Subgroups — C₂×C₃₇×#2897 #22681337

Order 9472.

5226 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×H(5,𝔽₂)×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#131×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#520	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2897	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃₇×#417	C₂	1	3	yes	maximal, complemented
6	C₂×C₃₇×#418	C₂	1	3	yes	maximal, complemented
7	C₂×C₃₇×#416	C₂	1	3	yes	maximal, complemented
8	C₂²×#102×C₃₇	C₂	1	3	yes	maximal, complemented
9	C₂×H(5,𝔽₂)×C₃₇	—	2	8	no	—
10	C₂×H(5,𝔽₂)×C₃₇	—	2	4	no	—
11	C₂×H(5,𝔽₂)×C₃₇	C₄	1	16	yes	complemented
12	C₂×H(5,𝔽₂)×C₃₇	C₂²	1	8	yes	—
13	C₂²×#41×C₃₇	—	2	1	no	—
14	C₂²×#41×C₃₇	C₂²	1	3	yes	—
15	C₂²×#41×C₃₇	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₃₇	—	2	3	no	—
17	C₂³×D₄×C₃₇	C₂²	1	3	yes	—
18	C₂×#131×C₃₇	—	2	8	no	—
19	C₂×#131×C₃₇	C₂²	1	8	yes	complemented
20	C₂²×M₁₆×C₃₇	C₂²	1	3	yes	complemented
21	C₂³×C₈×C₃₇	C₂²	1	3	yes	complemented
22	C₃₇×#520	—	2	4	no	—
23	C₃₇×#520	C₂²	1	8	yes	complemented
24	C₂×C₄×Q₈×C₃₇	—	2	1	no	—
25	C₂×C₄×D₄×C₃₇	—	2	3	no	—
26	C₂×#117×C₃₇	C₂²	1	3	yes	complemented
27	C₂²×C₄⋊C₄×C₃₇	C₂²	1	3	yes	complemented
28	C₃₇×#418	C₂²	1	24	yes	complemented
29	C₃₇×#417	C₂²	1	24	yes	complemented
30	C₃₇×#416	C₂²	1	24	yes	complemented
31	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×#103×C₃₇	C₂²	1	3	yes	complemented
33	C₂×#102×C₃₇	C₂²	1	3	yes	complemented
34	C₂×#102×C₃₇	C₂²	1	6	yes	complemented
35	C₂×#102×C₃₇	C₂²	1	3	yes	complemented
36	C₂×#102×C₃₇	C₂²	1	24	yes	complemented
37	C₂⁵×C₃₇	—	2	3	no	—
38	H(5,𝔽₂)×C₃₇	—	2	64	no	—
39	H(5,𝔽₂)×C₃₇	—	2	32	no	—
40	H(5,𝔽₂)×C₃₇	C₂×C₄	1	64	yes	complemented
41	C₂×#41×C₃₇	—	2	16	no	—
42	C₂×#41×C₃₇	—	2	8	no	—
43	C₂×#41×C₃₇	—	2	12	no	—
44	C₂×#41×C₃₇	—	2	6	no	—
45	C₂×#41×C₃₇	C₂×C₄	1	8	yes	—
46	C₂×#41×C₃₇	C₂×C₄	1	24	yes	complemented
47	C₂×#41×C₃₇	D₄	1	8	yes	—
48	C₂×#41×C₃₇	D₄	1	4	yes	—
49	C₂×#41×C₃₇	C₂³	1	12	yes	—
50	C₂×#41×C₃₇	C₂³	1	4	yes	—
51	C₂²×Q₈×C₃₇	D₄	1	1	yes	characteristic
52	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₃₇	—	2	3	no	—
