Finite Group Databasebeta

← #26026756

Subgroups — #26026756

Order 11392.

568 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 129 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×#15667994C212yesmaximal, complemented
2#19151540C212yesmaximal, complemented
3#19151520C212yesmaximal, complemented
4#19151507C211yesmaximal, characteristic
5#19151476C212yesmaximal, complemented
6#19151475C212yesmaximal, complemented
7#19151470C211yesmaximal, characteristic, complemented
8#19151457C212yesmaximal, complemented
9#397×C89C211yesmaximal, characteristic, complemented
10C22×D356C2211yescharacteristic
11C22×C22⋊D89C2212yes—
12C23×Dic89C2211yescharacteristic
13C22×C4×D89C2212yes—
14#15667994—28no—
15C2×C4⋊Dic89C2212yes—
16C2×#13083553C2212yes—
17C2×#13083553C2212yes—
18C2×C22⋊Dic89C2211yescharacteristic
19C2×#13083551C2212yes—
20C2×#13083551C2212yes—
21C2×#13083551C2212yes—
22C2×#13083551C2212yes—
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2212yes—
26#15667919C2211yescharacteristic
27C2×C4⋊C4×C89C2211yescharacteristic
28C2×C22⋊C4×C89C2212yes—
29C2×C22⋊C4×C89C2211yescharacteristic
30#95×C89C2211yescharacteristic
31#95×C89C2212yes—
32C23×D89C2312yes—
33C2×D356—24no—
34C2×D356—41no—
35C2×C22⋊D89—24no—
36C2×C22⋊D89—24no—
37C2×C22⋊D89—42no—
38C22×Dic89—41no—
39C22×Dic89—42no—
40C22×Dic89C2312yes—
41C22×Dic89C2312yes—
42C22×Dic89C2312yes—
43C2×C4×D89—24no—
44C2×C4×D89—24no—
45C2×C4×D89—42no—
46C4⋊Dic89—24no—
47#13083553—24no—
48#13083553—42no—
49C22⋊Dic89D414yescomplemented
50#13083551—24no—
51#13083551—42no—
52#13083551—42no—
53#13083551—42no—
54C24×C89C2311yescharacteristic
55C22×C4×C89C2312yes—
56C22×C4×C89C2311yescharacteristic
57C22×C4×C89C2312yes—
58C22×C4×C89C2311yescharacteristic
59C4⋊C4×C89—41no—
60C22⋊C4×C89—24no—
61C22⋊C4×C89—41no—
62C23×C89—22no—
63C23×C89—21no—
64C23×C89—22no—
65C23×C89—21no—
66C23×C89C2×D412yes—
67C23×C89C2411yescharacteristic
68C22×D89—22no—
69C22×D89—22no—
70C22×D89—22no—
71C22×D89—22no—
72C22×D89—22no—
73C22×D89—22no—
74C22×D89#4114yes—
75C2×C4×C89—22no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89—22no—
79C2×C4×C89—21no—
80C2×C4×C89—21no—
81C2×C4×C89—22no—
82C2×C4×C89—22no—
83C2×C4×C89—22no—
84C2×C4×C89—22no—
85C22⋊D89—48no—
86C2×Dic89—22no—
87C2×Dic89—22no—
88C2×Dic89—22no—
89C2×Dic89—22no—
90C2×Dic89—22no—
91C2×Dic89—22no—
92C2×Dic89—22no—
93C2×Dic89—22no—
94C2×Dic89—44no—
95C2×Dic89C2×D414yes—
96D356—44no—
97C4×D89—48no—
98C22×C89—22no—
99C22×C89—24no—
100C22×C89—42no—
101C22×C89—41no—
102C22×C89—41no—
103C22×C89C22×D411yescharacteristic
104C22×C89C2×#4112yes—
105C22×C89H(5,𝔽2)11yescharacteristic
106C22×C89H(5,𝔽2)12yes—
107C22×C892−1+411yescharacteristic
108C2×D89—24no—
109C2×D89—24no—
110C2×D89—24no—
111C2×D89—42no—
112C2×D89—42no—
113C2×D89—42no—
114C2×D89—42no—
115C4×C89—42no—
116C4×C89—42no—
117C4×C89—41no—
118C4×C89—41no—
119Dic89—24no—
120Dic89—42no—
121Dic89—42no—
122C2×C89—42no—
123C2×C89#53711yescharacteristic
124C2×C89#53912yes—
125C2×C89#54612yes—
