Subgroups — C₃₇×#61697 #22682950

Order 9472.

2082 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3496	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3335	C₂	1	8	yes	maximal, complemented
4	C₃₇×#3295	C₂	1	8	yes	maximal, complemented
5	C₃₇×#3227	C₂	1	2	yes	maximal, complemented
6	C₃₇×#3187	C₂	1	4	yes	maximal, complemented
7	C₃₇×#3103	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₇×#481	C₂	1	4	yes	maximal, complemented
9	C₃₇×#2972	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×H(5,𝔽₂)×C₃₇	—	2	1	no	—
11	C₃₇×#554	—	2	4	no	—
12	C₃₇×#554	C₂²	1	8	yes	complemented
13	C₃₇×#547	C₂²	1	4	yes	—
14	C₃₇×#546	—	2	4	no	—
15	D₄²×C₃₇	C₂²	1	4	yes	—
16	C₃₇×#537	—	2	1	no	—
17	C₃₇×#534	—	2	2	no	—
18	C₃₇×#532	C₂²	1	2	yes	—
19	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
20	C₂×#125×C₃₇	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₃₇	—	2	2	no	—
22	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	complemented
23	C₂×#121×C₃₇	C₂²	1	4	yes	—
24	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×D₄×C₃₇	—	2	1	no	—
26	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₃₇	C₂²	1	2	yes	complemented
28	C₃₇×#498	C₂²	1	4	yes	complemented
29	C₃₇×#486	C₂²	1	4	yes	complemented
30	C₃₇×#483	C₂²	1	8	yes	complemented
31	C₃₇×#481	C₂²	1	8	yes	complemented
32	C₃₇×#481	C₂²	1	16	yes	complemented
33	C₃₇×#481	C₂²	1	4	yes	complemented
34	C₃₇×#476	C₂²	1	8	yes	complemented
35	C₃₇×#475	C₂²	1	4	yes	complemented
36	C₃₇×#465	C₂²	1	16	yes	complemented
37	C₃₇×#460	C₂²	1	4	yes	complemented
38	C₃₇×#450	C₂²	1	8	yes	complemented
39	C₃₇×#448	C₂²	1	4	yes	complemented
40	C₄×SD₁₆×C₃₇	C₂²	1	8	yes	complemented
41	C₈×D₄×C₃₇	C₂²	1	8	yes	complemented
42	C₃₇×#431	C₂²	1	2	yes	complemented
43	C₂×#106×C₃₇	C₂²	1	8	yes	complemented
44	C₂×#102×C₃₇	C₂²	1	8	yes	complemented
45	C₂×C₂²⋊C₈×C₃₇	C₂²	1	4	yes	complemented
46	H(5,𝔽₂)×C₃₇	—	4	8	no	—
47	C₂×#41×C₃₇	—	2	4	no	—
48	C₂×#41×C₃₇	—	2	2	no	—
49	C₂²×Q₈×C₃₇	—	2	1	no	—
50	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₃₇	—	2	4	no	—
52	C₂²×D₄×C₃₇	—	2	4	no	—
53	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
54	C₂²×D₄×C₃₇	C₂³	1	4	yes	—
55	C₂³×C₄×C₃₇	—	2	2	no	—
56	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
57	C₂×SD₁₆×C₃₇	C₂³	1	8	yes	—
58	C₂²×C₈×C₃₇	C₂³	1	8	yes	—
59	C₄⋊Q₈×C₃₇	—	2	2	no	—
60	C₄⋊Q₈×C₃₇	C₂³	1	4	yes	—
61	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
62	#127×C₃₇	C₂³	1	2	yes	—
63	#125×C₃₇	—	2	8	no	—
64	#124×C₃₇	—	2	2	no	—
65	#123×C₃₇	—	2	8	no	—
66	C₂²⋊Q₈×C₃₇	—	2	4	no	—
67	C₂²⋊Q₈×C₃₇	—	2	4	no	—
68	C₂²⋊Q₈×C₃₇	—	2	16	no	—
69	C₂²⋊Q₈×C₃₇	C₂³	1	8	yes	—
70	#121×C₃₇	—	2	4	no	—
71	#121×C₃₇	—	2	4	no	—
