Subgroups — C₃₇×#33786 #22655039

Order 9472.

618 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3176	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3155	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2250	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2246	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2244	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2242	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2210	C₂	1	2	yes	maximal, complemented
8	C₃₇×#2206	C₂	1	2	yes	maximal, complemented
9	C₃₇×#2186	C₂	1	2	yes	maximal, complemented
10	C₃₇×#2184	C₂	1	2	yes	maximal, complemented
11	C₃₇×#2164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₃₇	—	2	1	no	—
13	C₂×#135×C₃₇	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₃₇×#540	—	2	1	no	—
16	C₃₇×#535	—	2	1	no	—
17	C₂×SD₃₂×C₃₇	C₂²	1	2	yes	complemented
18	C₂×D₁₆×C₃₇	C₂²	1	2	yes	—
19	C₂×D₁₆×C₃₇	C₂²	1	2	yes	—
20	C₂×D₁₆×C₃₇	C₂²	1	2	yes	complemented
21	C₃₇×#499	C₂²	1	1	yes	characteristic, complemented
22	C₃₇×#496	—	2	1	no	—
23	C₃₇×#496	—	2	1	no	—
24	C₃₇×#495	C₂²	1	1	yes	characteristic
25	C₃₇×#495	C₂²	1	1	yes	characteristic
26	C₃₇×#493	C₂²	1	1	yes	characteristic
27	C₃₇×#493	C₂²	1	1	yes	characteristic
28	C₃₇×#493	C₂²	1	1	yes	characteristic, complemented
29	C₃₇×#490	—	2	1	no	—
30	C₃₇×#469	—	2	1	no	—
31	C₃₇×#466	C₂²	1	2	yes	—
32	C₃₇×#442	—	2	1	no	—
33	C₄×D₈×C₃₇	C₂²	1	2	yes	complemented
34	C₃₇×#405	C₂²	1	1	yes	characteristic
35	C₃₇×C₄⋊C₁₆	C₂²	1	2	yes	complemented
36	C₃₇×#358	C₂²	1	2	yes	complemented
37	C₃₇×#357	C₂²	1	2	yes	—
38	C₃₇×#357	C₂²	1	2	yes	—
39	C₃₇×#357	C₂²	1	2	yes	complemented
40	C₃₇×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₃₇×#346	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₁₆×C₃₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#41×C₃₇	—	2	1	no	—
44	C₂²×D₄×C₃₇	—	2	1	no	—
45	AGL(1,ℤ/8)×C₃₇	—	4	4	no	—
46	#135×C₃₇	—	4	2	no	—
47	C₂×Q₁₆×C₃₇	C₂³	1	1	yes	characteristic
48	C₂×SD₁₆×C₃₇	—	2	1	no	—
49	C₂×SD₁₆×C₃₇	—	2	1	no	—
50	C₂×SD₁₆×C₃₇	—	2	1	no	—
51	C₂×D₈×C₃₇	—	2	1	no	—
52	C₂×D₈×C₃₇	—	2	1	no	—
53	C₂×D₈×C₃₇	—	2	1	no	—
54	C₂×D₈×C₃₇	—	2	1	no	—
55	C₂×D₈×C₃₇	—	4	2	no	—
56	C₂×D₈×C₃₇	C₂³	1	1	yes	characteristic
57	C₂×D₈×C₃₇	C₂³	1	1	yes	characteristic
58	C₂×D₈×C₃₇	C₂³	1	1	yes	characteristic
59	C₂×D₈×C₃₇	C₂³	1	2	yes	—
60	C₂×M₁₆×C₃₇	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
62	#127×C₃₇	—	2	1	no	—
63	#127×C₃₇	—	2	1	no	—
64	#127×C₃₇	—	2	1	no	—
65	#125×C₃₇	—	2	1	no	—
66	#124×C₃₇	—	2	1	no	—
67	#124×C₃₇	—	2	1	no	—
68	#123×C₃₇	—	4	2	no	—
69	#121×C₃₇	—	2	2	no	—
