Finite Group Databasebeta

← #31815253

Subgroups — #31815253

Order 17792.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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×D8×D139C211yesmaximal, characteristic
2#22581425C212yesmaximal, complemented
3#22581066C211yesmaximal, characteristic, complemented
4#22581065C211yesmaximal, characteristic, complemented
5#22581064C211yesmaximal, characteristic, complemented
6C4×#14555770C212yesmaximal, complemented
7#22581033C212yesmaximal, complemented
8#22580988C211yesmaximal, characteristic, complemented
9#22580956C212yesmaximal, complemented
10#22580910C211yesmaximal, characteristic, complemented
11#442×C139C211yesmaximal, characteristic, complemented
12C2×D4×D139C2212yes—
13C2×D1112C2211yescharacteristic
14C2×#14555770C2212yes—
15D8×D139C418yescomplemented
16C2×#14555768C2211yescharacteristic
17C2×C8×D139C2211yescharacteristic
18C4×D556C2212yescomplemented
19D4×Dic139C2212yescomplemented
20#17984804C2212yescomplemented
21C4×C22⋊D139—22no—
22(C22⋊D139)⋊C4—22no—
23#17984800C2212yes—
24#17984799C2211yescharacteristic
25C2×(C2×D139)⋊C4—22no—
26C22⋊C4×D139—22no—
27#17984775C2212yescomplemented
28#17984774C2211yescharacteristic, complemented
29#17984764C2212yescomplemented
30#17984763C2212yescomplemented
31#17984762C2212yescomplemented
32#17984752C2211yescharacteristic, complemented
33C4×C139⋊C8C2211yescharacteristic, complemented
34C8×Dic139C2211yescharacteristic, complemented
35C2×D8×C139C2211yescharacteristic
36C4×D4×C139C2212yescomplemented
37#106×C139C2211yescharacteristic, complemented
38#102×C139C2212yescomplemented
39#97×C139C2211yescharacteristic, complemented
40C23×D139—22no—
41C2×D556C2312yes—
42C2×C22⋊D139—22no—
43D4×D139—24no—
44D4×D139C2×C418yescomplemented
45C22×Dic139—22no—
46C2×C4×D139—22no—
47C2×C4×D139—22no—
48C2×C4×D139C2311yescharacteristic
49D1112C2×C414yescomplemented
50#14555770C2×C418yescomplemented
51#14555768—22no—
52C2×C139⋊C8C2311yescharacteristic
53C2×C139⋊C8C2311yescharacteristic
54C8×D139C2×C414yescomplemented
55C4⋊Dic139C2312yes—
56Dic139⋊C4D412yes—
57C22⋊Dic139—22no—
58(C2×D139)⋊C4—22no—
59(C2×D139)⋊C4—22no—
60(C2×D139)⋊C4—22no—
61(C2×D139)⋊C4D412yes—
62C4×Dic139—22no—
63C4×Dic139C2311yescharacteristic
64C2×D4×C139C2312yes—
65C22×C4×C139—22no—
66D8×C139C2×C414yescomplemented
67C2×C8×C139C2311yescharacteristic
68C2×C8×C139C2311yescharacteristic
69C4⋊C4×C139C2312yes—
70C22⋊C4×C139—22no—
71C42×C139C2311yescharacteristic
72C22×D139—22no—
73C22×D139—28no—
74C22×D139—82no—
75C22×D139—82no—
76C22×D139C2×D411yescharacteristic
77D556—22no—
78D556C22×C414yes—
79C22⋊D139—28no—
80C2×Dic139—22no—
81C2×Dic139—82no—
82C2×Dic139C2×D412yes—
83C2×Dic139C2×D411yescharacteristic
84C4×D139—82no—
85C4×D139—82no—
86C4×D139C22×C412yes—
87C4×D139#4112yes—
88C139⋊C8—21no—
89C139⋊C8C22×C412yes—
90C23×C139—22no—
91D4×C139—22no—
92D4×C139C22×C414yes—
93C2×C4×C139—22no—
94C2×C4×C139—82no—
95C2×C4×C139C2×D412yes—
96C2×C4×C139C2411yescharacteristic
97C8×C139—21no—
98C8×C139C22×C412yes—
99C22×C139—24no—
100C22×C139—42no—
101C22×C139—42no—
102C22×C139C22×D411yescharacteristic
103C2×D139—22no—
104C2×D139—24no—
105C2×D139—42no—
106C2×D139—42no—
107C2×D139—88no—
108C2×D139C4×D412yes—
109C4×C139—22no—
110C4×C139—42no—
111C4×C139C23×C411yescharacteristic
112C4×C139C2×#4111yescharacteristic
113Dic139—22no—
114Dic139—42no—
115Dic139C4×D412yes—
116C2×C139—44no—
117C2×C139C2×C4×D411yescharacteristic
118C2×C139#57612yes—
119D139—22no—
120D139—44no—
121C139#294811yescharacteristic, complemented, Sylow
122#2948—1391nomaximal, Sylow
123C22×D8—1391no—
124#518—1392no—
125#442—1391no—
126#442—1391no—
127#442—1391no—
