Subgroups — C₁₃₇×#21177 #46870563

Order 35072.

906 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#430×C₁₃₇	C₂	1	2	yes	maximal
2	C₂×#423×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#423×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×M₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#1950×C₁₃₇	C₂	1	8	yes	maximal, complemented
6	#1738×C₁₃₇	C₂	1	2	yes	maximal
7	C₂²×M₁₆×C₁₃₇	C₂²	1	2	yes	—
8	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₃₇	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
12	#430×C₁₃₇	—	2	8	no	—
13	C₂×#108×C₁₃₇	C₂²	1	8	yes	—
14	#423×C₁₃₇	—	2	1	no	—
15	#423×C₁₃₇	—	2	1	no	—
16	#423×C₁₃₇	C₄	1	2	yes	—
17	#423×C₁₃₇	C₄	1	4	yes	—
18	#423×C₁₃₇	C₄	1	2	yes	—
19	#423×C₁₃₇	C₂²	1	4	yes	—
20	C₂×C₄⋊C₈×C₁₃₇	—	2	2	no	—
21	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	4	yes	—
22	C₄×M₁₆×C₁₃₇	—	2	2	no	—
23	C₄×M₁₆×C₁₃₇	C₂²	1	4	yes	—
24	C₂×#97×C₁₃₇	—	2	1	no	—
25	C₂×C₄×C₈×C₁₃₇	—	2	1	no	—
26	#341×C₁₃₇	C₂²	1	8	yes	—
27	C₂³×C₄×C₁₃₇	Q₈	1	2	yes	—
28	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
29	C₂×M₁₆×C₁₃₇	—	2	1	no	—
30	C₂×M₁₆×C₁₃₇	—	2	1	no	—
31	C₂×M₁₆×C₁₃₇	—	2	4	no	—
32	C₂×M₁₆×C₁₃₇	—	2	2	no	—
33	C₂×M₁₆×C₁₃₇	—	2	2	no	—
34	C₂×M₁₆×C₁₃₇	—	2	4	no	—
35	C₂×M₁₆×C₁₃₇	—	2	2	no	—
36	C₂×M₁₆×C₁₃₇	—	2	4	no	—
37	C₂×M₁₆×C₁₃₇	—	2	4	no	—
38	C₂×M₁₆×C₁₃₇	C₂×C₄	1	4	yes	—
39	C₂×M₁₆×C₁₃₇	C₂×C₄	1	4	yes	—
40	C₂×M₁₆×C₁₃₇	D₄	1	4	yes	—
41	C₂×M₁₆×C₁₃₇	Q₈	1	4	yes	—
42	C₂×M₁₆×C₁₃₇	C₂³	1	4	yes	—
43	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
44	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃₇	—	2	1	no	—
46	C₂²×C₈×C₁₃₇	—	2	1	no	—
47	C₂²×C₈×C₁₃₇	—	2	2	no	—
48	C₂²×C₈×C₁₃₇	C₂³	1	4	yes	—
49	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
55	C₂×C₄²×C₁₃₇	Q₈	1	1	yes	characteristic
56	C₂×C₄²×C₁₃₇	Q₈	1	1	yes	characteristic
57	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
58	#108×C₁₃₇	—	2	16	no	—
59	C₄⋊C₈×C₁₃₇	—	2	4	no	—
60	C₄⋊C₈×C₁₃₇	—	2	4	no	—
61	C₄⋊C₈×C₁₃₇	C₂×C₄	1	8	yes	—
62	C₄⋊C₈×C₁₃₇	C₂×C₄	1	8	yes	—
63	#97×C₁₃₇	—	2	4	no	—
64	C₄×C₈×C₁₃₇	—	2	4	no	—
65	C₂⁴×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
66	C₂²×C₄×C₁₃₇	—	4	4	no	—
67	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
68	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
70	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
71	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
77	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
78	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
80	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
81	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
82	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
83	M₁₆×C₁₃₇	—	2	8	no	—
84	M₁₆×C₁₃₇	—	2	8	no	—
85	M₁₆×C₁₃₇	—	2	4	no	—
86	M₁₆×C₁₃₇	—	2	4	no	—
87	M₁₆×C₁₃₇	—	2	2	no	—
88	M₁₆×C₁₃₇	—	2	2	no	—
89	M₁₆×C₁₃₇	—	2	4	no	—
90	M₁₆×C₁₃₇	—	2	4	no	—
91	M₁₆×C₁₃₇	—	4	4	no	—
92	M₁₆×C₁₃₇	C₂×D₄	1	4	yes	—
93	M₁₆×C₁₃₇	C₂×Q₈	1	4	yes	—
94	C₂×C₈×C₁₃₇	—	2	4	no	—
95	C₂×C₈×C₁₃₇	—	2	4	no	—
96	C₂×C₈×C₁₃₇	—	2	4	no	—
97	C₂×C₈×C₁₃₇	—	2	2	no	—
98	C₂×C₈×C₁₃₇	—	2	2	no	—
99	C₂×C₈×C₁₃₇	—	2	4	no	—
100	C₂×C₈×C₁₃₇	—	2	4	no	—
101	C₂×C₈×C₁₃₇	—	4	4	no	—
102	C₂×C₈×C₁₃₇	C₂²×C₄	1	8	yes	—
