Subgroups — C₃₇×#60494 #22681747

Order 9472.

2090 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×H(5,𝔽₂)×C₃₇	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#3083	C₂	1	6	yes	maximal, complemented
4	C₃₇×#3081	C₂	1	6	yes	maximal, complemented
5	C₃₇×#3079	C₂	1	3	yes	maximal, complemented
6	C₃₇×#3077	C₂	1	3	yes	maximal, complemented
7	C₃₇×#3076	C₂	1	3	yes	maximal, complemented
8	C₂×C₃₇×#474	C₂	1	3	yes	maximal, complemented
9	C₃₇×#2913	C₂	1	2	yes	maximal, complemented
10	C₃₇×#2906	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#2897	C₂	1	2	yes	maximal
12	C₂×H(5,𝔽₂)×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#131×C₃₇	C₂²	1	2	yes	—
14	Q₈²×C₃₇	—	2	1	no	—
15	C₃₇×#557	—	2	1	no	—
16	C₃₇×#554	—	2	3	no	—
17	D₄×Q₈×C₃₇	—	2	3	no	—
18	C₃₇×#544	C₂²	1	6	yes	complemented
19	C₃₇×#533	C₂²	1	3	yes	complemented
20	C₂×C₄⋊Q₈×C₃₇	C₂²	1	3	yes	complemented
21	C₃₇×#520	—	2	1	no	—
22	C₃₇×#520	C₂²	1	3	yes	—
23	C₃₇×#520	C₂²	1	2	yes	—
24	C₃₇×#520	C₂²	1	1	yes	characteristic
25	C₃₇×#518	—	2	3	no	—
26	C₃₇×#518	C₂²	1	3	yes	—
27	C₄×#41×C₃₇	—	2	1	no	—
28	C₄×#41×C₃₇	C₂²	1	3	yes	—
29	C₄×#41×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₃₇	—	2	3	no	—
31	C₂×C₄×D₄×C₃₇	C₂²	1	3	yes	—
32	C₃₇×#479	C₂²	1	6	yes	complemented
33	C₃₇×#478	C₂²	1	6	yes	complemented
34	C₃₇×#478	C₂²	1	12	yes	complemented
35	C₃₇×#477	C₂²	1	1	yes	characteristic, complemented
36	C₃₇×#477	C₂²	1	6	yes	complemented
37	C₃₇×#476	C₂²	1	3	yes	complemented
38	C₃₇×#476	C₂²	1	6	yes	complemented
39	C₃₇×#475	C₂²	1	3	yes	complemented
40	C₃₇×#474	C₂²	1	3	yes	complemented
41	C₃₇×#474	C₂²	1	6	yes	complemented
42	C₃₇×#474	C₂²	1	12	yes	complemented
43	C₃₇×#428	C₂²	1	6	yes	complemented
44	C₃₇×#428	C₂²	1	6	yes	complemented
45	C₃₇×#427	C₂²	1	6	yes	complemented
46	C₂×#107×C₃₇	C₂²	1	6	yes	complemented
47	C₃₇×#424	C₂²	1	6	yes	complemented
48	C₃₇×#423	C₂²	1	3	yes	complemented
49	C₂×C₄⋊C₈×C₃₇	C₂²	1	3	yes	complemented
50	C₃₇×#418	C₂²	1	6	yes	—
51	C₃₇×#417	C₂²	1	6	yes	—
52	C₃₇×#416	C₂²	1	6	yes	—
53	C₂×#102×C₃₇	C₂²	1	6	yes	—
54	H(5,𝔽₂)×C₃₇	—	2	4	no	—
55	H(5,𝔽₂)×C₃₇	Q₈	1	8	yes	complemented
56	C₂×#41×C₃₇	—	2	1	no	—
57	C₂×#41×C₃₇	C₂³	1	3	yes	—
58	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₃₇	—	2	3	no	—
