Subgroups — C₁₃₇×#25909 #46875295

Order 35072.

1092 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#489×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	#1993×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1875×C₁₃₇	C₂	1	2	yes	maximal
8	#1873×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1749×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#533×C₁₃₇	—	2	8	no	—
11	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	2	yes	—
12	C₂×#125×C₁₃₇	C₂²	1	2	yes	—
13	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
15	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×#121×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₃₇	—	2	2	no	—
18	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
20	#489×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×#97×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	—	2	2	no	—
34	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
35	C₂²×D₄×C₁₃₇	—	2	1	no	—
36	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
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	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
41	C₄⋊Q₈×C₁₃₇	D₄	1	8	yes	complemented
42	#125×C₁₃₇	—	2	8	no	—
43	#124×C₁₃₇	—	2	4	no	—
44	C₂²⋊Q₈×C₁₃₇	—	2	16	no	—
45	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
46	#121×C₁₃₇	—	2	4	no	—
47	C₄×Q₈×C₁₃₇	—	2	16	no	—
48	#117×C₁₃₇	—	2	8	no	—
49	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
55	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
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	2	no	—
61	C₂×C₄²×C₁₃₇	—	2	4	no	—
62	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
63	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
65	#103×C₁₃₇	—	2	8	no	—
66	#102×C₁₃₇	—	2	8	no	—
67	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
68	#97×C₁₃₇	—	2	4	no	—
69	#95×C₁₃₇	—	2	2	no	—
70	#95×C₁₃₇	—	2	2	no	—
71	C₂⁴×C₁₃₇	—	2	1	no	—
72	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
73	C₂×Q₈×C₁₃₇	—	2	8	no	—
74	C₂×Q₈×C₁₃₇	—	2	2	no	—
75	C₂×Q₈×C₁₃₇	—	2	2	no	—
76	C₂×Q₈×C₁₃₇	—	2	2	no	—
77	C₂×Q₈×C₁₃₇	—	4	4	no	—
78	C₂×Q₈×C₁₃₇	—	4	4	no	—
79	C₂×D₄×C₁₃₇	—	2	2	no	—
80	C₂×D₄×C₁₃₇	—	2	2	no	—
81	C₂×D₄×C₁₃₇	—	2	2	no	—
82	C₂×D₄×C₁₃₇	—	4	4	no	—
83	C₂×D₄×C₁₃₇	—	4	2	no	—
84	C₂²×C₄×C₁₃₇	—	2	2	no	—
85	C₂²×C₄×C₁₃₇	—	2	2	no	—
86	C₂²×C₄×C₁₃₇	—	2	4	no	—
87	C₂²×C₄×C₁₃₇	—	2	4	no	—
88	C₂²×C₄×C₁₃₇	—	2	1	no	—
89	C₂²×C₄×C₁₃₇	—	2	1	no	—
90	C₂²×C₄×C₁₃₇	—	2	1	no	—
91	C₂²×C₄×C₁₃₇	—	4	2	no	—
92	C₂²×C₄×C₁₃₇	—	4	2	no	—
93	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
97	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₁₃₇	—	2	4	no	—
99	C₂×C₈×C₁₃₇	—	2	4	no	—
100	C₂×C₈×C₁₃₇	—	2	4	no	—
101	C₄⋊C₄×C₁₃₇	—	2	16	no	—
102	C₄⋊C₄×C₁₃₇	—	2	8	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	—	2	8	no	—
109	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
110	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
111	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
112	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
113	C₄²×C₁₃₇	—	2	8	no	—
114	C₄²×C₁₃₇	—	2	4	no	—
115	C₄²×C₁₃₇	—	2	2	no	—
116	C₄²×C₁₃₇	C₂×D₄	1	4	yes	—
117	C₂³×C₁₃₇	—	2	1	no	—
118	C₂³×C₁₃₇	—	2	1	no	—
119	C₂³×C₁₃₇	—	2	2	no	—
120	C₂³×C₁₃₇	—	2	2	no	—
121	C₂³×C₁₃₇	—	4	1	no	—
122	C₂³×C₁₃₇	—	4	1	no	—
123	C₂³×C₁₃₇	—	4	1	no	—
124	C₂³×C₁₃₇	—	4	2	no	—
125	C₂³×C₁₃₇	—	4	2	no	—
126	C₂³×C₁₃₇	#124	1	2	yes	—
127	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
128	Q₈×C₁₃₇	—	4	16	no	—
129	Q₈×C₁₃₇	—	4	4	no	—
