Subgroups — C₂×C₃₇×#3094 #22681762

Order 9472.

2670 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3094	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₇×#481	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₇×#482	C₂	1	4	yes	maximal, complemented
6	C₂×C₃₇×#480	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₇×#428	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₇×#418	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₇×#407	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₃₇	—	2	1	no	—
11	C₂³×D₄×C₃₇	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂×#121×C₃₇	—	2	1	no	—
15	C₂×#121×C₃₇	—	2	4	no	—
16	C₂×#121×C₃₇	—	2	1	no	—
17	C₂×#121×C₃₇	C₂²	1	2	yes	—
18	C₂×#121×C₃₇	C₂²	1	2	yes	—
19	C₂×#121×C₃₇	C₂²	1	8	yes	—
20	C₂×#117×C₃₇	—	2	1	no	—
21	C₂×#117×C₃₇	—	2	1	no	—
22	C₂×#117×C₃₇	—	2	4	no	—
23	C₂×#117×C₃₇	C₂²	1	2	yes	—
24	C₂×#117×C₃₇	C₂²	1	2	yes	complemented
25	C₂×#117×C₃₇	C₂²	1	8	yes	complemented
26	C₂²×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₂²⋊C₄×C₃₇	—	2	1	no	—
30	C₂²×C₂²⋊C₄×C₃₇	—	2	1	no	—
31	C₂²×C₄²×C₃₇	—	2	1	no	—
32	C₃₇×#482	C₂²	1	32	yes	complemented
33	C₃₇×#481	C₂²	1	16	yes	complemented
34	C₃₇×#480	C₂²	1	16	yes	complemented
35	C₃₇×#428	C₂²	1	16	yes	complemented
36	C₂×#107×C₃₇	C₂²	1	4	yes	complemented
37	C₂×#106×C₃₇	C₂²	1	4	yes	complemented
38	C₃₇×#418	C₂²	1	16	yes	complemented
39	C₂×#102×C₃₇	C₂²	1	4	yes	complemented
40	C₂×#102×C₃₇	C₂²	1	4	yes	complemented
41	C₃₇×#407	C₂²	1	8	yes	complemented
42	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	complemented
43	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	complemented
44	C₂⁵×C₃₇	—	2	1	no	—
45	C₂⁵×C₃₇	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₃₇	—	2	8	no	—
47	C₂²×D₄×C₃₇	—	2	2	no	—
48	C₂²×D₄×C₃₇	—	2	2	no	—
49	C₂²×D₄×C₃₇	—	2	2	no	—
50	C₂²×D₄×C₃₇	—	2	1	no	—
51	C₂²×D₄×C₃₇	—	2	8	no	—
52	C₂²×D₄×C₃₇	—	4	8	no	—
53	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
54	C₂²×D₄×C₃₇	C₂³	1	4	yes	—
55	C₂³×C₄×C₃₇	—	2	8	no	—
56	C₂³×C₄×C₃₇	—	2	1	no	—
57	C₂³×C₄×C₃₇	—	2	1	no	—
58	C₂³×C₄×C₃₇	—	2	1	no	—
59	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₃₇	D₄	1	4	yes	—
61	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₃₇	C₂³	1	4	yes	—
66	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₃₇	—	2	8	no	—
68	C₂×M₁₆×C₃₇	C₂³	1	8	yes	—
69	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
70	#121×C₃₇	—	2	8	no	—
71	#121×C₃₇	—	2	4	no	—
72	#121×C₃₇	—	2	4	no	—
73	#121×C₃₇	—	2	8	no	—
74	#121×C₃₇	C₂³	1	8	yes	—
75	#121×C₃₇	C₂³	1	8	yes	—
76	#117×C₃₇	—	2	4	no	—
77	#117×C₃₇	—	2	8	no	—
78	#117×C₃₇	—	2	8	no	—
