Subgroups — C₁₃₇×#25942 #46875328

Order 35072.

1054 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#489×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#464×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2592×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#2024×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2023×C₁₃₇	C₂	1	2	yes	maximal
7	#1988×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1985×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1880×C₁₃₇	C₂	1	2	yes	maximal
10	#1878×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	#1763×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
14	Q₈²×C₁₃₇	—	2	4	no	—
15	Q₈²×C₁₃₇	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₁₃₇	—	2	2	no	—
17	C₂×C₄⋊Q₈×C₁₃₇	—	2	1	no	—
18	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	2	yes	—
19	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃₇	—	2	1	no	—
22	C₂×C₄×Q₈×C₁₃₇	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
25	#489×C₁₃₇	—	2	4	no	—
26	#464×C₁₃₇	—	2	4	no	—
27	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
29	C₂×#103×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
31	C₂×#102×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
33	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
34	#397×C₁₃₇	—	2	1	no	—
35	#393×C₁₃₇	—	2	1	no	—
36	#391×C₁₃₇	C₂²	1	2	yes	—
37	#390×C₁₃₇	C₂²	1	2	yes	—
38	#388×C₁₃₇	—	2	2	no	—
39	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
40	#340×C₁₃₇	C₂²	1	2	yes	—
41	#340×C₁₃₇	C₂²	1	2	yes	—
42	#340×C₁₃₇	C₂²	1	2	yes	—
43	#336×C₁₃₇	C₂²	1	2	yes	—
44	#336×C₁₃₇	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃₇	—	2	2	no	—
46	C₂²×Q₈×C₁₃₇	—	2	1	no	—
47	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
51	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
52	C₂×Q₁₆×C₁₃₇	—	2	4	no	—
53	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
54	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
55	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₁₃₇	—	2	16	no	—
59	C₄⋊Q₈×C₁₃₇	—	2	8	no	—
60	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
61	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
62	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
63	C₄⋊Q₈×C₁₃₇	D₄	1	4	yes	—
64	#124×C₁₃₇	—	2	2	no	—
65	#124×C₁₃₇	—	2	2	no	—
66	C₄×Q₈×C₁₃₇	—	2	8	no	—
67	C₄×Q₈×C₁₃₇	—	2	4	no	—
68	C₄×Q₈×C₁₃₇	—	2	4	no	—
69	C₄×Q₈×C₁₃₇	—	2	2	no	—
70	C₄×Q₈×C₁₃₇	—	2	2	no	—
71	C₄×Q₈×C₁₃₇	—	2	2	no	—
72	C₄×Q₈×C₁₃₇	D₄	1	4	yes	—
73	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
86	C₂×C₄²×C₁₃₇	—	2	2	no	—
87	C₂×C₄²×C₁₃₇	—	2	1	no	—
88	C₂×C₄²×C₁₃₇	—	2	1	no	—
