Subgroups — C₂×C₃₇×#3222 #22682045

Order 9472.

2214 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	C₂×C₃₇×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#535	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#3222	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₇×#497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₇×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₇×#490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₇×#488	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₇×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₇×#460	C₂	1	2	yes	maximal, complemented
10	C₂×C₃₇×#452	C₂	1	2	yes	maximal, complemented
11	C₂×C₃₇×#450	C₂	1	2	yes	maximal, complemented
12	C₂×C₃₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₃₇	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₃₇	C₂²	1	1	yes	characteristic
15	C₂²×Q₁₆×C₃₇	C₂²	1	2	yes	complemented
16	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
17	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
18	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	complemented
19	C₃₇×#541	—	2	4	no	—
20	C₃₇×#541	C₂²	1	8	yes	complemented
21	C₃₇×#535	—	2	4	no	—
22	C₃₇×#535	C₂²	1	8	yes	—
23	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
24	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×#126×C₃₇	—	2	2	no	—
27	C₂×#125×C₃₇	—	2	2	no	—
28	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
32	C₂×#121×C₃₇	—	2	2	no	—
33	C₂×#120×C₃₇	—	2	2	no	—
34	C₂×C₄×Q₈×C₃₇	C₂²	1	2	yes	complemented
35	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic
36	C₃₇×#497	C₂²	1	8	yes	complemented
37	C₃₇×#492	C₂²	1	8	yes	complemented
38	C₃₇×#490	C₂²	1	8	yes	complemented
39	C₃₇×#488	C₂²	1	8	yes	complemented
40	C₃₇×#464	C₂²	1	16	yes	complemented
41	C₃₇×#460	C₂²	1	16	yes	complemented
42	C₃₇×#452	C₂²	1	16	yes	complemented
43	C₃₇×#450	C₂²	1	16	yes	complemented
44	C₃₇×#433	C₂²	1	8	yes	complemented
45	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	complemented
46	C₂×#103×C₃₇	C₂²	1	2	yes	complemented
47	C₂×#102×C₃₇	C₂²	1	2	yes	—
48	C₂×#102×C₃₇	C₂²	1	2	yes	—
49	C₂×#102×C₃₇	C₂²	1	2	yes	complemented
50	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	—
51	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
53	C₂⁵×C₃₇	—	2	1	no	—
54	C₂×#41×C₃₇	—	2	2	no	—
55	C₂×#41×C₃₇	—	4	4	no	—
56	C₂×#41×C₃₇	C₂³	1	4	yes	—
57	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
58	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₃₇	—	2	1	no	—
60	C₂²×D₄×C₃₇	—	2	1	no	—
61	C₂²×D₄×C₃₇	—	2	2	no	—
62	C₂²×D₄×C₃₇	—	2	2	no	—
63	C₂²×D₄×C₃₇	—	2	2	no	—
64	C₂²×D₄×C₃₇	—	4	4	no	—
65	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₃₇	C₂³	1	4	yes	—
69	C₂³×C₄×C₃₇	—	2	1	no	—
70	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
71	C₂×Q₁₆×C₃₇	—	4	4	no	—
72	C₂×Q₁₆×C₃₇	C₂³	1	8	yes	complemented
