Subgroups — C₃×#1434 #72149

Order 384.

568 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#95	C₂	1	2	yes	maximal
3	C₂×C₃×#95	C₂	1	2	yes	maximal
4	C₂×C₃×#95	C₂	1	2	yes	maximal
5	#1434	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂³×C₃×C₄	C₂²	1	4	yes	—
7	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
8	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₄²	—	2	4	no	—
11	C₂×C₃×C₄²	C₄	1	4	yes	complemented
12	C₃×#95	—	2	4	no	—
13	C₃×#95	—	2	4	no	—
14	C₃×#95	C₄	1	8	yes	complemented
15	C₂²×C₄²	C₂×C₃	1	1	yes	characteristic
16	C₂×#95	C₂×C₃	1	2	yes	—
17	C₂×#95	C₂×C₃	1	2	yes	—
18	C₂×#95	C₂×C₃	1	2	yes	—
19	C₂⁴×C₃	C₂³	1	1	yes	characteristic
20	C₂²×C₃×C₄	—	2	2	no	—
21	C₂²×C₃×C₄	—	2	2	no	—
22	C₂²×C₃×C₄	—	2	2	no	—
23	C₂²×C₃×C₄	—	2	2	no	—
24	C₂²×C₃×C₄	—	2	2	no	—
25	C₂²×C₃×C₄	—	2	2	no	—
26	C₂²×C₃×C₄	—	2	4	no	—
27	C₂²×C₃×C₄	—	2	4	no	—
28	C₂²×C₃×C₄	—	2	4	no	—
29	C₂²×C₃×C₄	—	2	4	no	—
30	C₂²×C₃×C₄	—	2	4	no	—
31	C₂²×C₃×C₄	—	2	4	no	—
32	C₂²×C₃×C₄	C₂×C₄	1	8	yes	—
33	C₂²×C₃×C₄	C₂×C₄	1	4	yes	—
34	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
35	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
36	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
37	C₂²×C₃×C₄	D₄	1	4	yes	—
38	C₂²×C₃×C₄	D₄	1	2	yes	—
39	C₂²×C₃×C₄	Q₈	1	2	yes	—
40	C₃×C₄²	—	2	8	no	—
41	C₂³×C₄	C₂²×C₃	1	4	yes	—
42	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
43	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
44	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
45	C₂×C₄²	—	2	4	no	—
46	C₂×C₄²	C₃×C₄	1	4	yes	complemented
47	#95	—	2	4	no	—
48	#95	—	2	4	no	—
49	#95	C₃×C₄	1	8	yes	complemented
50	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
51	C₂³×C₃	C₂²×C₄	1	2	yes	—
52	C₂³×C₃	C₂×D₄	1	2	yes	—
53	C₂³×C₃	C₂×D₄	1	1	yes	characteristic
54	C₂³×C₃	C₂×Q₈	1	1	yes	characteristic
55	C₂³×C₃	#41	1	2	yes	—
56	C₂³×C₃	#41	1	2	yes	—
57	C₂³×C₃	#41	1	2	yes	—
58	C₂³×C₃	#41	1	2	yes	—
59	C₂×C₃×C₄	—	2	2	no	—
60	C₂×C₃×C₄	—	2	2	no	—
61	C₂×C₃×C₄	—	2	2	no	—
62	C₂×C₃×C₄	—	2	2	no	—
63	C₂×C₃×C₄	—	2	2	no	—
64	C₂×C₃×C₄	—	2	2	no	—
65	C₂×C₃×C₄	—	2	8	no	—
66	C₂×C₃×C₄	—	2	4	no	—
67	C₂×C₃×C₄	—	2	4	no	—
68	C₂×C₃×C₄	—	2	8	no	—
69	C₂×C₃×C₄	—	2	8	no	—
70	C₂×C₃×C₄	—	2	8	no	—
71	C₂×C₃×C₄	—	2	8	no	—
72	C₂×C₃×C₄	—	4	4	no	—
73	C₂×C₃×C₄	—	4	4	no	—
74	C₂×C₃×C₄	—	4	4	no	—
75	C₂×C₃×C₄	—	4	4	no	—
76	C₂×C₃×C₄	C₄²	1	4	yes	—
77	C₂×C₃×C₄	C₂²⋊C₄	1	4	yes	—
78	C₂×C₃×C₄	C₄⋊C₄	1	4	yes	—
79	C₂⁴	C₂³×C₃	1	1	yes	characteristic
80	C₂²×C₄	—	2	2	no	—
81	C₂²×C₄	—	2	2	no	—
82	C₂²×C₄	—	2	2	no	—
83	C₂²×C₄	—	2	2	no	—
84	C₂²×C₄	—	2	2	no	—
85	C₂²×C₄	—	2	2	no	—
86	C₂²×C₄	—	2	4	no	—
87	C₂²×C₄	—	2	4	no	—
88	C₂²×C₄	—	2	4	no	—
89	C₂²×C₄	—	2	4	no	—
90	C₂²×C₄	—	2	4	no	—
91	C₂²×C₄	—	2	4	no	—
92	C₂²×C₄	C₂×C₃×C₄	1	8	yes	—
93	C₂²×C₄	C₂×C₃×C₄	1	4	yes	—
94	C₂²×C₄	C₂×C₃×C₄	1	2	yes	—
95	C₂²×C₄	C₂×C₃×C₄	1	2	yes	—
96	C₂²×C₄	C₂×C₃×C₄	1	2	yes	—
97	C₂²×C₄	C₃×D₄	1	4	yes	—
98	C₂²×C₄	C₃×D₄	1	2	yes	—
99	C₂²×C₄	C₃×Q₈	1	2	yes	—
100	C₄²	—	2	8	no	—
101	C₂²×C₃	C₂×C₄²	1	1	yes	characteristic
102	C₂²×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
