Finite Group Databasebeta

← #31819539

Subgroups — #31819539

Order 17792.

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×#17984865C211yesmaximal, characteristic, complemented
2#135×D139C211yesmaximal, characteristic, complemented
3#22581395C212yesmaximal, complemented
4#22581394C211yesmaximal, characteristic, complemented
5#22581391C211yesmaximal, characteristic, complemented
6#22581390C212yesmaximal, complemented
7#22581388C211yesmaximal, characteristic, complemented
8#22581386C212yesmaximal, complemented
9#22581384C212yesmaximal, complemented
10M32×D139C211yesmaximal, characteristic, complemented
11#510×C139C211yesmaximal, characteristic, complemented
12C2×#14555786—21no—
13#41×D139—21no—
14#17984865—21no—
15#17984865—21no—
16#17984865C2212yes—
17#17984865C2212yescomplemented
18#17984865C2211yescharacteristic, complemented
19#17984864C2211yescharacteristic
20#17984863—21no—
21#17984862—21no—
22#17984861C2211yescharacteristic, complemented
23Q16×D139C2211yescharacteristic, complemented
24C2×#14555772—21no—
25SD16×D139—21no—
26C2×D1112C2211yescharacteristic, complemented
27D8×D139C2211yescharacteristic, complemented
28C2×C8×D139C2211yescharacteristic
29#17984788C2212yescomplemented
30#17984787C2212yescomplemented
31#17984785C2212yescomplemented
32#17984785C2212yescomplemented
33D2224C2212yescomplemented
34#17984783C2212yescomplemented
35#17984782C2211yescharacteristic, complemented
36#17984781C2212yescomplemented
37C16×D139C2212yescomplemented
38#135×C139C2211yescharacteristic
39C2×Q16×C139C2211yescharacteristic, complemented
40Q32×C139C2212yescomplemented
41SD32×C139C2212yescomplemented
42M32×C139C2211yescharacteristic, complemented
43#14555786—21no—
44#14555786—22no—
45#14555786—22no—
46#14555786—41no—
47#14555786—41no—
48#14555785—21no—
49#14555785—41no—
50#14555784—21no—
51#14555784—41no—
52Q8×D139—21no—
53C2×D556—21no—
54C2×D556—41no—
55D4×D139—21no—
56D4×D139—41no—
57C2×C4×D139—41no—
58C2×C4×D139—41no—
59C2×C4×D139D411yescharacteristic
60Dic556C2311yescharacteristic
61#14555775—21no—
62#14555774—21no—
63#14555773—21no—
64#14555772—21no—
65#14555772—22no—
66#14555772—22no—
67D1112—21no—
68D1112C2312yes—
69D1112C2311yescharacteristic
70#14555770—21no—
71C2×C139⋊C8D411yescharacteristic
72C8×D139D411yescharacteristic
73C8×D139D411yescharacteristic
74C8×D139C2311yescharacteristic
75C8×D139C2311yescharacteristic
76C139⋊C16C2312yes—
77#41×C139—21no—
78C2×Q8×C139—21no—
79Q16×C139—21no—
80Q16×C139C2311yescharacteristic
81Q16×C139C2312yes—
82SD16×C139—21no—
83D8×C139C2311yescharacteristic
84C2×C8×C139C2311yescharacteristic
85C16×C139C2312yes—
86C22×D139—41no—
87C22×D139—41no—
88C22×D139D811yescharacteristic
89Dic278—21no—
90Dic278—41no—
91D556—21no—
92D556—22no—
93D556—41no—
94D556—42no—
95D556—42no—
96D556—41no—
97C22⋊D139—41no—
98C22⋊D139—41no—
99C22⋊D139—41no—
100C2×Dic139—41no—
101C2×Dic139D811yescharacteristic
102C4×D139—41no—
103C4×D139—41no—
104C4×D139—41no—
105C4×D139—42no—
106C4×D139—42no—
107C4×D139D811yescharacteristic
108C4×D139D811yescharacteristic
109C4×D139C2×D411yescharacteristic
110C4×D139C2×D411yescharacteristic
111C139⋊C8C2×D411yescharacteristic
112C139⋊C8C2×D411yescharacteristic
113Q8×C139—21no—
114Q8×C139—22no—
115Q8×C139—41no—
116D4×C139—21no—
117D4×C139—41no—
118C2×C4×C139—41no—
119C2×C4×C139—41no—
120C2×C4×C139C2×D411yescharacteristic
121C8×C139C2×D411yescharacteristic
122C8×C139C2411yescharacteristic
123C22×C139—41no—
124C22×C139C2×D811yescharacteristic
125C2×D139—41no—
126C2×D139—41no—
127C2×D139—42no—
128C2×D139—82no—
129C2×D139—82no—
130C2×D139C2×D811yescharacteristic
131C2×D139C2×D811yescharacteristic
132C4×C139—41no—
133C4×C139—42no—
134C4×C139C2×D811yescharacteristic
135C4×C139C22×D411yescharacteristic
136Dic139—41no—
137Dic139C2×D811yescharacteristic
138Dic139C2×D811yescharacteristic
139C2×C139—21no—
140C2×C139—81no—
141C2×C139C22×D811yescharacteristic
142D139—21no—
143D139—21no—
144D139—81no—
145D139—82no—
146C139#341411yescharacteristic, complemented, Sylow
