Subgroups — D₃×#433 #79370

Order 384.

412 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×#117	C₂	1	1	yes	maximal, characteristic
2	C₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	#5000	C₂	1	1	yes	maximal, characteristic, complemented
4	#4840	C₂	1	2	yes	maximal, complemented
5	D₃×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
6	D₃×C₂²⋊C₈	C₂	1	2	yes	maximal
7	#4720	C₂	1	2	yes	maximal, complemented
8	#4709	C₂	1	1	yes	maximal, characteristic, complemented
9	D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
10	#4690	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#433	—	3	1	no	maximal, Sylow
13	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
14	C₃×#117	C₂²	1	1	yes	characteristic
15	#926	C₂²	1	1	yes	characteristic
16	C₂×D₃×C₈	C₂²	1	2	yes	—
17	C₂×D₃×C₈	C₂²	1	2	yes	—
18	#892	C₄	1	2	yes	—
19	D₃×C₄⋊C₄	C₄	1	2	yes	—
20	D₃×C₂²⋊C₄	C₄	1	2	yes	—
21	#877	C₄	1	2	yes	—
22	#872	C₂²	1	1	yes	characteristic
23	#872	C₂²	1	1	yes	characteristic
24	C₄²×D₃	C₂²	1	1	yes	characteristic
25	C₄²×D₃	C₂²	1	1	yes	characteristic
26	C₃×C₄⋊C₈	C₂²	1	2	yes	complemented
27	C₃×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₃×#97	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
30	#830	C₂²	1	2	yes	—
31	(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
32	(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
33	#815	C₂²	1	2	yes	complemented
34	Dic₃⋊C₈	C₂²	1	2	yes	complemented
35	Dic₃⋊C₈	C₂²	1	2	yes	complemented
36	C₈×Dic₃	C₂²	1	2	yes	complemented
37	C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
38	#803	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×#117	—	3	1	no	—
41	#433	—	3	1	no	—
42	#433	—	3	2	no	—
43	#433	—	3	2	no	—
44	#433	—	3	1	no	—
45	#433	—	3	1	no	—
46	#433	D₃	1	1	yes	characteristic, direct product factor
47	C₂×C₄⋊C₈	—	3	2	no	—
48	C₂×C₂²⋊C₈	—	3	2	no	—
49	C₂×#97	—	3	1	no	—
50	C₂×C₄×C₈	—	3	1	no	—
51	C₂³×D₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
53	C₂²×Dic₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×D₃	—	2	4	no	—
55	C₂×C₄×D₃	C₂×C₄	1	2	yes	—
56	C₂×C₄×D₃	C₂×C₄	1	2	yes	—
57	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
60	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₈	C₂³	1	2	yes	—
62	C₂×C₃×C₈	C₂³	1	2	yes	—
63	C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
64	C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
65	C₃×C₄²	C₂³	1	1	yes	characteristic
66	C₃×C₄²	C₂³	1	1	yes	characteristic
67	#217	C₂×C₄	1	2	yes	—
68	(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
69	(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
70	C₄⋊Dic₃	C₂×C₄	1	2	yes	—
71	Dic₃⋊C₄	C₂×C₄	1	2	yes	—
72	Dic₃⋊C₄	C₂×C₄	1	2	yes	—
73	C₄×Dic₃	C₂×C₄	1	2	yes	—
74	C₄×Dic₃	C₂×C₄	1	2	yes	—
75	C₄×Dic₃	C₂³	1	1	yes	characteristic
76	C₄×Dic₃	C₂³	1	1	yes	characteristic
77	C₂×C₃⋊C₈	C₂³	1	2	yes	—
78	C₂×C₃⋊C₈	C₂³	1	2	yes	—
79	D₃×C₈	—	2	4	no	—
80	D₃×C₈	—	2	4	no	—
81	C₂³×C₄	—	3	1	no	—
82	C₂²×C₈	—	3	2	no	—
83	C₂²×C₈	—	3	2	no	—
84	#117	—	3	1	no	—
85	#117	—	3	2	no	—
86	#117	—	3	2	no	—
87	#117	—	3	1	no	—
88	#117	—	3	1	no	—
89	#117	C₂×D₃	1	1	yes	characteristic
90	C₂×C₄⋊C₄	—	3	2	no	—
91	C₂×C₂²⋊C₄	—	3	2	no	—
92	C₂×C₄²	—	3	1	no	—
93	C₂×C₄²	—	3	1	no	—
94	C₄⋊C₈	—	3	2	no	—
95	C₄⋊C₈	—	3	2	no	—
96	C₄⋊C₈	—	3	2	no	—
97	C₄⋊C₈	C₂×D₃	1	2	yes	complemented
98	C₂²⋊C₈	—	3	2	no	—
99	C₂²⋊C₈	—	3	2	no	—
100	C₂²⋊C₈	—	3	2	no	—
101	C₂²⋊C₈	C₂×D₃	1	2	yes	—
102	#97	—	3	2	no	—
103	#97	—	3	1	no	—
104	#97	C₂×D₃	1	1	yes	characteristic, complemented
105	C₄×C₈	—	3	2	no	—
106	C₄×C₈	—	3	1	no	—
