Subgroups — C₁₃₇×#11040 #46860426

Order 35072.

1278 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2896×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	C₂×#408×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	C₂×#338×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1729×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₁₃₇	C₂²	1	2	yes	—
7	#575×C₁₃₇	—	2	4	no	—
8	#575×C₁₃₇	—	2	2	no	—
9	#575×C₁₃₇	C₄	1	4	yes	complemented
10	C₂×#137×C₁₃₇	—	2	2	no	—
11	C₂×AGL(1,ℤ/8)×C₁₃₇	—	2	2	no	—
12	C₂×#135×C₁₃₇	—	2	2	no	—
13	C₂²×M₁₆×C₁₃₇	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
17	#419×C₁₃₇	—	2	2	no	—
18	#418×C₁₃₇	—	2	2	no	—
19	#417×C₁₃₇	—	2	4	no	—
20	#416×C₁₃₇	—	2	4	no	—
21	#408×C₁₃₇	—	2	4	no	—
22	#408×C₁₃₇	—	2	4	no	—
23	C₂×C₂²⋊C₈×C₁₃₇	—	2	4	no	—
24	#338×C₁₃₇	—	2	2	no	—
25	#336×C₁₃₇	—	2	2	no	—
26	C₂×#41×C₁₃₇	—	2	2	no	—
27	C₂×#41×C₁₃₇	—	2	2	no	—
28	C₂×#41×C₁₃₇	—	2	2	no	—
29	C₂×#41×C₁₃₇	—	2	2	no	—
30	C₂×#41×C₁₃₇	—	2	2	no	—
31	C₂×#41×C₁₃₇	—	2	2	no	—
32	C₂×#41×C₁₃₇	—	2	2	no	—
33	C₂×#41×C₁₃₇	—	2	2	no	—
34	C₂×#41×C₁₃₇	—	2	2	no	—
35	C₂×#41×C₁₃₇	—	2	2	no	—
36	C₂×#41×C₁₃₇	C₂×C₄	1	4	yes	—
37	C₂×#41×C₁₃₇	D₄	1	4	yes	—
38	C₂²×Q₈×C₁₃₇	D₄	1	2	yes	—
39	C₂²×D₄×C₁₃₇	—	2	2	no	—
40	C₂²×D₄×C₁₃₇	D₄	1	2	yes	—
41	C₂³×C₄×C₁₃₇	—	2	2	no	—
42	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
43	#137×C₁₃₇	—	2	8	no	—
44	#137×C₁₃₇	—	2	8	no	—
45	AGL(1,ℤ/8)×C₁₃₇	—	2	8	no	—
46	AGL(1,ℤ/8)×C₁₃₇	—	2	8	no	—
47	#135×C₁₃₇	—	2	8	no	—
48	#135×C₁₃₇	—	2	8	no	—
49	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
50	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
51	C₂×D₈×C₁₃₇	—	2	2	no	—
52	C₂×M₁₆×C₁₃₇	—	2	2	no	—
53	C₂×M₁₆×C₁₃₇	—	2	2	no	—
54	C₂×M₁₆×C₁₃₇	—	2	2	no	—
55	C₂×M₁₆×C₁₃₇	—	2	2	no	—
56	C₂×M₁₆×C₁₃₇	—	2	2	no	—
57	C₂×M₁₆×C₁₃₇	—	2	2	no	—
58	C₂×M₁₆×C₁₃₇	—	2	2	no	—
59	C₂×M₁₆×C₁₃₇	—	2	2	no	—
60	C₂×M₁₆×C₁₃₇	C₂×C₄	1	2	yes	—
61	C₂×M₁₆×C₁₃₇	D₄	1	2	yes	—
62	C₂²×C₈×C₁₃₇	—	2	2	no	—
63	C₂²×C₈×C₁₃₇	—	2	2	no	—
64	C₂²×C₈×C₁₃₇	—	2	1	no	—
65	C₂²×C₈×C₁₃₇	—	2	1	no	—
66	C₂²×C₈×C₁₃₇	D₄	1	4	yes	—
67	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
68	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
69	#117×C₁₃₇	—	2	2	no	—
70	#117×C₁₃₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
72	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
73	C₂×C₄²×C₁₃₇	—	2	1	no	—
74	#103×C₁₃₇	—	2	8	no	—
75	#102×C₁₃₇	—	2	8	no	—
76	C₂²⋊C₈×C₁₃₇	—	2	16	no	—
77	C₂⁴×C₁₃₇	—	2	2	no	—
78	C₂⁴×C₁₃₇	#41	1	1	yes	characteristic
79	#41×C₁₃₇	—	2	4	no	—
80	#41×C₁₃₇	—	2	4	no	—
81	#41×C₁₃₇	—	2	4	no	—
82	#41×C₁₃₇	—	2	4	no	—
83	#41×C₁₃₇	—	2	4	no	—
