Finite Group Databasebeta

← #26026568

Subgroups — #26026568

Order 11392.

544 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15668011C212yesmaximal, complemented
2C2×#15667989C212yesmaximal
3#19151529C212yesmaximal, complemented
4#19151518C212yesmaximal, complemented
5#19151510C211yesmaximal, characteristic
6#19151486C212yesmaximal
7#19151483C212yesmaximal, complemented
8#19151470C211yesmaximal, characteristic
9#399×C89C211yesmaximal, characteristic
10C22×Dic178C2211yescharacteristic
11C22×Dic178C2212yes—
12C23×Dic89C2211yescharacteristic
13#15668011—28no—
14#15667989—28no—
15C2×C4⋊Dic89C2212yes—
16C2×#13083553C2212yes—
17C2×#13083553C2212yes—
18C2×#13083553C2212yes—
19C2×#13083553C2212yes—
20C2×C22⋊Dic89C2212yes—
21C2×C22⋊Dic89C2211yescharacteristic
22C2×C4×Dic89C2212yes—
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2212yes—
26#15667919C2212yes—
27#15667919C2211yescharacteristic
28C2×C4⋊C4×C89C2212yes—
29C2×C4⋊C4×C89C2211yescharacteristic
30C2×C22⋊C4×C89C2212yes—
31C2×C22⋊C4×C89C2211yescharacteristic
32#95×C89C2211yescharacteristic
33C2×Dic178—24no—
34C2×Dic178—24no—
35C2×Dic178—24no—
36C2×Dic178—42no—
37C2×Dic178—41no—
38C22×Dic89—24no—
39C22×Dic89—41no—
40C22×Dic89C2312yes—
41C22×Dic89C2312yes—
42C22×Dic89C2312yes—
43C22×Dic89C2312yes—
44C4⋊Dic89D418yes—
45#13083553—24no—
46#13083553—24no—
47#13083553—24no—
48#13083553—24no—
49C22⋊Dic89—24no—
50C22⋊Dic89Q814yescomplemented
51C4×Dic89—24no—
52C24×C89C2311yescharacteristic
53C22×C4×C89C2312yes—
54C22×C4×C89C2311yescharacteristic
55C22×C4×C89C2311yescharacteristic
56C22×C4×C89C2312yes—
57C4⋊C4×C89—24no—
58C4⋊C4×C89—41no—
59C22⋊C4×C89—24no—
60C22⋊C4×C89—41no—
61C23×C89—22no—
62C23×C89—21no—
63C23×C89—21no—
64C23×C89—22no—
65C23×C89C2×Q812yes—
66C23×C89C2411yescharacteristic
67C2×C4×C89—22no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—22no—
72C2×C4×C89—21no—
73C2×C4×C89—21no—
74C2×C4×C89—22no—
75C2×C4×C89—22no—
76C2×C4×C89C2×D414yes—
77C2×Dic89—22no—
78C2×Dic89—22no—
79C2×Dic89—22no—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89—44no—
87C2×Dic89C2×D414yes—
88C2×Dic89C2×D414yes—
89C2×Dic89C2×Q814yes—
90Dic178—44no—
91Dic178—48no—
92C22×C89—22no—
93C22×C89—24no—
94C22×C89—42no—
95C22×C89—41no—
96C22×C89—41no—
97C22×C89C22×D412yes—
98C22×C89C22×Q811yescharacteristic
99C22×C89H(5,𝔽2)11yescharacteristic
100C22×C892−1+411yescharacteristic
101C22×C892−1+412yes—
102C4×C89—24no—
103C4×C89—42no—
104C4×C89—41no—
105C4×C89—41no—
106Dic89—24no—
107Dic89—24no—
108Dic89—24no—
109Dic89—42no—
110C2×C89—42no—
111C2×C89#53612yes—
112C2×C89#54411yescharacteristic
113C2×C89D4211yescharacteristic
114C2×C89D4×Q812yes—
115C2×C89#56311yescharacteristic
