Subgroups — C₁₃₇×#21400 #46870786

Order 35072.

1238 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2285×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1990×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1956×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1892×C₁₃₇	C₂	1	4	yes	maximal
7	C₄×#103×C₁₃₇	C₂	1	4	yes	maximal, complemented
8	C₂³×C₈×C₁₃₇	C₂²	1	2	yes	—
9	#533×C₁₃₇	—	2	4	no	—
10	#533×C₁₃₇	C₄	1	8	yes	complemented
11	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#125×C₁₃₇	—	2	1	no	—
14	C₂×C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃₇	—	2	1	no	—
17	C₂×C₄×Q₈×C₁₃₇	C₂²	1	2	yes	—
18	C₂×#117×C₁₃₇	—	2	1	no	—
19	C₂×#117×C₁₃₇	—	2	1	no	—
20	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×#103×C₁₃₇	C₂²	1	8	yes	—
22	C₂×C₄×C₈×C₁₃₇	—	2	4	no	—
23	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
25	#384×C₁₃₇	C₂²	1	2	yes	—
26	#382×C₁₃₇	—	2	1	no	—
27	#380×C₁₃₇	—	2	1	no	—
28	#380×C₁₃₇	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₁₃₇	—	2	1	no	—
30	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
31	#340×C₁₃₇	C₂²	1	8	yes	—
32	C₂²×Q₈×C₁₃₇	—	2	1	no	—
33	C₂²×Q₈×C₁₃₇	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₃₇	—	2	4	no	—
38	C₂²×C₈×C₁₃₇	—	2	8	no	—
39	C₂²×C₈×C₁₃₇	C₂³	1	4	yes	—
40	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
41	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
42	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	4	yes	—
43	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	4	yes	—
44	#125×C₁₃₇	—	2	8	no	—
45	C₂²⋊Q₈×C₁₃₇	—	2	8	no	—
46	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
47	C₂²⋊Q₈×C₁₃₇	C₂×C₄	1	8	yes	—
48	C₄×Q₈×C₁₃₇	—	2	8	no	—
49	C₄×Q₈×C₁₃₇	—	2	4	no	—
50	C₄×Q₈×C₁₃₇	C₂×C₄	1	8	yes	—
51	#117×C₁₃₇	—	2	8	no	—
52	#117×C₁₃₇	—	4	4	no	—
53	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
64	C₂×C₄²×C₁₃₇	—	2	2	no	—
65	C₂×C₄²×C₁₃₇	—	2	2	no	—
66	C₂×C₄²×C₁₃₇	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃₇	D₄	1	4	yes	—
70	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
72	#103×C₁₃₇	—	2	16	no	—
73	C₄×C₈×C₁₃₇	—	2	4	no	—
74	C₄×C₈×C₁₃₇	—	2	4	no	—
75	#95×C₁₃₇	—	2	2	no	—
76	#95×C₁₃₇	—	2	2	no	—
77	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
78	C₂×Q₈×C₁₃₇	—	2	4	no	—
79	C₂×Q₈×C₁₃₇	—	2	2	no	—
80	C₂×Q₈×C₁₃₇	—	2	8	no	—
81	C₂×Q₈×C₁₃₇	—	4	4	no	—
82	C₂×Q₈×C₁₃₇	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₁₃₇	—	2	4	no	—
84	C₂²×C₄×C₁₃₇	—	2	4	no	—
85	C₂²×C₄×C₁₃₇	—	2	2	no	—
86	C₂²×C₄×C₁₃₇	—	2	2	no	—
87	C₂²×C₄×C₁₃₇	—	2	4	no	—
88	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	4	yes	—