89	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₁₃₇	—	2	2	no	—
92	#103×C₁₃₇	—	2	4	no	—
93	#103×C₁₃₇	—	2	2	no	—
94	#103×C₁₃₇	—	2	4	no	—
95	#102×C₁₃₇	—	2	2	no	—
96	#102×C₁₃₇	—	2	4	no	—
97	#97×C₁₃₇	—	2	2	no	—
98	#95×C₁₃₇	—	2	1	no	—
99	#95×C₁₃₇	—	2	2	no	—
100	#95×C₁₃₇	—	2	2	no	—
101	C₂⁴×C₁₃₇	—	2	1	no	—
102	C₂×Q₈×C₁₃₇	—	2	8	no	—
103	C₂×Q₈×C₁₃₇	—	2	2	no	—
104	C₂×Q₈×C₁₃₇	—	2	4	no	—
105	C₂×Q₈×C₁₃₇	—	2	4	no	—
106	C₂×Q₈×C₁₃₇	—	2	1	no	—
107	C₂×Q₈×C₁₃₇	—	2	2	no	—
108	C₂×Q₈×C₁₃₇	—	2	1	no	—
109	C₂×Q₈×C₁₃₇	—	2	1	no	—
110	C₂×Q₈×C₁₃₇	—	2	2	no	—
111	C₂×Q₈×C₁₃₇	—	2	2	no	—
112	C₂×Q₈×C₁₃₇	—	8	1	no	—
113	C₂×Q₈×C₁₃₇	—	8	1	no	—
114	C₂×Q₈×C₁₃₇	—	8	2	no	—
115	C₂×Q₈×C₁₃₇	—	8	2	no	—
116	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
117	C₂×Q₈×C₁₃₇	#41	1	4	yes	—
118	C₂×D₄×C₁₃₇	—	2	1	no	—
119	C₂×D₄×C₁₃₇	—	2	1	no	—
120	C₂×D₄×C₁₃₇	—	2	2	no	—
121	C₂×D₄×C₁₃₇	—	2	2	no	—
122	C₂²×C₄×C₁₃₇	—	2	1	no	—
123	C₂²×C₄×C₁₃₇	—	2	2	no	—
124	C₂²×C₄×C₁₃₇	—	2	1	no	—
125	C₂²×C₄×C₁₃₇	—	2	1	no	—
126	C₂²×C₄×C₁₃₇	—	2	2	no	—
127	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
132	Q₁₆×C₁₃₇	—	4	4	no	—
133	SD₁₆×C₁₃₇	—	4	4	no	—
134	C₂×C₈×C₁₃₇	—	2	2	no	—
135	C₂×C₈×C₁₃₇	—	2	1	no	—
136	C₂×C₈×C₁₃₇	—	2	1	no	—
137	C₂×C₈×C₁₃₇	—	2	2	no	—
138	C₂×C₈×C₁₃₇	—	2	2	no	—
139	C₂×C₈×C₁₃₇	—	2	2	no	—
140	C₂×C₈×C₁₃₇	—	2	2	no	—
141	C₄⋊C₄×C₁₃₇	—	2	8	no	—
142	C₄⋊C₄×C₁₃₇	—	2	8	no	—
143	C₄⋊C₄×C₁₃₇	—	2	4	no	—
144	C₄⋊C₄×C₁₃₇	—	2	4	no	—
145	C₄⋊C₄×C₁₃₇	—	2	4	no	—
146	C₄⋊C₄×C₁₃₇	—	2	2	no	—
147	C₄⋊C₄×C₁₃₇	—	2	2	no	—
148	C₄⋊C₄×C₁₃₇	—	2	1	no	—
149	C₄⋊C₄×C₁₃₇	—	2	2	no	—
150	C₄⋊C₄×C₁₃₇	—	2	2	no	—
151	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
152	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
153	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
154	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
155	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
156	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
157	C₄²×C₁₃₇	—	2	8	no	—
158	C₄²×C₁₃₇	—	2	4	no	—
159	C₄²×C₁₃₇	—	2	2	no	—
160	C₄²×C₁₃₇	—	2	2	no	—
161	C₄²×C₁₃₇	—	8	1	no	—
162	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
163	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
164	C₂³×C₁₃₇	—	4	1	no	—
165	C₂³×C₁₃₇	—	4	2	no	—
166	C₂³×C₁₃₇	—	4	2	no	—
167	C₂³×C₁₃₇	—	4	1	no	—
168	C₂³×C₁₃₇	—	4	1	no	—
169	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₁₃₇	—	2	8	no	—
171	Q₈×C₁₃₇	—	2	2	no	—
172	Q₈×C₁₃₇	—	2	4	no	—
173	Q₈×C₁₃₇	—	4	1	no	—
174	Q₈×C₁₃₇	—	4	1	no	—
175	Q₈×C₁₃₇	—	4	2	no	—
176	Q₈×C₁₃₇	—	8	4	no	—
177	Q₈×C₁₃₇	—	8	8	no	—
178	Q₈×C₁₃₇	#124	1	4	yes	—
179	D₄×C₁₃₇	—	4	1	no	—
180	D₄×C₁₃₇	—	4	1	no	—
