Finite Group Databasebeta

← #26025941

Subgroups — #26025941

Order 11392.

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

normal subgroups only

This group has 576 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×#15667969C211yesmaximal, characteristic, complemented
2#19151517C211yesmaximal, characteristic, complemented
3#19151512C211yesmaximal, characteristic, complemented
4#19151509C211yesmaximal, characteristic, complemented
5#19151506C211yesmaximal, characteristic
6#19151498C212yesmaximal, complemented
7#19151492C212yesmaximal, complemented
8#19151486C212yesmaximal, complemented
9#19151474C212yesmaximal, complemented
10#19151444C211yesmaximal, characteristic, complemented
11C2×#124×C89C211yesmaximal, characteristic, complemented
12C22×C22⋊D89C2212yes—
13C22×C4×D89C2211yescharacteristic
14#15667969—24no—
15C2×#13083553C2211yescharacteristic
16C2×#13083553C2211yescharacteristic
17C2×#13083553C2212yes—
18C2×C22⋊Dic89C2212yes—
19C2×C22⋊Dic89C2212yes—
20C2×C22⋊Dic89C2212yes—
21C2×#13083551C2211yescharacteristic
22C2×#13083551C2211yescharacteristic
23C2×#13083551C2212yes—
24C2×C4×Dic89C2212yes—
25C2×C4×Dic89C2211yescharacteristic
26#15667919C2212yes—
27#15667919C2211yescharacteristic
28#15667919C2211yescharacteristic
29#15667919C2212yes—
30#15667919C2212yes—
31C22×Q8×C89C2211yescharacteristic
32C22×D4×C89C2211yescharacteristic
33#124×C89—24no—
34C2×C22⋊C4×C89C2212yes—
35C2×C22⋊C4×C89C2212yes—
36C2×C42×C89C2211yescharacteristic
37C23×D89C2311yescharacteristic
38C2×C22⋊D89—24no—
39C2×C22⋊D89—24no—
40C2×C22⋊D89—42no—
41C22×Dic89C2312yes—
42C22×Dic89C2311yescharacteristic
43C22×Dic89C2311yescharacteristic
44C22×Dic89C2311yescharacteristic
45C22×Dic89C2312yes—
46C2×C4×D89—22no—
47C2×C4×D89—22no—
48C2×C4×D89—22no—
49#13083553—22no—
50#13083553—22no—
51#13083553—42no—
52C22⋊Dic89—24no—
53C22⋊Dic89—24no—
54C22⋊Dic89—42no—
55#13083551—22no—
56#13083551—22no—
57#13083551—42no—
58C4×Dic89—22no—
59C4×Dic89—24no—
60C24×C89C2312yes—
61C2×Q8×C89—22no—
62C2×Q8×C89—42no—
63C2×D4×C89—22no—
64C2×D4×C89—42no—
65C22×C4×C89C2312yes—
66C22×C4×C89C2311yescharacteristic
67C22×C4×C89C2311yescharacteristic
68C22×C4×C89C2311yescharacteristic
69C22⋊C4×C89—24no—
70C22⋊C4×C89—24no—
71C42×C89D414yescomplemented
72C23×C89—22no—
73C23×C89—22no—
74C23×C89—22no—
75C23×C89—22no—
76C23×C89—22no—
77C23×C89—22no—
78C23×C89—22no—
79C23×C89C2411yescharacteristic
80C22×D89—21no—
81C22×D89—21no—
82C22×D89—22no—
83C22×D89—22no—
84C22×D89#4112yes—
85Q8×C89—44no—
86D4×C89—44no—
87C2×C4×C89—22no—
88C2×C4×C89—21no—
89C2×C4×C89—21no—
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—
97C22⋊D89—48no—
98C2×Dic89—21no—
99C2×Dic89—21no—
100C2×Dic89—22no—
101C2×Dic89—22no—
102C2×Dic89—21no—
103C2×Dic89—21no—
104C2×Dic89—22no—
105C2×Dic89—22no—
106C2×Dic89—22no—
107C2×Dic89—22no—
108C2×Dic89—22no—
109C2×Dic89#4114yes—
110C2×Dic89#4112yes—
111C4×D89—28no—
112C22×C89—42no—
113C22×C89—42no—
114C22×C89—42no—
115C22×C89—42no—
116C22×C89—42no—
117C22×C89—42no—
118C22×C89—42no—
119C22×C89C22×D411yescharacteristic
120C22×C89C2×#4111yescharacteristic
121C22×C89C2×#4111yescharacteristic
122C22×C89C2×#4112yes—
123C22×C89H(5,𝔽2)12yes—
124C2×D89—22no—
125C2×D89—24no—
126C2×D89—41no—
127C2×D89—41no—
128C2×D89—42no—
129C4×C89—22no—
130C4×C89—22no—
131C4×C89—22no—
132C4×C89—42no—
133Dic89—22no—
134Dic89—24no—
