Subgroups — C₁₃₇×#19393 #46868779

Order 35072.

642 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3230×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#3077×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#476×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2972×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#1683×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1675×C₁₃₇	C₂	1	4	yes	maximal, complemented
7	#1571×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1548×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1542×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#533×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
13	#500×C₁₃₇	C₂²	1	2	yes	complemented
14	#487×C₁₃₇	C₂²	1	2	yes	complemented
15	#484×C₁₃₇	—	2	2	no	—
16	#478×C₁₃₇	—	2	2	no	—
17	#477×C₁₃₇	—	2	2	no	—
18	#476×C₁₃₇	—	2	2	no	—
19	#476×C₁₃₇	C₂²	1	4	yes	—
20	#476×C₁₃₇	C₂²	1	2	yes	—
21	#474×C₁₃₇	C₂²	1	2	yes	—
22	C₈×D₄×C₁₃₇	—	2	2	no	—
23	C₈×D₄×C₁₃₇	C₂²	1	4	yes	—
24	#431×C₁₃₇	C₂²	1	1	yes	characteristic
25	#431×C₁₃₇	C₂²	1	1	yes	characteristic
26	#428×C₁₃₇	—	2	1	no	—
27	C₂×#106×C₁₃₇	—	2	1	no	—
28	#423×C₁₃₇	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
30	#418×C₁₃₇	—	2	1	no	—
31	C₂×#102×C₁₃₇	—	2	1	no	—
32	C₂×C₂²⋊C₈×C₁₃₇	—	2	2	no	—
33	#335×C₁₃₇	C₂²	1	4	yes	complemented
34	#333×C₁₃₇	C₂²	1	2	yes	complemented
35	#333×C₁₃₇	C₂²	1	4	yes	complemented
36	#332×C₁₃₇	C₂²	1	2	yes	complemented
37	C₂²×Q₈×C₁₃₇	—	2	1	no	—
38	C₂²×D₄×C₁₃₇	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃₇	—	2	1	no	—
40	C₂×M₁₆×C₁₃₇	—	2	1	no	—
41	C₂²×C₈×C₁₃₇	—	2	1	no	—
42	C₂²×C₈×C₁₃₇	—	2	4	no	—
43	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
44	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
45	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
46	C₄⋊Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
47	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
48	C₄⋊Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
49	#125×C₁₃₇	—	2	1	no	—
50	C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
51	C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
52	C₄×Q₈×C₁₃₇	—	2	1	no	—
53	C₄×Q₈×C₁₃₇	—	2	1	no	—
54	C₄×D₄×C₁₃₇	—	2	1	no	—
55	C₄×D₄×C₁₃₇	—	2	1	no	—
56	C₄×D₄×C₁₃₇	D₄	1	2	yes	—
57	C₄×D₄×C₁₃₇	C₂³	1	2	yes	—
58	#117×C₁₃₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
63	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
64	#107×C₁₃₇	—	2	4	no	—
65	#107×C₁₃₇	—	2	2	no	—
66	#106×C₁₃₇	—	2	4	no	—
67	#106×C₁₃₇	—	2	2	no	—
68	C₄⋊C₈×C₁₃₇	—	2	1	no	—
69	C₄⋊C₈×C₁₃₇	—	2	1	no	—
70	C₄⋊C₈×C₁₃₇	D₄	1	2	yes	—
71	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
72	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
73	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
74	#103×C₁₃₇	—	2	4	no	—
75	#102×C₁₃₇	—	2	4	no	—
76	#102×C₁₃₇	—	2	2	no	—
77	#102×C₁₃₇	—	2	2	no	—
78	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
79	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