54	C₂²×D₄×C₃₇	—	2	48	no	—
55	C₂²×D₄×C₃₇	—	2	24	no	—
56	C₂²×D₄×C₃₇	—	2	3	no	—
57	C₂²×D₄×C₃₇	—	2	6	no	—
58	C₂²×D₄×C₃₇	—	2	12	no	—
59	C₂²×D₄×C₃₇	C₂×C₄	1	24	yes	complemented
60	C₂²×D₄×C₃₇	D₄	1	3	yes	—
61	C₂²×D₄×C₃₇	C₂³	1	3	yes	—
62	C₂²×D₄×C₃₇	C₂³	1	12	yes	—
63	C₂³×C₄×C₃₇	—	2	3	no	—
64	C₂³×C₄×C₃₇	—	2	3	no	—
65	C₂³×C₄×C₃₇	C₂³	1	3	yes	—
66	#131×C₃₇	—	2	32	no	—
67	C₂×M₁₆×C₃₇	—	2	12	no	—
68	C₂×M₁₆×C₃₇	C₂³	1	12	yes	complemented
69	C₂²×C₈×C₃₇	—	2	12	no	—
70	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₃₇	C₂³	1	3	yes	—
72	C₂²×C₈×C₃₇	C₂³	1	12	yes	complemented
73	C₄×Q₈×C₃₇	—	2	8	no	—
74	C₄×D₄×C₃₇	—	2	24	no	—
75	#117×C₃₇	—	2	6	no	—
76	#117×C₃₇	C₂³	1	12	yes	complemented
77	C₂×C₄⋊C₄×C₃₇	—	2	6	no	—
78	C₂×C₄⋊C₄×C₃₇	—	2	3	no	—
79	C₂×C₄⋊C₄×C₃₇	C₂³	1	3	yes	—
80	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₃₇	C₂³	1	12	yes	complemented
82	C₂×C₂²⋊C₄×C₃₇	—	2	3	no	—
83	C₂×C₄²×C₃₇	—	2	3	no	—
84	#103×C₃₇	C₂³	1	4	yes	complemented
85	#103×C₃₇	C₂³	1	12	yes	complemented
86	#102×C₃₇	C₂³	1	12	yes	complemented
87	#102×C₃₇	C₂³	1	24	yes	complemented
88	#102×C₃₇	C₂³	1	12	yes	complemented
89	C₂⁴×C₃₇	—	2	3	no	—
90	C₂⁴×C₃₇	—	2	24	no	—
91	C₂⁴×C₃₇	—	2	12	no	—
92	C₂⁴×C₃₇	—	8	6	no	—
93	C₂⁴×C₃₇	—	8	6	no	—
94	C₂⁴×C₃₇	C₂×D₄	1	3	yes	—
95	#41×C₃₇	—	2	64	no	—
96	#41×C₃₇	—	2	48	no	—
97	#41×C₃₇	—	2	24	no	—
98	#41×C₃₇	C₂²⋊C₄	1	32	yes	—
99	#41×C₃₇	C₂²×C₄	1	16	yes	—
100	#41×C₃₇	C₂²×C₄	1	48	yes	complemented
101	#41×C₃₇	C₂×D₄	1	16	yes	—
102	C₂×Q₈×C₃₇	—	2	2	no	—
103	C₂×Q₈×C₃₇	—	2	1	no	—
104	C₂×Q₈×C₃₇	C₂²⋊C₄	1	8	yes	—
105	C₂×Q₈×C₃₇	C₂²×C₄	1	4	yes	—
106	C₂×Q₈×C₃₇	C₂×D₄	1	4	yes	—
107	C₂×Q₈×C₃₇	C₂⁴	1	2	yes	—
108	C₂×D₄×C₃₇	—	2	24	no	—
109	C₂×D₄×C₃₇	—	2	12	no	—
110	C₂×D₄×C₃₇	—	2	192	no	—
111	C₂×D₄×C₃₇	—	2	24	no	—
112	C₂×D₄×C₃₇	—	2	48	no	—
113	C₂×D₄×C₃₇	—	2	12	no	—
114	C₂×D₄×C₃₇	—	2	3	no	—
115	C₂×D₄×C₃₇	—	2	6	no	—
116	C₂×D₄×C₃₇	—	2	24	no	—
117	C₂×D₄×C₃₇	C₂²⋊C₄	1	24	yes	—
118	C₂×D₄×C₃₇	C₂²×C₄	1	12	yes	—
119	C₂×D₄×C₃₇	C₂²×C₄	1	48	yes	complemented
120	C₂×D₄×C₃₇	C₂×D₄	1	12	yes	—
121	C₂×D₄×C₃₇	C₂⁴	1	6	yes	—
122	C₂²×C₄×C₃₇	—	2	1	no	—
123	C₂²×C₄×C₃₇	—	2	24	no	—
124	C₂²×C₄×C₃₇	—	2	12	no	—