79	#117×C₃₇	—	2	4	no	—
80	#117×C₃₇	C₂³	1	8	yes	—
81	#117×C₃₇	C₂³	1	8	yes	complemented
82	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
83	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
85	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
86	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
88	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	complemented
93	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	complemented
94	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₃₇	—	2	8	no	—
96	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₃₇	—	2	8	no	—
98	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
100	C₂×C₄²×C₃₇	—	2	2	no	—
101	C₂×C₄²×C₃₇	—	2	8	no	—
102	C₂×C₄²×C₃₇	—	2	2	no	—
103	#107×C₃₇	C₂³	1	16	yes	complemented
104	#106×C₃₇	C₂³	1	16	yes	complemented
105	#102×C₃₇	C₂³	1	16	yes	complemented
106	#102×C₃₇	C₂³	1	16	yes	complemented
107	C₂²⋊C₈×C₃₇	C₂³	1	8	yes	complemented
108	C₂²⋊C₈×C₃₇	C₂³	1	8	yes	complemented
109	C₂⁴×C₃₇	—	2	4	no	—
110	C₂⁴×C₃₇	—	2	4	no	—
111	C₂⁴×C₃₇	—	2	4	no	—
112	C₂⁴×C₃₇	—	2	2	no	—
113	C₂⁴×C₃₇	—	4	2	no	—
114	C₂⁴×C₃₇	—	4	4	no	—
115	C₂⁴×C₃₇	—	4	4	no	—
116	C₂⁴×C₃₇	—	4	4	no	—
117	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
118	C₂⁴×C₃₇	C₂×D₄	1	4	yes	—
119	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
120	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
121	C₂×D₄×C₃₇	—	2	8	no	—
122	C₂×D₄×C₃₇	—	2	8	no	—
123	C₂×D₄×C₃₇	—	2	4	no	—
124	C₂×D₄×C₃₇	—	2	2	no	—
125	C₂×D₄×C₃₇	—	2	8	no	—
126	C₂×D₄×C₃₇	—	2	16	no	—
127	C₂×D₄×C₃₇	—	4	32	no	—
128	C₂×D₄×C₃₇	—	4	8	no	—
129	C₂×D₄×C₃₇	—	4	8	no	—
130	C₂×D₄×C₃₇	—	4	8	no	—
131	C₂×D₄×C₃₇	—	4	4	no	—
132	C₂×D₄×C₃₇	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₃₇	—	2	4	no	—
134	C₂²×C₄×C₃₇	—	2	4	no	—
135	C₂²×C₄×C₃₇	—	2	16	no	—
136	C₂²×C₄×C₃₇	—	2	4	no	—
137	C₂²×C₄×C₃₇	—	2	4	no	—
138	C₂²×C₄×C₃₇	—	2	4	no	—
139	C₂²×C₄×C₃₇	—	2	16	no	—
140	C₂²×C₄×C₃₇	—	2	4	no	—
141	C₂²×C₄×C₃₇	—	2	4	no	—
142	C₂²×C₄×C₃₇	—	2	4	no	—
143	C₂²×C₄×C₃₇	—	2	2	no	—
144	C₂²×C₄×C₃₇	—	2	2	no	—
145	C₂²×C₄×C₃₇	—	2	2	no	—
146	C₂²×C₄×C₃₇	—	4	4	no	—
147	C₂²×C₄×C₃₇	—	4	4	no	—
148	C₂²×C₄×C₃₇	—	4	4	no	—
149	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₃₇	#41	1	8	yes	—
159	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
163	M₁₆×C₃₇	—	2	16	no	—
164	C₂×C₈×C₃₇	—	2	8	no	—
165	C₂×C₈×C₃₇	C₂⁴	1	8	yes	—
166	C₄⋊C₄×C₃₇	—	2	2	no	—
167	C₄⋊C₄×C₃₇	—	2	2	no	—
168	C₄⋊C₄×C₃₇	—	2	4	no	—
169	C₄⋊C₄×C₃₇	—	2	2	no	—
170	C₄⋊C₄×C₃₇	—	2	4	no	—
171	C₄⋊C₄×C₃₇	—	2	4	no	—
172	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