70	#121×C₃₇	—	4	2	no	—
71	#121×C₃₇	—	4	2	no	—
72	#120×C₃₇	—	4	2	no	—
73	C₄×D₄×C₃₇	—	2	2	no	—
74	#117×C₃₇	D₄	1	1	yes	characteristic
75	SD₃₂×C₃₇	—	4	2	no	—
76	D₁₆×C₃₇	—	4	2	no	—
77	D₁₆×C₃₇	—	4	2	no	—
78	D₁₆×C₃₇	—	4	2	no	—
79	C₂×C₁₆×C₃₇	C₂³	1	2	yes	—
80	C₂×C₁₆×C₃₇	C₂³	1	2	yes	—
81	#107×C₃₇	C₂³	1	2	yes	—
82	#106×C₃₇	—	2	1	no	—
83	#102×C₃₇	—	2	2	no	—
84	#102×C₃₇	—	2	2	no	—
85	#97×C₃₇	D₄	1	1	yes	characteristic
86	#97×C₃₇	D₄	1	1	yes	characteristic
87	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
89	C₂⁴×C₃₇	—	4	1	no	—
90	#41×C₃₇	—	4	2	no	—
91	#41×C₃₇	—	4	2	no	—
92	C₂×Q₈×C₃₇	—	2	1	no	—
93	C₂×D₄×C₃₇	—	2	2	no	—
94	C₂×D₄×C₃₇	—	2	1	no	—
95	C₂×D₄×C₃₇	—	2	1	no	—
96	C₂×D₄×C₃₇	—	2	1	no	—
97	C₂×D₄×C₃₇	—	4	2	no	—
98	C₂×D₄×C₃₇	—	4	2	no	—
99	C₂×D₄×C₃₇	—	4	1	no	—
100	C₂×D₄×C₃₇	—	4	2	no	—
101	C₂×D₄×C₃₇	—	4	1	no	—
102	C₂×D₄×C₃₇	—	4	2	no	—
103	C₂×D₄×C₃₇	—	4	2	no	—
104	C₂×D₄×C₃₇	—	4	2	no	—
105	C₂²×C₄×C₃₇	—	4	1	no	—
106	C₂²×C₄×C₃₇	—	4	2	no	—
107	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
108	Q₁₆×C₃₇	—	2	2	no	—
109	SD₁₆×C₃₇	—	4	2	no	—
110	SD₁₆×C₃₇	—	4	2	no	—
111	SD₁₆×C₃₇	—	4	2	no	—
112	D₈×C₃₇	—	2	2	no	—
113	D₈×C₃₇	—	2	2	no	—
114	D₈×C₃₇	—	2	2	no	—
115	D₈×C₃₇	—	2	2	no	—
116	D₈×C₃₇	—	2	2	no	—
117	D₈×C₃₇	—	4	2	no	—
118	D₈×C₃₇	—	4	2	no	—
119	D₈×C₃₇	—	4	2	no	—
120	D₈×C₃₇	—	4	2	no	—
121	M₁₆×C₃₇	—	2	2	no	—
122	C₂×C₈×C₃₇	—	2	2	no	—
123	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₃₇	C₂⁴	1	1	yes	characteristic
127	C₄⋊C₄×C₃₇	—	2	2	no	—
128	C₄⋊C₄×C₃₇	—	4	2	no	—
129	C₄⋊C₄×C₃₇	D₈	1	2	yes	—
130	C₂²⋊C₄×C₃₇	—	4	2	no	—
131	C₂²⋊C₄×C₃₇	—	4	2	no	—
132	C₂²⋊C₄×C₃₇	—	4	2	no	—
133	C₂²⋊C₄×C₃₇	—	4	2	no	—
134	C₂²⋊C₄×C₃₇	D₈	1	2	yes	—
135	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
137	C₁₆×C₃₇	—	2	2	no	—
138	C₁₆×C₃₇	—	2	2	no	—
139	C₂³×C₃₇	—	4	2	no	—
140	C₂³×C₃₇	—	4	1	no	—
141	C₂³×C₃₇	—	4	1	no	—
142	C₂³×C₃₇	—	4	1	no	—
143	C₂³×C₃₇	—	8	2	no	—
144	C₂³×C₃₇	—	16	2	no	—
145	C₂³×C₃₇	C₂×D₈	1	1	yes	characteristic
146	Q₈×C₃₇	—	4	1	no	—
147	Q₈×C₃₇	—	4	1	no	—
148	D₄×C₃₇	—	4	1	no	—
149	D₄×C₃₇	—	4	1	no	—
150	D₄×C₃₇	—	4	1	no	—
151	D₄×C₃₇	—	4	2	no	—
152	D₄×C₃₇	—	4	1	no	—
153	D₄×C₃₇	—	4	1	no	—
154	D₄×C₃₇	—	4	1	no	—
155	D₄×C₃₇	—	4	2	no	—
156	D₄×C₃₇	—	8	2	no	—
157	D₄×C₃₇	—	8	2	no	—
158	D₄×C₃₇	—	16	2	no	—
159	D₄×C₃₇	—	16	2	no	—
160	D₄×C₃₇	—	16	2	no	—
161	D₄×C₃₇	—	16	2	no	—
162	C₂×C₄×C₃₇	—	2	1	no	—
163	C₂×C₄×C₃₇	—	2	1	no	—
164	C₂×C₄×C₃₇	—	4	1	no	—
165	C₂×C₄×C₃₇	—	4	2	no	—
166	C₂×C₄×C₃₇	—	8	2	no	—
167	C₂×C₄×C₃₇	—	16	2	no	—
168	C₂×C₄×C₃₇	C₂×D₈	1	2	yes	—
169	C₂×C₄×C₃₇	C₂×D₈	1	2	yes	—
