Subgroups — C₂×#72221820 #72243935

Order 8748.

1225 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10624709⋊C₂	C₃	1	1	yes	maximal, characteristic, complemented
2	C₂×#10624709⋊C₂	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×#4207⋊C₉	—	3	1	no	maximal
4	C₂×#92318⋊C₃	C₃	1	1	yes	maximal, characteristic
5	C₂×#14554150	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃⋊AGL(1,ℤ/27)	C₃	1	1	yes	maximal, characteristic, complemented
7	#72221820	C₂	1	2	yes	maximal, direct product factor
8	C₂×C₃×AGL(1,ℤ/27)	—	3	3	no	maximal
9	#14554150	C₂²	1	1	yes	characteristic, complemented, Sylow
10	#92318⋊C₃	C₂×C₃	1	2	yes	—
11	#4207⋊C₉	—	3	2	no	—
12	#10624709⋊C₂	C₂×C₃	1	2	yes	complemented
13	#10624709⋊C₂	C₂×C₃	1	2	yes	complemented
14	C₃⋊AGL(1,ℤ/27)	C₂×C₃	1	2	yes	complemented
15	C₃×AGL(1,ℤ/27)	—	3	6	no	—
16	C₂×#10624918	—	2	1	no	—
17	C₂×#10624918	C₂×C₃	1	1	yes	characteristic
18	C₂×#10624864	D₃	1	1	yes	characteristic
19	C₂×#10624709	—	2	3	no	—
20	C₂×#10624709	—	2	1	no	—
21	C₂×#10624709	—	2	1	no	—
22	C₂×#10624709	—	2	3	no	—
23	C₂×#10624709	—	2	3	no	—
24	C₂×#10624709	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×#10624709	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₃×#6875	—	2	1	no	—
27	C₂×C₃×#6875	—	2	3	no	—
28	C₂×C₃×#6875	D₃	1	3	yes	complemented
29	C₂×C₃×#6875	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₃×#4207	—	3	1	no	—
31	C₂×#92318	C₉	1	3	yes	complemented
32	C₂×C₃⋊(D₂₇⋊C₃)	C₃²	1	1	yes	characteristic
33	C₂×#92294	—	3	1	no	—
34	C₂×#92294	—	3	1	no	—
35	C₂×C₃⋊(D₉⋊C₉)	—	3	1	no	—
36	C₂×C₃×D₂₇⋊C₃	—	3	3	no	—
37	C₂×C₉×AGL(1,ℤ/9)	—	9	1	no	—
38	C₂×C₉×AGL(1,ℤ/9)	—	9	1	no	—
39	C₂×C₉×(C₃⋊D₃)⋊C₃	—	9	1	no	—
40	C₂×C₃×D₉⋊C₉	—	9	1	no	—
41	C₂×AGL(1,ℤ/27)	—	3	3	no	—
42	C₂×AGL(1,ℤ/27)	—	3	3	no	—
43	C₂×AGL(1,ℤ/27)	—	3	3	no	—
44	#10624918	—	2	1	no	—
45	#10624918	C₂²×C₃	1	1	yes	characteristic
46	#10624864	C₂×D₃	1	1	yes	characteristic
47	#10624709	—	2	3	no	—
48	#10624709	—	2	1	no	—
49	#10624709	—	2	1	no	—
50	#10624709	—	2	3	no	—
51	#10624709	—	2	3	no	—
52	#10624709	C₂²×C₃	1	1	yes	characteristic, complemented
53	#10624709	C₂²×C₃	1	1	yes	characteristic, complemented
54	C₃×#6875	—	2	1	no	—
55	C₃×#6875	—	2	3	no	—
56	C₃×#6875	C₂×D₃	1	3	yes	complemented
