Subgroups — C₃₇×#21419 #22642672

Order 9472.

1122 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3455	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2921	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#117×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#1995	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1994	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#1963	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#1962	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1897	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1896	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1759	C₂	1	2	yes	maximal, complemented
11	C₄×#104×C₃₇	C₂	1	2	yes	maximal, complemented
12	C₃₇×#542	C₄	1	4	yes	complemented
13	C₃₇×#541	C₄	1	2	yes	complemented
14	C₃₇×#540	C₄	1	2	yes	complemented
15	C₃₇×#539	—	2	2	no	—
16	C₃₇×#538	—	2	2	no	—
17	C₃₇×#533	C₂²	1	1	yes	characteristic
18	C₃₇×#532	C₂²	1	1	yes	characteristic
19	C₃₇×#529	—	2	4	no	—
20	C₃₇×#525	C₂²	1	2	yes	—
21	C₄×#41×C₃₇	C₂²	1	2	yes	—
22	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₃₇	C₂²	1	1	yes	characteristic
25	C₃₇×#433	—	2	4	no	—
26	C₃₇×#423	C₂²	1	1	yes	characteristic
27	C₃₇×#423	C₂²	1	1	yes	characteristic
28	C₂×#104×C₃₇	C₂²	1	2	yes	—
29	C₂×#104×C₃₇	C₂²	1	2	yes	—
30	C₂×#104×C₃₇	C₂²	1	2	yes	—
31	C₂×#104×C₃₇	C₂²	1	2	yes	—
32	C₃₇×#407	C₂²	1	2	yes	—
33	C₄×M₁₆×C₃₇	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₃₇	—	2	2	no	—
35	C₄×C₂²⋊C₄×C₃₇	—	2	2	no	—
36	C₃₇×#376	C₂²	1	1	yes	characteristic
37	C₃₇×#376	C₂²	1	1	yes	characteristic
38	C₄³×C₃₇	C₂²	1	1	yes	characteristic
39	C₄³×C₃₇	C₂²	1	1	yes	characteristic
40	C₃₇×#339	C₂²	1	2	yes	—
41	C₃₇×#339	C₂²	1	2	yes	—
42	C₃₇×#339	C₂²	1	2	yes	—
43	C₃₇×#339	C₂²	1	2	yes	—
44	C₂×#41×C₃₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₃₇	—	2	1	no	—
46	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
48	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₃₇	C₂×C₄	1	1	yes	characteristic, complemented
50	C₄⋊Q₈×C₃₇	C₂×C₄	1	2	yes	complemented
51	#127×C₃₇	C₂×C₄	1	1	yes	characteristic, complemented
52	#126×C₃₇	—	2	4	no	—
53	#126×C₃₇	—	2	4	no	—
54	#125×C₃₇	—	2	4	no	—
55	#125×C₃₇	C₂×C₄	1	2	yes	complemented
56	#124×C₃₇	—	2	4	no	—
57	#124×C₃₇	C₂×C₄	1	2	yes	complemented
58	#123×C₃₇	—	2	2	no	—
59	#123×C₃₇	—	2	4	no	—
60	#123×C₃₇	—	2	4	no	—
61	C₂²⋊Q₈×C₃₇	—	2	2	no	—
62	C₂²⋊Q₈×C₃₇	—	2	4	no	—
63	C₂²⋊Q₈×C₃₇	C₂×C₄	1	4	yes	—
64	#121×C₃₇	—	2	2	no	—
65	#121×C₃₇	—	2	4	no	—
66	#121×C₃₇	C₂×C₄	1	4	yes	—
67	#120×C₃₇	—	2	2	no	—
68	C₄×Q₈×C₃₇	—	2	2	no	—
69	C₄×Q₈×C₃₇	C₂×C₄	1	4	yes	complemented