181	D₄×C₁₃₇	—	4	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	1	no	—
188	C₂×C₄×C₁₃₇	—	2	1	no	—
189	C₂×C₄×C₁₃₇	—	2	2	no	—
190	C₂×C₄×C₁₃₇	—	2	4	no	—
191	C₂×C₄×C₁₃₇	—	2	2	no	—
192	C₂×C₄×C₁₃₇	—	2	2	no	—
193	C₂×C₄×C₁₃₇	—	2	2	no	—
194	C₂×C₄×C₁₃₇	—	4	2	no	—
195	C₂×C₄×C₁₃₇	—	4	1	no	—
196	C₂×C₄×C₁₃₇	—	4	2	no	—
197	C₂×C₄×C₁₃₇	—	4	1	no	—
198	C₂×C₄×C₁₃₇	—	4	1	no	—
199	C₂×C₄×C₁₃₇	—	4	2	no	—
200	C₂×C₄×C₁₃₇	—	4	2	no	—
201	C₂×C₄×C₁₃₇	—	4	2	no	—
202	C₂×C₄×C₁₃₇	—	4	2	no	—
203	C₂×C₄×C₁₃₇	#120	1	2	yes	—
204	C₂×C₄×C₁₃₇	#120	1	2	yes	—
205	C₂×C₄×C₁₃₇	#137	1	4	yes	—
206	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
209	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
210	C₈×C₁₃₇	—	4	1	no	—
211	C₈×C₁₃₇	—	4	1	no	—
212	C₈×C₁₃₇	—	4	2	no	—
213	C₂²×C₁₃₇	—	8	2	no	—
214	C₂²×C₁₃₇	—	8	2	no	—
215	C₂²×C₁₃₇	—	8	1	no	—
216	C₂²×C₁₃₇	—	8	1	no	—
217	C₂²×C₁₃₇	—	8	1	no	—
218	C₂²×C₁₃₇	C₂×#120	1	1	yes	characteristic
219	C₂²×C₁₃₇	#548	1	2	yes	—
220	C₂²×C₁₃₇	C₂×#137	1	2	yes	—
221	C₂²×C₁₃₇	#576	1	1	yes	characteristic
222	C₂²×C₁₃₇	#577	1	1	yes	characteristic
223	C₄×C₁₃₇	—	2	4	no	—
224	C₄×C₁₃₇	—	2	2	no	—
225	C₄×C₁₃₇	—	2	4	no	—
226	C₄×C₁₃₇	—	2	2	no	—
227	C₄×C₁₃₇	—	4	2	no	—
228	C₄×C₁₃₇	—	4	4	no	—
229	C₄×C₁₃₇	—	4	2	no	—
230	C₄×C₁₃₇	—	8	2	no	—
231	C₄×C₁₃₇	—	8	1	no	—
232	C₄×C₁₃₇	C₂×#124	1	1	yes	characteristic
233	C₄×C₁₃₇	#536	1	1	yes	characteristic
234	C₄×C₁₃₇	#548	1	2	yes	—
235	C₂×C₁₃₇	—	16	1	no	—
236	C₂×C₁₃₇	#2436	1	1	yes	characteristic
237	C₂×C₁₃₇	#3004	1	1	yes	characteristic
238	C₂×C₁₃₇	#3012	1	1	yes	characteristic
239	C₂×C₁₃₇	#3369	1	2	yes	—
240	C₂×C₁₃₇	#3375	1	2	yes	—
241	#25942	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₁₃₇	#25942	1	1	yes	characteristic, direct product factor, Sylow
243	C₂×Q₈²	C₂×C₁₃₇	1	1	yes	characteristic, complemented
244	C₂×#489	C₂×C₁₃₇	1	1	yes	characteristic
245	C₂×#464	C₂×C₁₃₇	1	1	yes	characteristic
246	#2592	C₂×C₁₃₇	1	1	yes	characteristic
247	#2024	C₂×C₁₃₇	1	2	yes	complemented
248	#2023	C₂×C₁₃₇	1	2	yes	—
249	#1988	C₂×C₁₃₇	1	1	yes	characteristic, complemented
250	#1985	C₂×C₁₃₇	1	1	yes	characteristic, complemented
251	#1880	C₂×C₁₃₇	1	2	yes	—
252	#1878	C₂×C₁₃₇	1	2	yes	complemented
253	#1763	C₂×C₁₃₇	1	1	yes	characteristic, complemented
254	C₂²×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
255	C₂²×SD₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
256	Q₈²	—	2	4	no	—
257	Q₈²	—	2	4	no	—
258	C₂×C₄⋊Q₈	—	2	2	no	—
259	C₂×C₄⋊Q₈	—	2	1	no	—
260	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
261	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
262	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
263	C₂×C₄×Q₈	—	2	1	no	—