57	C₃×#6875	C₂²×C₃	1	1	yes	characteristic, complemented
58	C₂×C₃×#737	C₃×D₃	1	1	yes	characteristic
59	C₃×#4207	—	3	2	no	—
60	C₂×#6903	—	2	3	no	—
61	C₂×#6903	—	2	6	no	—
62	C₂×#6903	—	2	3	no	—
63	C₂×#6903	—	6	3	no	—
64	C₂×#6903	—	6	3	no	—
65	C₂×#6903	—	6	3	no	—
66	C₂×#6903	C₂×C₉	1	3	yes	complemented
67	C₂×C₃×C₂₇⋊C₃	—	2	1	no	—
68	C₂×C₃×C₂₇⋊C₃	—	2	3	no	—
69	C₂×C₃×C₂₇⋊C₃	—	2	6	no	—
70	C₂×C₃×C₂₇⋊C₃	—	2	1	no	—
71	C₂×C₃×C₂₇⋊C₃	—	2	1	no	—
72	C₂×C₃×C₂₇⋊C₃	—	2	1	no	—
73	C₂×C₃×C₂₇⋊C₃	—	2	3	no	—
74	C₂×C₃×C₂₇⋊C₃	C₃×D₃	1	3	yes	—
75	C₂×C₃×C₂₇⋊C₃	C₂×C₃²	1	1	yes	characteristic
76	C₂×C₉×3₋¹⁺²	—	3	1	no	—
77	C₂×C₉×3₋¹⁺²	—	3	1	no	—
78	C₂×C₉×3₋¹⁺²	—	6	1	no	—
79	C₂×C₉×3₋¹⁺²	—	6	1	no	—
80	C₂×C₉×3₋¹⁺²	—	6	1	no	—
81	C₂×C₉×H(3,𝔽₃)	—	6	1	no	—
82	C₂×#6887	—	2	1	no	—
83	C₂×#6887	—	2	1	no	—
84	C₂×#6887	—	2	1	no	—
85	C₂×#6887	C₃×D₃	1	1	yes	characteristic
86	C₂×#6887	C₃×D₃	1	1	yes	characteristic
87	C₂×C₃×C₉⋊C₉	—	2	1	no	—
88	C₂×C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
89	C₂×C₃×C₉⋊C₉	C₃⋊D₃	1	1	yes	characteristic
90	#92318	C₂×C₉	1	6	yes	complemented
91	C₃⋊(D₂₇⋊C₃)	C₂×C₃²	1	2	yes	—
92	#92294	—	3	2	no	—
93	#92294	—	3	2	no	—
94	C₃⋊(D₉⋊C₉)	—	3	2	no	—
95	C₃×D₂₇⋊C₃	—	3	6	no	—
96	C₉×AGL(1,ℤ/9)	—	9	2	no	—
97	C₉×AGL(1,ℤ/9)	—	9	2	no	—
98	C₉×(C₃⋊D₃)⋊C₃	—	9	2	no	—
99	C₃×D₉⋊C₉	—	9	2	no	—
100	C₂×#6875	—	2	6	no	—
101	C₂×#6875	—	2	6	no	—
102	C₂×#6875	—	2	6	no	—
103	C₂×#6875	—	2	3	no	—
104	C₂×#6875	—	2	3	no	—
105	C₂×#6875	—	2	3	no	—
106	C₂×#6875	—	2	3	no	—
107	C₂×#6875	—	2	3	no	—
108	C₂×#6875	—	2	3	no	—
109	C₂×#6875	C₃×D₃	1	3	yes	—
110	C₂×#6875	C₃×D₃	1	3	yes	—
111	C₂×#6875	C₃×D₃	1	3	yes	—
112	AGL(1,ℤ/27)	—	3	6	no	—
113	AGL(1,ℤ/27)	—	3	6	no	—
114	AGL(1,ℤ/27)	—	3	6	no	—
115	C₂×#4207	—	3	3	no	—
116	C₂×C₉×C₃⋊D₃	—	9	1	no	—
117	C₂×C₃×C₃⋊D₉	—	3	1	no	—
118	C₂×C₃×AGL(1,ℤ/9)	—	9	1	no	—
119	C₂×C₃×AGL(1,ℤ/9)	—	9	1	no	—
120	C₂×C₃×(C₃⋊D₃)⋊C₃	—	9	1	no	—
121	C₂×C₃×D₃×C₉	—	27	1	no	—
122	C₂×C₃²×D₉	—	9	1	no	—
123	C₂×C₃⋊D₂₇	C₃×C₉	1	1	yes	characteristic, complemented
124	C₂×D₂₇⋊C₃	—	3	6	no	—
125	C₂×D₂₇⋊C₃	—	3	3	no	—
126	C₂×C₃×D₂₇	—	3	3	no	—
127	C₂×D₉⋊C₉	—	9	1	no	—
128	C₂×D₉⋊C₉	—	9	1	no	—
129	C₂×D₉⋊C₉	—	9	1	no	—
130	C₂×D₉⋊C₉	—	9	1	no	—
131	C₂×D₉⋊C₉	—	9	1	no	—
132	C₂×D₉⋊C₉	—	9	1	no	—
133	C₂×D₉⋊C₉	—	9	1	no	—
134	C₂×(C₃⋊D₃)⋊C₉	—	9	1	no	—