70	C₄×D₄×C₃₇	—	2	4	no	—
71	C₄×D₄×C₃₇	—	2	4	no	—
72	C₄×D₄×C₃₇	—	2	2	no	—
73	C₄×D₄×C₃₇	C₂×C₄	1	4	yes	complemented
74	#117×C₃₇	—	2	2	no	—
75	#117×C₃₇	—	2	2	no	—
76	#117×C₃₇	—	2	2	no	—
77	#117×C₃₇	C₂×C₄	1	2	yes	—
78	#117×C₃₇	C₂×C₄	1	2	yes	—
79	#117×C₃₇	D₄	1	4	yes	—
80	#117×C₃₇	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
83	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₃₇	D₄	1	2	yes	—
85	C₂×C₄²×C₃₇	—	2	1	no	—
86	C₂×C₄²×C₃₇	—	2	2	no	—
87	C₂×C₄²×C₃₇	—	2	2	no	—
88	C₂×C₄²×C₃₇	—	2	2	no	—
89	C₂×C₄²×C₃₇	—	2	2	no	—
90	C₂×C₄²×C₃₇	—	2	2	no	—
91	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₃₇	—	2	2	no	—
98	C₄⋊C₈×C₃₇	—	2	2	no	—
99	#104×C₃₇	—	2	4	no	—
100	#104×C₃₇	—	2	4	no	—
101	#104×C₃₇	—	2	4	no	—
102	#104×C₃₇	—	2	4	no	—
103	C₂²⋊C₈×C₃₇	—	2	4	no	—
104	#97×C₃₇	—	2	2	no	—
105	C₄×C₈×C₃₇	—	2	2	no	—
106	#95×C₃₇	—	2	2	no	—
107	#95×C₃₇	—	2	2	no	—
108	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
109	#41×C₃₇	—	2	2	no	—
110	#41×C₃₇	—	2	2	no	—
111	#41×C₃₇	—	2	2	no	—
112	#41×C₃₇	—	2	2	no	—
113	C₂×Q₈×C₃₇	—	2	2	no	—
114	C₂×Q₈×C₃₇	C₂²×C₄	1	2	yes	—
115	C₂×D₄×C₃₇	—	2	2	no	—
116	C₂×D₄×C₃₇	—	2	4	no	—
117	C₂×D₄×C₃₇	—	2	2	no	—
118	C₂×D₄×C₃₇	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₃₇	—	2	1	no	—
120	C₂²×C₄×C₃₇	—	2	1	no	—
121	C₂²×C₄×C₃₇	—	2	1	no	—
122	C₂²×C₄×C₃₇	—	2	1	no	—
123	C₂²×C₄×C₃₇	—	2	1	no	—
124	C₂²×C₄×C₃₇	—	2	4	no	—
125	C₂²×C₄×C₃₇	—	2	1	no	—
126	C₂²×C₄×C₃₇	—	2	1	no	—
127	C₂²×C₄×C₃₇	—	2	1	no	—
128	C₂²×C₄×C₃₇	—	2	2	no	—
129	C₂²×C₄×C₃₇	—	2	4	no	—
130	C₂²×C₄×C₃₇	—	4	4	no	—
131	C₂²×C₄×C₃₇	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
137	M₁₆×C₃₇	—	2	2	no	—
138	M₁₆×C₃₇	—	2	2	no	—
139	M₁₆×C₃₇	—	2	2	no	—
140	M₁₆×C₃₇	—	2	2	no	—
141	C₂×C₈×C₃₇	—	2	2	no	—
142	C₂×C₈×C₃₇	—	2	2	no	—
143	C₄⋊C₄×C₃₇	—	2	4	no	—
144	C₄⋊C₄×C₃₇	—	2	4	no	—
145	C₄⋊C₄×C₃₇	—	2	2	no	—
146	C₄⋊C₄×C₃₇	—	2	4	no	—
147	C₄⋊C₄×C₃₇	—	2	4	no	—
148	C₄⋊C₄×C₃₇	—	2	2	no	—
149	C₄⋊C₄×C₃₇	C₂²⋊C₄	1	4	yes	—
150	C₄⋊C₄×C₃₇	C₂²⋊C₄	1	4	yes	—
151	C₄⋊C₄×C₃₇	C₂²×C₄	1	4	yes	—
152	C₂²⋊C₄×C₃₇	—	2	4	no	—
153	C₂²⋊C₄×C₃₇	—	2	4	no	—
154	C₂²⋊C₄×C₃₇	—	2	2	no	—
155	C₂²⋊C₄×C₃₇	—	2	4	no	—
156	C₂²⋊C₄×C₃₇	—	2	4	no	—
157	C₂²⋊C₄×C₃₇	—	2	4	no	—
158	C₂²⋊C₄×C₃₇	C₂²⋊C₄	1	4	yes	—
159	C₂²⋊C₄×C₃₇	C₂²⋊C₄	1	4	yes	—
160	C₄²×C₃₇	—	2	4	no	—
161	C₄²×C₃₇	—	2	4	no	—
162	C₄²×C₃₇	—	2	2	no	—
163	C₄²×C₃₇	—	2	1	no	—
164	C₄²×C₃₇	—	2	1	no	—
165	C₄²×C₃₇	—	2	1	no	—
166	C₄²×C₃₇	—	2	1	no	—
167	C₄²×C₃₇	—	4	4	no	—
168	C₄²×C₃₇	—	4	4	no	—
169	C₄²×C₃₇	C₂²×C₄	1	2	yes	—
170	C₄²×C₃₇	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₃₇	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₃₇	C₂×D₄	1	2	yes	—
