Subgroups — C₃×#69842 #11786332

Order 1152.

497 conjugacy classes of subgroups.

The subgroup lattice has 186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#97	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#819	C₂	1	4	yes	maximal
3	C₃×#4924	C₂	1	2	yes	maximal
4	C₃×#1849	—	3	1	no	maximal
5	#69842	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₃²×C₈	C₂²	1	2	yes	—
7	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
8	C₂×C₃×#208	C₂²	1	4	yes	—
9	C₃²×#97	C₄	1	4	yes	—
10	C₃×#819	—	2	8	no	—
11	C₃×C₄⋊(C₃⋊C₈)	—	2	4	no	—
12	C₂×C₃×#108	—	3	4	no	—
13	C₃×#423	—	3	2	no	—
14	C₂×C₃×#97	—	2	1	no	—
15	C₂×C₃×#97	D₃	1	1	yes	characteristic
16	C₂×C₃×#97	C₂×C₃	1	1	yes	characteristic
17	C₂×#819	C₂×C₃	1	4	yes	—
18	#4924	C₂×C₃	1	2	yes	—
19	C₂²×C₃²×C₄	Q₈	1	2	yes	—
20	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
21	C₂×C₃²×C₈	C₂×C₄	1	4	yes	—
22	C₂×C₃²×C₈	D₄	1	4	yes	—
23	C₂×C₃²×C₈	Q₈	1	4	yes	—
24	C₃²×C₄²	C₂×C₄	1	2	yes	—
25	C₃²×C₄²	D₄	1	2	yes	—
26	C₃×#208	—	2	8	no	—
27	C₂×C₃×C₃⋊C₈	—	2	4	no	—
28	#1849	—	3	1	no	Sylow
29	C₂×C₃×M₁₆	—	3	4	no	—
30	C₂²×C₃×C₈	—	2	2	no	—
31	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
32	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
33	C₂×C₃×C₄²	—	2	1	no	—
34	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
35	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
36	C₂×#208	C₂²×C₃	1	4	yes	—
37	C₃×#108	—	6	8	no	—
38	C₃×C₄⋊C₈	—	6	4	no	—
39	C₃×#97	—	2	4	no	—
40	C₃×#97	Dic₃	1	4	yes	—
41	C₃×#97	C₃×C₄	1	4	yes	—
42	#819	—	2	8	no	—
43	C₄⋊(C₃⋊C₈)	—	2	4	no	—
44	C₂³×C₃²	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₃²×C₄	—	4	2	no	—
46	C₂×C₃²×C₄	C₄⋊C₄	1	4	yes	—
47	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
49	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
50	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
51	C₃²×C₈	C₄⋊C₄	1	8	yes	—
52	C₃×C₃⋊C₈	—	4	4	no	—
53	C₂×#108	—	3	4	no	—
54	#423	—	3	2	no	—
55	C₂×#97	C₃×D₃	1	1	yes	characteristic
56	C₂²×C₃×C₄	—	2	2	no	—
57	C₂²×C₃×C₄	—	2	1	no	—
58	C₂²×C₃×C₄	Dic₆	1	2	yes	—
59	C₂²×C₃×C₄	C₃×Q₈	1	2	yes	—
60	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
61	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
62	C₃×M₁₆	—	6	8	no	—
63	C₂×C₃×C₈	—	2	4	no	—
64	C₂×C₃×C₈	—	2	4	no	—
65	C₂×C₃×C₈	—	2	4	no	—
66	C₂×C₃×C₈	—	6	4	no	—
67	C₂×C₃×C₈	Dic₆	1	4	yes	—
68	C₂×C₃×C₈	D₁₂	1	4	yes	—
69	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	—
70	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	—
71	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
72	C₂×C₃×C₈	C₃×Q₈	1	4	yes	—
73	C₃×C₄²	—	2	2	no	—
74	C₃×C₄²	—	2	2	no	—
75	C₃×C₄²	D₁₂	1	2	yes	—
76	C₃×C₄²	C₂×Dic₃	1	2	yes	—
77	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
78	C₃×C₄²	C₃×D₄	1	2	yes	—
79	#208	—	2	8	no	—
80	C₂×C₃⋊C₈	—	2	4	no	—
81	C₂²×C₃²	—	2	2	no	—
82	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₃²	C₄⋊Q₈	1	2	yes	—
84	C₃²×C₄	—	2	4	no	—
85	C₃²×C₄	C₂×C₄⋊C₄	1	2	yes	—
86	C₃²×C₄	#127	1	1	yes	characteristic
87	C₃²×C₄	C₄⋊Q₈	1	1	yes	characteristic
88	C₂×M₁₆	—	3	4	no	—
89	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
90	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
91	#108	—	6	8	no	—
92	C₄⋊C₈	—	6	4	no	—
93	#97	C₃×Dic₃	1	4	yes	—
94	C₂³×C₃	—	2	1	no	—
95	C₂³×C₃	C₂×Dic₆	1	1	yes	characteristic
96	C₂³×C₃	C₂×C₃×Q₈	1	1	yes	characteristic
97	C₂×C₃×C₄	—	2	4	no	—
98	C₂×C₃×C₄	—	2	2	no	—
99	C₂×C₃×C₄	—	2	1	no	—
100	C₂×C₃×C₄	—	2	2	no	—
101	C₂×C₃×C₄	—	2	1	no	—
102	C₂×C₃×C₄	—	4	2	no	—
