Subgroups — C₁₃₇×#21148 #46870534

Order 35072.

1002 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#424×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#424×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#423×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#405×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#2296×C₁₃₇	C₂	1	1	yes	maximal, characteristic
6	#1940×C₁₃₇	C₂	1	4	yes	maximal, complemented
7	#1939×C₁₃₇	C₂	1	4	yes	maximal, complemented
8	#1729×C₁₃₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#336×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
17	#424×C₁₃₇	—	2	4	no	—
18	#424×C₁₃₇	—	2	4	no	—
19	#423×C₁₃₇	—	2	4	no	—
20	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	4	yes	—
21	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	4	yes	—
22	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	4	yes	—
23	#405×C₁₃₇	—	2	4	no	—
24	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
26	#389×C₁₃₇	C₄	1	2	yes	—
27	#389×C₁₃₇	C₄	1	2	yes	—
28	#385×C₁₃₇	C₄	1	4	yes	—
29	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	4	yes	—
30	#336×C₁₃₇	C₂²	1	2	yes	—
31	#336×C₁₃₇	C₂²	1	2	yes	—
32	#336×C₁₃₇	C₂²	1	2	yes	—
33	#336×C₁₃₇	C₂²	1	2	yes	—
34	C₂³×C₄×C₁₃₇	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₁₃₇	—	2	2	no	—
37	C₂×M₁₆×C₁₃₇	—	2	2	no	—
38	C₂×M₁₆×C₁₃₇	—	2	2	no	—
39	C₂×M₁₆×C₁₃₇	—	2	2	no	—
40	C₂×M₁₆×C₁₃₇	—	2	2	no	—
41	C₂×M₁₆×C₁₃₇	D₄	1	4	yes	—
42	C₂²×C₈×C₁₃₇	—	2	2	no	—
43	C₂²×C₈×C₁₃₇	—	2	2	no	—
44	C₂²×C₈×C₁₃₇	—	2	2	no	—
45	C₂²×C₈×C₁₃₇	—	2	2	no	—
46	C₂²×C₈×C₁₃₇	—	2	2	no	—
47	C₂²×C₈×C₁₃₇	Q₈	1	4	yes	—
48	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
53	#117×C₁₃₇	—	2	2	no	—
54	#117×C₁₃₇	—	2	2	no	—
55	#117×C₁₃₇	D₄	1	4	yes	—
56	#117×C₁₃₇	Q₈	1	4	yes	—
57	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₁₃₇	—	2	2	no	—
64	C₂×C₄²×C₁₃₇	—	2	2	no	—
65	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
70	C₄⋊C₈×C₁₃₇	—	2	8	no	—
71	C₄⋊C₈×C₁₃₇	—	2	8	no	—
72	C₄⋊C₈×C₁₃₇	—	2	8	no	—
73	#97×C₁₃₇	—	2	4	no	—
74	C₄×C₈×C₁₃₇	—	2	4	no	—
75	#95×C₁₃₇	C₂×C₄	1	4	yes	—
76	#95×C₁₃₇	C₂×C₄	1	4	yes	—
77	C₂⁴×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃₇	—	2	4	no	—
79	C₂²×C₄×C₁₃₇	—	2	4	no	—
80	C₂²×C₄×C₁₃₇	—	4	2	no	—
81	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
89	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
91	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
92	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
93	M₁₆×C₁₃₇	—	2	8	no	—
94	M₁₆×C₁₃₇	—	4	4	no	—
95	C₂×C₈×C₁₃₇	—	2	8	no	—
96	C₂×C₈×C₁₃₇	—	2	1	no	—
97	C₂×C₈×C₁₃₇	—	2	2	no	—
98	C₂×C₈×C₁₃₇	—	2	1	no	—
99	C₂×C₈×C₁₃₇	—	2	1	no	—
100	C₂×C₈×C₁₃₇	—	2	1	no	—
101	C₂×C₈×C₁₃₇	—	2	2	no	—
102	C₂×C₈×C₁₃₇	—	2	2	no	—
103	C₂×C₈×C₁₃₇	—	2	2	no	—
104	C₂×C₈×C₁₃₇	—	2	2	no	—
105	C₂×C₈×C₁₃₇	—	2	2	no	—
106	C₂×C₈×C₁₃₇	—	2	2	no	—
107	C₂×C₈×C₁₃₇	—	2	2	no	—
108	C₂×C₈×C₁₃₇	—	4	4	no	—
109	C₂×C₈×C₁₃₇	C₂×D₄	1	4	yes	—
110	C₂×C₈×C₁₃₇	C₂×Q₈	1	2	yes	—
111	C₂×C₈×C₁₃₇	C₂×Q₈	1	2	yes	—
112	C₄⋊C₄×C₁₃₇	—	2	4	no	—
113	C₄⋊C₄×C₁₃₇	—	2	8	no	—
114	C₄⋊C₄×C₁₃₇	—	4	4	no	—
115	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	8	yes	—
116	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
117	C₂²⋊C₄×C₁₃₇	C₄⋊C₄	1	8	yes	—
118	C₄²×C₁₃₇	—	2	2	no	—
119	C₄²×C₁₃₇	—	2	2	no	—
120	C₄²×C₁₃₇	—	2	2	no	—
121	C₄²×C₁₃₇	—	2	2	no	—
122	C₄²×C₁₃₇	—	2	2	no	—
123	C₄²×C₁₃₇	—	2	2	no	—
124	C₄²×C₁₃₇	C₂×D₄	1	4	yes	—
125	C₄²×C₁₃₇	C₂×Q₈	1	4	yes	—
126	C₂³×C₁₃₇	—	2	2	no	—
127	C₂³×C₁₃₇	—	2	2	no	—
128	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
129	C₂³×C₁₃₇	C₄×D₄	1	2	yes	—
130	C₂³×C₁₃₇	C₄×Q₈	1	2	yes	—
131	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₃₇	—	2	2	no	—
133	C₂×C₄×C₁₃₇	—	2	4	no	—
134	C₂×C₄×C₁₃₇	—	2	4	no	—
135	C₂×C₄×C₁₃₇	—	2	2	no	—
136	C₂×C₄×C₁₃₇	—	2	2	no	—
137	C₂×C₄×C₁₃₇	—	2	4	no	—
138	C₂×C₄×C₁₃₇	—	2	4	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	—	4	8	no	—
143	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	8	yes	—
