Finite Group Databasebeta

← #26024697

Subgroups — #26024697

Order 11392.

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

normal subgroups only

This group has 546 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×#15667997C211yesmaximal, characteristic
2C2×#15667970C211yesmaximal, characteristic, complemented
3#19151537C211yesmaximal, characteristic, complemented
4#19151535C211yesmaximal, characteristic, complemented
5#19151524C211yesmaximal, characteristic, complemented
6#19151488C212yesmaximal, complemented
7#19151481C212yesmaximal, complemented
8#19151476C212yesmaximal
9#19151455C212yesmaximal, complemented
10#95×D89C211yesmaximal, characteristic, complemented
11#398×C89C211yesmaximal, characteristic, complemented
12C22×D356C2211yescharacteristic
13C22×C4×D89C2212yes—
14C22×C4×D89C2211yescharacteristic
15#15667997—24no—
16#15667970—24no—
17C2×C4⋊Dic89C2212yes—
18C2×C4⋊Dic89C2211yescharacteristic
19C2×#13083553C2211yescharacteristic
20C2×#13083551C2211yescharacteristic
21C2×#13083551C2212yes—
22C2×#13083551C2212yes—
23C2×#13083551C2211yescharacteristic
24C2×#13083551C2211yescharacteristic
25C2×#13083551C2212yes—
26C2×C4×Dic89C2212yes—
27#15667919C2212yes—
28#15667919C2211yescharacteristic
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C2×C4⋊C4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34C2×C4⋊C4×C89C2212yes—
35#95×C89C2211yescharacteristic
36#95×C89C2212yes—
37C23×D89C2311yescharacteristic
38C23×D89C2311yescharacteristic
39C2×D356—22no—
40C2×D356—24no—
41C22×Dic89C2312yes—
42C22×Dic89C2312yes—
43C22×Dic89C2311yescharacteristic
44C22×Dic89C2311yescharacteristic
45C2×C4×D89—24no—
46C2×C4×D89—24no—
47C2×C4×D89—24no—
48C2×C4×D89—42no—
49C2×C4×D89D414yes—
50C4⋊Dic89—22no—
51C4⋊Dic89—24no—
52#13083553—22no—
53#13083551—24no—
54#13083551—22no—
55#13083551—22no—
56#13083551—24no—
57#13083551—22no—
58#13083551—42no—
59C4×Dic89—24no—
60C22×C4×C89C2311yescharacteristic
61C22×C4×C89C2312yes—
62C22×C4×C89C2311yescharacteristic
63C22×C4×C89C2311yescharacteristic
64C22×C4×C89C2312yes—
65C4⋊C4×C89—22no—
66C4⋊C4×C89—22no—
67C4⋊C4×C89—42no—
68C23×C89C2411yescharacteristic
69C22×D89—22no—
70C22×D89—21no—
71C22×D89—21no—
72C22×D89—21no—
73C22×D89—22no—
74C22×D89—22no—
75C22×D89—21no—
76C22×D89—21no—
77C22×D89C2×D412yes—
78C22×D89#4114yes—
79C2×C4×C89—22no—
80C2×C4×C89—22no—
81C2×C4×C89—22no—
82C2×C4×C89—22no—
83C2×C4×C89—21no—
84C2×C4×C89—21no—
85C2×C4×C89—22no—
86C2×C4×C89—21no—
87C2×C4×C89—22no—
88C2×C4×C89—22no—
89C2×C4×C89—21no—
90C2×C4×C89C2×D412yes—
91C2×C4×C89#4114yes—
92C2×Dic89—22no—
93C2×Dic89—22no—
94C2×Dic89—21no—
95C2×Dic89—22no—
96C2×Dic89—22no—
97C2×Dic89—22no—
98C2×Dic89—22no—
99C2×Dic89—22no—
100C2×Dic89—22no—
101C2×Dic89C2×D412yes—
102D356—44no—
103C4×D89—28no—
104C4×D89—48no—
105C22×C89C22×D411yescharacteristic
106C22×C89C2×#4112yes—
107C22×C89C2×#4112yes—
108C22×C89H(5,𝔽2)11yescharacteristic
109C22×C892−1+411yescharacteristic
110C2×D89—22no—
111C2×D89—22no—
112C2×D89—24no—
113C2×D89—24no—
114C2×D89—41no—
115C2×D89—41no—
116C2×D89—41no—
117C2×D89—42no—
118C2×D89—42no—
119C2×D89#12314yes—
120C4×C89—22no—
121C4×C89—24no—
122C4×C89—41no—
123C4×C89—42no—
124C4×C89—41no—
125Dic89—22no—
126Dic89—42no—
127Dic89—41no—
128Dic89—42no—
