Subgroups — C₁₃₇×#25834 #46875220

Order 35072.

1246 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#498×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#476×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2567×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2058×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1988×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1984×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1864×C₁₃₇	C₂	1	4	yes	maximal
9	C₄×#102×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₃₇	—	2	1	no	—
11	D₄×Q₈×C₁₃₇	—	2	4	no	—
12	D₄×Q₈×C₁₃₇	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	2	yes	—
15	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
18	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
21	#498×C₁₃₇	—	2	4	no	—
22	#476×C₁₃₇	—	2	4	no	—
23	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
24	C₂×#106×C₁₃₇	C₂²	1	4	yes	—
25	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
26	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
27	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
29	#395×C₁₃₇	—	2	2	no	—
30	#391×C₁₃₇	—	2	1	no	—
31	#389×C₁₃₇	C₂²	1	4	yes	—
32	#384×C₁₃₇	—	2	1	no	—
33	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
34	#340×C₁₃₇	C₂²	1	2	yes	—
35	#340×C₁₃₇	C₂²	1	4	yes	—
36	#336×C₁₃₇	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₃₇	—	2	8	no	—
38	C₂²×Q₈×C₁₃₇	—	2	2	no	—
39	C₂²×Q₈×C₁₃₇	—	2	1	no	—
40	C₂²×Q₈×C₁₃₇	—	2	1	no	—
41	C₂²×Q₈×C₁₃₇	—	4	4	no	—
42	C₂²×Q₈×C₁₃₇	—	4	4	no	—
43	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃₇	—	2	2	no	—
46	C₂³×C₄×C₁₃₇	—	2	1	no	—
47	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
50	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
51	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
52	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
53	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
54	C₄⋊Q₈×C₁₃₇	D₄	1	4	yes	—
55	C₂²⋊Q₈×C₁₃₇	—	2	8	no	—
56	C₂²⋊Q₈×C₁₃₇	—	2	16	no	—
57	C₄×Q₈×C₁₃₇	—	2	2	no	—
58	C₄×Q₈×C₁₃₇	—	2	2	no	—
59	C₄×D₄×C₁₃₇	—	2	4	no	—
60	C₄×D₄×C₁₃₇	—	2	4	no	—
61	C₄×D₄×C₁₃₇	—	2	2	no	—
62	C₄×D₄×C₁₃₇	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
67	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
75	C₂×C₄²×C₁₃₇	—	2	1	no	—
76	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
78	#106×C₁₃₇	—	2	4	no	—
79	#106×C₁₃₇	—	2	8	no	—
80	C₄⋊C₈×C₁₃₇	—	2	2	no	—
81	#102×C₁₃₇	—	2	4	no	—
82	#102×C₁₃₇	Q₈	1	8	yes	complemented
83	C₄×C₈×C₁₃₇	—	2	2	no	—
84	#95×C₁₃₇	—	2	1	no	—
85	#95×C₁₃₇	—	2	4	no	—
86	C₂⁴×C₁₃₇	—	2	1	no	—
87	C₂×Q₈×C₁₃₇	—	2	8	no	—
88	C₂×Q₈×C₁₃₇	—	2	2	no	—
89	C₂×Q₈×C₁₃₇	—	2	4	no	—
90	C₂×Q₈×C₁₃₇	—	2	2	no	—
91	C₂×Q₈×C₁₃₇	—	4	4	no	—
92	C₂×Q₈×C₁₃₇	—	4	32	no	—
93	C₂×Q₈×C₁₃₇	—	4	2	no	—
94	C₂×Q₈×C₁₃₇	—	4	4	no	—
95	C₂×Q₈×C₁₃₇	—	4	2	no	—
96	C₂×Q₈×C₁₃₇	—	4	2	no	—
97	C₂×Q₈×C₁₃₇	—	8	2	no	—
98	C₂×Q₈×C₁₃₇	SD₁₆	1	4	yes	—
99	C₂×D₄×C₁₃₇	—	2	1	no	—
100	C₂×D₄×C₁₃₇	—	2	2	no	—
101	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
102	C₂×D₄×C₁₃₇	C₂×Q₈	1	4	yes	—
103	C₂²×C₄×C₁₃₇	—	2	8	no	—
104	C₂²×C₄×C₁₃₇	—	2	2	no	—
105	C₂²×C₄×C₁₃₇	—	2	2	no	—
106	C₂²×C₄×C₁₃₇	—	2	1	no	—
107	C₂²×C₄×C₁₃₇	—	2	4	no	—
108	C₂²×C₄×C₁₃₇	—	2	2	no	—
