Subgroups — #2913⋊C₃ #73246

Order 384.

131 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#131⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#520⋊C₃	C₂	1	2	yes	maximal
3	#2913	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₂×#41⋊C₃	C₂²	1	1	yes	characteristic
5	#131⋊C₃	C₄	1	2	yes	complemented
6	C₄×SL(2,𝔽₃)	—	2	2	no	—
7	C₃×#107	—	4	1	no	maximal
8	C₂×#131	C₂×C₃	1	1	yes	characteristic
9	#520	C₂×C₃	1	2	yes	—
10	#428	—	3	2	no	—
11	#427	—	3	1	no	—
12	C₂×#107	—	3	1	no	—
13	#41⋊C₃	C₂×C₄	1	1	yes	characteristic
14	#41⋊C₃	Q₈	1	1	yes	characteristic
15	C₂×SL(2,𝔽₃)	D₄	1	1	yes	characteristic
16	C₂×C₃×C₈	—	4	1	no	—
17	C₃×C₄⋊C₄	—	4	2	no	—
18	C₂×#41	C₂²×C₃	1	1	yes	characteristic
19	#131	—	3	2	no	—
20	#131	C₃×C₄	1	2	yes	complemented
21	C₂×M₁₆	—	3	1	no	—
22	C₂²×C₈	—	3	1	no	—
23	C₄×Q₈	—	2	2	no	—
24	C₄×D₄	—	6	2	no	—
25	#117	—	3	2	no	—
26	C₂×C₄⋊C₄	—	3	2	no	—
27	#107	—	3	2	no	—
28	#107	—	3	1	no	—
29	#107	A₄	1	1	yes	characteristic
30	#106	—	3	2	no	—
31	C₂×C₃×C₄	—	4	1	no	—
32	C₂×C₃×C₄	—	8	2	no	—
33	SL(2,𝔽₃)	C₄⋊C₄	1	1	yes	characteristic
34	C₃×C₈	—	4	2	no	—
35	#41	—	3	1	no	—
36	#41	—	3	1	no	—
37	#41	C₂×C₃×C₄	1	1	yes	characteristic
38	#41	C₃×Q₈	1	1	yes	characteristic
39	C₂×Q₈	C₃×D₄	1	1	yes	characteristic
40	C₂×D₄	—	3	1	no	—
41	C₂²×C₄	—	3	1	no	—
42	C₂²×C₄	—	6	2	no	—
43	M₁₆	—	3	2	no	—
44	M₁₆	—	3	2	no	—
45	C₂×C₈	—	3	1	no	—
46	C₂×C₈	—	3	2	no	—
47	C₂×C₈	—	3	2	no	—
48	C₂×C₈	C₂×A₄	1	1	yes	characteristic
49	C₄⋊C₄	—	3	2	no	—
50	C₄⋊C₄	—	6	2	no	—
51	C₄⋊C₄	C₂×A₄	1	2	yes	—
52	C₂²⋊C₄	—	6	2	no	—
53	C₄²	—	6	2	no	—
54	C₂²×C₃	—	4	1	no	—
55	C₃×C₄	—	4	1	no	—
56	C₃×C₄	—	4	1	no	—
57	C₃×C₄	—	16	2	no	—
58	C₂³	—	3	1	no	—
59	Q₈	—	3	1	no	—
60	Q₈	C₃×C₄⋊C₄	1	1	yes	characteristic
61	D₄	—	3	1	no	—
62	D₄	—	3	1	no	—
63	D₄	—	3	2	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	3	1	no	—
66	C₂×C₄	—	3	1	no	—
67	C₂×C₄	—	3	1	no	—
68	C₂×C₄	—	3	1	no	—
69	C₂×C₄	—	3	1	no	—
70	C₂×C₄	—	6	2	no	—
71	C₂×C₄	—	24	2	no	—
72	C₂×C₄	C₂²×A₄	1	1	yes	characteristic
73	C₈	—	3	2	no	—
74	C₈	C₄×A₄	1	2	yes	—
75	C₂×C₃	—	4	1	no	—
76	C₂×C₃	—	4	1	no	—
77	C₂×C₃	—	4	1	no	—
78	C₂²	—	3	1	no	—
79	C₂²	—	3	1	no	—
80	C₂²	—	6	1	no	—
81	C₂²	—	6	1	no	—
82	C₂²	D₄×A₄	1	1	yes	characteristic
83	C₄	—	3	1	no	—
84	C₄	—	3	1	no	—
85	C₄	—	4	2	no	—
86	C₄	—	12	2	no	—
87	C₄	C₂×C₄×A₄	1	1	yes	characteristic
88	C₄	Q₈×A₄	1	1	yes	characteristic
89	C₃	—	4	1	no	Sylow
90	C₂	—	6	1	no	—
91	C₂	—	6	1	no	—
92	C₂	A₄×C₄⋊C₄	1	1	yes	characteristic
93	C₂	#576⋊C₃	1	1	yes	characteristic
94	C₂	#578⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	D₄×A₄
commutator	#41	C₂×C₃×C₄
Frattini	C₂×C₄	C₂²×A₄
Fitting	#2913	C₃
prime radical	C₂×#41⋊C₃	C₂²
cosocle	C₂×#41	C₂²×C₃
hypercenter	#107	A₄
hypocenter	Q₈	C₃×C₄⋊C₄
LCS	G ▷ #41 ▷ Q₈
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
3. #2913	C₃	semidirect
5. #131⋊C₃	C₄	semidirect
20. #131	C₃×C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#131⋊C₃	2
#520⋊C₃	2
#2913	3
C₃×#107	4

Subgroups — #2913⋊C3 #73246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2913⋊C₃ #73246