Finite Group Databasebeta

← #26026416

Subgroups — #26026416

Order 11392.

434 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15668005C211yesmaximal, characteristic
2C2×#15668003C211yesmaximal, characteristic, complemented
3#19151536C211yesmaximal, characteristic, complemented
4#19151530C211yesmaximal, characteristic, complemented
5#19151529C212yesmaximal, complemented
6#19151523C211yesmaximal, characteristic
7#19151521C212yesmaximal
8#19151497C212yesmaximal, complemented
9#19151491C212yesmaximal
10#19151449C211yesmaximal, characteristic, complemented
11#399×C89C211yesmaximal, characteristic
12#15668005—24no—
13#15668003—24no—
14C2×C4⋊Dic89C2212yes—
15C2×C4⋊Dic89C2211yescharacteristic
16C2×C4⋊Dic89C2211yescharacteristic
17C2×C4⋊Dic89C2212yes—
18C2×#13083553C2212yes—
19C2×#13083553C2212yes—
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2211yescharacteristic
22C2×C22⋊Dic89C2211yescharacteristic
23C2×C22⋊Dic89C2211yescharacteristic
24C2×C22⋊Dic89C2212yes—
25C2×C4×Dic89C2212yes—
26C2×C4×Dic89C2211yescharacteristic
27#15667919C2211yescharacteristic
28#15667919C2212yes—
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C2×C4⋊C4×C89C2212yes—
33C2×C4⋊C4×C89C2211yescharacteristic
34C2×C22⋊C4×C89C2212yes—
35C2×C22⋊C4×C89C2211yescharacteristic
36#95×C89C2211yescharacteristic
37C22×Dic89C2312yes—
38C22×Dic89C2311yescharacteristic
39C22×Dic89C2311yescharacteristic
40C22×Dic89C2312yes—
41C22×Dic89C2311yescharacteristic
42C22×Dic89C2311yescharacteristic
43C4⋊Dic89—22no—
44C4⋊Dic89—24no—
45C4⋊Dic89—22no—
46C4⋊Dic89—42no—
47#13083553—22no—
48#13083553—24no—
49#13083553—24no—
50#13083553—22no—
51C22⋊Dic89—22no—
52C22⋊Dic89—22no—
53C22⋊Dic89—42no—
54C4×Dic89—42no—
55C4×Dic89D414yes—
56C24×C89C2311yescharacteristic
57C22×C4×C89C2311yescharacteristic
58C22×C4×C89C2312yes—
59C22×C4×C89C2311yescharacteristic
60C22×C4×C89C2312yes—
61C4⋊C4×C89—22no—
62C4⋊C4×C89—24no—
63C22⋊C4×C89—22no—
64C22⋊C4×C89—24no—
65C23×C89—21no—
66C23×C89—22no—
67C23×C89—21no—
68C23×C89—22no—
69C23×C89—21no—
70C23×C89C2411yescharacteristic
71C2×C4×C89—22no—
72C2×C4×C89—22no—
73C2×C4×C89—22no—
74C2×C4×C89—21no—
75C2×C4×C89—22no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89—22no—
79C2×C4×C89C2×D412yes—
80C2×C4×C89#4114yes—
81C2×Dic89—22no—
82C2×Dic89—21no—
83C2×Dic89—21no—
84C2×Dic89—21no—
85C2×Dic89—21no—
86C2×Dic89—22no—
87C2×Dic89—22no—
88C2×Dic89—22no—
89C2×Dic89—22no—
90C2×Dic89—21no—
91C2×Dic89—22no—
92C2×Dic89—22no—
93C2×Dic89—21no—
94C2×Dic89—22no—
95C2×Dic89C2×D412yes—
96C2×Dic89C2×D412yes—
97C22×C89—41no—
98C22×C89—41no—
99C22×C89—41no—
100C22×C89—42no—
101C22×C89—42no—
102C22×C89C22×D411yescharacteristic
103C22×C89C2×#4112yes—
104C22×C89H(5,𝔽2)11yescharacteristic
105C22×C892−1+412yes—
106C22×C892−1+411yescharacteristic
107C4×C89—22no—
108C4×C89—24no—
109C4×C89—41no—
110C4×C89—42no—
111Dic89—22no—
112Dic89—22no—
113Dic89—41no—
114Dic89—41no—
115Dic89—42no—
116Dic89—42no—
117C2×C89—81no—
118C2×C89#53211yescharacteristic
