Subgroups — C₁₃₇×#28759 #46878145

Order 35072.

928 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#489×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#486×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2657×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2331×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2042×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2041×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1983×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1982×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1961×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1958×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1768×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
19	#489×C₁₃₇	—	2	4	no	—
20	#486×C₁₃₇	—	2	4	no	—
21	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
23	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
24	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
25	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
26	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
27	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
28	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
29	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
30	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
32	#392×C₁₃₇	—	2	2	no	—
33	#392×C₁₃₇	—	2	2	no	—
34	#391×C₁₃₇	—	2	2	no	—
35	#389×C₁₃₇	C₂²	1	2	yes	—
36	#387×C₁₃₇	—	2	2	no	—
37	#382×C₁₃₇	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
39	#376×C₁₃₇	C₂²	1	1	yes	characteristic
40	#336×C₁₃₇	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃₇	—	2	1	no	—
42	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₃₇	—	2	2	no	—
44	C₂²×D₄×C₁₃₇	—	2	1	no	—
45	C₂²×D₄×C₁₃₇	—	2	1	no	—
46	C₂²×D₄×C₁₃₇	—	2	2	no	—
47	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
53	C₄⋊Q₈×C₁₃₇	D₄	1	4	yes	complemented
54	#127×C₁₃₇	—	2	2	no	—
55	#127×C₁₃₇	—	2	2	no	—
56	#127×C₁₃₇	—	2	4	no	—
57	#127×C₁₃₇	—	4	2	no	—
58	#124×C₁₃₇	—	2	2	no	—
59	#124×C₁₃₇	—	2	2	no	—
60	#124×C₁₃₇	—	2	4	no	—
61	#124×C₁₃₇	—	4	2	no	—
62	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
70	C₂×C₄²×C₁₃₇	—	2	2	no	—
71	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₁₃₇	—	2	4	no	—
75	#103×C₁₃₇	—	2	4	no	—
76	#103×C₁₃₇	—	4	2	no	—
77	#102×C₁₃₇	—	2	4	no	—
78	#102×C₁₃₇	—	2	4	no	—
79	#102×C₁₃₇	—	2	4	no	—
80	#102×C₁₃₇	—	4	2	no	—
81	#102×C₁₃₇	—	4	2	no	—
82	#102×C₁₃₇	—	4	2	no	—
83	#97×C₁₃₇	—	2	2	no	—
84	C₄×C₈×C₁₃₇	—	2	2	no	—
85	#95×C₁₃₇	—	2	2	no	—
86	#95×C₁₃₇	—	2	1	no	—
87	#95×C₁₃₇	—	2	1	no	—
88	#95×C₁₃₇	—	2	2	no	—
89	#95×C₁₃₇	D₄	1	2	yes	—
90	#95×C₁₃₇	D₄	1	2	yes	—
91	C₂⁴×C₁₃₇	—	2	1	no	—
92	C₂⁴×C₁₃₇	—	2	1	no	—
93	C₂⁴×C₁₃₇	—	2	1	no	—
94	C₂×Q₈×C₁₃₇	—	2	4	no	—
95	C₂×Q₈×C₁₃₇	—	2	1	no	—
96	C₂×Q₈×C₁₃₇	—	2	1	no	—
97	C₂×Q₈×C₁₃₇	—	2	2	no	—
98	C₂×Q₈×C₁₃₇	—	2	2	no	—
99	C₂×Q₈×C₁₃₇	—	8	2	no	—
100	C₂×D₄×C₁₃₇	—	2	1	no	—
101	C₂×D₄×C₁₃₇	—	2	1	no	—
102	C₂×D₄×C₁₃₇	—	2	1	no	—
103	C₂×D₄×C₁₃₇	—	2	2	no	—
104	C₂×D₄×C₁₃₇	—	2	1	no	—
105	C₂×D₄×C₁₃₇	—	2	2	no	—
106	C₂×D₄×C₁₃₇	—	2	2	no	—
107	C₂×D₄×C₁₃₇	—	2	1	no	—
108	C₂×D₄×C₁₃₇	—	2	1	no	—
109	C₂×D₄×C₁₃₇	—	2	2	no	—
110	C₂×D₄×C₁₃₇	—	2	2	no	—
111	C₂×D₄×C₁₃₇	—	2	2	no	—
112	C₂×D₄×C₁₃₇	—	4	4	no	—
113	C₂×D₄×C₁₃₇	—	4	2	no	—
114	C₂×D₄×C₁₃₇	—	4	2	no	—
115	C₂×D₄×C₁₃₇	—	4	4	no	—