103	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₁₃₇	C₄⋊C₄	1	2	yes	—
107	C₄²×C₁₃₇	C₄⋊C₄	1	2	yes	—
108	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
110	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
111	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
112	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
113	C₂³×C₁₃₇	—	4	2	no	—
114	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
115	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
116	C₂³×C₁₃₇	#125	1	2	yes	—
117	C₂³×C₁₃₇	C₄⋊Q₈	1	2	yes	—
118	C₂³×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
119	C₂×C₄×C₁₃₇	—	2	4	no	—
120	C₂×C₄×C₁₃₇	—	2	4	no	—
121	C₂×C₄×C₁₃₇	—	2	4	no	—
122	C₂×C₄×C₁₃₇	—	4	2	no	—
123	C₂×C₄×C₁₃₇	—	4	2	no	—
124	C₂×C₄×C₁₃₇	—	4	2	no	—
125	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
126	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
131	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
132	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
133	C₂×C₄×C₁₃₇	C₄×Q₈	1	2	yes	—
134	C₂×C₄×C₁₃₇	C₄×Q₈	1	2	yes	—
135	C₂×C₄×C₁₃₇	#121	1	2	yes	—
136	C₂×C₄×C₁₃₇	#121	1	2	yes	—
137	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
138	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
139	C₂×C₄×C₁₃₇	#125	1	2	yes	—
140	C₂×C₄×C₁₃₇	C₄⋊Q₈	1	2	yes	—
141	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
146	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
147	C₈×C₁₃₇	—	2	8	no	—
148	C₈×C₁₃₇	—	2	4	no	—
149	C₈×C₁₃₇	—	2	4	no	—
150	C₈×C₁₃₇	—	4	4	no	—
151	C₂²×C₁₃₇	—	2	2	no	—
152	C₂²×C₁₃₇	—	2	2	no	—
153	C₂²×C₁₃₇	—	2	2	no	—
154	C₂²×C₁₃₇	—	4	2	no	—
155	C₂²×C₁₃₇	—	4	2	no	—
156	C₂²×C₁₃₇	#389	1	2	yes	—
157	C₂²×C₁₃₇	#389	1	2	yes	—
158	C₂²×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
159	C₂²×C₁₃₇	C₂×#125	1	1	yes	characteristic
160	C₂²×C₁₃₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
161	C₄×C₁₃₇	—	2	2	no	—
162	C₄×C₁₃₇	—	2	2	no	—
163	C₄×C₁₃₇	—	2	2	no	—
164	C₄×C₁₃₇	#389	1	2	yes	—
165	C₄×C₁₃₇	#389	1	2	yes	—
166	C₄×C₁₃₇	#430	1	4	yes	complemented
167	C₄×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
168	C₄×C₁₃₇	C₂×C₄×Q₈	1	1	yes	characteristic
169	C₄×C₁₃₇	C₂×#121	1	1	yes	characteristic
170	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
171	C₂×C₁₃₇	—	2	1	no	—
172	C₂×C₁₃₇	—	2	1	no	—
173	C₂×C₁₃₇	—	2	2	no	—
174	C₂×C₁₃₇	—	2	2	no	—
175	C₂×C₁₃₇	C₂×#389	1	1	yes	characteristic
176	C₂×C₁₃₇	C₂×#430	1	2	yes	—
177	#21177	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₁₃₇	#21177	1	1	yes	characteristic, direct product factor, Sylow
179	C₂×#430	C₂×C₁₃₇	1	2	yes	—
180	C₂×#423	C₂×C₁₃₇	1	1	yes	characteristic
181	C₂×#423	C₂×C₁₃₇	1	1	yes	characteristic
182	C₂×C₄×M₁₆	C₂×C₁₃₇	1	1	yes	characteristic
183	#1950	C₂×C₁₃₇	1	8	yes	complemented
184	#1738	C₂×C₁₃₇	1	2	yes	—
185	C₂²×M₁₆	C₂²×C₁₃₇	1	2	yes	—
186	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
187	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
188	C₂²×M₁₆	C₂²×C₁₃₇	1	2	yes	—
189	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
190	#430	—	2	8	no	—
191	C₂×#108	C₂²×C₁₃₇	1	8	yes	—
192	#423	—	2	1	no	—
193	#423	—	2	1	no	—
194	#423	C₄×C₁₃₇	1	2	yes	—
195	#423	C₄×C₁₃₇	1	4	yes	—
196	#423	C₄×C₁₃₇	1	2	yes	—
