Finite Group Databasebeta

← #46781196

Subgroups — #46781196

Order 33664.

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

normal subgroups only

This group has 276 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
1#30682485C211yesmaximal, characteristic
2#30681960C211yesmaximal, characteristic, complemented
3C4×C8×D263C211yesmaximal, characteristic, complemented
4#30681667C211yesmaximal, characteristic, complemented
5D4⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7D4⋊C8×C263C211yesmaximal, characteristic, complemented
8C2×#16862376—21no—
9C2×#16862359—21no—
10C2×C8×D263—21no—
11#22554469C411yescharacteristic
12#22554466C411yescharacteristic
13#22554456—21no—
14#22554445C411yescharacteristic
15#22554443—21no—
16#22554441C411yescharacteristic
17C4×D1052C2211yescharacteristic
18C4×C22⋊D263—21no—
19C42×D263C2211yescharacteristic
20C4⋊(C263⋊C8)C2211yescharacteristic
21Dic263⋊C8—21no—
22C4×C263⋊C8C2211yescharacteristic
23C8×Dic263—21no—
24C4×D4×C263C2211yescharacteristic
25C4⋊C8×C263C2211yescharacteristic
26C4×C8×C263C2211yescharacteristic
27#16862376—42no—
28#16862376—42no—
29C2×Dic526—21no—
30C2×D1052—21no—
31C2×D1052C2×C411yescharacteristic
32C2×C22⋊D263—21no—
33C2×C22⋊D263—21no—
34C2×C22⋊D263—21no—
35C2×C4×D263—21no—
36C2×C4×D263C2×C411yescharacteristic
37C2×C4×D263D411yescharacteristic
38C2×C4×D263D411yescharacteristic
39#16862359—42no—
40C2×C263⋊C8—21no—
41C2×C263⋊C8—21no—
42C8×D263—24no—
43C4⋊Dic263C2×C411yescharacteristic
44Dic263⋊C4—21no—
45C22⋊Dic263—21no—
46(C2×D263)⋊C4—21no—
47(C2×D263)⋊C4—21no—
48C4×Dic263C2×C411yescharacteristic
49C4×Dic263D411yescharacteristic
50C4×Dic263D411yescharacteristic
51C2×D4×C263C2×C411yescharacteristic
52C22×C4×C263—21no—
53C2×C8×C263—21no—
54C2×C8×C263—21no—
55C4⋊C4×C263C2×C411yescharacteristic
56C22⋊C4×C263—21no—
57C42×C263C2311yescharacteristic
58C22×D263—21no—
59C22×D263C22⋊C411yescharacteristic
60Dic526—42no—
61D1052—21no—
62D1052—21no—
63D1052—42no—
64C22⋊D263—42no—
65C22⋊D263—42no—
66C22⋊D263—42no—
67C2×Dic263—21no—
68C2×Dic263C22⋊C411yescharacteristic
69C2×Dic263C22⋊C411yescharacteristic
70C2×Dic263C22⋊C411yescharacteristic
71C4×D263—21no—
72C4×D263—21no—
73C4×D263—22no—
74C4×D263—41no—
75C4×D263—41no—
76C4×D263D812yes—
77C4×D263SD1612yes—
78C263⋊C8—22no—
79C263⋊C8—41no—
80C23×C263—21no—
81D4×C263—21no—
82D4×C263—21no—
83C2×C4×C263—21no—
84C2×C4×C263—41no—
85C2×C4×C263—41no—
86C2×C4×C263C22×C411yescharacteristic
87C2×C4×C263C2×D411yescharacteristic
88C2×C4×C263C2×D411yescharacteristic
89C8×C263—22no—
90C8×C263—41no—
91C22×C263—41no—
92C22×C263—41no—
93C22×C263—41no—
94C22×C263C2×C22⋊C411yescharacteristic
95C2×D263—21no—
96C2×D263—21no—
97C2×D263—41no—
98C2×D263—41no—
99C2×D263—41no—
100C2×D263#10212yes—
101C4×C263—21no—
102C4×C263—41no—
103C4×C263#13111yescharacteristic
104C4×C263#13111yescharacteristic
105C4×C263C2×D811yescharacteristic
106C4×C263C2×SD1611yescharacteristic
107Dic263—21no—
108Dic263—41no—
109Dic263#10212yes—
110Dic263#10412yes—
111C2×C263—81no—