125	C₂²×C₄×C₃₇	—	2	1	no	—
126	C₂²×C₄×C₃₇	—	2	3	no	—
127	C₂²×C₄×C₃₇	—	2	12	no	—
128	C₂²×C₄×C₃₇	—	8	6	no	—
129	C₂²×C₄×C₃₇	C₂²×C₄	1	12	yes	—
130	C₂²×C₄×C₃₇	C₂×D₄	1	6	yes	—
131	C₂²×C₄×C₃₇	C₂×D₄	1	3	yes	—
132	C₂²×C₄×C₃₇	C₂×D₄	1	12	yes	—
133	C₂²×C₄×C₃₇	C₂⁴	1	6	yes	—
134	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
135	M₁₆×C₃₇	—	2	24	no	—
136	C₂×C₈×C₃₇	—	2	2	no	—
137	C₂×C₈×C₃₇	—	2	6	no	—
138	C₂×C₈×C₃₇	—	2	24	no	—
139	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
140	C₂×C₈×C₃₇	C₂⁴	1	6	yes	—
141	C₄⋊C₄×C₃₇	—	2	3	no	—
142	C₄⋊C₄×C₃₇	—	2	12	no	—
143	C₄⋊C₄×C₃₇	—	2	1	no	—
144	C₄⋊C₄×C₃₇	C₂⁴	1	6	yes	—
145	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
146	C₂²⋊C₄×C₃₇	—	2	12	no	—
147	C₄²×C₃₇	—	2	12	no	—
148	C₂³×C₃₇	—	2	6	no	—
149	C₂³×C₃₇	—	2	6	no	—
150	C₂³×C₃₇	—	2	12	no	—
151	C₂³×C₃₇	—	2	6	no	—
152	C₂³×C₃₇	—	2	48	no	—
153	C₂³×C₃₇	—	4	6	no	—
154	C₂³×C₃₇	—	4	6	no	—
155	C₂³×C₃₇	—	8	48	no	—
156	C₂³×C₃₇	—	8	12	no	—
157	C₂³×C₃₇	—	8	12	no	—
158	C₂³×C₃₇	C₂×C₂²⋊C₄	1	12	yes	—
159	C₂³×C₃₇	C₂²×D₄	1	6	yes	—
160	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₃₇	—	2	4	no	—
162	Q₈×C₃₇	—	2	2	no	—
163	Q₈×C₃₇	C₂×C₂²⋊C₄	1	16	yes	—
164	Q₈×C₃₇	C₂³×C₄	1	4	yes	—
165	D₄×C₃₇	—	2	48	no	—
166	D₄×C₃₇	—	2	12	no	—
167	D₄×C₃₇	—	2	48	no	—
168	D₄×C₃₇	—	2	6	no	—
169	D₄×C₃₇	C₂×C₂²⋊C₄	1	48	yes	—
170	D₄×C₃₇	C₂³×C₄	1	12	yes	—
171	C₂×C₄×C₃₇	—	2	4	no	—
172	C₂×C₄×C₃₇	—	2	2	no	—
173	C₂×C₄×C₃₇	—	2	48	no	—
174	C₂×C₄×C₃₇	—	2	2	no	—
175	C₂×C₄×C₃₇	—	2	6	no	—
176	C₂×C₄×C₃₇	—	4	6	no	—
177	C₂×C₄×C₃₇	—	4	2	no	—
178	C₂×C₄×C₃₇	—	8	12	no	—
179	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	12	yes	—
180	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	24	yes	—
181	C₂×C₄×C₃₇	C₂³×C₄	1	2	yes	—
182	C₂×C₄×C₃₇	C₂³×C₄	1	12	yes	—
183	C₂×C₄×C₃₇	C₂²×D₄	1	6	yes	—
184	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
186	C₂×C₄×C₃₇	C₂²×D₄	1	12	yes	—
187	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
188	C₈×C₃₇	—	2	2	no	—
189	C₈×C₃₇	—	2	6	no	—
190	C₂×#2897	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂²×C₃₇	—	2	24	no	—
192	C₂²×C₃₇	—	2	6	no	—
