Subgroups — C₄×#14556527 #22609833

Order 9344.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556527	C₂	1	2	yes	maximal
2	C₄×#11924012	C₂	1	2	yes	maximal
3	#17988352	C₂	1	2	yes	maximal
4	C₂×C₄×C₈×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#11924012	C₂²	1	4	yes	—
6	#14556527	C₄	1	8	yes	direct product factor
7	#14556502	—	2	2	no	—
8	C₄×#10596831	—	2	2	no	—
9	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₇₃	C₄	1	4	yes	—
13	#11924012	—	2	4	no	—
14	#11924012	C₂×C₄	1	8	yes	—
15	C₂×#10596831	—	2	4	no	—
16	C₂²×C₄×C₇₃	Q₈	1	2	yes	—
17	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
18	C₂×C₈×C₇₃	—	2	2	no	—
19	C₂×C₈×C₇₃	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
22	C₄²×C₇₃	C₂×C₄	1	2	yes	—
23	C₄²×C₇₃	D₄	1	1	yes	characteristic
24	C₄²×C₇₃	D₄	1	1	yes	characteristic
25	C₂³×C₇₃	C₂×Q₈	1	1	yes	characteristic
26	C₂×C₄×C₇₃	—	2	4	no	—
27	C₂×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
30	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₇₃	#41	1	2	yes	—
33	C₈×C₇₃	—	2	2	no	—
34	C₈×C₇₃	C₄²	1	4	yes	—
35	#10596831	—	2	8	no	—
36	C₂²×C₇₃	—	2	2	no	—
37	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂²×C₇₃	C₄×Q₈	1	2	yes	—
39	C₄×C₇₃	—	2	2	no	—
40	C₄×C₇₃	#108	1	4	yes	complemented
41	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
42	C₄×C₇₃	#117	1	1	yes	characteristic
43	C₄×C₇₃	C₄×D₄	1	2	yes	—
44	C₂×C₇₃	—	2	2	no	—
45	C₂×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₇₃	C₂×#108	1	2	yes	—
47	C₄×#108	—	73	1	no	maximal, Sylow
48	C₇₃	C₄×#108	1	1	yes	characteristic, complemented, Sylow
49	C₂×#108	—	73	2	no	—
50	C₄×M₁₆	—	73	2	no	—
51	C₂×C₄×C₈	D₇₃	1	1	yes	characteristic
52	#341	—	73	2	no	—
53	C₂×M₁₆	—	73	4	no	—
54	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
55	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
56	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
57	#108	—	73	8	no	—
58	#97	—	146	2	no	—
59	C₄×C₈	—	146	2	no	—
60	C₄×C₈	Dic₇₃	1	4	yes	—
61	C₂²×C₄	Dic₁₄₆	1	2	yes	—
62	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
63	M₁₆	—	73	8	no	—
64	M₁₆	—	146	4	no	—
65	C₂×C₈	—	2	2	no	—
66	C₂×C₈	—	146	4	no	—
67	C₂×C₈	C₄×D₇₃	1	4	yes	—
68	C₂×C₈	C₂×Dic₇₃	1	2	yes	—
69	C₂×C₈	C₂×Dic₇₃	1	2	yes	—
70	C₄²	D₂₉₂	1	1	yes	characteristic
71	C₄²	D₂₉₂	1	1	yes	characteristic
72	C₄²	C₂×Dic₇₃	1	2	yes	—
73	C₂³	C₂×Dic₁₄₆	1	1	yes	characteristic
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	C₄⋊Dic₇₃	1	2	yes	—
76	C₂×C₄	C₄⋊Dic₇₃	1	2	yes	—
77	C₂×C₄	C₂×C₄×D₇₃	1	2	yes	—
78	C₂×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
79	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
80	C₂×C₄	#11924028	1	2	yes	—
81	C₈	—	2	2	no	—
82	C₈	—	146	8	no	—
83	C₈	C₄×Dic₇₃	1	4	yes	—
84	C₂²	—	2	2	no	—
85	C₂²	C₂×C₄⋊Dic₇₃	1	1	yes	characteristic
86	C₂²	C₄×Dic₁₄₆	1	2	yes	—
87	C₄	—	2	2	no	—
88	C₄	#14556527	1	4	yes	direct product factor
89	C₄	C₂×C₄×Dic₇₃	1	1	yes	characteristic
90	C₄	#14556550	1	1	yes	characteristic
91	C₄	C₄×D₂₉₂	1	2	yes	—
92	C₂	—	2	2	no	—
93	C₂	C₄×C₄⋊Dic₇₃	1	1	yes	characteristic
94	C₂	C₂×#14556527	1	2	yes	—

	subgroup	G/H
center	C₄²	D₂₉₂
commutator	C₄×C₇₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	C₂×C₄×C₈×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	C₂×C₄×C₈	D₇₃
hypocenter	C₇₃	C₄×#108
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #14556527	C₄	direct (N × H)
40. C₄×C₇₃	#108	semidirect
48. C₇₃	C₄×#108	semidirect
88. C₄	#14556527	direct (N × H)

Subgroups — C4×#14556527 #22609833

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#14556527 #22609833