Finite Group Databasebeta

← #46783778

Subgroups — #46783778

Order 33664.

394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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×#22554503C211yesmaximal, characteristic, complemented
2#30682505C211yesmaximal, characteristic
3C2×#22554457C211yesmaximal, characteristic, complemented
4C2×#22554396C211yesmaximal, characteristic, complemented
5#30681948C211yesmaximal, characteristic, complemented
6#30681699C211yesmaximal, characteristic, complemented
7C2×#100×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C22×Dic526C2211yescharacteristic
10#22554503—22no—
11#22554503—22no—
12C2×Dic1052—21no—
13C2×#16862365—21no—
14#22554466—21no—
15#22554457—21no—
16#22554457—22no—
17#22554457—22no—
18#22554441—22no—
19#22554439—22no—
20#22554429C2211yescharacteristic
21C2×C22⋊Dic263—22no—
22C2×C4×Dic263C2211yescharacteristic
23#22554396—22no—
24#22554395—22no—
25C22×D4×C263C2211yescharacteristic
26C2×M16×C263C2211yescharacteristic
27C2×M16×C263C2211yescharacteristic
28#100×C263—22no—
29#16862376—21no—
30#16862376—21no—
31#16862376—21no—
32#16862376—21no—
33C2×Dic526—21no—
34C2×Dic526—21no—
35C2×Dic526—21no—
36C2×Dic526—21no—
37C2×Dic526—21no—
38C2×Dic526D411yescharacteristic
39C2×Dic526D412yescomplemented
40C2×D1052D411yescharacteristic
41C2×C22⋊D263—24no—
42C2×C22⋊D263—21no—
43C22×Dic263—21no—
44C22×Dic263—21no—
45C2×C4×D263—21no—
46Dic1052—24no—
47#16862365—24no—
48C4⋊Dic263D412yes—
49C22⋊Dic263—28no—
50C22⋊Dic263—24no—
51C22⋊Dic263—21no—
52C4×Dic263—21no—
53C4×Dic263—21no—
54C4×Dic263D412yescomplemented
55C24×C263D412yes—
56C2×D4×C263—21no—
57C2×D4×C263—21no—
58C2×D4×C263—21no—
59C2×D4×C263—21no—
60C2×D4×C263—21no—
61C2×D4×C263—21no—
62C22×C4×C263C2311yescharacteristic
63M16×C263—21no—
64M16×C263—21no—
65M16×C263—21no—
66M16×C263D412yescomplemented
67C2×C8×C263—21no—
68C2×C8×C263—21no—
69C22×D263—21no—
70Dic526—22no—
71Dic526—21no—
72Dic526—22no—
73Dic526—21no—
74Dic526—41no—
75Dic526—41no—
76D1052—21no—
77D1052—21no—
78C22⋊D263—41no—
79C22⋊D263—41no—
80C22⋊D263—84no—
81C2×Dic263—22no—
82C2×Dic263—22no—
83C2×Dic263—21no—
84C2×Dic263—22no—
85C2×Dic263—42no—
86C2×Dic263—41no—
87C2×Dic263—41no—
88C4×D263—41no—
89C4×D263—41no—
90C23×C263—22no—
91C23×C263—22no—
92C23×C263—22no—
93C23×C263—44no—
94C23×C263C2×D411yescharacteristic
95D4×C263—41no—
96D4×C263—41no—
97D4×C263—41no—
98D4×C263—41no—
99C2×C4×C263C2×D411yescharacteristic
100C2×C4×C263C2×D411yescharacteristic
101C2×C4×C263C2×D411yescharacteristic
102C2×C4×C263C2×D411yescharacteristic
103C2×C4×C263C2×D411yescharacteristic
104C2×C4×C263#4111yescharacteristic
105C8×C263—22no—
106C8×C263—41no—
107C22×C263—22no—
108C22×C263—44no—
109C22×C263—42no—
110C22×C263—44no—
111C22×C263—82no—
112C22×C263#12011yescharacteristic
113C22×C263#12011yescharacteristic
114C22×C263#12111yescharacteristic
115C2×D263—41no—
116C2×D263—42no—
117C4×C263#12011yescharacteristic
118C4×C263#12111yescharacteristic
119C4×C263#12111yescharacteristic
120C4×C263#12711yescharacteristic
121Dic263—42no—
122Dic263—41no—
123Dic263—42no—
124Dic263—42no—
125C2×C263—21no—
126C2×C263—21no—
127C2×C263—82no—
128C2×C263#39211yescharacteristic
129C2×C263#45512yes—
