Finite Group Databasebeta

← #26024725

Subgroups — #26024725

Order 11392.

544 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 161 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#19151530C211yesmaximal, characteristic, complemented
4#19151529C211yesmaximal, characteristic, complemented
5#19151528C211yesmaximal, characteristic, complemented
6#19151502C212yesmaximal, complemented
7#19151472C212yesmaximal
8#19151469C212yesmaximal
9#19151467C212yesmaximal, complemented
10#19151445C211yesmaximal, characteristic
11#398×C89C211yesmaximal, characteristic, complemented
12C22×Dic178C2211yescharacteristic
13C22×C4×D89C2211yescharacteristic
14C22×C4×D89C2212yes—
15#15667990—24no—
16C2×C4⋊Dic89C2211yescharacteristic
17C2×C4⋊Dic89C2212yes—
18C2×#13083553C2211yescharacteristic
19C2×#13083553C2212yes—
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2212yes—
22C2×#13083553C2212yes—
23C4⋊C4×D89—24no—
24C2×#13083551C2211yescharacteristic
25C2×#13083551C2211yescharacteristic
26C2×#13083551C2212yes—
27C2×C4×Dic89C2212yes—
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
38C2×Dic178—22no—
39C2×Dic178—24no—
40C22×Dic89C2312yes—
41C22×Dic89C2311yescharacteristic
42C22×Dic89C2311yescharacteristic
43C22×Dic89C2312yes—
44C22×Dic89C2311yescharacteristic
45C2×C4×D89—24no—
46C2×C4×D89—24no—
47C2×C4×D89—42no—
48C2×C4×D89—42no—
49C2×C4×D89D414yes—
50C4⋊Dic89—22no—
51C4⋊Dic89—42no—
52#13083553—22no—
53#13083553—22no—
54#13083553—24no—
55#13083553—42no—
56#13083553—42no—
57#13083551—22no—
58#13083551—22no—
59#13083551Q818yescomplemented
60C4×Dic89—24no—
61C22×C4×C89C2312yes—
62C22×C4×C89C2311yescharacteristic
63C22×C4×C89C2311yescharacteristic
64C22×C4×C89C2311yescharacteristic
65C22×C4×C89C2312yes—
66C4⋊C4×C89—22no—
67C4⋊C4×C89—22no—
68C4⋊C4×C89—42no—
69C23×C89C2411yescharacteristic
70C22×D89—22no—
71C22×D89—21no—
72C22×D89—21no—
73C22×D89C2×D412yes—
74C22×D89C2×Q814yes—
75C2×C4×C89—22no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89—21no—
79C2×C4×C89—21no—
80C2×C4×C89—22no—
81C2×C4×C89—22no—
82C2×C4×C89—21no—
83C2×C4×C89—22no—
84C2×C4×C89—21no—
85C2×C4×C89—22no—
86C2×C4×C89C2×D412yes—
87C2×C4×C89C2×Q814yes—
88C2×Dic89—22no—
89C2×Dic89—22no—
90C2×Dic89—21no—
91C2×Dic89—21no—
92C2×Dic89—22no—
93C2×Dic89—22no—
94C2×Dic89—21no—
95C2×Dic89—22no—
96C2×Dic89—21no—
97C2×Dic89—22no—
98C2×Dic89C2×D412yes—
99C2×Dic89C2×Q814yes—
100C2×Dic89#4114yes—
101C4×D89—28no—
102C4×D89—48no—
103Dic178—44no—
104C22×C89C22×D411yescharacteristic
105C22×C89C22×Q812yes—
106C22×C89C2×#4112yes—
107C22×C89H(5,𝔽2)11yescharacteristic
108C22×C89H(5,𝔽2)11yescharacteristic
109C2×D89—22no—
110C2×D89—22no—
111C2×D89—24no—
112C2×D89—24no—
113C2×D89C4⋊Q814yes—
114C4×C89—22no—
115C4×C89—24no—
116C4×C89—41no—
117C4×C89—42no—
118C4×C89—41no—
119Dic89—24no—
120Dic89—41no—
121Dic89—42no—
122Dic89—41no—
123Dic89#12314yes—
124C2×C89C2×#12311yescharacteristic
125C2×C89C2×C4⋊Q811yescharacteristic
126C2×C89#53511yescharacteristic
127C2×C89#55412yes—
