Subgroups — #1407×C₁₇₃ #36349192

Order 22144.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#497×C₁₇₃	C₂	1	1	yes	maximal, characteristic
2	#355×C₁₇₃	C₂	1	1	yes	maximal, characteristic
3	#354×C₁₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₁₇₃	—	2	1	no	—
5	C₂×SD₁₆×C₁₇₃	—	2	1	no	—
6	C₄⋊Q₈×C₁₇₃	C₄	1	1	yes	characteristic, complemented
7	#124×C₁₇₃	C₂²	1	1	yes	characteristic
8	#101×C₁₇₃	—	2	1	no	—
9	#99×C₁₇₃	—	2	1	no	—
10	#97×C₁₇₃	C₄	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₁₇₃	—	2	1	no	—
12	C₂×Q₈×C₁₇₃	D₄	1	1	yes	characteristic
13	C₂×D₄×C₁₇₃	D₄	1	1	yes	characteristic
14	Q₁₆×C₁₇₃	—	4	2	no	—
15	SD₁₆×C₁₇₃	—	4	2	no	—
16	M₁₆×C₁₇₃	—	4	1	no	—
17	C₂×C₈×C₁₇₃	—	2	1	no	—
18	C₄⋊C₄×C₁₇₃	—	4	1	no	—
19	C₂²⋊C₄×C₁₇₃	—	4	1	no	—
20	C₂²⋊C₄×C₁₇₃	—	4	1	no	—
21	C₄²×C₁₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₁₇₃	—	2	1	no	—
23	Q₈×C₁₇₃	—	4	1	no	—
24	Q₈×C₁₇₃	—	4	1	no	—
25	Q₈×C₁₇₃	—	4	1	no	—
26	D₄×C₁₇₃	—	4	1	no	—
27	C₂×C₄×C₁₇₃	—	2	1	no	—
28	C₂×C₄×C₁₇₃	—	2	1	no	—
29	C₂×C₄×C₁₇₃	—	4	1	no	—
30	C₂×C₄×C₁₇₃	—	8	1	no	—
31	C₂×C₄×C₁₇₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₈×C₁₇₃	—	2	2	no	—
33	C₈×C₁₇₃	—	8	1	no	—
34	C₂²×C₁₇₃	—	4	1	no	—
35	C₂²×C₁₇₃	—	8	1	no	—
36	C₂²×C₁₇₃	#99	1	1	yes	characteristic
37	C₄×C₁₇₃	—	2	1	no	—
38	C₄×C₁₇₃	—	4	1	no	—
39	C₄×C₁₇₃	—	4	1	no	—
40	C₄×C₁₇₃	—	8	1	no	—
41	C₄×C₁₇₃	—	16	1	no	—
42	C₂×C₁₇₃	—	2	1	no	—
43	C₂×C₁₇₃	—	8	1	no	—
44	C₂×C₁₇₃	#353	1	1	yes	characteristic
45	C₁₇₃	#1407	1	1	yes	characteristic, direct product factor, Sylow
46	#1407	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	#497	C₂×C₁₇₃	1	1	yes	characteristic
48	#355	C₂×C₁₇₃	1	1	yes	characteristic
49	#354	C₂×C₁₇₃	1	1	yes	characteristic
50	C₂×Q₁₆	—	2	1	no	—
51	C₂×SD₁₆	—	2	1	no	—
52	C₄⋊Q₈	C₄×C₁₇₃	1	1	yes	characteristic, complemented
53	#124	C₂²×C₁₇₃	1	1	yes	characteristic
54	#101	—	2	1	no	—
55	#99	—	2	1	no	—
56	#97	C₄×C₁₇₃	1	1	yes	characteristic, complemented
57	C₂×Q₈	—	2	1	no	—
58	C₂×Q₈	D₄×C₁₇₃	1	1	yes	characteristic
59	C₂×D₄	D₄×C₁₇₃	1	1	yes	characteristic
60	Q₁₆	—	4	2	no	—
61	SD₁₆	—	4	2	no	—
62	M₁₆	—	4	1	no	—
63	C₂×C₈	—	2	1	no	—
64	C₄⋊C₄	—	4	1	no	—
65	C₂²⋊C₄	—	4	1	no	—
66	C₂²⋊C₄	—	4	1	no	—
67	C₄²	C₂×C₄×C₁₇₃	1	1	yes	characteristic
68	C₂³	—	2	1	no	—
69	Q₈	—	4	1	no	—
70	Q₈	—	4	1	no	—
71	Q₈	—	4	1	no	—
72	D₄	—	4	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	8	1	no	—
77	C₂×C₄	C₂²⋊C₄×C₁₇₃	1	1	yes	characteristic
78	C₈	—	2	2	no	—
79	C₈	—	8	1	no	—
80	C₂²	—	4	1	no	—
81	C₂²	—	8	1	no	—
82	C₂²	#99×C₁₇₃	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	8	1	no	—
87	C₄	—	16	1	no	—
88	C₂	—	2	1	no	—
89	C₂	—	8	1	no	—
90	C₂	#353×C₁₇₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₇₃	#353
commutator	C₄²	C₂×C₄×C₁₇₃
Frattini, cosocle	#124	C₂²×C₁₇₃
prime radical	C₂×D₄×C₁₇₃	D₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇₃ ◁ C₂²×C₁₇₃ ◁ C₂×C₄×C₁₇₃ ◁ #124×C₁₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₄⋊Q₈×C₁₇₃	C₄	semidirect
10. #97×C₁₇₃	C₄	semidirect
45. C₁₇₃	#1407	direct (N × H)
46. #1407	C₁₇₃	direct (N × H)
52. C₄⋊Q₈	C₄×C₁₇₃	semidirect
56. #97	C₄×C₁₇₃	semidirect

Maximal subgroups

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

subgroup	index
#497×C₁₇₃	2
#355×C₁₇₃	2
#354×C₁₇₃	2
#1407	173

Subgroups — #1407×C173 #36349192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1407×C₁₇₃ #36349192