Subgroups — C₁₃₇×#20662 #46870048

Order 35072.

1438 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#427×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#106×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2311×C₁₃₇	C₂	1	2	yes	maximal
5	#1809×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1807×C₁₃₇	C₂	1	4	yes	maximal, complemented
7	#1736×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₁₃₇	C₂²	1	1	yes	characteristic
9	C₂×#131×C₁₃₇	—	2	4	no	—
10	C₂×#131×C₁₃₇	—	2	4	no	—
11	C₂×#131×C₁₃₇	C₄	1	8	yes	complemented
12	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₃₇	C₂²	1	2	yes	—
14	C₂³×C₈×C₁₃₇	C₂²	1	2	yes	—
15	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
18	#427×C₁₃₇	—	2	4	no	—
19	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
20	C₂×#106×C₁₃₇	—	2	4	no	—
21	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
23	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
24	#391×C₁₃₇	—	2	2	no	—
25	#390×C₁₃₇	—	2	2	no	—
26	#386×C₁₃₇	—	2	4	no	—
27	#380×C₁₃₇	C₂²	1	8	yes	—
28	#340×C₁₃₇	C₂²	1	8	yes	—
29	C₂×#41×C₁₃₇	—	2	2	no	—
30	C₂×#41×C₁₃₇	—	2	2	no	—
31	C₂×#41×C₁₃₇	—	2	2	no	—
32	C₂×#41×C₁₃₇	—	2	2	no	—
33	C₂×#41×C₁₃₇	C₂×C₄	1	4	yes	—
34	C₂×#41×C₁₃₇	Q₈	1	4	yes	—
35	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₃₇	D₄	1	2	yes	—
37	C₂²×D₄×C₁₃₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃₇	—	2	2	no	—
39	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
41	#131×C₁₃₇	—	2	32	no	—
42	C₂×M₁₆×C₁₃₇	—	2	2	no	—
43	C₂×M₁₆×C₁₃₇	—	2	2	no	—
44	C₂×M₁₆×C₁₃₇	—	2	4	no	—
45	C₂×M₁₆×C₁₃₇	—	2	4	no	—
46	C₂×M₁₆×C₁₃₇	C₂×C₄	1	4	yes	—
47	C₂×M₁₆×C₁₃₇	C₂×C₄	1	8	yes	complemented
48	C₂²×C₈×C₁₃₇	—	2	4	no	—
49	C₂²×C₈×C₁₃₇	—	2	4	no	—
50	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
51	C₂²×C₈×C₁₃₇	C₂×C₄	1	8	yes	complemented
52	C₂²×C₈×C₁₃₇	D₄	1	4	yes	—
53	C₂²×C₈×C₁₃₇	D₄	1	4	yes	—
54	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
57	#117×C₁₃₇	—	2	4	no	—
58	#117×C₁₃₇	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
60	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
61	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
64	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₃₇	—	2	8	no	—
66	C₂×C₄²×C₁₃₇	—	2	2	no	—
67	#107×C₁₃₇	—	2	4	no	—
68	#106×C₁₃₇	—	2	4	no	—
69	#106×C₁₃₇	—	2	4	no	—
70	#106×C₁₃₇	—	2	4	no	—
71	#95×C₁₃₇	—	2	8	no	—
72	C₂⁴×C₁₃₇	C₂×D₄	1	2	yes	—
73	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
74	#41×C₁₃₇	—	2	8	no	—
75	#41×C₁₃₇	—	2	8	no	—
76	#41×C₁₃₇	—	2	8	no	—
77	#41×C₁₃₇	—	2	8	no	—
78	C₂×Q₈×C₁₃₇	—	2	2	no	—
79	C₂×Q₈×C₁₃₇	—	2	2	no	—
80	C₂×Q₈×C₁₃₇	C₄⋊C₄	1	4	yes	—
81	C₂×D₄×C₁₃₇	—	2	4	no	—
82	C₂×D₄×C₁₃₇	—	2	4	no	—
83	C₂×D₄×C₁₃₇	—	2	2	no	—
84	C₂×D₄×C₁₃₇	—	2	2	no	—
85	C₂×D₄×C₁₃₇	C₄⋊C₄	1	8	yes	—
86	C₂×D₄×C₁₃₇	C₄⋊C₄	1	4	yes	—
87	C₂²×C₄×C₁₃₇	—	2	2	no	—
88	C₂²×C₄×C₁₃₇	—	2	2	no	—
89	C₂²×C₄×C₁₃₇	—	2	2	no	—
90	C₂²×C₄×C₁₃₇	—	2	2	no	—
91	C₂²×C₄×C₁₃₇	—	2	4	no	—
92	C₂²×C₄×C₁₃₇	—	2	4	no	—
93	C₂²×C₄×C₁₃₇	—	4	4	no	—
94	C₂²×C₄×C₁₃₇	—	8	4	no	—
95	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₇	C₂×Q₈	1	4	yes	—
102	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
103	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
104	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
