Finite Group Databasebeta

← #392×D89 #26023446

Subgroups — #392×D89 #26023446

Order 11392.

1812 conjugacy classes of subgroups; only the 223 normal subgroups are shown.

normal subgroups only

This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 223 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
1C22×D4×D89C213yesmaximal, complemented
2C2×C22⋊C4×D89C213yesmaximal, complemented
3#19151508C211yesmaximal, characteristic, complemented
4#19151507C213yesmaximal, complemented
5#19151506C213yesmaximal, complemented
6#95×D89C211yesmaximal, characteristic, complemented
7#392×C89C211yesmaximal, characteristic, complemented
8C24×D89C2213yes—
9C22×D356C2213yescomplemented
10C22×C22⋊D89C2216yescomplemented
11C2×D4×D89—224no—
12C2×D4×D89—212no—
13C22×C4×D89C2211yescharacteristic
14C22×C4×D89C2213yes—
15C2×C22⋊Dic89C2213yescomplemented
16C2×#13083551C2213yescomplemented
17C2×#13083551C2213yescomplemented
18C22⋊C4×D89—212no—
19#15667919C2213yescomplemented
20C22×D4×C89C2213yescomplemented
21C2×C22⋊C4×C89C2213yescomplemented
22#95×C89C2211yescharacteristic, complemented
23C23×D89—212no—
24C23×D89—212no—
25C23×D89—26no—
26C23×D89—26no—
27C23×D89D4112yescomplemented
28C23×D89C2313yes—
29C23×D89C2311yescharacteristic
30C2×D356—212no—
31C2×D356—26no—
32C2×C22⋊D89—212no—
33C2×C22⋊D89—212no—
34C2×C22⋊D89—212no—
35D4×D89—296no—
36C22×Dic89C2311yescharacteristic
37C22×Dic89C2313yes—
38C2×C4×D89—212no—
39C2×C4×D89—26no—
40C2×C4×D89D4112yescomplemented
41C22⋊Dic89—26no—
42#13083551—26no—
43#13083551—26no—
44C24×C89C2313yes—
45C2×D4×C89—212no—
46C2×D4×C89—26no—
47C22×C4×C89C2311yescharacteristic
48C22×C4×C89C2313yes—
49C22⋊C4×C89—26no—
50C23×C89—23no—
51C23×C89—26no—
52C23×C89—26no—
53C23×C89—23no—
54C23×C89C2×D416yescomplemented
55C23×C89C2411yescharacteristic
56C22×D89—23no—
57C22×D89—26no—
58C22×D89—26no—
59C22×D89—23no—
60C22×D89—248no—
61C22×D89—224no—
62C22×D89—412no—
63C22×D89—424no—
64C22×D89—412no—
65C22×D89C2×D416yes—
66C22×D89C2×D416yes—
67C22×D89C2×D416yescomplemented
68C22×D89#4112yes—
69D4×C89—224no—
70C2×C4×C89—26no—
71C2×C4×C89—23no—
72C2×C4×C89C2×D416yescomplemented
73C22⋊D89—248no—
74C2×Dic89—26no—
75C2×Dic89—23no—
76C2×Dic89C2×D416yescomplemented
77D356—224no—
78C4×D89—224no—
79C4×D89—44no—
80C22×C89—212no—
81C22×C89—26no—
82C22×C89—43no—
83C22×C89—46no—
84C22×C89—43no—
85C22×C89C22×D413yes—
86C22×C89C22×D413yes—
87C22×C89C2×#4111yescharacteristic
88C2×D89—212no—
89C2×D89—26no—
90C2×D89—43no—
91C2×D89—46no—
92C2×D89—43no—
93C2×D89—448no—
94C2×D89#120112yes—
95C2×D89#121112yes—
96C2×D89#12714yes—
97C4×C89—26no—
98C4×C89—41no—
99Dic89—26no—
100Dic89—41no—
101C2×C89—46no—
102C2×C89C2×#12013yes—
103C2×C89C2×#12113yes—
104C2×C89C2×#12711yescharacteristic
105D89—46no—
106D89#39218yesdirect product factor
107C2×#392—891nomaximal, Sylow
108C89C2×#39211yescharacteristic, complemented, Sylow
109C23×D4—893no—
110C22×C22⋊C4—893no—
111#392—893no—
112#392—893no—