193	C₂²×C₃₇	—	2	6	no	—
194	C₂²×C₃₇	—	2	12	no	—
195	C₂²×C₃₇	—	4	24	no	—
196	C₂²×C₃₇	—	4	6	no	—
197	C₂²×C₃₇	—	4	6	no	—
198	C₂²×C₃₇	—	8	48	no	—
199	C₂²×C₃₇	C₂²×C₂²⋊C₄	1	12	yes	—
200	C₂²×C₃₇	C₂²×C₂²⋊C₄	1	2	yes	—
201	C₂²×C₃₇	#576	1	2	yes	—
202	C₂²×C₃₇	#577	1	2	yes	—
203	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
204	C₄×C₃₇	—	2	4	no	—
205	C₄×C₃₇	—	4	6	no	—
206	C₄×C₃₇	—	4	2	no	—
207	C₄×C₃₇	C₂²×C₂²⋊C₄	1	12	yes	—
208	C₄×C₃₇	C₂²×C₂²⋊C₄	1	2	yes	—
209	C₄×C₃₇	C₂⁴×C₄	1	1	yes	characteristic
210	C₄×C₃₇	C₂³×D₄	1	1	yes	characteristic
211	C₂²×H(5,𝔽₂)	C₂×C₃₇	1	1	yes	characteristic
212	C₂²×#131	C₂×C₃₇	1	1	yes	characteristic, complemented
213	C₂×#520	C₂×C₃₇	1	1	yes	characteristic, complemented
214	#2897	C₂×C₃₇	1	16	yes	direct product factor
215	C₂×#417	C₂×C₃₇	1	3	yes	complemented
216	C₂×#418	C₂×C₃₇	1	3	yes	complemented
217	C₂×#416	C₂×C₃₇	1	3	yes	complemented
218	C₂²×#102	C₂×C₃₇	1	3	yes	complemented
219	C₂×C₃₇	—	2	12	no	—
220	C₂×C₃₇	—	4	12	no	—
221	C₂×C₃₇	#2897	1	4	yes	direct product factor
222	C₂×C₃₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₃₇	C₂×#576	1	1	yes	characteristic
224	C₂×C₃₇	C₂×#577	1	1	yes	characteristic
225	C₂×H(5,𝔽₂)	—	2	8	no	—
226	C₂×H(5,𝔽₂)	—	2	4	no	—
227	C₂×H(5,𝔽₂)	C₄×C₃₇	1	16	yes	complemented
228	C₂×H(5,𝔽₂)	C₂²×C₃₇	1	8	yes	—
229	C₂²×#41	—	2	1	no	—
230	C₂²×#41	C₂²×C₃₇	1	3	yes	—
231	C₂²×#41	C₂²×C₃₇	1	1	yes	characteristic
232	C₂³×D₄	—	2	3	no	—
233	C₂³×D₄	C₂²×C₃₇	1	3	yes	—
234	C₂×#131	—	2	8	no	—
235	C₂×#131	C₂²×C₃₇	1	8	yes	complemented
236	C₂²×M₁₆	C₂²×C₃₇	1	3	yes	complemented
237	C₂³×C₈	C₂²×C₃₇	1	3	yes	complemented
238	#520	—	2	4	no	—
239	#520	C₂²×C₃₇	1	8	yes	complemented
240	C₂×C₄×Q₈	—	2	1	no	—
241	C₂×C₄×D₄	—	2	3	no	—
242	C₂×#117	C₂²×C₃₇	1	3	yes	complemented
243	C₂²×C₄⋊C₄	C₂²×C₃₇	1	3	yes	complemented
244	#418	C₂²×C₃₇	1	24	yes	complemented
245	#417	C₂²×C₃₇	1	24	yes	complemented
246	#416	C₂²×C₃₇	1	24	yes	complemented
247	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic, complemented
248	C₂×#103	C₂²×C₃₇	1	3	yes	complemented
249	C₂×#102	C₂²×C₃₇	1	3	yes	complemented
250	C₂×#102	C₂²×C₃₇	1	6	yes	complemented