103	C₂×C₃×C₄	—	4	2	no	—
104	C₂×C₃×C₄	—	4	4	no	—
105	C₂×C₃×C₄	C₄⋊Dic₃	1	4	yes	—
106	C₂×C₃×C₄	C₃×C₄⋊C₄	1	4	yes	—
107	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
108	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
109	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
110	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
111	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
113	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
114	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
115	C₃×C₈	—	2	8	no	—
116	C₃×C₈	—	12	4	no	—
117	C₃×C₈	C₄⋊Dic₃	1	8	yes	—
118	C₃×C₈	C₃×C₄⋊C₄	1	8	yes	—
119	C₃⋊C₈	—	4	4	no	—
120	C₂×C₃²	—	2	2	no	—
121	C₂×C₃²	#384	1	1	yes	characteristic
122	C₂×C₃²	#430	1	2	yes	—
123	C₂²×C₄	C₃×Dic₆	1	2	yes	—
124	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
125	M₁₆	—	6	8	no	—
126	C₂×C₈	—	6	4	no	—
127	C₂×C₈	C₃×Dic₆	1	4	yes	—
128	C₂×C₈	C₃×D₁₂	1	4	yes	—
129	C₂×C₈	C₂×C₃×Dic₃	1	4	yes	—
130	C₄²	C₃×D₁₂	1	2	yes	—
131	C₄²	C₂×C₃×Dic₃	1	2	yes	—
132	C₂²×C₃	—	2	4	no	—
133	C₂²×C₃	—	2	2	no	—
134	C₂²×C₃	—	2	2	no	—
135	C₂²×C₃	—	2	1	no	—
136	C₂²×C₃	—	2	2	no	—
137	C₂²×C₃	#869	1	2	yes	—
138	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
139	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
140	C₂²×C₃	C₃×C₄⋊Q₈	1	2	yes	—
141	C₃×C₄	—	2	4	no	—
142	C₃×C₄	—	2	4	no	—
143	C₃×C₄	—	2	2	no	—
144	C₃×C₄	—	2	1	no	—
145	C₃×C₄	—	2	1	no	—
146	C₃×C₄	—	4	4	no	—
147	C₃×C₄	#869	1	1	yes	characteristic
148	C₃×C₄	#874	1	1	yes	characteristic
149	C₃×C₄	C₂×C₄⋊Dic₃	1	2	yes	—
150	C₃×C₄	C₂×C₃×C₄⋊C₄	1	2	yes	—
151	C₃×C₄	C₃×#127	1	1	yes	characteristic
152	C₃×C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
153	C₃²	#1849	1	1	yes	characteristic, complemented, Sylow
154	C₂³	C₂×C₃×Dic₆	1	1	yes	characteristic
155	C₂×C₄	—	4	2	no	—
156	C₂×C₄	C₃×C₄⋊Dic₃	1	4	yes	—
157	C₂×C₄	C₂×C₃×Dic₆	1	2	yes	—
158	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
159	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
160	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
161	C₈	—	12	4	no	—
162	C₈	C₃×C₄⋊Dic₃	1	8	yes	—
163	C₂×C₃	—	2	4	no	—
164	C₂×C₃	—	2	2	no	—
165	C₂×C₃	—	2	2	no	—
166	C₂×C₃	—	2	1	no	—
167	C₂×C₃	—	2	2	no	—
168	C₂×C₃	#4935	1	1	yes	characteristic
169	C₂×C₃	#5125	1	2	yes	—
170	C₂×C₃	C₃×#384	1	1	yes	characteristic
171	C₂×C₃	C₃×#430	1	2	yes	—
172	C₂²	—	2	2	no	—
173	C₂²	C₃×#869	1	2	yes	—
174	C₂²	C₂×C₃×C₄⋊Dic₃	1	1	yes	characteristic
175	C₄	—	2	4	no	—
176	C₄	C₃×#869	1	1	yes	characteristic
177	C₄	C₃×#874	1	1	yes	characteristic
178	C₄	C₂×C₃×C₄⋊Dic₃	1	2	yes	—
179	C₃	—	2	1	no	—
180	C₃	#69842	1	1	yes	characteristic, direct product factor
181	C₃	C₃×#1849	1	1	yes	characteristic, complemented
182	C₂	—	2	2	no	—
183	C₂	C₃×#4935	1	1	yes	characteristic
184	C₂	C₃×#5125	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₁₂
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃²×#97	C₂
socle	C₂²×C₃²	C₂×C₄⋊C₄
prime radical	C₂³×C₃²	C₂×Q₈
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂×C₃×#97	D₃
hypocenter	C₃	C₃×#1849
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₂×C₃×#97

Complements

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

N	H ≅ G/N	type
5. #69842	C₃	direct (N × H)
153. C₃²	#1849	semidirect
180. C₃	#69842	direct (N × H)
181. C₃	C₃×#1849	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#97	2
C₂×C₃×#819	2
C₃×#4924	2
C₃×#1849	3
#69842	3

Subgroups — C3×#69842 #11786332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69842 #11786332