Subgroups — #41007701

Order 26973.

764 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582565	C₃	1	2	yes	maximal, complemented
2	#22582564	C₃	1	1	yes	maximal, characteristic, complemented
3	#22582563	C₃	1	2	yes	maximal, complemented
4	#22582563	C₃	1	2	yes	maximal, complemented
5	#22582563	C₃	1	2	yes	maximal, complemented
6	#22582561	C₃	1	2	yes	maximal, complemented
7	#22582558	C₃	1	1	yes	maximal, characteristic, complemented
8	#22582557	C₃	1	2	yes	maximal, complemented
9	#22582557	C₃	1	2	yes	maximal, complemented
10	#22582557	C₃	1	2	yes	maximal, 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	#22582556	C₃	1	2	yes	maximal, complemented
15	#22582555	C₃	1	2	yes	maximal, complemented
16	#22582555	C₃	1	2	yes	maximal, complemented
17	#22582555	C₃	1	2	yes	maximal, complemented
18	#22582553	C₃	1	1	yes	maximal, characteristic, complemented
19	#22582551	C₃	1	1	yes	maximal, characteristic, complemented
20	(C₃×C₃₇⋊C₃)⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
21	C₉×C₃²⋊(C₃₇⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
22	#22582539	C₃	1	2	yes	maximal, complemented
23	C₃²⋊C₉×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
24	C₃₇×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
25	C₃³×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
26	C₃×#11758608	C₃²	1	2	yes	—
27	C₃×#11758608	C₃²	1	2	yes	complemented
28	C₃×#11758608	C₃²	1	2	yes	complemented
29	C₃×#11758605	C₃²	1	2	yes	—
30	C₃×#11758605	C₃²	1	1	yes	characteristic
31	C₃×#11758605	C₃²	1	2	yes	complemented
32	C₃×#11758605	C₃²	1	2	yes	complemented
33	C₃×#11758605	C₃²	1	2	yes	complemented
34	C₃×#11758606	C₃²	1	2	yes	complemented
35	C₃×#11758606	C₃²	1	2	yes	complemented
36	C₃×#11758606	C₃²	1	2	yes	complemented
37	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	2	yes	—
38	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	1	yes	characteristic
39	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	2	yes	—
40	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	2	yes	—
41	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	1	yes	characteristic
42	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	1	yes	characteristic
43	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	2	yes	—
44	C₃²×#66524	C₃²	1	2	yes	complemented
45	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
46	C₃×C₉×C₃₇⋊C₃	C₃²	1	2	yes	—
47	C₃×C₉×C₃₇⋊C₃	C₃²	1	2	yes	complemented
48	C₃×C₉×C₃₇⋊C₃	C₃²	1	2	yes	complemented