173	C₄²×C₃₇	C₂×D₄	1	2	yes	—
174	C₄²×C₃₇	#41	1	2	yes	—
175	C₄²×C₃₇	#41	1	2	yes	—
176	C₄²×C₃₇	#41	1	2	yes	—
177	C₄²×C₃₇	#41	1	2	yes	—
178	C₂³×C₃₇	—	2	1	no	—
179	C₂³×C₃₇	—	2	1	no	—
180	C₂³×C₃₇	—	2	2	no	—
181	C₂³×C₃₇	—	4	2	no	—
182	C₂³×C₃₇	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₃₇	—	2	2	no	—
185	Q₈×C₃₇	—	2	2	no	—
186	Q₈×C₃₇	—	8	2	no	—
187	D₄×C₃₇	—	2	2	no	—
188	D₄×C₃₇	—	2	2	no	—
189	D₄×C₃₇	—	4	2	no	—
190	D₄×C₃₇	—	4	2	no	—
191	D₄×C₃₇	—	8	2	no	—
192	D₄×C₃₇	—	8	4	no	—
193	C₂×C₄×C₃₇	—	2	4	no	—
194	C₂×C₄×C₃₇	—	2	1	no	—
195	C₂×C₄×C₃₇	—	2	2	no	—
196	C₂×C₄×C₃₇	—	2	1	no	—
197	C₂×C₄×C₃₇	—	2	2	no	—
198	C₂×C₄×C₃₇	—	2	2	no	—
199	C₂×C₄×C₃₇	—	2	2	no	—
200	C₂×C₄×C₃₇	—	2	2	no	—
201	C₂×C₄×C₃₇	—	2	2	no	—
202	C₂×C₄×C₃₇	—	2	4	no	—
203	C₂×C₄×C₃₇	—	2	2	no	—
204	C₂×C₄×C₃₇	—	2	2	no	—
205	C₂×C₄×C₃₇	—	2	2	no	—
206	C₂×C₄×C₃₇	—	4	2	no	—
207	C₂×C₄×C₃₇	—	4	2	no	—
208	C₂×C₄×C₃₇	—	4	8	no	—
209	C₂×C₄×C₃₇	—	4	2	no	—
210	C₂×C₄×C₃₇	—	4	2	no	—
211	C₂×C₄×C₃₇	—	4	2	no	—
212	C₂×C₄×C₃₇	—	4	2	no	—
213	C₂×C₄×C₃₇	—	4	2	no	—
214	C₂×C₄×C₃₇	—	8	4	no	—
215	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	4	yes	—
216	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂×C₄×C₃₇	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
225	C₈×C₃₇	—	4	2	no	—
226	C₈×C₃₇	—	4	2	no	—
227	#21419	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂²×C₃₇	—	2	2	no	—
229	C₂²×C₃₇	—	2	4	no	—
230	C₂²×C₃₇	—	2	2	no	—
231	C₂²×C₃₇	—	4	2	no	—
232	C₂²×C₃₇	—	4	2	no	—
233	C₂²×C₃₇	—	4	4	no	—
234	C₂²×C₃₇	—	4	2	no	—
235	C₂²×C₃₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
236	C₂²×C₃₇	#525	1	1	yes	characteristic
237	C₂²×C₃₇	#525	1	1	yes	characteristic
238	C₄×C₃₇	—	2	4	no	—
239	C₄×C₃₇	—	2	4	no	—
240	C₄×C₃₇	—	2	2	no	—
241	C₄×C₃₇	—	2	2	no	—
242	C₄×C₃₇	—	2	2	no	—
243	C₄×C₃₇	—	4	2	no	—
244	C₄×C₃₇	—	4	2	no	—
245	C₄×C₃₇	—	4	2	no	—
246	C₄×C₃₇	—	4	4	no	—
247	C₄×C₃₇	—	4	2	no	—
248	C₄×C₃₇	C₄×#41	1	1	yes	characteristic
249	C₄×C₃₇	C₄×#41	1	1	yes	characteristic
250	C₄×C₃₇	#532	1	1	yes	characteristic
251	C₄×C₃₇	#532	1	1	yes	characteristic
252	#3455	C₂×C₃₇	1	1	yes	characteristic
253	#2921	C₂×C₃₇	1	1	yes	characteristic, complemented
254	C₄×#117	C₂×C₃₇	1	1	yes	characteristic, complemented
255	#1995	C₂×C₃₇	1	1	yes	characteristic, complemented
256	#1994	C₂×C₃₇	1	1	yes	characteristic, complemented
257	#1963	C₂×C₃₇	1	1	yes	characteristic, complemented
258	#1962	C₂×C₃₇	1	1	yes	characteristic, complemented
259	#1897	C₂×C₃₇	1	2	yes	complemented
260	#1896	C₂×C₃₇	1	2	yes	complemented
261	#1759	C₂×C₃₇	1	2	yes	complemented
262	C₄×#104	C₂×C₃₇	1	2	yes	complemented