84	#41×C₁₃₇	—	2	4	no	—
85	#41×C₁₃₇	—	2	4	no	—
86	#41×C₁₃₇	—	2	4	no	—
87	#41×C₁₃₇	—	4	2	no	—
88	#41×C₁₃₇	—	4	2	no	—
89	#41×C₁₃₇	—	4	2	no	—
90	#41×C₁₃₇	—	4	2	no	—
91	#41×C₁₃₇	—	4	2	no	—
92	#41×C₁₃₇	—	4	2	no	—
93	#41×C₁₃₇	—	4	2	no	—
94	#41×C₁₃₇	—	4	2	no	—
95	C₂×Q₈×C₁₃₇	—	2	2	no	—
96	C₂×Q₈×C₁₃₇	—	2	2	no	—
97	C₂×Q₈×C₁₃₇	—	2	2	no	—
98	C₂×Q₈×C₁₃₇	—	2	2	no	—
99	C₂×Q₈×C₁₃₇	—	2	2	no	—
100	C₂×Q₈×C₁₃₇	C₂²⋊C₄	1	4	yes	—
101	C₂×D₄×C₁₃₇	—	2	4	no	—
102	C₂×D₄×C₁₃₇	—	2	4	no	—
103	C₂×D₄×C₁₃₇	—	2	2	no	—
104	C₂×D₄×C₁₃₇	—	2	2	no	—
105	C₂×D₄×C₁₃₇	—	2	2	no	—
106	C₂×D₄×C₁₃₇	—	2	2	no	—
107	C₂×D₄×C₁₃₇	—	2	2	no	—
108	C₂×D₄×C₁₃₇	—	4	2	no	—
109	C₂×D₄×C₁₃₇	—	4	2	no	—
110	C₂×D₄×C₁₃₇	—	4	2	no	—
111	C₂×D₄×C₁₃₇	—	4	2	no	—
112	C₂×D₄×C₁₃₇	C₂²⋊C₄	1	4	yes	—
113	C₂²×C₄×C₁₃₇	—	2	2	no	—
114	C₂²×C₄×C₁₃₇	—	2	4	no	—
115	C₂²×C₄×C₁₃₇	—	2	4	no	—
116	C₂²×C₄×C₁₃₇	—	2	2	no	—
117	C₂²×C₄×C₁₃₇	—	4	2	no	—
118	C₂²×C₄×C₁₃₇	—	4	2	no	—
119	C₂²×C₄×C₁₃₇	—	4	2	no	—
120	C₂²×C₄×C₁₃₇	—	4	2	no	—
121	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
130	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
131	Q₁₆×C₁₃₇	—	2	8	no	—
132	SD₁₆×C₁₃₇	—	2	16	no	—
133	D₈×C₁₃₇	—	2	8	no	—
134	M₁₆×C₁₃₇	—	2	4	no	—
135	M₁₆×C₁₃₇	—	2	4	no	—
136	M₁₆×C₁₃₇	—	4	2	no	—
137	M₁₆×C₁₃₇	—	4	2	no	—
138	M₁₆×C₁₃₇	—	4	2	no	—
139	M₁₆×C₁₃₇	—	4	2	no	—
140	C₂×C₈×C₁₃₇	—	2	2	no	—
141	C₂×C₈×C₁₃₇	—	2	2	no	—
142	C₂×C₈×C₁₃₇	—	2	4	no	—
143	C₂×C₈×C₁₃₇	—	2	4	no	—
144	C₂×C₈×C₁₃₇	—	2	4	no	—
145	C₂×C₈×C₁₃₇	—	2	2	no	—
146	C₂×C₈×C₁₃₇	—	2	4	no	—
147	C₂×C₈×C₁₃₇	—	4	1	no	—
148	C₂×C₈×C₁₃₇	—	4	2	no	—
149	C₂×C₈×C₁₃₇	—	4	1	no	—
150	C₂×C₈×C₁₃₇	C₂²⋊C₄	1	4	yes	—
151	C₄⋊C₄×C₁₃₇	—	2	4	no	—
152	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
153	C₄²×C₁₃₇	—	4	1	no	—
154	C₄²×C₁₃₇	—	4	1	no	—
155	C₂³×C₁₃₇	—	2	4	no	—
156	C₂³×C₁₃₇	—	4	2	no	—
157	C₂³×C₁₃₇	—	4	8	no	—
158	C₂³×C₁₃₇	—	4	2	no	—
159	C₂³×C₁₃₇	—	4	2	no	—
160	C₂³×C₁₃₇	C₄×D₄	1	1	yes	characteristic
161	C₂³×C₁₃₇	#121	1	2	yes	—
162	C₂³×C₁₃₇	#121	1	1	yes	characteristic
163	C₂³×C₁₃₇	#123	1	2	yes	—
164	C₂³×C₁₃₇	#124	1	1	yes	characteristic
165	Q₈×C₁₃₇	—	2	4	no	—
166	Q₈×C₁₃₇	—	2	4	no	—
167	Q₈×C₁₃₇	—	4	2	no	—
168	Q₈×C₁₃₇	—	4	2	no	—
169	D₄×C₁₃₇	—	2	4	no	—
170	D₄×C₁₃₇	—	2	4	no	—
171	D₄×C₁₃₇	—	4	4	no	—
172	D₄×C₁₃₇	—	4	4	no	—
173	D₄×C₁₃₇	—	4	4	no	—
174	D₄×C₁₃₇	—	4	4	no	—
175	D₄×C₁₃₇	—	4	2	no	—
176	D₄×C₁₃₇	—	4	2	no	—
177	C₂×C₄×C₁₃₇	—	2	4	no	—
178	C₂×C₄×C₁₃₇	—	4	2	no	—
179	C₂×C₄×C₁₃₇	—	4	2	no	—
180	C₂×C₄×C₁₃₇	—	4	4	no	—
181	C₂×C₄×C₁₃₇	—	4	4	no	—
182	C₂×C₄×C₁₃₇	—	4	4	no	—
183	C₂×C₄×C₁₃₇	—	4	4	no	—
184	C₂×C₄×C₁₃₇	—	4	4	no	—
185	C₂×C₄×C₁₃₇	—	4	2	no	—
