Subgroups — C₁₃₇×#10807 #46860193

Order 35072.

914 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₄⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#340×C₁₃₇	C₂	1	2	yes	maximal
3	C₂×#340×C₁₃₇	C₂	1	2	yes	maximal
4	C₂×#336×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	C₄⋊#95×C₁₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃₇	C₂²	1	2	yes	—
7	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₁₃₇	—	2	1	no	—
11	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₄×C₄⋊C₄×C₁₃₇	—	2	2	no	—
13	C₄×C₄⋊C₄×C₁₃₇	C₄	1	4	yes	complemented
14	C₂×#95×C₁₃₇	—	2	1	no	—
15	C₂×#95×C₁₃₇	—	2	1	no	—
16	C₂×#95×C₁₃₇	—	2	1	no	—
17	#340×C₁₃₇	—	2	4	no	—
18	#340×C₁₃₇	C₄	1	8	yes	complemented
19	#336×C₁₃₇	—	2	2	no	—
20	C₂³×C₄×C₁₃₇	—	2	1	no	—
21	C₂³×C₄×C₁₃₇	—	2	1	no	—
22	C₂³×C₄×C₁₃₇	—	2	2	no	—
23	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
26	C₂²×C₈×C₁₃₇	—	2	2	no	—
27	C₂²×C₈×C₁₃₇	—	2	2	no	—
28	C₂²×C₈×C₁₃₇	—	2	2	no	—
29	C₂²×C₈×C₁₃₇	—	2	2	no	—
30	C₂²×C₈×C₁₃₇	—	2	2	no	—
31	C₂²×C₈×C₁₃₇	—	2	2	no	—
32	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
33	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
44	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₃₇	Q₈	1	2	yes	—
49	C₂×C₄²×C₁₃₇	—	2	2	no	—
50	C₂×C₄²×C₁₃₇	—	2	2	no	—
51	C₂×C₄²×C₁₃₇	—	2	4	no	—
52	C₂×C₄²×C₁₃₇	—	4	4	no	—
53	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
55	#95×C₁₃₇	—	2	4	no	—
56	#95×C₁₃₇	—	4	2	no	—
57	#95×C₁₃₇	—	4	2	no	—
58	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₃₇	—	2	2	no	—
60	C₂²×C₄×C₁₃₇	—	2	2	no	—
61	C₂²×C₄×C₁₃₇	—	2	2	no	—
62	C₂²×C₄×C₁₃₇	—	2	2	no	—
63	C₂²×C₄×C₁₃₇	—	2	4	no	—
64	C₂²×C₄×C₁₃₇	—	2	2	no	—
65	C₂²×C₄×C₁₃₇	—	2	2	no	—
66	C₂²×C₄×C₁₃₇	—	2	2	no	—
67	C₂²×C₄×C₁₃₇	—	2	2	no	—
68	C₂²×C₄×C₁₃₇	—	2	1	no	—
69	C₂²×C₄×C₁₃₇	—	2	1	no	—
70	C₂²×C₄×C₁₃₇	—	2	4	no	—
71	C₂²×C₄×C₁₃₇	—	4	2	no	—
72	C₂²×C₄×C₁₃₇	—	4	2	no	—
73	C₂²×C₄×C₁₃₇	—	4	2	no	—
74	C₂²×C₄×C₁₃₇	—	4	1	no	—
75	C₂²×C₄×C₁₃₇	—	4	1	no	—
76	C₂²×C₄×C₁₃₇	—	4	2	no	—
77	C₂²×C₄×C₁₃₇	—	4	2	no	—
78	C₂²×C₄×C₁₃₇	—	4	2	no	—
79	C₂²×C₄×C₁₃₇	—	4	2	no	—
80	C₂²×C₄×C₁₃₇	—	4	2	no	—
81	C₂²×C₄×C₁₃₇	—	4	2	no	—
82	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	2	yes	—
84	C₂²×C₄×C₁₃₇	SD₁₆	1	2	yes	—
85	C₂²×C₄×C₁₃₇	Q₁₆	1	2	yes	—
86	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
94	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
95	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
96	C₂×C₈×C₁₃₇	—	2	4	no	—
97	C₂×C₈×C₁₃₇	—	2	4	no	—
98	C₂×C₈×C₁₃₇	—	2	4	no	—