72	#121×C₃₇	—	2	2	no	—
73	#121×C₃₇	—	2	4	no	—
74	#121×C₃₇	C₂³	1	4	yes	—
75	#121×C₃₇	C₂³	1	8	yes	—
76	#120×C₃₇	—	2	8	no	—
77	C₄×Q₈×C₃₇	—	2	2	no	—
78	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
79	C₄×D₄×C₃₇	—	2	8	no	—
80	C₄×D₄×C₃₇	—	2	2	no	—
81	C₄×D₄×C₃₇	D₄	1	4	yes	—
82	C₄×D₄×C₃₇	C₂³	1	4	yes	—
83	C₄×D₄×C₃₇	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
86	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
87	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
88	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
89	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₃₇	C₂³	1	8	yes	—
93	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
96	C₂×C₂²⋊C₄×C₃₇	D₄	1	2	yes	—
97	C₂×C₄²×C₃₇	—	2	1	no	—
98	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
99	#106×C₃₇	C₂³	1	8	yes	—
100	#106×C₃₇	C₂³	1	16	yes	—
101	C₄⋊C₈×C₃₇	C₂³	1	4	yes	—
102	#103×C₃₇	C₂³	1	8	yes	—
103	#102×C₃₇	C₂³	1	8	yes	—
104	#102×C₃₇	C₂³	1	16	yes	—
105	C₂²⋊C₈×C₃₇	C₂³	1	4	yes	—
106	C₂²⋊C₈×C₃₇	C₂³	1	8	yes	—
107	C₄×C₈×C₃₇	C₂³	1	4	yes	—
108	C₂⁴×C₃₇	—	2	4	no	—
109	C₂⁴×C₃₇	C₂×D₄	1	2	yes	—
110	#41×C₃₇	—	4	16	no	—
111	#41×C₃₇	—	4	8	no	—
112	C₂×Q₈×C₃₇	—	2	1	no	—
113	C₂×Q₈×C₃₇	—	2	2	no	—
114	C₂×Q₈×C₃₇	—	2	4	no	—
115	C₂×Q₈×C₃₇	—	4	2	no	—
116	C₂×Q₈×C₃₇	—	8	2	no	—
117	C₂×Q₈×C₃₇	C₂⁴	1	2	yes	—
118	C₂×D₄×C₃₇	—	2	8	no	—
119	C₂×D₄×C₃₇	—	2	4	no	—
120	C₂×D₄×C₃₇	—	2	2	no	—
121	C₂×D₄×C₃₇	—	2	2	no	—
122	C₂×D₄×C₃₇	—	2	4	no	—
123	C₂×D₄×C₃₇	—	4	8	no	—
124	C₂×D₄×C₃₇	—	4	16	no	—
125	C₂×D₄×C₃₇	—	4	16	no	—
126	C₂×D₄×C₃₇	SD₁₆	1	8	yes	complemented
127	C₂×D₄×C₃₇	C₂×D₄	1	4	yes	—
128	C₂×D₄×C₃₇	C₂⁴	1	4	yes	—
129	C₂²×C₄×C₃₇	—	2	1	no	—
130	C₂²×C₄×C₃₇	—	2	1	no	—
131	C₂²×C₄×C₃₇	—	2	2	no	—
132	C₂²×C₄×C₃₇	—	2	4	no	—
133	C₂²×C₄×C₃₇	—	2	8	no	—
134	C₂²×C₄×C₃₇	—	2	4	no	—
135	C₂²×C₄×C₃₇	—	4	4	no	—
136	C₂²×C₄×C₃₇	—	8	4	no	—
137	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
143	SD₁₆×C₃₇	—	4	8	no	—
144	C₂×C₈×C₃₇	—	4	8	no	—
145	C₂×C₈×C₃₇	C₂⁴	1	8	yes	—
146	C₄⋊C₄×C₃₇	—	2	1	no	—
147	C₄⋊C₄×C₃₇	—	2	8	no	—
148	C₄⋊C₄×C₃₇	—	2	2	no	—
149	C₄⋊C₄×C₃₇	—	2	4	no	—
150	C₄⋊C₄×C₃₇	—	2	4	no	—
151	C₄⋊C₄×C₃₇	—	2	8	no	—
152	C₄⋊C₄×C₃₇	—	2	4	no	—
153	C₄⋊C₄×C₃₇	—	2	2	no	—
154	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
155	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
156	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
157	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
158	C₂²⋊C₄×C₃₇	—	2	8	no	—
159	C₂²⋊C₄×C₃₇	—	2	4	no	—
160	C₂²⋊C₄×C₃₇	—	2	8	no	—
161	C₂²⋊C₄×C₃₇	—	2	4	no	—
162	C₂²⋊C₄×C₃₇	C₂×D₄	1	8	yes	—
163	C₄²×C₃₇	—	2	4	no	—
164	C₄²×C₃₇	C₂×D₄	1	2	yes	—
165	C₄²×C₃₇	C₂⁴	1	2	yes	—
166	C₂³×C₃₇	—	2	4	no	—
