Subgroups — #3407⋊C₃ #73276

Order 384.

100 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	#504⋊C₃	C₂	1	2	yes	maximal, complemented
3	#3407	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₂×#41⋊C₃	C₄	1	1	yes	characteristic
5	#131⋊C₃	C₄	1	1	yes	characteristic
6	#131⋊C₃	C₂²	1	1	yes	characteristic
7	C₃×M₃₂	—	4	1	no	maximal
8	C₂×#131	C₂×C₃	1	1	yes	characteristic
9	#504	—	3	2	no	—
10	#504	C₂×C₃	1	2	yes	complemented
11	C₂×M₃₂	—	3	1	no	—
12	C₂×M₃₂	—	3	1	no	—
13	#41⋊C₃	C₈	1	1	yes	characteristic
14	#41⋊C₃	C₂×C₄	1	1	yes	characteristic
15	C₂×SL(2,𝔽₃)	C₈	1	1	yes	characteristic
16	C₂×C₃×C₈	—	4	1	no	—
17	C₃×C₁₆	—	4	2	no	—
18	C₂×#41	C₃×C₄	1	1	yes	characteristic
19	#131	—	3	1	no	—
20	#131	—	3	1	no	—
21	#131	C₃×C₄	1	1	yes	characteristic
22	#131	C₂²×C₃	1	1	yes	characteristic
23	C₂×M₁₆	—	3	1	no	—
24	C₂²×C₈	—	3	1	no	—
25	M₃₂	—	3	1	no	—
26	M₃₂	—	3	2	no	—
27	M₃₂	—	3	2	no	—
28	M₃₂	A₄	1	1	yes	characteristic
29	C₂×C₁₆	—	3	2	no	—
30	C₂×C₁₆	—	3	2	no	—
31	C₂×C₃×C₄	—	4	1	no	—
32	SL(2,𝔽₃)	C₂×C₈	1	1	yes	characteristic
33	C₃×C₈	—	4	1	no	—
34	C₃×C₈	—	4	1	no	—
35	#41	—	3	1	no	—
36	#41	—	3	1	no	—
37	#41	C₃×C₈	1	1	yes	characteristic
38	#41	C₂×C₃×C₄	1	1	yes	characteristic
39	C₂×Q₈	C₃×C₈	1	1	yes	characteristic
40	C₂×D₄	—	3	1	no	—
41	C₂²×C₄	—	3	1	no	—
42	M₁₆	—	3	2	no	—
43	M₁₆	—	3	1	no	—
44	M₁₆	—	3	1	no	—
45	C₂×C₈	—	3	1	no	—
46	C₂×C₈	—	3	1	no	—
47	C₂×C₈	—	3	1	no	—
48	C₂×C₈	—	3	1	no	—
49	C₂×C₈	—	3	1	no	—
50	C₂×C₈	C₂×A₄	1	1	yes	characteristic
51	C₁₆	—	3	2	no	—
52	C₁₆	C₂×A₄	1	2	yes	—
53	C₂²×C₃	—	4	1	no	—
54	C₃×C₄	—	4	1	no	—
55	C₃×C₄	—	4	1	no	—
56	C₂³	—	3	1	no	—
57	Q₈	—	3	1	no	—
58	Q₈	C₂×C₃×C₈	1	1	yes	characteristic
59	D₄	—	3	1	no	—
60	D₄	—	3	1	no	—
61	D₄	—	3	2	no	—
62	C₂×C₄	—	3	1	no	—
63	C₂×C₄	—	3	1	no	—
64	C₂×C₄	—	3	1	no	—
65	C₂×C₄	—	3	1	no	—
66	C₂×C₄	—	3	1	no	—
67	C₂×C₄	C₄×A₄	1	1	yes	characteristic
68	C₈	—	3	1	no	—
69	C₈	—	3	1	no	—
70	C₈	C₄×A₄	1	1	yes	characteristic
71	C₈	C₂²×A₄	1	1	yes	characteristic
72	C₂×C₃	—	4	1	no	—
73	C₂×C₃	—	8	1	no	—
74	C₂²	—	3	1	no	—
75	C₂²	—	3	1	no	—
76	C₂²	—	12	1	no	—
77	C₂²	C₈×A₄	1	1	yes	characteristic
78	C₄	—	3	1	no	—
79	C₄	—	3	1	no	—
80	C₄	C₈×A₄	1	1	yes	characteristic
81	C₄	C₂×C₄×A₄	1	1	yes	characteristic
82	C₃	—	4	1	no	Sylow
83	C₂	—	2	1	no	—
84	C₂	—	6	1	no	—
85	C₂	—	6	1	no	—
86	C₂	C₂×C₈×A₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×A₄
commutator, hypocenter	Q₈	C₂×C₃×C₈
Fitting	#3407	C₃
socle	C₂	C₂×C₈×A₄
prime radical	C₂×#41⋊C₃	C₄
cosocle	#131	C₂²×C₃
hypercenter	M₃₂	A₄
LCS	G ▷ Q₈
UCS	C₁ ◁ C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #504⋊C₃	C₂	semidirect
3. #3407	C₃	semidirect
10. #504	C₂×C₃	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
#504⋊C₃	2
#3407	3
C₃×M₃₂	4

Subgroups — #3407⋊C3 #73276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3407⋊C₃ #73276