144	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
146	C₂×C₄×C₁₃₇	C₄×Q₈	1	2	yes	—
147	C₂×C₄×C₁₃₇	#121	1	4	yes	—
148	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	4	yes	—
149	C₂×C₄×C₁₃₇	#125	1	4	yes	—
150	C₂×C₄×C₁₃₇	C₄⋊Q₈	1	4	yes	—
151	C₂×C₄×C₁₃₇	#131	1	4	yes	—
152	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
156	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
158	C₈×C₁₃₇	—	2	4	no	—
159	C₈×C₁₃₇	—	2	2	no	—
160	C₈×C₁₃₇	—	2	2	no	—
161	C₈×C₁₃₇	—	4	2	no	—
162	C₈×C₁₃₇	—	4	2	no	—
163	C₂²×C₁₃₇	—	2	4	no	—
164	C₂²×C₁₃₇	—	2	4	no	—
165	C₂²×C₁₃₇	—	2	2	no	—
166	C₂²×C₁₃₇	—	2	2	no	—
167	C₂²×C₁₃₇	#389	1	4	yes	—
168	C₂²×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
169	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
170	C₂²×C₁₃₇	C₂×C₄×Q₈	1	1	yes	characteristic
171	C₂²×C₁₃₇	C₂×#131	1	2	yes	—
172	C₂²×C₁₃₇	#568	1	2	yes	—
173	C₄×C₁₃₇	—	2	8	no	—
174	C₄×C₁₃₇	—	2	4	no	—
175	C₄×C₁₃₇	—	4	4	no	—
176	C₄×C₁₃₇	—	4	2	no	—
177	C₄×C₁₃₇	#389	1	4	yes	—
178	C₄×C₁₃₇	C₂×#121	1	1	yes	characteristic
179	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
180	C₄×C₁₃₇	C₂×#125	1	1	yes	characteristic
181	C₄×C₁₃₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
182	C₂×C₁₃₇	—	2	4	no	—
183	C₂×C₁₃₇	C₂×#389	1	1	yes	characteristic
184	C₂×C₁₃₇	#2906	1	2	yes	—
185	C₂×C₁₃₇	#2933	1	2	yes	—
186	C₂×C₁₃₇	#2960	1	1	yes	characteristic
187	C₂×C₁₃₇	#2961	1	1	yes	characteristic
188	#21148	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₁₃₇	#21148	1	1	yes	characteristic, direct product factor, Sylow
190	C₂×#424	C₂×C₁₃₇	1	1	yes	characteristic
191	C₂×#424	C₂×C₁₃₇	1	1	yes	characteristic
192	C₂×#423	C₂×C₁₃₇	1	1	yes	characteristic
193	C₂×#405	C₂×C₁₃₇	1	1	yes	characteristic
194	#2296	C₂×C₁₃₇	1	1	yes	characteristic
195	#1940	C₂×C₁₃₇	1	4	yes	complemented
196	#1939	C₂×C₁₃₇	1	4	yes	complemented
197	#1729	C₂×C₁₃₇	1	1	yes	characteristic
198	C₂×#336	C₂×C₁₃₇	1	1	yes	characteristic
199	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
200	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
201	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
202	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
203	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
204	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
205	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
206	#424	—	2	4	no	—
207	#424	—	2	4	no	—
208	#423	—	2	4	no	—
209	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	4	yes	—
210	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	4	yes	—
211	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	4	yes	—
212	#405	—	2	4	no	—
213	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
214	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
215	#389	C₄×C₁₃₇	1	2	yes	—
216	#389	C₄×C₁₃₇	1	2	yes	—
217	#385	C₄×C₁₃₇	1	4	yes	—
218	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	4	yes	—
219	#336	C₂²×C₁₃₇	1	2	yes	—
220	#336	C₂²×C₁₃₇	1	2	yes	—
221	#336	C₂²×C₁₃₇	1	2	yes	—
222	#336	C₂²×C₁₃₇	1	2	yes	—
223	C₂³×C₄	C₂×C₄×C₁₃₇	1	2	yes	—
224	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
225	C₂×M₁₆	—	2	2	no	—
226	C₂×M₁₆	—	2	2	no	—
227	C₂×M₁₆	—	2	2	no	—
228	C₂×M₁₆	—	2	2	no	—
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	D₄×C₁₃₇	1	4	yes	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	—	2	2	no	—
234	C₂²×C₈	—	2	2	no	—
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	Q₈×C₁₃₇	1	4	yes	—
237	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
238	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
239	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
240	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
242	#117	—	2	2	no	—
243	#117	—	2	2	no	—
244	#117	D₄×C₁₃₇	1	4	yes	—
245	#117	Q₈×C₁₃₇	1	4	yes	—
246	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
247	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
248	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
249	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