251	C₂×#102	C₂²×C₃₇	1	3	yes	complemented
252	C₂×#102	C₂²×C₃₇	1	24	yes	complemented
253	C₃₇	C₂×#2897	1	1	yes	characteristic, direct product factor, Sylow
254	C₂⁵	—	2	3	no	—
255	H(5,𝔽₂)	—	2	64	no	—
256	H(5,𝔽₂)	—	2	32	no	—
257	H(5,𝔽₂)	C₂×C₄×C₃₇	1	64	yes	complemented
258	C₂×#41	—	2	16	no	—
259	C₂×#41	—	2	8	no	—
260	C₂×#41	—	2	12	no	—
261	C₂×#41	—	2	6	no	—
262	C₂×#41	C₂×C₄×C₃₇	1	8	yes	—
263	C₂×#41	C₂×C₄×C₃₇	1	24	yes	complemented
264	C₂×#41	D₄×C₃₇	1	8	yes	—
265	C₂×#41	D₄×C₃₇	1	4	yes	—
266	C₂×#41	C₂³×C₃₇	1	12	yes	—
267	C₂×#41	C₂³×C₃₇	1	4	yes	—
268	C₂²×Q₈	D₄×C₃₇	1	1	yes	characteristic
269	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
270	C₂²×D₄	—	2	3	no	—
271	C₂²×D₄	—	2	48	no	—
272	C₂²×D₄	—	2	24	no	—
273	C₂²×D₄	—	2	3	no	—
274	C₂²×D₄	—	2	6	no	—
275	C₂²×D₄	—	2	12	no	—
276	C₂²×D₄	C₂×C₄×C₃₇	1	24	yes	complemented
277	C₂²×D₄	D₄×C₃₇	1	3	yes	—
278	C₂²×D₄	C₂³×C₃₇	1	3	yes	—
279	C₂²×D₄	C₂³×C₃₇	1	12	yes	—
280	C₂³×C₄	—	2	3	no	—
281	C₂³×C₄	—	2	3	no	—
282	C₂³×C₄	C₂³×C₃₇	1	3	yes	—
283	#131	—	2	32	no	—
284	C₂×M₁₆	—	2	12	no	—
285	C₂×M₁₆	C₂³×C₃₇	1	12	yes	complemented
286	C₂²×C₈	—	2	12	no	—
287	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₃₇	1	3	yes	—
289	C₂²×C₈	C₂³×C₃₇	1	12	yes	complemented
290	C₄×Q₈	—	2	8	no	—
291	C₄×D₄	—	2	24	no	—
292	#117	—	2	6	no	—
293	#117	C₂³×C₃₇	1	12	yes	complemented
294	C₂×C₄⋊C₄	—	2	3	no	—
295	C₂×C₄⋊C₄	—	2	6	no	—
296	C₂×C₄⋊C₄	C₂³×C₃₇	1	3	yes	—
297	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₃₇	1	12	yes	complemented
299	C₂×C₂²⋊C₄	—	2	3	no	—
300	C₂×C₄²	—	2	3	no	—
301	#103	C₂³×C₃₇	1	4	yes	complemented
302	#103	C₂³×C₃₇	1	12	yes	complemented
303	#102	C₂³×C₃₇	1	12	yes	complemented
304	#102	C₂³×C₃₇	1	24	yes	complemented
305	#102	C₂³×C₃₇	1	12	yes	complemented
306	C₂⁴	—	2	3	no	—
307	C₂⁴	—	2	24	no	—
308	C₂⁴	—	2	12	no	—
309	C₂⁴	—	8	6	no	—
310	C₂⁴	—	8	6	no	—
311	C₂⁴	C₂×D₄×C₃₇	1	3	yes	—
312	#41	—	2	64	no	—
313	#41	—	2	48	no	—
314	#41	—	2	24	no	—
315	#41	C₂²⋊C₄×C₃₇	1	32	yes	—
316	#41	C₂²×C₄×C₃₇	1	16	yes	—
317	#41	C₂²×C₄×C₃₇	1	48	yes	complemented
318	#41	C₂×D₄×C₃₇	1	16	yes	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	C₂²⋊C₄×C₃₇	1	8	yes	—
