Subgroups — C₁₃₇×#22682 #46872068

Order 35072.

1062 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₈×C₁₃₇	C₂	1	2	yes	maximal
2	C₂×C₄×D₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2349×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#1942×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1864×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1846×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1804×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	C₈×C₄⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₃₇	C₂²	1	4	yes	—
11	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
12	C₄×D₈×C₁₃₇	—	2	8	no	—
13	C₄×D₈×C₁₃₇	C₄	1	8	yes	complemented
14	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
15	C₂×#107×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×#102×C₁₃₇	C₂²	1	4	yes	—
19	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
22	#389×C₁₃₇	C₂²	1	4	yes	—
23	#385×C₁₃₇	—	2	4	no	—
24	#382×C₁₃₇	C₂²	1	2	yes	—
25	#380×C₁₃₇	—	2	2	no	—
26	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₂×#95×C₁₃₇	—	2	2	no	—
28	#340×C₁₃₇	C₂²	1	4	yes	—
29	#336×C₁₃₇	C₂²	1	2	yes	—
30	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
31	C₂³×C₄×C₁₃₇	—	2	2	no	—
32	C₂³×C₄×C₁₃₇	—	2	4	no	—
33	C₂×D₈×C₁₃₇	C₂×C₄	1	4	yes	—
34	C₂×D₈×C₁₃₇	D₄	1	4	yes	—
35	C₂×D₈×C₁₃₇	Q₈	1	4	yes	—
36	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
39	C₄×D₄×C₁₃₇	—	2	8	no	—
40	C₄×D₄×C₁₃₇	—	2	4	no	—
41	C₄×D₄×C₁₃₇	—	4	4	no	—
42	C₄×D₄×C₁₃₇	C₂×C₄	1	8	yes	complemented
43	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
47	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
49	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
50	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
51	#107×C₁₃₇	—	2	4	no	—
52	#107×C₁₃₇	C₂×C₄	1	4	yes	complemented
53	#106×C₁₃₇	—	4	2	no	—
54	C₄⋊C₈×C₁₃₇	—	2	2	no	—
55	#102×C₁₃₇	—	2	8	no	—
56	#102×C₁₃₇	C₂×C₄	1	8	yes	complemented
57	C₄×C₈×C₁₃₇	—	2	4	no	—
58	C₄×C₈×C₁₃₇	C₂×C₄	1	4	yes	complemented
59	#95×C₁₃₇	—	2	2	no	—
60	#95×C₁₃₇	—	2	4	no	—
61	#95×C₁₃₇	—	2	2	no	—
62	#95×C₁₃₇	D₄	1	1	yes	characteristic
63	#95×C₁₃₇	D₄	1	1	yes	characteristic
64	C₂⁴×C₁₃₇	—	2	2	no	—
65	C₂×D₄×C₁₃₇	—	2	2	no	—
66	C₂×D₄×C₁₃₇	—	2	2	no	—
67	C₂×D₄×C₁₃₇	—	2	2	no	—
68	C₂×D₄×C₁₃₇	C₂²×C₄	1	4	yes	—
69	C₂×D₄×C₁₃₇	C₂×D₄	1	4	yes	—
70	C₂×D₄×C₁₃₇	C₂×Q₈	1	4	yes	—
71	C₂²×C₄×C₁₃₇	—	2	2	no	—
72	C₂²×C₄×C₁₃₇	—	2	8	no	—
73	C₂²×C₄×C₁₃₇	—	2	4	no	—
74	C₂²×C₄×C₁₃₇	—	4	8	no	—
75	C₂²×C₄×C₁₃₇	—	4	8	no	—
76	C₂²×C₄×C₁₃₇	—	8	4	no	—
77	C₂²×C₄×C₁₃₇	—	8	4	no	—
78	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
83	D₈×C₁₃₇	C₄⋊C₄	1	16	yes	complemented
84	C₂×C₈×C₁₃₇	—	2	1	no	—
85	C₂×C₈×C₁₃₇	—	2	1	no	—
86	C₂×C₈×C₁₃₇	—	2	2	no	—
87	C₂×C₈×C₁₃₇	—	2	2	no	—
88	C₂×C₈×C₁₃₇	—	2	2	no	—
89	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
90	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
91	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
92	C₂×C₈×C₁₃₇	C₂×Q₈	1	2	yes	—
93	C₄⋊C₄×C₁₃₇	—	2	4	no	—
94	C₄⋊C₄×C₁₃₇	—	2	2	no	—
95	C₄⋊C₄×C₁₃₇	—	2	4	no	—
96	C₄⋊C₄×C₁₃₇	—	2	4	no	—
97	C₄⋊C₄×C₁₃₇	—	8	4	no	—
