Subgroups — C₃₇×#28295 #22649548

Order 9472.

738 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3077	C₂	1	2	yes	maximal, complemented
2	C₃₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₈×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2063	C₂	1	4	yes	maximal, complemented
5	C₃₇×#1978	C₂	1	2	yes	maximal
6	C₃₇×#1952	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1848	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1800	C₂	1	2	yes	maximal, complemented
9	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
10	C₃₇×#533	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	—
12	C₃₇×#478	—	2	4	no	—
13	C₃₇×#476	—	2	2	no	—
14	C₃₇×#474	—	2	2	no	—
15	C₃₇×#446	—	2	1	no	—
16	C₃₇×#446	—	2	1	no	—
17	C₈×Q₈×C₃₇	—	2	1	no	—
18	C₈×Q₈×C₃₇	—	2	1	no	—
19	C₄×D₈×C₃₇	—	2	1	no	—
20	C₄×D₈×C₃₇	—	2	1	no	—
21	C₄×D₈×C₃₇	—	2	1	no	—
22	C₄×D₈×C₃₇	—	2	1	no	—
23	C₂×#108×C₃₇	C₂²	1	2	yes	—
24	C₂×#108×C₃₇	C₂²	1	2	yes	—
25	C₃₇×#428	C₂²	1	4	yes	—
26	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
27	C₃₇×#424	C₂²	1	2	yes	—
28	C₃₇×#423	C₂²	1	2	yes	—
29	C₃₇×#423	C₂²	1	1	yes	characteristic
30	C₃₇×#418	C₂²	1	4	yes	—
31	C₂×#102×C₃₇	C₂²	1	2	yes	—
32	C₂×#100×C₃₇	C₂²	1	4	yes	—
33	C₃₇×#405	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
35	C₃₇×#343	C₂²	1	4	yes	—
36	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
37	C₂³×C₄×C₃₇	—	2	2	no	—
38	C₂×D₈×C₃₇	—	2	1	no	—
39	C₂×D₈×C₃₇	—	2	1	no	—
40	C₂×D₈×C₃₇	—	2	2	no	—
41	C₂×D₈×C₃₇	Q₈	1	4	yes	complemented
42	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
43	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
44	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
46	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
47	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
48	#125×C₃₇	D₄	1	2	yes	—
49	C₂²⋊Q₈×C₃₇	—	2	1	no	—
50	C₂²⋊Q₈×C₃₇	—	2	1	no	—
51	C₄×Q₈×C₃₇	—	2	1	no	—
52	C₄×Q₈×C₃₇	—	2	1	no	—
53	C₄×D₄×C₃₇	—	2	2	no	—
54	C₄×D₄×C₃₇	—	2	2	no	—
55	C₄×D₄×C₃₇	—	2	2	no	—
56	C₄×D₄×C₃₇	—	2	2	no	—
57	#117×C₃₇	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
59	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
60	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
61	#108×C₃₇	—	2	4	no	—
62	#108×C₃₇	—	4	2	no	—
63	#107×C₃₇	—	2	1	no	—
64	#107×C₃₇	—	2	1	no	—
65	#107×C₃₇	—	2	4	no	—
66	#106×C₃₇	—	2	4	no	—
67	C₄⋊C₈×C₃₇	—	2	2	no	—
68	C₄⋊C₈×C₃₇	—	2	2	no	—
69	C₄⋊C₈×C₃₇	—	2	1	no	—
70	C₄⋊C₈×C₃₇	—	2	1	no	—
71	C₄⋊C₈×C₃₇	—	2	2	no	—
72	C₄⋊C₈×C₃₇	—	2	2	no	—
73	#102×C₃₇	—	2	2	no	—
74	#102×C₃₇	—	2	2	no	—
75	#102×C₃₇	—	2	4	no	—
76	#102×C₃₇	—	2	4	no	—
77	#100×C₃₇	—	4	4	no	—
78	#97×C₃₇	—	2	2	no	—
79	C₄×C₈×C₃₇	—	2	2	no	—
80	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
81	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
82	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
83	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
84	C₂⁴×C₃₇	—	2	2	no	—
85	C₂×Q₈×C₃₇	—	2	1	no	—
86	C₂×Q₈×C₃₇	—	2	1	no	—
87	C₂×D₄×C₃₇	—	2	2	no	—
88	C₂×D₄×C₃₇	—	2	2	no	—
