Subgroups — C₁₃₇×#21885 #46871271

Order 35072.

1162 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2285×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1987×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1981×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1892×C₁₃₇	C₂	1	4	yes	maximal
7	#1803×C₁₃₇	C₂	1	4	yes	maximal, complemented
8	C₂³×C₈×C₁₃₇	C₂²	1	2	yes	—
9	#533×C₁₃₇	—	2	4	no	—
10	#533×C₁₃₇	C₄	1	8	yes	complemented
11	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#125×C₁₃₇	—	2	1	no	—
14	C₂×C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃₇	—	2	1	no	—
17	C₂×C₄×Q₈×C₁₃₇	C₂²	1	2	yes	—
18	C₂×#117×C₁₃₇	—	2	1	no	—
19	C₂×#117×C₁₃₇	—	2	1	no	—
20	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₁₃₇	—	2	4	no	—
22	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
23	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
24	C₂×#103×C₁₃₇	C₂²	1	8	yes	—
25	#384×C₁₃₇	C₂²	1	2	yes	—
26	#382×C₁₃₇	—	2	1	no	—
27	#380×C₁₃₇	—	2	1	no	—
28	#380×C₁₃₇	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₁₃₇	—	2	1	no	—
30	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
31	#340×C₁₃₇	C₂²	1	8	yes	—
32	C₂²×Q₈×C₁₃₇	—	2	1	no	—
33	C₂²×Q₈×C₁₃₇	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₃₇	—	2	4	no	—
38	C₂²×C₈×C₁₃₇	—	4	4	no	—
39	C₂²×C₈×C₁₃₇	C₂³	1	4	yes	—
40	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
41	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
42	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	4	yes	—
43	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	4	yes	—
44	#125×C₁₃₇	—	2	8	no	—
45	C₂²⋊Q₈×C₁₃₇	—	2	8	no	—
46	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
47	C₂²⋊Q₈×C₁₃₇	C₂×C₄	1	8	yes	—
48	C₄×Q₈×C₁₃₇	—	2	8	no	—
49	C₄×Q₈×C₁₃₇	—	2	4	no	—
50	C₄×Q₈×C₁₃₇	C₂×C₄	1	8	yes	—
51	#117×C₁₃₇	—	2	8	no	—
52	#117×C₁₃₇	—	4	4	no	—
53	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
64	C₂×C₄²×C₁₃₇	—	2	2	no	—
65	C₂×C₄²×C₁₃₇	—	2	2	no	—
66	C₂×C₄²×C₁₃₇	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃₇	D₄	1	4	yes	—
70	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₁₃₇	—	2	4	no	—
73	C₄⋊C₈×C₁₃₇	—	2	4	no	—
74	#103×C₁₃₇	—	4	8	no	—
75	#95×C₁₃₇	—	2	2	no	—
76	#95×C₁₃₇	—	2	2	no	—
77	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
78	C₂×Q₈×C₁₃₇	—	2	4	no	—
79	C₂×Q₈×C₁₃₇	—	2	2	no	—
80	C₂×Q₈×C₁₃₇	—	2	4	no	—
81	C₂×Q₈×C₁₃₇	—	2	4	no	—
82	C₂×Q₈×C₁₃₇	—	4	4	no	—
83	C₂×Q₈×C₁₃₇	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₁₃₇	—	2	2	no	—
85	C₂²×C₄×C₁₃₇	—	2	2	no	—
86	C₂²×C₄×C₁₃₇	—	2	2	no	—
87	C₂²×C₄×C₁₃₇	—	2	2	no	—
88	C₂²×C₄×C₁₃₇	—	2	4	no	—
89	C₂²×C₄×C₁₃₇	—	4	2	no	—
90	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	4	yes	—
91	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	4	yes	—
92	C₂²×C₄×C₁₃₇	SD₁₆	1	4	yes	—
93	C₂²×C₄×C₁₃₇	Q₁₆	1	4	yes	—
94	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
102	C₂×C₈×C₁₃₇	—	2	4	no	—
103	C₂×C₈×C₁₃₇	—	2	8	no	—
