Finite Group Databasebeta

← #31818199

Subgroups — #31818199

Order 17792.

460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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#22581764C212yesmaximal, complemented
2#22581763C212yesmaximal, complemented
3#22581325C211yesmaximal, characteristic, complemented
4#22581215C212yesmaximal, complemented
5#22581214C212yesmaximal, complemented
6#22581137C212yesmaximal, complemented
7#22581120C211yesmaximal, characteristic, complemented
8#22581067C212yesmaximal, complemented
9#453×C139C211yesmaximal, characteristic, complemented
10#17984889C2212yes—
11#17984887C2211yescharacteristic, complemented
12#17984875C2212yescomplemented
13#17984872—22no—
14#17984872C2212yescomplemented
15#17984871—22no—
16#17984868—22no—
17#17984868C2212yes—
18#17984866—22no—
19#17984862—22no—
20#17984862C2212yes—
21#17984861—22no—
22C2×#14555773—22no—
23C2×#14555773C2212yescomplemented
24C2×#14555773C2212yescomplemented
25SD16×D139—22no—
26#17984850C2212yescomplemented
27#17984849C2212yescomplemented
28#17984842C2211yescharacteristic, complemented
29#17984777C2212yescomplemented
30#17984770C2212yescomplemented
31#17984760C2212yescomplemented
32#17984759C2211yescharacteristic, complemented
33C4×C139⋊C8C2211yescharacteristic, complemented
34H(5,𝔽2)×C139C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C139C2212yes—
36#127×C139C2211yescharacteristic
37#104×C139C2212yescomplemented
38#100×C139C2211yescharacteristic, complemented
39#14555785—22no—
40#14555785C2312yes—
41#14555784—22no—
42#14555784—22no—
43#14555784—42no—
44C2×Dic278—22no—
45C2×Dic278C2312yes—
46Q8×D139—22no—
47C2×C22⋊D139—41no—
48D4×D139—22no—
49Dic556—22no—
50#14555775—22no—
51#14555775D412yescomplemented
52#14555774—22no—
53#14555773—22no—
54#14555773—22no—
55#14555773—22no—
56#14555773—22no—
57#14555773—22no—
58#14555773—22no—
59#14555773D412yescomplemented
60#14555772D412yescomplemented
61#14555770—22no—
62#14555770D412yescomplemented
63#14555769—22no—
64#14555769C2312yes—
65#14555768—22no—
66C2×C139⋊C8—22no—
67C2×C139⋊C8C2312yes—
68C8×D139—22no—
69C4⋊Dic139—41no—
70#41×C139—22no—
71#41×C139C2312yes—
72C2×D4×C139—22no—
73C2×D4×C139—41no—
74C2×D4×C139—41no—
75C2×D4×C139C2311yescharacteristic
76C2×D4×C139C2311yescharacteristic
77SD16×C139—22no—
78D8×C139—22no—
79M16×C139C2312yes—
80C42×C139C2311yescharacteristic
81C22×D139—41no—
82Dic278—22no—
83Dic278—22no—
84Dic278—42no—
85Dic278C2×D412yes—
86D556C2×D412yes—
87C22⋊D139—22no—
88C22⋊D139—42no—
89C22⋊D139—42no—
90C2×Dic139—22no—
91C2×Dic139—41no—
92C2×Dic139—42no—
93C4×D139—22no—
94C4×D139—42no—
95C139⋊C8—22no—
96C139⋊C8C2×D412yes—
97C139⋊C8C2×D412yes—
98C23×C139—21no—
99C23×C139—21no—
100C23×C139—41no—
101Q8×C139C2×D412yes—
102D4×C139—22no—
103D4×C139—22no—
104D4×C139—22no—
105D4×C139—42no—
106D4×C139—82no—
107D4×C139C2×D412yes—
108C2×C4×C139—21no—
109C2×C4×C139—22no—
110C2×C4×C139—41no—
111C2×C4×C139C2411yescharacteristic
112C8×C139—22no—
113C22×C139—22no—
114C22×C139—41no—
115C22×C139—41no—
116C22×C139—81no—
117C22×C139—81no—
118C22×C139—161no—
119C22×C139H(5,𝔽2)11yescharacteristic
120C2×D139—22no—
121C2×D139—161no—
122C4×C139—22no—
123C4×C139—22no—
124C4×C139C22×D412yes—
125Dic139—22no—
126Dic139—42no—
127C2×C139—21no—
128C2×C139—42no—
129C2×C139—81no—
130C2×C139—81no—
131C2×C139D4211yescharacteristic
132D139—42no—
133C139#329111yescharacteristic, complemented, Sylow
134#3291—1391nomaximal, Sylow
135#577—1392no—
136#577—1392no—
137#492—1391no—
138#471—1392no—
139#471—1392no—