99	C₂×C₈×C₁₃₇	—	4	2	no	—
100	C₂×C₈×C₁₃₇	—	4	2	no	—
101	C₂×C₈×C₁₃₇	—	4	2	no	—
102	C₂×C₈×C₁₃₇	—	4	2	no	—
103	C₄⋊C₄×C₁₃₇	—	2	2	no	—
104	C₄⋊C₄×C₁₃₇	—	2	2	no	—
105	C₄⋊C₄×C₁₃₇	—	2	4	no	—
106	C₄⋊C₄×C₁₃₇	—	2	2	no	—
107	C₄⋊C₄×C₁₃₇	—	2	2	no	—
108	C₄⋊C₄×C₁₃₇	—	2	4	no	—
109	C₄⋊C₄×C₁₃₇	—	2	4	no	—
110	C₄⋊C₄×C₁₃₇	—	4	2	no	—
111	C₄⋊C₄×C₁₃₇	—	4	2	no	—
112	C₄⋊C₄×C₁₃₇	C₄²	1	4	yes	—
113	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	4	yes	—
114	C₄²×C₁₃₇	—	2	2	no	—
115	C₄²×C₁₃₇	—	2	2	no	—
116	C₄²×C₁₃₇	—	2	4	no	—
117	C₄²×C₁₃₇	—	4	8	no	—
118	C₂³×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₁₃₇	C₄×D₄	1	2	yes	—
120	C₂³×C₁₃₇	#121	1	1	yes	characteristic
121	C₂³×C₁₃₇	C₂²⋊Q₈	1	1	yes	characteristic
122	C₂³×C₁₃₇	#123	1	2	yes	—
123	C₂³×C₁₃₇	C₂×SD₁₆	1	1	yes	characteristic
124	C₂³×C₁₃₇	C₂×Q₁₆	1	1	yes	characteristic
125	C₂³×C₁₃₇	#135	1	2	yes	—
126	C₂³×C₁₃₇	AGL(1,ℤ/8)	1	1	yes	characteristic
127	C₂³×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
128	C₂³×C₁₃₇	#137	1	1	yes	characteristic
129	C₂×C₄×C₁₃₇	—	2	2	no	—
130	C₂×C₄×C₁₃₇	—	2	2	no	—
131	C₂×C₄×C₁₃₇	—	2	4	no	—
132	C₂×C₄×C₁₃₇	—	2	4	no	—
133	C₂×C₄×C₁₃₇	—	2	4	no	—
134	C₂×C₄×C₁₃₇	—	2	4	no	—
135	C₂×C₄×C₁₃₇	—	2	2	no	—
136	C₂×C₄×C₁₃₇	—	2	2	no	—
137	C₂×C₄×C₁₃₇	—	2	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	4	no	—
143	C₂×C₄×C₁₃₇	—	4	4	no	—
144	C₂×C₄×C₁₃₇	—	4	4	no	—
145	C₂×C₄×C₁₃₇	—	4	4	no	—
146	C₂×C₄×C₁₃₇	—	4	2	no	—
147	C₂×C₄×C₁₃₇	—	4	2	no	—
148	C₂×C₄×C₁₃₇	—	4	4	no	—
149	C₂×C₄×C₁₃₇	—	4	4	no	—
150	C₂×C₄×C₁₃₇	—	4	4	no	—
151	C₂×C₄×C₁₃₇	—	8	2	no	—
152	C₂×C₄×C₁₃₇	—	8	2	no	—
153	C₂×C₄×C₁₃₇	—	8	2	no	—
154	C₂×C₄×C₁₃₇	—	8	2	no	—
155	C₂×C₄×C₁₃₇	#103	1	4	yes	—
156	C₂×C₄×C₁₃₇	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃₇	#117	1	1	yes	characteristic
159	C₂×C₄×C₁₃₇	#117	1	1	yes	characteristic
160	C₂×C₄×C₁₃₇	#117	1	2	yes	—
161	C₂×C₄×C₁₃₇	#117	1	2	yes	—
162	C₂×C₄×C₁₃₇	#117	1	1	yes	characteristic
163	C₂×C₄×C₁₃₇	#117	1	1	yes	characteristic
164	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₁₃₇	C₄×Q₈	1	2	yes	—
167	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
168	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃₇	#123	1	2	yes	—
170	C₂×C₄×C₁₃₇	#124	1	2	yes	—
171	C₂×C₄×C₁₃₇	#125	1	2	yes	—
172	C₂×C₄×C₁₃₇	#126	1	2	yes	—
173	C₂×C₄×C₁₃₇	#126	1	2	yes	—
174	C₈×C₁₃₇	—	4	4	no	—
175	C₂²×C₁₃₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×C₁₃₇	#380	1	1	yes	characteristic
177	C₂²×C₁₃₇	#381	1	1	yes	characteristic
178	C₂²×C₁₃₇	#387	1	2	yes	—