126C2×C89#55111yescharacteristic
127C2×C89#56011yescharacteristic
128D89—44no—
129#2693—891nomaximal, Sylow
130C89#269311yescharacteristic, complemented, Sylow
131C2×#123—892no—
132#400—892no—
133#397D8911yescharacteristic, complemented
134#396—892no—
135#392—891no—
136#386—892no—
137#386—892no—
138#385—891no—
139#380—892no—
140C22×D4—892no—
141C22×D4—891no—
142C23×C4—891no—
143C23×C4—892no—
144#123—1788no—
145C2×C4⋊C4—892no—
146C2×C4⋊C4—892no—
147C2×C4⋊C4—892no—
148C2×C4⋊C4C2×D8911yescharacteristic
149C2×C22⋊C4—891no—
150C2×C22⋊C4—892no—
151C2×C22⋊C4—892no—
152C2×C22⋊C4—892no—
153C2×C22⋊C4—892no—
154C2×C22⋊C4C2×D8912yes—
155C2×C22⋊C4C2×D8911yescharacteristic
156#95—892no—
157#95—892no—
158#95—892no—
159#95—891no—
160#95C2×D8911yescharacteristic
161#95C2×D8912yes—
162C24—892no—
163C24C22×D8911yescharacteristic
164C2×D4—3561no—
165C2×D4—3562no—
166C2×D4—1784no—
167C2×D4—1784no—
168C2×D4—1784no—
169C22×C4—892no—
170C22×C4—892no—
171C22×C4—892no—
172C22×C4—3562no—
173C22×C4—3561no—
174C22×C4—3562no—
175C22×C4—1784no—
176C22×C4—1784no—
177C22×C4C22×D8911yescharacteristic
178C22×C4C22×D8912yes—
179C22×C4C22×D8912yes—
180C22×C4C22×D8911yescharacteristic
181C4⋊C4—41no—
182C4⋊C4—3562no—
183C4⋊C4—1784no—
184C4⋊C4—1784no—
185C22⋊C4—24no—
186C22⋊C4—41no—
187C22⋊C4—894no—
188C22⋊C4—3562no—
189C22⋊C4—3562no—
190C22⋊C4—3562no—
191C22⋊C4—1784no—
192C23—22no—
193C23—21no—
194C23—22no—
195C23—21no—
196C23—894no—
197C23—1782no—
198C23—1782no—
199C23—1782no—
200C23—1782no—
201C23—1782no—
202C23—1782no—
203C23D4×D8912yes—
204C23C23×D8911yescharacteristic
205D4—3564no—
206D4—3568no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—894no—
218C2×C4—3568no—
219C2×C4—3564no—
220C2×C4—1782no—
221C2×C4—1782no—
222C2×C4—1782no—
223C2×C4—1782no—
224C2×C4—1782no—
225C2×C4—1782no—
226C2×C4—1782no—
227C2×C4—1782no—
228C22—22no—
229C22—24no—
230C22—42no—
231C22—41no—
232C22—41no—
233C22—3562no—
234C22—3562no—
235C22—3562no—
236C22—3562no—
237C22—1784no—
238C22—1784no—
239C22—1784no—
240C22C2×D4×D8911yescharacteristic
241C22#41×D8912yes—
242C22#1566805711yescharacteristic
243C22#1566805812yes—
244C22#1566805911yescharacteristic
245C4—42no—
246C4—42no—
247C4—41no—
248C4—41no—
249C4—3562no—
250C4—3562no—
251C4—1784no—
252C2—42no—
253C2—3564no—
254C2#1915217511yescharacteristic
255C2#1915218912yes—
256C2#1915224012yes—
257C2#1915227811yescharacteristic
258C2#1915233811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#397×C89C2
prime radical#19151507C2
hypercenter#397D89
hypocenterC89#2693
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#15667994C2semidirect
2. #19151540C2semidirect
3. #19151520C2semidirect
5. #19151476C2semidirect
6. #19151475C2semidirect
7. #19151470C2semidirect
8. #19151457C2semidirect
9. #397×C89C2semidirect
49. C22⋊Dic89D4semidirect
130. C89#2693semidirect
133. #397D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679942
#191515402
#191515202
#191515072
#191514762
#191514752
#191514702
#191514572
#397×C892
#269389