73	C₂×SD₁₆×C₃₇	—	4	4	no	—
74	C₂×SD₁₆×C₃₇	—	4	4	no	—
75	C₂×SD₁₆×C₃₇	—	4	4	no	—
76	C₂×SD₁₆×C₃₇	C₂³	1	8	yes	—
77	C₂×SD₁₆×C₃₇	C₂³	1	8	yes	—
78	C₂×SD₁₆×C₃₇	C₂³	1	8	yes	complemented
79	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
80	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
81	C₄⋊Q₈×C₃₇	—	2	2	no	—
82	C₄⋊Q₈×C₃₇	C₂³	1	4	yes	complemented
83	#127×C₃₇	—	2	2	no	—
84	#127×C₃₇	—	2	2	no	—
85	#127×C₃₇	C₂³	1	4	yes	—
86	#127×C₃₇	C₂³	1	4	yes	—
87	#126×C₃₇	—	2	16	no	—
88	#125×C₃₇	—	2	16	no	—
89	#125×C₃₇	—	2	2	no	—
90	#125×C₃₇	C₂³	1	4	yes	complemented
91	#124×C₃₇	—	2	2	no	—
92	#124×C₃₇	—	2	2	no	—
93	#124×C₃₇	C₂³	1	4	yes	—
94	#124×C₃₇	C₂³	1	4	yes	—
95	C₂²⋊Q₈×C₃₇	—	2	4	no	—
96	C₂²⋊Q₈×C₃₇	C₂³	1	8	yes	—
97	#121×C₃₇	—	2	16	no	—
98	#120×C₃₇	—	2	16	no	—
99	C₄×Q₈×C₃₇	—	2	4	no	—
100	C₄×Q₈×C₃₇	C₂³	1	8	yes	complemented
101	#117×C₃₇	D₄	1	4	yes	—
102	#117×C₃₇	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
104	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
105	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
106	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
107	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
108	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
110	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
111	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₃₇	D₄	1	2	yes	—
113	C₂×C₄²×C₃₇	—	2	2	no	—
114	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₃₇	C₂³	1	8	yes	complemented
117	#103×C₃₇	C₂³	1	8	yes	complemented
118	#102×C₃₇	C₂³	1	8	yes	—
119	#102×C₃₇	C₂³	1	8	yes	—
120	#102×C₃₇	C₂³	1	8	yes	complemented
121	C₂²⋊C₈×C₃₇	C₂³	1	8	yes	—
122	#97×C₃₇	C₂³	1	4	yes	complemented
123	C₄×C₈×C₃₇	C₂³	1	4	yes	complemented
124	C₂⁴×C₃₇	—	2	1	no	—
125	C₂⁴×C₃₇	—	2	1	no	—
126	C₂⁴×C₃₇	—	2	1	no	—
127	C₂⁴×C₃₇	—	2	4	no	—
128	C₂⁴×C₃₇	—	4	4	no	—
129	C₂⁴×C₃₇	—	8	4	no	—
130	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
131	#41×C₃₇	—	4	8	no	—
132	#41×C₃₇	—	4	8	no	—
133	C₂×Q₈×C₃₇	—	2	2	no	—
134	C₂×Q₈×C₃₇	—	2	1	no	—
135	C₂×Q₈×C₃₇	—	2	4	no	—
136	C₂×Q₈×C₃₇	—	2	4	no	—
137	C₂×Q₈×C₃₇	—	2	4	no	—
138	C₂×Q₈×C₃₇	C₂⁴	1	2	yes	—
139	C₂×Q₈×C₃₇	C₂⁴	1	4	yes	—
140	C₂×D₄×C₃₇	—	2	4	no	—
141	C₂×D₄×C₃₇	—	2	4	no	—
142	C₂×D₄×C₃₇	—	2	1	no	—
143	C₂×D₄×C₃₇	—	2	1	no	—
144	C₂×D₄×C₃₇	—	2	1	no	—
145	C₂×D₄×C₃₇	—	2	8	no	—
146	C₂×D₄×C₃₇	—	2	8	no	—
147	C₂×D₄×C₃₇	—	2	4	no	—
148	C₂×D₄×C₃₇	—	2	4	no	—
149	C₂×D₄×C₃₇	—	2	4	no	—
150	C₂×D₄×C₃₇	—	4	8	no	—
151	C₂×D₄×C₃₇	—	4	4	no	—
152	C₂×D₄×C₃₇	—	4	8	no	—
153	C₂×D₄×C₃₇	—	4	4	no	—
154	C₂×D₄×C₃₇	—	8	4	no	—
155	C₂×D₄×C₃₇	—	8	4	no	—
156	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
157	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
158	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₃₇	—	2	4	no	—
160	C₂²×C₄×C₃₇	—	2	2	no	—
161	C₂²×C₄×C₃₇	—	2	2	no	—
162	C₂²×C₄×C₃₇	—	2	1	no	—
163	C₂²×C₄×C₃₇	—	2	4	no	—
