Subgroups — #34001254

Order 18688.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22625063	C₂	1	2	yes	maximal
2	#22609538	C₂	1	1	yes	maximal, characteristic
3	#17989492	—	2	2	no	—
4	#17988964	C₂²	1	1	yes	characteristic
5	#17988935	—	2	2	no	—
6	C₈×#10596831	C₄	1	1	yes	characteristic, complemented
7	#494×C₇₃	C₄	1	1	yes	characteristic, complemented
8	#14556650	—	4	2	no	—
9	C₂×D₅₈₄	—	4	1	no	—
10	#14556588	D₄	1	2	yes	—
11	#14556511	—	4	4	no	—
12	C₄×#10596831	—	2	1	no	—
13	C₂×Q₁₆×C₇₃	—	4	1	no	—
14	C₄⋊Q₈×C₇₃	—	2	1	no	—
15	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
16	C₂²⋊#64408	—	8	2	no	—
17	C₂×D₂₉₂	—	2	2	no	—
18	C₂×D₂₉₂	—	4	2	no	—
19	D₅₈₄	—	8	2	no	—
20	C₂×#10596831	—	2	2	no	—
21	C₂×Q₈×C₇₃	—	4	1	no	—
22	Q₁₆×C₇₃	—	8	2	no	—
23	C₂×C₈×C₇₃	—	2	1	no	—
24	C₄⋊C₄×C₇₃	—	4	2	no	—
25	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂²×D₇₃	—	4	2	no	—
27	C₂×#64408	—	16	2	no	—
28	Q₈×C₇₃	—	8	2	no	—
29	C₂×C₄×C₇₃	—	2	1	no	—
30	C₂×C₄×C₇₃	—	8	1	no	—
31	C₂×C₄×C₇₃	#99	1	1	yes	characteristic
32	D₂₉₂	—	8	2	no	—
33	D₂₉₂	—	8	4	no	—
34	C₈×C₇₃	—	2	2	no	—
35	#10596831	—	4	2	no	—
36	C₂²×C₇₃	#353	1	1	yes	characteristic
37	C₂×D₇₃	—	8	2	no	—
38	C₂×D₇₃	—	16	2	no	—
39	#64408	—	32	2	no	—
40	C₄×C₇₃	—	2	2	no	—
41	C₄×C₇₃	—	2	1	no	—
42	C₄×C₇₃	—	16	1	no	—
43	#7530	—	73	1	no	maximal, Sylow
44	C₂×C₇₃	—	2	1	no	—
45	C₂×C₇₃	#1408	1	1	yes	characteristic
46	D₇₃	—	16	2	no	—
47	#1709	—	73	1	no	—
48	#1408	—	73	2	no	—
49	C₇₃	#7530	1	1	yes	characteristic, complemented, Sylow
50	#494	#64408	1	1	yes	characteristic, complemented
51	#493	—	73	1	no	—
52	#486	—	146	2	no	—
53	#353	—	146	2	no	—
54	C₈²	—	73	1	no	—
55	C₂×Q₁₆	—	4	1	no	—
56	C₂×D₈	—	292	1	no	—
57	C₄⋊Q₈	—	2	1	no	—
58	#127	—	73	2	no	—
59	#102	—	292	4	no	—
60	#99	—	292	2	no	—
61	C₄×C₈	—	146	1	no	—
62	C₄×C₈	C₂×#64408	1	1	yes	characteristic
63	C₂×Q₈	—	4	1	no	—
64	C₂×D₄	—	292	2	no	—
65	C₂×D₄	—	146	2	no	—
66	Q₁₆	—	8	2	no	—
67	D₈	—	584	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	146	2	no	—
70	C₄⋊C₄	—	4	2	no	—
71	C₂²⋊C₄	—	584	2	no	—
72	C₄²	C₂²⋊#64408	1	1	yes	characteristic
73	C₂³	—	292	2	no	—
74	Q₈	—	8	2	no	—
75	D₄	—	584	2	no	—
76	D₄	—	584	4	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	8	1	no	—
79	C₂×C₄	—	1168	2	no	—
80	C₂×C₄	#14556649	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	292	2	no	—
83	C₂²	—	584	2	no	—
84	C₂²	—	1168	2	no	—
85	C₂²	#17989491	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	2	1	no	—
88	C₄	—	16	1	no	—
89	C₄	—	2336	2	no	—
90	C₂	—	2	1	no	—
91	C₂	—	1168	2	no	—
92	C₂	#22625062	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22625062
commutator	C₄×C₈×C₇₃	C₂×C₄
Frattini	C₄×C₈	C₂×#64408
Fitting	#494×C₇₃	C₄
socle	C₂×C₇₃	#1408
prime radical, cosocle	#17988964	C₂²
hypercenter	#494	#64408
hypocenter	C₇₃	#7530
LCS	G ▷ C₄×C₈×C₇₃ ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
6. C₈×#10596831	C₄	semidirect
7. #494×C₇₃	C₄	semidirect
49. C₇₃	#7530	semidirect
50. #494	#64408	semidirect

Maximal subgroups

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

subgroup	index
#22625063	2
#22609538	2
#7530	73