Subgroups — C₁₃₇×#20393 #46869779

Order 35072.

1606 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#520×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#410×C₁₃₇	C₂	1	2	yes	maximal
3	#2274×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	C₄×#99×C₁₃₇	C₂	1	8	yes	maximal, complemented
5	#1740×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₁₃₇	C₂²	1	1	yes	characteristic
7	#520×C₁₃₇	—	2	8	no	—
8	C₂×C₄×Q₈×C₁₃₇	C₄	1	2	yes	complemented
9	C₂×C₄×D₄×C₁₃₇	C₄	1	2	yes	complemented
10	C₂×C₄×D₄×C₁₃₇	C₂²	1	4	yes	—
11	C₂×#117×C₁₃₇	C₄	1	2	yes	complemented
12	C₂×#117×C₁₃₇	C₂²	1	4	yes	—
13	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₃₇	C₄	1	2	yes	complemented
15	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
16	#410×C₁₃₇	C₄	1	16	yes	complemented
17	C₂×#99×C₁₃₇	C₂²	1	8	yes	—
18	C₄×C₄⋊C₄×C₁₃₇	—	2	8	no	—
19	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	8	yes	—
20	#342×C₁₃₇	C₂²	1	8	yes	—
21	C₂×#41×C₁₃₇	—	2	4	no	—
22	C₂×#41×C₁₃₇	—	2	4	no	—
23	C₂×#41×C₁₃₇	C₂×C₄	1	8	yes	—
24	C₂²×Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
25	C₂²×D₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
26	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
27	C₂³×C₄×C₁₃₇	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₁₃₇	C₂×C₄	1	4	yes	—
29	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
30	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
31	C₄×Q₈×C₁₃₇	—	2	8	no	—
32	C₄×D₄×C₁₃₇	—	2	16	no	—
33	C₄×D₄×C₁₃₇	—	2	8	no	—
34	#117×C₁₃₇	—	2	4	no	—
35	#117×C₁₃₇	—	2	8	no	—
36	#117×C₁₃₇	—	2	8	no	—
37	#117×C₁₃₇	C₂×C₄	1	16	yes	complemented
38	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
39	C₂×C₄⋊C₄×C₁₃₇	—	2	8	no	—
40	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
42	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
44	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₃₇	D₄	1	8	yes	—
46	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
47	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
48	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
49	C₂×C₄²×C₁₃₇	—	2	4	no	—
50	C₂×C₄²×C₁₃₇	—	2	8	no	—
51	C₂×C₄²×C₁₃₇	C₂×C₄	1	4	yes	—
52	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
53	#99×C₁₃₇	C₂×C₄	1	32	yes	complemented
54	#95×C₁₃₇	—	2	8	no	—
55	C₂⁴×C₁₃₇	C₂²×C₄	1	2	yes	—
56	C₂⁴×C₁₃₇	C₂⁴	1	1	yes	characteristic
57	#41×C₁₃₇	—	2	16	no	—
58	#41×C₁₃₇	—	2	16	no	—
59	C₂×Q₈×C₁₃₇	—	2	2	no	—
60	C₂×Q₈×C₁₃₇	—	2	2	no	—
61	C₂×Q₈×C₁₃₇	C₄²	1	4	yes	complemented
62	C₂×D₄×C₁₃₇	—	2	4	no	—
63	C₂×D₄×C₁₃₇	—	2	4	no	—
