Finite Group Databasebeta

← #46783127

Subgroups — #46783127

Order 33664.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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#30682704C211yesmaximal, characteristic, complemented
2#30682484C211yesmaximal, characteristic
3#30681955C211yesmaximal, characteristic, complemented
4#30681911C211yesmaximal, characteristic, complemented
5#30681699C211yesmaximal, characteristic, complemented
6#30681697C211yesmaximal, characteristic, complemented
7#421×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554478—22no—
10#22554476—22no—
11C2×#16862360C2211yescharacteristic
12M16×D263—22no—
13#22554468C411yescharacteristic, complemented
14#22554466C411yescharacteristic, complemented
15#22554459C411yescharacteristic, complemented
16#22554457C411yescharacteristic, complemented
17#22554442—22no—
18C4×C22⋊D263—22no—
19#22554429C2211yescharacteristic
20C2×C4×Dic263C2211yescharacteristic
21#22554397—22no—
22#22554384—22no—
23C2×#41×C263C2211yescharacteristic
24C2×M16×C263C2211yescharacteristic
25#117×C263C2211yescharacteristic
26#104×C263—22no—
27#16862376—21no—
28#16862376—21no—
29#16862376—21no—
30#16862376—21no—
31C2×Dic526C2×C411yescharacteristic
32C2×D1052C2×C411yescharacteristic
33C2×C22⋊D263—22no—
34C2×C22⋊D263D412yes—
35C22×Dic263—21no—
36C2×C4×D263D412yes—
37#16862360—21no—
38#16862360D412yescomplemented
39#16862359—24no—
40C2×C263⋊C8—21no—
41C8×D263—24no—
42C4⋊Dic263—21no—
43Dic263⋊C4—22no—
44C22⋊Dic263—22no—
45C22⋊Dic263—21no—
46(C2×D263)⋊C4—22no—
47C4×Dic263—21no—
48C4×Dic263—21no—
49C4×Dic263C2×C411yescharacteristic
50C4×Dic263C2×C411yescharacteristic
51#41×C263—21no—
52#41×C263—21no—
53#41×C263—21no—
54#41×C263—21no—
55C2×Q8×C263C2×C411yescharacteristic
56C2×D4×C263—21no—
57C2×D4×C263C2×C411yescharacteristic
58C22×C4×C263—21no—
59C22×C4×C263C2311yescharacteristic
60M16×C263—21no—
61M16×C263D412yescomplemented
62C2×C8×C263—21no—
63C4⋊C4×C263—21no—
64C22⋊C4×C263—21no—
65C42×C263—21no—
66C22×D263C22⋊C412yes—
67Dic526—21no—
68Dic526—21no—
69D1052—21no—
70D1052—21no—
71C22⋊D263—22no—
72C22⋊D263—22no—
73C22⋊D263—44no—
74C2×Dic263—21no—
75C2×Dic263—21no—
76C2×Dic263—42no—
77C2×Dic263—41no—
78C2×Dic263C22⋊C412yes—
79C4×D263—22no—
80C4×D263—22no—
81C263⋊C8—22no—
82C23×C263—21no—
83C23×C263C2×D411yescharacteristic
84Q8×C263—21no—
85Q8×C263—21no—
86D4×C263—21no—
87D4×C263—21no—
88D4×C263—41no—
89D4×C263—41no—
90C2×C4×C263—21no—
91C2×C4×C263—41no—
92C2×C4×C263—41no—
93C2×C4×C263—41no—
94C2×C4×C263C22×C411yescharacteristic
95C2×C4×C263C2×D411yescharacteristic
96C2×C4×C263C2×D411yescharacteristic
97C2×C4×C263C2×D411yescharacteristic
98C2×C4×C263#4111yescharacteristic
99C2×C4×C263#4111yescharacteristic
100C8×C263—22no—
101C22×C263—41no—
102C22×C263—42no—
103C22×C263—41no—
104C22×C263C2×C22⋊C411yescharacteristic
105C22×C263#12111yescharacteristic
106C22×C263#12111yescharacteristic
107C2×D263—22no—
108C2×D263—42no—
109C4×C263—41no—
110C4×C263—81no—
111C4×C263C4×D411yescharacteristic
112C4×C263C4×D411yescharacteristic
113C4×C263#12011yescharacteristic
114C4×C263#12311yescharacteristic
115Dic263—22no—
116Dic263—22no—
117Dic263—41no—
118Dic263—81no—
119C2×C263—21no—
120C2×C263—21no—
121C2×C263—21no—
122C2×C263—81no—
