Subgroups — #41007646

Order 26973.

1058 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688532	C₃	1	2	yes	maximal, complemented
2	C₃×#15688531	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×3₋¹⁺²×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	#22582563	C₃	1	2	yes	maximal, complemented
5	#22582563	C₃	1	2	yes	maximal, complemented
6	#22582563	C₃	1	2	yes	maximal, complemented
7	#22582561	C₃	1	2	yes	maximal, complemented
8	#22582560	C₃	1	2	yes	maximal, complemented
9	#22582559	C₃	1	1	yes	maximal, characteristic, complemented
10	#22582558	C₃	1	1	yes	maximal, characteristic, complemented
11	#22582557	C₃	1	2	yes	maximal, complemented
12	#22582557	C₃	1	2	yes	maximal, complemented
13	#22582557	C₃	1	2	yes	maximal, complemented
14	#22582557	C₃	1	2	yes	maximal, complemented
15	#22582557	C₃	1	2	yes	maximal, complemented
16	#22582557	C₃	1	2	yes	maximal, complemented
17	#22582556	C₃	1	2	yes	maximal, complemented
18	#22582555	C₃	1	2	yes	maximal, complemented
19	#22582555	C₃	1	2	yes	maximal, complemented
20	#22582555	C₃	1	2	yes	maximal, complemented
21	#22582553	C₃	1	1	yes	maximal, characteristic, complemented
22	#22582552	C₃	1	1	yes	maximal, characteristic, complemented
23	(C₃×C₃₇⋊C₃)⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
24	C₃₇×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
25	C₃³×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
26	#15688532	—	3	18	no	—
27	#15688531	—	3	9	no	—
28	C₃×#11758608	C₃²	1	2	yes	—
29	C₃×#11758608	C₃²	1	2	yes	complemented
30	C₃×#11758608	C₃²	1	2	yes	complemented
31	C₃×#11758605	C₃²	1	1	yes	characteristic
32	C₃×#11758605	C₃²	1	2	yes	—
33	C₃×#11758605	C₃²	1	1	yes	characteristic
34	C₃×#11758605	C₃²	1	2	yes	—
35	C₃×#11758605	C₃²	1	2	yes	complemented
36	C₃×#11758605	C₃²	1	2	yes	complemented
37	C₃×#11758605	C₃²	1	2	yes	complemented
38	C₃×#11758606	C₃²	1	1	yes	characteristic
39	C₃×#11758606	C₃²	1	2	yes	—
40	C₃×#11758606	C₃²	1	1	yes	characteristic
41	C₃×#11758606	C₃²	1	2	yes	—
42	C₃×#11758606	C₃²	1	2	yes	complemented
43	C₃×#11758606	C₃²	1	2	yes	complemented
44	C₃×#11758606	C₃²	1	2	yes	complemented
45	3₋¹⁺²×C₃₇⋊C₃	—	3	9	no	—
46	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	1	yes	characteristic
47	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	2	yes	—
48	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	2	yes	—
49	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	2	yes	—
50	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	2	yes	—