49	C₃×C₉×C₃₇⋊C₃	C₃²	1	2	yes	complemented
50	C₃²⋊#66524	C₃²	1	2	yes	—
51	C₃²⋊#66524	C₃²	1	2	yes	—
52	C₃²⋊#66524	C₃²	1	2	yes	complemented
53	C₃²⋊#66524	C₃²	1	2	yes	complemented
54	C₃²⋊#66524	C₃²	1	2	yes	complemented
55	C₃²⋊#66524	C₃²	1	2	yes	complemented
56	C₃²⋊#66524	C₃²	1	2	yes	complemented
57	C₃²⋊#66524	C₃²	1	2	yes	complemented
58	#15688502	C₃²	1	2	yes	—
59	#15688502	C₃²	1	1	yes	characteristic
60	#15688502	C₃²	1	1	yes	characteristic
61	#15688502	C₃²	1	2	yes	—
62	#15688502	C₃²	1	2	yes	—
63	#15688502	C₃²	1	2	yes	—
64	#15688502	C₃²	1	1	yes	characteristic
65	#15688502	C₃²	1	1	yes	characteristic
66	#15688502	C₃²	1	1	yes	characteristic
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	complemented
73	#15688502	C₃²	1	2	yes	complemented
74	#15688502	C₃²	1	2	yes	complemented
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	C₃×3₋¹⁺²×C₃₇	C₃²	1	1	yes	characteristic
91	C₃×3₋¹⁺²×C₃₇	C₃²	1	2	yes	complemented
92	C₃×H(3,𝔽₃)×C₃₇	C₃²	1	1	yes	characteristic
93	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic, complemented
94	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
95	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
96	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	complemented
97	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	complemented
98	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	complemented
99	C₃³×C₃₇	C₃³	1	1	yes	characteristic
100	C₃³×C₃₇	C₃³	1	1	yes	characteristic
101	C₃³×C₃₇	C₃³	1	2	yes	—
102	C₃²×C₃₇⋊C₃	—	3	3	no	—
103	C₃²×C₃₇⋊C₃	—	9	1	no	—
104	C₃²×C₃₇⋊C₃	—	9	1	no	—
105	C₃²×C₃₇⋊C₃	—	9	1	no	—
106	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
107	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
108	C₃²×C₃₇⋊C₃	C₃³	1	2	yes	—
109	C₃²×C₃₇⋊C₃	C₃³	1	2	yes	—
110	C₃²×C₃₇⋊C₃	C₃³	1	2	yes	—
111	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
112	3₋¹⁺²×C₃₇	—	9	1	no	—
113	3₋¹⁺²×C₃₇	—	9	2	no	—
114	H(3,𝔽₃)×C₃₇	—	9	1	no	—
115	C₃×C₉×C₃₇	—	9	1	no	—
116	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
117	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
118	C₃×C₉×C₃₇	C₃³	1	2	yes	—
119	C₃×C₉×C₃₇	C₃³	1	2	yes	—
120	C₃×C₉×C₃₇	C₃³	1	2	yes	—
121	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
122	C₃²⋊(C₃₇⋊C₃)	—	3	6	no	—
123	C₃²⋊(C₃₇⋊C₃)	—	3	3	no	—
124	C₃²⋊(C₃₇⋊C₃)	—	9	2	no	—
125	C₃²⋊(C₃₇⋊C₃)	—	9	1	no	—
126	C₃²⋊(C₃₇⋊C₃)	—	9	2	no	—
127	C₃²⋊(C₃₇⋊C₃)	—	9	1	no	—
128	C₃²⋊(C₃₇⋊C₃)	—	9	2	no	—
129	#11758608	—	9	2	no	—
130	#11758608	—	9	2	no	—
131	#11758608	—	9	2	no	—