130	D₄×C₁₃₇	—	4	4	no	—
131	D₄×C₁₃₇	—	8	4	no	—
132	C₂×C₄×C₁₃₇	—	2	1	no	—
133	C₂×C₄×C₁₃₇	—	2	1	no	—
134	C₂×C₄×C₁₃₇	—	2	2	no	—
135	C₂×C₄×C₁₃₇	—	2	2	no	—
136	C₂×C₄×C₁₃₇	—	2	8	no	—
137	C₂×C₄×C₁₃₇	—	2	2	no	—
138	C₂×C₄×C₁₃₇	—	2	8	no	—
139	C₂×C₄×C₁₃₇	—	2	2	no	—
140	C₂×C₄×C₁₃₇	—	2	2	no	—
141	C₂×C₄×C₁₃₇	—	4	8	no	—
142	C₂×C₄×C₁₃₇	—	4	4	no	—
143	C₂×C₄×C₁₃₇	—	4	4	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	1	no	—
148	C₂×C₄×C₁₃₇	—	4	1	no	—
149	C₂×C₄×C₁₃₇	—	4	2	no	—
150	C₂×C₄×C₁₃₇	—	4	2	no	—
151	C₂×C₄×C₁₃₇	#120	1	4	yes	—
152	C₂×C₄×C₁₃₇	#124	1	2	yes	—
153	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
154	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
155	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
156	C₈×C₁₃₇	—	4	4	no	—
157	C₂²×C₁₃₇	—	2	2	no	—
158	C₂²×C₁₃₇	—	2	2	no	—
159	C₂²×C₁₃₇	—	2	2	no	—
160	C₂²×C₁₃₇	—	4	2	no	—
161	C₂²×C₁₃₇	—	4	2	no	—
162	C₂²×C₁₃₇	—	8	1	no	—
163	C₂²×C₁₃₇	—	8	1	no	—
164	C₂²×C₁₃₇	—	8	1	no	—
165	C₂²×C₁₃₇	—	8	2	no	—
166	C₂²×C₁₃₇	—	8	2	no	—
167	C₂²×C₁₃₇	C₂×#120	1	1	yes	characteristic
168	C₂²×C₁₃₇	C₂×#124	1	1	yes	characteristic
169	C₂²×C₁₃₇	#536	1	1	yes	characteristic
170	C₂²×C₁₃₇	#575	1	2	yes	—
171	C₂²×C₁₃₇	#575	1	2	yes	—
172	C₄×C₁₃₇	—	2	2	no	—
173	C₄×C₁₃₇	—	2	4	no	—
174	C₄×C₁₃₇	—	4	2	no	—
175	C₄×C₁₃₇	—	4	8	no	—
176	C₄×C₁₃₇	—	8	1	no	—
177	C₄×C₁₃₇	—	8	1	no	—
178	C₄×C₁₃₇	—	8	1	no	—
179	C₄×C₁₃₇	#548	1	4	yes	—
180	C₂×C₁₃₇	—	4	2	no	—
181	C₂×C₁₃₇	—	16	1	no	—
182	C₂×C₁₃₇	#2436	1	1	yes	characteristic
183	C₂×C₁₃₇	#3005	1	2	yes	—
184	C₂×C₁₃₇	#3135	1	1	yes	characteristic
185	C₂×C₁₃₇	#3140	1	1	yes	characteristic
186	C₂×C₁₃₇	#3240	1	2	yes	—
187	#25909	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₁₃₇	#25909	1	1	yes	characteristic, direct product factor, Sylow
189	C₂×#533	C₂×C₁₃₇	1	1	yes	characteristic, complemented
190	C₂×#489	C₂×C₁₃₇	1	2	yes	complemented
191	#2850	C₂×C₁₃₇	1	1	yes	characteristic
192	#2026	C₂×C₁₃₇	1	2	yes	complemented
193	#2025	C₂×C₁₃₇	1	2	yes	complemented
194	#1993	C₂×C₁₃₇	1	2	yes	complemented
195	#1875	C₂×C₁₃₇	1	2	yes	—
196	#1873	C₂×C₁₃₇	1	2	yes	complemented
197	#1749	C₂×C₁₃₇	1	1	yes	characteristic, complemented
198	#533	—	2	8	no	—
199	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
200	C₂×#125	C₂²×C₁₃₇	1	2	yes	—
201	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
202	C₂×C₂²⋊Q₈	—	2	2	no	—
203	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
204	C₂×#121	C₂²×C₁₃₇	1	1	yes	characteristic
205	C₂×C₄×Q₈	—	2	2	no	—
206	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
207	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
208	#489	—	2	8	no	—
209	C₂×#103	C₂²×C₁₃₇	1	4	yes	—
210	C₂×#102	C₂²×C₁₃₇	1	4	yes	—
211	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
212	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
213	#391	C₂²×C₁₃₇	1	1	yes	characteristic
214	#390	C₂²×C₁₃₇	1	1	yes	characteristic
215	#388	—	2	2	no	—
216	#386	—	2	2	no	—
217	#382	C₂²×C₁₃₇	1	1	yes	characteristic
218	#340	C₂²×C₁₃₇	1	4	yes	—
219	#340	C₂²×C₁₃₇	1	4	yes	—
220	#336	C₂²×C₁₃₇	1	2	yes	—
221	C₂²×Q₈	—	2	2	no	—
222	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
223	C₂²×D₄	—	2	1	no	—
224	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
225	C₂³×C₄	D₄×C₁₃₇	1	2	yes	—
226	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
228	C₄⋊Q₈	—	2	4	no	—
229	C₄⋊Q₈	D₄×C₁₃₇	1	8	yes	complemented
230	#125	—	2	8	no	—
231	#124	—	2	4	no	—
232	C₂²⋊Q₈	—	2	16	no	—
233	C₂²⋊Q₈	—	2	4	no	—
234	#121	—	2	4	no	—
235	C₄×Q₈	—	2	16	no	—
