Subgroups — C₂×C₃₇×#3191 #22681986

Order 9472.

2394 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#525	C₂	1	2	yes	maximal, complemented
2	C₃₇×#3191	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃₇×#485	C₂	1	2	yes	maximal, complemented
4	C₂×C₃₇×#482	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₇×#467	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₇×#465	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₇×#452	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₇×#449	C₂	1	2	yes	maximal, complemented
10	C₂²×C₂²⋊C₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#41×C₃₇	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic, complemented
14	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	complemented
15	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
16	C₂³×C₈×C₃₇	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₃₇×#525	—	2	8	no	—
19	C₃₇×#525	C₂²	1	16	yes	complemented
20	C₂×#123×C₃₇	—	2	2	no	—
21	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
23	C₂×#121×C₃₇	C₂²	1	2	yes	—
24	C₂×#121×C₃₇	C₂²	1	2	yes	—
25	C₂×#120×C₃₇	—	2	2	no	—
26	C₂×C₄×D₄×C₃₇	—	2	2	no	—
27	C₂×C₄×D₄×C₃₇	—	2	2	no	—
28	C₂×#117×C₃₇	C₂²	1	2	yes	—
29	C₃₇×#485	C₂²	1	16	yes	complemented
30	C₃₇×#482	C₂²	1	16	yes	complemented
31	C₃₇×#467	C₂²	1	8	yes	complemented
32	C₃₇×#466	C₂²	1	8	yes	complemented
33	C₃₇×#465	C₂²	1	16	yes	complemented
34	C₃₇×#452	C₂²	1	16	yes	complemented
35	C₃₇×#449	C₂²	1	16	yes	complemented
36	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×#106×C₃₇	C₂²	1	2	yes	complemented
39	C₂×#103×C₃₇	C₂²	1	2	yes	complemented
40	C₂×#103×C₃₇	C₂²	1	2	yes	complemented
41	C₂×#102×C₃₇	C₂²	1	2	yes	complemented
42	C₂×#102×C₃₇	C₂²	1	2	yes	complemented
43	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	—
44	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	—
45	C₂×C₂²⋊C₈×C₃₇	C₂²	1	8	yes	complemented
46	C₂⁵×C₃₇	D₄	1	1	yes	characteristic
47	C₂×#41×C₃₇	—	2	4	no	—
48	C₂×#41×C₃₇	—	4	4	no	—
49	C₂×#41×C₃₇	—	4	4	no	—
50	C₂×#41×C₃₇	C₂³	1	8	yes	—
51	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
52	C₂²×D₄×C₃₇	—	2	2	no	—
53	C₂²×D₄×C₃₇	—	2	2	no	—
54	C₂²×D₄×C₃₇	—	2	2	no	—
55	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
56	C₂³×C₄×C₃₇	—	2	2	no	—
57	C₂³×C₄×C₃₇	—	4	2	no	—
58	C₂³×C₄×C₃₇	—	4	2	no	—
59	C₂³×C₄×C₃₇	D₄	1	2	yes	—
60	C₂³×C₄×C₃₇	D₄	1	4	yes	—
61	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
64	C₂³×C₄×C₃₇	C₂³	1	4	yes	—
65	C₂×Q₁₆×C₃₇	—	4	2	no	—
66	C₂×Q₁₆×C₃₇	C₂³	1	4	yes	complemented
67	C₂×SD₁₆×C₃₇	—	4	4	no	—
68	C₂×SD₁₆×C₃₇	C₂³	1	8	yes	complemented
69	C₂×D₈×C₃₇	—	4	2	no	—
70	C₂×D₈×C₃₇	C₂³	1	4	yes	complemented
71	C₂²×C₈×C₃₇	—	4	2	no	—
72	C₂²×C₈×C₃₇	—	4	2	no	—
