Finite Group Databasebeta

← #26024845

Subgroups — #26024845

Order 11392.

440 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 137 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
1#19151527C212yesmaximal, complemented
2#19151525C212yesmaximal, complemented
3#19151500C211yesmaximal, characteristic
4#19151499C211yesmaximal, characteristic
5#19151499C211yesmaximal, characteristic
6#19151497C211yesmaximal, characteristic, complemented
7#19151490C212yesmaximal, complemented
8#19151487C212yesmaximal, complemented
9C4⋊C4×Dic89C211yesmaximal, characteristic, complemented
10C4×#13083553C211yesmaximal, characteristic, complemented
11#382×C89C211yesmaximal, characteristic, complemented
12C22×D356C2211yescharacteristic
13C2×C4⋊Dic89C2211yescharacteristic
14C2×C4⋊Dic89C2212yes—
15C2×#13083553C2211yescharacteristic
16C2×#13083553C2211yescharacteristic
17C2×#13083551C2212yes—
18C2×#13083551C2212yes—
19C2×#13083551C2212yes—
20C2×#13083551C2212yes—
21C2×#13083551C2212yes—
22C2×#13083551C2212yes—
23C2×C4×Dic89C2211yescharacteristic
24C2×C4×Dic89C2211yescharacteristic
25C2×C4×Dic89C2212yes—
26#15667919C2211yescharacteristic
27#15667919C2211yescharacteristic
28#15667919C2212yes—
29#15667919C2212yes—
30C2×C4⋊C4×C89C2211yescharacteristic
31C2×C4⋊C4×C89C2211yescharacteristic
32C2×C42×C89C2211yescharacteristic
33#95×C89C2212yes—
34#95×C89C2212yes—
35C23×D89C2312yes—
36C2×D356—22no—
37C2×D356—22no—
38C2×D356—22no—
39C22×Dic89C2311yescharacteristic
40C22×Dic89C2311yescharacteristic
41C22×Dic89C2312yes—
42C22×Dic89C2311yescharacteristic
43C22×Dic89C2311yescharacteristic
44C4⋊Dic89—22no—
45C4⋊Dic89—42no—
46#13083553—22no—
47#13083553—22no—
48#13083551—24no—
49#13083551—24no—
50#13083551—42no—
51#13083551—42no—
52#13083551—42no—
53#13083551—42no—
54C4×Dic89—22no—
55C4×Dic89—22no—
56C4×Dic89—42no—
57C22×C4×C89C2311yescharacteristic
58C22×C4×C89C2311yescharacteristic
59C22×C4×C89C2312yes—
60C22×C4×C89C2312yes—
61C22×C4×C89C2311yescharacteristic
62C4⋊C4×C89—22no—
63C4⋊C4×C89—22no—
64C42×C89—22no—
65C23×C89C2411yescharacteristic
66C22×D89—22no—
67C22×D89—22no—
68C22×D89—22no—
69C22×D89—22no—
70C22×D89—22no—
71C22×D89—22no—
72C22×D89—22no—
73C2×C4×C89—21no—
74C2×C4×C89—21no—
75C2×C4×C89—22no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89—22no—
79C2×C4×C89—21no—
80C2×C4×C89—21no—
81C2×C4×C89—22no—
82C2×C4×C89—21no—
83C2×C4×C89—21no—
84C2×C4×C89—22no—
85C2×C4×C89#4112yes—
86C2×C4×C89#4112yes—
87C2×C4×C89#4112yes—
88C2×Dic89—21no—
89C2×Dic89—21no—
90C2×Dic89—21no—
91C2×Dic89—21no—
92C2×Dic89—21no—
93C2×Dic89—21no—
94C2×Dic89—21no—
95C2×Dic89—22no—
96C2×Dic89—22no—
97C2×Dic89—21no—
98C2×Dic89—21no—
99C2×Dic89—22no—
100C2×Dic89—21no—
101C2×Dic89#4112yes—
102C2×Dic89#4112yes—
103D356—44no—
104C22×C89C2×#4111yescharacteristic
105C22×C89C2×#4111yescharacteristic
106C22×C89C2×#4111yescharacteristic
107C22×C89C2×#4111yescharacteristic
108C22×C89C2×#4111yescharacteristic
109C22×C89H(5,𝔽2)11yescharacteristic
110C22×C89H(5,𝔽2)11yescharacteristic
111C2×D89—42no—
112C2×D89—42no—
113C2×D89—42no—
114C2×D89—42no—
115C2×D89—42no—
116C2×D89—42no—
117C2×D89—42no—
118C4×C89—41no—
119C4×C89—41no—
120C4×C89—42no—
121C4×C89—42no—
122C4×C89#12614yes—
123Dic89—22no—
124Dic89—22no—
125Dic89—41no—
126Dic89—42no—
127Dic89—41no—
128C2×C89C2×#12611yescharacteristic
129C2×C89#52911yescharacteristic
130C2×C89#54011yescharacteristic
