Finite Group Databasebeta

← #31816542

Subgroups — #31816542

Order 17792.

450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#22581487C211yesmaximal, characteristic, complemented
2#22581283C211yesmaximal, characteristic, complemented
3#22581266C211yesmaximal, characteristic, complemented
4#22581253C212yesmaximal, complemented
5#22581168C212yesmaximal, complemented
6#22581104C211yesmaximal, characteristic, complemented
7#22581087C211yesmaximal, characteristic
8#22581063C212yesmaximal, complemented
9#22581053C212yesmaximal, complemented
10#22581010C211yesmaximal, characteristic, complemented
11C2×C4×D4×C139C211yesmaximal, characteristic, complemented
12C2×#14555773C2212yes—
13C2×#14555770C2212yes—
14#17984836—21no—
15#17984834C2211yescharacteristic, complemented
16#17984830C2211yescharacteristic, complemented
17#17984825—21no—
18#17984821C2211yescharacteristic
19#17984816C2211yescharacteristic
20C4×Dic278C2211yescharacteristic, complemented
21C4×D556C2211yescharacteristic, complemented
22C4×C22⋊D139—21no—
23#17984799—21no—
24#17984775C2212yescomplemented
25#17984773C2212yescomplemented
26C4⋊(C139⋊C8)C2212yescomplemented
27#17984765C2212yescomplemented
28#17984763C2212yes—
29#17984763C2212yes—
30#17984762C2212yescomplemented
31C22⋊(C139⋊C8)C2211yescharacteristic
32C22⋊(C139⋊C8)C2211yescharacteristic
33#17984753C2212yescomplemented
34C22×D4×C139C2211yescharacteristic
35C23×C4×C139—21no—
36C4×D4×C139—21no—
37C4×D4×C139—21no—
38C4×D4×C139C2212yes—
39C4×D4×C139C2212yes—
40C2×C4⋊C4×C139C2211yescharacteristic
41C2×C22⋊C4×C139—21no—
42C2×C42×C139C2211yescharacteristic
43C2×Dic278C2311yescharacteristic
44C2×D556C2311yescharacteristic
45C2×C22⋊D139—21no—
46C2×C4×D139—21no—
47#14555773—24no—
48#14555770—24no—
49C2×C139⋊C8C2312yes—
50C2×C139⋊C8C2312yes—
51C4⋊Dic139C2311yescharacteristic
52C4⋊Dic139C2311yescharacteristic
53Dic139⋊C4—21no—
54Dic139⋊C4—21no—
55Dic139⋊C4—21no—
56Dic139⋊C4—21no—
57C22⋊Dic139—21no—
58(C2×D139)⋊C4—21no—
59(C2×D139)⋊C4—21no—
60(C2×D139)⋊C4—21no—
61(C2×D139)⋊C4—21no—
62C4×Dic139—21no—
63C24×C139—21no—
64C2×D4×C139—24no—
65C2×D4×C139—21no—
66C2×D4×C139C2312yes—
67C22×C4×C139—21no—
68C22×C4×C139—22no—
69C22×C4×C139—22no—
70C22×C4×C139—44no—
71C22×C4×C139D411yescharacteristic
72C22×C4×C139D411yescharacteristic
73C22×C4×C139C2311yescharacteristic
74C4⋊C4×C139—21no—
75C4⋊C4×C139C2312yes—
76C22⋊C4×C139—22no—
77C22⋊C4×C139—22no—
78C42×C139D411yescharacteristic
79C42×C139D411yescharacteristic
80C42×C139C2311yescharacteristic
81C42×C139C2311yescharacteristic
82C22×D139—21no—
83Dic278—22no—
84D556—22no—
85C22⋊D139—42no—
86C2×Dic139—21no—
87C2×Dic139—21no—
88C2×Dic139—21no—
89C4×D139—42no—
90C139⋊C8—22no—
91C139⋊C8—22no—
92C23×C139—24no—
93C23×C139—22no—
94C23×C139—42no—
95C23×C139—42no—
96C23×C139C2×D411yescharacteristic
97D4×C139—24no—
98D4×C139—22no—
99D4×C139#4114yes—
100C2×C4×C139—22no—
101C2×C4×C139—22no—
102C2×C4×C139—22no—
103C2×C4×C139—41no—
104C2×C4×C139—44no—
105C2×C4×C139—44no—
106C2×C4×C139—42no—
107C2×C4×C139C2×D411yescharacteristic
108C2×C4×C139C2×D411yescharacteristic
109C2×C4×C139C2×D411yescharacteristic
110C2×C4×C139C2×D411yescharacteristic
111C2×C4×C139C2×D411yescharacteristic
112C2×C4×C139C2411yescharacteristic
113C22×C139—21no—
114C22×C139—21no—
115C22×C139—24no—
116C22×C139—48no—
117C22×C139—42no—
118C22×C139—42no—
119C22×C139AGL(1,ℤ/8)12yes—
120C22×C139C22×D411yescharacteristic
121C2×D139—41no—
122C2×D139—41no—
123C2×D139—41no—
124C4×C139—21no—
125C4×C139—21no—
126C4×C139—21no—
127C4×C139—21no—
128C4×C139—21no—
129C4×C139—42no—
130C4×C139C2×#4112yes—
131Dic139—41no—
132Dic139—41no—
133Dic139—41no—
134C2×C139—22no—
135C2×C139—44no—
136C2×C139#52511yescharacteristic
137C2×C139C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C139#57511yescharacteristic
