Finite Group Databasebeta

← #26028140

Subgroups — #26028140

Order 11392.

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

normal subgroups only

This group has 376 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#19151538C212yesmaximal
2#19151532C212yesmaximal
3#19151518C211yesmaximal, characteristic
4#19151503C211yesmaximal, characteristic
5#19151502C212yesmaximal
6#19151502C212yesmaximal
7#19151485C212yesmaximal
8#19151479C212yesmaximal
9#400×C89C211yesmaximal, characteristic
10C22×Dic178C2211yescharacteristic
11C22×Dic178C2211yescharacteristic
12C2×C4⋊Dic89C2212yes—
13C2×#13083553C2212yes—
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×C4×Dic89C2212yes—
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—24no—
32C2×Dic178—41no—
33C2×Dic178—41no—
34C2×Dic178—41no—
35C2×Dic178Q814yescomplemented
36C22×Dic89C2312yes—
37C22×Dic89C2312yes—
38C22×Dic89C2312yes—
39C22×Dic89C2312yes—
40C4⋊Dic89—42no—
41#13083553—24no—
42#13083553—24no—
43#13083553—42no—
44C4×Dic89—42no—
45C4×Dic89—41no—
46C22×C4×C89C2311yescharacteristic
47C22×C4×C89C2312yes—
48C22×C4×C89C2312yes—
49C22×C4×C89C2311yescharacteristic
50C22×C4×C89C2311yescharacteristic
51C4⋊C4×C89—41no—
52C4⋊C4×C89—41no—
53C23×C89C2411yescharacteristic
54C2×C4×C89—21no—
55C2×C4×C89—21no—
56C2×C4×C89—22no—
57C2×C4×C89—22no—
58C2×C4×C89—22no—
59C2×C4×C89—21no—
60C2×C4×C89—22no—
61C2×C4×C89—21no—
62C2×C4×C89—22no—
63C2×C4×C89—22no—
64C2×C4×C89—24no—
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×Dic89C2×Q814yes—
77C2×Dic89#4114yes—
78Dic178—44no—
79Dic178—44no—
80C22×C89C22×Q811yescharacteristic
81C22×C89C2×#4112yes—
82C22×C89H(5,𝔽2)11yescharacteristic
83C22×C89H(5,𝔽2)11yescharacteristic
84C22×C892−1+412yes—
85C4×C89—22no—
86C4×C89—42no—
87C4×C89—41no—
88C4×C89—41no—
89C4×C89—42no—
90Dic89—24no—
91Dic89—24no—
92Dic89—42no—
93Dic89—42no—
94C2×C89#54212yes—
95C2×C89#54311yescharacteristic
96C2×C89#55111yescharacteristic
97C2×C89#55712yes—
98C2×C89#56311yescharacteristic
99#2799—891nomaximal, Sylow
100C89#279911yescharacteristic, complemented, Sylow
101#400—892no—
102#400D8911yescharacteristic
103#398—892no—
104#395—891no—
105#391—891no—
106#391—892no—
107#391—892no—
108#387—892no—
109#387—892no—
110C22×Q8—891no—
111C22×Q8—891no—
112C2×C4⋊C4—892no—
113C2×C4⋊C4—892no—
114C2×C4⋊C4—892no—
115C2×C4⋊C4—892no—
116C2×C4⋊C4C2×D8911yescharacteristic
117C2×C4⋊C4C2×D8911yescharacteristic
118C2×C42—891no—
119C2×C42—892no—
120#95—892no—
121#95—892no—
122#95—892no—
123#95—892no—
124#95—892no—
125#95—892no—
126#95—892no—
127#95—891no—
128#95C2×D8912yes—
129#95C2×D8912yes—
130#95C2×D8911yescharacteristic
131C2×Q8—894no—
132C2×Q8—3561no—
133C2×Q8—3561no—
134C2×Q8—3561no—
135C2×Q8—1784no—
136C22×C4—892no—
137C22×C4—892no—
138C22×C4—892no—
139C22×C4—892no—
140C22×C4C22×D8912yes—
141C22×C4C22×D8911yescharacteristic
142C22×C4C22×D8911yescharacteristic
143C22×C4C22×D8912yes—
144C22×C4C22×D8911yescharacteristic
145C4⋊C4—41no—
146C4⋊C4—41no—
147C4⋊C4—3562no—
148C4⋊C4—3562no—
149C4⋊C4—1784no—
150C4⋊C4—1784no—
151C42—3561no—
152C42—3562no—
153C23C23×D8911yescharacteristic
154Q8—3564no—
155Q8—3564no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—24no—
167C2×C4—894no—
168C2×C4—894no—
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×C4Q8×D8912yes—
180C22C2×Q8×D8911yescharacteristic
181C22#41×D8912yes—
182C22#1566805711yescharacteristic
183C22#1566805811yescharacteristic
184C22#1566805912yes—
185C4—22no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—42no—
190C4—3562no—
191C4—3562no—
192C4—1784no—
193C4—1784no—
194C2#1915221412yes—
195C2#1915222311yescharacteristic
196C2#1915227611yescharacteristic
197C2#1915232512yes—
198C2#1915234811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#400×C89C2
hypercenter#400D89
hypocenterC89#2799
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
35. C2×Dic178Q8semidirect
100. C89#2799semidirect

Maximal subgroups

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

subgroupindex
#191515382
#191515322
#191515182
#191515032
#191515022
#191514852
#191514792
#400×C892
#279989