Subgroups — C₁₃₇×#25907 #46875293

Order 35072.

1116 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#125×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#488×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#2850×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2026×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2025×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1991×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1874×C₁₃₇	C₂	1	2	yes	maximal
8	#1872×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	C₄×C₂²⋊C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#125×C₁₃₇	—	2	8	no	—
11	C₂×#125×C₁₃₇	—	2	2	no	—
12	C₂×#125×C₁₃₇	C₂²	1	2	yes	—
13	C₂×#125×C₁₃₇	C₂²	1	2	yes	—
14	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×#121×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₃₇	—	2	2	no	—
18	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
20	#488×C₁₃₇	—	2	8	no	—
21	C₂×#103×C₁₃₇	C₂²	1	4	yes	—
22	C₂×#102×C₁₃₇	C₂²	1	4	yes	—
23	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
25	#391×C₁₃₇	C₂²	1	1	yes	characteristic
26	#390×C₁₃₇	C₂²	1	1	yes	characteristic
27	#388×C₁₃₇	—	2	2	no	—
28	#386×C₁₃₇	—	2	2	no	—
29	#382×C₁₃₇	C₂²	1	1	yes	characteristic
30	#340×C₁₃₇	C₂²	1	4	yes	—
31	#340×C₁₃₇	C₂²	1	4	yes	—
32	#336×C₁₃₇	C₂²	1	2	yes	—
33	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
34	C₂²×D₄×C₁₃₇	—	2	1	no	—
35	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₁₃₇	—	2	2	no	—
37	C₂³×C₄×C₁₃₇	D₄	1	2	yes	—
38	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₁₃₇	C₂³	1	4	yes	—
40	#125×C₁₃₇	—	2	16	no	—
41	#125×C₁₃₇	—	2	8	no	—
42	#125×C₁₃₇	—	2	4	no	—
43	#125×C₁₃₇	D₄	1	8	yes	complemented
44	#124×C₁₃₇	—	2	4	no	—
45	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
46	#121×C₁₃₇	—	2	4	no	—
47	C₂×C₄⋊C₄×C₁₃₇	—	2	16	no	—
48	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₇	—	2	8	no	—
52	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
56	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
60	C₂×C₄²×C₁₃₇	—	2	4	no	—
61	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
62	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
64	#103×C₁₃₇	—	2	8	no	—
65	#102×C₁₃₇	—	2	8	no	—
66	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
67	C₄×C₈×C₁₃₇	—	2	4	no	—
68	#95×C₁₃₇	—	2	2	no	—
69	#95×C₁₃₇	—	2	2	no	—
70	C₂⁴×C₁₃₇	—	2	1	no	—
71	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
72	C₂×Q₈×C₁₃₇	—	2	2	no	—
73	C₂×Q₈×C₁₃₇	—	2	2	no	—
74	C₂×Q₈×C₁₃₇	—	2	2	no	—
75	C₂×D₄×C₁₃₇	—	2	2	no	—
76	C₂×D₄×C₁₃₇	—	2	2	no	—
77	C₂×D₄×C₁₃₇	—	2	2	no	—
78	C₂×D₄×C₁₃₇	—	4	2	no	—
79	C₂×D₄×C₁₃₇	—	4	4	no	—
80	C₂²×C₄×C₁₃₇	—	2	2	no	—
81	C₂²×C₄×C₁₃₇	—	2	2	no	—
82	C₂²×C₄×C₁₃₇	—	2	8	no	—
83	C₂²×C₄×C₁₃₇	—	2	4	no	—
84	C₂²×C₄×C₁₃₇	—	2	4	no	—
85	C₂²×C₄×C₁₃₇	—	2	4	no	—
86	C₂²×C₄×C₁₃₇	—	2	1	no	—
87	C₂²×C₄×C₁₃₇	—	2	1	no	—
