Subgroups — C₃₇×#29934 #22651187

Order 9472.

668 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#2621	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2314	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2096	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2095	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2074	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2074	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2036	C₂	1	2	yes	maximal
8	C₃₇×#2035	C₂	1	2	yes	maximal
9	C₃₇×#1981	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1949	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1798	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×#107×C₃₇	C₂²	1	2	yes	—
17	C₂×#106×C₃₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
19	C₂×#103×C₃₇	C₂²	1	2	yes	—
20	C₂×#103×C₃₇	C₂²	1	2	yes	—
21	C₂×#103×C₃₇	C₂²	1	2	yes	—
22	C₂×#103×C₃₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	—
24	C₃₇×#398	—	2	2	no	—
25	C₃₇×#397	—	2	2	no	—
26	C₃₇×#391	C₂²	1	1	yes	characteristic
27	C₃₇×#391	C₂²	1	1	yes	characteristic
28	C₃₇×#388	—	2	2	no	—
29	C₃₇×#387	—	2	2	no	—
30	C₃₇×#384	C₂²	1	1	yes	characteristic
31	C₃₇×#382	C₂²	1	1	yes	characteristic
32	C₃₇×#382	C₂²	1	1	yes	characteristic
33	C₃₇×#380	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
35	C₃₇×#340	C₂²	1	2	yes	—
36	C₃₇×#340	C₂²	1	2	yes	—
37	C₃₇×#336	C₂²	1	1	yes	characteristic
38	C₃₇×#336	C₂²	1	1	yes	characteristic
39	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
43	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
44	C₄⋊Q₈×C₃₇	—	2	4	no	—
45	C₂²⋊Q₈×C₃₇	—	4	2	no	—
46	C₂²⋊Q₈×C₃₇	—	4	2	no	—
47	#117×C₃₇	—	2	4	no	—
48	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
49	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
50	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₃₇	D₄	1	2	yes	—
61	C₂×C₄²×C₃₇	—	2	2	no	—
62	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
64	#107×C₃₇	—	4	2	no	—
65	#106×C₃₇	—	4	2	no	—
66	C₄⋊C₈×C₃₇	—	2	4	no	—
67	#103×C₃₇	—	4	2	no	—
68	#103×C₃₇	—	4	2	no	—
69	#103×C₃₇	—	4	2	no	—
70	#103×C₃₇	—	4	2	no	—
71	C₂²⋊C₈×C₃₇	—	4	2	no	—
72	#95×C₃₇	—	2	2	no	—
73	#95×C₃₇	—	2	2	no	—
74	#95×C₃₇	—	2	2	no	—
75	#95×C₃₇	—	2	2	no	—
76	#95×C₃₇	—	2	2	no	—
77	#95×C₃₇	—	2	2	no	—
78	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₃₇	—	2	2	no	—
80	C₂×Q₈×C₃₇	—	2	2	no	—
81	C₂×Q₈×C₃₇	—	2	1	no	—
82	C₂×Q₈×C₃₇	—	2	1	no	—
83	C₂×Q₈×C₃₇	—	2	2	no	—
84	C₂×Q₈×C₃₇	—	2	2	no	—
85	C₂×Q₈×C₃₇	—	2	1	no	—