164	C₂²×C₄×C₃₇	—	4	4	no	—
165	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
171	Q₁₆×C₃₇	—	4	8	no	—
172	SD₁₆×C₃₇	—	4	8	no	—
173	SD₁₆×C₃₇	—	4	8	no	—
174	SD₁₆×C₃₇	—	4	8	no	—
175	C₂×C₈×C₃₇	—	2	4	no	—
176	C₂×C₈×C₃₇	—	2	4	no	—
177	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
178	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
179	C₄⋊C₄×C₃₇	—	2	8	no	—
180	C₄⋊C₄×C₃₇	—	2	8	no	—
181	C₄⋊C₄×C₃₇	—	2	8	no	—
182	C₄⋊C₄×C₃₇	—	2	8	no	—
183	C₄⋊C₄×C₃₇	—	2	2	no	—
184	C₄⋊C₄×C₃₇	C₂×D₄	1	8	yes	—
185	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
186	C₂²⋊C₄×C₃₇	—	2	8	no	—
187	C₂²⋊C₄×C₃₇	—	2	8	no	—
188	C₂²⋊C₄×C₃₇	—	2	8	no	—
189	C₂²⋊C₄×C₃₇	C₂×D₄	1	8	yes	—
190	C₄²×C₃₇	—	2	8	no	—
191	C₄²×C₃₇	C₂×D₄	1	2	yes	—
192	C₄²×C₃₇	C₂×D₄	1	2	yes	—
193	C₄²×C₃₇	C₂⁴	1	2	yes	—
194	C₄²×C₃₇	C₂⁴	1	2	yes	—
195	C₂³×C₃₇	—	2	2	no	—
196	C₂³×C₃₇	—	2	4	no	—
197	C₂³×C₃₇	—	2	2	no	—
198	C₂³×C₃₇	—	2	2	no	—
199	C₂³×C₃₇	—	2	2	no	—
200	C₂³×C₃₇	—	4	8	no	—
201	C₂³×C₃₇	—	4	2	no	—
202	C₂³×C₃₇	—	4	2	no	—
203	C₂³×C₃₇	—	4	2	no	—
204	C₂³×C₃₇	—	4	4	no	—
205	C₂³×C₃₇	—	4	4	no	—
206	C₂³×C₃₇	—	4	4	no	—
207	C₂³×C₃₇	—	8	8	no	—
208	C₂³×C₃₇	—	8	16	no	—
209	C₂³×C₃₇	C₂²×D₄	1	2	yes	—
210	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₃₇	—	2	4	no	—
212	Q₈×C₃₇	—	2	4	no	—
213	Q₈×C₃₇	—	2	4	no	—
214	Q₈×C₃₇	—	4	4	no	—
215	Q₈×C₃₇	—	4	2	no	—
216	D₄×C₃₇	—	2	4	no	—
217	D₄×C₃₇	—	2	4	no	—
218	D₄×C₃₇	—	2	4	no	—
219	D₄×C₃₇	—	4	8	no	—
220	D₄×C₃₇	—	4	8	no	—
221	D₄×C₃₇	—	4	2	no	—
222	D₄×C₃₇	—	4	2	no	—
223	D₄×C₃₇	—	4	2	no	—
224	D₄×C₃₇	—	8	8	no	—
225	D₄×C₃₇	—	8	8	no	—
226	C₂×C₄×C₃₇	—	2	2	no	—
227	C₂×C₄×C₃₇	—	2	4	no	—
228	C₂×C₄×C₃₇	—	2	4	no	—
229	C₂×C₄×C₃₇	—	2	4	no	—
230	C₂×C₄×C₃₇	—	2	4	no	—
231	C₂×C₄×C₃₇	—	2	4	no	—
232	C₂×C₄×C₃₇	—	2	4	no	—
233	C₂×C₄×C₃₇	—	2	2	no	—
234	C₂×C₄×C₃₇	—	4	8	no	—
235	C₂×C₄×C₃₇	—	4	2	no	—
236	C₂×C₄×C₃₇	—	4	4	no	—
237	C₂×C₄×C₃₇	—	4	4	no	—
238	C₂×C₄×C₃₇	C₂²×D₄	1	4	yes	—
239	C₂×C₄×C₃₇	C₂²×D₄	1	4	yes	—
240	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
241	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₃₇	H(5,𝔽₂)	1	4	yes	—
243	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
244	C₈×C₃₇	—	2	4	no	—
245	C₈×C₃₇	—	2	4	no	—
246	C₂×#3222	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂²×C₃₇	—	2	2	no	—
248	C₂²×C₃₇	—	2	4	no	—
249	C₂²×C₃₇	—	4	4	no	—
250	C₂²×C₃₇	—	4	2	no	—
251	C₂²×C₃₇	—	4	2	no	—
252	C₂²×C₃₇	—	4	2	no	—
253	C₂²×C₃₇	—	4	4	no	—
254	C₂²×C₃₇	—	4	4	no	—
255	C₂²×C₃₇	—	4	4	no	—
256	C₂²×C₃₇	—	8	16	no	—
257	C₂²×C₃₇	—	8	4	no	—
258	C₂²×C₃₇	—	8	4	no	—
259	C₂²×C₃₇	—	8	4	no	—
260	C₂²×C₃₇	#535	1	2	yes	—
261	C₂²×C₃₇	#577	1	4	yes	—
262	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
263	C₄×C₃₇	—	2	2	no	—
264	C₄×C₃₇	—	2	4	no	—
265	C₄×C₃₇	—	2	4	no	—
266	C₄×C₃₇	—	4	2	no	—
267	C₄×C₃₇	—	4	4	no	—
268	C₄×C₃₇	—	4	4	no	—
269	C₄×C₃₇	#535	1	2	yes	—
270	C₄×C₃₇	C₂×H(5,𝔽₂)	1	2	yes	—