135	C₂×(C₃⋊D₃)⋊C₉	—	9	1	no	—
136	C₂×C₉×D₉	—	9	1	no	—
137	C₂×C₉×D₉	—	9	1	no	—
138	C₃×#737	C₂×C₃×D₃	1	1	yes	characteristic
139	#6903	—	2	3	no	—
140	#6903	—	2	6	no	—
141	#6903	—	2	3	no	—
142	#6903	—	6	3	no	—
143	#6903	—	6	3	no	—
144	#6903	—	6	3	no	—
145	#6903	C₂²×C₉	1	3	yes	complemented
146	C₃×C₂₇⋊C₃	—	2	1	no	—
147	C₃×C₂₇⋊C₃	—	2	3	no	—
148	C₃×C₂₇⋊C₃	—	2	6	no	—
149	C₃×C₂₇⋊C₃	—	2	1	no	—
150	C₃×C₂₇⋊C₃	—	2	1	no	—
151	C₃×C₂₇⋊C₃	—	2	1	no	—
152	C₃×C₂₇⋊C₃	—	2	3	no	—
153	C₃×C₂₇⋊C₃	C₂×C₃×D₃	1	3	yes	—
154	C₃×C₂₇⋊C₃	C₂²×C₃²	1	1	yes	characteristic
155	C₉×3₋¹⁺²	—	3	1	no	—
156	C₉×3₋¹⁺²	—	3	1	no	—
157	C₉×3₋¹⁺²	—	6	1	no	—
158	C₉×3₋¹⁺²	—	6	1	no	—
159	C₉×3₋¹⁺²	—	6	1	no	—
160	C₉×H(3,𝔽₃)	—	6	1	no	—
161	#6887	—	2	1	no	—
162	#6887	—	2	1	no	—
163	#6887	—	2	1	no	—
164	#6887	C₂×C₃×D₃	1	1	yes	characteristic
165	#6887	C₂×C₃×D₃	1	1	yes	characteristic
166	C₃×C₉⋊C₉	—	2	1	no	—
167	C₃×C₉⋊C₉	C₂×C₃×D₃	1	1	yes	characteristic
168	C₃×C₉⋊C₉	C₂×C₃⋊D₃	1	1	yes	characteristic
169	#6875	—	2	6	no	—
170	#6875	—	2	6	no	—
171	#6875	—	2	6	no	—
172	#6875	—	2	3	no	—
173	#6875	—	2	3	no	—
174	#6875	—	2	3	no	—
175	#6875	—	2	3	no	—
176	#6875	—	2	3	no	—
177	#6875	—	2	3	no	—
178	#6875	C₂×C₃×D₃	1	3	yes	—
179	#6875	C₂×C₃×D₃	1	3	yes	—
180	#6875	C₂×C₃×D₃	1	3	yes	—
181	C₂×#737	—	2	3	no	—
182	C₂×#737	—	2	3	no	—
183	C₂×#737	—	2	3	no	—
184	C₂×#737	—	2	3	no	—
185	C₂×#737	D₃×C₉	1	3	yes	—
186	C₂×C₃×3₋¹⁺²	—	2	1	no	—
187	C₂×C₃×3₋¹⁺²	—	2	1	no	—
188	C₂×C₃×3₋¹⁺²	—	2	1	no	—
189	C₂×C₃×3₋¹⁺²	AGL(1,ℤ/9)	1	1	yes	characteristic
190	C₂×C₃×3₋¹⁺²	AGL(1,ℤ/9)	1	1	yes	characteristic
191	C₂×C₃×H(3,𝔽₃)	AGL(1,ℤ/9)	1	1	yes	characteristic
192	C₂×C₃²×C₉	—	2	1	no	—
193	C₂×C₃²×C₉	—	6	1	no	—
194	C₂×C₃²×C₉	—	6	1	no	—
195	C₂×C₃²×C₉	—	6	1	no	—
196	C₂×C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
197	C₂×C₃²×C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
198	#4207	—	3	6	no	—
199	C₉×C₃⋊D₃	—	9	2	no	—
200	C₃×C₃⋊D₉	—	3	2	no	—
201	C₃×AGL(1,ℤ/9)	—	9	2	no	—
202	C₃×AGL(1,ℤ/9)	—	9	2	no	—
203	C₃×(C₃⋊D₃)⋊C₃	—	9	2	no	—
204	C₃×D₃×C₉	—	27	2	no	—
205	C₃²×D₉	—	9	2	no	—
206	C₂×C₂₇⋊C₃	—	2	2	no	—
207	C₂×C₂₇⋊C₃	—	2	6	no	—
208	C₂×C₂₇⋊C₃	—	2	6	no	—
209	C₂×C₂₇⋊C₃	—	2	1	no	—
210	C₂×C₂₇⋊C₃	—	2	3	no	—
211	C₂×C₂₇⋊C₃	—	2	6	no	—
212	C₂×C₂₇⋊C₃	—	2	3	no	—
213	C₂×C₂₇⋊C₃	—	2	6	no	—
