Subgroups — #465×D₃₇ #18004152

Order 4736.

564 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₈×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊Q₈×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#121×D₃₇	C₂	1	1	yes	maximal, characteristic
5	#14557765	C₂	1	1	yes	maximal, characteristic, complemented
6	#14557764	C₂	1	1	yes	maximal, characteristic, complemented
7	#14557763	C₂	1	1	yes	maximal, characteristic, complemented
8	#14557762	C₂	1	1	yes	maximal, characteristic, complemented
9	#14557761	C₂	1	1	yes	maximal, characteristic, complemented
10	#14557760	C₂	1	1	yes	maximal, characteristic, complemented
11	#14557759	C₂	1	1	yes	maximal, characteristic, complemented
12	#106×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#103×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#102×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#465	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₃₇	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₃₇	—	2	1	no	—
18	C₂×D₄×D₃₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₃₇	C₂²	1	1	yes	characteristic
20	C₂×#10596930	C₂²	1	1	yes	characteristic, complemented
21	C₂×#10596940	C₂²	1	1	yes	characteristic, complemented
22	C₂×#10596941	C₂²	1	1	yes	characteristic, complemented
23	SD₁₆×D₃₇	—	2	4	no	—
24	C₂²×#64436	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₈×D₃₇	—	2	4	no	—
26	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic, complemented
30	#11924516	C₂²	1	1	yes	characteristic, complemented
31	#11924515	C₂²	1	1	yes	characteristic, complemented
32	#11924514	—	2	1	no	—
33	#11924513	—	2	1	no	—
34	#11924512	C₂²	1	1	yes	characteristic, complemented
35	#11924511	C₂²	1	1	yes	characteristic
36	#11924510	C₂²	1	1	yes	characteristic
37	#11924509	—	2	1	no	—
38	#11924508	—	2	1	no	—
39	#11924507	C₂²	1	1	yes	characteristic
40	C₄⋊C₄×D₃₇	—	2	1	no	—
41	C₄⋊C₄×D₃₇	C₂²	1	1	yes	characteristic
42	C₄⋊C₄×D₃₇	C₂²	1	1	yes	characteristic
43	C₂²⋊C₄×D₃₇	—	2	1	no	—
44	C₂²⋊C₄×D₃₇	—	2	1	no	—
45	#11924468	C₂²	1	1	yes	characteristic, complemented
46	#11924467	C₂²	1	1	yes	characteristic, complemented
47	#11924467	C₂²	1	1	yes	characteristic, complemented
48	#11924461	C₂²	1	1	yes	characteristic, complemented
49	#11924460	C₂²	1	1	yes	characteristic, complemented
50	#11924459	C₂²	1	1	yes	characteristic, complemented
51	#11924458	C₂²	1	1	yes	characteristic, complemented
52	#11924457	C₂²	1	1	yes	characteristic, complemented
