Finite Group Databasebeta

← #46784061

Subgroups — #46784061

Order 33664.

324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C22×#16862363C211yesmaximal, characteristic
2C2×Dic263⋊C8C211yesmaximal, characteristic, complemented
3C2×#22554392C211yesmaximal, characteristic
4#30681845C211yesmaximal, characteristic, complemented
5#30681839C211yesmaximal, characteristic
6#30681700C211yesmaximal, characteristic, complemented
7C2×#103×C263C211yesmaximal, characteristic, complemented
8C22×D1052C2211yescharacteristic
9C2×#16862363—22no—
10C2×#16862363—22no—
11C2×#16862363—22no—
12C22×C263⋊C8C2211yescharacteristic
13C2×C4⋊Dic263C2211yescharacteristic
14C2×(C2×D263)⋊C4—21no—
15C2×(C2×D263)⋊C4—21no—
16C2×C4×Dic263C2211yescharacteristic
17Dic263⋊C8—22no—
18#22554392—22no—
19C263⋊#95—21no—
20C263⋊#95—21no—
21C22×Q8×C263C2211yescharacteristic
22C22×C8×C263C2211yescharacteristic
23C2×C4⋊C4×C263C2211yescharacteristic
24#103×C263—22no—
25C23×D263—21no—
26C2×D1052—21no—
27C2×D1052—21no—
28C2×D1052—21no—
29C2×D1052—21no—
30C2×D1052—21no—
31C2×D1052D412yes—
32C22×Dic263—21no—
33C22×Dic263D411yescharacteristic
34C22×Dic263D411yescharacteristic
35#16862363—28no—
36C2×C263⋊C8—21no—
37C2×C263⋊C8—21no—
38C2×C263⋊C8D412yes—
39C4⋊Dic263—21no—
40C4⋊Dic263—21no—
41(C2×D263)⋊C4—42no—
42(C2×D263)⋊C4—42no—
43C4×Dic263—21no—
44C4×Dic263—21no—
45C2×Q8×C263—21no—
46C2×Q8×C263—21no—
47C2×Q8×C263—21no—
48C2×Q8×C263—21no—
49C2×Q8×C263—21no—
50C2×Q8×C263D412yes—
51C22×C4×C263—21no—
52C22×C4×C263—21no—
53C22×C4×C263C2311yescharacteristic
54C2×C8×C263—21no—
55C2×C8×C263—21no—
56C2×C8×C263—21no—
57C4⋊C4×C263—21no—
58C4⋊C4×C263—21no—
59C22×D263—22no—
60C22×D263—41no—
61C22×D263—41no—
62C22×D263—41no—
63C22×D263—41no—
64C22×D263—41no—
65C22×D263—41no—
66D1052—22no—
67D1052—22no—
68D1052—41no—
69D1052—41no—
70C2×Dic263—21no—
71C2×Dic263—21no—
72C2×Dic263—21no—
73C2×Dic263—21no—
74C2×Dic263—21no—
75C2×Dic263—41no—
76C2×Dic263—41no—
77C2×Dic263—41no—
78C2×Dic263SD1612yescomplemented
79C263⋊C8—22no—
80C23×C263C2×D411yescharacteristic
81Q8×C263—22no—
82Q8×C263—22no—
83Q8×C263—41no—
84Q8×C263—41no—
85C2×C4×C263—22no—
86C2×C4×C263—41no—
87C2×C4×C263—41no—
88C2×C4×C263—41no—
89C2×C4×C263—41no—
90C2×C4×C263—41no—
91C2×C4×C263C2×D411yescharacteristic
92C2×C4×C263C2×D411yescharacteristic
93C2×C4×C263C2×D411yescharacteristic
94C2×C4×C263#4111yescharacteristic
95C2×C4×C263#4111yescharacteristic
96C2×C4×C263#4111yescharacteristic
97C8×C263—41no—
98C22×C263#12111yescharacteristic
99C22×C263#12111yescharacteristic
100C22×C263#12111yescharacteristic
101C22×C263C2×SD1611yescharacteristic
102C22×C263#13511yescharacteristic
103C22×C263AGL(1,ℤ/8)11yescharacteristic
104C22×C263#13711yescharacteristic
105C2×D263—42no—
106C2×D263—42no—
107C2×D263—42no—
108C2×D263—81no—
109C2×D263—81no—
110C2×D263—81no—
111C2×D263—81no—
112C4×C263—42no—
113C4×C263—81no—
114C4×C263#12011yescharacteristic
115C4×C263#12311yescharacteristic
116C4×C263#12311yescharacteristic
117C4×C263#12411yescharacteristic
118Dic263—22no—
119Dic263—41no—
120Dic263—81no—
121C2×C263#39411yescharacteristic
122C2×C263#46011yescharacteristic
123C2×C263#46111yescharacteristic
124C2×C263#46311yescharacteristic
125C2×C263#46411yescharacteristic
126C2×C263#46511yescharacteristic
127C2×C263#46811yescharacteristic
