Subgroups — C₂×#72221831 #72244050

Order 8748.

1241 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13091386	C₃	1	1	yes	maximal, characteristic
2	C₂×#13091566	C₃	1	2	yes	maximal
3	C₂×#13091566	C₃	1	1	yes	maximal, characteristic
4	C₂×#14554150	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₃×#6875	—	3	1	no	maximal
6	C₂×D₃×#6875	—	3	2	no	maximal
7	C₂×D₃×#6875	—	3	1	no	maximal
8	#72221831	C₂	1	2	yes	maximal, direct product factor
9	#14554150	C₂²	1	1	yes	characteristic, complemented, Sylow
10	#13091566	C₂×C₃	1	4	yes	—
11	#13091566	C₂×C₃	1	2	yes	—
12	#13091386	C₂×C₃	1	2	yes	—
13	D₃×#6875	—	3	2	no	—
14	D₃×#6875	—	3	4	no	—
15	D₃×#6875	—	3	2	no	—
16	C₂×#10624918	C₂×C₃	1	1	yes	characteristic
17	C₂×#10624918	C₂×C₃	1	2	yes	—
18	C₂×#10624864	C₂×C₃	1	1	yes	characteristic
19	C₂×#10624709	—	2	4	no	—
20	C₂×#10624709	—	2	2	no	—
21	C₂×#10624709	—	2	2	no	—
22	C₂×#10624709	—	2	2	no	—
23	C₂×#10624709	—	2	1	no	—
24	C₂×#10624709	—	2	1	no	—
25	C₂×C₃×#6875	—	2	1	no	—
26	C₂×C₃×#6875	—	2	2	no	—
27	C₂×C₃×#6875	—	2	1	no	—
28	C₂×C₃×#6875	D₃	1	1	yes	characteristic, complemented
29	C₂×C₃×#6875	D₃	1	2	yes	complemented
30	C₂×C₃×#6875	D₃	1	1	yes	characteristic, complemented
31	C₂×C₃×#4208	C₃²	1	1	yes	characteristic
32	C₂×#92319	—	3	2	no	—
33	C₂×#92319	C₉	1	3	yes	complemented
34	C₂×C₉×#272	—	3	1	no	—
35	C₂×D₃×C₂₇⋊C₃	—	3	2	no	—
36	C₂×D₃×C₂₇⋊C₃	—	3	1	no	—
37	C₂×D₃×C₂₇⋊C₃	—	3	1	no	—
38	C₂×D₃×C₂₇⋊C₃	—	3	4	no	—
39	C₂×D₃×C₂₇⋊C₃	—	3	2	no	—
40	C₂×D₃×C₂₇⋊C₃	—	3	2	no	—
41	C₂×D₃×C₉⋊C₉	—	3	1	no	—
42	C₂×D₃×C₉⋊C₉	—	3	2	no	—
43	C₂×D₃×C₉⋊C₉	—	3	1	no	—
44	C₂²×#6875	—	9	1	no	—
45	#10624918	C₂²×C₃	1	1	yes	characteristic
46	#10624918	C₂²×C₃	1	2	yes	—
47	#10624864	C₂²×C₃	1	1	yes	characteristic
48	#10624709	—	2	4	no	—
49	#10624709	—	2	2	no	—
50	#10624709	—	2	2	no	—
51	#10624709	—	2	2	no	—
52	#10624709	—	2	1	no	—
53	#10624709	—	2	1	no	—
54	C₃×#6875	—	2	1	no	—
55	C₃×#6875	—	2	2	no	—
56	C₃×#6875	—	2	1	no	—
57	C₃×#6875	C₂×D₃	1	1	yes	characteristic, complemented
58	C₃×#6875	C₂×D₃	1	2	yes	complemented
59	C₃×#6875	C₂×D₃	1	1	yes	characteristic, complemented
60	C₂×C₃×#737	C₂×C₃²	1	1	yes	characteristic