113#392—891no—
114#392D8911yescharacteristic, direct product factor
115C2×#95—891no—
116C25—893no—
117C22×D4—896no—
118C22×D4—893no—
119C22×D4—17812no—
120C22×D4—17824no—
121C22×D4C2×D8913yescomplemented
122C23×C4—893no—
123C23×C4—891no—
124C2×C22⋊C4—893no—
125C2×C22⋊C4—893no—
126C2×C22⋊C4—893no—
127C2×C22⋊C4—17812no—
128C2×C22⋊C4C2×D8913yescomplemented
129#95—893no—
130#95C2×D8911yescharacteristic, complemented
131C24—891no—
132C24—8912no—
133C24—893no—
134C24—1786no—
135C24—17812no—
136C24—17812no—
137C24—1786no—
138C24C22×D8913yes—
139C2×D4—212no—
140C2×D4—26no—
141C2×D4—17812no—
142C2×D4—17812no—
143C2×D4—17896no—
144C2×D4—17812no—
145C2×D4—17812no—
146C2×D4—1786no—
147C22×C4—893no—
148C22×C4—8912no—
149C22×C4—891no—
150C22×C4—1786no—
151C22×C4—17812no—
152C22×C4C22×D8911yescharacteristic
153C22×C4C22×D8913yes—
154C22⋊C4—26no—
155C22⋊C4—1786no—
156C22⋊C4—1786no—
157C22⋊C4—1786no—
158C23—23no—
159C23—26no—
160C23—26no—
161C23—23no—
162C23—896no—
163C23—896no—
164C23—892no—
165C23—896no—
166C23—35612no—
167C23—35612no—
168C23—35624no—
169C23—17848no—
170C23—17824no—
171C23—1783no—
172C23—1786no—
173C23—1786no—
174C23—1783no—
175C23D4×D8916yescomplemented
176C23C23×D8911yescharacteristic
177D4—224no—
178D4—17824no—
179D4—17848no—
180C2×C4—26no—
181C2×C4—23no—
182C2×C4—896no—
183C2×C4—3564no—
184C2×C4—17824no—
185C2×C4—1783no—
186C2×C4—1786no—
187C2×C4D4×D8916yescomplemented
188C22—212no—
189C22—26no—
190C22—43no—
191C22—43no—
192C22—46no—
193C22—894no—
194C22—8912no—
195C22—8912no—
196C22—35648no—
197C22—3563no—
198C22—3563no—
199C22—3566no—
200C22—17812no—
201C22—1786no—
202C22C2×D4×D8913yes—
203C22C2×D4×D8913yes—
204C22#41×D8911yescharacteristic
205C4—26no—
206C4—41no—
207C4—3561no—
208C4—1786no—
209C2—46no—
210C2—898no—
211C2—3566no—
212C2#120×D8913yes—
213C2#121×D8913yes—
214C2#127×D8911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#392×C89C2
hypercenter#392D89
hypocenterC89C2×#392
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D89C2semidirect
2. C2×C22⋊C4×D89C2semidirect
3. #19151508C2semidirect
4. #19151507C2semidirect
5. #19151506C2semidirect
6. #95×D89C2semidirect
7. #392×C89C2semidirect
9. C22×D356C22semidirect
10. C22×C22⋊D89C22semidirect
15. C2×C22⋊Dic89C22semidirect
16. C2×#13083551C22semidirect
17. C2×#13083551C22semidirect
19. #15667919C22semidirect
20. C22×D4×C89C22semidirect
21. C2×C22⋊C4×C89C22semidirect
22. #95×C89C22semidirect
27. C23×D89D4semidirect
40. C2×C4×D89D4semidirect
54. C23×C89C2×D4semidirect
67. C22×D89C2×D4semidirect
72. C2×C4×C89C2×D4semidirect
76. C2×Dic89C2×D4semidirect
106. D89#392direct (N × H)
108. C89C2×#392semidirect
114. #392D89direct (N × H)
121. C22×D4C2×D89semidirect
128. C2×C22⋊C4C2×D89semidirect
130. #95C2×D89semidirect
175. C23D4×D89semidirect
187. C2×C4D4×D89semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D892
C2×C22⋊C4×D892
#191515082
#191515072
#191515062
#95×D892
#392×C892
C2×#39289