Finite Group Databasebeta

← #26028290

Subgroups — #26028290

Order 11392.

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

normal subgroups only

This group has 444 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×#15667989C212yesmaximal
2#19151540C212yesmaximal, complemented
3#19151539C212yesmaximal, complemented
4#19151526C212yesmaximal
5#19151523C211yesmaximal, characteristic
6#19151519C212yesmaximal, complemented
7#19151518C212yesmaximal, complemented
8#19151459C211yesmaximal, characteristic
9#397×C89C211yesmaximal, characteristic
10C22×Dic178C2212yes—
11C23×Dic89C2211yescharacteristic
12#15667989—28no—
13C2×C4⋊Dic89C2212yes—
14C2×C4⋊Dic89C2211yescharacteristic
15C2×#13083553C2212yes—
16C2×#13083553C2212yes—
17C2×#13083553C2212yes—
18C2×C22⋊Dic89C2212yes—
19C2×C22⋊Dic89C2211yescharacteristic
20#15667919C2212yes—
21#15667919C2212yes—
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2211yescharacteristic
26#15667919C2212yes—
27C2×C4⋊C4×C89C2211yescharacteristic
28C2×C22⋊C4×C89C2212yes—
29C2×C22⋊C4×C89C2211yescharacteristic
30#95×C89C2212yes—
31#95×C89C2211yescharacteristic
32C2×Dic178—24no—
33C2×Dic178—42no—
34C2×Dic178—42no—
35C22×Dic89—41no—
36C22×Dic89—41no—
37C22×Dic89D414yes—
38C22×Dic89C2312yes—
39C22×Dic89C2312yes—
40C22×Dic89C2312yes—
41C22×Dic89C2312yes—
42C4⋊Dic89—24no—
43C4⋊Dic89—41no—
44#13083553—24no—
45#13083553—24no—
46#13083553—42no—
47C22⋊Dic89—24no—
48C22⋊Dic89—41no—
49C24×C89C2311yescharacteristic
50C22×C4×C89C2312yes—
51C22×C4×C89C2311yescharacteristic
52C22×C4×C89C2312yes—
53C22×C4×C89C2311yescharacteristic
54C4⋊C4×C89—41no—
55C22⋊C4×C89—24no—
56C22⋊C4×C89—41no—
57C23×C89—21no—
58C23×C89—21no—
59C23×C89—22no—
60C23×C89—22no—
61C23×C89C2×D412yes—
62C23×C89C2411yescharacteristic
63C2×C4×C89—22no—
64C2×C4×C89—22no—
65C2×C4×C89—21no—
66C2×C4×C89—21no—
67C2×C4×C89—22no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—22no—
72C2×C4×C89—22no—
73C2×Dic89—22no—
74C2×Dic89—22no—
75C2×Dic89—22no—
76C2×Dic89—22no—
77C2×Dic89—22no—
78C2×Dic89—22no—
79C2×Dic89—22no—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89—44no—
85C2×Dic89C2×D414yes—
86Dic178—48no—
87C22×C89—22no—
88C22×C89—24no—
89C22×C89—41no—
90C22×C89—42no—
91C22×C89—41no—
92C22×C89C22×D411yescharacteristic
93C22×C89H(5,𝔽2)11yescharacteristic
94C22×C89H(5,𝔽2)11yescharacteristic
95C22×C892−1+412yes—
96C22×C892−1+412yes—
97C4×C89—42no—
98C4×C89—42no—
99C4×C89—41no—
100C4×C89—41no—
101Dic89—24no—
102Dic89—42no—
103Dic89—42no—
104Dic89—42no—
105C2×C89—42no—
106C2×C89#53411yescharacteristic
107C2×C89#53612yes—
108C2×C89#56311yescharacteristic
109C2×C89#56312yes—
110C2×C89#56311yescharacteristic
111#2817—891nomaximal, Sylow
112C89#281711yescharacteristic, complemented, Sylow
113C2×C22⋊Q8—892no—
114#400—892no—
115#400—892no—
116#397—891no—
117#397—892no—
118#397D8911yescharacteristic
119#395—892no—
120#395—892no—
121#381—891no—
122C22×Q8—892no—
123C23×C4—891no—
124C22⋊Q8—1788no—
125C2×C4⋊C4—892no—
126C2×C4⋊C4—891no—
127C2×C4⋊C4—892no—
128C2×C4⋊C4—892no—
129C2×C4⋊C4—892no—
130C2×C4⋊C4C2×D8911yescharacteristic
131C2×C22⋊C4—891no—
132C2×C22⋊C4—892no—
133C2×C22⋊C4C2×D8912yes—
134C2×C22⋊C4C2×D8911yescharacteristic
135#95—892no—
136#95—892no—
137#95—892no—
138#95—892no—
139#95—892no—
140#95—892no—
141#95—891no—
142#95C2×D8912yes—
143#95C2×D8911yescharacteristic
144C24C22×D8911yescharacteristic
145C2×Q8—3562no—
146C2×Q8—3562no—
147C2×Q8—1784no—
148C22×C4—894no—
149C22×C4—892no—
150C22×C4—892no—
151C22×C4—892no—
152C22×C4—892no—
153C22×C4—3561no—
154C22×C4—3561no—
155C22×C4C22×D8911yescharacteristic
156C22×C4C22×D8911yescharacteristic
157C22×C4C22×D8912yes—
158C22×C4C22×D8912yes—
159C4⋊C4—41no—
160C4⋊C4—3562no—
161C4⋊C4—3561no—
162C4⋊C4—1784no—
163C4⋊C4—1784no—
164C4⋊C4—1784no—
165C22⋊C4—24no—
166C22⋊C4—41no—
167C22⋊C4—3561no—
168C22⋊C4—1784no—
169C23—21no—
170C23—21no—
171C23—22no—
172C23—22no—
173C23D4×D8912yes—
174C23C23×D8911yescharacteristic
175Q8—3568no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—894no—
187C2×C4—3564no—
188C2×C4—1782no—
189C2×C4—1782no—
190C2×C4—1782no—
191C2×C4—1782no—
192C2×C4—1782no—
193C2×C4—1782no—
194C2×C4—1782no—
195C2×C4—1782no—
196C2×C4—1782no—
197C2×C4—1782no—
198C2×C4—1782no—
199C22—22no—
200C22—24no—
201C22—41no—
202C22—42no—
203C22—41no—
204C22C2×D4×D8911yescharacteristic
205C22#1566805711yescharacteristic
206C22#1566805811yescharacteristic
207C22#1566805912yes—
208C22#1566805912yes—
209C4—42no—
210C4—42no—
211C4—41no—
212C4—41no—
213C4—3562no—
214C4—3562no—
215C4—3562no—
216C4—1784no—
217C2—42no—
218C2#1915215611yescharacteristic
219C2#1915217012yes—
220C2#1915234811yescharacteristic
221C2#1915235012yes—
222C2#1915235111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#397×C89C2
prime radicalC24×C89C23
hypercenter#397D89
hypocenterC89#2817
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #19151540C2semidirect
3. #19151539C2semidirect
6. #19151519C2semidirect
7. #19151518C2semidirect
112. C89#2817semidirect

Maximal subgroups

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

subgroupindex
C2×#156679892
#191515402
#191515392
#191515262
#191515232
#191515192
#191515182
#191514592
#397×C892
#281789