Subgroups — C₁₃₇×#28771 #46878157

Order 35072.

830 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2440×C₁₃₇	C₂	1	2	yes	maximal
2	#2084×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#2058×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#1990×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1941×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1853×C₁₃₇	C₂	1	2	yes	maximal
7	#1807×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	C₈×C₂²⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#340×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	2	yes	—
12	C₂×C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
13	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
14	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
15	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
16	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
19	#398×C₁₃₇	—	2	2	no	—
20	#395×C₁₃₇	—	2	2	no	—
21	#389×C₁₃₇	C₂²	1	2	yes	—
22	#389×C₁₃₇	C₂²	1	2	yes	—
23	#385×C₁₃₇	—	2	2	no	—
24	#384×C₁₃₇	C₂²	1	2	yes	—
25	#380×C₁₃₇	C₂²	1	2	yes	—
26	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
27	#340×C₁₃₇	C₂²	1	1	yes	characteristic
28	#340×C₁₃₇	C₂²	1	2	yes	—
29	#340×C₁₃₇	C₂²	1	1	yes	characteristic
30	#340×C₁₃₇	C₂²	1	1	yes	characteristic
31	#340×C₁₃₇	C₂²	1	1	yes	characteristic
32	#340×C₁₃₇	C₂²	1	2	yes	—
33	#340×C₁₃₇	C₂²	1	2	yes	—
34	#336×C₁₃₇	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₃₇	—	2	2	no	—
36	C₂³×C₄×C₁₃₇	—	2	2	no	—
37	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₁₃₇	—	4	2	no	—
39	C₂²×C₈×C₁₃₇	Q₈	1	4	yes	complemented
40	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
43	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
44	C₄⋊Q₈×C₁₃₇	—	4	2	no	—
45	C₂²⋊Q₈×C₁₃₇	—	4	8	no	—
46	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
47	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₃₇	—	4	2	no	—
54	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₃₇	D₄	1	2	yes	—
60	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
61	#106×C₁₃₇	—	2	4	no	—
62	#106×C₁₃₇	—	4	2	no	—
63	#106×C₁₃₇	—	4	2	no	—
64	C₂²⋊C₈×C₁₃₇	Q₈	1	4	yes	complemented
65	C₄×C₈×C₁₃₇	—	4	2	no	—
66	#95×C₁₃₇	—	2	2	no	—
67	#95×C₁₃₇	—	2	2	no	—
68	#95×C₁₃₇	—	2	2	no	—
69	#95×C₁₃₇	D₄	1	1	yes	characteristic
70	#95×C₁₃₇	D₄	1	1	yes	characteristic
71	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
72	C₂×Q₈×C₁₃₇	—	4	4	no	—
73	C₂×Q₈×C₁₃₇	—	4	4	no	—
74	C₂×Q₈×C₁₃₇	—	8	2	no	—
75	C₂²×C₄×C₁₃₇	—	2	2	no	—
76	C₂²×C₄×C₁₃₇	—	2	2	no	—
77	C₂²×C₄×C₁₃₇	—	2	2	no	—
78	C₂²×C₄×C₁₃₇	—	2	2	no	—
79	C₂²×C₄×C₁₃₇	—	2	2	no	—
80	C₂²×C₄×C₁₃₇	—	2	2	no	—
81	C₂²×C₄×C₁₃₇	—	4	4	no	—
82	C₂²×C₄×C₁₃₇	—	4	4	no	—
83	C₂²×C₄×C₁₃₇	—	8	2	no	—
84	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
88	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