214	C₂×C₂₇⋊C₃	—	2	3	no	—
215	C₂×C₂₇⋊C₃	—	2	3	no	—
216	C₂×C₂₇⋊C₃	—	2	3	no	—
217	C₂×C₂₇⋊C₃	—	2	3	no	—
218	C₂×C₂₇⋊C₃	—	6	12	no	—
219	C₂×C₂₇⋊C₃	—	6	1	no	—
220	C₂×C₂₇⋊C₃	—	6	1	no	—
221	C₂×C₂₇⋊C₃	—	6	6	no	—
222	C₂×C₂₇⋊C₃	—	6	1	no	—
223	C₂×C₂₇⋊C₃	—	6	1	no	—
224	C₂×C₂₇⋊C₃	—	6	1	no	—
225	C₂×C₂₇⋊C₃	—	6	1	no	—
226	C₂×C₂₇⋊C₃	D₃×C₉	1	6	yes	complemented
227	C₂×C₂₇⋊C₃	C₃²×D₃	1	3	yes	—
228	C₂×C₃×C₂₇	—	2	3	no	—
229	C₂×C₃×C₂₇	—	2	3	no	—
230	C₂×C₃×C₂₇	—	2	3	no	—
231	C₂×C₃×C₂₇	—	2	1	no	—
232	C₂×C₃×C₂₇	—	2	3	no	—
233	C₂×C₃×C₂₇	—	2	3	no	—
234	C₂×C₃×C₂₇	—	6	6	no	—
235	C₂×C₃×C₂₇	—	6	1	no	—
236	C₂×C₃×C₂₇	—	6	3	no	—
237	C₂×C₃×C₂₇	—	6	1	no	—
238	C₂×C₃×C₂₇	—	6	1	no	—
239	C₂×C₃×C₂₇	D₃×C₉	1	3	yes	complemented
240	C₂×C₃×C₂₇	C₂×C₃×C₉	1	1	yes	characteristic, complemented
241	C₂×C₉⋊C₉	—	2	1	no	—
242	C₂×C₉⋊C₉	—	2	1	no	—
243	C₂×C₉⋊C₉	—	2	1	no	—
244	C₂×C₉⋊C₉	—	3	1	no	—
245	C₂×C₉⋊C₉	—	6	1	no	—
246	C₂×C₉⋊C₉	—	6	1	no	—
247	C₂×C₉⋊C₉	—	6	1	no	—
248	C₂×C₉⋊C₉	—	6	1	no	—
249	C₂×C₉⋊C₉	—	6	1	no	—
250	C₂×C₉⋊C₉	—	6	1	no	—
251	C₂×C₉⋊C₉	—	6	1	no	—
252	C₂×C₉⋊C₉	—	6	1	no	—
253	C₂×C₉⋊C₉	—	6	1	no	—
254	C₂×C₉⋊C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
255	C₂×C₉⋊C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
256	C₂×C₉⋊C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
257	C₂×C₃²⋊C₉	—	6	1	no	—
258	C₂×C₃²⋊C₉	—	6	1	no	—
259	C₂×C₃²⋊C₉	—	6	1	no	—
260	C₂×C₃²⋊C₉	—	6	1	no	—
261	C₂×C₃²⋊C₉	—	6	1	no	—
262	C₂×C₉²	—	3	1	no	—
263	C₂×C₉²	—	3	1	no	—
264	C₂×C₉²	—	6	1	no	—
265	C₂×C₉²	—	6	1	no	—
266	C₂×C₉²	—	6	1	no	—
267	C₃⋊D₂₇	C₂×C₃×C₉	1	2	yes	complemented
268	D₂₇⋊C₃	—	3	12	no	—
269	D₂₇⋊C₃	—	3	6	no	—
270	C₃×D₂₇	—	3	6	no	—
271	D₉⋊C₉	—	9	2	no	—
272	D₉⋊C₉	—	9	2	no	—
273	D₉⋊C₉	—	9	2	no	—
274	D₉⋊C₉	—	9	2	no	—
275	D₉⋊C₉	—	9	2	no	—
276	D₉⋊C₉	—	9	2	no	—
277	D₉⋊C₉	—	9	2	no	—
278	(C₃⋊D₃)⋊C₉	—	9	2	no	—
279	(C₃⋊D₃)⋊C₉	—	9	2	no	—
280	C₉×D₉	—	9	2	no	—
281	C₉×D₉	—	9	2	no	—
282	C₂×C₃×C₃⋊D₃	—	9	1	no	—
283	C₂×C₃²×D₃	—	27	1	no	—
284	C₂²×C₃×C₉	—	81	1	no	—
285	C₂×C₃⋊D₉	—	3	1	no	—
286	C₂×AGL(1,ℤ/9)	—	9	3	no	—
287	C₂×AGL(1,ℤ/9)	—	9	3	no	—
288	C₂×(C₃⋊D₃)⋊C₃	—	9	3	no	—
289	C₂×D₃×C₉	—	27	1	no	—
290	C₂×D₃×C₉	—	27	1	no	—
291	C₂×D₃×C₉	—	27	1	no	—
292	C₂×D₃×C₉	—	81	1	no	—
293	C₂×C₃×D₉	—	9	1	no	—
294	C₂×C₃×D₉	—	9	1	no	—
295	C₂×C₃×D₉	—	9	3	no	—
