Subgroups — C₂×#10624901⋊C₂ #72244105

Order 2916.

755 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624901⋊C₂	C₂	1	2	yes	maximal, direct product factor
2	C₂×#10624901	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×#737	—	3	1	no	maximal
4	C₂×#92265	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×#92265	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂×#92265	C₃	1	1	yes	maximal, characteristic, complemented
7	C₂×#92264	C₃	1	1	yes	maximal, characteristic, complemented
8	C₂×#92264	C₃	1	1	yes	maximal, characteristic, complemented
9	C₂×#92264	C₃	1	1	yes	maximal, characteristic, complemented
10	C₂×#6894⋊C₂	C₃	1	1	yes	maximal, characteristic, complemented
11	C₂×D₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
12	C₂×D₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
13	C₂×C₉×AGL(1,ℤ/9)	C₃	1	1	yes	maximal, characteristic, complemented
14	C₂×C₉×AGL(1,ℤ/9)	C₃	1	1	yes	maximal, characteristic, complemented
15	C₂×C₉×AGL(1,ℤ/9)	C₃	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×D₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
17	#10624901	C₂²	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×#737	D₃	1	1	yes	characteristic
19	D₃×#737	—	3	2	no	—
20	C₂×#6900	C₂×C₃	1	1	yes	characteristic, complemented
21	C₂×#6900	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂×#6900	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂×#6899	—	2	1	no	—
24	C₂×#6899	—	2	1	no	—
25	C₂×#6899	—	2	1	no	—
26	C₂×#6896	—	2	1	no	—
27	C₂×#6896	—	2	1	no	—
28	C₂×#6896	—	2	1	no	—
29	C₂×#6896	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×#6896	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×#6896	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×#6895	—	2	1	no	—
33	C₂×#6894	—	2	1	no	—
34	C₂×#6894	—	2	1	no	—
35	C₂×#6894	—	2	1	no	—
36	C₂×#6894	—	2	1	no	—
37	C₂×#6894	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×C₉⋊H(3,𝔽₃)	—	2	1	no	—
39	C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
40	C₂×C₉×3₋¹⁺²	—	2	1	no	—
41	C₂×C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×C₃×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
46	#92265	C₂×C₃	1	2	yes	complemented
47	#92265	C₂×C₃	1	2	yes	complemented
48	#92265	C₂×C₃	1	2	yes	complemented
49	#92264	C₂×C₃	1	2	yes	complemented
50	#92264	C₂×C₃	1	2	yes	complemented
51	#92264	C₂×C₃	1	2	yes	complemented
52	#6894⋊C₂	C₂×C₃	1	2	yes	complemented
53	D₉⋊H(3,𝔽₃)	C₂×C₃	1	2	yes	—
54	D₉×3₋¹⁺²	C₂×C₃	1	2	yes	complemented
55	C₉×AGL(1,ℤ/9)	C₂×C₃	1	2	yes	complemented
56	C₉×AGL(1,ℤ/9)	C₂×C₃	1	2	yes	complemented
57	C₉×AGL(1,ℤ/9)	C₂×C₃	1	2	yes	complemented
58	C₃×D₉⋊C₉	C₂×C₃	1	2	yes	complemented
59	C₂²×#737	—	9	1	no	—
60	C₂×D₃×3₋¹⁺²	—	3	1	no	—
61	C₂×D₃×3₋¹⁺²	—	3	1	no	—
62	C₂×D₃×3₋¹⁺²	—	3	1	no	—
63	C₂×D₃×3₋¹⁺²	—	3	1	no	—
64	C₂×D₃×3₋¹⁺²	—	3	1	no	—
65	C₂×D₃×3₋¹⁺²	—	3	1	no	—
