Finite Group Databasebeta

← #26024732

Subgroups — #26024732

Order 11392.

512 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15667990C211yesmaximal, characteristic
2C2×C4⋊C4×D89C211yesmaximal, characteristic
3#19151538C211yesmaximal, characteristic, complemented
4#19151537C211yesmaximal, characteristic, complemented
5#19151536C211yesmaximal, characteristic, complemented
6#19151502C212yesmaximal, complemented
7#19151462C212yesmaximal, complemented
8#19151460C212yesmaximal
9#19151460C212yesmaximal
10#19151445C211yesmaximal, characteristic
11#400×C89C211yesmaximal, characteristic, complemented
12C22×Dic178C2211yescharacteristic
13C22×C4×D89C2212yes—
14C22×C4×D89C2211yescharacteristic
15#15667990—24no—
16C2×C4⋊Dic89C2211yescharacteristic
17C2×#13083553C2211yescharacteristic
18C2×#13083553C2212yes—
19C2×#13083553C2211yescharacteristic
20C4⋊C4×D89—24no—
21C2×#13083551C2212yes—
22C2×#13083551C2211yescharacteristic
23C2×#13083551C2211yescharacteristic
24C2×C4×Dic89C2212yes—
25#15667919C2211yescharacteristic
26#15667919C2212yes—
27#15667919C2212yes—
28#15667919C2212yes—
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C2×C4⋊C4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34#95×C89C2211yescharacteristic
35#95×C89C2212yes—
36#95×C89C2212yes—
37C23×D89C2311yescharacteristic
38C2×Dic178—22no—
39C2×Dic178—24no—
40C22×Dic89C2312yes—
41C22×Dic89C2311yescharacteristic
42C22×Dic89C2312yes—
43C22×Dic89C2311yescharacteristic
44C22×Dic89C2311yescharacteristic
45C2×C4×D89—24no—
46C2×C4×D89—24no—
47C2×C4×D89—28no—
48C2×C4×D89D414yes—
49C4⋊Dic89—22no—
50#13083553—22no—
51#13083553—22no—
52#13083553—24no—
53#13083551—22no—
54#13083551—22no—
55#13083551—24no—
56C4×Dic89—24no—
57C22×C4×C89C2312yes—
58C22×C4×C89C2311yescharacteristic
59C22×C4×C89C2312yes—
60C22×C4×C89C2311yescharacteristic
61C22×C4×C89C2311yescharacteristic
62C4⋊C4×C89—22no—
63C4⋊C4×C89—22no—
64C23×C89C2411yescharacteristic
65C22×D89—22no—
66C22×D89—21no—
67C22×D89—21no—
68C22×D89C2×D412yes—
69C22×D89#4114yes—
70C2×C4×C89—22no—
71C2×C4×C89—21no—
72C2×C4×C89—21no—
73C2×C4×C89—22no—
74C2×C4×C89—22no—
75C2×C4×C89—22no—
76C2×C4×C89—24no—
77C2×C4×C89—22no—
78C2×C4×C89—21no—
79C2×C4×C89—22no—
80C2×C4×C89—21no—
81C2×C4×C89C2×D412yes—
82C2×Dic89—21no—
83C2×Dic89—21no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89—22no—
87C2×Dic89—24no—
88C2×Dic89—22no—
89C2×Dic89—21no—
90C2×Dic89—21no—
91C2×Dic89—22no—
92C2×Dic89C2×D412yes—
93C2×Dic89#4114yes—
94C4×D89—28no—
95C4×D89—48no—
96Dic178—44no—
97C22×C89C22×D411yescharacteristic
98C22×C89C2×#4112yes—
99C22×C89C2×#4112yes—
100C22×C892−1+411yescharacteristic
101C22×C892−1+411yescharacteristic
102C2×D89—22no—
103C2×D89—22no—
104C2×D89—24no—
105C2×D89—24no—
106C2×D89#12414yes—
107C4×C89—22no—
108C4×C89—41no—
109C4×C89—42no—
110C4×C89—41no—
111C4×C89—42no—
112Dic89—41no—
113Dic89—42no—
114Dic89—41no—
115Dic89—42no—
116Dic89#12314yes—
117C2×C89C2×#12311yescharacteristic