167	C₂³×C₃₇	—	4	2	no	—
168	C₂³×C₃₇	—	4	2	no	—
169	C₂³×C₃₇	—	4	8	no	—
170	C₂³×C₃₇	—	8	4	no	—
171	C₂³×C₃₇	—	8	4	no	—
172	C₂³×C₃₇	C₂×SD₁₆	1	8	yes	—
173	C₂³×C₃₇	C₂²×D₄	1	4	yes	—
174	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₃₇	—	2	4	no	—
176	Q₈×C₃₇	—	4	2	no	—
177	Q₈×C₃₇	—	4	4	no	—
178	Q₈×C₃₇	—	8	4	no	—
179	D₄×C₃₇	—	2	8	no	—
180	D₄×C₃₇	—	4	16	no	—
181	D₄×C₃₇	—	4	8	no	—
182	D₄×C₃₇	—	4	4	no	—
183	D₄×C₃₇	—	8	2	no	—
184	D₄×C₃₇	—	8	4	no	—
185	D₄×C₃₇	C₂×SD₁₆	1	16	yes	—
186	C₂×C₄×C₃₇	—	2	8	no	—
187	C₂×C₄×C₃₇	—	2	2	no	—
188	C₂×C₄×C₃₇	—	2	2	no	—
189	C₂×C₄×C₃₇	—	2	2	no	—
190	C₂×C₄×C₃₇	—	2	4	no	—
191	C₂×C₄×C₃₇	—	2	4	no	—
192	C₂×C₄×C₃₇	—	4	4	no	—
193	C₂×C₄×C₃₇	—	4	2	no	—
194	C₂×C₄×C₃₇	—	4	1	no	—
195	C₂×C₄×C₃₇	—	4	2	no	—
196	C₂×C₄×C₃₇	—	4	4	no	—
197	C₂×C₄×C₃₇	—	4	2	no	—
198	C₂×C₄×C₃₇	—	4	8	no	—
199	C₂×C₄×C₃₇	—	4	8	no	—
200	C₂×C₄×C₃₇	—	8	8	no	—
201	C₂×C₄×C₃₇	C₂×SD₁₆	1	4	yes	—
202	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
204	C₂×C₄×C₃₇	C₂²×D₄	1	4	yes	—
205	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
206	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
207	C₈×C₃₇	—	2	8	no	—
208	#61697	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂²×C₃₇	—	2	1	no	—
210	C₂²×C₃₇	—	2	4	no	—
211	C₂²×C₃₇	—	2	1	no	—
212	C₂²×C₃₇	—	2	4	no	—
213	C₂²×C₃₇	—	4	8	no	—
214	C₂²×C₃₇	—	4	4	no	—
215	C₂²×C₃₇	—	4	4	no	—
216	C₂²×C₃₇	—	4	4	no	—
217	C₂²×C₃₇	—	16	8	no	—
218	C₂²×C₃₇	C₂²×SD₁₆	1	8	yes	—
219	C₂²×C₃₇	C₂²×SD₁₆	1	2	yes	—
220	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
221	C₄×C₃₇	—	2	2	no	—
222	C₄×C₃₇	—	2	1	no	—
223	C₄×C₃₇	—	2	4	no	—
224	C₄×C₃₇	—	4	2	no	—
225	C₄×C₃₇	—	4	4	no	—
226	C₄×C₃₇	—	4	2	no	—
227	C₄×C₃₇	—	4	4	no	—
228	C₄×C₃₇	C₂²×SD₁₆	1	4	yes	—
229	C₄×C₃₇	#585	1	2	yes	—
230	#3496	C₂×C₃₇	1	1	yes	characteristic
231	C₂×#554	C₂×C₃₇	1	1	yes	characteristic, complemented
232	#3335	C₂×C₃₇	1	8	yes	complemented
233	#3295	C₂×C₃₇	1	8	yes	complemented
234	#3227	C₂×C₃₇	1	2	yes	complemented
235	#3187	C₂×C₃₇	1	4	yes	complemented
236	#3103	C₂×C₃₇	1	2	yes	complemented
237	C₂×#481	C₂×C₃₇	1	4	yes	complemented
238	#2972	C₂×C₃₇	1	1	yes	characteristic, complemented
239	C₂×C₃₇	—	2	2	no	—
240	C₂×C₃₇	—	2	8	no	—
241	C₂×C₃₇	—	8	4	no	—
242	C₂×C₃₇	#3485	1	1	yes	characteristic
243	C₂×C₃₇	C₂³×SD₁₆	1	1	yes	characteristic
244	C₂×C₃₇	#3585	1	1	yes	characteristic
245	C₂×H(5,𝔽₂)	—	2	1	no	—
246	#554	—	2	4	no	—
247	#554	C₂²×C₃₇	1	8	yes	complemented
248	#547	C₂²×C₃₇	1	4	yes	—
249	#546	—	2	4	no	—
250	D₄²	C₂²×C₃₇	1	4	yes	—
251	#537	—	2	1	no	—
252	#534	—	2	2	no	—
253	#532	C₂²×C₃₇	1	2	yes	—
254	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
255	C₂×#125	—	2	1	no	—
256	C₂×C₂²⋊Q₈	—	2	2	no	—