296	C₂×C₃×D₉	—	9	1	no	—
297	C₂×D₂₇	—	3	3	no	—
298	#737	—	2	3	no	—
299	#737	—	2	3	no	—
300	#737	—	2	3	no	—
301	#737	—	2	3	no	—
302	#737	C₂×D₃×C₉	1	3	yes	—
303	C₃×3₋¹⁺²	—	2	1	no	—
304	C₃×3₋¹⁺²	—	2	1	no	—
305	C₃×3₋¹⁺²	—	2	1	no	—
306	C₃×3₋¹⁺²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
307	C₃×3₋¹⁺²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
308	C₃×H(3,𝔽₃)	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
309	C₃²×C₉	—	2	1	no	—
310	C₃²×C₉	—	6	1	no	—
311	C₃²×C₉	—	6	1	no	—
312	C₃²×C₉	—	6	1	no	—
313	C₃²×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
314	C₃²×C₉	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
315	C₂₇⋊C₃	—	2	2	no	—
316	C₂₇⋊C₃	—	2	6	no	—
317	C₂₇⋊C₃	—	2	6	no	—
318	C₂₇⋊C₃	—	2	1	no	—
319	C₂₇⋊C₃	—	2	3	no	—
320	C₂₇⋊C₃	—	2	6	no	—
321	C₂₇⋊C₃	—	2	3	no	—
322	C₂₇⋊C₃	—	2	6	no	—
323	C₂₇⋊C₃	—	2	3	no	—
324	C₂₇⋊C₃	—	2	3	no	—
325	C₂₇⋊C₃	—	2	3	no	—
326	C₂₇⋊C₃	—	2	3	no	—
327	C₂₇⋊C₃	—	6	12	no	—
328	C₂₇⋊C₃	—	6	1	no	—
329	C₂₇⋊C₃	—	6	1	no	—
330	C₂₇⋊C₃	—	6	6	no	—
331	C₂₇⋊C₃	—	6	1	no	—
332	C₂₇⋊C₃	—	6	1	no	—
333	C₂₇⋊C₃	—	6	1	no	—
334	C₂₇⋊C₃	—	6	1	no	—
335	C₂₇⋊C₃	C₂×D₃×C₉	1	6	yes	complemented
336	C₂₇⋊C₃	C₂×C₃²×D₃	1	3	yes	—
337	C₃×C₂₇	—	2	3	no	—
338	C₃×C₂₇	—	2	3	no	—
339	C₃×C₂₇	—	2	3	no	—
340	C₃×C₂₇	—	2	1	no	—
341	C₃×C₂₇	—	2	3	no	—
342	C₃×C₂₇	—	2	3	no	—
343	C₃×C₂₇	—	6	6	no	—
344	C₃×C₂₇	—	6	1	no	—
345	C₃×C₂₇	—	6	3	no	—
346	C₃×C₂₇	—	6	1	no	—
347	C₃×C₂₇	—	6	1	no	—
348	C₃×C₂₇	C₂×D₃×C₉	1	3	yes	complemented
349	C₃×C₂₇	C₂²×C₃×C₉	1	1	yes	characteristic, complemented
350	C₉⋊C₉	—	2	1	no	—
351	C₉⋊C₉	—	2	1	no	—
352	C₉⋊C₉	—	2	1	no	—
353	C₉⋊C₉	—	3	1	no	—
354	C₉⋊C₉	—	6	1	no	—
355	C₉⋊C₉	—	6	1	no	—
356	C₉⋊C₉	—	6	1	no	—
357	C₉⋊C₉	—	6	1	no	—
358	C₉⋊C₉	—	6	1	no	—
359	C₉⋊C₉	—	6	1	no	—
360	C₉⋊C₉	—	6	1	no	—
361	C₉⋊C₉	—	6	1	no	—
362	C₉⋊C₉	—	6	1	no	—
363	C₉⋊C₉	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
364	C₉⋊C₉	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
365	C₉⋊C₉	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
366	C₃²⋊C₉	—	6	1	no	—
367	C₃²⋊C₉	—	6	1	no	—
368	C₃²⋊C₉	—	6	1	no	—
369	C₃²⋊C₉	—	6	1	no	—
370	C₃²⋊C₉	—	6	1	no	—
371	C₉²	—	3	1	no	—
372	C₉²	—	3	1	no	—
373	C₉²	—	6	1	no	—
374	C₉²	—	6	1	no	—
375	C₉²	—	6	1	no	—
376	C₂×C₃³	—	2	1	no	—