132	C₃×#66524	—	9	2	no	—
133	C₃×#66524	C₃³	1	2	yes	—
134	C₃×#66524	C₃³	1	2	yes	—
135	C₃×#66524	C₃³	1	2	yes	—
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	#11758606	—	9	2	no	—
143	#11758606	—	9	2	no	—
144	#11758606	—	9	2	no	—
145	#11758605	—	9	2	no	—
146	#11758605	—	9	1	no	—
147	#11758605	—	9	2	no	—
148	#11758605	—	9	2	no	—
149	#11758605	—	9	2	no	—
150	C₉×C₃₇⋊C₃	—	9	1	no	—
151	C₉×C₃₇⋊C₃	—	9	2	no	—
152	C₉×C₃₇⋊C₃	—	9	2	no	—
153	C₉×C₃₇⋊C₃	—	9	2	no	—
154	C₉×C₃₇⋊C₃	—	9	2	no	—
155	#10624888	—	37	1	no	maximal, Sylow
156	C₃²×C₃₇	—	3	1	no	—
157	C₃²×C₃₇	—	3	2	no	—
158	C₃²×C₃₇	—	3	1	no	—
159	C₃²×C₃₇	—	3	2	no	—
160	C₃²×C₃₇	—	3	1	no	—
161	C₃²×C₃₇	—	3	1	no	—
162	C₃²×C₃₇	—	3	1	no	—
163	C₃²×C₃₇	—	3	1	no	—
164	C₃²×C₃₇	—	3	2	no	—
165	C₃²×C₃₇	—	3	1	no	—
166	C₃²×C₃₇	—	3	2	no	—
167	C₃²×C₃₇	—	3	1	no	—
168	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
169	C₃×C₃₇⋊C₃	—	3	1	no	—
170	C₃×C₃₇⋊C₃	—	3	1	no	—
171	C₃×C₃₇⋊C₃	—	3	1	no	—
172	C₃×C₃₇⋊C₃	—	3	2	no	—
173	C₃×C₃₇⋊C₃	—	3	2	no	—
174	C₃×C₃₇⋊C₃	—	3	2	no	—
175	C₃×C₃₇⋊C₃	—	3	1	no	—
176	C₃×C₃₇⋊C₃	—	3	1	no	—
177	C₃×C₃₇⋊C₃	—	3	2	no	—
178	C₃×C₃₇⋊C₃	—	3	2	no	—
179	C₃×C₃₇⋊C₃	—	3	2	no	—
180	C₃×C₃₇⋊C₃	—	3	1	no	—
181	C₃×C₃₇⋊C₃	—	3	1	no	—
182	C₃×C₃₇⋊C₃	—	3	1	no	—
183	C₃×C₃₇⋊C₃	—	3	2	no	—
184	C₃×C₃₇⋊C₃	—	3	2	no	—
185	C₃×C₃₇⋊C₃	—	3	2	no	—
186	C₃×C₃₇⋊C₃	—	3	2	no	—
187	C₃×C₃₇⋊C₃	—	3	2	no	—
188	C₃×C₃₇⋊C₃	—	3	2	no	—
189	C₃×C₃₇⋊C₃	—	3	1	no	—
190	C₃×C₃₇⋊C₃	—	3	1	no	—
191	C₃×C₃₇⋊C₃	—	3	1	no	—
192	C₃×C₃₇⋊C₃	—	9	9	no	—
193	C₃×C₃₇⋊C₃	#737	1	3	yes	—
194	C₉×C₃₇	—	3	1	no	—
195	C₉×C₃₇	—	3	2	no	—
196	C₉×C₃₇	—	3	2	no	—
197	C₉×C₃₇	—	3	2	no	—
198	C₉×C₃₇	—	3	1	no	—
199	C₉×C₃₇	—	3	1	no	—
200	#66524	—	3	2	no	—
201	#66524	—	3	2	no	—
202	#66524	—	3	2	no	—
203	#66524	—	3	2	no	—
204	#66524	—	3	2	no	—
205	#66524	—	3	2	no	—
206	#66524	—	3	2	no	—
207	#66524	—	3	2	no	—
208	#66524	—	3	2	no	—
209	#6893	—	37	2	no	—
210	#6893	—	37	1	no	—
211	#6893	—	37	2	no	—
212	#6893	—	37	2	no	—
213	#6893	—	37	2	no	—
214	C₉⋊H(3,𝔽₃)	—	37	2	no	—
215	C₉⋊H(3,𝔽₃)	—	37	2	no	—
216	C₉⋊H(3,𝔽₃)	—	37	2	no	—
217	C₉⋊H(3,𝔽₃)	—	37	2	no	—
218	C₉⋊H(3,𝔽₃)	—	37	1	no	—
219	C₉⋊H(3,𝔽₃)	—	37	2	no	—
220	C₉⋊H(3,𝔽₃)	—	37	2	no	—
221	C₉⋊H(3,𝔽₃)	—	37	2	no	—
222	C₉⋊H(3,𝔽₃)	—	37	2	no	—
223	C₉⋊H(3,𝔽₃)	—	37	2	no	—
224	C₉⋊H(3,𝔽₃)	—	37	2	no	—
225	C₉⋊H(3,𝔽₃)	—	37	2	no	—
226	C₉⋊H(3,𝔽₃)	C₃₇⋊C₃	1	1	yes	characteristic, complemented
227	#6891	—	37	1	no	—
228	#6891	—	37	1	no	—
229	C₃²⋊H(3,𝔽₃)	—	37	1	no	—
230	C₉×H(3,𝔽₃)	—	37	1	no	—
231	C₉×H(3,𝔽₃)	—	37	2	no	—