53	#11924456	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
57	#121×C₃₇	C₂²	1	1	yes	characteristic
58	#106×C₃₇	C₂²	1	1	yes	characteristic, complemented
59	#103×C₃₇	C₂²	1	1	yes	characteristic, complemented
60	#102×C₃₇	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₃₇	—	2	1	no	—
62	C₂³×D₃₇	D₄	1	1	yes	characteristic
63	C₂×Q₈×C₃₇	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₃₇	—	2	1	no	—
65	C₂×D₄×C₃₇	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊D₃₇	—	2	1	no	—
68	C₂×C₂²⋊D₃₇	—	2	1	no	—
69	C₂×C₂²⋊D₃₇	—	2	1	no	—
70	C₂²×Dic₃₇	D₄	1	1	yes	characteristic
71	Q₈×D₃₇	—	2	2	no	—
72	Q₈×D₃₇	—	2	2	no	—
73	D₄×D₃₇	—	2	2	no	—
74	D₄×D₃₇	—	2	2	no	—
75	D₄×D₃₇	—	4	4	no	—
76	C₂×D₁₄₈	—	2	1	no	—
77	C₂×D₁₄₈	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₃₇	—	2	2	no	—
79	C₂×C₄×D₃₇	—	2	2	no	—
80	C₂×C₄×D₃₇	—	2	1	no	—
81	C₂×C₄×D₃₇	—	2	1	no	—
82	C₂×C₄×D₃₇	—	2	1	no	—
83	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
84	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
85	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
86	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
87	C₂×Dic₇₄	—	2	1	no	—
88	C₂×Dic₇₄	C₂³	1	1	yes	characteristic
89	SD₁₆×C₃₇	—	2	2	no	—
90	C₂×C₈×C₃₇	—	2	2	no	—
91	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
92	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
93	C₄⋊C₄×C₃₇	—	2	1	no	—
94	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
95	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
96	C₂²⋊C₄×C₃₇	—	2	1	no	—
97	C₂²⋊C₄×C₃₇	—	2	1	no	—
98	C₂²⋊Dic₃₇	—	2	1	no	—
99	C₂²⋊Dic₃₇	—	2	1	no	—
100	#10596941	—	2	2	no	—
101	#10596940	—	2	2	no	—
102	#10596938	—	2	1	no	—
103	#10596938	—	2	1	no	—
104	#10596938	—	2	1	no	—
105	#10596938	—	2	1	no	—
106	C₄⋊Dic₃₇	—	2	1	no	—
107	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
108	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
109	#10596936	—	2	1	no	—
110	#10596936	—	2	1	no	—
111	#10596936	—	2	1	no	—
112	#10596936	—	2	1	no	—
113	C₂×#64436	—	2	2	no	—
114	C₂×#64436	C₂³	1	1	yes	characteristic
115	C₂×#64436	C₂³	1	1	yes	characteristic
116	#10596930	—	2	2	no	—
117	C₈×D₃₇	—	2	2	no	—
118	C₈×D₃₇	—	2	2	no	—
119	C₈×D₃₇	—	2	2	no	—
120	C₈×D₃₇	D₄	1	4	yes	complemented
121	C₂³×C₃₇	—	2	1	no	—
122	C₂³×C₃₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×D₃₇	—	2	2	no	—
124	C₂²×D₃₇	—	2	2	no	—
125	C₂²×D₃₇	—	2	1	no	—
126	C₂²×D₃₇	—	4	2	no	—
127	C₂²×D₃₇	—	4	2	no	—
