
177C8—10521no—
178C22—5262no—
179C22—10521no—
180C22—10521no—
181C22—21041no—
182C22—21041no—
183C22—21041no—
184C22#2255444011yescharacteristic
185C4—21no—
186C4—22no—
187C4—41no—
188C4—10522no—
189C4—10521no—
190C4C2×D210411yescharacteristic
191C4SD16×D26311yescharacteristic
192C4#2255449811yescharacteristic
193C4#2255450211yescharacteristic
194C2—10522no—
195C2—42081no—
196C2#3068207411yescharacteristic
197C2#3068207811yescharacteristic
198C2#3068211211yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingQ8⋊C8×C263C2
socleC22×C263#120
prime radical#30682134C2
hypercenterQ8⋊C8D263
hypocenterC263#1627
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. Q8×D1052C2semidirect
2. #30682285C2semidirect
3. #30682138C2semidirect
5. #30681683C2semidirect
6. #30681667C2semidirect
7. Q8⋊C8×C263C2semidirect
62. D1052SD16semidirect
70. Q8×C263D8semidirect
99. C263#1627semidirect
106. Q8⋊C8D263semidirect
157. Q8D2104semidirect

Maximal subgroups

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

subgroupindex
Q8×D10522
#306822852
#306821382
#306821342
#306816832
#306816672
Q8⋊C8×C2632
#1627263