232	C₃×C₃²⋊C₉	—	37	1	no	—
233	C₃×C₃₇	—	9	1	no	—
234	C₃×C₃₇	—	9	2	no	—
235	C₃×C₃₇	—	9	1	no	—
236	C₃×C₃₇	C₃×#737	1	1	yes	characteristic
237	C₃×C₃₇	H(5,𝔽₃)	1	1	yes	characteristic
238	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
239	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
240	C₃₇⋊C₃	—	3	3	no	—
241	C₃₇⋊C₃	—	9	2	no	—
242	C₃₇⋊C₃	—	9	2	no	—
243	C₃₇⋊C₃	—	9	2	no	—
244	C₃₇⋊C₃	—	9	1	no	—
245	C₃₇⋊C₃	—	9	1	no	—
246	C₃⁴	—	37	1	no	—
247	C₃×3₋¹⁺²	—	37	2	no	—
248	C₃×3₋¹⁺²	—	37	2	no	—
249	C₃×3₋¹⁺²	—	37	2	no	—
250	C₃×3₋¹⁺²	—	37	2	no	—
251	C₃×3₋¹⁺²	—	37	2	no	—
252	C₃×3₋¹⁺²	—	37	2	no	—
253	C₃×3₋¹⁺²	—	37	2	no	—
254	C₃×3₋¹⁺²	—	37	1	no	—
255	C₃×3₋¹⁺²	—	37	2	no	—
256	C₃×3₋¹⁺²	—	37	2	no	—
257	C₃×3₋¹⁺²	—	37	2	no	—
258	C₃×3₋¹⁺²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
259	C₃×3₋¹⁺²	C₃×C₃₇⋊C₃	1	2	yes	complemented
260	C₃×H(3,𝔽₃)	—	37	2	no	—
261	C₃×H(3,𝔽₃)	—	37	2	no	—
262	C₃×H(3,𝔽₃)	—	37	1	no	—
263	C₃×H(3,𝔽₃)	—	37	2	no	—
264	C₃×H(3,𝔽₃)	—	37	1	no	—
265	C₃×H(3,𝔽₃)	—	37	2	no	—
266	C₃×H(3,𝔽₃)	—	37	1	no	—
267	C₃×H(3,𝔽₃)	C₃×C₃₇⋊C₃	1	1	yes	characteristic
268	C₃²×C₉	—	37	2	no	—
269	C₃²×C₉	—	37	1	no	—
270	C₃²×C₉	—	37	2	no	—
271	C₃²×C₉	—	37	2	no	—
272	C₃²×C₉	—	37	2	no	—
273	C₃²×C₉	—	37	2	no	—
274	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented
275	C₃²⋊C₉	—	37	2	no	—
276	C₃²⋊C₉	—	37	2	no	—
277	C₃²⋊C₉	—	37	2	no	—
278	C₃²⋊C₉	—	37	2	no	—
279	C₃²⋊C₉	—	37	2	no	—
280	C₃²⋊C₉	—	37	2	no	—
281	C₃²⋊C₉	—	37	2	no	—
282	C₃²⋊C₉	—	37	2	no	—
283	C₃²⋊C₉	—	37	2	no	—
284	C₃²⋊C₉	—	37	1	no	—
285	C₃²⋊C₉	—	37	2	no	—
286	C₃²⋊C₉	—	37	1	no	—
287	C₃²⋊C₉	—	37	1	no	—
288	C₃²⋊C₉	—	37	2	no	—
289	C₃²⋊C₉	—	37	1	no	—
290	C₃²⋊C₉	—	37	2	no	—
291	C₃²⋊C₉	—	37	1	no	—
292	C₃²⋊C₉	—	37	2	no	—
293	C₃²⋊C₉	—	37	1	no	—
294	C₃²⋊C₉	—	37	2	no	—
295	C₃²⋊C₉	—	37	1	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	2	no	—
306	C₃²⋊C₉	—	37	2	no	—
307	C₃²⋊C₉	—	37	2	no	—
308	C₃²⋊C₉	—	37	2	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	C₃×C₃₇⋊C₃	1	1	yes	characteristic
316	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
317	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	2	yes	complemented
318	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	2	yes	complemented
319	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	2	yes	complemented
320	C₃₇	#10624888	1	1	yes	characteristic, complemented, Sylow
321	C₃³	—	37	1	no	—
322	C₃³	—	37	1	no	—
323	C₃³	—	37	2	no	—
324	C₃³	—	37	2	no	—
325	C₃³	—	37	2	no	—
326	C₃³	—	37	1	no	—
