Subgroups — C₂×C₃₇×#3076 #22681732

Order 9472.

2162 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₃₇	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#3076	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₇×#479	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₇×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₇×#478	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₇×#427	C₂	1	2	yes	maximal, complemented
11	C₂²×C₄⋊C₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₇×#416	C₂	1	2	yes	maximal
13	C₂²×#41×C₃₇	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₃₇	C₂²	1	2	yes	—
15	C₃₇×#533	—	2	4	no	—
16	C₃₇×#533	C₂²	1	8	yes	complemented
17	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×#125×C₃₇	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₃₇	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₃₇	—	2	1	no	—
22	C₄×#41×C₃₇	—	2	4	no	—
23	C₄×#41×C₃₇	C₂²	1	8	yes	—
24	C₂×C₄×Q₈×C₃₇	—	2	1	no	—
25	C₂×C₄×Q₈×C₃₇	—	2	1	no	—
26	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₃₇	—	2	1	no	—
29	C₂×C₄×D₄×C₃₇	—	2	1	no	—
30	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
32	C₂×#117×C₃₇	—	2	1	no	—
33	C₂×#117×C₃₇	C₂²	1	2	yes	—
34	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₃₇	—	2	1	no	—
36	C₂²×C₄²×C₃₇	C₂²	1	1	yes	characteristic
37	C₃₇×#479	C₂²	1	16	yes	complemented
38	C₃₇×#478	C₂²	1	16	yes	complemented
39	C₃₇×#477	C₂²	1	8	yes	complemented
40	C₃₇×#476	C₂²	1	8	yes	complemented
41	C₃₇×#475	C₂²	1	8	yes	complemented
42	C₃₇×#474	C₂²	1	8	yes	complemented
43	C₃₇×#427	C₂²	1	16	yes	complemented
44	C₂×#107×C₃₇	C₂²	1	2	yes	—
45	C₂×#107×C₃₇	C₂²	1	2	yes	—
46	C₂×#106×C₃₇	C₂²	1	2	yes	—
47	C₂×#106×C₃₇	C₂²	1	2	yes	—
48	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
49	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
51	C₂×C₄⋊C₈×C₃₇	C₂²	1	8	yes	complemented
52	C₃₇×#416	C₂²	1	16	yes	—
53	C₂×#103×C₃₇	C₂²	1	2	yes	—
54	C₂×#103×C₃₇	C₂²	1	2	yes	—
55	C₂×#102×C₃₇	C₂²	1	2	yes	—
56	C₂×#102×C₃₇	C₂²	1	2	yes	—
57	C₂×#41×C₃₇	—	2	2	no	—
58	C₂×#41×C₃₇	—	2	4	no	—
59	C₂×#41×C₃₇	Q₈	1	8	yes	complemented
60	C₂×#41×C₃₇	C₂³	1	4	yes	—
61	C₂²×Q₈×C₃₇	—	2	1	no	—
62	C₂²×Q₈×C₃₇	—	2	1	no	—
63	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₃₇	—	2	1	no	—
65	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₃₇	—	2	1	no	—
67	C₂³×C₄×C₃₇	—	2	1	no	—
68	C₂³×C₄×C₃₇	—	2	1	no	—
69	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
70	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
71	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₃₇	—	2	8	no	—
73	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
74	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
75	C₂²×C₈×C₃₇	C₂³	1	8	yes	—
76	C₄⋊Q₈×C₃₇	—	2	2	no	—
77	C₄⋊Q₈×C₃₇	—	2	2	no	—
