Finite Group Databasebeta

← #26025950

Subgroups — #26025950

Order 11392.

476 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 145 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×#15668004C211yesmaximal, characteristic, complemented
2#19151537C211yesmaximal, characteristic, complemented
3#19151534C211yesmaximal, characteristic
4#19151528C211yesmaximal, characteristic, complemented
5#19151523C211yesmaximal, characteristic
6#19151493C212yesmaximal, complemented
7#19151492C212yesmaximal
8#19151482C212yesmaximal, complemented
9#19151471C212yesmaximal
10#19151444C211yesmaximal, characteristic, complemented
11C2×#117×C89C211yesmaximal, characteristic
12#15668004—24no—
13C2×C4⋊Dic89C2211yescharacteristic
14C2×C4⋊Dic89C2211yescharacteristic
15C2×#13083553C2212yes—
16C2×#13083553C2212yes—
17C2×#13083553C2212yes—
18C2×#13083553C2212yes—
19C2×C22⋊Dic89C2212yes—
20C2×C22⋊Dic89C2212yes—
21C2×C4×Dic89C2212yes—
22#15667919C2212yes—
23#15667919C2211yescharacteristic
24#15667919C2211yescharacteristic
25#15667919C2212yes—
26#15667919C2212yes—
27#15667919C2212yes—
28#15667919C2212yes—
29C23×C4×C89C2211yescharacteristic
30#117×C89—24no—
31C2×C4⋊C4×C89C2211yescharacteristic
32C2×C4⋊C4×C89C2211yescharacteristic
33C2×C22⋊C4×C89C2211yescharacteristic
34C2×C22⋊C4×C89C2211yescharacteristic
35C2×C42×C89C2211yescharacteristic
36C2×C42×C89C2211yescharacteristic
37C22×Dic89C2312yes—
38C22×Dic89C2312yes—
39C22×Dic89C2312yes—
40C22×Dic89C2312yes—
41C4⋊Dic89—22no—
42C4⋊Dic89—22no—
43#13083553—24no—
44#13083553—24no—
45#13083553—24no—
46#13083553—24no—
47C22⋊Dic89—24no—
48C22⋊Dic89—24no—
49C4×Dic89—24no—
50C24×C89C2311yescharacteristic
51C22×C4×C89—22no—
52C22×C4×C89—22no—
53C22×C4×C89—22no—
54C22×C4×C89C2311yescharacteristic
55C22×C4×C89C2311yescharacteristic
56C22×C4×C89C2311yescharacteristic
57C22×C4×C89C2311yescharacteristic
58C22×C4×C89C2311yescharacteristic
59C22×C4×C89C2311yescharacteristic
60C4⋊C4×C89—22no—
61C4⋊C4×C89—22no—
62C22⋊C4×C89—22no—
63C22⋊C4×C89—22no—
64C42×C89—22no—
65C42×C89D414yes—
66C23×C89—21no—
67C23×C89—21no—
68C23×C89—22no—
69C23×C89—22no—
70C23×C89#4112yes—
71C23×C89C2411yescharacteristic
72C2×C4×C89—28no—
73C2×C4×C89—21no—
74C2×C4×C89—21no—
75C2×C4×C89—21no—
76C2×C4×C89—21no—
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×C89C2×D412yes—
84C2×C4×C89C2×D412yes—
85C2×C4×C89C2×D412yes—
86C2×C4×C89#4112yes—
87C2×Dic89—22no—
88C2×Dic89—22no—
89C2×Dic89—22no—
90C2×Dic89—22no—
91C2×Dic89—22no—
92C2×Dic89—22no—
93C2×Dic89—22no—
94C2×Dic89—22no—
95C2×Dic89—22no—
96C2×Dic89—22no—
97C2×Dic89—22no—
98C2×Dic89#4114yes—
99C22×C89—22no—
100C22×C89—24no—
101C22×C89—41no—
102C22×C89—41no—
103C22×C89—42no—
104C22×C89C22×D411yescharacteristic
105C22×C89C2×#4111yescharacteristic
106C22×C89C2×#4111yescharacteristic
107C22×C89C2×#4112yes—
108C22×C892−1+412yes—
109C4×C89—22no—
110C4×C89—22no—
111C4×C89—22no—
112C4×C89—22no—
113C4×C89—41no—
114C4×C89—41no—
115Dic89—24no—
116Dic89—42no—
117Dic89—42no—
118Dic89—42no—
119C2×C89—42no—
120C2×C89#52511yescharacteristic
121C2×C89#53211yescharacteristic