179	C₂²×C₁₃₇	#388	1	2	yes	—
180	C₂²×C₁₃₇	C₂×#103	1	1	yes	characteristic
181	C₂²×C₁₃₇	#416	1	1	yes	characteristic
182	C₂²×C₁₃₇	#417	1	1	yes	characteristic
183	C₂²×C₁₃₇	#418	1	1	yes	characteristic
184	C₂²×C₁₃₇	C₄×SD₁₆	1	2	yes	—
185	C₂²×C₁₃₇	C₄×Q₁₆	1	2	yes	—
186	C₂²×C₁₃₇	#440	1	2	yes	—
187	C₂²×C₁₃₇	#442	1	2	yes	—
188	C₂²×C₁₃₇	#460	1	1	yes	characteristic
189	C₂²×C₁₃₇	#462	1	1	yes	characteristic
190	C₂²×C₁₃₇	#463	1	2	yes	—
191	C₂²×C₁₃₇	#475	1	1	yes	characteristic
192	C₂²×C₁₃₇	#477	1	1	yes	characteristic
193	C₂²×C₁₃₇	#478	1	2	yes	—
194	C₂²×C₁₃₇	#481	1	2	yes	—
195	C₂²×C₁₃₇	#482	1	2	yes	—
196	C₂²×C₁₃₇	#484	1	2	yes	—
197	C₂²×C₁₃₇	#485	1	2	yes	—
198	C₄×C₁₃₇	—	2	4	no	—
199	C₄×C₁₃₇	—	4	4	no	—
200	C₄×C₁₃₇	—	4	2	no	—
201	C₄×C₁₃₇	—	4	4	no	—
202	C₄×C₁₃₇	—	8	4	no	—
203	C₄×C₁₃₇	#376	1	1	yes	characteristic
204	C₄×C₁₃₇	C₄×C₄⋊C₄	1	1	yes	characteristic
205	C₄×C₁₃₇	#382	1	1	yes	characteristic
206	C₄×C₁₃₇	#383	1	1	yes	characteristic
207	C₄×C₁₃₇	#387	1	2	yes	—
208	C₄×C₁₃₇	#388	1	2	yes	—
209	C₂×C₁₃₇	#1434	1	1	yes	characteristic
210	C₂×C₁₃₇	C₄×#103	1	1	yes	characteristic
211	C₂×C₁₃₇	#1762	1	1	yes	characteristic
212	C₂×C₁₃₇	#1803	1	1	yes	characteristic
213	C₂×C₁₃₇	#1804	1	1	yes	characteristic
214	C₂×C₁₃₇	#1824	1	1	yes	characteristic
215	C₂×C₁₃₇	#1825	1	1	yes	characteristic
216	C₂×C₁₃₇	#1919	1	2	yes	—
217	C₂×C₁₃₇	#1921	1	2	yes	—
218	C₂×C₁₃₇	#1926	1	2	yes	—
219	C₂×C₁₃₇	#1928	1	2	yes	—
220	#10807	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₁₃₇	#10807	1	1	yes	characteristic, direct product factor, Sylow
222	C₂×C₄×C₄⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic
223	C₂×#340	C₂×C₁₃₇	1	2	yes	—
224	C₂×#340	C₂×C₁₃₇	1	2	yes	—
225	C₂×#336	C₂×C₁₃₇	1	1	yes	characteristic
226	C₄⋊#95	C₂×C₁₃₇	1	1	yes	characteristic
227	C₂³×C₈	C₂²×C₁₃₇	1	2	yes	—
228	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
229	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
230	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
231	C₂²×C₄²	—	2	1	no	—
232	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
233	C₄×C₄⋊C₄	—	2	2	no	—
234	C₄×C₄⋊C₄	C₄×C₁₃₇	1	4	yes	complemented
235	C₂×#95	—	2	1	no	—
236	C₂×#95	—	2	1	no	—
237	C₂×#95	—	2	1	no	—
238	#340	—	2	4	no	—
239	#340	C₄×C₁₃₇	1	8	yes	complemented
240	#336	—	2	2	no	—
241	C₂³×C₄	—	2	1	no	—
242	C₂³×C₄	—	2	1	no	—
243	C₂³×C₄	—	2	2	no	—
244	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
245	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
