Finite Group Databasebeta

← #31818219

Subgroups — #31818219

Order 17792.

494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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#22581608C211yesmaximal, characteristic, complemented
2D4×D556C211yesmaximal, characteristic, complemented
3#22581300C211yesmaximal, characteristic, complemented
4#22581268C212yesmaximal, complemented
5#22581233C211yesmaximal, characteristic, complemented
6#22581188C212yesmaximal, complemented
7#22581148C211yesmaximal, characteristic, complemented
8#22581085C212yesmaximal, complemented
9C8×D556C211yesmaximal, characteristic, complemented
10#102×D139C212yesmaximal, complemented
11C4×D8×C139C211yesmaximal, characteristic, complemented
12C2×#14555785—21no—
13C22×D556—21no—
14C2×D4×D139C2212yes—
15C2×#14555770C2212yescomplemented
16C2×C8×D139C2212yescomplemented
17#17984842C2211yescharacteristic, complemented
18#17984839C2211yescharacteristic
19#17984824—22no—
20#17984821—21no—
21#17984817C2212yes—
22#17984816—21no—
23#17984813C2212yescomplemented
24#17984812—22no—
25C4×D556C2211yescharacteristic
26C4⋊C4×D139C2212yescomplemented
27#17984775C2212yescomplemented
28C4⋊(C139⋊C8)C2211yescharacteristic, complemented
29#17984764C2212yescomplemented
30#17984764C2212yescomplemented
31#17984763C2212yes—
32#17984762C2212yescomplemented
33(C2×D139)⋊C8C2212yescomplemented
34C2×D8×C139C2211yescharacteristic
35C4×D4×C139C2211yescharacteristic
36C4×D4×C139C2211yescharacteristic, complemented
37#107×C139C2211yescharacteristic, complemented
38#102×C139C2211yescharacteristic
39#102×C139C2211yescharacteristic, complemented
40C4×C8×C139C2211yescharacteristic, complemented
41C23×D139—22no—
42#14555785—44no—
43C2×Dic278—21no—
44C2×D556—22no—
45C2×D556—21no—
46C2×D556—21no—
47C2×D556—44no—
48C2×D556D411yescharacteristic
49C2×D556C2312yes—
50C2×C22⋊D139—22no—
51C2×C22⋊D139—22no—
52D4×D139—24no—
53D4×D139—42no—
54C2×C4×D139—22no—
55C2×C4×D139C2312yes—
56#14555770—42no—
57C2×C139⋊C8C2312yes—
58C8×D139—42no—
59C4⋊Dic139—21no—
60C4⋊Dic139D411yescharacteristic
61C4⋊Dic139C2312yes—
62Dic139⋊C4—22no—
63C22⋊Dic139—22no—
64(C2×D139)⋊C4—22no—
65(C2×D139)⋊C4D412yes—
66C2×D4×C139C2311yescharacteristic
67C2×D4×C139C2311yescharacteristic
68C22×C4×C139—21no—
69C22×C4×C139—21no—
70D8×C139—22no—
71C2×C8×C139C2311yescharacteristic
72C2×C8×C139C2311yescharacteristic
73C4⋊C4×C139C2311yescharacteristic
74C4⋊C4×C139C2311yescharacteristic
75C22⋊C4×C139—21no—
76C22⋊C4×C139—21no—
77C42×C139C2311yescharacteristic
78C22×D139—22no—
79C22×D139—44no—
80C22×D139—44no—
81C22×D139—82no—
82C22×D139C2×D412yes—
83Dic278—42no—
84D556—22no—
85D556—22no—
86D556—44no—
87D556—42no—
88D556—81no—
89D556D814yescomplemented
90C22⋊D139—44no—
91C22⋊D139—44no—
92C2×Dic139—22no—
93C2×Dic139C2×D412yes—
94C4×D139—22no—
95C4×D139—22no—
96C4×D139—44no—
97C139⋊C8—22no—
98C23×C139—21no—
99C23×C139—21no—
100D4×C139—21no—
101D4×C139—21no—
102D4×C139—21no—
103D4×C139#4112yescomplemented
104C2×C4×C139—21no—
105C2×C4×C139—21no—
106C2×C4×C139—42no—
107C2×C4×C139—42no—
108C2×C4×C139C2×D411yescharacteristic
109C2×C4×C139C2×D411yescharacteristic
110C2×C4×C139C2411yescharacteristic
111C8×C139—21no—
112C8×C139—21no—
113C22×C139—22no—
114C22×C139—41no—
115C22×C139—41no—
116C22×C139—41no—
117C22×C139—41no—
118C22×C139—41no—
119C22×C139C22×D411yescharacteristic
120C2×D139—22no—
121C2×D139—22no—
122C2×D139—42no—
123C2×D139—42no—
124C2×D139—42no—
125C2×D139—88no—
126C2×D139C2×D814yes—
127C4×C139—21no—
128C4×C139—41no—
129C4×C139—41no—
130C4×C139C2×D812yes—
131C4×C139C2×#4111yescharacteristic
132C4×C139H(5,𝔽2)11yescharacteristic
133Dic139—22no—
134Dic139—42no—
135C2×C139—42no—
136C2×C139—81no—
137C2×C139#54611yescharacteristic
138C2×C139C22×D811yescharacteristic
139C2×C139#57711yescharacteristic
140D139—24no—
141D139—82no—
142C139#329411yescharacteristic, complemented, Sylow
143#3294—1391nomaximal, Sylow
144#547—1391no—
145D42—1391no—
146#486—1391no—
147#480—1392no—
148#474—1391no—