322	C₂×Q₈	C₂²×C₄×C₃₇	1	4	yes	—
323	C₂×Q₈	C₂×D₄×C₃₇	1	4	yes	—
324	C₂×Q₈	C₂⁴×C₃₇	1	2	yes	—
325	C₂×D₄	—	2	24	no	—
326	C₂×D₄	—	2	12	no	—
327	C₂×D₄	—	2	192	no	—
328	C₂×D₄	—	2	24	no	—
329	C₂×D₄	—	2	48	no	—
330	C₂×D₄	—	2	6	no	—
331	C₂×D₄	—	2	12	no	—
332	C₂×D₄	—	2	3	no	—
333	C₂×D₄	—	2	24	no	—
334	C₂×D₄	C₂²⋊C₄×C₃₇	1	24	yes	—
335	C₂×D₄	C₂²×C₄×C₃₇	1	12	yes	—
336	C₂×D₄	C₂²×C₄×C₃₇	1	48	yes	complemented
337	C₂×D₄	C₂×D₄×C₃₇	1	12	yes	—
338	C₂×D₄	C₂⁴×C₃₇	1	6	yes	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	24	no	—
341	C₂²×C₄	—	2	12	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	3	no	—
344	C₂²×C₄	—	2	12	no	—
345	C₂²×C₄	—	8	6	no	—
346	C₂²×C₄	C₂²×C₄×C₃₇	1	12	yes	—
347	C₂²×C₄	C₂×D₄×C₃₇	1	3	yes	—
348	C₂²×C₄	C₂×D₄×C₃₇	1	6	yes	—
349	C₂²×C₄	C₂×D₄×C₃₇	1	12	yes	—
350	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
351	C₂²×C₄	C₂⁴×C₃₇	1	6	yes	—
352	M₁₆	—	2	24	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	6	no	—
355	C₂×C₈	—	2	24	no	—
356	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
357	C₂×C₈	C₂⁴×C₃₇	1	6	yes	—
358	C₄⋊C₄	—	2	3	no	—
359	C₄⋊C₄	—	2	12	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	C₂⁴×C₃₇	1	6	yes	—
362	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
363	C₂²⋊C₄	—	2	12	no	—
364	C₄²	—	2	12	no	—
365	C₂³	—	2	6	no	—
366	C₂³	—	2	6	no	—
367	C₂³	—	2	6	no	—
368	C₂³	—	2	12	no	—
369	C₂³	—	2	48	no	—
370	C₂³	—	4	6	no	—
371	C₂³	—	4	6	no	—
372	C₂³	—	8	48	no	—
373	C₂³	—	8	12	no	—
374	C₂³	—	8	12	no	—
375	C₂³	C₂×C₂²⋊C₄×C₃₇	1	12	yes	—
376	C₂³	C₂²×D₄×C₃₇	1	6	yes	—
377	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
378	Q₈	—	2	2	no	—
379	Q₈	—	2	4	no	—
380	Q₈	C₂×C₂²⋊C₄×C₃₇	1	16	yes	—
381	Q₈	C₂³×C₄×C₃₇	1	4	yes	—
382	D₄	—	2	48	no	—
383	D₄	—	2	6	no	—
384	D₄	—	2	12	no	—
385	D₄	—	2	48	no	—
386	D₄	C₂×C₂²⋊C₄×C₃₇	1	48	yes	—
387	D₄	C₂³×C₄×C₃₇	1	12	yes	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	48	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	6	no	—
393	C₂×C₄	—	4	6	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	8	12	no	—
