Subgroups — C₂³×#90770 #16836451

Order 3712.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#90770	C₂	1	14	yes	maximal, direct product factor
2	C₂³×#6597	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₄×C₂₉	C₄	1	1	yes	characteristic
4	C₂²×#6597	C₄	1	7	yes	—
5	C₂²×#6597	C₂²	1	7	yes	—
6	C₂×#90770	C₂²	1	28	yes	direct product factor
7	C₂⁴×C₂₉	C₈	1	1	yes	characteristic
8	C₂²×C₄×C₂₉	C₈	1	7	yes	—
9	C₂²×C₄×C₂₉	C₂×C₄	1	7	yes	—
10	C₂×#6597	C₂×C₄	1	21	yes	—
11	C₂×#6597	C₂³	1	7	yes	—
12	#90770	C₂³	1	8	yes	direct product factor
13	C₂³×C₂₉	C₁₆	1	8	yes	complemented
14	C₂³×C₂₉	C₂×C₈	1	7	yes	—
15	C₂×C₄×C₂₉	C₂×C₈	1	21	yes	—
16	C₂×C₄×C₂₉	C₂²×C₄	1	7	yes	—
17	#6597	C₂²×C₄	1	7	yes	—
18	#6597	C₂⁴	1	1	yes	characteristic
19	C₂³×C₁₆	—	29	1	no	maximal, Sylow
20	C₂²×C₂₉	C₂×C₁₆	1	28	yes	complemented
21	C₂²×C₂₉	C₂²×C₈	1	7	yes	—
22	C₄×C₂₉	C₂²×C₈	1	7	yes	—
23	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
24	C₂³×C₈	—	29	1	no	—
25	C₂²×C₁₆	—	29	14	no	—
26	C₂×C₂₉	C₂²×C₁₆	1	14	yes	complemented
27	C₂×C₂₉	C₂³×C₈	1	1	yes	characteristic
28	C₂³×C₄	#1181	1	1	yes	characteristic
29	C₂²×C₈	—	29	7	no	—
30	C₂²×C₈	—	29	7	no	—
31	C₂×C₁₆	—	29	28	no	—
32	C₂₉	C₂³×C₁₆	1	1	yes	characteristic, complemented, Sylow
33	C₂⁴	#6599	1	1	yes	characteristic
34	C₂²×C₄	#6599	1	7	yes	—
35	C₂²×C₄	C₂×#1181	1	7	yes	—
36	C₂×C₈	—	29	7	no	—
37	C₂×C₈	—	29	21	no	—
38	C₁₆	—	29	8	no	—
39	C₂³	#90770	1	8	yes	direct product factor
40	C₂³	C₂×#6599	1	7	yes	—
41	C₂×C₄	C₂×#6599	1	21	yes	—
42	C₂×C₄	C₂²×#1181	1	7	yes	—
43	C₈	—	29	1	no	—
44	C₈	—	29	7	no	—
45	C₂²	C₂×#90770	1	28	yes	direct product factor
46	C₂²	C₂²×#6599	1	7	yes	—
47	C₄	C₂²×#6599	1	7	yes	—
48	C₄	C₂³×#1181	1	1	yes	characteristic
49	C₂	C₂²×#90770	1	14	yes	direct product factor
50	C₂	C₂³×#6599	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₄	#1181
commutator, hypocenter	C₂₉	C₂³×C₁₆
Frattini	C₄	C₂³×#1181
Fitting	C₂³×C₄×C₂₉	C₄
socle, prime radical	C₂⁴×C₂₉	C₈
cosocle	#6597	C₂⁴
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#90770	C₂	direct (N × H)
6. C₂×#90770	C₂²	direct (N × H)
12. #90770	C₂³	direct (N × H)
13. C₂³×C₂₉	C₁₆	semidirect
20. C₂²×C₂₉	C₂×C₁₆	semidirect
26. C₂×C₂₉	C₂²×C₁₆	semidirect
32. C₂₉	C₂³×C₁₆	semidirect
39. C₂³	#90770	direct (N × H)
45. C₂²	C₂×#90770	direct (N × H)
49. C₂	C₂²×#90770	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#90770	2
C₂³×#6597	2
C₂³×C₁₆	29

Subgroups — C23×#90770 #16836451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#90770 #16836451