Finite Group Databasebeta

← #46783787

Subgroups — #46783787

Order 33664.

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

normal subgroups only

This group has 406 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
1C2×#22554496C211yesmaximal, characteristic, complemented
2#30682516C211yesmaximal, characteristic, complemented
3C2×#22554397C211yesmaximal, characteristic, complemented
4C2×#22554396C211yesmaximal, characteristic, complemented
5#30681841C211yesmaximal, characteristic, complemented
6#30681706C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554496—22no—
10#22554496—22no—
11C2×#16862364—21no—
12C2×#16862361—21no—
13C2×#16862360C2211yescharacteristic
14#22554449—21no—
15#22554446—21no—
16#22554444—21no—
17#22554442—22no—
18#22554441—21no—
19C2×C4⋊Dic263C2211yescharacteristic
20C2×C22⋊Dic263—22no—
21C2×C4×Dic263C2211yescharacteristic
22#22554397—22no—
23#22554396—22no—
24C2×#41×C263C2211yescharacteristic
25C22×D4×C263C2211yescharacteristic
26AGL(1,ℤ/8)×C263—22no—
27AGL(1,ℤ/8)×C263—22no—
28C2×SD16×C263—21no—
29C2×D8×C263—21no—
30C2×M16×C263C2211yescharacteristic
31#16862376—21no—
32#16862376—21no—
33#16862376—21no—
34#16862376—21no—
35C2×Dic526D411yescharacteristic
36C2×D1052D411yescharacteristic
37C2×C22⋊D263—22no—
38C2×C22⋊D263—21no—
39C22×Dic263—21no—
40C22×Dic263D412yes—
41C2×C4×D263—21no—
42#16862364—24no—
43#16862361—24no—
44#16862360—21no—
45#16862360D412yescomplemented
46C2×C263⋊C8—21no—
47C4⋊Dic263—21no—
48C4⋊Dic263—21no—
49Dic263⋊C4—22no—
50C22⋊Dic263—22no—
51C22⋊Dic263—44no—
52(C2×D263)⋊C4—22no—
53C4×Dic263—21no—
54C4×Dic263—21no—
55C24×C263—21no—
56#41×C263—21no—
57#41×C263—21no—
58#41×C263—21no—
59#41×C263—21no—
60C2×Q8×C263D411yescharacteristic
61C2×D4×C263—21no—
62C2×D4×C263—21no—
63C2×D4×C263—21no—
64C2×D4×C263—21no—
65C2×D4×C263—21no—
66C2×D4×C263—21no—
67C2×D4×C263D411yescharacteristic
68C2×D4×C263D412yescomplemented
69C22×C4×C263—21no—
70C22×C4×C263C2311yescharacteristic
71SD16×C263—24no—
72D8×C263—24no—
73M16×C263—21no—
74M16×C263D412yescomplemented
75C2×C8×C263—21no—
76C22×D263—21no—
77Dic526—21no—
78Dic526—21no—
79D1052—21no—
80D1052—21no—
81C22⋊D263—41no—
82C22⋊D263—41no—
83C22⋊D263—82no—
84C2×Dic263—22no—
85C2×Dic263—22no—
86C2×Dic263—21no—
87C2×Dic263—41no—
88C2×Dic263—41no—
89C2×Dic263—42no—
90C4×D263—41no—
91C4×D263—41no—
92C263⋊C8—22no—
93C23×C263—21no—
94C23×C263—22no—
95C23×C263—42no—
96C23×C263—42no—
97C23×C263—41no—
98C23×C263—41no—
99C23×C263C2×D411yescharacteristic
100Q8×C263—21no—
101Q8×C263—21no—
102D4×C263—21no—
103D4×C263—22no—
104D4×C263—22no—
105D4×C263—21no—
106D4×C263—41no—
107D4×C263—41no—
108D4×C263—41no—
109D4×C263—41no—
110C2×C4×C263—21no—
111C2×C4×C263—41no—
112C2×C4×C263—41no—
113C2×C4×C263C2×D411yescharacteristic
114C2×C4×C263C2×D411yescharacteristic
115C2×C4×C263C2×D411yescharacteristic
116C2×C4×C263C2×D411yescharacteristic
117C2×C4×C263C2×D411yescharacteristic
118C2×C4×C263#4111yescharacteristic
119C8×C263—22no—
120C22×C263—21no—
121C22×C263—21no—
122C22×C263—44no—
123C22×C263—41no—
124C22×C263—42no—
125C22×C263—41no—
126C22×C263—41no—
127C22×C263—82no—
128C22×C263—81no—
129C22×C263—81no—
130C22×C263#12011yescharacteristic
131C22×C263#12111yescharacteristic
132C22×C263#12711yescharacteristic
133C2×D263—41no—
134C2×D263—41no—
135C2×D263—41no—
136C4×C263—41no—
137C4×C263#12011yescharacteristic
138C4×C263#12011yescharacteristic
139C4×C263#12111yescharacteristic
140C4×C263#12111yescharacteristic
141Dic263—42no—
142Dic263—41no—
143Dic263—42no—
144C2×C263—21no—
145C2×C263—21no—
146C2×C263—81no—
147C2×C263—82no—
148C2×C263#39211yescharacteristic