89	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
90	C₂×C₈×C₁₃₇	—	2	2	no	—
91	C₂×C₈×C₁₃₇	—	2	2	no	—
92	C₂×C₈×C₁₃₇	—	2	2	no	—
93	C₂×C₈×C₁₃₇	—	2	2	no	—
94	C₂×C₈×C₁₃₇	—	4	4	no	—
95	C₂×C₈×C₁₃₇	C₂×Q₈	1	4	yes	—
96	C₂×C₈×C₁₃₇	C₂×Q₈	1	2	yes	—
97	C₂×C₈×C₁₃₇	C₂×Q₈	1	2	yes	—
98	C₄⋊C₄×C₁₃₇	—	2	2	no	—
99	C₄⋊C₄×C₁₃₇	—	2	2	no	—
100	C₄⋊C₄×C₁₃₇	—	2	2	no	—
101	C₄⋊C₄×C₁₃₇	—	2	2	no	—
102	C₄⋊C₄×C₁₃₇	—	2	2	no	—
103	C₄⋊C₄×C₁₃₇	—	2	2	no	—
104	C₄⋊C₄×C₁₃₇	—	2	2	no	—
105	C₄⋊C₄×C₁₃₇	—	4	4	no	—
106	C₄⋊C₄×C₁₃₇	—	4	4	no	—
107	C₄⋊C₄×C₁₃₇	—	4	4	no	—
108	C₄⋊C₄×C₁₃₇	—	4	4	no	—
109	C₄⋊C₄×C₁₃₇	—	4	4	no	—
110	C₄⋊C₄×C₁₃₇	—	8	2	no	—
111	C₄⋊C₄×C₁₃₇	#41	1	4	yes	—
112	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
113	C₂²⋊C₄×C₁₃₇	SD₁₆	1	8	yes	—
114	C₄²×C₁₃₇	—	2	2	no	—
115	C₄²×C₁₃₇	—	2	2	no	—
116	C₂³×C₁₃₇	—	2	2	no	—
117	C₂³×C₁₃₇	—	2	1	no	—
118	C₂³×C₁₃₇	—	2	1	no	—
119	C₂³×C₁₃₇	C₄⋊Q₈	1	2	yes	—
120	C₂³×C₁₃₇	C₂×SD₁₆	1	4	yes	—
121	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
122	Q₈×C₁₃₇	—	8	8	no	—
123	C₂×C₄×C₁₃₇	—	2	2	no	—
124	C₂×C₄×C₁₃₇	—	2	2	no	—
125	C₂×C₄×C₁₃₇	—	2	2	no	—
126	C₂×C₄×C₁₃₇	—	2	2	no	—
127	C₂×C₄×C₁₃₇	—	2	2	no	—
128	C₂×C₄×C₁₃₇	—	2	2	no	—
129	C₂×C₄×C₁₃₇	—	2	2	no	—
130	C₂×C₄×C₁₃₇	—	2	4	no	—
131	C₂×C₄×C₁₃₇	—	2	4	no	—
132	C₂×C₄×C₁₃₇	—	4	2	no	—
133	C₂×C₄×C₁₃₇	—	4	2	no	—
134	C₂×C₄×C₁₃₇	—	4	2	no	—
135	C₂×C₄×C₁₃₇	—	4	2	no	—
136	C₂×C₄×C₁₃₇	—	4	2	no	—
137	C₂×C₄×C₁₃₇	—	4	2	no	—
138	C₂×C₄×C₁₃₇	—	4	2	no	—
139	C₂×C₄×C₁₃₇	—	4	2	no	—
140	C₂×C₄×C₁₃₇	—	4	2	no	—
141	C₂×C₄×C₁₃₇	—	4	2	no	—
142	C₂×C₄×C₁₃₇	—	4	2	no	—
143	C₂×C₄×C₁₃₇	—	8	8	no	—
144	C₂×C₄×C₁₃₇	C₄⋊Q₈	1	2	yes	—
145	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	4	yes	—
146	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	4	yes	—
147	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
150	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
151	C₈×C₁₃₇	—	2	2	no	—
152	C₈×C₁₃₇	—	2	2	no	—
153	C₈×C₁₃₇	—	2	4	no	—
154	C₂²×C₁₃₇	—	2	2	no	—
155	C₂²×C₁₃₇	—	2	4	no	—
156	C₂²×C₁₃₇	—	2	4	no	—
157	C₂²×C₁₃₇	—	2	2	no	—
158	C₂²×C₁₃₇	#498	1	4	yes	—
159	C₂²×C₁₃₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
160	C₂²×C₁₃₇	#546	1	2	yes	—
161	C₂²×C₁₃₇	C₂²×SD₁₆	1	2	yes	—
162	C₂²×C₁₃₇	#576	1	1	yes	characteristic
163	C₂²×C₁₃₇	#578	1	1	yes	characteristic
164	C₄×C₁₃₇	—	2	4	no	—
165	C₄×C₁₃₇	—	2	4	no	—
166	C₄×C₁₃₇	—	2	2	no	—
167	C₄×C₁₃₇	—	4	4	no	—
168	C₄×C₁₃₇	—	8	2	no	—
169	C₄×C₁₃₇	—	8	2	no	—
170	C₄×C₁₃₇	—	8	2	no	—
171	C₄×C₁₃₇	#533	1	1	yes	characteristic
172	C₄×C₁₃₇	#543	1	1	yes	characteristic
173	C₄×C₁₃₇	#554	1	2	yes	—
174	C₂×C₁₃₇	—	2	4	no	—
175	C₂×C₁₃₇	#2549	1	1	yes	characteristic
176	C₂×C₁₃₇	C₂×#498	1	1	yes	characteristic
177	C₂×C₁₃₇	#3164	1	1	yes	characteristic
178	C₂×C₁₃₇	#3295	1	2	yes	—
179	C₂×C₁₃₇	#3298	1	2	yes	—
180	#28771	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₁₃₇	#28771	1	1	yes	characteristic, direct product factor, Sylow
