Finite Group Databasebeta

← #26025158

Subgroups — #26025158

Order 11392.

604 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 147 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×#15667990C212yesmaximal, complemented
2C2×#15667977C211yesmaximal, characteristic, complemented
3C2×#15667974C211yesmaximal, characteristic
4#19151529C211yesmaximal, characteristic, complemented
5#19151516C211yesmaximal, characteristic
6#19151515C211yesmaximal, characteristic
7#19151488C212yesmaximal, complemented
8#19151487C212yesmaximal, complemented
9#19151462C211yesmaximal, characteristic, complemented
10#19151457C212yesmaximal, complemented
11#398×C89C211yesmaximal, characteristic, complemented
12C22×Dic178C2211yescharacteristic
13C22×D356C2211yescharacteristic
14C22×C4×D89C2212yes—
15#15667990—28no—
16#15667977—24no—
17#15667974—24no—
18C2×#13083553C2211yescharacteristic
19C2×#13083553C2212yes—
20C2×#13083553C2212yes—
21C2×#13083553C2211yescharacteristic
22C2×#13083551C2212yes—
23C2×#13083551C2212yes—
24C2×#13083551C2212yes—
25C2×#13083551C2212yes—
26C2×#13083551C2212yes—
27C2×C4×Dic89C2211yescharacteristic
28C2×C4×Dic89C2211yescharacteristic
29C2×C4×Dic89C2211yescharacteristic
30#15667919C2212yes—
31#15667919C2212yes—
32#15667919C2211yescharacteristic
33C2×C4⋊C4×C89C2212yes—
34C2×C4⋊C4×C89C2211yescharacteristic
35C2×C4⋊C4×C89C2211yescharacteristic
36#95×C89C2212yes—
37#95×C89C2211yescharacteristic
38C23×D89C2312yes—
39C2×Dic178—22no—
40C2×Dic178—22no—
41C2×Dic178D414yescomplemented
42C2×D356—24no—
43C2×D356—22no—
44C22×Dic89C2312yes—
45C22×Dic89C2311yescharacteristic
46C22×Dic89C2311yescharacteristic
47C22×Dic89C2311yescharacteristic
48C22×Dic89C2311yescharacteristic
49C2×C4×D89—24no—
50C2×C4×D89—24no—
51C2×C4×D89—24no—
52#13083553—22no—
53#13083553—22no—
54#13083553—24no—
55#13083553—24no—
56#13083551—24no—
57#13083551—24no—
58#13083551—24no—
59#13083551—24no—
60#13083551—24no—
61C4×Dic89—22no—
62C4×Dic89—22no—
63C4×Dic89D414yes—
64C22×C4×C89C2312yes—
65C22×C4×C89C2312yes—
66C22×C4×C89C2311yescharacteristic
67C22×C4×C89C2311yescharacteristic
68C22×C4×C89C2311yescharacteristic
69C4⋊C4×C89—22no—
70C4⋊C4×C89—22no—
71C4⋊C4×C89—24no—
72C23×C89C2411yescharacteristic
73C22×D89—22no—
74C22×D89—22no—
75C22×D89—22no—
76C22×D89—22no—
77C22×D89—22no—
78C22×D89—22no—
79C22×D89#4114yes—
80C2×C4×C89—21no—
81C2×C4×C89—22no—
82C2×C4×C89—21no—
83C2×C4×C89—21no—
84C2×C4×C89—22no—
85C2×C4×C89—22no—
86C2×C4×C89—22no—
87C2×C4×C89—22no—
88C2×C4×C89—22no—
89C2×C4×C89—22no—
90C2×C4×C89—22no—
91C2×C4×C89C2×D412yes—
92C2×C4×C89C2×D412yes—
93C2×Dic89—21no—
94C2×Dic89—21no—
95C2×Dic89—22no—
96C2×Dic89—21no—
97C2×Dic89—22no—
98C2×Dic89—22no—
99C2×Dic89—22no—
100C2×Dic89—22no—
101C2×Dic89C2×D412yes—
102C2×Dic89C2×D412yes—
103C2×Dic89C2×D412yes—
104C2×Dic89C2×D412yes—
105C2×Dic89#4112yes—
106D356—28no—
107C4×D89—48no—
108Dic178—28no—
109C22×C89C22×D411yescharacteristic
110C22×C89C22×D411yescharacteristic
111C22×C89C2×#4111yescharacteristic
112C22×C89C2×#4112yes—
113C22×C892−1+412yes—
114C2×D89—24no—
115C2×D89—24no—
116C2×D89—24no—
117C2×D89—42no—
118C2×D89—42no—
119C2×D89—42no—
120C2×D89—42no—
121C4×C89—22no—
122C4×C89—22no—
123C4×C89—42no—
124C4×C89—41no—
125C4×C89—42no—
126Dic89—22no—
127Dic89—22no—
128Dic89—41no—
129Dic89—42no—