73	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
75	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
77	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
78	#123×C₃₇	—	2	16	no	—
79	C₂²⋊Q₈×C₃₇	—	2	4	no	—
80	C₂²⋊Q₈×C₃₇	—	2	4	no	—
81	C₂²⋊Q₈×C₃₇	C₂³	1	8	yes	—
82	C₂²⋊Q₈×C₃₇	C₂³	1	8	yes	—
83	#121×C₃₇	—	2	4	no	—
84	#121×C₃₇	—	2	4	no	—
85	#121×C₃₇	C₂³	1	8	yes	—
86	#121×C₃₇	C₂³	1	8	yes	—
87	#120×C₃₇	—	2	16	no	—
88	C₄×D₄×C₃₇	—	2	16	no	—
89	C₄×D₄×C₃₇	—	2	16	no	—
90	#117×C₃₇	—	2	4	no	—
91	#117×C₃₇	C₂³	1	8	yes	—
92	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
93	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
94	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
96	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
101	C₂×C₄²×C₃₇	—	2	2	no	—
102	#107×C₃₇	C₂³	1	4	yes	complemented
103	#107×C₃₇	C₂³	1	4	yes	complemented
104	#106×C₃₇	C₂³	1	8	yes	complemented
105	#103×C₃₇	C₂³	1	8	yes	complemented
106	#103×C₃₇	C₂³	1	8	yes	complemented
107	#102×C₃₇	C₂³	1	8	yes	complemented
108	#102×C₃₇	C₂³	1	8	yes	complemented
109	C₂²⋊C₈×C₃₇	C₂³	1	8	yes	—
110	C₂²⋊C₈×C₃₇	C₂³	1	8	yes	—
111	C₂⁴×C₃₇	—	2	4	no	—
112	C₂⁴×C₃₇	—	2	2	no	—
113	C₂⁴×C₃₇	—	4	2	no	—
114	C₂⁴×C₃₇	—	4	2	no	—
115	C₂⁴×C₃₇	C₂×D₄	1	2	yes	—
116	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
117	C₂⁴×C₃₇	C₂×D₄	1	4	yes	—
118	#41×C₃₇	—	4	8	no	—
119	#41×C₃₇	—	4	8	no	—
120	#41×C₃₇	—	4	16	no	—
121	C₂×Q₈×C₃₇	—	2	2	no	—
122	C₂×Q₈×C₃₇	—	2	4	no	—
123	C₂×Q₈×C₃₇	—	2	4	no	—
124	C₂×Q₈×C₃₇	C₂⁴	1	4	yes	—
125	C₂×D₄×C₃₇	—	2	8	no	—
126	C₂×D₄×C₃₇	—	2	8	no	—
127	C₂×D₄×C₃₇	—	2	8	no	—
128	C₂×D₄×C₃₇	—	2	2	no	—
129	C₂×D₄×C₃₇	—	2	4	no	—
130	C₂×D₄×C₃₇	—	2	4	no	—
131	C₂×D₄×C₃₇	—	4	8	no	—
132	C₂×D₄×C₃₇	—	4	8	no	—
133	C₂×D₄×C₃₇	—	4	8	no	—
134	C₂×D₄×C₃₇	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₃₇	—	2	2	no	—
136	C₂²×C₄×C₃₇	—	2	2	no	—
137	C₂²×C₄×C₃₇	—	2	4	no	—
138	C₂²×C₄×C₃₇	—	2	4	no	—
139	C₂²×C₄×C₃₇	—	2	2	no	—
140	C₂²×C₄×C₃₇	—	2	2	no	—
141	C₂²×C₄×C₃₇	—	2	2	no	—
142	C₂²×C₄×C₃₇	—	2	8	no	—
143	C₂²×C₄×C₃₇	—	4	8	no	—
144	C₂²×C₄×C₃₇	—	4	4	no	—
145	C₂²×C₄×C₃₇	—	4	4	no	—
146	C₂²×C₄×C₃₇	—	4	2	no	—
147	C₂²×C₄×C₃₇	—	4	4	no	—
148	C₂²×C₄×C₃₇	—	4	8	no	—
149	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₃₇	C₂×D₄	1	8	yes	—
155	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
158	Q₁₆×C₃₇	—	4	4	no	—
159	SD₁₆×C₃₇	—	4	8	no	—
160	D₈×C₃₇	—	4	4	no	—
161	C₂×C₈×C₃₇	—	2	2	no	—
162	C₂×C₈×C₃₇	—	2	4	no	—
163	C₂×C₈×C₃₇	—	2	2	no	—
164	C₂×C₈×C₃₇	—	4	4	no	—
165	C₂×C₈×C₃₇	—	4	4	no	—
166	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
167	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
168	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
