Finite Group Databasebeta

← #46781159

Subgroups — #46781159

Order 33664.

234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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#30682475C211yesmaximal, characteristic
2C4⋊C8×D263C211yesmaximal, characteristic, complemented
3C4×#16862359C211yesmaximal, characteristic, complemented
4Q8⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
5#30681667C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7Q8⋊C8×C263C211yesmaximal, characteristic, complemented
8C2×#16862359—21no—
9C2×C8×D263—21no—
10#22554465—21no—
11#22554461C411yescharacteristic
12#22554459C411yescharacteristic
13#22554455—21no—
14#22554446C411yescharacteristic
15#22554445C411yescharacteristic
16C4×D1052—21no—
17C4×D1052C2211yescharacteristic
18#22554427—21no—
19C42×D263C2211yescharacteristic
20C4⋊(C263⋊C8)C2211yescharacteristic
21Dic263⋊C8—21no—
22#22554380—21no—
23C4×C263⋊C8C2211yescharacteristic
24C4×Q8×C263C2211yescharacteristic
25C4⋊C8×C263C2211yescharacteristic
26C4×C8×C263C2211yescharacteristic
27C2×D1052—21no—
28C2×D1052C2×C411yescharacteristic
29C2×C4×D263—21no—
30C2×C4×D263C2×C411yescharacteristic
31C2×C4×D263D411yescharacteristic
32C2×C4×D263D411yescharacteristic
33#16862359—24no—
34C2×C263⋊C8—21no—
35C2×C263⋊C8—21no—
36C8×D263—42no—
37C4⋊Dic263—21no—
38C4⋊Dic263C2×C411yescharacteristic
39Dic263⋊C4—21no—
40Dic263⋊C4—21no—
41(C2×D263)⋊C4—21no—
42(C2×D263)⋊C4—21no—
43(C2×D263)⋊C4—21no—
44(C2×D263)⋊C4—21no—
45(C2×D263)⋊C4—21no—
46C4×Dic263C2×C411yescharacteristic
47C4×Dic263D411yescharacteristic
48C4×Dic263D411yescharacteristic
49C2×Q8×C263C2×C411yescharacteristic
50C2×C8×C263—21no—
51C2×C8×C263—21no—
52C4⋊C4×C263—21no—
53C4⋊C4×C263C2×C411yescharacteristic
54C42×C263—21no—
55C42×C263C2311yescharacteristic
56C22×D263—21no—
57C22×D263C22⋊C411yescharacteristic
58D1052—21no—
59D1052—21no—
60D1052—42no—
61C2×Dic263—21no—
62C2×Dic263C22⋊C411yescharacteristic
63C2×Dic263C22⋊C411yescharacteristic
64C2×Dic263C22⋊C411yescharacteristic
65C4×D263—22no—
66C4×D263—21no—
67C4×D263—21no—
68C4×D263—21no—
69C4×D263—21no—
70C4×D263—41no—
71C4×D263—41no—
72C263⋊C8—22no—
73C263⋊C8—41no—
74Q8×C263—21no—
75Q8×C263—21no—
76C2×C4×C263—21no—
77C2×C4×C263—21no—
78C2×C4×C263C22×C411yescharacteristic
79C2×C4×C263C2×D411yescharacteristic
80C2×C4×C263C2×D411yescharacteristic
81C8×C263—22no—
82C8×C263—41no—
83C22×C263C2×C22⋊C411yescharacteristic
84C2×D263—21no—
85C2×D263—21no—
86C2×D263—41no—
87C2×D263—41no—
88C2×D263—41no—
89C2×D263#10412yes—
90C4×C263—21no—
91C4×C263—41no—
92C4×C263—41no—
93C4×C263#13111yescharacteristic
94C4×C263#13111yescharacteristic
95C4×C263AGL(1,ℤ/8)11yescharacteristic
96C4×C263#13711yescharacteristic
97Dic263—21no—
98Dic263—21no—
99Dic263—21no—
100Dic263—41no—
101C2×C263#40811yescharacteristic
102C2×C263#41711yescharacteristic