86	C₂×Q₈×C₃₇	—	2	1	no	—
87	C₂²×C₄×C₃₇	—	2	2	no	—
88	C₂²×C₄×C₃₇	—	2	1	no	—
89	C₂²×C₄×C₃₇	—	2	2	no	—
90	C₂²×C₄×C₃₇	—	2	1	no	—
91	C₂²×C₄×C₃₇	—	2	2	no	—
92	C₂²×C₄×C₃₇	—	2	1	no	—
93	C₂²×C₄×C₃₇	—	2	1	no	—
94	C₂²×C₄×C₃₇	—	2	2	no	—
95	C₂²×C₄×C₃₇	—	2	1	no	—
96	C₂²×C₄×C₃₇	—	2	1	no	—
97	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
101	C₂×C₈×C₃₇	—	2	2	no	—
102	C₂×C₈×C₃₇	—	2	2	no	—
103	C₂×C₈×C₃₇	—	2	2	no	—
104	C₂×C₈×C₃₇	—	2	2	no	—
105	C₂×C₈×C₃₇	—	2	2	no	—
106	C₂×C₈×C₃₇	—	2	2	no	—
107	C₄⋊C₄×C₃₇	—	2	4	no	—
108	C₄⋊C₄×C₃₇	—	2	2	no	—
109	C₄⋊C₄×C₃₇	—	2	2	no	—
110	C₄⋊C₄×C₃₇	—	2	2	no	—
111	C₄⋊C₄×C₃₇	—	2	2	no	—
112	C₄⋊C₄×C₃₇	—	2	2	no	—
113	C₄⋊C₄×C₃₇	—	2	2	no	—
114	C₄⋊C₄×C₃₇	—	4	2	no	—
115	C₄⋊C₄×C₃₇	—	4	2	no	—
116	C₄⋊C₄×C₃₇	—	4	4	no	—
117	C₄⋊C₄×C₃₇	—	8	2	no	—
118	C₂²⋊C₄×C₃₇	—	2	4	no	—
119	C₂²⋊C₄×C₃₇	—	4	2	no	—
120	C₂²⋊C₄×C₃₇	—	4	2	no	—
121	C₂²⋊C₄×C₃₇	—	8	2	no	—
122	C₄²×C₃₇	—	2	2	no	—
123	C₄²×C₃₇	—	8	2	no	—
124	C₄²×C₃₇	#41	1	4	yes	—
125	C₂³×C₃₇	—	2	1	no	—
126	C₂³×C₃₇	—	2	1	no	—
127	C₂³×C₃₇	—	2	1	no	—
128	C₂³×C₃₇	—	2	2	no	—
129	C₂³×C₃₇	—	2	2	no	—
130	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
131	Q₈×C₃₇	—	4	2	no	—
132	Q₈×C₃₇	—	4	2	no	—
133	Q₈×C₃₇	—	4	2	no	—
134	Q₈×C₃₇	—	4	2	no	—
135	C₂×C₄×C₃₇	—	2	2	no	—
136	C₂×C₄×C₃₇	—	2	2	no	—
137	C₂×C₄×C₃₇	—	2	2	no	—
138	C₂×C₄×C₃₇	—	2	1	no	—
139	C₂×C₄×C₃₇	—	2	1	no	—
140	C₂×C₄×C₃₇	—	2	1	no	—
141	C₂×C₄×C₃₇	—	2	2	no	—
142	C₂×C₄×C₃₇	—	2	2	no	—
143	C₂×C₄×C₃₇	—	4	2	no	—
144	C₂×C₄×C₃₇	—	4	2	no	—
145	C₂×C₄×C₃₇	—	4	1	no	—
146	C₂×C₄×C₃₇	—	4	1	no	—
147	C₂×C₄×C₃₇	—	4	1	no	—
148	C₂×C₄×C₃₇	—	4	1	no	—
149	C₂×C₄×C₃₇	—	4	1	no	—
150	C₂×C₄×C₃₇	—	4	1	no	—
151	C₂×C₄×C₃₇	—	4	2	no	—
152	C₂×C₄×C₃₇	—	4	2	no	—
153	C₂×C₄×C₃₇	—	4	1	no	—
154	C₂×C₄×C₃₇	—	4	1	no	—
155	C₂×C₄×C₃₇	—	4	2	no	—
156	C₂×C₄×C₃₇	—	4	2	no	—
157	C₂×C₄×C₃₇	—	4	2	no	—
158	C₂×C₄×C₃₇	—	4	2	no	—
159	C₂×C₄×C₃₇	—	4	2	no	—
160	C₂×C₄×C₃₇	—	4	2	no	—
161	C₂×C₄×C₃₇	#123	1	4	yes	—
162	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
163	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
165	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
166	C₈×C₃₇	—	4	2	no	—
167	C₈×C₃₇	—	4	2	no	—
168	#29934	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂²×C₃₇	—	4	2	no	—
170	C₂²×C₃₇	—	4	1	no	—
171	C₂²×C₃₇	—	4	1	no	—
172	C₂²×C₃₇	—	4	1	no	—
173	C₂²×C₃₇	—	4	2	no	—
174	C₂²×C₃₇	C₂×#123	1	1	yes	characteristic
175	C₂²×C₃₇	#535	1	1	yes	characteristic
176	C₂²×C₃₇	#537	1	1	yes	characteristic
177	C₂²×C₃₇	#577	1	2	yes	—
178	C₂²×C₃₇	#578	1	2	yes	—