109	C₂²×C₄×C₁₃₇	—	4	4	no	—
110	C₂²×C₄×C₁₃₇	—	4	4	no	—
111	C₂²×C₄×C₁₃₇	—	4	2	no	—
112	C₂²×C₄×C₁₃₇	—	4	2	no	—
113	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
118	C₂×C₈×C₁₃₇	—	2	2	no	—
119	C₂×C₈×C₁₃₇	—	2	2	no	—
120	C₂×C₈×C₁₃₇	—	2	2	no	—
121	C₂×C₈×C₁₃₇	—	2	4	no	—
122	C₂×C₈×C₁₃₇	C₂×Q₈	1	4	yes	complemented
123	C₄⋊C₄×C₁₃₇	—	2	8	no	—
124	C₄⋊C₄×C₁₃₇	—	2	4	no	—
125	C₄⋊C₄×C₁₃₇	—	2	4	no	—
126	C₄⋊C₄×C₁₃₇	—	2	2	no	—
127	C₄⋊C₄×C₁₃₇	—	2	2	no	—
128	C₄⋊C₄×C₁₃₇	—	2	1	no	—
129	C₄⋊C₄×C₁₃₇	—	2	2	no	—
130	C₄⋊C₄×C₁₃₇	—	2	2	no	—
131	C₄⋊C₄×C₁₃₇	—	2	2	no	—
132	C₄⋊C₄×C₁₃₇	—	4	2	no	—
133	C₄⋊C₄×C₁₃₇	—	8	4	no	—
134	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
135	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₁₃₇	C₂×Q₈	1	4	yes	complemented
137	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
138	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
139	C₄²×C₁₃₇	—	2	2	no	—
140	C₄²×C₁₃₇	—	2	2	no	—
141	C₄²×C₁₃₇	—	4	2	no	—
142	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
143	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
144	C₂³×C₁₃₇	—	2	2	no	—
145	C₂³×C₁₃₇	—	2	4	no	—
146	C₂³×C₁₃₇	—	4	1	no	—
147	C₂³×C₁₃₇	—	4	1	no	—
148	C₂³×C₁₃₇	—	4	2	no	—
149	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₁₃₇	—	2	8	no	—
151	Q₈×C₁₃₇	—	4	16	no	—
152	Q₈×C₁₃₇	—	4	8	no	—
153	Q₈×C₁₃₇	—	8	4	no	—
154	D₄×C₁₃₇	—	2	2	no	—
155	D₄×C₁₃₇	—	2	4	no	—
156	D₄×C₁₃₇	C₄⋊Q₈	1	4	yes	—
157	C₂×C₄×C₁₃₇	—	2	2	no	—
158	C₂×C₄×C₁₃₇	—	2	2	no	—
159	C₂×C₄×C₁₃₇	—	2	2	no	—
160	C₂×C₄×C₁₃₇	—	2	2	no	—
161	C₂×C₄×C₁₃₇	—	2	4	no	—
162	C₂×C₄×C₁₃₇	—	2	2	no	—
163	C₂×C₄×C₁₃₇	—	2	4	no	—
164	C₂×C₄×C₁₃₇	—	2	4	no	—
165	C₂×C₄×C₁₃₇	—	4	16	no	—
166	C₂×C₄×C₁₃₇	—	4	2	no	—
167	C₂×C₄×C₁₃₇	—	4	1	no	—
168	C₂×C₄×C₁₃₇	—	4	2	no	—
169	C₂×C₄×C₁₃₇	—	4	2	no	—
170	C₂×C₄×C₁₃₇	—	4	1	no	—
171	C₂×C₄×C₁₃₇	—	4	2	no	—
172	C₂×C₄×C₁₃₇	—	4	8	no	—
173	C₂×C₄×C₁₃₇	—	4	2	no	—
174	C₂×C₄×C₁₃₇	—	4	4	no	—
175	C₂×C₄×C₁₃₇	#120	1	2	yes	—
176	C₂×C₄×C₁₃₇	#120	1	2	yes	—
177	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	4	yes	—
178	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	2	yes	—
179	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
180	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃₇	C₂²×Q₈	1	2	yes	—
183	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
184	C₈×C₁₃₇	—	2	4	no	—
185	C₈×C₁₃₇	—	4	2	no	—
186	C₂²×C₁₃₇	—	2	4	no	—
187	C₂²×C₁₃₇	—	4	4	no	—
188	C₂²×C₁₃₇	—	4	4	no	—
189	C₂²×C₁₃₇	—	4	2	no	—
190	C₂²×C₁₃₇	—	4	2	no	—
191	C₂²×C₁₃₇	C₂×#120	1	1	yes	characteristic
192	C₂²×C₁₃₇	D₄×Q₈	1	2	yes	—
193	C₂²×C₁₃₇	C₂²×SD₁₆	1	1	yes	characteristic
194	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂²×C₁₃₇	#577	1	2	yes	—
196	C₄×C₁₃₇	—	2	4	no	—
197	C₄×C₁₃₇	—	2	2	no	—
198	C₄×C₁₃₇	—	4	4	no	—
199	C₄×C₁₃₇	—	4	4	no	—
200	C₄×C₁₃₇	—	4	2	no	—
201	C₄×C₁₃₇	—	4	2	no	—
202	C₄×C₁₃₇	—	8	2	no	—
203	C₄×C₁₃₇	#450	1	4	yes	—
204	C₄×C₁₃₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
205	C₄×C₁₃₇	#536	1	1	yes	characteristic
206	C₄×C₁₃₇	D₄×Q₈	1	2	yes	—
207	C₂×C₁₃₇	—	4	4	no	—
208	C₂×C₁₃₇	#2434	1	1	yes	characteristic
209	C₂×C₁₃₇	C₂×#450	1	1	yes	characteristic
210	C₂×C₁₃₇	#3010	1	1	yes	characteristic
211	C₂×C₁₃₇	Q₈×SD₁₆	1	2	yes	—
212	C₂×C₁₃₇	#3384	1	2	yes	—