60	C₂²×D₄×C₃₇	—	2	3	no	—
61	C₂²×D₄×C₃₇	C₂³	1	3	yes	—
62	C₂³×C₄×C₃₇	—	2	3	no	—
63	#131×C₃₇	—	2	8	no	—
64	C₂×M₁₆×C₃₇	C₂³	1	6	yes	—
65	C₂²×C₈×C₃₇	C₂³	1	6	yes	—
66	C₄⋊Q₈×C₃₇	—	2	6	no	—
67	C₄⋊Q₈×C₃₇	—	2	3	no	—
68	C₄⋊Q₈×C₃₇	—	2	3	no	—
69	C₄⋊Q₈×C₃₇	C₂³	1	3	yes	—
70	C₄⋊Q₈×C₃₇	C₂³	1	6	yes	—
71	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
72	#125×C₃₇	—	2	6	no	—
73	#125×C₃₇	C₂³	1	6	yes	—
74	C₂²⋊Q₈×C₃₇	—	2	3	no	—
75	C₂²⋊Q₈×C₃₇	—	2	3	no	—
76	C₂²⋊Q₈×C₃₇	—	2	12	no	—
77	C₄×Q₈×C₃₇	—	2	1	no	—
78	C₄×Q₈×C₃₇	—	2	2	no	—
79	C₄×Q₈×C₃₇	—	2	3	no	—
80	C₄×Q₈×C₃₇	—	2	3	no	—
81	C₄×Q₈×C₃₇	D₄	1	1	yes	characteristic
82	C₄×Q₈×C₃₇	D₄	1	1	yes	characteristic
83	C₄×Q₈×C₃₇	C₂³	1	3	yes	—
84	C₄×Q₈×C₃₇	C₂³	1	1	yes	characteristic
85	C₄×D₄×C₃₇	—	2	6	no	—
86	C₄×D₄×C₃₇	—	2	3	no	—
87	C₄×D₄×C₃₇	—	2	3	no	—
88	C₄×D₄×C₃₇	—	2	3	no	—
89	C₄×D₄×C₃₇	—	2	3	no	—
90	C₄×D₄×C₃₇	—	2	3	no	—
91	C₄×D₄×C₃₇	—	2	6	no	—
92	C₄×D₄×C₃₇	—	2	3	no	—
93	C₄×D₄×C₃₇	—	2	3	no	—
94	C₄×D₄×C₃₇	D₄	1	3	yes	—
95	C₄×D₄×C₃₇	D₄	1	3	yes	—
96	C₄×D₄×C₃₇	C₂³	1	6	yes	—
97	C₄×D₄×C₃₇	C₂³	1	3	yes	—
98	C₄×D₄×C₃₇	C₂³	1	3	yes	—
99	#117×C₃₇	—	2	3	no	—
100	#117×C₃₇	—	2	3	no	—
101	#117×C₃₇	C₂³	1	6	yes	—
102	#117×C₃₇	C₂³	1	3	yes	—
103	#117×C₃₇	C₂³	1	3	yes	—
104	C₂×C₄⋊C₄×C₃₇	—	2	3	no	—
105	C₂×C₄⋊C₄×C₃₇	—	2	3	no	—
106	C₂×C₄⋊C₄×C₃₇	C₂³	1	3	yes	—
107	C₂×C₄⋊C₄×C₃₇	C₂³	1	6	yes	—
108	C₂×C₂²⋊C₄×C₃₇	—	2	3	no	—
109	C₂×C₂²⋊C₄×C₃₇	—	2	6	no	—
110	C₂×C₄²×C₃₇	—	2	3	no	—
111	C₂×C₄²×C₃₇	C₂³	1	3	yes	—
112	#107×C₃₇	C₂³	1	6	yes	—
113	#107×C₃₇	C₂³	1	12	yes	—
114	#107×C₃₇	C₂³	1	2	yes	—
115	#106×C₃₇	C₂³	1	6	yes	—
116	#106×C₃₇	C₂³	1	6	yes	—
117	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
118	C₄⋊C₈×C₃₇	C₂³	1	3	yes	—
119	C₄⋊C₈×C₃₇	C₂³	1	6	yes	—
120	C₄⋊C₈×C₃₇	C₂³	1	6	yes	—
121	#103×C₃₇	C₂³	1	2	yes	—
122	#103×C₃₇	C₂³	1	6	yes	—
123	#102×C₃₇	C₂³	1	6	yes	—
124	#102×C₃₇	C₂³	1	12	yes	—
125	#102×C₃₇	C₂³	1	6	yes	—
126	C₂⁴×C₃₇	—	2	3	no	—
127	#41×C₃₇	—	2	8	no	—
128	#41×C₃₇	—	2	6	no	—
129	#41×C₃₇	C₂×Q₈	1	4	yes	—
130	#41×C₃₇	C₂×Q₈	1	12	yes	complemented
131	#41×C₃₇	#41	1	4	yes	—
132	C₂×Q₈×C₃₇	—	2	1	no	—
133	C₂×Q₈×C₃₇	—	2	3	no	—
134	C₂×Q₈×C₃₇	—	2	6	no	—
135	C₂×Q₈×C₃₇	—	8	6	no	—
136	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
