Finite Group Databasebeta

← #46783798

Subgroups — #46783798

Order 33664.

380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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#30682736C211yesmaximal, characteristic, complemented
2#30682505C211yesmaximal, characteristic, complemented
3#30681954C211yesmaximal, characteristic, complemented
4#30681943C211yesmaximal, characteristic, complemented
5#30681912C211yesmaximal, characteristic, complemented
6#30681710C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554501—21no—
10#22554500—21no—
11#22554496—21no—
12#22554495—21no—
13#22554490—22no—
14C2×#16862360C2211yescharacteristic
15#22554466—21no—
16#22554457—21no—
17#22554441—22no—
18#22554439—22no—
19#22554429C2211yescharacteristic
20#22554429C2211yescharacteristic
21#22554396—22no—
22#22554391—22no—
23#22554385—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—24no—
38C2×C22⋊D263—21no—
39C2×C4×D263—21no—
40#16862366—22no—
41#16862364—22no—
42#16862363—22no—
43#16862361—22no—
44#16862360—21no—
45#16862360—21no—
46C2×C263⋊C8D412yescomplemented
47C4⋊Dic263—21no—
48C4⋊Dic263—21no—
49C22⋊Dic263—24no—
50C22⋊Dic263—21no—
51C22⋊Dic263D412yes—
52C4×Dic263—21no—
53C4×Dic263—21no—
54C24×C263—21no—
55#41×C263—21no—
56#41×C263—21no—
57#41×C263—21no—
58#41×C263—21no—
59C2×Q8×C263D411yescharacteristic, complemented
60C2×D4×C263—21no—
61C2×D4×C263—21no—
62C2×D4×C263—21no—
63C2×D4×C263—21no—
64C2×D4×C263—21no—
65C2×D4×C263—21no—
66C2×D4×C263D412yes—
67C2×D4×C263D411yescharacteristic, complemented
68C22×C4×C263—21no—
69C22×C4×C263C2311yescharacteristic
70SD16×C263—24no—
71D8×C263—24no—
72M16×C263—21no—
73M16×C263D412yescomplemented
74C2×C8×C263—21no—
75C22×D263—21no—
76Dic526—21no—
77Dic526—21no—
78D1052—21no—
79D1052—21no—
80C22⋊D263—41no—
81C22⋊D263—41no—
82C22⋊D263—84no—
83C2×Dic263—22no—
84C2×Dic263—21no—
85C2×Dic263—41no—
86C4×D263—41no—
87C4×D263—41no—
88C263⋊C8—22no—
89C23×C263—22no—
90C23×C263—21no—
91C23×C263—41no—
92C23×C263—41no—
93C23×C263—82no—
94C23×C263C2×D411yescharacteristic
95Q8×C263—21no—
96Q8×C263—21no—
97D4×C263—21no—
98D4×C263—22no—
99D4×C263—21no—
100D4×C263—22no—
101D4×C263—41no—
102D4×C263—41no—
103D4×C263—41no—
104D4×C263—41no—
105C2×C4×C263—21no—
106C2×C4×C263—41no—
107C2×C4×C263—41no—
108C2×C4×C263C2×D411yescharacteristic
109C2×C4×C263C2×D411yescharacteristic
110C2×C4×C263C2×D411yescharacteristic
111C2×C4×C263C2×D411yescharacteristic
112C2×C4×C263C2×D411yescharacteristic
113C2×C4×C263#4111yescharacteristic
114C8×C263—22no—
115C22×C263—41no—
116C22×C263—44no—
117C22×C263—41no—
118C22×C263—42no—
119C22×C263—81no—
120C22×C263—82no—
121C22×C263—82no—
122C22×C263#12011yescharacteristic
123C22×C263#12111yescharacteristic
124C22×C263#12711yescharacteristic
125C2×D263—42no—
126C2×D263—41no—
127C4×C263—41no—
128C4×C263#12011yescharacteristic
129C4×C263#12011yescharacteristic
130C4×C263#12111yescharacteristic
131C4×C263#12111yescharacteristic
132Dic263—42no—
133Dic263—41no—
134Dic263—81no—
135C2×C263—21no—
136C2×C263—21no—
137C2×C263—21no—
138C2×C263—82no—
139C2×C263—81no—
140C2×C263#39211yescharacteristic
141D263—81no—
142C263#200811yescharacteristic, complemented, Sylow
143#2008—2631nomaximal, Sylow
144#575—2631no—
145C2×AGL(1,ℤ/8)D26311yescharacteristic, complemented
146#535—2631no—
147#421—2631no—
148#418—2631no—
