Subgroups — C₁₃₇×#20863 #46870249

Order 35072.

1422 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3428×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2911×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#104×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2896×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#2285×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#1860×C₁₃₇	C₂	1	4	yes	maximal, complemented
7	#1859×C₁₃₇	C₂	1	4	yes	maximal, complemented
8	#1742×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#339×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
13	#520×C₁₃₇	—	2	2	no	—
14	#520×C₁₃₇	C₂²	1	4	yes	—
15	#519×C₁₃₇	—	2	1	no	—
16	#518×C₁₃₇	—	2	1	no	—
17	#518×C₁₃₇	—	2	2	no	—
18	C₄×#41×C₁₃₇	—	2	2	no	—
19	C₄×#41×C₁₃₇	—	2	2	no	—
20	C₂×#117×C₁₃₇	—	2	2	no	—
21	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
25	#428×C₁₃₇	—	2	2	no	—
26	#428×C₁₃₇	C₂²	1	4	yes	complemented
27	#427×C₁₃₇	—	2	2	no	—
28	C₂×#104×C₁₃₇	C₄	1	8	yes	complemented
29	C₂×#104×C₁₃₇	C₂²	1	2	yes	—
30	C₂×#104×C₁₃₇	C₂²	1	2	yes	—
31	#419×C₁₃₇	—	2	1	no	—
32	#418×C₁₃₇	—	2	1	no	—
33	#417×C₁₃₇	C₂²	1	4	yes	—
34	#416×C₁₃₇	—	2	2	no	—
35	#384×C₁₃₇	C₂²	1	2	yes	complemented
36	#382×C₁₃₇	C₂²	1	2	yes	complemented
37	#380×C₁₃₇	—	2	2	no	—
38	C₄×C₄⋊C₄×C₁₃₇	—	2	2	no	—
39	#343×C₁₃₇	C₂²	1	4	yes	complemented
40	#339×C₁₃₇	C₂²	1	2	yes	complemented
41	#339×C₁₃₇	C₂²	1	2	yes	complemented
42	C₂×#41×C₁₃₇	—	2	1	no	—
43	C₂×#41×C₁₃₇	—	2	1	no	—
44	C₂×#41×C₁₃₇	—	2	2	no	—
45	C₂×#41×C₁₃₇	—	2	2	no	—
46	C₂×#41×C₁₃₇	C₂×C₄	1	4	yes	—
47	C₂×#41×C₁₃₇	D₄	1	2	yes	—
48	C₂×#41×C₁₃₇	Q₈	1	4	yes	—
49	C₂×#41×C₁₃₇	C₂³	1	2	yes	—
50	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₁₃₇	—	2	1	no	—
52	C₂²×D₄×C₁₃₇	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₃₇	—	2	1	no	—
54	C₂³×C₄×C₁₃₇	—	2	1	no	—
55	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₁₃₇	—	2	1	no	—
57	C₂×M₁₆×C₁₃₇	—	2	2	no	—
58	C₂×M₁₆×C₁₃₇	—	2	1	no	—
59	C₂×M₁₆×C₁₃₇	—	2	2	no	—
60	C₂×M₁₆×C₁₃₇	—	2	2	no	—
61	C₂×M₁₆×C₁₃₇	C₂×C₄	1	4	yes	complemented
62	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
63	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₃₇	—	2	1	no	—
65	C₂²×C₈×C₁₃₇	—	2	1	no	—
66	C₄×Q₈×C₁₃₇	—	2	4	no	—
67	C₄×Q₈×C₁₃₇	—	2	4	no	—
68	C₄×D₄×C₁₃₇	—	2	8	no	—
69	C₄×D₄×C₁₃₇	—	2	4	no	—
70	C₄×D₄×C₁₃₇	—	2	4	no	—
71	C₄×D₄×C₁₃₇	—	2	8	no	—
72	#117×C₁₃₇	—	2	4	no	—
73	#117×C₁₃₇	—	2	4	no	—
74	#117×C₁₃₇	—	2	1	no	—
75	#117×C₁₃₇	—	2	1	no	—
76	#117×C₁₃₇	—	2	1	no	—
77	#117×C₁₃₇	—	2	1	no	—
78	#117×C₁₃₇	—	2	1	no	—
79	#117×C₁₃₇	—	2	1	no	—
80	#117×C₁₃₇	—	2	4	no	—
81	#117×C₁₃₇	—	2	1	no	—
82	#117×C₁₃₇	—	2	1	no	—
83	#117×C₁₃₇	—	2	1	no	—
84	#117×C₁₃₇	—	2	1	no	—
85	#117×C₁₃₇	D₄	1	2	yes	—
86	#117×C₁₃₇	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
88	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
89	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
90	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
92	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₃₇	D₄	1	2	yes	—
96	C₂×C₄²×C₁₃₇	—	2	4	no	—
97	C₂×C₄²×C₁₃₇	—	2	1	no	—
98	C₂×C₄²×C₁₃₇	—	2	1	no	—