64	C₂×D₄×C₁₃₇	—	2	2	no	—
65	C₂×D₄×C₁₃₇	—	2	2	no	—
66	C₂×D₄×C₁₃₇	C₄²	1	4	yes	complemented
67	C₂×D₄×C₁₃₇	C₂²×C₄	1	8	yes	—
68	C₂²×C₄×C₁₃₇	—	2	4	no	—
69	C₂²×C₄×C₁₃₇	—	2	4	no	—
70	C₂²×C₄×C₁₃₇	—	2	8	no	—
71	C₂²×C₄×C₁₃₇	—	2	8	no	—
72	C₂²×C₄×C₁₃₇	—	8	2	no	—
73	C₂²×C₄×C₁₃₇	—	8	4	no	—
74	C₂²×C₄×C₁₃₇	C₄²	1	8	yes	complemented
75	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₁₃₇	C₂×D₄	1	8	yes	—
83	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
84	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
85	C₄⋊C₄×C₁₃₇	—	2	2	no	—
86	C₄⋊C₄×C₁₃₇	—	2	8	no	—
87	C₄⋊C₄×C₁₃₇	—	2	2	no	—
88	C₄⋊C₄×C₁₃₇	—	2	16	no	—
89	C₄⋊C₄×C₁₃₇	C₂²⋊C₄	1	8	yes	—
90	C₄⋊C₄×C₁₃₇	C₂²⋊C₄	1	8	yes	—
91	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
92	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
93	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
94	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	16	yes	—
95	C₄²×C₁₃₇	—	2	8	no	—
96	C₄²×C₁₃₇	—	2	4	no	—
97	C₄²×C₁₃₇	—	2	16	no	—
98	C₄²×C₁₃₇	—	8	8	no	—
99	C₂³×C₁₃₇	—	2	2	no	—
100	C₂³×C₁₃₇	—	2	2	no	—
101	C₂³×C₁₃₇	—	4	1	no	—
102	C₂³×C₁₃₇	—	4	1	no	—
103	C₂³×C₁₃₇	—	4	2	no	—
104	C₂³×C₁₃₇	—	4	2	no	—
105	C₂³×C₁₃₇	C₂×C₄²	1	4	yes	—
106	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
107	C₂³×C₁₃₇	C₂³×C₄	1	2	yes	—
108	C₂³×C₁₃₇	C₂²×D₄	1	2	yes	—
109	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
110	Q₈×C₁₃₇	—	2	8	no	—
111	D₄×C₁₃₇	—	2	16	no	—
112	D₄×C₁₃₇	—	2	8	no	—
113	C₂×C₄×C₁₃₇	—	2	2	no	—
114	C₂×C₄×C₁₃₇	—	2	2	no	—
115	C₂×C₄×C₁₃₇	—	2	16	no	—
116	C₂×C₄×C₁₃₇	—	2	2	no	—
117	C₂×C₄×C₁₃₇	—	2	2	no	—
118	C₂×C₄×C₁₃₇	—	2	16	no	—
119	C₂×C₄×C₁₃₇	—	4	8	no	—
120	C₂×C₄×C₁₃₇	—	4	4	no	—
121	C₂×C₄×C₁₃₇	—	4	8	no	—
122	C₂×C₄×C₁₃₇	—	4	8	no	—
123	C₂×C₄×C₁₃₇	—	4	2	no	—
124	C₂×C₄×C₁₃₇	—	4	2	no	—
125	C₂×C₄×C₁₃₇	—	8	8	no	—
126	C₂×C₄×C₁₃₇	C₂×C₄²	1	4	yes	—
127	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
128	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
129	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	8	yes	—
130	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
131	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
132	C₂×C₄×C₁₃₇	#117	1	2	yes	—
133	C₂×C₄×C₁₃₇	#117	1	2	yes	—
134	C₂×C₄×C₁₃₇	C₄×D₄	1	8	yes	—
135	C₂×C₄×C₁₃₇	C₄×D₄	1	8	yes	—
136	C₂²×C₁₃₇	—	2	2	no	—
137	C₂²×C₁₃₇	—	2	1	no	—
138	C₂²×C₁₃₇	—	2	2	no	—
139	C₂²×C₁₃₇	—	2	1	no	—
140	C₂²×C₁₃₇	—	2	4	no	—
141	C₂²×C₁₃₇	—	4	2	no	—
142	C₂²×C₁₃₇	—	4	2	no	—
143	C₂²×C₁₃₇	—	4	4	no	—
144	C₂²×C₁₃₇	—	4	4	no	—
145	C₂²×C₁₃₇	—	4	2	no	—