105	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
106	M₁₆×C₁₃₇	—	2	8	no	—
107	M₁₆×C₁₃₇	—	2	16	no	—
108	C₂×C₈×C₁₃₇	—	2	2	no	—
109	C₂×C₈×C₁₃₇	—	2	2	no	—
110	C₂×C₈×C₁₃₇	—	2	16	no	—
111	C₂×C₈×C₁₃₇	C₂²⋊C₄	1	16	yes	complemented
112	C₂×C₈×C₁₃₇	C₂²×C₄	1	4	yes	—
113	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
119	C₄⋊C₄×C₁₃₇	—	2	4	no	—
120	C₄⋊C₄×C₁₃₇	—	2	4	no	—
121	C₄⋊C₄×C₁₃₇	—	2	4	no	—
122	C₄⋊C₄×C₁₃₇	—	2	4	no	—
123	C₄⋊C₄×C₁₃₇	—	4	4	no	—
124	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
125	C₂²⋊C₄×C₁₃₇	—	8	8	no	—
126	C₄²×C₁₃₇	—	4	4	no	—
127	C₂³×C₁₃₇	—	2	4	no	—
128	C₂³×C₁₃₇	—	2	2	no	—
129	C₂³×C₁₃₇	—	2	2	no	—
130	C₂³×C₁₃₇	—	2	8	no	—
131	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
132	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
133	C₂³×C₁₃₇	#121	1	2	yes	—
134	C₂³×C₁₃₇	#121	1	2	yes	—
135	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₁₃₇	—	2	8	no	—
137	D₄×C₁₃₇	—	2	16	no	—
138	D₄×C₁₃₇	—	2	8	no	—
139	C₂×C₄×C₁₃₇	—	2	2	no	—
140	C₂×C₄×C₁₃₇	—	2	2	no	—
141	C₂×C₄×C₁₃₇	—	2	4	no	—
142	C₂×C₄×C₁₃₇	—	2	4	no	—
143	C₂×C₄×C₁₃₇	—	2	4	no	—
144	C₂×C₄×C₁₃₇	—	2	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	8	no	—
149	C₂×C₄×C₁₃₇	—	4	4	no	—
150	C₂×C₄×C₁₃₇	—	8	8	no	—
151	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	4	yes	—
152	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
153	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
154	C₂×C₄×C₁₃₇	#117	1	4	yes	—
155	C₂×C₄×C₁₃₇	#121	1	2	yes	—
156	C₂×C₄×C₁₃₇	#121	1	2	yes	—
157	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	4	yes	—
158	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	4	yes	—
159	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
165	C₈×C₁₃₇	—	2	4	no	—
166	C₈×C₁₃₇	C₂×C₂²⋊C₄	1	4	yes	—
167	C₈×C₁₃₇	C₂×C₂²⋊C₄	1	4	yes	—
168	C₂²×C₁₃₇	—	2	4	no	—
169	C₂²×C₁₃₇	—	2	4	no	—
170	C₂²×C₁₃₇	—	2	4	no	—
171	C₂²×C₁₃₇	—	2	8	no	—
172	C₂²×C₁₃₇	—	2	4	no	—
173	C₂²×C₁₃₇	—	4	4	no	—
174	C₂²×C₁₃₇	—	4	4	no	—
175	C₂²×C₁₃₇	#380	1	4	yes	—
176	C₂²×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
177	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
178	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
179	C₂²×C₁₃₇	#577	1	4	yes	—
180	C₄×C₁₃₇	—	2	4	no	—
181	C₄×C₁₃₇	—	8	4	no	—
182	C₄×C₁₃₇	—	8	4	no	—
183	C₄×C₁₃₇	#380	1	4	yes	—
184	C₄×C₁₃₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
185	C₄×C₁₃₇	C₂×#117	1	1	yes	characteristic
186	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
187	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
188	C₂×C₁₃₇	—	2	4	no	—
189	C₂×C₁₃₇	—	4	4	no	—
190	C₂×C₁₃₇	C₂×#380	1	1	yes	characteristic
191	C₂×C₁₃₇	#2912	1	2	yes	—
192	C₂×C₁₃₇	#3057	1	2	yes	—
193	C₂×C₁₃₇	#3060	1	2	yes	—
194	#20662	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₁₃₇	#20662	1	1	yes	characteristic, direct product factor, Sylow
196	C₂²×#131	C₂×C₁₃₇	1	1	yes	characteristic
197	C₂×#427	C₂×C₁₃₇	1	1	yes	characteristic, complemented
198	C₂²×#106	C₂×C₁₃₇	1	1	yes	characteristic, complemented
199	#2311	C₂×C₁₃₇	1	2	yes	—
200	#1809	C₂×C₁₃₇	1	4	yes	complemented
201	#1807	C₂×C₁₃₇	1	4	yes	complemented
202	#1736	C₂×C₁₃₇	1	2	yes	complemented
203	C₂²×#41	C₂²×C₁₃₇	1	1	yes	characteristic
204	C₂×#131	—	2	4	no	—
205	C₂×#131	—	2	4	no	—