169	C₄⋊C₄×C₃₇	—	2	8	no	—
170	C₄⋊C₄×C₃₇	—	2	8	no	—
171	C₄⋊C₄×C₃₇	—	2	2	no	—
172	C₄⋊C₄×C₃₇	—	2	2	no	—
173	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
174	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
175	C₂²⋊C₄×C₃₇	—	2	8	no	—
176	C₂²⋊C₄×C₃₇	—	2	8	no	—
177	C₂²⋊C₄×C₃₇	—	2	8	no	—
178	C₂²⋊C₄×C₃₇	—	2	8	no	—
179	C₂²⋊C₄×C₃₇	—	2	8	no	—
180	C₄²×C₃₇	—	2	8	no	—
181	C₂³×C₃₇	—	2	2	no	—
182	C₂³×C₃₇	—	2	2	no	—
183	C₂³×C₃₇	—	2	4	no	—
184	C₂³×C₃₇	—	2	8	no	—
185	C₂³×C₃₇	—	2	4	no	—
186	C₂³×C₃₇	—	2	4	no	—
187	C₂³×C₃₇	—	2	4	no	—
188	C₂³×C₃₇	—	4	4	no	—
189	C₂³×C₃₇	—	4	4	no	—
190	C₂³×C₃₇	—	4	16	no	—
191	C₂³×C₃₇	—	4	4	no	—
192	C₂³×C₃₇	—	4	4	no	—
193	C₂³×C₃₇	—	4	4	no	—
194	C₂³×C₃₇	#135	1	4	yes	—
195	C₂³×C₃₇	C₂²×D₄	1	4	yes	—
196	C₂³×C₃₇	C₂²×D₄	1	2	yes	—
197	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₃₇	—	2	4	no	—
199	Q₈×C₃₇	—	2	4	no	—
200	Q₈×C₃₇	—	4	4	no	—
201	D₄×C₃₇	—	2	4	no	—
202	D₄×C₃₇	—	2	4	no	—
203	D₄×C₃₇	—	4	16	no	—
204	D₄×C₃₇	—	4	16	no	—
205	D₄×C₃₇	—	4	16	no	—
206	D₄×C₃₇	—	4	4	no	—
207	C₂×C₄×C₃₇	—	2	4	no	—
208	C₂×C₄×C₃₇	—	2	2	no	—
209	C₂×C₄×C₃₇	—	2	4	no	—
210	C₂×C₄×C₃₇	—	2	8	no	—
211	C₂×C₄×C₃₇	—	2	2	no	—
212	C₂×C₄×C₃₇	—	2	2	no	—
213	C₂×C₄×C₃₇	—	2	4	no	—
214	C₂×C₄×C₃₇	—	2	4	no	—
215	C₂×C₄×C₃₇	—	2	4	no	—
216	C₂×C₄×C₃₇	—	2	4	no	—
217	C₂×C₄×C₃₇	—	2	4	no	—
218	C₂×C₄×C₃₇	—	4	4	no	—
219	C₂×C₄×C₃₇	—	4	8	no	—
220	C₂×C₄×C₃₇	—	4	16	no	—
221	C₂×C₄×C₃₇	—	4	4	no	—
222	C₂×C₄×C₃₇	—	4	4	no	—
223	C₂×C₄×C₃₇	—	4	4	no	—
224	C₂×C₄×C₃₇	C₂²×D₄	1	4	yes	—
225	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
226	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
228	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
229	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
230	C₈×C₃₇	—	2	2	no	—
231	C₈×C₃₇	—	2	4	no	—
232	C₈×C₃₇	—	2	2	no	—
233	C₂×#3191	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂²×C₃₇	—	2	2	no	—
235	C₂²×C₃₇	—	2	8	no	—
236	C₂²×C₃₇	—	2	2	no	—
237	C₂²×C₃₇	—	2	4	no	—
238	C₂²×C₃₇	—	2	4	no	—
239	C₂²×C₃₇	—	2	4	no	—
240	C₂²×C₃₇	—	4	16	no	—
241	C₂²×C₃₇	—	4	8	no	—
242	C₂²×C₃₇	—	4	4	no	—
243	C₂²×C₃₇	—	4	4	no	—
244	C₂²×C₃₇	—	4	4	no	—
245	C₂²×C₃₇	—	8	8	no	—
246	C₂²×C₃₇	#534	1	2	yes	—
247	C₂²×C₃₇	C₂×#135	1	4	yes	—
248	C₂²×C₃₇	C₂×#135	1	2	yes	—
249	C₂²×C₃₇	#575	1	2	yes	—
250	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
251	C₄×C₃₇	—	2	4	no	—
252	C₄×C₃₇	—	2	2	no	—
253	C₄×C₃₇	—	4	4	no	—
254	C₄×C₃₇	—	4	4	no	—
255	C₄×C₃₇	—	4	4	no	—
256	C₄×C₃₇	#534	1	2	yes	—
257	C₄×C₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
258	C₄×C₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
259	C₂×#525	C₂×C₃₇	1	2	yes	complemented
260	#3191	C₂×C₃₇	1	16	yes	direct product factor
