Finite Group Databasebeta

← #46783126

Subgroups — #46783126

Order 33664.

370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#22554496C211yesmaximal, characteristic
2#30682419C211yesmaximal, characteristic, complemented
3C2×#22554398C211yesmaximal, characteristic, complemented
4#30681943C211yesmaximal, characteristic, complemented
5#30681707C211yesmaximal, characteristic, complemented
6#30681698C211yesmaximal, characteristic, complemented
7#390×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554496—22no—
10#22554496C414yescomplemented
11C2×#16862364—21no—
12C2×#16862361—21no—
13C2×#16862360C2211yescharacteristic
14C2×#16862360C2211yescharacteristic
15#22554435—21no—
16#22554432—21no—
17C4×C22⋊D263—22no—
18#22554429C2211yescharacteristic
19#22554428—21no—
20C4⋊C4×D263—21no—
21#22554398—22no—
22#22554391—21no—
23#22554391—21no—
24C22×D4×C263C2211yescharacteristic
25C2×C4⋊C4×C263C2211yescharacteristic
26C2×C22⋊C4×C263—22no—
27C2×C42×C263C2211yescharacteristic
28#16862376—21no—
29#16862376—21no—
30#16862376C2×C412yes—
31#16862376D412yes—
32C2×Dic526D411yescharacteristic
33C2×D1052D411yescharacteristic
34C2×C22⋊D263—21no—
35C2×C4×D263—22no—
36C2×C4×D263—21no—
37#16862364—24no—
38#16862361—24no—
39#16862360—21no—
40#16862360—21no—
41#16862360—21no—
42#16862360C2×C412yescomplemented
43C2×C263⋊C8—21no—
44C2×C263⋊C8—21no—
45C4⋊Dic263D411yescharacteristic
46C4⋊Dic263D411yescharacteristic
47Dic263⋊C4—22no—
48C22⋊Dic263—21no—
49(C2×D263)⋊C4—22no—
50C4×Dic263—22no—
51C4×Dic263—21no—
52C24×C263—21no—
53C2×D4×C263—21no—
54C2×D4×C263—21no—
55C2×D4×C263—21no—
56C2×D4×C263—21no—
57C2×D4×C263—21no—
58C2×D4×C263C2×C412yescomplemented
59C22×C4×C263—21no—
60C22×C4×C263D412yes—
61C22×C4×C263C2311yescharacteristic
62C4⋊C4×C263—21no—
63C4⋊C4×C263—21no—
64C22⋊C4×C263—44no—
65C42×C263—21no—
66C42×C263—21no—
67C22×D263—21no—
68Dic526—21no—
69Dic526C22⋊C412yescomplemented
70D1052—21no—
71D1052C22⋊C412yescomplemented
72C22⋊D263—22no—
73C22⋊D263—22no—
74C2×Dic263—21no—
75C2×Dic263—21no—
76C2×Dic263—21no—
77C4×D263—22no—
78C4×D263—22no—
79C4×D263—82no—
80C263⋊C8—22no—
81C263⋊C8—41no—
82C23×C263—22no—
83C23×C263—42no—
84C23×C263—42no—
85C23×C263—41no—
86C23×C263—41no—
87C23×C263C2×D411yescharacteristic
88D4×C263—22no—
89D4×C263—22no—
90D4×C263—41no—
91D4×C263—41no—
92C2×C4×C263—22no—
93C2×C4×C263—22no—
94C2×C4×C263—41no—
95C2×C4×C263—41no—
96C2×C4×C263—42no—
97C2×C4×C263C22×C411yescharacteristic
98C2×C4×C263C2×D411yescharacteristic
99C2×C4×C263C2×D411yescharacteristic
100C2×C4×C263C2×D411yescharacteristic
101C2×C4×C263#4111yescharacteristic
102C2×C4×C263#4111yescharacteristic
103C22×C263—21no—
104C22×C263—21no—
105C22×C263—44no—
106C22×C263—42no—
107C22×C263—82no—
108C22×C263—81no—
109C22×C263—81no—
110C22×C263C4×D411yescharacteristic
111C22×C263#12011yescharacteristic
112C22×C263#12111yescharacteristic
113C2×D263—22no—
114C2×D263—41no—
115C2×D263—41no—
116C4×C263—42no—
117C4×C263—42no—
118C4×C263C2×C22⋊C411yescharacteristic
119C4×C263C4×D411yescharacteristic
120C4×C263#12111yescharacteristic
121C4×C263#12311yescharacteristic
122Dic263—22no—
123Dic263—41no—
124Dic263—41no—
125C2×C263—21no—
126C2×C263—21no—
127C2×C263—82no—
128C2×C263#38611yescharacteristic
129C2×C263#45311yescharacteristic
130C2×C263#45411yescharacteristic
131D263—42no—
