Finite Group Databasebeta

← #46783944

Subgroups — #46783944

Order 33664.

316 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 89 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×#22554449C211yesmaximal, characteristic
2C2×#22554402C211yesmaximal, characteristic, complemented
3C2×#22554395C211yesmaximal, characteristic, complemented
4C2×#22554395C211yesmaximal, characteristic, complemented
5#30681798C211yesmaximal, characteristic
6#30681701C211yesmaximal, characteristic, complemented
7C2×C22⋊C8×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9#22554449—22no—
10#22554449—22no—
11C2×C4⋊Dic263C2211yescharacteristic
12C2×C4⋊Dic263C2211yescharacteristic
13C2×C4⋊Dic263C2211yescharacteristic
14C2×Dic263⋊C4—21no—
15C2×C22⋊Dic263—21no—
16C2×C22⋊Dic263—21no—
17#22554402—22no—
18#22554395—22no—
19#22554395—22no—
20C263⋊#95—21no—
21C23×C4×C263C2211yescharacteristic
22C22×C8×C263C2211yescharacteristic
23C22×C8×C263C2211yescharacteristic
24C22⋊C8×C263—22no—
25C2×Dic526—21no—
26C2×Dic526—21no—
27C2×Dic526—21no—
28C2×Dic526—21no—
29C2×Dic526—21no—
30C2×Dic526D412yes—
31C22×Dic263—21no—
32C22×Dic263—21no—
33C22×Dic263—21no—
34C22×Dic263—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263—21no—
37C4⋊Dic263—21no—
38C4⋊Dic263—21no—
39C4⋊Dic263—21no—
40C4⋊Dic263D412yes—
41Dic263⋊C4—24no—
42C22⋊Dic263—24no—
43C22⋊Dic263—42no—
44C24×C263D411yescharacteristic
45C22×C4×C263—21no—
46C22×C4×C263—21no—
47C22×C4×C263—21no—
48C22×C4×C263—21no—
49C22×C4×C263—21no—
50C22×C4×C263—21no—
51C22×C4×C263D411yescharacteristic
52C22×C4×C263C2311yescharacteristic
53C2×C8×C263—21no—
54C2×C8×C263—21no—
55C2×C8×C263—21no—
56C2×C8×C263—21no—
57C2×C8×C263—21no—
58C2×C8×C263D412yes—
59Dic526—22no—
60Dic526—22no—
61Dic526—41no—
62Dic526—41no—
63C2×Dic263—22no—
64C2×Dic263—22no—
65C2×Dic263—41no—
66C2×Dic263—41no—
67C2×Dic263—41no—
68C2×Dic263—41no—
69C2×Dic263—41no—
70C2×Dic263—41no—
71C2×Dic263—41no—
72C2×Dic263—41no—
73C2×Dic263—41no—
74C2×Dic263—41no—
75C23×C263—21no—
76C23×C263—21no—
77C23×C263—21no—
78C23×C263—21no—
79C23×C263—21no—
80C23×C263—21no—
81C23×C263SD1612yes—
82C23×C263C2×D411yescharacteristic
83C2×C4×C263—21no—
84C2×C4×C263—21no—
85C2×C4×C263—21no—
86C2×C4×C263—41no—
87C2×C4×C263—41no—
88C2×C4×C263—41no—
89C2×C4×C263—41no—
90C2×C4×C263C2×D411yescharacteristic
91C2×C4×C263C2×D411yescharacteristic
92C2×C4×C263C2×D411yescharacteristic
93C2×C4×C263#4111yescharacteristic
94C2×C4×C263#4111yescharacteristic
95C2×C4×C263#4111yescharacteristic
96C8×C263—22no—
97C8×C263—41no—
98C22×C263—22no—
99C22×C263—22no—
100C22×C263—22no—
101C22×C263—41no—
102C22×C263—41no—
103C22×C263—41no—
104C22×C263—41no—
105C22×C263#12011yescharacteristic
106C22×C263#12111yescharacteristic
107C22×C263#12311yescharacteristic
108C22×C263C2×SD1611yescharacteristic
109C22×C263#13511yescharacteristic
110C22×C263#13711yescharacteristic
111C22×C263#13711yescharacteristic
112C4×C263—41no—
113C4×C263#12111yescharacteristic
114C4×C263#12111yescharacteristic
115C4×C263#12311yescharacteristic
116C4×C263#12411yescharacteristic
117Dic263—42no—
118Dic263—42no—
119Dic263—81no—
120Dic263—81no—
121C2×C263—42no—
122C2×C263#39411yescharacteristic
123C2×C263#44811yescharacteristic
124C2×C263#45211yescharacteristic