263	C₂×C₃₇	—	2	1	no	—
264	C₂×C₃₇	—	2	1	no	—
265	C₂×C₃₇	—	4	2	no	—
266	C₂×C₃₇	—	8	2	no	—
267	C₂×C₃₇	#2297	1	1	yes	characteristic
268	C₂×C₃₇	#2901	1	2	yes	—
269	#542	C₄×C₃₇	1	4	yes	complemented
270	#541	C₄×C₃₇	1	2	yes	complemented
271	#540	C₄×C₃₇	1	2	yes	complemented
272	#539	—	2	2	no	—
273	#538	—	2	2	no	—
274	#533	C₂²×C₃₇	1	1	yes	characteristic
275	#532	C₂²×C₃₇	1	1	yes	characteristic
276	#529	—	2	4	no	—
277	#525	C₂²×C₃₇	1	2	yes	—
278	C₄×#41	C₂²×C₃₇	1	2	yes	—
279	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic
280	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic
281	C₂²×C₄²	C₂²×C₃₇	1	1	yes	characteristic
282	#433	—	2	4	no	—
283	#423	C₂²×C₃₇	1	1	yes	characteristic
284	#423	C₂²×C₃₇	1	1	yes	characteristic
285	C₂×#104	C₂²×C₃₇	1	2	yes	—
286	C₂×#104	C₂²×C₃₇	1	2	yes	—
287	C₂×#104	C₂²×C₃₇	1	2	yes	—
288	C₂×#104	C₂²×C₃₇	1	2	yes	—
289	#407	C₂²×C₃₇	1	2	yes	—
290	C₄×M₁₆	C₂²×C₃₇	1	2	yes	—
291	C₄×C₄⋊C₄	—	2	2	no	—
292	C₄×C₂²⋊C₄	—	2	2	no	—
293	#376	C₂²×C₃₇	1	1	yes	characteristic
294	#376	C₂²×C₃₇	1	1	yes	characteristic
295	C₄³	C₂²×C₃₇	1	1	yes	characteristic
296	C₄³	C₂²×C₃₇	1	1	yes	characteristic
297	#339	C₂²×C₃₇	1	2	yes	—
298	#339	C₂²×C₃₇	1	2	yes	—
299	#339	C₂²×C₃₇	1	2	yes	—
300	#339	C₂²×C₃₇	1	2	yes	—
301	C₃₇	#21419	1	1	yes	characteristic, direct product factor, Sylow
302	C₂×#41	C₂³×C₃₇	1	2	yes	—
303	C₂³×C₄	—	2	1	no	—
304	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
305	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
306	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
307	C₄⋊Q₈	C₂×C₄×C₃₇	1	1	yes	characteristic, complemented
308	C₄⋊Q₈	C₂×C₄×C₃₇	1	2	yes	complemented
309	#127	C₂×C₄×C₃₇	1	1	yes	characteristic, complemented
310	#126	—	2	4	no	—
311	#126	—	2	4	no	—
312	#125	—	2	4	no	—
313	#125	C₂×C₄×C₃₇	1	2	yes	complemented
314	#124	—	2	4	no	—
315	#124	C₂×C₄×C₃₇	1	2	yes	complemented
316	#123	—	2	2	no	—
317	#123	—	2	4	no	—
318	#123	—	2	4	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	—	2	4	no	—
321	C₂²⋊Q₈	C₂×C₄×C₃₇	1	4	yes	—
322	#121	—	2	2	no	—
323	#121	—	2	4	no	—
324	#121	C₂×C₄×C₃₇	1	4	yes	—
325	#120	—	2	2	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	C₂×C₄×C₃₇	1	4	yes	complemented
328	C₄×D₄	—	2	4	no	—
329	C₄×D₄	—	2	4	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	C₂×C₄×C₃₇	1	4	yes	complemented
332	#117	—	2	2	no	—
333	#117	—	2	2	no	—
334	#117	—	2	2	no	—
335	#117	C₂×C₄×C₃₇	1	2	yes	—
336	#117	C₂×C₄×C₃₇	1	2	yes	—
337	#117	D₄×C₃₇	1	4	yes	—
338	#117	C₂³×C₃₇	1	2	yes	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	D₄×C₃₇	1	2	yes	—
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	—	2	2	no	—
