Finite Group Databasebeta

← #26025495

Subgroups — #26025495

Order 11392.

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

normal subgroups only

This group has 476 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
1#19151537C211yesmaximal, characteristic, complemented
2#19151510C212yesmaximal, complemented
3#19151503C211yesmaximal, characteristic, complemented
4#19151491C212yesmaximal, complemented
5#19151478C212yesmaximal
6#19151465C212yesmaximal, complemented
7#19151459C212yesmaximal, complemented
8C22⋊C4×Dic89C212yesmaximal, complemented
9#394×C89C211yesmaximal, characteristic
10C22×Dic178C2211yescharacteristic
11C23×Dic89C2212yes—
12C2×C4⋊Dic89C2211yescharacteristic
13C2×C22⋊Dic89C2212yes—
14C2×C22⋊Dic89C2212yes—
15C2×C22⋊Dic89C2212yes—
16C2×C4×Dic89C2212yes—
17C2×C4×Dic89C2211yescharacteristic
18#15667919C2212yes—
19#15667919C2212yes—
20#15667919C2211yescharacteristic
21#15667919C2212yes—
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2212yes—
26C22×D4×C89C2211yescharacteristic
27C2×C4⋊C4×C89C2211yescharacteristic
28C2×C22⋊C4×C89C2212yes—
29C2×C22⋊C4×C89C2212yes—
30#95×C89C2211yescharacteristic
31C2×Dic178—22no—
32C2×Dic178—41no—
33C2×Dic178—41no—
34C22×Dic89—24no—
35C22×Dic89—24no—
36C22×Dic89—42no—
37C22×Dic89C2312yes—
38C22×Dic89C2312yes—
39C22×Dic89C2312yes—
40C22×Dic89C2312yes—
41C4⋊Dic89—41no—
42C22⋊Dic89—24no—
43C22⋊Dic89—42no—
44C22⋊Dic89—42no—
45C4×Dic89—24no—
46C4×Dic89—41no—
47C24×C89C2312yes—
48C2×D4×C89—24no—
49C2×D4×C89—41no—
50C22×C4×C89C2312yes—
51C22×C4×C89C2311yescharacteristic
52C22×C4×C89C2311yescharacteristic
53C22×C4×C89C2311yescharacteristic
54C4⋊C4×C89—41no—
55C22⋊C4×C89—24no—
56C22⋊C4×C89—24no—
57C23×C89—22no—
58C23×C89—22no—
59C23×C89—22no—
60C23×C89—22no—
61C23×C89—22no—
62C23×C89—22no—
63C23×C89#4114yes—
64C23×C89C2411yescharacteristic
65D4×C89—44no—
66C2×C4×C89—21no—
67C2×C4×C89—21no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—22no—
72C2×C4×C89—22no—
73C2×C4×C89—21no—
74C2×C4×C89—21no—
75C2×C4×C89#4112yes—
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—22no—
87C2×Dic89—48no—
88C2×Dic89#4114yes—
89Dic178—44no—
90C22×C89—24no—
91C22×C89—24no—
92C22×C89—24no—
93C22×C89—42no—
94C22×C89—42no—
95C22×C89—42no—
96C22×C89—42no—
97C22×C89C2×#4111yescharacteristic
98C22×C89C2×#4112yes—
99C22×C89C2×#4112yes—
100C22×C89H(5,𝔽2)11yescharacteristic
101C22×C89H(5,𝔽2)11yescharacteristic
102C4×C89—22no—
103C4×C89—42no—
104C4×C89—41no—
105C4×C89—41no—
106Dic89—24no—
107Dic89—42no—
108Dic89—42no—
109Dic89—42no—
110C2×C89—44no—
111C2×C89#52912yes—
112C2×C89#53811yescharacteristic
113C2×C89#55112yes—
114C2×C89#55111yescharacteristic
115C2×C89#55511yescharacteristic
116#2572—891nomaximal, Sylow
117C89#257211yescharacteristic, complemented, Sylow
118#400—891no—
119#394D8911yescharacteristic
120#393—892no—
121#391—891no—
122#388—892no—
123#386—892no—
124#383—892no—
125#381—892no—
126C4×C22⋊C4—892no—
127C22×Q8—891no—
128C22×D4C2×D8911yescharacteristic
129C23×C4—892no—
130C2×C4⋊C4—891no—
131C2×C4⋊C4C2×D8911yescharacteristic
132C2×C22⋊C4—892no—
133C2×C22⋊C4—892no—
134C2×C22⋊C4—892no—
135C2×C22⋊C4C2×D8912yes—
136C2×C22⋊C4C2×D8912yes—
137C2×C42—891no—
138C2×C42—892no—
139#95—892no—
140#95—892no—
141#95—891no—
142#95—892no—
143#95—892no—
144#95—892no—
145#95—892no—
146#95—892no—
147#95C2×D8911yescharacteristic
148C24C22×D8912yes—
149C2×Q8—3561no—
150C2×Q8—3561no—
151C2×Q8—1782no—
152C2×D4—24no—
153C2×D4—41no—
154C22×C4—892no—
155C22×C4—892no—
156C22×C4—892no—
157C22×C4—892no—
158C22×C4—3562no—
159C22×C4—1784no—
160C22×C4—1784no—
161C22×C4C22×D8911yescharacteristic
162C22×C4C22×D8912yes—
163C22×C4C22×D8911yescharacteristic
164C22×C4C22×D8911yescharacteristic
165C4⋊C4—41no—
166C4⋊C4—3561no—
167C22⋊C4—24no—
168C22⋊C4—24no—
169C22⋊C4—3562no—
170C22⋊C4—3562no—
171C22⋊C4—1784no—
172C42—3561no—
173C42—1784no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23#1308357314yes—
181C23C23×D8911yescharacteristic
182Q8—3564no—
183D4—44no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—894no—
194C2×C4—3568no—
195C2×C4—1782no—
196C2×C4—1782no—
197C2×C4—1782no—
198C2×C4—1782no—
199C2×C4—1782no—
200C2×C4—1782no—
201C2×C4—1782no—
202C2×C4—1782no—
203C2×C4—1782no—
204C2×C4—1782no—
205C2×C4—1782no—
206C2×C4#1308357312yes—
207C22—24no—
208C22—24no—
209C22—24no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—42no—
214C22#41×D8912yes—
215C22C2×#1308357311yescharacteristic
216C22C2×#1308357312yes—
217C22#1566805711yescharacteristic
218C22#1566805811yescharacteristic
219C4—22no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—3562no—
224C4—3562no—
225C4—3562no—
226C4—1784no—
227C2—44no—
228C2#1915212912yes—
229C2#1915218511yescharacteristic
230C2#1915227112yes—
231C2#1915227911yescharacteristic
232C2#1915231011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#394×C89C2
prime radicalC22×D4×C89C22
hypercenter#394D89
hypocenterC89#2572
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #19151537C2semidirect
2. #19151510C2semidirect
3. #19151503C2semidirect
4. #19151491C2semidirect
6. #19151465C2semidirect
7. #19151459C2semidirect
8. C22⋊C4×Dic89C2semidirect
117. C89#2572semidirect

Maximal subgroups

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

subgroupindex
#191515372
#191515102
#191515032
#191514912
#191514782
#191514652
#191514592
C22⋊C4×Dic892
#394×C892
#257289