Subgroups — C₁₃₇×#21717 #46871103

Order 35072.

766 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×#446×C₁₃₇	C₂	1	2	yes	maximal
2	#2399×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#1984×C₁₃₇	C₂	1	2	yes	maximal
4	#1940×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#1940×C₁₃₇	C₂	1	1	yes	maximal, characteristic
6	#1939×C₁₃₇	C₂	1	2	yes	maximal
7	#1843×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1771×C₁₃₇	C₂	1	2	yes	maximal
9	#1770×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	C₈×C₄⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic
11	#1726×C₁₃₇	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Q₈×C₁₃₇	C₂²	1	2	yes	—
13	#446×C₁₃₇	—	2	8	no	—
14	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
20	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
21	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
28	#398×C₁₃₇	C₄	1	2	yes	—
29	#398×C₁₃₇	C₄	1	2	yes	—
30	#395×C₁₃₇	C₄	1	2	yes	—
31	#395×C₁₃₇	C₄	1	2	yes	—
32	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
35	#376×C₁₃₇	C₂²	1	1	yes	characteristic
36	#336×C₁₃₇	C₂²	1	2	yes	—
37	#336×C₁₃₇	C₂²	1	2	yes	—
38	#336×C₁₃₇	C₂²	1	2	yes	—
39	#336×C₁₃₇	C₂²	1	2	yes	—
40	C₂²×Q₈×C₁₃₇	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
47	C₄×Q₈×C₁₃₇	—	2	4	no	—
48	C₄×Q₈×C₁₃₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
57	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
58	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₁₃₇	—	2	4	no	—
62	C₄⋊C₈×C₁₃₇	—	2	4	no	—
63	C₄⋊C₈×C₁₃₇	—	2	4	no	—
64	C₄⋊C₈×C₁₃₇	—	2	4	no	—
65	C₄⋊C₈×C₁₃₇	—	2	2	no	—
66	C₄⋊C₈×C₁₃₇	—	2	2	no	—
67	#97×C₁₃₇	—	2	4	no	—
68	#97×C₁₃₇	—	2	2	no	—
69	#97×C₁₃₇	D₄	1	4	yes	—
70	#97×C₁₃₇	Q₈	1	4	yes	complemented
71	C₄×C₈×C₁₃₇	—	2	4	no	—
72	C₄×C₈×C₁₃₇	—	2	2	no	—
73	C₄×C₈×C₁₃₇	—	2	2	no	—
74	C₄×C₈×C₁₃₇	Q₈	1	4	yes	complemented
75	#95×C₁₃₇	C₂×C₄	1	2	yes	—
76	#95×C₁₃₇	C₂×C₄	1	2	yes	—
77	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
78	#95×C₁₃₇	C₂×C₄	1	2	yes	—
79	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
80	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
81	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
82	#95×C₁₃₇	C₂×C₄	1	2	yes	—
83	C₂×Q₈×C₁₃₇	—	2	4	no	—
84	C₂×Q₈×C₁₃₇	—	2	4	no	—
85	C₂×Q₈×C₁₃₇	—	4	2	no	—
86	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
95	C₂×C₈×C₁₃₇	—	2	1	no	—
96	C₂×C₈×C₁₃₇	—	2	1	no	—
97	C₂×C₈×C₁₃₇	—	2	1	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	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₁₃₇	C₂×Q₈	1	2	yes	—
110	C₂×C₈×C₁₃₇	C₂×Q₈	1	2	yes	—
111	C₂×C₈×C₁₃₇	C₂×Q₈	1	2	yes	—
112	C₂×C₈×C₁₃₇	C₂×Q₈	1	2	yes	—
113	C₄⋊C₄×C₁₃₇	—	2	4	no	—
114	C₄⋊C₄×C₁₃₇	—	2	4	no	—
115	C₄⋊C₄×C₁₃₇	—	2	4	no	—
116	C₄⋊C₄×C₁₃₇	—	2	4	no	—
117	C₄⋊C₄×C₁₃₇	—	2	4	no	—
118	C₄⋊C₄×C₁₃₇	—	4	2	no	—
119	C₄⋊C₄×C₁₃₇	—	4	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	2	yes	—
125	C₄²×C₁₃₇	C₂×Q₈	1	2	yes	—
126	C₄²×C₁₃₇	C₂×Q₈	1	2	yes	—
127	C₄²×C₁₃₇	#41	1	2	yes	—
128	C₄²×C₁₃₇	#41	1	2	yes	—
129	C₄²×C₁₃₇	#41	1	2	yes	—
130	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
131	Q₈×C₁₃₇	—	4	8	no	—
132	C₂×C₄×C₁₃₇	—	2	2	no	—
133	C₂×C₄×C₁₃₇	—	2	2	no	—
134	C₂×C₄×C₁₃₇	—	2	2	no	—
135	C₂×C₄×C₁₃₇	—	2	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	2	no	—
140	C₂×C₄×C₁₃₇	—	2	2	no	—
141	C₂×C₄×C₁₃₇	—	2	2	no	—
142	C₂×C₄×C₁₃₇	—	2	2	no	—
143	C₂×C₄×C₁₃₇	—	2	2	no	—
144	C₂×C₄×C₁₃₇	—	2	2	no	—
145	C₂×C₄×C₁₃₇	—	2	2	no	—
146	C₂×C₄×C₁₃₇	—	2	2	no	—
147	C₂×C₄×C₁₃₇	—	2	2	no	—
148	C₂×C₄×C₁₃₇	—	2	2	no	—
149	C₂×C₄×C₁₃₇	C₄×D₄	1	4	yes	—
150	C₂×C₄×C₁₃₇	C₄×Q₈	1	2	yes	—
151	C₂×C₄×C₁₃₇	C₄×Q₈	1	2	yes	—
152	C₂×C₄×C₁₃₇	C₄×Q₈	1	4	yes	—
153	C₂×C₄×C₁₃₇	#131	1	4	yes	—
154	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