104	C₂×C₈×C₁₃₇	—	4	8	no	—
105	C₄⋊C₄×C₁₃₇	—	2	4	no	—
106	C₄⋊C₄×C₁₃₇	—	2	4	no	—
107	C₄⋊C₄×C₁₃₇	—	2	4	no	—
108	C₄⋊C₄×C₁₃₇	—	2	8	no	—
109	C₄⋊C₄×C₁₃₇	—	2	8	no	—
110	C₄⋊C₄×C₁₃₇	—	2	2	no	—
111	C₄⋊C₄×C₁₃₇	—	2	4	no	—
112	C₄⋊C₄×C₁₃₇	—	2	4	no	—
113	C₄⋊C₄×C₁₃₇	—	4	4	no	—
114	C₄⋊C₄×C₁₃₇	—	4	4	no	—
115	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
116	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
117	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
118	C₄²×C₁₃₇	—	2	8	no	—
119	C₄²×C₁₃₇	—	4	4	no	—
120	C₄²×C₁₃₇	C₂²⋊C₄	1	4	yes	—
121	C₄²×C₁₃₇	C₂²⋊C₄	1	4	yes	—
122	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
123	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
124	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
125	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
126	C₂³×C₁₃₇	—	2	2	no	—
127	C₂³×C₁₃₇	—	2	2	no	—
128	C₂³×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
129	C₂³×C₁₃₇	C₂×SD₁₆	1	2	yes	—
130	C₂³×C₁₃₇	C₂×Q₁₆	1	2	yes	—
131	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
132	Q₈×C₁₃₇	—	2	8	no	—
133	Q₈×C₁₃₇	—	4	8	no	—
134	Q₈×C₁₃₇	—	4	2	no	—
135	Q₈×C₁₃₇	—	4	2	no	—
136	C₂×C₄×C₁₃₇	—	2	2	no	—
137	C₂×C₄×C₁₃₇	—	2	2	no	—
138	C₂×C₄×C₁₃₇	—	2	2	no	—
139	C₂×C₄×C₁₃₇	—	2	4	no	—
140	C₂×C₄×C₁₃₇	—	2	2	no	—
141	C₂×C₄×C₁₃₇	—	2	2	no	—
142	C₂×C₄×C₁₃₇	—	2	4	no	—
143	C₂×C₄×C₁₃₇	—	2	4	no	—
144	C₂×C₄×C₁₃₇	—	4	4	no	—
145	C₂×C₄×C₁₃₇	—	4	4	no	—
146	C₂×C₄×C₁₃₇	—	4	4	no	—
147	C₂×C₄×C₁₃₇	—	4	4	no	—
148	C₂×C₄×C₁₃₇	—	4	4	no	—
149	C₂×C₄×C₁₃₇	—	4	4	no	—
150	C₂×C₄×C₁₃₇	#103	1	16	yes	complemented
151	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	2	yes	—
157	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	2	yes	—
158	C₂×C₄×C₁₃₇	C₂×Q₁₆	1	2	yes	—
159	C₂×C₄×C₁₃₇	C₂×Q₁₆	1	2	yes	—
160	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
163	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
164	C₈×C₁₃₇	—	4	4	no	—
165	C₂²×C₁₃₇	—	2	2	no	—
166	C₂²×C₁₃₇	—	2	2	no	—
167	C₂²×C₁₃₇	—	2	4	no	—
168	C₂²×C₁₃₇	—	2	4	no	—
169	C₂²×C₁₃₇	C₂×#103	1	4	yes	—
170	C₂²×C₁₃₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₁₃₇	#537	1	2	yes	—
172	C₂²×C₁₃₇	C₂²×SD₁₆	1	1	yes	characteristic
173	C₂²×C₁₃₇	C₂²×Q₁₆	1	1	yes	characteristic
174	C₂²×C₁₃₇	#575	1	2	yes	—
175	C₄×C₁₃₇	—	2	2	no	—
176	C₄×C₁₃₇	—	2	2	no	—
177	C₄×C₁₃₇	—	2	2	no	—
178	C₄×C₁₃₇	—	4	4	no	—
179	C₄×C₁₃₇	—	4	4	no	—
180	C₄×C₁₃₇	—	8	4	no	—
181	C₄×C₁₃₇	C₂×#103	1	4	yes	—
182	C₄×C₁₃₇	C₂×#103	1	4	yes	—
183	C₄×C₁₃₇	#520	1	2	yes	—
184	C₄×C₁₃₇	#535	1	1	yes	characteristic
185	C₄×C₁₃₇	#536	1	1	yes	characteristic
186	C₂×C₁₃₇	—	2	4	no	—
187	C₂×C₁₃₇	#2311	1	1	yes	characteristic
188	C₂×C₁₃₇	C₂²×#103	1	1	yes	characteristic
189	C₂×C₁₃₇	#2896	1	1	yes	characteristic
190	C₂×C₁₃₇	#3246	1	2	yes	—
191	C₂×C₁₃₇	#3249	1	2	yes	—
192	#21885	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₁₃₇	#21885	1	1	yes	characteristic, direct product factor, Sylow
194	C₂×#533	C₂×C₁₃₇	1	1	yes	characteristic