116	C₂×D₄×C₁₃₇	—	8	2	no	—
117	C₂×D₄×C₁₃₇	—	8	2	no	—
118	C₂×D₄×C₁₃₇	—	8	2	no	—
119	C₂×D₄×C₁₃₇	—	8	2	no	—
120	C₂×D₄×C₁₃₇	—	8	2	no	—
121	C₂×D₄×C₁₃₇	—	8	2	no	—
122	C₂²×C₄×C₁₃₇	—	2	2	no	—
123	C₂²×C₄×C₁₃₇	—	2	2	no	—
124	C₂²×C₄×C₁₃₇	—	2	1	no	—
125	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
130	C₂×C₈×C₁₃₇	—	2	2	no	—
131	C₂×C₈×C₁₃₇	—	2	2	no	—
132	C₂×C₈×C₁₃₇	—	2	2	no	—
133	C₂×C₈×C₁₃₇	—	2	2	no	—
134	C₂×C₈×C₁₃₇	—	2	2	no	—
135	C₂×C₈×C₁₃₇	—	2	2	no	—
136	C₄⋊C₄×C₁₃₇	—	2	4	no	—
137	C₄⋊C₄×C₁₃₇	—	2	2	no	—
138	C₄⋊C₄×C₁₃₇	—	2	2	no	—
139	C₄⋊C₄×C₁₃₇	—	2	2	no	—
140	C₄⋊C₄×C₁₃₇	—	8	2	no	—
141	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
142	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
143	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
144	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
145	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
146	C₄²×C₁₃₇	—	2	2	no	—
147	C₄²×C₁₃₇	—	8	2	no	—
148	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
149	C₄²×C₁₃₇	#41	1	2	yes	—
150	C₄²×C₁₃₇	#41	1	4	yes	—
151	C₂³×C₁₃₇	—	4	1	no	—
152	C₂³×C₁₃₇	—	4	1	no	—
153	C₂³×C₁₃₇	—	4	1	no	—
154	C₂³×C₁₃₇	—	4	1	no	—
155	C₂³×C₁₃₇	—	4	1	no	—
156	C₂³×C₁₃₇	—	4	1	no	—
157	C₂³×C₁₃₇	—	4	1	no	—
158	C₂³×C₁₃₇	—	4	1	no	—
159	C₂³×C₁₃₇	—	4	1	no	—
160	C₂³×C₁₃₇	—	4	2	no	—
161	C₂³×C₁₃₇	—	4	2	no	—
162	C₂³×C₁₃₇	—	4	2	no	—
163	C₂³×C₁₃₇	—	4	2	no	—
164	C₂³×C₁₃₇	—	4	2	no	—
165	C₂³×C₁₃₇	—	4	2	no	—
166	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₃₇	—	4	2	no	—
168	Q₈×C₁₃₇	—	4	2	no	—
169	Q₈×C₁₃₇	—	8	4	no	—
170	D₄×C₁₃₇	—	4	2	no	—
171	D₄×C₁₃₇	—	4	2	no	—
172	D₄×C₁₃₇	—	4	2	no	—
173	D₄×C₁₃₇	—	4	2	no	—
174	D₄×C₁₃₇	—	4	2	no	—
175	D₄×C₁₃₇	—	4	2	no	—
176	D₄×C₁₃₇	—	8	8	no	—
177	D₄×C₁₃₇	—	8	4	no	—
178	D₄×C₁₃₇	—	8	4	no	—
179	D₄×C₁₃₇	—	8	8	no	—
180	C₂×C₄×C₁₃₇	—	2	2	no	—
181	C₂×C₄×C₁₃₇	—	2	2	no	—
182	C₂×C₄×C₁₃₇	—	2	2	no	—
183	C₂×C₄×C₁₃₇	—	2	2	no	—
184	C₂×C₄×C₁₃₇	—	2	4	no	—
185	C₂×C₄×C₁₃₇	—	2	2	no	—
186	C₂×C₄×C₁₃₇	—	2	2	no	—
187	C₂×C₄×C₁₃₇	—	2	2	no	—
188	C₂×C₄×C₁₃₇	—	4	2	no	—
189	C₂×C₄×C₁₃₇	—	4	2	no	—
190	C₂×C₄×C₁₃₇	—	4	1	no	—
191	C₂×C₄×C₁₃₇	—	4	1	no	—
192	C₂×C₄×C₁₃₇	—	4	1	no	—
193	C₂×C₄×C₁₃₇	—	4	2	no	—
194	C₂×C₄×C₁₃₇	—	4	2	no	—
195	C₂×C₄×C₁₃₇	—	4	2	no	—
196	C₂×C₄×C₁₃₇	#121	1	2	yes	—
197	C₂×C₄×C₁₃₇	#121	1	2	yes	—
198	C₂×C₄×C₁₃₇	#124	1	4	yes	—
199	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
201	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
203	C₈×C₁₃₇	—	4	2	no	—
204	C₈×C₁₃₇	—	4	2	no	—
205	C₂²×C₁₃₇	—	8	2	no	—
206	C₂²×C₁₃₇	—	8	2	no	—
207	C₂²×C₁₃₇	—	8	2	no	—
208	C₂²×C₁₃₇	—	8	2	no	—
209	C₂²×C₁₃₇	—	8	2	no	—
210	C₂²×C₁₃₇	—	8	2	no	—
211	C₂²×C₁₃₇	—	8	1	no	—
212	C₂²×C₁₃₇	—	8	1	no	—
213	C₂²×C₁₃₇	—	8	1	no	—
214	C₂²×C₁₃₇	—	8	1	no	—
215	C₂²×C₁₃₇	—	8	1	no	—
216	C₂²×C₁₃₇	—	8	1	no	—
217	C₂²×C₁₃₇	—	8	1	no	—
218	C₂²×C₁₃₇	—	8	1	no	—
219	C₂²×C₁₃₇	—	8	1	no	—
220	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
221	C₂²×C₁₃₇	C₂×#124	1	1	yes	characteristic
222	C₂²×C₁₃₇	#535	1	1	yes	characteristic
223	C₂²×C₁₃₇	#576	1	2	yes	—
224	C₂²×C₁₃₇	#577	1	2	yes	—
225	C₄×C₁₃₇	—	2	4	no	—
226	C₄×C₁₃₇	—	2	2	no	—
227	C₄×C₁₃₇	—	2	2	no	—
228	C₄×C₁₃₇	—	4	2	no	—
229	C₄×C₁₃₇	—	4	4	no	—
230	C₄×C₁₃₇	—	8	2	no	—
231	C₄×C₁₃₇	—	8	1	no	—
232	C₄×C₁₃₇	#550	1	2	yes	—
233	C₄×C₁₃₇	#559	1	2	yes	—
234	C₂×C₁₃₇	—	16	1	no	—
235	C₂×C₁₃₇	—	16	1	no	—