129C2×C89C2×#12311yescharacteristic
130C2×C89#53211yescharacteristic
131C2×C89#53711yescharacteristic
132C2×C89#55112yes—
133C2×C89#55212yes—
134D89—24no—
135D89—81no—
136#2498—891nomaximal, Sylow
137C89#249811yescharacteristic, complemented, Sylow
138C2×#123—891no—
139C2×#117—891no—
140#400—891no—
141#399—891no—
142#398D8911yescharacteristic, complemented
143#397—891no—
144#388—892no—
145#387—892no—
146#386—892no—
147#380—892no—
148C2×#95—891no—
149C22×D4—891no—
150C23×C4—891no—
151C23×C4—892no—
152#123—1784no—
153#117—1784no—
154C2×C4⋊C4—891no—
155C2×C4⋊C4—891no—
156C2×C4⋊C4—892no—
157C2×C4⋊C4C2×D8911yescharacteristic
158C2×C4⋊C4C2×D8911yescharacteristic
159C2×C4⋊C4C2×D8912yes—
160C2×C22⋊C4—892no—
161C2×C22⋊C4—892no—
162C2×C22⋊C4—891no—
163C2×C22⋊C4—891no—
164C2×C22⋊C4—891no—
165C2×C22⋊C4—892no—
166C2×C42—892no—
167#95—892no—
168#95—891no—
169#95—892no—
170#95—892no—
171#95—892no—
172#95C2×D8911yescharacteristic
173#95C2×D8912yes—
174C24—891no—
175C24—891no—
176C2×D4—1782no—
177C2×D4—1784no—
178C22×C4—891no—
179C22×C4—894no—
180C22×C4—892no—
181C22×C4—892no—
182C22×C4—891no—
183C22×C4—3562no—
184C22×C4—1784no—
185C22×C4—1784no—
186C22×C4—1784no—
187C22×C4C22×D8911yescharacteristic
188C22×C4C22×D8911yescharacteristic
189C22×C4C22×D8912yes—
190C22×C4C22×D8911yescharacteristic
191C22×C4C22×D8912yes—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—1782no—
196C4⋊C4—1782no—
197C4⋊C4—1784no—
198C22⋊C4—3562no—
199C22⋊C4—1782no—
200C22⋊C4—1784no—
201C22⋊C4—1782no—
202C22⋊C4—1782no—
203C22⋊C4—1784no—
204C42—1784no—
205C23—892no—
206C23—894no—
207C23—1781no—
208C23—1782no—
209C23—1782no—
210C23—1781no—
211C23—1781no—
212C23—1782no—
213C23—1781no—
214C23—1781no—
215C23C23×D8911yescharacteristic
216D4—3564no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—892no—
229C2×C4—3568no—
230C2×C4—1788no—
231C2×C4—1782no—
232C2×C4—1781no—
233C2×C4—1782no—
234C2×C4—1782no—
235C2×C4—1782no—
236C2×C4—1782no—
237C2×C4—1782no—
238C2×C4—1782no—
239C2×C4—1782no—
240C2×C4D4×D8912yes—
241C2×C4#1308357514yes—
242C22—894no—
243C22—3561no—
244C22—3561no—
245C22—3562no—
246C22—3562no—
247C22—3561no—
248C22—1782no—
249C22—1782no—
250C22—1784no—
251C22—1784no—
252C22C2×D4×D8911yescharacteristic
253C22#41×D8912yes—
254C22C2×#1308357512yes—
255C22#1566805711yescharacteristic
256C22#1566805911yescharacteristic
257C4—24no—
258C4—22no—
259C4—42no—
260C4—41no—
261C4—41no—
262C4—3562no—
263C4—3561no—
264C4—3562no—
265C4—1782no—
266C2—1784no—
267C2—7121no—
268C2#123×D8911yescharacteristic
269C2#1915214911yescharacteristic
270C2#1915217711yescharacteristic
271C2#1915227512yes—
272C2#1915228612yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#398×C89C2
prime radicalC22×D356C22
hypercenter#398D89
hypocenterC89#2498
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#15667970C2semidirect
3. #19151537C2semidirect
4. #19151535C2semidirect
5. #19151524C2semidirect
6. #19151488C2semidirect
7. #19151481C2semidirect
9. #19151455C2semidirect
10. #95×D89C2semidirect
11. #398×C89C2semidirect
137. C89#2498semidirect
142. #398D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679972
C2×#156679702
#191515372
#191515352
#191515242
#191514882
#191514812
#191514762
#191514552
#95×D892
#398×C892
#249889