156	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
160	C₈×C₁₃₇	—	2	2	no	—
161	C₈×C₁₃₇	—	2	2	no	—
162	C₈×C₁₃₇	—	2	2	no	—
163	C₈×C₁₃₇	—	4	2	no	—
164	C₈×C₁₃₇	—	4	2	no	—
165	C₈×C₁₃₇	C₄⋊Q₈	1	4	yes	—
166	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
167	C₂²×C₁₃₇	C₂×C₄×Q₈	1	1	yes	characteristic
168	C₂²×C₁₃₇	C₂×C₄×Q₈	1	1	yes	characteristic
169	C₂²×C₁₃₇	C₂×#131	1	2	yes	—
170	C₂²×C₁₃₇	#568	1	2	yes	—
171	C₄×C₁₃₇	—	2	4	no	—
172	C₄×C₁₃₇	—	2	4	no	—
173	C₄×C₁₃₇	—	2	2	no	—
174	C₄×C₁₃₇	—	2	2	no	—
175	C₄×C₁₃₇	—	2	4	no	—
176	C₄×C₁₃₇	—	4	2	no	—
177	C₄×C₁₃₇	—	4	2	no	—
178	C₄×C₁₃₇	—	4	2	no	—
179	C₄×C₁₃₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
180	C₄×C₁₃₇	#532	1	1	yes	characteristic
181	C₄×C₁₃₇	#533	1	1	yes	characteristic
182	C₄×C₁₃₇	#533	1	1	yes	characteristic
183	C₂×C₁₃₇	C₄×C₄⋊Q₈	1	1	yes	characteristic
184	C₂×C₁₃₇	#2933	1	2	yes	—
185	C₂×C₁₃₇	#2960	1	1	yes	characteristic
186	C₂×C₁₃₇	#2961	1	1	yes	characteristic
187	C₂×C₁₃₇	#2962	1	2	yes	—
188	#21717	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₁₃₇	#21717	1	1	yes	characteristic, direct product factor, Sylow
190	C₂×#446	C₂×C₁₃₇	1	2	yes	—
191	#2399	C₂×C₁₃₇	1	1	yes	characteristic
192	#1984	C₂×C₁₃₇	1	2	yes	—
193	#1940	C₂×C₁₃₇	1	1	yes	characteristic
194	#1940	C₂×C₁₃₇	1	1	yes	characteristic
195	#1939	C₂×C₁₃₇	1	2	yes	—
196	#1843	C₂×C₁₃₇	1	1	yes	characteristic
197	#1771	C₂×C₁₃₇	1	2	yes	—
198	#1770	C₂×C₁₃₇	1	1	yes	characteristic
199	C₈×C₄⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic
200	#1726	C₂×C₁₃₇	1	1	yes	characteristic
201	C₂×C₄×Q₈	C₂²×C₁₃₇	1	2	yes	—
202	#446	—	2	8	no	—
203	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
205	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
206	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
207	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
208	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
209	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
210	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
211	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
212	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
213	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
214	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
215	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
217	#398	C₄×C₁₃₇	1	2	yes	—
218	#398	C₄×C₁₃₇	1	2	yes	—
219	#395	C₄×C₁₃₇	1	2	yes	—
220	#395	C₄×C₁₃₇	1	2	yes	—
221	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
222	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
223	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
224	#376	C₂²×C₁₃₇	1	1	yes	characteristic
225	#336	C₂²×C₁₃₇	1	2	yes	—
226	#336	C₂²×C₁₃₇	1	2	yes	—
227	#336	C₂²×C₁₃₇	1	2	yes	—
228	#336	C₂²×C₁₃₇	1	2	yes	—
229	C₂²×Q₈	C₂×C₄×C₁₃₇	1	2	yes	—
230	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
231	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
232	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
236	C₄×Q₈	—	2	4	no	—
237	C₄×Q₈	—	2	4	no	—
238	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
239	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
240	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
241	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
242	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
243	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
244	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
245	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
246	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
247	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
250	C₄⋊C₈	—	2	4	no	—
251	C₄⋊C₈	—	2	4	no	—
252	C₄⋊C₈	—	2	4	no	—
253	C₄⋊C₈	—	2	4	no	—
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	2	2	no	—