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	C₄²×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	2	no	—
184	C₂³×C₃₇	—	2	2	no	—
185	C₂³×C₃₇	—	2	8	no	—
186	C₂³×C₃₇	—	2	2	no	—
187	C₂³×C₃₇	—	2	8	no	—
188	C₂³×C₃₇	—	2	2	no	—
189	C₂³×C₃₇	—	2	2	no	—
190	C₂³×C₃₇	—	2	4	no	—
191	C₂³×C₃₇	—	4	4	no	—
192	C₂³×C₃₇	—	4	16	no	—
193	C₂³×C₃₇	—	4	8	no	—
194	C₂³×C₃₇	—	4	8	no	—
195	C₂³×C₃₇	—	4	8	no	—
196	C₂³×C₃₇	—	4	4	no	—
197	C₂³×C₃₇	—	4	4	no	—
198	C₂³×C₃₇	—	4	4	no	—
199	C₂³×C₃₇	—	8	16	no	—
200	C₂³×C₃₇	#123	1	4	yes	—
201	C₂³×C₃₇	AGL(1,ℤ/8)	1	4	yes	—
202	C₂³×C₃₇	C₂²×D₄	1	2	yes	—
203	C₂³×C₃₇	C₂²×D₄	1	2	yes	—
204	C₂³×C₃₇	C₂²×D₄	1	2	yes	—
205	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
206	D₄×C₃₇	—	2	8	no	—
207	D₄×C₃₇	—	4	16	no	—
208	D₄×C₃₇	—	4	16	no	—
209	D₄×C₃₇	—	4	8	no	—
210	D₄×C₃₇	—	4	4	no	—
211	C₂×C₄×C₃₇	—	2	8	no	—
212	C₂×C₄×C₃₇	—	2	2	no	—
213	C₂×C₄×C₃₇	—	2	2	no	—
214	C₂×C₄×C₃₇	—	2	8	no	—
215	C₂×C₄×C₃₇	—	2	4	no	—
216	C₂×C₄×C₃₇	—	2	4	no	—
217	C₂×C₄×C₃₇	—	2	8	no	—
218	C₂×C₄×C₃₇	—	2	4	no	—
219	C₂×C₄×C₃₇	—	2	4	no	—
220	C₂×C₄×C₃₇	—	2	4	no	—
221	C₂×C₄×C₃₇	—	2	4	no	—
222	C₂×C₄×C₃₇	—	2	4	no	—
223	C₂×C₄×C₃₇	—	4	8	no	—
224	C₂×C₄×C₃₇	—	4	8	no	—
225	C₂×C₄×C₃₇	—	4	8	no	—
226	C₂×C₄×C₃₇	—	4	4	no	—
227	C₂×C₄×C₃₇	—	4	4	no	—
228	C₂×C₄×C₃₇	—	4	4	no	—
229	C₂×C₄×C₃₇	#123	1	8	yes	—
230	C₂×C₄×C₃₇	#123	1	4	yes	—
231	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₃₇	C₂×#41	1	4	yes	—
236	C₂×C₄×C₃₇	C₂×#41	1	8	yes	—
237	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
238	C₈×C₃₇	—	2	8	no	—
239	C₂×#3094	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂²×C₃₇	—	2	8	no	—
241	C₂²×C₃₇	—	2	8	no	—
242	C₂²×C₃₇	—	2	2	no	—
243	C₂²×C₃₇	—	2	2	no	—
244	C₂²×C₃₇	—	2	2	no	—
245	C₂²×C₃₇	—	2	2	no	—
246	C₂²×C₃₇	—	2	2	no	—
247	C₂²×C₃₇	—	2	2	no	—
248	C₂²×C₃₇	—	2	2	no	—
249	C₂²×C₃₇	—	4	16	no	—
250	C₂²×C₃₇	—	4	4	no	—
251	C₂²×C₃₇	—	4	4	no	—
252	C₂²×C₃₇	—	4	4	no	—
253	C₂²×C₃₇	—	4	4	no	—
254	C₂²×C₃₇	—	8	16	no	—
255	C₂²×C₃₇	—	8	8	no	—
256	C₂²×C₃₇	C₂×#123	1	4	yes	—
257	C₂²×C₃₇	C₂×#123	1	2	yes	—
258	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
259	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
260	C₂²×C₃₇	#575	1	2	yes	—
261	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
262	C₄×C₃₇	—	2	2	no	—
263	C₄×C₃₇	—	2	2	no	—
264	C₄×C₃₇	—	4	4	no	—
265	C₄×C₃₇	—	4	4	no	—
266	C₄×C₃₇	—	4	4	no	—
267	C₄×C₃₇	C₂×#123	1	4	yes	—
268	C₄×C₃₇	C₂×#123	1	2	yes	—
269	C₄×C₃₇	C₂²×#41	1	2	yes	—
270	C₂²×#121	C₂×C₃₇	1	1	yes	characteristic
271	C₂²×#117	C₂×C₃₇	1	1	yes	characteristic, complemented
272	#3094	C₂×C₃₇	1	16	yes	direct product factor
273	C₂×#481	C₂×C₃₇	1	2	yes	complemented