213	#25834	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₁₃₇	#25834	1	1	yes	characteristic, direct product factor, Sylow
215	C₂×D₄×Q₈	C₂×C₁₃₇	1	1	yes	characteristic
216	C₂×#498	C₂×C₁₃₇	1	1	yes	characteristic, complemented
217	C₂×#476	C₂×C₁₃₇	1	1	yes	characteristic
218	#2567	C₂×C₁₃₇	1	1	yes	characteristic, complemented
219	#2058	C₂×C₁₃₇	1	4	yes	complemented
220	#1988	C₂×C₁₃₇	1	1	yes	characteristic, complemented
221	#1984	C₂×C₁₃₇	1	1	yes	characteristic, complemented
222	#1864	C₂×C₁₃₇	1	4	yes	—
223	C₄×#102	C₂×C₁₃₇	1	1	yes	characteristic
224	C₂³×Q₈	—	2	1	no	—
225	D₄×Q₈	—	2	4	no	—
226	D₄×Q₈	—	2	4	no	—
227	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
228	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
229	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
230	C₂×C₂²⋊Q₈	—	2	1	no	—
231	C₂×C₂²⋊Q₈	—	2	2	no	—
232	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
233	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
234	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
235	#498	—	2	4	no	—
236	#476	—	2	4	no	—
237	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
238	C₂×#106	C₂²×C₁₃₇	1	4	yes	—
239	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
240	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
241	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
242	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
243	#395	—	2	2	no	—
244	#391	—	2	1	no	—
245	#389	C₂²×C₁₃₇	1	4	yes	—
246	#384	—	2	1	no	—
247	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
248	#340	C₂²×C₁₃₇	1	2	yes	—
249	#340	C₂²×C₁₃₇	1	4	yes	—
250	#336	C₂²×C₁₃₇	1	4	yes	—
251	C₂²×Q₈	—	2	8	no	—
252	C₂²×Q₈	—	2	2	no	—
253	C₂²×Q₈	—	2	1	no	—
254	C₂²×Q₈	—	2	1	no	—
255	C₂²×Q₈	—	4	4	no	—
256	C₂²×Q₈	—	4	4	no	—
257	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
258	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
259	C₂³×C₄	—	2	2	no	—
260	C₂³×C₄	—	2	1	no	—
261	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
262	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
263	C₄⋊Q₈	—	2	4	no	—
264	C₄⋊Q₈	—	2	4	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	C₄⋊Q₈	—	2	2	no	—
267	C₄⋊Q₈	—	2	2	no	—
268	C₄⋊Q₈	D₄×C₁₃₇	1	4	yes	—
269	C₂²⋊Q₈	—	2	8	no	—
270	C₂²⋊Q₈	—	2	16	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	D₄×C₁₃₇	1	4	yes	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	4	no	—
281	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
282	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
291	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
292	#106	—	2	4	no	—
293	#106	—	2	8	no	—
294	C₄⋊C₈	—	2	2	no	—
295	#102	—	2	4	no	—
296	#102	Q₈×C₁₃₇	1	8	yes	complemented
297	C₄×C₈	—	2	2	no	—
298	#95	—	2	1	no	—
299	#95	—	2	4	no	—
300	C₂⁴	—	2	1	no	—
301	C₂×Q₈	—	2	8	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	4	4	no	—
306	C₂×Q₈	—	4	32	no	—
307	C₂×Q₈	—	4	2	no	—
308	C₂×Q₈	—	4	4	no	—
309	C₂×Q₈	—	4	2	no	—
310	C₂×Q₈	—	4	2	no	—
311	C₂×Q₈	—	8	2	no	—
312	C₂×Q₈	SD₁₆×C₁₃₇	1	4	yes	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
316	C₂×D₄	C₂×Q₈×C₁₃₇	1	4	yes	—
317	C₂²×C₄	—	2	8	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	4	4	no	—