246	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
265	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
266	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
267	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
268	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
269	C₂×C₄⋊C₄	Q₈×C₁₃₇	1	2	yes	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	—	2	4	no	—
273	C₂×C₄²	—	4	4	no	—
274	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
275	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
276	#95	—	2	4	no	—
277	#95	—	4	2	no	—
278	#95	—	4	2	no	—
279	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	2	yes	—
304	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	2	yes	—
305	C₂²×C₄	SD₁₆×C₁₃₇	1	2	yes	—
306	C₂²×C₄	Q₁₆×C₁₃₇	1	2	yes	—
307	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
308	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
312	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
313	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
314	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
315	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
316	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	4	2	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	—	4	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	C₄²×C₁₃₇	1	4	yes	—
334	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	4	yes	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	4	no	—
338	C₄²	—	4	8	no	—
339	C₂³	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
340	C₂³	C₄×D₄×C₁₃₇	1	2	yes	—
341	C₂³	#121×C₁₃₇	1	1	yes	characteristic
342	C₂³	C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
343	C₂³	#123×C₁₃₇	1	2	yes	—
344	C₂³	C₂×SD₁₆×C₁₃₇	1	1	yes	characteristic
345	C₂³	C₂×Q₁₆×C₁₃₇	1	1	yes	characteristic
346	C₂³	#135×C₁₃₇	1	2	yes	—
347	C₂³	AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
348	C₂³	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
349	C₂³	#137×C₁₃₇	1	1	yes	characteristic
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	8	2	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	—	8	2	no	—
375	C₂×C₄	—	8	2	no	—
376	C₂×C₄	#103×C₁₃₇	1	4	yes	—
377	C₂×C₄	C₂×C₄²×C₁₃₇	1	1	yes	characteristic
378	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
379	C₂×C₄	#117×C₁₃₇	1	1	yes	characteristic
380	C₂×C₄	#117×C₁₃₇	1	1	yes	characteristic
381	C₂×C₄	#117×C₁₃₇	1	2	yes	—
382	C₂×C₄	#117×C₁₃₇	1	2	yes	—
383	C₂×C₄	#117×C₁₃₇	1	1	yes	characteristic
384	C₂×C₄	#117×C₁₃₇	1	1	yes	characteristic