66	C₂×D₃×3₋¹⁺²	—	3	1	no	—
67	C₂×D₃×3₋¹⁺²	—	3	1	no	—
68	C₂×C₃×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic
69	C₂×C₃×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic
70	C₂×C₃×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic
71	C₂×D₃×H(3,𝔽₃)	—	3	1	no	—
72	C₂×C₃×D₃×C₉	—	3	1	no	—
73	C₂×C₃×D₃×C₉	—	3	1	no	—
74	C₂×C₃×D₃×C₉	—	3	1	no	—
75	C₂×C₃×D₃×C₉	—	3	1	no	—
76	C₂×C₃²×D₉	C₃²	1	1	yes	characteristic
77	C₂×D₉⋊C₉	C₃²	1	1	yes	characteristic
78	C₂×D₉⋊C₉	C₃²	1	1	yes	characteristic
79	C₂×D₉⋊C₉	C₃²	1	1	yes	characteristic
80	C₂×D₉⋊C₉	C₃²	1	1	yes	characteristic
81	C₂×D₉⋊C₉	C₃²	1	1	yes	characteristic
82	C₂×D₉⋊C₉	C₃²	1	1	yes	characteristic
83	C₂×C₉×D₉	C₃²	1	1	yes	characteristic
84	C₂×C₉×D₉	C₃²	1	1	yes	characteristic
85	C₂×C₉×D₉	C₃²	1	1	yes	characteristic
86	C₃×#737	C₂×D₃	1	1	yes	characteristic
87	#6900	C₂²×C₃	1	1	yes	characteristic, complemented
88	#6900	C₂²×C₃	1	1	yes	characteristic, complemented
89	#6900	C₂²×C₃	1	1	yes	characteristic, complemented
90	#6899	—	2	1	no	—
91	#6899	—	2	1	no	—
92	#6899	—	2	1	no	—
93	#6896	—	2	1	no	—
94	#6896	—	2	1	no	—
95	#6896	—	2	1	no	—
96	#6896	C₂²×C₃	1	1	yes	characteristic, complemented
97	#6896	C₂²×C₃	1	1	yes	characteristic, complemented
98	#6896	C₂²×C₃	1	1	yes	characteristic, complemented
99	#6895	—	2	1	no	—
100	#6894	—	2	1	no	—
101	#6894	—	2	1	no	—
102	#6894	—	2	1	no	—
103	#6894	—	2	1	no	—
104	#6894	C₂²×C₃	1	1	yes	characteristic, complemented
105	C₉⋊H(3,𝔽₃)	—	2	1	no	—
106	C₉⋊H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic
107	C₉×3₋¹⁺²	—	2	1	no	—
108	C₉×3₋¹⁺²	C₂²×C₃	1	1	yes	characteristic, complemented
109	C₉×3₋¹⁺²	C₂²×C₃	1	1	yes	characteristic, complemented
110	C₉×3₋¹⁺²	C₂²×C₃	1	1	yes	characteristic, complemented
111	C₉×3₋¹⁺²	C₂²×C₃	1	1	yes	characteristic, complemented
112	C₃×C₉⋊C₉	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₂×#737	—	6	1	no	—
114	C₂×#737	—	6	1	no	—
115	C₂×#737	—	6	1	no	—
116	C₂×#737	—	6	1	no	—
117	C₂×#737	—	6	1	no	—
118	C₂×#737	—	9	2	no	—
119	C₂×C₃×3₋¹⁺²	—	2	1	no	—
120	C₂×C₃×3₋¹⁺²	—	2	1	no	—
121	C₂×C₃×3₋¹⁺²	—	2	1	no	—
122	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
123	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
124	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
125	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
126	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
127	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
128	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
129	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
130	C₂×C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
131	C₂×C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
132	C₂×C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
133	C₂×C₃×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
134	C₂×C₃²×C₉	—	2	1	no	—
135	C₂×C₃²×C₉	C₃×D₃	1	1	yes	characteristic