140#456—1392no—
141#453—1391no—
142#453D13911yescharacteristic, complemented
143#443—1392no—
1442−1+4—1392no—
145H(5,𝔽2)—1391no—
146H(5,𝔽2)C2×D13911yescharacteristic, complemented
147#137—2782no—
148#137—2782no—
149#137—1392no—
150#137—1392no—
151AGL(1,ℤ/8)—2782no—
152AGL(1,ℤ/8)—2782no—
153AGL(1,ℤ/8)—1392no—
154AGL(1,ℤ/8)C2×D13912yes—
155#135—2782no—
156#135—2782no—
157#135—1392no—
158C2×SD16—2782no—
159C2×SD16—2782no—
160C2×SD16—1392no—
161C2×SD16—1392no—
162#131—1392no—
163#131—1392no—
164C4⋊Q8—1391no—
165#127C2×D13911yescharacteristic
166#108—1392no—
167#104—1392no—
168#104C2×D13912yescomplemented
169#101—1392no—
170#100—1391no—
171#100C2×D13911yescharacteristic, complemented
172C4×C8—1391no—
173#41—22no—
174#41—2782no—
175#41—2782no—
176#41—2782no—
177#41—5562no—
178#41—1392no—
179#41C22×D13912yes—
180C2×Q8—2782no—
181C2×Q8—2782no—
182C2×Q8—1392no—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—2782no—
187C2×D4—5561no—
188C2×D4C22×D13911yescharacteristic
189C2×D4C22×D13911yescharacteristic
190Q16—2782no—
191Q16—2782no—
192Q16—1392no—
193SD16—22no—
194SD16—2782no—
195SD16—2782no—
196SD16—2782no—
197SD16—2782no—
198SD16—2782no—
199SD16—2782no—
200SD16—2782no—
201SD16—1392no—
202SD16—1392no—
203D8—22no—
204D8—2782no—
205D8—1392no—
206M16—2782no—
207M16—2782no—
208M16—1392no—
209M16C22×D13912yes—
210C2×C8—2782no—
211C2×C8—2782no—
212C2×C8—1392no—
213C4⋊C4—5561no—
214C42C22×D13911yescharacteristic
215C23—21no—
216C23—21no—
217C23—41no—
218C23—5561no—
219Q8—2782no—
220Q8—2782no—
221Q8—5562no—
222Q8—1392no—
223Q8D4×D13912yes—
224D4—22no—
225D4—22no—
226D4—22no—
227D4—42no—
228D4—82no—
229D4—2782no—
230D4—5562no—
231D4—5562no—
232D4—1392no—
233D4D4×D13912yes—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—2782no—
238C2×C4—2782no—
239C2×C4—5562no—
240C2×C4—5561no—
241C2×C4—5562no—
242C2×C4C23×D13911yescharacteristic
243C8—22no—
244C8—2782no—
245C8—1392no—
246C8—1392no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—81no—
251C22—81no—
252C22—161no—
253C22—2782no—
254C22—22241no—
255C22#1798488711yescharacteristic
256C4—22no—
257C4—22no—
258C4—2782no—
259C4—5562no—
260C4C2×D4×D13912yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—81no—
265C2—5562no—
266C2#2258158511yescharacteristic
subgroupG/H
centerC2#22581585
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#453×C139C2
socleC2×C139D42
hypercenter#453D139
hypocenterC139#3291
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #22581764C2semidirect
2. #22581763C2semidirect
3. #22581325C2semidirect
4. #22581215C2semidirect
5. #22581214C2semidirect
6. #22581137C2semidirect
7. #22581120C2semidirect
8. #22581067C2semidirect
9. #453×C139C2semidirect
11. #17984887C22semidirect
12. #17984875C22semidirect
14. #17984872C22semidirect
23. C2×#14555773C22semidirect
24. C2×#14555773C22semidirect
26. #17984850C22semidirect
27. #17984849C22semidirect
28. #17984842C22semidirect
29. #17984777C22semidirect
30. #17984770C22semidirect
31. #17984760C22semidirect
32. #17984759C22semidirect
33. C4×C139⋊C8C22semidirect
34. H(5,𝔽2)×C139C22semidirect
37. #104×C139C22semidirect
38. #100×C139C22semidirect
51. #14555775D4semidirect
59. #14555773D4semidirect
60. #14555772D4semidirect
62. #14555770D4semidirect
133. C139#3291semidirect
142. #453D139semidirect
146. H(5,𝔽2)C2×D139semidirect
168. #104C2×D139semidirect
171. #100C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225817642
#225817632
#225813252
#225812152
#225812142
#225811372
#225811202
#225810672
#453×C1392
#3291139