Subgroups — C₃×#69437 #11785979

Order 1152.

521 conjugacy classes of subgroups.

The subgroup lattice has 177 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#376	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	2	yes	maximal
3	C₃×#4524	C₂	1	4	yes	maximal
4	C₃×#1832	—	3	1	no	maximal
5	#69437	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃²×C₄²	C₂²	1	2	yes	—
7	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₃⋊C₈	C₂²	1	4	yes	—
9	C₃²×#95	C₄	1	4	yes	—
10	C₃×C₄⋊(C₃⋊C₈)	—	2	4	no	—
11	C₂×C₃×C₄⋊C₈	—	3	2	no	—
12	C₃×#376	—	2	1	no	—
13	C₃×#376	D₃	1	1	yes	characteristic
14	C₃×#376	C₂×C₃	1	1	yes	characteristic
15	C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	1	2	yes	—
16	C₃×#336	—	3	4	no	—
17	#4524	C₂×C₃	1	4	yes	—
18	C₂²×C₃²×C₄	C₂×C₄	1	4	yes	—
19	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
20	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
21	C₃²×C₄²	—	2	4	no	—
22	C₃²×C₄²	D₄	1	2	yes	—
23	C₃²×C₄²	Q₈	1	2	yes	—
24	C₂×C₃×C₃⋊C₈	—	2	4	no	—
25	C₂×C₃×C₃⋊C₈	—	2	8	no	—
26	#1832	—	3	1	no	Sylow
27	C₂²×C₃×C₈	—	3	4	no	—
28	C₂×C₃×C₄²	—	2	2	no	—
29	C₂×C₃×C₄²	—	2	1	no	—
30	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
31	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
32	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
33	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
34	C₂²×C₃⋊C₈	C₂²×C₃	1	4	yes	—
35	C₃×C₄⋊C₈	—	6	4	no	—
36	C₃×#95	—	2	4	no	—
37	C₃×#95	Dic₃	1	4	yes	—
38	C₃×#95	C₃×C₄	1	4	yes	—
39	C₄⋊(C₃⋊C₈)	—	2	4	no	—
40	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₃²×C₄	—	2	4	no	—
42	C₂×C₃²×C₄	—	2	4	no	—
43	C₂×C₃²×C₄	—	2	8	no	—
44	C₂×C₃²×C₄	C₄⋊C₄	1	4	yes	—
45	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
46	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₃²×C₄	#41	1	4	yes	—
48	C₃×C₃⋊C₈	—	4	4	no	—
49	C₂×C₄⋊C₈	—	3	2	no	—
50	#376	C₃×D₃	1	1	yes	characteristic
51	#336	—	3	4	no	—
52	C₂²×C₃×C₄	—	2	4	no	—
53	C₂²×C₃×C₄	—	2	2	no	—
54	C₂²×C₃×C₄	—	2	1	no	—
55	C₂²×C₃×C₄	C₂×Dic₃	1	4	yes	—
56	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
57	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
58	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
59	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
60	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
61	C₂×C₃×C₈	—	6	4	no	—
62	C₂×C₃×C₈	—	6	8	no	—
63	C₃×C₄²	—	2	8	no	—
64	C₃×C₄²	—	2	4	no	—
65	C₃×C₄²	—	2	4	no	—
66	C₃×C₄²	—	2	2	no	—
67	C₃×C₄²	—	2	2	no	—
68	C₃×C₄²	Dic₆	1	2	yes	—
69	C₃×C₄²	D₁₂	1	2	yes	—
70	C₃×C₄²	C₃×D₄	1	2	yes	—
71	C₃×C₄²	C₃×Q₈	1	2	yes	—
72	C₂×C₃⋊C₈	—	2	4	no	—
73	C₂×C₃⋊C₈	—	2	8	no	—
74	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₃²	#117	1	2	yes	—
76	C₂²×C₃²	#131	1	4	yes	—
77	C₃²×C₄	—	2	4	no	—
78	C₃²×C₄	—	4	4	no	—
79	C₃²×C₄	#124	1	2	yes	—
80	C₃²×C₄	#125	1	2	yes	—
81	C₂²×C₈	—	3	4	no	—
82	C₂×C₄²	C₂×C₃×D₃	1	2	yes	—
83	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
84	C₄⋊C₈	—	6	4	no	—
85	#95	C₃×Dic₃	1	4	yes	—
86	C₂³×C₃	—	2	1	no	—
87	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
88	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄	—	2	4	no	—
90	C₂×C₃×C₄	—	2	4	no	—
91	C₂×C₃×C₄	—	2	8	no	—
92	C₂×C₃×C₄	—	2	4	no	—
93	C₂×C₃×C₄	—	2	8	no	—
94	C₂×C₃×C₄	—	2	4	no	—
