Finite Group Databasebeta

← #26028318

Subgroups — #26028318

Order 11392.

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

normal subgroups only

This group has 380 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
1C2×#15668002C212yesmaximal
2#19151540C212yesmaximal
3#19151539C212yesmaximal
4#19151532C212yesmaximal
5#19151531C212yesmaximal
6#19151531C212yesmaximal
7#19151528C211yesmaximal, characteristic
8#19151463C211yesmaximal, characteristic
9#398×C89C211yesmaximal, characteristic
10#15668002—28no—
11C2×C4⋊Dic89C2212yes—
12C2×C4⋊Dic89C2211yescharacteristic
13C2×C4⋊Dic89C2211yescharacteristic
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×#13083553C2212yes—
17C2×#13083553C2212yes—
18C2×#13083553C2212yes—
19C2×C4×Dic89C2211yescharacteristic
20#15667919C2212yes—
21#15667919C2212yes—
22#15667919C2212yes—
23#15667919C2211yescharacteristic
24#15667919C2212yes—
25#15667919C2212yes—
26#15667919C2212yes—
27C2×C4⋊C4×C89C2212yes—
28C2×C4⋊C4×C89C2211yescharacteristic
29C2×C4⋊C4×C89C2211yescharacteristic
30#95×C89C2212yes—
31#95×C89C2211yescharacteristic
32C22×Dic89C2312yes—
33C22×Dic89C2312yes—
34C22×Dic89C2312yes—
35C22×Dic89C2312yes—
36C4⋊Dic89—24no—
37C4⋊Dic89—41no—
38C4⋊Dic89—41no—
39#13083553—24no—
40#13083553—24no—
41#13083553—24no—
42#13083553—24no—
43#13083553—42no—
44C4×Dic89D414yes—
45C22×C4×C89C2311yescharacteristic
46C22×C4×C89C2312yes—
47C22×C4×C89C2311yescharacteristic
48C22×C4×C89C2312yes—
49C22×C4×C89C2311yescharacteristic
50C4⋊C4×C89—24no—
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—21no—
59C2×C4×C89—22no—
60C2×C4×C89—21no—
61C2×C4×C89—22no—
62C2×C4×C89—22no—
63C2×C4×C89—22no—
64C2×C4×C89—22no—
65C2×C4×C89—22no—
66C2×C4×C89C2×D412yes—
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—24no—
77C2×Dic89C2×D414yes—
78C22×C89C22×D411yescharacteristic
79C22×C89H(5,𝔽2)11yescharacteristic
80C22×C892−1+412yes—
81C22×C892−1+412yes—
82C22×C892−1+411yescharacteristic
83C4×C89—22no—
84C4×C89—42no—
85C4×C89—42no—
86C4×C89—41no—
87C4×C89—41no—
88Dic89—24no—
89Dic89—42no—
90Dic89—42no—
91Dic89—42no—
92C2×C89#53612yes—
93C2×C89#53711yescharacteristic
94C2×C89#56311yescharacteristic
95C2×C89#56311yescharacteristic
96C2×C89#56412yes—
97#2822—891nomaximal, Sylow
98C89#282211yescharacteristic, complemented, Sylow
99C2×#125—892no—
100#400—892no—
101#400—892no—
102#398—891no—
103#398—892no—
104#398—892no—
105#398—892no—
106#398D8911yescharacteristic
107#382—891no—
108#125—1788no—
109C2×C4⋊C4—891no—
110C2×C4⋊C4—892no—
111C2×C4⋊C4—891no—
112C2×C4⋊C4—892no—
113C2×C4⋊C4—892no—
114C2×C4⋊C4—892no—
115C2×C4⋊C4—892no—
116C2×C4⋊C4—892no—
117C2×C4⋊C4C2×D8912yes—
118C2×C4⋊C4C2×D8911yescharacteristic
119C2×C4⋊C4C2×D8911yescharacteristic
120C2×C42—891no—
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×D8911yescharacteristic
130C22×C4—892no—
131C22×C4—892no—
132C22×C4—892no—
133C22×C4—892no—
134C22×C4C22×D8911yescharacteristic
135C22×C4C22×D8911yescharacteristic
136C22×C4C22×D8912yes—
137C22×C4C22×D8912yes—
138C22×C4C22×D8911yescharacteristic
139C4⋊C4—24no—
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—3562no—
143C4⋊C4—3561no—
144C4⋊C4—3561no—
145C4⋊C4—1784no—
146C4⋊C4—1784no—
147C4⋊C4—1784no—
148C4⋊C4—1784no—
149C4⋊C4—1784no—
150C42—894no—
151C23C23×D8911yescharacteristic
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—894no—
165C2×C4—1782no—
166C2×C4—1782no—
167C2×C4—1782no—
168C2×C4—1782no—
169C2×C4—1782no—
170C2×C4—1782no—
171C2×C4—1782no—
172C2×C4—1784no—
173C2×C4—1782no—
174C2×C4—1782no—
175C2×C4D4×D8912yes—
176C22C2×D4×D8911yescharacteristic
177C22#1566805711yescharacteristic
178C22#1566805912yes—
179C22#1566805911yescharacteristic
180C22#1566806012yes—
181C4—22no—
182C4—42no—
183C4—42no—
184C4—41no—
185C4—41no—
186C4—3562no—
187C4—3562no—
188C4—3562no—
189C4—1784no—
190C2#1915217112yes—
191C2#1915217511yescharacteristic
192C2#1915234711yescharacteristic
193C2#1915235111yescharacteristic
194C2C89⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#398×C89C2
hypercenter#398D89
hypocenterC89#2822
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
98. C89#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#156680022
#191515402
#191515392
#191515322
#191515312
#191515282
#191514632
#398×C892
#282289