135Dic89—41no—
136Dic89—41no—
137Dic89—42no—
138C2×C89—82no—
139C2×C89#52511yescharacteristic
140C2×C89#53211yescharacteristic
141C2×C89#53511yescharacteristic
142C2×C89#55112yes—
143C2×C89#55512yes—
144D89—42no—
145#2610—891nomaximal, Sylow
146C89#261011yescharacteristic, complemented, Sylow
147C2×#124D8911yescharacteristic, complemented
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#376—891no—
158C22×Q8C2×D8911yescharacteristic
159C22×D4—892no—
160C22×D4C2×D8911yescharacteristic
161C23×C4—891no—
162#124—24no—
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—892no—
170C2×C22⋊C4—892no—
171C2×C22⋊C4—891no—
172C2×C22⋊C4—891no—
173C2×C22⋊C4C2×D8912yes—
174C2×C22⋊C4C2×D8912yes—
175C2×C42—891no—
176C2×C42—892no—
177C2×C42C2×D8911yescharacteristic
178#95—892no—
179#95—891no—
180#95—891no—
181#95—892no—
182#95—892no—
183C24—891no—
184C24C22×D8912yes—
185C2×Q8—22no—
186C2×Q8—42no—
187C2×D4—22no—
188C2×D4—42no—
189C2×D4—3562no—
190C2×D4—1784no—
191C2×D4—1784no—
192C22×C4—892no—
193C22×C4—891no—
194C22×C4—892no—
195C22×C4—891no—
196C22×C4—891no—
197C22×C4—1782no—
198C22×C4—1782no—
199C22×C4—1782no—
200C22×C4C22×D8912yes—
201C22×C4C22×D8911yescharacteristic
202C22×C4C22×D8911yescharacteristic
203C22×C4C22×D8911yescharacteristic
204C4⋊C4—3562no—
205C4⋊C4—1782no—
206C4⋊C4—1782no—
207C22⋊C4—24no—
208C22⋊C4—24no—
209C22⋊C4—3562no—
210C22⋊C4—3562no—
211C22⋊C4—1784no—
212C22⋊C4—1784no—
213C22⋊C4—1782no—
214C22⋊C4—1782no—
215C42—1784no—
216C42—1782no—
217C42C22⋊D8914yescomplemented
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—892no—
226C23—1781no—
227C23—1781no—
228C23—1782no—
229C23—1782no—
230C23C23×D8911yescharacteristic
231Q8—44no—
232D4—44no—
233D4—3568no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—894no—
242C2×C4—892no—
243C2×C4—1788no—
244C2×C4—1781no—
245C2×C4—1781no—
246C2×C4—1782no—
247C2×C4—1782no—
248C2×C4—1782no—
249C2×C4—1782no—
250C2×C4—1782no—
251C2×C4—1781no—
252C2×C4—1781no—
253C2×C4—1782no—
254C2×C4—1782no—
255C2×C4C2×C22⋊D8912yes—
256C2×C4C2×C22⋊D8912yes—
257C2×C4C2×C22⋊D8912yes—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—3561no—
266C22—3561no—
267C22—3562no—
268C22—1784no—
269C22—1782no—
270C22C22×C22⋊D8911yescharacteristic
271C22#41×D8912yes—
272C22#41×D8911yescharacteristic
273C22#41×D8911yescharacteristic
274C22#1566805712yes—
275C4—22no—
276C4—22no—
277C4—22no—
278C4—42no—
279C4—3561no—
280C4—3561no—
281C4—3562no—
282C4—1784no—
283C4—1782no—
284C2—82no—
285C2—3562no—
286C2#1915210511yescharacteristic
287C2#1915214411yescharacteristic
288C2#1915216511yescharacteristic
289C2#1915227812yes—
290C2#1915231012yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
FittingC2×#124×C89C2
prime radical#19151506C2
hypercenterC2×#124D89
hypocenterC89#2610
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#15667969C2semidirect
2. #19151517C2semidirect
3. #19151512C2semidirect
4. #19151509C2semidirect
6. #19151498C2semidirect
7. #19151492C2semidirect
8. #19151486C2semidirect
9. #19151474C2semidirect
10. #19151444C2semidirect
11. C2×#124×C89C2semidirect
71. C42×C89D4semidirect
146. C89#2610semidirect
147. C2×#124D89semidirect
217. C42C22⋊D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679692
#191515172
#191515122
#191515092
#191515062
#191514982
#191514922
#191514862
#191514742
#191514442
C2×#124×C892
#261089