146	C₂²×C₁₃₇	—	4	2	no	—
147	C₂²×C₁₃₇	C₂²×C₄²	1	1	yes	characteristic
148	C₂²×C₁₃₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
150	C₂²×C₁₃₇	C₂×C₄×D₄	1	4	yes	—
151	C₄×C₁₃₇	—	2	8	no	—
152	C₄×C₁₃₇	—	2	4	no	—
153	C₄×C₁₃₇	—	4	16	no	—
154	C₄×C₁₃₇	—	4	2	no	—
155	C₄×C₁₃₇	—	4	2	no	—
156	C₄×C₁₃₇	C₄×C₂²⋊C₄	1	4	yes	—
157	C₄×C₁₃₇	C₄×C₂²⋊C₄	1	4	yes	—
158	C₂×C₁₃₇	—	2	4	no	—
159	C₂×C₁₃₇	—	2	1	no	—
160	C₂×C₁₃₇	—	2	1	no	—
161	C₂×C₁₃₇	—	4	4	no	—
162	C₂×C₁₃₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₁₃₇	#2883	1	1	yes	characteristic
164	C₂×C₁₃₇	#2884	1	1	yes	characteristic
165	#20393	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₁₃₇	#20393	1	1	yes	characteristic, direct product factor, Sylow
167	C₂×#520	C₂×C₁₃₇	1	1	yes	characteristic
168	C₂×#410	C₂×C₁₃₇	1	2	yes	—
169	#2274	C₂×C₁₃₇	1	2	yes	complemented
170	C₄×#99	C₂×C₁₃₇	1	8	yes	complemented
171	#1740	C₂×C₁₃₇	1	2	yes	complemented
172	C₂²×#41	C₂²×C₁₃₇	1	1	yes	characteristic
173	#520	—	2	8	no	—
174	C₂×C₄×Q₈	C₄×C₁₃₇	1	2	yes	complemented
175	C₂×C₄×D₄	C₄×C₁₃₇	1	2	yes	complemented
176	C₂×C₄×D₄	C₂²×C₁₃₇	1	4	yes	—
177	C₂×#117	C₄×C₁₃₇	1	2	yes	complemented
178	C₂×#117	C₂²×C₁₃₇	1	4	yes	—
179	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
180	C₂²×C₄⋊C₄	C₄×C₁₃₇	1	2	yes	complemented
181	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
182	#410	C₄×C₁₃₇	1	16	yes	complemented
183	C₂×#99	C₂²×C₁₃₇	1	8	yes	—
184	C₄×C₄⋊C₄	—	2	8	no	—
185	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	8	yes	—
186	#342	C₂²×C₁₃₇	1	8	yes	—
187	C₂×#41	—	2	4	no	—
188	C₂×#41	—	2	4	no	—
189	C₂×#41	C₂×C₄×C₁₃₇	1	8	yes	—
190	C₂²×Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
191	C₂²×D₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
192	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
193	C₂³×C₄	C₂×C₄×C₁₃₇	1	2	yes	—
194	C₂³×C₄	C₂×C₄×C₁₃₇	1	4	yes	—
195	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
196	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
197	C₄×Q₈	—	2	8	no	—
198	C₄×D₄	—	2	16	no	—
199	C₄×D₄	—	2	8	no	—
200	#117	—	2	4	no	—
201	#117	—	2	8	no	—
202	#117	—	2	8	no	—
203	#117	C₂×C₄×C₁₃₇	1	16	yes	complemented
204	C₂×C₄⋊C₄	—	2	4	no	—
205	C₂×C₄⋊C₄	—	2	8	no	—
206	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
208	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
210	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
211	C₂×C₄⋊C₄	D₄×C₁₃₇	1	8	yes	—
212	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
213	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
