Subgroups — C₃₇×#10624914 #41004703

Order 26973.

578 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#6900	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#6899	C₃	1	2	yes	maximal, complemented
3	C₃₇×#6899	C₃	1	2	yes	maximal, complemented
4	C₃₇×#6899	C₃	1	2	yes	maximal, complemented
5	C₃₇×#6899	C₃	1	2	yes	maximal, complemented
6	C₃₇×#6898	C₃	1	2	yes	maximal, complemented
7	C₃₇×#6898	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#6897	C₃	1	2	yes	maximal, complemented
9	C₃₇×#6897	C₃	1	2	yes	maximal, complemented
10	C₃₇×#6897	C₃	1	2	yes	maximal, complemented
11	C₃₇×#6896	C₃	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#6896	C₃	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#6896	C₃	1	2	yes	maximal, complemented
14	C₃₇×#6896	C₃	1	2	yes	maximal, complemented
15	C₃₇×#6895	C₃	1	1	yes	maximal, characteristic, complemented
16	C₃₇×#6895	C₃	1	2	yes	maximal, complemented
17	C₃₇×#6894	C₃	1	2	yes	maximal, complemented
18	C₃₇×#6894	C₃	1	1	yes	maximal, characteristic, complemented
19	C₃₇×#6894	C₃	1	2	yes	maximal, complemented
20	C₃₇×#6894	C₃	1	2	yes	maximal, complemented
21	C₃₇×#6894	C₃	1	2	yes	maximal, complemented
22	C₃₇×#6893	C₃	1	1	yes	maximal, characteristic
23	C₃₇×C₉⋊H(3,𝔽₃)	C₃	1	2	yes	maximal
24	C₃₇×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
25	C₃×3₋¹⁺²×C₃₇	C₃²	1	2	yes	—
26	C₃×3₋¹⁺²×C₃₇	C₃²	1	2	yes	—
27	C₃×3₋¹⁺²×C₃₇	C₃²	1	2	yes	—
28	C₃×3₋¹⁺²×C₃₇	C₃²	1	1	yes	characteristic
29	C₃×3₋¹⁺²×C₃₇	C₃²	1	2	yes	—
30	C₃×3₋¹⁺²×C₃₇	C₃²	1	1	yes	characteristic
31	C₃×3₋¹⁺²×C₃₇	C₃²	1	1	yes	characteristic
32	C₃×H(3,𝔽₃)×C₃₇	C₃²	1	1	yes	characteristic
33	C₃²×C₉×C₃₇	C₃²	1	2	yes	—
34	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
35	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
36	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
37	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
38	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
39	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
40	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
41	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
42	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
43	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
44	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
45	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
46	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
47	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
48	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
49	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
50	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
51	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
52	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
53	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
54	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
55	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
56	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
57	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
58	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
59	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
60	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
61	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
62	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
63	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
64	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
65	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
66	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
67	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
68	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
69	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
70	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
71	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
72	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
73	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
