Subgroups — C₂×#22625100 #34014562

Order 18688.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22625100	C₂	1	4	yes	maximal, direct product factor
2	C₂×#17989426	C₂	1	2	yes	maximal, complemented
3	C₂²×#14556497	C₂	1	1	yes	maximal, characteristic
4	#17989426	C₂²	1	4	yes	complemented
5	C₂×#14556497	C₄	1	2	yes	—
6	C₂×#14556497	C₄	1	1	yes	characteristic
7	C₂×#14556497	C₂²	1	1	yes	characteristic
8	C₂×#14556497	C₂²	1	2	yes	—
9	C₂²×C₁₆×C₇₃	C₄	1	1	yes	characteristic
10	#14556497	C₂×C₄	1	1	yes	characteristic
11	#14556497	C₂×C₄	1	2	yes	—
12	#14556497	C₂³	1	1	yes	characteristic
13	C₂²×C₈×C₇₃	C₈	1	1	yes	characteristic
14	C₂×C₁₆×C₇₃	C₈	1	1	yes	characteristic
15	C₂×C₁₆×C₇₃	C₈	1	2	yes	—
16	C₂×C₁₆×C₇₃	C₂×C₄	1	2	yes	—
17	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₇₃	C₁₆	1	1	yes	characteristic
19	C₂×C₈×C₇₃	C₁₆	1	2	yes	—
20	C₂×C₈×C₇₃	C₁₆	1	1	yes	characteristic
21	C₂×C₈×C₇₃	C₂×C₈	1	2	yes	—
22	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
23	C₁₆×C₇₃	C₂×C₈	1	2	yes	—
24	C₁₆×C₇₃	C₂×C₈	1	1	yes	characteristic
25	C₁₆×C₇₃	C₂²×C₄	1	1	yes	characteristic
26	C₂³×C₇₃	C₃₂	1	1	yes	characteristic
27	C₂×C₄×C₇₃	C₃₂	1	2	yes	—
28	C₂×C₄×C₇₃	C₃₂	1	1	yes	characteristic
29	C₂×C₄×C₇₃	C₂×C₁₆	1	2	yes	—
30	C₂×C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
31	C₈×C₇₃	C₂×C₁₆	1	2	yes	—
32	C₈×C₇₃	C₂×C₁₆	1	1	yes	characteristic
33	C₈×C₇₃	C₂²×C₈	1	1	yes	characteristic
34	C₂²×C₇₃	—	2	2	no	—
35	C₂²×C₇₃	C₂×C₃₂	1	2	yes	—
36	C₂²×C₇₃	C₂×C₃₂	1	1	yes	characteristic
37	C₄×C₇₃	C₂×C₃₂	1	1	yes	characteristic
38	C₄×C₇₃	C₂×C₃₂	1	2	yes	—
39	C₄×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
40	C₂×M₁₂₈	—	73	1	no	maximal, Sylow
41	C₂×C₇₃	—	2	2	no	—
42	C₂×C₇₃	M₁₂₈	1	2	yes	complemented
43	C₂×C₇₃	C₂²×C₃₂	1	1	yes	characteristic
44	C₂²×C₃₂	—	73	1	no	—
45	M₁₂₈	—	73	4	no	—
46	C₂×C₆₄	—	73	2	no	—
47	C₇₃	C₂×M₁₂₈	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₁₆	#64408	1	1	yes	characteristic
49	C₂×C₃₂	—	73	2	no	—
50	C₂×C₃₂	—	73	2	no	—
51	C₂×C₃₂	—	73	1	no	—
52	C₂×C₃₂	—	73	1	no	—
53	C₆₄	—	73	4	no	—
54	C₂²×C₈	#10596833	1	1	yes	characteristic
55	C₂×C₁₆	#10596833	1	1	yes	characteristic
56	C₂×C₁₆	#10596833	1	2	yes	—
57	C₂×C₁₆	C₂×#64408	1	2	yes	—
58	C₂×C₁₆	C₂×#64408	1	1	yes	characteristic
59	C₃₂	—	73	1	no	—
60	C₃₂	—	73	1	no	—
61	C₃₂	—	73	2	no	—
62	C₂²×C₄	#11924031	1	1	yes	characteristic
63	C₂×C₈	#11924031	1	1	yes	characteristic
64	C₂×C₈	#11924031	1	2	yes	—
65	C₂×C₈	C₂×#10596833	1	2	yes	—
66	C₂×C₈	C₂×#10596833	1	1	yes	characteristic
67	C₁₆	C₂×#10596833	1	2	yes	—
68	C₁₆	C₂×#10596833	1	1	yes	characteristic
69	C₁₆	C₂²×#64408	1	1	yes	characteristic
70	C₂³	#14556641	1	1	yes	characteristic
71	C₂×C₄	#14556641	1	2	yes	—
72	C₂×C₄	#14556641	1	1	yes	characteristic
73	C₂×C₄	C₂×#11924031	1	2	yes	—
74	C₂×C₄	C₂×#11924031	1	1	yes	characteristic
75	C₈	C₂×#11924031	1	2	yes	—
76	C₈	C₂×#11924031	1	1	yes	characteristic
77	C₈	C₂²×#10596833	1	1	yes	characteristic
78	C₂²	—	2	2	no	—
79	C₂²	C₂×#14556641	1	2	yes	—
80	C₂²	C₂×#14556641	1	1	yes	characteristic
81	C₄	C₂×#14556641	1	1	yes	characteristic
82	C₄	C₂×#14556641	1	2	yes	—
83	C₄	C₂²×#11924031	1	1	yes	characteristic
84	C₂	—	2	2	no	—
85	C₂	#22625100	1	2	yes	direct product factor
86	C₂	C₂²×#14556641	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×#64408
commutator	C₂×C₇₃	C₂²×C₃₂
Frattini	C₁₆	C₂²×#64408
Fitting	C₂²×C₁₆×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₃₂
prime radical	C₂³×C₇₃	C₃₂
cosocle	#14556497	C₂³
hypercenter	C₂²×C₁₆	#64408
hypocenter	C₇₃	C₂×M₁₂₈
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
1. #22625100	C₂	direct (N × H)
2. C₂×#17989426	C₂	semidirect
4. #17989426	C₂²	semidirect
42. C₂×C₇₃	M₁₂₈	semidirect
47. C₇₃	C₂×M₁₂₈	semidirect
85. C₂	#22625100	direct (N × H)

Maximal subgroups

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

subgroup	index
#22625100	2
C₂×#17989426	2
C₂²×#14556497	2
C₂×M₁₂₈	73

Subgroups — C2×#22625100 #34014562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22625100 #34014562