104	C₂²×C₃	#117	1	1	yes	characteristic
105	C₂²×C₃	#117	1	1	yes	characteristic
106	C₂²×C₃	#117	1	4	yes	—
107	C₂²×C₃	#117	1	1	yes	characteristic
108	C₂²×C₃	#117	1	1	yes	characteristic
109	C₂²×C₃	C₄×D₄	1	4	yes	—
110	C₂²×C₃	C₄×D₄	1	2	yes	—
111	C₂²×C₃	C₄×Q₈	1	2	yes	—
112	C₂²×C₃	#121	1	2	yes	—
113	C₂²×C₃	C₂²⋊Q₈	1	2	yes	—
114	C₂²×C₃	#123	1	4	yes	—
115	C₂²×C₃	#124	1	2	yes	—
116	C₂²×C₃	#125	1	2	yes	—
117	C₂²×C₃	#126	1	4	yes	—
118	C₃×C₄	—	2	4	no	—
119	C₃×C₄	—	2	4	no	—
120	C₃×C₄	—	2	4	no	—
121	C₃×C₄	—	4	8	no	—
122	C₂³	C₂²×C₃×C₄	1	1	yes	characteristic
123	C₂³	C₂²×C₃×C₄	1	2	yes	—
124	C₂³	C₂×C₃×D₄	1	2	yes	—
125	C₂³	C₂×C₃×D₄	1	1	yes	characteristic
126	C₂³	C₂×C₃×Q₈	1	1	yes	characteristic
127	C₂³	C₃×#41	1	2	yes	—
128	C₂³	C₃×#41	1	2	yes	—
129	C₂³	C₃×#41	1	2	yes	—
130	C₂³	C₃×#41	1	2	yes	—
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	2	8	no	—
138	C₂×C₄	—	2	4	no	—
139	C₂×C₄	—	2	4	no	—
140	C₂×C₄	—	2	8	no	—
141	C₂×C₄	—	2	8	no	—
142	C₂×C₄	—	2	8	no	—
143	C₂×C₄	—	2	8	no	—
144	C₂×C₄	—	4	4	no	—
145	C₂×C₄	—	4	4	no	—
146	C₂×C₄	—	4	4	no	—
147	C₂×C₄	—	4	4	no	—
148	C₂×C₄	C₃×C₄²	1	4	yes	—
149	C₂×C₄	C₃×C₂²⋊C₄	1	4	yes	—
150	C₂×C₄	C₃×C₄⋊C₄	1	4	yes	—
151	C₂×C₃	#376	1	1	yes	characteristic
152	C₂×C₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₃	C₄×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₃	#380	1	1	yes	characteristic
155	C₂×C₃	#381	1	1	yes	characteristic
156	C₂×C₃	#382	1	1	yes	characteristic
157	C₂×C₃	#383	1	1	yes	characteristic
158	C₂×C₃	#387	1	4	yes	—
159	C₂×C₃	#388	1	4	yes	—
160	C₂²	C₂×C₃×C₄²	1	1	yes	characteristic
161	C₂²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
162	C₂²	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
163	C₂²	C₃×#117	1	1	yes	characteristic
164	C₂²	C₃×#117	1	1	yes	characteristic
165	C₂²	C₃×#117	1	4	yes	—
166	C₂²	C₃×#117	1	1	yes	characteristic
167	C₂²	C₃×#117	1	1	yes	characteristic
168	C₂²	C₃×C₄×D₄	1	4	yes	—
169	C₂²	C₃×C₄×D₄	1	2	yes	—
170	C₂²	C₃×C₄×Q₈	1	2	yes	—
171	C₂²	C₃×#121	1	2	yes	—
172	C₂²	C₃×C₂²⋊Q₈	1	2	yes	—
173	C₂²	C₃×#123	1	4	yes	—
174	C₂²	C₃×#124	1	2	yes	—
175	C₂²	C₃×#125	1	2	yes	—
176	C₂²	C₃×#126	1	4	yes	—
177	C₄	—	2	4	no	—
178	C₄	—	2	4	no	—
179	C₄	—	2	4	no	—
180	C₄	—	4	8	no	—
181	C₃	#1434	1	1	yes	characteristic, direct product factor, Sylow
182	C₂	C₃×#376	1	1	yes	characteristic
183	C₂	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
184	C₂	C₃×C₄×C₄⋊C₄	1	1	yes	characteristic
185	C₂	C₃×#380	1	1	yes	characteristic
186	C₂	C₃×#381	1	1	yes	characteristic
187	C₂	C₃×#382	1	1	yes	characteristic
188	C₂	C₃×#383	1	1	yes	characteristic
189	C₂	C₃×#387	1	4	yes	—
190	C₂	C₃×#388	1	4	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₃	C₂³
commutator	C₂²	C₂×C₃×C₄²
Frattini, cosocle	C₂⁴	C₂³×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
5. #1434	C₃	direct (N × H)
11. C₂×C₃×C₄²	C₄	semidirect
14. C₃×#95	C₄	semidirect
46. C₂×C₄²	C₃×C₄	semidirect
49. #95	C₃×C₄	semidirect
181. C₃	#1434	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄²	2
C₂×C₃×#95	2
#1434	3

Subgroups — C3×#1434 #72149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1434 #72149