Subgroups — #34014566

Order 18688.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22625101	C₂	1	2	yes	maximal, complemented
2	#22625100	C₂	1	1	yes	maximal, characteristic, complemented
3	#22625099	C₂	1	2	yes	maximal, complemented
4	C₂×#17989426	C₂	1	1	yes	maximal, characteristic, complemented
5	#22612226	C₂	1	1	yes	maximal, characteristic
6	#17989426	C₂²	1	1	yes	characteristic
7	#17989426	C₂²	1	1	yes	characteristic
8	#17989426	C₂²	1	2	yes	—
9	#17989003	C₄	1	1	yes	characteristic
10	#17988420	C₄	1	2	yes	—
11	C₂×#14556497	C₂²	1	1	yes	characteristic
12	C₃₂×D₇₃	C₂²	1	2	yes	—
13	M₆₄×C₇₃	C₄	1	1	yes	characteristic
14	#14556597	C₈	1	1	yes	characteristic
15	#14556531	C₈	1	1	yes	characteristic
16	#14556530	C₈	1	2	yes	—
17	C₁₆×D₇₃	C₂×C₄	1	2	yes	—
18	#14556497	C₂×C₄	1	1	yes	characteristic
19	#14556497	C₂³	1	1	yes	characteristic
20	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₃₂×C₇₃	C₂×C₄	1	2	yes	—
22	#11924028	C₁₆	1	1	yes	characteristic
23	#11924012	C₁₆	1	1	yes	characteristic
24	#11924011	C₁₆	1	2	yes	—
25	C₈×D₇₃	C₂×C₈	1	2	yes	—
26	#11924003	C₂×C₈	1	2	yes	—
27	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
28	C₁₆×C₇₃	C₂×C₈	1	1	yes	characteristic
29	C₁₆×C₇₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
31	C₂²⋊D₇₃	C₃₂	1	2	yes	—
32	D₂₉₂	C₃₂	1	1	yes	characteristic
33	C₄×D₇₃	C₂×C₁₆	1	2	yes	—
34	Dic₁₄₆	C₃₂	1	1	yes	characteristic
35	C₈×C₇₃	C₂×C₁₆	1	1	yes	characteristic
36	C₈×C₇₃	C₂²×C₈	1	1	yes	characteristic
37	#10596831	C₂×C₁₆	1	2	yes	—
38	C₂²×C₇₃	C₂×C₃₂	1	1	yes	characteristic
39	C₂×D₇₃	C₂×C₃₂	1	2	yes	—
40	C₄×C₇₃	C₂×C₃₂	1	1	yes	characteristic
41	C₄×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
42	Dic₇₃	C₂×C₃₂	1	2	yes	—
43	#13737	—	73	1	no	maximal, Sylow
44	C₂×C₇₃	—	2	1	no	—
45	C₂×C₇₃	C₂²×C₃₂	1	1	yes	characteristic
46	D₇₃	—	2	2	no	—
47	#2258	—	73	1	no	—
48	M₁₂₈	—	73	1	no	—
49	M₁₂₈	—	73	2	no	—
50	C₂×C₆₄	—	73	1	no	—
51	C₂×C₆₄	—	73	2	no	—
52	C₇₃	#13737	1	1	yes	characteristic, complemented, Sylow
53	#504	—	73	1	no	—
54	M₆₄	—	73	2	no	—
55	M₆₄	#64408	1	1	yes	characteristic
56	C₂×C₃₂	—	73	1	no	—
57	C₂×C₃₂	—	73	2	no	—
58	C₆₄	—	73	1	no	—
59	C₆₄	—	73	1	no	—
60	C₆₄	—	73	2	no	—
61	#131	—	73	1	no	—
62	M₃₂	—	73	1	no	—
63	M₃₂	—	73	2	no	—
64	C₂×C₁₆	—	73	2	no	—
65	C₂×C₁₆	C₂×#64408	1	1	yes	characteristic
66	C₃₂	—	73	1	no	—
67	C₃₂	—	73	1	no	—
68	C₃₂	C₂×#64408	1	2	yes	—
69	#41	—	73	1	no	—
70	M₁₆	—	73	1	no	—
71	M₁₆	—	73	2	no	—
72	C₂×C₈	—	73	2	no	—
73	C₂×C₈	#11924036	1	1	yes	characteristic
74	C₁₆	—	73	2	no	—
75	C₁₆	#11924036	1	1	yes	characteristic
76	C₁₆	C₂²×#64408	1	1	yes	characteristic
77	Q₈	—	73	1	no	—
78	D₄	—	73	2	no	—
79	D₄	—	73	1	no	—
80	C₂×C₄	—	73	2	no	—
81	C₂×C₄	#14556664	1	1	yes	characteristic
82	C₈	—	73	2	no	—
83	C₈	#14556664	1	1	yes	characteristic
84	C₈	C₂×#11924036	1	1	yes	characteristic
85	C₂²	—	73	2	no	—
86	C₂²	#17989518	1	1	yes	characteristic
87	C₄	—	73	2	no	—
88	C₄	#17989518	1	1	yes	characteristic
89	C₄	C₂×#14556664	1	1	yes	characteristic
90	C₂	—	2	1	no	—
91	C₂	—	146	2	no	—
92	C₂	C₂×#17989518	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂²×#64408
commutator, socle	C₂×C₇₃	C₂²×C₃₂
Fitting	M₆₄×C₇₃	C₄
prime radical	#11924028	C₁₆
cosocle	#14556497	C₂³
hypercenter	M₆₄	#64408
hypocenter	C₇₃	#13737
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
1. #22625101	C₂	semidirect
2. #22625100	C₂	semidirect
3. #22625099	C₂	semidirect
4. C₂×#17989426	C₂	semidirect
52. C₇₃	#13737	semidirect

Maximal subgroups

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

subgroup	index
#22625101	2
#22625100	2
#22625099	2
C₂×#17989426	2
#22612226	2
#13737	73