Subgroups — #18003504

Order 4736.

458 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558330	C₂	1	1	yes	maximal, characteristic
2	#14558298	C₂	1	2	yes	maximal, complemented
3	#14557656	C₂	1	1	yes	maximal, characteristic, complemented
4	#14557652	C₂	1	2	yes	maximal, complemented
5	#14557650	C₂	1	1	yes	maximal, characteristic, complemented
6	#14557649	C₂	1	1	yes	maximal, characteristic, complemented
7	#14557648	C₂	1	2	yes	maximal, complemented
8	#14557580	C₂	1	1	yes	maximal, characteristic, complemented
9	#104×D₃₇	C₂	1	2	yes	maximal, complemented
10	#14557485	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#444	C₂	1	1	yes	maximal, characteristic, complemented
12	#41×D₃₇	C₂²	1	2	yes	—
13	#11924568	C₄	1	2	yes	complemented
14	#11924565	C₄	1	2	yes	complemented
15	#11924563	C₄	1	2	yes	complemented
16	#11924560	C₄	1	2	yes	complemented
17	#11924558	C₂²	1	1	yes	characteristic
18	#11924556	C₂²	1	2	yes	—
19	#11924544	—	2	2	no	—
20	#11924544	C₂²	1	2	yes	complemented
21	#11924543	C₂²	1	2	yes	complemented
22	#11924542	—	2	2	no	—
23	#11924542	C₂²	1	2	yes	complemented
24	C₂×#10596929	—	2	2	no	—
25	C₂×#10596929	C₂²	1	1	yes	characteristic
26	C₂×#10596929	C₂²	1	1	yes	characteristic
27	M₁₆×D₃₇	—	2	2	no	—
28	M₁₆×D₃₇	C₂²	1	2	yes	—
29	C₄²×D₃₇	C₂²	1	1	yes	characteristic
30	#11924472	C₂²	1	1	yes	characteristic, complemented
31	#11924471	C₂²	1	2	yes	complemented
32	#11924464	C₂²	1	2	yes	complemented
33	#11924463	C₂²	1	2	yes	complemented
34	#11924462	C₂²	1	2	yes	complemented
35	#11924447	C₂²	1	1	yes	characteristic, complemented
36	C₈×Dic₃₇	C₂²	1	1	yes	characteristic, complemented
37	C₈×Dic₃₇	C₂²	1	1	yes	characteristic, complemented
38	#135×C₃₇	C₂²	1	1	yes	characteristic
39	#131×C₃₇	C₂²	1	2	yes	complemented
40	#108×C₃₇	C₂²	1	1	yes	characteristic, complemented
41	#104×C₃₇	C₂²	1	2	yes	complemented
42	#97×C₃₇	C₂²	1	1	yes	characteristic, complemented
43	#41×C₃₇	C₂³	1	2	yes	—
44	#10596966	C₂×C₄	1	2	yes	—
45	Q₈×D₃₇	C₂×C₄	1	2	yes	—
46	#10596964	—	2	2	no	—
47	#10596964	C₂×C₄	1	2	yes	—
48	D₄×D₃₇	—	2	2	no	—
49	D₄×D₃₇	C₂×C₄	1	2	yes	—
50	#10596962	—	2	2	no	—
51	#10596962	C₂³	1	2	yes	—
52	C₂×C₄×D₃₇	—	2	2	no	—
53	C₂×C₄×D₃₇	—	2	1	no	—
54	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
55	Q₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic, complemented
56	SD₁₆×C₃₇	C₂×C₄	1	2	yes	complemented
57	D₈×C₃₇	C₂×C₄	1	1	yes	characteristic, complemented
58	M₁₆×C₃₇	—	2	2	no	—
59	M₁₆×C₃₇	C₂³	1	2	yes	—
60	C₂×C₈×C₃₇	—	2	2	no	—
61	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
62	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
63	C₄²×C₃₇	C₂³	1	1	yes	characteristic
64	#10596942	C₂×C₄	1	2	yes	complemented
65	#10596941	C₂×C₄	1	2	yes	complemented
66	#10596940	C₂×C₄	1	2	yes	complemented
67	#10596939	C₂×C₄	1	2	yes	complemented
68	C₄×Dic₃₇	—	2	1	no	—
69	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
70	#10596934	—	2	2	no	—
