Subgroups — C₃₇×#28606 #22649859

Order 9472.

898 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#436	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2547	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2542	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2036	C₂	1	4	yes	maximal, complemented
6	C₃₇×#1988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#1981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1894	C₂	1	4	yes	maximal, complemented
9	C₄×#107×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×M₁₆×C₃₇	C₂²	1	2	yes	—
11	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#124×C₃₇	—	2	1	no	—
14	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	4	yes	—
15	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
16	C₃₇×#487	—	2	4	no	—
17	C₃₇×#436	—	2	4	no	—
18	C₂×#107×C₃₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×#103×C₃₇	C₂²	1	2	yes	—
21	C₂×#103×C₃₇	C₂²	1	2	yes	—
22	C₂×#103×C₃₇	C₂²	1	4	yes	—
23	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₃₇×#399	—	2	2	no	—
26	C₃₇×#397	—	2	2	no	—
27	C₃₇×#391	—	2	1	no	—
28	C₃₇×#390	—	2	1	no	—
29	C₃₇×#384	—	2	1	no	—
30	C₃₇×#380	C₂²	1	4	yes	—
31	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
33	C₃₇×#340	C₂²	1	2	yes	—
34	C₃₇×#340	C₂²	1	4	yes	—
35	C₂²×Q₈×C₃₇	—	2	1	no	—
36	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
37	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
39	C₂×M₁₆×C₃₇	—	2	4	no	—
40	C₂×M₁₆×C₃₇	—	4	4	no	—
41	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
42	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
44	C₄⋊Q₈×C₃₇	—	2	2	no	—
45	C₄⋊Q₈×C₃₇	—	2	2	no	—
46	C₄⋊Q₈×C₃₇	—	2	2	no	—
47	C₄⋊Q₈×C₃₇	—	2	2	no	—
48	#124×C₃₇	—	4	4	no	—
49	C₂²⋊Q₈×C₃₇	—	2	8	no	—
50	C₂²⋊Q₈×C₃₇	—	4	4	no	—
51	C₄×D₄×C₃₇	—	2	2	no	—
52	C₄×D₄×C₃₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₃₇	D₄	1	2	yes	—
64	C₂×C₄²×C₃₇	—	2	1	no	—
65	C₂×C₄²×C₃₇	—	2	1	no	—
66	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
67	#107×C₃₇	—	2	4	no	—
68	C₄⋊C₈×C₃₇	—	2	2	no	—
69	#103×C₃₇	—	2	4	no	—
70	#103×C₃₇	—	2	4	no	—
71	#103×C₃₇	—	4	4	no	—
72	C₂²⋊C₈×C₃₇	—	2	4	no	—
73	C₄×C₈×C₃₇	D₄	1	4	yes	—
74	#95×C₃₇	—	2	1	no	—
75	#95×C₃₇	—	2	1	no	—
76	#95×C₃₇	—	2	4	no	—
77	C₂⁴×C₃₇	C₂×D₄	1	2	yes	—
78	C₂×Q₈×C₃₇	—	2	2	no	—
79	C₂×Q₈×C₃₇	—	2	4	no	—
80	C₂×Q₈×C₃₇	—	2	2	no	—
81	C₂×Q₈×C₃₇	—	2	4	no	—
82	C₂×Q₈×C₃₇	—	4	2	no	—
83	C₂×Q₈×C₃₇	—	4	2	no	—
84	C₂×Q₈×C₃₇	—	4	2	no	—
85	C₂×D₄×C₃₇	—	2	2	no	—
86	C₂×D₄×C₃₇	—	2	2	no	—
87	C₂×D₄×C₃₇	—	2	2	no	—
88	C₂²×C₄×C₃₇	—	2	2	no	—
89	C₂²×C₄×C₃₇	—	2	2	no	—
90	C₂²×C₄×C₃₇	—	2	2	no	—
91	C₂²×C₄×C₃₇	—	2	4	no	—
92	C₂²×C₄×C₃₇	—	2	4	no	—
93	C₂²×C₄×C₃₇	—	2	2	no	—
94	C₂²×C₄×C₃₇	—	2	2	no	—
95	C₂²×C₄×C₃₇	—	2	2	no	—
96	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
100	M₁₆×C₃₇	—	4	8	no	—
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	4	no	—
105	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
107	C₄⋊C₄×C₃₇	—	2	2	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	—	4	8	no	—
114	C₄⋊C₄×C₃₇	—	4	2	no	—
115	C₄⋊C₄×C₃₇	—	4	2	no	—
116	C₄⋊C₄×C₃₇	—	4	2	no	—
117	C₄⋊C₄×C₃₇	#41	1	4	yes	—
118	C₂²⋊C₄×C₃₇	—	2	4	no	—
119	C₂²⋊C₄×C₃₇	—	4	8	no	—
120	C₂²⋊C₄×C₃₇	—	4	8	no	—
121	C₄²×C₃₇	—	4	2	no	—
122	C₄²×C₃₇	—	4	2	no	—
123	C₄²×C₃₇	C₂×D₄	1	2	yes	—
124	C₄²×C₃₇	#41	1	2	yes	—
125	C₂³×C₃₇	—	2	2	no	—
126	C₂³×C₃₇	—	2	4	no	—
127	C₂³×C₃₇	—	2	2	no	—
128	C₂³×C₃₇	—	2	2	no	—
