Subgroups — C₂×#10624907 #13090393

Order 1458.

622 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624907	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×#6899	C₃	1	3	yes	maximal, complemented
3	C₂×#6899	C₃	1	3	yes	maximal, complemented
4	C₂×#6898	C₃	1	3	yes	maximal, complemented
5	C₂×#6897	C₃	1	3	yes	maximal, complemented
6	C₂×#6897	C₃	1	3	yes	maximal, complemented
7	C₂×#6896	C₃	1	3	yes	maximal, complemented
8	C₂×#6895	C₃	1	1	yes	maximal, characteristic, complemented
9	C₂×#6895	C₃	1	3	yes	maximal, complemented
10	C₂×#6894	C₃	1	1	yes	maximal, characteristic, complemented
11	C₂×#6894	C₃	1	1	yes	maximal, characteristic, complemented
12	C₂×#6894	C₃	1	1	yes	maximal, characteristic, complemented
13	C₂×#6894	C₃	1	1	yes	maximal, characteristic, complemented
14	C₂×#6894	C₃	1	3	yes	maximal, complemented
15	C₂×#6893	C₃	1	1	yes	maximal, characteristic
16	C₂×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
17	C₂×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
18	C₂×C₉×3₋¹⁺²	C₃	1	3	yes	maximal, complemented
19	C₂×C₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
20	C₂×C₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
21	C₂×C₉×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
22	C₂×#6887	C₃	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
24	#6899	C₂×C₃	1	3	yes	complemented
25	#6899	C₂×C₃	1	3	yes	complemented
26	#6898	C₂×C₃	1	3	yes	complemented
27	#6897	C₂×C₃	1	3	yes	complemented
28	#6897	C₂×C₃	1	3	yes	complemented
29	#6896	C₂×C₃	1	3	yes	complemented
30	#6895	C₂×C₃	1	1	yes	characteristic, complemented
31	#6895	C₂×C₃	1	3	yes	complemented
32	#6894	C₂×C₃	1	1	yes	characteristic, complemented
33	#6894	C₂×C₃	1	1	yes	characteristic, complemented
34	#6894	C₂×C₃	1	1	yes	characteristic, complemented
35	#6894	C₂×C₃	1	1	yes	characteristic, complemented
36	#6894	C₂×C₃	1	3	yes	complemented
37	#6893	C₂×C₃	1	1	yes	characteristic
38	C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
39	C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
40	C₉×3₋¹⁺²	C₂×C₃	1	3	yes	complemented
41	C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic, complemented
42	C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic, complemented
43	C₉×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
44	#6887	C₂×C₃	1	1	yes	characteristic, complemented
45	C₃×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₃×3₋¹⁺²	C₃²	1	3	yes	—
47	C₂×C₃×3₋¹⁺²	C₃²	1	1	yes	characteristic
48	C₂×C₃×3₋¹⁺²	C₃²	1	1	yes	characteristic
49	C₂×C₃×3₋¹⁺²	C₃²	1	3	yes	—
50	C₂×C₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
51	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
52	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
53	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
54	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
55	C₂×C₃²×C₉	C₃²	1	3	yes	—
56	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
57	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
58	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
59	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
60	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
61	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