197	#423	C₂²×C₁₃₇	1	4	yes	—
198	C₂×C₄⋊C₈	—	2	2	no	—
199	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	4	yes	—
200	C₄×M₁₆	—	2	2	no	—
201	C₄×M₁₆	C₂²×C₁₃₇	1	4	yes	—
202	C₂×#97	—	2	1	no	—
203	C₂×C₄×C₈	—	2	1	no	—
204	#341	C₂²×C₁₃₇	1	8	yes	—
205	C₂³×C₄	Q₈×C₁₃₇	1	2	yes	—
206	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
207	C₂×M₁₆	—	2	1	no	—
208	C₂×M₁₆	—	2	1	no	—
209	C₂×M₁₆	—	2	4	no	—
210	C₂×M₁₆	—	2	2	no	—
211	C₂×M₁₆	—	2	2	no	—
212	C₂×M₁₆	—	2	4	no	—
213	C₂×M₁₆	—	2	2	no	—
214	C₂×M₁₆	—	2	4	no	—
215	C₂×M₁₆	—	2	4	no	—
216	C₂×M₁₆	C₂×C₄×C₁₃₇	1	4	yes	—
217	C₂×M₁₆	C₂×C₄×C₁₃₇	1	4	yes	—
218	C₂×M₁₆	D₄×C₁₃₇	1	4	yes	—
219	C₂×M₁₆	Q₈×C₁₃₇	1	4	yes	—
220	C₂×M₁₆	C₂³×C₁₃₇	1	4	yes	—
221	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
222	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
223	C₂²×C₈	—	2	1	no	—
224	C₂²×C₈	—	2	1	no	—
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
227	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
228	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
229	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
230	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
231	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
232	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
233	C₂×C₄²	Q₈×C₁₃₇	1	1	yes	characteristic
234	C₂×C₄²	Q₈×C₁₃₇	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
236	#108	—	2	16	no	—
237	C₄⋊C₈	—	2	4	no	—
238	C₄⋊C₈	—	2	4	no	—
239	C₄⋊C₈	C₂×C₄×C₁₃₇	1	8	yes	—
240	C₄⋊C₈	C₂×C₄×C₁₃₇	1	8	yes	—
241	#97	—	2	4	no	—
242	C₄×C₈	—	2	4	no	—
243	C₂⁴	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
244	C₂²×C₄	—	4	4	no	—
245	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
246	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
247	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
248	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
249	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
251	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
252	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
253	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
254	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
255	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
256	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
257	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
258	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
259	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
260	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
261	M₁₆	—	2	8	no	—
262	M₁₆	—	2	8	no	—
263	M₁₆	—	2	4	no	—
264	M₁₆	—	2	4	no	—
265	M₁₆	—	2	2	no	—
266	M₁₆	—	2	2	no	—
267	M₁₆	—	2	4	no	—
268	M₁₆	—	2	4	no	—
269	M₁₆	—	4	4	no	—
270	M₁₆	C₂×D₄×C₁₃₇	1	4	yes	—
271	M₁₆	C₂×Q₈×C₁₃₇	1	4	yes	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	4	4	no	—
280	C₂×C₈	C₂²×C₄×C₁₃₇	1	8	yes	—
281	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
282	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
283	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
284	C₄²	C₄⋊C₄×C₁₃₇	1	2	yes	—
285	C₄²	C₄⋊C₄×C₁₃₇	1	2	yes	—
286	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
287	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