179	C₄×C₃₇	—	2	4	no	—
180	C₄×C₃₇	—	4	2	no	—
181	C₄×C₃₇	—	4	1	no	—
182	C₄×C₃₇	—	8	1	no	—
183	C₄×C₃₇	—	8	1	no	—
184	C₄×C₃₇	—	8	1	no	—
185	C₄×C₃₇	—	8	2	no	—
186	C₄×C₃₇	—	8	1	no	—
187	C₄×C₃₇	—	8	2	no	—
188	C₄×C₃₇	#540	1	2	yes	—
189	C₄×C₃₇	#542	1	2	yes	—
190	#2621	C₂×C₃₇	1	1	yes	characteristic
191	#2314	C₂×C₃₇	1	1	yes	characteristic
192	#2096	C₂×C₃₇	1	1	yes	characteristic, complemented
193	#2095	C₂×C₃₇	1	1	yes	characteristic, complemented
194	#2074	C₂×C₃₇	1	1	yes	characteristic, complemented
195	#2074	C₂×C₃₇	1	1	yes	characteristic, complemented
196	#2036	C₂×C₃₇	1	2	yes	—
197	#2035	C₂×C₃₇	1	2	yes	—
198	#1981	C₂×C₃₇	1	2	yes	complemented
199	#1949	C₂×C₃₇	1	2	yes	complemented
200	#1798	C₂×C₃₇	1	1	yes	characteristic
201	C₂×C₃₇	—	8	1	no	—
202	C₂×C₃₇	#2624	1	1	yes	characteristic
203	C₂×C₃₇	#3097	1	2	yes	—
204	C₂×C₃₇	#3221	1	1	yes	characteristic
205	C₂×C₃₇	#3223	1	1	yes	characteristic
206	C₂×C₃₇	#3258	1	2	yes	—
207	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
208	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
209	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
210	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic
211	C₂×#107	C₂²×C₃₇	1	2	yes	—
212	C₂×#106	C₂²×C₃₇	1	2	yes	—
213	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
214	C₂×#103	C₂²×C₃₇	1	2	yes	—
215	C₂×#103	C₂²×C₃₇	1	2	yes	—
216	C₂×#103	C₂²×C₃₇	1	2	yes	—
217	C₂×#103	C₂²×C₃₇	1	2	yes	—
218	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
219	#398	—	2	2	no	—
220	#397	—	2	2	no	—
221	#391	C₂²×C₃₇	1	1	yes	characteristic
222	#391	C₂²×C₃₇	1	1	yes	characteristic
223	#388	—	2	2	no	—
224	#387	—	2	2	no	—
225	#384	C₂²×C₃₇	1	1	yes	characteristic
226	#382	C₂²×C₃₇	1	1	yes	characteristic
227	#382	C₂²×C₃₇	1	1	yes	characteristic
228	#380	C₂²×C₃₇	1	2	yes	—
229	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
230	#340	C₂²×C₃₇	1	2	yes	—
231	#340	C₂²×C₃₇	1	2	yes	—
232	#336	C₂²×C₃₇	1	1	yes	characteristic
233	#336	C₂²×C₃₇	1	1	yes	characteristic
234	C₃₇	#29934	1	1	yes	characteristic, direct product factor, Sylow
235	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
236	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
239	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
240	C₄⋊Q₈	—	2	4	no	—
241	C₂²⋊Q₈	—	4	2	no	—
242	C₂²⋊Q₈	—	4	2	no	—
243	#117	—	2	4	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	D₄×C₃₇	1	2	yes	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
260	#107	—	4	2	no	—
261	#106	—	4	2	no	—