71	#10596934	C₂³	1	2	yes	—
72	C₂×#64436	—	2	2	no	—
73	C₂×#64436	C₂³	1	1	yes	characteristic
74	C₂×#64436	C₂³	1	1	yes	characteristic
75	Dic₁₄₈	C₂×C₄	1	1	yes	characteristic, complemented
76	D₂₉₆	C₂×C₄	1	1	yes	characteristic, complemented
77	#10596930	C₂×C₄	1	2	yes	complemented
78	#10596929	—	2	2	no	—
79	#10596929	—	2	2	no	—
80	#10596929	—	2	2	no	—
81	#10596929	C₂×C₄	1	2	yes	—
82	#10596929	C₂×C₄	1	2	yes	—
83	#10596929	D₄	1	2	yes	—
84	#10596929	D₄	1	2	yes	—
85	C₈×D₃₇	—	2	2	no	—
86	C₈×D₃₇	—	2	2	no	—
87	C₈×D₃₇	—	2	2	no	—
88	C₂²×D₃₇	—	2	2	no	—
89	C₂²×D₃₇	#41	1	1	yes	characteristic
90	Q₈×C₃₇	C₂²×C₄	1	2	yes	—
91	D₄×C₃₇	—	2	2	no	—
92	D₄×C₃₇	C₂²×C₄	1	2	yes	—
93	C₂×C₄×C₃₇	—	2	2	no	—
94	C₂×C₄×C₃₇	—	2	1	no	—
95	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
96	C₂²⋊D₃₇	—	2	2	no	—
97	C₂²⋊D₃₇	—	2	2	no	—
98	C₂²⋊D₃₇	—	2	2	no	—
99	C₂×Dic₃₇	—	2	1	no	—
100	C₂×Dic₃₇	—	2	2	no	—
101	C₂×Dic₃₇	#41	1	1	yes	characteristic
102	D₁₄₈	—	2	2	no	—
103	D₁₄₈	C₂²×C₄	1	2	yes	—
104	C₄×D₃₇	—	2	2	no	—
105	C₄×D₃₇	—	2	2	no	—
106	C₄×D₃₇	—	2	2	no	—
107	C₄×D₃₇	—	4	2	no	—
108	C₄×D₃₇	C₂²×C₄	1	2	yes	—
109	C₄×D₃₇	C₂×D₄	1	2	yes	—
110	Dic₇₄	—	2	2	no	—
111	Dic₇₄	C₂²×C₄	1	2	yes	—
112	C₈×C₃₇	—	2	2	no	—
113	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
114	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
115	C₈×C₃₇	C₂×D₄	1	2	yes	—
116	#64436	—	2	2	no	—
117	#64436	C₂²×C₄	1	2	yes	—
118	#64436	C₂×D₄	1	1	yes	characteristic
119	#64436	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₃₇	—	2	2	no	—
121	C₂²×C₃₇	C₂×#41	1	1	yes	characteristic
122	C₂×D₃₇	—	2	2	no	—
123	C₂×D₃₇	—	4	1	no	—
124	C₂×D₃₇	—	8	2	no	—
125	C₂×D₃₇	C₄×D₄	1	2	yes	—
126	C₄×C₃₇	—	2	2	no	—
127	C₄×C₃₇	—	4	1	no	—
128	C₄×C₃₇	C₂³×C₄	1	1	yes	characteristic
129	C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
130	Dic₃₇	—	2	2	no	—
131	Dic₃₇	—	2	2	no	—
132	Dic₃₇	C₄×D₄	1	2	yes	—
133	#2956	—	37	1	no	maximal, Sylow
134	C₂×C₃₇	—	2	1	no	—
135	C₂×C₃₇	—	4	2	no	—
136	C₂×C₃₇	C₂×C₄×D₄	1	1	yes	characteristic
137	D₃₇	—	2	2	no	—
138	D₃₇	—	4	2	no	—
139	#575	—	37	1	no	—
140	#568	—	37	2	no	—
141	#444	—	37	2	no	—
142	#444	—	37	1	no	—
143	#444	D₃₇	1	1	yes	characteristic, complemented
144	#443	—	37	1	no	—
145	#443	—	37	2	no	—
146	#443	—	37	1	no	—
147	#430	—	37	1	no	—
148	C₂×#104	—	37	2	no	—
149	C₄×M₁₆	—	37	1	no	—
150	C₃₇	#2956	1	1	yes	characteristic, complemented, Sylow
151	C₂×#41	—	37	2	no	—
152	#137	—	37	2	no	—
153	#137	—	37	2	no	—
154	AGL(1,ℤ/8)	—	37	2	no	—
155	AGL(1,ℤ/8)	—	37	2	no	—
156	#135	—	37	2	no	—
157	#135	—	37	1	no	—
158	#135	C₂×D₃₇	1	1	yes	characteristic
159	#131	—	37	2	no	—
160	#131	—	37	2	no	—
161	#131	—	37	2	no	—
162	#131	—	74	2	no	—
163	#131	—	74	2	no	—
164	#131	C₂×D₃₇	1	2	yes	complemented
165	C₂×M₁₆	—	37	1	no	—
166	C₂×M₁₆	—	37	1	no	—
167	C₂×M₁₆	—	37	2	no	—
168	C₂×M₁₆	—	74	2	no	—
169	C₂×M₁₆	—	74	2	no	—
170	C₂×C₄²	—	37	1	no	—
171	#108	—	37	2	no	—
172	#108	—	37	1	no	—