51	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	1	yes	characteristic
52	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	1	yes	characteristic
53	C₃²×#66524	C₃²	1	2	yes	complemented
54	C₃×C₉×C₃₇⋊C₃	C₃²	1	2	yes	—
55	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
56	C₃×C₉×C₃₇⋊C₃	C₃²	1	2	yes	complemented
57	C₃×C₉×C₃₇⋊C₃	C₃²	1	2	yes	complemented
58	C₃×C₉×C₃₇⋊C₃	C₃²	1	2	yes	complemented
59	C₃²⋊#66524	C₃²	1	2	yes	—
60	C₃²⋊#66524	C₃²	1	2	yes	—
61	C₃²⋊#66524	C₃²	1	2	yes	complemented
62	C₃²⋊#66524	C₃²	1	2	yes	complemented
63	C₃²⋊#66524	C₃²	1	2	yes	complemented
64	C₃²⋊#66524	C₃²	1	2	yes	complemented
65	C₃²⋊#66524	C₃²	1	2	yes	complemented
66	C₃²⋊#66524	C₃²	1	2	yes	complemented
67	#15688502	C₃²	1	2	yes	—
68	#15688502	C₃²	1	2	yes	—
69	#15688502	C₃²	1	1	yes	characteristic
70	#15688502	C₃²	1	1	yes	characteristic
71	#15688502	C₃²	1	2	yes	—
72	#15688502	C₃²	1	2	yes	—
73	#15688502	C₃²	1	1	yes	characteristic
74	#15688502	C₃²	1	1	yes	characteristic
75	#15688502	C₃²	1	2	yes	complemented
76	#15688502	C₃²	1	2	yes	complemented
77	#15688502	C₃²	1	2	yes	complemented
78	#15688502	C₃²	1	2	yes	complemented
79	#15688502	C₃²	1	2	yes	complemented
80	#15688502	C₃²	1	2	yes	complemented
81	#15688502	C₃²	1	2	yes	complemented
82	#15688502	C₃²	1	2	yes	complemented
83	#15688502	C₃²	1	2	yes	complemented
84	#15688502	C₃²	1	2	yes	complemented
85	#15688502	C₃²	1	2	yes	complemented
86	#15688502	C₃²	1	2	yes	complemented
87	#15688502	C₃²	1	2	yes	complemented
88	#15688502	C₃²	1	2	yes	complemented
89	#15688502	C₃²	1	2	yes	complemented
90	#15688502	C₃²	1	2	yes	complemented
91	#15688502	C₃²	1	2	yes	complemented
92	#15688502	C₃²	1	2	yes	complemented
93	C₃×3₋¹⁺²×C₃₇	C₃²	1	1	yes	characteristic
94	C₃×3₋¹⁺²×C₃₇	C₃²	1	2	yes	complemented
95	C₃×H(3,𝔽₃)×C₃₇	C₃²	1	1	yes	characteristic
96	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic, complemented
97	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
98	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
99	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	complemented
100	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	complemented
101	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	complemented
102	C₃³×C₃₇	C₃³	1	1	yes	characteristic
103	C₃³×C₃₇	C₃³	1	1	yes	characteristic
104	C₃³×C₃₇	C₃³	1	2	yes	—
105	C₃²×C₃₇⋊C₃	—	3	3	no	—
106	C₃²×C₃₇⋊C₃	—	9	1	no	—
107	C₃²×C₃₇⋊C₃	—	9	1	no	—
108	C₃²×C₃₇⋊C₃	—	9	1	no	—