345	C₂×C₄²	—	2	2	no	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	—	2	2	no	—
349	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
350	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
351	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
355	C₄⋊C₈	—	2	2	no	—
356	C₄⋊C₈	—	2	2	no	—
357	#104	—	2	4	no	—
358	#104	—	2	4	no	—
359	#104	—	2	4	no	—
360	#104	—	2	4	no	—
361	C₂²⋊C₈	—	2	4	no	—
362	#97	—	2	2	no	—
363	C₄×C₈	—	2	2	no	—
364	#95	—	2	2	no	—
365	#95	—	2	2	no	—
366	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
367	#41	—	2	2	no	—
368	#41	—	2	2	no	—
369	#41	—	2	2	no	—
370	#41	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	C₂²×C₄×C₃₇	1	2	yes	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	C₂²×C₄×C₃₇	1	2	yes	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	4	4	no	—
389	C₂²×C₄	C₂²×C₄×C₃₇	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
392	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
393	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
394	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
395	M₁₆	—	2	2	no	—
396	M₁₆	—	2	2	no	—
397	M₁₆	—	2	2	no	—
398	M₁₆	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	C₂²⋊C₄×C₃₇	1	4	yes	—
408	C₄⋊C₄	C₂²⋊C₄×C₃₇	1	4	yes	—
409	C₄⋊C₄	C₂²×C₄×C₃₇	1	4	yes	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	C₂²⋊C₄×C₃₇	1	4	yes	—
417	C₂²⋊C₄	C₂²⋊C₄×C₃₇	1	4	yes	—
418	C₄²	—	2	4	no	—
419	C₄²	—	2	4	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	4	4	no	—
426	C₄²	—	4	4	no	—
427	C₄²	C₂²×C₄×C₃₇	1	2	yes	—
428	C₄²	C₂²×C₄×C₃₇	1	1	yes	characteristic
429	C₄²	C₂²×C₄×C₃₇	1	1	yes	characteristic
430	C₄²	C₂×D₄×C₃₇	1	2	yes	—
431	C₄²	C₂×D₄×C₃₇	1	2	yes	—
432	C₄²	#41×C₃₇	1	2	yes	—
433	C₄²	#41×C₃₇	1	2	yes	—
434	C₄²	#41×C₃₇	1	2	yes	—
435	C₄²	#41×C₃₇	1	2	yes	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	C₂×C₂²⋊C₄×C₃₇	1	2	yes	—
441	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
442	Q₈	—	2	2	no	—
443	Q₈	—	2	2	no	—
444	Q₈	—	8	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	8	2	no	—
450	D₄	—	8	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	8	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	8	4	no	—
473	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	4	yes	—
474	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	2	yes	—
475	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	2	yes	—
476	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	2	yes	—
477	C₂×C₄	C₂³×C₄×C₃₇	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
479	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