136	C₂×C₃²×C₉	C₃×D₃	1	1	yes	characteristic
137	C₂×C₃²×C₉	C₃×D₃	1	1	yes	characteristic
138	C₂×C₃²×C₉	C₃×D₃	1	1	yes	characteristic
139	C₂×C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
140	D₃×3₋¹⁺²	—	3	2	no	—
141	D₃×3₋¹⁺²	—	3	2	no	—
142	D₃×3₋¹⁺²	—	3	2	no	—
143	D₃×3₋¹⁺²	—	3	2	no	—
144	D₃×3₋¹⁺²	—	3	2	no	—
145	D₃×3₋¹⁺²	—	3	2	no	—
146	D₃×3₋¹⁺²	—	3	2	no	—
147	D₃×3₋¹⁺²	—	3	2	no	—
148	C₃×AGL(1,ℤ/9)	C₂×C₃²	1	2	yes	—
149	C₃×AGL(1,ℤ/9)	C₂×C₃²	1	2	yes	—
150	C₃×AGL(1,ℤ/9)	C₂×C₃²	1	2	yes	—
151	D₃×H(3,𝔽₃)	—	3	2	no	—
152	C₃×D₃×C₉	—	3	2	no	—
153	C₃×D₃×C₉	—	3	2	no	—
154	C₃×D₃×C₉	—	3	2	no	—
155	C₃×D₃×C₉	—	3	2	no	—
156	C₃²×D₉	C₂×C₃²	1	2	yes	—
157	C₂×C₉⋊C₉	—	2	1	no	—
158	C₂×C₉⋊C₉	—	2	1	no	—
159	C₂×C₉⋊C₉	—	2	1	no	—
160	C₂×C₉⋊C₉	—	2	1	no	—
161	C₂×C₉⋊C₉	—	2	1	no	—
162	C₂×C₉⋊C₉	—	2	1	no	—
163	C₂×C₉⋊C₉	—	2	1	no	—
164	C₂×C₉⋊C₉	—	2	1	no	—
165	C₂×C₉⋊C₉	—	2	1	no	—
166	C₂×C₉⋊C₉	—	2	1	no	—
167	C₂×C₉⋊C₉	—	2	1	no	—
168	C₂×C₉⋊C₉	—	2	1	no	—
169	C₂×C₉⋊C₉	—	2	1	no	—
170	C₂×C₉⋊C₉	—	2	1	no	—
171	C₂×C₉⋊C₉	—	2	1	no	—
172	C₂×C₉⋊C₉	—	2	1	no	—
173	C₂×C₉⋊C₉	—	2	1	no	—
174	C₂×C₉⋊C₉	—	2	1	no	—
175	C₂×C₉⋊C₉	—	2	1	no	—
176	C₂×C₉⋊C₉	—	2	1	no	—
177	C₂×C₉⋊C₉	—	2	1	no	—
178	C₂×C₉⋊C₉	—	2	1	no	—
179	C₂×C₉⋊C₉	—	2	1	no	—
180	C₂×C₉⋊C₉	—	2	1	no	—
181	C₂×C₉⋊C₉	—	2	1	no	—
182	C₂×C₉⋊C₉	—	2	1	no	—
183	C₂×C₉⋊C₉	—	2	1	no	—
184	C₂×C₉⋊C₉	—	2	1	no	—
185	C₂×C₉⋊C₉	—	2	1	no	—
186	C₂×C₉⋊C₉	—	2	1	no	—
187	C₂×C₉⋊C₉	—	2	1	no	—
188	C₂×C₉⋊C₉	—	2	1	no	—
189	C₂×C₉⋊C₉	—	2	1	no	—
190	C₂×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
191	C₂×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
192	C₂×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
193	C₂×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
194	C₂×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
195	C₂×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
196	C₂×C₃²⋊C₉	—	2	1	no	—
197	C₂×C₃²⋊C₉	—	2	1	no	—
198	C₂×C₃²⋊C₉	—	2	1	no	—
199	C₂×C₃²⋊C₉	—	2	1	no	—
200	C₂×C₃²⋊C₉	—	2	1	no	—
201	C₂×C₃²⋊C₉	—	2	1	no	—
202	C₂×C₃²⋊C₉	—	2	1	no	—
203	C₂×C₃²⋊C₉	—	2	1	no	—
204	C₂×C₃²⋊C₉	—	2	1	no	—
205	C₂×C₃²⋊C₉	—	2	1	no	—
206	C₂×C₃²⋊C₉	—	2	1	no	—
207	C₂×C₃²⋊C₉	—	2	1	no	—
208	C₂×C₉²	—	2	1	no	—
209	C₂×C₉²	—	2	1	no	—
210	C₂×C₉²	—	2	1	no	—
211	C₂×C₉²	C₂×C₃²	1	1	yes	characteristic
212	C₂×C₉²	C₂×C₃²	1	1	yes	characteristic
213	C₂×C₉²	C₂×C₃²	1	1	yes	characteristic
214	D₉⋊C₉	C₂×C₃²	1	2	yes	—
215	D₉⋊C₉	C₂×C₃²	1	2	yes	—
216	D₉⋊C₉	C₂×C₃²	1	2	yes	—
217	D₉⋊C₉	C₂×C₃²	1	2	yes	—
218	D₉⋊C₉	C₂×C₃²	1	2	yes	—
219	D₉⋊C₉	C₂×C₃²	1	2	yes	—
220	C₉×D₉	C₂×C₃²	1	2	yes	—
221	C₉×D₉	C₂×C₃²	1	2	yes	—
222	C₉×D₉	C₂×C₃²	1	2	yes	—
223	C₂×C₃²×D₃	—	3	1	no	—
224	C₂×C₃²×D₃	—	3	1	no	—
225	C₂×C₃²×D₃	—	3	1	no	—
226	C₂×C₃²×D₃	—	3	1	no	—
227	C₂²×3₋¹⁺²	—	9	1	no	—
228	C₂²×3₋¹⁺²	—	9	1	no	—
229	C₂²×3₋¹⁺²	—	9	1	no	—
230	C₂²×3₋¹⁺²	—	9	1	no	—
231	C₂²×3₋¹⁺²	—	9	1	no	—
232	C₂²×3₋¹⁺²	—	9	1	no	—
