Finite Group Databasebeta

← #26033384

Subgroups — #26033384

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×#15668031C211yesmaximal, characteristic, complemented
2#135×D89C211yesmaximal, characteristic, complemented
3#19152041C211yesmaximal, characteristic, complemented
4#19152038C211yesmaximal, characteristic, complemented
5#19152037C212yesmaximal, complemented
6#19152034C211yesmaximal, characteristic, complemented
7#19152032C212yesmaximal, complemented
8#19152029C212yesmaximal, complemented
9#19152027C212yesmaximal, complemented
10M32×D89C211yesmaximal, characteristic, complemented
11#509×C89C211yesmaximal, characteristic, complemented
12C2×#13083573—21no—
13#41×D89—21no—
14#15668035C2211yescharacteristic, complemented
15#15668034C2211yescharacteristic
16#15668033—21no—
17#15668032—21no—
18#15668031—21no—
19#15668031—21no—
20#15668031C2212yes—
21#15668031C2211yescharacteristic, complemented
22#15668031C2212yescomplemented
23C2×Dic356C2211yescharacteristic, complemented
24Q16×D89C2211yescharacteristic, complemented
25C2×#13083562—21no—
26SD16×D89—21no—
27D8×D89C2211yescharacteristic, complemented
28C2×C8×D89C2211yescharacteristic
29Dic712C2212yescomplemented
30#15667958C2212yescomplemented
31#15667957C2212yescomplemented
32#15667956C2212yescomplemented
33#15667956C2212yescomplemented
34#15667953C2212yescomplemented
35#15667952C2211yescharacteristic, complemented
36#15667951C2212yescomplemented
37C16×D89C2212yescomplemented
38#135×C89C2211yescharacteristic
39C2×D8×C89C2211yescharacteristic, complemented
40SD32×C89C2212yescomplemented
41D16×C89C2212yescomplemented
42M32×C89C2211yescharacteristic, complemented
43#13083575—21no—
44#13083574—21no—
45#13083574—41no—
46#13083573—22no—
47#13083573—22no—
48#13083573—21no—
49#13083573—41no—
50#13083573—41no—
51#13083573—41no—
52C2×Dic178—21no—
53Q8×D89—21no—
54C2×C22⋊D89—41no—
55D4×D89—21no—
56D4×D89—41no—
57C22×Dic89—41no—
58C2×C4×D89—41no—
59C2×C4×D89D411yescharacteristic
60Dic356—21no—
61Dic356C2311yescharacteristic
62Dic356C2312yes—
63#13083564—21no—
64#13083563—21no—
65#13083562—21no—
66#13083562—22no—
67#13083562—22no—
68#13083561—21no—
69D712C2311yescharacteristic
70#13083559—21no—
71C2×#10623494D411yescharacteristic
72C8×D89D411yescharacteristic
73C8×D89D411yescharacteristic
74C8×D89C2311yescharacteristic
75C8×D89C2311yescharacteristic
76#13083549C2312yes—
77#41×C89—21no—
78C2×D4×C89—21no—
79Q16×C89C2311yescharacteristic
80SD16×C89—21no—
81D8×C89—21no—
82D8×C89C2311yescharacteristic
83D8×C89C2312yes—
84C2×C8×C89C2311yescharacteristic
85C16×C89C2312yes—
86C23×C89—41no—
87C22×D89—41no—
88C22×D89D811yescharacteristic
89Q8×C89—21no—
90D4×C89—22no—
91D4×C89—21no—
92D4×C89—41no—
93D4×C89—41no—
94C2×C4×C89—41no—
95C2×C4×C89C2×D411yescharacteristic
96C22⋊D89—41no—
97C22⋊D89—41no—
98C22⋊D89—42no—
99C22⋊D89—42no—
100C22⋊D89—41no—
101C2×Dic89—41no—
102C2×Dic89—41no—
103C2×Dic89—42no—
104C2×Dic89—42no—
105C2×Dic89D811yescharacteristic
106D356—21no—
107D356—41no—
108C4×D89—41no—
109C4×D89—41no—
110C4×D89—41no—
111C4×D89D811yescharacteristic
112C4×D89D811yescharacteristic
113C4×D89C2×D411yescharacteristic
114C4×D89C2×D411yescharacteristic
115Dic178—22no—
116Dic178—21no—
117Dic178—41no—
118Dic178—41no—
119C8×C89C2×D411yescharacteristic
120C8×C89C2411yescharacteristic
121#10623494C2×D411yescharacteristic
122#10623494C2×D411yescharacteristic
123C22×C89—42no—
124C22×C89—41no—
125C22×C89—82no—
126C22×C89C2×D811yescharacteristic
127C2×D89—41no—
128C2×D89—41no—
129C2×D89—82no—
130C2×D89C2×D811yescharacteristic
131C2×D89C2×D811yescharacteristic
132C4×C89—41no—
133C4×C89C2×D811yescharacteristic
134C4×C89C22×D411yescharacteristic
135Dic89—41no—
136Dic89—42no—
