Subgroups — C₁₃₇×#19458 #46868844

Order 35072.

744 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3205×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#3109×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#459×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2974×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1697×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1687×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1677×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1667×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1573×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1555×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1551×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₁₃₇	—	2	1	no	—
13	#532×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
16	#493×C₁₃₇	C₂²	1	2	yes	complemented
17	#486×C₁₃₇	C₂²	1	2	yes	complemented
18	#481×C₁₃₇	—	2	1	no	—
19	#476×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
20	#476×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
21	#459×C₁₃₇	—	2	1	no	—
22	#459×C₁₃₇	—	2	1	no	—
23	#459×C₁₃₇	—	2	2	no	—
24	#459×C₁₃₇	C₂²	1	2	yes	—
25	#459×C₁₃₇	C₂²	1	2	yes	—
26	#459×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
27	#459×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
28	#447×C₁₃₇	—	2	1	no	—
29	#447×C₁₃₇	—	2	1	no	—
30	#447×C₁₃₇	—	2	1	no	—
31	#442×C₁₃₇	—	2	1	no	—
32	#442×C₁₃₇	—	2	1	no	—
33	#436×C₁₃₇	C₂²	1	2	yes	complemented
34	#435×C₁₃₇	—	2	2	no	—
35	C₈×D₄×C₁₃₇	C₂²	1	2	yes	complemented
36	#432×C₁₃₇	C₂²	1	1	yes	characteristic
37	#432×C₁₃₇	C₂²	1	1	yes	characteristic
38	#431×C₁₃₇	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
40	C₂×#102×C₁₃₇	—	2	1	no	—
41	#407×C₁₃₇	—	2	1	no	—
42	C₂×C₂²⋊C₈×C₁₃₇	—	2	1	no	—
43	#335×C₁₃₇	C₂²	1	2	yes	complemented
44	#334×C₁₃₇	C₂²	1	2	yes	complemented
45	#333×C₁₃₇	C₂²	1	2	yes	complemented
46	#331×C₁₃₇	C₂²	1	2	yes	complemented
47	#331×C₁₃₇	C₂²	1	2	yes	complemented
48	#331×C₁₃₇	C₂²	1	2	yes	complemented
49	C₂×#41×C₁₃₇	—	2	1	no	—
50	C₂²×D₄×C₁₃₇	—	2	1	no	—
51	C₂²×D₄×C₁₃₇	—	2	1	no	—
52	C₂²×D₄×C₁₃₇	—	2	1	no	—
53	C₂²×D₄×C₁₃₇	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₃₇	—	2	1	no	—
55	C₂×D₈×C₁₃₇	—	2	1	no	—
56	C₂×D₈×C₁₃₇	—	2	1	no	—
57	C₂×D₈×C₁₃₇	—	2	2	no	—
58	C₂×D₈×C₁₃₇	—	2	2	no	—
59	C₂×D₈×C₁₃₇	—	2	2	no	—
60	C₂×D₈×C₁₃₇	—	2	2	no	—
61	C₂×D₈×C₁₃₇	—	4	4	no	—
62	C₂×M₁₆×C₁₃₇	—	2	2	no	—
63	C₂²×C₈×C₁₃₇	—	2	1	no	—
64	C₂²×C₈×C₁₃₇	—	2	2	no	—
65	C₄⋊Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
66	#127×C₁₃₇	—	2	1	no	—
67	#127×C₁₃₇	—	2	1	no	—
68	#127×C₁₃₇	—	2	1	no	—
69	#127×C₁₃₇	C₂³	1	2	yes	—
70	#127×C₁₃₇	C₂³	1	1	yes	characteristic
71	#124×C₁₃₇	—	2	1	no	—
72	#121×C₁₃₇	—	2	1	no	—
73	#121×C₁₃₇	—	2	1	no	—
74	C₄×D₄×C₁₃₇	—	2	1	no	—
75	C₄×D₄×C₁₃₇	—	2	1	no	—
76	C₄×D₄×C₁₃₇	—	2	1	no	—
77	C₄×D₄×C₁₃₇	—	2	1	no	—