233	C₂²×3₋¹⁺²	—	9	1	no	—
234	C₂²×3₋¹⁺²	—	9	1	no	—
235	C₂²×H(3,𝔽₃)	—	9	1	no	—
236	C₂²×C₃×C₉	—	9	1	no	—
237	C₂²×C₃×C₉	—	9	1	no	—
238	C₂²×C₃×C₉	—	9	1	no	—
239	C₂²×C₃×C₉	—	9	1	no	—
240	C₂×AGL(1,ℤ/9)	—	3	1	no	—
241	C₂×AGL(1,ℤ/9)	—	3	1	no	—
242	C₂×AGL(1,ℤ/9)	—	3	1	no	—
243	C₂×D₃×C₉	—	3	1	no	—
244	C₂×D₃×C₉	—	3	1	no	—
245	C₂×D₃×C₉	—	3	1	no	—
246	C₂×D₃×C₉	—	3	1	no	—
247	C₂×D₃×C₉	—	3	1	no	—
248	C₂×D₃×C₉	—	3	1	no	—
249	C₂×D₃×C₉	—	3	1	no	—
250	C₂×D₃×C₉	—	3	1	no	—
251	C₂×D₃×C₉	—	3	1	no	—
252	C₂×C₃×D₉	—	3	1	no	—
253	C₂×C₃×D₉	C₃³	1	1	yes	characteristic
254	#737	—	6	1	no	—
255	#737	—	6	1	no	—
256	#737	—	6	1	no	—
257	#737	—	6	1	no	—
258	#737	—	6	1	no	—
259	C₃×3₋¹⁺²	—	2	1	no	—
260	C₃×3₋¹⁺²	—	2	1	no	—
261	C₃×3₋¹⁺²	—	2	1	no	—
262	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic
263	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic
264	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic
265	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic
266	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic
267	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic
268	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic
269	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic
270	C₃×3₋¹⁺²	C₂²×C₃²	1	1	yes	characteristic
271	C₃×3₋¹⁺²	C₂²×C₃²	1	1	yes	characteristic
272	C₃×3₋¹⁺²	C₂²×C₃²	1	1	yes	characteristic
273	C₃×H(3,𝔽₃)	C₂×C₃×D₃	1	1	yes	characteristic
274	C₃²×C₉	—	2	1	no	—
275	C₃²×C₉	C₂×C₃×D₃	1	1	yes	characteristic
276	C₃²×C₉	C₂×C₃×D₃	1	1	yes	characteristic
277	C₃²×C₉	C₂×C₃×D₃	1	1	yes	characteristic
278	C₃²×C₉	C₂×C₃×D₃	1	1	yes	characteristic
279	C₃²×C₉	C₂²×C₃²	1	1	yes	characteristic
280	C₉⋊C₉	—	2	1	no	—
281	C₉⋊C₉	—	2	1	no	—
282	C₉⋊C₉	—	2	1	no	—
283	C₉⋊C₉	—	2	1	no	—
284	C₉⋊C₉	—	2	1	no	—
285	C₉⋊C₉	—	2	1	no	—
286	C₉⋊C₉	—	2	1	no	—
287	C₉⋊C₉	—	2	1	no	—
288	C₉⋊C₉	—	2	1	no	—
289	C₉⋊C₉	—	2	1	no	—
290	C₉⋊C₉	—	2	1	no	—
291	C₉⋊C₉	—	2	1	no	—
292	C₉⋊C₉	—	2	1	no	—
293	C₉⋊C₉	—	2	1	no	—
294	C₉⋊C₉	—	2	1	no	—
295	C₉⋊C₉	—	2	1	no	—
296	C₉⋊C₉	—	2	1	no	—
297	C₉⋊C₉	—	2	1	no	—
298	C₉⋊C₉	—	2	1	no	—
299	C₉⋊C₉	—	2	1	no	—
300	C₉⋊C₉	—	2	1	no	—
301	C₉⋊C₉	—	2	1	no	—
302	C₉⋊C₉	—	2	1	no	—
303	C₉⋊C₉	—	2	1	no	—
304	C₉⋊C₉	—	2	1	no	—
305	C₉⋊C₉	—	2	1	no	—
306	C₉⋊C₉	—	2	1	no	—
307	C₉⋊C₉	—	2	1	no	—
308	C₉⋊C₉	—	2	1	no	—
309	C₉⋊C₉	—	2	1	no	—
310	C₉⋊C₉	—	2	1	no	—
311	C₉⋊C₉	—	2	1	no	—
312	C₉⋊C₉	—	2	1	no	—
313	C₉⋊C₉	C₂²×C₃²	1	1	yes	characteristic
314	C₉⋊C₉	C₂²×C₃²	1	1	yes	characteristic
315	C₉⋊C₉	C₂²×C₃²	1	1	yes	characteristic
316	C₉⋊C₉	C₂²×C₃²	1	1	yes	characteristic
317	C₉⋊C₉	C₂²×C₃²	1	1	yes	characteristic
318	C₉⋊C₉	C₂²×C₃²	1	1	yes	characteristic
319	C₃²⋊C₉	—	2	1	no	—
320	C₃²⋊C₉	—	2	1	no	—
321	C₃²⋊C₉	—	2	1	no	—
322	C₃²⋊C₉	—	2	1	no	—
323	C₃²⋊C₉	—	2	1	no	—
324	C₃²⋊C₉	—	2	1	no	—
325	C₃²⋊C₉	—	2	1	no	—
326	C₃²⋊C₉	—	2	1	no	—
327	C₃²⋊C₉	—	2	1	no	—
328	C₃²⋊C₉	—	2	1	no	—
329	C₃²⋊C₉	—	2	1	no	—
330	C₃²⋊C₉	—	2	1	no	—
