Subgroups — C₁₃₇×#9222 #46858608

Order 35072.

590 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#460×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#1957×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1803×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#331×C₁₃₇	C₂	1	1	yes	maximal, characteristic
6	#1296×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1277×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₁₃₇	—	2	1	no	—
9	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
11	#460×C₁₃₇	—	2	2	no	—
12	#460×C₁₃₇	C₄	1	4	yes	complemented
13	C₈×Q₈×C₁₃₇	—	2	2	no	—
14	C₈×Q₈×C₁₃₇	—	2	2	no	—
15	C₂×C₄⋊C₈×C₁₃₇	—	2	1	no	—
16	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×#103×C₁₃₇	—	2	1	no	—
20	C₂×#102×C₁₃₇	—	2	1	no	—
21	C₂×#102×C₁₃₇	—	2	1	no	—
22	C₂×#102×C₁₃₇	—	2	1	no	—
23	C₂×C₄×C₈×C₁₃₇	—	2	1	no	—
24	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
25	#384×C₁₃₇	C₂²	1	1	yes	characteristic
26	#340×C₁₃₇	—	2	1	no	—
27	#331×C₁₃₇	—	2	2	no	—
28	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₃₇	—	2	1	no	—
30	C₂²×D₄×C₁₃₇	—	2	1	no	—
31	C₂²×D₄×C₁₃₇	—	2	1	no	—
32	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
33	C₂×SD₁₆×C₁₃₇	—	4	2	no	—
34	C₂×SD₁₆×C₁₃₇	—	4	2	no	—
35	C₂²×C₈×C₁₃₇	—	2	1	no	—
36	C₂²×C₈×C₁₃₇	—	2	1	no	—
37	C₂²×C₈×C₁₃₇	—	2	1	no	—
38	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
40	#127×C₁₃₇	—	2	1	no	—
41	#127×C₁₃₇	—	2	1	no	—
42	#127×C₁₃₇	—	2	1	no	—
43	#127×C₁₃₇	C₂×C₄	1	2	yes	—
44	C₄×Q₈×C₁₃₇	—	2	1	no	—
45	C₄×Q₈×C₁₃₇	—	2	1	no	—
46	C₄×Q₈×C₁₃₇	C₂×C₄	1	2	yes	—
47	C₄×Q₈×C₁₃₇	D₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃₇	—	2	1	no	—
54	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
55	C₄⋊C₈×C₁₃₇	—	2	4	no	—
56	C₄⋊C₈×C₁₃₇	—	2	1	no	—
57	C₄⋊C₈×C₁₃₇	—	2	1	no	—
58	C₄⋊C₈×C₁₃₇	—	2	1	no	—
59	C₄⋊C₈×C₁₃₇	—	2	1	no	—
60	C₄⋊C₈×C₁₃₇	C₂×C₄	1	2	yes	—
61	C₄⋊C₈×C₁₃₇	D₄	1	2	yes	—
62	#103×C₁₃₇	—	4	2	no	—
63	#102×C₁₃₇	—	2	4	no	—
64	#102×C₁₃₇	—	4	2	no	—
65	#102×C₁₃₇	—	4	2	no	—
66	C₄×C₈×C₁₃₇	—	2	4	no	—
67	C₄×C₈×C₁₃₇	—	2	1	no	—
68	C₄×C₈×C₁₃₇	—	2	1	no	—
69	C₂⁴×C₁₃₇	—	4	1	no	—
70	C₂×Q₈×C₁₃₇	—	2	1	no	—
71	C₂×Q₈×C₁₃₇	—	2	1	no	—
72	C₂×Q₈×C₁₃₇	—	2	1	no	—
73	C₂×Q₈×C₁₃₇	C₂²⋊C₄	1	2	yes	—
74	C₂×Q₈×C₁₃₇	D₈	1	2	yes	—
75	C₂×Q₈×C₁₃₇	SD₁₆	1	2	yes	—
76	C₂×D₄×C₁₃₇	—	2	2	no	—
77	C₂×D₄×C₁₃₇	—	2	2	no	—
78	C₂×D₄×C₁₃₇	—	2	2	no	—
79	C₂×D₄×C₁₃₇	—	4	1	no	—
80	C₂×D₄×C₁₃₇	—	4	1	no	—
81	C₂×D₄×C₁₃₇	—	4	1	no	—
82	C₂×D₄×C₁₃₇	—	4	1	no	—
83	C₂×D₄×C₁₃₇	—	4	1	no	—
84	C₂×D₄×C₁₃₇	—	4	1	no	—
85	C₂×D₄×C₁₃₇	—	4	1	no	—