128	C₂²×D₃₇	—	4	2	no	—
129	C₂²×D₃₇	SD₁₆	1	4	yes	complemented
130	C₂²×D₃₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×D₃₇	C₂×D₄	1	1	yes	characteristic
132	Q₈×C₃₇	—	2	1	no	—
133	Q₈×C₃₇	—	2	1	no	—
134	D₄×C₃₇	—	2	1	no	—
135	D₄×C₃₇	—	2	1	no	—
136	D₄×C₃₇	—	4	2	no	—
137	C₂×C₄×C₃₇	—	2	1	no	—
138	C₂×C₄×C₃₇	—	2	1	no	—
139	C₂×C₄×C₃₇	—	2	1	no	—
140	C₂×C₄×C₃₇	—	2	1	no	—
141	C₂×C₄×C₃₇	—	2	1	no	—
142	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
144	C₂²⋊D₃₇	—	4	2	no	—
145	C₂²⋊D₃₇	—	4	2	no	—
146	C₂²⋊D₃₇	—	4	2	no	—
147	C₂×Dic₃₇	—	2	2	no	—
148	C₂×Dic₃₇	—	2	1	no	—
149	C₂×Dic₃₇	—	2	1	no	—
150	C₂×Dic₃₇	—	2	1	no	—
151	C₂×Dic₃₇	C₂×D₄	1	1	yes	characteristic
152	C₂×Dic₃₇	C₂×D₄	1	1	yes	characteristic
153	D₁₄₈	—	2	1	no	—
154	D₁₄₈	—	2	1	no	—
155	D₁₄₈	—	4	2	no	—
156	C₄×D₃₇	—	2	2	no	—
157	C₄×D₃₇	—	2	1	no	—
158	C₄×D₃₇	—	2	1	no	—
159	C₄×D₃₇	—	2	2	no	—
160	C₄×D₃₇	—	4	2	no	—
161	C₄×D₃₇	—	4	2	no	—
162	C₄×D₃₇	—	4	2	no	—
163	C₄×D₃₇	C₂×D₄	1	2	yes	—
164	C₄×D₃₇	#41	1	2	yes	—
165	Dic₇₄	—	2	1	no	—
166	Dic₇₄	—	2	1	no	—
167	Dic₇₄	—	4	2	no	—
168	C₈×C₃₇	—	2	1	no	—
169	C₈×C₃₇	C₂×D₄	1	2	yes	complemented
170	#64436	—	2	1	no	—
171	#64436	C₂×D₄	1	2	yes	complemented
172	C₂²×C₃₇	—	2	1	no	—
173	C₂²×C₃₇	—	2	1	no	—
174	C₂²×C₃₇	—	4	1	no	—
175	C₂²×C₃₇	—	4	1	no	—
176	C₂²×C₃₇	—	4	1	no	—
177	C₂²×C₃₇	C₂×SD₁₆	1	2	yes	complemented
178	C₂²×C₃₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×D₃₇	—	2	1	no	—
180	C₂×D₃₇	—	2	1	no	—
181	C₂×D₃₇	—	2	8	no	—
182	C₂×D₃₇	—	4	1	no	—
183	C₂×D₃₇	—	4	1	no	—
184	C₂×D₃₇	—	4	1	no	—
185	C₂×D₃₇	—	8	4	no	—
186	C₂×D₃₇	#121	1	2	yes	—
187	C₂×D₃₇	C₂×SD₁₆	1	2	yes	—
188	C₂×D₃₇	C₂×SD₁₆	1	2	yes	complemented
189	C₂×D₃₇	#135	1	2	yes	—
190	C₄×C₃₇	—	2	1	no	—
191	C₄×C₃₇	—	4	1	no	—
192	C₄×C₃₇	—	4	1	no	—
193	C₄×C₃₇	—	4	1	no	—
194	C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
195	C₄×C₃₇	C₂×#41	1	1	yes	characteristic
196	Dic₃₇	—	2	1	no	—
197	Dic₃₇	—	4	1	no	—
198	Dic₃₇	—	4	1	no	—
199	Dic₃₇	—	4	1	no	—
200	Dic₃₇	#121	1	2	yes	—
201	C₂×#465	—	37	1	no	maximal, Sylow
202	C₂×C₃₇	—	2	2	no	—
203	C₂×C₃₇	—	8	1	no	—
204	C₂×C₃₇	C₂×#121	1	1	yes	characteristic
205	C₂×C₃₇	C₂²×SD₁₆	1	1	yes	characteristic
206	C₂×C₃₇	C₂×#135	1	1	yes	characteristic
207	D₃₇	—	2	2	no	—
208	D₃₇	—	8	1	no	—
209	D₃₇	#465	1	4	yes	direct product factor
210	C₂²×SD₁₆	—	37	1	no	—
211	C₂³×C₈	—	37	1	no	—
212	C₂×C₂²⋊Q₈	—	37	1	no	—
213	C₂×#121	—	37	1	no	—
214	#465	—	37	1	no	—
215	#465	—	37	1	no	—
216	#465	—	37	1	no	—
217	#465	—	37	1	no	—