74	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
75	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
76	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
77	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
78	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
79	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
80	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
81	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
82	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
83	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
84	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
85	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
86	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
87	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
88	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
89	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
90	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
91	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
92	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
93	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
94	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
95	C₉²×C₃₇	C₃²	1	1	yes	characteristic
96	C₉²×C₃₇	C₃²	1	2	yes	—
97	C₉²×C₃₇	C₃²	1	2	yes	—
98	C₉²×C₃₇	C₃²	1	1	yes	characteristic
99	C₃³×C₃₇	C₃³	1	2	yes	—
100	C₃³×C₃₇	C₃³	1	1	yes	characteristic
101	C₃³×C₃₇	C₃³	1	1	yes	characteristic
102	3₋¹⁺²×C₃₇	—	9	2	no	—
103	3₋¹⁺²×C₃₇	—	9	2	no	—
104	3₋¹⁺²×C₃₇	—	9	2	no	—
105	3₋¹⁺²×C₃₇	—	9	1	no	—
106	3₋¹⁺²×C₃₇	—	9	2	no	—
107	3₋¹⁺²×C₃₇	—	9	1	no	—
108	3₋¹⁺²×C₃₇	—	9	1	no	—
109	H(3,𝔽₃)×C₃₇	—	9	1	no	—
110	C₃×C₉×C₃₇	—	9	1	no	—
111	C₃×C₉×C₃₇	—	9	2	no	—
112	C₃×C₉×C₃₇	—	9	1	no	—
113	C₃×C₉×C₃₇	C₃³	1	2	yes	—
114	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
115	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
116	C₃×C₉×C₃₇	C₃³	1	2	yes	—
117	C₃×C₉×C₃₇	C₃³	1	2	yes	—
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	2	yes	—
122	C₃×C₉×C₃₇	C₃³	1	2	yes	—
123	C₃×C₉×C₃₇	C₃³	1	2	yes	—
124	C₃×C₉×C₃₇	C₃³	1	2	yes	—
125	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
126	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
127	C₃×C₉×C₃₇	C₃³	1	2	yes	—
128	C₃×C₉×C₃₇	C₃³	1	2	yes	—
129	C₃×C₉×C₃₇	C₃³	1	2	yes	—
130	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
131	C₃×C₉×C₃₇	C₃³	1	2	yes	—
132	C₃×C₉×C₃₇	C₃³	1	2	yes	—
133	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
134	#10624914	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₃²×C₃₇	—	3	1	no	—
136	C₃²×C₃₇	—	3	2	no	—
137	C₃²×C₃₇	—	3	1	no	—
138	C₃²×C₃₇	—	3	2	no	—
139	C₃²×C₃₇	—	3	1	no	—
140	C₃²×C₃₇	—	3	2	no	—
141	C₃²×C₃₇	—	3	2	no	—
142	C₃²×C₃₇	—	3	2	no	—
143	C₃²×C₃₇	—	3	2	no	—
144	C₃²×C₃₇	—	3	1	no	—
145	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
146	C₉×C₃₇	—	3	1	no	—
147	C₉×C₃₇	—	3	2	no	—
148	C₉×C₃₇	—	3	2	no	—
149	C₉×C₃₇	—	3	2	no	—
150	C₉×C₃₇	—	3	2	no	—
151	C₉×C₃₇	—	3	2	no	—
152	C₉×C₃₇	—	3	1	no	—
153	C₉×C₃₇	—	3	1	no	—
154	C₉×C₃₇	—	3	2	no	—
155	C₉×C₃₇	—	3	2	no	—
156	C₉×C₃₇	—	3	1	no	—
157	C₉×C₃₇	—	3	2	no	—
158	C₉×C₃₇	—	3	1	no	—
159	C₉×C₃₇	—	3	2	no	—
160	C₉×C₃₇	—	3	2	no	—
161	C₉×C₃₇	—	3	2	no	—
162	C₉×C₃₇	—	3	2	no	—
163	C₉×C₃₇	—	3	2	no	—
164	C₉×C₃₇	—	3	2	no	—
165	C₉×C₃₇	—	3	2	no	—
166	C₉×C₃₇	—	3	1	no	—
167	#6900	C₃×C₃₇	1	1	yes	characteristic, complemented
168	#6899	C₃×C₃₇	1	2	yes	complemented
169	#6899	C₃×C₃₇	1	2	yes	complemented
170	#6899	C₃×C₃₇	1	2	yes	complemented
171	#6899	C₃×C₃₇	1	2	yes	complemented
172	#6898	C₃×C₃₇	1	2	yes	complemented
173	#6898	C₃×C₃₇	1	1	yes	characteristic, complemented
174	#6897	C₃×C₃₇	1	2	yes	complemented
175	#6897	C₃×C₃₇	1	2	yes	complemented
176	#6897	C₃×C₃₇	1	2	yes	complemented
177	#6896	C₃×C₃₇	1	1	yes	characteristic, complemented
178	#6896	C₃×C₃₇	1	1	yes	characteristic, complemented
179	#6896	C₃×C₃₇	1	2	yes	complemented
180	#6896	C₃×C₃₇	1	2	yes	complemented
181	#6895	C₃×C₃₇	1	1	yes	characteristic, complemented
182	#6895	C₃×C₃₇	1	2	yes	complemented