86	C₂×D₄×C₁₃₇	—	4	1	no	—
87	C₂×D₄×C₁₃₇	—	4	1	no	—
88	C₂×D₄×C₁₃₇	—	4	1	no	—
89	C₂×D₄×C₁₃₇	—	4	1	no	—
90	C₂×D₄×C₁₃₇	—	8	1	no	—
91	C₂×D₄×C₁₃₇	—	8	1	no	—
92	C₂²×C₄×C₁₃₇	—	2	1	no	—
93	C₂²×C₄×C₁₃₇	—	2	1	no	—
94	C₂²×C₄×C₁₃₇	—	4	1	no	—
95	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
98	SD₁₆×C₁₃₇	—	4	8	no	—
99	C₂×C₈×C₁₃₇	—	2	1	no	—
100	C₂×C₈×C₁₃₇	—	2	1	no	—
101	C₂×C₈×C₁₃₇	—	2	2	no	—
102	C₂×C₈×C₁₃₇	—	2	1	no	—
103	C₂×C₈×C₁₃₇	—	2	2	no	—
104	C₂×C₈×C₁₃₇	—	2	1	no	—
105	C₂×C₈×C₁₃₇	—	2	1	no	—
106	C₂×C₈×C₁₃₇	—	4	1	no	—
107	C₂×C₈×C₁₃₇	—	4	1	no	—
108	C₂×C₈×C₁₃₇	—	4	1	no	—
109	C₂×C₈×C₁₃₇	—	4	1	no	—
110	C₂×C₈×C₁₃₇	—	4	1	no	—
111	C₂×C₈×C₁₃₇	—	4	1	no	—
112	C₂×C₈×C₁₃₇	—	4	1	no	—
113	C₂×C₈×C₁₃₇	SD₁₆	1	2	yes	complemented
114	C₄⋊C₄×C₁₃₇	—	2	2	no	—
115	C₄⋊C₄×C₁₃₇	—	2	1	no	—
116	C₄⋊C₄×C₁₃₇	—	2	2	no	—
117	C₄⋊C₄×C₁₃₇	—	4	1	no	—
118	C₄⋊C₄×C₁₃₇	—	4	1	no	—
119	C₄⋊C₄×C₁₃₇	—	4	1	no	—
120	C₄⋊C₄×C₁₃₇	—	4	1	no	—
121	C₄⋊C₄×C₁₃₇	—	8	1	no	—
122	C₄⋊C₄×C₁₃₇	C₂²⋊C₄	1	2	yes	—
123	C₄²×C₁₃₇	—	2	2	no	—
124	C₄²×C₁₃₇	—	2	2	no	—
125	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₃₇	#41	1	1	yes	characteristic
129	C₂³×C₁₃₇	—	4	2	no	—
130	C₂³×C₁₃₇	—	8	1	no	—
131	C₂³×C₁₃₇	—	8	1	no	—
132	C₂³×C₁₃₇	—	8	1	no	—
133	C₂³×C₁₃₇	—	8	1	no	—
134	C₂³×C₁₃₇	—	8	1	no	—
135	C₂³×C₁₃₇	—	8	1	no	—
136	C₂³×C₁₃₇	#121	1	1	yes	characteristic
137	Q₈×C₁₃₇	—	2	2	no	—
138	Q₈×C₁₃₇	—	2	2	no	—
139	Q₈×C₁₃₇	—	2	2	no	—
140	Q₈×C₁₃₇	#102	1	4	yes	complemented
141	D₄×C₁₃₇	—	4	2	no	—
142	D₄×C₁₃₇	—	4	2	no	—
143	D₄×C₁₃₇	—	4	2	no	—
144	D₄×C₁₃₇	—	4	2	no	—
145	D₄×C₁₃₇	—	8	2	no	—
146	D₄×C₁₃₇	—	8	2	no	—
147	D₄×C₁₃₇	—	8	1	no	—
148	D₄×C₁₃₇	—	8	1	no	—
149	D₄×C₁₃₇	—	8	1	no	—
150	D₄×C₁₃₇	—	8	1	no	—
151	C₂×C₄×C₁₃₇	—	2	2	no	—
152	C₂×C₄×C₁₃₇	—	2	2	no	—
153	C₂×C₄×C₁₃₇	—	2	2	no	—
154	C₂×C₄×C₁₃₇	—	2	1	no	—
155	C₂×C₄×C₁₃₇	—	2	1	no	—
156	C₂×C₄×C₁₃₇	—	2	2	no	—
157	C₂×C₄×C₁₃₇	—	4	1	no	—
158	C₂×C₄×C₁₃₇	—	4	1	no	—
159	C₂×C₄×C₁₃₇	—	8	1	no	—
160	C₂×C₄×C₁₃₇	—	8	1	no	—
161	C₂×C₄×C₁₃₇	—	8	1	no	—
162	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
166	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
167	C₂×C₄×C₁₃₇	#123	1	1	yes	characteristic
168	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	1	yes	characteristic
170	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	1	yes	characteristic
171	C₂×C₄×C₁₃₇	#135	1	1	yes	characteristic
172	C₂×C₄×C₁₃₇	#135	1	1	yes	characteristic
173	C₂×C₄×C₁₃₇	#135	1	1	yes	characteristic
174	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₂×C₄×C₁₃₇	#137	1	1	yes	characteristic
