Subgroups — C₃×#2931 #84795

Order 384.

500 conjugacy classes of subgroups.

The subgroup lattice has 168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#131	C₂	1	2	yes	maximal, complemented
2	C₃×#532	C₂	1	1	yes	maximal, characteristic
3	C₃×#436	C₂	1	4	yes	maximal, complemented
4	C₃×C₈×D₄	C₂	1	4	yes	maximal, complemented
5	C₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#408	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#2931	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂×C₃×#41	C₂²	1	2	yes	—
10	C₃×#131	—	2	8	no	—
11	C₂×C₃×M₁₆	C₂²	1	2	yes	—
12	C₂×C₃×M₁₆	C₂²	1	4	yes	—
13	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₈	C₂²	1	4	yes	—
15	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₄⋊Q₈	C₄	1	1	yes	characteristic
17	C₃×#127	C₄	1	1	yes	characteristic
18	C₃×#124	C₄	1	2	yes	—
19	C₃×#121	C₄	1	4	yes	—
20	C₃×C₄×D₄	C₂²	1	4	yes	—
21	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
22	C₃×C₄⋊C₈	C₂²	1	4	yes	—
23	C₃×C₂²⋊C₈	C₂²	1	8	yes	—
24	C₃×C₄×C₈	C₂²	1	2	yes	—
25	C₃×C₄×C₈	C₂²	1	2	yes	—
26	C₂×#131	C₂×C₃	1	2	yes	complemented
27	#532	C₂×C₃	1	1	yes	characteristic
28	#436	C₂×C₃	1	4	yes	complemented
29	C₈×D₄	C₂×C₃	1	4	yes	complemented
30	#423	C₂×C₃	1	1	yes	characteristic, complemented
31	#408	C₂×C₃	1	2	yes	complemented
32	C₂×C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
33	C₃×#41	—	2	4	no	—
34	C₃×#41	—	2	4	no	—
35	C₂×C₃×Q₈	C₂×C₄	1	2	yes	—
36	C₂×C₃×D₄	C₂×C₄	1	4	yes	—
37	C₂×C₃×D₄	C₂×C₄	1	4	yes	—
38	C₂×C₃×D₄	C₂×C₄	1	2	yes	—
39	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
40	C₂²×C₃×C₄	C₂³	1	4	yes	—
41	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
42	C₃×M₁₆	—	2	4	no	—
43	C₃×M₁₆	—	2	8	no	—
44	C₂×C₃×C₈	—	2	2	no	—
45	C₂×C₃×C₈	—	2	8	no	—
46	C₂×C₃×C₈	D₄	1	4	yes	complemented
47	C₂×C₃×C₈	C₂³	1	2	yes	—
48	C₂×C₃×C₈	C₂³	1	4	yes	—
49	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
51	C₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
52	C₃×C₂²⋊C₄	C₂×C₄	1	8	yes	—
53	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
54	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
55	C₃×C₄²	C₂³	1	2	yes	—
56	C₂×#41	C₂²×C₃	1	2	yes	—
57	#131	—	2	8	no	—
58	C₂×M₁₆	C₂²×C₃	1	2	yes	—
59	C₂×M₁₆	C₂²×C₃	1	4	yes	—
60	C₂²×C₈	C₂²×C₃	1	4	yes	—
61	C₂²×C₈	C₂²×C₃	1	1	yes	characteristic
62	C₂²×C₈	C₂²×C₃	1	1	yes	characteristic
63	C₄⋊Q₈	C₃×C₄	1	1	yes	characteristic
64	#127	C₃×C₄	1	1	yes	characteristic
65	#124	C₃×C₄	1	2	yes	—
66	#121	C₃×C₄	1	4	yes	—
67	C₄×D₄	C₂²×C₃	1	4	yes	—
68	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
69	C₄⋊C₈	C₂²×C₃	1	4	yes	—
70	C₂²⋊C₈	C₂²×C₃	1	8	yes	—
71	C₄×C₈	C₂²×C₃	1	2	yes	—
72	C₄×C₈	C₂²×C₃	1	2	yes	—
73	C₂³×C₃	C₂²×C₄	1	4	yes	—
74	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
75	C₃×Q₈	—	2	4	no	—
76	C₃×D₄	—	2	8	no	—
77	C₃×D₄	—	2	4	no	—
78	C₃×D₄	—	2	8	no	—
79	C₂×C₃×C₄	—	2	4	no	—
80	C₂×C₃×C₄	—	2	4	no	—
81	C₂×C₃×C₄	—	2	4	no	—
82	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
83	C₂×C₃×C₄	C₂²×C₄	1	4	yes	—
84	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
86	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
87	C₂×C₃×C₄	#41	1	2	yes	—
88	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
89	C₃×C₈	—	2	4	no	—
90	C₃×C₈	—	2	2	no	—
91	C₃×C₈	C₂×D₄	1	2	yes	—
92	C₃×C₈	C₂×D₄	1	2	yes	—