147#3414—1391nomaximal, Sylow
148C2×#135—1391no—
149C2×#135—1391no—
150#510—1391no—
151#510—1392no—
152#510D13911yescharacteristic, complemented
153#509—1391no—
154#509—1392no—
155#509—1391no—
156#508—1392no—
157#508—1392no—
158C2×M32—1391no—
159C2×#41—2781no—
160C2×#41—2781no—
161#135—2781no—
162#135—2781no—
163#135—2781no—
164#135—2781no—
165#135—1392no—
166#135—1391no—
167#135—1392no—
168#135—1391no—
169#135—1391no—
170#135C2×D13911yescharacteristic
171C2×Q16—1391no—
172C2×Q16C2×D13911yescharacteristic, complemented
173C2×SD16—2781no—
174C2×SD16—2781no—
175C2×D8—1391no—
176C2×D8—1391no—
177C22×C8—1391no—
178Q32—1392no—
179Q32C2×D13912yescomplemented
180SD32—1392no—
181SD32—1392no—
182SD32—1392no—
183SD32C2×D13912yescomplemented
184D16—1392no—
185D16—1392no—
186M32—1391no—
187M32—1392no—
188M32C2×D13911yescharacteristic, complemented
189C2×C16—1392no—
190#41—21no—
191#41—2781no—
192#41—2782no—
193#41—2781no—
194#41—2782no—
195#41—2781no—
196#41—5561no—
197#41—5561no—
198#41—5561no—
199#41—5561no—
200C2×Q8—21no—
201C2×Q8—2781no—
202C2×D4—2781no—
203C2×D4—2781no—
204C2×D4—5561no—
205C2×D4—5561no—
206C22×C4—5561no—
207C22×C4—5561no—
208C22×C4—1391no—
209Q16—21no—
210Q16—2781no—
211Q16—1391no—
212Q16C22×D13911yescharacteristic
213Q16C22×D13912yes—
214SD16—21no—
215SD16—2781no—
216SD16—2782no—
217SD16—2781no—
218SD16—2782no—
219SD16—2781no—
220D8—2781no—
221D8—2781no—
222D8—1392no—
223D8—1391no—
224D8C22×D13911yescharacteristic
225C2×C8—1391no—
226C2×C8—1391no—
227C2×C8—1391no—
228C2×C8—1391no—
229C2×C8—1391no—
230C2×C8C22×D13911yescharacteristic
231C16—1392no—
232C16C22×D13912yes—
233C23—5561no—
234C23—5561no—
235C23—1391no—
236Q8—21no—
237Q8—22no—
238Q8—41no—
239Q8—2781no—
240Q8—5561no—
241D4—21no—
242D4—41no—
243D4—2781no—
244D4—2782no—
245D4—5561no—
246D4—5562no—
247D4—5562no—
248D4—5561no—
249D4—5561no—
250D4—5561no—
251D4—5561no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—5561no—
255C2×C4—5561no—
256C2×C4—5562no—
257C2×C4—5562no—
258C2×C4—5561no—
259C2×C4—5561no—
260C2×C4—1391no—
261C2×C4—1391no—
262C2×C4—1391no—
263C2×C4—1391no—
264C2×C4—1391no—
265C2×C4D4×D13911yescharacteristic
266C8—1391no—
267C8—1391no—
268C8D4×D13911yescharacteristic
269C8C23×D13911yescharacteristic
270C22—41no—
271C22—5561no—
272C22—5562no—
273C22—5561no—
274C22—11122no—
275C22—11122no—
276C22—1391no—
277C22—1391no—
278C22D8×D13911yescharacteristic
279C4—41no—
280C4—42no—
281C4—5561no—
282C4—1391no—
283C4—1391no—
284C4D8×D13911yescharacteristic
285C4C2×D4×D13911yescharacteristic
286C2—21no—
287C2—81no—
288C2—2781no—
289C2—2781no—
290C2—11122no—
291C2—11121no—
292C2C2×D8×D13911yescharacteristic
subgroupG/H
centerC2C2×D8×D139
commutator, cosocleC8×C139C24
FrattiniC8C23×D139
Fitting#510×C139C2
socleC2×C139C22×D8
hypercenter#510D139
hypocenterC139#3414
LCSG ▷ C8×C139 ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
1. C2×#17984865C2semidirect
2. #135×D139C2semidirect
3. #22581395C2semidirect
4. #22581394C2semidirect
5. #22581391C2semidirect
6. #22581390C2semidirect
7. #22581388C2semidirect
8. #22581386C2semidirect
9. #22581384C2semidirect
10. M32×D139C2semidirect
11. #510×C139C2semidirect
17. #17984865C22semidirect
18. #17984865C22semidirect
22. #17984861C22semidirect
23. Q16×D139C22semidirect
26. C2×D1112C22semidirect
27. D8×D139C22semidirect
29. #17984788C22semidirect
30. #17984787C22semidirect
31. #17984785C22semidirect
32. #17984785C22semidirect
33. D2224C22semidirect
34. #17984783C22semidirect
35. #17984782C22semidirect
36. #17984781C22semidirect
37. C16×D139C22semidirect
39. C2×Q16×C139C22semidirect
40. Q32×C139C22semidirect
41. SD32×C139C22semidirect
42. M32×C139C22semidirect
146. C139#3414semidirect
152. #510D139semidirect
172. C2×Q16C2×D139semidirect
179. Q32C2×D139semidirect
183. SD32C2×D139semidirect
188. M32C2×D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848652
#135×D1392
#225813952
#225813942
#225813912
#225813902
#225813882
#225813862
#225813842
M32×D1392
#510×C1392
#3414139