Subgroups — C₃×#2949 #84813

Order 384.

492 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#518	C₂	1	1	yes	maximal, characteristic
4	C₃×#440	C₂	1	4	yes	maximal, complemented
5	C₃×C₄×SD₁₆	C₂	1	4	yes	maximal, complemented
6	C₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#418	C₂	1	1	yes	maximal, characteristic
9	C₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
10	#2949	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂²×C₃×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×SD₁₆	C₄	1	8	yes	complemented
14	C₂×C₃×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₃×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic
18	C₃×C₄×Q₈	—	2	2	no	—
19	C₃×C₄×Q₈	C₂²	1	4	yes	complemented
20	C₃×C₄×D₄	—	2	2	no	—
21	C₃×C₄×D₄	C₂²	1	4	yes	—
22	C₃×#117	—	2	2	no	—
23	C₃×#117	C₂²	1	1	yes	characteristic
24	C₃×#117	C₂²	1	1	yes	characteristic
25	C₃×#117	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
27	C₃×#107	C₂²	1	2	yes	complemented
28	C₃×#106	C₂²	1	2	yes	complemented
29	C₃×#103	C₂²	1	4	yes	complemented
30	C₃×#102	C₂²	1	4	yes	—
31	C₃×#97	C₂²	1	2	yes	complemented
32	C₃×C₄×C₈	C₂²	1	2	yes	complemented
33	C₂²×SD₁₆	C₂×C₃	1	1	yes	characteristic
34	#519	C₂×C₃	1	1	yes	characteristic, complemented
35	#518	C₂×C₃	1	1	yes	characteristic
36	#440	C₂×C₃	1	4	yes	complemented
37	C₄×SD₁₆	C₂×C₃	1	4	yes	complemented
38	#427	C₂×C₃	1	1	yes	characteristic, complemented
39	#419	C₂×C₃	1	1	yes	characteristic, complemented
40	#418	C₂×C₃	1	1	yes	characteristic
41	#405	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂⁴×C₃	—	2	1	no	—
43	C₂×C₃×Q₈	—	2	1	no	—
44	C₂×C₃×Q₈	—	2	2	no	—
45	C₂×C₃×Q₈	C₂×C₄	1	4	yes	complemented
46	C₂×C₃×Q₈	C₂³	1	2	yes	—
47	C₂×C₃×D₄	—	2	1	no	—
48	C₂×C₃×D₄	—	2	2	no	—
49	C₂×C₃×D₄	C₂×C₄	1	4	yes	—
50	C₂×C₃×D₄	C₂³	1	2	yes	—
51	C₂²×C₃×C₄	—	2	1	no	—
52	C₂²×C₃×C₄	—	2	4	no	—
53	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
54	C₃×SD₁₆	C₂×C₄	1	8	yes	complemented
55	C₃×SD₁₆	C₂×C₄	1	8	yes	complemented
56	C₃×M₁₆	—	2	2	no	—
57	C₂×C₃×C₈	C₂×C₄	1	4	yes	complemented
58	C₂×C₃×C₈	C₂³	1	2	yes	—
59	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
61	C₃×C₄⋊C₄	—	2	4	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	1	no	—
66	C₃×C₂²⋊C₄	—	2	1	no	—
67	C₃×C₂²⋊C₄	—	2	4	no	—
68	C₃×C₂²⋊C₄	D₄	1	2	yes	—
69	C₃×C₄²	—	2	4	no	—
70	C₃×C₄²	—	2	1	no	—
71	C₃×C₄²	—	2	1	no	—
72	C₃×C₄²	C₂³	1	2	yes	—
73	C₂²×Q₈	C₂²×C₃	1	1	yes	characteristic
74	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
75	C₂×SD₁₆	C₃×C₄	1	8	yes	complemented
76	C₂×SD₁₆	C₂²×C₃	1	2	yes	—
77	C₂×SD₁₆	C₂²×C₃	1	2	yes	—
