Subgroups — #18002989

Order 4736.

418 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557425	C₂	1	1	yes	maximal, characteristic
2	#14557425	C₂	1	1	yes	maximal, characteristic
3	#14557424	C₂	1	1	yes	maximal, characteristic
4	#14557423	C₂	1	1	yes	maximal, characteristic
5	#14557423	C₂	1	1	yes	maximal, characteristic
6	#14557422	C₂	1	1	yes	maximal, characteristic
7	#14557422	C₂	1	1	yes	maximal, characteristic
8	#14557420	C₂	1	1	yes	maximal, characteristic, complemented
9	#14557419	C₂	1	1	yes	maximal, characteristic, complemented
10	#14557418	C₂	1	1	yes	maximal, characteristic, complemented
11	#14557416	C₂	1	1	yes	maximal, characteristic, complemented
12	#14557415	C₂	1	1	yes	maximal, characteristic, complemented
13	#14557414	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄²×Dic₃₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#387	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
18	C₂×#10596936	C₂²	1	1	yes	characteristic
19	C₂×#10596936	C₂²	1	1	yes	characteristic
20	C₂×#10596936	C₂²	1	1	yes	characteristic
21	C₂×#10596938	C₂²	1	1	yes	characteristic
22	C₂×#10596938	C₂²	1	1	yes	characteristic
23	C₂×#10596938	C₂²	1	1	yes	characteristic
24	C₂×#10596938	C₂²	1	1	yes	characteristic
25	C₂×#10596938	C₂²	1	1	yes	characteristic
26	C₂×#10596938	C₂²	1	1	yes	characteristic
27	C₂×#10596938	C₂²	1	1	yes	characteristic
28	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
34	#11924443	C₂²	1	1	yes	characteristic
35	#11924443	C₂²	1	1	yes	characteristic
36	#11924443	C₂²	1	1	yes	characteristic
37	#11924443	C₂²	1	1	yes	characteristic
38	#11924443	C₂²	1	1	yes	characteristic
39	#11924443	C₂²	1	1	yes	characteristic
40	#11924443	C₂²	1	1	yes	characteristic
41	#11924443	C₂²	1	1	yes	characteristic
42	#11924443	C₂²	1	1	yes	characteristic
43	#11924443	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
46	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
47	#95×C₃₇	C₂²	1	1	yes	characteristic
48	#95×C₃₇	C₂²	1	1	yes	characteristic
49	#95×C₃₇	C₂²	1	1	yes	characteristic
50	#95×C₃₇	C₂²	1	1	yes	characteristic
51	C₂³×D₃₇	C₂³	1	1	yes	characteristic
52	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
53	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
54	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
55	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
56	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
59	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
60	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
61	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
62	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
63	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
64	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