218	#465	—	37	1	no	—
219	#465	—	37	1	no	—
220	#465	—	37	1	no	—
221	#465	D₃₇	1	1	yes	characteristic, direct product factor
222	C₂×#106	—	37	1	no	—
223	C₂×#103	—	37	1	no	—
224	C₂×#102	—	37	1	no	—
225	C₃₇	C₂×#465	1	1	yes	characteristic, complemented, Sylow
226	C₂²×Q₈	—	37	1	no	—
227	C₂²×D₄	—	37	1	no	—
228	C₂²×D₄	—	74	1	no	—
229	C₂³×C₄	—	37	1	no	—
230	C₂×SD₁₆	—	37	1	no	—
231	C₂×SD₁₆	—	37	1	no	—
232	C₂×SD₁₆	—	37	1	no	—
233	C₂×SD₁₆	—	74	4	no	—
234	C₂×SD₁₆	C₂×D₃₇	1	1	yes	characteristic, complemented
235	C₂²×C₈	—	37	1	no	—
236	C₂²×C₈	—	37	1	no	—
237	C₂²×C₈	—	37	1	no	—
238	C₂²×C₈	—	37	1	no	—
239	C₂²×C₈	—	37	1	no	—
240	C₂²×C₈	—	74	4	no	—
241	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic, complemented
242	C₂²⋊Q₈	—	37	1	no	—
243	C₂²⋊Q₈	—	37	1	no	—
244	C₂²⋊Q₈	—	37	1	no	—
245	C₂²⋊Q₈	—	74	1	no	—
246	C₂²⋊Q₈	—	74	1	no	—
247	C₂²⋊Q₈	C₂×D₃₇	1	1	yes	characteristic, complemented
248	#121	—	37	1	no	—
249	#121	—	37	1	no	—
250	#121	—	37	1	no	—
251	#121	—	74	1	no	—
252	#121	—	74	1	no	—
253	#121	C₂×D₃₇	1	1	yes	characteristic
254	C₂×C₄⋊C₄	—	37	1	no	—
255	C₂×C₄⋊C₄	—	37	1	no	—
256	C₂×C₄⋊C₄	—	74	1	no	—
257	C₂×C₂²⋊C₄	—	74	1	no	—
258	C₂×C₂²⋊C₄	—	74	1	no	—
259	#106	—	37	1	no	—
260	#106	—	37	1	no	—
261	#106	—	37	1	no	—
262	#106	C₂×D₃₇	1	1	yes	characteristic, complemented
263	#103	—	37	1	no	—
264	#103	—	37	1	no	—
265	#103	—	37	1	no	—
266	#103	C₂×D₃₇	1	1	yes	characteristic, complemented
267	#102	—	37	1	no	—
268	#102	—	37	1	no	—
269	#102	—	37	1	no	—
270	#102	C₂×D₃₇	1	1	yes	characteristic, complemented
271	C₂⁴	—	37	1	no	—
272	C₂⁴	—	74	1	no	—
273	C₂×Q₈	—	37	1	no	—
274	C₂×Q₈	—	74	1	no	—
275	C₂×Q₈	—	74	2	no	—
276	C₂×Q₈	—	74	2	no	—
277	C₂×Q₈	C₂²×D₃₇	1	1	yes	characteristic
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	37	1	no	—
280	C₂×D₄	—	74	1	no	—
281	C₂×D₄	—	74	2	no	—
282	C₂×D₄	—	74	2	no	—
283	C₂×D₄	—	74	1	no	—
284	C₂×D₄	—	74	1	no	—
285	C₂×D₄	—	74	1	no	—
286	C₂×D₄	—	148	4	no	—
287	C₂×D₄	C₂²×D₃₇	1	1	yes	characteristic
288	C₂²×C₄	—	37	1	no	—
289	C₂²×C₄	—	37	1	no	—
290	C₂²×C₄	—	37	1	no	—
291	C₂²×C₄	—	37	1	no	—
292	C₂²×C₄	—	37	1	no	—
293	C₂²×C₄	—	74	2	no	—
294	C₂²×C₄	—	74	2	no	—
295	C₂²×C₄	—	74	1	no	—
296	C₂²×C₄	—	74	1	no	—
297	C₂²×C₄	—	74	1	no	—
298	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
299	SD₁₆	—	2	2	no	—
300	SD₁₆	—	74	2	no	—
301	SD₁₆	—	74	2	no	—
302	SD₁₆	—	74	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	37	1	no	—
305	C₂×C₈	—	37	4	no	—