61	C₃×#4208	C₂×C₃²	1	2	yes	—
62	C₂×#6903	—	2	6	no	—
63	C₂×#6903	—	2	3	no	—
64	C₂×#6903	—	2	3	no	—
65	C₂×#6903	—	3	2	no	—
66	C₂×#6903	—	6	4	no	—
67	C₂×#6903	—	6	2	no	—
68	C₂×#6903	—	6	2	no	—
69	C₂×#6903	C₂×C₉	1	3	yes	complemented
70	C₂×C₃×C₂₇⋊C₃	—	2	2	no	—
71	C₂×C₃×C₂₇⋊C₃	—	2	1	no	—
72	C₂×C₃×C₂₇⋊C₃	—	2	1	no	—
73	C₂×C₃×C₂₇⋊C₃	—	2	4	no	—
74	C₂×C₃×C₂₇⋊C₃	—	2	2	no	—
75	C₂×C₃×C₂₇⋊C₃	—	2	2	no	—
76	C₂×C₃×C₂₇⋊C₃	C₃×D₃	1	4	yes	—
77	C₂×C₃×C₂₇⋊C₃	C₃×D₃	1	2	yes	—
78	C₂×C₃×C₂₇⋊C₃	C₃×D₃	1	2	yes	—
79	C₂×C₃×C₂₇⋊C₃	C₃×D₃	1	2	yes	—
80	C₂×C₃×C₂₇⋊C₃	C₃×D₃	1	1	yes	characteristic
81	C₂×C₃×C₂₇⋊C₃	C₃×D₃	1	1	yes	characteristic
82	C₂×C₉×3₋¹⁺²	—	6	1	no	—
83	C₂×C₉×3₋¹⁺²	—	6	2	no	—
84	C₂×C₉×3₋¹⁺²	—	6	1	no	—
85	C₂×C₉×H(3,𝔽₃)	—	3	1	no	—
86	C₂×#6887	—	2	2	no	—
87	C₂×#6887	—	2	1	no	—
88	C₂×#6887	—	2	1	no	—
89	C₂×C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
90	C₂×C₃×C₉⋊C₉	C₃×D₃	1	2	yes	—
91	C₂×C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
92	#92319	—	3	4	no	—
93	#92319	C₂×C₉	1	6	yes	complemented
94	C₉×#272	—	3	2	no	—
95	D₃×C₂₇⋊C₃	—	3	4	no	—
96	D₃×C₂₇⋊C₃	—	3	2	no	—
97	D₃×C₂₇⋊C₃	—	3	2	no	—
98	D₃×C₂₇⋊C₃	—	3	8	no	—
99	D₃×C₂₇⋊C₃	—	3	4	no	—
100	D₃×C₂₇⋊C₃	—	3	4	no	—
101	D₃×C₉⋊C₉	—	3	2	no	—
102	D₃×C₉⋊C₉	—	3	4	no	—
103	D₃×C₉⋊C₉	—	3	2	no	—
104	C₂×#6875	—	2	2	no	—
105	C₂×#6875	—	2	4	no	—
106	C₂×#6875	—	2	4	no	—
107	C₂×#6875	—	2	4	no	—
108	C₂×#6875	—	2	4	no	—
109	C₂×#6875	—	2	2	no	—
110	C₂×#6875	—	2	4	no	—
111	C₂×#6875	—	2	2	no	—
112	C₂×#6875	—	2	4	no	—
113	C₂×#6875	—	2	2	no	—
114	C₂×#6875	—	2	1	no	—
115	C₂×#6875	—	2	2	no	—
116	C₂×#6875	—	2	1	no	—
117	C₂×#6875	—	2	1	no	—
118	C₂×#6875	—	2	2	no	—
119	C₂×#6875	—	2	1	no	—
120	C₂×#6875	—	9	2	no	—
121	C₂×#6875	C₃⋊D₃	1	1	yes	characteristic
122	C₂×#4208	C₃×C₉	1	1	yes	characteristic
123	C₂×#4208	3₋¹⁺²	1	2	yes	—
124	C₂×C₃×#272	3₋¹⁺²	1	1	yes	characteristic
125	C₂×C₃×D₃×C₉	—	3	2	no	—
126	C₂×C₃×D₃×C₉	—	3	1	no	—
127	C₂×C₃×D₃×C₉	—	3	1	no	—
128	C₂×C₃×D₃×C₉	—	9	1	no	—
129	C₂×C₃×D₃×C₉	—	9	2	no	—
130	C₂×C₃×D₃×C₉	—	9	1	no	—
131	C₂²×C₂₇⋊C₃	—	9	1	no	—
132	C₂²×C₂₇⋊C₃	—	9	2	no	—
133	C₂²×C₉⋊C₉	—	9	1	no	—
134	C₂×D₃×C₂₇	—	3	6	no	—
135	C₂×D₃×C₂₇	—	3	3	no	—
136	C₂×D₃×C₂₇	—	3	3	no	—
