Subgroups — #41007687

Order 26973.

698 conjugacy classes of subgroups.

The subgroup lattice has 598 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	1	yes	maximal, characteristic
2	#22582605	C₃	1	1	yes	maximal, characteristic, complemented
3	#22582604	C₃	1	1	yes	maximal, characteristic, complemented
4	#22582601	C₃	1	1	yes	maximal, characteristic, complemented
5	#22582598	C₃	1	1	yes	maximal, characteristic, complemented
6	#22582598	C₃	1	1	yes	maximal, characteristic, complemented
7	#22582597	C₃	1	1	yes	maximal, characteristic, complemented
8	#22582597	C₃	1	1	yes	maximal, characteristic, complemented
9	#22582593	C₃	1	1	yes	maximal, characteristic, complemented
10	#22582593	C₃	1	1	yes	maximal, characteristic, complemented
11	#22582584	C₃	1	1	yes	maximal, characteristic, complemented
12	#22582584	C₃	1	1	yes	maximal, characteristic, complemented
13	#22582583	C₃	1	1	yes	maximal, characteristic, complemented
14	#22582583	C₃	1	1	yes	maximal, characteristic, complemented
15	#22582581	C₃	1	1	yes	maximal, characteristic, complemented
16	#22582581	C₃	1	1	yes	maximal, characteristic, complemented
17	#22582580	C₃	1	1	yes	maximal, characteristic, complemented
18	#22582580	C₃	1	1	yes	maximal, characteristic, complemented
19	#22582574	C₃	1	1	yes	maximal, characteristic, complemented
20	#22582573	C₃	1	1	yes	maximal, characteristic, complemented
21	#22582570	C₃	1	1	yes	maximal, characteristic, complemented
22	#22582570	C₃	1	1	yes	maximal, characteristic, complemented
23	#22582570	C₃	1	1	yes	maximal, characteristic, complemented
24	#22582570	C₃	1	1	yes	maximal, characteristic, complemented
25	#22582570	C₃	1	1	yes	maximal, characteristic, complemented
26	#22582569	C₃	1	1	yes	maximal, characteristic, complemented
27	#22582569	C₃	1	1	yes	maximal, characteristic, complemented
28	#22582569	C₃	1	1	yes	maximal, characteristic, complemented
29	#22582569	C₃	1	1	yes	maximal, characteristic, complemented
30	#22582569	C₃	1	1	yes	maximal, characteristic, complemented
31	#22582568	C₃	1	1	yes	maximal, characteristic, complemented
32	#22582567	C₃	1	1	yes	maximal, characteristic, complemented
33	#22582566	C₃	1	1	yes	maximal, characteristic, complemented
34	#22582557	C₃	1	1	yes	maximal, characteristic
35	#22582557	C₃	1	1	yes	maximal, characteristic
36	#22582555	C₃	1	1	yes	maximal, characteristic
37	#22582537	C₃	1	1	yes	maximal, characteristic, complemented
38	#22582536	C₃	1	1	yes	maximal, characteristic, complemented
39	C₉⋊C₉×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
40	C₃₇×#6896	C₃	1	1	yes	maximal, characteristic, complemented
41	#15688532	—	3	9	no	—
42	C₃×#11758608	C₃²	1	1	yes	characteristic
43	C₃×#11758608	C₃²	1	1	yes	characteristic
44	C₃×#11758608	C₃²	1	1	yes	characteristic
45	C₃×#11758605	C₃²	1	1	yes	characteristic