78	C₄⋊Q₈×C₃₇	C₂³	1	4	yes	—
79	C₄⋊Q₈×C₃₇	C₂³	1	4	yes	—
80	#125×C₃₇	—	2	4	no	—
81	#125×C₃₇	C₂³	1	8	yes	—
82	C₂²⋊Q₈×C₃₇	—	2	8	no	—
83	C₂²⋊Q₈×C₃₇	—	2	8	no	—
84	C₄×Q₈×C₃₇	—	2	8	no	—
85	C₄×Q₈×C₃₇	—	2	8	no	—
86	C₄×Q₈×C₃₇	—	2	2	no	—
87	C₄×Q₈×C₃₇	—	2	2	no	—
88	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
89	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
90	C₄×D₄×C₃₇	—	2	8	no	—
91	C₄×D₄×C₃₇	—	2	8	no	—
92	C₄×D₄×C₃₇	—	2	2	no	—
93	C₄×D₄×C₃₇	—	2	2	no	—
94	C₄×D₄×C₃₇	C₂³	1	4	yes	—
95	C₄×D₄×C₃₇	C₂³	1	4	yes	—
96	#117×C₃₇	—	2	4	no	—
97	#117×C₃₇	—	2	2	no	—
98	#117×C₃₇	—	2	8	no	—
99	#117×C₃₇	C₂³	1	8	yes	—
100	#117×C₃₇	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
102	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
103	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
104	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
105	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
106	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
107	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
115	C₂×C₄²×C₃₇	—	2	1	no	—
116	C₂×C₄²×C₃₇	—	2	1	no	—
117	C₂×C₄²×C₃₇	—	2	1	no	—
118	C₂×C₄²×C₃₇	—	2	2	no	—
119	C₂×C₄²×C₃₇	—	2	8	no	—
120	C₂×C₄²×C₃₇	D₄	1	4	yes	—
121	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
122	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₃₇	C₂³	1	4	yes	—
126	#107×C₃₇	C₂³	1	8	yes	—
127	#107×C₃₇	C₂³	1	8	yes	—
128	#106×C₃₇	C₂³	1	8	yes	—
129	#106×C₃₇	C₂³	1	8	yes	—
130	C₄⋊C₈×C₃₇	C₂³	1	4	yes	—
131	C₄⋊C₈×C₃₇	C₂³	1	4	yes	—
132	C₄⋊C₈×C₃₇	C₂³	1	8	yes	—
133	#103×C₃₇	C₂³	1	8	yes	—
134	#103×C₃₇	C₂³	1	8	yes	—
135	#102×C₃₇	C₂³	1	8	yes	—
136	#102×C₃₇	C₂³	1	8	yes	—
137	C₂⁴×C₃₇	—	2	1	no	—
138	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
139	#41×C₃₇	—	2	16	no	—
140	#41×C₃₇	—	2	8	no	—
141	#41×C₃₇	C₂×Q₈	1	16	yes	complemented
142	C₂×Q₈×C₃₇	—	2	1	no	—
143	C₂×Q₈×C₃₇	—	2	4	no	—
144	C₂×Q₈×C₃₇	—	2	4	no	—
145	C₂×Q₈×C₃₇	—	2	2	no	—
146	C₂×Q₈×C₃₇	—	4	4	no	—
147	C₂×Q₈×C₃₇	—	4	4	no	—
148	C₂×Q₈×C₃₇	C₂×Q₈	1	4	yes	—
149	C₂×Q₈×C₃₇	C₂⁴	1	2	yes	—
150	C₂×D₄×C₃₇	—	2	8	no	—
151	C₂×D₄×C₃₇	—	2	4	no	—
152	C₂×D₄×C₃₇	—	2	1	no	—
153	C₂×D₄×C₃₇	—	2	2	no	—
154	C₂×D₄×C₃₇	C₂×Q₈	1	4	yes	—
155	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₃₇	—	2	1	no	—
157	C₂²×C₄×C₃₇	—	2	8	no	—
158	C₂²×C₄×C₃₇	—	2	4	no	—
159	C₂²×C₄×C₃₇	—	2	4	no	—
160	C₂²×C₄×C₃₇	—	2	1	no	—
161	C₂²×C₄×C₃₇	—	2	1	no	—
162	C₂²×C₄×C₃₇	—	2	2	no	—
163	C₂²×C₄×C₃₇	—	2	2	no	—
164	C₂²×C₄×C₃₇	—	2	4	no	—
165	C₂²×C₄×C₃₇	—	2	4	no	—
166	C₂²×C₄×C₃₇	—	4	2	no	—
167	C₂²×C₄×C₃₇	—	4	4	no	—
168	C₂²×C₄×C₃₇	—	4	4	no	—
169	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
173	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₃₇	C₂×Q₈	1	4	yes	—
178	C₂²×C₄×C₃₇	#41	1	4	yes	—
179	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