137	C₂×D₃×C₂₇	—	9	4	no	—
138	C₂×D₃×C₂₇	—	9	2	no	—
139	C₂×D₃×C₂₇	—	9	2	no	—
140	C₃×#737	C₂²×C₃²	1	1	yes	characteristic
141	#6903	—	2	6	no	—
142	#6903	—	2	3	no	—
143	#6903	—	2	3	no	—
144	#6903	—	3	2	no	—
145	#6903	—	6	4	no	—
146	#6903	—	6	2	no	—
147	#6903	—	6	2	no	—
148	#6903	C₂²×C₉	1	3	yes	complemented
149	C₃×C₂₇⋊C₃	—	2	2	no	—
150	C₃×C₂₇⋊C₃	—	2	1	no	—
151	C₃×C₂₇⋊C₃	—	2	1	no	—
152	C₃×C₂₇⋊C₃	—	2	4	no	—
153	C₃×C₂₇⋊C₃	—	2	2	no	—
154	C₃×C₂₇⋊C₃	—	2	2	no	—
155	C₃×C₂₇⋊C₃	C₂×C₃×D₃	1	4	yes	—
156	C₃×C₂₇⋊C₃	C₂×C₃×D₃	1	2	yes	—
157	C₃×C₂₇⋊C₃	C₂×C₃×D₃	1	2	yes	—
158	C₃×C₂₇⋊C₃	C₂×C₃×D₃	1	2	yes	—
159	C₃×C₂₇⋊C₃	C₂×C₃×D₃	1	1	yes	characteristic
160	C₃×C₂₇⋊C₃	C₂×C₃×D₃	1	1	yes	characteristic
161	C₉×3₋¹⁺²	—	6	1	no	—
162	C₉×3₋¹⁺²	—	6	2	no	—
163	C₉×3₋¹⁺²	—	6	1	no	—
164	C₉×H(3,𝔽₃)	—	3	1	no	—
165	#6887	—	2	2	no	—
166	#6887	—	2	1	no	—
167	#6887	—	2	1	no	—
168	C₃×C₉⋊C₉	C₂×C₃×D₃	1	1	yes	characteristic
169	C₃×C₉⋊C₉	C₂×C₃×D₃	1	2	yes	—
170	C₃×C₉⋊C₉	C₂×C₃×D₃	1	1	yes	characteristic
171	#6875	—	2	2	no	—
172	#6875	—	2	4	no	—
173	#6875	—	2	4	no	—
174	#6875	—	2	4	no	—
175	#6875	—	2	4	no	—
176	#6875	—	2	2	no	—
177	#6875	—	2	4	no	—
178	#6875	—	2	2	no	—
179	#6875	—	2	4	no	—
180	#6875	—	2	2	no	—
181	#6875	—	2	1	no	—
182	#6875	—	2	2	no	—
183	#6875	—	2	1	no	—
184	#6875	—	2	1	no	—
185	#6875	—	2	2	no	—
186	#6875	—	2	1	no	—
187	#6875	C₂×C₃⋊D₃	1	1	yes	characteristic
188	C₂×#737	—	2	2	no	—
189	C₂×#737	—	2	1	no	—
190	C₂×#737	—	2	1	no	—
191	C₂×#737	—	2	4	no	—
192	C₂×#737	—	2	2	no	—
193	C₂×#737	—	2	2	no	—
194	C₂×#737	C₂×C₃×C₉	1	1	yes	characteristic
195	C₂×#737	C₂×3₋¹⁺²	1	2	yes	—
196	C₂×C₃×3₋¹⁺²	—	2	2	no	—
197	C₂×C₃×3₋¹⁺²	—	2	1	no	—
198	C₂×C₃×3₋¹⁺²	—	2	1	no	—
199	C₂×C₃×H(3,𝔽₃)	C₂×3₋¹⁺²	1	1	yes	characteristic
200	C₂×C₃²×C₉	—	3	1	no	—
201	C₂×C₃²×C₉	—	3	2	no	—
202	C₂×C₃²×C₉	—	3	1	no	—
203	C₂×C₃²×C₉	C₃²×D₃	1	2	yes	—
204	C₂×C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
205	C₂×C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
206	#4208	C₂×C₃×C₉	1	2	yes	—
207	#4208	C₂×3₋¹⁺²	1	4	yes	—
208	C₃×#272	C₂×3₋¹⁺²	1	2	yes	—
209	C₃×D₃×C₉	—	3	4	no	—
210	C₃×D₃×C₉	—	3	2	no	—
211	C₃×D₃×C₉	—	3	2	no	—