88	C₂²×C₄×C₁₃₇	—	2	1	no	—
89	C₂²×C₄×C₁₃₇	—	4	2	no	—
90	C₂²×C₄×C₁₃₇	—	4	4	no	—
91	C₂²×C₄×C₁₃₇	—	4	4	no	—
92	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
96	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
97	C₂×C₈×C₁₃₇	—	2	4	no	—
98	C₂×C₈×C₁₃₇	—	2	4	no	—
99	C₂×C₈×C₁₃₇	—	2	4	no	—
100	C₄⋊C₄×C₁₃₇	—	2	8	no	—
101	C₄⋊C₄×C₁₃₇	—	2	16	no	—
102	C₄⋊C₄×C₁₃₇	—	2	16	no	—
103	C₄⋊C₄×C₁₃₇	—	2	4	no	—
104	C₄⋊C₄×C₁₃₇	—	2	2	no	—
105	C₄⋊C₄×C₁₃₇	—	2	2	no	—
106	C₄⋊C₄×C₁₃₇	—	4	2	no	—
107	C₄⋊C₄×C₁₃₇	C₂×D₄	1	8	yes	—
108	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
109	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
110	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
111	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
112	C₄²×C₁₃₇	—	2	4	no	—
113	C₄²×C₁₃₇	—	2	2	no	—
114	C₄²×C₁₃₇	C₂×D₄	1	4	yes	—
115	C₂³×C₁₃₇	—	2	1	no	—
116	C₂³×C₁₃₇	—	2	1	no	—
117	C₂³×C₁₃₇	—	2	2	no	—
118	C₂³×C₁₃₇	—	4	1	no	—
119	C₂³×C₁₃₇	—	4	1	no	—
120	C₂³×C₁₃₇	—	4	1	no	—
121	C₂³×C₁₃₇	—	4	2	no	—
122	C₂³×C₁₃₇	—	4	2	no	—
123	C₂³×C₁₃₇	#124	1	2	yes	—
124	C₂³×C₁₃₇	#135	1	4	yes	—
125	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
126	Q₈×C₁₃₇	—	4	4	no	—
127	D₄×C₁₃₇	—	4	4	no	—
128	D₄×C₁₃₇	—	8	4	no	—
129	C₂×C₄×C₁₃₇	—	2	1	no	—
130	C₂×C₄×C₁₃₇	—	2	1	no	—
131	C₂×C₄×C₁₃₇	—	2	2	no	—
132	C₂×C₄×C₁₃₇	—	2	2	no	—
133	C₂×C₄×C₁₃₇	—	2	8	no	—
134	C₂×C₄×C₁₃₇	—	2	2	no	—
135	C₂×C₄×C₁₃₇	—	2	8	no	—
136	C₂×C₄×C₁₃₇	—	2	2	no	—
137	C₂×C₄×C₁₃₇	—	2	2	no	—
138	C₂×C₄×C₁₃₇	—	4	8	no	—
139	C₂×C₄×C₁₃₇	—	4	16	no	—
140	C₂×C₄×C₁₃₇	—	4	4	no	—
141	C₂×C₄×C₁₃₇	—	4	4	no	—
142	C₂×C₄×C₁₃₇	—	4	1	no	—
143	C₂×C₄×C₁₃₇	—	4	1	no	—
144	C₂×C₄×C₁₃₇	—	4	1	no	—
145	C₂×C₄×C₁₃₇	—	4	1	no	—
146	C₂×C₄×C₁₃₇	—	4	1	no	—
147	C₂×C₄×C₁₃₇	—	4	2	no	—
148	C₂×C₄×C₁₃₇	—	4	2	no	—
149	C₂×C₄×C₁₃₇	#120	1	4	yes	—
150	C₂×C₄×C₁₃₇	#124	1	2	yes	—
151	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
152	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
153	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
154	C₈×C₁₃₇	—	4	4	no	—
155	C₂²×C₁₃₇	—	2	2	no	—
156	C₂²×C₁₃₇	—	2	2	no	—
157	C₂²×C₁₃₇	—	2	4	no	—
158	C₂²×C₁₃₇	—	2	4	no	—
159	C₂²×C₁₃₇	—	8	1	no	—
160	C₂²×C₁₃₇	—	8	1	no	—
161	C₂²×C₁₃₇	—	8	1	no	—
162	C₂²×C₁₃₇	—	8	2	no	—
163	C₂²×C₁₃₇	—	8	2	no	—
164	C₂²×C₁₃₇	#488	1	4	yes	complemented
165	C₂²×C₁₃₇	C₂×#120	1	1	yes	characteristic
166	C₂²×C₁₃₇	C₂×#124	1	1	yes	characteristic
167	C₂²×C₁₃₇	#536	1	1	yes	characteristic
168	C₂²×C₁₃₇	C₂×#135	1	2	yes	—
169	C₂²×C₁₃₇	#575	1	2	yes	—
170	C₄×C₁₃₇	—	2	2	no	—
171	C₄×C₁₃₇	—	2	4	no	—
172	C₄×C₁₃₇	—	4	2	no	—
173	C₄×C₁₃₇	—	4	8	no	—
174	C₄×C₁₃₇	—	8	1	no	—
175	C₄×C₁₃₇	—	8	1	no	—
176	C₄×C₁₃₇	—	8	1	no	—
177	C₄×C₁₃₇	#548	1	4	yes	—
178	C₂×C₁₃₇	—	2	4	no	—
179	C₂×C₁₃₇	—	16	1	no	—
180	C₂×C₁₃₇	#2436	1	1	yes	characteristic
181	C₂×C₁₃₇	#3002	1	2	yes	—
182	C₂×C₁₃₇	C₂×#488	1	1	yes	characteristic
183	C₂×C₁₃₇	#3142	1	1	yes	characteristic