78	C₄×D₄×C₁₃₇	D₄	1	1	yes	characteristic
79	C₄×D₄×C₁₃₇	D₄	1	1	yes	characteristic
80	C₄×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
81	C₄×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
84	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
85	#106×C₁₃₇	—	2	1	no	—
86	#106×C₁₃₇	—	2	1	no	—
87	C₄⋊C₈×C₁₃₇	—	2	1	no	—
88	C₄⋊C₈×C₁₃₇	D₄	1	2	yes	—
89	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
90	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
91	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
93	#102×C₁₃₇	—	2	1	no	—
94	#102×C₁₃₇	—	2	1	no	—
95	#102×C₁₃₇	—	2	2	no	—
96	#102×C₁₃₇	—	2	2	no	—
97	#102×C₁₃₇	—	2	2	no	—
98	#102×C₁₃₇	—	2	2	no	—
99	#102×C₁₃₇	—	2	1	no	—
100	#102×C₁₃₇	—	2	1	no	—
101	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
102	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
103	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
104	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
105	C₂²⋊C₈×C₁₃₇	D₄	1	1	yes	characteristic
106	C₂²⋊C₈×C₁₃₇	D₄	1	1	yes	characteristic
107	#97×C₁₃₇	—	2	1	no	—
108	#97×C₁₃₇	—	2	1	no	—
109	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
110	C₂⁴×C₁₃₇	—	2	1	no	—
111	C₂⁴×C₁₃₇	—	4	1	no	—
112	#41×C₁₃₇	—	8	2	no	—
113	C₂×Q₈×C₁₃₇	—	2	1	no	—
114	C₂×D₄×C₁₃₇	—	2	2	no	—
115	C₂×D₄×C₁₃₇	—	2	1	no	—
116	C₂×D₄×C₁₃₇	—	2	1	no	—
117	C₂×D₄×C₁₃₇	—	2	2	no	—
118	C₂×D₄×C₁₃₇	—	2	2	no	—
119	C₂×D₄×C₁₃₇	—	2	1	no	—
120	C₂×D₄×C₁₃₇	—	2	1	no	—
121	C₂×D₄×C₁₃₇	—	2	2	no	—
122	C₂×D₄×C₁₃₇	—	4	1	no	—
123	C₂×D₄×C₁₃₇	—	4	2	no	—
124	C₂×D₄×C₁₃₇	—	4	2	no	—
125	C₂×D₄×C₁₃₇	—	4	1	no	—
126	C₂×D₄×C₁₃₇	—	4	1	no	—
127	C₂×D₄×C₁₃₇	—	4	1	no	—
128	C₂×D₄×C₁₃₇	—	4	1	no	—
129	C₂×D₄×C₁₃₇	—	8	2	no	—
130	C₂×D₄×C₁₃₇	—	8	2	no	—
131	C₂×D₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
132	C₂×D₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃₇	—	2	1	no	—
134	C₂²×C₄×C₁₃₇	—	2	1	no	—
135	C₂²×C₄×C₁₃₇	—	2	1	no	—
136	C₂²×C₄×C₁₃₇	—	2	1	no	—
137	C₂²×C₄×C₁₃₇	—	2	1	no	—
138	C₂²×C₄×C₁₃₇	—	4	1	no	—
139	C₂²×C₄×C₁₃₇	—	8	2	no	—
140	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
143	D₈×C₁₃₇	—	4	2	no	—
144	D₈×C₁₃₇	—	4	4	no	—
145	D₈×C₁₃₇	—	4	2	no	—
146	D₈×C₁₃₇	—	4	4	no	—
147	D₈×C₁₃₇	—	8	2	no	—
148	D₈×C₁₃₇	—	8	2	no	—
149	M₁₆×C₁₃₇	—	8	2	no	—
150	C₂×C₈×C₁₃₇	—	2	2	no	—
151	C₂×C₈×C₁₃₇	—	2	1	no	—
152	C₂×C₈×C₁₃₇	—	2	1	no	—
153	C₂×C₈×C₁₃₇	—	2	2	no	—
154	C₂×C₈×C₁₃₇	—	4	2	no	—
155	C₂×C₈×C₁₃₇	—	8	2	no	—
156	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
157	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
158	C₄⋊C₄×C₁₃₇	—	2	1	no	—
159	C₄⋊C₄×C₁₃₇	—	2	1	no	—
160	C₄⋊C₄×C₁₃₇	—	2	1	no	—
161	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
162	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
163	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
164	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