331	C₉²	—	2	1	no	—
332	C₉²	—	2	1	no	—
333	C₉²	—	2	1	no	—
334	C₉²	C₂²×C₃²	1	1	yes	characteristic
335	C₉²	C₂²×C₃²	1	1	yes	characteristic
336	C₉²	C₂²×C₃²	1	1	yes	characteristic
337	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
338	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
339	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
340	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
341	C₃²×D₃	—	3	2	no	—
342	C₃²×D₃	—	3	2	no	—
343	C₃²×D₃	—	3	2	no	—
344	C₃²×D₃	—	3	2	no	—
345	C₂×3₋¹⁺²	—	2	1	no	—
346	C₂×3₋¹⁺²	—	2	1	no	—
347	C₂×3₋¹⁺²	—	2	1	no	—
348	C₂×3₋¹⁺²	—	2	1	no	—
349	C₂×3₋¹⁺²	—	3	1	no	—
350	C₂×3₋¹⁺²	—	3	1	no	—
351	C₂×3₋¹⁺²	—	3	1	no	—
352	C₂×3₋¹⁺²	—	3	1	no	—
353	C₂×3₋¹⁺²	—	3	1	no	—
354	C₂×3₋¹⁺²	—	3	1	no	—
355	C₂×3₋¹⁺²	—	3	1	no	—
356	C₂×3₋¹⁺²	—	3	1	no	—
357	C₂×3₋¹⁺²	—	3	1	no	—
358	C₂×3₋¹⁺²	—	6	1	no	—
359	C₂×3₋¹⁺²	—	6	1	no	—
360	C₂×3₋¹⁺²	—	6	1	no	—
361	C₂×3₋¹⁺²	—	6	1	no	—
362	C₂×3₋¹⁺²	—	6	1	no	—
363	C₂×3₋¹⁺²	—	6	1	no	—
364	C₂×3₋¹⁺²	—	6	1	no	—
365	C₂×3₋¹⁺²	—	6	1	no	—
366	C₂×3₋¹⁺²	—	6	1	no	—
367	C₂×3₋¹⁺²	—	6	1	no	—
368	C₂×3₋¹⁺²	—	6	1	no	—
369	C₂×3₋¹⁺²	—	9	2	no	—
370	C₂×3₋¹⁺²	—	9	2	no	—
371	C₂×3₋¹⁺²	—	9	2	no	—
372	C₂×3₋¹⁺²	—	9	2	no	—
373	C₂×3₋¹⁺²	—	9	2	no	—
374	C₂×3₋¹⁺²	—	9	2	no	—
375	C₂×3₋¹⁺²	—	9	2	no	—
376	C₂×3₋¹⁺²	—	9	2	no	—
377	C₂×3₋¹⁺²	—	18	1	no	—
378	C₂×3₋¹⁺²	—	18	1	no	—
379	C₂×3₋¹⁺²	—	18	1	no	—
380	C₂×3₋¹⁺²	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
381	C₂×H(3,𝔽₃)	—	3	1	no	—
382	C₂×H(3,𝔽₃)	—	6	1	no	—
383	C₂×H(3,𝔽₃)	—	9	2	no	—
384	C₂×C₃×C₉	—	2	1	no	—
385	C₂×C₃×C₉	—	2	1	no	—
386	C₂×C₃×C₉	—	2	1	no	—
387	C₂×C₃×C₉	—	2	1	no	—
388	C₂×C₃×C₉	—	2	1	no	—
389	C₂×C₃×C₉	—	2	1	no	—
390	C₂×C₃×C₉	—	2	1	no	—
391	C₂×C₃×C₉	—	2	1	no	—
392	C₂×C₃×C₉	—	2	1	no	—
393	C₂×C₃×C₉	—	2	1	no	—
394	C₂×C₃×C₉	—	2	1	no	—
395	C₂×C₃×C₉	—	2	1	no	—
396	C₂×C₃×C₉	—	2	1	no	—
397	C₂×C₃×C₉	—	3	1	no	—
398	C₂×C₃×C₉	—	3	1	no	—
399	C₂×C₃×C₉	—	3	1	no	—
400	C₂×C₃×C₉	—	6	1	no	—
401	C₂×C₃×C₉	—	6	1	no	—
402	C₂×C₃×C₉	—	6	1	no	—
403	C₂×C₃×C₉	—	6	1	no	—
404	C₂×C₃×C₉	—	6	1	no	—
405	C₂×C₃×C₉	—	6	1	no	—
406	C₂×C₃×C₉	—	6	1	no	—
407	C₂×C₃×C₉	—	9	2	no	—
408	C₂×C₃×C₉	—	9	2	no	—
409	C₂×C₃×C₉	—	9	2	no	—
410	C₂×C₃×C₉	—	9	2	no	—
411	C₂×C₃×C₉	—	18	1	no	—
412	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
413	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
414	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
415	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
416	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
417	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
418	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
419	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
420	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
421	C₂×C₃×C₉	C₂×C₃³	1	1	yes	characteristic
422	AGL(1,ℤ/9)	—	3	2	no	—
423	AGL(1,ℤ/9)	—	3	2	no	—
