Finite Group Databasebeta

← #46781249

Subgroups — #46781249

Order 33664.

334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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#30682449C211yesmaximal, characteristic
2#30681902C211yesmaximal, characteristic, complemented
3#30681674C212yesmaximal, complemented
4#30681671C212yesmaximal, complemented
5C2×#95×C263C211yesmaximal, characteristic, complemented
6C2×#16862376C411yescharacteristic, complemented
7C2×#16862360—21no—
8#22554453—21no—
9#22554449C411yescharacteristic, complemented
10#22554449C2211yescharacteristic
11#22554444C411yescharacteristic, complemented
12#22554444C2211yescharacteristic
13#22554439—21no—
14C4×C22⋊D263—21no—
15C4×C22⋊D263—21no—
16#22554429C411yescharacteristic, complemented
17C22⋊(C263⋊C8)—21no—
18C22⋊(C263⋊C8)C2212yes—
19C23×C4×C263—21no—
20C23×C4×C263C2211yescharacteristic
21#95×C263—21no—
22#95×C263C2212yes—
23#16862376—42no—
24C2×Dic526C2×C411yescharacteristic, complemented
25C2×D1052C2×C411yescharacteristic, complemented
26C2×C22⋊D263—21no—
27C2×C22⋊D263—21no—
28C2×C22⋊D263—21no—
29C2×C4×D263—21no—
30#16862360—42no—
31C2×C263⋊C8—22no—
32C4⋊Dic263C2×C411yescharacteristic, complemented
33C4⋊Dic263C2×C411yescharacteristic, complemented
34Dic263⋊C4—21no—
35Dic263⋊C4—21no—
36C22⋊Dic263—21no—
37C22⋊Dic263—21no—
38C22⋊Dic263—21no—
39(C2×D263)⋊C4—21no—
40(C2×D263)⋊C4—21no—
41C4×Dic263—21no—
42C24×C263D411yescharacteristic
43C22×C4×C263—24no—
44C22×C4×C263—22no—
45C22×C4×C263—42no—
46C22×C4×C263—42no—
47C22×C4×C263—42no—
48C22×C4×C263C2×C411yescharacteristic
49C22×C4×C263C2×C411yescharacteristic
50C22×C4×C263D411yescharacteristic
51C22×C4×C263D411yescharacteristic
52C22×C4×C263D411yescharacteristic
53C22×C4×C263C2311yescharacteristic
54C22×D263—21no—
55Dic526—41no—
56D1052—41no—
57C22⋊D263—42no—
58C22⋊D263—42no—
59C22⋊D263—41no—
60C22⋊D263—41no—
61C2×Dic263—21no—
62C2×Dic263—21no—
63C2×Dic263—21no—
64C4×D263—42no—
65C263⋊C8—42no—
66C23×C263—22no—
67C23×C263—22no—
68C23×C263—21no—
69C23×C263—21no—
70C23×C263C22⋊C411yescharacteristic
71C23×C263C22⋊C411yescharacteristic
72C23×C263C2×D411yescharacteristic
73C2×C4×C263—22no—
74C2×C4×C263—22no—
75C2×C4×C263—24no—
76C2×C4×C263—41no—
77C2×C4×C263—41no—
78C2×C4×C263—41no—
79C2×C4×C263—41no—
80C2×C4×C263—48no—
81C2×C4×C263—42no—
82C2×C4×C263—42no—
83C2×C4×C263C22⋊C411yescharacteristic
84C2×C4×C263C22⋊C411yescharacteristic
85C2×C4×C263C22×C411yescharacteristic
86C2×C4×C263C2×D411yescharacteristic
87C22×C263—24no—
88C22×C263—24no—
89C22×C263—21no—
90C22×C263—21no—
91C22×C263—21no—
92C22×C263—21no—
93C22×C263—21no—
94C22×C263—21no—
95C22×C263#9912yes—
96C22×C263#10412yes—
97C22×C263C2×C22⋊C411yescharacteristic
98C22×C263AGL(1,ℤ/8)11yescharacteristic
99C22×C263#13711yescharacteristic
100C2×D263—41no—
101C2×D263—41no—
102C2×D263—41no—
103C4×C263—21no—
104C4×C263—21no—
105C4×C263—21no—
106C4×C263—21no—
107C4×C263—44no—
108Dic263—41no—
109Dic263—41no—
110Dic263—41no—
111C2×C263—21no—
112C2×C263—22no—
113C2×C263—22no—
114C2×C263—21no—
115C2×C263C2×#9911yescharacteristic
116C2×C263#41711yescharacteristic
117C2×C263C2×#10411yescharacteristic
118D263—81no—