80	C₂²⋊C₈×C₁₃₇	D₄	1	2	yes	—
81	C₄×C₈×C₁₃₇	—	2	1	no	—
82	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
83	C₂⁴×C₁₃₇	—	2	1	no	—
84	C₂×Q₈×C₁₃₇	—	2	1	no	—
85	C₂×Q₈×C₁₃₇	—	2	1	no	—
86	C₂×Q₈×C₁₃₇	—	2	2	no	—
87	C₂×Q₈×C₁₃₇	—	4	1	no	—
88	C₂×Q₈×C₁₃₇	—	8	2	no	—
89	C₂×D₄×C₁₃₇	—	2	1	no	—
90	C₂×D₄×C₁₃₇	—	2	2	no	—
91	C₂×D₄×C₁₃₇	Q₁₆	1	4	yes	—
92	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃₇	—	2	1	no	—
94	C₂²×C₄×C₁₃₇	—	2	2	no	—
95	C₂²×C₄×C₁₃₇	—	2	2	no	—
96	C₂²×C₄×C₁₃₇	—	4	1	no	—
97	C₂²×C₄×C₁₃₇	—	8	2	no	—
98	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
101	M₁₆×C₁₃₇	—	4	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	—	4	2	no	—
106	C₂×C₈×C₁₃₇	—	8	4	no	—
107	C₂×C₈×C₁₃₇	C₂×D₄	1	4	yes	—
108	C₄⋊C₄×C₁₃₇	—	2	1	no	—
109	C₄⋊C₄×C₁₃₇	—	2	2	no	—
110	C₄⋊C₄×C₁₃₇	—	2	1	no	—
111	C₄⋊C₄×C₁₃₇	—	2	1	no	—
112	C₄⋊C₄×C₁₃₇	—	2	2	no	—
113	C₄⋊C₄×C₁₃₇	—	2	1	no	—
114	C₄⋊C₄×C₁₃₇	—	2	1	no	—
115	C₄⋊C₄×C₁₃₇	—	4	1	no	—
116	C₄⋊C₄×C₁₃₇	—	4	1	no	—
117	C₄⋊C₄×C₁₃₇	—	4	1	no	—
118	C₄⋊C₄×C₁₃₇	—	4	1	no	—
119	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
120	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
121	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
122	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
123	C₄²×C₁₃₇	—	4	1	no	—
124	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₃₇	#41	1	1	yes	characteristic
127	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
128	C₂³×C₁₃₇	—	2	2	no	—
129	C₂³×C₁₃₇	—	2	4	no	—
130	C₂³×C₁₃₇	—	8	1	no	—
131	C₂³×C₁₃₇	—	8	1	no	—
132	C₂³×C₁₃₇	#121	1	1	yes	characteristic
133	Q₈×C₁₃₇	—	4	2	no	—
134	Q₈×C₁₃₇	—	8	1	no	—
135	Q₈×C₁₃₇	—	8	2	no	—
136	Q₈×C₁₃₇	—	8	2	no	—
137	D₄×C₁₃₇	—	2	2	no	—
138	D₄×C₁₃₇	—	2	4	no	—
139	D₄×C₁₃₇	C₂×Q₁₆	1	4	yes	—
140	C₂×C₄×C₁₃₇	—	2	2	no	—
141	C₂×C₄×C₁₃₇	—	2	2	no	—
142	C₂×C₄×C₁₃₇	—	4	1	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	2	no	—
147	C₂×C₄×C₁₃₇	—	8	2	no	—
148	C₂×C₄×C₁₃₇	—	8	1	no	—
149	C₂×C₄×C₁₃₇	—	8	2	no	—
150	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
153	C₂×C₄×C₁₃₇	C₂×Q₁₆	1	2	yes	—
154	C₂×C₄×C₁₃₇	#135	1	2	yes	—
155	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
158	C₈×C₁₃₇	—	2	4	no	—
159	C₈×C₁₃₇	—	4	2	no	—
160	C₈×C₁₃₇	—	4	2	no	—
161	C₈×C₁₃₇	—	4	2	no	—
162	C₂²×C₁₃₇	—	2	1	no	—
163	C₂²×C₁₃₇	—	2	1	no	—
164	C₂²×C₁₃₇	—	2	4	no	—
165	C₂²×C₁₃₇	—	4	2	no	—
166	C₂²×C₁₃₇	—	4	2	no	—
167	C₂²×C₁₃₇	—	8	4	no	—
168	C₂²×C₁₃₇	#467	1	2	yes	—
169	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
170	C₄×C₁₃₇	—	2	1	no	—
171	C₄×C₁₃₇	—	2	1	no	—
172	C₄×C₁₃₇	—	2	1	no	—
173	C₄×C₁₃₇	—	4	2	no	—
174	C₄×C₁₃₇	—	8	1	no	—
175	C₄×C₁₃₇	—	8	2	no	—
176	C₄×C₁₃₇	—	8	1	no	—
177	C₄×C₁₃₇	#467	1	2	yes	—
178	C₄×C₁₃₇	C₂²×Q₁₆	1	1	yes	characteristic
179	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
180	C₄×C₁₃₇	#577	1	2	yes	—
181	C₂×C₁₃₇	—	2	2	no	—
182	C₂×C₁₃₇	—	4	4	no	—
183	C₂×C₁₃₇	#3042	1	1	yes	characteristic
184	C₂×C₁₃₇	C₂×#467	1	1	yes	characteristic
185	C₂×C₁₃₇	#3068	1	1	yes	characteristic