274	C₂×#482	C₂×C₃₇	1	4	yes	complemented
275	C₂×#480	C₂×C₃₇	1	2	yes	complemented
276	C₂×#428	C₂×C₃₇	1	2	yes	complemented
277	C₂×#418	C₂×C₃₇	1	2	yes	complemented
278	C₂×#407	C₂×C₃₇	1	1	yes	characteristic, complemented
279	C₂×C₃₇	—	2	4	no	—
280	C₂×C₃₇	—	2	4	no	—
281	C₂×C₃₇	—	4	2	no	—
282	C₂×C₃₇	—	8	4	no	—
283	C₂×C₃₇	#3094	1	4	yes	direct product factor
284	C₂×C₃₇	C₂²×#123	1	1	yes	characteristic
285	C₂×C₃₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
286	C₂×C₃₇	C₂×#575	1	1	yes	characteristic
287	C₂³×D₄	—	2	1	no	—
288	C₂³×D₄	C₂²×C₃₇	1	1	yes	characteristic
289	C₂⁴×C₄	C₂²×C₃₇	1	1	yes	characteristic
290	C₂²×M₁₆	C₂²×C₃₇	1	2	yes	—
291	C₂×#121	—	2	1	no	—
292	C₂×#121	—	2	4	no	—
293	C₂×#121	—	2	1	no	—
294	C₂×#121	C₂²×C₃₇	1	2	yes	—
295	C₂×#121	C₂²×C₃₇	1	2	yes	—
296	C₂×#121	C₂²×C₃₇	1	8	yes	—
297	C₂×#117	—	2	1	no	—
298	C₂×#117	—	2	1	no	—
299	C₂×#117	—	2	4	no	—
300	C₂×#117	C₂²×C₃₇	1	2	yes	—
301	C₂×#117	C₂²×C₃₇	1	2	yes	complemented
302	C₂×#117	C₂²×C₃₇	1	8	yes	complemented
303	C₂²×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
304	C₂²×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic, complemented
305	C₂²×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic, complemented
306	C₂²×C₂²⋊C₄	—	2	1	no	—
307	C₂²×C₂²⋊C₄	—	2	1	no	—
308	C₂²×C₄²	—	2	1	no	—
309	#482	C₂²×C₃₇	1	32	yes	complemented
310	#481	C₂²×C₃₇	1	16	yes	complemented
311	#480	C₂²×C₃₇	1	16	yes	complemented
312	#428	C₂²×C₃₇	1	16	yes	complemented
313	C₂×#107	C₂²×C₃₇	1	4	yes	complemented
314	C₂×#106	C₂²×C₃₇	1	4	yes	complemented
315	#418	C₂²×C₃₇	1	16	yes	complemented
316	C₂×#102	C₂²×C₃₇	1	4	yes	complemented
317	C₂×#102	C₂²×C₃₇	1	4	yes	complemented
318	#407	C₂²×C₃₇	1	8	yes	complemented
319	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	complemented
320	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	complemented
321	C₃₇	C₂×#3094	1	1	yes	characteristic, direct product factor, Sylow
322	C₂⁵	—	2	1	no	—
323	C₂⁵	D₄×C₃₇	1	1	yes	characteristic
324	C₂²×D₄	—	2	2	no	—
325	C₂²×D₄	—	2	8	no	—
326	C₂²×D₄	—	2	2	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	2	8	no	—
330	C₂²×D₄	—	4	8	no	—
331	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
332	C₂²×D₄	C₂³×C₃₇	1	4	yes	—
333	C₂³×C₄	—	2	8	no	—
334	C₂³×C₄	—	2	1	no	—
335	C₂³×C₄	—	2	1	no	—
336	C₂³×C₄	—	2	1	no	—
337	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
338	C₂³×C₄	D₄×C₃₇	1	4	yes	—
339	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
340	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
341	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
342	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