118C2×C89C2×#12411yescharacteristic
119C2×C89#53611yescharacteristic
120C2×C89#55212yes—
121C2×C89#55212yes—
122D89—24no—
123#2503—891nomaximal, Sylow
124C89#250311yescharacteristic, complemented, Sylow
125C2×C22⋊Q8—891no—
126C22×C4⋊C4—891no—
127#400—891no—
128#400—891no—
129#400—891no—
130#400D8911yescharacteristic, complemented
131#391—892no—
132#382—892no—
133#381—892no—
134#381—892no—
135C4×C22⋊C4—891no—
136C22×Q8—891no—
137C23×C4—891no—
138C23×C4—892no—
139C22⋊Q8—1784no—
140C2×C4⋊C4—892no—
141C2×C4⋊C4—891no—
142C2×C4⋊C4—891no—
143C2×C4⋊C4—891no—
144C2×C4⋊C4—1784no—
145C2×C4⋊C4C2×D8911yescharacteristic
146C2×C4⋊C4C2×D8911yescharacteristic
147C2×C22⋊C4—891no—
148C2×C22⋊C4—891no—
149C2×C22⋊C4—892no—
150C2×C42—892no—
151#95—891no—
152#95—892no—
153#95—892no—
154#95—892no—
155#95—892no—
156#95—892no—
157#95—892no—
158#95C2×D8911yescharacteristic
159#95C2×D8912yes—
160#95C2×D8912yes—
161C24—891no—
162C2×Q8—1782no—
163C2×Q8—1784no—
164C22×C4—891no—
165C22×C4—894no—
166C22×C4—892no—
167C22×C4—891no—
168C22×C4—891no—
169C22×C4—892no—
170C22×C4—1784no—
171C22×C4—1784no—
172C22×C4—1788no—
173C22×C4C22×D8912yes—
174C22×C4C22×D8911yescharacteristic
175C22×C4C22×D8911yescharacteristic
176C22×C4C22×D8912yes—
177C22×C4C22×D8911yescharacteristic
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—1784no—
181C4⋊C4—1782no—
182C4⋊C4—1782no—
183C4⋊C4—1782no—
184C22⋊C4—1782no—
185C22⋊C4—1782no—
186C22⋊C4—1784no—
187C42—1784no—
188C23—892no—
189C23—894no—
190C23—1782no—
191C23—1781no—
192C23—1781no—
193C23C23×D8911yescharacteristic
194Q8—3564no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—892no—
207C2×C4—894no—
208C2×C4—3568no—
209C2×C4—1788no—
210C2×C4—1781no—
211C2×C4—1781no—
212C2×C4—1782no—
213C2×C4—1782no—
214C2×C4—1782no—
215C2×C4—1784no—
216C2×C4—1782no—
217C2×C4—1781no—
218C2×C4—1781no—
219C2×C4—1782no—
220C2×C4D4×D8912yes—
221C22—894no—
222C22—1782no—
223C22—1784no—
224C22—1784no—
225C22—1782no—
226C22C2×D4×D8911yescharacteristic
227C22#41×D8912yes—
228C22#41×D8912yes—
229C22#1566805911yescharacteristic
230C22#1566806011yescharacteristic
231C4—22no—
232C4—41no—
233C4—42no—
234C4—41no—
235C4—42no—
236C4—894no—
237C4—3561no—
238C4—3562no—
239C4—3561no—
240C4—3562no—
241C2—1784no—
242C2#123×D8911yescharacteristic
243C2#124×D8911yescharacteristic
244C2#1915217111yescharacteristic
245C2#1915228012yes—
246C2#1915228412yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#400×C89C2
prime radicalC23×D89C23
hypercenter#400D89
hypocenterC89#2503
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #19151538C2semidirect
4. #19151537C2semidirect
5. #19151536C2semidirect
6. #19151502C2semidirect
7. #19151462C2semidirect
11. #400×C89C2semidirect
124. C89#2503semidirect
130. #400D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679902
C2×C4⋊C4×D892
#191515382
#191515372
#191515362
#191515022
#191514622
#191514602
#191514452
#400×C892
#250389