78	C₂×M₁₆	C₂²×C₃	1	1	yes	characteristic
79	C₂²×C₈	C₂²×C₃	1	1	yes	characteristic
80	C₄×Q₈	—	2	2	no	—
81	C₄×Q₈	C₂²×C₃	1	4	yes	complemented
82	C₄×D₄	—	2	2	no	—
83	C₄×D₄	C₂²×C₃	1	4	yes	—
84	#117	—	2	2	no	—
85	#117	C₂²×C₃	1	1	yes	characteristic
86	#117	C₂²×C₃	1	1	yes	characteristic
87	#117	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₂²⋊C₄	—	2	2	no	—
89	#107	C₂²×C₃	1	2	yes	complemented
90	#106	C₂²×C₃	1	2	yes	complemented
91	#103	C₂²×C₃	1	4	yes	complemented
92	#102	C₂²×C₃	1	4	yes	—
93	#97	C₂²×C₃	1	2	yes	complemented
94	C₄×C₈	C₂²×C₃	1	2	yes	complemented
95	C₂³×C₃	—	2	2	no	—
96	C₂³×C₃	—	2	4	no	—
97	C₂³×C₃	—	8	2	no	—
98	C₂³×C₃	C₂×D₄	1	1	yes	characteristic
99	C₃×Q₈	—	2	4	no	—
100	C₃×Q₈	—	2	2	no	—
101	C₃×Q₈	C₂²×C₄	1	4	yes	—
102	C₃×D₄	—	2	4	no	—
103	C₃×D₄	—	2	2	no	—
104	C₃×D₄	C₂²×C₄	1	4	yes	—
105	C₂×C₃×C₄	—	2	4	no	—
106	C₂×C₃×C₄	—	2	2	no	—
107	C₂×C₃×C₄	—	2	2	no	—
108	C₂×C₃×C₄	—	2	2	no	—
109	C₂×C₃×C₄	—	8	4	no	—
110	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
111	C₂×C₃×C₄	C₂×D₄	1	4	yes	—
112	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄	#41	1	2	yes	—
114	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
115	C₃×C₈	—	2	2	no	—
116	C₃×C₈	C₂²×C₄	1	2	yes	—
117	C₃×C₈	C₂²×C₄	1	2	yes	—
118	C₂⁴	—	2	1	no	—
119	C₂×Q₈	—	2	1	no	—
120	C₂×Q₈	—	2	2	no	—
121	C₂×Q₈	C₂×C₃×C₄	1	4	yes	complemented
122	C₂×Q₈	C₂³×C₃	1	2	yes	—
123	C₂×D₄	—	2	1	no	—
124	C₂×D₄	—	2	2	no	—
125	C₂×D₄	C₂×C₃×C₄	1	4	yes	—
126	C₂×D₄	C₂³×C₃	1	2	yes	—
127	C₂²×C₄	—	2	1	no	—
128	C₂²×C₄	—	2	4	no	—
129	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
130	SD₁₆	C₂×C₃×C₄	1	8	yes	complemented
131	SD₁₆	C₂×C₃×C₄	1	8	yes	complemented
132	M₁₆	—	2	2	no	—
133	C₂×C₈	C₂×C₃×C₄	1	4	yes	complemented
134	C₂×C₈	C₂³×C₃	1	2	yes	—
135	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
136	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
137	C₄⋊C₄	—	2	4	no	—
138	C₄⋊C₄	C₃×D₄	1	2	yes	—
139	C₄⋊C₄	C₂³×C₃	1	2	yes	—
140	C₄⋊C₄	C₂³×C₃	1	2	yes	—
141	C₂²⋊C₄	—	2	1	no	—
142	C₂²⋊C₄	—	2	1	no	—
143	C₂²⋊C₄	—	2	4	no	—
144	C₂²⋊C₄	C₃×D₄	1	2	yes	—
145	C₄²	—	2	4	no	—
146	C₄²	—	2	1	no	—
147	C₄²	—	2	1	no	—
148	C₄²	C₂³×C₃	1	2	yes	—
149	C₂²×C₃	—	2	2	no	—
150	C₂²×C₃	—	2	4	no	—
151	C₂²×C₃	—	4	4	no	—
152	C₂²×C₃	—	8	4	no	—
153	C₂²×C₃	C₄×D₄	1	2	yes	—
154	C₂²×C₃	C₂²×D₄	1	1	yes	characteristic
155	C₃×C₄	—	2	4	no	—
156	C₃×C₄	—	2	4	no	—
157	C₃×C₄	—	4	2	no	—
158	C₃×C₄	—	4	2	no	—
159	C₃×C₄	C₄×D₄	1	2	yes	—
160	C₃×C₄	C₂³×C₄	1	1	yes	characteristic
161	C₃×C₄	C₂×#41	1	1	yes	characteristic
162	C₂³	—	2	2	no	—
163	C₂³	—	2	4	no	—
164	C₂³	—	8	2	no	—
165	C₂³	C₂×C₃×D₄	1	1	yes	characteristic