257	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	complemented
258	C₂×#121	C₂²×C₃₇	1	4	yes	—
259	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
260	C₂×C₄×D₄	—	2	1	no	—
261	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
262	C₂²×C₄⋊C₄	C₂²×C₃₇	1	2	yes	complemented
263	#498	C₂²×C₃₇	1	4	yes	complemented
264	#486	C₂²×C₃₇	1	4	yes	complemented
265	#483	C₂²×C₃₇	1	8	yes	complemented
266	#481	C₂²×C₃₇	1	16	yes	complemented
267	#481	C₂²×C₃₇	1	4	yes	complemented
268	#481	C₂²×C₃₇	1	8	yes	complemented
269	#476	C₂²×C₃₇	1	8	yes	complemented
270	#475	C₂²×C₃₇	1	4	yes	complemented
271	#465	C₂²×C₃₇	1	16	yes	complemented
272	#460	C₂²×C₃₇	1	4	yes	complemented
273	#450	C₂²×C₃₇	1	8	yes	complemented
274	#448	C₂²×C₃₇	1	4	yes	complemented
275	C₄×SD₁₆	C₂²×C₃₇	1	8	yes	complemented
276	C₈×D₄	C₂²×C₃₇	1	8	yes	complemented
277	#431	C₂²×C₃₇	1	2	yes	complemented
278	C₂×#106	C₂²×C₃₇	1	8	yes	complemented
279	C₂×#102	C₂²×C₃₇	1	8	yes	complemented
280	C₂×C₂²⋊C₈	C₂²×C₃₇	1	4	yes	complemented
281	C₃₇	#61697	1	1	yes	characteristic, direct product factor, Sylow
282	H(5,𝔽₂)	—	4	8	no	—
283	C₂×#41	—	2	4	no	—
284	C₂×#41	—	2	2	no	—
285	C₂²×Q₈	—	2	1	no	—
286	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
287	C₂²×D₄	—	2	4	no	—
288	C₂²×D₄	—	2	4	no	—
289	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
290	C₂²×D₄	C₂³×C₃₇	1	4	yes	—
291	C₂³×C₄	—	2	2	no	—
292	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
293	C₂×SD₁₆	C₂³×C₃₇	1	8	yes	—
294	C₂²×C₈	C₂³×C₃₇	1	8	yes	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₄⋊Q₈	C₂³×C₃₇	1	4	yes	—
297	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
298	#127	C₂³×C₃₇	1	2	yes	—
299	#125	—	2	8	no	—
300	#124	—	2	2	no	—
301	#123	—	2	8	no	—
302	C₂²⋊Q₈	—	2	4	no	—
303	C₂²⋊Q₈	—	2	4	no	—
304	C₂²⋊Q₈	—	2	16	no	—
305	C₂²⋊Q₈	C₂³×C₃₇	1	8	yes	—
306	#121	—	2	4	no	—
307	#121	—	2	4	no	—
308	#121	—	2	2	no	—
309	#121	—	2	4	no	—
310	#121	C₂³×C₃₇	1	4	yes	—
311	#121	C₂³×C₃₇	1	8	yes	—
312	#120	—	2	8	no	—
313	C₄×Q₈	—	2	2	no	—
314	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
315	C₄×D₄	—	2	8	no	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	D₄×C₃₇	1	4	yes	—
318	C₄×D₄	C₂³×C₃₇	1	4	yes	—
319	C₄×D₄	C₂³×C₃₇	1	4	yes	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	4	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₃₇	1	8	yes	—
329	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	4	no	—
332	C₂×C₂²⋊C₄	D₄×C₃₇	1	2	yes	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
335	#106	C₂³×C₃₇	1	8	yes	—
336	#106	C₂³×C₃₇	1	16	yes	—
337	C₄⋊C₈	C₂³×C₃₇	1	4	yes	—
338	#103	C₂³×C₃₇	1	8	yes	—
339	#102	C₂³×C₃₇	1	8	yes	—
340	#102	C₂³×C₃₇	1	16	yes	—