62	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
63	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
64	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
65	C₂×C₉⋊C₉	C₃²	1	3	yes	—
66	C₂×C₉⋊C₉	C₃²	1	3	yes	—
67	C₂×C₉⋊C₉	C₃²	1	3	yes	—
68	C₂×C₉⋊C₉	C₃²	1	3	yes	—
69	C₂×C₉⋊C₉	C₃²	1	3	yes	—
70	C₂×C₉⋊C₉	C₃²	1	3	yes	—
71	C₂×C₉⋊C₉	C₃²	1	3	yes	—
72	C₂×C₉⋊C₉	C₃²	1	3	yes	—
73	C₂×C₉⋊C₉	C₃²	1	3	yes	—
74	C₂×C₉⋊C₉	C₃²	1	3	yes	—
75	C₂×C₉⋊C₉	C₃²	1	3	yes	—
76	C₂×C₉⋊C₉	C₃²	1	3	yes	—
77	C₂×C₉⋊C₉	C₃²	1	3	yes	—
78	C₂×C₉⋊C₉	C₃²	1	3	yes	—
79	C₂×C₉⋊C₉	C₃²	1	3	yes	—
80	C₂×C₉⋊C₉	C₃²	1	3	yes	—
81	C₂×C₉⋊C₉	C₃²	1	3	yes	—
82	C₂×C₉⋊C₉	C₃²	1	3	yes	—
83	C₂×C₉⋊C₉	C₃²	1	3	yes	—
84	C₂×C₉⋊C₉	C₃²	1	3	yes	—
85	C₂×C₉⋊C₉	C₃²	1	3	yes	—
86	C₂×C₃²⋊C₉	C₃²	1	1	yes	characteristic
87	C₂×C₃²⋊C₉	C₃²	1	1	yes	characteristic
88	C₂×C₃²⋊C₉	C₃²	1	1	yes	characteristic
89	C₂×C₃²⋊C₉	C₃²	1	1	yes	characteristic
90	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
91	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
92	C₂×C₃²⋊C₉	C₃²	1	1	yes	characteristic
93	C₂×C₃²⋊C₉	C₃²	1	1	yes	characteristic
94	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
95	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
96	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
97	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
98	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
99	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
100	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
101	C₂×C₉²	C₃²	1	3	yes	—
102	C₂×C₉²	C₃²	1	3	yes	—
103	C₂×C₉²	C₃²	1	3	yes	—
104	C₃×3₋¹⁺²	C₂×C₃²	1	3	yes	—
105	C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
106	C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
107	C₃×3₋¹⁺²	C₂×C₃²	1	3	yes	—
108	C₃×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
109	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
110	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
111	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
112	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
113	C₃²×C₉	C₂×C₃²	1	3	yes	—
114	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
115	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
116	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
117	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
118	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
119	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
120	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
121	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
122	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
123	C₉⋊C₉	C₂×C₃²	1	3	yes	—
124	C₉⋊C₉	C₂×C₃²	1	3	yes	—
125	C₉⋊C₉	C₂×C₃²	1	3	yes	—
126	C₉⋊C₉	C₂×C₃²	1	3	yes	—
127	C₉⋊C₉	C₂×C₃²	1	3	yes	—
128	C₉⋊C₉	C₂×C₃²	1	3	yes	—
129	C₉⋊C₉	C₂×C₃²	1	3	yes	—
130	C₉⋊C₉	C₂×C₃²	1	3	yes	—
131	C₉⋊C₉	C₂×C₃²	1	3	yes	—
132	C₉⋊C₉	C₂×C₃²	1	3	yes	—
133	C₉⋊C₉	C₂×C₃²	1	3	yes	—
134	C₉⋊C₉	C₂×C₃²	1	3	yes	—
135	C₉⋊C₉	C₂×C₃²	1	3	yes	—
136	C₉⋊C₉	C₂×C₃²	1	3	yes	—
137	C₉⋊C₉	C₂×C₃²	1	3	yes	—
138	C₉⋊C₉	C₂×C₃²	1	3	yes	—
139	C₉⋊C₉	C₂×C₃²	1	3	yes	—
140	C₉⋊C₉	C₂×C₃²	1	3	yes	—
141	C₉⋊C₉	C₂×C₃²	1	3	yes	—
142	C₉⋊C₉	C₂×C₃²	1	3	yes	—
143	C₉⋊C₉	C₂×C₃²	1	3	yes	—