212	C₃×D₃×C₉	—	9	2	no	—
213	C₃×D₃×C₉	—	9	4	no	—
214	C₃×D₃×C₉	—	9	2	no	—
215	C₂×C₂₇⋊C₃	—	2	6	no	—
216	C₂×C₂₇⋊C₃	—	2	3	no	—
217	C₂×C₂₇⋊C₃	—	2	3	no	—
218	C₂×C₂₇⋊C₃	—	2	6	no	—
219	C₂×C₂₇⋊C₃	—	2	3	no	—
220	C₂×C₂₇⋊C₃	—	2	3	no	—
221	C₂×C₂₇⋊C₃	—	2	1	no	—
222	C₂×C₂₇⋊C₃	—	2	1	no	—
223	C₂×C₂₇⋊C₃	—	2	2	no	—
224	C₂×C₂₇⋊C₃	—	2	6	no	—
225	C₂×C₂₇⋊C₃	—	2	3	no	—
226	C₂×C₂₇⋊C₃	—	2	3	no	—
227	C₂×C₂₇⋊C₃	—	2	2	no	—
228	C₂×C₂₇⋊C₃	—	2	2	no	—
229	C₂×C₂₇⋊C₃	—	2	4	no	—
230	C₂×C₂₇⋊C₃	—	6	4	no	—
231	C₂×C₂₇⋊C₃	—	6	2	no	—
232	C₂×C₂₇⋊C₃	—	6	2	no	—
233	C₂×C₂₇⋊C₃	—	6	4	no	—
234	C₂×C₂₇⋊C₃	—	6	2	no	—
235	C₂×C₂₇⋊C₃	—	6	2	no	—
236	C₂×C₂₇⋊C₃	—	6	4	no	—
237	C₂×C₂₇⋊C₃	—	6	2	no	—
238	C₂×C₂₇⋊C₃	—	6	2	no	—
239	C₂×C₂₇⋊C₃	—	9	2	no	—
240	C₂×C₂₇⋊C₃	—	9	4	no	—
241	C₂×C₂₇⋊C₃	C₃×C₃⋊D₃	1	2	yes	—
242	C₂×C₂₇⋊C₃	C₃×C₃⋊D₃	1	1	yes	characteristic
243	C₂×C₃×C₂₇	—	2	6	no	—
244	C₂×C₃×C₂₇	—	2	3	no	—
245	C₂×C₃×C₂₇	—	2	3	no	—
246	C₂×C₃×C₂₇	—	3	4	no	—
247	C₂×C₃×C₂₇	—	3	2	no	—
248	C₂×C₃×C₂₇	—	3	2	no	—
249	C₂×C₃×C₂₇	—	6	4	no	—
250	C₂×C₃×C₂₇	—	6	2	no	—
251	C₂×C₃×C₂₇	—	6	2	no	—
252	C₂×C₃×C₂₇	D₃×C₉	1	6	yes	complemented
253	C₂×C₃×C₂₇	D₃×C₉	1	3	yes	complemented
254	C₂×C₃×C₂₇	D₃×C₉	1	3	yes	complemented
255	C₂×C₉⋊C₉	—	2	1	no	—
256	C₂×C₉⋊C₉	—	2	2	no	—
257	C₂×C₉⋊C₉	—	2	1	no	—
258	C₂×C₉⋊C₉	—	6	1	no	—
259	C₂×C₉⋊C₉	—	6	2	no	—
260	C₂×C₉⋊C₉	—	6	1	no	—
261	C₂×C₉⋊C₉	—	6	2	no	—
262	C₂×C₉⋊C₉	—	6	1	no	—
263	C₂×C₉⋊C₉	—	6	1	no	—
264	C₂×C₉⋊C₉	—	9	2	no	—
265	C₂×C₉⋊C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
266	C₂×C₃²⋊C₉	—	6	2	no	—
267	C₂×C₃²⋊C₉	—	6	1	no	—
268	C₂×C₃²⋊C₉	—	6	1	no	—
269	C₂×C₉²	—	6	2	no	—
270	C₂×C₉²	—	6	1	no	—
271	C₂×C₉²	—	6	1	no	—
272	D₃×C₂₇	—	3	12	no	—
273	D₃×C₂₇	—	3	6	no	—
274	D₃×C₂₇	—	3	6	no	—
275	D₃×C₂₇	—	9	8	no	—
276	D₃×C₂₇	—	9	4	no	—
277	D₃×C₂₇	—	9	4	no	—
278	C₂×C₃²×D₃	—	3	2	no	—
279	C₂×C₃²×D₃	—	3	1	no	—
280	C₂×C₃²×D₃	—	3	1	no	—
281	C₂²×C₃×C₉	—	9	1	no	—
282	C₂²×C₃×C₉	—	27	1	no	—
283	C₂×#272	C₉⋊C₉	1	1	yes	characteristic
284	C₂×D₃×C₉	—	3	2	no	—
285	C₂×D₃×C₉	—	3	1	no	—
286	C₂×D₃×C₉	—	3	1	no	—
287	C₂×D₃×C₉	—	3	4	no	—
288	C₂×D₃×C₉	—	3	2	no	—
289	C₂×D₃×C₉	—	3	2	no	—
290	C₂×D₃×C₉	—	27	1	no	—
291	C₂×D₃×C₉	—	27	2	no	—