139D139—81no—
140C139#311411yescharacteristic, complemented, Sylow
141#3114—1391nomaximal, Sylow
142#529—1391no—
143C2×C4×D4D13911yescharacteristic, complemented
144#483—1391no—
145#480—1391no—
146#478—1392no—
147#463—1392no—
148#450—1391no—
149#447—1391no—
150#442—1392no—
151#440—1392no—
152#432—1391no—
153C22×D4C2×D13911yescharacteristic
154C23×C4—21no—
155C2×SD16—1392no—
156C2×D8—1392no—
157#126—2781no—
158#125—1391no—
159#124—1391no—
160#123—2781no—
161C22⋊Q8—1391no—
162#121—1391no—
163C4×Q8—1391no—
164C4×D4—21no—
165C4×D4—21no—
166C4×D4—2781no—
167C4×D4—1391no—
168C4×D4C2×D13912yes—
169C4×D4C2×D13912yes—
170#117—2781no—
171C2×C4⋊C4C2×D13911yescharacteristic
172C2×C22⋊C4—21no—
173C2×C42C2×D13911yescharacteristic
174#107—1392no—
175#106—1392no—
176C4⋊C8—1392no—
177#103—1392no—
178#102—1392no—
179#102—1392no—
180#102—1392no—
181C22⋊C8—1391no—
182C22⋊C8—1391no—
183#97—1392no—
184C24—21no—
185C2×Q8—1391no—
186C2×D4—24no—
187C2×D4—21no—
188C2×D4—2781no—
189C2×D4—1391no—
190C2×D4C22×D13912yes—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—44no—
195C22×C4—2781no—
196C22×C4C22⋊D13911yescharacteristic
197C22×C4C22⋊D13911yescharacteristic
198C22×C4C22×D13911yescharacteristic
199SD16—2784no—
200D8—2784no—
201C2×C8—1392no—
202C2×C8—1392no—
203C4⋊C4—21no—
204C4⋊C4—2781no—
205C4⋊C4—2781no—
206C4⋊C4—2781no—
207C4⋊C4—2781no—
208C4⋊C4—1391no—
209C4⋊C4—1391no—
210C4⋊C4C22×D13912yes—
211C22⋊C4—22no—
212C22⋊C4—22no—
213C22⋊C4—2781no—
214C22⋊C4—2781no—
215C22⋊C4—2781no—
216C22⋊C4—2781no—
217C22⋊C4—2781no—
218C42—2781no—
219C42C22⋊D13911yescharacteristic
220C42C22⋊D13911yescharacteristic
221C42C22×D13911yescharacteristic
222C42C22×D13911yescharacteristic
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—2781no—
228C23C2×C22⋊D13911yescharacteristic
229Q8—2782no—
230D4—24no—
231D4—22no—
232D4—2782no—
233D4—5562no—
234D4#1455578514yes—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—44no—
240C2×C4—44no—
241C2×C4—42no—
242C2×C4—2781no—
243C2×C4—2781no—
244C2×C4—2781no—
245C2×C4—5562no—
246C2×C4C2×C22⋊D13911yescharacteristic
247C2×C4C2×C22⋊D13911yescharacteristic
248C2×C4C2×C22⋊D13911yescharacteristic
249C2×C4C2×C22⋊D13911yescharacteristic
250C2×C4C2×C22⋊D13911yescharacteristic
251C2×C4C23×D13911yescharacteristic
252C8—2782no—
253C8—2782no—
254C22—21no—
255C22—21no—
256C22—24no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22—5561no—
261C22—5561no—
262C22—5561no—
263C22#1798486812yes—
264C22C22×C22⋊D13911yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—5561no—
272C4—5561no—
273C4—5561no—
274C4C2×#1455578512yes—
275C2—22no—
276C2—44no—
277C2—11121no—
278C2#2258146411yescharacteristic
279C2C2×#1798486811yescharacteristic
280C2#2258175111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC2×C4×D4×C139C2
socleC22×C139C22×D4
prime radical#22581087C2
hypercenterC2×C4×D4D139
hypocenterC139#3114
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #22581487C2semidirect
2. #22581283C2semidirect
3. #22581266C2semidirect
4. #22581253C2semidirect
5. #22581168C2semidirect
6. #22581104C2semidirect
8. #22581063C2semidirect
9. #22581053C2semidirect
10. #22581010C2semidirect
11. C2×C4×D4×C139C2semidirect
15. #17984834C22semidirect
16. #17984830C22semidirect
20. C4×Dic278C22semidirect
21. C4×D556C22semidirect
24. #17984775C22semidirect
25. #17984773C22semidirect
26. C4⋊(C139⋊C8)C22semidirect
27. #17984765C22semidirect
30. #17984762C22semidirect
33. #17984753C22semidirect
140. C139#3114semidirect
143. C2×C4×D4D139semidirect

Maximal subgroups

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

subgroupindex
#225814872
#225812832
#225812662
#225812532
#225811682
#225811042
#225810872
#225810632
#225810532
#225810102
C2×C4×D4×C1392
#3114139