165	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
166	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
167	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
168	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
169	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₃₇	#41	1	1	yes	characteristic
172	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
173	C₂³×C₁₃₇	—	2	1	no	—
174	C₂³×C₁₃₇	—	2	1	no	—
175	C₂³×C₁₃₇	—	4	2	no	—
176	C₂³×C₁₃₇	—	4	2	no	—
177	C₂³×C₁₃₇	—	4	1	no	—
178	C₂³×C₁₃₇	—	4	2	no	—
179	C₂³×C₁₃₇	—	8	1	no	—
180	C₂³×C₁₃₇	—	8	2	no	—
181	C₂³×C₁₃₇	—	8	2	no	—
182	C₂³×C₁₃₇	—	8	2	no	—
183	C₂³×C₁₃₇	#121	1	1	yes	characteristic
184	Q₈×C₁₃₇	—	8	1	no	—
185	D₄×C₁₃₇	—	2	1	no	—
186	D₄×C₁₃₇	—	2	1	no	—
187	D₄×C₁₃₇	—	2	1	no	—
188	D₄×C₁₃₇	—	4	2	no	—
189	D₄×C₁₃₇	—	4	2	no	—
190	D₄×C₁₃₇	—	4	1	no	—
191	D₄×C₁₃₇	—	4	1	no	—
192	D₄×C₁₃₇	—	4	2	no	—
193	D₄×C₁₃₇	—	4	2	no	—
194	D₄×C₁₃₇	—	4	2	no	—
195	D₄×C₁₃₇	—	4	2	no	—
196	D₄×C₁₃₇	—	8	2	no	—
197	D₄×C₁₃₇	—	8	1	no	—
198	D₄×C₁₃₇	—	8	2	no	—
199	D₄×C₁₃₇	—	8	2	no	—
200	D₄×C₁₃₇	—	8	2	no	—
201	D₄×C₁₃₇	—	8	2	no	—
202	D₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
203	C₂×C₄×C₁₃₇	—	2	2	no	—
204	C₂×C₄×C₁₃₇	—	2	1	no	—
205	C₂×C₄×C₁₃₇	—	2	1	no	—
206	C₂×C₄×C₁₃₇	—	2	2	no	—
207	C₂×C₄×C₁₃₇	—	2	1	no	—
208	C₂×C₄×C₁₃₇	—	2	1	no	—
209	C₂×C₄×C₁₃₇	—	4	2	no	—
210	C₂×C₄×C₁₃₇	—	4	2	no	—
211	C₂×C₄×C₁₃₇	—	4	1	no	—
212	C₂×C₄×C₁₃₇	—	8	1	no	—
213	C₂×C₄×C₁₃₇	—	8	1	no	—
214	C₂×C₄×C₁₃₇	—	8	2	no	—
215	C₂×C₄×C₁₃₇	—	8	1	no	—
216	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
217	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
218	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
219	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
222	C₈×C₁₃₇	—	2	2	no	—
223	C₈×C₁₃₇	—	2	2	no	—
224	C₈×C₁₃₇	—	4	2	no	—
225	C₈×C₁₃₇	—	4	1	no	—
226	C₈×C₁₃₇	—	4	1	no	—
227	C₈×C₁₃₇	—	4	2	no	—
228	C₂²×C₁₃₇	—	2	1	no	—
229	C₂²×C₁₃₇	—	2	1	no	—
230	C₂²×C₁₃₇	—	2	2	no	—
231	C₂²×C₁₃₇	—	4	1	no	—
232	C₂²×C₁₃₇	—	4	1	no	—
233	C₂²×C₁₃₇	—	4	1	no	—
234	C₂²×C₁₃₇	—	4	1	no	—
235	C₂²×C₁₃₇	—	4	1	no	—
236	C₂²×C₁₃₇	—	8	4	no	—
237	C₂²×C₁₃₇	—	8	2	no	—
238	C₂²×C₁₃₇	—	8	1	no	—
239	C₂²×C₁₃₇	—	8	2	no	—
240	C₂²×C₁₃₇	—	8	1	no	—
241	C₂²×C₁₃₇	—	8	1	no	—
242	C₂²×C₁₃₇	—	8	2	no	—
243	C₂²×C₁₃₇	—	16	4	no	—
244	C₂²×C₁₃₇	#472	1	2	yes	—
245	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
246	C₄×C₁₃₇	—	2	1	no	—
247	C₄×C₁₃₇	—	2	1	no	—
248	C₄×C₁₃₇	—	2	1	no	—
249	C₄×C₁₃₇	—	2	1	no	—
250	C₄×C₁₃₇	—	4	1	no	—
251	C₄×C₁₃₇	—	4	1	no	—
252	C₄×C₁₃₇	—	8	1	no	—
253	C₄×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
254	C₄×C₁₃₇	#575	1	1	yes	characteristic
255	C₄×C₁₃₇	#576	1	2	yes	—
256	C₂×C₁₃₇	—	2	2	no	—
257	C₂×C₁₃₇	—	4	2	no	—
258	C₂×C₁₃₇	—	8	1	no	—
259	C₂×C₁₃₇	—	16	1	no	—
260	C₂×C₁₃₇	—	16	2	no	—
261	C₂×C₁₃₇	#3041	1	1	yes	characteristic