250	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
251	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
255	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
257	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
258	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
259	C₄⋊C₈	—	2	8	no	—
260	C₄⋊C₈	—	2	8	no	—
261	C₄⋊C₈	—	2	8	no	—
262	#97	—	2	4	no	—
263	C₄×C₈	—	2	4	no	—
264	#95	C₂×C₄×C₁₃₇	1	4	yes	—
265	#95	C₂×C₄×C₁₃₇	1	4	yes	—
266	C₂⁴	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
272	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
273	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
274	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
277	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
278	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
279	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
280	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
281	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
282	M₁₆	—	2	8	no	—
283	M₁₆	—	4	4	no	—
284	C₂×C₈	—	2	8	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	4	4	no	—
298	C₂×C₈	C₂×D₄×C₁₃₇	1	4	yes	—
299	C₂×C₈	C₂×Q₈×C₁₃₇	1	2	yes	—
300	C₂×C₈	C₂×Q₈×C₁₃₇	1	2	yes	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	8	no	—
303	C₄⋊C₄	—	4	4	no	—
304	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	8	yes	—
305	C₂²⋊C₄	—	2	4	no	—
306	C₂²⋊C₄	C₄⋊C₄×C₁₃₇	1	8	yes	—
307	C₄²	—	2	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	C₂×D₄×C₁₃₇	1	4	yes	—
314	C₄²	C₂×Q₈×C₁₃₇	1	4	yes	—
315	C₂³	—	2	2	no	—
316	C₂³	—	2	2	no	—
317	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
318	C₂³	C₄×D₄×C₁₃₇	1	2	yes	—
319	C₂³	C₄×Q₈×C₁₃₇	1	2	yes	—
320	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	4	8	no	—
332	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	8	yes	—
333	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
334	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
335	C₂×C₄	C₄×Q₈×C₁₃₇	1	2	yes	—
336	C₂×C₄	#121×C₁₃₇	1	4	yes	—
337	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	4	yes	—
338	C₂×C₄	#125×C₁₃₇	1	4	yes	—
339	C₂×C₄	C₄⋊Q₈×C₁₃₇	1	4	yes	—
340	C₂×C₄	#131×C₁₃₇	1	4	yes	—
341	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
342	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
343	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
344	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
345	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
346	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
347	C₈	—	2	4	no	—
348	C₈	—	2	2	no	—
349	C₈	—	2	2	no	—
350	C₈	—	4	2	no	—
351	C₈	—	4	2	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	2	4	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	#389×C₁₃₇	1	4	yes	—
357	C₂²	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
358	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
359	C₂²	C₂×C₄×Q₈×C₁₃₇	1	1	yes	characteristic
360	C₂²	C₂×#131×C₁₃₇	1	2	yes	—
361	C₂²	#568×C₁₃₇	1	2	yes	—
362	C₄	—	2	8	no	—
363	C₄	—	2	4	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	4	no	—
366	C₄	#389×C₁₃₇	1	4	yes	—
367	C₄	C₂×#121×C₁₃₇	1	1	yes	characteristic
368	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
369	C₄	C₂×#125×C₁₃₇	1	1	yes	characteristic
370	C₄	C₂×C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
371	C₂	—	2	4	no	—
372	C₂	C₂×#389×C₁₃₇	1	1	yes	characteristic
373	C₂	#2906×C₁₃₇	1	2	yes	—
374	C₂	#2933×C₁₃₇	1	2	yes	—
375	C₂	#2960×C₁₃₇	1	1	yes	characteristic
376	C₂	#2961×C₁₃₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
6. #1940×C₁₃₇	C₂	semidirect
7. #1939×C₁₃₇	C₂	semidirect
188. #21148	C₁₃₇	direct (N × H)
189. C₁₃₇	#21148	direct (N × H)
195. #1940	C₂×C₁₃₇	semidirect
196. #1939	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×#424×C₁₃₇	2
C₂×#423×C₁₃₇	2
C₂×#405×C₁₃₇	2
#2296×C₁₃₇	2
#1940×C₁₃₇	2
#1939×C₁₃₇	2
#1729×C₁₃₇	2
C₂×#336×C₁₃₇	2
#21148	137

Subgroups — C137×#21148 #46870534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21148 #46870534