343	C₂³×C₄	C₂³×C₃₇	1	4	yes	—
344	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
345	C₂×M₁₆	—	2	8	no	—
346	C₂×M₁₆	C₂³×C₃₇	1	8	yes	—
347	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
348	#121	—	2	8	no	—
349	#121	—	2	4	no	—
350	#121	—	2	4	no	—
351	#121	—	2	8	no	—
352	#121	C₂³×C₃₇	1	8	yes	—
353	#121	C₂³×C₃₇	1	8	yes	—
354	#117	—	2	4	no	—
355	#117	—	2	8	no	—
356	#117	—	2	8	no	—
357	#117	—	2	4	no	—
358	#117	C₂³×C₃₇	1	8	yes	—
359	#117	C₂³×C₃₇	1	8	yes	complemented
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	2	no	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
368	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	complemented
371	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	complemented
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	8	no	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	—	2	8	no	—
378	C₂×C₄²	—	2	2	no	—
379	C₂×C₄²	—	2	8	no	—
380	C₂×C₄²	—	2	2	no	—
381	#107	C₂³×C₃₇	1	16	yes	complemented
382	#106	C₂³×C₃₇	1	16	yes	complemented
383	#102	C₂³×C₃₇	1	16	yes	complemented
384	#102	C₂³×C₃₇	1	16	yes	complemented
385	C₂²⋊C₈	C₂³×C₃₇	1	8	yes	complemented
386	C₂²⋊C₈	C₂³×C₃₇	1	8	yes	complemented
387	C₂⁴	—	2	4	no	—
388	C₂⁴	—	2	4	no	—
389	C₂⁴	—	2	4	no	—
390	C₂⁴	—	2	2	no	—
391	C₂⁴	—	4	2	no	—
392	C₂⁴	—	4	4	no	—
393	C₂⁴	—	4	4	no	—
394	C₂⁴	—	4	4	no	—
395	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
396	C₂⁴	C₂×D₄×C₃₇	1	4	yes	—
397	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
398	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
399	C₂×D₄	—	2	8	no	—
400	C₂×D₄	—	2	8	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	8	no	—
404	C₂×D₄	—	2	16	no	—
405	C₂×D₄	—	4	32	no	—
406	C₂×D₄	—	4	8	no	—
407	C₂×D₄	—	4	8	no	—
408	C₂×D₄	—	4	8	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	C₂⁴×C₃₇	1	4	yes	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	16	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	16	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	4	4	no	—
425	C₂²×C₄	—	4	4	no	—
426	C₂²×C₄	—	4	4	no	—
427	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
429	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
431	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
432	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
433	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
434	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
436	C₂²×C₄	#41×C₃₇	1	8	yes	—
437	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
439	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
440	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