186	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
190	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
191	C₂×C₄×C₁₃₇	#120	1	2	yes	—
192	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
193	C₂×C₄×C₁₃₇	#120	1	2	yes	—
194	C₂×C₄×C₁₃₇	#120	1	2	yes	—
195	C₂×C₄×C₁₃₇	#121	1	2	yes	—
196	C₂×C₄×C₁₃₇	#121	1	2	yes	—
197	C₂×C₄×C₁₃₇	#121	1	2	yes	—
198	C₂×C₄×C₁₃₇	#121	1	2	yes	—
199	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
200	C₂×C₄×C₁₃₇	#123	1	2	yes	—
201	C₂×C₄×C₁₃₇	#124	1	1	yes	characteristic
202	C₂×C₄×C₁₃₇	#127	1	1	yes	characteristic
203	C₂×C₄×C₁₃₇	#127	1	1	yes	characteristic
204	C₈×C₁₃₇	—	2	4	no	—
205	C₈×C₁₃₇	—	4	2	no	—
206	C₈×C₁₃₇	—	4	4	no	—
207	C₂²×C₁₃₇	—	2	2	no	—
208	C₂²×C₁₃₇	—	2	4	no	—
209	C₂²×C₁₃₇	—	4	1	no	—
210	C₂²×C₁₃₇	—	4	2	no	—
211	C₂²×C₁₃₇	—	4	1	no	—
212	C₂²×C₁₃₇	—	4	8	no	—
213	C₂²×C₁₃₇	—	4	4	no	—
214	C₂²×C₁₃₇	—	8	4	no	—
215	C₂²×C₁₃₇	—	8	4	no	—
216	C₂²×C₁₃₇	#386	1	2	yes	—
217	C₂²×C₁₃₇	#390	1	1	yes	characteristic
218	C₂²×C₁₃₇	#392	1	1	yes	characteristic
219	C₂²×C₁₃₇	#394	1	2	yes	—
220	C₂²×C₁₃₇	#394	1	1	yes	characteristic
221	C₄×C₁₃₇	—	4	4	no	—
222	C₄×C₁₃₇	—	8	2	no	—
223	C₄×C₁₃₇	#379	1	1	yes	characteristic
224	C₄×C₁₃₇	#386	1	2	yes	—
225	C₄×C₁₃₇	#390	1	1	yes	characteristic
226	C₄×C₁₃₇	#392	1	1	yes	characteristic
227	C₄×C₁₃₇	#392	1	2	yes	—
228	C₄×C₁₃₇	#394	1	1	yes	characteristic
229	C₂×C₁₃₇	—	2	2	no	—
230	C₂×C₁₃₇	—	2	2	no	—
231	C₂×C₁₃₇	—	2	1	no	—
232	C₂×C₁₃₇	—	2	1	no	—
233	C₂×C₁₃₇	—	8	4	no	—
234	C₂×C₁₃₇	#1438	1	1	yes	characteristic
235	C₂×C₁₃₇	#2017	1	2	yes	—
236	#11040	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₁₃₇	#11040	1	1	yes	characteristic, direct product factor, Sylow
238	C₂×#575	C₂×C₁₃₇	1	1	yes	characteristic
239	#2896	C₂×C₁₃₇	1	2	yes	complemented
240	C₂×#408	C₂×C₁₃₇	1	2	yes	complemented
241	C₂×#338	C₂×C₁₃₇	1	1	yes	characteristic, complemented
242	#1729	C₂×C₁₃₇	1	1	yes	characteristic, complemented
243	C₂²×#41	C₂²×C₁₃₇	1	2	yes	—
244	#575	—	2	4	no	—
245	#575	—	2	2	no	—
246	#575	C₄×C₁₃₇	1	4	yes	complemented
247	C₂×#137	—	2	2	no	—
248	C₂×AGL(1,ℤ/8)	—	2	2	no	—
249	C₂×#135	—	2	2	no	—
250	C₂²×M₁₆	C₂²×C₁₃₇	1	2	yes	—
251	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
252	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
253	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
254	#419	—	2	2	no	—
255	#418	—	2	2	no	—
256	#417	—	2	4	no	—
257	#416	—	2	4	no	—
258	#408	—	2	4	no	—
259	#408	—	2	4	no	—
260	C₂×C₂²⋊C₈	—	2	4	no	—
261	#338	—	2	2	no	—
262	#336	—	2	2	no	—
263	C₂×#41	—	2	2	no	—
264	C₂×#41	—	2	2	no	—
265	C₂×#41	—	2	2	no	—
266	C₂×#41	—	2	2	no	—