149#410—2631no—
150#344—2631no—
151C2×#41—2631no—
152C2×#41C2×D26311yescharacteristic
153C22×D4C2×D26311yescharacteristic
154#137—5261no—
155#137—5261no—
156AGL(1,ℤ/8)—22no—
157AGL(1,ℤ/8)—22no—
158AGL(1,ℤ/8)—5261no—
159AGL(1,ℤ/8)—5261no—
160#135—5262no—
161C2×SD16—21no—
162C2×D8—21no—
163C2×M16—2631no—
164C2×M16C2×D26311yescharacteristic
165#127—5261no—
166#124—5261no—
167#121—5262no—
168#120—5262no—
169#117—2631no—
170#117—2631no—
171#104—5262no—
172#102—5262no—
173#99—5262no—
174C24—21no—
175#41—21no—
176#41—21no—
177#41—21no—
178#41—21no—
179#41—5261no—
180#41—5261no—
181#41—5261no—
182#41—5261no—
183C2×Q8—2631no—
184C2×Q8C22⋊D26311yescharacteristic, complemented
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—21no—
190C2×D4—21no—
191C2×D4—2631no—
192C2×D4—5261no—
193C2×D4—5264no—
194C2×D4C22⋊D26312yes—
195C2×D4C22⋊D26311yescharacteristic, complemented
196C22×C4—21no—
197C22×C4—5261no—
198C22×C4C22×D26311yescharacteristic
199Q16—5262no—
200SD16—24no—
201SD16—5262no—
202SD16—5262no—
203D8—24no—
204D8—5262no—
205M16—21no—
206M16—5261no—
207M16—5261no—
208M16C22⋊D26312yescomplemented
209C2×C8—21no—
210C2×C8—2632no—
211C4⋊C4—5261no—
212C4⋊C4—5261no—
213C22⋊C4—2632no—
214C22⋊C4—5264no—
215C22⋊C4—5261no—
216C42—5261no—
217C42—5261no—
218C23—22no—
219C23—21no—
220C23—41no—
221C23—41no—
222C23—82no—
223C23—5261no—
224C23D4×D26311yescharacteristic
225Q8—21no—
226Q8—21no—
227Q8—5261no—
228Q8—5261no—
229D4—21no—
230D4—21no—
231D4—22no—
232D4—22no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—41no—
237D4—5261no—
238D4—5261no—
239D4—10521no—
240D4—10521no—
241D4—21044no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—5262no—
246C2×C4—5261no—
247C2×C4—10521no—
248C2×C4—10521no—
249C2×C4—10521no—
250C2×C4D4×D26311yescharacteristic
251C2×C4D4×D26311yescharacteristic
252C2×C4C2×C22⋊D26311yescharacteristic
253C2×C4C2×C22⋊D26311yescharacteristic
254C2×C4C2×C22⋊D26311yescharacteristic
255C2×C4#1686237511yescharacteristic
256C8—22no—
257C8—5262no—
258C22—41no—
259C22—44no—
260C22—41no—
261C22—42no—
262C22—81no—
263C22—82no—
264C22—82no—
265C22—10522no—
266C22—10521no—
267C22#2255443811yescharacteristic
268C22#2255444211yescharacteristic
269C22#2255446611yescharacteristic
270C4—41no—
271C4—10522no—
272C4—10521no—
273C4—21041no—
274C4#2255443811yescharacteristic
275C4#2255443911yescharacteristic
276C4#2255444111yescharacteristic
277C4#2255444211yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—82no—
282C2—81no—
283C2—21041no—
284C2#3068184611yescharacteristic
subgroupG/H
centerC2#30681846
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×AGL(1,ℤ/8)×C263C2
socleC2×C263#392
hypercenterC2×AGL(1,ℤ/8)D263
hypocenterC263#2008
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #30682736C2semidirect
2. #30682505C2semidirect
3. #30681954C2semidirect
4. #30681943C2semidirect
5. #30681912C2semidirect
6. #30681710C2semidirect
7. C2×AGL(1,ℤ/8)×C263C2semidirect
46. C2×C263⋊C8D4semidirect
59. C2×Q8×C263D4semidirect
67. C2×D4×C263D4semidirect
73. M16×C263D4semidirect
142. C263#2008semidirect
145. C2×AGL(1,ℤ/8)D263semidirect
184. C2×Q8C22⋊D263semidirect
195. C2×D4C22⋊D263semidirect
208. M16C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
#306827362
#306825052
#306819542
#306819432
#306819122
#306817102
C2×AGL(1,ℤ/8)×C2632
#2008263