Subgroups — C₃₇×#19391 #22640644

Order 9472.

696 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3227	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3036	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2972	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1677	C₂	1	4	yes	maximal, complemented
6	C₃₇×#1671	C₂	1	4	yes	maximal, complemented
7	C₃₇×#1570	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1540	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₃₇	—	2	1	no	—
11	C₃₇×#532	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
14	C₃₇×#498	C₂²	1	2	yes	complemented
15	C₃₇×#486	C₂²	1	2	yes	complemented
16	C₃₇×#481	—	2	2	no	—
17	C₃₇×#476	—	2	2	no	—
18	C₃₇×#476	—	2	2	no	—
19	C₃₇×#476	C₂²	1	4	yes	—
20	C₃₇×#463	—	2	2	no	—
21	C₃₇×#461	C₂²	1	2	yes	—
22	C₃₇×#459	C₂²	1	2	yes	—
23	C₈×D₄×C₃₇	—	2	2	no	—
24	C₈×D₄×C₃₇	C₂²	1	4	yes	—
25	C₃₇×#431	C₂²	1	1	yes	characteristic
26	C₃₇×#431	C₂²	1	1	yes	characteristic
27	C₂×#106×C₃₇	—	2	1	no	—
28	C₃₇×#423	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
30	C₃₇×#417	—	2	1	no	—
31	C₂×#102×C₃₇	—	2	1	no	—
32	C₂×C₂²⋊C₈×C₃₇	—	2	2	no	—
33	C₃₇×#334	C₂²	1	4	yes	complemented
34	C₃₇×#333	C₂²	1	4	yes	complemented
35	C₃₇×#332	C₂²	1	2	yes	complemented
36	C₃₇×#331	C₂²	1	2	yes	complemented
37	C₂×#41×C₃₇	—	2	1	no	—
38	C₂²×Q₈×C₃₇	—	2	1	no	—
39	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₃₇	—	2	1	no	—
41	AGL(1,ℤ/8)×C₃₇	—	4	4	no	—
42	C₂×SD₁₆×C₃₇	—	2	2	no	—
43	C₂×D₈×C₃₇	—	2	2	no	—
44	C₂×M₁₆×C₃₇	—	2	1	no	—
45	C₂²×C₈×C₃₇	—	2	1	no	—
46	C₂²×C₈×C₃₇	—	2	4	no	—
47	C₄⋊Q₈×C₃₇	—	2	1	no	—
48	C₄⋊Q₈×C₃₇	—	2	1	no	—
49	C₄⋊Q₈×C₃₇	—	2	1	no	—
50	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
52	#127×C₃₇	C₂³	1	1	yes	characteristic
53	#124×C₃₇	—	2	1	no	—
54	#121×C₃₇	—	2	1	no	—
55	#121×C₃₇	—	2	1	no	—
56	C₄×D₄×C₃₇	—	2	1	no	—
57	C₄×D₄×C₃₇	—	2	1	no	—
58	C₄×D₄×C₃₇	—	2	1	no	—
59	C₄×D₄×C₃₇	—	2	1	no	—
60	C₄×D₄×C₃₇	D₄	1	2	yes	—
61	C₄×D₄×C₃₇	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
66	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
67	#106×C₃₇	—	2	4	no	—
68	#106×C₃₇	—	2	4	no	—
69	C₄⋊C₈×C₃₇	—	2	1	no	—
70	C₄⋊C₈×C₃₇	—	2	1	no	—
71	C₄⋊C₈×C₃₇	D₄	1	2	yes	—
72	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
73	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
74	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
75	#103×C₃₇	—	2	2	no	—
76	#102×C₃₇	—	2	4	no	—
77	#102×C₃₇	—	2	4	no	—
78	#102×C₃₇	—	2	2	no	—
79	C₂²⋊C₈×C₃₇	—	2	1	no	—
80	C₂²⋊C₈×C₃₇	—	2	4	no	—
81	C₂²⋊C₈×C₃₇	D₄	1	2	yes	—
82	C₄×C₈×C₃₇	—	2	1	no	—
83	C₄×C₈×C₃₇	C₂³	1	2	yes	—
84	C₂⁴×C₃₇	—	2	1	no	—
85	#41×C₃₇	—	4	2	no	—
86	#41×C₃₇	—	4	2	no	—
87	C₂×Q₈×C₃₇	—	2	1	no	—
88	C₂×Q₈×C₃₇	—	2	2	no	—
89	C₂×Q₈×C₃₇	—	4	1	no	—
90	C₂×Q₈×C₃₇	—	8	2	no	—
91	C₂×D₄×C₃₇	—	2	1	no	—
92	C₂×D₄×C₃₇	—	2	2	no	—
93	C₂×D₄×C₃₇	—	2	1	no	—
94	C₂×D₄×C₃₇	—	2	1	no	—
95	C₂×D₄×C₃₇	—	2	1	no	—
96	C₂×D₄×C₃₇	—	4	1	no	—
97	C₂×D₄×C₃₇	SD₁₆	1	4	yes	—
98	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₃₇	—	2	1	no	—