170	C₂×C₄×C₃₇	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
172	C₈×C₃₇	—	2	1	no	—
173	C₈×C₃₇	—	2	1	no	—
174	C₈×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
175	C₈×C₃₇	H(5,𝔽₂)	1	2	yes	—
176	#33786	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂²×C₃₇	—	2	2	no	—
178	C₂²×C₃₇	—	2	1	no	—
179	C₂²×C₃₇	—	8	2	no	—
180	C₂²×C₃₇	—	8	2	no	—
181	C₂²×C₃₇	—	8	2	no	—
182	C₂²×C₃₇	—	8	2	no	—
183	C₂²×C₃₇	—	8	2	no	—
184	C₂²×C₃₇	—	8	1	no	—
185	C₂²×C₃₇	—	8	1	no	—
186	C₂²×C₃₇	—	8	1	no	—
187	C₂²×C₃₇	—	8	2	no	—
188	C₂²×C₃₇	—	16	4	no	—
189	C₂²×C₃₇	C₂²×D₈	1	1	yes	characteristic
190	C₄×C₃₇	—	2	2	no	—
191	C₄×C₃₇	—	2	2	no	—
192	C₄×C₃₇	—	2	1	no	—
193	C₄×C₃₇	—	8	2	no	—
194	C₄×C₃₇	—	8	1	no	—
195	C₄×C₃₇	#535	1	1	yes	characteristic
196	C₄×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	#3176	C₂×C₃₇	1	1	yes	characteristic, complemented
198	#3155	C₂×C₃₇	1	1	yes	characteristic, complemented
199	#2250	C₂×C₃₇	1	1	yes	characteristic, complemented
200	#2246	C₂×C₃₇	1	1	yes	characteristic, complemented
201	#2244	C₂×C₃₇	1	1	yes	characteristic, complemented
202	#2242	C₂×C₃₇	1	1	yes	characteristic, complemented
203	#2210	C₂×C₃₇	1	2	yes	complemented
204	#2206	C₂×C₃₇	1	2	yes	complemented
205	#2186	C₂×C₃₇	1	2	yes	complemented
206	#2184	C₂×C₃₇	1	2	yes	complemented
207	#2164	C₂×C₃₇	1	1	yes	characteristic, complemented
208	C₂×C₃₇	—	4	1	no	—
209	C₂×C₃₇	—	16	2	no	—
210	C₂×C₃₇	—	16	1	no	—
211	C₂×C₃₇	—	16	1	no	—
212	C₂×C₃₇	—	16	1	no	—
213	C₂×C₃₇	#3205	1	1	yes	characteristic
214	C₂×C₃₇	#3415	1	2	yes	—
215	C₂×AGL(1,ℤ/8)	—	2	1	no	—
216	C₂×#135	C₂²×C₃₇	1	1	yes	characteristic
217	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
218	#540	—	2	1	no	—
219	#535	—	2	1	no	—
220	C₂×SD₃₂	C₂²×C₃₇	1	2	yes	complemented
221	C₂×D₁₆	C₂²×C₃₇	1	2	yes	—
222	C₂×D₁₆	C₂²×C₃₇	1	2	yes	—
223	C₂×D₁₆	C₂²×C₃₇	1	2	yes	complemented
224	#499	C₂²×C₃₇	1	1	yes	characteristic, complemented
225	#496	—	2	1	no	—
226	#496	—	2	1	no	—
227	#495	C₂²×C₃₇	1	1	yes	characteristic
228	#495	C₂²×C₃₇	1	1	yes	characteristic
229	#493	C₂²×C₃₇	1	1	yes	characteristic
230	#493	C₂²×C₃₇	1	1	yes	characteristic
231	#493	C₂²×C₃₇	1	1	yes	characteristic, complemented
232	#490	—	2	1	no	—
233	#469	—	2	1	no	—
234	#466	C₂²×C₃₇	1	2	yes	—
235	#442	—	2	1	no	—
236	C₄×D₈	C₂²×C₃₇	1	2	yes	complemented
237	#405	C₂²×C₃₇	1	1	yes	characteristic
238	C₄⋊C₁₆	C₂²×C₃₇	1	2	yes	complemented
239	#358	C₂²×C₃₇	1	2	yes	complemented
240	#357	C₂²×C₃₇	1	2	yes	—
241	#357	C₂²×C₃₇	1	2	yes	—
242	#357	C₂²×C₃₇	1	2	yes	complemented
243	C₂²⋊C₁₆	C₂²×C₃₇	1	2	yes	—