195	C₂²×C₄⋊C₈	C₂×C₁₃₇	1	1	yes	characteristic
196	#2285	C₂×C₁₃₇	1	1	yes	characteristic
197	#1987	C₂×C₁₃₇	1	2	yes	complemented
198	#1981	C₂×C₁₃₇	1	2	yes	complemented
199	#1892	C₂×C₁₃₇	1	4	yes	—
200	#1803	C₂×C₁₃₇	1	4	yes	complemented
201	C₂³×C₈	C₂²×C₁₃₇	1	2	yes	—
202	#533	—	2	4	no	—
203	#533	C₄×C₁₃₇	1	8	yes	complemented
204	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
205	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
206	C₂×#125	—	2	1	no	—
207	C₂×C₂²⋊Q₈	—	2	1	no	—
208	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
209	C₂×C₄×Q₈	—	2	1	no	—
210	C₂×C₄×Q₈	C₂²×C₁₃₇	1	2	yes	—
211	C₂×#117	—	2	1	no	—
212	C₂×#117	—	2	1	no	—
213	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
214	C₂×C₄⋊C₈	—	2	4	no	—
215	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
216	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
217	C₂×#103	C₂²×C₁₃₇	1	8	yes	—
218	#384	C₂²×C₁₃₇	1	2	yes	—
219	#382	—	2	1	no	—
220	#380	—	2	1	no	—
221	#380	C₂²×C₁₃₇	1	2	yes	—
222	C₄×C₄⋊C₄	—	2	1	no	—
223	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
224	#340	C₂²×C₁₃₇	1	8	yes	—
225	C₂²×Q₈	—	2	1	no	—
226	C₂²×Q₈	C₂³×C₁₃₇	1	2	yes	—
227	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
228	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
230	C₂²×C₈	—	2	4	no	—
231	C₂²×C₈	—	4	4	no	—
232	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
233	C₄⋊Q₈	—	2	2	no	—
234	C₄⋊Q₈	—	2	2	no	—
235	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	4	yes	—
236	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	4	yes	—
237	#125	—	2	8	no	—
238	C₂²⋊Q₈	—	2	8	no	—
239	C₂²⋊Q₈	—	2	4	no	—
240	C₂²⋊Q₈	C₂×C₄×C₁₃₇	1	8	yes	—
241	C₄×Q₈	—	2	8	no	—
242	C₄×Q₈	—	2	4	no	—
243	C₄×Q₈	C₂×C₄×C₁₃₇	1	8	yes	—
244	#117	—	2	8	no	—
245	#117	—	4	4	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
254	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	C₂×C₄×C₁₃₇	1	4	yes	—
260	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
261	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
262	C₂×C₄²	D₄×C₁₃₇	1	4	yes	—
263	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
265	C₄⋊C₈	—	2	4	no	—
266	C₄⋊C₈	—	2	4	no	—
267	#103	—	4	8	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
271	C₂×Q₈	—	2	4	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	4	4	no	—
276	C₂×Q₈	C₂²×C₄×C₁₃₇	1	4	yes	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	4	yes	—
284	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	4	yes	—
285	C₂²×C₄	SD₁₆×C₁₃₇	1	4	yes	—
286	C₂²×C₄	Q₁₆×C₁₃₇	1	4	yes	—
287	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
294	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	8	no	—
297	C₂×C₈	—	4	8	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	8	no	—
302	C₄⋊C₄	—	2	8	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	4	4	no	—
307	C₄⋊C₄	—	4	4	no	—
308	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
309	C₂²⋊C₄	—	2	8	no	—
310	C₂²⋊C₄	—	4	4	no	—
