Subgroups — C₃₇×#12577 #22633830

Order 9472.

768 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#410	C₂	1	2	yes	maximal
2	C₃₇×#2879	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#1391	C₂	1	4	yes	maximal, complemented
4	C₂²×#41×C₃₇	C₂²	1	1	yes	characteristic
5	C₂²×M₁₆×C₃₇	C₄	1	1	yes	characteristic, complemented
6	C₂²×M₁₆×C₃₇	C₄	1	1	yes	characteristic, complemented
7	C₂×#117×C₃₇	—	2	2	no	—
8	C₃₇×#410	—	2	2	no	—
9	C₃₇×#410	—	2	2	no	—
10	C₃₇×#410	C₄	1	4	yes	complemented
11	C₃₇×#410	C₂²	1	4	yes	—
12	C₂×#99×C₃₇	—	2	2	no	—
13	C₂×#99×C₃₇	C₄	1	4	yes	complemented
14	C₃₇×#408	—	2	2	no	—
15	C₃₇×#408	C₄	1	2	yes	complemented
16	C₃₇×#408	C₂²	1	2	yes	—
17	C₃₇×#407	—	2	2	no	—
18	C₂×#41×C₃₇	—	4	2	no	—
19	C₂×#41×C₃₇	—	4	2	no	—
20	C₂×#41×C₃₇	C₂×C₄	1	2	yes	—
21	C₂×#41×C₃₇	C₂×C₄	1	1	yes	characteristic
22	C₂×#41×C₃₇	D₄	1	1	yes	characteristic
23	C₂×#41×C₃₇	D₄	1	2	yes	—
24	C₂×#41×C₃₇	Q₈	1	1	yes	characteristic
25	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
26	C₂²×Q₈×C₃₇	Q₈	1	1	yes	characteristic
27	C₂²×D₄×C₃₇	C₂×C₄	1	2	yes	—
28	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₃₇	D₄	1	2	yes	—
31	C₂×M₁₆×C₃₇	—	2	1	no	—
32	C₂×M₁₆×C₃₇	—	2	1	no	—
33	C₂×M₁₆×C₃₇	—	2	1	no	—
34	C₂×M₁₆×C₃₇	—	4	2	no	—
35	C₂×M₁₆×C₃₇	—	4	2	no	—
36	C₂×M₁₆×C₃₇	C₂×C₄	1	2	yes	complemented
37	C₂²×C₈×C₃₇	—	2	1	no	—
38	C₂²×C₈×C₃₇	C₂×C₄	1	2	yes	complemented
39	#117×C₃₇	—	2	4	no	—
40	#117×C₃₇	—	2	4	no	—
41	#117×C₃₇	—	4	2	no	—
42	#117×C₃₇	—	4	2	no	—
43	C₂×C₄⋊C₄×C₃₇	—	4	2	no	—
44	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
45	C₂×C₄²×C₃₇	—	4	2	no	—
46	#99×C₃₇	—	2	4	no	—
47	#99×C₃₇	—	2	4	no	—
48	#99×C₃₇	—	2	4	no	—
49	#99×C₃₇	C₂×C₄	1	8	yes	complemented
50	C₂²⋊C₈×C₃₇	—	2	4	no	—
51	C₂²⋊C₈×C₃₇	—	2	4	no	—
52	C₂⁴×C₃₇	C₄²	1	1	yes	characteristic
53	C₂⁴×C₃₇	C₂²⋊C₄	1	2	yes	—
54	#41×C₃₇	—	4	2	no	—
55	#41×C₃₇	—	4	2	no	—
56	#41×C₃₇	—	4	1	no	—
57	#41×C₃₇	—	4	1	no	—
58	#41×C₃₇	—	4	2	no	—
59	#41×C₃₇	—	4	2	no	—
60	#41×C₃₇	—	4	2	no	—
61	#41×C₃₇	—	4	2	no	—
62	#41×C₃₇	—	4	1	no	—
63	#41×C₃₇	—	4	1	no	—
64	C₂×Q₈×C₃₇	—	4	2	no	—
65	C₂×Q₈×C₃₇	C₄⋊C₄	1	2	yes	—
66	C₂×Q₈×C₃₇	C₄⋊C₄	1	1	yes	characteristic
67	C₂×Q₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
68	C₂×D₄×C₃₇	—	4	2	no	—