109	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
110	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
111	C₃²×C₃₇⋊C₃	C₃³	1	2	yes	—
112	C₃²×C₃₇⋊C₃	C₃³	1	2	yes	—
113	C₃²×C₃₇⋊C₃	C₃³	1	2	yes	—
114	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
115	3₋¹⁺²×C₃₇	—	3	3	no	—
116	3₋¹⁺²×C₃₇	—	3	6	no	—
117	H(3,𝔽₃)×C₃₇	—	9	1	no	—
118	C₃×C₉×C₃₇	—	3	3	no	—
119	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
120	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
121	C₃×C₉×C₃₇	C₃³	1	2	yes	—
122	C₃×C₉×C₃₇	C₃³	1	2	yes	—
123	C₃×C₉×C₃₇	C₃³	1	2	yes	—
124	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
125	C₃²⋊(C₃₇⋊C₃)	—	3	3	no	—
126	C₃²⋊(C₃₇⋊C₃)	—	3	6	no	—
127	C₃²⋊(C₃₇⋊C₃)	—	9	2	no	—
128	C₃²⋊(C₃₇⋊C₃)	—	9	2	no	—
129	C₃²⋊(C₃₇⋊C₃)	—	9	1	no	—
130	C₃²⋊(C₃₇⋊C₃)	—	9	1	no	—
131	C₃²⋊(C₃₇⋊C₃)	—	9	2	no	—
132	#11758608	—	3	6	no	—
133	#11758608	—	3	6	no	—
134	#11758608	—	3	6	no	—
135	C₃×#66524	—	3	6	no	—
136	C₃×#66524	C₃³	1	2	yes	—
137	C₃×#66524	C₃³	1	2	yes	—
138	C₃×#66524	C₃³	1	2	yes	—
139	C₃×#66524	C₃³	1	2	yes	—
140	C₃×#66524	C₃³	1	2	yes	—
141	C₃×#66524	C₃³	1	2	yes	—
142	C₃×#66524	C₃³	1	2	yes	—
143	C₃×#66524	C₃³	1	2	yes	—
144	C₃×#66524	C₃³	1	2	yes	—
145	#11758606	—	3	3	no	—
146	#11758606	—	3	6	no	—
147	#11758606	—	3	3	no	—
148	#11758606	—	3	6	no	—
149	#11758606	—	3	6	no	—
150	#11758606	—	3	6	no	—
151	#11758606	—	3	6	no	—
152	#11758605	—	3	3	no	—
153	#11758605	—	3	6	no	—
154	#11758605	—	3	3	no	—
155	#11758605	—	3	6	no	—
156	#11758605	—	3	6	no	—
157	#11758605	—	3	6	no	—
158	#11758605	—	3	6	no	—
159	C₉×C₃₇⋊C₃	—	3	6	no	—
160	C₉×C₃₇⋊C₃	—	3	6	no	—
161	C₉×C₃₇⋊C₃	—	3	6	no	—
162	C₉×C₃₇⋊C₃	—	3	6	no	—
163	C₉×C₃₇⋊C₃	H(3,𝔽₃)	1	9	yes	complemented
164	#10624882	—	37	1	no	maximal, Sylow
165	C₃²×C₃₇	—	3	2	no	—
166	C₃²×C₃₇	—	3	1	no	—
167	C₃²×C₃₇	—	3	1	no	—
168	C₃²×C₃₇	—	3	1	no	—
169	C₃²×C₃₇	—	3	1	no	—
170	C₃²×C₃₇	—	3	2	no	—
171	C₃²×C₃₇	—	3	1	no	—
172	C₃²×C₃₇	—	3	2	no	—
173	C₃²×C₃₇	—	3	1	no	—
174	C₃²×C₃₇	—	3	2	no	—
175	C₃²×C₃₇	—	3	1	no	—
176	C₃²×C₃₇	—	3	1	no	—
177	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
178	C₃×C₃₇⋊C₃	—	3	1	no	—
179	C₃×C₃₇⋊C₃	—	3	1	no	—
180	C₃×C₃₇⋊C₃	—	3	1	no	—
181	C₃×C₃₇⋊C₃	—	3	2	no	—
182	C₃×C₃₇⋊C₃	—	3	2	no	—
183	C₃×C₃₇⋊C₃	—	3	2	no	—
184	C₃×C₃₇⋊C₃	—	3	1	no	—
185	C₃×C₃₇⋊C₃	—	3	1	no	—
186	C₃×C₃₇⋊C₃	—	3	1	no	—
187	C₃×C₃₇⋊C₃	—	3	1	no	—
188	C₃×C₃₇⋊C₃	—	3	2	no	—
189	C₃×C₃₇⋊C₃	—	3	2	no	—
190	C₃×C₃₇⋊C₃	—	3	2	no	—
191	C₃×C₃₇⋊C₃	—	3	2	no	—
192	C₃×C₃₇⋊C₃	—	3	2	no	—
193	C₃×C₃₇⋊C₃	—	3	2	no	—