128D263—82no—
129C263#205511yescharacteristic, complemented, Sylow
130#2055—2631nomaximal, Sylow
131C22×SD16—2631no—
132C2×C4⋊C8—2631no—
133C2×#103D26311yescharacteristic, complemented
134C2×#102—2631no—
135#391—2631no—
136#390—2631no—
137#340—2631no—
138C22×Q8C2×D26311yescharacteristic
139C22×D4—2631no—
140C2×SD16—5262no—
141C2×SD16—5262no—
142C2×SD16—5262no—
143C22×C8—2631no—
144C22×C8C2×D26311yescharacteristic
145C2×C4⋊C4—2631no—
146C2×C4⋊C4C2×D26311yescharacteristic
147C2×C22⋊C4—5261no—
148C2×C22⋊C4—5261no—
149C2×C42—2631no—
150C4⋊C8—5262no—
151#103—22no—
152#102—5262no—
153#95—5261no—
154#95—5261no—
155C24—5261no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8C22⋊D26312yes—
162C2×D4—2632no—
163C2×D4—5261no—
164C2×D4—5261no—
165C2×D4—5261no—
166C2×D4—5261no—
167C2×D4—5261no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—2631no—
171C22×C4—2631no—
172C22×C4—5261no—
173C22×C4C22×D26311yescharacteristic
174SD16—5268no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—2632no—
179C2×C8—5261no—
180C2×C8—5261no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—5261no—
184C4⋊C4—5261no—
185C22⋊C4—10522no—
186C22⋊C4—10522no—
187C42—5261no—
188C42—5261no—
189C23—5262no—
190C23—10521no—
191C23—10521no—
192C23—10521no—
193C23—10521no—
194C23—10521no—
195C23—10521no—
196C23D4×D26311yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—5262no—
202D4—5262no—
203D4—10521no—
204D4—10521no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—2632no—
212C2×C4—5261no—
213C2×C4—5261no—
214C2×C4—5261no—
215C2×C4—5261no—
216C2×C4—5261no—
217C2×C4—10521no—
218C2×C4—10521no—
219C2×C4—10521no—
220C2×C4D4×D26311yescharacteristic
221C2×C4D4×D26311yescharacteristic
222C2×C4C2×C22⋊D26311yescharacteristic
223C2×C4#1686237511yescharacteristic
224C2×C4#1686237611yescharacteristic
225C2×C4#1686237611yescharacteristic
226C8—41no—
227C8—5262no—
228C22—10522no—
229C22—10522no—
230C22—10522no—
231C22—21041no—
232C22—21041no—
233C22—21041no—
234C22—21041no—
235C22#2255444211yescharacteristic
236C22#2255444311yescharacteristic
237C22#2255444311yescharacteristic
238C22SD16×D26311yescharacteristic
239C22#2255449311yescharacteristic
240C22#2255449711yescharacteristic
241C22#2255450211yescharacteristic
242C4—42no—
243C4—81no—
244C4—5262no—
245C4—10521no—
246C4—21041no—
247C4#2255443811yescharacteristic
248C4#2255445211yescharacteristic
249C4#2255445311yescharacteristic
250C4#2255445611yescharacteristic
251C2—21042no—
252C2#3068185311yescharacteristic
253C2#3068213611yescharacteristic
254C2#3068214211yescharacteristic
255C2#3068215611yescharacteristic
256C2#3068216211yescharacteristic
257C2#3068217011yescharacteristic
258C2#3068218711yescharacteristic
subgroupG/H
centerC23D4×D263
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#103×C263C2
socleC23×C263C2×D4
prime radicalC22×D1052C22
hypercenterC2×#103D263
hypocenterC263#2055
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×Dic263⋊C8C2semidirect
4. #30681845C2semidirect
6. #30681700C2semidirect
7. C2×#103×C263C2semidirect
78. C2×Dic263SD16semidirect
129. C263#2055semidirect
133. C2×#103D263semidirect

Maximal subgroups

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

subgroupindex
C22×#168623632
C2×Dic263⋊C82
C2×#225543922
#306818452
#306818392
#306817002
C2×#103×C2632
#2055263