46	C₃×#11758605	C₃²	1	1	yes	characteristic
47	C₃×#11758605	C₃²	1	1	yes	characteristic
48	C₃×#11758605	C₃²	1	1	yes	characteristic
49	C₃×#11758605	C₃²	1	1	yes	characteristic
50	C₃×#11758605	C₃²	1	1	yes	characteristic
51	C₃×#11758606	C₃²	1	1	yes	characteristic
52	C₃×#11758606	C₃²	1	1	yes	characteristic
53	C₃×#11758606	C₃²	1	1	yes	characteristic
54	C₃×#11758606	C₃²	1	1	yes	characteristic
55	C₃×#11758606	C₃²	1	1	yes	characteristic
56	C₃×#11758606	C₃²	1	1	yes	characteristic
57	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	1	yes	characteristic
58	C₃²×#66524	C₃²	1	1	yes	characteristic
59	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
60	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
61	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
62	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
63	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
64	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
65	#15688506	C₃²	1	1	yes	characteristic
66	#15688506	C₃²	1	1	yes	characteristic
67	#15688506	C₃²	1	1	yes	characteristic
68	#15688506	C₃²	1	1	yes	characteristic
69	#15688506	C₃²	1	1	yes	characteristic
70	#15688506	C₃²	1	1	yes	characteristic
71	#15688506	C₃²	1	1	yes	characteristic
72	#15688506	C₃²	1	1	yes	characteristic
73	#15688505	C₃²	1	1	yes	characteristic
74	#15688505	C₃²	1	1	yes	characteristic
75	#15688505	C₃²	1	1	yes	characteristic
76	#15688505	C₃²	1	1	yes	characteristic
77	#15688505	C₃²	1	1	yes	characteristic
78	#15688505	C₃²	1	1	yes	characteristic
79	#15688505	C₃²	1	1	yes	characteristic
80	#15688505	C₃²	1	1	yes	characteristic
81	#15688504	C₃²	1	1	yes	characteristic
82	#15688504	C₃²	1	1	yes	characteristic
83	#15688504	C₃²	1	1	yes	characteristic
84	#15688504	C₃²	1	1	yes	characteristic
85	#15688504	C₃²	1	1	yes	characteristic
86	#15688504	C₃²	1	1	yes	characteristic
87	#15688504	C₃²	1	1	yes	characteristic
88	#15688504	C₃²	1	1	yes	characteristic
89	#15688504	C₃²	1	1	yes	characteristic
90	#15688504	C₃²	1	1	yes	characteristic
91	#15688504	C₃²	1	1	yes	characteristic
92	#15688504	C₃²	1	1	yes	characteristic
93	#15688504	C₃²	1	1	yes	characteristic
94	#15688504	C₃²	1	1	yes	characteristic
95	#15688504	C₃²	1	1	yes	characteristic
96	#15688504	C₃²	1	1	yes	characteristic
97	#15688504	C₃²	1	1	yes	characteristic
98	#15688504	C₃²	1	1	yes	characteristic
99	#15688504	C₃²	1	1	yes	characteristic
100	#15688504	C₃²	1	1	yes	characteristic
101	#15688504	C₃²	1	1	yes	characteristic
102	#15688504	C₃²	1	1	yes	characteristic
103	#15688504	C₃²	1	1	yes	characteristic
104	#15688504	C₃²	1	1	yes	characteristic
105	#15688504	C₃²	1	1	yes	characteristic
106	#15688504	C₃²	1	1	yes	characteristic
107	#15688504	C₃²	1	1	yes	characteristic
108	#15688504	C₃²	1	1	yes	characteristic