119C263#150411yescharacteristic, complemented, Sylow
120#1504—2631nomaximal, Sylow
121#525—2631no—
122#407—2631no—
123C2×#95D26311yescharacteristic, complemented
124#328—2632no—
125#327—2632no—
126C2×#41—2631no—
127C23×C4—21no—
128C23×C4C2×D26311yescharacteristic
129C2×M16—5261no—
130#123—5261no—
131C22⋊Q8—2631no—
132C22⋊Q8—2631no—
133#121—2631no—
134#121—2631no—
135#120—5261no—
136C4×D4—5261no—
137C4×D4—5261no—
138#117—2631no—
139C22⋊C8—2632no—
140C22⋊C8—5261no—
141#95—21no—
142#95C2×D26312yes—
143C24C22⋊D26311yescharacteristic
144#41—10522no—
145C2×Q8—2631no—
146C2×D4—2631no—
147C2×D4—5261no—
148C2×D4—5261no—
149C2×D4—5261no—
150C22×C4—24no—
151C22×C4—22no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4—42no—
155C22×C4—5261no—
156C22×C4C4×D26311yescharacteristic
157C22×C4C4×D26311yescharacteristic
158C22×C4C22⋊D26311yescharacteristic
159C22×C4D105211yescharacteristic
160C22×C4D105211yescharacteristic
161C22×C4C22×D26311yescharacteristic
162M16—10522no—
163C2×C8—5262no—
164C4⋊C4—2631no—
165C4⋊C4—2631no—
166C4⋊C4—5261no—
167C4⋊C4—5261no—
168C22⋊C4—5261no—
169C22⋊C4—5261no—
170C22⋊C4—5261no—
171C22⋊C4—5261no—
172C22⋊C4—5261no—
173C42—5261no—
174C23—22no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—5261no—
179C23(C2×D263)⋊C411yescharacteristic
180C23(C2×D263)⋊C411yescharacteristic
181C23C2×C22⋊D26311yescharacteristic
182Q8—10521no—
183D4—10521no—
184D4—10522no—
185D4—10522no—
186D4—10521no—
187D4—10521no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—48no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—5261no—
199C2×C4—5261no—
200C2×C4—5261no—
201C2×C4—10522no—
202C2×C4(C2×D263)⋊C411yescharacteristic
203C2×C4(C2×D263)⋊C411yescharacteristic
204C2×C4C2×C4×D26311yescharacteristic
205C2×C4C2×D105211yescharacteristic
206C8—10522no—
207C22—24no—
208C22—24no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—10521no—
216C22—10521no—
217C22—10521no—
218C22#2255438412yes—
219C22#2255439812yes—
220C22C2×(C2×D263)⋊C411yescharacteristic
221C22#2255449611yescharacteristic
222C22#2255450111yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—44no—
228C4—10521no—
229C4—10521no—
230C4—10521no—
231C2—21no—
232C2—22no—
233C2—22no—
234C2—21no—
235C2—21041no—
236C2C2×#2255438411yescharacteristic
237C2#3068193711yescharacteristic
238C2C2×#2255439811yescharacteristic
subgroupG/H
centerC22C2×(C2×D263)⋊C4
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#95×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682449C2
cosocleC22×C4×C263C23
hypercenterC2×#95D263
hypocenterC263#1504
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
2. #30681902C2semidirect
3. #30681674C2semidirect
4. #30681671C2semidirect
5. C2×#95×C263C2semidirect
6. C2×#16862376C4semidirect
9. #22554449C4semidirect
11. #22554444C4semidirect
16. #22554429C4semidirect
24. C2×Dic526C2×C4semidirect
25. C2×D1052C2×C4semidirect
32. C4⋊Dic263C2×C4semidirect
33. C4⋊Dic263C2×C4semidirect
119. C263#1504semidirect
123. C2×#95D263semidirect

Maximal subgroups

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

subgroupindex
#306824492
#306819022
#306816742
#306816712
C2×#95×C2632
#1504263