Subgroups — C₄×#14556641 #22625035

Order 9344.

72 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	C₄	1	4	yes	direct product factor
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	C₈	1	2	yes	—
8	#11924003	C₂×C₄	1	2	yes	—
9	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic
10	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
11	C₄²×C₇₃	C₈	1	1	yes	characteristic
12	C₂×C₄×C₇₃	C₁₆	1	2	yes	—
13	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
14	C₈×C₇₃	C₁₆	1	2	yes	—
15	C₈×C₇₃	C₄²	1	1	yes	characteristic
16	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
17	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
18	C₄×C₇₃	C₃₂	1	4	yes	complemented
19	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
20	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
21	C₂×C₇₃	C₄×C₁₆	1	1	yes	characteristic
22	C₂×C₇₃	C₂×C₃₂	1	2	yes	—
23	C₄×C₃₂	—	73	1	no	maximal, Sylow
24	C₇₃	C₄×C₃₂	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃₂	—	73	2	no	—
26	C₄×C₁₆	—	73	1	no	—
27	C₂×C₁₆	—	73	1	no	—
28	C₂×C₁₆	—	73	1	no	—
29	C₄×C₈	#64408	1	1	yes	characteristic
30	C₃₂	—	73	4	no	—
31	C₂×C₈	#10596833	1	1	yes	characteristic
32	C₂×C₈	C₂×#64408	1	1	yes	characteristic
33	C₄²	#10596833	1	1	yes	characteristic
34	C₁₆	—	73	2	no	—
35	C₁₆	—	73	2	no	—
36	C₂×C₄	#11924031	1	2	yes	—
37	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
38	C₈	#11924031	1	2	yes	—
39	C₈	C₄×#64408	1	1	yes	characteristic
40	C₈	#11924036	1	1	yes	characteristic
41	C₂²	C₂×#11924031	1	1	yes	characteristic
42	C₄	#14556641	1	4	yes	direct product factor
43	C₄	C₄×#10596833	1	1	yes	characteristic
44	C₄	C₂×#11924031	1	1	yes	characteristic
45	C₂	C₄×#11924031	1	1	yes	characteristic
46	C₂	C₂×#14556641	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. #14556641	C₄	direct (N × H)
18. C₄×C₇₃	C₃₂	semidirect
24. C₇₃	C₄×C₃₂	semidirect
42. C₄	#14556641	direct (N × H)

Subgroups — C4×#14556641 #22625035

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#14556641 #22625035