144	C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
145	C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
146	C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
147	C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
148	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
149	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
150	C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
151	C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
152	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
153	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
154	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
155	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
156	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
157	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
158	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
159	C₉²	C₂×C₃²	1	3	yes	—
160	C₉²	C₂×C₃²	1	3	yes	—
161	C₉²	C₂×C₃²	1	3	yes	—
162	C₂×C₃³	C₃³	1	3	yes	—
163	C₂×C₃³	C₃³	1	1	yes	characteristic
164	C₂×3₋¹⁺²	—	3	3	no	—
165	C₂×3₋¹⁺²	—	3	3	no	—
166	C₂×3₋¹⁺²	—	3	9	no	—
167	C₂×3₋¹⁺²	—	9	3	no	—
168	C₂×H(3,𝔽₃)	—	3	3	no	—
169	C₂×C₃×C₉	—	3	3	no	—
170	C₂×C₃×C₉	—	3	3	no	—
171	C₂×C₃×C₉	—	9	1	no	—
172	C₂×C₃×C₉	—	9	3	no	—
173	C₂×C₃×C₉	—	9	1	no	—
174	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
175	C₂×C₃×C₉	C₃³	1	3	yes	—
176	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
177	C₂×C₃×C₉	C₃³	1	3	yes	—
178	C₂×C₃×C₉	C₃³	1	3	yes	—
179	C₂×C₃×C₉	C₃³	1	3	yes	—
180	C₂×C₃×C₉	C₃³	1	3	yes	—
181	C₂×C₃×C₉	C₃³	1	3	yes	—
182	C₂×C₃×C₉	C₃³	1	3	yes	—
183	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
184	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
185	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
186	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
187	C₂×C₃×C₉	C₃³	1	3	yes	—
188	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
189	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
190	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
191	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
192	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
193	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
194	C₃³	C₂×C₃³	1	3	yes	—
195	C₃³	C₂×C₃³	1	1	yes	characteristic
196	3₋¹⁺²	—	3	3	no	—
197	3₋¹⁺²	—	3	3	no	—
198	3₋¹⁺²	—	3	9	no	—
199	3₋¹⁺²	—	9	3	no	—
200	H(3,𝔽₃)	—	3	3	no	—
201	C₃×C₉	—	3	3	no	—
202	C₃×C₉	—	3	3	no	—
203	C₃×C₉	—	9	1	no	—
204	C₃×C₉	—	9	3	no	—
205	C₃×C₉	—	9	1	no	—
206	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
207	C₃×C₉	C₂×C₃³	1	3	yes	—
208	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
209	C₃×C₉	C₂×C₃³	1	3	yes	—
210	C₃×C₉	C₂×C₃³	1	3	yes	—
211	C₃×C₉	C₂×C₃³	1	3	yes	—
212	C₃×C₉	C₂×C₃³	1	3	yes	—
213	C₃×C₉	C₂×C₃³	1	3	yes	—
214	C₃×C₉	C₂×C₃³	1	3	yes	—
215	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
216	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
217	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
218	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
219	C₃×C₉	C₂×C₃³	1	3	yes	—
220	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
221	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
222	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