424	AGL(1,ℤ/9)	—	3	2	no	—
425	D₃×C₉	—	3	2	no	—
426	D₃×C₉	—	3	2	no	—
427	D₃×C₉	—	3	2	no	—
428	D₃×C₉	—	3	2	no	—
429	D₃×C₉	—	3	2	no	—
430	D₃×C₉	—	3	2	no	—
431	D₃×C₉	—	3	2	no	—
432	D₃×C₉	—	3	2	no	—
433	D₃×C₉	—	3	2	no	—
434	C₃×D₉	—	3	2	no	—
435	C₃×D₉	C₂×C₃³	1	2	yes	—
436	C₂²×C₃²	—	9	1	no	—
437	C₂²×C₃²	—	9	1	no	—
438	C₂²×C₃²	—	9	1	no	—
439	C₂²×C₃²	—	9	1	no	—
440	C₂×C₃×D₃	—	3	1	no	—
441	C₂×C₃×D₃	—	9	1	no	—
442	C₂×C₃×D₃	—	9	1	no	—
443	C₂×C₃×D₃	—	9	1	no	—
444	C₂×C₃×D₃	—	9	1	no	—
445	C₂²×C₉	—	9	1	no	—
446	C₂²×C₉	—	9	1	no	—
447	C₂²×C₉	—	9	1	no	—
448	C₂²×C₉	—	9	1	no	—
449	C₂²×C₉	—	9	1	no	—
450	C₂²×C₉	—	9	1	no	—
451	C₂²×C₉	—	9	1	no	—
452	C₂²×C₉	—	9	1	no	—
453	C₂²×C₉	—	9	1	no	—
454	C₂×D₉	#737	1	1	yes	characteristic, complemented
455	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
456	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
457	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
458	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
459	3₋¹⁺²	—	2	1	no	—
460	3₋¹⁺²	—	2	1	no	—
461	3₋¹⁺²	—	2	1	no	—
462	3₋¹⁺²	—	2	1	no	—
463	3₋¹⁺²	—	3	1	no	—
464	3₋¹⁺²	—	3	1	no	—
465	3₋¹⁺²	—	3	1	no	—
466	3₋¹⁺²	—	3	1	no	—
467	3₋¹⁺²	—	3	1	no	—
468	3₋¹⁺²	—	3	1	no	—
469	3₋¹⁺²	—	3	1	no	—
470	3₋¹⁺²	—	3	1	no	—
471	3₋¹⁺²	—	3	1	no	—
472	3₋¹⁺²	—	6	1	no	—
473	3₋¹⁺²	—	6	1	no	—
474	3₋¹⁺²	—	6	1	no	—
475	3₋¹⁺²	—	6	1	no	—
476	3₋¹⁺²	—	6	1	no	—
477	3₋¹⁺²	—	6	1	no	—
478	3₋¹⁺²	—	6	1	no	—
479	3₋¹⁺²	—	6	1	no	—
480	3₋¹⁺²	—	6	1	no	—
481	3₋¹⁺²	—	6	1	no	—
482	3₋¹⁺²	—	6	1	no	—
483	3₋¹⁺²	—	18	1	no	—
484	3₋¹⁺²	—	18	1	no	—
485	3₋¹⁺²	—	18	1	no	—
486	3₋¹⁺²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
487	H(3,𝔽₃)	—	3	1	no	—
488	H(3,𝔽₃)	—	6	1	no	—
489	C₃×C₉	—	2	1	no	—
490	C₃×C₉	—	2	1	no	—
491	C₃×C₉	—	2	1	no	—
492	C₃×C₉	—	2	1	no	—
493	C₃×C₉	—	2	1	no	—
494	C₃×C₉	—	2	1	no	—
495	C₃×C₉	—	2	1	no	—
496	C₃×C₉	—	2	1	no	—
497	C₃×C₉	—	2	1	no	—
498	C₃×C₉	—	2	1	no	—
499	C₃×C₉	—	2	1	no	—
500	C₃×C₉	—	2	1	no	—
501	C₃×C₉	—	2	1	no	—
502	C₃×C₉	—	3	1	no	—
503	C₃×C₉	—	3	1	no	—
504	C₃×C₉	—	3	1	no	—
505	C₃×C₉	—	6	1	no	—
506	C₃×C₉	—	6	1	no	—
507	C₃×C₉	—	6	1	no	—
508	C₃×C₉	—	6	1	no	—
509	C₃×C₉	—	6	1	no	—
510	C₃×C₉	—	6	1	no	—
511	C₃×C₉	—	6	1	no	—
512	C₃×C₉	—	18	1	no	—
513	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
514	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
515	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
516	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
517	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
518	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
519	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
520	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
521	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
522	C₃×C₉	C₂²×C₃³	1	1	yes	characteristic
523	C₂×C₃²	—	2	1	no	—
524	C₂×C₃²	—	3	1	no	—
525	C₂×C₃²	—	3	1	no	—
526	C₂×C₃²	—	3	1	no	—
527	C₂×C₃²	—	3	1	no	—