149C2×C263#45311yescharacteristic
150C2×C263#45411yescharacteristic
151D263—81no—
152C263#200611yescharacteristic, complemented, Sylow
153#2006—2631nomaximal, Sylow
154C2×AGL(1,ℤ/8)—2631no—
155C2×AGL(1,ℤ/8)D26311yescharacteristic, complemented
156#537—2631no—
157C2×#104—2631no—
158C2×#104—2631no—
159#390—2631no—
160#343—2631no—
161C2×#41—2631no—
162C2×#41C2×D26311yescharacteristic
163C22×D4C2×D26311yescharacteristic
164AGL(1,ℤ/8)—22no—
165AGL(1,ℤ/8)—22no—
166AGL(1,ℤ/8)—5262no—
167AGL(1,ℤ/8)—5262no—
168C2×SD16—21no—
169C2×SD16—5261no—
170C2×D8—21no—
171C2×D8—5261no—
172C2×M16—2631no—
173C2×M16C2×D26311yescharacteristic
174C22⋊Q8—5261no—
175C22⋊Q8—5261no—
176#121—5261no—
177#121—5262no—
178#121—5261no—
179C2×C4⋊C4—2631no—
180C2×C22⋊C4—5262no—
181C2×C42—2631no—
182#104—5262no—
183#104—5262no—
184C24—21no—
185#41—21no—
186#41—21no—
187#41—21no—
188#41—21no—
189#41—5261no—
190#41—5261no—
191#41—5261no—
192#41—5261no—
193C2×Q8—2631no—
194C2×Q8C22⋊D26311yescharacteristic
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—2631no—
202C2×D4—5261no—
203C2×D4—5262no—
204C2×D4C22⋊D26311yescharacteristic
205C2×D4C22⋊D26312yescomplemented
206C22×C4—21no—
207C22×C4—2632no—
208C22×C4—5261no—
209C22×C4—5261no—
210C22×C4C22×D26311yescharacteristic
211SD16—24no—
212SD16—5264no—
213D8—24no—
214D8—5264no—
215M16—21no—
216M16—2632no—
217M16—5261no—
218M16C22⋊D26312yescomplemented
219C2×C8—21no—
220C2×C8—5261no—
221C4⋊C4—5262no—
222C4⋊C4—5261no—
223C4⋊C4—5261no—
224C22⋊C4—5262no—
225C22⋊C4—5262no—
226C22⋊C4—10524no—
227C42—5261no—
228C42—5261no—
229C23—21no—
230C23—22no—
231C23—42no—
232C23—42no—
233C23—41no—
234C23—41no—
235C23—5261no—
236C23D4×D26311yescharacteristic
237Q8—21no—
238Q8—21no—
239Q8—5261no—
240Q8—5261no—
241D4—22no—
242D4—21no—
243D4—22no—
244D4—21no—
245D4—41no—
246D4—41no—
247D4—41no—
248D4—41no—
249D4—5261no—
250D4—5261no—
251D4—10521no—
252D4—10521no—
253D4—21042no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—5262no—
258C2×C4—5262no—
259C2×C4—5261no—
260C2×C4—10521no—
261C2×C4—10521no—
262C2×C4—10521no—
263C2×C4—10521no—
264C2×C4—10522no—
265C2×C4D4×D26311yescharacteristic
266C2×C4D4×D26311yescharacteristic
267C2×C4C2×C22⋊D26311yescharacteristic
268C2×C4C2×C22⋊D26311yescharacteristic
269C2×C4C2×C22⋊D26311yescharacteristic
270C2×C4#1686237511yescharacteristic
271C8—22no—
272C8—5262no—
273C22—21no—
274C22—21no—
275C22—44no—
276C22—41no—
277C22—42no—
278C22—41no—
279C22—41no—
280C22—82no—
281C22—81no—
282C22—81no—
283C22—10521no—
284C22—10521no—
285C22—10521no—
286C22#2255443811yescharacteristic
287C22#2255444211yescharacteristic
288C22#2255446611yescharacteristic
289C4—41no—
290C4—10522no—
291C4—10521no—
292C4—10522no—
293C4#2255443811yescharacteristic
294C4#2255443911yescharacteristic
295C4#2255444111yescharacteristic
296C4#2255444211yescharacteristic
297C2—21no—
298C2—21no—
299C2—82no—
300C2—81no—
301C2—21041no—
302C2#3068184611yescharacteristic
303C2#3068210411yescharacteristic
304C2#3068210911yescharacteristic
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#2006
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. C2×#22554496C2semidirect
2. #30682516C2semidirect
3. C2×#22554397C2semidirect
4. C2×#22554396C2semidirect
5. #30681841C2semidirect
6. #30681706C2semidirect
7. C2×AGL(1,ℤ/8)×C263C2semidirect
45. #16862360D4semidirect
68. C2×D4×C263D4semidirect
74. M16×C263D4semidirect
152. C263#2006semidirect
155. C2×AGL(1,ℤ/8)D263semidirect
205. C2×D4C22⋊D263semidirect
218. M16C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225544962
#306825162
C2×#225543972
C2×#225543962
#306818412
#306817062
C2×AGL(1,ℤ/8)×C2632
#2006263