Finite Group Databasebeta

← #36447965

Subgroups — #36447965

Order 22784.

394 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 91 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#26022855C211yesmaximal, characteristic
2#26018582C211yesmaximal, characteristic
3#26018159C212yesmaximal
4#26018157C212yesmaximal
5C89×#1463C211yesmaximal, characteristic
6#19151562C2212yes—
7#19151484—22no—
8#19151484—22no—
9#19151461C412yes—
10#19151458C2211yescharacteristic
11#19151458C2211yescharacteristic
12C4×C22⋊Dic89C412yes—
13#19151324—22no—
14C22×C4⋊C4×C89C2211yescharacteristic
15#407×C89C2212yes—
16#324×C89—22no—
17C2×#13083558—22no—
18C2×C4⋊Dic89—21no—
19C2×C4⋊Dic89—21no—
20C2×C22⋊Dic89C2×C412yes—
21C2×C22⋊Dic89C2×C412yes—
22C2×C4×Dic89—22no—
23C22⋊#10623494—22no—
24C22⋊#10623494—22no—
25#15667919—22no—
26#15667919—24no—
27#15667919—21no—
28#15667919—21no—
29C23×C4×C89C2×C411yescharacteristic
30C23×C4×C89C2×C411yescharacteristic
31C23×C4×C89C2311yescharacteristic
32C2×M16×C89—22no—
33C2×C4⋊C4×C89—22no—
34C2×C4⋊C4×C89—22no—
35C2×C4⋊C4×C89D412yes—
36C2×C4⋊C4×C89D412yes—
37C22⋊C8×C89—22no—
38C22⋊C8×C89—22no—
39C22×Dic89—22no—
40C22×Dic89—22no—
41#13083558—82no—
42C2×#10623494—42no—
43C4⋊Dic89—81no—
44C4⋊Dic89—81no—
45C22⋊Dic89—42no—
46C22⋊Dic89—42no—
47C4×Dic89—82no—
48C24×C89C22×C411yescharacteristic
49C22×C4×C89—21no—
50C22×C4×C89—21no—
51C22×C4×C89—21no—
52C22×C4×C89—21no—
53C22×C4×C89—41no—
54C22×C4×C89—41no—
55C22×C4×C89—81no—
56C22×C4×C89—81no—
57C22×C4×C89C22⋊C412yes—
58C22×C4×C89C22⋊C412yes—
59C22×C4×C89C2×D411yescharacteristic
60C22×C4×C89C2×D411yescharacteristic
61C22×C4×C89#4112yes—
62C22×C4×C89#4112yes—
63M16×C89—82no—
64C2×C8×C89—42no—
65C4⋊C4×C89—24no—
66C4⋊C4×C89—24no—
67C23×C89—21no—
68C23×C89—21no—
69C23×C89—41no—
70C23×C89—41no—
71C23×C89C2×C22⋊C411yescharacteristic
72C23×C89#11711yescharacteristic
73C23×C89#11711yescharacteristic
74C2×C4×C89—22no—
75C2×C4×C89—22no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89—42no—
79C2×C4×C89—41no—
80C2×C4×C89—41no—
81C2×C4×C89—42no—
82C2×C4×C89—42no—
83C2×C4×C89—42no—
84C2×C4×C89—42no—
85C2×C4×C89—81no—
86C2×C4×C89—81no—
87C2×C4×C89#12312yes—
88C2×C4×C89#12312yes—
89C2×Dic89—42no—
90C2×Dic89—42no—
91C2×Dic89—42no—
92C2×Dic89—42no—
93C2×Dic89—42no—
94C2×Dic89—42no—
95C8×C89—82no—
96#10623494—82no—
97C22×C89—21no—
98C22×C89—21no—
99C22×C89—21no—
100C22×C89—21no—
101C22×C89—21no—
102C22×C89—21no—
103C22×C89—21no—
104C22×C89—21no—
105C22×C89—42no—
106C22×C89—42no—
107C22×C89#38111yescharacteristic
108C22×C89#41311yescharacteristic
109C22×C89#41311yescharacteristic
110C4×C89—22no—
111C4×C89—22no—
112C4×C89—42no—
113C4×C89—42no—
114Dic89—82no—
115Dic89—82no—
116#8758—891nomaximal, Sylow
