Subgroups — C₃×#3260 #85124

Order 384.

346 conjugacy classes of subgroups.

The subgroup lattice has 202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#540	C₂	1	1	yes	maximal, characteristic
3	C₃×#479	C₂	1	2	yes	maximal, complemented
4	C₃×#478	C₂	1	2	yes	maximal, complemented
5	C₃×#468	C₂	1	2	yes	maximal, complemented
6	C₃×#465	C₂	1	2	yes	maximal, complemented
7	C₃×#461	C₂	1	2	yes	maximal, complemented
8	C₃×#460	C₂	1	2	yes	maximal, complemented
9	C₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
10	#3260	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂×C₃×SD₁₆	C₂²	1	2	yes	—
12	C₂×C₃×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic
15	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₃×#127	C₂²	1	1	yes	characteristic
17	C₃×#126	—	2	2	no	—
18	C₃×#125	—	2	2	no	—
19	C₃×#125	C₂²	1	1	yes	characteristic
20	C₃×#125	C₂²	1	1	yes	characteristic
21	C₃×#123	—	2	2	no	—
22	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₃×#121	—	2	2	no	—
24	C₃×#121	C₂²	1	2	yes	—
25	C₃×C₄×Q₈	C₂²	1	2	yes	—
26	C₃×C₄×D₄	C₂²	1	2	yes	—
27	C₃×#117	C₂²	1	1	yes	characteristic
28	C₃×#107	C₂²	1	2	yes	—
29	C₃×#106	C₂²	1	2	yes	—
30	C₃×C₄⋊C₈	C₂²	1	2	yes	—
31	C₃×C₄⋊C₈	C₂²	1	2	yes	—
32	C₃×#103	C₂²	1	2	yes	—
33	C₃×#103	C₂²	1	2	yes	—
34	C₃×#102	C₂²	1	2	yes	—
35	C₃×#102	C₂²	1	2	yes	—
36	#541	C₂×C₃	1	1	yes	characteristic, complemented
37	#540	C₂×C₃	1	1	yes	characteristic
38	#479	C₂×C₃	1	2	yes	complemented
39	#478	C₂×C₃	1	2	yes	complemented
40	#468	C₂×C₃	1	2	yes	complemented
41	#465	C₂×C₃	1	2	yes	complemented
42	#461	C₂×C₃	1	2	yes	complemented
43	#460	C₂×C₃	1	2	yes	complemented
44	#424	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×C₃×Q₈	C₂³	1	2	yes	—
46	C₂×C₃×D₄	—	2	2	no	—
47	C₂×C₃×D₄	—	2	2	no	—
48	C₂×C₃×D₄	C₂³	1	2	yes	—
49	C₂²×C₃×C₄	—	2	2	no	—
50	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
51	C₃×SD₁₆	—	4	2	no	—
52	C₃×SD₁₆	—	4	2	no	—
53	C₃×M₁₆	—	4	1	no	—
54	C₂×C₃×C₈	—	4	1	no	—
55	C₂×C₃×C₈	C₂³	1	2	yes	—
56	C₂×C₃×C₈	C₂³	1	2	yes	—
57	C₃×C₄⋊C₄	—	2	2	no	—
58	C₃×C₄⋊C₄	—	2	2	no	—
59	C₃×C₄⋊C₄	—	2	2	no	—
60	C₃×C₄⋊C₄	—	2	2	no	—
61	C₃×C₄⋊C₄	—	2	2	no	—
62	C₃×C₄⋊C₄	D₄	1	2	yes	—
63	C₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₃×C₂²⋊C₄	—	2	2	no	—
66	C₃×C₂²⋊C₄	—	2	2	no	—
67	C₃×C₂²⋊C₄	—	2	2	no	—
68	C₃×C₂²⋊C₄	D₄	1	2	yes	—
69	C₃×C₄²	—	2	2	no	—
70	C₃×C₄²	C₂³	1	1	yes	characteristic
71	C₃×C₄²	C₂³	1	1	yes	characteristic
72	C₂×SD₁₆	C₂²×C₃	1	2	yes	—
73	C₂×SD₁₆	C₂²×C₃	1	2	yes	—
74	C₂×M₁₆	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₈	C₂²×C₃	1	1	yes	characteristic
76	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
77	#127	C₂²×C₃	1	1	yes	characteristic
78	#126	—	2	2	no	—
79	#125	—	2	2	no	—
80	#125	C₂²×C₃	1	1	yes	characteristic
81	#125	C₂²×C₃	1	1	yes	characteristic
82	#123	—	2	2	no	—
83	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
84	#121	—	2	2	no	—
85	#121	C₂²×C₃	1	2	yes	—
86	C₄×Q₈	C₂²×C₃	1	2	yes	—
87	C₄×D₄	C₂²×C₃	1	2	yes	—
88	#117	C₂²×C₃	1	1	yes	characteristic
89	#107	C₂²×C₃	1	2	yes	—
90	#106	C₂²×C₃	1	2	yes	—
91	C₄⋊C₈	C₂²×C₃	1	2	yes	—
92	C₄⋊C₈	C₂²×C₃	1	2	yes	—
93	#103	C₂²×C₃	1	2	yes	—
94	#103	C₂²×C₃	1	2	yes	—
95	#102	C₂²×C₃	1	2	yes	—
96	#102	C₂²×C₃	1	2	yes	—
97	C₂³×C₃	—	2	2	no	—
98	C₂³×C₃	C₂×D₄	1	1	yes	characteristic
99	C₃×Q₈	—	2	2	no	—
100	C₃×Q₈	—	2	2	no	—
101	C₃×D₄	—	2	2	no	—
102	C₃×D₄	—	2	2	no	—
103	C₃×D₄	—	8	2	no	—
104	C₃×D₄	—	8	2	no	—
105	C₂×C₃×C₄	—	2	1	no	—