176	C₈×C₁₃₇	—	2	2	no	—
177	C₈×C₁₃₇	—	4	2	no	—
178	C₈×C₁₃₇	—	4	1	no	—
179	C₈×C₁₃₇	—	4	2	no	—
180	C₈×C₁₃₇	—	8	1	no	—
181	C₂²×C₁₃₇	—	8	2	no	—
182	C₂²×C₁₃₇	—	8	2	no	—
183	C₂²×C₁₃₇	—	8	2	no	—
184	C₂²×C₁₃₇	—	16	1	no	—
185	C₂²×C₁₃₇	—	16	1	no	—
186	C₂²×C₁₃₇	—	16	1	no	—
187	C₂²×C₁₃₇	—	16	1	no	—
188	C₂²×C₁₃₇	#386	1	1	yes	characteristic
189	C₂²×C₁₃₇	#460	1	1	yes	characteristic
190	C₂²×C₁₃₇	#464	1	1	yes	characteristic
191	C₂²×C₁₃₇	#465	1	1	yes	characteristic
192	C₂²×C₁₃₇	#466	1	1	yes	characteristic
193	C₂²×C₁₃₇	#471	1	1	yes	characteristic
194	C₂²×C₁₃₇	#472	1	1	yes	characteristic
195	C₄×C₁₃₇	—	2	4	no	—
196	C₄×C₁₃₇	—	2	1	no	—
197	C₄×C₁₃₇	—	2	1	no	—
198	C₄×C₁₃₇	—	4	2	no	—
199	C₄×C₁₃₇	—	16	1	no	—
200	C₄×C₁₃₇	C₂×#102	1	1	yes	characteristic
201	C₄×C₁₃₇	#416	1	1	yes	characteristic
202	C₄×C₁₃₇	C₄×SD₁₆	1	1	yes	characteristic
203	C₄×C₁₃₇	#440	1	1	yes	characteristic
204	C₄×C₁₃₇	#448	1	1	yes	characteristic
205	C₄×C₁₃₇	#449	1	1	yes	characteristic
206	C₄×C₁₃₇	#465	1	1	yes	characteristic
207	C₄×C₁₃₇	#466	1	1	yes	characteristic
208	C₂×C₁₃₇	—	16	2	no	—
209	C₂×C₁₃₇	#1666	1	1	yes	characteristic
210	C₂×C₁₃₇	#1668	1	1	yes	characteristic
211	C₂×C₁₃₇	#1678	1	1	yes	characteristic
212	C₂×C₁₃₇	#1682	1	1	yes	characteristic
213	C₂×C₁₃₇	#1880	1	1	yes	characteristic
214	C₂×C₁₃₇	#1893	1	1	yes	characteristic
215	C₂×C₁₃₇	#1907	1	1	yes	characteristic
216	#9222	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₁₃₇	#9222	1	1	yes	characteristic, direct product factor, Sylow
218	C₂×#460	C₂×C₁₃₇	1	1	yes	characteristic
219	C₂×C₈×Q₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
220	#1957	C₂×C₁₃₇	1	1	yes	characteristic
221	#1803	C₂×C₁₃₇	1	1	yes	characteristic, complemented
222	C₂×#331	C₂×C₁₃₇	1	1	yes	characteristic
223	#1296	C₂×C₁₃₇	1	1	yes	characteristic, complemented
224	#1277	C₂×C₁₃₇	1	1	yes	characteristic, complemented
225	C₂²×SD₁₆	—	2	1	no	—
226	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
228	#460	—	2	2	no	—
229	#460	C₄×C₁₃₇	1	4	yes	complemented
230	C₈×Q₈	—	2	2	no	—
231	C₈×Q₈	—	2	2	no	—
232	C₂×C₄⋊C₈	—	2	1	no	—
233	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
234	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
235	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
236	C₂×#103	—	2	1	no	—
237	C₂×#102	—	2	1	no	—
238	C₂×#102	—	2	1	no	—
239	C₂×#102	—	2	1	no	—
240	C₂×C₄×C₈	—	2	1	no	—
241	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
242	#384	C₂²×C₁₃₇	1	1	yes	characteristic
243	#340	—	2	1	no	—
244	#331	—	2	2	no	—