262	C₂×C₁₃₇	#3055	1	1	yes	characteristic
263	C₂×C₁₃₇	C₂×#472	1	1	yes	characteristic
264	#19458	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₁₃₇	#19458	1	1	yes	characteristic, direct product factor, Sylow
266	#3205	C₂×C₁₃₇	1	1	yes	characteristic, complemented
267	#3109	C₂×C₁₃₇	1	1	yes	characteristic, complemented
268	C₂×#459	C₂×C₁₃₇	1	1	yes	characteristic, complemented
269	#2974	C₂×C₁₃₇	1	1	yes	characteristic, complemented
270	#1697	C₂×C₁₃₇	1	2	yes	complemented
271	#1687	C₂×C₁₃₇	1	2	yes	complemented
272	#1677	C₂×C₁₃₇	1	2	yes	complemented
273	#1667	C₂×C₁₃₇	1	2	yes	complemented
274	#1573	C₂×C₁₃₇	1	1	yes	characteristic, complemented
275	#1555	C₂×C₁₃₇	1	1	yes	characteristic, complemented
276	#1551	C₂×C₁₃₇	1	1	yes	characteristic, complemented
277	C₂²×D₈	—	2	1	no	—
278	#532	C₂²×C₁₃₇	1	1	yes	characteristic
279	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
280	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
281	#493	C₂²×C₁₃₇	1	2	yes	complemented
282	#486	C₂²×C₁₃₇	1	2	yes	complemented
283	#481	—	2	1	no	—
284	#476	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
285	#476	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
286	#459	—	2	1	no	—
287	#459	—	2	1	no	—
288	#459	—	2	2	no	—
289	#459	C₂²×C₁₃₇	1	2	yes	—
290	#459	C₂²×C₁₃₇	1	2	yes	—
291	#459	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
292	#459	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
293	#447	—	2	1	no	—
294	#447	—	2	1	no	—
295	#447	—	2	1	no	—
296	#442	—	2	1	no	—
297	#442	—	2	1	no	—
298	#436	C₂²×C₁₃₇	1	2	yes	complemented
299	#435	—	2	2	no	—
300	C₈×D₄	C₂²×C₁₃₇	1	2	yes	complemented
301	#432	C₂²×C₁₃₇	1	1	yes	characteristic
302	#432	C₂²×C₁₃₇	1	1	yes	characteristic
303	#431	C₂²×C₁₃₇	1	1	yes	characteristic
304	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
305	C₂×#102	—	2	1	no	—
306	#407	—	2	1	no	—
307	C₂×C₂²⋊C₈	—	2	1	no	—
308	#335	C₂²×C₁₃₇	1	2	yes	complemented
309	#334	C₂²×C₁₃₇	1	2	yes	complemented
310	#333	C₂²×C₁₃₇	1	2	yes	complemented
311	#331	C₂²×C₁₃₇	1	2	yes	complemented
312	#331	C₂²×C₁₃₇	1	2	yes	complemented
313	#331	C₂²×C₁₃₇	1	2	yes	complemented
314	C₂×#41	—	2	1	no	—
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	D₄×C₁₃₇	1	1	yes	characteristic
319	C₂³×C₄	—	2	1	no	—
320	C₂×D₈	—	2	2	no	—
321	C₂×D₈	—	2	2	no	—
322	C₂×D₈	—	2	1	no	—
323	C₂×D₈	—	2	1	no	—
324	C₂×D₈	—	2	2	no	—
325	C₂×D₈	—	2	2	no	—
326	C₂×D₈	—	4	4	no	—
327	C₂×M₁₆	—	2	2	no	—
328	C₂²×C₈	—	2	1	no	—
329	C₂²×C₈	—	2	2	no	—
330	C₄⋊Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
331	#127	—	2	1	no	—
332	#127	—	2	1	no	—
333	#127	—	2	1	no	—
334	#127	C₂³×C₁₃₇	1	2	yes	—
335	#127	C₂³×C₁₃₇	1	1	yes	characteristic
336	#124	—	2	1	no	—
337	#121	—	2	1	no	—
338	#121	—	2	1	no	—
339	C₄×D₄	—	2	1	no	—
340	C₄×D₄	—	2	1	no	—
341	C₄×D₄	—	2	1	no	—
342	C₄×D₄	—	2	1	no	—