109	#15688504	C₃²	1	1	yes	characteristic
110	#15688504	C₃²	1	1	yes	characteristic
111	#15688504	C₃²	1	1	yes	characteristic
112	#15688504	C₃²	1	1	yes	characteristic
113	#15688504	C₃²	1	1	yes	characteristic
114	#15688504	C₃²	1	1	yes	characteristic
115	#15688504	C₃²	1	1	yes	characteristic
116	#15688504	C₃²	1	1	yes	characteristic
117	#15688504	C₃²	1	1	yes	characteristic
118	#15688504	C₃²	1	1	yes	characteristic
119	#15688504	C₃²	1	1	yes	characteristic
120	#15688504	C₃²	1	1	yes	characteristic
121	#15688504	C₃²	1	1	yes	characteristic
122	#15688504	C₃²	1	1	yes	characteristic
123	#15688504	C₃²	1	1	yes	characteristic
124	#15688504	C₃²	1	1	yes	characteristic
125	#15688504	C₃²	1	1	yes	characteristic
126	#15688504	C₃²	1	1	yes	characteristic
127	#15688504	C₃²	1	1	yes	characteristic
128	#15688504	C₃²	1	1	yes	characteristic
129	#15688504	C₃²	1	1	yes	characteristic
130	#15688504	C₃²	1	1	yes	characteristic
131	#15688504	C₃²	1	1	yes	characteristic
132	C₃²⋊#66524	C₃²	1	1	yes	characteristic
133	C₃²⋊#66524	C₃²	1	1	yes	characteristic
134	C₃²⋊#66524	C₃²	1	1	yes	characteristic
135	C₃²⋊#66524	C₃²	1	1	yes	characteristic
136	#15688502	C₃²	1	1	yes	characteristic
137	#15688502	C₃²	1	1	yes	characteristic
138	#15688502	C₃²	1	1	yes	characteristic
139	#15688502	C₃²	1	1	yes	characteristic
140	#15688502	C₃²	1	1	yes	characteristic
141	#15688502	C₃²	1	1	yes	characteristic
142	#15688502	C₃²	1	1	yes	characteristic
143	#15688502	C₃²	1	1	yes	characteristic
144	#15688502	C₃²	1	1	yes	characteristic
145	#15688502	C₃²	1	1	yes	characteristic
146	#15688502	C₃²	1	1	yes	characteristic
147	#15688502	C₃²	1	1	yes	characteristic
148	#15688502	C₃²	1	1	yes	characteristic
149	#15688502	C₃²	1	1	yes	characteristic
150	#15688502	C₃²	1	1	yes	characteristic
151	#15688502	C₃²	1	1	yes	characteristic
152	#15688502	C₃²	1	1	yes	characteristic
153	#15688502	C₃²	1	1	yes	characteristic
154	C₉×#66524	C₃²	1	1	yes	characteristic
155	C₉×#66524	C₃²	1	1	yes	characteristic
156	C₉×#66524	C₃²	1	1	yes	characteristic
157	C₉×#66524	C₃²	1	1	yes	characteristic
158	C₉×#66524	C₃²	1	1	yes	characteristic
159	C₃×3₋¹⁺²×C₃₇	C₃²	1	1	yes	characteristic
160	C₃×3₋¹⁺²×C₃₇	C₃²	1	1	yes	characteristic
161	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
162	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
163	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
164	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
165	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
166	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
167	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
168	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
169	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
170	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
171	C₉²×C₃₇	C₃²	1	1	yes	characteristic