244	#346	C₂²×C₃₇	1	1	yes	characteristic, complemented
245	C₄×C₁₆	C₂²×C₃₇	1	1	yes	characteristic, complemented
246	C₃₇	#33786	1	1	yes	characteristic, direct product factor, Sylow
247	C₂×#41	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	AGL(1,ℤ/8)	—	4	4	no	—
250	#135	—	4	2	no	—
251	C₂×Q₁₆	C₂³×C₃₇	1	1	yes	characteristic
252	C₂×SD₁₆	—	2	1	no	—
253	C₂×SD₁₆	—	2	1	no	—
254	C₂×SD₁₆	—	2	1	no	—
255	C₂×D₈	—	2	1	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	—	2	1	no	—
259	C₂×D₈	—	4	2	no	—
260	C₂×D₈	C₂³×C₃₇	1	1	yes	characteristic
261	C₂×D₈	C₂³×C₃₇	1	1	yes	characteristic
262	C₂×D₈	C₂³×C₃₇	1	1	yes	characteristic
263	C₂×D₈	C₂³×C₃₇	1	2	yes	—
264	C₂×M₁₆	D₄×C₃₇	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
266	#127	—	2	1	no	—
267	#127	—	2	1	no	—
268	#127	—	2	1	no	—
269	#125	—	2	1	no	—
270	#124	—	2	1	no	—
271	#124	—	2	1	no	—
272	#123	—	4	2	no	—
273	#121	—	2	2	no	—
274	#121	—	4	2	no	—
275	#121	—	4	2	no	—
276	#120	—	4	2	no	—
277	C₄×D₄	—	2	2	no	—
278	#117	D₄×C₃₇	1	1	yes	characteristic
279	SD₃₂	—	4	2	no	—
280	D₁₆	—	4	2	no	—
281	D₁₆	—	4	2	no	—
282	D₁₆	—	4	2	no	—
283	C₂×C₁₆	C₂³×C₃₇	1	2	yes	—
284	C₂×C₁₆	C₂³×C₃₇	1	2	yes	—
285	#107	C₂³×C₃₇	1	2	yes	—
286	#106	—	2	1	no	—
287	#102	—	2	2	no	—
288	#102	—	2	2	no	—
289	#97	D₄×C₃₇	1	1	yes	characteristic
290	#97	D₄×C₃₇	1	1	yes	characteristic
291	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
292	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
293	C₂⁴	—	4	1	no	—
294	#41	—	4	2	no	—
295	#41	—	4	2	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
312	Q₁₆	—	2	2	no	—
313	SD₁₆	—	4	2	no	—
314	SD₁₆	—	4	2	no	—
315	SD₁₆	—	4	2	no	—
316	D₈	—	2	2	no	—
317	D₈	—	2	2	no	—
318	D₈	—	2	2	no	—
319	D₈	—	2	2	no	—
320	D₈	—	2	2	no	—
321	D₈	—	4	2	no	—
322	D₈	—	4	2	no	—
323	D₈	—	4	2	no	—
324	D₈	—	4	2	no	—
325	M₁₆	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
329	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
330	C₂×C₈	C₂⁴×C₃₇	1	1	yes	characteristic
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	D₈×C₃₇	1	2	yes	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	D₈×C₃₇	1	2	yes	—
339	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
341	C₁₆	—	2	2	no	—
342	C₁₆	—	2	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	8	2	no	—
348	C₂³	—	16	2	no	—
349	C₂³	C₂×D₈×C₃₇	1	1	yes	characteristic
350	Q₈	—	4	1	no	—
351	Q₈	—	4	1	no	—
352	D₄	—	4	1	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	1	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	1	no	—
357	D₄	—	4	1	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	2	no	—