341	C₂²⋊C₈	C₂³×C₃₇	1	4	yes	—
342	C₂²⋊C₈	C₂³×C₃₇	1	8	yes	—
343	C₄×C₈	C₂³×C₃₇	1	4	yes	—
344	C₂⁴	—	2	4	no	—
345	C₂⁴	C₂×D₄×C₃₇	1	2	yes	—
346	#41	—	4	16	no	—
347	#41	—	4	8	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	4	no	—
351	C₂×Q₈	—	4	2	no	—
352	C₂×Q₈	—	8	2	no	—
353	C₂×Q₈	C₂⁴×C₃₇	1	2	yes	—
354	C₂×D₄	—	2	8	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	4	8	no	—
360	C₂×D₄	—	4	16	no	—
361	C₂×D₄	—	4	16	no	—
362	C₂×D₄	SD₁₆×C₃₇	1	8	yes	complemented
363	C₂×D₄	C₂×D₄×C₃₇	1	4	yes	—
364	C₂×D₄	C₂⁴×C₃₇	1	4	yes	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	8	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	8	4	no	—
373	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
375	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
376	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
378	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
379	SD₁₆	—	4	8	no	—
380	C₂×C₈	—	4	8	no	—
381	C₂×C₈	C₂⁴×C₃₇	1	8	yes	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
391	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
392	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
393	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
394	C₂²⋊C₄	—	2	8	no	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	2	8	no	—
397	C₂²⋊C₄	—	2	4	no	—
398	C₂²⋊C₄	C₂×D₄×C₃₇	1	8	yes	—
399	C₄²	—	2	4	no	—
400	C₄²	C₂×D₄×C₃₇	1	2	yes	—
401	C₄²	C₂⁴×C₃₇	1	2	yes	—
402	C₂³	—	2	4	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	8	no	—
406	C₂³	—	8	4	no	—
407	C₂³	—	8	4	no	—
408	C₂³	C₂×SD₁₆×C₃₇	1	8	yes	—
409	C₂³	C₂²×D₄×C₃₇	1	4	yes	—
410	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
411	Q₈	—	2	4	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	4	4	no	—
414	Q₈	—	8	4	no	—
415	D₄	—	2	8	no	—
416	D₄	—	4	16	no	—
417	D₄	—	4	8	no	—
418	D₄	—	4	4	no	—
419	D₄	—	8	4	no	—
420	D₄	—	8	2	no	—
421	D₄	C₂×SD₁₆×C₃₇	1	16	yes	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	8	no	—
435	C₂×C₄	—	4	8	no	—
436	C₂×C₄	—	8	8	no	—
437	C₂×C₄	C₂×SD₁₆×C₃₇	1	4	yes	—
438	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
440	C₂×C₄	C₂²×D₄×C₃₇	1	4	yes	—
441	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
442	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
443	C₈	—	2	8	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	4	8	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	16	8	no	—
453	C₂²	C₂²×SD₁₆×C₃₇	1	8	yes	—
454	C₂²	C₂²×SD₁₆×C₃₇	1	2	yes	—
455	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
456	C₄	—	2	1	no	—
457	C₄	—	2	4	no	—
458	C₄	—	2	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	4	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	4	no	—