441	M₁₆	—	2	16	no	—
442	C₂×C₈	—	2	8	no	—
443	C₂×C₈	C₂⁴×C₃₇	1	8	yes	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
451	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
452	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
453	C₂²⋊C₄	—	2	8	no	—
454	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₄²	—	2	8	no	—
458	C₄²	—	2	8	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	8	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	8	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	4	no	—
469	C₂³	—	4	4	no	—
470	C₂³	—	4	16	no	—
471	C₂³	—	4	8	no	—
472	C₂³	—	4	8	no	—
473	C₂³	—	4	8	no	—
474	C₂³	—	4	4	no	—
475	C₂³	—	4	4	no	—
476	C₂³	—	4	4	no	—
477	C₂³	—	8	16	no	—
478	C₂³	#123×C₃₇	1	4	yes	—
479	C₂³	AGL(1,ℤ/8)×C₃₇	1	4	yes	—
480	C₂³	C₂²×D₄×C₃₇	1	2	yes	—
481	C₂³	C₂²×D₄×C₃₇	1	2	yes	—
482	C₂³	C₂²×D₄×C₃₇	1	2	yes	—
483	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
484	D₄	—	2	8	no	—
485	D₄	—	4	16	no	—
486	D₄	—	4	16	no	—
487	D₄	—	4	8	no	—
488	D₄	—	4	4	no	—
489	C₂×C₄	—	2	8	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	8	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	4	8	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	—	4	8	no	—
505	C₂×C₄	—	4	4	no	—
506	C₂×C₄	—	4	4	no	—
507	C₂×C₄	#123×C₃₇	1	8	yes	—
508	C₂×C₄	#123×C₃₇	1	4	yes	—
509	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
511	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
512	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
513	C₂×C₄	C₂×#41×C₃₇	1	4	yes	—
514	C₂×C₄	C₂×#41×C₃₇	1	8	yes	—
515	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
516	C₈	—	2	8	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	8	no	—
522	C₂²	—	2	8	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	4	16	no	—
527	C₂²	—	4	4	no	—
528	C₂²	—	4	4	no	—
529	C₂²	—	4	4	no	—
530	C₂²	—	4	4	no	—
531	C₂²	—	8	16	no	—
532	C₂²	—	8	8	no	—
533	C₂²	C₂×#123×C₃₇	1	4	yes	—
534	C₂²	C₂×#123×C₃₇	1	2	yes	—
535	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	4	yes	—
536	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	2	yes	—
537	C₂²	C₃₇×#575	1	2	yes	—
538	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
539	C₄	—	2	2	no	—
540	C₄	—	2	2	no	—
541	C₄	—	4	4	no	—
542	C₄	—	4	4	no	—
543	C₄	—	4	4	no	—
544	C₄	C₂×#123×C₃₇	1	4	yes	—
545	C₄	C₂×#123×C₃₇	1	2	yes	—
546	C₄	C₂²×#41×C₃₇	1	2	yes	—
547	C₂	—	2	4	no	—
548	C₂	—	2	4	no	—
549	C₂	—	4	2	no	—
550	C₂	—	8	4	no	—
551	C₂	C₃₇×#3094	1	4	yes	direct product factor
552	C₂	C₂²×#123×C₃₇	1	1	yes	characteristic
553	C₂	C₂²×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