311	C₄²	—	2	8	no	—
312	C₄²	—	4	4	no	—
313	C₄²	C₂²⋊C₄×C₁₃₇	1	4	yes	—
314	C₄²	C₂²⋊C₄×C₁₃₇	1	4	yes	—
315	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
316	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
317	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
318	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
322	C₂³	C₂×SD₁₆×C₁₃₇	1	2	yes	—
323	C₂³	C₂×Q₁₆×C₁₃₇	1	2	yes	—
324	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
325	Q₈	—	2	8	no	—
326	Q₈	—	4	8	no	—
327	Q₈	—	4	2	no	—
328	Q₈	—	4	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	#103×C₁₃₇	1	16	yes	complemented
344	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
345	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
346	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
347	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
348	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
349	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	2	yes	—
350	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	2	yes	—
351	C₂×C₄	C₂×Q₁₆×C₁₃₇	1	2	yes	—
352	C₂×C₄	C₂×Q₁₆×C₁₃₇	1	2	yes	—
353	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
354	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
355	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
356	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
357	C₈	—	4	4	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	4	no	—
361	C₂²	—	2	4	no	—
362	C₂²	C₂×#103×C₁₃₇	1	4	yes	—
363	C₂²	C₂²×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
364	C₂²	#537×C₁₃₇	1	2	yes	—
365	C₂²	C₂²×SD₁₆×C₁₃₇	1	1	yes	characteristic
366	C₂²	C₂²×Q₁₆×C₁₃₇	1	1	yes	characteristic
367	C₂²	#575×C₁₃₇	1	2	yes	—
368	C₄	—	2	2	no	—
369	C₄	—	2	2	no	—
370	C₄	—	2	2	no	—
371	C₄	—	4	4	no	—
372	C₄	—	4	4	no	—
373	C₄	—	8	4	no	—
374	C₄	C₂×#103×C₁₃₇	1	4	yes	—
375	C₄	C₂×#103×C₁₃₇	1	4	yes	—
376	C₄	#520×C₁₃₇	1	2	yes	—
377	C₄	#535×C₁₃₇	1	1	yes	characteristic
378	C₄	#536×C₁₃₇	1	1	yes	characteristic
379	C₂	—	2	4	no	—
380	C₂	#2311×C₁₃₇	1	1	yes	characteristic
381	C₂	C₂²×#103×C₁₃₇	1	1	yes	characteristic
382	C₂	#2896×C₁₃₇	1	1	yes	characteristic
383	C₂	#3246×C₁₃₇	1	2	yes	—
384	C₂	#3249×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂⁴×C₁₃₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂²×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1987×C₁₃₇	C₂	semidirect
5. #1981×C₁₃₇	C₂	semidirect
7. #1803×C₁₃₇	C₂	semidirect
10. #533×C₁₃₇	C₄	semidirect
150. C₂×C₄×C₁₃₇	#103	semidirect
192. #21885	C₁₃₇	direct (N × H)
193. C₁₃₇	#21885	direct (N × H)
197. #1987	C₂×C₁₃₇	semidirect
198. #1981	C₂×C₁₃₇	semidirect
200. #1803	C₂×C₁₃₇	semidirect
203. #533	C₄×C₁₃₇	semidirect
343. C₂×C₄	#103×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₁₃₇	2
C₂²×C₄⋊C₈×C₁₃₇	2
#2285×C₁₃₇	2
#1987×C₁₃₇	2
#1981×C₁₃₇	2
#1892×C₁₃₇	2
#1803×C₁₃₇	2
#21885	137

Subgroups — C137×#21885 #46871271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21885 #46871271