385	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
386	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
387	C₂×C₄	C₄×Q₈×C₁₃₇	1	2	yes	—
388	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
389	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
390	C₂×C₄	#123×C₁₃₇	1	2	yes	—
391	C₂×C₄	#124×C₁₃₇	1	2	yes	—
392	C₂×C₄	#125×C₁₃₇	1	2	yes	—
393	C₂×C₄	#126×C₁₃₇	1	2	yes	—
394	C₂×C₄	#126×C₁₃₇	1	2	yes	—
395	C₈	—	4	4	no	—
396	C₂²	C₄×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
397	C₂²	#380×C₁₃₇	1	1	yes	characteristic
398	C₂²	#381×C₁₃₇	1	1	yes	characteristic
399	C₂²	#387×C₁₃₇	1	2	yes	—
400	C₂²	#388×C₁₃₇	1	2	yes	—
401	C₂²	C₂×#103×C₁₃₇	1	1	yes	characteristic
402	C₂²	#416×C₁₃₇	1	1	yes	characteristic
403	C₂²	#417×C₁₃₇	1	1	yes	characteristic
404	C₂²	#418×C₁₃₇	1	1	yes	characteristic
405	C₂²	C₄×SD₁₆×C₁₃₇	1	2	yes	—
406	C₂²	C₄×Q₁₆×C₁₃₇	1	2	yes	—
407	C₂²	#440×C₁₃₇	1	2	yes	—
408	C₂²	#442×C₁₃₇	1	2	yes	—
409	C₂²	#460×C₁₃₇	1	1	yes	characteristic
410	C₂²	#462×C₁₃₇	1	1	yes	characteristic
411	C₂²	#463×C₁₃₇	1	2	yes	—
412	C₂²	#475×C₁₃₇	1	1	yes	characteristic
413	C₂²	#477×C₁₃₇	1	1	yes	characteristic
414	C₂²	#478×C₁₃₇	1	2	yes	—
415	C₂²	#481×C₁₃₇	1	2	yes	—
416	C₂²	#482×C₁₃₇	1	2	yes	—
417	C₂²	#484×C₁₃₇	1	2	yes	—
418	C₂²	#485×C₁₃₇	1	2	yes	—
419	C₄	—	2	4	no	—
420	C₄	—	4	4	no	—
421	C₄	—	4	4	no	—
422	C₄	—	4	2	no	—
423	C₄	—	8	4	no	—
424	C₄	#376×C₁₃₇	1	1	yes	characteristic
425	C₄	C₄×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
426	C₄	#382×C₁₃₇	1	1	yes	characteristic
427	C₄	#383×C₁₃₇	1	1	yes	characteristic
428	C₄	#387×C₁₃₇	1	2	yes	—
429	C₄	#388×C₁₃₇	1	2	yes	—
430	C₂	#1434×C₁₃₇	1	1	yes	characteristic
431	C₂	C₄×#103×C₁₃₇	1	1	yes	characteristic
432	C₂	#1762×C₁₃₇	1	1	yes	characteristic
433	C₂	#1803×C₁₃₇	1	1	yes	characteristic
434	C₂	#1804×C₁₃₇	1	1	yes	characteristic
435	C₂	#1824×C₁₃₇	1	1	yes	characteristic
436	C₂	#1825×C₁₃₇	1	1	yes	characteristic
437	C₂	#1919×C₁₃₇	1	2	yes	—
438	C₂	#1921×C₁₃₇	1	2	yes	—
439	C₂	#1926×C₁₃₇	1	2	yes	—
440	C₂	#1928×C₁₃₇	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
13. C₄×C₄⋊C₄×C₁₃₇	C₄	semidirect
18. #340×C₁₃₇	C₄	semidirect
220. #10807	C₁₃₇	direct (N × H)
221. C₁₃₇	#10807	direct (N × H)
234. C₄×C₄⋊C₄	C₄×C₁₃₇	semidirect
239. #340	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×C₄⋊C₄×C₁₃₇	2
C₂×#340×C₁₃₇	2
C₂×#336×C₁₃₇	2
C₄⋊#95×C₁₃₇	2
#10807	137

Subgroups — C137×#10807 #46860193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#10807 #46860193