98	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
99	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
100	C₂²⋊C₄×C₁₃₇	—	4	8	no	—
101	C₄²×C₁₃₇	—	2	2	no	—
102	C₄²×C₁₃₇	—	2	2	no	—
103	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
104	C₄²×C₁₃₇	#41	1	2	yes	—
105	C₂³×C₁₃₇	—	2	4	no	—
106	C₂³×C₁₃₇	—	2	4	no	—
107	C₂³×C₁₃₇	—	2	4	no	—
108	C₂³×C₁₃₇	—	4	4	no	—
109	C₂³×C₁₃₇	—	4	4	no	—
110	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
111	D₄×C₁₃₇	—	2	4	no	—
112	D₄×C₁₃₇	—	2	4	no	—
113	D₄×C₁₃₇	—	2	4	no	—
114	D₄×C₁₃₇	C₂×C₄⋊C₄	1	8	yes	—
115	C₂×C₄×C₁₃₇	—	2	2	no	—
116	C₂×C₄×C₁₃₇	—	2	2	no	—
117	C₂×C₄×C₁₃₇	—	2	2	no	—
118	C₂×C₄×C₁₃₇	—	2	2	no	—
119	C₂×C₄×C₁₃₇	—	2	4	no	—
120	C₂×C₄×C₁₃₇	—	2	2	no	—
121	C₂×C₄×C₁₃₇	—	2	2	no	—
122	C₂×C₄×C₁₃₇	—	2	2	no	—
123	C₂×C₄×C₁₃₇	—	4	4	no	—
124	C₂×C₄×C₁₃₇	—	4	4	no	—
125	C₂×C₄×C₁₃₇	—	4	4	no	—
126	C₂×C₄×C₁₃₇	—	4	4	no	—
127	C₂×C₄×C₁₃₇	—	8	8	no	—
128	C₂×C₄×C₁₃₇	—	8	16	no	—
129	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
130	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
131	C₂×C₄×C₁₃₇	#135	1	4	yes	—
132	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
135	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
136	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
137	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
138	C₈×C₁₃₇	—	2	2	no	—
139	C₈×C₁₃₇	—	4	2	no	—
140	C₈×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
141	C₂²×C₁₃₇	—	2	8	no	—
142	C₂²×C₁₃₇	—	4	8	no	—
143	C₂²×C₁₃₇	—	4	4	no	—
144	C₂²×C₁₃₇	—	4	4	no	—
145	C₂²×C₁₃₇	—	4	8	no	—
146	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
147	C₂²×C₁₃₇	D₄²	1	1	yes	characteristic
148	C₂²×C₁₃₇	D₄×Q₈	1	1	yes	characteristic
149	C₂²×C₁₃₇	C₂×#135	1	2	yes	—
150	C₂²×C₁₃₇	#576	1	2	yes	—
151	C₄×C₁₃₇	—	2	2	no	—
152	C₄×C₁₃₇	—	2	2	no	—
153	C₄×C₁₃₇	—	2	4	no	—
154	C₄×C₁₃₇	—	4	4	no	—
155	C₄×C₁₃₇	—	4	2	no	—
156	C₄×C₁₃₇	—	8	4	no	—
157	C₄×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
158	C₄×C₁₃₇	#520	1	1	yes	characteristic
159	C₄×C₁₃₇	#547	1	1	yes	characteristic
160	C₄×C₁₃₇	#554	1	1	yes	characteristic
161	C₂×C₁₃₇	—	4	8	no	—
162	C₂×C₁₃₇	D₄×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₁₃₇	C₄×#135	1	1	yes	characteristic
164	C₂×C₁₃₇	#2948	1	1	yes	characteristic
165	C₂×C₁₃₇	#3280	1	2	yes	—
166	C₂×C₁₃₇	#3380	1	2	yes	—
167	#22682	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₁₃₇	#22682	1	1	yes	characteristic, direct product factor, Sylow
169	C₂×C₄×D₈	C₂×C₁₃₇	1	2	yes	—
170	C₂×C₄×D₈	C₂×C₁₃₇	1	1	yes	characteristic
171	#2349	C₂×C₁₃₇	1	2	yes	complemented
172	#1942	C₂×C₁₃₇	1	2	yes	complemented
173	#1864	C₂×C₁₃₇	1	4	yes	complemented
174	#1846	C₂×C₁₃₇	1	1	yes	characteristic, complemented
175	#1804	C₂×C₁₃₇	1	2	yes	complemented
176	C₈×C₄⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic, complemented
177	C₂²×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
178	C₂×C₄×D₄	C₂²×C₁₃₇	1	4	yes	—
179	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
180	C₄×D₈	—	2	8	no	—
181	C₄×D₈	C₄×C₁₃₇	1	8	yes	complemented
182	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