128#442D13911yescharacteristic, complemented
129C4×D8—1392no—
130C4×D8—1392no—
131#427—1391no—
132#418—1392no—
133#405—1391no—
134C22×D4—1392no—
135C2×D8—1392no—
136C2×D8—1398no—
137C2×D8—1391no—
138C2×D8C2×D13911yescharacteristic
139C2×M16—1391no—
140C22×C8—1391no—
141C4×D4—2782no—
142C4×D4—2782no—
143C4×D4—1392no—
144C4×D4—1392no—
145C4×D4—1392no—
146C4×D4C2×D13912yescomplemented
147#117—1392no—
148#117—1391no—
149C2×C22⋊C4—2782no—
150C2×C22⋊C4—2782no—
151#107—1392no—
152#106—1391no—
153#106C2×D13911yescharacteristic, complemented
154#102—1392no—
155#102—1392no—
156#102—1392no—
157#102C2×D13912yescomplemented
158#97—1391no—
159#97C2×D13911yescharacteristic, complemented
160C4×C8—1391no—
161C4×C8—1391no—
162C24—2782no—
163C2×D4—2784no—
164C2×D4—2782no—
165C2×D4—1398no—
166C2×D4—1392no—
167C2×D4C22×D13912yes—
168C22×C4—22no—
169C22×C4—2782no—
170C22×C4—2782no—
171C22×C4—2782no—
172C22×C4—1391no—
173D8—1398no—
174D8—1394no—
175D8C4×D13914yescomplemented
176M16—2782no—
177C2×C8—1391no—
178C2×C8—1391no—
179C2×C8—1394no—
180C2×C8C22×D13911yescharacteristic
181C2×C8C22×D13911yescharacteristic
182C4⋊C4—1392no—
183C4⋊C4—1392no—
184C4⋊C4C22×D13912yes—
185C22⋊C4—22no—
186C22⋊C4—2782no—
187C22⋊C4—2782no—
188C22⋊C4—2782no—
189C22⋊C4—2782no—
190C22⋊C4—1392no—
191C42—2782no—
192C42—1391no—
193C42C22×D13911yescharacteristic
194C23—22no—
195C23—2788no—
196C23—2782no—
197C23—11122no—
198C23—11122no—
199C23—1391no—
200D4—22no—
201D4—2788no—
202D4—2782no—
203D4—1394no—
204D4C2×C4×D13914yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—2782no—
208C2×C4—11122no—
209C2×C4—11122no—
210C2×C4—11122no—
211C2×C4—1392no—
212C2×C4—1391no—
213C2×C4—1392no—
214C2×C4—1392no—
215C2×C4D4×D13912yes—
216C2×C4C23×D13911yescharacteristic
217C8—21no—
218C8—2781no—
219C8—1392no—
220C8C2×C4×D13912yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—2782no—
225C22—2784no—
226C22—5562no—
227C22—5562no—
228C22—11128no—
229C22—1392no—
230C22C2×D4×D13911yescharacteristic
231C4—22no—
232C4—42no—
233C4—2782no—
234C4—5562no—
235C4—1392no—
236C4C22×C4×D13911yescharacteristic
237C4#41×D13911yescharacteristic
238C2—44no—
239C2—2782no—
240C2—5564no—
241C2C4×D4×D13911yescharacteristic
242C2#2258175712yes—
subgroupG/H
centerC22C2×D4×D139
commutatorC4×C139C23×C4
FrattiniC2×C4C23×D139
Fitting#442×C139C2
socleC22×C139C22×D4
prime radicalC2×D8×D139C2
cosocleC2×C4×C139C24
hypercenter#442D139
hypocenterC139#2948
LCSG ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #22581425C2semidirect
3. #22581066C2semidirect
4. #22581065C2semidirect
5. #22581064C2semidirect
6. C4×#14555770C2semidirect
7. #22581033C2semidirect
8. #22580988C2semidirect
9. #22580956C2semidirect
10. #22580910C2semidirect
11. #442×C139C2semidirect
15. D8×D139C4semidirect
18. C4×D556C22semidirect
19. D4×Dic139C22semidirect
20. #17984804C22semidirect
27. #17984775C22semidirect
28. #17984774C22semidirect
29. #17984764C22semidirect
30. #17984763C22semidirect
31. #17984762C22semidirect
32. #17984752C22semidirect
33. C4×C139⋊C8C22semidirect
34. C8×Dic139C22semidirect
36. C4×D4×C139C22semidirect
37. #106×C139C22semidirect
38. #102×C139C22semidirect
39. #97×C139C22semidirect
44. D4×D139C2×C4semidirect
49. D1112C2×C4semidirect
50. #14555770C2×C4semidirect
54. C8×D139C2×C4semidirect
66. D8×C139C2×C4semidirect
121. C139#2948semidirect
128. #442D139semidirect
146. C4×D4C2×D139semidirect
153. #106C2×D139semidirect
157. #102C2×D139semidirect
159. #97C2×D139semidirect
175. D8C4×D139semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1392
#225814252
#225810662
#225810652
#225810642
C4×#145557702
#225810332
#225809882
#225809562
#225809102
#442×C1392
#2948139