99	C₂×C₄²×C₁₃₇	—	2	2	no	—
100	C₂×C₄²×C₁₃₇	—	2	1	no	—
101	C₂×C₄²×C₁₃₇	C₂×C₄	1	4	yes	complemented
102	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
103	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
105	#107×C₁₃₇	—	2	4	no	—
106	#106×C₁₃₇	—	2	4	no	—
107	#104×C₁₃₇	C₂×C₄	1	8	yes	complemented
108	#104×C₁₃₇	C₂×C₄	1	8	yes	complemented
109	#103×C₁₃₇	—	2	4	no	—
110	#102×C₁₃₇	—	2	4	no	—
111	#95×C₁₃₇	—	2	4	no	—
112	C₂⁴×C₁₃₇	—	2	1	no	—
113	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
114	#41×C₁₃₇	—	2	4	no	—
115	#41×C₁₃₇	—	2	4	no	—
116	#41×C₁₃₇	—	2	4	no	—
117	#41×C₁₃₇	—	2	4	no	—
118	#41×C₁₃₇	—	2	4	no	—
119	#41×C₁₃₇	—	2	2	no	—
120	#41×C₁₃₇	—	2	2	no	—
121	#41×C₁₃₇	C₄⋊C₄	1	8	yes	complemented
122	#41×C₁₃₇	C₂²×C₄	1	4	yes	—
123	#41×C₁₃₇	C₂×Q₈	1	4	yes	—
124	C₂×Q₈×C₁₃₇	—	2	1	no	—
125	C₂×Q₈×C₁₃₇	—	2	2	no	—
126	C₂×Q₈×C₁₃₇	C₄⋊C₄	1	4	yes	complemented
127	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
128	C₂×D₄×C₁₃₇	—	2	4	no	—
129	C₂×D₄×C₁₃₇	—	2	2	no	—
130	C₂×D₄×C₁₃₇	—	2	4	no	—
131	C₂×D₄×C₁₃₇	—	2	2	no	—
132	C₂×D₄×C₁₃₇	—	2	1	no	—
133	C₂×D₄×C₁₃₇	—	2	2	no	—
134	C₂×D₄×C₁₃₇	C₄⋊C₄	1	4	yes	complemented
135	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃₇	—	2	1	no	—
137	C₂²×C₄×C₁₃₇	—	2	1	no	—
138	C₂²×C₄×C₁₃₇	—	2	4	no	—
139	C₂²×C₄×C₁₃₇	—	2	2	no	—
140	C₂²×C₄×C₁₃₇	—	2	4	no	—
141	C₂²×C₄×C₁₃₇	—	2	2	no	—
142	C₂²×C₄×C₁₃₇	—	2	4	no	—
143	C₂²×C₄×C₁₃₇	—	2	1	no	—
144	C₂²×C₄×C₁₃₇	—	2	8	no	—
145	C₂²×C₄×C₁₃₇	—	2	2	no	—
146	C₂²×C₄×C₁₃₇	—	2	2	no	—
147	C₂²×C₄×C₁₃₇	—	4	4	no	—
148	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
156	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
157	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
158	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
159	M₁₆×C₁₃₇	—	2	4	no	—
160	M₁₆×C₁₃₇	—	2	2	no	—
161	M₁₆×C₁₃₇	—	2	2	no	—
162	M₁₆×C₁₃₇	—	2	2	no	—
163	M₁₆×C₁₃₇	—	4	2	no	—
164	M₁₆×C₁₃₇	C₂²×C₄	1	4	yes	—
165	C₂×C₈×C₁₃₇	—	2	4	no	—
166	C₂×C₈×C₁₃₇	—	2	2	no	—
167	C₂×C₈×C₁₃₇	—	2	2	no	—
168	C₂×C₈×C₁₃₇	—	4	2	no	—
169	C₄⋊C₄×C₁₃₇	—	2	8	no	—
170	C₄⋊C₄×C₁₃₇	—	2	2	no	—
171	C₄⋊C₄×C₁₃₇	—	2	2	no	—
172	C₄⋊C₄×C₁₃₇	—	2	2	no	—
173	C₄⋊C₄×C₁₃₇	—	2	2	no	—
174	C₄⋊C₄×C₁₃₇	—	2	2	no	—
175	C₄⋊C₄×C₁₃₇	—	4	8	no	—
176	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
177	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
178	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
179	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
180	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
181	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
182	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
183	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
184	C₄²×C₁₃₇	—	2	8	no	—
185	C₄²×C₁₃₇	—	2	4	no	—
186	C₄²×C₁₃₇	—	2	2	no	—
187	C₄²×C₁₃₇	—	2	2	no	—
188	C₄²×C₁₃₇	—	2	2	no	—
189	C₄²×C₁₃₇	—	2	2	no	—
190	C₄²×C₁₃₇	—	2	1	no	—
191	C₄²×C₁₃₇	—	2	1	no	—
192	C₄²×C₁₃₇	—	4	1	no	—
193	C₄²×C₁₃₇	—	4	1	no	—
194	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
195	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
196	C₂³×C₁₃₇	—	2	2	no	—
197	C₂³×C₁₃₇	—	2	4	no	—
198	C₂³×C₁₃₇	—	4	2	no	—