173	#108	C₂×D₃₇	1	1	yes	characteristic, complemented
174	#104	—	37	2	no	—
175	#104	—	37	2	no	—
176	#104	—	37	2	no	—
177	#104	C₂×D₃₇	1	2	yes	complemented
178	#97	—	37	1	no	—
179	#97	C₂×D₃₇	1	1	yes	characteristic, complemented
180	C₄×C₈	—	37	1	no	—
181	C₄×C₈	—	37	1	no	—
182	#41	—	37	2	no	—
183	#41	—	37	2	no	—
184	#41	—	37	2	no	—
185	#41	—	74	2	no	—
186	#41	—	74	2	no	—
187	#41	C₂²×D₃₇	1	2	yes	—
188	C₂×Q₈	—	37	2	no	—
189	C₂×D₄	—	37	2	no	—
190	C₂×D₄	—	74	2	no	—
191	C₂²×C₄	—	37	1	no	—
192	C₂²×C₄	—	74	2	no	—
193	C₂²×C₄	—	74	1	no	—
194	Q₁₆	—	37	2	no	—
195	Q₁₆	—	37	1	no	—
196	Q₁₆	C₄×D₃₇	1	1	yes	characteristic, complemented
197	SD₁₆	—	37	2	no	—
198	SD₁₆	—	37	2	no	—
199	SD₁₆	—	37	2	no	—
200	SD₁₆	C₄×D₃₇	1	2	yes	complemented
201	D₈	—	37	2	no	—
202	D₈	—	37	1	no	—
203	D₈	C₄×D₃₇	1	1	yes	characteristic, complemented
204	M₁₆	—	2	2	no	—
205	M₁₆	—	37	2	no	—
206	M₁₆	—	37	2	no	—
207	M₁₆	—	37	2	no	—
208	M₁₆	—	37	2	no	—
209	M₁₆	—	37	2	no	—
210	M₁₆	—	74	2	no	—
211	M₁₆	—	74	2	no	—
212	M₁₆	—	74	2	no	—
213	M₁₆	—	74	2	no	—
214	M₁₆	C₂²×D₃₇	1	2	yes	—
215	C₂×C₈	—	2	2	no	—
216	C₂×C₈	—	37	1	no	—
217	C₂×C₈	—	37	1	no	—
218	C₂×C₈	—	74	2	no	—
219	C₂×C₈	—	74	2	no	—
220	C₂×C₈	—	74	2	no	—
221	C₂×C₈	—	74	2	no	—
222	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
223	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
224	C₄²	—	37	1	no	—
225	C₄²	—	74	1	no	—
226	C₄²	C₂²×D₃₇	1	1	yes	characteristic
227	C₂³	—	37	1	no	—
228	C₂³	—	74	2	no	—
229	Q₈	—	37	2	no	—
230	Q₈	—	74	2	no	—
231	Q₈	C₂×C₄×D₃₇	1	2	yes	—
232	D₄	—	2	2	no	—
233	D₄	—	37	2	no	—
234	D₄	—	74	2	no	—
235	D₄	—	74	2	no	—
236	D₄	—	74	2	no	—
237	D₄	—	74	2	no	—
238	D₄	C₂×C₄×D₃₇	1	2	yes	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	37	1	no	—
242	C₂×C₄	—	37	2	no	—
243	C₂×C₄	—	37	2	no	—
244	C₂×C₄	—	74	2	no	—
245	C₂×C₄	—	74	2	no	—
246	C₂×C₄	—	74	2	no	—
247	C₂×C₄	—	74	1	no	—
248	C₂×C₄	—	74	2	no	—
249	C₂×C₄	—	148	2	no	—
250	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
251	C₈	—	2	2	no	—
252	C₈	—	37	2	no	—
253	C₈	—	37	1	no	—
254	C₈	—	37	1	no	—
255	C₈	—	74	2	no	—
256	C₈	C₂×C₄×D₃₇	1	1	yes	characteristic
257	C₈	C₂×C₄×D₃₇	1	1	yes	characteristic
258	C₈	D₄×D₃₇	1	2	yes	—
259	C₂²	—	2	2	no	—
260	C₂²	—	37	2	no	—
261	C₂²	—	296	2	no	—
262	C₂²	—	74	2	no	—
263	C₂²	—	148	1	no	—
264	C₂²	#41×D₃₇	1	1	yes	characteristic
265	C₄	—	2	2	no	—
266	C₄	—	4	1	no	—
267	C₄	—	37	2	no	—
268	C₄	—	74	2	no	—
269	C₄	—	74	2	no	—
270	C₄	C₂²×C₄×D₃₇	1	1	yes	characteristic
271	C₄	C₂×D₄×D₃₇	1	1	yes	characteristic
272	C₂	—	2	1	no	—
273	C₂	—	4	2	no	—
274	C₂	—	74	2	no	—
275	C₂	—	148	2	no	—
276	C₂	C₄×D₄×D₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×D₃₇
commutator	C₄×C₃₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₃₇
Fitting	C₃₇×#444	C₂
socle	C₂×C₃₇	C₂×C₄×D₄
prime radical	#14558330	C₂
cosocle	C₂×C₄×C₃₇	C₂⁴
hypercenter	#444	D₃₇
hypocenter	C₃₇	#2956
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #444