137	C₂×Q₈×C₃₇	C₂⁴	1	1	yes	characteristic
138	C₂×D₄×C₃₇	—	2	3	no	—
139	C₂×D₄×C₃₇	—	2	24	no	—
140	C₂×D₄×C₃₇	—	2	3	no	—
141	C₂×D₄×C₃₇	—	2	6	no	—
142	C₂×D₄×C₃₇	C₂×D₄	1	3	yes	—
143	C₂×D₄×C₃₇	C₂×Q₈	1	12	yes	complemented
144	C₂×D₄×C₃₇	C₂⁴	1	3	yes	—
145	C₂²×C₄×C₃₇	—	2	3	no	—
146	C₂²×C₄×C₃₇	—	2	3	no	—
147	C₂²×C₄×C₃₇	—	2	6	no	—
148	C₂²×C₄×C₃₇	—	2	3	no	—
149	C₂²×C₄×C₃₇	—	2	3	no	—
150	C₂²×C₄×C₃₇	—	2	6	no	—
151	C₂²×C₄×C₃₇	—	8	6	no	—
152	C₂²×C₄×C₃₇	C₂×D₄	1	3	yes	—
153	C₂²×C₄×C₃₇	C₂×D₄	1	3	yes	—
154	C₂²×C₄×C₃₇	C₂⁴	1	3	yes	—
155	M₁₆×C₃₇	—	2	12	no	—
156	C₂×C₈×C₃₇	—	2	12	no	—
157	C₂×C₈×C₃₇	C₂⁴	1	6	yes	—
158	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
159	C₄⋊C₄×C₃₇	—	2	3	no	—
160	C₄⋊C₄×C₃₇	—	2	3	no	—
161	C₄⋊C₄×C₃₇	—	2	3	no	—
162	C₄⋊C₄×C₃₇	—	2	6	no	—
163	C₄⋊C₄×C₃₇	—	2	6	no	—
164	C₄⋊C₄×C₃₇	—	2	1	no	—
165	C₄⋊C₄×C₃₇	—	2	1	no	—
166	C₄⋊C₄×C₃₇	—	2	6	no	—
167	C₄⋊C₄×C₃₇	—	2	6	no	—
168	C₄⋊C₄×C₃₇	C₂×D₄	1	3	yes	—
169	C₄⋊C₄×C₃₇	C₂×D₄	1	3	yes	—
170	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
171	C₄⋊C₄×C₃₇	C₂⁴	1	6	yes	—
172	C₄⋊C₄×C₃₇	C₂⁴	1	1	yes	characteristic
173	C₄⋊C₄×C₃₇	C₂⁴	1	3	yes	—
174	C₂²⋊C₄×C₃₇	—	2	3	no	—
175	C₂²⋊C₄×C₃₇	—	2	6	no	—
176	C₂²⋊C₄×C₃₇	—	2	3	no	—
177	C₂²⋊C₄×C₃₇	—	2	6	no	—
178	C₂²⋊C₄×C₃₇	—	2	3	no	—
179	C₂²⋊C₄×C₃₇	C₂×D₄	1	6	yes	—
180	C₄²×C₃₇	—	2	1	no	—
181	C₄²×C₃₇	—	2	3	no	—
182	C₄²×C₃₇	—	2	3	no	—
183	C₄²×C₃₇	—	2	6	no	—
184	C₄²×C₃₇	C₂×D₄	1	3	yes	—
185	C₄²×C₃₇	C₂×D₄	1	3	yes	—
186	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
187	C₄²×C₃₇	C₂⁴	1	3	yes	—
188	C₂³×C₃₇	—	2	3	no	—
189	C₂³×C₃₇	—	2	12	no	—
190	C₂³×C₃₇	—	8	3	no	—
191	C₂³×C₃₇	—	8	3	no	—
192	C₂³×C₃₇	C₂²×D₄	1	3	yes	—
193	Q₈×C₃₇	—	2	1	no	—
194	Q₈×C₃₇	—	4	2	no	—
195	Q₈×C₃₇	—	4	6	no	—
196	Q₈×C₃₇	—	8	6	no	—
197	Q₈×C₃₇	C₂²⋊Q₈	1	4	yes	—
198	Q₈×C₃₇	C₂²×Q₈	1	2	yes	—
199	D₄×C₃₇	—	2	12	no	—
200	D₄×C₃₇	—	2	12	no	—
201	D₄×C₃₇	—	2	3	no	—
202	D₄×C₃₇	C₂²⋊Q₈	1	12	yes	—
203	D₄×C₃₇	C₂²×Q₈	1	6	yes	—
204	C₂×C₄×C₃₇	—	2	1	no	—
205	C₂×C₄×C₃₇	—	2	12	no	—
206	C₂×C₄×C₃₇	—	2	6	no	—
207	C₂×C₄×C₃₇	—	2	1	no	—
208	C₂×C₄×C₃₇	—	2	2	no	—
209	C₂×C₄×C₃₇	—	2	3	no	—
210	C₂×C₄×C₃₇	—	2	6	no	—
211	C₂×C₄×C₃₇	—	4	3	no	—
212	C₂×C₄×C₃₇	—	4	6	no	—
213	C₂×C₄×C₃₇	—	8	3	no	—
214	C₂×C₄×C₃₇	—	8	6	no	—
215	C₂×C₄×C₃₇	—	8	3	no	—