271	C₂×#541	C₂×C₃₇	1	1	yes	characteristic, complemented
272	C₂×#535	C₂×C₃₇	1	1	yes	characteristic
273	#3222	C₂×C₃₇	1	16	yes	direct product factor
274	C₂×#497	C₂×C₃₇	1	1	yes	characteristic, complemented
275	C₂×#492	C₂×C₃₇	1	1	yes	characteristic, complemented
276	C₂×#490	C₂×C₃₇	1	1	yes	characteristic, complemented
277	C₂×#488	C₂×C₃₇	1	1	yes	characteristic, complemented
278	C₂×#464	C₂×C₃₇	1	2	yes	complemented
279	C₂×#460	C₂×C₃₇	1	2	yes	complemented
280	C₂×#452	C₂×C₃₇	1	2	yes	complemented
281	C₂×#450	C₂×C₃₇	1	2	yes	complemented
282	C₂×#433	C₂×C₃₇	1	1	yes	characteristic, complemented
283	C₂×C₃₇	—	4	2	no	—
284	C₂×C₃₇	—	8	2	no	—
285	C₂×C₃₇	—	8	2	no	—
286	C₂×C₃₇	—	8	2	no	—
287	C₂×C₃₇	#3222	1	4	yes	direct product factor
288	C₂×C₃₇	C₂×#535	1	1	yes	characteristic
289	C₂×C₃₇	C₂×#577	1	2	yes	—
290	C₂²×#41	C₂²×C₃₇	1	1	yes	characteristic
291	C₂³×D₄	C₂²×C₃₇	1	1	yes	characteristic
292	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	complemented
293	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
294	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
295	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	complemented
296	#541	—	2	4	no	—
297	#541	C₂²×C₃₇	1	8	yes	complemented
298	#535	—	2	4	no	—
299	#535	C₂²×C₃₇	1	8	yes	—
300	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
301	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
302	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
303	C₂×#126	—	2	2	no	—
304	C₂×#125	—	2	2	no	—
305	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic, complemented
306	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
307	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
308	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
309	C₂×#121	—	2	2	no	—
310	C₂×#120	—	2	2	no	—
311	C₂×C₄×Q₈	C₂²×C₃₇	1	2	yes	complemented
312	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic
313	#497	C₂²×C₃₇	1	8	yes	complemented
314	#492	C₂²×C₃₇	1	8	yes	complemented
315	#490	C₂²×C₃₇	1	8	yes	complemented
316	#488	C₂²×C₃₇	1	8	yes	complemented
317	#464	C₂²×C₃₇	1	16	yes	complemented
318	#460	C₂²×C₃₇	1	16	yes	complemented
319	#452	C₂²×C₃₇	1	16	yes	complemented
320	#450	C₂²×C₃₇	1	16	yes	complemented
321	#433	C₂²×C₃₇	1	8	yes	complemented
322	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	complemented
323	C₂×#103	C₂²×C₃₇	1	2	yes	complemented
324	C₂×#102	C₂²×C₃₇	1	2	yes	—
325	C₂×#102	C₂²×C₃₇	1	2	yes	—
326	C₂×#102	C₂²×C₃₇	1	2	yes	complemented
327	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
328	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic, complemented
329	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
330	C₃₇	C₂×#3222	1	1	yes	characteristic, direct product factor, Sylow
331	C₂⁵	—	2	1	no	—
332	C₂×#41	—	2	2	no	—
333	C₂×#41	—	4	4	no	—
334	C₂×#41	C₂³×C₃₇	1	4	yes	—