261	C₂×#485	C₂×C₃₇	1	2	yes	complemented
262	C₂×#482	C₂×C₃₇	1	2	yes	complemented
263	C₂×#467	C₂×C₃₇	1	1	yes	characteristic, complemented
264	C₂×#466	C₂×C₃₇	1	1	yes	characteristic, complemented
265	C₂×#465	C₂×C₃₇	1	2	yes	complemented
266	C₂×#452	C₂×C₃₇	1	2	yes	complemented
267	C₂×#449	C₂×C₃₇	1	2	yes	complemented
268	C₂²×C₂²⋊C₈	C₂×C₃₇	1	1	yes	characteristic, complemented
269	C₂×C₃₇	—	2	4	no	—
270	C₂×C₃₇	—	4	4	no	—
271	C₂×C₃₇	—	8	4	no	—
272	C₂×C₃₇	#3191	1	4	yes	direct product factor
273	C₂×C₃₇	C₂×#534	1	1	yes	characteristic
274	C₂×C₃₇	C₂²×#135	1	1	yes	characteristic
275	C₂×C₃₇	C₂×#575	1	1	yes	characteristic
276	C₂²×#41	C₂²×C₃₇	1	2	yes	—
277	C₂⁴×C₄	C₂²×C₃₇	1	1	yes	characteristic
278	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic, complemented
279	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	complemented
280	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
281	C₂³×C₈	C₂²×C₃₇	1	1	yes	characteristic
282	C₂³×C₈	C₂²×C₃₇	1	1	yes	characteristic
283	#525	—	2	8	no	—
284	#525	C₂²×C₃₇	1	16	yes	complemented
285	C₂×#123	—	2	2	no	—
286	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
287	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
288	C₂×#121	C₂²×C₃₇	1	2	yes	—
289	C₂×#121	C₂²×C₃₇	1	2	yes	—
290	C₂×#120	—	2	2	no	—
291	C₂×C₄×D₄	—	2	2	no	—
292	C₂×C₄×D₄	—	2	2	no	—
293	C₂×#117	C₂²×C₃₇	1	2	yes	—
294	#485	C₂²×C₃₇	1	16	yes	complemented
295	#482	C₂²×C₃₇	1	16	yes	complemented
296	#467	C₂²×C₃₇	1	8	yes	complemented
297	#466	C₂²×C₃₇	1	8	yes	complemented
298	#465	C₂²×C₃₇	1	16	yes	complemented
299	#452	C₂²×C₃₇	1	16	yes	complemented
300	#449	C₂²×C₃₇	1	16	yes	complemented
301	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic, complemented
302	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic, complemented
303	C₂×#106	C₂²×C₃₇	1	2	yes	complemented
304	C₂×#103	C₂²×C₃₇	1	2	yes	complemented
305	C₂×#103	C₂²×C₃₇	1	2	yes	complemented
306	C₂×#102	C₂²×C₃₇	1	2	yes	complemented
307	C₂×#102	C₂²×C₃₇	1	2	yes	complemented
308	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
309	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
310	C₂×C₂²⋊C₈	C₂²×C₃₇	1	8	yes	complemented
311	C₃₇	C₂×#3191	1	1	yes	characteristic, direct product factor, Sylow
312	C₂⁵	D₄×C₃₇	1	1	yes	characteristic
313	C₂×#41	—	2	4	no	—
314	C₂×#41	—	4	4	no	—
315	C₂×#41	—	4	4	no	—
316	C₂×#41	C₂³×C₃₇	1	8	yes	—
317	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
318	C₂²×D₄	—	2	2	no	—
319	C₂²×D₄	—	2	2	no	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
322	C₂³×C₄	—	2	2	no	—
323	C₂³×C₄	—	4	2	no	—
324	C₂³×C₄	—	4	2	no	—
325	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
326	C₂³×C₄	D₄×C₃₇	1	2	yes	—
327	C₂³×C₄	D₄×C₃₇	1	4	yes	—