236	C₂×C₁₃₇	—	16	1	no	—
237	C₂×C₁₃₇	#2548	1	1	yes	characteristic
238	C₂×C₁₃₇	#3041	1	1	yes	characteristic
239	C₂×C₁₃₇	#3043	1	1	yes	characteristic
240	C₂×C₁₃₇	#3136	1	2	yes	—
241	C₂×C₁₃₇	#3224	1	2	yes	—
242	#28759	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₁₃₇	#28759	1	1	yes	characteristic, direct product factor, Sylow
244	C₂×#489	C₂×C₁₃₇	1	1	yes	characteristic, complemented
245	C₂×#486	C₂×C₁₃₇	1	1	yes	characteristic, complemented
246	#2657	C₂×C₁₃₇	1	1	yes	characteristic
247	#2331	C₂×C₁₃₇	1	1	yes	characteristic, complemented
248	#2042	C₂×C₁₃₇	1	2	yes	complemented
249	#2041	C₂×C₁₃₇	1	2	yes	complemented
250	#1983	C₂×C₁₃₇	1	2	yes	complemented
251	#1982	C₂×C₁₃₇	1	2	yes	complemented
252	#1961	C₂×C₁₃₇	1	1	yes	characteristic, complemented
253	#1958	C₂×C₁₃₇	1	1	yes	characteristic, complemented
254	#1768	C₂×C₁₃₇	1	1	yes	characteristic, complemented
255	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
256	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
257	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
258	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
259	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
260	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
261	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
262	#489	—	2	4	no	—
263	#486	—	2	4	no	—
264	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
265	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
266	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
267	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
268	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
269	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
270	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
271	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
272	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
273	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
274	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
275	#392	—	2	2	no	—
276	#392	—	2	2	no	—
277	#391	—	2	2	no	—
278	#389	C₂²×C₁₃₇	1	2	yes	—
279	#387	—	2	2	no	—
280	#382	C₂²×C₁₃₇	1	1	yes	characteristic
281	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
282	#376	C₂²×C₁₃₇	1	1	yes	characteristic
283	#336	C₂²×C₁₃₇	1	2	yes	—
284	C₂²×Q₈	—	2	1	no	—
285	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
286	C₂²×D₄	—	2	2	no	—
287	C₂²×D₄	—	2	1	no	—
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	—	2	2	no	—
290	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
291	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
292	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
294	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₄⋊Q₈	D₄×C₁₃₇	1	4	yes	complemented
297	#127	—	2	2	no	—
298	#127	—	2	2	no	—
299	#127	—	2	4	no	—
300	#127	—	4	2	no	—
301	#124	—	2	2	no	—
302	#124	—	2	2	no	—
303	#124	—	2	4	no	—
304	#124	—	4	2	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₄²	—	2	2	no	—
314	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
317	C₄⋊C₈	—	2	4	no	—
318	#103	—	2	4	no	—
319	#103	—	4	2	no	—
320	#102	—	2	4	no	—
321	#102	—	2	4	no	—
322	#102	—	2	4	no	—
323	#102	—	4	2	no	—
324	#102	—	4	2	no	—
325	#102	—	4	2	no	—
326	#97	—	2	2	no	—
327	C₄×C₈	—	2	2	no	—
328	#95	—	2	2	no	—
329	#95	—	2	1	no	—