172	C₃³×C₃₇	C₃³	1	1	yes	characteristic
173	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
174	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
175	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
176	3₋¹⁺²×C₃₇	—	3	3	no	—
177	3₋¹⁺²×C₃₇	—	9	1	no	—
178	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
179	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
180	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
181	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
182	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
183	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
184	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
185	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
186	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
187	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
188	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
189	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
190	C₃²⋊(C₃₇⋊C₃)	—	3	3	no	—
191	#11758608	—	3	3	no	—
192	#11758608	—	9	1	no	—
193	#11758608	—	9	1	no	—
194	C₃×#66524	—	3	3	no	—
195	C₃×#66524	C₃³	1	1	yes	characteristic
196	C₃×#66524	C₃³	1	1	yes	characteristic
197	C₃×#66524	C₃³	1	1	yes	characteristic
198	C₃×#66524	C₃³	1	1	yes	characteristic
199	C₃×#66524	C₃³	1	1	yes	characteristic
200	C₃×#66524	C₃³	1	1	yes	characteristic
201	C₃×#66524	C₃³	1	1	yes	characteristic
202	C₃×#66524	C₃³	1	1	yes	characteristic
203	C₃×#66524	C₃³	1	1	yes	characteristic
204	C₃×#66524	C₃³	1	1	yes	characteristic
205	C₃×#66524	C₃³	1	1	yes	characteristic
206	C₃×#66524	C₃³	1	1	yes	characteristic
207	C₃×#66524	C₃³	1	1	yes	characteristic
208	C₃×#66524	C₃³	1	1	yes	characteristic
209	C₃×#66524	C₃³	1	1	yes	characteristic
210	C₃×#66524	C₃³	1	1	yes	characteristic
211	C₃×#66524	C₃³	1	1	yes	characteristic
212	C₃×#66524	C₃³	1	1	yes	characteristic
213	C₃×#66524	C₃³	1	1	yes	characteristic
214	C₃×#66524	C₃³	1	1	yes	characteristic
215	C₃×#66524	C₃³	1	1	yes	characteristic
216	C₃×#66524	C₃³	1	1	yes	characteristic
217	C₃×#66524	C₃³	1	1	yes	characteristic
218	C₃×#66524	C₃³	1	1	yes	characteristic
219	#11758606	—	3	3	no	—
220	#11758606	—	3	3	no	—
221	#11758606	—	3	3	no	—
222	#11758606	—	9	1	no	—
223	#11758606	—	9	1	no	—
224	#11758606	—	9	1	no	—
225	#11758605	—	3	3	no	—
226	#11758605	—	3	3	no	—
227	#11758605	—	3	3	no	—
228	#11758605	—	9	1	no	—
229	#11758605	—	9	1	no	—
230	#11758605	—	9	1	no	—
231	C₉×C₃₇⋊C₃	—	3	3	no	—
232	C₉×C₃₇⋊C₃	—	3	3	no	—
233	C₉×C₃₇⋊C₃	—	9	1	no	—
234	C₉×C₃₇⋊C₃	—	9	1	no	—
235	C₉×C₃₇⋊C₃	—	9	1	no	—
236	C₉×C₃₇⋊C₃	3₋¹⁺²	1	9	yes	complemented
237	#10624887	—	37	1	no	maximal, Sylow
238	C₃²×C₃₇	—	3	1	no	—
239	C₃²×C₃₇	—	3	1	no	—
240	C₃²×C₃₇	—	3	1	no	—
241	C₃²×C₃₇	—	3	1	no	—
242	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
