Finite Group Databasebeta

← #26027670

Subgroups — #26027670

Order 11392.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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#19151539C212yesmaximal, complemented
2#19151517C212yesmaximal, complemented
3#19151510C211yesmaximal, characteristic
4#19151502C212yesmaximal, complemented
5#19151492C212yesmaximal
6#19151470C212yesmaximal
7#19151470C211yesmaximal, characteristic
8#19151462C212yesmaximal, complemented
9#393×C89C211yesmaximal, characteristic
10C22×Dic178C2211yescharacteristic
11C23×Dic89C2211yescharacteristic
12C2×#13083553C2212yes—
13C2×#13083553C2212yes—
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×C22⋊Dic89C2212yes—
17C2×C22⋊Dic89C2211yescharacteristic
18C2×C4×Dic89C2212yes—
19#15667919C2212yes—
20#15667919C2212yes—
21#15667919C2212yes—
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2211yescharacteristic
26C22×Q8×C89C2211yescharacteristic
27C2×C22⋊C4×C89C2212yes—
28C2×C22⋊C4×C89C2211yescharacteristic
29#95×C89C2211yescharacteristic
30#95×C89C2212yes—
31C2×Dic178—24no—
32C2×Dic178—41no—
33C22×Dic89—42no—
34C22×Dic89—41no—
35C22×Dic89C2312yes—
36C22×Dic89C2312yes—
37C22×Dic89C2312yes—
38C22×Dic89C2312yes—
39#13083553—42no—
40#13083553—42no—
41#13083553—42no—
42#13083553—42no—
43C22⋊Dic89—24no—
44C22⋊Dic89Q814yescomplemented
45C4×Dic89—24no—
46C24×C89C2311yescharacteristic
47C2×Q8×C89—42no—
48C2×Q8×C89—41no—
49C22×C4×C89C2311yescharacteristic
50C22×C4×C89C2312yes—
51C22×C4×C89C2311yescharacteristic
52C22×C4×C89C2312yes—
53C22⋊C4×C89—42no—
54C22⋊C4×C89—41no—
55C23×C89—22no—
56C23×C89—21no—
57C23×C89—22no—
58C23×C89—21no—
59C23×C89C2×Q812yes—
60C23×C89C2411yescharacteristic
61Q8×C89—44no—
62C2×C4×C89—22no—
63C2×C4×C89—22no—
64C2×C4×C89—22no—
65C2×C4×C89—21no—
66C2×C4×C89—22no—
67C2×C4×C89—21no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—22no—
72C2×Dic89—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—44no—
83C2×Dic89C2×Q814yes—
84C2×Dic89#4114yes—
85Dic178—44no—
86C22×C89—22no—
87C22×C89—24no—
88C22×C89—42no—
89C22×C89—41no—
90C22×C89—41no—
91C22×C89C22×Q811yescharacteristic
92C22×C89C2×#4112yes—
93C22×C89H(5,𝔽2)12yes—
94C22×C89H(5,𝔽2)11yescharacteristic
95C22×C892−1+411yescharacteristic
96C4×C89—42no—
97C4×C89—41no—
98C4×C89—42no—
99C4×C89—41no—
100Dic89—24no—
101Dic89—24no—
102Dic89—42no—
103Dic89—42no—
104C2×C89—42no—
105C2×C89#54212yes—
106C2×C89#54411yescharacteristic
107C2×C89#55111yescharacteristic
108C2×C89#55412yes—
109C2×C89H(3,𝔽4)11yescharacteristic
110#2763—891nomaximal, Sylow
111C89#276311yescharacteristic, complemented, Sylow
112#400—892no—
113#395—892no—
114#393—891no—
115#393D8911yescharacteristic
116#391—892no—
117#388—892no—
118#385—892no—
119#385—891no—
120#382—892no—
121C22×Q8—891no—
122C22×Q8C2×D8911yescharacteristic
123C23×C4—891no—
124C2×C4⋊C4—892no—
125C2×C4⋊C4—892no—
126C2×C4⋊C4—892no—
127C2×C4⋊C4—892no—
128C2×C22⋊C4—891no—
129C2×C22⋊C4—892no—
130C2×C22⋊C4C2×D8912yes—
131C2×C22⋊C4C2×D8911yescharacteristic
132C2×C42—892no—
133#95—892no—
134#95—892no—
135#95—892no—
136#95—892no—
137#95—892no—
138#95—892no—
139#95—891no—
140#95C2×D8911yescharacteristic
141#95C2×D8912yes—
142C24C22×D8911yescharacteristic
143C2×Q8—42no—
144C2×Q8—41no—
145C2×Q8—3561no—
146C2×Q8—1784no—
147C22×C4—892no—
148C22×C4—892no—
149C22×C4—892no—
150C22×C4—892no—
151C22×C4—3562no—
152C22×C4—3561no—
153C22×C4C22×D8911yescharacteristic
154C22×C4C22×D8912yes—
155C22×C4C22×D8911yescharacteristic
156C22×C4C22×D8912yes—
157C4⋊C4—3562no—
158C4⋊C4—3562no—
159C4⋊C4—3562no—
160C4⋊C4—3562no—
161C22⋊C4—42no—
162C22⋊C4—41no—
163C22⋊C4—894no—
164C22⋊C4—1784no—
165C42—1784no—
166C23—22no—
167C23—21no—
168C23—22no—
169C23—21no—
170C23Q8×D8912yes—
171C23C23×D8911yescharacteristic
172Q8—44no—
173Q8—3564no—
174C2×C4—22no—
175C2×C4—22no—
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—894no—
185C2×C4—894no—
186C2×C4—3564no—
187C2×C4—1782no—
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—
197C22—22no—
198C22—24no—
199C22—42no—
200C22—41no—
201C22—41no—
202C22C2×Q8×D8911yescharacteristic
203C22#41×D8912yes—
204C22#1566805712yes—
205C22#1566805711yescharacteristic
206C22#1566805911yescharacteristic
207C4—42no—
208C4—41no—
209C4—42no—
210C4—41no—
211C4—3562no—
212C4—3562no—
213C4—1784no—
214C4—1784no—
215C2—42no—
216C2#1915221212yes—
217C2#1915222711yescharacteristic
218C2#1915227811yescharacteristic
219C2#1915230212yes—
220C2#1915234111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#393×C89C2
prime radicalC24×C89C23
hypercenter#393D89
hypocenterC89#2763
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. #19151539C2semidirect
2. #19151517C2semidirect
4. #19151502C2semidirect
8. #19151462C2semidirect
44. C22⋊Dic89Q8semidirect
111. C89#2763semidirect

Maximal subgroups

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

subgroupindex
#191515392
#191515172
#191515102
#191515022
#191514922
#191514702
#191514622
#393×C892
#276389