396	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	12	yes	—
397	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	24	yes	—
398	C₂×C₄	C₂³×C₄×C₃₇	1	2	yes	—
399	C₂×C₄	C₂³×C₄×C₃₇	1	12	yes	—
400	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
401	C₂×C₄	C₂²×D₄×C₃₇	1	12	yes	—
402	C₂×C₄	C₂²×D₄×C₃₇	1	6	yes	—
403	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
404	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
405	C₈	—	2	2	no	—
406	C₈	—	2	6	no	—
407	C₂²	—	2	24	no	—
408	C₂²	—	2	6	no	—
409	C₂²	—	2	6	no	—
410	C₂²	—	2	12	no	—
411	C₂²	—	4	24	no	—
412	C₂²	—	4	6	no	—
413	C₂²	—	4	6	no	—
414	C₂²	—	8	48	no	—
415	C₂²	C₂²×C₂²⋊C₄×C₃₇	1	12	yes	—
416	C₂²	C₂²×C₂²⋊C₄×C₃₇	1	2	yes	—
417	C₂²	C₃₇×#576	1	2	yes	—
418	C₂²	C₃₇×#577	1	2	yes	—
419	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
420	C₄	—	2	4	no	—
421	C₄	—	4	6	no	—
422	C₄	—	4	2	no	—
423	C₄	C₂²×C₂²⋊C₄×C₃₇	1	12	yes	—
424	C₄	C₂²×C₂²⋊C₄×C₃₇	1	2	yes	—
425	C₄	C₂⁴×C₄×C₃₇	1	1	yes	characteristic
426	C₄	C₂³×D₄×C₃₇	1	1	yes	characteristic
427	C₂	—	2	12	no	—
428	C₂	—	4	12	no	—
429	C₂	C₃₇×#2897	1	4	yes	direct product factor
430	C₂	C₂³×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
431	C₂	C₂×C₃₇×#576	1	1	yes	characteristic
432	C₂	C₂×C₃₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator	C₄	C₂⁴×C₄×C₃₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
prime radical	C₂²×H(5,𝔽₂)×C₃₇	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂²×#41×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#131×C₃₇	C₂	semidirect
3. C₂×C₃₇×#520	C₂	semidirect
4. C₃₇×#2897	C₂	direct (N × H)
5. C₂×C₃₇×#417	C₂	semidirect
6. C₂×C₃₇×#418	C₂	semidirect
7. C₂×C₃₇×#416	C₂	semidirect
8. C₂²×#102×C₃₇	C₂	semidirect
11. C₂×H(5,𝔽₂)×C₃₇	C₄	semidirect
19. C₂×#131×C₃₇	C₂²	semidirect
20. C₂²×M₁₆×C₃₇	C₂²	semidirect
21. C₂³×C₈×C₃₇	C₂²	semidirect
23. C₃₇×#520	C₂²	semidirect
26. C₂×#117×C₃₇	C₂²	semidirect
27. C₂²×C₄⋊C₄×C₃₇	C₂²	semidirect
28. C₃₇×#418	C₂²	semidirect
29. C₃₇×#417	C₂²	semidirect
30. C₃₇×#416	C₂²	semidirect
31. C₂×#103×C₃₇	C₂²	semidirect
32. C₂×#103×C₃₇	C₂²	semidirect
33. C₂×#102×C₃₇	C₂²	semidirect
34. C₂×#102×C₃₇	C₂²	semidirect