182	#2440	C₂×C₁₃₇	1	2	yes	—
183	#2084	C₂×C₁₃₇	1	2	yes	complemented
184	#2058	C₂×C₁₃₇	1	2	yes	complemented
185	#1990	C₂×C₁₃₇	1	2	yes	complemented
186	#1941	C₂×C₁₃₇	1	2	yes	complemented
187	#1853	C₂×C₁₃₇	1	2	yes	—
188	#1807	C₂×C₁₃₇	1	1	yes	characteristic
189	C₈×C₂²⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic
190	C₂×#340	C₂×C₁₃₇	1	1	yes	characteristic
191	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
192	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
193	C₂×C₂²⋊Q₈	—	2	2	no	—
194	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
195	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
196	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
197	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
198	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
199	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
200	#398	—	2	2	no	—
201	#395	—	2	2	no	—
202	#389	C₂²×C₁₃₇	1	2	yes	—
203	#389	C₂²×C₁₃₇	1	2	yes	—
204	#385	—	2	2	no	—
205	#384	C₂²×C₁₃₇	1	2	yes	—
206	#380	C₂²×C₁₃₇	1	2	yes	—
207	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
208	#340	C₂²×C₁₃₇	1	1	yes	characteristic
209	#340	C₂²×C₁₃₇	1	2	yes	—
210	#340	C₂²×C₁₃₇	1	1	yes	characteristic
211	#340	C₂²×C₁₃₇	1	1	yes	characteristic
212	#340	C₂²×C₁₃₇	1	1	yes	characteristic
213	#340	C₂²×C₁₃₇	1	2	yes	—
214	#340	C₂²×C₁₃₇	1	2	yes	—
215	#336	C₂²×C₁₃₇	1	2	yes	—
216	C₂²×Q₈	—	2	2	no	—
217	C₂³×C₄	—	2	2	no	—
218	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
219	C₂²×C₈	—	4	2	no	—
220	C₂²×C₈	Q₈×C₁₃₇	1	4	yes	complemented
221	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
222	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
224	C₄⋊Q₈	—	2	4	no	—
225	C₄⋊Q₈	—	4	2	no	—
226	C₂²⋊Q₈	—	4	8	no	—
227	C₂×C₄⋊C₄	—	2	4	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	4	2	no	—
235	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
236	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
237	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
238	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
239	C₂×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₂²⋊C₄	D₄×C₁₃₇	1	2	yes	—
241	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
242	#106	—	2	4	no	—
243	#106	—	4	2	no	—
244	#106	—	4	2	no	—
245	C₂²⋊C₈	Q₈×C₁₃₇	1	4	yes	complemented
246	C₄×C₈	—	4	2	no	—
247	#95	—	2	2	no	—
248	#95	—	2	2	no	—
249	#95	—	2	2	no	—
250	#95	D₄×C₁₃₇	1	1	yes	characteristic
251	#95	D₄×C₁₃₇	1	1	yes	characteristic
252	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
253	C₂×Q₈	—	4	4	no	—
254	C₂×Q₈	—	4	4	no	—
255	C₂×Q₈	—	8	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	4	4	no	—
263	C₂²×C₄	—	4	4	no	—
264	C₂²×C₄	—	8	2	no	—
265	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
267	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