181	C₂×C₈×C₃₇	—	2	4	no	—
182	C₂×C₈×C₃₇	—	2	4	no	—
183	C₂×C₈×C₃₇	—	2	16	no	—
184	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
185	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
186	C₄⋊C₄×C₃₇	—	2	4	no	—
187	C₄⋊C₄×C₃₇	—	2	4	no	—
188	C₄⋊C₄×C₃₇	—	2	8	no	—
189	C₄⋊C₄×C₃₇	—	2	8	no	—
190	C₄⋊C₄×C₃₇	—	2	4	no	—
191	C₄⋊C₄×C₃₇	—	2	4	no	—
192	C₄⋊C₄×C₃₇	—	2	1	no	—
193	C₄⋊C₄×C₃₇	—	2	1	no	—
194	C₄⋊C₄×C₃₇	—	2	2	no	—
195	C₄⋊C₄×C₃₇	—	2	2	no	—
196	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
197	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
198	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
199	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
200	C₂²⋊C₄×C₃₇	—	2	4	no	—
201	C₂²⋊C₄×C₃₇	—	2	8	no	—
202	C₂²⋊C₄×C₃₇	—	2	4	no	—
203	C₂²⋊C₄×C₃₇	—	2	4	no	—
204	C₄²×C₃₇	—	2	4	no	—
205	C₄²×C₃₇	—	2	4	no	—
206	C₄²×C₃₇	—	2	4	no	—
207	C₄²×C₃₇	—	2	8	no	—
208	C₄²×C₃₇	C₂×D₄	1	4	yes	—
209	C₄²×C₃₇	C₂×D₄	1	4	yes	—
210	C₄²×C₃₇	C₂×D₄	1	2	yes	—
211	C₄²×C₃₇	C₂×D₄	1	2	yes	—
212	C₄²×C₃₇	C₂⁴	1	2	yes	—
213	C₄²×C₃₇	C₂⁴	1	2	yes	—
214	C₂³×C₃₇	—	2	2	no	—
215	C₂³×C₃₇	—	2	2	no	—
216	C₂³×C₃₇	—	2	4	no	—
217	C₂³×C₃₇	—	2	2	no	—
218	C₂³×C₃₇	—	4	2	no	—
219	C₂³×C₃₇	—	4	2	no	—
220	C₂³×C₃₇	C₂²⋊Q₈	1	4	yes	—
221	C₂³×C₃₇	C₂²×D₄	1	2	yes	—
222	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
223	Q₈×C₃₇	—	2	4	no	—
224	Q₈×C₃₇	—	2	2	no	—
225	Q₈×C₃₇	—	4	8	no	—
226	Q₈×C₃₇	—	4	8	no	—
227	Q₈×C₃₇	C₂²×Q₈	1	4	yes	—
228	D₄×C₃₇	—	2	16	no	—
229	D₄×C₃₇	—	2	4	no	—
230	D₄×C₃₇	—	2	2	no	—
231	D₄×C₃₇	C₂²×Q₈	1	4	yes	—
232	C₂×C₄×C₃₇	—	2	4	no	—
233	C₂×C₄×C₃₇	—	2	2	no	—
234	C₂×C₄×C₃₇	—	2	2	no	—
235	C₂×C₄×C₃₇	—	2	2	no	—
236	C₂×C₄×C₃₇	—	2	2	no	—
237	C₂×C₄×C₃₇	—	2	16	no	—
238	C₂×C₄×C₃₇	—	2	8	no	—
239	C₂×C₄×C₃₇	—	2	2	no	—
240	C₂×C₄×C₃₇	—	2	2	no	—
241	C₂×C₄×C₃₇	—	2	4	no	—
242	C₂×C₄×C₃₇	—	2	4	no	—
243	C₂×C₄×C₃₇	—	4	4	no	—
244	C₂×C₄×C₃₇	—	4	8	no	—
245	C₂×C₄×C₃₇	—	4	2	no	—
246	C₂×C₄×C₃₇	—	4	4	no	—
247	C₂×C₄×C₃₇	—	4	2	no	—
248	C₂×C₄×C₃₇	—	4	4	no	—
249	C₂×C₄×C₃₇	—	4	8	no	—
250	C₂×C₄×C₃₇	C₂²⋊Q₈	1	4	yes	—
251	C₂×C₄×C₃₇	C₂²⋊Q₈	1	8	yes	—
252	C₂×C₄×C₃₇	#135	1	4	yes	—
253	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₃₇	C₂²×Q₈	1	2	yes	—
260	C₂×C₄×C₃₇	C₂²×Q₈	1	4	yes	—
261	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
262	C₂×C₄×C₃₇	C₂×#41	1	4	yes	—
263	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
264	C₈×C₃₇	—	2	4	no	—
265	C₈×C₃₇	—	2	4	no	—
266	C₂×#3076	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂²×C₃₇	—	2	8	no	—
268	C₂²×C₃₇	—	2	2	no	—
269	C₂²×C₃₇	—	2	2	no	—
270	C₂²×C₃₇	—	2	4	no	—
271	C₂²×C₃₇	—	4	8	no	—
272	C₂²×C₃₇	—	4	2	no	—
273	C₂²×C₃₇	—	4	2	no	—
274	C₂²×C₃₇	C₂×C₂²⋊Q₈	1	4	yes	—
275	C₂²×C₃₇	C₂×C₂²⋊Q₈	1	2	yes	—
276	C₂²×C₃₇	C₂×#135	1	2	yes	—
