Subgroups — C₂×#10624891 #13090377

Order 1458.

602 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624891	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×#6899	C₃	1	6	yes	maximal, complemented
3	C₂×#6898	C₃	1	3	yes	maximal, complemented
4	C₂×#6897	C₃	1	6	yes	maximal, complemented
5	C₂×#6896	C₃	1	3	yes	maximal, complemented
6	C₂×#6895	C₃	1	2	yes	maximal, complemented
7	C₂×#6895	C₃	1	3	yes	maximal, complemented
8	C₂×#6894	C₃	1	2	yes	maximal, complemented
9	C₂×#6894	C₃	1	2	yes	maximal, complemented
10	C₂×#6894	C₃	1	6	yes	maximal, complemented
11	C₂×#6893	C₃	1	1	yes	maximal, characteristic
12	C₂×C₉⋊H(3,𝔽₃)	C₃	1	2	yes	maximal
13	C₂×C₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
14	C₂×C₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
15	C₂×C₉×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
16	C₂×C₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
17	#6899	C₂×C₃	1	6	yes	complemented
18	#6898	C₂×C₃	1	3	yes	complemented
19	#6897	C₂×C₃	1	6	yes	complemented
20	#6896	C₂×C₃	1	3	yes	complemented
21	#6895	C₂×C₃	1	2	yes	complemented
22	#6895	C₂×C₃	1	3	yes	complemented
23	#6894	C₂×C₃	1	2	yes	complemented
24	#6894	C₂×C₃	1	2	yes	complemented
25	#6894	C₂×C₃	1	6	yes	complemented
26	#6893	C₂×C₃	1	1	yes	characteristic
27	C₉⋊H(3,𝔽₃)	C₂×C₃	1	2	yes	—
28	C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic, complemented
29	C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic, complemented
30	C₉×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
31	C₃×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×C₃×3₋¹⁺²	C₃²	1	1	yes	characteristic
33	C₂×C₃×3₋¹⁺²	C₃²	1	1	yes	characteristic
34	C₂×C₃×3₋¹⁺²	C₃²	1	6	yes	—
35	C₂×C₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
36	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
37	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
38	C₂×C₃²×C₉	C₃²	1	2	yes	—
39	C₂×C₃²×C₉	C₃²	1	3	yes	—
40	C₂×C₉⋊C₉	C₃²	1	2	yes	—
41	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
42	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
43	C₂×C₉⋊C₉	C₃²	1	2	yes	—
44	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
45	C₂×C₉⋊C₉	C₃²	1	2	yes	—
46	C₂×C₉⋊C₉	C₃²	1	3	yes	—
47	C₂×C₉⋊C₉	C₃²	1	3	yes	—
48	C₂×C₉⋊C₉	C₃²	1	3	yes	—
49	C₂×C₉⋊C₉	C₃²	1	3	yes	—
50	C₂×C₉⋊C₉	C₃²	1	6	yes	—
51	C₂×C₉⋊C₉	C₃²	1	6	yes	—
52	C₂×C₉⋊C₉	C₃²	1	6	yes	—
53	C₂×C₉⋊C₉	C₃²	1	6	yes	—
54	C₂×C₉⋊C₉	C₃²	1	6	yes	—
55	C₂×C₉⋊C₉	C₃²	1	6	yes	—
56	C₂×C₉⋊C₉	C₃²	1	12	yes	—
57	C₂×C₉⋊C₉	C₃²	1	6	yes	—
58	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
59	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
60	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
61	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
62	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
63	C₂×C₃²⋊C₉	C₃²	1	6	yes	—
64	C₂×C₃²⋊C₉	C₃²	1	6	yes	—
65	C₂×C₃²⋊C₉	C₃²	1	6	yes	—
66	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
67	C₂×C₉²	C₃²	1	3	yes	—
68	C₂×C₉²	C₃²	1	3	yes	—
69	C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
70	C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
71	C₃×3₋¹⁺²	C₂×C₃²	1	6	yes	—
72	C₃×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
73	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
74	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
75	C₃²×C₉	C₂×C₃²	1	2	yes	—
76	C₃²×C₉	C₂×C₃²	1	3	yes	—
77	C₉⋊C₉	C₂×C₃²	1	2	yes	—
78	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
79	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
80	C₉⋊C₉	C₂×C₃²	1	2	yes	—
81	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
82	C₉⋊C₉	C₂×C₃²	1	2	yes	—
83	C₉⋊C₉	C₂×C₃²	1	3	yes	—
84	C₉⋊C₉	C₂×C₃²	1	3	yes	—