129	C₂³×C₃₇	—	2	4	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	4	no	—
134	Q₈×C₃₇	—	8	4	no	—
135	D₄×C₃₇	—	4	4	no	—
136	C₂×C₄×C₃₇	—	2	2	no	—
137	C₂×C₄×C₃₇	—	2	2	no	—
138	C₂×C₄×C₃₇	—	2	4	no	—
139	C₂×C₄×C₃₇	—	2	4	no	—
140	C₂×C₄×C₃₇	—	4	2	no	—
141	C₂×C₄×C₃₇	—	4	2	no	—
142	C₂×C₄×C₃₇	—	4	2	no	—
143	C₂×C₄×C₃₇	—	4	2	no	—
144	C₂×C₄×C₃₇	—	4	4	no	—
145	C₂×C₄×C₃₇	—	4	2	no	—
146	C₂×C₄×C₃₇	—	4	2	no	—
147	C₂×C₄×C₃₇	—	4	4	no	—
148	C₂×C₄×C₃₇	—	4	2	no	—
149	C₂×C₄×C₃₇	—	4	2	no	—
150	C₂×C₄×C₃₇	—	4	2	no	—
151	C₂×C₄×C₃₇	—	4	2	no	—
152	C₂×C₄×C₃₇	—	4	2	no	—
153	C₂×C₄×C₃₇	#121	1	2	yes	—
154	C₂×C₄×C₃₇	#121	1	2	yes	—
155	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
156	C₂×C₄×C₃₇	#137	1	2	yes	—
157	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
159	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
161	C₈×C₃₇	—	2	2	no	—
162	C₈×C₃₇	—	2	2	no	—
163	C₈×C₃₇	—	4	2	no	—
164	#28606	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂²×C₃₇	—	4	4	no	—
166	C₂²×C₃₇	—	4	4	no	—
167	C₂²×C₃₇	—	4	2	no	—
168	C₂²×C₃₇	—	4	2	no	—
169	C₂²×C₃₇	—	4	2	no	—
170	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
171	C₂²×C₃₇	#546	1	2	yes	—
172	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
174	C₂²×C₃₇	#578	1	2	yes	—
175	C₄×C₃₇	—	2	2	no	—
176	C₄×C₃₇	—	4	4	no	—
177	C₄×C₃₇	—	4	2	no	—
178	C₄×C₃₇	—	8	2	no	—
179	C₄×C₃₇	—	8	2	no	—
180	C₄×C₃₇	—	8	2	no	—
181	C₄×C₃₇	#468	1	4	yes	—
182	C₄×C₃₇	#532	1	1	yes	characteristic
183	C₄×C₃₇	#535	1	1	yes	characteristic
184	C₄×C₃₇	#559	1	2	yes	—
185	C₂×#487	C₂×C₃₇	1	1	yes	characteristic, complemented
186	C₂×#436	C₂×C₃₇	1	1	yes	characteristic
187	#2547	C₂×C₃₇	1	1	yes	characteristic
188	#2542	C₂×C₃₇	1	1	yes	characteristic
189	#2036	C₂×C₃₇	1	4	yes	complemented
190	#1988	C₂×C₃₇	1	1	yes	characteristic, complemented
191	#1981	C₂×C₃₇	1	1	yes	characteristic, complemented
192	#1894	C₂×C₃₇	1	4	yes	complemented
193	C₄×#107	C₂×C₃₇	1	1	yes	characteristic, complemented
194	C₂×C₃₇	—	8	2	no	—
195	C₂×C₃₇	#2544	1	1	yes	characteristic
196	C₂×C₃₇	C₂×#468	1	1	yes	characteristic
197	C₂×C₃₇	#3059	1	1	yes	characteristic
198	C₂×C₃₇	#3328	1	2	yes	—
199	C₂×C₃₇	#3330	1	2	yes	—
200	C₂²×M₁₆	C₂²×C₃₇	1	2	yes	—
201	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
202	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
203	C₂×#124	—	2	1	no	—
204	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	4	yes	—
205	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
206	#487	—	2	4	no	—
207	#436	—	2	4	no	—
208	C₂×#107	C₂²×C₃₇	1	2	yes	—
209	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
210	C₂×#103	C₂²×C₃₇	1	2	yes	—
211	C₂×#103	C₂²×C₃₇	1	2	yes	—
212	C₂×#103	C₂²×C₃₇	1	4	yes	—
213	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
214	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
215	#399	—	2	2	no	—
216	#397	—	2	2	no	—
217	#391	—	2	1	no	—
218	#390	—	2	1	no	—
219	#384	—	2	1	no	—
220	#380	C₂²×C₃₇	1	4	yes	—
221	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
222	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
223	#340	C₂²×C₃₇	1	2	yes	—
224	#340	C₂²×C₃₇	1	4	yes	—
225	C₃₇	#28606	1	1	yes	characteristic, direct product factor, Sylow
226	C₂²×Q₈	—	2	1	no	—
227	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
228	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
230	C₂×M₁₆	—	2	4	no	—
231	C₂×M₁₆	—	4	4	no	—
232	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
233	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