65	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
66	C₄⋊C₄×C₃₇	—	2	2	no	—
67	C₄⋊C₄×C₃₇	—	2	2	no	—
68	C₄²×C₃₇	—	2	2	no	—
69	#10596938	—	2	2	no	—
70	#10596938	—	2	2	no	—
71	#10596938	—	2	2	no	—
72	#10596938	—	2	2	no	—
73	#10596938	—	2	2	no	—
74	#10596938	—	2	2	no	—
75	#10596938	—	2	2	no	—
76	C₄⋊Dic₃₇	—	2	2	no	—
77	C₄⋊Dic₃₇	—	2	2	no	—
78	#10596936	—	2	2	no	—
79	#10596936	—	2	2	no	—
80	#10596936	—	2	2	no	—
81	C₄×Dic₃₇	—	2	2	no	—
82	C₄×Dic₃₇	—	2	2	no	—
83	C₄×Dic₃₇	—	2	2	no	—
84	C₄×Dic₃₇	—	2	2	no	—
85	C₄×Dic₃₇	—	2	2	no	—
86	C₄×Dic₃₇	—	2	2	no	—
87	C₂³×C₃₇	C₂⁴	1	1	yes	characteristic
88	C₂²×D₃₇	—	2	1	no	—
89	C₂²×D₃₇	—	2	1	no	—
90	C₂²×D₃₇	—	2	1	no	—
91	C₂²×D₃₇	—	2	1	no	—
92	C₂²×D₃₇	—	2	1	no	—
93	C₂²×D₃₇	—	2	1	no	—
94	C₂²×D₃₇	—	2	1	no	—
95	C₂×C₄×C₃₇	—	2	1	no	—
96	C₂×C₄×C₃₇	—	2	1	no	—
97	C₂×C₄×C₃₇	—	2	1	no	—
98	C₂×C₄×C₃₇	—	2	1	no	—
99	C₂×C₄×C₃₇	—	2	1	no	—
100	C₂×C₄×C₃₇	—	2	1	no	—
101	C₂×C₄×C₃₇	—	2	1	no	—
102	C₂×C₄×C₃₇	—	2	1	no	—
103	C₂×C₄×C₃₇	—	2	1	no	—
104	C₂×C₄×C₃₇	—	2	1	no	—
105	C₂×C₄×C₃₇	—	2	1	no	—
106	C₂×C₄×C₃₇	—	2	1	no	—
107	C₂×C₄×C₃₇	—	2	1	no	—
108	C₂×C₄×C₃₇	—	2	1	no	—
109	C₂×C₄×C₃₇	—	2	1	no	—
110	C₂×C₄×C₃₇	—	2	1	no	—
111	C₂×C₄×C₃₇	—	2	1	no	—
112	C₂×C₄×C₃₇	—	2	1	no	—
113	C₂×C₄×C₃₇	#41	1	2	yes	—
114	C₂×C₄×C₃₇	#41	1	2	yes	—
115	C₂×C₄×C₃₇	#41	1	2	yes	—
116	C₂×Dic₃₇	—	2	1	no	—
117	C₂×Dic₃₇	—	2	1	no	—
118	C₂×Dic₃₇	—	2	1	no	—
119	C₂×Dic₃₇	—	2	1	no	—
120	C₂×Dic₃₇	—	2	1	no	—
121	C₂×Dic₃₇	—	2	1	no	—
122	C₂×Dic₃₇	—	2	1	no	—
123	C₂×Dic₃₇	—	2	1	no	—
124	C₂×Dic₃₇	—	2	1	no	—
125	C₂×Dic₃₇	—	2	1	no	—
126	C₂×Dic₃₇	—	2	1	no	—
127	C₂×Dic₃₇	—	2	1	no	—
128	C₂×Dic₃₇	—	2	1	no	—
129	C₂×Dic₃₇	—	2	1	no	—
130	C₂×Dic₃₇	—	2	1	no	—
131	C₂×Dic₃₇	—	2	1	no	—
132	C₂×Dic₃₇	—	2	1	no	—
133	C₂×Dic₃₇	#41	1	2	yes	—
134	C₂×Dic₃₇	#41	1	2	yes	—
135	C₂×Dic₃₇	#41	1	2	yes	—
136	C₂×Dic₃₇	#41	1	2	yes	—
137	C₂²×C₃₇	C₂×#41	1	1	yes	characteristic
138	C₂²×C₃₇	C₂×#41	1	1	yes	characteristic
139	C₂²×C₃₇	C₂×#41	1	1	yes	characteristic
140	C₂²×C₃₇	C₂×#41	1	1	yes	characteristic
141	C₂²×C₃₇	C₂×#41	1	1	yes	characteristic
142	C₂²×C₃₇	C₂×#41	1	1	yes	characteristic
143	C₂²×C₃₇	C₂×#41	1	1	yes	characteristic
144	C₂×D₃₇	—	4	1	no	—
145	C₂×D₃₇	—	4	1	no	—
146	C₂×D₃₇	—	4	1	no	—
147	C₂×D₃₇	—	4	1	no	—
148	C₂×D₃₇	—	4	1	no	—
149	C₂×D₃₇	—	4	1	no	—
150	C₂×D₃₇	—	4	1	no	—
151	C₄×C₃₇	—	2	2	no	—
152	C₄×C₃₇	—	2	2	no	—
153	C₄×C₃₇	—	2	2	no	—
154	C₄×C₃₇	—	4	1	no	—
155	C₄×C₃₇	—	4	1	no	—
156	C₄×C₃₇	—	4	1	no	—
157	C₄×C₃₇	—	4	1	no	—
158	Dic₃₇	—	2	2	no	—
159	Dic₃₇	—	2	2	no	—
160	Dic₃₇	—	2	2	no	—
161	Dic₃₇	—	2	2	no	—
162	Dic₃₇	—	4	1	no	—
163	Dic₃₇	—	4	1	no	—
164	Dic₃₇	—	4	1	no	—
165	#2866	—	37	1	no	maximal, Sylow
166	C₂×C₃₇	#529	1	1	yes	characteristic
167	C₂×C₃₇	#529	1	1	yes	characteristic
168	C₂×C₃₇	#529	1	1	yes	characteristic