199	C₂³×C₁₃₇	—	8	2	no	—
200	C₂³×C₁₃₇	C₄×D₄	1	2	yes	—
201	C₂³×C₁₃₇	#120	1	1	yes	characteristic
202	C₂³×C₁₃₇	#120	1	1	yes	characteristic
203	C₂³×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
204	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
205	Q₈×C₁₃₇	—	2	2	no	—
206	Q₈×C₁₃₇	—	2	4	no	—
207	Q₈×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
208	D₄×C₁₃₇	—	2	4	no	—
209	D₄×C₁₃₇	—	2	4	no	—
210	D₄×C₁₃₇	—	2	8	no	—
211	D₄×C₁₃₇	—	2	2	no	—
212	D₄×C₁₃₇	—	2	4	no	—
213	D₄×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
214	C₂×C₄×C₁₃₇	—	2	4	no	—
215	C₂×C₄×C₁₃₇	—	2	2	no	—
216	C₂×C₄×C₁₃₇	—	2	2	no	—
217	C₂×C₄×C₁₃₇	—	2	4	no	—
218	C₂×C₄×C₁₃₇	—	2	4	no	—
219	C₂×C₄×C₁₃₇	—	2	4	no	—
220	C₂×C₄×C₁₃₇	—	2	8	no	—
221	C₂×C₄×C₁₃₇	—	2	2	no	—
222	C₂×C₄×C₁₃₇	—	2	4	no	—
223	C₂×C₄×C₁₃₇	—	2	4	no	—
224	C₂×C₄×C₁₃₇	—	4	8	no	—
225	C₂×C₄×C₁₃₇	—	4	2	no	—
226	C₂×C₄×C₁₃₇	—	4	4	no	—
227	C₂×C₄×C₁₃₇	—	4	4	no	—
228	C₂×C₄×C₁₃₇	—	4	2	no	—
229	C₂×C₄×C₁₃₇	—	8	2	no	—
230	C₂×C₄×C₁₃₇	—	8	8	no	—
231	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
232	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
233	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
234	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
235	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
236	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
237	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
238	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
239	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
240	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
241	C₂×C₄×C₁₃₇	#123	1	2	yes	—
242	C₂×C₄×C₁₃₇	#123	1	2	yes	—
243	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
247	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
249	C₈×C₁₃₇	—	2	4	no	—
250	C₈×C₁₃₇	—	4	2	no	—
251	C₂²×C₁₃₇	—	2	2	no	—
252	C₂²×C₁₃₇	—	2	2	no	—
253	C₂²×C₁₃₇	—	2	2	no	—
254	C₂²×C₁₃₇	—	2	4	no	—
255	C₂²×C₁₃₇	—	4	2	no	—
256	C₂²×C₁₃₇	—	4	2	no	—
257	C₂²×C₁₃₇	—	4	4	no	—
258	C₂²×C₁₃₇	—	8	4	no	—
259	C₂²×C₁₃₇	#385	1	2	yes	—
260	C₂²×C₁₃₇	#385	1	2	yes	—
261	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
262	C₂²×C₁₃₇	C₂×#120	1	1	yes	characteristic
263	C₂²×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
264	C₄×C₁₃₇	—	2	4	no	—
265	C₄×C₁₃₇	—	2	4	no	—
266	C₄×C₁₃₇	—	4	2	no	—
267	C₄×C₁₃₇	—	4	4	no	—
268	C₄×C₁₃₇	—	4	4	no	—
269	C₄×C₁₃₇	—	8	2	no	—
270	C₄×C₁₃₇	#385	1	2	yes	—
271	C₄×C₁₃₇	#385	1	2	yes	—
272	C₄×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
273	C₄×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
274	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
275	C₄×C₁₃₇	C₂×#123	1	1	yes	characteristic
276	C₂×C₁₃₇	—	2	1	no	—
277	C₂×C₁₃₇	—	2	2	no	—
278	C₂×C₁₃₇	—	2	1	no	—
279	C₂×C₁₃₇	—	2	2	no	—
280	C₂×C₁₃₇	—	4	4	no	—
281	C₂×C₁₃₇	C₂×#385	1	1	yes	characteristic
282	C₂×C₁₃₇	#3018	1	2	yes	—
283	#20863	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₁₃₇	#20863	1	1	yes	characteristic, direct product factor, Sylow
285	#3428	C₂×C₁₃₇	1	1	yes	characteristic
286	#2911	C₂×C₁₃₇	1	1	yes	characteristic, complemented
287	C₂²×#104	C₂×C₁₃₇	1	1	yes	characteristic