236	#117	—	2	8	no	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	1	no	—
245	C₂×C₂²⋊C₄	—	2	1	no	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₄²	—	2	2	no	—
249	C₂×C₄²	—	2	4	no	—
250	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
251	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
253	#103	—	2	8	no	—
254	#102	—	2	8	no	—
255	C₂²⋊C₈	—	2	4	no	—
256	#97	—	2	4	no	—
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	C₂⁴	—	2	1	no	—
260	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
261	C₂×Q₈	—	2	8	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	4	4	no	—
266	C₂×Q₈	—	4	4	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	4	4	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
284	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
285	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₄⋊C₄	—	2	16	no	—
290	C₄⋊C₄	—	2	8	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	4	2	no	—
295	C₄⋊C₄	C₂×D₄×C₁₃₇	1	8	yes	—
296	C₂²⋊C₄	—	2	8	no	—
297	C₂²⋊C₄	—	4	4	no	—
298	C₂²⋊C₄	—	4	2	no	—
299	C₂²⋊C₄	—	4	4	no	—
300	C₂²⋊C₄	—	4	2	no	—
301	C₄²	—	2	8	no	—
302	C₄²	—	2	4	no	—
303	C₄²	—	2	2	no	—
304	C₄²	C₂×D₄×C₁₃₇	1	4	yes	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	4	1	no	—
310	C₂³	—	4	1	no	—
311	C₂³	—	4	1	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	#124×C₁₃₇	1	2	yes	—
315	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
316	Q₈	—	4	16	no	—
317	Q₈	—	4	4	no	—
318	D₄	—	4	4	no	—
319	D₄	—	8	4	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	8	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	#120×C₁₃₇	1	4	yes	—
340	C₂×C₄	#124×C₁₃₇	1	2	yes	—
341	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
342	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
343	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
344	C₈	—	4	4	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	4	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	8	1	no	—
351	C₂²	—	8	1	no	—
352	C₂²	—	8	1	no	—
353	C₂²	—	8	2	no	—
354	C₂²	—	8	2	no	—
355	C₂²	C₂×#120×C₁₃₇	1	1	yes	characteristic
356	C₂²	C₂×#124×C₁₃₇	1	1	yes	characteristic
357	C₂²	#536×C₁₃₇	1	1	yes	characteristic
358	C₂²	#575×C₁₃₇	1	2	yes	—
359	C₂²	#575×C₁₃₇	1	2	yes	—
360	C₄	—	2	2	no	—
361	C₄	—	2	4	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	8	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	1	no	—
366	C₄	—	8	1	no	—
367	C₄	#548×C₁₃₇	1	4	yes	—
368	C₂	—	4	2	no	—
369	C₂	—	16	1	no	—
370	C₂	#2436×C₁₃₇	1	1	yes	characteristic
371	C₂	#3005×C₁₃₇	1	2	yes	—
372	C₂	#3135×C₁₃₇	1	1	yes	characteristic
373	C₂	#3140×C₁₃₇	1	1	yes	characteristic
374	C₂	#3240×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. C₂×#533×C₁₃₇	C₂	semidirect
2. C₂×#489×C₁₃₇	C₂	semidirect
4. #2026×C₁₃₇	C₂	semidirect
5. #2025×C₁₃₇	C₂	semidirect
6. #1993×C₁₃₇	C₂	semidirect
8. #1873×C₁₃₇	C₂	semidirect
9. #1749×C₁₃₇	C₂	semidirect
41. C₄⋊Q₈×C₁₃₇	D₄	semidirect
187. #25909	C₁₃₇	direct (N × H)
188. C₁₃₇	#25909	direct (N × H)
189. C₂×#533	C₂×C₁₃₇	semidirect
190. C₂×#489	C₂×C₁₃₇	semidirect
192. #2026	C₂×C₁₃₇	semidirect
193. #2025	C₂×C₁₃₇	semidirect
194. #1993	C₂×C₁₃₇	semidirect
196. #1873	C₂×C₁₃₇	semidirect
197. #1749	C₂×C₁₃₇	semidirect
229. C₄⋊Q₈	D₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₁₃₇	2
C₂×#489×C₁₃₇	2
#2850×C₁₃₇	2
#2026×C₁₃₇	2
#2025×C₁₃₇	2
#1993×C₁₃₇	2
#1875×C₁₃₇	2
#1873×C₁₃₇	2
#1749×C₁₃₇	2
#25909	137

Subgroups — C137×#25909 #46875295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#25909 #46875295