Subgroups — #34000069

Order 18688.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22624961	C₂	1	2	yes	maximal
2	#22609547	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11924031	—	2	2	no	—
4	#17988990	—	2	2	no	—
5	#17988967	C₄	1	1	yes	characteristic
6	C₈×#10596831	C₂²	1	1	yes	characteristic
7	#494×C₇₃	C₄	1	1	yes	characteristic
8	C₂×#11924031	—	4	2	no	—
9	C₂×Dic₂₉₂	—	4	1	no	—
10	#14556591	—	2	1	no	—
11	#14556524	—	4	2	no	—
12	#14556524	—	4	2	no	—
13	C₄×#10596831	D₄	1	2	yes	—
14	C₂×Q₁₆×C₇₃	—	4	1	no	—
15	C₄⋊Q₈×C₇₃	—	2	1	no	—
16	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
17	#11924031	—	8	2	no	—
18	C₂×Dic₁₄₆	—	4	1	no	—
19	Dic₂₉₂	—	8	2	no	—
20	C₂×#10596831	D₈	1	2	yes	—
21	C₂×#10596831	SD₁₆	1	2	yes	—
22	C₄⋊Dic₇₃	—	4	2	no	—
23	C₂×Q₈×C₇₃	—	4	1	no	—
24	Q₁₆×C₇₃	—	8	2	no	—
25	C₂×C₈×C₇₃	—	2	1	no	—
26	C₄⋊C₄×C₇₃	—	4	2	no	—
27	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
28	Q₈×C₇₃	—	8	2	no	—
29	C₂×C₄×C₇₃	—	8	1	no	—
30	C₂×C₄×C₇₃	#100	1	1	yes	characteristic
31	C₂×C₄×C₇₃	#102	1	2	yes	—
32	C₂×Dic₇₃	—	8	1	no	—
33	Dic₁₄₆	—	8	2	no	—
34	C₈×C₇₃	—	2	2	no	—
35	#10596831	—	2	2	no	—
36	#10596831	SD₃₂	1	2	yes	—
37	#10596831	Q₃₂	1	2	yes	—
38	C₂²×C₇₃	#331	1	1	yes	characteristic
39	C₄×C₇₃	—	2	1	no	—
40	C₄×C₇₃	—	16	1	no	—
41	C₄×C₇₃	#358	1	2	yes	—
42	C₄×C₇₃	#362	1	2	yes	—
43	Dic₇₃	—	16	1	no	—
44	#7098	—	73	1	no	maximal, Sylow
45	C₂×C₇₃	#1357	1	1	yes	characteristic
46	C₂×C₇₃	#1362	1	2	yes	—
47	#1713	—	73	1	no	—
48	#1370	—	73	2	no	—
49	C₇₃	#7098	1	1	yes	characteristic, complemented, Sylow
50	#500	—	146	2	no	—
51	#494	—	73	1	no	—
52	#494	#64408	1	1	yes	characteristic
53	C₄⋊C₁₆	—	146	2	no	—
54	C₈²	—	73	1	no	—
55	C₂×Q₁₆	—	4	1	no	—
56	C₂×Q₁₆	—	292	1	no	—
57	C₄⋊Q₈	—	2	1	no	—
58	C₄⋊Q₈	—	146	1	no	—
59	C₂×C₁₆	—	292	2	no	—
60	#107	—	292	2	no	—
61	#107	—	292	2	no	—
62	C₄×C₈	—	73	2	no	—
63	C₄×C₈	C₂×#64408	1	1	yes	characteristic
64	C₂×Q₈	—	4	1	no	—
65	C₂×Q₈	—	292	1	no	—
66	Q₁₆	—	8	2	no	—
67	Q₁₆	—	584	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	73	2	no	—
70	C₂×C₈	—	73	2	no	—
71	C₄⋊C₄	—	4	2	no	—
72	C₄⋊C₄	—	292	2	no	—
73	C₄²	C₂²⋊#64408	1	1	yes	characteristic
74	C₁₆	—	584	2	no	—
75	Q₈	—	8	2	no	—
76	Q₈	—	584	2	no	—
77	C₂×C₄	—	8	1	no	—
78	C₂×C₄	—	584	1	no	—
79	C₂×C₄	#14556651	1	1	yes	characteristic
80	C₂×C₄	#14556653	1	2	yes	—
81	C₈	—	2	2	no	—
82	C₈	—	73	2	no	—
83	C₈	—	73	2	no	—
84	C₈	—	146	2	no	—
85	C₂²	#17989445	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	16	1	no	—
88	C₄	—	1168	1	no	—
89	C₄	#17989500	1	2	yes	—
90	C₄	#17989506	1	2	yes	—
91	C₂	#22624939	1	1	yes	characteristic
92	C₂	#22624946	1	2	yes	—

	subgroup	G/H
center	C₂²	#17989445
commutator	C₄×C₈×C₇₃	C₂×C₄
Frattini	C₄×C₈	C₂×#64408
Fitting	#494×C₇₃	C₄
socle, prime radical	C₂²×C₇₃	#331
cosocle	C₈×#10596831	C₂²
hypercenter	#494	#64408
hypocenter	C₇₃	#7098
LCS	G ▷ C₄×C₈×C₇₃ ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
49. C₇₃	#7098	semidirect

Maximal subgroups

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

subgroup	index
#22624961	2
#22609547	2
#7098	73