100	C₂²×C₄×C₃₇	—	2	2	no	—
101	C₂²×C₄×C₃₇	—	2	2	no	—
102	C₂²×C₄×C₃₇	—	4	1	no	—
103	C₂²×C₄×C₃₇	—	4	1	no	—
104	C₂²×C₄×C₃₇	—	8	2	no	—
105	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
108	SD₁₆×C₃₇	—	4	4	no	—
109	D₈×C₃₇	—	4	4	no	—
110	M₁₆×C₃₇	—	4	2	no	—
111	C₂×C₈×C₃₇	—	2	2	no	—
112	C₂×C₈×C₃₇	—	2	2	no	—
113	C₂×C₈×C₃₇	—	2	2	no	—
114	C₂×C₈×C₃₇	—	4	2	no	—
115	C₂×C₈×C₃₇	—	8	4	no	—
116	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
117	C₄⋊C₄×C₃₇	—	2	1	no	—
118	C₄⋊C₄×C₃₇	—	2	2	no	—
119	C₄⋊C₄×C₃₇	—	2	2	no	—
120	C₄⋊C₄×C₃₇	—	2	1	no	—
121	C₄⋊C₄×C₃₇	—	2	1	no	—
122	C₄⋊C₄×C₃₇	—	4	1	no	—
123	C₄⋊C₄×C₃₇	—	4	1	no	—
124	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
125	C₂²⋊C₄×C₃₇	—	2	2	no	—
126	C₂²⋊C₄×C₃₇	—	2	2	no	—
127	C₂²⋊C₄×C₃₇	—	4	1	no	—
128	C₂²⋊C₄×C₃₇	—	4	1	no	—
129	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₃₇	#41	1	1	yes	characteristic
132	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
133	C₂³×C₃₇	—	2	2	no	—
134	C₂³×C₃₇	—	2	4	no	—
135	C₂³×C₃₇	—	4	1	no	—
136	C₂³×C₃₇	—	8	1	no	—
137	C₂³×C₃₇	—	8	1	no	—
138	C₂³×C₃₇	#121	1	1	yes	characteristic
139	Q₈×C₃₇	—	4	1	no	—
140	Q₈×C₃₇	—	4	1	no	—
141	Q₈×C₃₇	—	8	2	no	—
142	Q₈×C₃₇	—	8	2	no	—
143	D₄×C₃₇	—	2	2	no	—
144	D₄×C₃₇	—	2	4	no	—
145	D₄×C₃₇	—	4	1	no	—
146	D₄×C₃₇	—	4	1	no	—
147	D₄×C₃₇	—	4	2	no	—
148	D₄×C₃₇	—	8	1	no	—
149	D₄×C₃₇	—	8	2	no	—
150	D₄×C₃₇	C₂×SD₁₆	1	4	yes	—
151	C₂×C₄×C₃₇	—	2	2	no	—
152	C₂×C₄×C₃₇	—	2	2	no	—
153	C₂×C₄×C₃₇	—	4	1	no	—
154	C₂×C₄×C₃₇	—	4	4	no	—
155	C₂×C₄×C₃₇	—	4	1	no	—
156	C₂×C₄×C₃₇	—	4	2	no	—
157	C₂×C₄×C₃₇	—	8	2	no	—
158	C₂×C₄×C₃₇	—	8	1	no	—
159	C₂×C₄×C₃₇	—	8	2	no	—
160	C₂×C₄×C₃₇	—	8	2	no	—
161	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
162	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
163	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
164	C₂×C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
165	C₂×C₄×C₃₇	#135	1	2	yes	—
166	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
169	C₈×C₃₇	—	2	4	no	—
170	C₈×C₃₇	—	4	2	no	—
171	C₈×C₃₇	—	4	2	no	—
172	C₈×C₃₇	—	4	2	no	—
173	#19391	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₃₇	—	2	1	no	—
175	C₂²×C₃₇	—	2	1	no	—
176	C₂²×C₃₇	—	2	4	no	—
177	C₂²×C₃₇	—	4	2	no	—
178	C₂²×C₃₇	—	4	2	no	—
179	C₂²×C₃₇	—	8	4	no	—
180	C₂²×C₃₇	—	8	1	no	—
181	C₂²×C₃₇	—	8	1	no	—
182	C₂²×C₃₇	—	8	1	no	—
183	C₂²×C₃₇	#465	1	2	yes	—
184	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
185	C₄×C₃₇	—	2	1	no	—
186	C₄×C₃₇	—	2	1	no	—
187	C₄×C₃₇	—	2	1	no	—
188	C₄×C₃₇	—	4	2	no	—
189	C₄×C₃₇	—	8	1	no	—
190	C₄×C₃₇	—	8	2	no	—
191	C₄×C₃₇	#465	1	2	yes	—
192	C₄×C₃₇	C₂²×SD₁₆	1	1	yes	characteristic
193	C₄×C₃₇	C₂×#135	1	1	yes	characteristic
194	C₄×C₃₇	#577	1	2	yes	—
195	#3227	C₂×C₃₇	1	1	yes	characteristic, complemented
196	C₂×#476	C₂×C₃₇	1	1	yes	characteristic, complemented
197	#3036	C₂×C₃₇	1	1	yes	characteristic
198	#2972	C₂×C₃₇	1	1	yes	characteristic, complemented
199	#1677	C₂×C₃₇	1	4	yes	complemented
200	#1671	C₂×C₃₇	1	4	yes	complemented
201	#1570	C₂×C₃₇	1	1	yes	characteristic, complemented
