Subgroups — C₃₇×#29752 #22651005

Order 9472.

890 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	C₂×C₃₇×#470	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3007	C₂	1	2	yes	maximal
3	C₃₇×#2879	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2079	C₂	1	2	yes	maximal, complemented
5	C₃₇×#2052	C₂	1	4	yes	maximal, complemented
6	C₃₇×#2020	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1901	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1811	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₃₇	C₂²	1	1	yes	characteristic
10	C₂×#137×C₃₇	C₂²	1	4	yes	—
11	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic, complemented
12	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
15	C₃₇×#470	—	2	2	no	—
16	C₃₇×#470	—	2	2	no	—
17	C₃₇×#452	—	2	4	no	—
18	C₃₇×#451	—	2	2	no	—
19	C₃₇×#450	—	2	2	no	—
20	C₂×#108×C₃₇	C₂²	1	2	yes	complemented
21	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic, complemented
22	C₃₇×#417	C₂²	1	4	yes	—
23	C₂×#103×C₃₇	C₂²	1	2	yes	complemented
24	C₂×#101×C₃₇	C₂²	1	4	yes	complemented
25	C₃₇×#408	—	2	2	no	—
26	C₃₇×#408	C₂²	1	2	yes	—
27	C₃₇×#408	C₂²	1	2	yes	—
28	C₃₇×#407	—	2	2	no	—
29	C₃₇×#407	C₂²	1	2	yes	—
30	C₃₇×#343	C₂²	1	4	yes	complemented
31	C₃₇×#341	C₂²	1	2	yes	complemented
32	C₂×#41×C₃₇	—	2	1	no	—
33	C₂×#41×C₃₇	—	2	1	no	—
34	C₂×#41×C₃₇	—	4	2	no	—
35	C₂×#41×C₃₇	—	4	2	no	—
36	C₂×#41×C₃₇	D₄	1	2	yes	—
37	C₂×#41×C₃₇	C₂³	1	2	yes	—
38	C₂²×Q₈×C₃₇	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
40	C₂²×D₄×C₃₇	—	2	1	no	—
41	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₃₇	—	2	1	no	—
43	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
44	#137×C₃₇	—	4	4	no	—
45	#137×C₃₇	—	4	4	no	—
46	C₂×Q₁₆×C₃₇	—	2	4	no	—
47	C₂×Q₁₆×C₃₇	—	2	2	no	—
48	C₂×Q₁₆×C₃₇	—	4	2	no	—
49	C₂×SD₁₆×C₃₇	—	2	4	no	—
50	C₂×M₁₆×C₃₇	—	2	1	no	—
51	C₂×M₁₆×C₃₇	—	4	2	no	—
52	C₂×M₁₆×C₃₇	—	4	2	no	—
53	C₂×M₁₆×C₃₇	D₄	1	2	yes	—
54	C₂×M₁₆×C₃₇	D₄	1	2	yes	—
55	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
56	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
57	C₂²×C₈×C₃₇	—	2	1	no	—
58	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
60	C₂²⋊Q₈×C₃₇	—	2	2	no	—
61	C₂²⋊Q₈×C₃₇	—	2	2	no	—
62	C₂²⋊Q₈×C₃₇	—	2	2	no	—
63	C₂²⋊Q₈×C₃₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
67	#108×C₃₇	—	4	2	no	—
68	#106×C₃₇	—	2	2	no	—
69	#103×C₃₇	—	2	4	no	—
70	#103×C₃₇	—	2	4	no	—
71	#102×C₃₇	—	2	4	no	—
72	#101×C₃₇	—	4	4	no	—
73	C₂²⋊C₈×C₃₇	—	2	2	no	—
74	C₂²⋊C₈×C₃₇	—	2	2	no	—
75	C₂²⋊C₈×C₃₇	—	2	4	no	—
76	C₂²⋊C₈×C₃₇	—	2	4	no	—
77	C₂⁴×C₃₇	—	2	1	no	—
78	C₂⁴×C₃₇	#41	1	1	yes	characteristic
79	#41×C₃₇	—	2	4	no	—
80	#41×C₃₇	—	2	4	no	—
81	#41×C₃₇	—	4	4	no	—
82	#41×C₃₇	—	4	4	no	—
83	#41×C₃₇	—	4	2	no	—
84	#41×C₃₇	—	4	2	no	—
85	C₂×Q₈×C₃₇	—	2	1	no	—
86	C₂×Q₈×C₃₇	—	2	2	no	—
87	C₂×Q₈×C₃₇	—	2	2	no	—
88	C₂×Q₈×C₃₇	—	2	4	no	—
89	C₂×Q₈×C₃₇	—	2	4	no	—
90	C₂×Q₈×C₃₇	—	4	2	no	—
