Finite Group Databasebeta

← #46783049

Subgroups — #46783049

Order 33664.

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

normal subgroups only

This group has 376 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
1#30682449C211yesmaximal, characteristic
2C2×#22554396C212yesmaximal, complemented
3C4×C22⋊Dic263C211yesmaximal, characteristic, complemented
4#30681699C212yesmaximal, complemented
5C22×M16×C263C211yesmaximal, characteristic, complemented
6C2×#16862376C2211yescharacteristic
7#22554453—21no—
8#22554449C411yescharacteristic, complemented
9#22554449C411yescharacteristic, complemented
10#22554444C411yescharacteristic, complemented
11#22554444C411yescharacteristic, complemented
12#22554439—21no—
13C4×C22⋊D263—21no—
14C4×C22⋊D263—21no—
15#22554429C2211yescharacteristic
16C2×C22⋊Dic263—21no—
17C2×C4×Dic263C2212yes—
18#22554396—24no—
19C263⋊#95—21no—
20C23×C4×C263C2211yescharacteristic
21C2×M16×C263—21no—
22C2×M16×C263—24no—
23C2×M16×C263C2212yes—
24C22×C8×C263—21no—
25#16862376—22no—
26#16862376—22no—
27C2×Dic526C2×C411yescharacteristic
28C2×D1052C2×C411yescharacteristic
29C2×C22⋊D263—21no—
30C2×C22⋊D263—21no—
31C2×C22⋊D263—21no—
32C22×Dic263—22no—
33C2×C4×D263—21no—
34C4⋊Dic263C2×C411yescharacteristic
35C4⋊Dic263C2×C411yescharacteristic
36Dic263⋊C4—21no—
37Dic263⋊C4—21no—
38C22⋊Dic263—24no—
39C22⋊Dic263—21no—
40C22⋊Dic263—21no—
41C22⋊Dic263—21no—
42(C2×D263)⋊C4—21no—
43(C2×D263)⋊C4—21no—
44C4×Dic263—21no—
45C4×Dic263—22no—
46C4×Dic263—22no—
47C24×C263D411yescharacteristic
48C22×C4×C263—22no—
49C22×C4×C263—22no—
50C22×C4×C263C2×C411yescharacteristic
51C22×C4×C263C2×C411yescharacteristic
52C22×C4×C263D411yescharacteristic
53C22×C4×C263D411yescharacteristic
54C22×C4×C263D411yescharacteristic
55C22×C4×C263C2311yescharacteristic
56M16×C263—24no—
57M16×C263—22no—
58M16×C263D414yescomplemented
59C2×C8×C263—24no—
60C2×C8×C263—22no—
61C22×D263—21no—
62Dic526—22no—
63D1052—22no—
64C22⋊D263—42no—
65C22⋊D263—42no—
66C22⋊D263—42no—
67C2×Dic263—24no—
68C2×Dic263—21no—
69C2×Dic263—21no—
70C2×Dic263—21no—
71C2×Dic263—42no—
72C2×Dic263—42no—
73C4×D263—41no—
74C4×D263—41no—
75C23×C263—22no—
76C23×C263—22no—
77C23×C263—41no—
78C23×C263C22⋊C411yescharacteristic
79C23×C263C22⋊C411yescharacteristic
80C23×C263C2×D411yescharacteristic
81C2×C4×C263—22no—
82C2×C4×C263—22no—
83C2×C4×C263—22no—
84C2×C4×C263—21no—
85C2×C4×C263—21no—
86C2×C4×C263—21no—
87C2×C4×C263—21no—
88C2×C4×C263C22⋊C411yescharacteristic
89C2×C4×C263C22⋊C411yescharacteristic
90C2×C4×C263C22×C411yescharacteristic
91C2×C4×C263C2×D412yes—
92C2×C4×C263C2×D411yescharacteristic
93C2×C4×C263#4112yes—
94C8×C263—24no—
95C22×C263—21no—
96C22×C263—21no—
97C22×C263—21no—
98C22×C263—21no—
99C22×C263—21no—
100C22×C263—21no—
101C22×C263—21no—
102C22×C263—44no—
103C22×C263#10412yescomplemented
104C22×C263C2×C22⋊C411yescharacteristic
105C22×C263#12112yes—
106C2×D263—41no—
107C2×D263—41no—
108C2×D263—41no—
109C4×C263—21no—
110C4×C263—21no—
111C4×C263C4×D412yes—
112C4×C263#12011yescharacteristic
113C4×C263#12311yescharacteristic
114Dic263—44no—
115Dic263—41no—
116Dic263—41no—
117Dic263—41no—
118C2×C263—22no—
119C2×C263—22no—
120C2×C263—41no—
121C2×C263#38611yescharacteristic
122C2×C263C2×#10411yescharacteristic
123C2×C263#42111yescharacteristic