306	C₂×C₈	—	37	1	no	—
307	C₂×C₈	—	74	2	no	—
308	C₂×C₈	—	74	2	no	—
309	C₂×C₈	—	74	2	no	—
310	C₂×C₈	—	74	2	no	—
311	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
312	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	37	1	no	—
315	C₄⋊C₄	—	37	1	no	—
316	C₄⋊C₄	—	74	1	no	—
317	C₄⋊C₄	—	74	1	no	—
318	C₄⋊C₄	—	74	1	no	—
319	C₄⋊C₄	—	74	1	no	—
320	C₄⋊C₄	—	74	1	no	—
321	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
322	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
323	C₂²⋊C₄	—	2	1	no	—
324	C₂²⋊C₄	—	2	1	no	—
325	C₂²⋊C₄	—	74	1	no	—
326	C₂²⋊C₄	—	74	1	no	—
327	C₂²⋊C₄	—	74	1	no	—
328	C₂²⋊C₄	—	74	1	no	—
329	C₂²⋊C₄	—	74	1	no	—
330	C₂²⋊C₄	—	74	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	37	1	no	—
333	C₂³	—	37	4	no	—
334	C₂³	—	37	1	no	—
335	C₂³	—	74	2	no	—
336	C₂³	—	74	2	no	—
337	C₂³	—	74	1	no	—
338	C₂³	—	148	2	no	—
339	C₂³	—	148	2	no	—
340	C₂³	—	148	2	no	—
341	C₂³	D₄×D₃₇	1	1	yes	characteristic
342	Q₈	—	2	1	no	—
343	Q₈	—	2	1	no	—
344	Q₈	—	74	1	no	—
345	Q₈	—	74	1	no	—
346	Q₈	—	148	2	no	—
347	D₄	—	2	1	no	—
348	D₄	—	2	1	no	—
349	D₄	—	4	2	no	—
350	D₄	—	74	1	no	—
351	D₄	—	74	1	no	—
352	D₄	—	148	2	no	—
353	D₄	—	148	2	no	—
354	D₄	—	148	2	no	—
355	D₄	—	148	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	37	1	no	—
362	C₂×C₄	—	37	2	no	—
363	C₂×C₄	—	37	2	no	—
364	C₂×C₄	—	37	1	no	—
365	C₂×C₄	—	74	2	no	—
366	C₂×C₄	—	74	2	no	—
367	C₂×C₄	—	74	2	no	—
368	C₂×C₄	—	74	1	no	—
369	C₂×C₄	—	74	1	no	—
370	C₂×C₄	—	74	1	no	—
371	C₂×C₄	—	74	1	no	—
372	C₂×C₄	—	74	1	no	—
373	C₂×C₄	—	148	2	no	—
374	C₂×C₄	—	148	2	no	—
375	C₂×C₄	—	148	2	no	—
376	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
377	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
378	C₈	—	2	1	no	—
379	C₈	—	37	2	no	—
380	C₈	—	74	1	no	—
381	C₈	D₄×D₃₇	1	2	yes	complemented
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	37	2	no	—
388	C₂²	—	37	2	no	—
389	C₂²	—	37	2	no	—
390	C₂²	—	37	2	no	—
391	C₂²	—	296	4	no	—
392	C₂²	—	74	8	no	—
393	C₂²	—	74	1	no	—
394	C₂²	—	74	1	no	—
395	C₂²	—	148	1	no	—
396	C₂²	—	148	1	no	—
397	C₂²	—	148	1	no	—
398	C₂²	SD₁₆×D₃₇	1	2	yes	complemented
399	C₂²	C₂×D₄×D₃₇	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	37	2	no	—
405	C₄	—	74	1	no	—
406	C₄	—	148	1	no	—
407	C₄	—	148	1	no	—
408	C₄	—	148	1	no	—
409	C₄	C₂×D₄×D₃₇	1	1	yes	characteristic
410	C₄	#41×D₃₇	1	1	yes	characteristic
411	C₂	—	2	2	no	—
412	C₂	—	8	1	no	—
413	C₂	—	37	4	no	—
414	C₂	—	296	1	no	—
415	C₂	—	74	2	no	—
