Finite Group Databasebeta

← #26028085

Subgroups — #26028085

Order 11392.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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#19151537C211yesmaximal, characteristic, complemented
2#19151521C212yesmaximal, complemented
3#19151512C212yesmaximal
4#19151491C212yesmaximal, complemented
5#19151486C212yesmaximal, complemented
6#19151486C212yesmaximal, complemented
7#19151480C212yesmaximal, complemented
8#19151467C211yesmaximal, characteristic, complemented
9#394×C89C211yesmaximal, characteristic
10C2×C4⋊Dic89C2211yescharacteristic
11C2×C4⋊Dic89C2211yescharacteristic
12C2×#13083553C2212yes—
13C2×#13083553C2212yes—
14C2×#13083553C2212yes—
15C2×C22⋊Dic89C2212yes—
16C2×C22⋊Dic89C2212yes—
17C2×C22⋊Dic89C2212yes—
18C2×C22⋊Dic89C2212yes—
19C2×C4×Dic89C2211yescharacteristic
20C2×C4×Dic89C2212yes—
21#15667919C2212yes—
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2211yescharacteristic
25#15667919C2212yes—
26C22×D4×C89C2211yescharacteristic
27C2×C4⋊C4×C89C2211yescharacteristic
28C2×C22⋊C4×C89C2212yes—
29C2×C22⋊C4×C89C2212yes—
30#95×C89C2211yescharacteristic
31C22×Dic89C2312yes—
32C22×Dic89C2312yes—
33C22×Dic89C2312yes—
34C22×Dic89C2312yes—
35C4⋊Dic89—41no—
36C4⋊Dic89—41no—
37#13083553—24no—
38#13083553—42no—
39#13083553—42no—
40C22⋊Dic89—24no—
41C22⋊Dic89—24no—
42C22⋊Dic89—42no—
43C22⋊Dic89—42no—
44C4×Dic89—22no—
45C4×Dic89—42no—
46C24×C89C2312yes—
47C2×D4×C89—41no—
48C2×D4×C89—42no—
49C22×C4×C89C2312yes—
50C22×C4×C89C2311yescharacteristic
51C22×C4×C89C2311yescharacteristic
52C22×C4×C89C2311yescharacteristic
53C4⋊C4×C89—41no—
54C22⋊C4×C89—24no—
55C22⋊C4×C89—42no—
56C23×C89—22no—
57C23×C89—22no—
58C23×C89—22no—
59C23×C89—22no—
60C23×C89—22no—
61C23×C89—22no—
62C23×C89—22no—
63C23×C89C2411yescharacteristic
64D4×C89—44no—
65C2×C4×C89—21no—
66C2×C4×C89—21no—
67C2×C4×C89—22no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—21no—
72C2×C4×C89—21no—
73C2×C4×C89—22no—
74C2×C4×C89#4112yes—
75C2×Dic89—22no—
76C2×Dic89—22no—
77C2×Dic89—22no—
78C2×Dic89—22no—
79C2×Dic89—22no—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89#4114yes—
87C22×C89—42no—
88C22×C89—42no—
89C22×C89—42no—
90C22×C89—42no—
91C22×C89—42no—
92C22×C89—42no—
93C22×C89—42no—
94C22×C89C2×#4111yescharacteristic
95C22×C89C2×#4112yes—
96C22×C89H(5,𝔽2)11yescharacteristic
97C22×C89H(5,𝔽2)12yes—
98C22×C892−1+411yescharacteristic
99C4×C89—22no—
100C4×C89—42no—
101C4×C89—41no—
102C4×C89—41no—
103Dic89—24no—
104Dic89—42no—
105Dic89—42no—
106Dic89—42no—
107C2×C89—82no—
108C2×C89#53911yescharacteristic
109C2×C89#54212yes—
110C2×C89#55312yes—
111C2×C89#55511yescharacteristic
112C2×C89#56011yescharacteristic
113#2795—891nomaximal, Sylow
114C89#279511yescharacteristic, complemented, Sylow
115#400—891no—
116#396—892no—
117#394—892no—
118#394D8911yescharacteristic
119#388—892no—
120#388—892no—
121#388—892no—
122#387—892no—
123#384—891no—
124C22×D4C2×D8911yescharacteristic
125C2×C4⋊C4—892no—
126C2×C4⋊C4—891no—
127C2×C4⋊C4—892no—
128C2×C4⋊C4—891no—
129C2×C4⋊C4—892no—
130C2×C4⋊C4C2×D8911yescharacteristic
131C2×C22⋊C4—892no—
132C2×C22⋊C4—892no—
133C2×C22⋊C4—892no—
134C2×C22⋊C4—892no—
135C2×C22⋊C4C2×D8912yes—
136C2×C22⋊C4C2×D8912yes—
137C2×C42—892no—
138C2×C42—891no—
139#95—892no—
140#95—892no—
141#95—892no—
142#95—891no—
143#95—892no—
144#95C2×D8911yescharacteristic
145C24C22×D8912yes—
146C2×D4—41no—
147C2×D4—42no—
148C22×C4—892no—
149C22×C4—892no—
150C22×C4—892no—
151C22×C4—892no—
152C22×C4C22×D8912yes—
153C22×C4C22×D8911yescharacteristic
154C22×C4C22×D8911yescharacteristic
155C22×C4C22×D8911yescharacteristic
156C4⋊C4—41no—
157C4⋊C4—3562no—
158C4⋊C4—3562no—
159C4⋊C4—3561no—
160C4⋊C4—3561no—
161C4⋊C4—1784no—
162C22⋊C4—24no—
163C22⋊C4—42no—
164C22⋊C4—3562no—
165C22⋊C4—3562no—
166C22⋊C4—1784no—
167C22⋊C4—1784no—
168C42—3562no—
169C42—1782no—
170C23—22no—
171C23—22no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23C23×D8911yescharacteristic
178D4—44no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—894no—
189C2×C4—1782no—
190C2×C4—1782no—
191C2×C4—1782no—
192C2×C4—1782no—
193C2×C4—1782no—
194C2×C4—1782no—
195C2×C4—1782no—
196C2×C4—1782no—
197C2×C4—1782no—
198C2×C4—1782no—
199C2×C4—1782no—
200C2×C4#1308357312yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—42no—
208C22#41×D8912yes—
209C22C2×#1308357311yescharacteristic
210C22#1566805711yescharacteristic
211C22#1566805712yes—
212C22#1566805911yescharacteristic
213C4—22no—
214C4—42no—
215C4—41no—
216C4—41no—
217C4—3562no—
218C4—3562no—
219C4—3562no—
220C4—1784no—
221C2—82no—
222C2#1915219311yescharacteristic
223C2#1915221612yes—
224C2#1915229512yes—
225C2#1915231011yescharacteristic
226C2#1915233711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#394×C89C2
prime radicalC22×D4×C89C22
hypercenter#394D89
hypocenterC89#2795
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #19151537C2semidirect
2. #19151521C2semidirect
4. #19151491C2semidirect
5. #19151486C2semidirect
6. #19151486C2semidirect
7. #19151480C2semidirect
8. #19151467C2semidirect
114. C89#2795semidirect

Maximal subgroups

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

subgroupindex
#191515372
#191515212
#191515122
#191514912
#191514862
#191514802
#191514672
#394×C892
#279589