292	C₂×D₃×C₉	—	27	1	no	—
293	C₂²×C₂₇	—	9	3	no	—
294	C₂²×C₂₇	—	27	2	no	—
295	#737	—	2	2	no	—
296	#737	—	2	1	no	—
297	#737	—	2	1	no	—
298	#737	—	2	4	no	—
299	#737	—	2	2	no	—
300	#737	—	2	2	no	—
301	#737	C₂²×C₃×C₉	1	1	yes	characteristic
302	#737	C₂²×3₋¹⁺²	1	2	yes	—
303	C₃×3₋¹⁺²	—	2	2	no	—
304	C₃×3₋¹⁺²	—	2	1	no	—
305	C₃×3₋¹⁺²	—	2	1	no	—
306	C₃×H(3,𝔽₃)	C₂²×3₋¹⁺²	1	1	yes	characteristic
307	C₃²×C₉	—	3	1	no	—
308	C₃²×C₉	—	3	2	no	—
309	C₃²×C₉	—	3	1	no	—
310	C₃²×C₉	C₂×C₃²×D₃	1	2	yes	—
311	C₃²×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
312	C₃²×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
313	C₂₇⋊C₃	—	2	6	no	—
314	C₂₇⋊C₃	—	2	3	no	—
315	C₂₇⋊C₃	—	2	3	no	—
316	C₂₇⋊C₃	—	2	6	no	—
317	C₂₇⋊C₃	—	2	3	no	—
318	C₂₇⋊C₃	—	2	3	no	—
319	C₂₇⋊C₃	—	2	1	no	—
320	C₂₇⋊C₃	—	2	1	no	—
321	C₂₇⋊C₃	—	2	2	no	—
322	C₂₇⋊C₃	—	2	6	no	—
323	C₂₇⋊C₃	—	2	3	no	—
324	C₂₇⋊C₃	—	2	3	no	—
325	C₂₇⋊C₃	—	2	2	no	—
326	C₂₇⋊C₃	—	2	2	no	—
327	C₂₇⋊C₃	—	2	4	no	—
328	C₂₇⋊C₃	—	6	4	no	—
329	C₂₇⋊C₃	—	6	2	no	—
330	C₂₇⋊C₃	—	6	2	no	—
331	C₂₇⋊C₃	—	6	4	no	—
332	C₂₇⋊C₃	—	6	2	no	—
333	C₂₇⋊C₃	—	6	2	no	—
334	C₂₇⋊C₃	—	6	4	no	—
335	C₂₇⋊C₃	—	6	2	no	—
336	C₂₇⋊C₃	—	6	2	no	—
337	C₂₇⋊C₃	C₂×C₃×C₃⋊D₃	1	2	yes	—
338	C₂₇⋊C₃	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
339	C₃×C₂₇	—	2	6	no	—
340	C₃×C₂₇	—	2	3	no	—
341	C₃×C₂₇	—	2	3	no	—
342	C₃×C₂₇	—	3	4	no	—
343	C₃×C₂₇	—	3	2	no	—
344	C₃×C₂₇	—	3	2	no	—
345	C₃×C₂₇	—	6	4	no	—
346	C₃×C₂₇	—	6	2	no	—
347	C₃×C₂₇	—	6	2	no	—
348	C₃×C₂₇	C₂×D₃×C₉	1	6	yes	complemented
349	C₃×C₂₇	C₂×D₃×C₉	1	3	yes	complemented
350	C₃×C₂₇	C₂×D₃×C₉	1	3	yes	complemented
351	C₉⋊C₉	—	2	1	no	—
352	C₉⋊C₉	—	2	2	no	—
353	C₉⋊C₉	—	2	1	no	—
354	C₉⋊C₉	—	6	1	no	—
355	C₉⋊C₉	—	6	2	no	—
356	C₉⋊C₉	—	6	1	no	—
357	C₉⋊C₉	—	6	2	no	—
358	C₉⋊C₉	—	6	1	no	—
359	C₉⋊C₉	—	6	1	no	—
360	C₉⋊C₉	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
361	C₃²⋊C₉	—	6	2	no	—
362	C₃²⋊C₉	—	6	1	no	—
363	C₃²⋊C₉	—	6	1	no	—
364	C₉²	—	6	2	no	—
365	C₉²	—	6	1	no	—
366	C₉²	—	6	1	no	—
367	C₂×C₃³	D₃×3₋¹⁺²	1	2	yes	—
368	C₂×C₃³	D₃×3₋¹⁺²	1	1	yes	characteristic
369	C₂×C₃³	D₃×3₋¹⁺²	1	1	yes	characteristic
370	C₃²×D₃	—	3	4	no	—
371	C₃²×D₃	—	3	2	no	—
372	C₃²×D₃	—	3	2	no	—