122C2×C89#53611yescharacteristic
123C2×C89#55212yes—
124C2×C89#55212yes—
125#2611—891nomaximal, Sylow
126C89#261111yescharacteristic, complemented, Sylow
127C2×#125—891no—
128C2×#117D8911yescharacteristic
129#400—891no—
130#399—891no—
131#398—891no—
132#397—891no—
133#389—892no—
134#388—892no—
135#387—892no—
136#385—892no—
137#376—891no—
138C23×C4C2×D8911yescharacteristic
139#125—1784no—
140#117—24no—
141C2×C4⋊C4—892no—
142C2×C4⋊C4—892no—
143C2×C4⋊C4—891no—
144C2×C4⋊C4—891no—
145C2×C4⋊C4—892no—
146C2×C4⋊C4—892no—
147C2×C4⋊C4C2×D8911yescharacteristic
148C2×C4⋊C4C2×D8911yescharacteristic
149C2×C22⋊C4—892no—
150C2×C22⋊C4—892no—
151C2×C22⋊C4C2×D8911yescharacteristic
152C2×C22⋊C4C2×D8911yescharacteristic
153C2×C42—892no—
154C2×C42C2×D8911yescharacteristic
155C2×C42C2×D8911yescharacteristic
156#95—892no—
157#95—891no—
158#95—891no—
159#95—892no—
160#95—892no—
161#95—892no—
162#95—892no—
163C24C22×D8911yescharacteristic
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—892no—
168C22×C4—892no—
169C22×C4—892no—
170C22×C4—892no—
171C22×C4C22×D8911yescharacteristic
172C22×C4C22×D8911yescharacteristic
173C22×C4C22×D8911yescharacteristic
174C22×C4C22×D8911yescharacteristic
175C22×C4C22×D8911yescharacteristic
176C22×C4C22×D8911yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—1784no—
180C4⋊C4—1784no—
181C4⋊C4—1784no—
182C4⋊C4—1782no—
183C4⋊C4—1782no—
184C4⋊C4—1784no—
185C22⋊C4—22no—
186C22⋊C4—22no—
187C22⋊C4—1784no—
188C22⋊C4—1784no—
189C42—22no—
190C42—1784no—
191C42C22⋊D8914yes—
192C23—21no—
193C23—22no—
194C23—21no—
195C23—22no—
196C23#1308357412yes—
197C23C23×D8911yescharacteristic
198C2×C4—28no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—894no—
210C2×C4—1782no—
211C2×C4—1782no—
212C2×C4—1782no—
213C2×C4—1782no—
214C2×C4—1782no—
215C2×C4—1782no—
216C2×C4—1782no—
217C2×C4—1782no—
218C2×C4—1782no—
219C2×C4—1782no—
220C2×C4—1782no—
221C2×C4C2×C22⋊D8912yes—
222C2×C4C2×C22⋊D8912yes—
223C2×C4C2×C22⋊D8912yes—
224C2×C4#1308357412yes—
225C22—24no—
226C22—22no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22C22×C22⋊D8911yescharacteristic
231C22#41×D8912yes—
232C22C2×#1308357411yescharacteristic
233C22C2×#1308357411yescharacteristic
234C22#1566805912yes—
235C4—22no—
236C4—22no—
237C4—22no—
238C4—22no—
239C4—41no—
240C4—41no—
241C4—3562no—
242C4—3562no—
243C4—3562no—
244C4—1784no—
245C2—42no—
246C2#1915210911yescharacteristic
247C2#1915214411yescharacteristic
248C2#1915216911yescharacteristic
249C2#1915228112yes—
250C2#1915228712yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
FittingC2×#117×C89C2
prime radicalC24×C89C23
hypercenterC2×#117D89
hypocenterC89#2611
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×#15668004C2semidirect
2. #19151537C2semidirect
4. #19151528C2semidirect
6. #19151493C2semidirect
8. #19151482C2semidirect
10. #19151444C2semidirect
126. C89#2611semidirect

Maximal subgroups

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

subgroupindex
C2×#156680042
#191515372
#191515342
#191515282
#191515232
#191514932
#191514922
#191514822
#191514712
#191514442
C2×#117×C892
#261189