93	#41	—	2	4	no	—
94	#41	—	2	4	no	—
95	C₂×Q₈	C₂×C₃×C₄	1	2	yes	—
96	C₂×D₄	C₂×C₃×C₄	1	4	yes	—
97	C₂×D₄	C₂×C₃×C₄	1	4	yes	—
98	C₂×D₄	C₂×C₃×C₄	1	2	yes	—
99	C₂²×C₄	C₂×C₃×C₄	1	2	yes	—
100	C₂²×C₄	C₂³×C₃	1	4	yes	—
101	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
102	M₁₆	—	2	4	no	—
103	M₁₆	—	2	8	no	—
104	C₂×C₈	—	2	2	no	—
105	C₂×C₈	—	2	8	no	—
106	C₂×C₈	C₃×D₄	1	4	yes	complemented
107	C₂×C₈	C₂³×C₃	1	2	yes	—
108	C₂×C₈	C₂³×C₃	1	4	yes	—
109	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
110	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
111	C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
112	C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
113	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
114	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
115	C₄²	C₂³×C₃	1	2	yes	—
116	C₂²×C₃	—	2	2	no	—
117	C₂²×C₃	—	2	4	no	—
118	C₂²×C₃	—	2	8	no	—
119	C₂²×C₃	C₄×D₄	1	2	yes	—
120	C₂²×C₃	C₂³×C₄	1	1	yes	characteristic
121	C₃×C₄	—	2	4	no	—
122	C₃×C₄	—	2	2	no	—
123	C₃×C₄	C₄×D₄	1	2	yes	—
124	C₃×C₄	#131	1	4	yes	complemented
125	C₃×C₄	C₂²×D₄	1	1	yes	characteristic
126	C₃×C₄	C₂×#41	1	1	yes	characteristic
127	C₂³	C₂²×C₃×C₄	1	4	yes	—
128	C₂³	C₂²×C₃×C₄	1	1	yes	characteristic
129	Q₈	—	2	4	no	—
130	D₄	—	2	8	no	—
131	D₄	—	2	4	no	—
132	D₄	—	2	8	no	—
133	C₂×C₄	—	2	4	no	—
134	C₂×C₄	—	2	4	no	—
135	C₂×C₄	—	2	4	no	—
136	C₂×C₄	C₂²×C₃×C₄	1	2	yes	—
137	C₂×C₄	C₂²×C₃×C₄	1	4	yes	—
138	C₂×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
139	C₂×C₄	C₂²×C₃×C₄	1	2	yes	—
140	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
141	C₂×C₄	C₃×#41	1	2	yes	—
142	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
143	C₈	—	2	4	no	—
144	C₈	—	2	2	no	—
145	C₈	C₂×C₃×D₄	1	2	yes	—
146	C₈	C₂×C₃×D₄	1	2	yes	—
147	C₂×C₃	—	2	2	no	—
148	C₂×C₃	—	4	4	no	—
149	C₂×C₃	C₂×C₄×D₄	1	1	yes	characteristic
150	C₂×C₃	C₂×#131	1	2	yes	—
151	C₂²	—	2	2	no	—
152	C₂²	—	2	8	no	—
153	C₂²	—	2	4	no	—
154	C₂²	C₃×C₄×D₄	1	2	yes	—
155	C₂²	C₂³×C₃×C₄	1	1	yes	characteristic
156	C₄	—	2	2	no	—
157	C₄	—	2	4	no	—
158	C₄	C₃×C₄×D₄	1	2	yes	—
159	C₄	C₃×#131	1	4	yes	complemented
160	C₄	C₂²×C₃×D₄	1	1	yes	characteristic
161	C₄	C₂×C₃×#41	1	1	yes	characteristic
162	C₃	#2931	1	1	yes	characteristic, direct product factor, Sylow
163	C₂	—	2	2	no	—
164	C₂	—	4	4	no	—
165	C₂	C₂×C₃×C₄×D₄	1	1	yes	characteristic
166	C₂	C₂×C₃×#131	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₈	C₂³
commutator	C₂²	C₂³×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂³×C₄
prime radical	C₃×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#131	C₂	semidirect
3. C₃×#436	C₂	semidirect
4. C₃×C₈×D₄	C₂	semidirect
5. C₃×#423	C₂	semidirect
6. C₃×#408	C₂	semidirect
7. C₂×C₃×C₄×C₈	C₂	semidirect
8. #2931	C₃	direct (N × H)
26. C₂×#131	C₂×C₃	semidirect
28. #436	C₂×C₃	semidirect
29. C₈×D₄	C₂×C₃	semidirect
30. #423	C₂×C₃	semidirect
31. #408	C₂×C₃	semidirect
32. C₂×C₄×C₈	C₂×C₃	semidirect
46. C₂×C₃×C₈	D₄	semidirect
106. C₂×C₈	C₃×D₄	semidirect
124. C₃×C₄	#131	semidirect
159. C₄	C₃×#131	semidirect
162. C₃	#2931	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×#131	2
C₃×#532	2
C₃×#436	2
C₃×C₈×D₄	2
C₃×#423	2
C₃×#408	2
C₂×C₃×C₄×C₈	2
#2931	3

Subgroups — C3×#2931 #84795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2931 #84795