463	C₄	C₂²×SD₁₆×C₃₇	1	4	yes	—
464	C₄	C₃₇×#585	1	2	yes	—
465	C₂	—	2	2	no	—
466	C₂	—	2	8	no	—
467	C₂	—	8	4	no	—
468	C₂	C₃₇×#3485	1	1	yes	characteristic
469	C₂	C₂³×SD₁₆×C₃₇	1	1	yes	characteristic
470	C₂	C₃₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
prime radical	C₃₇×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄×D₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₇×#554	C₂	semidirect
3. C₃₇×#3335	C₂	semidirect
4. C₃₇×#3295	C₂	semidirect
5. C₃₇×#3227	C₂	semidirect
6. C₃₇×#3187	C₂	semidirect
7. C₃₇×#3103	C₂	semidirect
8. C₂×C₃₇×#481	C₂	semidirect
9. C₃₇×#2972	C₂	semidirect
12. C₃₇×#554	C₂²	semidirect
19. C₂×C₄⋊Q₈×C₃₇	C₂²	semidirect
22. C₂×C₂²⋊Q₈×C₃₇	C₂²	semidirect
24. C₂×C₄×Q₈×C₃₇	C₂²	semidirect
27. C₂²×C₄⋊C₄×C₃₇	C₂²	semidirect
28. C₃₇×#498	C₂²	semidirect
29. C₃₇×#486	C₂²	semidirect
30. C₃₇×#483	C₂²	semidirect
31. C₃₇×#481	C₂²	semidirect
32. C₃₇×#481	C₂²	semidirect
33. C₃₇×#481	C₂²	semidirect
34. C₃₇×#476	C₂²	semidirect
35. C₃₇×#475	C₂²	semidirect
36. C₃₇×#465	C₂²	semidirect
37. C₃₇×#460	C₂²	semidirect
38. C₃₇×#450	C₂²	semidirect
39. C₃₇×#448	C₂²	semidirect
40. C₄×SD₁₆×C₃₇	C₂²	semidirect
41. C₈×D₄×C₃₇	C₂²	semidirect
42. C₃₇×#431	C₂²	semidirect
43. C₂×#106×C₃₇	C₂²	semidirect
44. C₂×#102×C₃₇	C₂²	semidirect
45. C₂×C₂²⋊C₈×C₃₇	C₂²	semidirect
126. C₂×D₄×C₃₇	SD₁₆	semidirect
208. #61697	C₃₇	direct (N × H)
231. C₂×#554	C₂×C₃₇	semidirect
232. #3335	C₂×C₃₇	semidirect
233. #3295	C₂×C₃₇	semidirect
234. #3227	C₂×C₃₇	semidirect
235. #3187	C₂×C₃₇	semidirect
236. #3103	C₂×C₃₇	semidirect
237. C₂×#481	C₂×C₃₇	semidirect
238. #2972	C₂×C₃₇	semidirect
247. #554	C₂²×C₃₇	semidirect
254. C₂×C₄⋊Q₈	C₂²×C₃₇	semidirect
257. C₂×C₂²⋊Q₈	C₂²×C₃₇	semidirect
259. C₂×C₄×Q₈	C₂²×C₃₇	semidirect
262. C₂²×C₄⋊C₄	C₂²×C₃₇	semidirect
263. #498	C₂²×C₃₇	semidirect
264. #486	C₂²×C₃₇	semidirect
265. #483	C₂²×C₃₇	semidirect
266. #481	C₂²×C₃₇	semidirect
267. #481	C₂²×C₃₇	semidirect
268. #481	C₂²×C₃₇	semidirect
269. #476	C₂²×C₃₇	semidirect
270. #475	C₂²×C₃₇	semidirect
271. #465	C₂²×C₃₇	semidirect
272. #460	C₂²×C₃₇	semidirect
273. #450	C₂²×C₃₇	semidirect
274. #448	C₂²×C₃₇	semidirect
275. C₄×SD₁₆	C₂²×C₃₇	semidirect
276. C₈×D₄	C₂²×C₃₇	semidirect
277. #431	C₂²×C₃₇	semidirect
278. C₂×#106	C₂²×C₃₇	semidirect
279. C₂×#102	C₂²×C₃₇	semidirect
280. C₂×C₂²⋊C₈	C₂²×C₃₇	semidirect
281. C₃₇	#61697	direct (N × H)
362. C₂×D₄	SD₁₆×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3496	2
C₂×C₃₇×#554	2
C₃₇×#3335	2
C₃₇×#3295	2
C₃₇×#3227	2
C₃₇×#3187	2
C₃₇×#3103	2
C₂×C₃₇×#481	2
C₃₇×#2972	2
#61697	37

Subgroups — C37×#61697 #22682950

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#61697 #22682950