Finite Group Databasebeta

← #26028433

Subgroups — #26028433

Order 11392.

332 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C89⋊#401C212yesmaximal
2#19151540C212yesmaximal
3#19151537C212yesmaximal
4#19151530C212yesmaximal
5#19151528C211yesmaximal, characteristic
6#19151519C212yesmaximal
7#19151503C211yesmaximal, characteristic
8#19151480C212yesmaximal
9#400×C89C211yesmaximal, characteristic
10C22×Dic178C2211yescharacteristic
11C2×C4⋊Dic89C2212yes—
12C2×C4⋊Dic89C2212yes—
13C2×C4⋊Dic89C2211yescharacteristic
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×C4×Dic89C2211yescharacteristic
17#15667919C2212yes—
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—22no—
32C2×Dic178—41no—
33C2×Dic178—41no—
34C22×Dic89C2312yes—
35C22×Dic89C2312yes—
36C22×Dic89C2312yes—
37C22×Dic89C2312yes—
38C4⋊Dic89—42no—
39C4⋊Dic89—41no—
40C4⋊Dic89—42no—
41#13083553—24no—
42#13083553—42no—
43C4×Dic89—41no—
44C22×C4×C89C2312yes—
45C22×C4×C89C2312yes—
46C22×C4×C89C2311yescharacteristic
47C22×C4×C89C2311yescharacteristic
48C22×C4×C89C2311yescharacteristic
49C4⋊C4×C89—41no—
50C4⋊C4×C89—41no—
51C23×C89C2411yescharacteristic
52C2×C4×C89—21no—
53C2×C4×C89—21no—
54C2×C4×C89—21no—
55C2×C4×C89—22no—
56C2×C4×C89—21no—
57C2×C4×C89—22no—
58C2×C4×C89—22no—
59C2×C4×C89—22no—
60C2×C4×C89—24no—
61C2×C4×C89—22no—
62C2×C4×C89—22no—
63C2×C4×C89#4112yes—
64C2×Dic89—22no—
65C2×Dic89—22no—
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—
76Dic178—44no—
77C22×C89C2×#4111yescharacteristic
78C22×C89H(5,𝔽2)11yescharacteristic
79C22×C89H(5,𝔽2)11yescharacteristic
80C22×C892−1+412yes—
81C22×C892−1+412yes—
82C4×C89—22no—
83C4×C89—42no—
84C4×C89—42no—
85C4×C89—41no—
86C4×C89—41no—
87Dic89—42no—
88Dic89—42no—
89Dic89—42no—
90Dic89—42no—
91C2×C89#53811yescharacteristic
92C2×C89#54112yes—
93C2×C89#56311yescharacteristic
94C2×C89#56312yes—
95C2×C89#56311yescharacteristic
96#2833—891nomaximal, Sylow
97C89#283311yescharacteristic, complemented, Sylow
98#401—892no—
99#400—892no—
100#400—892no—
101#400D8911yescharacteristic
102#398—891no—
103#398—892no—
104#395—892no—
105#391—891no—
106#387—892no—
107C22×Q8—891no—
108C2×C4⋊C4—892no—
109C2×C4⋊C4—892no—
110C2×C4⋊C4—892no—
111C2×C4⋊C4—891no—
112C2×C4⋊C4—892no—
113C2×C4⋊C4C2×D8911yescharacteristic
114C2×C4⋊C4C2×D8911yescharacteristic
115C2×C42—891no—
116#95—892no—
117#95—892no—
118#95—892no—
119#95—892no—
120#95—892no—
121#95—892no—
122#95—892no—
123#95—892no—
124#95—891no—
125#95C2×D8912yes—
126#95C2×D8912yes—
127#95C2×D8911yescharacteristic
128C2×Q8—3561no—
129C2×Q8—3561no—
130C2×Q8—1782no—
131C22×C4—892no—
132C22×C4—892no—
133C22×C4—892no—
134C22×C4—892no—
135C22×C4C22×D8911yescharacteristic
136C22×C4C22×D8912yes—
137C22×C4C22×D8911yescharacteristic
138C22×C4C22×D8912yes—
139C22×C4C22×D8911yescharacteristic
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—3562no—
143C4⋊C4—3561no—
144C4⋊C4—3562no—
145C4⋊C4—3562no—
146C4⋊C4—1784no—
147C42—3561no—
148C23C23×D8911yescharacteristic
149Q8—3564no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—1782no—
162C2×C4—1782no—
163C2×C4—1782no—
164C2×C4—1782no—
165C2×C4—1782no—
166C2×C4—1782no—
167C2×C4—1782no—
168C2×C4—1782no—
169C2×C4—1782no—
170C2×C4—1782no—
171C2×C4—1782no—
172C2×C4—1782no—
173C2×C4#1308357512yes—
174C22C2×#1308357511yescharacteristic
175C22#1566805711yescharacteristic
176C22#1566805811yescharacteristic
177C22#1566805912yes—
178C22#1566805912yes—
179C4—22no—
180C4—42no—
181C4—42no—
182C4—41no—
183C4—41no—
184C4—3562no—
185C4—3562no—
186C4—3562no—
187C4—3562no—
188C2#1915218811yescharacteristic
189C2#1915221112yes—
190C2#1915234811yescharacteristic
191C2#1915235012yes—
192C2#1915235111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#400×C89C2
hypercenter#400D89
hypocenterC89#2833
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
97. C89#2833semidirect

Maximal subgroups

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

subgroupindex
C89⋊#4012
#191515402
#191515372
#191515302
#191515282
#191515192
#191515032
#191514802
#400×C892
#283389