91	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
92	C₂×D₄×C₃₇	—	2	2	no	—
93	C₂×D₄×C₃₇	—	2	2	no	—
94	C₂×D₄×C₃₇	—	2	1	no	—
95	C₂×D₄×C₃₇	—	4	2	no	—
96	C₂×D₄×C₃₇	—	4	4	no	—
97	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₃₇	—	2	2	no	—
99	C₂²×C₄×C₃₇	—	2	2	no	—
100	C₂²×C₄×C₃₇	—	2	1	no	—
101	C₂²×C₄×C₃₇	—	2	2	no	—
102	C₂²×C₄×C₃₇	—	2	2	no	—
103	C₂²×C₄×C₃₇	—	2	2	no	—
104	C₂²×C₄×C₃₇	—	2	2	no	—
105	C₂²×C₄×C₃₇	—	4	2	no	—
106	C₂²×C₄×C₃₇	—	4	2	no	—
107	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
112	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
113	Q₁₆×C₃₇	—	4	4	no	—
114	Q₁₆×C₃₇	—	4	8	no	—
115	SD₁₆×C₃₇	—	4	8	no	—
116	M₁₆×C₃₇	—	2	4	no	—
117	M₁₆×C₃₇	—	2	4	no	—
118	M₁₆×C₃₇	—	2	4	no	—
119	M₁₆×C₃₇	—	4	2	no	—
120	M₁₆×C₃₇	—	4	2	no	—
121	M₁₆×C₃₇	—	4	2	no	—
122	C₂×C₈×C₃₇	—	2	2	no	—
123	C₂×C₈×C₃₇	—	2	2	no	—
124	C₂×C₈×C₃₇	—	2	2	no	—
125	C₂×C₈×C₃₇	—	2	4	no	—
126	C₂×C₈×C₃₇	—	4	2	no	—
127	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₃₇	—	2	2	no	—
130	C₄⋊C₄×C₃₇	—	2	2	no	—
131	C₄⋊C₄×C₃₇	—	4	2	no	—
132	C₄⋊C₄×C₃₇	—	4	2	no	—
133	C₂²⋊C₄×C₃₇	—	4	2	no	—
134	C₂²⋊C₄×C₃₇	—	4	2	no	—
135	C₂³×C₃₇	—	2	2	no	—
136	C₂³×C₃₇	—	2	2	no	—
137	C₂³×C₃₇	—	4	2	no	—
138	C₂³×C₃₇	—	4	2	no	—
139	C₂³×C₃₇	—	8	2	no	—
140	C₂³×C₃₇	#121	1	1	yes	characteristic
141	C₂³×C₃₇	#121	1	1	yes	characteristic
142	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
143	Q₈×C₃₇	—	2	4	no	—
144	Q₈×C₃₇	—	4	2	no	—
145	Q₈×C₃₇	—	4	4	no	—
146	Q₈×C₃₇	—	4	2	no	—
147	Q₈×C₃₇	—	4	2	no	—
148	D₄×C₃₇	—	2	4	no	—
149	D₄×C₃₇	—	4	2	no	—
150	D₄×C₃₇	—	4	4	no	—
151	D₄×C₃₇	—	4	4	no	—
152	C₂×C₄×C₃₇	—	2	2	no	—
153	C₂×C₄×C₃₇	—	2	1	no	—
154	C₂×C₄×C₃₇	—	2	1	no	—
155	C₂×C₄×C₃₇	—	2	2	no	—
156	C₂×C₄×C₃₇	—	2	2	no	—
157	C₂×C₄×C₃₇	—	2	1	no	—
158	C₂×C₄×C₃₇	—	2	1	no	—
159	C₂×C₄×C₃₇	—	2	2	no	—
160	C₂×C₄×C₃₇	—	4	4	no	—
161	C₂×C₄×C₃₇	—	4	2	no	—
162	C₂×C₄×C₃₇	—	4	2	no	—
163	C₂×C₄×C₃₇	—	4	2	no	—
164	C₂×C₄×C₃₇	—	4	2	no	—
165	C₂×C₄×C₃₇	—	4	2	no	—
166	C₂×C₄×C₃₇	—	4	4	no	—
167	C₂×C₄×C₃₇	—	8	2	no	—
168	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
169	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
170	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
173	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
174	C₈×C₃₇	—	2	2	no	—
175	C₈×C₃₇	—	2	2	no	—
176	C₈×C₃₇	—	4	4	no	—
177	C₈×C₃₇	—	4	2	no	—
178	#29752	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₃₇	—	2	2	no	—
180	C₂²×C₃₇	—	2	1	no	—
181	C₂²×C₃₇	—	2	1	no	—
182	C₂²×C₃₇	—	2	2	no	—
183	C₂²×C₃₇	—	2	2	no	—
184	C₂²×C₃₇	—	4	2	no	—
185	C₂²×C₃₇	—	4	4	no	—
186	C₂²×C₃₇	—	8	2	no	—
187	C₂²×C₃₇	—	8	4	no	—
188	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
189	C₂²×C₃₇	#538	1	2	yes	—
190	C₄×C₃₇	—	2	1	no	—
191	C₄×C₃₇	—	2	1	no	—
192	C₄×C₃₇	—	4	2	no	—
193	C₄×C₃₇	—	8	2	no	—
194	C₄×C₃₇	—	8	2	no	—
195	C₄×C₃₇	#534	1	1	yes	characteristic
196	C₄×C₃₇	#534	1	2	yes	—