327	C₃³	—	333	1	no	—
328	C₃³	—	333	1	no	—
329	C₃³	—	333	1	no	—
330	C₃³	—	111	3	no	—
331	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
332	C₃³	C₃²×C₃₇⋊C₃	1	2	yes	—
333	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
334	3₋¹⁺²	—	9	1	no	—
335	3₋¹⁺²	—	9	2	no	—
336	3₋¹⁺²	—	333	2	no	—
337	3₋¹⁺²	—	333	1	no	—
338	3₋¹⁺²	—	333	2	no	—
339	3₋¹⁺²	—	333	2	no	—
340	3₋¹⁺²	—	333	2	no	—
341	3₋¹⁺²	—	333	2	no	—
342	3₋¹⁺²	—	333	2	no	—
343	3₋¹⁺²	—	333	2	no	—
344	3₋¹⁺²	—	333	2	no	—
345	3₋¹⁺²	—	333	2	no	—
346	3₋¹⁺²	—	333	2	no	—
347	H(3,𝔽₃)	—	9	1	no	—
348	H(3,𝔽₃)	—	333	1	no	—
349	H(3,𝔽₃)	—	333	2	no	—
350	H(3,𝔽₃)	—	333	2	no	—
351	H(3,𝔽₃)	—	333	1	no	—
352	H(3,𝔽₃)	—	333	2	no	—
353	H(3,𝔽₃)	—	111	6	no	—
354	H(3,𝔽₃)	—	111	3	no	—
355	C₃×C₉	—	9	1	no	—
356	C₃×C₉	—	37	2	no	—
357	C₃×C₉	—	37	2	no	—
358	C₃×C₉	—	37	2	no	—
359	C₃×C₉	—	37	2	no	—
360	C₃×C₉	—	37	2	no	—
361	C₃×C₉	—	37	2	no	—
362	C₃×C₉	—	37	2	no	—
363	C₃×C₉	—	37	2	no	—
364	C₃×C₉	—	37	2	no	—
365	C₃×C₉	—	333	1	no	—
366	C₃×C₉	—	333	2	no	—
367	C₃×C₉	—	333	2	no	—
368	C₃×C₉	—	333	2	no	—
369	C₃×C₉	—	333	2	no	—
370	C₃×C₉	—	333	2	no	—
371	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
372	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
373	C₃×C₉	C₃²×C₃₇⋊C₃	1	2	yes	—
374	C₃×C₉	C₃²×C₃₇⋊C₃	1	2	yes	—
375	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
376	C₃×C₉	C₃²×C₃₇⋊C₃	1	2	yes	—
377	C₃²	—	3	2	no	—
378	C₃²	—	3	1	no	—
379	C₃²	—	3	1	no	—
380	C₃²	—	3	1	no	—
381	C₃²	—	3	2	no	—
382	C₃²	—	3	1	no	—
383	C₃²	—	3	2	no	—
384	C₃²	—	3	1	no	—
385	C₃²	—	3	1	no	—
386	C₃²	—	3	1	no	—
387	C₃²	—	3	2	no	—
388	C₃²	—	3	1	no	—
389	C₃²	—	37	3	no	—
390	C₃²	—	333	9	no	—
391	C₃²	—	111	2	no	—
392	C₃²	—	111	2	no	—
393	C₃²	—	111	2	no	—
394	C₃²	—	111	1	no	—
395	C₃²	—	111	1	no	—
396	C₃²	—	111	2	no	—
397	C₃²	—	111	2	no	—
398	C₃²	—	111	2	no	—
399	C₃²	—	111	1	no	—
400	C₃²	—	111	1	no	—
401	C₃²	—	111	1	no	—
402	C₃²	—	111	2	no	—
403	C₃²	—	111	2	no	—
404	C₃²	—	111	2	no	—
405	C₃²	—	111	1	no	—
406	C₃²	—	111	2	no	—
407	C₃²	—	111	2	no	—
408	C₃²	—	111	2	no	—
409	C₃²	—	111	1	no	—
410	C₃²	—	111	1	no	—
411	C₃²	—	111	1	no	—
412	C₃²	—	111	1	no	—
413	C₃²	—	111	1	no	—
414	C₃²	C₃³×C₃₇⋊C₃	1	1	yes	characteristic
415	C₉	—	3	1	no	—
416	C₉	—	3	1	no	—
417	C₉	—	3	1	no	—
418	C₉	—	3	2	no	—
419	C₉	—	3	2	no	—
420	C₉	—	3	2	no	—
421	C₉	—	111	2	no	—
422	C₉	—	111	2	no	—
423	C₉	—	111	2	no	—
424	C₉	—	111	2	no	—
425	C₉	—	111	2	no	—
426	C₉	—	111	2	no	—
427	C₉	—	111	2	no	—
428	C₉	—	111	2	no	—
429	C₉	—	111	2	no	—
430	C₃	—	9	1	no	—