202	#1548	C₂×C₃₇	1	1	yes	characteristic, complemented
203	#1540	C₂×C₃₇	1	1	yes	characteristic, complemented
204	C₂×C₃₇	—	2	2	no	—
205	C₂×C₃₇	—	4	4	no	—
206	C₂×C₃₇	—	16	1	no	—
207	C₂×C₃₇	#3042	1	1	yes	characteristic
208	C₂×C₃₇	C₂×#465	1	1	yes	characteristic
209	C₂×C₃₇	#3068	1	1	yes	characteristic
210	C₂×AGL(1,ℤ/8)	—	2	1	no	—
211	#532	C₂²×C₃₇	1	1	yes	characteristic
212	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
213	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
214	#498	C₂²×C₃₇	1	2	yes	complemented
215	#486	C₂²×C₃₇	1	2	yes	complemented
216	#481	—	2	2	no	—
217	#476	—	2	2	no	—
218	#476	—	2	2	no	—
219	#476	C₂²×C₃₇	1	4	yes	—
220	#463	—	2	2	no	—
221	#461	C₂²×C₃₇	1	2	yes	—
222	#459	C₂²×C₃₇	1	2	yes	—
223	C₈×D₄	—	2	2	no	—
224	C₈×D₄	C₂²×C₃₇	1	4	yes	—
225	#431	C₂²×C₃₇	1	1	yes	characteristic
226	#431	C₂²×C₃₇	1	1	yes	characteristic
227	C₂×#106	—	2	1	no	—
228	#423	C₂²×C₃₇	1	1	yes	characteristic
229	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
230	#417	—	2	1	no	—
231	C₂×#102	—	2	1	no	—
232	C₂×C₂²⋊C₈	—	2	2	no	—
233	#334	C₂²×C₃₇	1	4	yes	complemented
234	#333	C₂²×C₃₇	1	4	yes	complemented
235	#332	C₂²×C₃₇	1	2	yes	complemented
236	#331	C₂²×C₃₇	1	2	yes	complemented
237	C₃₇	#19391	1	1	yes	characteristic, direct product factor, Sylow
238	C₂×#41	—	2	1	no	—
239	C₂²×Q₈	—	2	1	no	—
240	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
241	C₂³×C₄	—	2	1	no	—
242	AGL(1,ℤ/8)	—	4	4	no	—
243	C₂×SD₁₆	—	2	2	no	—
244	C₂×D₈	—	2	2	no	—
245	C₂×M₁₆	—	2	1	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	2	4	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
252	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
253	#127	C₂³×C₃₇	1	1	yes	characteristic
254	#124	—	2	1	no	—
255	#121	—	2	1	no	—
256	#121	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	D₄×C₃₇	1	2	yes	—
262	C₄×D₄	C₂³×C₃₇	1	2	yes	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
268	#106	—	2	4	no	—
269	#106	—	2	4	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	D₄×C₃₇	1	2	yes	—
273	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
274	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
275	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
276	#103	—	2	2	no	—
277	#102	—	2	4	no	—
278	#102	—	2	4	no	—
279	#102	—	2	2	no	—
280	C₂²⋊C₈	—	2	1	no	—
281	C₂²⋊C₈	—	2	4	no	—
282	C₂²⋊C₈	D₄×C₃₇	1	2	yes	—
283	C₄×C₈	—	2	1	no	—
284	C₄×C₈	C₂³×C₃₇	1	2	yes	—
285	C₂⁴	—	2	1	no	—
286	#41	—	4	2	no	—
287	#41	—	4	2	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	4	1	no	—
291	C₂×Q₈	—	8	2	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	SD₁₆×C₃₇	1	4	yes	—
299	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	8	2	no	—
306	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
308	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
309	SD₁₆	—	4	4	no	—
310	D₈	—	4	4	no	—
311	M₁₆	—	4	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	4	2	no	—
316	C₂×C₈	—	8	4	no	—
317	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	4	1	no	—
