Finite Group Databasebeta

← #46783759

Subgroups — #46783759

Order 33664.

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

normal subgroups only

This group has 478 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#30682502C211yesmaximal, characteristic, complemented
2C2×#22554466C211yesmaximal, characteristic, complemented
3C2×#22554397C211yesmaximal, characteristic, complemented
4#30681943C211yesmaximal, characteristic, complemented
5C2×#22554386C211yesmaximal, characteristic, complemented
6#30681699C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C263C211yesmaximal, characteristic, complemented
8C22×D1052C2211yescharacteristic
9C22×C22⋊D263—22no—
10C2×#16862360C2211yescharacteristic
11#22554466—22no—
12#22554466—22no—
13#22554466—21no—
14#22554459—21no—
15#22554444—22no—
16#22554438—22no—
17#22554429C2211yescharacteristic
18C2×C4×Dic263C2211yescharacteristic
19#22554397—22no—
20#22554391—22no—
21#22554386—22no—
22C2×#41×C263C2211yescharacteristic
23C22×D4×C263C2211yescharacteristic
24AGL(1,ℤ/8)×C263—22no—
25AGL(1,ℤ/8)×C263—22no—
26C2×SD16×C263—21no—
27C2×D8×C263—21no—
28C2×M16×C263C2211yescharacteristic
29C23×D263D412yes—
30C2×D1052—21no—
31C2×D1052—21no—
32C2×D1052—21no—
33C2×D1052—21no—
34C2×D1052—21no—
35C2×D1052—21no—
36C2×C22⋊D263—28no—
37C2×C22⋊D263—24no—
38C2×C22⋊D263—48no—
39C22×Dic263—21no—
40#16862360—21no—
41#16862360—21no—
42C2×C263⋊C8—21no—
43C4⋊Dic263D412yescomplemented
44C22⋊Dic263—21no—
45(C2×D263)⋊C4—24no—
46C4×Dic263—21no—
47C4×Dic263—21no—
48C4×Dic263D412yescomplemented
49C24×C263—21no—
50#41×C263—21no—
51#41×C263—21no—
52#41×C263—21no—
53#41×C263—21no—
54C2×Q8×C263D411yescharacteristic, complemented
55C2×D4×C263—21no—
56C2×D4×C263—21no—
57C2×D4×C263—21no—
58C2×D4×C263—21no—
59C2×D4×C263—21no—
60C2×D4×C263—21no—
61C2×D4×C263D412yescomplemented
62C2×D4×C263D411yescharacteristic, complemented
63C22×C4×C263—21no—
64C22×C4×C263C2311yescharacteristic
65SD16×C263—24no—
66D8×C263—24no—
67M16×C263—21no—
68M16×C263D412yescomplemented
69C2×C8×C263—21no—
70C22×D263—22no—
71C22×D263—22no—
72C22×D263—22no—
73C22×D263—44no—
74D1052—41no—
75D1052—41no—
76D1052—41no—
77D1052—41no—
78C22⋊D263—416no—
79C22⋊D263—84no—
80C2×Dic263—24no—
81C2×Dic263—22no—
82C2×Dic263—22no—
83C263⋊C8—41no—
84C23×C263—21no—
85C23×C263—22no—
86C23×C263—44no—
87C23×C263—41no—
88C23×C263—41no—
89C23×C263C2×D411yescharacteristic
90Q8×C263—21no—
91Q8×C263—21no—
92D4×C263—21no—
93D4×C263—22no—
94D4×C263—22no—
95D4×C263—21no—
96D4×C263—41no—
97D4×C263—41no—
98D4×C263—41no—
99D4×C263—41no—
100C2×C4×C263—21no—
101C2×C4×C263—41no—
102C2×C4×C263—41no—
103C2×C4×C263C2×D411yescharacteristic
104C2×C4×C263C2×D411yescharacteristic
105C2×C4×C263C2×D411yescharacteristic
106C2×C4×C263C2×D411yescharacteristic
107C2×C4×C263C2×D411yescharacteristic
108C2×C4×C263#4111yescharacteristic
109C8×C263—22no—
110C22×C263—22no—
111C22×C263—44no—
112C22×C263—41no—
113C22×C263—42no—
114C22×C263—42no—
115C22×C263—82no—
116C22×C263—82no—
117C22×C263#12011yescharacteristic
118C22×C263#12011yescharacteristic
119C22×C263#12111yescharacteristic
120C2×D263—44no—
121C2×D263—42no—
122C2×D263—44no—
123C2×D263—82no—
124C4×C263—41no—
125C4×C263#12011yescharacteristic
126C4×C263#12111yescharacteristic
127C4×C263#12111yescharacteristic
128C4×C263#12711yescharacteristic
129Dic263—24no—
130Dic263—42no—
131C2×C263—21no—
132C2×C263—21no—
133C2×C263—81no—
134C2×C263—82no—
135C2×C263#39211yescharacteristic
136C2×C263#45312yes—
137D263—82no—
