Subgroups — C₄×#131⋊C₃ #73225

Order 384.

157 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#131⋊C₃	C₂	1	2	yes	maximal
2	C₄×#41⋊C₃	C₂	1	1	yes	maximal, characteristic
3	C₄×#131	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₂×#41⋊C₃	C₂²	1	1	yes	characteristic
5	#131⋊C₃	C₄	1	4	yes	direct product factor
6	C₄×SL(2,𝔽₃)	C₄	1	2	yes	—
7	C₃×C₄×C₈	—	4	1	no	maximal
8	C₂×#131	C₂×C₃	1	2	yes	—
9	C₄×#41	C₂×C₃	1	1	yes	characteristic
10	#405	—	3	2	no	—
11	C₄×M₁₆	—	3	1	no	—
12	C₂×C₄×C₈	—	3	1	no	—
13	#41⋊C₃	C₂×C₄	1	2	yes	—
14	C₂×SL(2,𝔽₃)	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃×C₈	—	4	2	no	—
16	C₃×C₄²	—	4	1	no	—
17	C₂×#41	C₂²×C₃	1	1	yes	characteristic
18	#131	—	3	4	no	—
19	#131	C₃×C₄	1	4	yes	complemented
20	C₂×M₁₆	—	3	2	no	—
21	C₂²×C₈	—	3	2	no	—
22	C₄×Q₈	C₃×C₄	1	2	yes	—
23	C₄×D₄	—	3	2	no	—
24	#117	—	3	1	no	—
25	C₂×C₄²	—	3	1	no	—
26	#97	—	3	2	no	—
27	C₄×C₈	—	3	2	no	—
28	C₄×C₈	—	3	1	no	—
29	C₄×C₈	A₄	1	1	yes	characteristic
30	C₂×C₃×C₄	—	4	2	no	—
31	C₂×C₃×C₄	—	4	1	no	—
32	SL(2,𝔽₃)	C₄²	1	1	yes	characteristic
33	C₃×C₈	—	4	4	no	—
34	#41	—	3	2	no	—
35	#41	C₂×C₃×C₄	1	2	yes	—
36	C₂×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
37	C₂×D₄	—	3	1	no	—
38	C₂²×C₄	—	3	1	no	—
39	C₂²×C₄	—	3	2	no	—
40	M₁₆	—	3	4	no	—
41	M₁₆	—	3	4	no	—
42	C₂×C₈	—	3	2	no	—
43	C₂×C₈	—	3	4	no	—
44	C₂×C₈	—	3	4	no	—
45	C₂×C₈	C₂×A₄	1	2	yes	—
46	C₄⋊C₄	—	3	2	no	—
47	C₂²⋊C₄	—	3	2	no	—
48	C₄²	—	3	2	no	—
49	C₄²	—	3	1	no	—
50	C₄²	C₂×A₄	1	1	yes	characteristic
51	C₂²×C₃	—	4	1	no	—
52	C₃×C₄	—	4	4	no	—
53	C₃×C₄	—	4	2	no	—
54	C₂³	—	3	1	no	—
55	Q₈	—	3	1	no	—
56	Q₈	C₃×C₄²	1	1	yes	characteristic
57	D₄	—	3	2	no	—
58	D₄	—	3	2	no	—
59	C₂×C₄	—	3	1	no	—
60	C₂×C₄	—	3	2	no	—
61	C₂×C₄	—	3	2	no	—
62	C₂×C₄	—	3	2	no	—
63	C₂×C₄	—	6	4	no	—
64	C₂×C₄	C₄×A₄	1	2	yes	—
65	C₂×C₄	C₂²×A₄	1	1	yes	characteristic
66	C₈	—	3	4	no	—
67	C₈	C₄×A₄	1	4	yes	—
68	C₂×C₃	—	4	1	no	—
69	C₂×C₃	—	4	2	no	—
70	C₂²	—	3	2	no	—
71	C₂²	—	6	2	no	—
72	C₂²	C₂×C₄×A₄	1	1	yes	characteristic
73	C₄	—	3	1	no	—
74	C₄	—	3	1	no	—
75	C₄	—	6	2	no	—
76	C₄	#131⋊C₃	1	4	yes	direct product factor
77	C₄	C₂×C₄×A₄	1	2	yes	—
78	C₃	—	4	1	no	Sylow
79	C₂	—	6	2	no	—
80	C₂	C₄²×A₄	1	1	yes	characteristic
81	C₂	C₂×#131⋊C₃	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄×C₈	A₄
commutator, hypocenter	Q₈	C₃×C₄²
Frattini	C₂×C₄	C₂²×A₄
Fitting	C₄×#131	C₃
socle	C₂²	C₂×C₄×A₄
prime radical	C₂×#41⋊C₃	C₂²
cosocle	C₂×#41	C₂²×C₃
LCS	G ▷ Q₈
UCS	C₁ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₄×#131	C₃	semidirect
5. #131⋊C₃	C₄	direct (N × H)
19. #131	C₃×C₄	semidirect
76. C₄	#131⋊C₃	direct (N × H)

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
C₄×#41⋊C₃	2
C₄×#131	3
C₃×C₄×C₈	4

Subgroups — C4×#131⋊C3 #73225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#131⋊C₃ #73225