329	C₂²⋊C₄	—	4	1	no	—
330	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
331	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
332	C₄²	#41×C₃₇	1	1	yes	characteristic
333	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
334	C₂³	—	2	2	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	4	1	no	—
337	C₂³	—	8	1	no	—
338	C₂³	—	8	1	no	—
339	C₂³	#121×C₃₇	1	1	yes	characteristic
340	Q₈	—	4	1	no	—
341	Q₈	—	4	1	no	—
342	Q₈	—	8	2	no	—
343	Q₈	—	8	2	no	—
344	D₄	—	2	2	no	—
345	D₄	—	2	4	no	—
346	D₄	—	4	1	no	—
347	D₄	—	4	1	no	—
348	D₄	—	4	2	no	—
349	D₄	—	8	1	no	—
350	D₄	—	8	2	no	—
351	D₄	C₂×SD₁₆×C₃₇	1	4	yes	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	—	8	1	no	—
360	C₂×C₄	—	8	2	no	—
361	C₂×C₄	—	8	2	no	—
362	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
363	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
364	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
365	C₂×C₄	C₂×SD₁₆×C₃₇	1	2	yes	—
366	C₂×C₄	#135×C₃₇	1	2	yes	—
367	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
369	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
370	C₈	—	2	4	no	—
371	C₈	—	4	2	no	—
372	C₈	—	4	2	no	—
373	C₈	—	4	2	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	8	4	no	—
380	C₂²	—	8	1	no	—
381	C₂²	—	8	1	no	—
382	C₂²	—	8	1	no	—
383	C₂²	C₃₇×#465	1	2	yes	—
384	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	2	no	—
389	C₄	—	8	1	no	—
390	C₄	—	8	2	no	—
391	C₄	C₃₇×#465	1	2	yes	—
392	C₄	C₂²×SD₁₆×C₃₇	1	1	yes	characteristic
393	C₄	C₂×#135×C₃₇	1	1	yes	characteristic
394	C₄	C₃₇×#577	1	2	yes	—
395	C₂	—	2	2	no	—
396	C₂	—	4	4	no	—
397	C₂	—	16	1	no	—
398	C₂	C₃₇×#3042	1	1	yes	characteristic
399	C₂	C₂×C₃₇×#465	1	1	yes	characteristic
400	C₂	C₃₇×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
prime radical	C₃₇×#3036	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3227	C₂	semidirect
2. C₂×C₃₇×#476	C₂	semidirect
4. C₃₇×#2972	C₂	semidirect
5. C₃₇×#1677	C₂	semidirect
6. C₃₇×#1671	C₂	semidirect
7. C₃₇×#1570	C₂	semidirect
8. C₃₇×#1548	C₂	semidirect
9. C₃₇×#1540	C₂	semidirect
14. C₃₇×#498	C₂²	semidirect
15. C₃₇×#486	C₂²	semidirect
33. C₃₇×#334	C₂²	semidirect
34. C₃₇×#333	C₂²	semidirect
35. C₃₇×#332	C₂²	semidirect
36. C₃₇×#331	C₂²	semidirect
173. #19391	C₃₇	direct (N × H)
195. #3227	C₂×C₃₇	semidirect
196. C₂×#476	C₂×C₃₇	semidirect
198. #2972	C₂×C₃₇	semidirect
199. #1677	C₂×C₃₇	semidirect
200. #1671	C₂×C₃₇	semidirect
201. #1570	C₂×C₃₇	semidirect
202. #1548	C₂×C₃₇	semidirect
203. #1540	C₂×C₃₇	semidirect
214. #498	C₂²×C₃₇	semidirect
215. #486	C₂²×C₃₇	semidirect
233. #334	C₂²×C₃₇	semidirect
234. #333	C₂²×C₃₇	semidirect
235. #332	C₂²×C₃₇	semidirect
236. #331	C₂²×C₃₇	semidirect
237. C₃₇	#19391	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×#3227	2
C₂×C₃₇×#476	2
C₃₇×#3036	2
C₃₇×#2972	2
C₃₇×#1677	2
C₃₇×#1671	2
C₃₇×#1570	2
C₃₇×#1548	2
C₃₇×#1540	2
#19391	37

Subgroups — C37×#19391 #22640644

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#19391 #22640644