184	C₂×C₁₃₇	#3232	1	2	yes	—
185	#25907	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₁₃₇	#25907	1	1	yes	characteristic, direct product factor, Sylow
187	C₂²×#125	C₂×C₁₃₇	1	1	yes	characteristic, complemented
188	C₂×#488	C₂×C₁₃₇	1	2	yes	complemented
189	#2850	C₂×C₁₃₇	1	1	yes	characteristic
190	#2026	C₂×C₁₃₇	1	2	yes	complemented
191	#2025	C₂×C₁₃₇	1	2	yes	complemented
192	#1991	C₂×C₁₃₇	1	2	yes	complemented
193	#1874	C₂×C₁₃₇	1	2	yes	—
194	#1872	C₂×C₁₃₇	1	2	yes	complemented
195	C₄×C₂²⋊C₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
196	C₂×#125	—	2	8	no	—
197	C₂×#125	—	2	2	no	—
198	C₂×#125	C₂²×C₁₃₇	1	2	yes	—
199	C₂×#125	C₂²×C₁₃₇	1	2	yes	—
200	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
201	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
202	C₂×#121	C₂²×C₁₃₇	1	1	yes	characteristic
203	C₂²×C₄⋊C₄	—	2	2	no	—
204	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
205	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
206	#488	—	2	8	no	—
207	C₂×#103	C₂²×C₁₃₇	1	4	yes	—
208	C₂×#102	C₂²×C₁₃₇	1	4	yes	—
209	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
210	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
211	#391	C₂²×C₁₃₇	1	1	yes	characteristic
212	#390	C₂²×C₁₃₇	1	1	yes	characteristic
213	#388	—	2	2	no	—
214	#386	—	2	2	no	—
215	#382	C₂²×C₁₃₇	1	1	yes	characteristic
216	#340	C₂²×C₁₃₇	1	4	yes	—
217	#340	C₂²×C₁₃₇	1	4	yes	—
218	#336	C₂²×C₁₃₇	1	2	yes	—
219	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
220	C₂²×D₄	—	2	1	no	—
221	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
222	C₂³×C₄	—	2	2	no	—
223	C₂³×C₄	D₄×C₁₃₇	1	2	yes	—
224	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
225	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
226	#125	—	2	16	no	—
227	#125	—	2	8	no	—
228	#125	—	2	4	no	—
229	#125	D₄×C₁₃₇	1	8	yes	complemented
230	#124	—	2	4	no	—
231	C₂²⋊Q₈	—	2	4	no	—
232	#121	—	2	4	no	—
233	C₂×C₄⋊C₄	—	2	16	no	—
234	C₂×C₄⋊C₄	—	2	4	no	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	8	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
242	C₂×C₂²⋊C₄	—	2	1	no	—
243	C₂×C₂²⋊C₄	—	2	1	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₄²	—	2	4	no	—
247	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
248	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
250	#103	—	2	8	no	—
251	#102	—	2	8	no	—
252	C₂²⋊C₈	—	2	4	no	—
253	C₄×C₈	—	2	4	no	—
254	#95	—	2	2	no	—
255	#95	—	2	2	no	—
256	C₂⁴	—	2	1	no	—
257	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	2	2	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	2	2	no	—
264	C₂×D₄	—	4	2	no	—
265	C₂×D₄	—	4	4	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
280	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
281	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
282	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	2	4	no	—