125C2×C263#46511yescharacteristic
126C2×C263#47011yescharacteristic
127C2×C263#48311yescharacteristic
128C2×C263#48511yescharacteristic
129C263#203511yescharacteristic, complemented, Sylow
130#2035—2631nomaximal, Sylow
131C2×C22⋊Q8—2631no—
132C2×#106—2631no—
133C2×#103—2631no—
134C2×#103—2631no—
135C2×C22⋊C8D26311yescharacteristic
136#380—2631no—
137#340—2631no—
138C22×Q8—2631no—
139C23×C4C2×D26311yescharacteristic
140C22×C8C2×D26311yescharacteristic
141C22×C8C2×D26311yescharacteristic
142C22⋊Q8—5262no—
143C22⋊Q8—5262no—
144C2×C4⋊C4—2631no—
145C2×C4⋊C4—2631no—
146C2×C4⋊C4—2631no—
147C2×C4⋊C4—5261no—
148C2×C22⋊C4—5261no—
149C2×C22⋊C4—5261no—
150#106—5262no—
151#103—5262no—
152#103—5262no—
153C22⋊C8—22no—
154#95—5261no—
155C24D105211yescharacteristic
156C2×Q8—2632no—
157C2×Q8—5261no—
158C2×Q8—5261no—
159C2×Q8—5261no—
160C2×Q8—5261no—
161C2×Q8—5261no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—5261no—
169C22×C4—5261no—
170C22×C4—5261no—
171C22×C4—5261no—
172C22×C4D105211yescharacteristic
173C22×C4C22×D26311yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8C22⋊D26312yes—
180C4⋊C4—2632no—
181C4⋊C4—5264no—
182C4⋊C4—5261no—
183C4⋊C4—5261no—
184C4⋊C4—5261no—
185C4⋊C4—5261no—
186C4⋊C4—5261no—
187C22⋊C4—5264no—
188C22⋊C4—10522no—
189C23—21no—
190C23—21no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23#1686236512yes—
196C23C2×D105211yescharacteristic
197Q8—5262no—
198Q8—5262no—
199Q8—10521no—
200Q8—10521no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—5262no—
209C2×C4—5262no—
210C2×C4—10521no—
211C2×C4—10521no—
212C2×C4—10521no—
213C2×C4—10521no—
214C2×C4—10521no—
215C2×C4—10521no—
216C2×C4—10521no—
217C2×C4—10521no—
218C2×C4—10521no—
219C2×C4—10521no—
220C2×C4D4×D26311yescharacteristic
221C2×C4D4×D26311yescharacteristic
222C2×C4C2×C22⋊D26311yescharacteristic
223C2×C4#1686237511yescharacteristic
224C2×C4#1686237511yescharacteristic
225C2×C4#1686237611yescharacteristic
226C8—22no—
227C8—41no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22#2255444011yescharacteristic
236C22#2255444411yescharacteristic
237C22#2255445411yescharacteristic
238C22C2×#1686236511yescharacteristic
239C22#2255449211yescharacteristic
240C22#2255450311yescharacteristic
241C22#2255450311yescharacteristic
242C4—41no—
243C4—10522no—
244C4—10522no—
245C4—21041no—
246C4—21041no—
247C4#2255444111yescharacteristic
248C4#2255444211yescharacteristic
249C4#2255445211yescharacteristic
250C4#2255445611yescharacteristic
251C2—42no—
252C2#3068185411yescharacteristic
253C2#3068207911yescharacteristic
254C2#3068210211yescharacteristic
255C2#3068216711yescharacteristic
256C2#3068219611yescharacteristic
257C2#3068226911yescharacteristic
258C2#3068228011yescharacteristic
subgroupG/H
centerC23C2×D1052
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×C22⋊C8×C263C2
socleC23×C263C2×D4
prime radicalC24×C263D4
hypercenterC2×C22⋊C8D263
hypocenterC263#2035
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#22554402C2semidirect
3. C2×#22554395C2semidirect
4. C2×#22554395C2semidirect
6. #30681701C2semidirect
129. C263#2035semidirect

Maximal subgroups

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

subgroupindex
C2×#225544492
C2×#225544022
C2×#225543952
#306817982
#306817012
C2×C22⋊C8×C2632
#2035263