194	C₃×C₃₇⋊C₃	—	3	2	no	—
195	C₃×C₃₇⋊C₃	—	3	2	no	—
196	C₃×C₃₇⋊C₃	—	3	2	no	—
197	C₃×C₃₇⋊C₃	—	3	1	no	—
198	C₃×C₃₇⋊C₃	—	3	1	no	—
199	C₃×C₃₇⋊C₃	—	3	1	no	—
200	C₃×C₃₇⋊C₃	—	3	1	no	—
201	C₃×C₃₇⋊C₃	—	9	9	no	—
202	C₃×C₃₇⋊C₃	C₃×H(3,𝔽₃)	1	3	yes	—
203	C₉×C₃₇	—	3	2	no	—
204	C₉×C₃₇	—	3	2	no	—
205	C₉×C₃₇	—	3	2	no	—
206	C₉×C₃₇	—	3	1	no	—
207	C₉×C₃₇	—	3	1	no	—
208	C₉×C₃₇	C₃×H(3,𝔽₃)	1	3	yes	—
209	#66524	—	3	2	no	—
210	#66524	—	3	2	no	—
211	#66524	—	3	2	no	—
212	#66524	—	3	2	no	—
213	#66524	—	3	2	no	—
214	#66524	—	3	2	no	—
215	#66524	—	3	2	no	—
216	#66524	—	3	2	no	—
217	#66524	C₃×H(3,𝔽₃)	1	6	yes	—
218	C₃×#737	—	37	2	no	—
219	C₃×#737	—	37	1	no	—
220	C₃²×3₋¹⁺²	—	37	1	no	—
221	#6893	—	37	2	no	—
222	#6893	—	37	2	no	—
223	#6893	—	37	2	no	—
224	C₉⋊H(3,𝔽₃)	—	37	2	no	—
225	C₉⋊H(3,𝔽₃)	—	37	2	no	—
226	C₉⋊H(3,𝔽₃)	—	37	2	no	—
227	C₉⋊H(3,𝔽₃)	—	37	2	no	—
228	C₉⋊H(3,𝔽₃)	—	37	1	no	—
229	C₉⋊H(3,𝔽₃)	—	37	1	no	—
230	C₉⋊H(3,𝔽₃)	—	37	2	no	—
231	C₉⋊H(3,𝔽₃)	—	37	2	no	—
232	C₉⋊H(3,𝔽₃)	—	37	2	no	—
233	C₉⋊H(3,𝔽₃)	—	37	2	no	—
234	C₉⋊H(3,𝔽₃)	—	37	2	no	—
235	C₉⋊H(3,𝔽₃)	—	37	2	no	—
236	C₉⋊H(3,𝔽₃)	—	37	2	no	—
237	C₉⋊H(3,𝔽₃)	—	37	2	no	—
238	C₉⋊H(3,𝔽₃)	C₃₇⋊C₃	1	1	yes	characteristic, complemented
239	#6891	—	37	1	no	—
240	#6891	—	37	1	no	—
241	C₃²⋊H(3,𝔽₃)	—	37	1	no	—
242	C₃×C₃₇	—	9	1	no	—
243	C₃×C₃₇	—	9	2	no	—
244	C₃×C₃₇	—	9	1	no	—
245	C₃×C₃₇	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
246	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
247	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
248	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
249	C₃₇⋊C₃	—	3	3	no	—
250	C₃₇⋊C₃	—	9	2	no	—
251	C₃₇⋊C₃	—	9	2	no	—
252	C₃₇⋊C₃	—	9	2	no	—
253	C₃₇⋊C₃	—	9	1	no	—
254	C₃₇⋊C₃	—	9	1	no	—
255	C₃⁴	—	37	1	no	—
256	#737	—	111	9	no	—
257	#737	—	111	18	no	—
258	C₃×3₋¹⁺²	—	37	2	no	—
259	C₃×3₋¹⁺²	—	37	2	no	—
260	C₃×3₋¹⁺²	—	37	2	no	—
261	C₃×3₋¹⁺²	—	37	2	no	—
262	C₃×3₋¹⁺²	—	37	1	no	—
263	C₃×3₋¹⁺²	—	37	2	no	—
264	C₃×3₋¹⁺²	—	37	1	no	—
265	C₃×3₋¹⁺²	—	37	2	no	—
266	C₃×3₋¹⁺²	—	37	1	no	—
267	C₃×3₋¹⁺²	—	37	2	no	—
268	C₃×3₋¹⁺²	—	37	2	no	—
269	C₃×3₋¹⁺²	—	37	2	no	—
270	C₃×3₋¹⁺²	—	37	2	no	—
271	C₃×3₋¹⁺²	—	37	1	no	—
272	C₃×3₋¹⁺²	—	37	2	no	—
273	C₃×3₋¹⁺²	—	37	2	no	—
274	C₃×3₋¹⁺²	—	37	2	no	—
275	C₃×3₋¹⁺²	—	111	9	no	—
276	C₃×3₋¹⁺²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
277	C₃×3₋¹⁺²	C₃×C₃₇⋊C₃	1	2	yes	complemented
278	C₃×H(3,𝔽₃)	—	37	2	no	—
279	C₃×H(3,𝔽₃)	—	37	2	no	—
280	C₃×H(3,𝔽₃)	—	37	2	no	—
281	C₃×H(3,𝔽₃)	—	37	1	no	—