288	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
289	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
290	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
291	C₂³	—	4	2	no	—
292	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
293	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
294	C₂³	#125×C₁₃₇	1	2	yes	—
295	C₂³	C₄⋊Q₈×C₁₃₇	1	2	yes	—
296	C₂³	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	4	2	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	—	4	2	no	—
303	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
304	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
305	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
306	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
307	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
308	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
309	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
310	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
311	C₂×C₄	C₄×Q₈×C₁₃₇	1	2	yes	—
312	C₂×C₄	C₄×Q₈×C₁₃₇	1	2	yes	—
313	C₂×C₄	#121×C₁₃₇	1	2	yes	—
314	C₂×C₄	#121×C₁₃₇	1	2	yes	—
315	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
316	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
317	C₂×C₄	#125×C₁₃₇	1	2	yes	—
318	C₂×C₄	C₄⋊Q₈×C₁₃₇	1	2	yes	—
319	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
320	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
321	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
322	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
323	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
324	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
325	C₈	—	2	8	no	—
326	C₈	—	2	4	no	—
327	C₈	—	2	4	no	—
328	C₈	—	4	4	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	4	2	no	—
333	C₂²	—	4	2	no	—
334	C₂²	#389×C₁₃₇	1	2	yes	—
335	C₂²	#389×C₁₃₇	1	2	yes	—
336	C₂²	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
337	C₂²	C₂×#125×C₁₃₇	1	1	yes	characteristic
338	C₂²	C₂×C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
339	C₄	—	2	2	no	—
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	#389×C₁₃₇	1	2	yes	—
343	C₄	#389×C₁₃₇	1	2	yes	—
344	C₄	#430×C₁₃₇	1	4	yes	complemented
345	C₄	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
346	C₄	C₂×C₄×Q₈×C₁₃₇	1	1	yes	characteristic
347	C₄	C₂×#121×C₁₃₇	1	1	yes	characteristic
348	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
349	C₂	—	2	2	no	—
350	C₂	—	2	2	no	—
351	C₂	—	2	1	no	—
352	C₂	—	2	1	no	—
353	C₂	C₂×#389×C₁₃₇	1	1	yes	characteristic
354	C₂	C₂×#430×C₁₃₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle	C₂²×C₁₃₇	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₃₇	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₇ ◁ C₂²×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
5. #1950×C₁₃₇	C₂	semidirect
166. C₄×C₁₃₇	#430	semidirect
177. #21177	C₁₃₇	direct (N × H)
178. C₁₃₇	#21177	direct (N × H)
183. #1950	C₂×C₁₃₇	semidirect
344. C₄	#430×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#430×C₁₃₇	2
C₂×#423×C₁₃₇	2
C₂×C₄×M₁₆×C₁₃₇	2
#1950×C₁₃₇	2
#1738×C₁₃₇	2
#21177	137

Subgroups — C137×#21177 #46870563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21177 #46870563