Subgroups — C₂×C₃×#433 #84783

Order 384.

412 conjugacy classes of subgroups.

The subgroup lattice has 142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#117	C₂	1	1	yes	maximal, characteristic
2	C₃×#433	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₃×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₂²⋊C₈	C₂	1	2	yes	maximal
5	C₂×C₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#433	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₈	C₂²	1	2	yes	—
10	C₂²×C₃×C₈	C₂²	1	2	yes	—
11	C₃×#117	C₄	1	4	yes	—
12	C₃×#117	C₂²	1	4	yes	—
13	C₂×C₃×C₄⋊C₄	C₄	1	2	yes	—
14	C₂×C₃×C₂²⋊C₄	C₄	1	2	yes	—
15	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
17	C₃×C₄⋊C₈	C₂²	1	8	yes	complemented
18	C₃×C₂²⋊C₈	C₂²	1	8	yes	—
19	C₃×#97	C₂²	1	4	yes	complemented
20	C₃×C₄×C₈	C₂²	1	4	yes	complemented
21	C₂×#117	C₂×C₃	1	1	yes	characteristic
22	#433	C₂×C₃	1	8	yes	direct product factor
23	C₂×C₄⋊C₈	C₂×C₃	1	2	yes	complemented
24	C₂×C₂²⋊C₈	C₂×C₃	1	2	yes	—
25	C₂×#97	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂⁴×C₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃×C₄	—	2	4	no	—
29	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
30	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
31	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
33	C₂²×C₃×C₄	C₂³	1	2	yes	—
34	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
35	C₂×C₃×C₈	—	2	4	no	—
36	C₂×C₃×C₈	—	2	4	no	—
37	C₂×C₃×C₈	C₂³	1	4	yes	—
38	C₂×C₃×C₈	C₂³	1	4	yes	—
39	C₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
40	C₃×C₂²⋊C₄	C₂×C₄	1	8	yes	—
41	C₃×C₄²	C₂×C₄	1	2	yes	—
42	C₃×C₄²	C₂×C₄	1	2	yes	—
43	C₃×C₄²	C₂³	1	2	yes	—
44	C₃×C₄²	C₂³	1	2	yes	—
45	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
46	C₂²×C₈	C₂²×C₃	1	2	yes	—
47	C₂²×C₈	C₂²×C₃	1	2	yes	—
48	#117	C₃×C₄	1	4	yes	—
49	#117	C₂²×C₃	1	4	yes	—
50	C₂×C₄⋊C₄	C₃×C₄	1	2	yes	—
51	C₂×C₂²⋊C₄	C₃×C₄	1	2	yes	—
52	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
53	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
54	C₄⋊C₈	C₂²×C₃	1	8	yes	complemented
55	C₂²⋊C₈	C₂²×C₃	1	8	yes	—
56	#97	C₂²×C₃	1	4	yes	complemented
57	C₄×C₈	C₂²×C₃	1	4	yes	complemented
58	C₂³×C₃	—	2	2	no	—
59	C₂³×C₃	—	2	4	no	—
60	C₂³×C₃	C₂²×C₄	1	2	yes	—
61	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₃×C₄	—	2	2	no	—
63	C₂×C₃×C₄	—	2	4	no	—
64	C₂×C₃×C₄	—	2	4	no	—
65	C₂×C₃×C₄	—	2	4	no	—
66	C₂×C₃×C₄	—	2	4	no	—
67	C₂×C₃×C₄	C₂²×C₄	1	4	yes	—
68	C₂×C₃×C₄	C₂²×C₄	1	4	yes	—
69	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
70	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₃×C₄	#41	1	4	yes	—
72	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
73	C₃×C₈	—	2	4	no	—
74	C₃×C₈	—	2	4	no	—
75	C₂⁴	C₂×C₃×C₄	1	1	yes	characteristic
76	C₂²×C₄	—	2	4	no	—
77	C₂²×C₄	C₂×C₃×C₄	1	2	yes	—
78	C₂²×C₄	C₂×C₃×C₄	1	2	yes	—
79	C₂²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