137Dic89C2×D811yescharacteristic
138Dic89C2×D811yescharacteristic
139C2×C89—21no—
140C2×C89—81no—
141C2×C89—82no—
142C2×C89C22×D811yescharacteristic
143D89—21no—
144D89—21no—
145D89—81no—
146#3414—891nomaximal, Sylow
147C89#341411yescharacteristic, complemented, Sylow
148C2×#135—891no—
149C2×#135—891no—
150#510—891no—
151#510—892no—
152#510—891no—
153#509—891no—
154#509—892no—
155#509D8911yescharacteristic, complemented
156#508—892no—
157#508—892no—
158C2×M32—891no—
159C2×#41—1781no—
160C2×#41—1781no—
161#135—891no—
162#135—892no—
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×Q16—891no—
173C2×SD16—1781no—
174C2×SD16—1781no—
175C2×D8—891no—
176C2×D8C2×D8911yescharacteristic, complemented
177C22×C8—891no—
178Q32—892no—
179Q32—892no—
180SD32—892no—
181SD32—892no—
182SD32—892no—
183SD32C2×D8912yescomplemented
184D16—892no—
185D16C2×D8912yescomplemented
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—1782no—
196#41—1782no—
197#41—1781no—
198#41—1781no—
199#41—1781no—
200C2×Q8—1781no—
201C2×Q8—1781no—
202C2×D4—21no—
203C2×D4—3561no—
204C2×D4—3561no—
205C2×D4—1781no—
206C22×C4—891no—
207C22×C4—3561no—
208C22×C4—3561no—
209Q16—891no—
210Q16—892no—
211Q16—1781no—
212Q16—1781no—
213Q16C22×D8911yescharacteristic
214SD16—21no—
215SD16—1782no—
216SD16—1782no—
217SD16—1781no—
218SD16—1781no—
219SD16—1781no—
220D8—21no—
221D8—891no—
222D8—1781no—
223D8C22×D8912yes—
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—41no—
234C23—891no—
235C23—3561no—
236Q8—21no—
237Q8—3561no—
238Q8—3561no—
239Q8—1782no—
240Q8—1781no—
241D4—22no—
242D4—21no—
243D4—41no—
244D4—41no—
245D4—3561no—
246D4—3561no—
247D4—3561no—
248D4—3562no—
249D4—3562no—
250D4—3561no—
251D4—1781no—
252C2×C4—41no—
253C2×C4—891no—
254C2×C4—891no—
255C2×C4—891no—
256C2×C4—891no—
257C2×C4—891no—
258C2×C4—3561no—
259C2×C4—3561no—
260C2×C4—3561no—
261C2×C4—3562no—
262C2×C4—3562no—
263C2×C4—3561no—
264C2×C4—3561no—
265C2×C4D4×D8911yescharacteristic
266C8—891no—
267C8—891no—
268C8D4×D8911yescharacteristic
269C8C23×D8911yescharacteristic
270C22—41no—
271C22—42no—
272C22—82no—
273C22—891no—
274C22—891no—
275C22—3561no—
276C22—3561no—
277C22—7122no—
278C22D8×D8911yescharacteristic
279C4—41no—
280C4—891no—
281C4—891no—
282C4—3561no—
283C4—3562no—
284C4D8×D8911yescharacteristic
285C4C2×D4×D8911yescharacteristic
286C2—21no—
287C2—82no—
288C2—81no—
289C2—1781no—
290C2—1781no—
291C2—7121no—
292C2C2×D8×D8911yescharacteristic
subgroupG/H
centerC2C2×D8×D89
commutator, cosocleC8×C89C24
FrattiniC8C23×D89
Fitting#509×C89C2
socleC2×C89C22×D8
hypercenter#509D89
hypocenterC89#3414
LCSG ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. C2×#15668031C2semidirect
2. #135×D89C2semidirect
3. #19152041C2semidirect
4. #19152038C2semidirect
5. #19152037C2semidirect
6. #19152034C2semidirect
7. #19152032C2semidirect
8. #19152029C2semidirect
9. #19152027C2semidirect
10. M32×D89C2semidirect
11. #509×C89C2semidirect
14. #15668035C22semidirect
21. #15668031C22semidirect
22. #15668031C22semidirect
23. C2×Dic356C22semidirect
24. Q16×D89C22semidirect
27. D8×D89C22semidirect
29. Dic712C22semidirect
30. #15667958C22semidirect
31. #15667957C22semidirect
32. #15667956C22semidirect
33. #15667956C22semidirect
34. #15667953C22semidirect
35. #15667952C22semidirect
36. #15667951C22semidirect
37. C16×D89C22semidirect
39. C2×D8×C89C22semidirect
40. SD32×C89C22semidirect
41. D16×C89C22semidirect
42. M32×C89C22semidirect
147. C89#3414semidirect
155. #509D89semidirect
176. C2×D8C2×D89semidirect
183. SD32C2×D89semidirect
185. D16C2×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×#156680312
#135×D892
#191520412
#191520382
#191520372
#191520342
#191520322
#191520292
#191520272
M32×D892
#509×C892
#341489