138C263#200211yescharacteristic, complemented, Sylow
139#2002—2631nomaximal, Sylow
140C2×AGL(1,ℤ/8)D26311yescharacteristic, complemented
141#535—2631no—
142C2×#127—2631no—
143C2×#104—2631no—
144#418—2631no—
145C2×#100—2631no—
146#339—2631no—
147C2×#41C2×D26311yescharacteristic
148C22×D4—2631no—
149C22×D4—5262no—
150C22×D4C2×D26311yescharacteristic
151AGL(1,ℤ/8)—22no—
152AGL(1,ℤ/8)—22no—
153C2×SD16—21no—
154C2×D8—21no—
155C2×M16—2631no—
156C2×M16C2×D26311yescharacteristic
157#127—5262no—
158#127—5262no—
159#127—5261no—
160#124—5261no—
161#121—5262no—
162#120—5262no—
163#117—2631no—
164C2×C42—2631no—
165#104—5262no—
166#102—5262no—
167#100—5262no—
168C24—21no—
169C24—2632no—
170#41—21no—
171#41—21no—
172#41—21no—
173#41—21no—
174C2×Q8C22⋊D26311yescharacteristic, complemented
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—5268no—
182C2×D4—5264no—
183C2×D4—5261no—
184C2×D4—5261no—
185C2×D4—5261no—
186C2×D4—5261no—
187C2×D4—5261no—
188C2×D4—5261no—
189C2×D4—10528no—
190C2×D4C22⋊D26311yescharacteristic, complemented
191C2×D4C22⋊D26312yescomplemented
192C22×C4—21no—
193C22×C4—5261no—
194C22×C4C22×D26311yescharacteristic
195SD16—24no—
196D8—24no—
197M16—21no—
198M16—5261no—
199M16—5261no—
200M16C22⋊D26312yescomplemented
201C2×C8—21no—
202C2×C8—5261no—
203C4⋊C4—2632no—
204C22⋊C4—5264no—
205C22⋊C4—5261no—
206C42—2632no—
207C42—5261no—
208C42—5261no—
209C23—22no—
210C23—21no—
211C23—44no—
212C23—41no—
213C23—41no—
214C23—5262no—
215C23—5262no—
216C23—5262no—
217C23—10524no—
218C23D4×D26311yescharacteristic
219Q8—21no—
220Q8—21no—
221D4—21no—
222D4—22no—
223D4—22no—
224D4—21no—
225D4—41no—
226D4—41no—
227D4—41no—
228D4—41no—
229D4—105216no—
230D4—10521no—
231D4—10521no—
232D4—10521no—
233D4—10521no—
234D4—21044no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—5264no—
239C2×C4—5262no—
240C2×C4—5262no—
241C2×C4D4×D26311yescharacteristic
242C2×C4D4×D26311yescharacteristic
243C2×C4C2×C22⋊D26311yescharacteristic
244C2×C4C2×C22⋊D26311yescharacteristic
245C2×C4C2×C22⋊D26311yescharacteristic
246C2×C4#1686237511yescharacteristic
247C8—22no—
248C8—10521no—
249C22—22no—
250C22—44no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—82no—
255C22—82no—
256C22—10524no—
257C22—10522no—
258C22—10524no—
259C22—21042no—
260C22#2255443811yescharacteristic
261C22#2255443811yescharacteristic
262C22#2255444111yescharacteristic
263C4—41no—
264C4—5264no—
265C4—10522no—
266C4#2255443911yescharacteristic
267C4#2255444211yescharacteristic
268C4#2255444211yescharacteristic
269C4#2255446611yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—81no—
274C2—21042no—
275C2#3068184611yescharacteristic
276C2#3068210412yes—
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×AGL(1,ℤ/8)×C263C2
socleC22×C263#120
hypercenterC2×AGL(1,ℤ/8)D263
hypocenterC263#2002
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #30682502C2semidirect
2. C2×#22554466C2semidirect
3. C2×#22554397C2semidirect
4. #30681943C2semidirect
5. C2×#22554386C2semidirect
6. #30681699C2semidirect
7. C2×AGL(1,ℤ/8)×C263C2semidirect
43. C4⋊Dic263D4semidirect
48. C4×Dic263D4semidirect
54. C2×Q8×C263D4semidirect
61. C2×D4×C263D4semidirect
62. C2×D4×C263D4semidirect
68. M16×C263D4semidirect
138. C263#2002semidirect
140. C2×AGL(1,ℤ/8)D263semidirect
174. C2×Q8C22⋊D263semidirect
190. C2×D4C22⋊D263semidirect
191. C2×D4C22⋊D263semidirect
200. M16C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
#306825022
C2×#225544662
C2×#225543972
#306819432
C2×#225543862
#306816992
C2×AGL(1,ℤ/8)×C2632
#2002263