373	C₂×3₋¹⁺²	—	2	4	no	—
374	C₂×3₋¹⁺²	—	2	4	no	—
375	C₂×3₋¹⁺²	—	2	4	no	—
376	C₂×3₋¹⁺²	—	2	4	no	—
377	C₂×3₋¹⁺²	—	2	4	no	—
378	C₂×3₋¹⁺²	—	2	2	no	—
379	C₂×3₋¹⁺²	—	2	2	no	—
380	C₂×3₋¹⁺²	—	2	2	no	—
381	C₂×3₋¹⁺²	—	2	1	no	—
382	C₂×3₋¹⁺²	—	2	1	no	—
383	C₂×3₋¹⁺²	—	2	4	no	—
384	C₂×3₋¹⁺²	—	2	2	no	—
385	C₂×3₋¹⁺²	—	2	2	no	—
386	C₂×H(3,𝔽₃)	—	2	2	no	—
387	C₂×H(3,𝔽₃)	—	2	1	no	—
388	C₂×H(3,𝔽₃)	—	2	1	no	—
389	C₂×H(3,𝔽₃)	C₂×C₉⋊C₉	1	1	yes	characteristic
390	C₂×C₃×C₉	—	2	2	no	—
391	C₂×C₃×C₉	—	2	1	no	—
392	C₂×C₃×C₉	—	2	1	no	—
393	C₂×C₃×C₉	—	2	2	no	—
394	C₂×C₃×C₉	—	2	1	no	—
395	C₂×C₃×C₉	—	2	1	no	—
396	C₂×C₃×C₉	—	2	4	no	—
397	C₂×C₃×C₉	—	2	2	no	—
398	C₂×C₃×C₉	—	2	2	no	—
399	C₂×C₃×C₉	—	3	1	no	—
400	C₂×C₃×C₉	—	6	1	no	—
401	C₂×C₃×C₉	—	6	2	no	—
402	C₂×C₃×C₉	—	6	1	no	—
403	C₂×C₃×C₉	—	9	2	no	—
404	C₂×C₃×C₉	—	27	1	no	—
405	C₂×C₃×C₉	—	27	2	no	—
406	C₂×C₃×C₉	—	54	2	no	—
407	C₂×C₃×C₉	—	54	1	no	—
408	C₂×C₃×C₉	C₃×D₃×C₉	1	2	yes	—
409	C₂×C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
410	C₂×C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
411	C₂×C₃×C₉	D₃×3₋¹⁺²	1	4	yes	—
412	C₂×C₃×C₉	D₃×3₋¹⁺²	1	2	yes	—
413	C₂×C₃×C₉	D₃×3₋¹⁺²	1	2	yes	—
414	C₂×C₃×C₉	C₃²×C₃⋊D₃	1	1	yes	characteristic
415	#272	C₂×C₉⋊C₉	1	2	yes	—
416	D₃×C₉	—	3	4	no	—
417	D₃×C₉	—	3	2	no	—
418	D₃×C₉	—	3	2	no	—
419	D₃×C₉	—	3	8	no	—
420	D₃×C₉	—	3	4	no	—
421	D₃×C₉	—	3	4	no	—
422	D₃×C₉	—	27	2	no	—
423	D₃×C₉	—	27	4	no	—
424	D₃×C₉	—	27	2	no	—
425	C₂×C₂₇	—	2	6	no	—
426	C₂×C₂₇	—	2	3	no	—
427	C₂×C₂₇	—	2	3	no	—
428	C₂×C₂₇	—	3	2	no	—
429	C₂×C₂₇	—	6	4	no	—
430	C₂×C₂₇	—	6	2	no	—
431	C₂×C₂₇	—	6	2	no	—
432	C₂×C₂₇	—	9	6	no	—
433	C₂×C₂₇	—	27	4	no	—
434	C₂×C₂₇	C₉×C₃⋊D₃	1	3	yes	—
435	C₂²×C₃²	—	9	1	no	—
436	C₂×C₃×D₃	—	3	2	no	—
437	C₂×C₃×D₃	—	3	1	no	—
438	C₂×C₃×D₃	—	3	1	no	—
439	C₂×C₃×D₃	—	9	2	no	—
440	C₂×C₃×D₃	—	9	1	no	—
441	C₂×C₃×D₃	—	9	1	no	—
442	C₂²×C₉	—	9	1	no	—
443	C₂²×C₉	—	9	2	no	—
444	C₂²×C₉	—	81	1	no	—
445	C₃³	C₂×D₃×3₋¹⁺²	1	2	yes	—
446	C₃³	C₂×D₃×3₋¹⁺²	1	1	yes	characteristic
447	C₃³	C₂×D₃×3₋¹⁺²	1	1	yes	characteristic
448	3₋¹⁺²	—	2	4	no	—
449	3₋¹⁺²	—	2	4	no	—
450	3₋¹⁺²	—	2	4	no	—
451	3₋¹⁺²	—	2	4	no	—
452	3₋¹⁺²	—	2	4	no	—
453	3₋¹⁺²	—	2	2	no	—