214	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
215	C₂×C₄²	—	2	4	no	—
216	C₂×C₄²	—	2	8	no	—
217	C₂×C₄²	C₂×C₄×C₁₃₇	1	4	yes	—
218	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
219	#99	C₂×C₄×C₁₃₇	1	32	yes	complemented
220	#95	—	2	8	no	—
221	C₂⁴	C₂²×C₄×C₁₃₇	1	2	yes	—
222	C₂⁴	C₂⁴×C₁₃₇	1	1	yes	characteristic
223	#41	—	2	16	no	—
224	#41	—	2	16	no	—
225	C₂×Q₈	—	2	2	no	—
226	C₂×Q₈	—	2	2	no	—
227	C₂×Q₈	C₄²×C₁₃₇	1	4	yes	complemented
228	C₂×D₄	—	2	4	no	—
229	C₂×D₄	—	2	4	no	—
230	C₂×D₄	—	2	2	no	—
231	C₂×D₄	—	2	2	no	—
232	C₂×D₄	C₄²×C₁₃₇	1	4	yes	complemented
233	C₂×D₄	C₂²×C₄×C₁₃₇	1	8	yes	—
234	C₂²×C₄	—	2	4	no	—
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	2	8	no	—
237	C₂²×C₄	—	2	8	no	—
238	C₂²×C₄	—	8	2	no	—
239	C₂²×C₄	—	8	4	no	—
240	C₂²×C₄	C₄²×C₁₃₇	1	8	yes	complemented
241	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
242	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
243	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
244	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
245	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
246	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
247	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
248	C₂²×C₄	C₂×D₄×C₁₃₇	1	8	yes	—
249	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
250	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
251	C₄⋊C₄	—	2	2	no	—
252	C₄⋊C₄	—	2	8	no	—
253	C₄⋊C₄	—	2	2	no	—
254	C₄⋊C₄	—	2	16	no	—
255	C₄⋊C₄	C₂²⋊C₄×C₁₃₇	1	8	yes	—
256	C₄⋊C₄	C₂²⋊C₄×C₁₃₇	1	8	yes	—
257	C₂²⋊C₄	—	2	4	no	—
258	C₂²⋊C₄	—	2	8	no	—
259	C₂²⋊C₄	—	2	8	no	—
260	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	16	yes	—
261	C₄²	—	2	8	no	—
262	C₄²	—	2	4	no	—
263	C₄²	—	2	16	no	—
264	C₄²	—	8	8	no	—
265	C₂³	—	2	2	no	—
266	C₂³	—	2	2	no	—
267	C₂³	—	4	1	no	—
268	C₂³	—	4	1	no	—
269	C₂³	—	4	2	no	—
270	C₂³	—	4	2	no	—
271	C₂³	C₂×C₄²×C₁₃₇	1	4	yes	—
272	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
273	C₂³	C₂³×C₄×C₁₃₇	1	2	yes	—
274	C₂³	C₂²×D₄×C₁₃₇	1	2	yes	—
275	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
276	Q₈	—	2	8	no	—
277	D₄	—	2	16	no	—
278	D₄	—	2	8	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	16	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	16	no	—
285	C₂×C₄	—	4	8	no	—
286	C₂×C₄	—	4	4	no	—
287	C₂×C₄	—	4	8	no	—
288	C₂×C₄	—	4	8	no	—
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	4	2	no	—
291	C₂×C₄	—	8	8	no	—
292	C₂×C₄	C₂×C₄²×C₁₃₇	1	4	yes	—
293	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