197	C₄×C₃₇	#535	1	1	yes	characteristic
198	C₂×#470	C₂×C₃₇	1	1	yes	characteristic, complemented
199	#3007	C₂×C₃₇	1	2	yes	—
200	#2879	C₂×C₃₇	1	1	yes	characteristic
201	#2079	C₂×C₃₇	1	2	yes	complemented
202	#2052	C₂×C₃₇	1	4	yes	complemented
203	#2020	C₂×C₃₇	1	2	yes	complemented
204	#1901	C₂×C₃₇	1	2	yes	complemented
205	#1811	C₂×C₃₇	1	1	yes	characteristic, complemented
206	C₂×C₃₇	—	2	2	no	—
207	C₂×C₃₇	—	4	1	no	—
208	C₂×C₃₇	—	4	1	no	—
209	C₂×C₃₇	—	8	2	no	—
210	C₂×C₃₇	#2617	1	1	yes	characteristic
211	C₂×C₃₇	#3069	1	2	yes	—
212	C₂²×#41	C₂²×C₃₇	1	1	yes	characteristic
213	C₂×#137	C₂²×C₃₇	1	4	yes	—
214	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic, complemented
215	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
216	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
217	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
218	#470	—	2	2	no	—
219	#470	—	2	2	no	—
220	#452	—	2	4	no	—
221	#451	—	2	2	no	—
222	#450	—	2	2	no	—
223	C₂×#108	C₂²×C₃₇	1	2	yes	complemented
224	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic, complemented
225	#417	C₂²×C₃₇	1	4	yes	—
226	C₂×#103	C₂²×C₃₇	1	2	yes	complemented
227	C₂×#101	C₂²×C₃₇	1	4	yes	complemented
228	#408	—	2	2	no	—
229	#408	C₂²×C₃₇	1	2	yes	—
230	#408	C₂²×C₃₇	1	2	yes	—
231	#407	—	2	2	no	—
232	#407	C₂²×C₃₇	1	2	yes	—
233	#343	C₂²×C₃₇	1	4	yes	complemented
234	#341	C₂²×C₃₇	1	2	yes	complemented
235	C₃₇	#29752	1	1	yes	characteristic, direct product factor, Sylow
236	C₂×#41	—	2	1	no	—
237	C₂×#41	—	2	1	no	—
238	C₂×#41	—	4	2	no	—
239	C₂×#41	—	4	2	no	—
240	C₂×#41	D₄×C₃₇	1	2	yes	—
241	C₂×#41	C₂³×C₃₇	1	2	yes	—
242	C₂²×Q₈	D₄×C₃₇	1	1	yes	characteristic
243	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
246	C₂³×C₄	—	2	1	no	—
247	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
248	#137	—	4	4	no	—
249	#137	—	4	4	no	—
250	C₂×Q₁₆	—	2	4	no	—
251	C₂×Q₁₆	—	2	2	no	—
252	C₂×Q₁₆	—	4	2	no	—
253	C₂×SD₁₆	—	2	4	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	4	2	no	—
256	C₂×M₁₆	—	4	2	no	—
257	C₂×M₁₆	D₄×C₃₇	1	2	yes	—
258	C₂×M₁₆	D₄×C₃₇	1	2	yes	—
259	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
260	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
264	C₂²⋊Q₈	—	2	2	no	—
265	C₂²⋊Q₈	—	2	2	no	—
266	C₂²⋊Q₈	—	2	2	no	—
267	C₂²⋊Q₈	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	#108	—	4	2	no	—
272	#106	—	2	2	no	—
273	#103	—	2	4	no	—
274	#103	—	2	4	no	—
275	#102	—	2	4	no	—
276	#101	—	4	4	no	—
277	C₂²⋊C₈	—	2	2	no	—
278	C₂²⋊C₈	—	2	2	no	—
279	C₂²⋊C₈	—	2	4	no	—
280	C₂²⋊C₈	—	2	4	no	—
281	C₂⁴	—	2	1	no	—
282	C₂⁴	#41×C₃₇	1	1	yes	characteristic
283	#41	—	2	4	no	—
284	#41	—	2	4	no	—
285	#41	—	4	4	no	—
286	#41	—	4	4	no	—
287	#41	—	4	2	no	—
288	#41	—	4	2	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	4	no	—
301	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
315	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