183	C₂×#107	C₂²×C₁₃₇	1	1	yes	characteristic
184	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
185	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
186	C₂×#102	C₂²×C₁₃₇	1	4	yes	—
187	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
188	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
189	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
190	#389	C₂²×C₁₃₇	1	4	yes	—
191	#385	—	2	4	no	—
192	#382	C₂²×C₁₃₇	1	2	yes	—
193	#380	—	2	2	no	—
194	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
195	C₂×#95	—	2	2	no	—
196	#340	C₂²×C₁₃₇	1	4	yes	—
197	#336	C₂²×C₁₃₇	1	2	yes	—
198	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
199	C₂³×C₄	—	2	2	no	—
200	C₂³×C₄	—	2	4	no	—
201	C₂×D₈	C₂×C₄×C₁₃₇	1	4	yes	—
202	C₂×D₈	D₄×C₁₃₇	1	4	yes	—
203	C₂×D₈	Q₈×C₁₃₇	1	4	yes	—
204	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
205	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
206	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
207	C₄×D₄	—	2	8	no	—
208	C₄×D₄	—	2	4	no	—
209	C₄×D₄	—	4	4	no	—
210	C₄×D₄	C₂×C₄×C₁₃₇	1	8	yes	complemented
211	C₂×C₄⋊C₄	—	2	4	no	—
212	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
213	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
214	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
215	C₂×C₂²⋊C₄	—	2	2	no	—
216	C₂×C₂²⋊C₄	—	2	4	no	—
217	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
218	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
219	#107	—	2	4	no	—
220	#107	C₂×C₄×C₁₃₇	1	4	yes	complemented
221	#106	—	4	2	no	—
222	C₄⋊C₈	—	2	2	no	—
223	#102	—	2	8	no	—
224	#102	C₂×C₄×C₁₃₇	1	8	yes	complemented
225	C₄×C₈	—	2	4	no	—
226	C₄×C₈	C₂×C₄×C₁₃₇	1	4	yes	complemented
227	#95	—	2	2	no	—
228	#95	—	2	4	no	—
229	#95	—	2	2	no	—
230	#95	D₄×C₁₃₇	1	1	yes	characteristic
231	#95	D₄×C₁₃₇	1	1	yes	characteristic
232	C₂⁴	—	2	2	no	—
233	C₂×D₄	—	2	2	no	—
234	C₂×D₄	—	2	2	no	—
235	C₂×D₄	—	2	2	no	—
236	C₂×D₄	C₂²×C₄×C₁₃₇	1	4	yes	—
237	C₂×D₄	C₂×D₄×C₁₃₇	1	4	yes	—
238	C₂×D₄	C₂×Q₈×C₁₃₇	1	4	yes	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	8	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	4	8	no	—
243	C₂²×C₄	—	4	8	no	—
244	C₂²×C₄	—	8	4	no	—
245	C₂²×C₄	—	8	4	no	—
246	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
247	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
248	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
249	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
250	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
251	D₈	C₄⋊C₄×C₁₃₇	1	16	yes	complemented
252	C₂×C₈	—	2	1	no	—
253	C₂×C₈	—	2	1	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
258	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
259	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
260	C₂×C₈	C₂×Q₈×C₁₃₇	1	2	yes	—
261	C₄⋊C₄	—	2	4	no	—
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	2	4	no	—
264	C₄⋊C₄	—	2	4	no	—
265	C₄⋊C₄	—	8	4	no	—
266	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
267	C₂²⋊C₄	—	2	8	no	—
268	C₂²⋊C₄	—	4	8	no	—
269	C₄²	—	2	2	no	—
270	C₄²	—	2	2	no	—
271	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