324	C₂²×C₄	—	4	4	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
331	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	4	no	—
336	C₂×C₈	C₂×Q₈×C₁₃₇	1	4	yes	complemented
337	C₄⋊C₄	—	2	8	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	8	4	no	—
348	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
349	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
350	C₄⋊C₄	C₂×Q₈×C₁₃₇	1	4	yes	complemented
351	C₂²⋊C₄	—	2	8	no	—
352	C₂²⋊C₄	—	2	4	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	4	2	no	—
356	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
357	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	2	no	—
363	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
364	Q₈	—	2	8	no	—
365	Q₈	—	4	16	no	—
366	Q₈	—	4	8	no	—
367	Q₈	—	8	4	no	—
368	D₄	—	2	2	no	—
369	D₄	—	2	4	no	—
370	D₄	C₄⋊Q₈×C₁₃₇	1	4	yes	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	4	16	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	8	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	#120×C₁₃₇	1	2	yes	—
390	C₂×C₄	#120×C₁₃₇	1	2	yes	—
391	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	4	yes	—
392	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	2	yes	—
393	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
394	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
396	C₂×C₄	C₂²×Q₈×C₁₃₇	1	2	yes	—
397	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
398	C₈	—	2	4	no	—
399	C₈	—	4	2	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	C₂×#120×C₁₃₇	1	1	yes	characteristic
406	C₂²	D₄×Q₈×C₁₃₇	1	2	yes	—
407	C₂²	C₂²×SD₁₆×C₁₃₇	1	1	yes	characteristic
408	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
409	C₂²	#577×C₁₃₇	1	2	yes	—
410	C₄	—	2	4	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	4	no	—
413	C₄	—	4	4	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	8	2	no	—
417	C₄	#450×C₁₃₇	1	4	yes	—
418	C₄	C₂×C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
419	C₄	#536×C₁₃₇	1	1	yes	characteristic
420	C₄	D₄×Q₈×C₁₃₇	1	2	yes	—
421	C₂	—	4	4	no	—
422	C₂	#2434×C₁₃₇	1	1	yes	characteristic
423	C₂	C₂×#450×C₁₃₇	1	1	yes	characteristic
424	C₂	#3010×C₁₃₇	1	1	yes	characteristic
425	C₂	Q₈×SD₁₆×C₁₃₇	1	2	yes	—
426	C₂	#3384×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂²×D₄×C₁₃₇	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂×C₄×Q₈×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#498×C₁₃₇	C₂	semidirect
4. #2567×C₁₃₇	C₂	semidirect
5. #2058×C₁₃₇	C₂	semidirect
6. #1988×C₁₃₇	C₂	semidirect
7. #1984×C₁₃₇	C₂	semidirect
82. #102×C₁₃₇	Q₈	semidirect
122. C₂×C₈×C₁₃₇	C₂×Q₈	semidirect
136. C₄⋊C₄×C₁₃₇	C₂×Q₈	semidirect
213. #25834	C₁₃₇	direct (N × H)
214. C₁₃₇	#25834	direct (N × H)
216. C₂×#498	C₂×C₁₃₇	semidirect
218. #2567	C₂×C₁₃₇	semidirect
219. #2058	C₂×C₁₃₇	semidirect
220. #1988	C₂×C₁₃₇	semidirect
221. #1984	C₂×C₁₃₇	semidirect
296. #102	Q₈×C₁₃₇	semidirect
336. C₂×C₈	C₂×Q₈×C₁₃₇	semidirect
350. C₄⋊C₄	C₂×Q₈×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₁₃₇	2
C₂×#498×C₁₃₇	2
C₂×#476×C₁₃₇	2
#2567×C₁₃₇	2
#2058×C₁₃₇	2
#1988×C₁₃₇	2
#1984×C₁₃₇	2
#1864×C₁₃₇	2
C₄×#102×C₁₃₇	2
#25834	137

Subgroups — C137×#25834 #46875220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#25834 #46875220