116#2677—891nomaximal, Sylow
117C89#267711yescharacteristic, complemented, Sylow
118C2×C4⋊Q8—892no—
119C2×C22⋊Q8—892no—
120#399D8911yescharacteristic
121#398—892no—
122#395—892no—
123#393—891no—
124#388—892no—
125#387—892no—
126#385—891no—
127C22×Q8—892no—
128C22×Q8—891no—
129C23×C4—891no—
130C4⋊Q8—1788no—
131C22⋊Q8—1788no—
132C2×C4⋊C4—892no—
133C2×C4⋊C4—892no—
134C2×C4⋊C4—892no—
135C2×C4⋊C4—892no—
136C2×C4⋊C4—892no—
137C2×C4⋊C4C2×D8912yes—
138C2×C4⋊C4C2×D8911yescharacteristic
139C2×C22⋊C4—891no—
140C2×C22⋊C4—892no—
141C2×C22⋊C4C2×D8912yes—
142C2×C22⋊C4C2×D8911yescharacteristic
143C2×C42—892no—
144#95—892no—
145#95—892no—
146#95—892no—
147#95—892no—
148#95—891no—
149#95C2×D8911yescharacteristic
150C24C22×D8911yescharacteristic
151C2×Q8—3561no—
152C2×Q8—3562no—
153C2×Q8—1784no—
154C2×Q8—1784no—
155C2×Q8—1784no—
156C22×C4—892no—
157C22×C4—892no—
158C22×C4—892no—
159C22×C4—892no—
160C22×C4—3561no—
161C22×C4—1784no—
162C22×C4C22×D8911yescharacteristic
163C22×C4C22×D8912yes—
164C22×C4C22×D8911yescharacteristic
165C22×C4C22×D8912yes—
166C4⋊C4—24no—
167C4⋊C4—41no—
168C4⋊C4—898no—
169C4⋊C4—1784no—
170C4⋊C4—1784no—
171C4⋊C4—1784no—
172C4⋊C4—1784no—
173C22⋊C4—24no—
174C22⋊C4—41no—
175C22⋊C4—894no—
176C22⋊C4—1784no—
177C42—1784no—
178C23—22no—
179C23—21no—
180C23—21no—
181C23—22no—
182C23Q8×D8912yes—
183C23C23×D8911yescharacteristic
184Q8—3568no—
185Q8—3564no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—894no—
196C2×C4—894no—
197C2×C4—894no—
198C2×C4—3564no—
199C2×C4—1782no—
200C2×C4—1782no—
201C2×C4—1782no—
202C2×C4—1782no—
203C2×C4—1782no—
204C2×C4—1782no—
205C2×C4—1782no—
206C2×C4—1782no—
207C2×C4—1782no—
208C2×C4D4×D8914yes—
209C22—22no—
210C22—24no—
211C22—42no—
212C22—41no—
213C22—41no—
214C22C2×D4×D8912yes—
215C22C2×Q8×D8911yescharacteristic
216C22#1566805711yescharacteristic
217C22#1566805911yescharacteristic
218C22#1566805912yes—
219C4—24no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—3562no—
224C4—1784no—
225C4—1784no—
226C4—1784no—
227C2—42no—
228C2#1915217012yes—
229C2#1915222711yescharacteristic
230C2#1915223311yescharacteristic
231C2#1915226112yes—
232C2#1915235111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#399×C89C2
prime radicalC24×C89C23
hypercenter#399D89
hypocenterC89#2677
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#15668011C2semidirect
3. #19151529C2semidirect
4. #19151518C2semidirect
7. #19151483C2semidirect
50. C22⋊Dic89Q8semidirect
117. C89#2677semidirect

Maximal subgroups

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

subgroupindex
C2×#156680112
C2×#156679892
#191515292
#191515182
#191515102
#191514862
#191514832
#191514702
#399×C892
#267789