328	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
329	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
330	C₂³×C₄	C₂³×C₃₇	1	4	yes	—
331	C₂×Q₁₆	—	4	2	no	—
332	C₂×Q₁₆	C₂³×C₃₇	1	4	yes	complemented
333	C₂×SD₁₆	—	4	4	no	—
334	C₂×SD₁₆	C₂³×C₃₇	1	8	yes	complemented
335	C₂×D₈	—	4	2	no	—
336	C₂×D₈	C₂³×C₃₇	1	4	yes	complemented
337	C₂²×C₈	—	4	2	no	—
338	C₂²×C₈	—	4	2	no	—
339	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
341	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
342	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
343	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
344	#123	—	2	16	no	—
345	C₂²⋊Q₈	—	2	4	no	—
346	C₂²⋊Q₈	—	2	4	no	—
347	C₂²⋊Q₈	C₂³×C₃₇	1	8	yes	—
348	C₂²⋊Q₈	C₂³×C₃₇	1	8	yes	—
349	#121	—	2	4	no	—
350	#121	—	2	4	no	—
351	#121	C₂³×C₃₇	1	8	yes	—
352	#121	C₂³×C₃₇	1	8	yes	—
353	#120	—	2	16	no	—
354	C₄×D₄	—	2	16	no	—
355	C₄×D₄	—	2	16	no	—
356	#117	—	2	4	no	—
357	#117	C₂³×C₃₇	1	8	yes	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₄²	—	2	2	no	—
368	#107	C₂³×C₃₇	1	4	yes	complemented
369	#107	C₂³×C₃₇	1	4	yes	complemented
370	#106	C₂³×C₃₇	1	8	yes	complemented
371	#103	C₂³×C₃₇	1	8	yes	complemented
372	#103	C₂³×C₃₇	1	8	yes	complemented
373	#102	C₂³×C₃₇	1	8	yes	complemented
374	#102	C₂³×C₃₇	1	8	yes	complemented
375	C₂²⋊C₈	C₂³×C₃₇	1	8	yes	—
376	C₂²⋊C₈	C₂³×C₃₇	1	8	yes	—
377	C₂⁴	—	2	4	no	—
378	C₂⁴	—	2	2	no	—
379	C₂⁴	—	4	2	no	—
380	C₂⁴	—	4	2	no	—
381	C₂⁴	C₂×D₄×C₃₇	1	2	yes	—
382	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
383	C₂⁴	C₂×D₄×C₃₇	1	4	yes	—
384	#41	—	4	8	no	—
385	#41	—	4	8	no	—
386	#41	—	4	16	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	4	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	C₂⁴×C₃₇	1	4	yes	—
391	C₂×D₄	—	2	8	no	—
392	C₂×D₄	—	2	8	no	—
393	C₂×D₄	—	2	8	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	4	8	no	—
398	C₂×D₄	—	4	8	no	—
399	C₂×D₄	—	4	8	no	—
400	C₂×D₄	C₂⁴×C₃₇	1	4	yes	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	8	no	—
409	C₂²×C₄	—	4	8	no	—
410	C₂²×C₄	—	4	4	no	—
411	C₂²×C₄	—	4	4	no	—
412	C₂²×C₄	—	4	2	no	—
413	C₂²×C₄	—	4	4	no	—
414	C₂²×C₄	—	4	8	no	—
415	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
416	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
418	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
419	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
420	C₂²×C₄	C₂×D₄×C₃₇	1	8	yes	—
421	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
422	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
423	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
424	Q₁₆	—	4	4	no	—
425	SD₁₆	—	4	8	no	—
426	D₈	—	4	4	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	4	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	4	4	no	—