80	C₂²×C₄	C₂×C₃×C₄	1	2	yes	—
81	C₂²×C₄	C₂³×C₃	1	2	yes	—
82	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
83	C₂×C₈	—	2	4	no	—
84	C₂×C₈	—	2	4	no	—
85	C₂×C₈	C₂³×C₃	1	4	yes	—
86	C₂×C₈	C₂³×C₃	1	4	yes	—
87	C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
88	C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
89	C₄²	C₂×C₃×C₄	1	2	yes	—
90	C₄²	C₂×C₃×C₄	1	2	yes	—
91	C₄²	C₂³×C₃	1	2	yes	—
92	C₄²	C₂³×C₃	1	2	yes	—
93	C₂²×C₃	—	2	2	no	—
94	C₂²×C₃	—	2	4	no	—
95	C₂²×C₃	—	4	4	no	—
96	C₂²×C₃	#117	1	2	yes	—
97	C₂²×C₃	#131	1	4	yes	—
98	C₂²×C₃	C₂³×C₄	1	1	yes	characteristic
99	C₃×C₄	—	2	2	no	—
100	C₃×C₄	—	2	4	no	—
101	C₃×C₄	—	2	4	no	—
102	C₃×C₄	#117	1	2	yes	—
103	C₃×C₄	C₂×#41	1	2	yes	—
104	C₂³	—	2	2	no	—
105	C₂³	—	2	4	no	—
106	C₂³	C₂²×C₃×C₄	1	2	yes	—
107	C₂³	C₂²×C₃×C₄	1	1	yes	characteristic
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	2	4	no	—
110	C₂×C₄	—	2	4	no	—
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	—	2	4	no	—
113	C₂×C₄	C₂²×C₃×C₄	1	4	yes	—
114	C₂×C₄	C₂²×C₃×C₄	1	4	yes	—
115	C₂×C₄	C₂²×C₃×C₄	1	2	yes	—
116	C₂×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
117	C₂×C₄	C₃×#41	1	4	yes	—
118	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
119	C₈	—	2	4	no	—
120	C₈	—	2	4	no	—
121	C₂×C₃	—	4	2	no	—
122	C₂×C₃	#433	1	4	yes	direct product factor
123	C₂×C₃	C₂×#117	1	1	yes	characteristic
124	C₂×C₃	C₂×#131	1	2	yes	—
125	C₂²	—	2	4	no	—
126	C₂²	—	2	2	no	—
127	C₂²	—	4	4	no	—
128	C₂²	C₃×#117	1	2	yes	—
129	C₂²	C₃×#131	1	4	yes	—
130	C₂²	C₂³×C₃×C₄	1	1	yes	characteristic
131	C₄	—	2	4	no	—
132	C₄	—	2	4	no	—
133	C₄	—	2	2	no	—
134	C₄	C₃×#117	1	2	yes	—
135	C₄	C₂×C₃×#41	1	2	yes	—
136	C₃	C₂×#433	1	1	yes	characteristic, direct product factor, Sylow
137	C₂	—	4	2	no	—
138	C₂	C₃×#433	1	4	yes	direct product factor
139	C₂	C₂×C₃×#117	1	1	yes	characteristic
140	C₂	C₂×C₃×#131	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂³
commutator	C₂²	C₂³×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂⁴×C₃
socle	C₂³×C₃	C₂²×C₄
prime radical	C₂⁴×C₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#433	C₂	direct (N × H)
3. C₂×C₃×C₄⋊C₈	C₂	semidirect
5. C₂×C₃×#97	C₂	semidirect
6. C₂×C₃×C₄×C₈	C₂	semidirect
7. C₂×#433	C₃	direct (N × H)
17. C₃×C₄⋊C₈	C₂²	semidirect
19. C₃×#97	C₂²	semidirect
20. C₃×C₄×C₈	C₂²	semidirect
22. #433	C₂×C₃	direct (N × H)
23. C₂×C₄⋊C₈	C₂×C₃	semidirect
25. C₂×#97	C₂×C₃	semidirect
26. C₂×C₄×C₈	C₂×C₃	semidirect
54. C₄⋊C₈	C₂²×C₃	semidirect
56. #97	C₂²×C₃	semidirect
57. C₄×C₈	C₂²×C₃	semidirect
122. C₂×C₃	#433	direct (N × H)
136. C₃	C₂×#433	direct (N × H)
138. C₂	C₃×#433	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×#117	2
C₃×#433	2
C₂×C₃×C₄⋊C₈	2
C₂×C₃×C₂²⋊C₈	2
C₂×C₃×#97	2
C₂×C₃×C₄×C₈	2
C₂×#433	3

Subgroups — C2×C3×#433 #84783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#433 #84783