Finite Group Databasebeta

← #26025933

Subgroups — #26025933

Order 11392.

576 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 145 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×#15668000C211yesmaximal, characteristic, complemented
2C2×#15667969C211yesmaximal, characteristic, complemented
3#19151519C211yesmaximal, characteristic, complemented
4#19151516C211yesmaximal, characteristic, complemented
5#19151511C211yesmaximal, characteristic, complemented
6#19151508C211yesmaximal, characteristic
7#19151500C212yesmaximal, complemented
8#19151490C212yesmaximal, complemented
9#19151489C212yesmaximal, complemented
10#19151476C212yesmaximal, complemented
11#376×C89C211yesmaximal, characteristic, complemented
12C22×Dic178C2211yescharacteristic
13C22×D356C2212yes—
14C22×D356C2211yescharacteristic
15C22×C4×D89C2211yescharacteristic
16#15668000—24no—
17#15667969—24no—
18C2×C4⋊Dic89C2212yes—
19C2×#13083553C2211yescharacteristic
20C2×#13083553C2211yescharacteristic
21C2×#13083551C2212yes—
22C2×#13083551C2212yes—
23C2×#13083551C2212yes—
24C2×#13083551C2212yes—
25C2×#13083551C2211yescharacteristic
26C2×#13083551C2211yescharacteristic
27C2×#13083551C2212yes—
28C2×#13083551C2212yes—
29C2×C4×Dic89C2211yescharacteristic
30#15667919C2212yes—
31#15667919C2212yes—
32C2×C42×C89C2212yes—
33C2×C42×C89C2211yescharacteristic
34#95×C89C2212yes—
35#95×C89C2211yescharacteristic
36#95×C89C2211yescharacteristic
37C23×D89C2312yes—
38C23×D89C2311yescharacteristic
39C2×Dic178—22no—
40C2×Dic178—42no—
41C2×D356—24no—
42C2×D356—22no—
43C2×D356—24no—
44C2×D356—42no—
45C2×D356—42no—
46C22×Dic89C2312yes—
47C22×Dic89C2311yescharacteristic
48C22×Dic89C2311yescharacteristic
49C22×Dic89C2311yescharacteristic
50C2×C4×D89—22no—
51C2×C4×D89—22no—
52C2×C4×D89—22no—
53C4⋊Dic89—42no—
54#13083553—22no—
55#13083553—22no—
56#13083551—22no—
57#13083551—22no—
58#13083551—24no—
59#13083551—24no—
60#13083551—24no—
61#13083551—24no—
62#13083551—42no—
63#13083551—42no—
64C4×Dic89—22no—
65C22×C4×C89C2312yes—
66C22×C4×C89C2311yescharacteristic
67C22×C4×C89C2311yescharacteristic
68C22×C4×C89C2311yescharacteristic
69C22×C4×C89C2312yes—
70C42×C89—24no—
71C42×C89D414yescomplemented
72C23×C89C2411yescharacteristic
73C22×D89—21no—
74C22×D89—21no—
75C22×D89—22no—
76C22×D89—22no—
77C22×D89—22no—
78C22×D89—22no—
79C22×D89—22no—
80C22×D89—22no—
81C22×D89—22no—
82C22×D89—22no—
83C22×D89—22no—
84C22×D89#4112yes—
85C2×C4×C89—22no—
86C2×C4×C89—21no—
87C2×C4×C89—21no—
88C2×C4×C89—22no—
89C2×C4×C89—22no—
90C2×C4×C89—22no—
91C2×C4×C89—22no—
92C2×C4×C89—22no—
93C2×C4×C89—22no—
94C2×C4×C89C2×D412yes—
95C2×C4×C89C2×D412yes—
96C2×C4×C89C2×D412yes—
97C2×C4×C89#4114yes—
98C2×Dic89—21no—
99C2×Dic89—21no—
100C2×Dic89—21no—
101C2×Dic89—21no—
102C2×Dic89—22no—
103C2×Dic89—22no—
104C2×Dic89—22no—
105C2×Dic89—22no—
106C2×Dic89—22no—
107C2×Dic89#4112yes—
108D356—48no—
109D356—44no—
110C4×D89—28no—
111Dic178—44no—
112C22×C89C22×D411yescharacteristic
113C22×C89C2×#4111yescharacteristic
114C22×C89C2×#4111yescharacteristic
115C22×C89C2×#4112yes—
116C22×C89H(5,𝔽2)12yes—
117C2×D89—22no—
118C2×D89—24no—
119C2×D89—41no—
120C2×D89—41no—
121C2×D89—42no—
122C2×D89—42no—
123C2×D89—42no—
124C2×D89—42no—
125C2×D89—42no—
126C2×D89—42no—
127C2×D89—42no—
128C2×D89—42no—
129C4×C89—22no—
130C4×C89—22no—
131C4×C89—22no—
132C4×C89—24no—
133C4×C89—42no—
134Dic89—22no—
135Dic89—41no—
136Dic89—42no—
137Dic89—41no—
138C2×C89#52511yescharacteristic
139C2×C89#53211yescharacteristic
140C2×C89#53511yescharacteristic
141C2×C89#55112yes—
142C2×C89#55512yes—