89	C₂×D₄×C₃₇	—	2	2	no	—
90	C₂×D₄×C₃₇	—	2	2	no	—
91	C₂×D₄×C₃₇	—	2	2	no	—
92	C₂×D₄×C₃₇	C₂×Q₈	1	4	yes	—
93	C₂²×C₄×C₃₇	—	2	2	no	—
94	C₂²×C₄×C₃₇	—	4	2	no	—
95	C₂²×C₄×C₃₇	—	4	2	no	—
96	C₂²×C₄×C₃₇	—	8	4	no	—
97	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
98	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
99	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
100	D₈×C₃₇	—	2	4	no	—
101	D₈×C₃₇	—	2	4	no	—
102	M₁₆×C₃₇	—	2	4	no	—
103	M₁₆×C₃₇	—	2	2	no	—
104	M₁₆×C₃₇	—	2	4	no	—
105	M₁₆×C₃₇	—	2	2	no	—
106	C₂×C₈×C₃₇	—	2	1	no	—
107	C₂×C₈×C₃₇	—	2	1	no	—
108	C₂×C₈×C₃₇	—	2	2	no	—
109	C₂×C₈×C₃₇	—	2	4	no	—
110	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₃₇	C₂×Q₈	1	2	yes	—
115	C₂×C₈×C₃₇	#41	1	2	yes	—
116	C₄⋊C₄×C₃₇	—	2	2	no	—
117	C₄⋊C₄×C₃₇	—	2	2	no	—
118	C₄⋊C₄×C₃₇	—	2	1	no	—
119	C₄⋊C₄×C₃₇	—	2	1	no	—
120	C₄⋊C₄×C₃₇	—	2	2	no	—
121	C₄⋊C₄×C₃₇	—	2	2	no	—
122	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
123	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
124	C₂²⋊C₄×C₃₇	—	2	2	no	—
125	C₂²⋊C₄×C₃₇	—	4	2	no	—
126	C₂²⋊C₄×C₃₇	—	4	2	no	—
127	C₄²×C₃₇	—	2	2	no	—
128	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
132	C₂³×C₃₇	—	2	4	no	—
133	C₂³×C₃₇	—	4	2	no	—
134	C₂³×C₃₇	—	4	2	no	—
135	C₂³×C₃₇	—	8	2	no	—
136	C₂³×C₃₇	—	8	2	no	—
137	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
138	Q₈×C₃₇	—	4	2	no	—
139	Q₈×C₃₇	—	4	2	no	—
140	D₄×C₃₇	—	2	4	no	—
141	D₄×C₃₇	—	2	4	no	—
142	D₄×C₃₇	—	4	2	no	—
143	D₄×C₃₇	—	4	2	no	—
144	C₂×C₄×C₃₇	—	2	2	no	—
145	C₂×C₄×C₃₇	—	2	2	no	—
146	C₂×C₄×C₃₇	—	2	2	no	—
147	C₂×C₄×C₃₇	—	4	1	no	—
148	C₂×C₄×C₃₇	—	4	2	no	—
149	C₂×C₄×C₃₇	—	8	4	no	—
150	C₂×C₄×C₃₇	—	8	4	no	—
151	C₂×C₄×C₃₇	—	8	2	no	—
152	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
153	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
154	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
155	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
156	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
159	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
162	C₈×C₃₇	—	2	1	no	—
163	C₈×C₃₇	—	2	1	no	—
164	C₈×C₃₇	—	4	2	no	—
165	C₈×C₃₇	—	4	4	no	—
166	C₈×C₃₇	C₂²⋊Q₈	1	2	yes	—
167	C₈×C₃₇	C₂²⋊Q₈	1	2	yes	—
168	#28295	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂²×C₃₇	—	2	1	no	—
170	C₂²×C₃₇	—	2	1	no	—
171	C₂²×C₃₇	—	4	4	no	—
172	C₂²×C₃₇	—	8	4	no	—
173	C₂²×C₃₇	—	8	4	no	—
174	C₂²×C₃₇	—	8	2	no	—
175	C₂²×C₃₇	—	8	2	no	—
176	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
177	C₂²×C₃₇	#554	1	1	yes	characteristic
178	C₂²×C₃₇	#556	1	1	yes	characteristic
179	C₄×C₃₇	—	2	1	no	—
180	C₄×C₃₇	—	2	1	no	—
181	C₄×C₃₇	—	2	1	no	—
182	C₄×C₃₇	—	4	2	no	—
183	C₄×C₃₇	—	4	2	no	—
184	C₄×C₃₇	—	8	2	no	—
185	C₄×C₃₇	#472	1	2	yes	—
186	C₄×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
187	C₄×C₃₇	#537	1	1	yes	characteristic
188	C₄×C₃₇	D₄×Q₈	1	1	yes	characteristic
189	C₄×C₃₇	#550	1	1	yes	characteristic
190	#3077	C₂×C₃₇	1	2	yes	complemented
191	#2960	C₂×C₃₇	1	1	yes	characteristic, complemented
192	C₂×C₄×D₈	C₂×C₃₇	1	1	yes	characteristic
