Finite Group Databasebeta

← #46783278

Subgroups — #46783278

Order 33664.

362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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#30682507C211yesmaximal, characteristic
2#30682412C211yesmaximal, characteristic, complemented
3#30681956C211yesmaximal, characteristic, complemented
4#30681954C211yesmaximal, characteristic, complemented
5C2×#22554386C211yesmaximal, characteristic, complemented
6#30681694C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C22×D1052C2211yescharacteristic
10C2×#16862360C2211yescharacteristic
11#22554467C412yescomplemented
12#22554458C412yescomplemented
13#22554445—22no—
14#22554440—22no—
15C4×D1052—22no—
16#22554432—22no—
17#22554429C2211yescharacteristic
18C22⋊C4×D263—22no—
19#22554398—22no—
20#22554396—22no—
21#22554386—22no—
22C2×M16×C263C2211yescharacteristic
23#117×C263C2211yescharacteristic
24#117×C263C2211yescharacteristic
25C23×D263D412yes—
26#16862376—21no—
27#16862376—21no—
28#16862376—21no—
29#16862376—21no—
30C2×Dic526C2×C411yescharacteristic, complemented
31C2×D1052—24no—
32C2×D1052—21no—
33C2×D1052—21no—
34C2×D1052—21no—
35C2×D1052—21no—
36C2×D1052C2×C412yes—
37C2×D1052C2×C411yescharacteristic, complemented
38C2×D1052D412yes—
39C2×C22⋊D263—21no—
40C2×C4×D263—24no—
41C2×C4×D263—21no—
42#16862360—21no—
43#16862360—21no—
44C2×C263⋊C8—21no—
45C4⋊Dic263—21no—
46C22⋊Dic263—21no—
47(C2×D263)⋊C4—24no—
48(C2×D263)⋊C4—24no—
49C4×Dic263D412yescomplemented
50C22×C4×C263C2311yescharacteristic
51M16×C263—21no—
52M16×C263—21no—
53C2×C8×C263—21no—
54C4⋊C4×C263—21no—
55C4⋊C4×C263—21no—
56C22⋊C4×C263—21no—
57C22⋊C4×C263—21no—
58C42×C263C2×C412yescomplemented
59C42×C263D412yescomplemented
60C22×D263—22no—
61C22×D263—22no—
62C22×D263—21no—
63C22×D263—82no—
64C22×D263C22⋊C414yes—
65Dic526—21no—
66Dic526—21no—
67D1052—22no—
68D1052—22no—
69D1052—21no—
70D1052—21no—
71D1052—22no—
72D1052—22no—
73D1052—84no—
74C22⋊D263—41no—
75C22⋊D263—41no—
76C2×Dic263—21no—
77C2×Dic263—22no—
78C4×D263—41no—
79C4×D263—41no—
80C4×D263—84no—
81C263⋊C8—41no—
82C23×C263C2×D411yescharacteristic
83C2×C4×C263—22no—
84C2×C4×C263—22no—
85C2×C4×C263C22×C411yescharacteristic
86C2×C4×C263C2×D411yescharacteristic
87C2×C4×C263C2×D411yescharacteristic
88C2×C4×C263C2×D411yescharacteristic
89C2×C4×C263#4111yescharacteristic
90C2×C4×C263#4111yescharacteristic
91C8×C263—41no—
92C22×C263—41no—
93C22×C263C2×C22⋊C411yescharacteristic
94C22×C263#12011yescharacteristic
95C22×C263#12311yescharacteristic
96C2×D263—24no—
97C2×D263—44no—
98C2×D263—44no—
99C2×D263—42no—
100C2×D263—41no—
101C2×D263—82no—
102C4×C263—42no—
103C4×C263—42no—
104C4×C263C4×D411yescharacteristic
105C4×C263C4×D411yescharacteristic
106C4×C263#12111yescharacteristic
107C4×C263#12111yescharacteristic
108Dic263—42no—
109Dic263—41no—
110C2×C263—21no—
111C2×C263—21no—
112C2×C263—21no—
113C2×C263#38611yescharacteristic
114D263—44no—
115D263—81no—
116C263#191111yescharacteristic, complemented, Sylow
117#1911—2631nomaximal, Sylow
118#535—2631no—
119#518—2631no—
120#421—2631no—
121#421—2631no—
122C2×#100—2631no—