262	C₄⋊C₈	—	2	4	no	—
263	#103	—	4	2	no	—
264	#103	—	4	2	no	—
265	#103	—	4	2	no	—
266	#103	—	4	2	no	—
267	C₂²⋊C₈	—	4	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	#95	—	2	2	no	—
271	#95	—	2	2	no	—
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
296	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	4	no	—
313	C₄⋊C₄	—	8	2	no	—
314	C₂²⋊C₄	—	2	4	no	—
315	C₂²⋊C₄	—	4	2	no	—
316	C₂²⋊C₄	—	4	2	no	—
317	C₂²⋊C₄	—	8	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	8	2	no	—
320	C₄²	#41×C₃₇	1	4	yes	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
327	Q₈	—	4	2	no	—
328	Q₈	—	4	2	no	—
329	Q₈	—	4	2	no	—
330	Q₈	—	4	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	#123×C₃₇	1	4	yes	—
358	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
359	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
360	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
361	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
362	C₈	—	4	2	no	—
363	C₈	—	4	2	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	C₂×#123×C₃₇	1	1	yes	characteristic
370	C₂²	C₃₇×#535	1	1	yes	characteristic
371	C₂²	C₃₇×#537	1	1	yes	characteristic
372	C₂²	C₃₇×#577	1	2	yes	—
373	C₂²	C₃₇×#578	1	2	yes	—
374	C₄	—	2	4	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	8	1	no	—
378	C₄	—	8	1	no	—
379	C₄	—	8	1	no	—
380	C₄	—	8	2	no	—
381	C₄	—	8	1	no	—
382	C₄	—	8	2	no	—
383	C₄	C₃₇×#540	1	2	yes	—
384	C₄	C₃₇×#542	1	2	yes	—
385	C₂	—	8	1	no	—
386	C₂	C₃₇×#2624	1	1	yes	characteristic
387	C₂	C₃₇×#3097	1	2	yes	—
388	C₂	C₃₇×#3221	1	1	yes	characteristic
389	C₂	C₃₇×#3223	1	1	yes	characteristic
390	C₂	C₃₇×#3258	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂⁴×C₃₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂×#117×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₇×#2096	C₂	semidirect
4. C₃₇×#2095	C₂	semidirect
5. C₃₇×#2074	C₂	semidirect
6. C₃₇×#2074	C₂	semidirect
9. C₃₇×#1981	C₂	semidirect
10. C₃₇×#1949	C₂	semidirect
168. #29934	C₃₇	direct (N × H)
192. #2096	C₂×C₃₇	semidirect
193. #2095	C₂×C₃₇	semidirect
194. #2074	C₂×C₃₇	semidirect
195. #2074	C₂×C₃₇	semidirect
198. #1981	C₂×C₃₇	semidirect
199. #1949	C₂×C₃₇	semidirect
234. C₃₇	#29934	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×#2621	2
C₃₇×#2314	2
C₃₇×#2096	2
C₃₇×#2095	2
C₃₇×#2074	2
C₃₇×#2036	2
C₃₇×#2035	2
C₃₇×#1981	2
C₃₇×#1949	2
C₃₇×#1798	2
#29934	37

Subgroups — C37×#29934 #22651187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29934 #22651187