Finite Group Databasebeta

← #46783257

Subgroups — #46783257

Order 33664.

332 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 97 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×#22554477C211yesmaximal, characteristic, complemented
2#30681939C211yesmaximal, characteristic, complemented
3C2×#22554391C211yesmaximal, characteristic, complemented
4C2×#22554387C211yesmaximal, characteristic, complemented
5#30681706C211yesmaximal, characteristic, complemented
6#30681702C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C263C211yesmaximal, characteristic
8#22554477—22no—
9#22554477—22no—
10C2×#16862360—21no—
11C2×#16862360C2211yescharacteristic
12C2×#16862360C2211yescharacteristic
13C22×C263⋊C8—21no—
14C22×C263⋊C8C2211yescharacteristic
15C2×C4⋊Dic263C2211yescharacteristic
16#22554394—21no—
17#22554391—21no—
18#22554391—21no—
19#22554391—21no—
20#22554387—22no—
21C2×#41×C263C2211yescharacteristic
22C22×D4×C263C2211yescharacteristic
23AGL(1,ℤ/8)×C263—22no—
24AGL(1,ℤ/8)×C263C414yescomplemented
25C2×SD16×C263—21no—
26C2×D8×C263—21no—
27C2×M16×C263C2211yescharacteristic
28C22×Dic263—21no—
29#16862360—24no—
30#16862360—21no—
31#16862360—21no—
32#16862360—21no—
33#16862360D412yes—
34C2×C263⋊C8—24no—
35C2×C263⋊C8—21no—
36C2×C263⋊C8—21no—
37C2×C263⋊C8—21no—
38C2×C263⋊C8—21no—
39C2×C263⋊C8D411yescharacteristic
40C2×C263⋊C8D411yescharacteristic
41C4⋊Dic263—21no—
42C4⋊Dic263—21no—
43C24×C263—21no—
44#41×C263—21no—
45#41×C263—21no—
46#41×C263C2×C412yes—
47#41×C263D412yes—
48C2×Q8×C263D411yescharacteristic
49C2×D4×C263—21no—
50C2×D4×C263—21no—
51C2×D4×C263—21no—
52C2×D4×C263—21no—
53C2×D4×C263—21no—
54C2×D4×C263—21no—
55C2×D4×C263C2×C412yes—
56C2×D4×C263D411yescharacteristic
57C22×C4×C263—21no—
58C22×C4×C263C2311yescharacteristic
59SD16×C263—24no—
60D8×C263—24no—
61M16×C263—21no—
62M16×C263C2×C412yes—
63C2×C8×C263—21no—
64C2×Dic263—41no—
65C2×Dic263—81no—
66C263⋊C8—21no—
67C263⋊C8—22no—
68C263⋊C8—21no—
69C263⋊C8—41no—
70C23×C263—21no—
71C23×C263—22no—
72C23×C263—41no—
73C23×C263—41no—
74C23×C263—81no—
75C23×C263—81no—
76C23×C263#4111yescharacteristic
77Q8×C263—21no—
78Q8×C263C22⋊C412yes—
79D4×C263—22no—
80D4×C263—22no—
81D4×C263—22no—
82D4×C263—22no—
83D4×C263—21no—
84D4×C263—41no—
85D4×C263—41no—
86D4×C263C22⋊C412yes—
87C2×C4×C263—21no—
88C2×C4×C263—22no—
89C2×C4×C263—22no—
90C2×C4×C263C22×C411yescharacteristic
91C2×C4×C263C2×D411yescharacteristic
92C2×C4×C263C2×D411yescharacteristic
93C2×C4×C263C2×D411yescharacteristic
94C2×C4×C263C2×D411yescharacteristic
95C2×C4×C263#4111yescharacteristic
96C8×C263—22no—
97C22×C263—21no—
98C22×C263—21no—
99C22×C263—22no—
100C22×C263—41no—
101C22×C263—41no—
102C22×C263—42no—
103C22×C263—82no—
104C22×C263—82no—
105C22×C263—81no—
106C22×C263—81no—
107C22×C263C4×D411yescharacteristic
108C22×C263#12111yescharacteristic
109C22×C263#12311yescharacteristic
110C4×C263—22no—
111C4×C263C2×C22⋊C411yescharacteristic
112C4×C263C4×D411yescharacteristic
113C4×C263#12011yescharacteristic
114C4×C263#12111yescharacteristic
115Dic263—81no—
116C2×C263—21no—
117C2×C263—21no—
118C2×C263—42no—
119C2×C263—82no—
120C2×C263#38611yescharacteristic
121C2×C263#47111yescharacteristic