267	C₂×#41	—	2	2	no	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	C₂×C₄×C₁₃₇	1	4	yes	—
274	C₂×#41	D₄×C₁₃₇	1	4	yes	—
275	C₂²×Q₈	D₄×C₁₃₇	1	2	yes	—
276	C₂²×D₄	—	2	2	no	—
277	C₂²×D₄	D₄×C₁₃₇	1	2	yes	—
278	C₂³×C₄	—	2	2	no	—
279	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
280	#137	—	2	8	no	—
281	#137	—	2	8	no	—
282	AGL(1,ℤ/8)	—	2	8	no	—
283	AGL(1,ℤ/8)	—	2	8	no	—
284	#135	—	2	8	no	—
285	#135	—	2	8	no	—
286	C₂×Q₁₆	—	2	2	no	—
287	C₂×SD₁₆	—	2	4	no	—
288	C₂×D₈	—	2	2	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	—	2	2	no	—
292	C₂×M₁₆	—	2	2	no	—
293	C₂×M₁₆	—	2	2	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	C₂×C₄×C₁₃₇	1	2	yes	—
298	C₂×M₁₆	D₄×C₁₃₇	1	2	yes	—
299	C₂²×C₈	—	2	1	no	—
300	C₂²×C₈	—	2	2	no	—
301	C₂²×C₈	—	2	2	no	—
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
304	C₂²×C₈	D₄×C₁₃₇	1	4	yes	—
305	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
306	#117	—	2	2	no	—
307	#117	—	2	2	no	—
308	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₄²	—	2	1	no	—
311	#103	—	2	8	no	—
312	#102	—	2	8	no	—
313	C₂²⋊C₈	—	2	16	no	—
314	C₂⁴	—	2	2	no	—
315	C₂⁴	#41×C₁₃₇	1	1	yes	characteristic
316	#41	—	2	4	no	—
317	#41	—	2	4	no	—
318	#41	—	2	4	no	—
319	#41	—	2	4	no	—
320	#41	—	2	4	no	—
321	#41	—	2	4	no	—
322	#41	—	2	4	no	—
323	#41	—	2	4	no	—
324	#41	—	4	2	no	—
325	#41	—	4	2	no	—
326	#41	—	4	2	no	—
327	#41	—	4	2	no	—
328	#41	—	4	2	no	—
329	#41	—	4	2	no	—
330	#41	—	4	2	no	—
331	#41	—	4	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	C₂²⋊C₄×C₁₃₇	1	4	yes	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	C₂²⋊C₄×C₁₃₇	1	4	yes	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
366	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
367	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
368	Q₁₆	—	2	8	no	—
369	SD₁₆	—	2	16	no	—
370	D₈	—	2	8	no	—
371	M₁₆	—	2	4	no	—
372	M₁₆	—	2	4	no	—
373	M₁₆	—	4	2	no	—
374	M₁₆	—	4	2	no	—
375	M₁₆	—	4	2	no	—
376	M₁₆	—	4	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	4	no	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	—	2	4	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	4	no	—
384	C₂×C₈	—	4	1	no	—
385	C₂×C₈	—	4	2	no	—
386	C₂×C₈	—	4	1	no	—
387	C₂×C₈	C₂²⋊C₄×C₁₃₇	1	4	yes	—
388	C₄⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₄²	—	4	1	no	—
391	C₄²	—	4	1	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	8	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	C₄×D₄×C₁₃₇	1	1	yes	characteristic
398	C₂³	#121×C₁₃₇	1	2	yes	—
399	C₂³	#121×C₁₃₇	1	1	yes	characteristic
400	C₂³	#123×C₁₃₇	1	2	yes	—
401	C₂³	#124×C₁₃₇	1	1	yes	characteristic