216	C₂×C₄×C₃₇	—	8	6	no	—
217	C₂×C₄×C₃₇	C₂²×D₄	1	3	yes	—
218	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₃₇	C₂²×D₄	1	3	yes	—
220	C₂×C₄×C₃₇	C₂²×D₄	1	3	yes	—
221	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₃₇	C₂²×Q₈	1	6	yes	—
223	C₂×C₄×C₃₇	C₂×#41	1	6	yes	—
224	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
225	C₈×C₃₇	—	2	2	no	—
226	C₈×C₃₇	—	2	6	no	—
227	#60494	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂²×C₃₇	—	2	3	no	—
229	C₂²×C₃₇	—	2	3	no	—
230	C₂²×C₃₇	—	2	6	no	—
231	C₂²×C₃₇	—	4	3	no	—
232	C₂²×C₃₇	—	4	3	no	—
233	C₂²×C₃₇	—	8	12	no	—
234	C₂²×C₃₇	C₂×C₂²⋊Q₈	1	6	yes	—
235	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
236	C₄×C₃₇	—	2	1	no	—
237	C₄×C₃₇	—	2	3	no	—
238	C₄×C₃₇	—	2	2	no	—
239	C₄×C₃₇	—	2	3	no	—
240	C₄×C₃₇	—	4	1	no	—
241	C₄×C₃₇	—	4	2	no	—
242	C₄×C₃₇	—	4	3	no	—
243	C₄×C₃₇	—	4	6	no	—
244	C₄×C₃₇	C₂×C₂²⋊Q₈	1	6	yes	—
245	C₄×C₃₇	#576	1	2	yes	—
246	C₄×C₃₇	C₂³×Q₈	1	1	yes	characteristic
247	C₄×C₃₇	C₂²×#41	1	1	yes	characteristic
248	#3503	C₂×C₃₇	1	1	yes	characteristic, complemented
249	C₄×H(5,𝔽₂)	C₂×C₃₇	1	1	yes	characteristic
250	#3083	C₂×C₃₇	1	6	yes	complemented
251	#3081	C₂×C₃₇	1	6	yes	complemented
252	#3079	C₂×C₃₇	1	3	yes	complemented
253	#3077	C₂×C₃₇	1	3	yes	complemented
254	#3076	C₂×C₃₇	1	3	yes	complemented
255	C₂×#474	C₂×C₃₇	1	3	yes	complemented
256	#2913	C₂×C₃₇	1	2	yes	complemented
257	#2906	C₂×C₃₇	1	1	yes	characteristic, complemented
258	#2897	C₂×C₃₇	1	2	yes	—
259	C₂×C₃₇	—	2	6	no	—
260	C₂×C₃₇	—	4	6	no	—
261	C₂×C₃₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
262	C₂×C₃₇	C₂×#576	1	1	yes	characteristic
263	C₂×C₃₇	#3586	1	1	yes	characteristic
264	C₂×H(5,𝔽₂)	C₂²×C₃₇	1	1	yes	characteristic
265	C₂×#131	C₂²×C₃₇	1	2	yes	—
266	Q₈²	—	2	1	no	—
267	#557	—	2	1	no	—
268	#554	—	2	3	no	—
269	D₄×Q₈	—	2	3	no	—
270	#544	C₂²×C₃₇	1	6	yes	complemented
271	#533	C₂²×C₃₇	1	3	yes	complemented
272	C₂×C₄⋊Q₈	C₂²×C₃₇	1	3	yes	complemented
273	#520	—	2	1	no	—
274	#520	C₂²×C₃₇	1	3	yes	—
275	#520	C₂²×C₃₇	1	2	yes	—
276	#520	C₂²×C₃₇	1	1	yes	characteristic
277	#518	—	2	3	no	—
278	#518	C₂²×C₃₇	1	3	yes	—
279	C₄×#41	—	2	1	no	—
280	C₄×#41	C₂²×C₃₇	1	3	yes	—
281	C₄×#41	C₂²×C₃₇	1	1	yes	characteristic
282	C₂×C₄×D₄	—	2	3	no	—