264	C₂×C₄×Q₈	C₂²×C₁₃₇	1	2	yes	—
265	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
266	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
267	#489	—	2	4	no	—
268	#464	—	2	4	no	—
269	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
270	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
271	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
272	C₂×#103	C₂²×C₁₃₇	1	1	yes	characteristic
273	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
274	C₂×#102	C₂²×C₁₃₇	1	1	yes	characteristic
275	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
276	#397	—	2	1	no	—
277	#393	—	2	1	no	—
278	#391	C₂²×C₁₃₇	1	2	yes	—
279	#390	C₂²×C₁₃₇	1	2	yes	—
280	#388	—	2	2	no	—
281	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
282	#340	C₂²×C₁₃₇	1	2	yes	—
283	#340	C₂²×C₁₃₇	1	2	yes	—
284	#340	C₂²×C₁₃₇	1	2	yes	—
285	#336	C₂²×C₁₃₇	1	2	yes	—
286	#336	C₂²×C₁₃₇	1	2	yes	—
287	C₂²×Q₈	—	2	2	no	—
288	C₂²×Q₈	—	2	1	no	—
289	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
290	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
291	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
292	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
293	C₂×Q₁₆	—	2	2	no	—
294	C₂×Q₁₆	—	2	4	no	—
295	C₂×SD₁₆	—	2	2	no	—
296	C₂×SD₁₆	—	2	4	no	—
297	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
300	C₄⋊Q₈	—	2	16	no	—
301	C₄⋊Q₈	—	2	8	no	—
302	C₄⋊Q₈	—	2	4	no	—
303	C₄⋊Q₈	—	2	4	no	—
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	D₄×C₁₃₇	1	4	yes	—
306	#124	—	2	2	no	—
307	#124	—	2	2	no	—
308	C₄×Q₈	—	2	8	no	—
309	C₄×Q₈	—	2	4	no	—
310	C₄×Q₈	—	2	4	no	—
311	C₄×Q₈	—	2	2	no	—
312	C₄×Q₈	—	2	2	no	—
313	C₄×Q₈	—	2	2	no	—
314	C₄×Q₈	D₄×C₁₃₇	1	4	yes	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
320	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₄²	—	2	2	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
332	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
333	C₄⋊C₈	—	2	2	no	—
334	#103	—	2	4	no	—
335	#103	—	2	2	no	—
336	#103	—	2	4	no	—
337	#102	—	2	2	no	—
338	#102	—	2	4	no	—
339	#97	—	2	2	no	—
340	#95	—	2	1	no	—
341	#95	—	2	2	no	—
342	#95	—	2	2	no	—
343	C₂⁴	—	2	1	no	—
344	C₂×Q₈	—	2	8	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	4	no	—
347	C₂×Q₈	—	2	4	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	8	1	no	—
355	C₂×Q₈	—	8	1	no	—
356	C₂×Q₈	—	8	2	no	—
357	C₂×Q₈	—	8	2	no	—
358	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
359	C₂×Q₈	#41×C₁₃₇	1	4	yes	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
374	Q₁₆	—	4	4	no	—
375	SD₁₆	—	4	4	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
394	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	—	4	4	no	—
