Subgroups — #1845×C₁₆₇ #36320205

Order 21376.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#107×C₁₆₇	C₂	1	4	yes	maximal
2	C₂×C₄×C₈×C₁₆₇	C₂	1	1	yes	maximal, characteristic
3	#384×C₁₆₇	C₂	1	2	yes	maximal
4	C₂²×C₈×C₁₆₇	C₂²	1	2	yes	—
5	C₂×C₄⋊C₄×C₁₆₇	—	2	4	no	—
6	C₂×C₄⋊C₄×C₁₆₇	C₂²	1	4	yes	—
7	C₂×C₄²×C₁₆₇	C₂²	1	1	yes	characteristic
8	#107×C₁₆₇	—	2	8	no	—
9	C₄×C₈×C₁₆₇	C₄	1	4	yes	complemented
10	C₂²×C₄×C₁₆₇	—	2	4	no	—
11	C₂²×C₄×C₁₆₇	D₄	1	2	yes	—
12	C₂²×C₄×C₁₆₇	C₂³	1	1	yes	characteristic
13	C₂×C₈×C₁₆₇	C₂×C₄	1	4	yes	—
14	C₂×C₈×C₁₆₇	D₄	1	4	yes	—
15	C₂×C₈×C₁₆₇	Q₈	1	4	yes	—
16	C₄⋊C₄×C₁₆₇	—	2	8	no	—
17	C₄⋊C₄×C₁₆₇	—	4	8	no	—
18	C₄²×C₁₆₇	C₂×C₄	1	2	yes	—
19	C₄²×C₁₆₇	Q₈	1	2	yes	—
20	C₂³×C₁₆₇	C₂×D₄	1	1	yes	characteristic
21	C₂×C₄×C₁₆₇	—	4	4	no	—
22	C₂×C₄×C₁₆₇	—	4	8	no	—
23	C₂×C₄×C₁₆₇	C₄⋊C₄	1	4	yes	—
24	C₂×C₄×C₁₆₇	D₈	1	4	yes	—
25	C₂×C₄×C₁₆₇	Q₁₆	1	4	yes	—
26	C₂×C₄×C₁₆₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₆₇	C₂×D₄	1	2	yes	—
28	C₂×C₄×C₁₆₇	C₂×Q₈	1	2	yes	—
29	C₂×C₄×C₁₆₇	C₂×Q₈	1	1	yes	characteristic
30	C₈×C₁₆₇	C₄⋊C₄	1	8	yes	complemented
31	C₂²×C₁₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₂²×C₁₆₇	#127	1	1	yes	characteristic
33	C₂²×C₁₆₇	C₄⋊Q₈	1	1	yes	characteristic
34	C₂²×C₁₆₇	C₂×D₈	1	2	yes	—
35	C₂²×C₁₆₇	C₂×Q₁₆	1	2	yes	—
36	C₄×C₁₆₇	—	8	4	no	—
37	C₄×C₁₆₇	#107	1	8	yes	complemented
38	C₄×C₁₆₇	C₂×C₄⋊C₄	1	2	yes	—
39	C₄×C₁₆₇	C₄⋊Q₈	1	2	yes	—
40	C₂×C₁₆₇	#384	1	1	yes	characteristic
41	C₂×C₁₆₇	C₂×#107	1	2	yes	—
42	C₂×C₁₆₇	#493	1	1	yes	characteristic
43	C₂×C₁₆₇	#494	1	1	yes	characteristic
44	C₂×C₁₆₇	#500	1	2	yes	—
45	C₁₆₇	#1845	1	1	yes	characteristic, direct product factor, Sylow
46	#1845	C₁₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂×#107	C₂×C₁₆₇	1	4	yes	—
48	C₂×C₄×C₈	C₂×C₁₆₇	1	1	yes	characteristic
49	#384	C₂×C₁₆₇	1	2	yes	—
50	C₂²×C₈	C₂²×C₁₆₇	1	2	yes	—
51	C₂×C₄⋊C₄	—	2	4	no	—
52	C₂×C₄⋊C₄	C₂²×C₁₆₇	1	4	yes	—