268	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
269	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
270	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	4	4	no	—
276	C₂×C₈	C₂×Q₈×C₁₃₇	1	4	yes	—
277	C₂×C₈	C₂×Q₈×C₁₃₇	1	2	yes	—
278	C₂×C₈	C₂×Q₈×C₁₃₇	1	2	yes	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	2	2	no	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	4	4	no	—
287	C₄⋊C₄	—	4	4	no	—
288	C₄⋊C₄	—	4	4	no	—
289	C₄⋊C₄	—	4	4	no	—
290	C₄⋊C₄	—	4	4	no	—
291	C₄⋊C₄	—	8	2	no	—
292	C₄⋊C₄	#41×C₁₃₇	1	4	yes	—
293	C₂²⋊C₄	—	4	4	no	—
294	C₂²⋊C₄	SD₁₆×C₁₃₇	1	8	yes	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	—	2	1	no	—
299	C₂³	—	2	1	no	—
300	C₂³	C₄⋊Q₈×C₁₃₇	1	2	yes	—
301	C₂³	C₂×SD₁₆×C₁₃₇	1	4	yes	—
302	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
303	Q₈	—	8	8	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	8	8	no	—
325	C₂×C₄	C₄⋊Q₈×C₁₃₇	1	2	yes	—
326	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	4	yes	—
327	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	4	yes	—
328	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
329	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
330	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
331	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
332	C₈	—	2	2	no	—
333	C₈	—	2	2	no	—
334	C₈	—	2	4	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	#498×C₁₃₇	1	4	yes	—
340	C₂²	C₂×C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
341	C₂²	#546×C₁₃₇	1	2	yes	—
342	C₂²	C₂²×SD₁₆×C₁₃₇	1	2	yes	—
343	C₂²	#576×C₁₃₇	1	1	yes	characteristic
344	C₂²	#578×C₁₃₇	1	1	yes	characteristic
345	C₄	—	2	4	no	—
346	C₄	—	2	4	no	—
347	C₄	—	2	2	no	—
348	C₄	—	4	4	no	—
349	C₄	—	8	2	no	—
350	C₄	—	8	2	no	—
351	C₄	—	8	2	no	—
352	C₄	#533×C₁₃₇	1	1	yes	characteristic
353	C₄	#543×C₁₃₇	1	1	yes	characteristic
354	C₄	#554×C₁₃₇	1	2	yes	—
355	C₂	—	2	4	no	—
356	C₂	#2549×C₁₃₇	1	1	yes	characteristic
357	C₂	C₂×#498×C₁₃₇	1	1	yes	characteristic
358	C₂	#3164×C₁₃₇	1	1	yes	characteristic
359	C₂	#3295×C₁₃₇	1	2	yes	—
360	C₂	#3298×C₁₃₇	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. #2084×C₁₃₇	C₂	semidirect
3. #2058×C₁₃₇	C₂	semidirect
4. #1990×C₁₃₇	C₂	semidirect
5. #1941×C₁₃₇	C₂	semidirect
39. C₂²×C₈×C₁₃₇	Q₈	semidirect
64. C₂²⋊C₈×C₁₃₇	Q₈	semidirect
180. #28771	C₁₃₇	direct (N × H)
181. C₁₃₇	#28771	direct (N × H)
183. #2084	C₂×C₁₃₇	semidirect
184. #2058	C₂×C₁₃₇	semidirect
185. #1990	C₂×C₁₃₇	semidirect
186. #1941	C₂×C₁₃₇	semidirect
220. C₂²×C₈	Q₈×C₁₃₇	semidirect
245. C₂²⋊C₈	Q₈×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#2440×C₁₃₇	2
#2084×C₁₃₇	2
#2058×C₁₃₇	2
#1990×C₁₃₇	2
#1941×C₁₃₇	2
#1853×C₁₃₇	2
#1807×C₁₃₇	2
C₈×C₂²⋊C₄×C₁₃₇	2
C₂×#340×C₁₃₇	2
#28771	137

Subgroups — C137×#28771 #46878157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28771 #46878157