85	C₉⋊C₉	C₂×C₃²	1	3	yes	—
86	C₉⋊C₉	C₂×C₃²	1	3	yes	—
87	C₉⋊C₉	C₂×C₃²	1	6	yes	—
88	C₉⋊C₉	C₂×C₃²	1	6	yes	—
89	C₉⋊C₉	C₂×C₃²	1	6	yes	—
90	C₉⋊C₉	C₂×C₃²	1	6	yes	—
91	C₉⋊C₉	C₂×C₃²	1	6	yes	—
92	C₉⋊C₉	C₂×C₃²	1	6	yes	—
93	C₉⋊C₉	C₂×C₃²	1	12	yes	—
94	C₉⋊C₉	C₂×C₃²	1	6	yes	—
95	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
96	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
97	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
98	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
99	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
100	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
101	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
102	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
103	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
104	C₉²	C₂×C₃²	1	3	yes	—
105	C₉²	C₂×C₃²	1	3	yes	—
106	C₂×C₃³	C₃³	1	3	yes	—
107	C₂×C₃³	C₃³	1	1	yes	characteristic
108	C₂×3₋¹⁺²	—	3	3	no	—
109	C₂×3₋¹⁺²	—	3	3	no	—
110	C₂×3₋¹⁺²	—	9	6	no	—
111	C₂×H(3,𝔽₃)	—	3	3	no	—
112	C₂×C₃×C₉	—	3	3	no	—
113	C₂×C₃×C₉	—	9	1	no	—
114	C₂×C₃×C₉	—	9	3	no	—
115	C₂×C₃×C₉	—	9	2	no	—
116	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
117	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
118	C₂×C₃×C₉	C₃³	1	3	yes	—
119	C₂×C₃×C₉	C₃³	1	3	yes	—
120	C₂×C₃×C₉	C₃³	1	6	yes	—
121	C₂×C₃×C₉	C₃³	1	6	yes	—
122	C₂×C₃×C₉	C₃³	1	2	yes	—
123	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
124	C₂×C₃×C₉	C₃³	1	6	yes	—
125	C₂×C₃×C₉	C₃³	1	2	yes	—
126	C₂×C₃×C₉	C₃³	1	2	yes	—
127	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
128	C₂×C₃×C₉	C₃³	1	2	yes	—
129	C₃³	C₂×C₃³	1	3	yes	—
130	C₃³	C₂×C₃³	1	1	yes	characteristic
131	3₋¹⁺²	—	3	3	no	—
132	3₋¹⁺²	—	3	3	no	—
133	3₋¹⁺²	—	9	6	no	—
134	H(3,𝔽₃)	—	3	3	no	—
135	C₃×C₉	—	3	3	no	—
136	C₃×C₉	—	9	1	no	—
137	C₃×C₉	—	9	3	no	—
138	C₃×C₉	—	9	2	no	—
139	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
140	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
141	C₃×C₉	C₂×C₃³	1	3	yes	—
142	C₃×C₉	C₂×C₃³	1	3	yes	—
143	C₃×C₉	C₂×C₃³	1	6	yes	—
144	C₃×C₉	C₂×C₃³	1	6	yes	—
145	C₃×C₉	C₂×C₃³	1	2	yes	—
146	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
147	C₃×C₉	C₂×C₃³	1	6	yes	—
148	C₃×C₉	C₂×C₃³	1	2	yes	—
149	C₃×C₉	C₂×C₃³	1	2	yes	—
150	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
151	C₃×C₉	C₂×C₃³	1	2	yes	—
152	C₂×C₃²	—	3	1	no	—
153	C₂×C₃²	—	3	2	no	—
154	C₂×C₃²	—	3	3	no	—
155	C₂×C₃²	—	3	3	no	—
156	C₂×C₃²	—	3	6	no	—
157	C₂×C₃²	#737	1	3	yes	—
158	C₂×C₃²	C₃⁴	1	1	yes	characteristic
159	C₂×C₉	—	3	2	no	—
160	C₂×C₉	—	3	1	no	—
161	C₂×C₉	—	3	3	no	—
162	C₂×C₉	—	3	3	no	—
163	C₂×C₉	—	3	1	no	—
164	C₂×C₉	—	3	1	no	—
165	C₂×C₉	—	3	1	no	—
166	C₂×C₉	—	3	6	no	—
167	C₂×C₉	—	3	2	no	—
168	C₂×C₉	—	3	2	no	—
169	C₂×C₉	—	3	2	no	—
170	C₂×C₉	—	3	6	no	—
171	C₂×C₉	—	3	6	no	—
172	C₃²	—	3	1	no	—
173	C₃²	—	3	2	no	—
174	C₃²	—	3	3	no	—
175	C₃²	—	3	3	no	—
176	C₃²	—	3	6	no	—
177	C₃²	C₂×#737	1	3	yes	—
178	C₃²	C₂×C₃⁴	1	1	yes	characteristic
179	C₉	—	3	2	no	—
180	C₉	—	3	1	no	—
181	C₉	—	3	3	no	—
182	C₉	—	3	3	no	—
183	C₉	—	3	1	no	—
184	C₉	—	3	1	no	—
185	C₉	—	3	1	no	—
186	C₉	—	3	6	no	—
187	C₉	—	3	2	no	—
188	C₉	—	3	2	no	—
189	C₉	—	3	2	no	—
190	C₉	—	3	6	no	—
191	C₉	—	3	6	no	—
192	C₂×C₃	—	3	3	no	—
193	C₂×C₃	—	9	3	no	—
194	C₂×C₃	C₃×#737	1	1	yes	characteristic
195	C₂×C₃	3₋¹⁺⁴	1	1	yes	characteristic
196	C₂×C₃	3₋¹⁺⁴	1	2	yes	—
197	C₃	—	3	3	no	—
198	C₃	—	9	3	no	—
199	C₃	C₂×C₃×#737	1	1	yes	characteristic
200	C₃	C₂×3₋¹⁺⁴	1	1	yes	characteristic
201	C₃	C₂×3₋¹⁺⁴	1	2	yes	—
202	C₂	#10624891	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃²	C₃⁴
commutator, Frattini, cosocle	C₃²	C₂×C₃⁴
prime radical	C₂×C₃×H(3,𝔽₃)	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ G