243	C₃×C₃₇⋊C₃	—	3	1	no	—
244	C₃×C₃₇⋊C₃	—	3	1	no	—
245	C₃×C₃₇⋊C₃	—	3	1	no	—
246	C₃×C₃₇⋊C₃	—	3	1	no	—
247	C₃×C₃₇⋊C₃	—	3	1	no	—
248	C₃×C₃₇⋊C₃	—	3	1	no	—
249	C₃×C₃₇⋊C₃	—	3	1	no	—
250	C₃×C₃₇⋊C₃	—	3	1	no	—
251	C₃×C₃₇⋊C₃	—	3	1	no	—
252	C₃×C₃₇⋊C₃	—	3	1	no	—
253	C₃×C₃₇⋊C₃	—	3	1	no	—
254	C₃×C₃₇⋊C₃	C₃×3₋¹⁺²	1	3	yes	—
255	C₉×C₃₇	—	3	1	no	—
256	C₉×C₃₇	—	3	1	no	—
257	C₉×C₃₇	—	3	1	no	—
258	C₉×C₃₇	—	3	1	no	—
259	C₉×C₃₇	—	3	1	no	—
260	C₉×C₃₇	—	3	1	no	—
261	C₉×C₃₇	—	3	1	no	—
262	C₉×C₃₇	—	3	1	no	—
263	C₉×C₃₇	—	3	1	no	—
264	C₉×C₃₇	—	3	1	no	—
265	C₉×C₃₇	—	3	1	no	—
266	C₉×C₃₇	C₃×3₋¹⁺²	1	3	yes	—
267	#66524	—	3	1	no	—
268	#66524	—	3	1	no	—
269	#66524	—	3	1	no	—
270	#66524	—	3	1	no	—
271	#66524	—	3	1	no	—
272	#66524	—	3	1	no	—
273	#66524	—	3	1	no	—
274	#66524	—	3	1	no	—
275	#66524	—	3	1	no	—
276	#66524	—	3	1	no	—
277	#66524	—	3	1	no	—
278	#66524	—	3	1	no	—
279	#66524	—	3	1	no	—
280	#66524	—	3	1	no	—
281	#66524	—	3	1	no	—
282	#66524	—	3	1	no	—
283	#66524	—	3	1	no	—
284	#66524	—	3	1	no	—
285	#66524	—	3	1	no	—
286	#66524	—	3	1	no	—
287	#66524	—	3	1	no	—
288	#66524	—	3	1	no	—
289	#66524	C₃×3₋¹⁺²	1	3	yes	—
290	#66524	C₃×3₋¹⁺²	1	3	yes	—
291	C₃×#737	—	37	1	no	—
292	#6900	—	37	1	no	—
293	#6900	—	37	1	no	—
294	#6900	—	37	1	no	—
295	#6899	—	37	1	no	—
296	#6899	—	37	1	no	—
297	#6899	—	37	1	no	—
298	#6899	—	37	1	no	—
299	#6899	—	37	1	no	—
300	#6899	—	37	1	no	—
301	#6896	—	37	1	no	—
302	#6896	—	37	1	no	—
303	#6896	—	37	1	no	—
304	#6896	—	37	1	no	—
305	#6896	—	37	1	no	—
306	#6896	—	37	1	no	—
307	#6896	—	37	1	no	—
308	#6896	—	37	1	no	—
309	#6896	C₃₇⋊C₃	1	1	yes	characteristic, complemented
310	#6894	—	37	1	no	—
311	#6894	—	37	1	no	—
312	#6894	—	37	1	no	—
313	#6894	—	37	1	no	—
314	#6894	—	37	1	no	—
315	#6894	—	37	1	no	—
316	#6894	—	37	1	no	—
317	#6894	—	37	1	no	—
318	#6894	—	37	1	no	—
319	#6894	—	37	1	no	—
320	#6894	—	37	1	no	—
321	#6894	—	37	1	no	—
322	#6894	—	37	1	no	—
323	#6894	—	37	1	no	—
324	#6894	—	37	1	no	—
325	C₉⋊H(3,𝔽₃)	—	37	1	no	—
326	C₉⋊H(3,𝔽₃)	—	37	1	no	—
327	C₉⋊H(3,𝔽₃)	—	37	1	no	—
328	#6887	—	37	1	no	—
329	#6887	—	37	1	no	—
330	C₃×C₉⋊C₉	—	37	1	no	—
331	C₃×C₃₇	—	9	1	no	—
332	C₃×C₃₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
333	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
334	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
335	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
336	C₃₇⋊C₃	—	3	3	no	—
337	C₃₇⋊C₃	—	9	1	no	—
338	C₃₇⋊C₃	—	9	1	no	—
339	#737	—	111	9	no	—
340	C₃×3₋¹⁺²	—	37	1	no	—
341	C₃×3₋¹⁺²	—	37	1	no	—
342	C₃×3₋¹⁺²	—	37	1	no	—
343	C₃×3₋¹⁺²	—	37	1	no	—
344	C₃×3₋¹⁺²	—	37	1	no	—
345	C₃×3₋¹⁺²	—	37	1	no	—
346	C₃×3₋¹⁺²	—	37	1	no	—
347	C₃×3₋¹⁺²	—	37	1	no	—
348	C₃×3₋¹⁺²	—	37	1	no	—
349	C₃×3₋¹⁺²	—	37	1	no	—
350	C₃×3₋¹⁺²	—	37	1	no	—
351	C₃×3₋¹⁺²	—	37	1	no	—
352	C₃×3₋¹⁺²	—	37	1	no	—