35. C₂×#102×C₃₇	C₂²	semidirect
36. C₂×#102×C₃₇	C₂²	semidirect
40. H(5,𝔽₂)×C₃₇	C₂×C₄	semidirect
46. C₂×#41×C₃₇	C₂×C₄	semidirect
59. C₂²×D₄×C₃₇	C₂×C₄	semidirect
68. C₂×M₁₆×C₃₇	C₂³	semidirect
72. C₂²×C₈×C₃₇	C₂³	semidirect
76. #117×C₃₇	C₂³	semidirect
81. C₂×C₄⋊C₄×C₃₇	C₂³	semidirect
84. #103×C₃₇	C₂³	semidirect
85. #103×C₃₇	C₂³	semidirect
86. #102×C₃₇	C₂³	semidirect
87. #102×C₃₇	C₂³	semidirect
88. #102×C₃₇	C₂³	semidirect
100. #41×C₃₇	C₂²×C₄	semidirect
119. C₂×D₄×C₃₇	C₂²×C₄	semidirect
190. C₂×#2897	C₃₇	direct (N × H)
212. C₂²×#131	C₂×C₃₇	semidirect
213. C₂×#520	C₂×C₃₇	semidirect
214. #2897	C₂×C₃₇	direct (N × H)
215. C₂×#417	C₂×C₃₇	semidirect
216. C₂×#418	C₂×C₃₇	semidirect
217. C₂×#416	C₂×C₃₇	semidirect
218. C₂²×#102	C₂×C₃₇	semidirect
221. C₂×C₃₇	#2897	direct (N × H)
227. C₂×H(5,𝔽₂)	C₄×C₃₇	semidirect
235. C₂×#131	C₂²×C₃₇	semidirect
236. C₂²×M₁₆	C₂²×C₃₇	semidirect
237. C₂³×C₈	C₂²×C₃₇	semidirect
239. #520	C₂²×C₃₇	semidirect
242. C₂×#117	C₂²×C₃₇	semidirect
243. C₂²×C₄⋊C₄	C₂²×C₃₇	semidirect
244. #418	C₂²×C₃₇	semidirect
245. #417	C₂²×C₃₇	semidirect
246. #416	C₂²×C₃₇	semidirect
247. C₂×#103	C₂²×C₃₇	semidirect
248. C₂×#103	C₂²×C₃₇	semidirect
249. C₂×#102	C₂²×C₃₇	semidirect
250. C₂×#102	C₂²×C₃₇	semidirect
251. C₂×#102	C₂²×C₃₇	semidirect
252. C₂×#102	C₂²×C₃₇	semidirect
253. C₃₇	C₂×#2897	direct (N × H)
257. H(5,𝔽₂)	C₂×C₄×C₃₇	semidirect
263. C₂×#41	C₂×C₄×C₃₇	semidirect
276. C₂²×D₄	C₂×C₄×C₃₇	semidirect
285. C₂×M₁₆	C₂³×C₃₇	semidirect
289. C₂²×C₈	C₂³×C₃₇	semidirect
293. #117	C₂³×C₃₇	semidirect
298. C₂×C₄⋊C₄	C₂³×C₃₇	semidirect
301. #103	C₂³×C₃₇	semidirect
302. #103	C₂³×C₃₇	semidirect
303. #102	C₂³×C₃₇	semidirect
304. #102	C₂³×C₃₇	semidirect
305. #102	C₂³×C₃₇	semidirect
317. #41	C₂²×C₄×C₃₇	semidirect
336. C₂×D₄	C₂²×C₄×C₃₇	semidirect
429. C₂	C₃₇×#2897	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×H(5,𝔽₂)×C₃₇	2
C₂²×#131×C₃₇	2
C₂×C₃₇×#520	2
C₃₇×#2897	2
C₂×C₃₇×#417	2
C₂×C₃₇×#418	2
C₂×C₃₇×#416	2
C₂²×#102×C₃₇	2
C₂×#2897	37

Subgroups — C2×C37×#2897 #22681337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₇×#2897 #22681337