294	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
295	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	8	yes	—
296	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
297	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
298	C₂×C₄	#117×C₁₃₇	1	2	yes	—
299	C₂×C₄	#117×C₁₃₇	1	2	yes	—
300	C₂×C₄	C₄×D₄×C₁₃₇	1	8	yes	—
301	C₂×C₄	C₄×D₄×C₁₃₇	1	8	yes	—
302	C₂²	—	2	2	no	—
303	C₂²	—	2	1	no	—
304	C₂²	—	2	2	no	—
305	C₂²	—	2	1	no	—
306	C₂²	—	2	4	no	—
307	C₂²	—	4	2	no	—
308	C₂²	—	4	2	no	—
309	C₂²	—	4	4	no	—
310	C₂²	—	4	4	no	—
311	C₂²	—	4	2	no	—
312	C₂²	—	4	2	no	—
313	C₂²	C₂²×C₄²×C₁₃₇	1	1	yes	characteristic
314	C₂²	C₂²×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
315	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
316	C₂²	C₂×C₄×D₄×C₁₃₇	1	4	yes	—
317	C₄	—	2	8	no	—
318	C₄	—	2	4	no	—
319	C₄	—	4	16	no	—
320	C₄	—	4	2	no	—
321	C₄	—	4	2	no	—
322	C₄	C₄×C₂²⋊C₄×C₁₃₇	1	4	yes	—
323	C₄	C₄×C₂²⋊C₄×C₁₃₇	1	4	yes	—
324	C₂	—	2	4	no	—
325	C₂	—	2	1	no	—
326	C₂	—	2	1	no	—
327	C₂	—	4	4	no	—
328	C₂	C₂×C₄×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
329	C₂	#2883×C₁₃₇	1	1	yes	characteristic
330	C₂	#2884×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂²×C₂²⋊C₄
commutator	C₂²	C₂²×C₄²×C₁₃₇
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃₇
prime radical	C₂²×#41×C₁₃₇	C₂²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₂²×C₄⋊C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. #2274×C₁₃₇	C₂	semidirect
4. C₄×#99×C₁₃₇	C₂	semidirect
5. #1740×C₁₃₇	C₂	semidirect
8. C₂×C₄×Q₈×C₁₃₇	C₄	semidirect
9. C₂×C₄×D₄×C₁₃₇	C₄	semidirect
11. C₂×#117×C₁₃₇	C₄	semidirect
14. C₂²×C₄⋊C₄×C₁₃₇	C₄	semidirect
16. #410×C₁₃₇	C₄	semidirect
37. #117×C₁₃₇	C₂×C₄	semidirect
53. #99×C₁₃₇	C₂×C₄	semidirect
61. C₂×Q₈×C₁₃₇	C₄²	semidirect
66. C₂×D₄×C₁₃₇	C₄²	semidirect
74. C₂²×C₄×C₁₃₇	C₄²	semidirect
165. #20393	C₁₃₇	direct (N × H)
166. C₁₃₇	#20393	direct (N × H)
169. #2274	C₂×C₁₃₇	semidirect
170. C₄×#99	C₂×C₁₃₇	semidirect
171. #1740	C₂×C₁₃₇	semidirect
174. C₂×C₄×Q₈	C₄×C₁₃₇	semidirect
175. C₂×C₄×D₄	C₄×C₁₃₇	semidirect
177. C₂×#117	C₄×C₁₃₇	semidirect
180. C₂²×C₄⋊C₄	C₄×C₁₃₇	semidirect
182. #410	C₄×C₁₃₇	semidirect
203. #117	C₂×C₄×C₁₃₇	semidirect
219. #99	C₂×C₄×C₁₃₇	semidirect
227. C₂×Q₈	C₄²×C₁₃₇	semidirect
232. C₂×D₄	C₄²×C₁₃₇	semidirect
240. C₂²×C₄	C₄²×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#520×C₁₃₇	2
C₂×#410×C₁₃₇	2
#2274×C₁₃₇	2
C₄×#99×C₁₃₇	2
#1740×C₁₃₇	2
#20393	137

Subgroups — C137×#20393 #46869779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#20393 #46869779