95	C₂×C₃×C₄	—	2	8	no	—
96	C₂×C₃×C₄	—	2	4	no	—
97	C₂×C₃×C₄	—	2	1	no	—
98	C₂×C₃×C₄	—	2	1	no	—
99	C₂×C₃×C₄	—	2	4	no	—
100	C₂×C₃×C₄	—	4	4	no	—
101	C₂×C₃×C₄	—	4	8	no	—
102	C₂×C₃×C₄	C₄⋊Dic₃	1	4	yes	—
103	C₂×C₃×C₄	C₃×C₄⋊C₄	1	4	yes	—
104	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
105	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
106	C₂×C₃×C₄	#235	1	4	yes	—
107	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
109	C₂×C₃×C₄	C₃×#41	1	4	yes	—
110	C₃×C₈	—	12	4	no	—
111	C₃⋊C₈	—	4	4	no	—
112	C₂×C₃²	#382	1	1	yes	characteristic
113	C₂×C₃²	#424	1	2	yes	—
114	C₂×C₃²	#433	1	4	yes	—
115	C₂²×C₄	C₂×C₃×Dic₃	1	4	yes	—
116	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
117	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
118	C₂×C₈	—	6	4	no	—
119	C₂×C₈	—	6	8	no	—
120	C₄²	—	2	4	no	—
121	C₄²	C₃×Dic₆	1	2	yes	—
122	C₄²	C₃×D₁₂	1	2	yes	—
123	C₂²×C₃	—	2	1	no	—
124	C₂²×C₃	—	2	2	no	—
125	C₂²×C₃	—	2	4	no	—
126	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
127	C₂²×C₃	#926	1	2	yes	—
128	C₂²×C₃	#948	1	4	yes	—
129	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
130	C₂²×C₃	C₃×#117	1	2	yes	—
131	C₂²×C₃	C₃×#131	1	4	yes	—
132	C₃×C₄	—	2	4	no	—
133	C₃×C₄	—	2	4	no	—
134	C₃×C₄	—	2	2	no	—
135	C₃×C₄	—	2	2	no	—
136	C₃×C₄	—	4	4	no	—
137	C₃×C₄	—	4	8	no	—
138	C₃×C₄	—	4	4	no	—
139	C₃×C₄	—	4	4	no	—
140	C₃×C₄	#870	1	2	yes	—
141	C₃×C₄	#875	1	2	yes	—
142	C₃×C₄	C₃×#124	1	2	yes	—
143	C₃×C₄	C₃×#125	1	2	yes	—
144	C₃²	#1832	1	1	yes	characteristic, complemented, Sylow
145	C₂³	C₂²×C₃×Dic₃	1	1	yes	characteristic
146	C₂×C₄	—	2	4	no	—
147	C₂×C₄	—	2	4	no	—
148	C₂×C₄	—	2	8	no	—
149	C₂×C₄	C₃×C₄⋊Dic₃	1	4	yes	—
150	C₂×C₄	C₂×C₃×Dic₆	1	1	yes	characteristic
151	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
152	C₂×C₄	C₃×#235	1	4	yes	—
153	C₈	—	12	4	no	—
154	C₂×C₃	—	2	1	no	—
155	C₂×C₃	—	2	2	no	—
156	C₂×C₃	—	2	4	no	—
157	C₂×C₃	#4936	1	1	yes	characteristic
158	C₂×C₃	#4999	1	2	yes	—
159	C₂×C₃	#5000	1	4	yes	—
160	C₂×C₃	C₃×#382	1	1	yes	characteristic
161	C₂×C₃	C₃×#424	1	2	yes	—
162	C₂×C₃	C₃×#433	1	4	yes	—
163	C₂²	C₂×C₃×C₄⋊Dic₃	1	1	yes	characteristic
164	C₂²	C₃×#926	1	2	yes	—
165	C₂²	C₃×#948	1	4	yes	—
166	C₄	—	2	4	no	—
167	C₄	—	4	4	no	—
168	C₄	C₃×#870	1	2	yes	—
169	C₄	C₃×#875	1	2	yes	—
170	C₃	—	2	1	no	—
171	C₃	#69437	1	1	yes	characteristic, direct product factor
172	C₃	C₃×#1832	1	1	yes	characteristic, complemented
173	C₂	C₃×#4936	1	1	yes	characteristic
174	C₂	C₃×#4999	1	2	yes	—
175	C₂	C₃×#5000	1	4	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₃
commutator	C₂³×C₃	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₃²×#376	C₂
socle, prime radical	C₂³×C₃²	C₂²×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₃×#376	D₃
hypocenter	C₃	C₃×#1832
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₃×#376

Complements

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

N	H ≅ G/N	type
5. #69437	C₃	direct (N × H)
144. C₃²	#1832	semidirect
171. C₃	#69437	direct (N × H)
172. C₃	C₃×#1832	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#376	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₃×#4524	2
C₃×#1832	3
#69437	3

Subgroups — C3×#69437 #11785979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69437 #11785979