335	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
336	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
337	C₂²×D₄	—	2	1	no	—
338	C₂²×D₄	—	2	1	no	—
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	—	2	2	no	—
341	C₂²×D₄	—	2	2	no	—
342	C₂²×D₄	—	4	4	no	—
343	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
344	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
345	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
346	C₂²×D₄	C₂³×C₃₇	1	4	yes	—
347	C₂³×C₄	—	2	1	no	—
348	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
349	C₂×Q₁₆	—	4	4	no	—
350	C₂×Q₁₆	C₂³×C₃₇	1	8	yes	complemented
351	C₂×SD₁₆	—	4	4	no	—
352	C₂×SD₁₆	—	4	4	no	—
353	C₂×SD₁₆	—	4	4	no	—
354	C₂×SD₁₆	C₂³×C₃₇	1	8	yes	—
355	C₂×SD₁₆	C₂³×C₃₇	1	8	yes	—
356	C₂×SD₁₆	C₂³×C₃₇	1	8	yes	complemented
357	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
358	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
359	C₄⋊Q₈	—	2	2	no	—
360	C₄⋊Q₈	C₂³×C₃₇	1	4	yes	complemented
361	#127	—	2	2	no	—
362	#127	—	2	2	no	—
363	#127	C₂³×C₃₇	1	4	yes	—
364	#127	C₂³×C₃₇	1	4	yes	—
365	#126	—	2	16	no	—
366	#125	—	2	16	no	—
367	#125	—	2	2	no	—
368	#125	C₂³×C₃₇	1	4	yes	complemented
369	#124	—	2	2	no	—
370	#124	—	2	2	no	—
371	#124	C₂³×C₃₇	1	4	yes	—
372	#124	C₂³×C₃₇	1	4	yes	—
373	C₂²⋊Q₈	—	2	4	no	—
374	C₂²⋊Q₈	C₂³×C₃₇	1	8	yes	—
375	#121	—	2	16	no	—
376	#120	—	2	16	no	—
377	C₄×Q₈	—	2	4	no	—
378	C₄×Q₈	C₂³×C₃₇	1	8	yes	complemented
379	#117	D₄×C₃₇	1	4	yes	—
380	#117	C₂³×C₃₇	1	4	yes	—
381	C₂×C₄⋊C₄	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	2	no	—
383	C₂×C₄⋊C₄	—	2	2	no	—
384	C₂×C₄⋊C₄	—	2	2	no	—
385	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	—	2	2	no	—
390	C₂×C₂²⋊C₄	D₄×C₃₇	1	2	yes	—
391	C₂×C₄²	—	2	2	no	—
392	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
394	C₄⋊C₈	C₂³×C₃₇	1	8	yes	complemented
395	#103	C₂³×C₃₇	1	8	yes	complemented
396	#102	C₂³×C₃₇	1	8	yes	—
397	#102	C₂³×C₃₇	1	8	yes	—
398	#102	C₂³×C₃₇	1	8	yes	complemented
399	C₂²⋊C₈	C₂³×C₃₇	1	8	yes	—
400	#97	C₂³×C₃₇	1	4	yes	complemented
401	C₄×C₈	C₂³×C₃₇	1	4	yes	complemented
402	C₂⁴	—	2	1	no	—
403	C₂⁴	—	2	1	no	—
404	C₂⁴	—	2	1	no	—
405	C₂⁴	—	2	4	no	—
406	C₂⁴	—	4	4	no	—
407	C₂⁴	—	8	4	no	—
408	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
409	#41	—	4	8	no	—
410	#41	—	4	8	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	4	no	—
414	C₂×Q₈	—	2	4	no	—
415	C₂×Q₈	—	2	4	no	—
416	C₂×Q₈	C₂⁴×C₃₇	1	2	yes	—
417	C₂×Q₈	C₂⁴×C₃₇	1	4	yes	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	8	no	—
424	C₂×D₄	—	2	8	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	4	8	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	—	4	8	no	—
431	C₂×D₄	—	4	4	no	—
432	C₂×D₄	—	8	4	no	—
433	C₂×D₄	—	8	4	no	—
434	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
435	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