288	#2896	C₂×C₁₃₇	1	1	yes	characteristic
289	#2285	C₂×C₁₃₇	1	1	yes	characteristic, complemented
290	#1860	C₂×C₁₃₇	1	4	yes	complemented
291	#1859	C₂×C₁₃₇	1	4	yes	complemented
292	#1742	C₂×C₁₃₇	1	1	yes	characteristic, complemented
293	C₂×#339	C₂×C₁₃₇	1	1	yes	characteristic, complemented
294	C₂²×#41	C₂²×C₁₃₇	1	1	yes	characteristic
295	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
296	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
297	#520	—	2	2	no	—
298	#520	C₂²×C₁₃₇	1	4	yes	—
299	#519	—	2	1	no	—
300	#518	—	2	1	no	—
301	#518	—	2	2	no	—
302	C₄×#41	—	2	2	no	—
303	C₄×#41	—	2	2	no	—
304	C₂×#117	—	2	2	no	—
305	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
306	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
307	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
308	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
309	#428	—	2	2	no	—
310	#428	C₂²×C₁₃₇	1	4	yes	complemented
311	#427	—	2	2	no	—
312	C₂×#104	C₄×C₁₃₇	1	8	yes	complemented
313	C₂×#104	C₂²×C₁₃₇	1	2	yes	—
314	C₂×#104	C₂²×C₁₃₇	1	2	yes	—
315	#419	—	2	1	no	—
316	#418	—	2	1	no	—
317	#417	C₂²×C₁₃₇	1	4	yes	—
318	#416	—	2	2	no	—
319	#384	C₂²×C₁₃₇	1	2	yes	complemented
320	#382	C₂²×C₁₃₇	1	2	yes	complemented
321	#380	—	2	2	no	—
322	C₄×C₄⋊C₄	—	2	2	no	—
323	#343	C₂²×C₁₃₇	1	4	yes	complemented
324	#339	C₂²×C₁₃₇	1	2	yes	complemented
325	#339	C₂²×C₁₃₇	1	2	yes	complemented
326	C₂×#41	—	2	1	no	—
327	C₂×#41	—	2	1	no	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	2	2	no	—
330	C₂×#41	C₂×C₄×C₁₃₇	1	4	yes	—
331	C₂×#41	D₄×C₁₃₇	1	2	yes	—
332	C₂×#41	Q₈×C₁₃₇	1	4	yes	—
333	C₂×#41	C₂³×C₁₃₇	1	2	yes	—
334	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	D₄×C₁₃₇	1	1	yes	characteristic
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	—	2	1	no	—
339	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	2	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	2	2	no	—
344	C₂×M₁₆	—	2	2	no	—
345	C₂×M₁₆	C₂×C₄×C₁₃₇	1	4	yes	complemented
346	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
347	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
348	C₂²×C₈	—	2	1	no	—
349	C₂²×C₈	—	2	1	no	—
350	C₄×Q₈	—	2	4	no	—
351	C₄×Q₈	—	2	4	no	—
352	C₄×D₄	—	2	8	no	—
353	C₄×D₄	—	2	4	no	—
354	C₄×D₄	—	2	4	no	—
355	C₄×D₄	—	2	8	no	—
356	#117	—	2	4	no	—
357	#117	—	2	4	no	—
358	#117	—	2	1	no	—
359	#117	—	2	1	no	—
360	#117	—	2	1	no	—
361	#117	—	2	1	no	—
362	#117	—	2	1	no	—
363	#117	—	2	1	no	—
364	#117	—	2	4	no	—
365	#117	—	2	1	no	—
366	#117	—	2	1	no	—
367	#117	—	2	1	no	—
368	#117	—	2	1	no	—
369	#117	D₄×C₁₃₇	1	2	yes	—
370	#117	C₂³×C₁₃₇	1	2	yes	—
371	C₂×C₄⋊C₄	—	2	4	no	—
372	C₂×C₄⋊C₄	—	2	4	no	—
373	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
376	C₂×C₂²⋊C₄	—	2	4	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	D₄×C₁₃₇	1	2	yes	—
380	C₂×C₄²	—	2	4	no	—
381	C₂×C₄²	—	2	1	no	—
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	2	2	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	C₂×C₄×C₁₃₇	1	4	yes	complemented
386	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
387	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