277	C₂²×C₃₇	#575	1	2	yes	—
278	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
279	C₄×C₃₇	—	2	4	no	—
280	C₄×C₃₇	—	2	2	no	—
281	C₄×C₃₇	—	2	2	no	—
282	C₄×C₃₇	—	2	2	no	—
283	C₄×C₃₇	—	4	2	no	—
284	C₄×C₃₇	—	4	4	no	—
285	C₄×C₃₇	—	4	2	no	—
286	C₄×C₃₇	—	4	4	no	—
287	C₄×C₃₇	C₂×C₂²⋊Q₈	1	4	yes	—
288	C₄×C₃₇	C₂×C₂²⋊Q₈	1	2	yes	—
289	C₄×C₃₇	C₂×#135	1	4	yes	—
290	C₄×C₃₇	C₂³×Q₈	1	1	yes	characteristic
291	C₄×C₃₇	C₂²×#41	1	1	yes	characteristic
292	C₂×#533	C₂×C₃₇	1	1	yes	characteristic, complemented
293	C₂×C₄×#41	C₂×C₃₇	1	1	yes	characteristic
294	#3076	C₂×C₃₇	1	16	yes	direct product factor
295	C₂×#479	C₂×C₃₇	1	2	yes	complemented
296	C₂×#477	C₂×C₃₇	1	1	yes	characteristic, complemented
297	C₂×#475	C₂×C₃₇	1	1	yes	characteristic, complemented
298	C₂×#478	C₂×C₃₇	1	2	yes	complemented
299	C₂×#476	C₂×C₃₇	1	1	yes	characteristic, complemented
300	C₂×#474	C₂×C₃₇	1	1	yes	characteristic, complemented
301	C₂×#427	C₂×C₃₇	1	2	yes	complemented
302	C₂²×C₄⋊C₈	C₂×C₃₇	1	1	yes	characteristic, complemented
303	C₂×#416	C₂×C₃₇	1	2	yes	—
304	C₂×C₃₇	—	2	4	no	—
305	C₂×C₃₇	—	4	4	no	—
306	C₂×C₃₇	#3076	1	4	yes	direct product factor
307	C₂×C₃₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
308	C₂×C₃₇	C₂²×#135	1	1	yes	characteristic
309	C₂×C₃₇	C₂×#575	1	1	yes	characteristic
310	C₂²×#41	C₂²×C₃₇	1	1	yes	characteristic
311	C₂³×C₈	C₂²×C₃₇	1	2	yes	—
312	#533	—	2	4	no	—
313	#533	C₂²×C₃₇	1	8	yes	complemented
314	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
315	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
316	C₂×#125	C₂²×C₃₇	1	2	yes	—
317	C₂×C₂²⋊Q₈	—	2	1	no	—
318	C₂×C₂²⋊Q₈	—	2	1	no	—
319	C₄×#41	—	2	4	no	—
320	C₄×#41	C₂²×C₃₇	1	8	yes	—
321	C₂×C₄×Q₈	—	2	1	no	—
322	C₂×C₄×Q₈	—	2	1	no	—
323	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
324	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
325	C₂×C₄×D₄	—	2	1	no	—
326	C₂×C₄×D₄	—	2	1	no	—
327	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
328	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
329	C₂×#117	—	2	1	no	—
330	C₂×#117	C₂²×C₃₇	1	2	yes	—
331	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic
332	C₂²×C₄²	—	2	1	no	—
333	C₂²×C₄²	C₂²×C₃₇	1	1	yes	characteristic
334	#479	C₂²×C₃₇	1	16	yes	complemented
335	#478	C₂²×C₃₇	1	16	yes	complemented
336	#477	C₂²×C₃₇	1	8	yes	complemented
337	#476	C₂²×C₃₇	1	8	yes	complemented
338	#475	C₂²×C₃₇	1	8	yes	complemented
339	#474	C₂²×C₃₇	1	8	yes	complemented
340	#427	C₂²×C₃₇	1	16	yes	complemented
341	C₂×#107	C₂²×C₃₇	1	2	yes	—
342	C₂×#107	C₂²×C₃₇	1	2	yes	—
343	C₂×#106	C₂²×C₃₇	1	2	yes	—
344	C₂×#106	C₂²×C₃₇	1	2	yes	—
345	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
346	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
347	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