193	#2063	C₂×C₃₇	1	4	yes	complemented
194	#1978	C₂×C₃₇	1	2	yes	—
195	#1952	C₂×C₃₇	1	2	yes	complemented
196	#1848	C₂×C₃₇	1	1	yes	characteristic, complemented
197	#1800	C₂×C₃₇	1	2	yes	complemented
198	C₂×C₃₇	—	2	1	no	—
199	C₂×C₃₇	—	2	1	no	—
200	C₂×C₃₇	—	8	4	no	—
201	C₂×C₃₇	#2538	1	1	yes	characteristic
202	C₂×C₃₇	C₂×#472	1	1	yes	characteristic
203	C₂×C₃₇	#3067	1	1	yes	characteristic
204	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
205	#533	C₂²×C₃₇	1	1	yes	characteristic
206	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	—
207	#478	—	2	4	no	—
208	#476	—	2	2	no	—
209	#474	—	2	2	no	—
210	#446	—	2	1	no	—
211	#446	—	2	1	no	—
212	C₈×Q₈	—	2	1	no	—
213	C₈×Q₈	—	2	1	no	—
214	C₄×D₈	—	2	1	no	—
215	C₄×D₈	—	2	1	no	—
216	C₄×D₈	—	2	1	no	—
217	C₄×D₈	—	2	1	no	—
218	C₂×#108	C₂²×C₃₇	1	2	yes	—
219	C₂×#108	C₂²×C₃₇	1	2	yes	—
220	#428	C₂²×C₃₇	1	4	yes	—
221	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
222	#424	C₂²×C₃₇	1	2	yes	—
223	#423	C₂²×C₃₇	1	2	yes	—
224	#423	C₂²×C₃₇	1	1	yes	characteristic
225	#418	C₂²×C₃₇	1	4	yes	—
226	C₂×#102	C₂²×C₃₇	1	2	yes	—
227	C₂×#100	C₂²×C₃₇	1	4	yes	—
228	#405	C₂²×C₃₇	1	2	yes	—
229	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
230	#343	C₂²×C₃₇	1	4	yes	—
231	C₃₇	#28295	1	1	yes	characteristic, direct product factor, Sylow
232	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
233	C₂³×C₄	—	2	2	no	—
234	C₂×D₈	—	2	1	no	—
235	C₂×D₈	—	2	1	no	—
236	C₂×D₈	—	2	2	no	—
237	C₂×D₈	Q₈×C₃₇	1	4	yes	complemented
238	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
239	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
240	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
242	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
243	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
244	#125	D₄×C₃₇	1	2	yes	—
245	C₂²⋊Q₈	—	2	1	no	—
246	C₂²⋊Q₈	—	2	1	no	—
247	C₄×Q₈	—	2	1	no	—
248	C₄×Q₈	—	2	1	no	—
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	—	2	2	no	—
253	#117	C₂³×C₃₇	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
257	#108	—	2	4	no	—
258	#108	—	4	2	no	—
259	#107	—	2	1	no	—
260	#107	—	2	1	no	—
261	#107	—	2	4	no	—
262	#106	—	2	4	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	2	no	—
269	#102	—	2	2	no	—
270	#102	—	2	2	no	—
271	#102	—	2	4	no	—
272	#102	—	2	4	no	—
273	#100	—	4	4	no	—
274	#97	—	2	2	no	—
275	C₄×C₈	—	2	2	no	—
276	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
277	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
278	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
279	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
280	C₂⁴	—	2	2	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	C₂×Q₈×C₃₇	1	4	yes	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	8	4	no	—
293	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
294	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
295	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
296	D₈	—	2	4	no	—
297	D₈	—	2	4	no	—
298	M₁₆	—	2	4	no	—
299	M₁₆	—	2	2	no	—