436	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	4	4	no	—
443	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
444	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
445	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
449	Q₁₆	—	4	8	no	—
450	SD₁₆	—	4	8	no	—
451	SD₁₆	—	4	8	no	—
452	SD₁₆	—	4	8	no	—
453	C₂×C₈	—	2	4	no	—
454	C₂×C₈	—	2	4	no	—
455	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
456	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	2	8	no	—
459	C₄⋊C₄	—	2	8	no	—
460	C₄⋊C₄	—	2	8	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	C₂×D₄×C₃₇	1	8	yes	—
463	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
464	C₂²⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	—	2	8	no	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	C₂×D₄×C₃₇	1	8	yes	—
468	C₄²	—	2	8	no	—
469	C₄²	C₂×D₄×C₃₇	1	2	yes	—
470	C₄²	C₂×D₄×C₃₇	1	2	yes	—
471	C₄²	C₂⁴×C₃₇	1	2	yes	—
472	C₄²	C₂⁴×C₃₇	1	2	yes	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	4	8	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	4	no	—
483	C₂³	—	4	4	no	—
484	C₂³	—	4	4	no	—
485	C₂³	—	8	8	no	—
486	C₂³	—	8	16	no	—
487	C₂³	C₂²×D₄×C₃₇	1	2	yes	—
488	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
489	Q₈	—	2	4	no	—
490	Q₈	—	2	4	no	—
491	Q₈	—	2	4	no	—
492	Q₈	—	4	2	no	—
493	Q₈	—	4	4	no	—
494	D₄	—	2	4	no	—
495	D₄	—	2	4	no	—
496	D₄	—	2	4	no	—
497	D₄	—	4	8	no	—
498	D₄	—	4	8	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	8	8	no	—
503	D₄	—	8	8	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	4	8	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	C₂²×D₄×C₃₇	1	4	yes	—
517	C₂×C₄	C₂²×D₄×C₃₇	1	4	yes	—
518	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
519	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
520	C₂×C₄	H(5,𝔽₂)×C₃₇	1	4	yes	—
521	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
522	C₈	—	2	4	no	—
523	C₈	—	2	4	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	4	no	—
531	C₂²	—	4	4	no	—
532	C₂²	—	4	4	no	—
533	C₂²	—	8	16	no	—
534	C₂²	—	8	4	no	—
535	C₂²	—	8	4	no	—
536	C₂²	—	8	4	no	—
537	C₂²	C₃₇×#535	1	2	yes	—
538	C₂²	C₃₇×#577	1	4	yes	—
539	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
540	C₄	—	2	2	no	—
541	C₄	—	2	4	no	—
542	C₄	—	2	4	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	4	no	—
545	C₄	—	4	4	no	—
546	C₄	C₃₇×#535	1	2	yes	—
547	C₄	C₂×H(5,𝔽₂)×C₃₇	1	2	yes	—
548	C₂	—	4	2	no	—
549	C₂	—	8	2	no	—
550	C₂	—	8	2	no	—
551	C₂	—	8	2	no	—
552	C₂	C₃₇×#3222	1	4	yes	direct product factor
553	C₂	C₂×C₃₇×#535	1	1	yes	characteristic
554	C₂	C₂×C₃₇×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
prime radical	C₂×C₃₇×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂×#117×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#541	C₂	semidirect
3. C₃₇×#3222	C₂	direct (N × H)
4. C₂×C₃₇×#497	C₂	semidirect
5. C₂×C₃₇×#492	C₂	semidirect