69	C₂×D₄×C₃₇	—	4	2	no	—
70	C₂×D₄×C₃₇	—	4	2	no	—
71	C₂×D₄×C₃₇	C₄²	1	2	yes	—
72	C₂×D₄×C₃₇	C₂²⋊C₄	1	2	yes	—
73	C₂×D₄×C₃₇	C₂²⋊C₄	1	2	yes	—
74	C₂×D₄×C₃₇	C₄⋊C₄	1	2	yes	—
75	C₂×D₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
76	C₂×D₄×C₃₇	C₂²×C₄	1	2	yes	—
77	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₃₇	—	2	2	no	—
79	C₂²×C₄×C₃₇	—	2	2	no	—
80	C₂²×C₄×C₃₇	—	2	2	no	—
81	C₂²×C₄×C₃₇	—	2	2	no	—
82	C₂²×C₄×C₃₇	—	2	2	no	—
83	C₂²×C₄×C₃₇	—	2	2	no	—
84	C₂²×C₄×C₃₇	—	4	4	no	—
85	C₂²×C₄×C₃₇	C₄²	1	1	yes	characteristic
86	C₂²×C₄×C₃₇	C₂²⋊C₄	1	2	yes	—
87	C₂²×C₄×C₃₇	C₂²⋊C₄	1	2	yes	—
88	C₂²×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
93	C₂²×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
94	C₂²×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
96	M₁₆×C₃₇	—	4	2	no	—
97	M₁₆×C₃₇	—	4	2	no	—
98	M₁₆×C₃₇	—	4	2	no	—
99	M₁₆×C₃₇	—	4	2	no	—
100	C₂×C₈×C₃₇	—	2	2	no	—
101	C₂×C₈×C₃₇	—	2	2	no	—
102	C₂×C₈×C₃₇	—	4	2	no	—
103	C₂×C₈×C₃₇	—	4	2	no	—
104	C₄⋊C₄×C₃₇	—	4	4	no	—
105	C₄⋊C₄×C₃₇	—	4	4	no	—
106	C₂²⋊C₄×C₃₇	—	2	8	no	—
107	C₂²⋊C₄×C₃₇	—	4	4	no	—
108	C₄²×C₃₇	—	4	4	no	—
109	C₄²×C₃₇	—	4	4	no	—
110	C₂³×C₃₇	—	2	2	no	—
111	C₂³×C₃₇	—	2	2	no	—
112	C₂³×C₃₇	—	2	2	no	—
113	C₂³×C₃₇	—	8	2	no	—
114	C₂³×C₃₇	—	8	1	no	—
115	C₂³×C₃₇	#95	1	2	yes	—
116	C₂³×C₃₇	#95	1	1	yes	characteristic
117	C₂³×C₃₇	#95	1	1	yes	characteristic
118	C₂³×C₃₇	C₂×C₄²	1	1	yes	characteristic
119	C₂³×C₃₇	C₂×C₂²⋊C₄	1	2	yes	—
120	Q₈×C₃₇	—	4	1	no	—
121	Q₈×C₃₇	—	4	2	no	—
122	Q₈×C₃₇	—	4	1	no	—
123	D₄×C₃₇	—	4	2	no	—
124	D₄×C₃₇	—	4	2	no	—
125	D₄×C₃₇	—	4	2	no	—
126	D₄×C₃₇	—	4	2	no	—
127	D₄×C₃₇	—	4	1	no	—
128	D₄×C₃₇	—	4	2	no	—
129	D₄×C₃₇	—	4	1	no	—
130	C₂×C₄×C₃₇	—	2	2	no	—
131	C₂×C₄×C₃₇	—	2	2	no	—
132	C₂×C₄×C₃₇	—	2	2	no	—
133	C₂×C₄×C₃₇	—	2	2	no	—
134	C₂×C₄×C₃₇	—	2	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	2	no	—
139	C₂×C₄×C₃₇	—	2	2	no	—
140	C₂×C₄×C₃₇	—	2	1	no	—
141	C₂×C₄×C₃₇	—	2	1	no	—
142	C₂×C₄×C₃₇	—	2	2	no	—
143	C₂×C₄×C₃₇	—	2	2	no	—
144	C₂×C₄×C₃₇	—	2	1	no	—
145	C₂×C₄×C₃₇	—	2	1	no	—
146	C₂×C₄×C₃₇	—	2	2	no	—
147	C₂×C₄×C₃₇	—	4	8	no	—
148	C₂×C₄×C₃₇	—	8	8	no	—
149	C₂×C₄×C₃₇	#95	1	1	yes	characteristic
150	C₂×C₄×C₃₇	#95	1	2	yes	—
151	C₂×C₄×C₃₇	#95	1	1	yes	characteristic