300	M₁₆	—	2	4	no	—
301	M₁₆	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
307	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
308	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
309	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
310	C₂×C₈	C₂×Q₈×C₃₇	1	2	yes	—
311	C₂×C₈	#41×C₃₇	1	2	yes	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
319	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
325	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
326	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
327	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
328	C₂³	—	2	4	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	8	2	no	—
332	C₂³	—	8	2	no	—
333	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
334	Q₈	—	4	2	no	—
335	Q₈	—	4	2	no	—
336	D₄	—	2	4	no	—
337	D₄	—	2	4	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	8	4	no	—
346	C₂×C₄	—	8	4	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
349	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
350	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
351	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
352	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
353	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
354	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
355	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
356	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
357	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	4	2	no	—
361	C₈	—	4	4	no	—
362	C₈	C₂²⋊Q₈×C₃₇	1	2	yes	—
363	C₈	C₂²⋊Q₈×C₃₇	1	2	yes	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	8	4	no	—
368	C₂²	—	8	4	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
372	C₂²	C₃₇×#554	1	1	yes	characteristic
373	C₂²	C₃₇×#556	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	8	2	no	—
380	C₄	C₃₇×#472	1	2	yes	—
381	C₄	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
382	C₄	C₃₇×#537	1	1	yes	characteristic
383	C₄	D₄×Q₈×C₃₇	1	1	yes	characteristic
384	C₄	C₃₇×#550	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	8	4	no	—
388	C₂	C₃₇×#2538	1	1	yes	characteristic
389	C₂	C₂×C₃₇×#472	1	1	yes	characteristic
390	C₂	C₃₇×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂²×D₈×C₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3077	C₂	semidirect
2. C₃₇×#2960	C₂	semidirect
4. C₃₇×#2063	C₂	semidirect
6. C₃₇×#1952	C₂	semidirect
7. C₃₇×#1848	C₂	semidirect
8. C₃₇×#1800	C₂	semidirect
41. C₂×D₈×C₃₇	Q₈	semidirect
168. #28295	C₃₇	direct (N × H)
190. #3077	C₂×C₃₇	semidirect
191. #2960	C₂×C₃₇	semidirect
193. #2063	C₂×C₃₇	semidirect
195. #1952	C₂×C₃₇	semidirect
196. #1848	C₂×C₃₇	semidirect
197. #1800	C₂×C₃₇	semidirect
231. C₃₇	#28295	direct (N × H)
237. C₂×D₈	Q₈×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3077	2
C₃₇×#2960	2
C₂×C₄×D₈×C₃₇	2
C₃₇×#2063	2
C₃₇×#1978	2
C₃₇×#1952	2
C₃₇×#1848	2
C₃₇×#1800	2
#28295	37

Subgroups — C37×#28295 #22649548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28295 #22649548