169	C₂×C₃₇	#529	1	1	yes	characteristic
170	C₂×C₃₇	#529	1	1	yes	characteristic
171	C₂×C₃₇	#529	1	1	yes	characteristic
172	C₂×C₃₇	#529	1	1	yes	characteristic
173	D₃₇	—	8	1	no	—
174	#388	—	37	1	no	—
175	#388	—	37	1	no	—
176	#388	—	37	1	no	—
177	#388	—	37	1	no	—
178	#388	—	37	1	no	—
179	#388	—	37	1	no	—
180	#388	—	37	1	no	—
181	#387	—	37	1	no	—
182	#387	—	37	1	no	—
183	#387	—	37	1	no	—
184	#387	—	37	1	no	—
185	#387	—	37	1	no	—
186	#387	—	37	1	no	—
187	#387	D₃₇	1	1	yes	characteristic, complemented
188	C₄³	—	37	1	no	—
189	C₃₇	#2866	1	1	yes	characteristic, complemented, Sylow
190	C₂×C₄⋊C₄	—	37	1	no	—
191	C₂×C₄⋊C₄	—	37	1	no	—
192	C₂×C₄⋊C₄	—	37	1	no	—
193	C₂×C₄⋊C₄	—	37	1	no	—
194	C₂×C₄⋊C₄	—	37	1	no	—
195	C₂×C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
196	C₂×C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
197	C₂×C₂²⋊C₄	—	37	1	no	—
198	C₂×C₂²⋊C₄	—	37	1	no	—
199	C₂×C₂²⋊C₄	—	37	1	no	—
200	C₂×C₂²⋊C₄	—	37	1	no	—
201	C₂×C₂²⋊C₄	—	37	1	no	—
202	C₂×C₂²⋊C₄	—	37	1	no	—
203	C₂×C₂²⋊C₄	—	37	1	no	—
204	C₂×C₄²	—	37	1	no	—
205	C₂×C₄²	—	37	1	no	—
206	C₂×C₄²	—	37	1	no	—
207	C₂×C₄²	—	37	1	no	—
208	C₂×C₄²	—	37	1	no	—
209	C₂×C₄²	—	37	1	no	—
210	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
211	#95	—	37	1	no	—
212	#95	—	37	1	no	—
213	#95	—	37	1	no	—
214	#95	—	37	1	no	—
215	#95	—	37	1	no	—
216	#95	—	37	1	no	—
217	#95	—	37	1	no	—
218	#95	—	37	1	no	—
219	#95	—	37	1	no	—
220	#95	—	37	1	no	—
221	#95	C₂×D₃₇	1	1	yes	characteristic
222	#95	C₂×D₃₇	1	1	yes	characteristic
223	#95	C₂×D₃₇	1	1	yes	characteristic
224	#95	C₂×D₃₇	1	1	yes	characteristic
225	C₂⁴	—	37	1	no	—
226	C₂²×C₄	—	37	1	no	—
227	C₂²×C₄	—	37	1	no	—
228	C₂²×C₄	—	37	1	no	—
229	C₂²×C₄	—	37	1	no	—
230	C₂²×C₄	—	37	1	no	—
231	C₂²×C₄	—	37	1	no	—
232	C₂²×C₄	—	37	1	no	—
233	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
234	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
235	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
236	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
237	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
238	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
239	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
240	C₄⋊C₄	—	2	2	no	—
241	C₄⋊C₄	—	2	2	no	—
242	C₄⋊C₄	—	74	2	no	—
243	C₄⋊C₄	—	74	2	no	—
244	C₄⋊C₄	—	74	2	no	—
245	C₄⋊C₄	—	74	2	no	—
246	C₄⋊C₄	—	74	2	no	—
247	C₂²⋊C₄	—	74	2	no	—
248	C₂²⋊C₄	—	74	2	no	—
249	C₂²⋊C₄	—	74	2	no	—
250	C₂²⋊C₄	—	74	2	no	—
251	C₂²⋊C₄	—	74	2	no	—
252	C₂²⋊C₄	—	74	2	no	—
253	C₂²⋊C₄	—	74	2	no	—
254	C₄²	—	2	2	no	—
255	C₄²	—	74	2	no	—
256	C₄²	—	74	2	no	—
257	C₄²	—	74	2	no	—
258	C₄²	—	74	2	no	—
259	C₄²	—	74	2	no	—
260	C₄²	—	74	2	no	—
261	C₂³	—	74	1	no	—
262	C₂³	—	74	1	no	—
263	C₂³	—	74	1	no	—
264	C₂³	—	74	1	no	—
265	C₂³	—	74	1	no	—
266	C₂³	—	74	1	no	—