245	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂×SD₁₆	—	2	4	no	—
250	C₂×SD₁₆	—	4	2	no	—
251	C₂×SD₁₆	—	4	2	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
256	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
257	#127	—	2	1	no	—
258	#127	—	2	1	no	—
259	#127	—	2	1	no	—
260	#127	C₂×C₄×C₁₃₇	1	2	yes	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	—	2	1	no	—
263	C₄×Q₈	C₂×C₄×C₁₃₇	1	2	yes	—
264	C₄×Q₈	D₄×C₁₃₇	1	2	yes	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
272	C₄⋊C₈	—	2	4	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
278	C₄⋊C₈	D₄×C₁₃₇	1	2	yes	—
279	#103	—	4	2	no	—
280	#102	—	2	4	no	—
281	#102	—	4	2	no	—
282	#102	—	4	2	no	—
283	C₄×C₈	—	2	4	no	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	—	2	1	no	—
286	C₂⁴	—	4	1	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	C₂²⋊C₄×C₁₃₇	1	2	yes	—
291	C₂×Q₈	D₈×C₁₃₇	1	2	yes	—
292	C₂×Q₈	SD₁₆×C₁₃₇	1	2	yes	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	8	1	no	—
308	C₂×D₄	—	8	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
314	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
315	SD₁₆	—	4	8	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	SD₁₆×C₁₃₇	1	2	yes	complemented
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	8	1	no	—
339	C₄⋊C₄	C₂²⋊C₄×C₁₃₇	1	2	yes	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
343	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
344	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
345	C₄²	#41×C₁₃₇	1	1	yes	characteristic
346	C₂³	—	4	2	no	—
347	C₂³	—	8	1	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	8	1	no	—
350	C₂³	—	8	1	no	—
351	C₂³	—	8	1	no	—
352	C₂³	—	8	1	no	—
353	C₂³	#121×C₁₃₇	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	2	2	no	—
356	Q₈	—	2	2	no	—
357	Q₈	#102×C₁₃₇	1	4	yes	complemented
358	D₄	—	4	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	8	2	no	—
363	D₄	—	8	2	no	—
364	D₄	—	8	1	no	—
365	D₄	—	8	1	no	—
366	D₄	—	8	1	no	—
367	D₄	—	8	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	8	1	no	—
377	C₂×C₄	—	8	1	no	—
378	C₂×C₄	—	8	1	no	—
379	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
380	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
381	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
382	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
383	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
384	C₂×C₄	#123×C₁₃₇	1	1	yes	characteristic
385	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
386	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	1	yes	characteristic