183	#6894	C₃×C₃₇	1	2	yes	complemented
184	#6894	C₃×C₃₇	1	1	yes	characteristic, complemented
185	#6894	C₃×C₃₇	1	2	yes	complemented
186	#6894	C₃×C₃₇	1	2	yes	complemented
187	#6894	C₃×C₃₇	1	2	yes	complemented
188	#6893	C₃×C₃₇	1	1	yes	characteristic
189	C₉⋊H(3,𝔽₃)	C₃×C₃₇	1	2	yes	—
190	C₉⋊H(3,𝔽₃)	C₃×C₃₇	1	1	yes	characteristic
191	C₃×C₃₇	—	9	1	no	—
192	C₃×C₃₇	—	9	2	no	—
193	C₃×C₃₇	—	9	1	no	—
194	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
195	C₃×C₃₇	3₋¹⁺⁴	1	2	yes	—
196	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
197	C₃×3₋¹⁺²	C₃²×C₃₇	1	2	yes	—
198	C₃×3₋¹⁺²	C₃²×C₃₇	1	2	yes	—
199	C₃×3₋¹⁺²	C₃²×C₃₇	1	2	yes	—
200	C₃×3₋¹⁺²	C₃²×C₃₇	1	1	yes	characteristic
201	C₃×3₋¹⁺²	C₃²×C₃₇	1	2	yes	—
202	C₃×3₋¹⁺²	C₃²×C₃₇	1	1	yes	characteristic
203	C₃×3₋¹⁺²	C₃²×C₃₇	1	1	yes	characteristic
204	C₃×H(3,𝔽₃)	C₃²×C₃₇	1	1	yes	characteristic
205	C₃²×C₉	C₃²×C₃₇	1	2	yes	—
206	C₃²×C₉	C₃²×C₃₇	1	1	yes	characteristic
207	C₃²×C₉	C₃²×C₃₇	1	1	yes	characteristic
208	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
209	C₉⋊C₉	C₃²×C₃₇	1	1	yes	characteristic
210	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
211	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
212	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
213	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
214	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
215	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
216	C₉⋊C₉	C₃²×C₃₇	1	1	yes	characteristic
217	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
218	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
219	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
220	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
221	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
222	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
223	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
224	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
225	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
226	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
227	C₉⋊C₉	C₃²×C₃₇	1	1	yes	characteristic
228	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
229	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
230	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
231	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
232	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
233	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
234	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
235	C₉⋊C₉	C₃²×C₃₇	1	1	yes	characteristic
236	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
237	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
238	C₉⋊C₉	C₃²×C₃₇	1	1	yes	characteristic
239	C₉⋊C₉	C₃²×C₃₇	1	1	yes	characteristic
240	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
241	C₉⋊C₉	C₃²×C₃₇	1	1	yes	characteristic
242	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
243	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
244	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
245	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
246	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
247	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
248	C₉⋊C₉	C₃²×C₃₇	1	2	yes	—
249	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
250	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
251	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
252	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
253	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
254	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
255	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
256	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
257	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
258	C₃²⋊C₉	C₃²×C₃₇	1	1	yes	characteristic
259	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
260	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
261	C₃²⋊C₉	C₃²×C₃₇	1	1	yes	characteristic
