Subgroups — C₃×#2606 #84470

Order 384.

380 conjugacy classes of subgroups.

The subgroup lattice has 194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#398	C₂	1	2	yes	maximal
2	C₃×#398	C₂	1	2	yes	maximal
3	C₃×#389	C₂	1	2	yes	maximal
4	C₃×#389	C₂	1	2	yes	maximal
5	C₃×#387	C₂	1	2	yes	maximal
6	C₃×#387	C₂	1	2	yes	maximal
7	C₃×#383	C₂	1	1	yes	maximal, characteristic
8	C₃×C₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₃×#376	C₂	1	1	yes	maximal, characteristic
10	#2606	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₄²	C₂²	1	2	yes	—
19	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
22	C₃×#95	C₂²	1	2	yes	—
23	C₃×#95	C₂²	1	1	yes	characteristic
24	C₃×#95	C₂²	1	1	yes	characteristic
25	C₃×#95	C₂²	1	2	yes	—
26	C₃×#95	C₂²	1	1	yes	characteristic
27	C₃×#95	C₂²	1	2	yes	—
28	C₃×#95	C₂²	1	1	yes	characteristic
29	C₃×#95	C₂²	1	2	yes	—
30	C₃×#95	C₂²	1	2	yes	—
31	C₃×#95	C₂²	1	2	yes	—
32	#398	C₂×C₃	1	2	yes	—
33	#398	C₂×C₃	1	2	yes	—
34	#389	C₂×C₃	1	2	yes	—
35	#389	C₂×C₃	1	2	yes	—
36	#387	C₂×C₃	1	2	yes	—
37	#387	C₂×C₃	1	2	yes	—
38	#383	C₂×C₃	1	1	yes	characteristic
39	C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
40	#376	C₂×C₃	1	1	yes	characteristic
41	C₂²×C₃×C₄	C₂³	1	2	yes	—
42	C₂²×C₃×C₄	C₂³	1	2	yes	—
43	C₂²×C₃×C₄	C₂³	1	2	yes	—
44	C₂²×C₃×C₄	C₂³	1	2	yes	—
45	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
47	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
48	C₂²×C₃×C₄	C₂³	1	2	yes	—
49	C₂²×C₃×C₄	C₂³	1	2	yes	—
50	C₃×C₄⋊C₄	—	2	4	no	—
51	C₃×C₄⋊C₄	—	2	4	no	—
52	C₃×C₄⋊C₄	—	2	4	no	—
53	C₃×C₄⋊C₄	—	2	4	no	—
54	C₃×C₄⋊C₄	—	2	4	no	—
55	C₃×C₄⋊C₄	—	4	2	no	—
56	C₃×C₄⋊C₄	—	4	2	no	—
57	C₃×C₄²	—	2	4	no	—
58	C₃×C₄²	—	4	1	no	—
59	C₃×C₄²	—	4	1	no	—
60	C₃×C₄²	Q₈	1	4	yes	—
61	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
62	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
63	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
64	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
65	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
66	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
67	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
68	C₂×C₄²	C₂²×C₃	1	2	yes	—
69	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
72	#95	C₂²×C₃	1	2	yes	—
73	#95	C₂²×C₃	1	1	yes	characteristic
74	#95	C₂²×C₃	1	1	yes	characteristic
75	#95	C₂²×C₃	1	2	yes	—
76	#95	C₂²×C₃	1	1	yes	characteristic
77	#95	C₂²×C₃	1	2	yes	—
78	#95	C₂²×C₃	1	1	yes	characteristic
79	#95	C₂²×C₃	1	2	yes	—
80	#95	C₂²×C₃	1	2	yes	—
81	#95	C₂²×C₃	1	2	yes	—
82	C₂³×C₃	C₂⁴	1	1	yes	characteristic
83	C₂×C₃×C₄	—	2	2	no	—
84	C₂×C₃×C₄	—	2	2	no	—
85	C₂×C₃×C₄	—	2	2	no	—
86	C₂×C₃×C₄	—	2	2	no	—
87	C₂×C₃×C₄	—	2	1	no	—
88	C₂×C₃×C₄	—	2	2	no	—
89	C₂×C₃×C₄	—	2	1	no	—
90	C₂×C₃×C₄	—	2	2	no	—