353	C₃×3₋¹⁺²	—	37	1	no	—
354	C₃×3₋¹⁺²	—	37	1	no	—
355	C₃×3₋¹⁺²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
356	C₃×3₋¹⁺²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
357	C₃×H(3,𝔽₃)	—	37	1	no	—
358	C₃²×C₉	—	37	1	no	—
359	C₃²×C₉	—	37	1	no	—
360	C₃²×C₉	—	37	1	no	—
361	C₃²×C₉	—	37	1	no	—
362	C₃²×C₉	—	37	1	no	—
363	C₃²×C₉	—	37	1	no	—
364	C₃²×C₉	—	37	1	no	—
365	C₉⋊C₉	—	37	1	no	—
366	C₉⋊C₉	—	37	1	no	—
367	C₉⋊C₉	—	37	1	no	—
368	C₉⋊C₉	—	37	1	no	—
369	C₉⋊C₉	—	37	1	no	—
370	C₉⋊C₉	—	37	1	no	—
371	C₉⋊C₉	—	37	1	no	—
372	C₉⋊C₉	—	37	1	no	—
373	C₉⋊C₉	—	37	1	no	—
374	C₉⋊C₉	—	37	1	no	—
375	C₉⋊C₉	—	37	1	no	—
376	C₉⋊C₉	—	37	1	no	—
377	C₉⋊C₉	—	37	1	no	—
378	C₉⋊C₉	—	37	1	no	—
379	C₉⋊C₉	—	37	1	no	—
380	C₉⋊C₉	—	37	1	no	—
381	C₉⋊C₉	—	37	1	no	—
382	C₉⋊C₉	—	37	1	no	—
383	C₉⋊C₉	—	37	1	no	—
384	C₉⋊C₉	—	37	1	no	—
385	C₉⋊C₉	—	37	1	no	—
386	C₉⋊C₉	—	37	1	no	—
387	C₉⋊C₉	—	37	1	no	—
388	C₉⋊C₉	—	37	1	no	—
389	C₉⋊C₉	—	37	1	no	—
390	C₉⋊C₉	—	37	1	no	—
391	C₉⋊C₉	—	37	1	no	—
392	C₉⋊C₉	—	37	1	no	—
393	C₉⋊C₉	—	37	1	no	—
394	C₉⋊C₉	—	37	1	no	—
395	C₉⋊C₉	—	37	1	no	—
396	C₉⋊C₉	—	37	1	no	—
397	C₉⋊C₉	—	37	1	no	—
398	C₉⋊C₉	—	37	1	no	—
399	C₉⋊C₉	—	37	1	no	—
400	C₉⋊C₉	—	37	1	no	—
401	C₉⋊C₉	—	37	1	no	—
402	C₉⋊C₉	—	37	1	no	—
403	C₉⋊C₉	—	37	1	no	—
404	C₉⋊C₉	—	37	1	no	—
405	C₉⋊C₉	—	37	1	no	—
406	C₉⋊C₉	—	37	1	no	—
407	C₉⋊C₉	—	37	1	no	—
408	C₉⋊C₉	—	37	1	no	—
409	C₉⋊C₉	—	37	1	no	—
410	C₉⋊C₉	—	37	1	no	—
411	C₉⋊C₉	—	37	1	no	—
412	C₉⋊C₉	—	37	1	no	—
413	C₉⋊C₉	—	37	1	no	—
414	C₉⋊C₉	—	37	1	no	—
415	C₉⋊C₉	—	37	1	no	—
416	C₉⋊C₉	—	37	1	no	—
417	C₉⋊C₉	—	37	1	no	—
418	C₉⋊C₉	—	37	1	no	—
419	C₉⋊C₉	—	37	1	no	—
420	C₉⋊C₉	—	37	1	no	—
421	C₉⋊C₉	—	37	1	no	—
422	C₉⋊C₉	—	37	1	no	—
423	C₉⋊C₉	—	37	1	no	—
424	C₉⋊C₉	—	37	1	no	—
425	C₉⋊C₉	—	37	1	no	—
426	C₉⋊C₉	—	37	1	no	—
427	C₉⋊C₉	—	37	1	no	—
428	C₉⋊C₉	—	37	1	no	—
429	C₉⋊C₉	—	37	1	no	—
430	C₉⋊C₉	—	37	1	no	—
431	C₉⋊C₉	—	37	1	no	—
432	C₉⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
433	C₉⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
434	C₉⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
435	C₉⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
436	C₉⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
437	C₉⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
438	C₉⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
439	C₉⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
440	C₃²⋊C₉	—	37	1	no	—
441	C₃²⋊C₉	—	37	1	no	—
442	C₃²⋊C₉	—	37	1	no	—
443	C₃²⋊C₉	—	37	1	no	—
444	C₃²⋊C₉	—	37	1	no	—
445	C₃²⋊C₉	—	37	1	no	—
446	C₃²⋊C₉	—	37	1	no	—
447	C₃²⋊C₉	—	37	1	no	—
448	C₃²⋊C₉	—	37	1	no	—
449	C₃²⋊C₉	—	37	1	no	—
450	C₃²⋊C₉	—	37	1	no	—
451	C₃²⋊C₉	—	37	1	no	—
452	C₃²⋊C₉	—	37	1	no	—
453	C₃²⋊C₉	—	37	1	no	—
454	C₃²⋊C₉	—	37	1	no	—
455	C₃²⋊C₉	—	37	1	no	—
456	C₃²⋊C₉	—	37	1	no	—
