Finite Group Databasebeta

← #26028052

Subgroups — #26028052

Order 11392.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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#19151528C212yesmaximal
2#19151519C212yesmaximal
3#19151518C211yesmaximal, characteristic
4#19151497C212yesmaximal
5#19151495C212yesmaximal
6#19151480C212yesmaximal
7#19151479C212yesmaximal
8#19151467C211yesmaximal, characteristic
9#398×C89C211yesmaximal, characteristic
10C22×Dic178C2211yescharacteristic
11C2×C4⋊Dic89C2211yescharacteristic
12C2×C4⋊Dic89C2212yes—
13C2×C4⋊Dic89C2212yes—
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×#13083553C2212yes—
17C2×#13083553C2212yes—
18C2×C4×Dic89C2211yescharacteristic
19C2×C4×Dic89C2212yes—
20#15667919C2212yes—
21#15667919C2212yes—
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2211yescharacteristic
25#15667919C2212yes—
26C2×C4⋊C4×C89C2212yes—
27C2×C4⋊C4×C89C2211yescharacteristic
28C2×C4⋊C4×C89C2211yescharacteristic
29#95×C89C2212yes—
30#95×C89C2211yescharacteristic
31C2×Dic178—42no—
32C2×Dic178—41no—
33C22×Dic89C2312yes—
34C22×Dic89C2312yes—
35C22×Dic89C2312yes—
36C22×Dic89C2312yes—
37C4⋊Dic89—42no—
38C4⋊Dic89—41no—
39C4⋊Dic89—42no—
40#13083553—42no—
41#13083553—42no—
42#13083553—42no—
43#13083553Q818yescomplemented
44C4×Dic89—22no—
45C4×Dic89—42no—
46C22×C4×C89C2311yescharacteristic
47C22×C4×C89C2312yes—
48C22×C4×C89C2311yescharacteristic
49C22×C4×C89C2312yes—
50C22×C4×C89C2311yescharacteristic
51C4⋊C4×C89—24no—
52C4⋊C4×C89—41no—
53C4⋊C4×C89—41no—
54C23×C89C2411yescharacteristic
55C2×C4×C89—22no—
56C2×C4×C89—21no—
57C2×C4×C89—22no—
58C2×C4×C89—21no—
59C2×C4×C89—22no—
60C2×C4×C89—21no—
61C2×C4×C89—22no—
62C2×C4×C89—21no—
63C2×C4×C89—22no—
64C2×C4×C89—22no—
65C2×C4×C89—22no—
66C2×C4×C89C2×Q814yes—
67C2×C4×C89#4112yes—
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×Dic89C2×Q814yes—
79C2×Dic89C2×Q814yes—
80Dic178—44no—
81C22×C89C22×Q812yes—
82C22×C89C2×#4111yescharacteristic
83C22×C89H(5,𝔽2)11yescharacteristic
84C22×C89H(5,𝔽2)12yes—
85C22×C892−1+411yescharacteristic
86C4×C89—22no—
87C4×C89—24no—
88C4×C89—42no—
89C4×C89—41no—
90C4×C89—41no—
91Dic89—24no—
92Dic89—24no—
93Dic89—42no—
94Dic89—42no—
95C2×C89#53911yescharacteristic
96C2×C89#54412yes—
97C2×C89#55412yes—
98C2×C89Q8211yescharacteristic
99C2×C89#56011yescharacteristic
100#2792—891nomaximal, Sylow
101C89#279211yescharacteristic, complemented, Sylow
102#398—892no—
103#398D8911yescharacteristic
104#395—891no—
105#395—892no—
106#389—892no—
107#389—892no—
108#387—892no—
109#387—892no—
110#384—891no—
111C22×Q8—891no—
112C2×C4⋊C4—892no—
113C2×C4⋊C4—892no—
114C2×C4⋊C4—891no—
115C2×C4⋊C4—892no—
116C2×C4⋊C4—892no—
117C2×C4⋊C4—892no—
118C2×C4⋊C4—892no—
119C2×C4⋊C4C2×D8912yes—
120C2×C4⋊C4C2×D8911yescharacteristic
121C2×C4⋊C4C2×D8911yescharacteristic
122C2×C42—892no—
123C2×C42—891no—
124#95—891no—
125#95—892no—
126#95—892no—
127#95—892no—
128#95—892no—
129#95—892no—
130#95C2×D8912yes—
131#95C2×D8911yescharacteristic
132C2×Q8—3561no—
133C2×Q8—3562no—
134C22×C4—892no—
135C22×C4—892no—
136C22×C4—892no—
137C22×C4—892no—
138C22×C4C22×D8912yes—
139C22×C4C22×D8911yescharacteristic
140C22×C4C22×D8911yescharacteristic
141C22×C4C22×D8912yes—
142C22×C4C22×D8911yescharacteristic
143C4⋊C4—24no—
144C4⋊C4—41no—
145C4⋊C4—41no—
146C4⋊C4—898no—
147C4⋊C4—3562no—
148C4⋊C4—3562no—
149C4⋊C4—3562no—
150C4⋊C4—3561no—
151C4⋊C4—3562no—
152C4⋊C4—3562no—
153C42—3562no—
154C42—1782no—
155C23C23×D8911yescharacteristic
156Q8—3564no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—894no—
169C2×C4—894no—
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—1782no—
180C2×C4Q8×D8914yes—
181C2×C4#1308357312yes—
182C22C2×Q8×D8912yes—
183C22C2×#1308357311yescharacteristic
184C22#1566805711yescharacteristic
185C22#1566805812yes—
186C22#1566805911yescharacteristic
187C4—22no—
188C4—24no—
189C4—42no—
190C4—41no—
191C4—41no—
192C4—3562no—
193C4—3562no—
194C4—1784no—
195C4—1784no—
196C2#1915219311yescharacteristic
197C2#1915222812yes—
198C2#1915230612yes—
199C2#1915232811yescharacteristic
200C2#1915233811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#398×C89C2
hypercenter#398D89
hypocenterC89#2792
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
43. #13083553Q8semidirect
101. C89#2792semidirect

Maximal subgroups

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

subgroupindex
#191515282
#191515192
#191515182
#191514972
#191514952
#191514802
#191514792
#191514672
#398×C892
#279289