267	C₂³	—	74	1	no	—
268	C₂³	C₂³×D₃₇	1	1	yes	characteristic
269	C₂×C₄	—	2	1	no	—
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	2	1	no	—
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	—	2	1	no	—
274	C₂×C₄	—	2	1	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	1	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	37	2	no	—
288	C₂×C₄	—	37	2	no	—
289	C₂×C₄	—	37	2	no	—
290	C₂×C₄	—	37	2	no	—
291	C₂×C₄	—	74	1	no	—
292	C₂×C₄	—	74	1	no	—
293	C₂×C₄	—	74	1	no	—
294	C₂×C₄	—	74	1	no	—
295	C₂×C₄	—	74	1	no	—
296	C₂×C₄	—	74	1	no	—
297	C₂×C₄	—	74	1	no	—
298	C₂×C₄	—	74	1	no	—
299	C₂×C₄	—	74	1	no	—
300	C₂×C₄	—	74	1	no	—
301	C₂×C₄	—	74	1	no	—
302	C₂×C₄	—	74	1	no	—
303	C₂×C₄	—	74	1	no	—
304	C₂×C₄	—	74	1	no	—
305	C₂×C₄	—	74	1	no	—
306	C₂×C₄	—	74	1	no	—
307	C₂×C₄	—	74	1	no	—
308	C₂×C₄	#10596962	1	2	yes	—
309	C₂×C₄	#10596964	1	2	yes	—
310	C₂×C₄	#10596966	1	2	yes	—
311	C₂²	—	148	1	no	—
312	C₂²	—	148	1	no	—
313	C₂²	—	148	1	no	—
314	C₂²	—	148	1	no	—
315	C₂²	—	148	1	no	—
316	C₂²	—	148	1	no	—
317	C₂²	—	148	1	no	—
318	C₂²	#41×D₃₇	1	1	yes	characteristic
319	C₂²	#41×D₃₇	1	1	yes	characteristic
320	C₂²	#41×D₃₇	1	1	yes	characteristic
321	C₂²	#41×D₃₇	1	1	yes	characteristic
322	C₂²	C₂×#10596964	1	1	yes	characteristic
323	C₂²	C₂×#10596962	1	1	yes	characteristic
324	C₂²	C₂×#10596966	1	1	yes	characteristic
325	C₄	—	2	2	no	—
326	C₄	—	2	2	no	—
327	C₄	—	2	2	no	—
328	C₄	—	4	1	no	—
329	C₄	—	4	1	no	—
330	C₄	—	4	1	no	—
331	C₄	—	4	1	no	—
332	C₄	—	74	2	no	—
333	C₄	—	74	2	no	—
334	C₄	—	74	2	no	—
335	C₄	—	74	2	no	—
336	C₄	—	148	1	no	—
337	C₄	—	148	1	no	—
338	C₄	—	148	1	no	—
339	C₂	—	296	1	no	—
340	C₂	#14558060	1	1	yes	characteristic
341	C₂	#14558061	1	1	yes	characteristic
342	C₂	#14558063	1	1	yes	characteristic
343	C₂	#14558066	1	1	yes	characteristic
344	C₂	#14558068	1	1	yes	characteristic
345	C₂	#14558069	1	1	yes	characteristic
346	C₂	#14558070	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₃₇
commutator, socle, cosocle	C₂³×C₃₇	C₂⁴
Fitting	C₃₇×#387	C₂
prime radical	C₂³×D₃₇	C₂³
hypercenter	#387	D₃₇
hypocenter	C₃₇	#2866
LCS	G ▷ C₂³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ #387

Complements

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

N	H ≅ G/N	type
8. #14557420	C₂	semidirect
9. #14557419	C₂	semidirect
10. #14557418	C₂	semidirect
11. #14557416	C₂	semidirect
12. #14557415	C₂	semidirect
13. #14557414	C₂	semidirect
14. C₄²×Dic₃₇	C₂	semidirect
15. C₃₇×#387	C₂	semidirect
187. #387	D₃₇	semidirect
189. C₃₇	#2866	semidirect

Maximal subgroups

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

subgroup	index
#14557425	2
#14557424	2
#14557423	2
#14557422	2
#14557420	2
#14557419	2
#14557418	2
#14557416	2
#14557415	2
#14557414	2
C₄²×Dic₃₇	2
C₃₇×#387	2
#2866	37