454	3₋¹⁺²	—	2	2	no	—
455	3₋¹⁺²	—	2	2	no	—
456	3₋¹⁺²	—	2	1	no	—
457	3₋¹⁺²	—	2	1	no	—
458	3₋¹⁺²	—	2	4	no	—
459	3₋¹⁺²	—	2	2	no	—
460	3₋¹⁺²	—	2	2	no	—
461	H(3,𝔽₃)	—	2	2	no	—
462	H(3,𝔽₃)	—	2	1	no	—
463	H(3,𝔽₃)	—	2	1	no	—
464	H(3,𝔽₃)	C₂²×C₉⋊C₉	1	1	yes	characteristic
465	C₃×C₉	—	2	2	no	—
466	C₃×C₉	—	2	1	no	—
467	C₃×C₉	—	2	1	no	—
468	C₃×C₉	—	2	2	no	—
469	C₃×C₉	—	2	1	no	—
470	C₃×C₉	—	2	1	no	—
471	C₃×C₉	—	2	4	no	—
472	C₃×C₉	—	2	2	no	—
473	C₃×C₉	—	2	2	no	—
474	C₃×C₉	—	3	1	no	—
475	C₃×C₉	—	6	1	no	—
476	C₃×C₉	—	6	2	no	—
477	C₃×C₉	—	6	1	no	—
478	C₃×C₉	—	27	1	no	—
479	C₃×C₉	—	54	2	no	—
480	C₃×C₉	—	54	1	no	—
481	C₃×C₉	C₂×C₃×D₃×C₉	1	2	yes	—
482	C₃×C₉	C₂×C₃×D₃×C₉	1	1	yes	characteristic
483	C₃×C₉	C₂×C₃×D₃×C₉	1	1	yes	characteristic
484	C₃×C₉	C₂×D₃×3₋¹⁺²	1	4	yes	—
485	C₃×C₉	C₂×D₃×3₋¹⁺²	1	2	yes	—
486	C₃×C₉	C₂×D₃×3₋¹⁺²	1	2	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	—	3	2	no	—
492	C₂₇	—	6	4	no	—
493	C₂₇	—	6	2	no	—
494	C₂₇	—	6	2	no	—
495	C₂₇	C₂×C₉×C₃⋊D₃	1	3	yes	—
496	C₂×C₃²	—	2	2	no	—
497	C₂×C₃²	—	2	1	no	—
498	C₂×C₃²	—	2	1	no	—
499	C₂×C₃²	—	9	2	no	—
500	C₂×C₃²	—	9	2	no	—
501	C₂×C₃²	—	18	1	no	—
502	C₂×C₃²	—	18	1	no	—
503	C₂×C₃²	D₃×C₉⋊C₉	1	2	yes	—
504	C₂×C₃²	D₃×C₉⋊C₉	1	1	yes	characteristic
505	C₂×C₃²	D₃×C₉⋊C₉	1	1	yes	characteristic
506	C₂×C₃²	C₃⋊D₃×3₋¹⁺²	1	1	yes	characteristic
507	C₃×D₃	—	3	4	no	—
508	C₃×D₃	—	3	2	no	—
509	C₃×D₃	—	3	2	no	—
510	C₃×D₃	—	9	4	no	—
511	C₃×D₃	—	9	2	no	—
512	C₃×D₃	—	9	2	no	—
513	C₂×C₉	—	2	2	no	—
514	C₂×C₉	—	2	1	no	—
515	C₂×C₉	—	2	1	no	—
516	C₂×C₉	—	2	4	no	—
517	C₂×C₉	—	2	2	no	—
518	C₂×C₉	—	2	2	no	—
519	C₂×C₉	—	9	1	no	—
520	C₂×C₉	—	9	2	no	—
521	C₂×C₉	—	9	4	no	—
522	C₂×C₉	—	18	1	no	—
523	C₂×C₉	—	18	2	no	—
524	C₂×C₉	—	18	1	no	—
525	C₂×C₉	—	81	2	no	—
526	C₂×C₉	C₃×C₉×C₃⋊D₃	1	1	yes	characteristic
527	C₂×C₉	C₃⋊D₃×3₋¹⁺²	1	2	yes	—
528	C₂²×C₃	—	9	1	no	—
529	C₂²×C₃	—	27	1	no	—
530	C₂×D₃	—	3	2	no	—
531	C₂×D₃	—	3	1	no	—
532	C₂×D₃	—	3	1	no	—
533	C₃²	—	2	2	no	—
534	C₃²	—	2	1	no	—
535	C₃²	—	2	1	no	—
536	C₃²	—	9	2	no	—
537	C₃²	—	18	1	no	—
538	C₃²	—	18	1	no	—
539	C₃²	C₂×D₃×C₉⋊C₉	1	2	yes	—
540	C₃²	C₂×D₃×C₉⋊C₉	1	1	yes	characteristic
541	C₃²	C₂×D₃×C₉⋊C₉	1	1	yes	characteristic