119C2×C89#53611yescharacteristic
120C2×C89#53711yescharacteristic
121C2×C89#53912yes—
122C2×C89#54112yes—
123#2664—891nomaximal, Sylow
124C89#266411yescharacteristic, complemented, Sylow
125C2×#126—891no—
126C2×#125—891no—
127#400—891no—
128#399D8911yescharacteristic
129#398—892no—
130#398—891no—
131#397—891no—
132#396—892no—
133#389—892no—
134#388—892no—
135C4×C4⋊C4—891no—
136#126—1784no—
137#125—1784no—
138C2×C4⋊C4—892no—
139C2×C4⋊C4—892no—
140C2×C4⋊C4—892no—
141C2×C4⋊C4—891no—
142C2×C4⋊C4—891no—
143C2×C4⋊C4—891no—
144C2×C4⋊C4—891no—
145C2×C4⋊C4—892no—
146C2×C4⋊C4C2×D8911yescharacteristic
147C2×C4⋊C4C2×D8912yes—
148C2×C22⋊C4—892no—
149C2×C22⋊C4—891no—
150C2×C22⋊C4—891no—
151C2×C22⋊C4C2×D8911yescharacteristic
152C2×C22⋊C4C2×D8912yes—
153C2×C42—891no—
154C2×C42—892no—
155#95—891no—
156#95—892no—
157#95—892no—
158#95—892no—
159#95—892no—
160#95C2×D8911yescharacteristic
161C24C22×D8911yescharacteristic
162C22×C4—891no—
163C22×C4—891no—
164C22×C4—892no—
165C22×C4—891no—
166C22×C4—891no—
167C22×C4—892no—
168C22×C4C22×D8911yescharacteristic
169C22×C4C22×D8912yes—
170C22×C4C22×D8911yescharacteristic
171C22×C4C22×D8912yes—
172C4⋊C4—22no—
173C4⋊C4—24no—
174C4⋊C4—3562no—
175C4⋊C4—1784no—
176C4⋊C4—1784no—
177C4⋊C4—1782no—
178C4⋊C4—1782no—
179C4⋊C4—1782no—
180C4⋊C4—1782no—
181C4⋊C4—1784no—
182C22⋊C4—22no—
183C22⋊C4—24no—
184C22⋊C4—3562no—
185C22⋊C4—1782no—
186C22⋊C4—1782no—
187C42—894no—
188C42—3562no—
189C23—21no—
190C23—22no—
191C23—21no—
192C23—22no—
193C23—21no—
194C23C23×D8911yescharacteristic
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—892no—
204C2×C4—892no—
205C2×C4—1781no—
206C2×C4—1781no—
207C2×C4—1782no—
208C2×C4—1782no—
209C2×C4—1782no—
210C2×C4—1782no—
211C2×C4—1781no—
212C2×C4—1782no—
213C2×C4—1782no—
214C2×C4—1781no—
215C2×C4—1782no—
216C2×C4—1782no—
217C2×C4—1781no—
218C2×C4—1781no—
219C2×C4D4×D8912yes—
220C2×C4#1308357314yes—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—42no—
225C22—42no—
226C22C2×D4×D8911yescharacteristic
227C22C2×#1308357312yes—
228C22#1566805811yescharacteristic
229C22#1566805912yes—
230C22#1566806011yescharacteristic
231C4—22no—
232C4—24no—
233C4—41no—
234C4—42no—
235C4—3561no—
236C4—3561no—
237C4—3562no—
238C4—3562no—
239C4—1782no—
240C4—1782no—
241C2—81no—
242C2#1915214611yescharacteristic
243C2#1915217011yescharacteristic
244C2#1915217811yescharacteristic
245C2#1915219212yes—
246C2#1915220812yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#399×C89C2
prime radicalC24×C89C23
hypercenter#399D89
hypocenterC89#2664
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. C2×#15668003C2semidirect
3. #19151536C2semidirect
4. #19151530C2semidirect
5. #19151529C2semidirect
8. #19151497C2semidirect
10. #19151449C2semidirect
124. C89#2664semidirect

Maximal subgroups

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

subgroupindex
C2×#156680052
C2×#156680032
#191515362
#191515302
#191515292
#191515232
#191515212
#191514972
#191514912
#191514492
#399×C892
#266489