Finite Group Databasebeta

← #26033387

Subgroups — #26033387

Order 11392.

364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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×#15668035C211yesmaximal, characteristic, complemented
2#135×D89C211yesmaximal, characteristic, complemented
3#19152040C212yesmaximal, complemented
4#19152039C211yesmaximal, characteristic, complemented
5#19152036C211yesmaximal, characteristic, complemented
6#19152035C212yesmaximal, complemented
7#19152033C211yesmaximal, characteristic, complemented
8#19152031C212yesmaximal, complemented
9#19152029C212yesmaximal, complemented
10M32×D89C211yesmaximal, characteristic, complemented
11#510×C89C211yesmaximal, characteristic, complemented
12C2×#13083575—21no—
13#41×D89—21no—
14#15668035—21no—
15#15668035—21no—
16#15668035C2212yes—
17#15668035C2212yescomplemented
18#15668035C2211yescharacteristic, complemented
19#15668034C2211yescharacteristic
20#15668033—21no—
21#15668032—21no—
22#15668031C2211yescharacteristic, complemented
23Q16×D89C2211yescharacteristic, complemented
24C2×#13083561—21no—
25SD16×D89—21no—
26C2×D712C2211yescharacteristic, complemented
27D8×D89C2211yescharacteristic, complemented
28C2×C8×D89C2211yescharacteristic
29#15667958C2212yescomplemented
30#15667957C2212yescomplemented
31#15667955C2212yescomplemented
32#15667955C2212yescomplemented
33D1424C2212yescomplemented
34#15667953C2212yescomplemented
35#15667952C2211yescharacteristic, complemented
36#15667951C2212yescomplemented
37C16×D89C2212yescomplemented
38#135×C89C2211yescharacteristic
39C2×Q16×C89C2211yescharacteristic, complemented
40Q32×C89C2212yescomplemented
41SD32×C89C2212yescomplemented
42M32×C89C2211yescharacteristic, complemented
43#13083575—21no—
44#13083575—22no—
45#13083575—22no—
46#13083575—41no—
47#13083575—41no—
48#13083574—21no—
49#13083574—41no—
50#13083573—21no—
51#13083573—41no—
52Q8×D89—21no—
53C2×D356—21no—
54C2×D356—41no—
55D4×D89—21no—
56D4×D89—41no—
57C2×C4×D89—41no—
58C2×C4×D89—41no—
59C2×C4×D89D411yescharacteristic
60Dic356C2311yescharacteristic
61#13083564—21no—
62#13083563—21no—
63#13083562—21no—
64#13083561—21no—
65#13083561—22no—
66#13083561—22no—
67D712—21no—
68D712C2311yescharacteristic
69D712C2312yes—
70#13083559—21no—
71C2×#10623494D411yescharacteristic
72C8×D89D411yescharacteristic
73C8×D89D411yescharacteristic
74C8×D89C2311yescharacteristic
75C8×D89C2311yescharacteristic
76#13083549C2312yes—
77#41×C89—21no—
78C2×Q8×C89—21no—
79Q16×C89—21no—
80Q16×C89C2311yescharacteristic
81Q16×C89C2312yes—
82SD16×C89—21no—
83D8×C89C2311yescharacteristic
84C2×C8×C89C2311yescharacteristic
85C16×C89C2312yes—
86C22×D89—41no—
87C22×D89—41no—
88C22×D89D811yescharacteristic
89Q8×C89—21no—
90Q8×C89—22no—
91Q8×C89—41no—
92D4×C89—21no—
93D4×C89—41no—
94C2×C4×C89—41no—
95C2×C4×C89—41no—
96C2×C4×C89C2×D411yescharacteristic
97C22⋊D89—41no—
98C22⋊D89—41no—
99C22⋊D89—41no—
100C2×Dic89—41no—
101C2×Dic89D811yescharacteristic
102D356—21no—
103D356—22no—
104D356—41no—
105D356—42no—
106D356—42no—
107D356—41no—
108C4×D89—41no—
109C4×D89—41no—
110C4×D89—41no—
111C4×D89—42no—
112C4×D89—42no—
113C4×D89D811yescharacteristic
114C4×D89D811yescharacteristic
115C4×D89C2×D411yescharacteristic
116C4×D89C2×D411yescharacteristic
117Dic178—21no—
118Dic178—41no—
119C8×C89C2×D411yescharacteristic
120C8×C89C2411yescharacteristic
121#10623494C2×D411yescharacteristic
122#10623494C2×D411yescharacteristic
123C22×C89—41no—
124C22×C89C2×D811yescharacteristic
125C2×D89—41no—
126C2×D89—42no—
127C2×D89—41no—
128C2×D89—82no—
129C2×D89—82no—
130C2×D89C2×D811yescharacteristic
131C2×D89C2×D811yescharacteristic
132C4×C89—41no—
133C4×C89—42no—
134C4×C89C2×D811yescharacteristic
135C4×C89C22×D411yescharacteristic
136Dic89—41no—
137Dic89C2×D811yescharacteristic
138Dic89C2×D811yescharacteristic
139C2×C89—21no—
140C2×C89—81no—
141C2×C89C22×D811yescharacteristic
142D89—21no—
143D89—21no—
144D89—82no—
145D89—81no—