377	C₂×C₃³	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
378	C₂×C₃³	C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
379	C₃×C₃⋊D₃	—	9	2	no	—
380	C₃²×D₃	—	27	2	no	—
381	C₂×3₋¹⁺²	—	2	6	no	—
382	C₂×3₋¹⁺²	—	2	6	no	—
383	C₂×3₋¹⁺²	—	2	6	no	—
384	C₂×3₋¹⁺²	—	2	3	no	—
385	C₂×3₋¹⁺²	—	2	3	no	—
386	C₂×3₋¹⁺²	—	2	3	no	—
387	C₂×3₋¹⁺²	—	2	3	no	—
388	C₂×3₋¹⁺²	—	2	3	no	—
389	C₂×3₋¹⁺²	D₉⋊C₉	1	3	yes	—
390	C₂×3₋¹⁺²	D₉⋊C₉	1	3	yes	—
391	C₂×H(3,𝔽₃)	—	2	3	no	—
392	C₂×H(3,𝔽₃)	D₉⋊C₉	1	3	yes	—
393	C₂×C₃×C₉	—	2	6	no	—
394	C₂×C₃×C₉	—	2	1	no	—
395	C₂×C₃×C₉	—	2	3	no	—
396	C₂×C₃×C₉	—	2	1	no	—
397	C₂×C₃×C₉	—	2	1	no	—
398	C₂×C₃×C₉	—	2	1	no	—
399	C₂×C₃×C₉	—	2	1	no	—
400	C₂×C₃×C₉	—	2	1	no	—
401	C₂×C₃×C₉	—	2	3	no	—
402	C₂×C₃×C₉	—	2	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	—	6	1	no	—
408	C₂×C₃×C₉	—	6	1	no	—
409	C₂×C₃×C₉	—	54	1	no	—
410	C₂×C₃×C₉	—	54	1	no	—
411	C₂×C₃×C₉	—	54	1	no	—
412	C₂×C₃×C₉	—	81	2	no	—
413	C₂×C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
414	C₂×C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
415	C₂×C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
416	C₂×C₃×C₉	C₉×C₃⋊D₃	1	3	yes	—
417	C₂×C₃×C₉	C₃²×C₃⋊D₃	1	1	yes	characteristic
418	C₃⋊D₉	—	3	2	no	—
419	AGL(1,ℤ/9)	—	9	6	no	—
420	AGL(1,ℤ/9)	—	9	6	no	—
421	(C₃⋊D₃)⋊C₃	—	9	6	no	—
422	D₃×C₉	—	27	2	no	—
423	D₃×C₉	—	27	2	no	—
424	D₃×C₉	—	27	2	no	—
425	D₃×C₉	—	81	2	no	—
426	C₃×D₉	—	9	2	no	—
427	C₃×D₉	—	9	2	no	—
428	C₃×D₉	—	9	6	no	—
429	C₃×D₉	—	9	2	no	—
430	C₂×C₂₇	—	2	6	no	—
431	C₂×C₂₇	—	2	3	no	—
432	C₂×C₂₇	—	2	3	no	—
433	C₂×C₂₇	—	6	3	no	—
434	C₂×C₂₇	—	6	3	no	—
435	C₂×C₂₇	—	6	3	no	—
436	C₂×C₂₇	C₃×D₃×C₉	1	3	yes	—
437	D₂₇	—	3	6	no	—
438	C₂²×C₃²	—	81	1	no	—
439	C₂×C₃⋊D₃	—	9	1	no	—
440	C₂×C₃×D₃	—	27	3	no	—
441	C₂×C₃×D₃	—	27	1	no	—
442	C₂×C₃×D₃	—	81	1	no	—
443	C₂²×C₉	—	81	1	no	—
444	C₂²×C₉	—	81	1	no	—
445	C₂²×C₉	—	81	1	no	—
446	C₂×D₉	—	9	1	no	—
447	C₂×D₉	—	9	1	no	—
448	C₂×D₉	—	9	1	no	—
449	C₃³	—	2	1	no	—
450	C₃³	C₂×C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
451	C₃³	C₂×C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
452	3₋¹⁺²	—	2	6	no	—
453	3₋¹⁺²	—	2	6	no	—
454	3₋¹⁺²	—	2	6	no	—
455	3₋¹⁺²	—	2	3	no	—
456	3₋¹⁺²	—	2	3	no	—
457	3₋¹⁺²	—	2	3	no	—
458	3₋¹⁺²	—	2	3	no	—
459	3₋¹⁺²	—	2	3	no	—
460	3₋¹⁺²	C₂×D₉⋊C₉	1	3	yes	—