283	C₂×C₄×D₄	C₂²×C₃₇	1	3	yes	—
284	#479	C₂²×C₃₇	1	6	yes	complemented
285	#478	C₂²×C₃₇	1	6	yes	complemented
286	#478	C₂²×C₃₇	1	12	yes	complemented
287	#477	C₂²×C₃₇	1	1	yes	characteristic, complemented
288	#477	C₂²×C₃₇	1	6	yes	complemented
289	#476	C₂²×C₃₇	1	3	yes	complemented
290	#476	C₂²×C₃₇	1	6	yes	complemented
291	#475	C₂²×C₃₇	1	3	yes	complemented
292	#474	C₂²×C₃₇	1	3	yes	complemented
293	#474	C₂²×C₃₇	1	6	yes	complemented
294	#474	C₂²×C₃₇	1	12	yes	complemented
295	#428	C₂²×C₃₇	1	6	yes	complemented
296	#428	C₂²×C₃₇	1	6	yes	complemented
297	#427	C₂²×C₃₇	1	6	yes	complemented
298	C₂×#107	C₂²×C₃₇	1	6	yes	complemented
299	#424	C₂²×C₃₇	1	6	yes	complemented
300	#423	C₂²×C₃₇	1	3	yes	complemented
301	C₂×C₄⋊C₈	C₂²×C₃₇	1	3	yes	complemented
302	#418	C₂²×C₃₇	1	6	yes	—
303	#417	C₂²×C₃₇	1	6	yes	—
304	#416	C₂²×C₃₇	1	6	yes	—
305	C₂×#102	C₂²×C₃₇	1	6	yes	—
306	C₃₇	#60494	1	1	yes	characteristic, direct product factor, Sylow
307	H(5,𝔽₂)	—	2	4	no	—
308	H(5,𝔽₂)	Q₈×C₃₇	1	8	yes	complemented
309	C₂×#41	—	2	1	no	—
310	C₂×#41	C₂³×C₃₇	1	3	yes	—
311	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
312	C₂²×Q₈	—	2	3	no	—
313	C₂²×D₄	—	2	3	no	—
314	C₂²×D₄	C₂³×C₃₇	1	3	yes	—
315	C₂³×C₄	—	2	3	no	—
316	#131	—	2	8	no	—
317	C₂×M₁₆	C₂³×C₃₇	1	6	yes	—
318	C₂²×C₈	C₂³×C₃₇	1	6	yes	—
319	C₄⋊Q₈	—	2	6	no	—
320	C₄⋊Q₈	—	2	3	no	—
321	C₄⋊Q₈	—	2	3	no	—
322	C₄⋊Q₈	C₂³×C₃₇	1	3	yes	—
323	C₄⋊Q₈	C₂³×C₃₇	1	6	yes	—
324	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
325	#125	—	2	6	no	—
326	#125	C₂³×C₃₇	1	6	yes	—
327	C₂²⋊Q₈	—	2	3	no	—
328	C₂²⋊Q₈	—	2	3	no	—
329	C₂²⋊Q₈	—	2	12	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	2	3	no	—
333	C₄×Q₈	—	2	3	no	—
334	C₄×Q₈	D₄×C₃₇	1	1	yes	characteristic
335	C₄×Q₈	D₄×C₃₇	1	1	yes	characteristic
336	C₄×Q₈	C₂³×C₃₇	1	1	yes	characteristic
337	C₄×Q₈	C₂³×C₃₇	1	3	yes	—
338	C₄×D₄	—	2	3	no	—
339	C₄×D₄	—	2	6	no	—
340	C₄×D₄	—	2	3	no	—
341	C₄×D₄	—	2	3	no	—
342	C₄×D₄	—	2	3	no	—
343	C₄×D₄	—	2	3	no	—
344	C₄×D₄	—	2	6	no	—
345	C₄×D₄	—	2	3	no	—
346	C₄×D₄	—	2	3	no	—
347	C₄×D₄	D₄×C₃₇	1	3	yes	—
348	C₄×D₄	D₄×C₃₇	1	3	yes	—
349	C₄×D₄	C₂³×C₃₇	1	3	yes	—
350	C₄×D₄	C₂³×C₃₇	1	6	yes	—
351	C₄×D₄	C₂³×C₃₇	1	3	yes	—
352	#117	—	2	3	no	—
353	#117	—	2	3	no	—