360	D₄	—	8	2	no	—
361	D₄	—	8	2	no	—
362	D₄	—	16	2	no	—
363	D₄	—	16	2	no	—
364	D₄	—	16	2	no	—
365	D₄	—	16	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	—	16	2	no	—
372	C₂×C₄	C₂×D₈×C₃₇	1	2	yes	—
373	C₂×C₄	C₂×D₈×C₃₇	1	2	yes	—
374	C₂×C₄	C₂×D₈×C₃₇	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
379	C₈	H(5,𝔽₂)×C₃₇	1	2	yes	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	1	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	16	4	no	—
392	C₂²	C₂²×D₈×C₃₇	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	1	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	1	no	—
398	C₄	C₃₇×#535	1	1	yes	characteristic
399	C₄	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
400	C₂	—	4	1	no	—
401	C₂	—	16	1	no	—
402	C₂	—	16	1	no	—
403	C₂	—	16	2	no	—
404	C₂	—	16	1	no	—
405	C₂	C₃₇×#3205	1	1	yes	characteristic
406	C₂	C₃₇×#3415	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ #117×C₃₇ ◁ C₃₇×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3176	C₂	semidirect
2. C₃₇×#3155	C₂	semidirect
3. C₃₇×#2250	C₂	semidirect
4. C₃₇×#2246	C₂	semidirect
5. C₃₇×#2244	C₂	semidirect
6. C₃₇×#2242	C₂	semidirect
7. C₃₇×#2210	C₂	semidirect
8. C₃₇×#2206	C₂	semidirect
9. C₃₇×#2186	C₂	semidirect
10. C₃₇×#2184	C₂	semidirect
11. C₃₇×#2164	C₂	semidirect
17. C₂×SD₃₂×C₃₇	C₂²	semidirect
20. C₂×D₁₆×C₃₇	C₂²	semidirect
21. C₃₇×#499	C₂²	semidirect
28. C₃₇×#493	C₂²	semidirect
33. C₄×D₈×C₃₇	C₂²	semidirect
35. C₃₇×C₄⋊C₁₆	C₂²	semidirect
36. C₃₇×#358	C₂²	semidirect
39. C₃₇×#357	C₂²	semidirect
41. C₃₇×#346	C₂²	semidirect
42. C₄×C₁₆×C₃₇	C₂²	semidirect
176. #33786	C₃₇	direct (N × H)
197. #3176	C₂×C₃₇	semidirect
198. #3155	C₂×C₃₇	semidirect
199. #2250	C₂×C₃₇	semidirect
200. #2246	C₂×C₃₇	semidirect
201. #2244	C₂×C₃₇	semidirect
202. #2242	C₂×C₃₇	semidirect
203. #2210	C₂×C₃₇	semidirect
204. #2206	C₂×C₃₇	semidirect
205. #2186	C₂×C₃₇	semidirect
206. #2184	C₂×C₃₇	semidirect
207. #2164	C₂×C₃₇	semidirect
220. C₂×SD₃₂	C₂²×C₃₇	semidirect
223. C₂×D₁₆	C₂²×C₃₇	semidirect
224. #499	C₂²×C₃₇	semidirect
231. #493	C₂²×C₃₇	semidirect
236. C₄×D₈	C₂²×C₃₇	semidirect
238. C₄⋊C₁₆	C₂²×C₃₇	semidirect
239. #358	C₂²×C₃₇	semidirect
242. #357	C₂²×C₃₇	semidirect
244. #346	C₂²×C₃₇	semidirect
245. C₄×C₁₆	C₂²×C₃₇	semidirect
246. C₃₇	#33786	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×#3176	2
C₃₇×#3155	2
C₃₇×#2250	2
C₃₇×#2246	2
C₃₇×#2244	2
C₃₇×#2242	2
C₃₇×#2210	2
C₃₇×#2206	2
C₃₇×#2186	2
C₃₇×#2184	2
C₃₇×#2164	2
#33786	37

Subgroups — C37×#33786 #22655039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#33786 #22655039