Subgroups — C₄⋊#14556641 #22625088

Order 9344.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556641	C₂	1	2	yes	maximal
2	C₄×#11924003	C₂	1	1	yes	maximal, characteristic
3	#14556641	—	2	2	no	—
4	C₂×#11924003	C₄	1	1	yes	characteristic
5	C₂×#11924003	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
7	#11924003	—	2	1	no	—
8	#11924003	D₄	1	1	yes	characteristic
9	#11924003	Q₈	1	1	yes	characteristic
10	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic
11	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
12	C₄²×C₇₃	C₈	1	1	yes	characteristic
13	C₂×C₄×C₇₃	C₁₆	1	1	yes	characteristic
14	C₂×C₄×C₇₃	C₁₆	1	1	yes	characteristic
15	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
16	C₈×C₇₃	—	2	1	no	—
17	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₇₃	M₁₆	1	1	yes	characteristic
19	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
20	C₄×C₇₃	—	2	1	no	—
21	C₄×C₇₃	C₃₂	1	2	yes	complemented
22	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₇₃	M₃₂	1	1	yes	characteristic
24	C₂×C₇₃	C₄⋊C₁₆	1	1	yes	characteristic
25	C₂×C₇₃	C₂×C₃₂	1	1	yes	characteristic
26	C₂×C₇₃	M₆₄	1	1	yes	characteristic
27	C₄⋊C₃₂	—	73	1	no	maximal, Sylow
28	C₇₃	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃₂	—	73	2	no	—
30	C₄×C₁₆	—	73	1	no	—
31	C₂×C₁₆	—	73	1	no	—
32	C₂×C₁₆	—	73	1	no	—
33	C₄×C₈	#64408	1	1	yes	characteristic
34	C₃₂	—	146	2	no	—
35	C₂×C₈	#10596833	1	1	yes	characteristic
36	C₂×C₈	C₂×#64408	1	1	yes	characteristic
37	C₄²	#10596833	1	1	yes	characteristic
38	C₁₆	—	73	1	no	—
39	C₁₆	—	73	1	no	—
40	C₁₆	—	146	1	no	—
41	C₂×C₄	#11924031	1	1	yes	characteristic
42	C₂×C₄	#11924031	1	1	yes	characteristic
43	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	C₄⋊#64408	1	1	yes	characteristic
46	C₈	#11924038	1	1	yes	characteristic
47	C₂²	C₂×#11924031	1	1	yes	characteristic
48	C₄	—	2	1	no	—
49	C₄	#14556641	1	2	yes	complemented
50	C₄	C₄⋊#10596833	1	1	yes	characteristic
51	C₄	#14556665	1	1	yes	characteristic
52	C₂	C₄⋊#11924031	1	1	yes	characteristic
53	C₂	C₂×#14556641	1	1	yes	characteristic
54	C₂	#17989519	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#64408
commutator	C₂×C₇₃	C₂×C₃₂
Fitting	C₄×C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₁₆
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	C₄⋊C₃₂
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
21. C₄×C₇₃	C₃₂	semidirect
28. C₇₃	C₄⋊C₃₂	semidirect
49. C₄	#14556641	semidirect

Subgroups — C4⋊#14556641 #22625088

Conjugacy classes of subgroups

Complements

Subgroups — C₄⋊#14556641 #22625088