389	#107	—	2	4	no	—
390	#106	—	2	4	no	—
391	#104	C₂×C₄×C₁₃₇	1	8	yes	complemented
392	#104	C₂×C₄×C₁₃₇	1	8	yes	complemented
393	#103	—	2	4	no	—
394	#102	—	2	4	no	—
395	#95	—	2	4	no	—
396	C₂⁴	—	2	1	no	—
397	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
398	#41	—	2	4	no	—
399	#41	—	2	4	no	—
400	#41	—	2	4	no	—
401	#41	—	2	4	no	—
402	#41	—	2	4	no	—
403	#41	—	2	2	no	—
404	#41	—	2	2	no	—
405	#41	C₄⋊C₄×C₁₃₇	1	8	yes	complemented
406	#41	C₂²×C₄×C₁₃₇	1	4	yes	—
407	#41	C₂×Q₈×C₁₃₇	1	4	yes	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	C₄⋊C₄×C₁₃₇	1	4	yes	complemented
411	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	C₄⋊C₄×C₁₃₇	1	4	yes	complemented
419	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	8	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	4	4	no	—
432	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
433	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
434	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
439	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
440	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
441	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
443	M₁₆	—	2	4	no	—
444	M₁₆	—	2	2	no	—
445	M₁₆	—	2	2	no	—
446	M₁₆	—	2	2	no	—
447	M₁₆	—	4	2	no	—
448	M₁₆	C₂²×C₄×C₁₃₇	1	4	yes	—
449	C₂×C₈	—	2	4	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	4	2	no	—
453	C₄⋊C₄	—	2	8	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	4	8	no	—
460	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	4	1	no	—
467	C₂²⋊C₄	—	4	1	no	—
468	C₄²	—	2	8	no	—
469	C₄²	—	2	4	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	2	2	no	—
472	C₄²	—	2	2	no	—
473	C₄²	—	2	2	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	4	1	no	—
477	C₄²	—	4	1	no	—
478	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
479	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	8	2	no	—
484	C₂³	C₄×D₄×C₁₃₇	1	2	yes	—
485	C₂³	#120×C₁₃₇	1	1	yes	characteristic
486	C₂³	#120×C₁₃₇	1	1	yes	characteristic
487	C₂³	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
488	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
489	Q₈	—	2	4	no	—
490	Q₈	—	2	2	no	—
491	Q₈	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
492	D₄	—	2	8	no	—
493	D₄	—	2	4	no	—
494	D₄	—	2	4	no	—
495	D₄	—	2	4	no	—
496	D₄	—	2	2	no	—
497	D₄	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	4	8	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	8	2	no	—
514	C₂×C₄	—	8	8	no	—
515	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
516	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
517	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
518	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
519	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
520	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
521	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
522	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
523	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
524	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
525	C₂×C₄	#123×C₁₃₇	1	2	yes	—