431	C₃	—	9	1	no	—
432	C₃	—	9	2	no	—
433	C₃	—	333	1	no	—
434	C₃	—	333	1	no	—
435	C₃	—	333	2	no	—
436	C₃	—	333	2	no	—
437	C₃	—	333	2	no	—
438	C₃	—	111	3	no	—
439	C₃	#737×C₃₇⋊C₃	1	1	yes	characteristic
440	C₃	C₃₇⋊H(5,𝔽₃)	1	1	yes	characteristic
441	C₃	#22582678	1	1	yes	characteristic
442	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	#10624888
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. #22582565	C₃	semidirect
2. #22582564	C₃	semidirect
3. #22582563	C₃	semidirect
4. #22582563	C₃	semidirect
5. #22582563	C₃	semidirect
6. #22582561	C₃	semidirect
7. #22582558	C₃	semidirect
8. #22582557	C₃	semidirect
9. #22582557	C₃	semidirect
10. #22582557	C₃	semidirect
11. #22582557	C₃	semidirect
12. #22582557	C₃	semidirect
13. #22582557	C₃	semidirect
14. #22582556	C₃	semidirect
15. #22582555	C₃	semidirect
16. #22582555	C₃	semidirect
17. #22582555	C₃	semidirect
18. #22582553	C₃	semidirect
19. #22582551	C₃	semidirect
21. C₉×C₃²⋊(C₃₇⋊C₃)	C₃	semidirect
22. #22582539	C₃	semidirect
23. C₃²⋊C₉×C₃₇⋊C₃	C₃	semidirect
24. C₃₇×C₉⋊H(3,𝔽₃)	C₃	semidirect
27. C₃×#11758608	C₃²	semidirect
28. C₃×#11758608	C₃²	semidirect
31. C₃×#11758605	C₃²	semidirect
32. C₃×#11758605	C₃²	semidirect
33. C₃×#11758605	C₃²	semidirect
34. C₃×#11758606	C₃²	semidirect
35. C₃×#11758606	C₃²	semidirect
36. C₃×#11758606	C₃²	semidirect
44. C₃²×#66524	C₃²	semidirect
47. C₃×C₉×C₃₇⋊C₃	C₃²	semidirect
48. C₃×C₉×C₃₇⋊C₃	C₃²	semidirect
49. C₃×C₉×C₃₇⋊C₃	C₃²	semidirect
52. C₃²⋊#66524	C₃²	semidirect
53. C₃²⋊#66524	C₃²	semidirect
54. C₃²⋊#66524	C₃²	semidirect
55. C₃²⋊#66524	C₃²	semidirect
56. C₃²⋊#66524	C₃²	semidirect
57. C₃²⋊#66524	C₃²	semidirect
72. #15688502	C₃²	semidirect
73. #15688502	C₃²	semidirect
74. #15688502	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
91. C₃×3₋¹⁺²×C₃₇	C₃²	semidirect
93. C₃²×C₉×C₃₇	C₃²	semidirect
96. C₃₇×C₃²⋊C₉	C₃²	semidirect
97. C₃₇×C₃²⋊C₉	C₃²	semidirect
98. C₃₇×C₃²⋊C₉	C₃²	semidirect
226. C₉⋊H(3,𝔽₃)	C₃₇⋊C₃	semidirect
259. C₃×3₋¹⁺²	C₃×C₃₇⋊C₃	semidirect
274. C₃²×C₉	C₃×C₃₇⋊C₃	semidirect
317. C₃²⋊C₉	C₃×C₃₇⋊C₃	semidirect
318. C₃²⋊C₉	C₃×C₃₇⋊C₃	semidirect
319. C₃²⋊C₉	C₃×C₃₇⋊C₃	semidirect
320. C₃₇	#10624888	semidirect

Maximal subgroups

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

subgroup	index
#22582565	3
#22582564	3
#22582563	3
#22582561	3
#22582558	3
#22582557	3
#22582556	3
#22582555	3
#22582553	3
#22582551	3
(C₃×C₃₇⋊C₃)⋊H(3,𝔽₃)	3
C₉×C₃²⋊(C₃₇⋊C₃)	3
#22582539	3
C₃²⋊C₉×C₃₇⋊C₃	3
C₃₇×C₉⋊H(3,𝔽₃)	3
#10624888	37