480	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
481	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
482	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
483	C₈	—	4	2	no	—
484	C₈	—	4	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	2	no	—
492	C₂²	C₂²×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
493	C₂²	C₃₇×#525	1	1	yes	characteristic
494	C₂²	C₃₇×#525	1	1	yes	characteristic
495	C₄	—	2	4	no	—
496	C₄	—	2	4	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	4	no	—
504	C₄	—	4	2	no	—
505	C₄	C₄×#41×C₃₇	1	1	yes	characteristic
506	C₄	C₄×#41×C₃₇	1	1	yes	characteristic
507	C₄	C₃₇×#532	1	1	yes	characteristic
508	C₄	C₃₇×#532	1	1	yes	characteristic
509	C₂	—	2	1	no	—
510	C₂	—	2	1	no	—
511	C₂	—	4	2	no	—
512	C₂	—	8	2	no	—
513	C₂	C₃₇×#2297	1	1	yes	characteristic
514	C₂	C₃₇×#2901	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
socle	C₂²×C₃₇	C₂²×C₂²⋊C₄
prime radical	C₃₇×#3455	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ C₂×#117×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#2921	C₂	semidirect
3. C₄×#117×C₃₇	C₂	semidirect
4. C₃₇×#1995	C₂	semidirect
5. C₃₇×#1994	C₂	semidirect
6. C₃₇×#1963	C₂	semidirect
7. C₃₇×#1962	C₂	semidirect
8. C₃₇×#1897	C₂	semidirect
9. C₃₇×#1896	C₂	semidirect
10. C₃₇×#1759	C₂	semidirect
11. C₄×#104×C₃₇	C₂	semidirect
12. C₃₇×#542	C₄	semidirect
13. C₃₇×#541	C₄	semidirect
14. C₃₇×#540	C₄	semidirect
49. C₄⋊Q₈×C₃₇	C₂×C₄	semidirect
50. C₄⋊Q₈×C₃₇	C₂×C₄	semidirect
51. #127×C₃₇	C₂×C₄	semidirect
55. #125×C₃₇	C₂×C₄	semidirect
57. #124×C₃₇	C₂×C₄	semidirect
69. C₄×Q₈×C₃₇	C₂×C₄	semidirect
73. C₄×D₄×C₃₇	C₂×C₄	semidirect
227. #21419	C₃₇	direct (N × H)
253. #2921	C₂×C₃₇	semidirect
254. C₄×#117	C₂×C₃₇	semidirect
255. #1995	C₂×C₃₇	semidirect
256. #1994	C₂×C₃₇	semidirect
257. #1963	C₂×C₃₇	semidirect
258. #1962	C₂×C₃₇	semidirect
259. #1897	C₂×C₃₇	semidirect
260. #1896	C₂×C₃₇	semidirect
261. #1759	C₂×C₃₇	semidirect
262. C₄×#104	C₂×C₃₇	semidirect
269. #542	C₄×C₃₇	semidirect
270. #541	C₄×C₃₇	semidirect
271. #540	C₄×C₃₇	semidirect
301. C₃₇	#21419	direct (N × H)
307. C₄⋊Q₈	C₂×C₄×C₃₇	semidirect
308. C₄⋊Q₈	C₂×C₄×C₃₇	semidirect
309. #127	C₂×C₄×C₃₇	semidirect
313. #125	C₂×C₄×C₃₇	semidirect
315. #124	C₂×C₄×C₃₇	semidirect
327. C₄×Q₈	C₂×C₄×C₃₇	semidirect
331. C₄×D₄	C₂×C₄×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3455	2
C₃₇×#2921	2
C₄×#117×C₃₇	2
C₃₇×#1995	2
C₃₇×#1994	2
C₃₇×#1963	2
C₃₇×#1962	2
C₃₇×#1897	2
C₃₇×#1896	2
C₃₇×#1759	2
C₄×#104×C₃₇	2
#21419	37

Subgroups — C37×#21419 #22642672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#21419 #22642672