152	C₂×C₄×C₃₇	#99	1	2	yes	—
153	C₂×C₄×C₃₇	#99	1	2	yes	—
154	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₃₇	C₂×C₄⋊C₄	1	2	yes	—
157	C₈×C₃₇	—	4	2	no	—
158	C₈×C₃₇	—	4	2	no	—
159	#12577	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂²×C₃₇	—	2	2	no	—
161	C₂²×C₃₇	—	2	2	no	—
162	C₂²×C₃₇	—	2	1	no	—
163	C₂²×C₃₇	—	2	1	no	—
164	C₂²×C₃₇	—	4	1	no	—
165	C₂²×C₃₇	—	4	2	no	—
166	C₂²×C₃₇	—	4	1	no	—
167	C₂²×C₃₇	—	4	1	no	—
168	C₂²×C₃₇	—	4	2	no	—
169	C₂²×C₃₇	—	4	4	no	—
170	C₂²×C₃₇	—	8	2	no	—
171	C₂²×C₃₇	—	8	2	no	—
172	C₂²×C₃₇	#342	1	2	yes	—
173	C₂²×C₃₇	C₂×#95	1	1	yes	characteristic
174	C₄×C₃₇	—	2	2	no	—
175	C₄×C₃₇	—	2	1	no	—
176	C₄×C₃₇	—	2	2	no	—
177	C₄×C₃₇	—	2	1	no	—
178	C₄×C₃₇	—	8	8	no	—
179	C₄×C₃₇	#342	1	2	yes	—
180	C₄×C₃₇	C₂×#99	1	1	yes	characteristic
181	C₄×C₃₇	C₂×#99	1	1	yes	characteristic
182	C₂×#410	C₂×C₃₇	1	2	yes	—
183	#2879	C₂×C₃₇	1	1	yes	characteristic
184	#1391	C₂×C₃₇	1	4	yes	complemented
185	C₂×C₃₇	—	2	1	no	—
186	C₂×C₃₇	—	2	2	no	—
187	C₂×C₃₇	—	4	2	no	—
188	C₂×C₃₇	—	4	2	no	—
189	C₂×C₃₇	—	4	1	no	—
190	C₂×C₃₇	—	4	1	no	—
191	C₂×C₃₇	C₂×#342	1	1	yes	characteristic
192	C₂²×#41	C₂²×C₃₇	1	1	yes	characteristic
193	C₂²×M₁₆	C₄×C₃₇	1	1	yes	characteristic, complemented
194	C₂²×M₁₆	C₄×C₃₇	1	1	yes	characteristic, complemented
195	C₂×#117	—	2	2	no	—
196	#410	—	2	2	no	—
197	#410	—	2	2	no	—
198	#410	C₄×C₃₇	1	4	yes	complemented
199	#410	C₂²×C₃₇	1	4	yes	—
200	C₂×#99	—	2	2	no	—
201	C₂×#99	C₄×C₃₇	1	4	yes	complemented
202	#408	—	2	2	no	—
203	#408	C₄×C₃₇	1	2	yes	complemented
204	#408	C₂²×C₃₇	1	2	yes	—
205	#407	—	2	2	no	—
206	C₃₇	#12577	1	1	yes	characteristic, direct product factor, Sylow
207	C₂×#41	—	4	2	no	—
208	C₂×#41	—	4	2	no	—
209	C₂×#41	C₂×C₄×C₃₇	1	2	yes	—
210	C₂×#41	C₂×C₄×C₃₇	1	1	yes	characteristic
211	C₂×#41	D₄×C₃₇	1	1	yes	characteristic
212	C₂×#41	D₄×C₃₇	1	2	yes	—
213	C₂×#41	Q₈×C₃₇	1	1	yes	characteristic
214	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
215	C₂²×Q₈	Q₈×C₃₇	1	1	yes	characteristic
216	C₂²×D₄	C₂×C₄×C₃₇	1	2	yes	—
217	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
218	C₂³×C₄	C₂×C₄×C₃₇	1	1	yes	characteristic
219	C₂³×C₄	D₄×C₃₇	1	2	yes	—
220	C₂×M₁₆	—	2	1	no	—
221	C₂×M₁₆	—	2	1	no	—
222	C₂×M₁₆	—	2	1	no	—
