Subgroups — #34015601

Order 18688.

1278 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22625107	C₂	1	14	yes	maximal
2	C₄³×D₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×(C₂×#64408)⋊C₄	C₂²	1	28	yes	—
4	C₂×C₄²×D₇₃	C₂²	1	7	yes	—
5	C₄²×Dic₇₃	C₄	1	7	yes	complemented
6	C₄³×C₇₃	C₄	1	1	yes	characteristic, complemented
7	C₂³×#64408	C₂³	1	8	yes	—
8	(C₂×#64408)⋊C₄	—	2	56	no	—
9	C₂²×C₄×D₇₃	C₂³	1	7	yes	—
10	C₂×C₄×Dic₇₃	C₂×C₄	1	7	yes	—
11	C₂×C₄×Dic₇₃	C₂×C₄	1	14	yes	—
12	C₄²×D₇₃	—	2	28	no	—
13	C₂×C₄²×C₇₃	C₂×C₄	1	7	yes	—
14	C₂²×#64408	—	2	56	no	—
15	C₂³×D₇₃	C₂⁴	1	1	yes	characteristic
16	C₂²×Dic₇₃	C₂²×C₄	1	7	yes	—
17	C₂×C₄×D₇₃	—	2	28	no	—
18	C₂×C₄×D₇₃	#41	1	28	yes	—
19	C₄×Dic₇₃	—	2	14	no	—
20	C₄×Dic₇₃	—	2	28	no	—
21	C₂²×C₄×C₇₃	C₂²×C₄	1	7	yes	—
22	C₄²×C₇₃	—	2	14	no	—
23	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
24	C₂²×D₇₃	C₂×#41	1	14	yes	—
25	C₂×#64408	—	4	56	no	—
26	C₂×C₄×C₇₃	—	2	14	no	—
27	C₂×C₄×C₇₃	#117	1	14	yes	—
28	C₂×Dic₇₃	—	2	14	no	—
29	C₂×Dic₇₃	#117	1	14	yes	—
30	C₄×D₇₃	—	2	56	no	—
31	C₂²×C₇₃	C₂×#117	1	7	yes	—
32	C₂×D₇₃	#529	1	28	yes	—
33	#64408	—	8	8	no	—
34	C₄×C₇₃	—	2	14	no	—
35	Dic₇₃	—	2	14	no	—
36	#14690	—	73	1	no	maximal, Sylow
37	C₂×C₇₃	#2283	1	7	yes	—
38	D₇₃	#2865	1	8	yes	—
39	C₂×C₄³	—	73	1	no	—
40	#1434	—	73	14	no	—
41	C₇₃	#14690	1	1	yes	characteristic, complemented, Sylow
42	C₂²×C₄²	—	73	7	no	—
43	C₂×#95	—	73	28	no	—
44	C₄³	—	73	7	no	—
45	C₄³	#64408	1	1	yes	characteristic, complemented
46	C₂³×C₄	—	73	7	no	—
47	C₂³×C₄	—	73	8	no	—
48	C₂×C₄²	—	73	14	no	—
49	C₂×C₄²	—	73	7	no	—
50	C₂×C₄²	—	146	28	no	—
51	C₂×C₄²	C₂×#64408	1	7	yes	—
52	#95	—	146	56	no	—
53	C₂⁴	—	73	1	no	—
54	C₂²×C₄	—	73	7	no	—
55	C₂²×C₄	—	73	28	no	—
56	C₂²×C₄	—	146	28	no	—
57	C₂²×C₄	—	146	56	no	—
58	C₂²×C₄	C₂²×#64408	1	7	yes	—
59	C₄²	—	2	14	no	—
60	C₄²	—	146	28	no	—
61	C₄²	—	146	14	no	—
62	C₂³	—	73	14	no	—
63	C₂³	C₂³×#64408	1	1	yes	characteristic
64	C₂×C₄	—	2	14	no	—
65	C₂×C₄	—	292	56	no	—
66	C₂×C₄	—	73	14	no	—
67	C₂×C₄	—	146	56	no	—
68	C₂×C₄	—	146	14	no	—
69	C₂×C₄	#14556670	1	14	yes	—
70	C₂²	—	73	28	no	—
71	C₂²	C₂×#14556670	1	7	yes	—
72	C₄	—	2	14	no	—
73	C₄	—	584	8	no	—
74	C₄	—	146	14	no	—
75	C₂	—	73	8	no	—
76	C₂	#22626378	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×#64408
commutator, socle	C₂³×C₇₃	C₂³×C₄
Fitting	C₄³×C₇₃	C₄
prime radical, cosocle	C₂³×D₇₃	C₂⁴
hypercenter	C₄³	#64408
hypocenter	C₇₃	#14690
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
5. C₄²×Dic₇₃	C₄	semidirect
6. C₄³×C₇₃	C₄	semidirect
41. C₇₃	#14690	semidirect
45. C₄³	#64408	semidirect

Maximal subgroups

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

subgroup	index
#22625107	2
C₄³×D₇₃	2
#14690	73