107	C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
108	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×D₃	—	2	2	no	—
110	C₂²×D₃	—	2	4	no	—
111	C₂²×D₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×D₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄	—	2	2	no	—
114	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
115	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
116	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
118	C₂×Dic₃	—	2	2	no	—
119	C₂×Dic₃	C₂²×C₄	1	2	yes	—
120	C₂×Dic₃	C₂²×C₄	1	2	yes	—
121	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
123	C₄×D₃	—	2	2	no	—
124	C₄×D₃	—	2	4	no	—
125	C₄×D₃	—	2	4	no	—
126	C₄×D₃	—	2	2	no	—
127	C₄×D₃	—	2	2	no	—
128	C₄×D₃	#41	1	4	yes	—
129	C₃×C₈	—	2	2	no	—
130	C₃×C₈	—	2	2	no	—
131	C₃⋊C₈	—	2	2	no	—
132	C₃⋊C₈	—	2	2	no	—
133	C₂⁴	—	3	1	no	—
134	C₂²×C₄	—	3	1	no	—
135	C₂²×C₄	—	3	1	no	—
136	C₂²×C₄	—	3	2	no	—
137	C₂²×C₄	—	3	2	no	—
138	C₂²×C₄	—	3	1	no	—
139	C₂²×C₄	—	3	1	no	—
140	C₂²×C₄	—	3	1	no	—
141	C₂²×C₄	—	6	4	no	—
142	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
143	C₂×C₈	—	3	2	no	—
144	C₂×C₈	—	3	2	no	—
145	C₂×C₈	—	6	4	no	—
146	C₂×C₈	—	6	4	no	—
147	C₂×C₈	C₂²×D₃	1	2	yes	—
148	C₂×C₈	C₂²×D₃	1	2	yes	—
149	C₄⋊C₄	—	3	2	no	—
150	C₄⋊C₄	—	3	2	no	—
151	C₄⋊C₄	—	3	2	no	—
152	C₄⋊C₄	C₄×D₃	1	2	yes	—
153	C₂²⋊C₄	—	3	2	no	—
154	C₂²⋊C₄	—	3	2	no	—
155	C₂²⋊C₄	—	3	2	no	—
156	C₂²⋊C₄	C₄×D₃	1	2	yes	—
157	C₄²	—	3	2	no	—
158	C₄²	—	3	2	no	—
159	C₄²	—	3	1	no	—
160	C₄²	—	3	1	no	—
161	C₄²	C₂²×D₃	1	1	yes	characteristic
162	C₄²	C₂²×D₃	1	1	yes	characteristic
163	C₂²×C₃	—	2	1	no	—
164	C₂²×C₃	—	2	2	no	—
165	C₂²×C₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×D₃	—	2	1	no	—
167	C₂×D₃	—	2	2	no	—
168	C₂×D₃	—	4	4	no	—
169	C₂×D₃	#117	1	2	yes	—
170	C₂×D₃	#131	1	4	yes	—
171	C₃×C₄	—	2	1	no	—
172	C₃×C₄	—	2	2	no	—
173	C₃×C₄	—	2	2	no	—
174	C₃×C₄	C₂×#41	1	2	yes	—
175	Dic₃	—	2	1	no	—
176	Dic₃	—	2	2	no	—
177	Dic₃	—	2	2	no	—
178	Dic₃	#117	1	2	yes	—
179	C₂³	—	3	1	no	—
180	C₂³	—	3	1	no	—
181	C₂³	—	6	2	no	—
182	C₂³	—	6	4	no	—
183	C₂³	C₂×C₄×D₃	1	1	yes	characteristic
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	3	1	no	—
186	C₂×C₄	—	3	4	no	—
187	C₂×C₄	—	3	2	no	—
188	C₂×C₄	—	3	2	no	—
189	C₂×C₄	—	3	1	no	—
190	C₂×C₄	—	6	2	no	—
191	C₂×C₄	—	6	2	no	—
192	C₂×C₄	—	6	4	no	—
193	C₂×C₄	—	6	4	no	—
194	C₂×C₄	—	6	2	no	—
195	C₂×C₄	—	6	2	no	—
196	C₂×C₄	C₂×C₄×D₃	1	2	yes	—
197	C₂×C₄	C₂×C₄×D₃	1	2	yes	—
198	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
199	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
200	C₈	—	2	2	no	—
201	C₈	—	2	2	no	—
202	C₈	—	6	2	no	—
203	C₈	—	6	2	no	—
204	C₂×C₃	—	4	1	no	—
205	C₂×C₃	C₂×#117	1	1	yes	characteristic
206	C₂×C₃	C₂×#131	1	2	yes	—
207	D₃	—	4	1	no	—
208	D₃	#433	1	4	yes	direct product factor
209	C₂²	—	2	2	no	—
210	C₂²	—	2	1	no	—
211	C₂²	—	3	4	no	—
212	C₂²	—	3	2	no	—
213	C₂²	—	6	2	no	—
214	C₂²	—	6	1	no	—
215	C₂²	—	12	4	no	—
216	C₂²	C₂²×C₄×D₃	1	1	yes	characteristic
217	C₄	—	2	2	no	—
218	C₄	—	2	2	no	—
219	C₄	—	2	1	no	—
220	C₄	—	3	2	no	—
221	C₄	—	6	2	no	—
222	C₄	—	6	2	no	—
223	C₄	—	6	1	no	—
224	C₄	D₃×#41	1	2	yes	—
225	C₃	C₂×#433	1	1	yes	characteristic, complemented, Sylow
226	C₂	—	3	4	no	—
227	C₂	—	4	1	no	—
228	C₂	—	12	1	no	—
229	C₂	D₃×#117	1	1	yes	characteristic
230	C₂	D₃×#131	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₃
commutator, socle	C₂²×C₃	C₂³×C₄
Fitting	C₃×#433	C₂
prime radical	C₂³×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴
hypercenter	#433	D₃
hypocenter	C₃	C₂×#433
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ #433