117C2×C89—21no—
118C2×C89—21no—
119C2×C89—41no—
120C2×C89—41no—
121C2×C89#182211yescharacteristic
122C2×C89#182811yescharacteristic
123C2×C89#183011yescharacteristic
124#2313—891no—
125#1463—891no—
126#1463D8911yescharacteristic
127#1305—892no—
128#1305—892no—
129C89#875811yescharacteristic, complemented, Sylow
130C22×C4⋊C4C2×D8911yescharacteristic
131#407—892no—
132#407C2×D8912yes—
133#387—1782no—
134#387—1782no—
135#381—892no—
136#380—891no—
137#380—891no—
138C4×C22⋊C4—892no—
139#324—22no—
140#324—1782no—
141C23×C4C4×D8911yescharacteristic
142C23×C4C4×D8911yescharacteristic
143C23×C4C22×D8911yescharacteristic
144C2×M16—22no—
145C2×M16—1782no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—1781no—
149C2×C4⋊C4—1781no—
150C2×C4⋊C4D35612yes—
151C2×C4⋊C4C22⋊D8912yes—
152C2×C22⋊C4—892no—
153C2×C22⋊C4—892no—
154C2×C42—1782no—
155C22⋊C8—22no—
156C22⋊C8—22no—
157C22⋊C8—1782no—
158C22⋊C8—1782no—
159#95—1782no—
160#95—1784no—
161#95—1781no—
162#95—1781no—
163C24C2×C4×D8911yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—81no—
171C22×C4—81no—
172C22×C4—1782no—
173C22×C4—1782no—
174C22×C4#1308355112yes—
175C22×C4#1308355112yes—
176C22×C4C2×C22⋊D8911yescharacteristic
177C22×C4C2×D35611yescharacteristic
178C22×C4#1308357312yes—
179C22×C4#1308357312yes—
180M16—82no—
181M16—7122no—
182C2×C8—42no—
183C2×C8—3562no—
184C4⋊C4—24no—
185C4⋊C4—24no—
186C4⋊C4—7121no—
187C4⋊C4—7121no—
188C22⋊C4—3562no—
189C22⋊C4—3562no—
190C42—7122no—
191C23—21no—
192C23—21no—
193C23—41no—
194C23—41no—
195C23C2×#1308355111yescharacteristic
196C23#1566796811yescharacteristic
197C23#1566796811yescharacteristic
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—81no—
210C2×C4—81no—
211C2×C4—3562no—
212C2×C4—3562no—
213C2×C4—3562no—
214C2×C4—3562no—
215C2×C4—3562no—
216C2×C4—3562no—
217C2×C4#1566799312yes—
218C2×C4#1566799612yes—
219C8—82no—
220C8—7122no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—42no—
230C22—42no—
231C22#1915145911yescharacteristic
232C22#1915158011yescharacteristic
233C22#1915158011yescharacteristic
234C4—22no—
235C4—22no—
236C4—42no—
237C4—42no—
238C4—7122no—
239C4—7122no—
240C2—21no—
241C2—21no—
242C2—41no—
243C2—41no—
244C2#2602033311yescharacteristic
245C2#2602035811yescharacteristic
246C2#2602036411yescharacteristic
subgroupG/H
centerC22#19151459
commutator, prime radicalC24×C89C22×C4
FrattiniC23×C4C22×D89
FittingC89×#1463C2
socleC22×C89#381
cosocleC23×C4×C89C23
hypercenter#1463D89
hypocenterC89#8758
LCSG ▷ C24×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
129. C89#8758semidirect

Maximal subgroups

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

subgroupindex
#260228552
#260185822
#260181592
#260181572
C89×#14632
#875889