235	C₄⋊Q₈	—	2	2	no	—
236	C₄⋊Q₈	—	2	2	no	—
237	C₄⋊Q₈	—	2	2	no	—
238	C₄⋊Q₈	—	2	2	no	—
239	#124	—	4	4	no	—
240	C₂²⋊Q₈	—	2	8	no	—
241	C₂²⋊Q₈	—	4	4	no	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
252	C₂×C₂²⋊C₄	—	2	4	no	—
253	C₂×C₂²⋊C₄	—	2	4	no	—
254	C₂×C₂²⋊C₄	D₄×C₃₇	1	2	yes	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
258	#107	—	2	4	no	—
259	C₄⋊C₈	—	2	2	no	—
260	#103	—	2	4	no	—
261	#103	—	2	4	no	—
262	#103	—	4	4	no	—
263	C₂²⋊C₈	—	2	4	no	—
264	C₄×C₈	D₄×C₃₇	1	4	yes	—
265	#95	—	2	1	no	—
266	#95	—	2	1	no	—
267	#95	—	2	4	no	—
268	C₂⁴	C₂×D₄×C₃₇	1	2	yes	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	4	2	no	—
274	C₂×Q₈	—	4	2	no	—
275	C₂×Q₈	—	4	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
290	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
291	M₁₆	—	4	8	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
297	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	4	8	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	#41×C₃₇	1	4	yes	—
309	C₂²⋊C₄	—	2	4	no	—
310	C₂²⋊C₄	—	4	8	no	—
311	C₂²⋊C₄	—	4	8	no	—
312	C₄²	—	4	2	no	—
313	C₄²	—	4	2	no	—
314	C₄²	C₂×D₄×C₃₇	1	2	yes	—
315	C₄²	#41×C₃₇	1	2	yes	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	4	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	4	no	—
321	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
322	Q₈	—	4	2	no	—
323	Q₈	—	4	2	no	—
324	Q₈	—	4	4	no	—
325	Q₈	—	8	4	no	—
326	D₄	—	4	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	#121×C₃₇	1	2	yes	—
345	C₂×C₄	#121×C₃₇	1	2	yes	—
346	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
347	C₂×C₄	#137×C₃₇	1	2	yes	—
348	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
349	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
350	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
351	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
352	C₈	—	2	2	no	—
353	C₈	—	2	2	no	—
354	C₈	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	4	no	—
359	C₂²	—	4	4	no	—
360	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
361	C₂²	C₃₇×#546	1	2	yes	—
362	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
363	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
364	C₂²	C₃₇×#578	1	2	yes	—
365	C₄	—	2	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	4	no	—
368	C₄	—	8	2	no	—
369	C₄	—	8	2	no	—
370	C₄	—	8	2	no	—
371	C₄	C₃₇×#468	1	4	yes	—
372	C₄	C₃₇×#532	1	1	yes	characteristic
373	C₄	C₃₇×#535	1	1	yes	characteristic
374	C₄	C₃₇×#559	1	2	yes	—
375	C₂	—	8	2	no	—
376	C₂	C₃₇×#2544	1	1	yes	characteristic
377	C₂	C₂×C₃₇×#468	1	1	yes	characteristic
378	C₂	C₃₇×#3059	1	1	yes	characteristic
379	C₂	C₃₇×#3328	1	2	yes	—
380	C₂	C₃₇×#3330	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#487	C₂	semidirect
5. C₃₇×#2036	C₂	semidirect
6. C₃₇×#1988	C₂	semidirect
7. C₃₇×#1981	C₂	semidirect
8. C₃₇×#1894	C₂	semidirect
9. C₄×#107×C₃₇	C₂	semidirect
164. #28606	C₃₇	direct (N × H)
185. C₂×#487	C₂×C₃₇	semidirect
189. #2036	C₂×C₃₇	semidirect
190. #1988	C₂×C₃₇	semidirect
191. #1981	C₂×C₃₇	semidirect
192. #1894	C₂×C₃₇	semidirect
193. C₄×#107	C₂×C₃₇	semidirect
225. C₃₇	#28606	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#487	2
C₂×C₃₇×#436	2
C₃₇×#2547	2
C₃₇×#2542	2
C₃₇×#2036	2
C₃₇×#1988	2
C₃₇×#1981	2
C₃₇×#1894	2
C₄×#107×C₃₇	2
#28606	37

Subgroups — C37×#28606 #22649859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28606 #22649859