6. C₂×C₃₇×#490	C₂	semidirect
7. C₂×C₃₇×#488	C₂	semidirect
8. C₂×C₃₇×#464	C₂	semidirect
9. C₂×C₃₇×#460	C₂	semidirect
10. C₂×C₃₇×#452	C₂	semidirect
11. C₂×C₃₇×#450	C₂	semidirect
12. C₂×C₃₇×#433	C₂	semidirect
15. C₂²×Q₁₆×C₃₇	C₂²	semidirect
18. C₂²×SD₁₆×C₃₇	C₂²	semidirect
20. C₃₇×#541	C₂²	semidirect
23. C₂×C₄⋊Q₈×C₃₇	C₂²	semidirect
28. C₂×#125×C₃₇	C₂²	semidirect
34. C₂×C₄×Q₈×C₃₇	C₂²	semidirect
36. C₃₇×#497	C₂²	semidirect
37. C₃₇×#492	C₂²	semidirect
38. C₃₇×#490	C₂²	semidirect
39. C₃₇×#488	C₂²	semidirect
40. C₃₇×#464	C₂²	semidirect
41. C₃₇×#460	C₂²	semidirect
42. C₃₇×#452	C₂²	semidirect
43. C₃₇×#450	C₂²	semidirect
44. C₃₇×#433	C₂²	semidirect
45. C₂×C₄⋊C₈×C₃₇	C₂²	semidirect
46. C₂×#103×C₃₇	C₂²	semidirect
49. C₂×#102×C₃₇	C₂²	semidirect
51. C₂×#97×C₃₇	C₂²	semidirect
52. C₂×C₄×C₈×C₃₇	C₂²	semidirect
72. C₂×Q₁₆×C₃₇	C₂³	semidirect
78. C₂×SD₁₆×C₃₇	C₂³	semidirect
82. C₄⋊Q₈×C₃₇	C₂³	semidirect
90. #125×C₃₇	C₂³	semidirect
100. C₄×Q₈×C₃₇	C₂³	semidirect
116. C₄⋊C₈×C₃₇	C₂³	semidirect
117. #103×C₃₇	C₂³	semidirect
120. #102×C₃₇	C₂³	semidirect
122. #97×C₃₇	C₂³	semidirect
123. C₄×C₈×C₃₇	C₂³	semidirect
246. C₂×#3222	C₃₇	direct (N × H)
271. C₂×#541	C₂×C₃₇	semidirect
273. #3222	C₂×C₃₇	direct (N × H)
274. C₂×#497	C₂×C₃₇	semidirect
275. C₂×#492	C₂×C₃₇	semidirect
276. C₂×#490	C₂×C₃₇	semidirect
277. C₂×#488	C₂×C₃₇	semidirect
278. C₂×#464	C₂×C₃₇	semidirect
279. C₂×#460	C₂×C₃₇	semidirect
280. C₂×#452	C₂×C₃₇	semidirect
281. C₂×#450	C₂×C₃₇	semidirect
282. C₂×#433	C₂×C₃₇	semidirect
287. C₂×C₃₇	#3222	direct (N × H)
292. C₂²×Q₁₆	C₂²×C₃₇	semidirect
295. C₂²×SD₁₆	C₂²×C₃₇	semidirect
297. #541	C₂²×C₃₇	semidirect
300. C₂×C₄⋊Q₈	C₂²×C₃₇	semidirect
305. C₂×#125	C₂²×C₃₇	semidirect
311. C₂×C₄×Q₈	C₂²×C₃₇	semidirect
313. #497	C₂²×C₃₇	semidirect
314. #492	C₂²×C₃₇	semidirect
315. #490	C₂²×C₃₇	semidirect
316. #488	C₂²×C₃₇	semidirect
317. #464	C₂²×C₃₇	semidirect
318. #460	C₂²×C₃₇	semidirect
319. #452	C₂²×C₃₇	semidirect
320. #450	C₂²×C₃₇	semidirect
321. #433	C₂²×C₃₇	semidirect
322. C₂×C₄⋊C₈	C₂²×C₃₇	semidirect
323. C₂×#103	C₂²×C₃₇	semidirect
326. C₂×#102	C₂²×C₃₇	semidirect
328. C₂×#97	C₂²×C₃₇	semidirect
329. C₂×C₄×C₈	C₂²×C₃₇	semidirect
330. C₃₇	C₂×#3222	direct (N × H)
350. C₂×Q₁₆	C₂³×C₃₇	semidirect
356. C₂×SD₁₆	C₂³×C₃₇	semidirect
360. C₄⋊Q₈	C₂³×C₃₇	semidirect
368. #125	C₂³×C₃₇	semidirect
378. C₄×Q₈	C₂³×C₃₇	semidirect
394. C₄⋊C₈	C₂³×C₃₇	semidirect
395. #103	C₂³×C₃₇	semidirect
398. #102	C₂³×C₃₇	semidirect
400. #97	C₂³×C₃₇	semidirect
401. C₄×C₈	C₂³×C₃₇	semidirect
552. C₂	C₃₇×#3222	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×#541	2
C₂×C₃₇×#535	2
C₃₇×#3222	2
C₂×C₃₇×#497	2
C₂×C₃₇×#492	2
C₂×C₃₇×#490	2
C₂×C₃₇×#488	2
C₂×C₃₇×#464	2
C₂×C₃₇×#460	2
C₂×C₃₇×#452	2
C₂×C₃₇×#450	2
C₂×C₃₇×#433	2
C₂×#3222	37

Subgroups — C2×C37×#3222 #22682045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₇×#3222 #22682045