256	#97	—	2	4	no	—
257	#97	—	2	2	no	—
258	#97	D₄×C₁₃₇	1	4	yes	—
259	#97	Q₈×C₁₃₇	1	4	yes	complemented
260	C₄×C₈	—	2	4	no	—
261	C₄×C₈	—	2	2	no	—
262	C₄×C₈	—	2	2	no	—
263	C₄×C₈	Q₈×C₁₃₇	1	4	yes	complemented
264	#95	C₂×C₄×C₁₃₇	1	2	yes	—
265	#95	C₂×C₄×C₁₃₇	1	2	yes	—
266	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
267	#95	C₂×C₄×C₁₃₇	1	2	yes	—
268	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
269	#95	C₂×C₄×C₁₃₇	1	2	yes	—
270	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
271	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	—	4	2	no	—
275	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
276	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
277	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
278	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
279	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
281	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
282	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
283	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	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	C₂×D₄×C₁₃₇	1	2	yes	—
297	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
298	C₂×C₈	C₂×Q₈×C₁₃₇	1	2	yes	—
299	C₂×C₈	C₂×Q₈×C₁₃₇	1	2	yes	—
300	C₂×C₈	C₂×Q₈×C₁₃₇	1	2	yes	—
301	C₂×C₈	C₂×Q₈×C₁₃₇	1	2	yes	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	—	4	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	2	yes	—
314	C₄²	C₂×Q₈×C₁₃₇	1	2	yes	—
315	C₄²	C₂×Q₈×C₁₃₇	1	2	yes	—
316	C₄²	#41×C₁₃₇	1	2	yes	—
317	C₄²	#41×C₁₃₇	1	2	yes	—
318	C₄²	#41×C₁₃₇	1	2	yes	—
319	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
320	Q₈	—	4	8	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	C₄×D₄×C₁₃₇	1	4	yes	—
339	C₂×C₄	C₄×Q₈×C₁₃₇	1	2	yes	—
340	C₂×C₄	C₄×Q₈×C₁₃₇	1	2	yes	—
341	C₂×C₄	C₄×Q₈×C₁₃₇	1	4	yes	—
342	C₂×C₄	#131×C₁₃₇	1	4	yes	—
343	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
344	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
345	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
346	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
347	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
348	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
349	C₈	—	2	2	no	—
350	C₈	—	2	2	no	—
351	C₈	—	2	2	no	—
352	C₈	—	4	2	no	—
353	C₈	—	4	2	no	—
354	C₈	C₄⋊Q₈×C₁₃₇	1	4	yes	—
355	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
356	C₂²	C₂×C₄×Q₈×C₁₃₇	1	1	yes	characteristic
357	C₂²	C₂×C₄×Q₈×C₁₃₇	1	1	yes	characteristic
358	C₂²	C₂×#131×C₁₃₇	1	2	yes	—
359	C₂²	#568×C₁₃₇	1	2	yes	—
360	C₄	—	2	4	no	—
361	C₄	—	2	4	no	—
362	C₄	—	2	2	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	4	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	C₂×C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
369	C₄	#532×C₁₃₇	1	1	yes	characteristic
370	C₄	#533×C₁₃₇	1	1	yes	characteristic
371	C₄	#533×C₁₃₇	1	1	yes	characteristic
372	C₂	C₄×C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
373	C₂	#2933×C₁₃₇	1	2	yes	—
374	C₂	#2960×C₁₃₇	1	1	yes	characteristic
375	C₂	#2961×C₁₃₇	1	1	yes	characteristic
376	C₂	#2962×C₁₃₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle, prime radical	C₂³×C₁₃₇	C₂³×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
70. #97×C₁₃₇	Q₈	semidirect
74. C₄×C₈×C₁₃₇	Q₈	semidirect
188. #21717	C₁₃₇	direct (N × H)
189. C₁₃₇	#21717	direct (N × H)
259. #97	Q₈×C₁₃₇	semidirect
263. C₄×C₈	Q₈×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#446×C₁₃₇	2
#2399×C₁₃₇	2
#1984×C₁₃₇	2
#1940×C₁₃₇	2
#1939×C₁₃₇	2
#1843×C₁₃₇	2
#1771×C₁₃₇	2
#1770×C₁₃₇	2
C₈×C₄⋊C₄×C₁₃₇	2
#1726×C₁₃₇	2
#21717	137

Subgroups — C137×#21717 #46871103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21717 #46871103