Complements

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

N	H ≅ G/N	type
2. C₃×#433	C₂	semidirect
3. #5000	C₂	semidirect
4. #4840	C₂	semidirect
5. D₃×C₄⋊C₈	C₂	semidirect
7. #4720	C₂	semidirect
8. #4709	C₂	semidirect
9. D₃×#97	C₂	semidirect
10. #4690	C₂	semidirect
11. C₄×D₃×C₈	C₂	semidirect
26. C₃×C₄⋊C₈	C₂²	semidirect
28. C₃×#97	C₂²	semidirect
29. C₃×C₄×C₈	C₂²	semidirect
33. #815	C₂²	semidirect
34. Dic₃⋊C₈	C₂²	semidirect
35. Dic₃⋊C₈	C₂²	semidirect
36. C₈×Dic₃	C₂²	semidirect
37. C₄⋊(C₃⋊C₈)	C₂²	semidirect
38. #803	C₂²	semidirect
39. C₄×C₃⋊C₈	C₂²	semidirect
46. #433	D₃	direct (N × H)
97. C₄⋊C₈	C₂×D₃	semidirect
104. #97	C₂×D₃	semidirect
107. C₄×C₈	C₂×D₃	semidirect
208. D₃	#433	direct (N × H)
225. C₃	C₂×#433	semidirect

Maximal subgroups

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

subgroup	index
D₃×#117	2
C₃×#433	2
#5000	2
#4840	2
D₃×C₄⋊C₈	2
D₃×C₂²⋊C₈	2
#4720	2
#4709	2
D₃×#97	2
#4690	2
C₄×D₃×C₈	2
C₂×#433	3

Subgroups — D3×#433 #79370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#433 #79370