343	C₄×D₄	D₄×C₁₃₇	1	1	yes	characteristic
344	C₄×D₄	D₄×C₁₃₇	1	1	yes	characteristic
345	C₄×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
346	C₄×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
347	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
350	#106	—	2	1	no	—
351	#106	—	2	1	no	—
352	C₄⋊C₈	—	2	1	no	—
353	C₄⋊C₈	D₄×C₁₃₇	1	2	yes	—
354	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
355	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
356	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
357	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
358	#102	—	2	1	no	—
359	#102	—	2	1	no	—
360	#102	—	2	2	no	—
361	#102	—	2	2	no	—
362	#102	—	2	2	no	—
363	#102	—	2	2	no	—
364	#102	—	2	1	no	—
365	#102	—	2	1	no	—
366	C₂²⋊C₈	—	2	1	no	—
367	C₂²⋊C₈	—	2	1	no	—
368	C₂²⋊C₈	—	2	2	no	—
369	C₂²⋊C₈	—	2	2	no	—
370	C₂²⋊C₈	D₄×C₁₃₇	1	1	yes	characteristic
371	C₂²⋊C₈	D₄×C₁₃₇	1	1	yes	characteristic
372	#97	—	2	1	no	—
373	#97	—	2	1	no	—
374	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
375	C₂⁴	—	2	1	no	—
376	C₂⁴	—	4	1	no	—
377	#41	—	8	2	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	4	1	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂×D₄	—	4	2	no	—
390	C₂×D₄	—	4	1	no	—
391	C₂×D₄	—	4	1	no	—
392	C₂×D₄	—	4	1	no	—
393	C₂×D₄	—	4	1	no	—
394	C₂×D₄	—	8	2	no	—
395	C₂×D₄	—	8	2	no	—
396	C₂×D₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
397	C₂×D₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	4	1	no	—
404	C₂²×C₄	—	8	2	no	—
405	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
407	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
408	D₈	—	4	2	no	—
409	D₈	—	4	4	no	—
410	D₈	—	4	2	no	—
411	D₈	—	4	4	no	—
412	D₈	—	8	2	no	—
413	D₈	—	8	2	no	—
414	M₁₆	—	8	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	4	2	no	—
420	C₂×C₈	—	8	2	no	—
421	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
422	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
427	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	4	1	no	—
433	C₂²⋊C₄	—	4	1	no	—
434	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
435	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
436	C₄²	#41×C₁₃₇	1	1	yes	characteristic
437	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	8	1	no	—
445	C₂³	—	8	2	no	—
446	C₂³	—	8	2	no	—
447	C₂³	—	8	2	no	—
448	C₂³	#121×C₁₃₇	1	1	yes	characteristic
449	Q₈	—	8	1	no	—
450	D₄	—	2	1	no	—
451	D₄	—	2	1	no	—
452	D₄	—	2	1	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	1	no	—
456	D₄	—	4	1	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	8	2	no	—
462	D₄	—	8	1	no	—
463	D₄	—	8	2	no	—
464	D₄	—	8	2	no	—
465	D₄	—	8	2	no	—
466	D₄	—	8	2	no	—
467	D₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	8	1	no	—
478	C₂×C₄	—	8	1	no	—
479	C₂×C₄	—	8	2	no	—
480	C₂×C₄	—	8	1	no	—
481	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