317	Q₁₆	—	4	4	no	—
318	Q₁₆	—	4	8	no	—
319	SD₁₆	—	4	8	no	—
320	M₁₆	—	2	4	no	—
321	M₁₆	—	2	4	no	—
322	M₁₆	—	2	4	no	—
323	M₁₆	—	4	2	no	—
324	M₁₆	—	4	2	no	—
325	M₁₆	—	4	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	4	no	—
330	C₂×C₈	—	4	2	no	—
331	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
332	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	8	2	no	—
344	C₂³	#121×C₃₇	1	1	yes	characteristic
345	C₂³	#121×C₃₇	1	1	yes	characteristic
346	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
347	Q₈	—	2	4	no	—
348	Q₈	—	4	2	no	—
349	Q₈	—	4	4	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	D₄	—	2	4	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	4	no	—
355	D₄	—	4	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	8	2	no	—
372	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
373	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
376	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
377	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
378	C₈	—	2	2	no	—
379	C₈	—	2	2	no	—
380	C₈	—	4	4	no	—
381	C₈	—	4	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	8	4	no	—
391	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
392	C₂²	C₃₇×#538	1	2	yes	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	4	2	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	2	no	—
398	C₄	C₃₇×#534	1	1	yes	characteristic
399	C₄	C₃₇×#534	1	2	yes	—
400	C₄	C₃₇×#535	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	4	1	no	—
403	C₂	—	4	1	no	—
404	C₂	—	8	2	no	—
405	C₂	C₃₇×#2617	1	1	yes	characteristic
406	C₂	C₃₇×#3069	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂²×#41×C₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂³×C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#470	C₂	semidirect
4. C₃₇×#2079	C₂	semidirect
5. C₃₇×#2052	C₂	semidirect
6. C₃₇×#2020	C₂	semidirect
7. C₃₇×#1901	C₂	semidirect
8. C₃₇×#1811	C₂	semidirect
11. C₂²×Q₁₆×C₃₇	C₂²	semidirect
20. C₂×#108×C₃₇	C₂²	semidirect
21. C₂×#106×C₃₇	C₂²	semidirect
23. C₂×#103×C₃₇	C₂²	semidirect
24. C₂×#101×C₃₇	C₂²	semidirect
30. C₃₇×#343	C₂²	semidirect
31. C₃₇×#341	C₂²	semidirect
178. #29752	C₃₇	direct (N × H)
198. C₂×#470	C₂×C₃₇	semidirect
201. #2079	C₂×C₃₇	semidirect
202. #2052	C₂×C₃₇	semidirect
203. #2020	C₂×C₃₇	semidirect
204. #1901	C₂×C₃₇	semidirect
205. #1811	C₂×C₃₇	semidirect
214. C₂²×Q₁₆	C₂²×C₃₇	semidirect
223. C₂×#108	C₂²×C₃₇	semidirect
224. C₂×#106	C₂²×C₃₇	semidirect
226. C₂×#103	C₂²×C₃₇	semidirect
227. C₂×#101	C₂²×C₃₇	semidirect
233. #343	C₂²×C₃₇	semidirect
234. #341	C₂²×C₃₇	semidirect
235. C₃₇	#29752	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×#470	2
C₃₇×#3007	2
C₃₇×#2879	2
C₃₇×#2079	2
C₃₇×#2052	2
C₃₇×#2020	2
C₃₇×#1901	2
C₃₇×#1811	2
#29752	37

Subgroups — C37×#29752 #22651005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29752 #22651005