103C2×C263C2×#10411yescharacteristic
104D263—22no—
105D263—81no—
106C263#148311yescharacteristic, complemented, Sylow
107#1483—2631nomaximal, Sylow
108#529—2631no—
109C2×C4⋊C8—2631no—
110C4×M16—2631no—
111Q8⋊C8—2631no—
112Q8⋊C8D26311yescharacteristic, complemented
113D4⋊C8—2631no—
114D4⋊C8—2631no—
115C2×M16—5261no—
116C22×C8—5261no—
117#126—5261no—
118#125—2631no—
119#124—2631no—
120#123—5261no—
121C22⋊Q8—2631no—
122#121—2631no—
123C4×Q8C2×D26311yescharacteristic
124C4×D4—2631no—
125C4×D4—5261no—
126#117—5261no—
127C2×C42—2631no—
128C4⋊C8—2631no—
129C4⋊C8—5261no—
130C4⋊C8C2×D26311yescharacteristic
131#97—5261no—
132C4×C8—2631no—
133C4×C8C2×D26311yescharacteristic
134C2×Q8C4×D26311yescharacteristic
135C2×D4—2631no—
136C2×D4—5261no—
137C22×C4—2631no—
138C22×C4—2631no—
139C22×C4—2631no—
140C22×C4—5261no—
141M16—5264no—
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—5261no—
145C2×C8—5261no—
146C2×C8—10522no—
147C4⋊C4—21no—
148C4⋊C4—2631no—
149C4⋊C4—5261no—
150C4⋊C4—5261no—
151C4⋊C4—5261no—
152C4⋊C4C4×D26311yescharacteristic
153C22⋊C4—5261no—
154C22⋊C4—5261no—
155C22⋊C4—5261no—
156C22⋊C4—5261no—
157C22⋊C4—5261no—
158C42—21no—
159C42—2631no—
160C42—2631no—
161C42—2631no—
162C42C22×D26311yescharacteristic
163C23—2631no—
164C23—5261no—
165Q8—21no—
166Q8—21no—
167D4—5261no—
168D4—5261no—
169D4—10522no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—2631no—
173C2×C4—2631no—
174C2×C4—2631no—
175C2×C4—5262no—
176C2×C4—5261no—
177C2×C4—5261no—
178C2×C4—5261no—
179C2×C4—5261no—
180C2×C4—5261no—
181C2×C4—10521no—
182C2×C4—10521no—
183C2×C4C2×C4×D26311yescharacteristic
184C2×C4D4×D26311yescharacteristic
185C2×C4D4×D26311yescharacteristic
186C8—22no—
187C8—41no—
188C8—5262no—
189C8—10521no—
190C22—2632no—
191C22—5261no—
192C22—5261no—
193C22—10521no—
194C22—10521no—
195C22—10521no—
196C22C22⋊C4×D26311yescharacteristic
197C4—21no—
198C4—41no—
199C4—41no—
200C4—5261no—
201C4—5261no—
202C4—5261no—
203C4—10521no—
204C4#2255447611yescharacteristic
205C4#2255447811yescharacteristic
206C4#2255449711yescharacteristic
207C4#2255450211yescharacteristic
208C2—5262no—
209C2—21041no—
210C2#3068190311yescharacteristic
211C2#3068193811yescharacteristic
212C2#104×D26311yescharacteristic
subgroupG/H
centerC2×C4D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
FittingQ8⋊C8×C263C2
socleC22×C263C2×C22⋊C4
prime radical#22554445C4
cosocleC42×C263C23
hypercenterQ8⋊C8D263
hypocenterC263#1483
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C4⋊C8×D263C2semidirect
3. C4×#16862359C2semidirect
4. Q8⋊(C263⋊C8)C2semidirect
5. #30681667C2semidirect
6. #30681665C2semidirect
7. Q8⋊C8×C263C2semidirect
106. C263#1483semidirect
112. Q8⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
#306824752
C4⋊C8×D2632
C4×#168623592
Q8⋊(C263⋊C8)2
#306816672
#306816652
Q8⋊C8×C2632
#1483263