Subgroups — C₃×#1534 #72249

Order 384.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#125	C₂	1	1	yes	maximal, characteristic
2	C₃×#432	C₂	1	2	yes	maximal
3	C₃×#330	C₂	1	4	yes	maximal, complemented
4	#1534	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×#125	—	2	2	no	—
6	C₃×#125	C₄	1	2	yes	—
7	C₃×#125	C₂²	1	2	yes	—
8	C₂×C₃×C₄⋊C₄	—	2	2	no	—
9	C₂×C₃×C₄⋊C₄	C₄	1	2	yes	—
10	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
11	C₃×C₄⋊C₈	—	2	2	no	—
12	C₃×C₂²⋊C₈	—	2	2	no	—
13	C₃×#97	C₂²	1	4	yes	—
14	C₂×#125	C₂×C₃	1	1	yes	characteristic
15	#432	C₂×C₃	1	2	yes	—
16	#330	C₂×C₃	1	4	yes	complemented
17	C₂²×C₃×C₄	—	2	2	no	—
18	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₃×C₄	D₄	1	2	yes	—
20	C₂×C₃×C₈	—	2	4	no	—
21	C₃×C₄⋊C₄	—	2	4	no	—
22	C₃×C₄⋊C₄	—	2	2	no	—
23	C₃×C₄⋊C₄	—	2	4	no	—
24	C₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
25	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
26	C₃×C₄²	D₄	1	2	yes	—
27	C₃×C₄²	C₂³	1	1	yes	characteristic
28	#125	—	2	2	no	—
29	#125	C₃×C₄	1	2	yes	—
30	#125	C₂²×C₃	1	2	yes	—
31	C₂×C₄⋊C₄	—	2	2	no	—
32	C₂×C₄⋊C₄	C₃×C₄	1	2	yes	—
33	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
34	C₄⋊C₈	—	2	2	no	—
35	C₂²⋊C₈	—	2	2	no	—
36	#97	C₂²×C₃	1	4	yes	—
37	C₂³×C₃	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₃×C₄	—	2	2	no	—
39	C₂×C₃×C₄	—	2	4	no	—
40	C₂×C₃×C₄	—	4	2	no	—
41	C₂×C₃×C₄	—	4	4	no	—
42	C₂×C₃×C₄	C₂²⋊C₄	1	2	yes	—
43	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
44	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
46	C₃×C₈	—	4	4	no	—
47	C₂²×C₄	—	2	2	no	—
48	C₂²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
49	C₂²×C₄	C₃×D₄	1	2	yes	—
50	C₂×C₈	—	2	4	no	—
51	C₄⋊C₄	—	2	4	no	—
52	C₄⋊C₄	—	2	2	no	—
53	C₄⋊C₄	—	2	4	no	—
54	C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
55	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
56	C₄²	C₃×D₄	1	2	yes	—
57	C₄²	C₂³×C₃	1	1	yes	characteristic
58	C₂²×C₃	—	2	2	no	—
59	C₂²×C₃	#101	1	2	yes	—
60	C₂²×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
61	C₃×C₄	—	2	1	no	—
62	C₃×C₄	—	2	1	no	—
63	C₃×C₄	—	2	2	no	—
64	C₃×C₄	—	2	2	no	—
65	C₃×C₄	—	4	4	no	—
66	C₂³	C₃×C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄	—	2	2	no	—
68	C₂×C₄	—	2	4	no	—
69	C₂×C₄	—	4	2	no	—
70	C₂×C₄	—	4	4	no	—
71	C₂×C₄	C₃×C₂²⋊C₄	1	2	yes	—
72	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
74	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
75	C₈	—	4	4	no	—
76	C₂×C₃	—	2	2	no	—
77	C₂×C₃	C₂×#101	1	1	yes	characteristic
78	C₂×C₃	#421	1	2	yes	—
79	C₂²	—	2	2	no	—
80	C₂²	C₃×#101	1	2	yes	—
81	C₂²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	2	1	no	—
84	C₄	—	2	2	no	—
85	C₄	—	2	2	no	—
86	C₄	—	4	4	no	—
87	C₃	#1534	1	1	yes	characteristic, direct product factor, Sylow
88	C₂	—	2	2	no	—
89	C₂	C₂×C₃×#101	1	1	yes	characteristic
90	C₂	C₃×#421	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₃×C₄
Frattini, cosocle	C₄²	C₂³×C₃
prime radical	C₂³×C₃	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×#330	C₂	semidirect
4. #1534	C₃	direct (N × H)
16. #330	C₂×C₃	semidirect
87. C₃	#1534	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×C₃×#125	2
C₃×#432	2
C₃×#330	2
#1534	3

Subgroups — C3×#1534 #72249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1534 #72249