402	Q₈	—	2	4	no	—
403	Q₈	—	2	4	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	4	4	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	4	no	—
411	D₄	—	4	4	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
424	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
425	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
426	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
427	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
428	C₂×C₄	#120×C₁₃₇	1	2	yes	—
429	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
430	C₂×C₄	#120×C₁₃₇	1	2	yes	—
431	C₂×C₄	#120×C₁₃₇	1	2	yes	—
432	C₂×C₄	#121×C₁₃₇	1	2	yes	—
433	C₂×C₄	#121×C₁₃₇	1	2	yes	—
434	C₂×C₄	#121×C₁₃₇	1	2	yes	—
435	C₂×C₄	#121×C₁₃₇	1	2	yes	—
436	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
437	C₂×C₄	#123×C₁₃₇	1	2	yes	—
438	C₂×C₄	#124×C₁₃₇	1	1	yes	characteristic
439	C₂×C₄	#127×C₁₃₇	1	1	yes	characteristic
440	C₂×C₄	#127×C₁₃₇	1	1	yes	characteristic
441	C₈	—	2	4	no	—
442	C₈	—	4	2	no	—
443	C₈	—	4	4	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	8	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	8	4	no	—
452	C₂²	—	8	4	no	—
453	C₂²	#386×C₁₃₇	1	2	yes	—
454	C₂²	#390×C₁₃₇	1	1	yes	characteristic
455	C₂²	#392×C₁₃₇	1	1	yes	characteristic
456	C₂²	#394×C₁₃₇	1	2	yes	—
457	C₂²	#394×C₁₃₇	1	1	yes	characteristic
458	C₄	—	4	4	no	—
459	C₄	—	8	2	no	—
460	C₄	#379×C₁₃₇	1	1	yes	characteristic
461	C₄	#386×C₁₃₇	1	2	yes	—
462	C₄	#390×C₁₃₇	1	1	yes	characteristic
463	C₄	#392×C₁₃₇	1	1	yes	characteristic
464	C₄	#392×C₁₃₇	1	2	yes	—
465	C₄	#394×C₁₃₇	1	1	yes	characteristic
466	C₂	—	2	2	no	—
467	C₂	—	2	2	no	—
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	—	8	4	no	—
471	C₂	#1438×C₁₃₇	1	1	yes	characteristic
472	C₂	#2017×C₁₃₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃₇	#127
commutator	C₂²×C₄	C₂²×C₄×C₁₃₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₇
socle	C₂²×C₁₃₇	#392
prime radical	C₂×#575×C₁₃₇	C₂
LCS	G ▷ C₂²×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. #2896×C₁₃₇	C₂	semidirect
3. C₂×#408×C₁₃₇	C₂	semidirect
4. C₂×#338×C₁₃₇	C₂	semidirect
5. #1729×C₁₃₇	C₂	semidirect
9. #575×C₁₃₇	C₄	semidirect
236. #11040	C₁₃₇	direct (N × H)
237. C₁₃₇	#11040	direct (N × H)
239. #2896	C₂×C₁₃₇	semidirect
240. C₂×#408	C₂×C₁₃₇	semidirect
241. C₂×#338	C₂×C₁₃₇	semidirect
242. #1729	C₂×C₁₃₇	semidirect
246. #575	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×#575×C₁₃₇	2
#2896×C₁₃₇	2
C₂×#408×C₁₃₇	2
C₂×#338×C₁₃₇	2
#1729×C₁₃₇	2
#11040	137

Subgroups — C137×#11040 #46860426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#11040 #46860426