206	C₂×#131	C₄×C₁₃₇	1	8	yes	complemented
207	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
208	C₂²×M₁₆	C₂²×C₁₃₇	1	2	yes	—
209	C₂³×C₈	C₂²×C₁₃₇	1	2	yes	—
210	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
211	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
212	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
213	#427	—	2	4	no	—
214	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
215	C₂×#106	—	2	4	no	—
216	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
217	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
218	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
219	#391	—	2	2	no	—
220	#390	—	2	2	no	—
221	#386	—	2	4	no	—
222	#380	C₂²×C₁₃₇	1	8	yes	—
223	#340	C₂²×C₁₃₇	1	8	yes	—
224	C₂×#41	—	2	2	no	—
225	C₂×#41	—	2	2	no	—
226	C₂×#41	—	2	2	no	—
227	C₂×#41	—	2	2	no	—
228	C₂×#41	C₂×C₄×C₁₃₇	1	4	yes	—
229	C₂×#41	Q₈×C₁₃₇	1	4	yes	—
230	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
231	C₂²×D₄	D₄×C₁₃₇	1	2	yes	—
232	C₂²×D₄	D₄×C₁₃₇	1	1	yes	characteristic
233	C₂³×C₄	—	2	2	no	—
234	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
235	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
236	#131	—	2	32	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	—	2	4	no	—
240	C₂×M₁₆	—	2	4	no	—
241	C₂×M₁₆	C₂×C₄×C₁₃₇	1	4	yes	—
242	C₂×M₁₆	C₂×C₄×C₁₃₇	1	8	yes	complemented
243	C₂²×C₈	—	2	4	no	—
244	C₂²×C₈	—	2	4	no	—
245	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
246	C₂²×C₈	C₂×C₄×C₁₃₇	1	8	yes	complemented
247	C₂²×C₈	D₄×C₁₃₇	1	4	yes	—
248	C₂²×C₈	D₄×C₁₃₇	1	4	yes	—
249	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
250	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
252	#117	—	2	4	no	—
253	#117	—	2	4	no	—
254	C₂×C₄⋊C₄	—	2	4	no	—
255	C₂×C₄⋊C₄	—	2	4	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
258	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	8	no	—
261	C₂×C₄²	—	2	2	no	—
262	#107	—	2	4	no	—
263	#106	—	2	4	no	—
264	#106	—	2	4	no	—
265	#106	—	2	4	no	—
266	#95	—	2	8	no	—
267	C₂⁴	C₂×D₄×C₁₃₇	1	2	yes	—
268	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
269	#41	—	2	8	no	—
270	#41	—	2	8	no	—
271	#41	—	2	8	no	—
272	#41	—	2	8	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	C₄⋊C₄×C₁₃₇	1	4	yes	—
276	C₂×D₄	—	2	4	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	C₄⋊C₄×C₁₃₇	1	8	yes	—
281	C₂×D₄	C₄⋊C₄×C₁₃₇	1	4	yes	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	4	4	no	—
289	C₂²×C₄	—	8	4	no	—
290	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
291	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
296	C₂²×C₄	C₂×Q₈×C₁₃₇	1	4	yes	—
297	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
298	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
299	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
300	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
301	M₁₆	—	2	8	no	—
302	M₁₆	—	2	16	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	16	no	—
306	C₂×C₈	C₂²⋊C₄×C₁₃₇	1	16	yes	complemented
307	C₂×C₈	C₂²×C₄×C₁₃₇	1	4	yes	—
308	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
309	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
310	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
311	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