272	C₄²	#41×C₁₃₇	1	2	yes	—
273	C₂³	—	2	4	no	—
274	C₂³	—	2	4	no	—
275	C₂³	—	2	4	no	—
276	C₂³	—	4	4	no	—
277	C₂³	—	4	4	no	—
278	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
279	D₄	—	2	4	no	—
280	D₄	—	2	4	no	—
281	D₄	—	2	4	no	—
282	D₄	C₂×C₄⋊C₄×C₁₃₇	1	8	yes	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	4	4	no	—
292	C₂×C₄	—	4	4	no	—
293	C₂×C₄	—	4	4	no	—
294	C₂×C₄	—	4	4	no	—
295	C₂×C₄	—	8	8	no	—
296	C₂×C₄	—	8	16	no	—
297	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
298	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
299	C₂×C₄	#135×C₁₃₇	1	4	yes	—
300	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
301	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
302	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
303	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
304	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
305	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
306	C₈	—	2	2	no	—
307	C₈	—	4	2	no	—
308	C₈	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
309	C₂²	—	2	8	no	—
310	C₂²	—	4	8	no	—
311	C₂²	—	4	4	no	—
312	C₂²	—	4	4	no	—
313	C₂²	—	4	8	no	—
314	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
315	C₂²	D₄²×C₁₃₇	1	1	yes	characteristic
316	C₂²	D₄×Q₈×C₁₃₇	1	1	yes	characteristic
317	C₂²	C₂×#135×C₁₃₇	1	2	yes	—
318	C₂²	#576×C₁₃₇	1	2	yes	—
319	C₄	—	2	2	no	—
320	C₄	—	2	2	no	—
321	C₄	—	2	4	no	—
322	C₄	—	4	4	no	—
323	C₄	—	4	2	no	—
324	C₄	—	8	4	no	—
325	C₄	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
326	C₄	#520×C₁₃₇	1	1	yes	characteristic
327	C₄	#547×C₁₃₇	1	1	yes	characteristic
328	C₄	#554×C₁₃₇	1	1	yes	characteristic
329	C₂	—	4	8	no	—
330	C₂	D₄×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
331	C₂	C₄×#135×C₁₃₇	1	1	yes	characteristic
332	C₂	#2948×C₁₃₇	1	1	yes	characteristic
333	C₂	#3280×C₁₃₇	1	2	yes	—
334	C₂	#3380×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×D₈×C₁₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₄×C₄⋊C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. #2349×C₁₃₇	C₂	semidirect
4. #1942×C₁₃₇	C₂	semidirect
5. #1864×C₁₃₇	C₂	semidirect
6. #1846×C₁₃₇	C₂	semidirect
7. #1804×C₁₃₇	C₂	semidirect
8. C₈×C₄⋊C₄×C₁₃₇	C₂	semidirect
13. C₄×D₈×C₁₃₇	C₄	semidirect
42. C₄×D₄×C₁₃₇	C₂×C₄	semidirect
52. #107×C₁₃₇	C₂×C₄	semidirect
56. #102×C₁₃₇	C₂×C₄	semidirect
58. C₄×C₈×C₁₃₇	C₂×C₄	semidirect
83. D₈×C₁₃₇	C₄⋊C₄	semidirect
167. #22682	C₁₃₇	direct (N × H)
168. C₁₃₇	#22682	direct (N × H)
171. #2349	C₂×C₁₃₇	semidirect
172. #1942	C₂×C₁₃₇	semidirect
173. #1864	C₂×C₁₃₇	semidirect
174. #1846	C₂×C₁₃₇	semidirect
175. #1804	C₂×C₁₃₇	semidirect
176. C₈×C₄⋊C₄	C₂×C₁₃₇	semidirect
181. C₄×D₈	C₄×C₁₃₇	semidirect
210. C₄×D₄	C₂×C₄×C₁₃₇	semidirect
220. #107	C₂×C₄×C₁₃₇	semidirect
224. #102	C₂×C₄×C₁₃₇	semidirect
226. C₄×C₈	C₂×C₄×C₁₃₇	semidirect
251. D₈	C₄⋊C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₈×C₁₃₇	2
#2349×C₁₃₇	2
#1942×C₁₃₇	2
#1864×C₁₃₇	2
#1846×C₁₃₇	2
#1804×C₁₃₇	2
C₈×C₄⋊C₄×C₁₃₇	2
#22682	137

Subgroups — C137×#22682 #46872068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#22682 #46872068