461	3₋¹⁺²	C₂×D₉⋊C₉	1	3	yes	—
462	H(3,𝔽₃)	—	2	3	no	—
463	H(3,𝔽₃)	C₂×D₉⋊C₉	1	3	yes	—
464	C₃×C₉	—	2	6	no	—
465	C₃×C₉	—	2	1	no	—
466	C₃×C₉	—	2	1	no	—
467	C₃×C₉	—	2	1	no	—
468	C₃×C₉	—	2	1	no	—
469	C₃×C₉	—	2	3	no	—
470	C₃×C₉	—	2	3	no	—
471	C₃×C₉	—	2	1	no	—
472	C₃×C₉	—	2	1	no	—
473	C₃×C₉	—	2	1	no	—
474	C₃×C₉	—	6	1	no	—
475	C₃×C₉	—	6	1	no	—
476	C₃×C₉	—	6	1	no	—
477	C₃×C₉	—	6	1	no	—
478	C₃×C₉	—	6	1	no	—
479	C₃×C₉	—	6	1	no	—
480	C₃×C₉	—	54	1	no	—
481	C₃×C₉	—	54	1	no	—
482	C₃×C₉	—	54	1	no	—
483	C₃×C₉	C₂×C₃×D₃×C₉	1	1	yes	characteristic
484	C₃×C₉	C₂×C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
485	C₃×C₉	C₂×C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
486	C₃×C₉	C₂×C₉×C₃⋊D₃	1	3	yes	—
487	C₃×C₉	C₂×C₃²×C₃⋊D₃	1	1	yes	characteristic
488	C₂₇	—	2	6	no	—
489	C₂₇	—	2	3	no	—
490	C₂₇	—	2	3	no	—
491	C₂₇	—	6	3	no	—
492	C₂₇	—	6	3	no	—
493	C₂₇	—	6	3	no	—
494	C₂₇	C₂×C₃×D₃×C₉	1	3	yes	—
495	C₂×C₃²	—	2	1	no	—
496	C₂×C₃²	—	2	3	no	—
497	C₂×C₃²	—	18	1	no	—
498	C₂×C₃²	—	18	1	no	—
499	C₂×C₃²	—	18	1	no	—
500	C₂×C₃²	—	81	2	no	—
501	C₂×C₃²	C₃×D₉⋊C₉	1	1	yes	characteristic
502	C₂×C₃²	C₃⋊(D₉⋊C₉)	1	3	yes	—
503	C₂×C₃²	C₃×C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
504	C₃⋊D₃	—	9	2	no	—
505	C₃×D₃	—	27	2	no	—
506	C₃×D₃	—	27	6	no	—
507	C₃×D₃	—	81	2	no	—
508	C₂×C₉	—	2	1	no	—
509	C₂×C₉	—	2	3	no	—
510	C₂×C₉	—	2	3	no	—
511	C₂×C₉	—	2	1	no	—
512	C₂×C₉	—	2	1	no	—
513	C₂×C₉	—	2	3	no	—
514	C₂×C₉	—	18	1	no	—
515	C₂×C₉	—	18	1	no	—
516	C₂×C₉	—	18	1	no	—
517	C₂×C₉	—	18	1	no	—
518	C₂×C₉	—	18	1	no	—
519	C₂×C₉	—	18	1	no	—
520	C₂×C₉	—	81	2	no	—
521	C₂×C₉	—	81	2	no	—
522	C₂×C₉	—	81	2	no	—
523	C₂×C₉	C₃×D₉⋊C₉	1	1	yes	characteristic
524	C₂×C₉	C₃×D₉⋊C₉	1	1	yes	characteristic
525	C₂×C₉	C₃×C₉×C₃⋊D₃	1	1	yes	characteristic
526	D₉	—	9	2	no	—
527	D₉	—	9	2	no	—
528	D₉	—	9	2	no	—
529	C₂²×C₃	—	81	1	no	—
530	C₂²×C₃	—	81	3	no	—
531	C₂×D₃	—	27	1	no	—
532	C₂×D₃	—	81	1	no	—
533	C₃²	—	2	1	no	—
534	C₃²	—	2	3	no	—
535	C₃²	—	18	1	no	—
536	C₃²	—	18	1	no	—
537	C₃²	—	18	1	no	—
538	C₃²	C₂×C₃×D₉⋊C₉	1	1	yes	characteristic
539	C₃²	C₂×C₃⋊(D₉⋊C₉)	1	3	yes	—
540	C₃²	C₂×C₃×C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
541	C₉	—	2	1	no	—
542	C₉	—	2	3	no	—
543	C₉	—	2	3	no	—
544	C₉	—	2	1	no	—
545	C₉	—	2	1	no	—