542	C₃²	C₂×C₃⋊D₃×3₋¹⁺²	1	1	yes	characteristic
543	C₉	—	2	2	no	—
544	C₉	—	2	1	no	—
545	C₉	—	2	1	no	—
546	C₉	—	2	4	no	—
547	C₉	—	2	2	no	—
548	C₉	—	2	2	no	—
549	C₉	—	9	1	no	—
550	C₉	—	18	1	no	—
551	C₉	—	18	2	no	—
552	C₉	—	18	1	no	—
553	C₉	C₂×C₃×C₉×C₃⋊D₃	1	1	yes	characteristic
554	C₉	C₂×C₃⋊D₃×3₋¹⁺²	1	2	yes	—
555	C₂×C₃	—	3	2	no	—
556	C₂×C₃	—	3	1	no	—
557	C₂×C₃	—	6	1	no	—
558	C₂×C₃	—	6	1	no	—
559	C₂×C₃	—	6	2	no	—
560	C₂×C₃	—	6	1	no	—
561	C₂×C₃	—	6	1	no	—
562	C₂×C₃	—	9	2	no	—
563	C₂×C₃	—	27	2	no	—
564	C₂×C₃	C₃⋊D₃×C₉⋊C₉	1	1	yes	characteristic
565	D₃	—	3	4	no	—
566	D₃	—	3	2	no	—
567	D₃	—	3	2	no	—
568	C₂²	—	9	1	no	Sylow
569	C₃	—	3	2	no	—
570	C₃	—	3	1	no	—
571	C₃	—	6	1	no	—
572	C₃	—	6	1	no	—
573	C₃	—	6	2	no	—
574	C₃	—	6	1	no	—
575	C₃	—	6	1	no	—
576	C₃	C₂×C₃⋊D₃×C₉⋊C₉	1	1	yes	characteristic
577	C₂	—	9	2	no	—
578	C₂	#72221831	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, socle	C₂×C₃	C₃⋊D₃×C₉⋊C₉
commutator	#737	C₂²×C₃×C₉
Frattini	C₃×C₉	C₂×C₃²×C₃⋊D₃
Fitting	C₂×#14554150	C₂
prime radical	C₂×C₃×#272	3₋¹⁺²
cosocle	C₃×#737	C₂²×C₃²
hypercenter	C₂×#6875	C₃⋊D₃
hypocenter	H(3,𝔽₃)	C₂²×C₉⋊C₉
LCS	G ▷ #737 ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₉ ◁ C₂×#6875

Complements

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

N	H ≅ G/N	type
4. C₂×#14554150	C₂	semidirect
8. #72221831	C₂	direct (N × H)
9. #14554150	C₂²	semidirect
28. C₂×C₃×#6875	D₃	semidirect
29. C₂×C₃×#6875	D₃	semidirect
30. C₂×C₃×#6875	D₃	semidirect
33. C₂×#92319	C₉	semidirect
57. C₃×#6875	C₂×D₃	semidirect
58. C₃×#6875	C₂×D₃	semidirect
59. C₃×#6875	C₂×D₃	semidirect
69. C₂×#6903	C₂×C₉	semidirect
93. #92319	C₂×C₉	semidirect
148. #6903	C₂²×C₉	semidirect
252. C₂×C₃×C₂₇	D₃×C₉	semidirect
253. C₂×C₃×C₂₇	D₃×C₉	semidirect
254. C₂×C₃×C₂₇	D₃×C₉	semidirect
348. C₃×C₂₇	C₂×D₃×C₉	semidirect
349. C₃×C₂₇	C₂×D₃×C₉	semidirect
350. C₃×C₂₇	C₂×D₃×C₉	semidirect
578. C₂	#72221831	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×#13091386	3
C₂×#13091566	3
C₂×#14554150	2
C₂×D₃×#6875	3
#72221831	2

Subgroups — C2×#72221831 #72244050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72221831 #72244050