91	C₂×C₃×C₄	—	2	2	no	—
92	C₂×C₃×C₄	—	2	2	no	—
93	C₂×C₃×C₄	—	2	2	no	—
94	C₂×C₃×C₄	—	2	2	no	—
95	C₂×C₃×C₄	—	2	2	no	—
96	C₂×C₃×C₄	—	2	2	no	—
97	C₂×C₃×C₄	—	2	2	no	—
98	C₂×C₃×C₄	—	2	2	no	—
99	C₂×C₃×C₄	—	2	2	no	—
100	C₂×C₃×C₄	—	2	2	no	—
101	C₂×C₃×C₄	—	2	2	no	—
102	C₂×C₃×C₄	—	2	2	no	—
103	C₂×C₃×C₄	C₂×Q₈	1	2	yes	—
104	C₂×C₃×C₄	C₂×Q₈	1	2	yes	—
105	C₂×C₃×C₄	C₂×Q₈	1	2	yes	—
106	C₂×C₃×C₄	#41	1	4	yes	—
107	C₂×C₃×C₄	#41	1	4	yes	—
108	C₂²×C₄	C₂³×C₃	1	2	yes	—
109	C₂²×C₄	C₂³×C₃	1	2	yes	—
110	C₂²×C₄	C₂³×C₃	1	2	yes	—
111	C₂²×C₄	C₂³×C₃	1	2	yes	—
112	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
113	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
114	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
115	C₂²×C₄	C₂³×C₃	1	2	yes	—
116	C₂²×C₄	C₂³×C₃	1	2	yes	—
117	C₄⋊C₄	—	2	4	no	—
118	C₄⋊C₄	—	2	4	no	—
119	C₄⋊C₄	—	2	4	no	—
120	C₄⋊C₄	—	2	4	no	—
121	C₄⋊C₄	—	2	4	no	—
122	C₄⋊C₄	—	4	2	no	—
123	C₄⋊C₄	—	4	2	no	—
124	C₄²	—	2	4	no	—
125	C₄²	—	4	1	no	—
126	C₄²	—	4	1	no	—
127	C₄²	C₃×Q₈	1	4	yes	—
128	C₂²×C₃	C₂²×Q₈	1	1	yes	characteristic
129	C₂²×C₃	C₂×#41	1	2	yes	—
130	C₂²×C₃	C₂×#41	1	2	yes	—
131	C₂²×C₃	H(5,𝔽₂)	1	1	yes	characteristic
132	C₂²×C₃	2₋¹⁺⁴	1	1	yes	characteristic
133	C₃×C₄	—	2	2	no	—
134	C₃×C₄	—	2	2	no	—
135	C₃×C₄	—	2	2	no	—
136	C₃×C₄	—	2	4	no	—
137	C₃×C₄	—	2	4	no	—
138	C₃×C₄	—	4	2	no	—
139	C₃×C₄	—	4	2	no	—
140	C₃×C₄	—	4	2	no	—
141	C₃×C₄	—	4	2	no	—
142	C₂³	C₂⁴×C₃	1	1	yes	characteristic
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	2	1	no	—
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	C₂×C₃×Q₈	1	2	yes	—
164	C₂×C₄	C₂×C₃×Q₈	1	2	yes	—
165	C₂×C₄	C₂×C₃×Q₈	1	2	yes	—
166	C₂×C₄	C₃×#41	1	4	yes	—
167	C₂×C₄	C₃×#41	1	4	yes	—
168	C₂×C₃	#533	1	1	yes	characteristic
169	C₂×C₃	#533	1	1	yes	characteristic
170	C₂×C₃	#544	1	1	yes	characteristic
171	C₂×C₃	#552	1	2	yes	—
172	C₂×C₃	#553	1	2	yes	—
173	C₂²	C₂²×C₃×Q₈	1	1	yes	characteristic
174	C₂²	C₂×C₃×#41	1	2	yes	—
175	C₂²	C₂×C₃×#41	1	2	yes	—
176	C₂²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
177	C₂²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
178	C₄	—	2	2	no	—
179	C₄	—	2	2	no	—
180	C₄	—	2	2	no	—
181	C₄	—	2	4	no	—
182	C₄	—	2	4	no	—
183	C₄	—	4	2	no	—
184	C₄	—	4	2	no	—
185	C₄	—	4	2	no	—
186	C₄	—	4	2	no	—
187	C₃	#2606	1	1	yes	characteristic, direct product factor, Sylow
188	C₂	C₃×#533	1	1	yes	characteristic
189	C₂	C₃×#533	1	1	yes	characteristic
190	C₂	C₃×#544	1	1	yes	characteristic
191	C₂	C₃×#552	1	2	yes	—
192	C₂	C₃×#553	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
10. #2606	C₃	direct (N × H)
187. C₃	#2606	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#398	2
C₃×#389	2
C₃×#387	2
C₃×#383	2
C₃×C₄×C₄⋊C₄	2
C₃×#376	2
#2606	3

Subgroups — C3×#2606 #84470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2606 #84470