Finite Group Databasebeta

← #26028319

Subgroups — #26028319

Order 11392.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15668004C211yesmaximal, characteristic
2#19151537C212yesmaximal
3#19151536C212yesmaximal
4#19151531C214yesmaximal
5#19151529C212yesmaximal
6#19151528C212yesmaximal
7#19151464C211yesmaximal, characteristic
8C2×#125×C89C211yesmaximal, characteristic
9#15668004—24no—
10C2×C4⋊Dic89C2211yescharacteristic
11C2×C4⋊Dic89C2211yescharacteristic
12C2×C4⋊Dic89C2212yes—
13C2×#13083553C2212yes—
14C2×#13083553C2212yes—
15C2×#13083553C2214yes—
16#15667919C2212yes—
17#15667919C2212yes—
18#15667919C2214yes—
19#15667919C2214yes—
20#15667919C2214yes—
21#125×C89—24no—
22C2×C4⋊C4×C89C2212yes—
23C2×C4⋊C4×C89C2211yescharacteristic
24C2×C4⋊C4×C89C2212yes—
25C2×C4⋊C4×C89C2211yescharacteristic
26C2×C42×C89C2211yescharacteristic
27C22×Dic89C2314yes—
28C22×Dic89C2312yes—
29C22×Dic89C2312yes—
30C4⋊Dic89—22no—
31C4⋊Dic89—22no—
32C4⋊Dic89—42no—
33#13083553—24no—
34#13083553—24no—
35#13083553—44no—
36C22×C4×C89C2312yes—
37C22×C4×C89C2312yes—
38C22×C4×C89C2311yescharacteristic
39C22×C4×C89C2311yescharacteristic
40C22×C4×C89C2311yescharacteristic
41C4⋊C4×C89—22no—
42C4⋊C4×C89—24no—
43C4⋊C4×C89—22no—
44C4⋊C4×C89—24no—
45C42×C89D414yes—
46C23×C89C2411yescharacteristic
47C2×C4×C89—21no—
48C2×C4×C89—22no—
49C2×C4×C89—21no—
50C2×C4×C89—22no—
51C2×C4×C89—22no—
52C2×C4×C89—22no—
53C2×C4×C89—22no—
54C2×C4×C89—24no—
55C2×C4×C89—22no—
56C2×C4×C89C2×D412yes—
57C2×C4×C89C2×D412yes—
58C2×C4×C89C2×D412yes—
59C2×Dic89—22no—
60C2×Dic89—22no—
61C2×Dic89—22no—
62C2×Dic89—24no—
63C2×Dic89—22no—
64C2×Dic89—24no—
65C2×Dic89—24no—
66C2×Dic89—24no—
67C22×C89C22×D411yescharacteristic
68C22×C89H(5,𝔽2)11yescharacteristic
69C22×C892−1+412yes—
70C22×C892−1+412yes—
71C22×C892−1+411yescharacteristic
72C4×C89—22no—
73C4×C89—22no—
74C4×C89—22no—
75C4×C89—42no—
76C4×C89—42no—
77Dic89—42no—
78Dic89—42no—
79Dic89—44no—
80C2×C89#53611yescharacteristic
81C2×C89#53611yescharacteristic
82C2×C89#53711yescharacteristic
83C2×C89#56312yes—
84C2×C89#56412yes—
85#2822—891nomaximal, Sylow
86C89#282211yescharacteristic, complemented, Sylow
87C2×#125—891no—
88C2×#125D8911yescharacteristic
89#400—892no—
90#400—892no—
91#398—892no—
92#398—892no—
93#398—894no—
94#382—891no—
95#125—24no—
96#125—1784no—
97C2×C4⋊C4—892no—
98C2×C4⋊C4—894no—
99C2×C4⋊C4—892no—
100C2×C4⋊C4—891no—
101C2×C4⋊C4—892no—
102C2×C4⋊C4—891no—
103C2×C4⋊C4C2×D8912yes—
104C2×C4⋊C4C2×D8911yescharacteristic
105C2×C4⋊C4C2×D8912yes—
106C2×C4⋊C4C2×D8911yescharacteristic
107C2×C42C2×D8911yescharacteristic
108#95—892no—
109#95—892no—
110#95—894no—
111#95—894no—
112#95—894no—
113C22×C4—894no—
114C22×C4—892no—
115C22×C4—892no—
116C22×C4C22×D8912yes—
117C22×C4C22×D8912yes—
118C22×C4C22×D8911yescharacteristic
119C22×C4C22×D8911yescharacteristic
120C22×C4C22×D8911yescharacteristic
121C4⋊C4—24no—
122C4⋊C4—22no—
123C4⋊C4—24no—
124C4⋊C4—22no—
125C4⋊C4—3564no—
126C4⋊C4—3562no—
127C4⋊C4—1784no—
128C4⋊C4—1784no—
129C4⋊C4—1782no—
130C4⋊C4—1782no—
131C42C22⋊D8914yes—
132C23C23×D8911yescharacteristic
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—21no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—24no—
141C2×C4—22no—
142C2×C4—1782no—
143C2×C4—1782no—
144C2×C4—1782no—
145C2×C4—1784no—
146C2×C4—1782no—
147C2×C4—1784no—
148C2×C4—1784no—
149C2×C4—1784no—
150C2×C4C2×C22⋊D8912yes—
151C2×C4C2×C22⋊D8912yes—
152C2×C4C2×C22⋊D8912yes—
153C22C22×C22⋊D8911yescharacteristic
154C22#1566805811yescharacteristic
155C22#1566805912yes—
156C22#1566805911yescharacteristic
157C22#1566806012yes—
158C4—22no—
159C4—22no—
160C4—22no—
161C4—42no—
162C4—42no—
163C4—3562no—
164C4—3562no—
165C4—3564no—
166C2#1915216911yescharacteristic
167C2#1915217211yescharacteristic
168C2#1915217611yescharacteristic
169C2#1915235212yes—
170C2C89⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
FittingC2×#125×C89C2
hypercenterC2×#125D89
hypocenterC89#2822
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
86. C89#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#156680042
#191515372
#191515362
#191515312
#191515292
#191515282
#191514642
C2×#125×C892
#282289