262	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
263	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
264	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
265	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
266	C₃²⋊C₉	C₃²×C₃₇	1	1	yes	characteristic
267	C₉²	C₃²×C₃₇	1	1	yes	characteristic
268	C₉²	C₃²×C₃₇	1	2	yes	—
269	C₉²	C₃²×C₃₇	1	2	yes	—
270	C₉²	C₃²×C₃₇	1	1	yes	characteristic
271	C₃₇	#10624914	1	1	yes	characteristic, direct product factor, Sylow
272	C₃³	C₃³×C₃₇	1	2	yes	—
273	C₃³	C₃³×C₃₇	1	1	yes	characteristic
274	C₃³	C₃³×C₃₇	1	1	yes	characteristic
275	3₋¹⁺²	—	9	2	no	—
276	3₋¹⁺²	—	9	2	no	—
277	3₋¹⁺²	—	9	2	no	—
278	3₋¹⁺²	—	9	1	no	—
279	3₋¹⁺²	—	9	2	no	—
280	3₋¹⁺²	—	9	1	no	—
281	3₋¹⁺²	—	9	1	no	—
282	H(3,𝔽₃)	—	9	1	no	—
283	C₃×C₉	—	9	2	no	—
284	C₃×C₉	—	9	1	no	—
285	C₃×C₉	—	9	1	no	—
286	C₃×C₉	C₃³×C₃₇	1	2	yes	—
287	C₃×C₉	C₃³×C₃₇	1	1	yes	characteristic
288	C₃×C₉	C₃³×C₃₇	1	1	yes	characteristic
289	C₃×C₉	C₃³×C₃₇	1	2	yes	—
290	C₃×C₉	C₃³×C₃₇	1	2	yes	—
291	C₃×C₉	C₃³×C₃₇	1	2	yes	—
292	C₃×C₉	C₃³×C₃₇	1	2	yes	—
293	C₃×C₉	C₃³×C₃₇	1	2	yes	—
294	C₃×C₉	C₃³×C₃₇	1	2	yes	—
295	C₃×C₉	C₃³×C₃₇	1	2	yes	—
296	C₃×C₉	C₃³×C₃₇	1	2	yes	—
297	C₃×C₉	C₃³×C₃₇	1	2	yes	—
298	C₃×C₉	C₃³×C₃₇	1	1	yes	characteristic
299	C₃×C₉	C₃³×C₃₇	1	1	yes	characteristic
300	C₃×C₉	C₃³×C₃₇	1	2	yes	—
301	C₃×C₉	C₃³×C₃₇	1	2	yes	—
302	C₃×C₉	C₃³×C₃₇	1	2	yes	—
303	C₃×C₉	C₃³×C₃₇	1	1	yes	characteristic
304	C₃×C₉	C₃³×C₃₇	1	2	yes	—
305	C₃×C₉	C₃³×C₃₇	1	2	yes	—
306	C₃×C₉	C₃³×C₃₇	1	1	yes	characteristic
307	C₃²	—	3	1	no	—
308	C₃²	—	3	2	no	—
309	C₃²	—	3	1	no	—
310	C₃²	—	3	2	no	—
311	C₃²	—	3	1	no	—
312	C₃²	—	3	2	no	—
313	C₃²	—	3	2	no	—
314	C₃²	—	3	2	no	—
315	C₃²	—	3	2	no	—
316	C₃²	—	3	1	no	—
317	C₃²	C₃⁴×C₃₇	1	1	yes	characteristic
318	C₉	—	3	2	no	—
319	C₉	—	3	1	no	—
320	C₉	—	3	2	no	—
321	C₉	—	3	2	no	—
322	C₉	—	3	2	no	—
323	C₉	—	3	1	no	—
324	C₉	—	3	2	no	—
325	C₉	—	3	2	no	—
326	C₉	—	3	1	no	—
327	C₉	—	3	2	no	—
328	C₉	—	3	2	no	—
329	C₉	—	3	2	no	—
330	C₉	—	3	2	no	—
331	C₉	—	3	2	no	—
332	C₉	—	3	2	no	—
333	C₉	—	3	2	no	—
334	C₉	—	3	1	no	—
335	C₉	—	3	1	no	—
336	C₉	—	3	2	no	—
337	C₉	—	3	2	no	—
338	C₉	—	3	1	no	—
339	C₃	—	9	1	no	—
340	C₃	—	9	2	no	—
341	C₃	—	9	1	no	—
342	C₃	C₃₇×3₋¹⁺⁴	1	2	yes	—
343	C₃	C₃₇×3₋¹⁺⁴	1	1	yes	characteristic
344	C₃	C₃₇×3₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃²×C₃₇	C₃⁴
commutator, Frattini, cosocle	C₃²	C₃⁴×C₃₇
prime radical	C₃×H(3,𝔽₃)×C₃₇	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#6900	C₃	semidirect
2. C₃₇×#6899	C₃	semidirect
3. C₃₇×#6899	C₃	semidirect
4. C₃₇×#6899	C₃	semidirect
5. C₃₇×#6899	C₃	semidirect
6. C₃₇×#6898	C₃	semidirect
7. C₃₇×#6898	C₃	semidirect
8. C₃₇×#6897	C₃	semidirect
9. C₃₇×#6897	C₃	semidirect
10. C₃₇×#6897	C₃	semidirect
11. C₃₇×#6896	C₃	semidirect
12. C₃₇×#6896	C₃	semidirect
13. C₃₇×#6896	C₃	semidirect
14. C₃₇×#6896	C₃	semidirect
15. C₃₇×#6895	C₃	semidirect
16. C₃₇×#6895	C₃	semidirect
17. C₃₇×#6894	C₃	semidirect
18. C₃₇×#6894	C₃	semidirect
19. C₃₇×#6894	C₃	semidirect
20. C₃₇×#6894	C₃	semidirect
21. C₃₇×#6894	C₃	semidirect
134. #10624914	C₃₇	direct (N × H)
167. #6900	C₃×C₃₇	semidirect
168. #6899	C₃×C₃₇	semidirect
169. #6899	C₃×C₃₇	semidirect
170. #6899	C₃×C₃₇	semidirect
171. #6899	C₃×C₃₇	semidirect
172. #6898	C₃×C₃₇	semidirect
173. #6898	C₃×C₃₇	semidirect
174. #6897	C₃×C₃₇	semidirect
175. #6897	C₃×C₃₇	semidirect
176. #6897	C₃×C₃₇	semidirect
177. #6896	C₃×C₃₇	semidirect
178. #6896	C₃×C₃₇	semidirect
179. #6896	C₃×C₃₇	semidirect
180. #6896	C₃×C₃₇	semidirect
181. #6895	C₃×C₃₇	semidirect
182. #6895	C₃×C₃₇	semidirect
183. #6894	C₃×C₃₇	semidirect
184. #6894	C₃×C₃₇	semidirect
185. #6894	C₃×C₃₇	semidirect
186. #6894	C₃×C₃₇	semidirect
187. #6894	C₃×C₃₇	semidirect
271. C₃₇	#10624914	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₇×#6900	3
C₃₇×#6899	3
C₃₇×#6898	3
C₃₇×#6897	3
C₃₇×#6896	3
C₃₇×#6895	3
C₃₇×#6894	3
C₃₇×#6893	3
C₃₇×C₉⋊H(3,𝔽₃)	3
#10624914	37

Subgroups — C37×#10624914 #41004703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624914 #41004703