Complements

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

N	H ≅ G/N	type
1. #10624891	C₂	direct (N × H)
2. C₂×#6899	C₃	semidirect
3. C₂×#6898	C₃	semidirect
4. C₂×#6897	C₃	semidirect
5. C₂×#6896	C₃	semidirect
6. C₂×#6895	C₃	semidirect
7. C₂×#6895	C₃	semidirect
8. C₂×#6894	C₃	semidirect
9. C₂×#6894	C₃	semidirect
10. C₂×#6894	C₃	semidirect
13. C₂×C₉×3₋¹⁺²	C₃	semidirect
14. C₂×C₉×3₋¹⁺²	C₃	semidirect
16. C₂×C₃×C₉⋊C₉	C₃	semidirect
17. #6899	C₂×C₃	semidirect
18. #6898	C₂×C₃	semidirect
19. #6897	C₂×C₃	semidirect
20. #6896	C₂×C₃	semidirect
21. #6895	C₂×C₃	semidirect
22. #6895	C₂×C₃	semidirect
23. #6894	C₂×C₃	semidirect
24. #6894	C₂×C₃	semidirect
25. #6894	C₂×C₃	semidirect
28. C₉×3₋¹⁺²	C₂×C₃	semidirect
29. C₉×3₋¹⁺²	C₂×C₃	semidirect
31. C₃×C₉⋊C₉	C₂×C₃	semidirect
202. C₂	#10624891	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624891	2
C₂×#6899	3
C₂×#6898	3
C₂×#6897	3
C₂×#6896	3
C₂×#6895	3
C₂×#6894	3
C₂×#6893	3
C₂×C₉⋊H(3,𝔽₃)	3
C₂×C₉×3₋¹⁺²	3
C₂×C₉×H(3,𝔽₃)	3
C₂×C₃×C₉⋊C₉	3

Subgroups — C2×#10624891 #13090377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624891 #13090377