Subgroups — #433×C₂₃₉ #29504337

Order 15296.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#117×C₂₃₉	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈×C₂₃₉	C₂	1	2	yes	maximal, complemented
3	C₂²⋊C₈×C₂₃₉	C₂	1	2	yes	maximal
4	#97×C₂₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₈×C₂₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×C₂₃₉	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₂₃₉	C₂²	1	2	yes	—
8	C₂×C₈×C₂₃₉	C₂²	1	2	yes	—
9	C₄⋊C₄×C₂₃₉	C₄	1	2	yes	—
10	C₂²⋊C₄×C₂₃₉	C₄	1	2	yes	—
11	C₄²×C₂₃₉	C₂²	1	1	yes	characteristic
12	C₄²×C₂₃₉	C₂²	1	1	yes	characteristic
13	C₂³×C₂₃₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₂₃₉	—	2	2	no	—
15	C₂×C₄×C₂₃₉	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₂₃₉	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₂₃₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₃₉	C₂³	1	1	yes	characteristic
19	C₈×C₂₃₉	—	2	2	no	—
20	C₈×C₂₃₉	—	2	2	no	—
21	C₂²×C₂₃₉	—	2	1	no	—
22	C₂²×C₂₃₉	—	2	2	no	—
23	C₂²×C₂₃₉	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₂₃₉	—	2	1	no	—
25	C₄×C₂₃₉	—	2	2	no	—
26	C₄×C₂₃₉	—	2	2	no	—
27	C₄×C₂₃₉	#41	1	2	yes	—
28	C₂×C₂₃₉	—	4	1	no	—
29	C₂×C₂₃₉	#117	1	1	yes	characteristic
30	C₂×C₂₃₉	#131	1	2	yes	—
31	C₂₃₉	#433	1	1	yes	characteristic, direct product factor, Sylow
32	#433	C₂₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	#117	C₂×C₂₃₉	1	1	yes	characteristic
34	C₄⋊C₈	C₂×C₂₃₉	1	2	yes	complemented
35	C₂²⋊C₈	C₂×C₂₃₉	1	2	yes	—
36	#97	C₂×C₂₃₉	1	1	yes	characteristic, complemented
37	C₄×C₈	C₂×C₂₃₉	1	1	yes	characteristic, complemented
38	C₂²×C₄	C₂²×C₂₃₉	1	1	yes	characteristic
39	C₂×C₈	C₂²×C₂₃₉	1	2	yes	—
40	C₂×C₈	C₂²×C₂₃₉	1	2	yes	—
41	C₄⋊C₄	C₄×C₂₃₉	1	2	yes	—
42	C₂²⋊C₄	C₄×C₂₃₉	1	2	yes	—
43	C₄²	C₂²×C₂₃₉	1	1	yes	characteristic
44	C₄²	C₂²×C₂₃₉	1	1	yes	characteristic
45	C₂³	C₂×C₄×C₂₃₉	1	1	yes	characteristic
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	C₂×C₄×C₂₃₉	1	2	yes	—
48	C₂×C₄	C₂×C₄×C₂₃₉	1	2	yes	—
49	C₂×C₄	C₂×C₄×C₂₃₉	1	1	yes	characteristic
50	C₂×C₄	C₂³×C₂₃₉	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₈	—	2	2	no	—
53	C₂²	—	2	1	no	—
54	C₂²	—	2	2	no	—
55	C₂²	C₂²×C₄×C₂₃₉	1	1	yes	characteristic
56	C₄	—	2	1	no	—
57	C₄	—	2	2	no	—
58	C₄	—	2	2	no	—
59	C₄	#41×C₂₃₉	1	2	yes	—
60	C₂	—	4	1	no	—
61	C₂	#117×C₂₃₉	1	1	yes	characteristic
62	C₂	#131×C₂₃₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃₉	C₂³
commutator	C₂²	C₂²×C₄×C₂₃₉
Frattini, cosocle	C₂×C₄	C₂³×C₂₃₉
socle	C₂²×C₂₃₉	C₂²×C₄
prime radical	C₂³×C₂₃₉	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄⋊C₈×C₂₃₉	C₂	semidirect
4. #97×C₂₃₉	C₂	semidirect
5. C₄×C₈×C₂₃₉	C₂	semidirect
31. C₂₃₉	#433	direct (N × H)
32. #433	C₂₃₉	direct (N × H)
34. C₄⋊C₈	C₂×C₂₃₉	semidirect
36. #97	C₂×C₂₃₉	semidirect
37. C₄×C₈	C₂×C₂₃₉	semidirect

Maximal subgroups

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

subgroup	index
#117×C₂₃₉	2
C₄⋊C₈×C₂₃₉	2
C₂²⋊C₈×C₂₃₉	2
#97×C₂₃₉	2
C₄×C₈×C₂₃₉	2
#433	239

Subgroups — #433×C239 #29504337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #433×C₂₃₉ #29504337