106	C₂×C₃×C₄	—	2	1	no	—
107	C₂×C₃×C₄	—	2	2	no	—
108	C₂×C₃×C₄	—	2	2	no	—
109	C₂×C₃×C₄	—	2	2	no	—
110	C₂×C₃×C₄	—	8	2	no	—
111	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
112	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
113	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
115	C₃×C₈	—	2	2	no	—
116	C₃×C₈	—	2	2	no	—
117	C₂×Q₈	C₂³×C₃	1	2	yes	—
118	C₂×D₄	—	2	2	no	—
119	C₂×D₄	—	2	2	no	—
120	C₂×D₄	C₂³×C₃	1	2	yes	—
121	C₂²×C₄	—	2	2	no	—
122	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
123	SD₁₆	—	4	2	no	—
124	SD₁₆	—	4	2	no	—
125	M₁₆	—	4	1	no	—
126	C₂×C₈	—	4	1	no	—
127	C₂×C₈	C₂³×C₃	1	2	yes	—
128	C₂×C₈	C₂³×C₃	1	2	yes	—
129	C₄⋊C₄	—	2	2	no	—
130	C₄⋊C₄	—	2	2	no	—
131	C₄⋊C₄	—	2	2	no	—
132	C₄⋊C₄	—	2	2	no	—
133	C₄⋊C₄	—	2	2	no	—
134	C₄⋊C₄	C₃×D₄	1	2	yes	—
135	C₄⋊C₄	C₂³×C₃	1	2	yes	—
136	C₄⋊C₄	C₂³×C₃	1	2	yes	—
137	C₂²⋊C₄	—	2	2	no	—
138	C₂²⋊C₄	—	2	2	no	—
139	C₂²⋊C₄	—	2	2	no	—
140	C₂²⋊C₄	C₃×D₄	1	2	yes	—
141	C₄²	—	2	2	no	—
142	C₄²	C₂³×C₃	1	1	yes	characteristic
143	C₄²	C₂³×C₃	1	1	yes	characteristic
144	C₂²×C₃	—	2	1	no	—
145	C₂²×C₃	—	2	2	no	—
146	C₂²×C₃	—	4	2	no	—
147	C₂²×C₃	—	4	2	no	—
148	C₂²×C₃	—	4	2	no	—
149	C₂²×C₃	C₂²×D₄	1	1	yes	characteristic
150	C₃×C₄	—	2	1	no	—
151	C₃×C₄	—	2	2	no	—
152	C₃×C₄	—	2	2	no	—
153	C₃×C₄	—	4	2	no	—
154	C₃×C₄	—	4	2	no	—
155	C₃×C₄	—	4	2	no	—
156	C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
157	C₃×C₄	2₋¹⁺⁴	1	1	yes	characteristic
158	C₂³	—	2	2	no	—
159	C₂³	C₂×C₃×D₄	1	1	yes	characteristic
160	Q₈	—	2	2	no	—
161	Q₈	—	2	2	no	—
162	D₄	—	2	2	no	—
163	D₄	—	2	2	no	—
164	D₄	—	8	2	no	—
165	D₄	—	8	2	no	—
166	C₂×C₄	—	2	1	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	8	2	no	—
172	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
173	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
174	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
175	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
176	C₈	—	2	2	no	—
177	C₈	—	2	2	no	—
178	C₂×C₃	—	4	1	no	—
179	C₂×C₃	—	8	2	no	—
180	C₂×C₃	#537	1	1	yes	characteristic
181	C₂×C₃	#577	1	2	yes	—
182	C₂²	—	2	2	no	—
183	C₂²	—	2	1	no	—
184	C₂²	—	4	2	no	—
185	C₂²	—	4	2	no	—
186	C₂²	—	4	2	no	—
187	C₂²	C₂²×C₃×D₄	1	1	yes	characteristic
188	C₄	—	2	2	no	—
189	C₄	—	2	2	no	—
190	C₄	—	2	1	no	—
191	C₄	—	4	2	no	—
192	C₄	—	4	2	no	—
193	C₄	—	4	2	no	—
194	C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
195	C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
196	C₃	#3260	1	1	yes	characteristic, direct product factor, Sylow
197	C₂	—	4	1	no	—
198	C₂	—	8	2	no	—
199	C₂	C₃×#537	1	1	yes	characteristic
200	C₂	C₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃
prime radical	C₃×#540	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#541	C₂	semidirect
3. C₃×#479	C₂	semidirect
4. C₃×#478	C₂	semidirect
5. C₃×#468	C₂	semidirect
6. C₃×#465	C₂	semidirect
7. C₃×#461	C₂	semidirect
8. C₃×#460	C₂	semidirect
9. C₃×#424	C₂	semidirect
10. #3260	C₃	direct (N × H)
36. #541	C₂×C₃	semidirect
38. #479	C₂×C₃	semidirect
39. #478	C₂×C₃	semidirect
40. #468	C₂×C₃	semidirect
41. #465	C₂×C₃	semidirect
42. #461	C₂×C₃	semidirect
43. #460	C₂×C₃	semidirect
44. #424	C₂×C₃	semidirect
196. C₃	#3260	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×#541	2
C₃×#540	2
C₃×#479	2
C₃×#478	2
C₃×#468	2
C₃×#465	2
C₃×#461	2
C₃×#460	2
C₃×#424	2
#3260	3

Subgroups — C3×#3260 #85124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3260 #85124