112C2×C263#40811yescharacteristic
113C2×C263C2×#10211yescharacteristic
114C2×C263C2×#10411yescharacteristic
115D263—22no—
116D263—81no—
117C263#149211yescharacteristic, complemented, Sylow
118#1492—2631nomaximal, Sylow
119#532—2631no—
120#423—2631no—
121C2×C4×C8—2631no—
122D4⋊C8—2631no—
123D4⋊C8—2631no—
124D4⋊C8—2631no—
125D4⋊C8D26311yescharacteristic, complemented
126C2×#41—5261no—
127C2×M16—5261no—
128C22×C8—5261no—
129C4⋊Q8—2631no—
130#127—2631no—
131#124—5261no—
132#121—2631no—
133#121—2631no—
134#121—5261no—
135C4×D4—2631no—
136C4×D4—5261no—
137C4×D4C2×D26311yescharacteristic
138C2×C42—2631no—
139C4⋊C8—2631no—
140C4⋊C8—5261no—
141C4⋊C8C2×D26311yescharacteristic
142C4×C8—2631no—
143C4×C8—5261no—
144C4×C8C2×D26311yescharacteristic
145#41—10522no—
146#41—10522no—
147C2×Q8—5261no—
148C2×D4—2631no—
149C2×D4—5261no—
150C2×D4—5261no—
151C2×D4—5261no—
152C2×D4—5261no—
153C2×D4C4×D26311yescharacteristic
154C22×C4—21no—
155C22×C4—2631no—
156C22×C4—2631no—
157C22×C4—2631no—
158C22×C4—5261no—
159M16—10522no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—5264no—
163C2×C8—5261no—
164C2×C8—5261no—
165C4⋊C4—2631no—
166C4⋊C4—5261no—
167C4⋊C4C4×D26311yescharacteristic
168C22⋊C4—21no—
169C22⋊C4—5261no—
170C22⋊C4—5261no—
171C22⋊C4—5261no—
172C42—2631no—
173C42—2631no—
174C42—2631no—
175C42C22×D26311yescharacteristic
176C23—21no—
177C23—2631no—
178C23—5261no—
179Q8—10522no—
180D4—21no—
181D4—21no—
182D4—5261no—
183D4—5261no—
184D4—10522no—
185D4—10522no—
186D4—10522no—
187D4—10522no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—2631no—
192C2×C4—2631no—
193C2×C4—2632no—
194C2×C4—2632no—
195C2×C4—2631no—
196C2×C4—5262no—
197C2×C4—5261no—
198C2×C4—5261no—
199C2×C4—5261no—
200C2×C4—10521no—
201C2×C4—10521no—
202C2×C4C2×C4×D26311yescharacteristic
203C2×C4D4×D26311yescharacteristic
204C2×C4D4×D26311yescharacteristic
205C8—22no—
206C8—41no—
207C8—5262no—
208C8—10521no—
209C22—41no—
210C22—41no—
211C22—41no—
212C22—2632no—
213C22—5261no—
214C22—5261no—
215C22—10521no—
216C22—10521no—
217C22—10521no—
218C22C22⋊C4×D26311yescharacteristic
219C4—21no—
220C4—41no—
221C4—2632no—
222C4—2632no—
223C4—5261no—
224C4—10521no—
225C4#2255447611yescharacteristic
226C4#2255447811yescharacteristic
227C4D8×D26311yescharacteristic
228C4SD16×D26311yescharacteristic
229C2—81no—
230C2—5262no—
231C2—21041no—
232C2#3068190311yescharacteristic
233C2#102×D26311yescharacteristic
234C2#104×D26311yescharacteristic
subgroupG/H
centerC2×C4D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
FittingD4⋊C8×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682485C2
cosocleC42×C263C23
hypercenterD4⋊C8D263
hypocenterC263#1492
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #30681960C2semidirect
3. C4×C8×D263C2semidirect
4. #30681667C2semidirect
5. D4⋊(C263⋊C8)C2semidirect
6. #30681665C2semidirect
7. D4⋊C8×C263C2semidirect
117. C263#1492semidirect
125. D4⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
#306824852
#306819602
C4×C8×D2632
#306816672
D4⋊(C263⋊C8)2
#306816652
D4⋊C8×C2632
#1492263