166	Q₈	—	2	4	no	—
167	Q₈	—	2	2	no	—
168	Q₈	C₂²×C₃×C₄	1	4	yes	—
169	D₄	—	2	4	no	—
170	D₄	—	2	2	no	—
171	D₄	C₂²×C₃×C₄	1	4	yes	—
172	C₂×C₄	—	2	4	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	8	4	no	—
177	C₂×C₄	C₂²×C₃×C₄	1	2	yes	—
178	C₂×C₄	C₂×C₃×D₄	1	4	yes	—
179	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
180	C₂×C₄	C₃×#41	1	2	yes	—
181	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
182	C₈	—	2	2	no	—
183	C₈	C₂²×C₃×C₄	1	2	yes	—
184	C₈	C₂²×C₃×C₄	1	2	yes	—
185	C₂×C₃	—	2	2	no	—
186	C₂×C₃	—	4	4	no	—
187	C₂×C₃	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂×C₃	#577	1	2	yes	—
189	C₂²	—	2	2	no	—
190	C₂²	—	2	4	no	—
191	C₂²	—	4	4	no	—
192	C₂²	—	8	4	no	—
193	C₂²	C₃×C₄×D₄	1	2	yes	—
194	C₂²	C₂²×C₃×D₄	1	1	yes	characteristic
195	C₄	—	2	4	no	—
196	C₄	—	2	4	no	—
197	C₄	—	4	2	no	—
198	C₄	—	4	2	no	—
199	C₄	C₃×C₄×D₄	1	2	yes	—
200	C₄	C₂³×C₃×C₄	1	1	yes	characteristic
201	C₄	C₂×C₃×#41	1	1	yes	characteristic
202	C₃	#2949	1	1	yes	characteristic, direct product factor, Sylow
203	C₂	—	2	2	no	—
204	C₂	—	4	4	no	—
205	C₂	C₂×C₃×C₄×D₄	1	1	yes	characteristic
206	C₂	C₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂²×D₄
commutator	C₄	C₂³×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂⁴×C₃
prime radical	C₂²×C₃×D₄	C₂²
LCS	G ▷ 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
2. C₃×#519	C₂	semidirect
4. C₃×#440	C₂	semidirect
5. C₃×C₄×SD₁₆	C₂	semidirect
6. C₃×#427	C₂	semidirect
7. C₃×#419	C₂	semidirect
9. C₃×#405	C₂	semidirect
10. #2949	C₃	direct (N × H)
13. C₂×C₃×SD₁₆	C₄	semidirect
19. C₃×C₄×Q₈	C₂²	semidirect
27. C₃×#107	C₂²	semidirect
28. C₃×#106	C₂²	semidirect
29. C₃×#103	C₂²	semidirect
31. C₃×#97	C₂²	semidirect
32. C₃×C₄×C₈	C₂²	semidirect
34. #519	C₂×C₃	semidirect
36. #440	C₂×C₃	semidirect
37. C₄×SD₁₆	C₂×C₃	semidirect
38. #427	C₂×C₃	semidirect
39. #419	C₂×C₃	semidirect
41. #405	C₂×C₃	semidirect
45. C₂×C₃×Q₈	C₂×C₄	semidirect
54. C₃×SD₁₆	C₂×C₄	semidirect
55. C₃×SD₁₆	C₂×C₄	semidirect
57. C₂×C₃×C₈	C₂×C₄	semidirect
75. C₂×SD₁₆	C₃×C₄	semidirect
81. C₄×Q₈	C₂²×C₃	semidirect
89. #107	C₂²×C₃	semidirect
90. #106	C₂²×C₃	semidirect
91. #103	C₂²×C₃	semidirect
93. #97	C₂²×C₃	semidirect
94. C₄×C₈	C₂²×C₃	semidirect
121. C₂×Q₈	C₂×C₃×C₄	semidirect
130. SD₁₆	C₂×C₃×C₄	semidirect
131. SD₁₆	C₂×C₃×C₄	semidirect
133. C₂×C₈	C₂×C₃×C₄	semidirect
202. C₃	#2949	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×SD₁₆	2
C₃×#519	2
C₃×#518	2
C₃×#440	2
C₃×C₄×SD₁₆	2
C₃×#427	2
C₃×#419	2
C₃×#418	2
C₃×#405	2
#2949	3

Subgroups — C3×#2949 #84813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2949 #84813