53	C₂×C₄²	C₂²×C₁₆₇	1	1	yes	characteristic
54	#107	—	2	8	no	—
55	C₄×C₈	C₄×C₁₆₇	1	4	yes	complemented
56	C₂²×C₄	—	2	4	no	—
57	C₂²×C₄	D₄×C₁₆₇	1	2	yes	—
58	C₂²×C₄	C₂³×C₁₆₇	1	1	yes	characteristic
59	C₂×C₈	C₂×C₄×C₁₆₇	1	4	yes	—
60	C₂×C₈	D₄×C₁₆₇	1	4	yes	—
61	C₂×C₈	Q₈×C₁₆₇	1	4	yes	—
62	C₄⋊C₄	—	2	8	no	—
63	C₄⋊C₄	—	4	8	no	—
64	C₄²	C₂×C₄×C₁₆₇	1	2	yes	—
65	C₄²	Q₈×C₁₆₇	1	2	yes	—
66	C₂³	C₂×D₄×C₁₆₇	1	1	yes	characteristic
67	C₂×C₄	—	4	4	no	—
68	C₂×C₄	—	4	8	no	—
69	C₂×C₄	C₄⋊C₄×C₁₆₇	1	4	yes	—
70	C₂×C₄	D₈×C₁₆₇	1	4	yes	—
71	C₂×C₄	Q₁₆×C₁₆₇	1	4	yes	—
72	C₂×C₄	C₂²×C₄×C₁₆₇	1	1	yes	characteristic
73	C₂×C₄	C₂×D₄×C₁₆₇	1	2	yes	—
74	C₂×C₄	C₂×Q₈×C₁₆₇	1	2	yes	—
75	C₂×C₄	C₂×Q₈×C₁₆₇	1	1	yes	characteristic
76	C₈	C₄⋊C₄×C₁₆₇	1	8	yes	complemented
77	C₂²	C₂×C₄⋊C₄×C₁₆₇	1	1	yes	characteristic
78	C₂²	#127×C₁₆₇	1	1	yes	characteristic
79	C₂²	C₄⋊Q₈×C₁₆₇	1	1	yes	characteristic
80	C₂²	C₂×D₈×C₁₆₇	1	2	yes	—
81	C₂²	C₂×Q₁₆×C₁₆₇	1	2	yes	—
82	C₄	—	8	4	no	—
83	C₄	#107×C₁₆₇	1	8	yes	complemented
84	C₄	C₂×C₄⋊C₄×C₁₆₇	1	2	yes	—
85	C₄	C₄⋊Q₈×C₁₆₇	1	2	yes	—
86	C₂	#384×C₁₆₇	1	1	yes	characteristic
87	C₂	C₂×#107×C₁₆₇	1	2	yes	—
88	C₂	#493×C₁₆₇	1	1	yes	characteristic
89	C₂	#494×C₁₆₇	1	1	yes	characteristic
90	C₂	#500×C₁₆₇	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₆₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₆₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₆₇ ◁ C₂×C₄²×C₁₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₄×C₈×C₁₆₇	C₄	semidirect
30. C₈×C₁₆₇	C₄⋊C₄	semidirect
37. C₄×C₁₆₇	#107	semidirect
45. C₁₆₇	#1845	direct (N × H)
46. #1845	C₁₆₇	direct (N × H)
55. C₄×C₈	C₄×C₁₆₇	semidirect
76. C₈	C₄⋊C₄×C₁₆₇	semidirect
83. C₄	#107×C₁₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#107×C₁₆₇	2
C₂×C₄×C₈×C₁₆₇	2
#384×C₁₆₇	2
#1845	167

Subgroups — #1845×C167 #36320205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1845×C₁₆₇ #36320205