528	C₂×C₃²	—	3	1	no	—
529	C₂×C₃²	—	3	1	no	—
530	C₂×C₃²	—	6	1	no	—
531	C₂×C₃²	—	6	1	no	—
532	C₂×C₃²	—	6	1	no	—
533	C₂×C₃²	—	6	1	no	—
534	C₂×C₃²	—	6	1	no	—
535	C₂×C₃²	—	9	2	no	—
536	C₂×C₃²	—	9	2	no	—
537	C₂×C₃²	—	9	2	no	—
538	C₂×C₃²	—	9	2	no	—
539	C₂×C₃²	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
540	C₂×C₃²	C₃³×D₃	1	1	yes	characteristic
541	C₃×D₃	—	3	2	no	—
542	C₃×D₃	—	9	2	no	—
543	C₃×D₃	—	9	2	no	—
544	C₃×D₃	—	9	2	no	—
545	C₃×D₃	—	9	2	no	—
546	C₂×C₉	—	2	1	no	—
547	C₂×C₉	—	2	1	no	—
548	C₂×C₉	—	2	1	no	—
549	C₂×C₉	—	2	1	no	—
550	C₂×C₉	—	3	1	no	—
551	C₂×C₉	—	3	1	no	—
552	C₂×C₉	—	3	1	no	—
553	C₂×C₉	—	3	1	no	—
554	C₂×C₉	—	6	1	no	—
555	C₂×C₉	—	6	1	no	—
556	C₂×C₉	—	6	1	no	—
557	C₂×C₉	—	6	1	no	—
558	C₂×C₉	—	6	1	no	—
559	C₂×C₉	—	6	1	no	—
560	C₂×C₉	—	6	1	no	—
561	C₂×C₉	—	6	1	no	—
562	C₂×C₉	—	6	1	no	—
563	C₂×C₉	—	6	1	no	—
564	C₂×C₉	—	6	1	no	—
565	C₂×C₉	—	6	1	no	—
566	C₂×C₉	—	6	1	no	—
567	C₂×C₉	—	6	1	no	—
568	C₂×C₉	—	6	1	no	—
569	C₂×C₉	—	9	2	no	—
570	C₂×C₉	—	9	2	no	—
571	C₂×C₉	—	9	2	no	—
572	C₂×C₉	—	9	2	no	—
573	C₂×C₉	—	9	2	no	—
574	C₂×C₉	—	9	2	no	—
575	C₂×C₉	—	9	2	no	—
576	C₂×C₉	—	9	2	no	—
577	C₂×C₉	—	9	2	no	—
578	C₂×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
579	C₂×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
580	C₂×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
581	C₂×C₉	C₂×#737	1	1	yes	characteristic, complemented
582	D₉	C₂×#737	1	2	yes	complemented
583	C₂²×C₃	—	9	1	no	—
584	C₂²×C₃	—	27	1	no	—
585	C₂²×C₃	—	27	1	no	—
586	C₂²×C₃	—	27	1	no	—
587	C₂²×C₃	—	27	1	no	—
588	C₂×D₃	—	3	1	no	—
589	C₃²	—	2	1	no	—
590	C₃²	—	3	1	no	—
591	C₃²	—	3	1	no	—
592	C₃²	—	3	1	no	—
593	C₃²	—	3	1	no	—
594	C₃²	—	3	1	no	—
595	C₃²	—	3	1	no	—
596	C₃²	—	6	1	no	—
597	C₃²	—	6	1	no	—
598	C₃²	—	6	1	no	—
599	C₃²	—	6	1	no	—
600	C₃²	—	6	1	no	—
601	C₃²	C₂×C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
602	C₃²	C₂×C₃³×D₃	1	1	yes	characteristic
603	C₉	—	2	1	no	—
604	C₉	—	2	1	no	—
605	C₉	—	2	1	no	—
606	C₉	—	2	1	no	—
607	C₉	—	3	1	no	—
608	C₉	—	3	1	no	—
609	C₉	—	3	1	no	—
610	C₉	—	3	1	no	—
611	C₉	—	6	1	no	—
612	C₉	—	6	1	no	—
613	C₉	—	6	1	no	—
614	C₉	—	6	1	no	—
615	C₉	—	6	1	no	—
616	C₉	—	6	1	no	—
617	C₉	—	6	1	no	—
618	C₉	—	6	1	no	—
619	C₉	—	6	1	no	—
620	C₉	—	6	1	no	—
621	C₉	—	6	1	no	—
622	C₉	—	6	1	no	—
623	C₉	—	6	1	no	—
624	C₉	—	6	1	no	—
625	C₉	—	6	1	no	—
626	C₉	C₂×C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
627	C₉	C₂×C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
628	C₉	C₂×C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
629	C₉	C₂²×#737	1	1	yes	characteristic, complemented
630	C₂×C₃	—	2	1	no	—
631	C₂×C₃	—	3	1	no	—
632	C₂×C₃	—	6	1	no	—
633	C₂×C₃	—	9	2	no	—
634	C₂×C₃	—	9	1	no	—
635	C₂×C₃	—	18	1	no	—
636	C₂×C₃	—	18	1	no	—
637	C₂×C₃	—	27	2	no	—
638	C₂×C₃	—	27	2	no	—
639	C₂×C₃	—	27	2	no	—
640	C₂×C₃	—	27	2	no	—