123H(3,ℤ/4)—2631no—
124H(3,ℤ/4)D26311yescharacteristic, complemented
125C2×#41—2631no—
126C22×D4—2631no—
127C2×M16—2631no—
128C2×M16C2×D26311yescharacteristic
129#127—2632no—
130#124—2632no—
131#121—5262no—
132#120—5262no—
133C4×D4—5262no—
134C4×D4—5262no—
135#117—2631no—
136#117C2×D26311yescharacteristic
137#117C2×D26311yescharacteristic
138C2×C22⋊C4—5262no—
139#104—5262no—
140#104—5262no—
141#100—5262no—
142C24—2632no—
143#41—5261no—
144#41—5261no—
145#41—5261no—
146#41—5261no—
147C2×Q8—2631no—
148C2×D4—2632no—
149C2×D4—2631no—
150C2×D4—2632no—
151C2×D4—5264no—
152C2×D4—5261no—
153C2×D4—5261no—
154C2×D4—5261no—
155C2×D4—5261no—
156C2×D4—5261no—
157C22×C4—5264no—
158C22×C4—5261no—
159C22×C4C22×D26311yescharacteristic
160M16—21no—
161M16—21no—
162M16—5261no—
163M16—5261no—
164C2×C8—21no—
165C2×C8—5261no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—5261no—
169C22⋊C4—21no—
170C22⋊C4—21no—
171C22⋊C4—5264no—
172C22⋊C4—5264no—
173C22⋊C4—5261no—
174C42—2632no—
175C42C4×D26312yescomplemented
176C42D105212yescomplemented
177C23—2634no—
178C23—5262no—
179C23—5262no—
180C23—5261no—
181C23—21042no—
182C23D4×D26311yescharacteristic
183Q8—5261no—
184Q8—5261no—
185D4—5262no—
186D4—5261no—
187D4—5262no—
188D4—5261no—
189D4—5262no—
190D4—5262no—
191D4—10521no—
192D4—10521no—
193D4—21044no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—5261no—
197C2×C4—5262no—
198C2×C4—10521no—
199C2×C4—10521no—
200C2×C4—21044no—
201C2×C4C2×C4×D26311yescharacteristic
202C2×C4D4×D26311yescharacteristic
203C2×C4D4×D26311yescharacteristic
204C2×C4C2×D105211yescharacteristic
205C2×C4#1686237611yescharacteristic
206C2×C4#1686237711yescharacteristic
207C8—41no—
208C8—10521no—
209C22—41no—
210C22—5264no—
211C22—10524no—
212C22—10524no—
213C22—10522no—
214C22—10521no—
215C22—21042no—
216C22C22⋊C4×D26311yescharacteristic
217C22#2255444011yescharacteristic
218C22#2255445511yescharacteristic
219C4—42no—
220C4—42no—
221C4—10522no—
222C4—10521no—
223C4#2255443211yescharacteristic
224C4C4×D105211yescharacteristic
225C4#2255444311yescharacteristic
226C4#2255444511yescharacteristic
227C2—21no—
228C2—21no—
229C2—21no—
230C2—10524no—
231C2—21041no—
232C2#3068181611yescharacteristic
subgroupG/H
centerC2#30681816
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingH(3,ℤ/4)×C263C2
socleC2×C263#386
prime radical#30682507C2
cosocleC22×C4×C263C23
hypercenterH(3,ℤ/4)D263
hypocenterC263#1911
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. #30682412C2semidirect
3. #30681956C2semidirect
4. #30681954C2semidirect
5. C2×#22554386C2semidirect
6. #30681694C2semidirect
7. H(3,ℤ/4)×C263C2semidirect
11. #22554467C4semidirect
12. #22554458C4semidirect
30. C2×Dic526C2×C4semidirect
37. C2×D1052C2×C4semidirect
49. C4×Dic263D4semidirect
58. C42×C263C2×C4semidirect
59. C42×C263D4semidirect
116. C263#1911semidirect
124. H(3,ℤ/4)D263semidirect
175. C42C4×D263semidirect
176. C42D1052semidirect

Maximal subgroups

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

subgroupindex
#306825072
#306824122
#306819562
#306819542
C2×#225543862
#306816942
H(3,ℤ/4)×C2632
#1911263