431	C₂×C₈	—	4	4	no	—
432	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
433	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
434	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	2	8	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
440	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂²⋊C₄	—	2	8	no	—
443	C₂²⋊C₄	—	2	8	no	—
444	C₂²⋊C₄	—	2	8	no	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₄²	—	2	8	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	2	8	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	2	4	no	—
453	C₂³	—	2	4	no	—
454	C₂³	—	4	4	no	—
455	C₂³	—	4	4	no	—
456	C₂³	—	4	16	no	—
457	C₂³	—	4	4	no	—
458	C₂³	—	4	4	no	—
459	C₂³	—	4	4	no	—
460	C₂³	#135×C₃₇	1	4	yes	—
461	C₂³	C₂²×D₄×C₃₇	1	4	yes	—
462	C₂³	C₂²×D₄×C₃₇	1	2	yes	—
463	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
464	Q₈	—	2	4	no	—
465	Q₈	—	2	4	no	—
466	Q₈	—	4	4	no	—
467	D₄	—	2	4	no	—
468	D₄	—	2	4	no	—
469	D₄	—	4	16	no	—
470	D₄	—	4	16	no	—
471	D₄	—	4	16	no	—
472	D₄	—	4	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	8	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	8	no	—
486	C₂×C₄	—	4	16	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	C₂²×D₄×C₃₇	1	4	yes	—
491	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
492	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
493	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
494	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
495	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
496	C₈	—	2	2	no	—
497	C₈	—	2	4	no	—
498	C₈	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	8	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	4	16	no	—
506	C₂²	—	4	8	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	8	8	no	—
511	C₂²	C₃₇×#534	1	2	yes	—
512	C₂²	C₂×#135×C₃₇	1	4	yes	—
513	C₂²	C₂×#135×C₃₇	1	2	yes	—
514	C₂²	C₃₇×#575	1	2	yes	—
515	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
516	C₄	—	2	4	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	4	4	no	—
520	C₄	—	4	4	no	—
521	C₄	C₃₇×#534	1	2	yes	—
522	C₄	C₂×H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
523	C₄	C₂×H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
524	C₂	—	2	4	no	—
525	C₂	—	4	4	no	—
526	C₂	—	8	4	no	—
527	C₂	C₃₇×#3191	1	4	yes	direct product factor
528	C₂	C₂×C₃₇×#534	1	1	yes	characteristic
529	C₂	C₂²×#135×C₃₇	1	1	yes	characteristic
530	C₂	C₂×C₃₇×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂⁴×C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#525	C₂	semidirect
2. C₃₇×#3191	C₂	direct (N × H)
3. C₂×C₃₇×#485	C₂	semidirect
4. C₂×C₃₇×#482	C₂	semidirect
5. C₂×C₃₇×#467	C₂	semidirect