122C2×C263#47211yescharacteristic
123C263#190711yescharacteristic, complemented, Sylow
124#1907—2631nomaximal, Sylow
125C2×AGL(1,ℤ/8)D26311yescharacteristic
126C2×#131—2631no—
127#417—2631no—
128C2×#102—2631no—
129C2×#100—2631no—
130#343—2631no—
131#341—2631no—
132C2×#41C2×D26311yescharacteristic
133C22×D4C2×D26311yescharacteristic
134AGL(1,ℤ/8)—22no—
135AGL(1,ℤ/8)Dic26314yescomplemented
136C2×SD16—21no—
137C2×D8—21no—
138#131—5262no—
139#131—5262no—
140C2×M16—2631no—
141C2×M16—2631no—
142C2×M16—5261no—
143C2×M16C2×D26311yescharacteristic
144C22×C8—2631no—
145C22×C8—5261no—
146C2×C4⋊C4—2631no—
147#103—5261no—
148#102—5261no—
149#102—5261no—
150#102—5261no—
151#100—5262no—
152C24—21no—
153#41—21no—
154#41—21no—
155#41C2×Dic26312yes—
156#41C22⋊D26312yes—
157C2×Q8C22⋊D26311yescharacteristic
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4C2×Dic26312yes—
165C2×D4C22⋊D26311yescharacteristic
166C22×C4—21no—
167C22×C4—5261no—
168C22×C4C22×D26311yescharacteristic
169SD16—24no—
170D8—24no—
171M16—21no—
172M16—2632no—
173M16—5264no—
174M16—5261no—
175M16—5261no—
176M16—5261no—
177M16C2×Dic26312yes—
178C2×C8—21no—
179C2×C8—2631no—
180C2×C8—2631no—
181C2×C8—5264no—
182C2×C8—5261no—
183C2×C8—5261no—
184C2×C8—5261no—
185C2×C8—5261no—
186C4⋊C4—5261no—
187C4⋊C4—5261no—
188C23—21no—
189C23—22no—
190C23—41no—
191C23—41no—
192C23—81no—
193C23—81no—
194C23#1686237511yescharacteristic
195Q8—21no—
196Q8C22⋊Dic26312yes—
197D4—22no—
198D4—22no—
199D4—22no—
200D4—22no—
201D4—21no—
202D4—41no—
203D4—41no—
204D4C22⋊Dic26312yes—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—10521no—
209C2×C4—21041no—
210C2×C4C22×Dic26311yescharacteristic
211C2×C4D4×D26311yescharacteristic
212C2×C4D4×D26311yescharacteristic
213C2×C4C2×C22⋊D26311yescharacteristic
214C2×C4C2×C22⋊D26311yescharacteristic
215C2×C4#1686237511yescharacteristic
216C8—22no—
217C8—5261no—
218C8—5261no—
219C8—5262no—
220C8—10521no—
221C22—21no—
222C22—21no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—42no—
227C22—82no—
228C22—82no—
229C22—81no—
230C22—81no—
231C22D4×Dic26311yescharacteristic
232C22#2255444211yescharacteristic
233C22#2255445111yescharacteristic
234C4—22no—
235C4—21041no—
236C4C2×C22⋊Dic26311yescharacteristic
237C4D4×Dic26311yescharacteristic
238C4#2255443811yescharacteristic
239C4#2255444211yescharacteristic
240C2—21no—
241C2—21no—
242C2—42no—
243C2—82no—
244C2#3068181811yescharacteristic
245C2#3068219911yescharacteristic
246C2#3068220611yescharacteristic
subgroupG/H
centerC22#22554442
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting, prime radicalC2×AGL(1,ℤ/8)×C263C2
socleC22×C263#121
cosocleC22×C4×C263C23
hypercenterC2×AGL(1,ℤ/8)D263
hypocenterC263#1907
LCSG ▷ C2×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×#22554477C2semidirect
2. #30681939C2semidirect
3. C2×#22554391C2semidirect
4. C2×#22554387C2semidirect
5. #30681706C2semidirect
6. #30681702C2semidirect
24. AGL(1,ℤ/8)×C263C4semidirect
123. C263#1907semidirect
135. AGL(1,ℤ/8)Dic263semidirect

Maximal subgroups

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

subgroupindex
C2×#225544772
#306819392
C2×#225543912
C2×#225543872
#306817062
#306817022
C2×AGL(1,ℤ/8)×C2632
#1907263