Subgroups — C₃×#2593 #84457

Order 384.

440 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#400	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#394	C₂	1	2	yes	maximal
4	C₃×#390	C₂	1	1	yes	maximal, characteristic
5	C₃×#388	C₂	1	2	yes	maximal, complemented
6	C₃×#388	C₂	1	2	yes	maximal, complemented
7	C₃×#388	C₂	1	2	yes	maximal, complemented
8	C₃×#388	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
10	#2593	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
15	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₄²	C₂²	1	2	yes	—
24	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄²	C₂²	1	2	yes	—
26	C₃×#95	C₂²	1	2	yes	—
27	C₃×#95	C₂²	1	2	yes	—
28	C₃×#95	C₂²	1	2	yes	—
29	C₃×#95	C₂²	1	1	yes	characteristic
30	C₃×#95	C₂²	1	2	yes	—
31	C₃×#95	C₂²	1	1	yes	characteristic
32	#400	C₂×C₃	1	1	yes	characteristic, complemented
33	#398	C₂×C₃	1	1	yes	characteristic, complemented
34	#394	C₂×C₃	1	2	yes	—
35	#390	C₂×C₃	1	1	yes	characteristic
36	#388	C₂×C₃	1	2	yes	complemented
37	#388	C₂×C₃	1	2	yes	complemented
38	#388	C₂×C₃	1	2	yes	complemented
39	#388	C₂×C₃	1	2	yes	complemented
40	C₄×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
41	C₂⁴×C₃	C₂³	1	2	yes	—
42	C₂×C₃×D₄	—	2	2	no	—
43	C₂×C₃×D₄	—	4	1	no	—
44	C₂×C₃×D₄	—	4	1	no	—
45	C₂²×C₃×C₄	C₂³	1	2	yes	—
46	C₂²×C₃×C₄	C₂³	1	2	yes	—
47	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
48	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄	C₂³	1	2	yes	—
50	C₂²×C₃×C₄	C₂³	1	2	yes	—
51	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄	C₂³	1	2	yes	—
53	C₃×C₄⋊C₄	—	2	4	no	—
54	C₃×C₄⋊C₄	—	2	4	no	—
55	C₃×C₄⋊C₄	—	4	1	no	—
56	C₃×C₄⋊C₄	—	4	1	no	—
57	C₃×C₄⋊C₄	—	4	1	no	—
58	C₃×C₂²⋊C₄	—	2	4	no	—
59	C₃×C₂²⋊C₄	—	2	4	no	—
60	C₃×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₂²⋊C₄	—	2	4	no	—
62	C₃×C₂²⋊C₄	—	4	2	no	—
63	C₃×C₂²⋊C₄	—	4	2	no	—
64	C₃×C₄²	—	2	4	no	—
65	C₃×C₄²	—	4	1	no	—
66	C₃×C₄²	—	4	2	no	—
67	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
69	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
70	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
74	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
75	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
76	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
77	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
78	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₄²	C₂²×C₃	1	2	yes	—
80	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₄²	C₂²×C₃	1	2	yes	—
82	#95	C₂²×C₃	1	2	yes	—
83	#95	C₂²×C₃	1	2	yes	—
84	#95	C₂²×C₃	1	2	yes	—
85	#95	C₂²×C₃	1	1	yes	characteristic
86	#95	C₂²×C₃	1	2	yes	—
87	#95	C₂²×C₃	1	1	yes	characteristic
88	C₂³×C₃	—	2	2	no	—
89	C₂³×C₃	—	2	2	no	—
90	C₂³×C₃	—	2	2	no	—
91	C₂³×C₃	—	2	2	no	—
92	C₂³×C₃	—	2	2	no	—
93	C₂³×C₃	—	2	2	no	—
94	C₂³×C₃	—	2	2	no	—
95	C₂³×C₃	C₂⁴	1	1	yes	characteristic
96	C₃×D₄	—	4	4	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	1	no	—
102	C₂×C₃×C₄	—	2	1	no	—
103	C₂×C₃×C₄	—	2	2	no	—
104	C₂×C₃×C₄	—	2	2	no	—
105	C₂×C₃×C₄	—	2	2	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	—	2	2	no	—
110	C₂×C₃×C₄	—	2	2	no	—
111	C₂×C₃×C₄	—	2	2	no	—
112	C₂×C₃×C₄	—	2	2	no	—
113	C₂×C₃×C₄	—	2	2	no	—
114	C₂×C₃×C₄	—	2	1	no	—
115	C₂×C₃×C₄	—	2	1	no	—
116	C₂×C₃×C₄	#41	1	4	yes	—
117	C₂×C₃×C₄	#41	1	4	yes	—
118	C₂×C₃×C₄	#41	1	2	yes	—