348	C₂×C₄⋊C₈	C₂²×C₃₇	1	8	yes	complemented
349	#416	C₂²×C₃₇	1	16	yes	—
350	C₂×#103	C₂²×C₃₇	1	2	yes	—
351	C₂×#103	C₂²×C₃₇	1	2	yes	—
352	C₂×#102	C₂²×C₃₇	1	2	yes	—
353	C₂×#102	C₂²×C₃₇	1	2	yes	—
354	C₃₇	C₂×#3076	1	1	yes	characteristic, direct product factor, Sylow
355	C₂×#41	—	2	2	no	—
356	C₂×#41	—	2	4	no	—
357	C₂×#41	Q₈×C₃₇	1	8	yes	complemented
358	C₂×#41	C₂³×C₃₇	1	4	yes	—
359	C₂²×Q₈	—	2	1	no	—
360	C₂²×Q₈	—	2	1	no	—
361	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
362	C₂²×D₄	—	2	1	no	—
363	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
364	C₂³×C₄	—	2	1	no	—
365	C₂³×C₄	—	2	1	no	—
366	C₂³×C₄	—	2	1	no	—
367	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
368	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
370	C₂²×C₈	—	2	8	no	—
371	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
372	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
373	C₂²×C₈	C₂³×C₃₇	1	8	yes	—
374	C₄⋊Q₈	—	2	2	no	—
375	C₄⋊Q₈	—	2	2	no	—
376	C₄⋊Q₈	C₂³×C₃₇	1	4	yes	—
377	C₄⋊Q₈	C₂³×C₃₇	1	4	yes	—
378	#125	—	2	4	no	—
379	#125	C₂³×C₃₇	1	8	yes	—
380	C₂²⋊Q₈	—	2	8	no	—
381	C₂²⋊Q₈	—	2	8	no	—
382	C₄×Q₈	—	2	8	no	—
383	C₄×Q₈	—	2	8	no	—
384	C₄×Q₈	—	2	2	no	—
385	C₄×Q₈	—	2	2	no	—
386	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
387	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
388	C₄×D₄	—	2	8	no	—
389	C₄×D₄	—	2	8	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	C₂³×C₃₇	1	4	yes	—
393	C₄×D₄	C₂³×C₃₇	1	4	yes	—
394	#117	—	2	2	no	—
395	#117	—	2	4	no	—
396	#117	—	2	8	no	—
397	#117	C₂³×C₃₇	1	4	yes	—
398	#117	C₂³×C₃₇	1	8	yes	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	2	no	—
402	C₂×C₄⋊C₄	—	2	2	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	2	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	—	2	2	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	—	2	1	no	—
417	C₂×C₄²	—	2	8	no	—
418	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
419	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
420	C₂×C₄²	D₄×C₃₇	1	4	yes	—
421	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₃₇	1	4	yes	—
424	#107	C₂³×C₃₇	1	8	yes	—
425	#107	C₂³×C₃₇	1	8	yes	—
426	#106	C₂³×C₃₇	1	8	yes	—
427	#106	C₂³×C₃₇	1	8	yes	—
428	C₄⋊C₈	C₂³×C₃₇	1	4	yes	—
429	C₄⋊C₈	C₂³×C₃₇	1	4	yes	—
430	C₄⋊C₈	C₂³×C₃₇	1	8	yes	—
431	#103	C₂³×C₃₇	1	8	yes	—
432	#103	C₂³×C₃₇	1	8	yes	—
433	#102	C₂³×C₃₇	1	8	yes	—
434	#102	C₂³×C₃₇	1	8	yes	—
435	C₂⁴	—	2	1	no	—
436	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
437	#41	—	2	16	no	—
438	#41	—	2	8	no	—
439	#41	C₂×Q₈×C₃₇	1	16	yes	complemented
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	4	no	—
442	C₂×Q₈	—	2	4	no	—
443	C₂×Q₈	—	2	2	no	—
444	C₂×Q₈	—	4	4	no	—
445	C₂×Q₈	—	4	4	no	—
446	C₂×Q₈	C₂×Q₈×C₃₇	1	4	yes	—
447	C₂×Q₈	C₂⁴×C₃₇	1	2	yes	—