286	C₄⋊C₄	—	2	8	no	—
287	C₄⋊C₄	—	2	16	no	—
288	C₄⋊C₄	—	2	16	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	4	2	no	—
293	C₄⋊C₄	C₂×D₄×C₁₃₇	1	8	yes	—
294	C₂²⋊C₄	—	4	4	no	—
295	C₂²⋊C₄	—	4	2	no	—
296	C₂²⋊C₄	—	4	4	no	—
297	C₂²⋊C₄	—	4	2	no	—
298	C₄²	—	2	4	no	—
299	C₄²	—	2	2	no	—
300	C₄²	C₂×D₄×C₁₃₇	1	4	yes	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	4	1	no	—
305	C₂³	—	4	1	no	—
306	C₂³	—	4	1	no	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	2	no	—
309	C₂³	#124×C₁₃₇	1	2	yes	—
310	C₂³	#135×C₁₃₇	1	4	yes	—
311	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
312	Q₈	—	4	4	no	—
313	D₄	—	4	4	no	—
314	D₄	—	8	4	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	8	no	—
325	C₂×C₄	—	4	16	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	#120×C₁₃₇	1	4	yes	—
336	C₂×C₄	#124×C₁₃₇	1	2	yes	—
337	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
338	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
339	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
340	C₈	—	4	4	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	8	1	no	—
346	C₂²	—	8	1	no	—
347	C₂²	—	8	1	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	8	2	no	—
350	C₂²	#488×C₁₃₇	1	4	yes	complemented
351	C₂²	C₂×#120×C₁₃₇	1	1	yes	characteristic
352	C₂²	C₂×#124×C₁₃₇	1	1	yes	characteristic
353	C₂²	#536×C₁₃₇	1	1	yes	characteristic
354	C₂²	C₂×#135×C₁₃₇	1	2	yes	—
355	C₂²	#575×C₁₃₇	1	2	yes	—
356	C₄	—	2	2	no	—
357	C₄	—	2	4	no	—
358	C₄	—	4	2	no	—
359	C₄	—	4	8	no	—
360	C₄	—	8	1	no	—
361	C₄	—	8	1	no	—
362	C₄	—	8	1	no	—
363	C₄	#548×C₁₃₇	1	4	yes	—
364	C₂	—	2	4	no	—
365	C₂	—	16	1	no	—
366	C₂	#2436×C₁₃₇	1	1	yes	characteristic
367	C₂	#3002×C₁₃₇	1	2	yes	—
368	C₂	C₂×#488×C₁₃₇	1	1	yes	characteristic
369	C₂	#3142×C₁₃₇	1	1	yes	characteristic
370	C₂	#3232×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂×#121×C₁₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂²×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#125×C₁₃₇	C₂	semidirect
2. C₂×#488×C₁₃₇	C₂	semidirect
4. #2026×C₁₃₇	C₂	semidirect
5. #2025×C₁₃₇	C₂	semidirect
6. #1991×C₁₃₇	C₂	semidirect
8. #1872×C₁₃₇	C₂	semidirect
9. C₄×C₂²⋊C₈×C₁₃₇	C₂	semidirect
43. #125×C₁₃₇	D₄	semidirect
164. C₂²×C₁₃₇	#488	semidirect
185. #25907	C₁₃₇	direct (N × H)
186. C₁₃₇	#25907	direct (N × H)
187. C₂²×#125	C₂×C₁₃₇	semidirect
188. C₂×#488	C₂×C₁₃₇	semidirect
190. #2026	C₂×C₁₃₇	semidirect
191. #2025	C₂×C₁₃₇	semidirect
192. #1991	C₂×C₁₃₇	semidirect
194. #1872	C₂×C₁₃₇	semidirect
195. C₄×C₂²⋊C₈	C₂×C₁₃₇	semidirect
229. #125	D₄×C₁₃₇	semidirect
350. C₂²	#488×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#125×C₁₃₇	2
C₂×#488×C₁₃₇	2
#2850×C₁₃₇	2
#2026×C₁₃₇	2
#2025×C₁₃₇	2
#1991×C₁₃₇	2
#1874×C₁₃₇	2
#1872×C₁₃₇	2
C₄×C₂²⋊C₈×C₁₃₇	2
#25907	137

Subgroups — C137×#25907 #46875293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#25907 #46875293