Complements

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

N	H ≅ G/N	type
2. #14558298	C₂	semidirect
3. #14557656	C₂	semidirect
4. #14557652	C₂	semidirect
5. #14557650	C₂	semidirect
6. #14557649	C₂	semidirect
7. #14557648	C₂	semidirect
8. #14557580	C₂	semidirect
9. #104×D₃₇	C₂	semidirect
10. #14557485	C₂	semidirect
11. C₃₇×#444	C₂	semidirect
13. #11924568	C₄	semidirect
14. #11924565	C₄	semidirect
15. #11924563	C₄	semidirect
16. #11924560	C₄	semidirect
20. #11924544	C₂²	semidirect
21. #11924543	C₂²	semidirect
23. #11924542	C₂²	semidirect
30. #11924472	C₂²	semidirect
31. #11924471	C₂²	semidirect
32. #11924464	C₂²	semidirect
33. #11924463	C₂²	semidirect
34. #11924462	C₂²	semidirect
35. #11924447	C₂²	semidirect
36. C₈×Dic₃₇	C₂²	semidirect
37. C₈×Dic₃₇	C₂²	semidirect
39. #131×C₃₇	C₂²	semidirect
40. #108×C₃₇	C₂²	semidirect
41. #104×C₃₇	C₂²	semidirect
42. #97×C₃₇	C₂²	semidirect
55. Q₁₆×C₃₇	C₂×C₄	semidirect
56. SD₁₆×C₃₇	C₂×C₄	semidirect
57. D₈×C₃₇	C₂×C₄	semidirect
64. #10596942	C₂×C₄	semidirect
65. #10596941	C₂×C₄	semidirect
66. #10596940	C₂×C₄	semidirect
67. #10596939	C₂×C₄	semidirect
75. Dic₁₄₈	C₂×C₄	semidirect
76. D₂₉₆	C₂×C₄	semidirect
77. #10596930	C₂×C₄	semidirect
143. #444	D₃₇	semidirect
150. C₃₇	#2956	semidirect
164. #131	C₂×D₃₇	semidirect
173. #108	C₂×D₃₇	semidirect
177. #104	C₂×D₃₇	semidirect
179. #97	C₂×D₃₇	semidirect
196. Q₁₆	C₄×D₃₇	semidirect
200. SD₁₆	C₄×D₃₇	semidirect
203. D₈	C₄×D₃₇	semidirect

Maximal subgroups

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

subgroup	index
#14558330	2
#14558298	2
#14557656	2
#14557652	2
#14557650	2
#14557649	2
#14557648	2
#14557580	2
#104×D₃₇	2
#14557485	2
C₃₇×#444	2
#2956	37