448	C₂×D₄	—	2	8	no	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	C₂×Q₈×C₃₇	1	4	yes	—
453	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	8	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	—	4	4	no	—
466	C₂²×C₄	—	4	4	no	—
467	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
471	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
472	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
473	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
475	C₂²×C₄	C₂×Q₈×C₃₇	1	4	yes	—
476	C₂²×C₄	#41×C₃₇	1	4	yes	—
477	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
478	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
479	C₂×C₈	—	2	4	no	—
480	C₂×C₈	—	2	4	no	—
481	C₂×C₈	—	2	16	no	—
482	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
483	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	2	8	no	—
487	C₄⋊C₄	—	2	8	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
495	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
496	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
497	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	2	8	no	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₄²	—	2	4	no	—
503	C₄²	—	2	4	no	—
504	C₄²	—	2	4	no	—
505	C₄²	—	2	8	no	—
506	C₄²	C₂×D₄×C₃₇	1	4	yes	—
507	C₄²	C₂×D₄×C₃₇	1	4	yes	—
508	C₄²	C₂×D₄×C₃₇	1	2	yes	—
509	C₄²	C₂×D₄×C₃₇	1	2	yes	—
510	C₄²	C₂⁴×C₃₇	1	2	yes	—
511	C₄²	C₂⁴×C₃₇	1	2	yes	—
512	C₂³	—	2	2	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	C₂²⋊Q₈×C₃₇	1	4	yes	—
519	C₂³	C₂²×D₄×C₃₇	1	2	yes	—
520	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
521	Q₈	—	2	4	no	—
522	Q₈	—	2	2	no	—
523	Q₈	—	4	8	no	—
524	Q₈	—	4	8	no	—
525	Q₈	C₂²×Q₈×C₃₇	1	4	yes	—
526	D₄	—	2	16	no	—
527	D₄	—	2	4	no	—
528	D₄	—	2	2	no	—
529	D₄	C₂²×Q₈×C₃₇	1	4	yes	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	16	no	—
536	C₂×C₄	—	2	8	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	4	4	no	—
542	C₂×C₄	—	4	8	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	4	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	4	no	—
547	C₂×C₄	—	4	8	no	—
548	C₂×C₄	C₂²⋊Q₈×C₃₇	1	4	yes	—
549	C₂×C₄	C₂²⋊Q₈×C₃₇	1	8	yes	—
550	C₂×C₄	#135×C₃₇	1	4	yes	—
551	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
552	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
553	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
555	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
556	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
557	C₂×C₄	C₂²×Q₈×C₃₇	1	2	yes	—
558	C₂×C₄	C₂²×Q₈×C₃₇	1	4	yes	—
559	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
560	C₂×C₄	C₂×#41×C₃₇	1	4	yes	—
561	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
562	C₈	—	2	4	no	—
563	C₈	—	2	4	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	8	no	—