124D263—81no—
125C263#187111yescharacteristic, complemented, Sylow
126#1871—2631nomaximal, Sylow
127C22×M16D26311yescharacteristic, complemented
128#525—2631no—
129C2×#104—2632no—
130C4×C22⋊C4—2631no—
131#339—2632no—
132C2×#41—2631no—
133C23×C4C2×D26311yescharacteristic
134C2×M16—21no—
135C2×M16—24no—
136C2×M16C2×D26312yes—
137C22×C8—21no—
138#123—5261no—
139C22⋊Q8—2631no—
140C22⋊Q8—2631no—
141#121—2631no—
142#121—2631no—
143#120—5261no—
144C4×D4—5261no—
145C4×D4—5261no—
146#117—2631no—
147C2×C22⋊C4—5261no—
148C2×C42—2632no—
149#104—5264no—
150#95—5261no—
151C24D105211yescharacteristic
152#41—5262no—
153#41—5262no—
154C2×Q8—2631no—
155C2×D4—2631no—
156C2×D4—5261no—
157C2×D4—5261no—
158C2×D4—5261no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—5262no—
162C22×C4—5261no—
163C22×C4C4×D26311yescharacteristic
164C22×C4C4×D26311yescharacteristic
165C22×C4C22⋊D26311yescharacteristic
166C22×C4C22⋊D26311yescharacteristic
167C22×C4D105211yescharacteristic
168C22×C4C22×D26311yescharacteristic
169M16—24no—
170M16—22no—
171M16C22⋊D26314yescomplemented
172C2×C8—24no—
173C2×C8—22no—
174C4⋊C4—2631no—
175C4⋊C4—2631no—
176C4⋊C4—5261no—
177C4⋊C4—5261no—
178C22⋊C4—5264no—
179C22⋊C4—5261no—
180C22⋊C4—5261no—
181C22⋊C4—5261no—
182C22⋊C4—5261no—
183C22⋊C4—5261no—
184C42—5261no—
185C42—5262no—
186C42—5262no—
187C23—22no—
188C23—22no—
189C23—41no—
190C23—5261no—
191C23(C2×D263)⋊C411yescharacteristic
192C23(C2×D263)⋊C411yescharacteristic
193C23C2×D105211yescharacteristic
194Q8—5262no—
195D4—5262no—
196D4—10522no—
197D4—10522no—
198D4—10522no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—5264no—
207C2×C4—5261no—
208C2×C4—5261no—
209C2×C4—5261no—
210C2×C4—10522no—
211C2×C4—10522no—
212C2×C4—10521no—
213C2×C4—10521no—
214C2×C4(C2×D263)⋊C411yescharacteristic
215C2×C4(C2×D263)⋊C411yescharacteristic
216C2×C4C2×C4×D26311yescharacteristic
217C2×C4C2×C22⋊D26312yes—
218C2×C4C2×C22⋊D26311yescharacteristic
219C2×C4#1686237612yes—
220C8—24no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—44no—
229C22—10521no—
230C22—10521no—
231C22—10521no—
232C22#2255439612yescomplemented
233C22C2×(C2×D263)⋊C411yescharacteristic
234C22#2255444412yes—
235C4—21no—
236C4—21no—
237C4—10524no—
238C4—10521no—
239C4—10521no—
240C4—10521no—
241C4C4×C22⋊D26312yes—
242C4#2255443911yescharacteristic
243C4#2255445311yescharacteristic
244C2—22no—
245C2—22no—
246C2—41no—
247C2—21041no—
248C2#3068181711yescharacteristic
249C2C2×#2255439611yescharacteristic
250C2#3068195411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC22×M16×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682449C2
cosocleC22×C4×C263C23
hypercenterC22×M16D263
hypocenterC263#1871
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#22554396C2semidirect
3. C4×C22⋊Dic263C2semidirect
4. #30681699C2semidirect
5. C22×M16×C263C2semidirect
8. #22554449C4semidirect
9. #22554449C4semidirect
10. #22554444C4semidirect
11. #22554444C4semidirect
58. M16×C263D4semidirect
103. C22×C263#104semidirect
125. C263#1871semidirect
127. C22×M16D263semidirect
171. M16C22⋊D263semidirect
232. C22#22554396semidirect

Maximal subgroups

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

subgroupindex
#306824492
C2×#225543962
C4×C22⋊Dic2632
#306816992
C22×M16×C2632
#1871263