132C263#188311yescharacteristic, complemented, Sylow
133#1883—2631nomaximal, Sylow
134C2×AGL(1,ℤ/8)—2631no—
135#520—2631no—
136C2×#104—2631no—
137#418—2631no—
138#390D26311yescharacteristic, complemented
139#343—2631no—
140#339—2631no—
141C2×#41—2631no—
142C22×D4C2×D26311yescharacteristic
143AGL(1,ℤ/8)—2634no—
144AGL(1,ℤ/8)—5262no—
145C2×SD16—5261no—
146C2×D8—5261no—
147C2×M16—2631no—
148C2×M16—2631no—
149C4×Q8—5261no—
150C4×D4—5261no—
151C4×D4—5262no—
152#117—2631no—
153#117—5261no—
154C2×C4⋊C4—5261no—
155C2×C4⋊C4C2×D26311yescharacteristic
156C2×C22⋊C4—22no—
157C2×C42C2×D26311yescharacteristic
158#104—5262no—
159#102—5261no—
160#102—5261no—
161C24—21no—
162#41—2632no—
163#41—2632no—
164#41—5261no—
165#41—5261no—
166C2×Q8—2631no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—2631no—
173C2×D4—5261no—
174C2×D4C4×D26312yescomplemented
175C22×C4—21no—
176C22×C4—5262no—
177C22×C4—5261no—
178C22×C4C22⋊D26312yes—
179C22×C4C22×D26311yescharacteristic
180SD16—5264no—
181D8—5264no—
182M16—2632no—
183M16—5261no—
184M16—5261no—
185M16—5261no—
186C2×C8—5261no—
187C2×C8—5261no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—2631no—
191C4⋊C4—2631no—
192C4⋊C4—5262no—
193C22⋊C4—44no—
194C22⋊C4—5262no—
195C22⋊C4—5261no—
196C42—21no—
197C42—21no—
198C42—5262no—
199C42—5261no—
200C23—22no—
201C23—42no—
202C23—42no—
203C23—41no—
204C23—41no—
205C23—5261no—
206C23C2×C22⋊D26311yescharacteristic
207Q8—2632no—
208Q8—5261no—
209D4—22no—
210D4—22no—
211D4—41no—
212D4—41no—
213D4—2632no—
214D4—5262no—
215D4—5262no—
216D4—5261no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—5261no—
223C2×C4—5262no—
224C2×C4—5262no—
225C2×C4—5261no—
226C2×C4—5261no—
227C2×C4—21042no—
228C2×C4C2×C4×D26311yescharacteristic
229C2×C4D4×D26311yescharacteristic
230C2×C4D4×D26311yescharacteristic
231C2×C4D4×D26311yescharacteristic
232C2×C4#1686237511yescharacteristic
233C2×C4#1686237611yescharacteristic
234C8—5262no—
235C8—10521no—
236C22—21no—
237C22—21no—
238C22—44no—
239C22—42no—
240C22—82no—
241C22—81no—
242C22—81no—
243C22—5262no—
244C22—10521no—
245C22—10521no—
246C22C4×C22⋊D26311yescharacteristic
247C22#2255443811yescharacteristic
248C22#2255444111yescharacteristic
249C4—42no—
250C4—42no—
251C4—5262no—
252C4—10521no—
253C4—10521no—
254C4C22⋊C4×D26311yescharacteristic
255C4(C22⋊D263)⋊C411yescharacteristic
256C4#2255444311yescharacteristic
257C4#2255445211yescharacteristic
258C2—21no—
259C2—21no—
260C2—82no—
261C2—10522no—
262C2#3068181411yescharacteristic
263C2#3068210511yescharacteristic
264C2#3068211011yescharacteristic
subgroupG/H
centerC22#22554438
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#390×C263C2
socleC22×C263#120
prime radicalC2×#22554496C2
cosocleC22×C4×C263C23
hypercenter#390D263
hypocenterC263#1883
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. #30682419C2semidirect
3. C2×#22554398C2semidirect
4. #30681943C2semidirect
5. #30681707C2semidirect
6. #30681698C2semidirect
7. #390×C263C2semidirect
10. #22554496C4semidirect
42. #16862360C2×C4semidirect
58. C2×D4×C263C2×C4semidirect
69. Dic526C22⋊C4semidirect
71. D1052C22⋊C4semidirect
132. C263#1883semidirect
138. #390D263semidirect
174. C2×D4C4×D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225544962
#306824192
C2×#225543982
#306819432
#306817072
#306816982
#390×C2632
#1883263