546	C₉	—	2	3	no	—
547	C₉	—	18	1	no	—
548	C₉	—	18	1	no	—
549	C₉	—	18	1	no	—
550	C₉	—	18	1	no	—
551	C₉	—	18	1	no	—
552	C₉	—	18	1	no	—
553	C₉	C₂×C₃×D₉⋊C₉	1	1	yes	characteristic
554	C₉	C₂×C₃×D₉⋊C₉	1	1	yes	characteristic
555	C₉	C₂×C₃×C₉×C₃⋊D₃	1	1	yes	characteristic
556	C₂×C₃	—	3	1	no	—
557	C₂×C₃	—	6	1	no	—
558	C₂×C₃	—	6	3	no	—
559	C₂×C₃	—	6	1	no	—
560	C₂×C₃	—	6	3	no	—
561	C₂×C₃	—	81	2	no	—
562	C₂×C₃	—	81	6	no	—
563	C₂×C₃	C₃×C₃⋊(D₉⋊C₉)	1	1	yes	characteristic
564	D₃	—	27	2	no	—
565	D₃	—	81	2	no	—
566	C₂²	—	81	1	no	Sylow
567	C₃	—	3	1	no	—
568	C₃	—	6	1	no	—
569	C₃	—	6	3	no	—
570	C₃	—	6	1	no	—
571	C₃	—	6	3	no	—
572	C₃	C₂×C₃×C₃⋊(D₉⋊C₉)	1	1	yes	characteristic
573	C₂	—	81	2	no	—
574	C₂	#72221820	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#72221820
commutator, hypocenter	C₃×C₂₇	C₂²×C₃×C₉
Frattini	C₃×C₉	C₂×C₃²×C₃⋊D₃
Fitting	C₂×#14554150	C₂
socle	C₂×C₃	C₃×C₃⋊(D₉⋊C₉)
prime radical	C₂×#92318⋊C₃	C₃
cosocle	C₃×C₂₇⋊C₃	C₂²×C₃²
LCS	G ▷ C₃×C₂₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×#10624709⋊C₂	C₃	semidirect
2. C₂×#10624709⋊C₂	C₃	semidirect
5. C₂×#14554150	C₂	semidirect
6. C₂×C₃⋊AGL(1,ℤ/27)	C₃	semidirect
7. #72221820	C₂	direct (N × H)
9. #14554150	C₂²	semidirect
12. #10624709⋊C₂	C₂×C₃	semidirect
13. #10624709⋊C₂	C₂×C₃	semidirect
14. C₃⋊AGL(1,ℤ/27)	C₂×C₃	semidirect
24. C₂×#10624709	C₂×C₃	semidirect
25. C₂×#10624709	C₂×C₃	semidirect
28. C₂×C₃×#6875	D₃	semidirect
29. C₂×C₃×#6875	C₂×C₃	semidirect
31. C₂×#92318	C₉	semidirect
52. #10624709	C₂²×C₃	semidirect
53. #10624709	C₂²×C₃	semidirect
56. C₃×#6875	C₂×D₃	semidirect
57. C₃×#6875	C₂²×C₃	semidirect
66. C₂×#6903	C₂×C₉	semidirect
90. #92318	C₂×C₉	semidirect
123. C₂×C₃⋊D₂₇	C₃×C₉	semidirect
145. #6903	C₂²×C₉	semidirect
226. C₂×C₂₇⋊C₃	D₃×C₉	semidirect
239. C₂×C₃×C₂₇	D₃×C₉	semidirect
240. C₂×C₃×C₂₇	C₂×C₃×C₉	semidirect
267. C₃⋊D₂₇	C₂×C₃×C₉	semidirect
335. C₂₇⋊C₃	C₂×D₃×C₉	semidirect
348. C₃×C₂₇	C₂×D₃×C₉	semidirect
349. C₃×C₂₇	C₂²×C₃×C₉	semidirect
574. C₂	#72221820	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#10624709⋊C₂	3
C₂×#4207⋊C₉	3
C₂×#92318⋊C₃	3
C₂×#14554150	2
C₂×C₃⋊AGL(1,ℤ/27)	3
#72221820	2
C₂×C₃×AGL(1,ℤ/27)	3

Subgroups — C2×#72221820 #72243935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72221820 #72243935