554	C₂	C₂×C₃₇×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
prime radical	C₂²×#121×C₃₇	C₂
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
2. C₂²×#117×C₃₇	C₂	semidirect
3. C₃₇×#3094	C₂	direct (N × H)
4. C₂×C₃₇×#481	C₂	semidirect
5. C₂×C₃₇×#482	C₂	semidirect
6. C₂×C₃₇×#480	C₂	semidirect
7. C₂×C₃₇×#428	C₂	semidirect
8. C₂×C₃₇×#418	C₂	semidirect
9. C₂×C₃₇×#407	C₂	semidirect
24. C₂×#117×C₃₇	C₂²	semidirect
25. C₂×#117×C₃₇	C₂²	semidirect
27. C₂²×C₄⋊C₄×C₃₇	C₂²	semidirect
28. C₂²×C₄⋊C₄×C₃₇	C₂²	semidirect
32. C₃₇×#482	C₂²	semidirect
33. C₃₇×#481	C₂²	semidirect
34. C₃₇×#480	C₂²	semidirect
35. C₃₇×#428	C₂²	semidirect
36. C₂×#107×C₃₇	C₂²	semidirect
37. C₂×#106×C₃₇	C₂²	semidirect
38. C₃₇×#418	C₂²	semidirect
39. C₂×#102×C₃₇	C₂²	semidirect
40. C₂×#102×C₃₇	C₂²	semidirect
41. C₃₇×#407	C₂²	semidirect
42. C₂×C₂²⋊C₈×C₃₇	C₂²	semidirect
43. C₂×C₂²⋊C₈×C₃₇	C₂²	semidirect
81. #117×C₃₇	C₂³	semidirect
92. C₂×C₄⋊C₄×C₃₇	C₂³	semidirect
93. C₂×C₄⋊C₄×C₃₇	C₂³	semidirect
103. #107×C₃₇	C₂³	semidirect
104. #106×C₃₇	C₂³	semidirect
105. #102×C₃₇	C₂³	semidirect
106. #102×C₃₇	C₂³	semidirect
107. C₂²⋊C₈×C₃₇	C₂³	semidirect
108. C₂²⋊C₈×C₃₇	C₂³	semidirect
239. C₂×#3094	C₃₇	direct (N × H)
271. C₂²×#117	C₂×C₃₇	semidirect
272. #3094	C₂×C₃₇	direct (N × H)
273. C₂×#481	C₂×C₃₇	semidirect
274. C₂×#482	C₂×C₃₇	semidirect
275. C₂×#480	C₂×C₃₇	semidirect
276. C₂×#428	C₂×C₃₇	semidirect
277. C₂×#418	C₂×C₃₇	semidirect
278. C₂×#407	C₂×C₃₇	semidirect
283. C₂×C₃₇	#3094	direct (N × H)
301. C₂×#117	C₂²×C₃₇	semidirect
302. C₂×#117	C₂²×C₃₇	semidirect
304. C₂²×C₄⋊C₄	C₂²×C₃₇	semidirect
305. C₂²×C₄⋊C₄	C₂²×C₃₇	semidirect
309. #482	C₂²×C₃₇	semidirect
310. #481	C₂²×C₃₇	semidirect
311. #480	C₂²×C₃₇	semidirect
312. #428	C₂²×C₃₇	semidirect
313. C₂×#107	C₂²×C₃₇	semidirect
314. C₂×#106	C₂²×C₃₇	semidirect
315. #418	C₂²×C₃₇	semidirect
316. C₂×#102	C₂²×C₃₇	semidirect
317. C₂×#102	C₂²×C₃₇	semidirect
318. #407	C₂²×C₃₇	semidirect
319. C₂×C₂²⋊C₈	C₂²×C₃₇	semidirect
320. C₂×C₂²⋊C₈	C₂²×C₃₇	semidirect
321. C₃₇	C₂×#3094	direct (N × H)
359. #117	C₂³×C₃₇	semidirect
370. C₂×C₄⋊C₄	C₂³×C₃₇	semidirect
371. C₂×C₄⋊C₄	C₂³×C₃₇	semidirect
381. #107	C₂³×C₃₇	semidirect
382. #106	C₂³×C₃₇	semidirect
383. #102	C₂³×C₃₇	semidirect
384. #102	C₂³×C₃₇	semidirect
385. C₂²⋊C₈	C₂³×C₃₇	semidirect
386. C₂²⋊C₈	C₂³×C₃₇	semidirect
551. C₂	C₃₇×#3094	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×#121×C₃₇	2
C₂²×#117×C₃₇	2
C₃₇×#3094	2
C₂×C₃₇×#481	2
C₂×C₃₇×#482	2
C₂×C₃₇×#480	2
C₂×C₃₇×#428	2
C₂×C₃₇×#418	2
C₂×C₃₇×#407	2
C₂×#3094	37

Subgroups — C2×C37×#3094 #22681762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₇×#3094 #22681762