146#3414—891nomaximal, Sylow
147C89#341411yescharacteristic, complemented, Sylow
148C2×#135—891no—
149C2×#135—891no—
150#510—891no—
151#510—892no—
152#510D8911yescharacteristic, complemented
153#509—891no—
154#509—892no—
155#509—891no—
156#508—892no—
157#508—892no—
158C2×M32—891no—
159C2×#41—1781no—
160C2×#41—1781no—
161#135—892no—
162#135—891no—
163#135—892no—
164#135—891no—
165#135—891no—
166#135—1781no—
167#135—1781no—
168#135—1781no—
169#135—1781no—
170#135C2×D8911yescharacteristic
171C2×Q16—891no—
172C2×Q16C2×D8911yescharacteristic, complemented
173C2×SD16—1781no—
174C2×SD16—1781no—
175C2×D8—891no—
176C2×D8—891no—
177C22×C8—891no—
178Q32—892no—
179Q32C2×D8912yescomplemented
180SD32—892no—
181SD32—892no—
182SD32—892no—
183SD32C2×D8912yescomplemented
184D16—892no—
185D16—892no—
186M32—891no—
187M32—892no—
188M32C2×D8911yescharacteristic, complemented
189C2×C16—892no—
190#41—21no—
191#41—3561no—
192#41—3561no—
193#41—3561no—
194#41—3561no—
195#41—1781no—
196#41—1782no—
197#41—1781no—
198#41—1782no—
199#41—1781no—
200C2×Q8—21no—
201C2×Q8—1781no—
202C2×D4—3561no—
203C2×D4—3561no—
204C2×D4—1781no—
205C2×D4—1781no—
206C22×C4—891no—
207C22×C4—3561no—
208C22×C4—3561no—
209Q16—21no—
210Q16—891no—
211Q16—1781no—
212Q16C22×D8911yescharacteristic
213Q16C22×D8912yes—
214SD16—21no—
215SD16—1781no—
216SD16—1782no—
217SD16—1781no—
218SD16—1782no—
219SD16—1781no—
220D8—892no—
221D8—891no—
222D8—1781no—
223D8—1781no—
224D8C22×D8911yescharacteristic
225C2×C8—891no—
226C2×C8—891no—
227C2×C8—891no—
228C2×C8—891no—
229C2×C8—891no—
230C2×C8C22×D8911yescharacteristic
231C16—892no—
232C16C22×D8912yes—
233C23—891no—
234C23—3561no—
235C23—3561no—
236Q8—21no—
237Q8—22no—
238Q8—41no—
239Q8—3561no—
240Q8—1781no—
241D4—21no—
242D4—41no—
243D4—3561no—
244D4—3562no—
245D4—3562no—
246D4—3561no—
247D4—3561no—
248D4—3561no—
249D4—3561no—
250D4—1781no—
251D4—1782no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—891no—
255C2×C4—891no—
256C2×C4—891no—
257C2×C4—891no—
258C2×C4—891no—
259C2×C4—3561no—
260C2×C4—3562no—
261C2×C4—3562no—
262C2×C4—3561no—
263C2×C4—3561no—
264C2×C4—3561no—
265C2×C4D4×D8911yescharacteristic
266C8—891no—
267C8—891no—
268C8D4×D8911yescharacteristic
269C8C23×D8911yescharacteristic
270C22—41no—
271C22—891no—
272C22—891no—
273C22—3561no—
274C22—3562no—
275C22—3561no—
276C22—7122no—
277C22—7122no—
278C22D8×D8911yescharacteristic
279C4—41no—
280C4—42no—
281C4—891no—
282C4—891no—
283C4—3561no—
284C4D8×D8911yescharacteristic
285C4C2×D4×D8911yescharacteristic
286C2—21no—
287C2—81no—
288C2—1781no—
289C2—1781no—
290C2—7122no—
291C2—7121no—
292C2C2×D8×D8911yescharacteristic
subgroupG/H
centerC2C2×D8×D89
commutator, cosocleC8×C89C24
FrattiniC8C23×D89
Fitting#510×C89C2
socleC2×C89C22×D8
hypercenter#510D89
hypocenterC89#3414
LCSG ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
1. C2×#15668035C2semidirect
2. #135×D89C2semidirect
3. #19152040C2semidirect
4. #19152039C2semidirect
5. #19152036C2semidirect
6. #19152035C2semidirect
7. #19152033C2semidirect
8. #19152031C2semidirect
9. #19152029C2semidirect
10. M32×D89C2semidirect
11. #510×C89C2semidirect
17. #15668035C22semidirect
18. #15668035C22semidirect
22. #15668031C22semidirect
23. Q16×D89C22semidirect
26. C2×D712C22semidirect
27. D8×D89C22semidirect
29. #15667958C22semidirect
30. #15667957C22semidirect
31. #15667955C22semidirect
32. #15667955C22semidirect
33. D1424C22semidirect
34. #15667953C22semidirect
35. #15667952C22semidirect
36. #15667951C22semidirect
37. C16×D89C22semidirect
39. C2×Q16×C89C22semidirect
40. Q32×C89C22semidirect
41. SD32×C89C22semidirect
42. M32×C89C22semidirect
147. C89#3414semidirect
152. #510D89semidirect
172. C2×Q16C2×D89semidirect
179. Q32C2×D89semidirect
183. SD32C2×D89semidirect
188. M32C2×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156680352
#135×D892
#191520402
#191520392
#191520362
#191520352
#191520332
#191520312
#191520292
M32×D892
#510×C892
#341489