387	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	1	yes	characteristic
388	C₂×C₄	#135×C₁₃₇	1	1	yes	characteristic
389	C₂×C₄	#135×C₁₃₇	1	1	yes	characteristic
390	C₂×C₄	#135×C₁₃₇	1	1	yes	characteristic
391	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
392	C₂×C₄	#137×C₁₃₇	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	4	2	no	—
395	C₈	—	4	1	no	—
396	C₈	—	4	2	no	—
397	C₈	—	8	1	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	16	1	no	—
402	C₂²	—	16	1	no	—
403	C₂²	—	16	1	no	—
404	C₂²	—	16	1	no	—
405	C₂²	#386×C₁₃₇	1	1	yes	characteristic
406	C₂²	#460×C₁₃₇	1	1	yes	characteristic
407	C₂²	#464×C₁₃₇	1	1	yes	characteristic
408	C₂²	#465×C₁₃₇	1	1	yes	characteristic
409	C₂²	#466×C₁₃₇	1	1	yes	characteristic
410	C₂²	#471×C₁₃₇	1	1	yes	characteristic
411	C₂²	#472×C₁₃₇	1	1	yes	characteristic
412	C₄	—	2	4	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	16	1	no	—
417	C₄	C₂×#102×C₁₃₇	1	1	yes	characteristic
418	C₄	#416×C₁₃₇	1	1	yes	characteristic
419	C₄	C₄×SD₁₆×C₁₃₇	1	1	yes	characteristic
420	C₄	#440×C₁₃₇	1	1	yes	characteristic
421	C₄	#448×C₁₃₇	1	1	yes	characteristic
422	C₄	#449×C₁₃₇	1	1	yes	characteristic
423	C₄	#465×C₁₃₇	1	1	yes	characteristic
424	C₄	#466×C₁₃₇	1	1	yes	characteristic
425	C₂	—	16	2	no	—
426	C₂	#1666×C₁₃₇	1	1	yes	characteristic
427	C₂	#1668×C₁₃₇	1	1	yes	characteristic
428	C₂	#1678×C₁₃₇	1	1	yes	characteristic
429	C₂	#1682×C₁₃₇	1	1	yes	characteristic
430	C₂	#1880×C₁₃₇	1	1	yes	characteristic
431	C₂	#1893×C₁₃₇	1	1	yes	characteristic
432	C₂	#1907×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₇	#121
commutator	C₄²	C₂²×C₄×C₁₃₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₇
prime radical	C₂×#127×C₁₃₇	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×Q₈×C₁₃₇	C₂	semidirect
4. #1803×C₁₃₇	C₂	semidirect
6. #1296×C₁₃₇	C₂	semidirect
7. #1277×C₁₃₇	C₂	semidirect
12. #460×C₁₃₇	C₄	semidirect
113. C₂×C₈×C₁₃₇	SD₁₆	semidirect
140. Q₈×C₁₃₇	#102	semidirect
216. #9222	C₁₃₇	direct (N × H)
217. C₁₃₇	#9222	direct (N × H)
219. C₂×C₈×Q₈	C₂×C₁₃₇	semidirect
221. #1803	C₂×C₁₃₇	semidirect
223. #1296	C₂×C₁₃₇	semidirect
224. #1277	C₂×C₁₃₇	semidirect
229. #460	C₄×C₁₃₇	semidirect
330. C₂×C₈	SD₁₆×C₁₃₇	semidirect
357. Q₈	#102×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#460×C₁₃₇	2
C₂×C₈×Q₈×C₁₃₇	2
#1957×C₁₃₇	2
#1803×C₁₃₇	2
C₂×#331×C₁₃₇	2
#1296×C₁₃₇	2
#1277×C₁₃₇	2
#9222	137

Subgroups — C137×#9222 #46858608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#9222 #46858608