186	#19393	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₁₃₇	#19393	1	1	yes	characteristic, direct product factor, Sylow
188	#3230	C₂×C₁₃₇	1	1	yes	characteristic, complemented
189	#3077	C₂×C₁₃₇	1	1	yes	characteristic
190	C₂×#476	C₂×C₁₃₇	1	1	yes	characteristic
191	#2972	C₂×C₁₃₇	1	1	yes	characteristic
192	#1683	C₂×C₁₃₇	1	4	yes	complemented
193	#1675	C₂×C₁₃₇	1	4	yes	complemented
194	#1571	C₂×C₁₃₇	1	1	yes	characteristic, complemented
195	#1548	C₂×C₁₃₇	1	1	yes	characteristic, complemented
196	#1542	C₂×C₁₃₇	1	1	yes	characteristic, complemented
197	#533	C₂²×C₁₃₇	1	1	yes	characteristic
198	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
199	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
200	#500	C₂²×C₁₃₇	1	2	yes	complemented
201	#487	C₂²×C₁₃₇	1	2	yes	complemented
202	#484	—	2	2	no	—
203	#478	—	2	2	no	—
204	#477	—	2	2	no	—
205	#476	—	2	2	no	—
206	#476	C₂²×C₁₃₇	1	2	yes	—
207	#476	C₂²×C₁₃₇	1	4	yes	—
208	#474	C₂²×C₁₃₇	1	2	yes	—
209	C₈×D₄	—	2	2	no	—
210	C₈×D₄	C₂²×C₁₃₇	1	4	yes	—
211	#431	C₂²×C₁₃₇	1	1	yes	characteristic
212	#431	C₂²×C₁₃₇	1	1	yes	characteristic
213	#428	—	2	1	no	—
214	C₂×#106	—	2	1	no	—
215	#423	C₂²×C₁₃₇	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
217	#418	—	2	1	no	—
218	C₂×#102	—	2	1	no	—
219	C₂×C₂²⋊C₈	—	2	2	no	—
220	#335	C₂²×C₁₃₇	1	4	yes	complemented
221	#333	C₂²×C₁₃₇	1	2	yes	complemented
222	#333	C₂²×C₁₃₇	1	4	yes	complemented
223	#332	C₂²×C₁₃₇	1	2	yes	complemented
224	C₂²×Q₈	—	2	1	no	—
225	C₂²×D₄	D₄×C₁₃₇	1	1	yes	characteristic
226	C₂³×C₄	—	2	1	no	—
227	C₂×M₁₆	—	2	1	no	—
228	C₂²×C₈	—	2	1	no	—
229	C₂²×C₈	—	2	4	no	—
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
234	C₄⋊Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
235	C₄⋊Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
236	#125	—	2	1	no	—
237	C₂²⋊Q₈	—	2	1	no	—
238	C₂²⋊Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	—	2	1	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	D₄×C₁₃₇	1	2	yes	—
244	C₄×D₄	C₂³×C₁₃₇	1	2	yes	—
245	#117	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
251	#107	—	2	4	no	—
252	#107	—	2	2	no	—
253	#106	—	2	4	no	—
254	#106	—	2	2	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	D₄×C₁₃₇	1	2	yes	—
258	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
259	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
260	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
261	#103	—	2	4	no	—
262	#102	—	2	4	no	—
263	#102	—	2	2	no	—
264	#102	—	2	2	no	—
265	C₂²⋊C₈	—	2	1	no	—
266	C₂²⋊C₈	—	2	4	no	—
267	C₂²⋊C₈	D₄×C₁₃₇	1	2	yes	—
268	C₄×C₈	—	2	1	no	—
269	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
270	C₂⁴	—	2	1	no	—
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	2	1	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	4	1	no	—
275	C₂×Q₈	—	8	2	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	Q₁₆×C₁₃₇	1	4	yes	—
279	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	8	2	no	—
285	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