482	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
483	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
486	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
487	C₈	—	2	2	no	—
488	C₈	—	2	2	no	—
489	C₈	—	4	2	no	—
490	C₈	—	4	1	no	—
491	C₈	—	4	1	no	—
492	C₈	—	4	2	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	8	4	no	—
502	C₂²	—	8	2	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	1	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	16	4	no	—
509	C₂²	#472×C₁₃₇	1	2	yes	—
510	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	8	1	no	—
518	C₄	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
519	C₄	#575×C₁₃₇	1	1	yes	characteristic
520	C₄	#576×C₁₃₇	1	2	yes	—
521	C₂	—	2	2	no	—
522	C₂	—	4	2	no	—
523	C₂	—	8	1	no	—
524	C₂	—	16	2	no	—
525	C₂	—	16	1	no	—
526	C₂	#3041×C₁₃₇	1	1	yes	characteristic
527	C₂	#3055×C₁₃₇	1	1	yes	characteristic
528	C₂	C₂×#472×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3205×C₁₃₇	C₂	semidirect
2. #3109×C₁₃₇	C₂	semidirect
3. C₂×#459×C₁₃₇	C₂	semidirect
4. #2974×C₁₃₇	C₂	semidirect
5. #1697×C₁₃₇	C₂	semidirect
6. #1687×C₁₃₇	C₂	semidirect
7. #1677×C₁₃₇	C₂	semidirect
8. #1667×C₁₃₇	C₂	semidirect
9. #1573×C₁₃₇	C₂	semidirect
10. #1555×C₁₃₇	C₂	semidirect
11. #1551×C₁₃₇	C₂	semidirect
16. #493×C₁₃₇	C₂²	semidirect
17. #486×C₁₃₇	C₂²	semidirect
19. #476×C₁₃₇	C₂²	semidirect
20. #476×C₁₃₇	C₂²	semidirect
26. #459×C₁₃₇	C₂²	semidirect
27. #459×C₁₃₇	C₂²	semidirect
33. #436×C₁₃₇	C₂²	semidirect
35. C₈×D₄×C₁₃₇	C₂²	semidirect
43. #335×C₁₃₇	C₂²	semidirect
44. #334×C₁₃₇	C₂²	semidirect
45. #333×C₁₃₇	C₂²	semidirect
46. #331×C₁₃₇	C₂²	semidirect
47. #331×C₁₃₇	C₂²	semidirect
48. #331×C₁₃₇	C₂²	semidirect
264. #19458	C₁₃₇	direct (N × H)
265. C₁₃₇	#19458	direct (N × H)
266. #3205	C₂×C₁₃₇	semidirect
267. #3109	C₂×C₁₃₇	semidirect
268. C₂×#459	C₂×C₁₃₇	semidirect
269. #2974	C₂×C₁₃₇	semidirect
270. #1697	C₂×C₁₃₇	semidirect
271. #1687	C₂×C₁₃₇	semidirect
272. #1677	C₂×C₁₃₇	semidirect
273. #1667	C₂×C₁₃₇	semidirect
274. #1573	C₂×C₁₃₇	semidirect
275. #1555	C₂×C₁₃₇	semidirect
276. #1551	C₂×C₁₃₇	semidirect
281. #493	C₂²×C₁₃₇	semidirect
282. #486	C₂²×C₁₃₇	semidirect
284. #476	C₂²×C₁₃₇	semidirect
285. #476	C₂²×C₁₃₇	semidirect
291. #459	C₂²×C₁₃₇	semidirect
292. #459	C₂²×C₁₃₇	semidirect
298. #436	C₂²×C₁₃₇	semidirect
300. C₈×D₄	C₂²×C₁₃₇	semidirect
308. #335	C₂²×C₁₃₇	semidirect
309. #334	C₂²×C₁₃₇	semidirect
310. #333	C₂²×C₁₃₇	semidirect
311. #331	C₂²×C₁₃₇	semidirect
312. #331	C₂²×C₁₃₇	semidirect
313. #331	C₂²×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3205×C₁₃₇	2
#3109×C₁₃₇	2
C₂×#459×C₁₃₇	2
#2974×C₁₃₇	2
#1697×C₁₃₇	2
#1687×C₁₃₇	2
#1677×C₁₃₇	2
#1667×C₁₃₇	2
#1573×C₁₃₇	2
#1555×C₁₃₇	2
#1551×C₁₃₇	2
#19458	137

Subgroups — C137×#19458 #46868844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19458 #46868844