282	C₃×H(3,𝔽₃)	—	37	1	no	—
283	C₃×H(3,𝔽₃)	—	37	2	no	—
284	C₃×H(3,𝔽₃)	—	37	1	no	—
285	C₃×H(3,𝔽₃)	C₃×C₃₇⋊C₃	1	1	yes	characteristic
286	C₃²×C₉	—	37	1	no	—
287	C₃²×C₉	—	37	2	no	—
288	C₃²×C₉	—	37	2	no	—
289	C₃²×C₉	—	37	2	no	—
290	C₃²×C₉	—	37	2	no	—
291	C₃²×C₉	—	37	2	no	—
292	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented
293	C₃²⋊C₉	—	37	2	no	—
294	C₃²⋊C₉	—	37	2	no	—
295	C₃²⋊C₉	—	37	2	no	—
296	C₃²⋊C₉	—	37	2	no	—
297	C₃²⋊C₉	—	37	2	no	—
298	C₃²⋊C₉	—	37	2	no	—
299	C₃²⋊C₉	—	37	2	no	—
300	C₃²⋊C₉	—	37	2	no	—
301	C₃²⋊C₉	—	37	2	no	—
302	C₃²⋊C₉	—	37	2	no	—
303	C₃²⋊C₉	—	37	2	no	—
304	C₃²⋊C₉	—	37	2	no	—
305	C₃²⋊C₉	—	37	1	no	—
306	C₃²⋊C₉	—	37	1	no	—
307	C₃²⋊C₉	—	37	1	no	—
308	C₃²⋊C₉	—	37	1	no	—
309	C₃²⋊C₉	—	37	2	no	—
310	C₃²⋊C₉	—	37	2	no	—
311	C₃²⋊C₉	—	37	2	no	—
312	C₃²⋊C₉	—	37	2	no	—
313	C₃²⋊C₉	—	37	2	no	—
314	C₃²⋊C₉	—	37	2	no	—
315	C₃²⋊C₉	—	37	2	no	—
316	C₃²⋊C₉	—	37	2	no	—
317	C₃²⋊C₉	—	37	2	no	—
318	C₃²⋊C₉	—	37	2	no	—
319	C₃²⋊C₉	—	37	2	no	—
320	C₃²⋊C₉	—	37	2	no	—
321	C₃²⋊C₉	—	37	2	no	—
322	C₃²⋊C₉	—	37	2	no	—
323	C₃²⋊C₉	—	37	2	no	—
324	C₃²⋊C₉	—	37	2	no	—
325	C₃²⋊C₉	—	37	2	no	—
326	C₃²⋊C₉	—	37	2	no	—
327	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
328	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
329	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	2	yes	complemented
330	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	2	yes	complemented
331	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	2	yes	complemented
332	C₃₇	#10624882	1	1	yes	characteristic, complemented, Sylow
333	C₃³	—	37	1	no	—
334	C₃³	—	37	2	no	—
335	C₃³	—	37	2	no	—
336	C₃³	—	37	2	no	—
337	C₃³	—	37	1	no	—
338	C₃³	—	37	1	no	—
339	C₃³	—	333	1	no	—
340	C₃³	—	333	1	no	—
341	C₃³	—	333	1	no	—
342	C₃³	—	111	3	no	—
343	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
344	C₃³	C₃²×C₃₇⋊C₃	1	2	yes	—
345	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
346	3₋¹⁺²	—	3	3	no	—
347	3₋¹⁺²	—	3	6	no	—
348	3₋¹⁺²	—	111	6	no	—
349	3₋¹⁺²	—	111	6	no	—
350	3₋¹⁺²	—	111	6	no	—
351	3₋¹⁺²	—	111	6	no	—
352	3₋¹⁺²	—	111	6	no	—
353	3₋¹⁺²	—	111	6	no	—
354	3₋¹⁺²	—	111	3	no	—
355	3₋¹⁺²	—	111	6	no	—
356	3₋¹⁺²	—	111	3	no	—
357	3₋¹⁺²	—	111	6	no	—
358	3₋¹⁺²	—	111	6	no	—
359	3₋¹⁺²	—	111	6	no	—
360	3₋¹⁺²	—	111	6	no	—
361	3₋¹⁺²	—	111	3	no	—
362	3₋¹⁺²	—	111	6	no	—
363	3₋¹⁺²	—	111	3	no	—
364	3₋¹⁺²	—	111	6	no	—
365	H(3,𝔽₃)	—	9	1	no	—
366	H(3,𝔽₃)	—	333	2	no	—
367	H(3,𝔽₃)	—	333	1	no	—
368	H(3,𝔽₃)	—	333	2	no	—
369	H(3,𝔽₃)	—	333	1	no	—