287	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
288	M₁₆	—	4	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	4	2	no	—
293	C₂×C₈	—	8	4	no	—
294	C₂×C₈	C₂×D₄×C₁₃₇	1	4	yes	—
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₄²	—	4	1	no	—
311	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
312	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
313	C₄²	#41×C₁₃₇	1	1	yes	characteristic
314	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
315	C₂³	—	2	2	no	—
316	C₂³	—	2	4	no	—
317	C₂³	—	8	1	no	—
318	C₂³	—	8	1	no	—
319	C₂³	#121×C₁₃₇	1	1	yes	characteristic
320	Q₈	—	4	2	no	—
321	Q₈	—	8	2	no	—
322	Q₈	—	8	1	no	—
323	Q₈	—	8	2	no	—
324	D₄	—	2	4	no	—
325	D₄	—	2	2	no	—
326	D₄	C₂×Q₁₆×C₁₃₇	1	4	yes	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	8	2	no	—
335	C₂×C₄	—	8	1	no	—
336	C₂×C₄	—	8	2	no	—
337	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
338	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
339	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
340	C₂×C₄	C₂×Q₁₆×C₁₃₇	1	2	yes	—
341	C₂×C₄	#135×C₁₃₇	1	2	yes	—
342	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
344	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
345	C₈	—	2	4	no	—
346	C₈	—	4	2	no	—
347	C₈	—	4	2	no	—
348	C₈	—	4	2	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	4	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	8	4	no	—
355	C₂²	#467×C₁₃₇	1	2	yes	—
356	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	4	2	no	—
361	C₄	—	8	1	no	—
362	C₄	—	8	2	no	—
363	C₄	—	8	1	no	—
364	C₄	#467×C₁₃₇	1	2	yes	—
365	C₄	C₂²×Q₁₆×C₁₃₇	1	1	yes	characteristic
366	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
367	C₄	#577×C₁₃₇	1	2	yes	—
368	C₂	—	2	2	no	—
369	C₂	—	4	4	no	—
370	C₂	#3042×C₁₃₇	1	1	yes	characteristic
371	C₂	C₂×#467×C₁₃₇	1	1	yes	characteristic
372	C₂	#3068×C₁₃₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #3230×C₁₃₇	C₂	semidirect
5. #1683×C₁₃₇	C₂	semidirect
6. #1675×C₁₃₇	C₂	semidirect
7. #1571×C₁₃₇	C₂	semidirect
8. #1548×C₁₃₇	C₂	semidirect
9. #1542×C₁₃₇	C₂	semidirect
13. #500×C₁₃₇	C₂²	semidirect
14. #487×C₁₃₇	C₂²	semidirect
33. #335×C₁₃₇	C₂²	semidirect
34. #333×C₁₃₇	C₂²	semidirect
35. #333×C₁₃₇	C₂²	semidirect
36. #332×C₁₃₇	C₂²	semidirect
186. #19393	C₁₃₇	direct (N × H)
187. C₁₃₇	#19393	direct (N × H)
188. #3230	C₂×C₁₃₇	semidirect
192. #1683	C₂×C₁₃₇	semidirect
193. #1675	C₂×C₁₃₇	semidirect
194. #1571	C₂×C₁₃₇	semidirect
195. #1548	C₂×C₁₃₇	semidirect
196. #1542	C₂×C₁₃₇	semidirect
200. #500	C₂²×C₁₃₇	semidirect
201. #487	C₂²×C₁₃₇	semidirect
220. #335	C₂²×C₁₃₇	semidirect
221. #333	C₂²×C₁₃₇	semidirect
222. #333	C₂²×C₁₃₇	semidirect
223. #332	C₂²×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3230×C₁₃₇	2
#3077×C₁₃₇	2
C₂×#476×C₁₃₇	2
#2972×C₁₃₇	2
#1683×C₁₃₇	2
#1675×C₁₃₇	2
#1571×C₁₃₇	2
#1548×C₁₃₇	2
#1542×C₁₃₇	2
#19393	137

Subgroups — C137×#19393 #46868779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19393 #46868779