143D89—42no—
144D89—82no—
145#2610—891nomaximal, Sylow
146C89#261011yescharacteristic, complemented, Sylow
147C2×#124—891no—
148C2×#117—891no—
149#395—891no—
150#394—891no—
151#393—891no—
152#392—891no—
153#390—892no—
154#388—892no—
155#388—892no—
156#386—892no—
157#376D8911yescharacteristic, complemented
158C22×Q8—891no—
159C22×D4—891no—
160C22×D4—892no—
161C23×C4—891no—
162#124—1784no—
163#117—1784no—
164C2×C4⋊C4—892no—
165C2×C4⋊C4—891no—
166C2×C4⋊C4—891no—
167C2×C22⋊C4—892no—
168C2×C22⋊C4—892no—
169C2×C22⋊C4—891no—
170C2×C22⋊C4—891no—
171C2×C22⋊C4—892no—
172C2×C22⋊C4—892no—
173C2×C22⋊C4—892no—
174C2×C22⋊C4—892no—
175C2×C42—891no—
176C2×C42C2×D8912yes—
177C2×C42C2×D8911yescharacteristic
178#95—892no—
179#95—892no—
180#95C2×D8912yes—
181#95C2×D8911yescharacteristic
182#95C2×D8911yescharacteristic
183C24—891no—
184C24—892no—
185C2×Q8—3562no—
186C2×Q8—1782no—
187C2×D4—3562no—
188C2×D4—3562no—
189C2×D4—1784no—
190C2×D4—1782no—
191C2×D4—1784no—
192C22×C4—891no—
193C22×C4—891no—
194C22×C4—892no—
195C22×C4—891no—
196C22×C4—1782no—
197C22×C4—1782no—
198C22×C4—1782no—
199C22×C4C22×D8912yes—
200C22×C4C22×D8911yescharacteristic
201C22×C4C22×D8911yescharacteristic
202C22×C4C22×D8911yescharacteristic
203C22×C4C22×D8912yes—
204C4⋊C4—3562no—
205C4⋊C4—1782no—
206C4⋊C4—1782no—
207C22⋊C4—3562no—
208C22⋊C4—3562no—
209C22⋊C4—1784no—
210C22⋊C4—1782no—
211C22⋊C4—1782no—
212C22⋊C4—1784no—
213C22⋊C4—1784no—
214C22⋊C4—1784no—
215C42—24no—
216C42—1782no—
217C42D35614yescomplemented
218C23—892no—
219C23—1782no—
220C23—1782no—
221C23—1782no—
222C23—1782no—
223C23—1782no—
224C23—1782no—
225C23—1782no—
226C23—1781no—
227C23—1781no—
228C23—1782no—
229C23—1782no—
230C23C23×D8911yescharacteristic
231Q8—3564no—
232D4—3564no—
233D4—3568no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—892no—
244C2×C4—1788no—
245C2×C4—1781no—
246C2×C4—1781no—
247C2×C4—1782no—
248C2×C4—1782no—
249C2×C4—1782no—
250C2×C4—1782no—
251C2×C4—1782no—
252C2×C4—1781no—
253C2×C4—1781no—
254C2×C4C2×D35612yes—
255C2×C4C2×D35612yes—
256C2×C4C2×D35612yes—
257C2×C4#1308357414yes—
258C22—3561no—
259C22—3561no—
260C22—3562no—
261C22—3562no—
262C22—3562no—
263C22—3562no—
264C22—3562no—
265C22—3562no—
266C22—3562no—
267C22—3562no—
268C22—1784no—
269C22—1782no—
270C22C22×D35611yescharacteristic
271C22#41×D8911yescharacteristic
272C22#41×D8911yescharacteristic
273C22C2×#1308357412yes—
274C22#1566805812yes—
275C4—22no—
276C4—22no—
277C4—24no—
278C4—22no—
279C4—42no—
280C4—3561no—
281C4—3562no—
282C4—3561no—
283C4—1782no—
284C2—3562no—
285C2—7122no—
286C2#1915211011yescharacteristic
287C2#1915214811yescharacteristic
288C2#1915216711yescharacteristic
289C2#1915227212yes—
290C2#1915231112yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#376×C89C2
prime radical#19151508C2
hypercenter#376D89
hypocenterC89#2610
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #376

Complements

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

NH ≅ G/Ntype
1. C2×#15668000C2semidirect
2. C2×#15667969C2semidirect
3. #19151519C2semidirect
4. #19151516C2semidirect
5. #19151511C2semidirect
7. #19151500C2semidirect
8. #19151490C2semidirect
9. #19151489C2semidirect
10. #19151476C2semidirect
11. #376×C89C2semidirect
71. C42×C89D4semidirect
146. C89#2610semidirect
157. #376D89semidirect
217. C42D356semidirect

Maximal subgroups

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

subgroupindex
C2×#156680002
C2×#156679692
#191515192
#191515162
#191515112
#191515082
#191515002
#191514902
#191514892
#191514762
#376×C892
#261089