6. C₂×C₃₇×#466	C₂	semidirect
7. C₂×C₃₇×#465	C₂	semidirect
8. C₂×C₃₇×#452	C₂	semidirect
9. C₂×C₃₇×#449	C₂	semidirect
10. C₂²×C₂²⋊C₈×C₃₇	C₂	semidirect
13. C₂²×Q₁₆×C₃₇	C₂²	semidirect
14. C₂²×SD₁₆×C₃₇	C₂²	semidirect
15. C₂²×D₈×C₃₇	C₂²	semidirect
19. C₃₇×#525	C₂²	semidirect
29. C₃₇×#485	C₂²	semidirect
30. C₃₇×#482	C₂²	semidirect
31. C₃₇×#467	C₂²	semidirect
32. C₃₇×#466	C₂²	semidirect
33. C₃₇×#465	C₂²	semidirect
34. C₃₇×#452	C₂²	semidirect
35. C₃₇×#449	C₂²	semidirect
36. C₂×#107×C₃₇	C₂²	semidirect
37. C₂×#107×C₃₇	C₂²	semidirect
38. C₂×#106×C₃₇	C₂²	semidirect
39. C₂×#103×C₃₇	C₂²	semidirect
40. C₂×#103×C₃₇	C₂²	semidirect
41. C₂×#102×C₃₇	C₂²	semidirect
42. C₂×#102×C₃₇	C₂²	semidirect
45. C₂×C₂²⋊C₈×C₃₇	C₂²	semidirect
66. C₂×Q₁₆×C₃₇	C₂³	semidirect
68. C₂×SD₁₆×C₃₇	C₂³	semidirect
70. C₂×D₈×C₃₇	C₂³	semidirect
102. #107×C₃₇	C₂³	semidirect
103. #107×C₃₇	C₂³	semidirect
104. #106×C₃₇	C₂³	semidirect
105. #103×C₃₇	C₂³	semidirect
106. #103×C₃₇	C₂³	semidirect
107. #102×C₃₇	C₂³	semidirect
108. #102×C₃₇	C₂³	semidirect
233. C₂×#3191	C₃₇	direct (N × H)
259. C₂×#525	C₂×C₃₇	semidirect
260. #3191	C₂×C₃₇	direct (N × H)
261. C₂×#485	C₂×C₃₇	semidirect
262. C₂×#482	C₂×C₃₇	semidirect
263. C₂×#467	C₂×C₃₇	semidirect
264. C₂×#466	C₂×C₃₇	semidirect
265. C₂×#465	C₂×C₃₇	semidirect
266. C₂×#452	C₂×C₃₇	semidirect
267. C₂×#449	C₂×C₃₇	semidirect
268. C₂²×C₂²⋊C₈	C₂×C₃₇	semidirect
272. C₂×C₃₇	#3191	direct (N × H)
278. C₂²×Q₁₆	C₂²×C₃₇	semidirect
279. C₂²×SD₁₆	C₂²×C₃₇	semidirect
280. C₂²×D₈	C₂²×C₃₇	semidirect
284. #525	C₂²×C₃₇	semidirect
294. #485	C₂²×C₃₇	semidirect
295. #482	C₂²×C₃₇	semidirect
296. #467	C₂²×C₃₇	semidirect
297. #466	C₂²×C₃₇	semidirect
298. #465	C₂²×C₃₇	semidirect
299. #452	C₂²×C₃₇	semidirect
300. #449	C₂²×C₃₇	semidirect
301. C₂×#107	C₂²×C₃₇	semidirect
302. C₂×#107	C₂²×C₃₇	semidirect
303. C₂×#106	C₂²×C₃₇	semidirect
304. C₂×#103	C₂²×C₃₇	semidirect
305. C₂×#103	C₂²×C₃₇	semidirect
306. C₂×#102	C₂²×C₃₇	semidirect
307. C₂×#102	C₂²×C₃₇	semidirect
310. C₂×C₂²⋊C₈	C₂²×C₃₇	semidirect
311. C₃₇	C₂×#3191	direct (N × H)
332. C₂×Q₁₆	C₂³×C₃₇	semidirect
334. C₂×SD₁₆	C₂³×C₃₇	semidirect
336. C₂×D₈	C₂³×C₃₇	semidirect
368. #107	C₂³×C₃₇	semidirect
369. #107	C₂³×C₃₇	semidirect
370. #106	C₂³×C₃₇	semidirect
371. #103	C₂³×C₃₇	semidirect
372. #103	C₂³×C₃₇	semidirect
373. #102	C₂³×C₃₇	semidirect
374. #102	C₂³×C₃₇	semidirect
527. C₂	C₃₇×#3191	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×#525	2
C₃₇×#3191	2
C₂×C₃₇×#485	2
C₂×C₃₇×#482	2
C₂×C₃₇×#467	2
C₂×C₃₇×#466	2
C₂×C₃₇×#465	2
C₂×C₃₇×#452	2
C₂×C₃₇×#449	2
C₂²×C₂²⋊C₈×C₃₇	2
C₂×#3191	37

Subgroups — C2×C37×#3191 #22681986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₇×#3191 #22681986