Subgroups — #34005461

Order 18688.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22624798	C₂	1	3	yes	maximal
2	#22624791	C₂	1	3	yes	maximal
3	#22608233	C₂	1	1	yes	maximal, characteristic
4	#17989610	C₂²	1	3	yes	—
5	#17989532	C₂²	1	1	yes	characteristic
6	C₄×#11924011	C₂²	1	3	yes	—
7	#17988308	C₄	1	3	yes	complemented
8	C₈²×C₇₃	C₄	1	1	yes	characteristic, complemented
9	#14556658	—	2	3	no	—
10	#14556648	—	2	3	no	—
11	#14556646	—	2	3	no	—
12	(C₂×#64408)⋊C₄	—	2	3	no	—
13	C₂×#11924011	—	2	3	no	—
14	C₄²×D₇₃	C₂³	1	1	yes	characteristic
15	#14556501	—	2	3	no	—
16	C₄×#10596831	C₂×C₄	1	3	yes	—
17	C₄×C₈×C₇₃	C₂×C₄	1	3	yes	—
18	C₂²×#64408	—	4	1	no	—
19	C₂×#10596833	—	4	3	no	—
20	C₂×C₄×D₇₃	#41	1	3	yes	—
21	#11924011	—	4	6	no	—
22	C₂×#10596831	—	2	3	no	—
23	C₄×Dic₇₃	#41	1	3	yes	—
24	C₂×C₈×C₇₃	—	2	3	no	—
25	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
26	C₂²×D₇₃	#126	1	1	yes	characteristic
27	C₂×#64408	—	8	3	no	—
28	C₂×C₄×C₇₃	#117	1	3	yes	—
29	C₂×Dic₇₃	#126	1	3	yes	—
30	C₄×D₇₃	—	4	3	no	—
31	#10596833	—	8	3	no	—
32	C₈×C₇₃	—	2	6	no	—
33	#10596831	—	4	3	no	—
34	C₂²×C₇₃	#383	1	1	yes	characteristic
35	C₂×D₇₃	—	2	3	no	—
36	#64408	—	16	1	no	—
37	C₄×C₇₃	—	2	3	no	—
38	Dic₇₃	—	2	3	no	—
39	#8803	—	73	1	no	maximal, Sylow
40	C₂×C₇₃	#1841	1	3	yes	—
41	D₇₃	—	4	1	no	—
42	#1455	—	73	1	no	—
43	#1291	—	73	3	no	—
44	#1288	—	73	3	no	—
45	C₇₃	#8803	1	1	yes	characteristic, complemented, Sylow
46	#432	—	73	3	no	—
47	C₄×M₁₆	—	73	3	no	—
48	#383	—	73	1	no	—
49	#322	—	73	3	no	—
50	C₈²	#64408	1	1	yes	characteristic, complemented
51	C₂×M₁₆	—	146	3	no	—
52	C₂×C₄²	—	73	1	no	—
53	C₄⋊C₈	—	146	3	no	—
54	C₂²⋊C₈	—	146	3	no	—
55	#97	—	146	3	no	—
56	#97	—	146	3	no	—
57	C₄×C₈	—	73	3	no	—
58	C₄×C₈	C₂×#64408	1	3	yes	—
59	#95	—	146	3	no	—
60	C₂²×C₄	—	292	1	no	—
61	C₂²×C₄	—	73	3	no	—
62	M₁₆	—	292	6	no	—
63	C₂×C₈	—	2	3	no	—
64	C₂×C₈	—	292	3	no	—
65	C₂×C₈	—	146	3	no	—
66	C₄²	—	73	3	no	—
67	C₄²	C₂²×#64408	1	1	yes	characteristic
68	C₂³	—	73	1	no	—
69	C₂×C₄	—	292	3	no	—
70	C₂×C₄	—	584	3	no	—
71	C₂×C₄	—	73	3	no	—
72	C₂×C₄	#14556670	1	3	yes	—
73	C₈	—	2	6	no	—
74	C₈	—	292	3	no	—
75	C₈	—	584	3	no	—
76	C₂²	—	146	3	no	—
77	C₂²	#17989532	1	1	yes	characteristic
78	C₄	—	2	3	no	—
79	C₄	—	1168	1	no	—
80	C₄	—	146	3	no	—
81	C₂	—	292	1	no	—
82	C₂	#22625861	1	3	yes	—

	subgroup	G/H
center	C₂²	#17989532
commutator	C₄²×C₇₃	C₂²×C₄
Frattini	C₄²	C₂²×#64408
Fitting	C₈²×C₇₃	C₄
socle	C₂²×C₇₃	#383
prime radical	C₂²×D₇₃	#126
cosocle	C₄²×D₇₃	C₂³
hypercenter	C₈²	#64408
hypocenter	C₇₃	#8803
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
7. #17988308	C₄	semidirect
8. C₈²×C₇₃	C₄	semidirect
45. C₇₃	#8803	semidirect
50. C₈²	#64408	semidirect

Maximal subgroups

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

subgroup	index
#22624798	2
#22624791	2
#22608233	2
#8803	73