223	C₂×M₁₆	—	4	2	no	—
224	C₂×M₁₆	—	4	2	no	—
225	C₂×M₁₆	C₂×C₄×C₃₇	1	2	yes	complemented
226	C₂²×C₈	—	2	1	no	—
227	C₂²×C₈	C₂×C₄×C₃₇	1	2	yes	complemented
228	#117	—	2	4	no	—
229	#117	—	2	4	no	—
230	#117	—	4	2	no	—
231	#117	—	4	2	no	—
232	C₂×C₄⋊C₄	—	4	2	no	—
233	C₂×C₂²⋊C₄	—	2	4	no	—
234	C₂×C₄²	—	4	2	no	—
235	#99	—	2	4	no	—
236	#99	—	2	4	no	—
237	#99	—	2	4	no	—
238	#99	C₂×C₄×C₃₇	1	8	yes	complemented
239	C₂²⋊C₈	—	2	4	no	—
240	C₂²⋊C₈	—	2	4	no	—
241	C₂⁴	C₄²×C₃₇	1	1	yes	characteristic
242	C₂⁴	C₂²⋊C₄×C₃₇	1	2	yes	—
243	#41	—	4	2	no	—
244	#41	—	4	2	no	—
245	#41	—	4	1	no	—
246	#41	—	4	1	no	—
247	#41	—	4	2	no	—
248	#41	—	4	2	no	—
249	#41	—	4	2	no	—
250	#41	—	4	2	no	—
251	#41	—	4	1	no	—
252	#41	—	4	1	no	—
253	C₂×Q₈	—	4	2	no	—
254	C₂×Q₈	C₄⋊C₄×C₃₇	1	2	yes	—
255	C₂×Q₈	C₄⋊C₄×C₃₇	1	1	yes	characteristic
256	C₂×Q₈	C₂×Q₈×C₃₇	1	1	yes	characteristic
257	C₂×D₄	—	4	2	no	—
258	C₂×D₄	—	4	2	no	—
259	C₂×D₄	—	4	2	no	—
260	C₂×D₄	C₄²×C₃₇	1	2	yes	—
261	C₂×D₄	C₂²⋊C₄×C₃₇	1	2	yes	—
262	C₂×D₄	C₂²⋊C₄×C₃₇	1	2	yes	—
263	C₂×D₄	C₄⋊C₄×C₃₇	1	2	yes	—
264	C₂×D₄	C₄⋊C₄×C₃₇	1	1	yes	characteristic
265	C₂×D₄	C₂²×C₄×C₃₇	1	2	yes	—
266	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	4	4	no	—
274	C₂²×C₄	C₄²×C₃₇	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊C₄×C₃₇	1	2	yes	—
276	C₂²×C₄	C₂²⋊C₄×C₃₇	1	2	yes	—
277	C₂²×C₄	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
278	C₂²×C₄	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
279	C₂²×C₄	C₄⋊C₄×C₃₇	1	1	yes	characteristic
280	C₂²×C₄	C₄⋊C₄×C₃₇	1	1	yes	characteristic
281	C₂²×C₄	C₄⋊C₄×C₃₇	1	2	yes	—
282	C₂²×C₄	C₄⋊C₄×C₃₇	1	2	yes	—
283	C₂²×C₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
285	M₁₆	—	4	2	no	—
286	M₁₆	—	4	2	no	—
287	M₁₆	—	4	2	no	—
288	M₁₆	—	4	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	—	4	2	no	—
293	C₄⋊C₄	—	4	4	no	—
294	C₄⋊C₄	—	4	4	no	—
295	C₂²⋊C₄	—	2	8	no	—
296	C₂²⋊C₄	—	4	4	no	—
297	C₄²	—	4	4	no	—
298	C₄²	—	4	4	no	—
299	C₂³	—	2	2	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	—	8	2	no	—
303	C₂³	—	8	1	no	—
304	C₂³	#95×C₃₇	1	2	yes	—
305	C₂³	#95×C₃₇	1	1	yes	characteristic
306	C₂³	#95×C₃₇	1	1	yes	characteristic
307	C₂³	C₂×C₄²×C₃₇	1	1	yes	characteristic
308	C₂³	C₂×C₂²⋊C₄×C₃₇	1	2	yes	—