223	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
224	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
225	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
226	C₂×C₃²	—	3	1	no	—
227	C₂×C₃²	—	3	1	no	—
228	C₂×C₃²	—	3	1	no	—
229	C₂×C₃²	—	3	3	no	—
230	C₂×C₃²	—	3	3	no	—
231	C₂×C₃²	—	3	3	no	—
232	C₂×C₃²	—	3	3	no	—
233	C₂×C₃²	#737	1	3	yes	—
234	C₂×C₃²	C₃⁴	1	1	yes	characteristic
235	C₂×C₉	—	3	1	no	—
236	C₂×C₉	—	3	1	no	—
237	C₂×C₉	—	3	1	no	—
238	C₂×C₉	—	3	1	no	—
239	C₂×C₉	—	3	1	no	—
240	C₂×C₉	—	3	3	no	—
241	C₂×C₉	—	3	3	no	—
242	C₂×C₉	—	3	3	no	—
243	C₂×C₉	—	3	3	no	—
244	C₂×C₉	—	3	1	no	—
245	C₂×C₉	—	3	3	no	—
246	C₂×C₉	—	3	1	no	—
247	C₂×C₉	—	3	1	no	—
248	C₂×C₉	—	3	1	no	—
249	C₂×C₉	—	3	3	no	—
250	C₂×C₉	—	3	1	no	—
251	C₂×C₉	—	3	1	no	—
252	C₂×C₉	—	3	3	no	—
253	C₂×C₉	—	3	3	no	—
254	C₂×C₉	#737	1	3	yes	—
255	C₃²	—	3	1	no	—
256	C₃²	—	3	1	no	—
257	C₃²	—	3	1	no	—
258	C₃²	—	3	3	no	—
259	C₃²	—	3	3	no	—
260	C₃²	—	3	3	no	—
261	C₃²	—	3	3	no	—
262	C₃²	C₂×#737	1	3	yes	—
263	C₃²	C₂×C₃⁴	1	1	yes	characteristic
264	C₉	—	3	1	no	—
265	C₉	—	3	1	no	—
266	C₉	—	3	1	no	—
267	C₉	—	3	1	no	—
268	C₉	—	3	1	no	—
269	C₉	—	3	3	no	—
270	C₉	—	3	3	no	—
271	C₉	—	3	3	no	—
272	C₉	—	3	3	no	—
273	C₉	—	3	1	no	—
274	C₉	—	3	3	no	—
275	C₉	—	3	1	no	—
276	C₉	—	3	1	no	—
277	C₉	—	3	1	no	—
278	C₉	—	3	3	no	—
279	C₉	—	3	1	no	—
280	C₉	—	3	1	no	—
281	C₉	—	3	3	no	—
282	C₉	—	3	3	no	—
283	C₉	C₂×#737	1	3	yes	—
284	C₂×C₃	—	3	3	no	—
285	C₂×C₃	—	9	3	no	—
286	C₂×C₃	C₃×#737	1	1	yes	characteristic
287	C₂×C₃	C₃×#737	1	1	yes	characteristic
288	C₂×C₃	3₋¹⁺⁴	1	1	yes	characteristic
289	C₂×C₃	3₋¹⁺⁴	1	1	yes	characteristic
290	C₃	—	3	3	no	—
291	C₃	—	9	3	no	—
292	C₃	C₂×C₃×#737	1	1	yes	characteristic
293	C₃	C₂×C₃×#737	1	1	yes	characteristic
294	C₃	C₂×3₋¹⁺⁴	1	1	yes	characteristic
295	C₃	C₂×3₋¹⁺⁴	1	1	yes	characteristic
296	C₂	#10624907	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. #10624907	C₂	direct (N × H)
2. C₂×#6899	C₃	semidirect
3. C₂×#6899	C₃	semidirect
4. C₂×#6898	C₃	semidirect
5. C₂×#6897	C₃	semidirect
6. C₂×#6897	C₃	semidirect
7. C₂×#6896	C₃	semidirect
8. C₂×#6895	C₃	semidirect
9. C₂×#6895	C₃	semidirect
10. C₂×#6894	C₃	semidirect
11. C₂×#6894	C₃	semidirect
12. C₂×#6894	C₃	semidirect
13. C₂×#6894	C₃	semidirect
14. C₂×#6894	C₃	semidirect
18. C₂×C₉×3₋¹⁺²	C₃	semidirect
19. C₂×C₉×3₋¹⁺²	C₃	semidirect
20. C₂×C₉×3₋¹⁺²	C₃	semidirect
22. C₂×#6887	C₃	semidirect
23. C₂×C₃×C₉⋊C₉	C₃	semidirect
24. #6899	C₂×C₃	semidirect
25. #6899	C₂×C₃	semidirect
26. #6898	C₂×C₃	semidirect
27. #6897	C₂×C₃	semidirect
28. #6897	C₂×C₃	semidirect
29. #6896	C₂×C₃	semidirect
30. #6895	C₂×C₃	semidirect
31. #6895	C₂×C₃	semidirect
32. #6894	C₂×C₃	semidirect
33. #6894	C₂×C₃	semidirect
34. #6894	C₂×C₃	semidirect
35. #6894	C₂×C₃	semidirect
36. #6894	C₂×C₃	semidirect
40. C₉×3₋¹⁺²	C₂×C₃	semidirect
41. C₉×3₋¹⁺²	C₂×C₃	semidirect
42. C₉×3₋¹⁺²	C₂×C₃	semidirect
44. #6887	C₂×C₃	semidirect
45. C₃×C₉⋊C₉	C₂×C₃	semidirect
296. C₂	#10624907	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624907	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×#6887	3
C₂×C₃×C₉⋊C₉	3

Subgroups — C2×#10624907 #13090393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624907 #13090393