330	#95	—	2	1	no	—
331	#95	—	2	2	no	—
332	#95	D₄×C₁₃₇	1	2	yes	—
333	#95	D₄×C₁₃₇	1	2	yes	—
334	C₂⁴	—	2	1	no	—
335	C₂⁴	—	2	1	no	—
336	C₂⁴	—	2	1	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	8	2	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	4	4	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	—	8	2	no	—
360	C₂×D₄	—	8	2	no	—
361	C₂×D₄	—	8	2	no	—
362	C₂×D₄	—	8	2	no	—
363	C₂×D₄	—	8	2	no	—
364	C₂×D₄	—	8	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	8	2	no	—
384	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
385	C₂²⋊C₄	—	4	4	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₂²⋊C₄	—	4	2	no	—
388	C₂²⋊C₄	—	4	4	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	8	2	no	—
391	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
392	C₄²	#41×C₁₃₇	1	2	yes	—
393	C₄²	#41×C₁₃₇	1	4	yes	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
410	Q₈	—	4	2	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	8	4	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	8	4	no	—
420	D₄	—	8	4	no	—
421	D₄	—	8	8	no	—
422	D₄	—	8	8	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	#121×C₁₃₇	1	2	yes	—
440	C₂×C₄	#121×C₁₃₇	1	2	yes	—
441	C₂×C₄	#124×C₁₃₇	1	4	yes	—
442	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
443	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
444	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
445	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
446	C₈	—	4	2	no	—
447	C₈	—	4	2	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
464	C₂²	C₂×#124×C₁₃₇	1	1	yes	characteristic
465	C₂²	#535×C₁₃₇	1	1	yes	characteristic
466	C₂²	#576×C₁₃₇	1	2	yes	—
467	C₂²	#577×C₁₃₇	1	2	yes	—
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	4	no	—
471	C₄	—	4	4	no	—
472	C₄	—	4	2	no	—
473	C₄	—	8	1	no	—
474	C₄	—	8	2	no	—
475	C₄	#550×C₁₃₇	1	2	yes	—
476	C₄	#559×C₁₃₇	1	2	yes	—
477	C₂	—	16	1	no	—
478	C₂	—	16	1	no	—
479	C₂	—	16	1	no	—
480	C₂	#2548×C₁₃₇	1	1	yes	characteristic
481	C₂	#3041×C₁₃₇	1	1	yes	characteristic
482	C₂	#3043×C₁₃₇	1	1	yes	characteristic
483	C₂	#3136×C₁₃₇	1	2	yes	—
484	C₂	#3224×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	#2657×C₁₃₇	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ #376×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#489×C₁₃₇	C₂	semidirect
2. C₂×#486×C₁₃₇	C₂	semidirect
4. #2331×C₁₃₇	C₂	semidirect
5. #2042×C₁₃₇	C₂	semidirect
6. #2041×C₁₃₇	C₂	semidirect
7. #1983×C₁₃₇	C₂	semidirect
8. #1982×C₁₃₇	C₂	semidirect
9. #1961×C₁₃₇	C₂	semidirect
10. #1958×C₁₃₇	C₂	semidirect
11. #1768×C₁₃₇	C₂	semidirect
53. C₄⋊Q₈×C₁₃₇	D₄	semidirect
242. #28759	C₁₃₇	direct (N × H)
243. C₁₃₇	#28759	direct (N × H)
244. C₂×#489	C₂×C₁₃₇	semidirect
245. C₂×#486	C₂×C₁₃₇	semidirect
247. #2331	C₂×C₁₃₇	semidirect
248. #2042	C₂×C₁₃₇	semidirect
249. #2041	C₂×C₁₃₇	semidirect
250. #1983	C₂×C₁₃₇	semidirect
251. #1982	C₂×C₁₃₇	semidirect
252. #1961	C₂×C₁₃₇	semidirect
253. #1958	C₂×C₁₃₇	semidirect
254. #1768	C₂×C₁₃₇	semidirect
296. C₄⋊Q₈	D₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#489×C₁₃₇	2
C₂×#486×C₁₃₇	2
#2657×C₁₃₇	2
#2331×C₁₃₇	2
#2042×C₁₃₇	2
#2041×C₁₃₇	2
#1983×C₁₃₇	2
#1982×C₁₃₇	2
#1961×C₁₃₇	2
#1958×C₁₃₇	2
#1768×C₁₃₇	2
#28759	137

Subgroups — C137×#28759 #46878145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28759 #46878145