457	C₃²⋊C₉	—	37	1	no	—
458	C₃²⋊C₉	—	37	1	no	—
459	C₃²⋊C₉	—	37	1	no	—
460	C₃²⋊C₉	—	37	1	no	—
461	C₃²⋊C₉	—	37	1	no	—
462	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
463	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
464	C₉²	—	37	1	no	—
465	C₉²	—	37	1	no	—
466	C₉²	—	37	1	no	—
467	C₉²	—	37	1	no	—
468	C₉²	—	37	1	no	—
469	C₉²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
470	C₃₇	#10624887	1	1	yes	characteristic, complemented, Sylow
471	C₃³	—	37	1	no	—
472	C₃³	—	37	1	no	—
473	C₃³	—	37	1	no	—
474	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
475	3₋¹⁺²	—	3	3	no	—
476	3₋¹⁺²	—	9	1	no	—
477	3₋¹⁺²	—	333	1	no	—
478	3₋¹⁺²	—	333	1	no	—
479	3₋¹⁺²	—	333	1	no	—
480	3₋¹⁺²	—	333	1	no	—
481	3₋¹⁺²	—	333	1	no	—
482	3₋¹⁺²	—	333	1	no	—
483	3₋¹⁺²	—	333	1	no	—
484	3₋¹⁺²	—	333	1	no	—
485	3₋¹⁺²	—	111	3	no	—
486	3₋¹⁺²	—	111	3	no	—
487	3₋¹⁺²	—	111	3	no	—
488	3₋¹⁺²	—	111	3	no	—
489	3₋¹⁺²	—	111	3	no	—
490	3₋¹⁺²	—	111	3	no	—
491	3₋¹⁺²	—	111	3	no	—
492	H(3,𝔽₃)	—	111	3	no	—
493	C₃×C₉	—	37	1	no	—
494	C₃×C₉	—	37	1	no	—
495	C₃×C₉	—	37	9	no	—
496	C₃×C₉	—	37	1	no	—
497	C₃×C₉	—	37	1	no	—
498	C₃×C₉	—	37	1	no	—
499	C₃×C₉	—	37	1	no	—
500	C₃×C₉	—	37	1	no	—
501	C₃×C₉	—	37	1	no	—
502	C₃×C₉	—	37	1	no	—
503	C₃×C₉	—	37	1	no	—
504	C₃×C₉	—	37	1	no	—
505	C₃×C₉	—	37	1	no	—
506	C₃×C₉	—	37	1	no	—
507	C₃×C₉	—	37	1	no	—
508	C₃×C₉	—	37	1	no	—
509	C₃×C₉	—	37	1	no	—
510	C₃×C₉	—	37	1	no	—
511	C₃×C₉	—	37	1	no	—
512	C₃×C₉	—	37	1	no	—
513	C₃×C₉	—	37	1	no	—
514	C₃×C₉	—	37	1	no	—
515	C₃×C₉	—	37	1	no	—
516	C₃×C₉	—	37	1	no	—
517	C₃×C₉	—	37	1	no	—
518	C₃×C₉	—	333	1	no	—
519	C₃×C₉	—	333	1	no	—
520	C₃×C₉	—	333	1	no	—
521	C₃×C₉	—	111	3	no	—
522	C₃×C₉	—	111	3	no	—
523	C₃×C₉	—	111	3	no	—
524	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
525	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
526	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
527	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
528	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
529	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
530	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
531	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
532	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
533	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
534	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
535	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
536	C₃²	—	3	1	no	—
537	C₃²	—	3	1	no	—
538	C₃²	—	3	1	no	—
539	C₃²	—	3	1	no	—
540	C₃²	—	37	3	no	—
541	C₃²	—	111	1	no	—
542	C₃²	—	111	1	no	—
543	C₃²	—	111	1	no	—
544	C₃²	—	111	1	no	—
545	C₃²	—	111	1	no	—
546	C₃²	—	111	1	no	—
547	C₃²	—	111	1	no	—
548	C₃²	—	111	1	no	—
549	C₃²	—	111	1	no	—
550	C₃²	—	111	1	no	—
551	C₃²	—	111	1	no	—
552	C₃²	C₃³×C₃₇⋊C₃	1	1	yes	characteristic