370	H(3,𝔽₃)	—	333	2	no	—
371	H(3,𝔽₃)	—	111	3	no	—
372	H(3,𝔽₃)	—	111	6	no	—
373	C₃×C₉	—	3	3	no	—
374	C₃×C₉	—	37	2	no	—
375	C₃×C₉	—	37	9	no	—
376	C₃×C₉	—	37	2	no	—
377	C₃×C₉	—	37	2	no	—
378	C₃×C₉	—	37	2	no	—
379	C₃×C₉	—	37	2	no	—
380	C₃×C₉	—	37	2	no	—
381	C₃×C₉	—	37	2	no	—
382	C₃×C₉	—	37	2	no	—
383	C₃×C₉	—	37	2	no	—
384	C₃×C₉	—	111	6	no	—
385	C₃×C₉	—	111	6	no	—
386	C₃×C₉	—	111	6	no	—
387	C₃×C₉	—	111	6	no	—
388	C₃×C₉	—	111	6	no	—
389	C₃×C₉	C₃²×C₃₇⋊C₃	1	2	yes	—
390	C₃×C₉	C₃²×C₃₇⋊C₃	1	2	yes	—
391	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
392	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
393	C₃×C₉	C₃²×C₃₇⋊C₃	1	2	yes	—
394	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
395	C₃²	—	3	1	no	—
396	C₃²	—	3	2	no	—
397	C₃²	—	3	1	no	—
398	C₃²	—	3	2	no	—
399	C₃²	—	3	1	no	—
400	C₃²	—	3	1	no	—
401	C₃²	—	3	2	no	—
402	C₃²	—	3	1	no	—
403	C₃²	—	3	1	no	—
404	C₃²	—	3	1	no	—
405	C₃²	—	3	2	no	—
406	C₃²	—	3	1	no	—
407	C₃²	—	37	3	no	—
408	C₃²	—	333	9	no	—
409	C₃²	—	111	2	no	—
410	C₃²	—	111	2	no	—
411	C₃²	—	111	2	no	—
412	C₃²	—	111	1	no	—
413	C₃²	—	111	1	no	—
414	C₃²	—	111	1	no	—
415	C₃²	—	111	2	no	—
416	C₃²	—	111	2	no	—
417	C₃²	—	111	2	no	—
418	C₃²	—	111	1	no	—
419	C₃²	—	111	1	no	—
420	C₃²	—	111	2	no	—
421	C₃²	—	111	2	no	—
422	C₃²	—	111	2	no	—
423	C₃²	—	111	1	no	—
424	C₃²	—	111	2	no	—
425	C₃²	—	111	2	no	—
426	C₃²	—	111	2	no	—
427	C₃²	—	111	1	no	—
428	C₃²	—	111	1	no	—
429	C₃²	—	111	1	no	—
430	C₃²	—	111	1	no	—
431	C₃²	—	111	1	no	—
432	C₃²	C₃³×C₃₇⋊C₃	1	1	yes	characteristic
433	C₉	—	3	1	no	—
434	C₉	—	3	1	no	—
435	C₉	—	3	2	no	—
436	C₉	—	3	2	no	—
437	C₉	—	3	2	no	—
438	C₉	—	37	6	no	—
439	C₉	—	111	2	no	—
440	C₉	—	111	2	no	—
441	C₉	—	111	2	no	—
442	C₉	—	111	2	no	—
443	C₉	—	111	2	no	—
444	C₉	—	111	2	no	—
445	C₉	—	111	2	no	—
446	C₉	—	111	2	no	—
447	C₉	H(3,𝔽₃)×C₃₇⋊C₃	1	3	yes	—
448	C₃	—	9	1	no	—
449	C₃	—	9	1	no	—
450	C₃	—	9	2	no	—
451	C₃	—	333	1	no	—
452	C₃	—	333	1	no	—
453	C₃	—	333	2	no	—
454	C₃	—	333	2	no	—
455	C₃	—	333	2	no	—
456	C₃	—	111	3	no	—
457	C₃	C₃×H(3,𝔽₃)×C₃₇⋊C₃	1	1	yes	characteristic
458	C₃	#22582677	1	1	yes	characteristic
459	C₃	#22582678	1	1	yes	characteristic
460	C₃	#22582679	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₃₇⋊C₃
commutator, socle, cosocle	C₃²×C₃₇	C₃⁴
Fitting	C₃₇×C₉⋊H(3,𝔽₃)	C₃
prime radical	(C₃×C₃₇⋊C₃)⋊H(3,𝔽₃)	C₃
hypercenter	C₉⋊H(3,𝔽₃)	C₃₇⋊C₃
hypocenter	C₃₇	#10624882
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₉⋊H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃×#15688532	C₃	semidirect