128C2×C89#55412yes—
129D89—24no—
130#2502—891nomaximal, Sylow
131C89#250211yescharacteristic, complemented, Sylow
132C2×C22⋊Q8—891no—
133C22×C4⋊C4—891no—
134#398—891no—
135#398—891no—
136#398—891no—
137#398D8911yescharacteristic, complemented
138#391—892no—
139#385—892no—
140#385—892no—
141#384—892no—
142C4×C22⋊C4—891no—
143C22×Q8—891no—
144C23×C4—891no—
145C23×C4—892no—
146C22⋊Q8—1784no—
147C2×C4⋊C4—892no—
148C2×C4⋊C4—892no—
149C2×C4⋊C4—892no—
150C2×C4⋊C4—892no—
151C2×C4⋊C4—891no—
152C2×C4⋊C4—891no—
153C2×C4⋊C4—891no—
154C2×C4⋊C4—1784no—
155C2×C4⋊C4C2×D8911yescharacteristic
156C2×C4⋊C4C2×D8911yescharacteristic
157C2×C4⋊C4C2×D8912yes—
158C2×C22⋊C4—892no—
159C2×C22⋊C4—891no—
160C2×C22⋊C4—891no—
161C2×C42—892no—
162#95—891no—
163#95—892no—
164#95—892no—
165#95—892no—
166#95C2×D8911yescharacteristic
167#95C2×D8912yes—
168C24—891no—
169C2×Q8—1782no—
170C2×Q8—1784no—
171C22×C4—891no—
172C22×C4—892no—
173C22×C4—894no—
174C22×C4—891no—
175C22×C4—892no—
176C22×C4—891no—
177C22×C4—3562no—
178C22×C4—3562no—
179C22×C4—1784no—
180C22×C4—1784no—
181C22×C4C22×D8911yescharacteristic
182C22×C4C22×D8912yes—
183C22×C4C22×D8911yescharacteristic
184C22×C4C22×D8911yescharacteristic
185C22×C4C22×D8912yes—
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—42no—
189C4⋊C4—3562no—
190C4⋊C4—3562no—
191C4⋊C4—3562no—
192C4⋊C4—1784no—
193C4⋊C4—1782no—
194C4⋊C4—1782no—
195C4⋊C4—1782no—
196C22⋊C4—898no—
197C22⋊C4—1782no—
198C22⋊C4—1782no—
199C42—1784no—
200C23—892no—
201C23—894no—
202C23—1782no—
203C23—1781no—
204C23—1781no—
205C23C23×D8911yescharacteristic
206Q8—3564no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—892no—
219C2×C4—894no—
220C2×C4—894no—
221C2×C4—3568no—
222C2×C4—1788no—
223C2×C4—1781no—
224C2×C4—1781no—
225C2×C4—1782no—
226C2×C4—1782no—
227C2×C4—1781no—
228C2×C4—1782no—
229C2×C4—1781no—
230C2×C4—1782no—
231C2×C4—1782no—
232C2×C4—1782no—
233C2×C4D4×D8912yes—
234C2×C4Q8×D8914yes—
235C22—894no—
236C22—1782no—
237C22—1784no—
238C22—1784no—
239C22—1782no—
240C22C2×D4×D8911yescharacteristic
241C22C2×Q8×D8912yes—
242C22#41×D8912yes—
243C22#1566805711yescharacteristic
244C22#1566805811yescharacteristic
245C4—24no—
246C4—22no—
247C4—42no—
248C4—41no—
249C4—41no—
250C4—894no—
251C4—3562no—
252C4—3561no—
253C4—3561no—
254C4—1784no—
255C2—1784no—
256C2#123×D8911yescharacteristic
257C2C4⋊Q8×D8911yescharacteristic
258C2#1915216411yescharacteristic
259C2#1915230212yes—
260C2#1915230412yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#398×C89C2
prime radicalC23×D89C23
hypercenter#398D89
hypocenterC89#2502
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #19151530C2semidirect
4. #19151529C2semidirect
5. #19151528C2semidirect
6. #19151502C2semidirect
9. #19151467C2semidirect
11. #398×C89C2semidirect
59. #13083551Q8semidirect
131. C89#2502semidirect
137. #398D89semidirect

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
#191515302
#191515292
#191515282
#191515022
#191514722
#191514692
#191514672
#191514452
#398×C892
#250289