123C2×C263#38611yescharacteristic
124D263—42no—
125C263#188411yescharacteristic, complemented, Sylow
126#1884—2631nomaximal, Sylow
127#568—2631no—
128#532—2631no—
129#421—2631no—
130#421D26311yescharacteristic, complemented
131#410—2631no—
132#339—2631no—
133#339—2631no—
134C2×#41—2631no—
135C2×#41C2×D26311yescharacteristic
136#131—5262no—
137#131—5262no—
138C2×M16—2631no—
139C2×M16—5262no—
140C2×M16C2×D26311yescharacteristic
141C4⋊Q8—2631no—
142#127—2631no—
143#124—2631no—
144#124—2631no—
145#121—5262no—
146C4×D4—5262no—
147#117—2631no—
148#117C2×D26311yescharacteristic
149C2×C42—2631no—
150#104—22no—
151#104—5262no—
152#99—5262no—
153#41—21no—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—5261no—
158#41—5261no—
159#41—5261no—
160#41—5261no—
161C2×Q8—2631no—
162C2×Q8C4×D26311yescharacteristic
163C2×D4—21no—
164C2×D4—2632no—
165C2×D4—2631no—
166C2×D4—5262no—
167C2×D4C4×D26311yescharacteristic
168C22×C4—21no—
169C22×C4—2632no—
170C22×C4—5261no—
171C22×C4C22×D26311yescharacteristic
172M16—21no—
173M16—2632no—
174M16—5264no—
175M16—5261no—
176M16C22⋊D26312yescomplemented
177C2×C8—21no—
178C2×C8—5264no—
179C2×C8—5261no—
180C4⋊C4—21no—
181C4⋊C4—5262no—
182C4⋊C4—5261no—
183C22⋊C4—21no—
184C22⋊C4—5262no—
185C22⋊C4—5262no—
186C22⋊C4—5261no—
187C42—21no—
188C42—2631no—
189C42—2631no—
190C42—5261no—
191C42—5261no—
192C23—21no—
193C23—2632no—
194C23D4×D26311yescharacteristic
195Q8—21no—
196Q8—21no—
197Q8—5261no—
198Q8—5261no—
199D4—21no—
200D4—21no—
201D4—41no—
202D4—41no—
203D4—5262no—
204D4—5262no—
205D4—5261no—
206D4—5261no—
207D4—10524no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—2632no—
213C2×C4—5261no—
214C2×C4—5262no—
215C2×C4—5262no—
216C2×C4—5261no—
217C2×C4—10522no—
218C2×C4—10521no—
219C2×C4C2×C4×D26311yescharacteristic
220C2×C4D4×D26311yescharacteristic
221C2×C4D4×D26311yescharacteristic
222C2×C4C2×C22⋊D26311yescharacteristic
223C2×C4#1686237511yescharacteristic
224C2×C4#1686237611yescharacteristic
225C8—22no—
226C8—5262no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—5262no—
231C22—10522no—
232C22C22⋊C4×D26311yescharacteristic
233C22#2255444111yescharacteristic
234C22#2255444311yescharacteristic
235C4—41no—
236C4—81no—
237C4—5262no—
238C4—5262no—
239C4—10521no—
240C4—21041no—
241C4(C22⋊D263)⋊C411yescharacteristic
242C4C4×C22⋊D26311yescharacteristic
243C4#2255443811yescharacteristic
244C4#2255445211yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—81no—
249C2—10522no—
250C2#3068181411yescharacteristic
subgroupG/H
centerC4#22554438
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#421×C263C2
socleC2×C263#386
prime radical#30682484C2
cosocleC22×C4×C263C23
hypercenter#421D263
hypocenterC263#1884
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #30682704C2semidirect
3. #30681955C2semidirect
4. #30681911C2semidirect
5. #30681699C2semidirect
6. #30681697C2semidirect
7. #421×C263C2semidirect
13. #22554468C4semidirect
14. #22554466C4semidirect
15. #22554459C4semidirect
16. #22554457C4semidirect
38. #16862360D4semidirect
61. M16×C263D4semidirect
125. C263#1884semidirect
130. #421D263semidirect
176. M16C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
#306827042
#306824842
#306819552
#306819112
#306816992
#306816972
#421×C2632
#1884263