641	C₂×C₃	C₃²×AGL(1,ℤ/9)	1	1	yes	characteristic
642	C₂×C₃	D₃×#737	1	1	yes	characteristic
643	D₃	—	3	2	no	—
644	C₂²	—	9	1	no	Sylow
645	C₃	—	2	1	no	—
646	C₃	—	3	1	no	—
647	C₃	—	6	1	no	—
648	C₃	—	9	1	no	—
649	C₃	—	18	1	no	—
650	C₃	—	18	1	no	—
651	C₃	C₂×C₃²×AGL(1,ℤ/9)	1	1	yes	characteristic
652	C₃	C₂×D₃×#737	1	1	yes	characteristic
653	C₂	—	9	2	no	—
654	C₂	#10624901⋊C₂	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center	C₂×C₃	C₃²×AGL(1,ℤ/9)
commutator, cosocle	C₃×C₉	C₂²×C₃³
Frattini	C₃²	C₂×C₃³×D₃
Fitting	C₂×#10624901	C₂
socle	C₂×C₃²	C₃³×D₃
prime radical	C₂×D₉⋊H(3,𝔽₃)	C₃
hypercenter	C₂×3₋¹⁺²	AGL(1,ℤ/9)
hypocenter	C₉	C₂²×#737
LCS	G ▷ C₃×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃ ◁ C₂×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. #10624901⋊C₂	C₂	direct (N × H)
2. C₂×#10624901	C₂	semidirect
4. C₂×#92265	C₃	semidirect
5. C₂×#92265	C₃	semidirect
6. C₂×#92265	C₃	semidirect
7. C₂×#92264	C₃	semidirect
8. C₂×#92264	C₃	semidirect
9. C₂×#92264	C₃	semidirect
10. C₂×#6894⋊C₂	C₃	semidirect
12. C₂×D₉×3₋¹⁺²	C₃	semidirect
13. C₂×C₉×AGL(1,ℤ/9)	C₃	semidirect
14. C₂×C₉×AGL(1,ℤ/9)	C₃	semidirect
15. C₂×C₉×AGL(1,ℤ/9)	C₃	semidirect
16. C₂×C₃×D₉⋊C₉	C₃	semidirect
17. #10624901	C₂²	semidirect
20. C₂×#6900	C₂×C₃	semidirect
21. C₂×#6900	C₂×C₃	semidirect
22. C₂×#6900	C₂×C₃	semidirect
29. C₂×#6896	C₂×C₃	semidirect
30. C₂×#6896	C₂×C₃	semidirect
31. C₂×#6896	C₂×C₃	semidirect
37. C₂×#6894	C₂×C₃	semidirect
41. C₂×C₉×3₋¹⁺²	C₂×C₃	semidirect
42. C₂×C₉×3₋¹⁺²	C₂×C₃	semidirect
43. C₂×C₉×3₋¹⁺²	C₂×C₃	semidirect
44. C₂×C₉×3₋¹⁺²	C₂×C₃	semidirect
45. C₂×C₃×C₉⋊C₉	C₂×C₃	semidirect
46. #92265	C₂×C₃	semidirect
47. #92265	C₂×C₃	semidirect
48. #92265	C₂×C₃	semidirect
49. #92264	C₂×C₃	semidirect
50. #92264	C₂×C₃	semidirect
51. #92264	C₂×C₃	semidirect
52. #6894⋊C₂	C₂×C₃	semidirect
54. D₉×3₋¹⁺²	C₂×C₃	semidirect
55. C₉×AGL(1,ℤ/9)	C₂×C₃	semidirect
56. C₉×AGL(1,ℤ/9)	C₂×C₃	semidirect
57. C₉×AGL(1,ℤ/9)	C₂×C₃	semidirect
58. C₃×D₉⋊C₉	C₂×C₃	semidirect
87. #6900	C₂²×C₃	semidirect
88. #6900	C₂²×C₃	semidirect
89. #6900	C₂²×C₃	semidirect
96. #6896	C₂²×C₃	semidirect
97. #6896	C₂²×C₃	semidirect
98. #6896	C₂²×C₃	semidirect
104. #6894	C₂²×C₃	semidirect
108. C₉×3₋¹⁺²	C₂²×C₃	semidirect
109. C₉×3₋¹⁺²	C₂²×C₃	semidirect
110. C₉×3₋¹⁺²	C₂²×C₃	semidirect
111. C₉×3₋¹⁺²	C₂²×C₃	semidirect
112. C₃×C₉⋊C₉	C₂²×C₃	semidirect
380. C₂×3₋¹⁺²	AGL(1,ℤ/9)	semidirect
454. C₂×D₉	#737	semidirect
486. 3₋¹⁺²	C₂×AGL(1,ℤ/9)	semidirect
581. C₂×C₉	C₂×#737	semidirect
582. D₉	C₂×#737	semidirect
629. C₉	C₂²×#737	semidirect
654. C₂	#10624901⋊C₂	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624901⋊C₂	2
C₂×#10624901	2
C₂×D₃×#737	3
C₂×#92265	3
C₂×#92264	3
C₂×#6894⋊C₂	3
C₂×D₉⋊H(3,𝔽₃)	3
C₂×D₉×3₋¹⁺²	3
C₂×C₉×AGL(1,ℤ/9)	3
C₂×C₃×D₉⋊C₉	3

Subgroups — C2×#10624901⋊C2 #72244105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624901⋊C₂ #72244105