Finite Group Databasebeta

← #26028525

Subgroups — #26028525

Order 11392.

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

normal subgroups only

This group has 356 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#19151539C212yesmaximal
2#19151538C212yesmaximal
3#19151537C211yesmaximal, characteristic
4#19151519C212yesmaximal
5#19151519C212yesmaximal
6#19151518C212yesmaximal
7#19151463C211yesmaximal, characteristic
8#19151462C212yesmaximal
9#400×C89C211yesmaximal, characteristic
10C22×Dic178C2212yes—
11C2×C4⋊Dic89C2211yescharacteristic
12C2×C4⋊Dic89C2211yescharacteristic
13C2×C4⋊Dic89C2212yes—
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×#13083553C2212yes—
17C2×C4×Dic89C2211yescharacteristic
18#15667919C2212yes—
19#15667919C2212yes—
20#15667919C2212yes—
21#15667919C2212yes—
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2211yescharacteristic
26C2×C4⋊C4×C89C2211yescharacteristic
27C2×C4⋊C4×C89C2211yescharacteristic
28#95×C89C2212yes—
29#95×C89C2212yes—
30#95×C89C2211yescharacteristic
31C2×Dic178—42no—
32C2×Dic178—42no—
33C2×Dic178—42no—
34C22×Dic89C2312yes—
35C22×Dic89C2312yes—
36C22×Dic89C2312yes—
37C22×Dic89C2312yes—
38C4⋊Dic89—41no—
39C4⋊Dic89—41no—
40C4⋊Dic89—42no—
41#13083553—42no—
42#13083553—42no—
43#13083553—42no—
44C4×Dic89Q814yescomplemented
45C22×C4×C89C2312yes—
46C22×C4×C89C2312yes—
47C22×C4×C89C2311yescharacteristic
48C22×C4×C89C2311yescharacteristic
49C22×C4×C89C2311yescharacteristic
50C4⋊C4×C89—41no—
51C4⋊C4×C89—41no—
52C23×C89C2411yescharacteristic
53C2×C4×C89—21no—
54C2×C4×C89—21no—
55C2×C4×C89—21no—
56C2×C4×C89—21no—
57C2×C4×C89—22no—
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—22no—
65C2×C4×C89C2×Q812yes—
66C2×Dic89—22no—
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×Dic89C2×Q814yes—
78Dic178—48no—
79C22×C89C22×Q811yescharacteristic
80C22×C89H(5,𝔽2)11yescharacteristic
81C22×C89H(5,𝔽2)12yes—
82C22×C892−1+411yescharacteristic
83C22×C892−1+412yes—
84C4×C89—22no—
85C4×C89—42no—
86C4×C89—42no—
87C4×C89—41no—
88C4×C89—41no—
89Dic89—24no—
90Dic89—42no—
91Dic89—42no—
92Dic89—42no—
93C2×C89#54411yescharacteristic
94C2×C89#54412yes—
95C2×C89H(3,𝔽4)11yescharacteristic
96C2×C89#56312yes—
97C2×C89#56311yescharacteristic
98#2844—891nomaximal, Sylow
99C89#284411yescharacteristic, complemented, Sylow
100#400—891no—
101#400—892no—
102#400—892no—
103#400D8911yescharacteristic
104#395—892no—
105#395—892no—
106#395—892no—
107#382—891no—
108#382—892no—
109C22×Q8—892no—
110C2×C4⋊C4—892no—
111C2×C4⋊C4—891no—
112C2×C4⋊C4—892no—
113C2×C4⋊C4—892no—
114C2×C4⋊C4—891no—
115C2×C4⋊C4—892no—
116C2×C4⋊C4C2×D8911yescharacteristic
117C2×C4⋊C4C2×D8911yescharacteristic
118C2×C42—891no—
119#95—892no—
120#95—892no—
121#95—892no—
122#95—892no—
123#95—892no—
124#95—892no—
125#95—892no—
126#95—891no—
127#95C2×D8912yes—
128#95C2×D8912yes—
129#95C2×D8911yescharacteristic
130C2×Q8—3562no—
131C2×Q8—3562no—
132C2×Q8—3562no—
133C22×C4—892no—
134C22×C4—892no—
135C22×C4—892no—
136C22×C4—892no—
137C22×C4C22×D8911yescharacteristic
138C22×C4C22×D8911yescharacteristic
139C22×C4C22×D8912yes—
140C22×C4C22×D8912yes—
141C22×C4C22×D8911yescharacteristic
142C4⋊C4—41no—
143C4⋊C4—41no—
144C4⋊C4—3562no—
145C4⋊C4—3562no—
146C4⋊C4—3562no—
147C4⋊C4—3561no—
148C4⋊C4—3561no—
149C4⋊C4—3562no—
150C42—894no—
151C23C23×D8911yescharacteristic
152Q8—3568no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—894no—
166C2×C4—1782no—
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×C4Q8×D8912yes—
178C22C2×Q8×D8911yescharacteristic
179C22#1566805711yescharacteristic
180C22#1566805812yes—
181C22#1566805911yescharacteristic
182C22#1566805912yes—
183C4—22no—
184C4—42no—
185C4—42no—
186C4—41no—
187C4—41no—
188C4—3562no—
189C4—3562no—
190C4—3562no—
191C4—1784no—
192C2#1915222711yescharacteristic
193C2#1915222812yes—
194C2#1915234011yescharacteristic
195C2#1915235012yes—
196C2#1915235111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#400×C89C2
hypercenter#400D89
hypocenterC89#2844
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
44. C4×Dic89Q8semidirect
99. C89#2844semidirect

Maximal subgroups

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

subgroupindex
#191515392
#191515382
#191515372
#191515192
#191515182
#191514632
#191514622
#400×C892
#284489