416	C₂	#121×D₃₇	1	1	yes	characteristic
417	C₂	C₂×SD₁₆×D₃₇	1	1	yes	characteristic
418	C₂	#135×D₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₃₇
commutator, cosocle	C₂×C₄×C₃₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₃₇
Fitting	C₃₇×#465	C₂
socle	C₂²×C₃₇	C₂²×D₄
prime radical	#121×D₃₇	C₂
hypercenter	#465	D₃₇
hypocenter	C₃₇	C₂×#465
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #465

Complements

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

N	H ≅ G/N	type
1. C₂×SD₁₆×D₃₇	C₂	semidirect
2. C₂²×C₈×D₃₇	C₂	semidirect
3. C₂²⋊Q₈×D₃₇	C₂	semidirect
5. #14557765	C₂	semidirect
6. #14557764	C₂	semidirect
7. #14557763	C₂	semidirect
8. #14557762	C₂	semidirect
9. #14557761	C₂	semidirect
10. #14557760	C₂	semidirect
11. #14557759	C₂	semidirect
12. #106×D₃₇	C₂	semidirect
13. #103×D₃₇	C₂	semidirect
14. #102×D₃₇	C₂	semidirect
15. C₃₇×#465	C₂	semidirect
20. C₂×#10596930	C₂²	semidirect
21. C₂×#10596940	C₂²	semidirect
22. C₂×#10596941	C₂²	semidirect
24. C₂²×#64436	C₂²	semidirect
28. C₂×C₈×D₃₇	C₂²	semidirect
29. C₂×C₈×D₃₇	C₂²	semidirect
30. #11924516	C₂²	semidirect
31. #11924515	C₂²	semidirect
34. #11924512	C₂²	semidirect
45. #11924468	C₂²	semidirect
46. #11924467	C₂²	semidirect
47. #11924467	C₂²	semidirect
48. #11924461	C₂²	semidirect
49. #11924460	C₂²	semidirect
50. #11924459	C₂²	semidirect
51. #11924458	C₂²	semidirect
52. #11924457	C₂²	semidirect
53. #11924456	C₂²	semidirect
54. C₂×SD₁₆×C₃₇	C₂²	semidirect
55. C₂²×C₈×C₃₇	C₂²	semidirect
56. C₂²⋊Q₈×C₃₇	C₂²	semidirect
58. #106×C₃₇	C₂²	semidirect
59. #103×C₃₇	C₂²	semidirect
60. #102×C₃₇	C₂²	semidirect
120. C₈×D₃₇	D₄	semidirect
129. C₂²×D₃₇	SD₁₆	semidirect
169. C₈×C₃₇	C₂×D₄	semidirect
171. #64436	C₂×D₄	semidirect
177. C₂²×C₃₇	C₂×SD₁₆	semidirect
188. C₂×D₃₇	C₂×SD₁₆	semidirect
209. D₃₇	#465	direct (N × H)
221. #465	D₃₇	direct (N × H)
225. C₃₇	C₂×#465	semidirect
234. C₂×SD₁₆	C₂×D₃₇	semidirect
241. C₂²×C₈	C₂×D₃₇	semidirect
247. C₂²⋊Q₈	C₂×D₃₇	semidirect
262. #106	C₂×D₃₇	semidirect
266. #103	C₂×D₃₇	semidirect
270. #102	C₂×D₃₇	semidirect
381. C₈	D₄×D₃₇	semidirect
398. C₂²	SD₁₆×D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×D₃₇	2
C₂²×C₈×D₃₇	2
C₂²⋊Q₈×D₃₇	2
#121×D₃₇	2
#14557765	2
#14557764	2
#14557763	2
#14557762	2
#14557761	2
#14557760	2
#14557759	2
#106×D₃₇	2
#103×D₃₇	2
#102×D₃₇	2
C₃₇×#465	2
C₂×#465	37

Subgroups — #465×D37 #18004152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #465×D₃₇ #18004152