312	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
313	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	—	8	8	no	—
321	C₄²	—	4	4	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	8	no	—
326	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
327	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
328	C₂³	#121×C₁₃₇	1	2	yes	—
329	C₂³	#121×C₁₃₇	1	2	yes	—
330	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
331	Q₈	—	2	8	no	—
332	D₄	—	2	16	no	—
333	D₄	—	2	8	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	8	8	no	—
346	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	4	yes	—
347	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
348	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
349	C₂×C₄	#117×C₁₃₇	1	4	yes	—
350	C₂×C₄	#121×C₁₃₇	1	2	yes	—
351	C₂×C₄	#121×C₁₃₇	1	2	yes	—
352	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	4	yes	—
353	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	4	yes	—
354	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
356	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
357	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
358	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
359	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
360	C₈	—	2	4	no	—
361	C₈	C₂×C₂²⋊C₄×C₁₃₇	1	4	yes	—
362	C₈	C₂×C₂²⋊C₄×C₁₃₇	1	4	yes	—
363	C₂²	—	2	4	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	4	no	—
367	C₂²	—	2	8	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	4	4	no	—
370	C₂²	#380×C₁₃₇	1	4	yes	—
371	C₂²	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
372	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
373	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
374	C₂²	#577×C₁₃₇	1	4	yes	—
375	C₄	—	2	4	no	—
376	C₄	—	8	4	no	—
377	C₄	—	8	4	no	—
378	C₄	#380×C₁₃₇	1	4	yes	—
379	C₄	C₂²×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
380	C₄	C₂×#117×C₁₃₇	1	1	yes	characteristic
381	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
382	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
383	C₂	—	2	4	no	—
384	C₂	—	4	4	no	—
385	C₂	C₂×#380×C₁₃₇	1	1	yes	characteristic
386	C₂	#2912×C₁₃₇	1	2	yes	—
387	C₂	#3057×C₁₃₇	1	2	yes	—
388	C₂	#3060×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	C₂²×#41×C₁₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂²×#41×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#427×C₁₃₇	C₂	semidirect
3. C₂²×#106×C₁₃₇	C₂	semidirect
5. #1809×C₁₃₇	C₂	semidirect
6. #1807×C₁₃₇	C₂	semidirect
7. #1736×C₁₃₇	C₂	semidirect
11. C₂×#131×C₁₃₇	C₄	semidirect
47. C₂×M₁₆×C₁₃₇	C₂×C₄	semidirect
51. C₂²×C₈×C₁₃₇	C₂×C₄	semidirect
111. C₂×C₈×C₁₃₇	C₂²⋊C₄	semidirect
194. #20662	C₁₃₇	direct (N × H)
195. C₁₃₇	#20662	direct (N × H)
197. C₂×#427	C₂×C₁₃₇	semidirect
198. C₂²×#106	C₂×C₁₃₇	semidirect
200. #1809	C₂×C₁₃₇	semidirect
201. #1807	C₂×C₁₃₇	semidirect
202. #1736	C₂×C₁₃₇	semidirect
206. C₂×#131	C₄×C₁₃₇	semidirect
242. C₂×M₁₆	C₂×C₄×C₁₃₇	semidirect
246. C₂²×C₈	C₂×C₄×C₁₃₇	semidirect
306. C₂×C₈	C₂²⋊C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#131×C₁₃₇	2
C₂×#427×C₁₃₇	2
C₂²×#106×C₁₃₇	2
#2311×C₁₃₇	2
#1809×C₁₃₇	2
#1807×C₁₃₇	2
#1736×C₁₃₇	2
#20662	137

Subgroups — C137×#20662 #46870048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#20662 #46870048