2. C₃×#15688531	C₃	semidirect
3. C₃×3₋¹⁺²×C₃₇⋊C₃	C₃	semidirect
4. #22582563	C₃	semidirect
5. #22582563	C₃	semidirect
6. #22582563	C₃	semidirect
7. #22582561	C₃	semidirect
8. #22582560	C₃	semidirect
9. #22582559	C₃	semidirect
10. #22582558	C₃	semidirect
11. #22582557	C₃	semidirect
12. #22582557	C₃	semidirect
13. #22582557	C₃	semidirect
14. #22582557	C₃	semidirect
15. #22582557	C₃	semidirect
16. #22582557	C₃	semidirect
17. #22582556	C₃	semidirect
18. #22582555	C₃	semidirect
19. #22582555	C₃	semidirect
20. #22582555	C₃	semidirect
21. #22582553	C₃	semidirect
22. #22582552	C₃	semidirect
24. C₃₇×C₉⋊H(3,𝔽₃)	C₃	semidirect
29. C₃×#11758608	C₃²	semidirect
30. C₃×#11758608	C₃²	semidirect
35. C₃×#11758605	C₃²	semidirect
36. C₃×#11758605	C₃²	semidirect
37. C₃×#11758605	C₃²	semidirect
42. C₃×#11758606	C₃²	semidirect
43. C₃×#11758606	C₃²	semidirect
44. C₃×#11758606	C₃²	semidirect
53. C₃²×#66524	C₃²	semidirect
56. C₃×C₉×C₃₇⋊C₃	C₃²	semidirect
57. C₃×C₉×C₃₇⋊C₃	C₃²	semidirect
58. C₃×C₉×C₃₇⋊C₃	C₃²	semidirect
61. C₃²⋊#66524	C₃²	semidirect
62. C₃²⋊#66524	C₃²	semidirect
63. C₃²⋊#66524	C₃²	semidirect
64. C₃²⋊#66524	C₃²	semidirect
65. C₃²⋊#66524	C₃²	semidirect
66. C₃²⋊#66524	C₃²	semidirect
75. #15688502	C₃²	semidirect
76. #15688502	C₃²	semidirect
77. #15688502	C₃²	semidirect
78. #15688502	C₃²	semidirect
79. #15688502	C₃²	semidirect
80. #15688502	C₃²	semidirect
81. #15688502	C₃²	semidirect
82. #15688502	C₃²	semidirect
83. #15688502	C₃²	semidirect
84. #15688502	C₃²	semidirect
85. #15688502	C₃²	semidirect
86. #15688502	C₃²	semidirect
87. #15688502	C₃²	semidirect
88. #15688502	C₃²	semidirect
89. #15688502	C₃²	semidirect
90. #15688502	C₃²	semidirect
91. #15688502	C₃²	semidirect
92. #15688502	C₃²	semidirect
94. C₃×3₋¹⁺²×C₃₇	C₃²	semidirect
96. C₃²×C₉×C₃₇	C₃²	semidirect
99. C₃₇×C₃²⋊C₉	C₃²	semidirect
100. C₃₇×C₃²⋊C₉	C₃²	semidirect
101. C₃₇×C₃²⋊C₉	C₃²	semidirect
163. C₉×C₃₇⋊C₃	H(3,𝔽₃)	semidirect
238. C₉⋊H(3,𝔽₃)	C₃₇⋊C₃	semidirect
277. C₃×3₋¹⁺²	C₃×C₃₇⋊C₃	semidirect
292. C₃²×C₉	C₃×C₃₇⋊C₃	semidirect
329. C₃²⋊C₉	C₃×C₃₇⋊C₃	semidirect
330. C₃²⋊C₉	C₃×C₃₇⋊C₃	semidirect
331. C₃²⋊C₉	C₃×C₃₇⋊C₃	semidirect
332. C₃₇	#10624882	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688532	3
C₃×#15688531	3
C₃×3₋¹⁺²×C₃₇⋊C₃	3
#22582563	3
#22582561	3
#22582560	3
#22582559	3
#22582558	3
#22582557	3
#22582556	3
#22582555	3
#22582553	3
#22582552	3
(C₃×C₃₇⋊C₃)⋊H(3,𝔽₃)	3
C₃₇×C₉⋊H(3,𝔽₃)	3
#10624882	37