131C2×C89#55311yescharacteristic
132C2×C89#55511yescharacteristic
133C2×C89#55911yescharacteristic
134C2×C89#55911yescharacteristic
135D89—82no—
136#2513—891nomaximal, Sylow
137C89#251311yescharacteristic, complemented, Sylow
138#397—892no—
139#397—892no—
140#390—891no—
141#390—891no—
142#390—891no—
143#389—891no—
144#388—892no—
145#388—892no—
146#382D8911yescharacteristic, complemented
147C4×C4⋊C4—891no—
148C4×C4⋊C4—891no—
149C22×D4—891no—
150C2×C4⋊C4—892no—
151C2×C4⋊C4—891no—
152C2×C4⋊C4—891no—
153C2×C4⋊C4—891no—
154C2×C4⋊C4C2×D8911yescharacteristic
155C2×C4⋊C4C2×D8911yescharacteristic
156C2×C22⋊C4—892no—
157C2×C22⋊C4—892no—
158C2×C22⋊C4—892no—
159C2×C22⋊C4—892no—
160C2×C22⋊C4—892no—
161C2×C22⋊C4—892no—
162C2×C42—892no—
163C2×C42—891no—
164C2×C42—891no—
165C2×C42C2×D8911yescharacteristic
166#95—891no—
167#95—892no—
168#95—891no—
169#95—892no—
170#95C2×D8912yes—
171#95C2×D8912yes—
172C24—892no—
173C2×D4—1782no—
174C2×D4—1782no—
175C2×D4—1782no—
176C22×C4—891no—
177C22×C4—891no—
178C22×C4—891no—
179C22×C4—891no—
180C22×C4—892no—
181C22×C4C22×D8912yes—
182C22×C4C22×D8911yescharacteristic
183C22×C4C22×D8911yescharacteristic
184C22×C4C22×D8912yes—
185C22×C4C22×D8911yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—3562no—
189C4⋊C4—1782no—
190C4⋊C4—1782no—
191C4⋊C4—1782no—
192C22⋊C4—3562no—
193C22⋊C4—3562no—
194C22⋊C4—3562no—
195C22⋊C4—3562no—
196C22⋊C4—1784no—
197C22⋊C4—1784no—
198C42—22no—
199C42—3562no—
200C42—1782no—
201C42—1782no—
202C23—1782no—
203C23—1782no—
204C23—1782no—
205C23—1782no—
206C23—1782no—
207C23—1782no—
208C23—1782no—
209C23C23×D8911yescharacteristic
210D4—3564no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—892no—
224C2×C4—892no—
225C2×C4—1781no—
226C2×C4—1781no—
227C2×C4—1781no—
228C2×C4—1782no—
229C2×C4—1782no—
230C2×C4—1781no—
231C2×C4—1781no—
232C2×C4—1782no—
233C2×C4—1781no—
234C2×C4—1781no—
235C2×C4—1781no—
236C2×C4—1781no—
237C2×C4—1781no—
238C2×C4#1308357312yes—
239C2×C4#1308357412yes—
240C2×C4#1308357512yes—
241C22—3562no—
242C22—3562no—
243C22—3562no—
244C22—3562no—
245C22—3562no—
246C22—3562no—
247C22—3562no—
248C22#41×D8911yescharacteristic
249C22#41×D8911yescharacteristic
250C22C2×#1308357311yescharacteristic
251C22C2×#1308357411yescharacteristic
252C22C2×#1308357511yescharacteristic
253C22#1566805811yescharacteristic
254C22#1566805811yescharacteristic
255C4—41no—
256C4—41no—
257C4—42no—
258C4—42no—
259C4—3561no—
260C4—3562no—
261C4—3561no—
262C4—1782no—
263C4—1782no—
264C4#1566800714yes—
265C2—7122no—
266C2C2×#1566800711yescharacteristic
267C2#1915213311yescharacteristic
268C2#1915220411yescharacteristic
269C2#1915229211yescharacteristic
270C2#1915231111yescharacteristic
271C2#1915233011yescharacteristic
272C2#1915233011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#382×C89C2
prime radicalC22×D356C22
hypercenter#382D89
hypocenterC89#2513
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. #19151527C2semidirect
2. #19151525C2semidirect
6. #19151497C2semidirect
7. #19151490C2semidirect
8. #19151487C2semidirect
9. C4⋊C4×Dic89C2semidirect
10. C4×#13083553C2semidirect
11. #382×C89C2semidirect
137. C89#2513semidirect
146. #382D89semidirect

Maximal subgroups

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

subgroupindex
#191515272
#191515252
#191515002
#191514992
#191514972
#191514902
#191514872
C4⋊C4×Dic892
C4×#130835532
#382×C892
#251389