398	C₂²⋊C₄	—	8	2	no	—
399	C₄²	—	2	8	no	—
400	C₄²	—	2	4	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	8	1	no	—
404	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
405	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
412	Q₈	—	2	8	no	—
413	Q₈	—	2	2	no	—
414	Q₈	—	2	4	no	—
415	Q₈	—	4	1	no	—
416	Q₈	—	4	1	no	—
417	Q₈	—	4	2	no	—
418	Q₈	—	8	4	no	—
419	Q₈	—	8	8	no	—
420	Q₈	#124×C₁₃₇	1	4	yes	—
421	D₄	—	4	1	no	—
422	D₄	—	4	1	no	—
423	D₄	—	4	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	#120×C₁₃₇	1	2	yes	—
446	C₂×C₄	#120×C₁₃₇	1	2	yes	—
447	C₂×C₄	#137×C₁₃₇	1	4	yes	—
448	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
449	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
450	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
451	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
452	C₈	—	4	1	no	—
453	C₈	—	4	1	no	—
454	C₈	—	4	2	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	8	2	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	8	1	no	—
460	C₂²	C₂×#120×C₁₃₇	1	1	yes	characteristic
461	C₂²	#548×C₁₃₇	1	2	yes	—
462	C₂²	C₂×#137×C₁₃₇	1	2	yes	—
463	C₂²	#576×C₁₃₇	1	1	yes	characteristic
464	C₂²	#577×C₁₃₇	1	1	yes	characteristic
465	C₄	—	2	4	no	—
466	C₄	—	2	2	no	—
467	C₄	—	2	4	no	—
468	C₄	—	2	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	4	no	—
471	C₄	—	4	2	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	1	no	—
474	C₄	C₂×#124×C₁₃₇	1	1	yes	characteristic
475	C₄	#536×C₁₃₇	1	1	yes	characteristic
476	C₄	#548×C₁₃₇	1	2	yes	—
477	C₂	—	16	1	no	—
478	C₂	#2436×C₁₃₇	1	1	yes	characteristic
479	C₂	#3004×C₁₃₇	1	1	yes	characteristic
480	C₂	#3012×C₁₃₇	1	1	yes	characteristic
481	C₂	#3369×C₁₃₇	1	2	yes	—
482	C₂	#3375×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂²×D₄×C₁₃₇	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂×C₄×Q₈×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈²×C₁₃₇	C₂	semidirect
5. #2024×C₁₃₇	C₂	semidirect
7. #1988×C₁₃₇	C₂	semidirect
8. #1985×C₁₃₇	C₂	semidirect
10. #1878×C₁₃₇	C₂	semidirect
11. #1763×C₁₃₇	C₂	semidirect
241. #25942	C₁₃₇	direct (N × H)
242. C₁₃₇	#25942	direct (N × H)
243. C₂×Q₈²	C₂×C₁₃₇	semidirect
247. #2024	C₂×C₁₃₇	semidirect
249. #1988	C₂×C₁₃₇	semidirect
250. #1985	C₂×C₁₃₇	semidirect
252. #1878	C₂×C₁₃₇	semidirect
253. #1763	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈²×C₁₃₇	2
C₂×#489×C₁₃₇	2
C₂×#464×C₁₃₇	2
#2592×C₁₃₇	2
#2024×C₁₃₇	2
#2023×C₁₃₇	2
#1988×C₁₃₇	2
#1985×C₁₃₇	2
#1880×C₁₃₇	2
#1878×C₁₃₇	2
#1763×C₁₃₇	2
#25942	137

Subgroups — C137×#25942 #46875328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#25942 #46875328