Subgroups — #22625065

Order 9344.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989492	C₂	1	2	yes	maximal
2	#17988960	C₂	1	1	yes	maximal, characteristic
3	#14556650	—	2	2	no	—
4	C₂×#11924017	—	2	2	no	—
5	#14556591	C₄	1	1	yes	characteristic, complemented
6	#14556588	C₂²	1	1	yes	characteristic
7	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic, complemented
8	C₂²⋊#64408	—	4	2	no	—
9	C₂×Dic₁₄₆	—	2	1	no	—
10	C₂×D₂₉₂	—	4	1	no	—
11	C₂×D₂₉₂	D₄	1	2	yes	—
12	#11924017	—	4	4	no	—
13	C₄⋊Dic₇₃	—	4	1	no	—
14	C₂×C₈×C₇₃	—	2	1	no	—
15	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×D₇₃	—	2	2	no	—
17	C₂×#64408	—	8	2	no	—
18	C₂×C₄×C₇₃	—	2	1	no	—
19	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×Dic₇₃	—	4	1	no	—
21	D₂₉₂	—	4	2	no	—
22	D₂₉₂	—	8	2	no	—
23	Dic₁₄₆	—	4	2	no	—
24	C₈×C₇₃	—	2	2	no	—
25	C₂²×C₇₃	#99	1	1	yes	characteristic
26	C₂×D₇₃	—	4	2	no	—
27	C₂×D₇₃	—	8	2	no	—
28	#64408	—	16	2	no	—
29	C₄×C₇₃	—	2	2	no	—
30	C₄×C₇₃	—	2	1	no	—
31	Dic₇₃	—	8	1	no	—
32	C₂×C₇₃	—	2	1	no	—
33	C₂×C₇₃	#353	1	1	yes	characteristic
34	D₇₃	—	8	2	no	—
35	#1409	—	73	1	no	maximal, Sylow
36	C₇₃	#1409	1	1	yes	characteristic, complemented, Sylow
37	#492	—	73	1	no	—
38	#353	—	73	2	no	—
39	C₂×SD₁₆	—	146	2	no	—
40	C₄⋊Q₈	—	73	1	no	—
41	#127	—	73	1	no	—
42	#99	—	146	2	no	—
43	C₄×C₈	#64408	1	1	yes	characteristic, complemented
44	C₂×Q₈	—	146	1	no	—
45	C₂×D₄	—	292	1	no	—
46	C₂×D₄	—	73	2	no	—
47	SD₁₆	—	292	4	no	—
48	C₂×C₈	—	2	1	no	—
49	C₄⋊C₄	—	292	1	no	—
50	C₂²⋊C₄	—	292	2	no	—
51	C₄²	C₂×#64408	1	1	yes	characteristic
52	C₂³	—	146	2	no	—
53	Q₈	—	292	2	no	—
54	D₄	—	292	2	no	—
55	D₄	—	584	2	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	292	1	no	—
58	C₂×C₄	—	584	2	no	—
59	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
60	C₈	—	2	2	no	—
61	C₂²	—	292	2	no	—
62	C₂²	—	584	2	no	—
63	C₂²	#14556650	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	2	1	no	—
66	C₄	—	584	1	no	—
67	C₄	—	1168	2	no	—
68	C₂	—	2	1	no	—
69	C₂	—	584	2	no	—
70	C₂	#17989492	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17989492
commutator	C₄²×C₇₃	C₂×C₄
Frattini	C₄²	C₂×#64408
Fitting	C₄×C₈×C₇₃	C₄
socle	C₂×C₇₃	#353
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	#1409
LCS	G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
5. #14556591	C₄	semidirect
7. C₄×C₈×C₇₃	C₄	semidirect
36. C₇₃	#1409	semidirect
43. C₄×C₈	#64408	semidirect