354	#117	C₂³×C₃₇	1	3	yes	—
355	#117	C₂³×C₃₇	1	6	yes	—
356	#117	C₂³×C₃₇	1	3	yes	—
357	C₂×C₄⋊C₄	—	2	3	no	—
358	C₂×C₄⋊C₄	—	2	3	no	—
359	C₂×C₄⋊C₄	C₂³×C₃₇	1	3	yes	—
360	C₂×C₄⋊C₄	C₂³×C₃₇	1	6	yes	—
361	C₂×C₂²⋊C₄	—	2	3	no	—
362	C₂×C₂²⋊C₄	—	2	6	no	—
363	C₂×C₄²	—	2	3	no	—
364	C₂×C₄²	C₂³×C₃₇	1	3	yes	—
365	#107	C₂³×C₃₇	1	6	yes	—
366	#107	C₂³×C₃₇	1	12	yes	—
367	#107	C₂³×C₃₇	1	2	yes	—
368	#106	C₂³×C₃₇	1	6	yes	—
369	#106	C₂³×C₃₇	1	6	yes	—
370	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
371	C₄⋊C₈	C₂³×C₃₇	1	3	yes	—
372	C₄⋊C₈	C₂³×C₃₇	1	6	yes	—
373	C₄⋊C₈	C₂³×C₃₇	1	6	yes	—
374	#103	C₂³×C₃₇	1	2	yes	—
375	#103	C₂³×C₃₇	1	6	yes	—
376	#102	C₂³×C₃₇	1	6	yes	—
377	#102	C₂³×C₃₇	1	12	yes	—
378	#102	C₂³×C₃₇	1	6	yes	—
379	C₂⁴	—	2	3	no	—
380	#41	—	2	8	no	—
381	#41	—	2	6	no	—
382	#41	C₂×Q₈×C₃₇	1	4	yes	—
383	#41	C₂×Q₈×C₃₇	1	12	yes	complemented
384	#41	#41×C₃₇	1	4	yes	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	3	no	—
387	C₂×Q₈	—	2	6	no	—
388	C₂×Q₈	—	8	6	no	—
389	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
390	C₂×Q₈	C₂⁴×C₃₇	1	1	yes	characteristic
391	C₂×D₄	—	2	3	no	—
392	C₂×D₄	—	2	24	no	—
393	C₂×D₄	—	2	3	no	—
394	C₂×D₄	—	2	6	no	—
395	C₂×D₄	C₂×D₄×C₃₇	1	3	yes	—
396	C₂×D₄	C₂×Q₈×C₃₇	1	12	yes	complemented
397	C₂×D₄	C₂⁴×C₃₇	1	3	yes	—
398	C₂²×C₄	—	2	3	no	—
399	C₂²×C₄	—	2	3	no	—
400	C₂²×C₄	—	2	6	no	—
401	C₂²×C₄	—	2	3	no	—
402	C₂²×C₄	—	2	3	no	—
403	C₂²×C₄	—	2	6	no	—
404	C₂²×C₄	—	8	6	no	—
405	C₂²×C₄	C₂×D₄×C₃₇	1	3	yes	—
406	C₂²×C₄	C₂×D₄×C₃₇	1	3	yes	—
407	C₂²×C₄	C₂⁴×C₃₇	1	3	yes	—
408	M₁₆	—	2	12	no	—
409	C₂×C₈	—	2	12	no	—
410	C₂×C₈	C₂⁴×C₃₇	1	6	yes	—
411	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
412	C₄⋊C₄	—	2	3	no	—
413	C₄⋊C₄	—	2	3	no	—
414	C₄⋊C₄	—	2	3	no	—
415	C₄⋊C₄	—	2	6	no	—
416	C₄⋊C₄	—	2	6	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	6	no	—
420	C₄⋊C₄	—	2	6	no	—
421	C₄⋊C₄	C₂×D₄×C₃₇	1	3	yes	—
422	C₄⋊C₄	C₂×D₄×C₃₇	1	3	yes	—
423	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
424	C₄⋊C₄	C₂⁴×C₃₇	1	6	yes	—
425	C₄⋊C₄	C₂⁴×C₃₇	1	1	yes	characteristic
426	C₄⋊C₄	C₂⁴×C₃₇	1	3	yes	—
427	C₂²⋊C₄	—	2	3	no	—
428	C₂²⋊C₄	—	2	6	no	—
429	C₂²⋊C₄	—	2	3	no	—
430	C₂²⋊C₄	—	2	6	no	—
431	C₂²⋊C₄	—	2	3	no	—
432	C₂²⋊C₄	C₂×D₄×C₃₇	1	6	yes	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	3	no	—