309	Q₈	—	4	1	no	—
310	Q₈	—	4	2	no	—
311	Q₈	—	4	1	no	—
312	D₄	—	4	2	no	—
313	D₄	—	4	2	no	—
314	D₄	—	4	2	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	1	no	—
317	D₄	—	4	2	no	—
318	D₄	—	4	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	8	no	—
337	C₂×C₄	—	8	8	no	—
338	C₂×C₄	#95×C₃₇	1	1	yes	characteristic
339	C₂×C₄	#95×C₃₇	1	2	yes	—
340	C₂×C₄	#95×C₃₇	1	1	yes	characteristic
341	C₂×C₄	#99×C₃₇	1	2	yes	—
342	C₂×C₄	#99×C₃₇	1	2	yes	—
343	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄⋊C₄×C₃₇	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄⋊C₄×C₃₇	1	2	yes	—
346	C₈	—	4	2	no	—
347	C₈	—	4	2	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	4	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	8	2	no	—
360	C₂²	C₃₇×#342	1	2	yes	—
361	C₂²	C₂×#95×C₃₇	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	1	no	—
366	C₄	—	8	8	no	—
367	C₄	C₃₇×#342	1	2	yes	—
368	C₄	C₂×#99×C₃₇	1	1	yes	characteristic
369	C₄	C₂×#99×C₃₇	1	1	yes	characteristic
370	C₂	—	2	1	no	—
371	C₂	—	2	2	no	—
372	C₂	—	4	2	no	—
373	C₂	—	4	2	no	—
374	C₂	—	4	1	no	—
375	C₂	—	4	1	no	—
376	C₂	C₂×C₃₇×#342	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₃₇	C₂×#99
commutator	C₂³	C₂×C₄²×C₃₇
Frattini, cosocle	C₂×#41	C₂³×C₃₇
socle	C₂×C₃₇	C₂×#342
prime radical	C₂²×#41×C₃₇	C₂²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ C₂²×#41×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₇×#1391	C₂	semidirect
5. C₂²×M₁₆×C₃₇	C₄	semidirect
6. C₂²×M₁₆×C₃₇	C₄	semidirect
10. C₃₇×#410	C₄	semidirect
13. C₂×#99×C₃₇	C₄	semidirect
15. C₃₇×#408	C₄	semidirect
36. C₂×M₁₆×C₃₇	C₂×C₄	semidirect
38. C₂²×C₈×C₃₇	C₂×C₄	semidirect
49. #99×C₃₇	C₂×C₄	semidirect
159. #12577	C₃₇	direct (N × H)
184. #1391	C₂×C₃₇	semidirect
193. C₂²×M₁₆	C₄×C₃₇	semidirect
194. C₂²×M₁₆	C₄×C₃₇	semidirect
198. #410	C₄×C₃₇	semidirect
201. C₂×#99	C₄×C₃₇	semidirect
203. #408	C₄×C₃₇	semidirect
206. C₃₇	#12577	direct (N × H)
225. C₂×M₁₆	C₂×C₄×C₃₇	semidirect
227. C₂²×C₈	C₂×C₄×C₃₇	semidirect
238. #99	C₂×C₄×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#410	2
C₃₇×#2879	2
C₃₇×#1391	2
#12577	37

Subgroups — C37×#12577 #22633830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#12577 #22633830