149#466—1392no—
150#459—1391no—
151#447—1392no—
152C4×D8D13911yescharacteristic, complemented
153C8×D4—1391no—
154C2×#102—1392no—
155C2×#41—2781no—
156C22×D4—2781no—
157C22×D4—1392no—
158C2×D8—1392no—
159C2×D8C2×D13911yescharacteristic
160C22×C8—1392no—
161C4⋊Q8—1391no—
162#127—1391no—
163#123—2782no—
164C22⋊Q8—2781no—
165#121—2781no—
166#121—1392no—
167#121—1392no—
168#120—2782no—
169C4×D4—1391no—
170C4×D4C2×D13911yescharacteristic
171C4×D4C2×D13911yescharacteristic, complemented
172C2×C4⋊C4—1392no—
173#107—1392no—
174#107C2×D13911yescharacteristic, complemented
175C4⋊C8—1391no—
176#102—1392no—
177#102—1392no—
178#102—1392no—
179#102—1392no—
180#102C2×D13911yescharacteristic
181#102C2×D13911yescharacteristic, complemented
182C22⋊C8—1392no—
183C4×C8C2×D13911yescharacteristic, complemented
184C24—2782no—
185#41—5564no—
186C2×Q8—2781no—
187C2×D4—2782no—
188C2×D4—2784no—
189C2×D4—2782no—
190C2×D4—2782no—
191C2×D4—2781no—
192C2×D4—2781no—
193C2×D4—5564no—
194C2×D4—5562no—
195C2×D4—1391no—
196C2×D4—1392no—
197C2×D4C22×D13911yescharacteristic
198C2×D4C22×D13911yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—2782no—
202C22×C4—1392no—
203D8—22no—
204D8—5562no—
205C2×C8—5562no—
206C2×C8—1392no—
207C2×C8C22×D13911yescharacteristic
208C2×C8C22×D13911yescharacteristic
209C4⋊C4—2782no—
210C4⋊C4—2781no—
211C4⋊C4—1392no—
212C4⋊C4—1391no—
213C4⋊C4C22×D13911yescharacteristic
214C4⋊C4C22×D13911yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—2782no—
218C22⋊C4—2782no—
219C22⋊C4—1392no—
220C42C22×D13911yescharacteristic
221C23—21no—
222C23—21no—
223C23—2782no—
224C23—5564no—
225C23—5564no—
226C23—11122no—
227C23—1392no—
228Q8—5562no—
229D4—21no—
230D4—21no—
231D4—21no—
232D4—2782no—
233D4—2782no—
234D4—5564no—
235D4—5564no—
236D4—5564no—
237D4—5562no—
238D4—11121no—
239D4—1394no—
240D4#1455578512yescomplemented
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—2782no—
246C2×C4—2782no—
247C2×C4—2782no—
248C2×C4—5564no—
249C2×C4—1392no—
250C2×C4D4×D13911yescharacteristic
251C2×C4D4×D13911yescharacteristic
252C2×C4C23×D13911yescharacteristic
253C8—21no—
254C8—21no—
255C8—2782no—
256C22—22no—
257C22—41no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—2782no—
263C22—2782no—
264C22—5562no—
265C22—5562no—
266C22—5562no—
267C22—11128no—
268C22—1394no—
269C22C2×D4×D13911yescharacteristic
270C4—21no—
271C4—41no—
272C4—41no—
273C4—2782no—
274C4—5562no—
275C4D8×D13912yes—
276C4C2×#1455578511yescharacteristic
277C4#1798488811yescharacteristic
278C2—42no—
279C2—81no—
280C2—2784no—
281C2—11122no—
282C2#2258159911yescharacteristic
283C2C2×D8×D13911yescharacteristic
284C2#2258176011yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC4×D8×C139C2
socleC22×C139C22×D4
hypercenterC4×D8D139
hypocenterC139#3294
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #22581608C2semidirect
2. D4×D556C2semidirect
3. #22581300C2semidirect
4. #22581268C2semidirect
5. #22581233C2semidirect
6. #22581188C2semidirect
7. #22581148C2semidirect
8. #22581085C2semidirect
9. C8×D556C2semidirect
10. #102×D139C2semidirect
11. C4×D8×C139C2semidirect
15. C2×#14555770C22semidirect
16. C2×C8×D139C22semidirect
17. #17984842C22semidirect
23. #17984813C22semidirect
26. C4⋊C4×D139C22semidirect
27. #17984775C22semidirect
28. C4⋊(C139⋊C8)C22semidirect
29. #17984764C22semidirect
30. #17984764C22semidirect
32. #17984762C22semidirect
33. (C2×D139)⋊C8C22semidirect
36. C4×D4×C139C22semidirect
37. #107×C139C22semidirect
39. #102×C139C22semidirect
40. C4×C8×C139C22semidirect
89. D556D8semidirect
103. D4×C139#41semidirect
142. C139#3294semidirect
152. C4×D8D139semidirect
171. C4×D4C2×D139semidirect
174. #107C2×D139semidirect
181. #102C2×D139semidirect
183. C4×C8C2×D139semidirect
240. D4#14555785semidirect

Maximal subgroups

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

subgroupindex
#225816082
D4×D5562
#225813002
#225812682
#225812332
#225811882
#225811482
#225810852
C8×D5562
#102×D1392
C4×D8×C1392
#3294139