435	C₄²	—	2	3	no	—
436	C₄²	—	2	6	no	—
437	C₄²	C₂×D₄×C₃₇	1	3	yes	—
438	C₄²	C₂×D₄×C₃₇	1	3	yes	—
439	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
440	C₄²	C₂⁴×C₃₇	1	3	yes	—
441	C₂³	—	2	3	no	—
442	C₂³	—	2	12	no	—
443	C₂³	—	8	3	no	—
444	C₂³	—	8	3	no	—
445	C₂³	C₂²×D₄×C₃₇	1	3	yes	—
446	Q₈	—	2	1	no	—
447	Q₈	—	4	2	no	—
448	Q₈	—	4	6	no	—
449	Q₈	—	8	6	no	—
450	Q₈	C₂²⋊Q₈×C₃₇	1	4	yes	—
451	Q₈	C₂²×Q₈×C₃₇	1	2	yes	—
452	D₄	—	2	12	no	—
453	D₄	—	2	12	no	—
454	D₄	—	2	3	no	—
455	D₄	C₂²⋊Q₈×C₃₇	1	12	yes	—
456	D₄	C₂²×Q₈×C₃₇	1	6	yes	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	12	no	—
459	C₂×C₄	—	2	6	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	3	no	—
463	C₂×C₄	—	2	6	no	—
464	C₂×C₄	—	4	3	no	—
465	C₂×C₄	—	4	6	no	—
466	C₂×C₄	—	8	6	no	—
467	C₂×C₄	—	8	3	no	—
468	C₂×C₄	—	8	3	no	—
469	C₂×C₄	—	8	6	no	—
470	C₂×C₄	C₂²×D₄×C₃₇	1	3	yes	—
471	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
472	C₂×C₄	C₂²×D₄×C₃₇	1	3	yes	—
473	C₂×C₄	C₂²×D₄×C₃₇	1	3	yes	—
474	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
475	C₂×C₄	C₂²×Q₈×C₃₇	1	6	yes	—
476	C₂×C₄	C₂×#41×C₃₇	1	6	yes	—
477	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
478	C₈	—	2	2	no	—
479	C₈	—	2	6	no	—
480	C₂²	—	2	3	no	—
481	C₂²	—	2	3	no	—
482	C₂²	—	2	6	no	—
483	C₂²	—	4	3	no	—
484	C₂²	—	4	3	no	—
485	C₂²	—	8	12	no	—
486	C₂²	C₂×C₂²⋊Q₈×C₃₇	1	6	yes	—
487	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
488	C₄	—	2	2	no	—
489	C₄	—	2	3	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	3	no	—
492	C₄	—	4	3	no	—
493	C₄	—	4	6	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	2	no	—
496	C₄	C₂×C₂²⋊Q₈×C₃₇	1	6	yes	—
497	C₄	C₃₇×#576	1	2	yes	—
498	C₄	C₂³×Q₈×C₃₇	1	1	yes	characteristic
499	C₄	C₂²×#41×C₃₇	1	1	yes	characteristic
500	C₂	—	2	6	no	—
501	C₂	—	4	6	no	—
502	C₂	C₂²×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
503	C₂	C₂×C₃₇×#576	1	1	yes	characteristic
504	C₂	C₃₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
prime radical	C₂×H(5,𝔽₂)×C₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄×#41×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3503	C₂	semidirect
3. C₃₇×#3083	C₂	semidirect
4. C₃₇×#3081	C₂	semidirect