567	C₂²	—	2	4	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	8	no	—
571	C₂²	C₂×C₂²⋊Q₈×C₃₇	1	4	yes	—
572	C₂²	C₂×C₂²⋊Q₈×C₃₇	1	2	yes	—
573	C₂²	C₂×#135×C₃₇	1	2	yes	—
574	C₂²	C₃₇×#575	1	2	yes	—
575	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
576	C₄	—	2	4	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	4	2	no	—
581	C₄	—	4	4	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	4	no	—
584	C₄	C₂×C₂²⋊Q₈×C₃₇	1	4	yes	—
585	C₄	C₂×C₂²⋊Q₈×C₃₇	1	2	yes	—
586	C₄	C₂×#135×C₃₇	1	4	yes	—
587	C₄	C₂³×Q₈×C₃₇	1	1	yes	characteristic
588	C₄	C₂²×#41×C₃₇	1	1	yes	characteristic
589	C₂	—	2	4	no	—
590	C₂	—	4	4	no	—
591	C₂	C₃₇×#3076	1	4	yes	direct product factor
592	C₂	C₂²×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
593	C₂	C₂²×#135×C₃₇	1	1	yes	characteristic
594	C₂	C₂×C₃₇×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
socle	C₂³×C₃₇	C₂²×D₄
prime radical	C₂²×#41×C₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₇ ◁ C₂²×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#533	C₂	semidirect
3. C₃₇×#3076	C₂	direct (N × H)
4. C₂×C₃₇×#479	C₂	semidirect
5. C₂×C₃₇×#477	C₂	semidirect
6. C₂×C₃₇×#475	C₂	semidirect
7. C₂×C₃₇×#478	C₂	semidirect
8. C₂×C₃₇×#476	C₂	semidirect
9. C₂×C₃₇×#474	C₂	semidirect
10. C₂×C₃₇×#427	C₂	semidirect
11. C₂²×C₄⋊C₈×C₃₇	C₂	semidirect
16. C₃₇×#533	C₂²	semidirect
37. C₃₇×#479	C₂²	semidirect
38. C₃₇×#478	C₂²	semidirect
39. C₃₇×#477	C₂²	semidirect
40. C₃₇×#476	C₂²	semidirect
41. C₃₇×#475	C₂²	semidirect
42. C₃₇×#474	C₂²	semidirect
43. C₃₇×#427	C₂²	semidirect
51. C₂×C₄⋊C₈×C₃₇	C₂²	semidirect
59. C₂×#41×C₃₇	Q₈	semidirect
141. #41×C₃₇	C₂×Q₈	semidirect
266. C₂×#3076	C₃₇	direct (N × H)
292. C₂×#533	C₂×C₃₇	semidirect
294. #3076	C₂×C₃₇	direct (N × H)
295. C₂×#479	C₂×C₃₇	semidirect
296. C₂×#477	C₂×C₃₇	semidirect
297. C₂×#475	C₂×C₃₇	semidirect
298. C₂×#478	C₂×C₃₇	semidirect
299. C₂×#476	C₂×C₃₇	semidirect
300. C₂×#474	C₂×C₃₇	semidirect
301. C₂×#427	C₂×C₃₇	semidirect
302. C₂²×C₄⋊C₈	C₂×C₃₇	semidirect
306. C₂×C₃₇	#3076	direct (N × H)
313. #533	C₂²×C₃₇	semidirect
334. #479	C₂²×C₃₇	semidirect
335. #478	C₂²×C₃₇	semidirect
336. #477	C₂²×C₃₇	semidirect
337. #476	C₂²×C₃₇	semidirect
338. #475	C₂²×C₃₇	semidirect
339. #474	C₂²×C₃₇	semidirect
340. #427	C₂²×C₃₇	semidirect
348. C₂×C₄⋊C₈	C₂²×C₃₇	semidirect
354. C₃₇	C₂×#3076	direct (N × H)
357. C₂×#41	Q₈×C₃₇	semidirect
439. #41	C₂×Q₈×C₃₇	semidirect
591. C₂	C₃₇×#3076	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×#533	2
C₂×C₄×#41×C₃₇	2
C₃₇×#3076	2
C₂×C₃₇×#479	2
C₂×C₃₇×#477	2
C₂×C₃₇×#475	2
C₂×C₃₇×#478	2
C₂×C₃₇×#476	2
C₂×C₃₇×#474	2
C₂×C₃₇×#427	2
C₂²×C₄⋊C₈×C₃₇	2
C₂×C₃₇×#416	2
C₂×#3076	37

Subgroups — C2×C37×#3076 #22681732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₇×#3076 #22681732