526	C₂×C₄	#123×C₁₃₇	1	2	yes	—
527	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
529	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
530	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
531	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
532	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
533	C₈	—	2	4	no	—
534	C₈	—	4	2	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	4	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	8	4	no	—
543	C₂²	#385×C₁₃₇	1	2	yes	—
544	C₂²	#385×C₁₃₇	1	2	yes	—
545	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
546	C₂²	C₂×#120×C₁₃₇	1	1	yes	characteristic
547	C₂²	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
548	C₄	—	2	4	no	—
549	C₄	—	2	4	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	4	no	—
553	C₄	—	8	2	no	—
554	C₄	#385×C₁₃₇	1	2	yes	—
555	C₄	#385×C₁₃₇	1	2	yes	—
556	C₄	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
557	C₄	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
558	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
559	C₄	C₂×#123×C₁₃₇	1	1	yes	characteristic
560	C₂	—	2	1	no	—
561	C₂	—	2	2	no	—
562	C₂	—	2	2	no	—
563	C₂	—	2	1	no	—
564	C₂	—	4	4	no	—
565	C₂	C₂×#385×C₁₃₇	1	1	yes	characteristic
566	C₂	#3018×C₁₃₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃₇	#120
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle	C₂²×C₁₃₇	C₂×#120
prime radical	C₂²×#41×C₁₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₇ ◁ C₂³×C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2911×C₁₃₇	C₂	semidirect
5. #2285×C₁₃₇	C₂	semidirect
6. #1860×C₁₃₇	C₂	semidirect
7. #1859×C₁₃₇	C₂	semidirect
8. #1742×C₁₃₇	C₂	semidirect
9. C₂×#339×C₁₃₇	C₂	semidirect
26. #428×C₁₃₇	C₂²	semidirect
28. C₂×#104×C₁₃₇	C₄	semidirect
35. #384×C₁₃₇	C₂²	semidirect
36. #382×C₁₃₇	C₂²	semidirect
39. #343×C₁₃₇	C₂²	semidirect
40. #339×C₁₃₇	C₂²	semidirect
41. #339×C₁₃₇	C₂²	semidirect
61. C₂×M₁₆×C₁₃₇	C₂×C₄	semidirect
101. C₂×C₄²×C₁₃₇	C₂×C₄	semidirect
107. #104×C₁₃₇	C₂×C₄	semidirect
108. #104×C₁₃₇	C₂×C₄	semidirect
121. #41×C₁₃₇	C₄⋊C₄	semidirect
126. C₂×Q₈×C₁₃₇	C₄⋊C₄	semidirect
134. C₂×D₄×C₁₃₇	C₄⋊C₄	semidirect
283. #20863	C₁₃₇	direct (N × H)
284. C₁₃₇	#20863	direct (N × H)
286. #2911	C₂×C₁₃₇	semidirect
289. #2285	C₂×C₁₃₇	semidirect
290. #1860	C₂×C₁₃₇	semidirect
291. #1859	C₂×C₁₃₇	semidirect
292. #1742	C₂×C₁₃₇	semidirect
293. C₂×#339	C₂×C₁₃₇	semidirect
310. #428	C₂²×C₁₃₇	semidirect
312. C₂×#104	C₄×C₁₃₇	semidirect
319. #384	C₂²×C₁₃₇	semidirect
320. #382	C₂²×C₁₃₇	semidirect
323. #343	C₂²×C₁₃₇	semidirect
324. #339	C₂²×C₁₃₇	semidirect
325. #339	C₂²×C₁₃₇	semidirect
345. C₂×M₁₆	C₂×C₄×C₁₃₇	semidirect
385. C₂×C₄²	C₂×C₄×C₁₃₇	semidirect
391. #104	C₂×C₄×C₁₃₇	semidirect
392. #104	C₂×C₄×C₁₃₇	semidirect
405. #41	C₄⋊C₄×C₁₃₇	semidirect
410. C₂×Q₈	C₄⋊C₄×C₁₃₇	semidirect
418. C₂×D₄	C₄⋊C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3428×C₁₃₇	2
#2911×C₁₃₇	2
C₂²×#104×C₁₃₇	2
#2896×C₁₃₇	2
#2285×C₁₃₇	2
#1860×C₁₃₇	2
#1859×C₁₃₇	2
#1742×C₁₃₇	2
C₂×#339×C₁₃₇	2
#20863	137

Subgroups — C137×#20863 #46870249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#20863 #46870249