5. C₃₇×#3079	C₂	semidirect
6. C₃₇×#3077	C₂	semidirect
7. C₃₇×#3076	C₂	semidirect
8. C₂×C₃₇×#474	C₂	semidirect
9. C₃₇×#2913	C₂	semidirect
10. C₃₇×#2906	C₂	semidirect
18. C₃₇×#544	C₂²	semidirect
19. C₃₇×#533	C₂²	semidirect
20. C₂×C₄⋊Q₈×C₃₇	C₂²	semidirect
32. C₃₇×#479	C₂²	semidirect
33. C₃₇×#478	C₂²	semidirect
34. C₃₇×#478	C₂²	semidirect
35. C₃₇×#477	C₂²	semidirect
36. C₃₇×#477	C₂²	semidirect
37. C₃₇×#476	C₂²	semidirect
38. C₃₇×#476	C₂²	semidirect
39. C₃₇×#475	C₂²	semidirect
40. C₃₇×#474	C₂²	semidirect
41. C₃₇×#474	C₂²	semidirect
42. C₃₇×#474	C₂²	semidirect
43. C₃₇×#428	C₂²	semidirect
44. C₃₇×#428	C₂²	semidirect
45. C₃₇×#427	C₂²	semidirect
46. C₂×#107×C₃₇	C₂²	semidirect
47. C₃₇×#424	C₂²	semidirect
48. C₃₇×#423	C₂²	semidirect
49. C₂×C₄⋊C₈×C₃₇	C₂²	semidirect
55. H(5,𝔽₂)×C₃₇	Q₈	semidirect
130. #41×C₃₇	C₂×Q₈	semidirect
143. C₂×D₄×C₃₇	C₂×Q₈	semidirect
227. #60494	C₃₇	direct (N × H)
248. #3503	C₂×C₃₇	semidirect
250. #3083	C₂×C₃₇	semidirect
251. #3081	C₂×C₃₇	semidirect
252. #3079	C₂×C₃₇	semidirect
253. #3077	C₂×C₃₇	semidirect
254. #3076	C₂×C₃₇	semidirect
255. C₂×#474	C₂×C₃₇	semidirect
256. #2913	C₂×C₃₇	semidirect
257. #2906	C₂×C₃₇	semidirect
270. #544	C₂²×C₃₇	semidirect
271. #533	C₂²×C₃₇	semidirect
272. C₂×C₄⋊Q₈	C₂²×C₃₇	semidirect
284. #479	C₂²×C₃₇	semidirect
285. #478	C₂²×C₃₇	semidirect
286. #478	C₂²×C₃₇	semidirect
287. #477	C₂²×C₃₇	semidirect
288. #477	C₂²×C₃₇	semidirect
289. #476	C₂²×C₃₇	semidirect
290. #476	C₂²×C₃₇	semidirect
291. #475	C₂²×C₃₇	semidirect
292. #474	C₂²×C₃₇	semidirect
293. #474	C₂²×C₃₇	semidirect
294. #474	C₂²×C₃₇	semidirect
295. #428	C₂²×C₃₇	semidirect
296. #428	C₂²×C₃₇	semidirect
297. #427	C₂²×C₃₇	semidirect
298. C₂×#107	C₂²×C₃₇	semidirect
299. #424	C₂²×C₃₇	semidirect
300. #423	C₂²×C₃₇	semidirect
301. C₂×C₄⋊C₈	C₂²×C₃₇	semidirect
306. C₃₇	#60494	direct (N × H)
308. H(5,𝔽₂)	Q₈×C₃₇	semidirect
383. #41	C₂×Q₈×C₃₇	semidirect
396. C₂×D₄	C₂×Q₈×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3503	2
C₄×H(5,𝔽₂)×C₃₇	2
C₃₇×#3083	2
C₃₇×#3081	2
C₃₇×#3079	2
C₃₇×#3077	2
C₃₇×#3076	2
C₂×C₃₇×#474	2
C₃₇×#2913	2
C₃₇×#2906	2
C₃₇×#2897	2
#60494	37

Subgroups — C37×#60494 #22681747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#60494 #22681747