553	C₉	—	3	1	no	—
554	C₉	—	3	1	no	—
555	C₉	—	3	1	no	—
556	C₉	—	3	1	no	—
557	C₉	—	3	1	no	—
558	C₉	—	3	1	no	—
559	C₉	—	3	1	no	—
560	C₉	—	3	1	no	—
561	C₉	—	3	1	no	—
562	C₉	—	3	1	no	—
563	C₉	—	3	1	no	—
564	C₉	—	37	3	no	—
565	C₉	—	37	3	no	—
566	C₉	—	111	1	no	—
567	C₉	—	111	1	no	—
568	C₉	—	111	1	no	—
569	C₉	—	111	1	no	—
570	C₉	—	111	1	no	—
571	C₉	—	111	1	no	—
572	C₉	—	111	1	no	—
573	C₉	—	111	1	no	—
574	C₉	—	111	1	no	—
575	C₉	—	111	1	no	—
576	C₉	—	111	1	no	—
577	C₉	—	111	1	no	—
578	C₉	—	111	1	no	—
579	C₉	—	111	1	no	—
580	C₉	—	111	1	no	—
581	C₉	—	111	1	no	—
582	C₉	—	111	1	no	—
583	C₉	—	111	1	no	—
584	C₉	—	111	1	no	—
585	C₉	—	111	1	no	—
586	C₉	—	111	1	no	—
587	C₉	—	111	1	no	—
588	C₉	3₋¹⁺²×C₃₇⋊C₃	1	3	yes	—
589	C₃	—	9	1	no	—
590	C₃	—	333	1	no	—
591	C₃	—	333	1	no	—
592	C₃	—	111	3	no	—
593	C₃	C₃×3₋¹⁺²×C₃₇⋊C₃	1	1	yes	characteristic
594	C₃	#22582677	1	1	yes	characteristic
595	C₃	#22582678	1	1	yes	characteristic
596	C₃	#22582679	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₃₇⋊C₃
commutator, socle, cosocle	C₃²×C₃₇	C₃⁴
Fitting	C₃₇×#6896	C₃
prime radical	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²
hypercenter	#6896	C₃₇⋊C₃
hypocenter	C₃₇	#10624887
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ #6896

Complements

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

N	H ≅ G/N	type
2. #22582605	C₃	semidirect
3. #22582604	C₃	semidirect
4. #22582601	C₃	semidirect
5. #22582598	C₃	semidirect
6. #22582598	C₃	semidirect
7. #22582597	C₃	semidirect
8. #22582597	C₃	semidirect
9. #22582593	C₃	semidirect
10. #22582593	C₃	semidirect
11. #22582584	C₃	semidirect
12. #22582584	C₃	semidirect
13. #22582583	C₃	semidirect
14. #22582583	C₃	semidirect
15. #22582581	C₃	semidirect
16. #22582581	C₃	semidirect
17. #22582580	C₃	semidirect
18. #22582580	C₃	semidirect
19. #22582574	C₃	semidirect
20. #22582573	C₃	semidirect
21. #22582570	C₃	semidirect
22. #22582570	C₃	semidirect
23. #22582570	C₃	semidirect
24. #22582570	C₃	semidirect
25. #22582570	C₃	semidirect
26. #22582569	C₃	semidirect
27. #22582569	C₃	semidirect
28. #22582569	C₃	semidirect
29. #22582569	C₃	semidirect
30. #22582569	C₃	semidirect
31. #22582568	C₃	semidirect
32. #22582567	C₃	semidirect
33. #22582566	C₃	semidirect
37. #22582537	C₃	semidirect
38. #22582536	C₃	semidirect
39. C₉⋊C₉×C₃₇⋊C₃	C₃	semidirect
40. C₃₇×#6896	C₃	semidirect
236. C₉×C₃₇⋊C₃	3₋¹⁺²	semidirect
309. #6896	C₃₇⋊C₃	semidirect
470. C₃₇	#10624887	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
#22582605	3
#22582604	3
#22582601	3
#22582598	3
#22582597	3
#22582593	3
#22582584	3
#22582583	3
#22582581	3
#22582580	3
#22582574	3
#22582573	3
#22582570	3
#22582569	3
#22582568	3
#22582567	3
#22582566	3
#22582557	3
#22582555	3
#22582537	3
#22582536	3
C₉⋊C₉×C₃₇⋊C₃	3
C₃₇×#6896	3
#10624887	37