Finite Group Databasebeta

← #26028243

Subgroups — #26028243

Order 11392.

344 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 125 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#19151538C212yesmaximal
2#19151537C212yesmaximal
3#19151536C212yesmaximal
4#19151496C211yesmaximal, characteristic
5#19151496C211yesmaximal, characteristic
6#19151485C212yesmaximal
7#19151484C212yesmaximal
8#19151479C212yesmaximal
9#389×C89C211yesmaximal, characteristic
10C2×C4⋊Dic89C2211yescharacteristic
11C2×C4⋊Dic89C2211yescharacteristic
12C2×C4⋊Dic89C2211yescharacteristic
13C2×C4⋊Dic89C2211yescharacteristic
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×C4×Dic89C2212yes—
17#15667919C2212yes—
18#15667919C2212yes—
19#15667919C2212yes—
20#15667919C2212yes—
21#15667919C2212yes—
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2212yes—
26C2×C4⋊C4×C89C2212yes—
27C2×C4⋊C4×C89C2211yescharacteristic
28C2×C4⋊C4×C89C2211yescharacteristic
29C2×C42×C89C2211yescharacteristic
30#95×C89C2212yes—
31C22×Dic89C2312yes—
32C22×Dic89C2312yes—
33C22×Dic89C2312yes—
34C22×Dic89C2312yes—
35C4⋊Dic89—22no—
36C4⋊Dic89—22no—
37C4⋊Dic89—41no—
38C4⋊Dic89—41no—
39#13083553—24no—
40#13083553—24no—
41C4×Dic89—42no—
42C22×C4×C89C2312yes—
43C22×C4×C89C2312yes—
44C22×C4×C89C2311yescharacteristic
45C22×C4×C89C2311yescharacteristic
46C22×C4×C89C2311yescharacteristic
47C4⋊C4×C89—24no—
48C4⋊C4×C89—22no—
49C4⋊C4×C89—41no—
50C42×C89—41no—
51C23×C89C2411yescharacteristic
52C2×C4×C89—21no—
53C2×C4×C89—21no—
54C2×C4×C89—21no—
55C2×C4×C89—21no—
56C2×C4×C89—21no—
57C2×C4×C89—21no—
58C2×C4×C89—22no—
59C2×C4×C89—22no—
60C2×C4×C89—22no—
61C2×C4×C89—22no—
62C2×C4×C89—22no—
63C2×C4×C89—22no—
64C2×C4×C89#4112yes—
65C2×C4×C89#4112yes—
66C2×C4×C89#4112yes—
67C2×Dic89—22no—
68C2×Dic89—22no—
69C2×Dic89—22no—
70C2×Dic89—22no—
71C2×Dic89—22no—
72C2×Dic89—22no—
73C2×Dic89—22no—
74C2×Dic89—22no—
75C2×Dic89—22no—
76C2×Dic89—22no—
77C2×Dic89—22no—
78C2×Dic89—22no—
79C22×C89C2×#4111yescharacteristic
80C22×C89C2×#4111yescharacteristic
81C22×C89C2×#4111yescharacteristic
82C22×C89H(5,𝔽2)11yescharacteristic
83C22×C892−1+411yescharacteristic
84C22×C892−1+411yescharacteristic
85C22×C892−1+411yescharacteristic
86C4×C89—22no—
87C4×C89—22no—
88C4×C89—22no—
89C4×C89—42no—
90C4×C89—42no—
91Dic89—42no—
92Dic89—42no—
93Dic89—42no—
94Dic89—42no—
95C2×C89#53911yescharacteristic
96C2×C89#53911yescharacteristic
97C2×C89#53911yescharacteristic
98C2×C89#55611yescharacteristic
99C2×C89#55611yescharacteristic
100C2×C89#55611yescharacteristic
101C2×C89#56411yescharacteristic
102#2810—891nomaximal, Sylow
103C89#281011yescharacteristic, complemented, Sylow
104#400—892no—
105#400—892no—
106#400—892no—
107#389—891no—
108#389—891no—
109#389D8911yescharacteristic
110#387—892no—
111#387—892no—
112#387—892no—
113C2×C4⋊C4—891no—
114C2×C4⋊C4—891no—
115C2×C4⋊C4—892no—
116C2×C4⋊C4—892no—
117C2×C4⋊C4—891no—
118C2×C4⋊C4—891no—
119C2×C4⋊C4C2×D8912yes—
120C2×C4⋊C4C2×D8911yescharacteristic
121C2×C4⋊C4C2×D8911yescharacteristic
122C2×C42—892no—
123C2×C42C2×D8911yescharacteristic
124#95—892no—
125#95—892no—
126#95—892no—
127#95—892no—
128#95—892no—
129#95—892no—
130#95—892no—
131#95—892no—
132#95—892no—
133#95C2×D8912yes—
134C22×C4—892no—
135C22×C4—892no—
136C22×C4—892no—
137C22×C4—892no—
138C22×C4C22×D8912yes—
139C22×C4C22×D8912yes—
140C22×C4C22×D8911yescharacteristic
141C22×C4C22×D8911yescharacteristic
142C22×C4C22×D8911yescharacteristic
143C4⋊C4—24no—
144C4⋊C4—22no—
145C4⋊C4—41no—
146C4⋊C4—3561no—
147C4⋊C4—3561no—
148C4⋊C4—1782no—
149C4⋊C4—1784no—
150C4⋊C4—1784no—
151C4⋊C4—1782no—
152C42—41no—
153C42—3562no—
154C23C23×D8911yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—1782no—
168C2×C4—1782no—
169C2×C4—1782no—
170C2×C4—1782no—
171C2×C4—1782no—
172C2×C4—1782no—
173C2×C4—1782no—
174C2×C4—1782no—
175C2×C4—1782no—
176C2×C4—1782no—
177C2×C4—1782no—
178C2×C4—1782no—
179C2×C4#1308357312yes—
180C2×C4#1308357412yes—
181C2×C4#1308357512yes—
182C22C2×#1308357311yescharacteristic
183C22C2×#1308357411yescharacteristic
184C22C2×#1308357511yescharacteristic
185C22#1566805711yescharacteristic
186C22#1566805911yescharacteristic
187C22#1566805911yescharacteristic
188C22#1566806011yescharacteristic
189C4—22no—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—42no—
194C4—3562no—
195C4—3562no—
196C4—3562no—
197C4—3562no—
198C2#1915219311yescharacteristic
199C2#1915219511yescharacteristic
200C2#1915219711yescharacteristic
201C2#1915231811yescharacteristic
202C2#1915232111yescharacteristic
203C2#1915232211yescharacteristic
204C2C89⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#389×C89C2
hypercenter#389D89
hypocenterC89#2810
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
103. C89#2810semidirect

Maximal subgroups

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

subgroupindex
#191515382
#191515372
#191515362
#191514962
#191514852
#191514842
#191514792
#389×C892
#281089