119	C₂⁴	C₂³×C₃	1	2	yes	—
120	C₂×D₄	—	2	2	no	—
121	C₂×D₄	—	4	1	no	—
122	C₂×D₄	—	4	1	no	—
123	C₂²×C₄	C₂³×C₃	1	2	yes	—
124	C₂²×C₄	C₂³×C₃	1	2	yes	—
125	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
126	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
127	C₂²×C₄	C₂³×C₃	1	2	yes	—
128	C₂²×C₄	C₂³×C₃	1	2	yes	—
129	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
130	C₂²×C₄	C₂³×C₃	1	2	yes	—
131	C₄⋊C₄	—	2	4	no	—
132	C₄⋊C₄	—	2	4	no	—
133	C₄⋊C₄	—	4	1	no	—
134	C₄⋊C₄	—	4	1	no	—
135	C₄⋊C₄	—	4	1	no	—
136	C₂²⋊C₄	—	2	4	no	—
137	C₂²⋊C₄	—	2	4	no	—
138	C₂²⋊C₄	—	2	4	no	—
139	C₂²⋊C₄	—	2	4	no	—
140	C₂²⋊C₄	—	4	2	no	—
141	C₂²⋊C₄	—	4	2	no	—
142	C₄²	—	2	4	no	—
143	C₄²	—	4	1	no	—
144	C₄²	—	4	2	no	—
145	C₂²×C₃	—	4	2	no	—
146	C₂²×C₃	—	4	2	no	—
147	C₂²×C₃	—	4	2	no	—
148	C₂²×C₃	—	4	2	no	—
149	C₂²×C₃	—	4	2	no	—
150	C₂²×C₃	—	4	2	no	—
151	C₂²×C₃	—	4	2	no	—
152	C₂²×C₃	C₂×#41	1	1	yes	characteristic
153	C₂²×C₃	C₂×#41	1	2	yes	—
154	C₂²×C₃	C₂×#41	1	2	yes	—
155	C₂²×C₃	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂²×C₃	H(5,𝔽₂)	1	1	yes	characteristic
157	C₃×C₄	—	2	4	no	—
158	C₃×C₄	—	2	2	no	—
159	C₃×C₄	—	2	4	no	—
160	C₃×C₄	—	4	2	no	—
161	C₃×C₄	—	4	2	no	—
162	C₃×C₄	—	4	2	no	—
163	C₃×C₄	—	4	1	no	—
164	C₃×C₄	—	4	1	no	—
165	C₂³	—	2	2	no	—
166	C₂³	—	2	2	no	—
167	C₂³	—	2	2	no	—
168	C₂³	—	2	2	no	—
169	C₂³	—	2	2	no	—
170	C₂³	—	2	2	no	—
171	C₂³	—	2	2	no	—
172	C₂³	C₂⁴×C₃	1	1	yes	characteristic
173	D₄	—	4	4	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	1	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	C₃×#41	1	4	yes	—
194	C₂×C₄	C₃×#41	1	4	yes	—
195	C₂×C₄	C₃×#41	1	2	yes	—
196	C₂×C₃	—	8	2	no	—
197	C₂×C₃	#529	1	2	yes	—
198	C₂×C₃	#538	1	1	yes	characteristic
199	C₂×C₃	#553	1	2	yes	—
200	C₂×C₃	#555	1	1	yes	characteristic
201	C₂×C₃	#559	1	1	yes	characteristic
202	C₂²	—	4	2	no	—
203	C₂²	—	4	2	no	—
204	C₂²	—	4	2	no	—
205	C₂²	—	4	2	no	—
206	C₂²	—	4	2	no	—
207	C₂²	—	4	2	no	—
208	C₂²	—	4	2	no	—
209	C₂²	C₂×C₃×#41	1	2	yes	—
210	C₂²	C₂×C₃×#41	1	1	yes	characteristic
211	C₂²	C₂×C₃×#41	1	2	yes	—
212	C₂²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
213	C₂²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
214	C₄	—	2	4	no	—
215	C₄	—	2	2	no	—
216	C₄	—	2	4	no	—
217	C₄	—	4	1	no	—
218	C₄	—	4	1	no	—
219	C₄	—	4	2	no	—
220	C₄	—	4	2	no	—
221	C₄	—	4	2	no	—
222	C₃	#2593	1	1	yes	characteristic, direct product factor, Sylow
223	C₂	—	8	2	no	—
224	C₂	C₃×#529	1	2	yes	—
225	C₂	C₃×#538	1	1	yes	characteristic
226	C₂	C₃×#553	1	2	yes	—
227	C₂	C₃×#555	1	1	yes	characteristic
228	C₂	C₃×#559	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃
prime radical	C₂²×C₃×D₄	C₂²
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
1. C₃×#400	C₂	semidirect
2. C₃×#398	C₂	semidirect
5. C₃×#388	C₂	semidirect
6. C₃×#388	C₂	semidirect
7. C₃×#388	C₂	semidirect
8. C₃×#388	C₂	semidirect
9. C₃×C₄×C₄⋊C₄	C₂	semidirect
10. #2593	C₃	direct (N × H)
32. #400	C₂×C₃	semidirect
33. #398	C₂×C₃	semidirect
36. #388	C₂×C₃	semidirect
37. #388	C₂×C₃	semidirect
38. #388	C₂×C₃	semidirect
39. #388	C₂×C₃	semidirect
40. C₄×C₄⋊C₄	C₂×C₃	semidirect
222. C₃	#2593	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×#400	2
C₃×#398	2
C₃×#394	2
C₃×#390	2
C₃×#388	2
C₃×C₄×C₄⋊C₄	2
#2593	3

Subgroups — C3×#2593 #84457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2593 #84457