130Dic89#12114yes—
131C2×C89C2×#12111yescharacteristic
132C2×C89#52511yescharacteristic
133C2×C89#53611yescharacteristic
134C2×C89#54812yes—
135C2×C89#55212yes—
136D89—44no—
137#2536—891nomaximal, Sylow
138C89#253611yescharacteristic, complemented, Sylow
139C2×C22⋊Q8—892no—
140C2×C4×Q8—891no—
141C2×C4×D4—891no—
142#398—891no—
143#398D8911yescharacteristic, complemented
144#394—891no—
145#394—891no—
146#388—892no—
147#388—892no—
148#382—891no—
149#380—892no—
150C22×Q8—891no—
151C22×D4—891no—
152C23×C4—892no—
153C22⋊Q8—1788no—
154C4×Q8—1784no—
155C4×D4—1784no—
156C2×C4⋊C4—891no—
157C2×C4⋊C4—891no—
158C2×C4⋊C4—892no—
159C2×C4⋊C4—892no—
160C2×C4⋊C4C2×D8911yescharacteristic
161C2×C4⋊C4C2×D8911yescharacteristic
162C2×C4⋊C4C2×D8912yes—
163C2×C22⋊C4—892no—
164C2×C22⋊C4—892no—
165C2×C22⋊C4—892no—
166C2×C22⋊C4—892no—
167C2×C22⋊C4—892no—
168C2×C42—891no—
169C2×C42—891no—
170C2×C42—891no—
171#95—892no—
172#95—892no—
173#95—891no—
174#95C2×D8912yes—
175#95C2×D8911yescharacteristic
176C24—892no—
177C2×Q8—894no—
178C2×Q8—1782no—
179C2×Q8—1782no—
180C2×D4—1784no—
181C2×D4—1782no—
182C22×C4—891no—
183C22×C4—891no—
184C22×C4—891no—
185C22×C4—892no—
186C22×C4—891no—
187C22×C4—1784no—
188C22×C4—1784no—
189C22×C4—1784no—
190C22×C4C22×D8912yes—
191C22×C4C22×D8912yes—
192C22×C4C22×D8911yescharacteristic
193C22×C4C22×D8911yescharacteristic
194C22×C4C22×D8911yescharacteristic
195C4⋊C4—22no—
196C4⋊C4—22no—
197C4⋊C4—24no—
198C4⋊C4—1782no—
199C4⋊C4—1784no—
200C4⋊C4—1784no—
201C4⋊C4—1782no—
202C22⋊C4—1784no—
203C22⋊C4—1784no—
204C22⋊C4—1784no—
205C22⋊C4—1784no—
206C22⋊C4—1784no—
207C42—894no—
208C42—1782no—
209C42—1782no—
210C23—894no—
211C23—1782no—
212C23—1782no—
213C23—1782no—
214C23—1782no—
215C23—1782no—
216C23—1782no—
217C23C23×D8911yescharacteristic
218Q8—1788no—
219D4—1788no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—892no—
232C2×C4—892no—
233C2×C4—892no—
234C2×C4—892no—
235C2×C4—892no—
236C2×C4—3568no—
237C2×C4—1781no—
238C2×C4—1782no—
239C2×C4—1782no—
240C2×C4—1782no—
241C2×C4—1782no—
242C2×C4—1781no—
243C2×C4—1781no—
244C2×C4—1782no—
245C2×C4D4×D8912yes—
246C2×C4D4×D8912yes—
247C22—3562no—
248C22—3562no—
249C22—3562no—
250C22—3562no—
251C22—1784no—
252C22—1784no—
253C22—1784no—
254C22C2×D4×D8911yescharacteristic
255C22C2×D4×D8911yescharacteristic
256C22#41×D8912yes—
257C22#41×D8911yescharacteristic
258C22#1566806012yes—
259C4—22no—
260C4—22no—
261C4—42no—
262C4—42no—
263C4—41no—
264C4—894no—
265C4—3562no—
266C4—3561no—
267C4—1782no—
268C4—1782no—
269C2—3564no—
270C2#121×D8911yescharacteristic
271C2#1915210611yescharacteristic
272C2#1915217311yescharacteristic
273C2#1915225812yes—
274C2#1915228012yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#398×C89C2
prime radicalC22×D356C22
hypercenter#398D89
hypocenterC89#2536
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#15667990C2semidirect
2. C2×#15667977C2semidirect
4. #19151529C2semidirect
7. #19151488C2semidirect
8. #19151487C2semidirect
9. #19151462C2semidirect
10. #19151457C2semidirect
11. #398×C89C2semidirect
41. C2×Dic178D4semidirect
138. C89#2536semidirect
143. #398D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679902
C2×#156679772
C2×#156679742
#191515292
#191515162
#191515152
#191514882
#191514872
#191514622
#191514572
#398×C892
#253689