130D263—81no—
131C263#200411yescharacteristic, complemented, Sylow
132#2004—2631nomaximal, Sylow
133C2×#137—2631no—
134#535—2631no—
135C2×#124—2631no—
136C2×#104—2631no—
137#419—2631no—
138C2×#100D26311yescharacteristic, complemented
139#339—2631no—
140C2×#41—2631no—
141C22×Q8—2631no—
142C22×D4C2×D26311yescharacteristic
143#137—5262no—
144#137—5262no—
145C2×Q16—5261no—
146C2×SD16—5261no—
147C2×M16C2×D26311yescharacteristic
148C2×M16C2×D26311yescharacteristic
149#127—5261no—
150#124—5262no—
151#124—5262no—
152#124—5261no—
153#121—5262no—
154#120—5262no—
155#117—2631no—
156C2×C22⋊C4—5262no—
157C2×C42—2631no—
158#104—5262no—
159#103—5262no—
160#100—22no—
161C24D105212yes—
162#41—5261no—
163#41—5261no—
164#41—5261no—
165#41—5261no—
166C2×Q8—2631no—
167C2×Q8—2632no—
168C2×Q8—5261no—
169C2×Q8—5261no—
170C2×Q8—5261no—
171C2×Q8—5261no—
172C2×Q8—5261no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—2631no—
180C2×D4—5261no—
181C2×D4—5264no—
182C22×C4—5261no—
183C22×C4—5261no—
184C22×C4—5261no—
185C22×C4C22×D26311yescharacteristic
186Q16—5264no—
187SD16—5264no—
188M16—21no—
189M16—21no—
190M16—21no—
191M16C22⋊D26312yescomplemented
192C2×C8—21no—
193C2×C8—21no—
194C4⋊C4—2632no—
195C22⋊C4—5268no—
196C22⋊C4—5264no—
197C22⋊C4—5261no—
198C42—2632no—
199C42—5261no—
200C42—5261no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—44no—
205C23—5261no—
206C23C2×D105211yescharacteristic
207Q8—5262no—
208Q8—5261no—
209Q8—5262no—
210Q8—5261no—
211Q8—10521no—
212Q8—10521no—
213D4—41no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—5261no—
218D4—5261no—
219D4—10521no—
220D4—10521no—
221D4—21044no—
222C2×C4—5262no—
223C2×C4—5262no—
224C2×C4—5262no—
225C2×C4—5261no—
226C2×C4—10522no—
227C2×C4—10521no—
228C2×C4—10521no—
229C2×C4—10521no—
230C2×C4—10521no—
231C2×C4D4×D26311yescharacteristic
232C2×C4D4×D26311yescharacteristic
233C2×C4D4×D26311yescharacteristic
234C2×C4D4×D26311yescharacteristic
235C2×C4C2×C22⋊D26311yescharacteristic
236C2×C4#1686237611yescharacteristic
237C8—22no—
238C8—41no—
239C22—22no—
240C22—44no—
241C22—44no—
242C22—42no—
243C22—82no—
244C22—10522no—
245C22—10521no—
246C22#2255444011yescharacteristic
247C22#2255444011yescharacteristic
248C22#2255444411yescharacteristic
249C4—10522no—
250C4—10522no—
251C4—10521no—
252C4—10522no—
253C4#2255443811yescharacteristic
254C4#2255444311yescharacteristic
255C4#2255444311yescharacteristic
256C4#2255446611yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—21041no—
261C2#3068184711yescharacteristic
262C2#3068211812yes—
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#100×C263C2
socleC22×C263#120
prime radical#30682505C2
hypercenterC2×#100D263
hypocenterC263#2004
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#22554503C2semidirect
3. C2×#22554457C2semidirect
4. C2×#22554396C2semidirect
5. #30681948C2semidirect
6. #30681699C2semidirect
7. C2×#100×C263C2semidirect
39. C2×Dic526D4semidirect
54. C4×Dic263D4semidirect
66. M16×C263D4semidirect
131. C263#2004semidirect
138. C2×#100D263semidirect
191. M16C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225545032
#306825052
C2×#225544572
C2×#225543962
#306819482
#306816992
C2×#100×C2632
#2004263