Finite Group Databasebeta

← #26018589

Subgroups — #26018589

Order 11392.

316 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 69 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×#15667974C211yesmaximal, characteristic
2#19151560C212yesmaximal, complemented
3#19151324C211yesmaximal, characteristic, complemented
4#19151321C212yesmaximal, complemented
5#324×C89C211yesmaximal, characteristic, complemented
6C22×D356C411yescharacteristic
7C22×C4×D89C411yescharacteristic
8C22×C4×D89C2211yescharacteristic
9C2×#13083557—22no—
10#15667974—22no—
11#15667974—22no—
12C2×#13083551C411yescharacteristic
13C2×#13083551C2211yescharacteristic
14C2×C4×Dic89C411yescharacteristic
15C22⋊#10623494C2212yes—
16#15667924—22no—
17C2×C4⋊C4×C89C2211yescharacteristic
18C22⋊C8×C89C2212yes—
19C23×D89C2×C411yescharacteristic
20C23×D89C2×C411yescharacteristic
21C2×D356—22no—
22C2×D356—22no—
23C2×D356—22no—
24C22×Dic89C2×C411yescharacteristic
25C22×Dic89C2×C411yescharacteristic
26C2×C4×D89—21no—
27C2×C4×D89—21no—
28C2×C4×D89—42no—
29C2×C4×D89—42no—
30C2×C4×D89D412yes—
31C2×C4×D89D412yes—
32#13083557—44no—
33C2×#10623494—22no—
34#13083551—22no—
35#13083551—22no—
36C4×Dic89—21no—
37C4×Dic89—21no—
38C22×C4×C89C2×C411yescharacteristic
39C22×C4×C89C2×C411yescharacteristic
40C22×C4×C89C2311yescharacteristic
41C2×C8×C89—22no—
42C4⋊C4×C89—22no—
43C23×C89C22×C411yescharacteristic
44C22×D89—21no—
45C22×D89—21no—
46C22×D89—21no—
47C22×D89—21no—
48C22×D89—41no—
49C22×D89—41no—
50C22×D89—41no—
51C22×D89—41no—
52C22×D89C22⋊C412yes—
53C22×D89M1612yescomplemented
54C2×C4×C89—21no—
55C2×C4×C89—21no—
56C2×C4×C89—21no—
57C2×C4×C89—41no—
58C2×C4×C89—41no—
59C2×C4×C89M1612yescomplemented
60C2×C4×C89C2×D412yes—
61C2×Dic89—22no—
62C2×Dic89—21no—
63C2×Dic89—41no—
64C2×Dic89C22⋊C411yescharacteristic
65C2×Dic89C22⋊C411yescharacteristic
66D356—28no—
67C4×D89—24no—
68C4×D89—42no—
69C4×D89—42no—
70C4×D89—42no—
71C8×C89—42no—
72#10623494—42no—
73C22×C89—21no—
74C22×C89—21no—
75C22×C89C2×C22⋊C411yescharacteristic
76C22×C89C2×M1611yescharacteristic
77C22×C89C2×M1611yescharacteristic
78C2×D89—22no—
79C2×D89—22no—
80C2×D89—22no—
81C2×D89—22no—
82C2×D89—42no—
83C2×D89—42no—
84C2×D89—42no—
85C2×D89—41no—
86C2×D89—41no—
87C2×D89—42no—
88C4×C89—22no—
89C4×C89—22no—
90C4×C89—41no—
91Dic89—21no—
92Dic89—41no—
93Dic89#9912yes—
94C2×C89—21no—
95C2×C89—21no—
96C2×C89#40711yescharacteristic
97C2×C89C2×#9911yescharacteristic
98C2×C89#41311yescharacteristic
99D89—42no—
100D89—42no—
101#1465—891nomaximal, Sylow
102C89#146511yescharacteristic, complemented, Sylow
103C2×C4×D4—891no—
104#407—892no—
105#324—891no—
106#324D8911yescharacteristic, complemented
107#323—892no—
108C22×D4—891no—
109C23×C4—891no—
110C23×C4—891no—
111C2×M16—1782no—
112C4×D4—1782no—
113C4×D4—1782no—
114C2×C4⋊C4C2×D8911yescharacteristic
115C2×C22⋊C4—891no—
116C2×C22⋊C4—891no—
117C2×C42—891no—
118C22⋊C8—892no—
119C22⋊C8—1782no—
120C22⋊C8C2×D8912yes—
121C24—891no—
122C24—891no—
123C2×D4—1782no—
124C2×D4—1782no—
125C2×D4—1782no—
126C22×C4—891no—
127C22×C4—892no—
128C22×C4—892no—
129C22×C4—891no—
130C22×C4—3562no—
131C22×C4—3562no—
132C22×C4—1781no—
133C22×C4—1781no—
134C22×C4C4×D8911yescharacteristic
135C22×C4C4×D8911yescharacteristic
136C22×C4C22×D8911yescharacteristic
137M16—3564no—
138C2×C8—22no—
139C2×C8—1782no—
140C4⋊C4—22no—
141C22⋊C4—1782no—
142C22⋊C4—1782no—
143C42—1781no—
144C42—1781no—
145C23—892no—
146C23—892no—
147C23—3561no—
148C23—3561no—
149C23—3561no—
150C23—3561no—
151C23—1781no—
152C23—1781no—
153C23—1781no—
154C23—1781no—
155C23C2×C4×D8911yescharacteristic
156D4—1788no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—891no—
163C2×C4—891no—
164C2×C4—3562no—
165C2×C4—3562no—
166C2×C4—3562no—
167C2×C4—3561no—
168C2×C4—1784no—
169C2×C4—1782no—
170C2×C4—1781no—
171C2×C4#1308355712yescomplemented
172C2×C4D4×D8912yes—
173C8—42no—
174C8—3562no—
175C22—21no—
176C22—21no—
177C22—3562no—
178C22—3562no—
179C22—3562no—
180C22—3562no—
181C22—3561no—
182C22—3561no—
183C22—1782no—
184C22—1782no—
185C22—1782no—
186C22—1782no—
187C22C22⋊C4×D8911yescharacteristic
188C22M16×D8911yescharacteristic
189C22C2×#1308355711yescharacteristic
190C4—22no—
191C4—22no—
192C4—41no—
193C4—892no—
194C4—3561no—
195C4—1781no—
196C2—21no—
197C2—21no—
198C2—3562no—
199C2—3562no—
200C2#1915156011yescharacteristic
201C2#99×D8911yescharacteristic
202C2#1915158111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D89
commutatorC23×C89C22×C4
FrattiniC22×C4C22×D89
Fitting#324×C89C2
socleC22×C89C2×C22⋊C4
prime radicalC22×D356C4
cosocleC22×C4×C89C23
hypercenter#324D89
hypocenterC89#1465
LCSG ▷ C23×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #19151560C2semidirect
3. #19151324C2semidirect
4. #19151321C2semidirect
5. #324×C89C2semidirect
53. C22×D89M16semidirect
59. C2×C4×C89M16semidirect
102. C89#1465semidirect
106. #324D89semidirect
171. C2×C4#13083557semidirect

Maximal subgroups

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

subgroupindex
C2×#156679742
#191515602
#191513242
#191513212
#324×C892
#146589