89	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	4	yes	—
90	C₂²×C₄×C₁₃₇	SD₁₆	1	4	yes	—
91	C₂²×C₄×C₁₃₇	Q₁₆	1	4	yes	—
92	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
100	C₂×C₈×C₁₃₇	—	2	16	no	—
101	C₂×C₈×C₁₃₇	—	2	4	no	—
102	C₂×C₈×C₁₃₇	—	2	4	no	—
103	C₂×C₈×C₁₃₇	#41	1	8	yes	—
104	C₄⋊C₄×C₁₃₇	—	2	4	no	—
105	C₄⋊C₄×C₁₃₇	—	2	4	no	—
106	C₄⋊C₄×C₁₃₇	—	2	4	no	—
107	C₄⋊C₄×C₁₃₇	—	2	8	no	—
108	C₄⋊C₄×C₁₃₇	—	2	8	no	—
109	C₄⋊C₄×C₁₃₇	—	2	2	no	—
110	C₄⋊C₄×C₁₃₇	—	2	8	no	—
111	C₄⋊C₄×C₁₃₇	—	4	4	no	—
112	C₄⋊C₄×C₁₃₇	—	4	4	no	—
113	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
114	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
115	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
116	C₄²×C₁₃₇	—	2	8	no	—
117	C₄²×C₁₃₇	—	4	4	no	—
118	C₄²×C₁₃₇	C₂²⋊C₄	1	4	yes	—
119	C₄²×C₁₃₇	C₂²⋊C₄	1	4	yes	—
120	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
121	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
122	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
123	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
124	C₂³×C₁₃₇	—	2	2	no	—
125	C₂³×C₁₃₇	—	2	2	no	—
126	C₂³×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
127	C₂³×C₁₃₇	C₂×SD₁₆	1	2	yes	—
128	C₂³×C₁₃₇	C₂×Q₁₆	1	2	yes	—
129	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
130	Q₈×C₁₃₇	—	2	8	no	—
131	Q₈×C₁₃₇	—	4	4	no	—
132	Q₈×C₁₃₇	—	4	8	no	—
133	C₂×C₄×C₁₃₇	—	2	2	no	—
134	C₂×C₄×C₁₃₇	—	2	2	no	—
135	C₂×C₄×C₁₃₇	—	2	4	no	—
136	C₂×C₄×C₁₃₇	—	2	4	no	—
137	C₂×C₄×C₁₃₇	—	2	8	no	—
138	C₂×C₄×C₁₃₇	—	2	4	no	—
139	C₂×C₄×C₁₃₇	—	2	4	no	—
140	C₂×C₄×C₁₃₇	—	4	4	no	—
141	C₂×C₄×C₁₃₇	—	4	4	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	#103	1	16	yes	complemented
146	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
147	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
148	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	2	yes	—
152	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	2	yes	—
153	C₂×C₄×C₁₃₇	C₂×Q₁₆	1	2	yes	—
154	C₂×C₄×C₁₃₇	C₂×Q₁₆	1	2	yes	—
155	C₂×C₄×C₁₃₇	#135	1	4	yes	—
156	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃₇	C₂×#41	1	4	yes	—
159	C₈×C₁₃₇	—	2	8	no	—
160	C₂²×C₁₃₇	—	2	2	no	—
161	C₂²×C₁₃₇	—	2	4	no	—
162	C₂²×C₁₃₇	—	2	4	no	—
163	C₂²×C₁₃₇	—	2	2	no	—
164	C₂²×C₁₃₇	C₂×#103	1	4	yes	—
165	C₂²×C₁₃₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
166	C₂²×C₁₃₇	#532	1	2	yes	—
167	C₂²×C₁₃₇	C₂²×SD₁₆	1	1	yes	characteristic
168	C₂²×C₁₃₇	C₂²×Q₁₆	1	1	yes	characteristic
169	C₂²×C₁₃₇	C₂×#135	1	2	yes	—
170	C₄×C₁₃₇	—	2	2	no	—
171	C₄×C₁₃₇	—	2	2	no	—
172	C₄×C₁₃₇	—	4	4	no	—
173	C₄×C₁₃₇	—	4	4	no	—
174	C₄×C₁₃₇	—	8	4	no	—
175	C₄×C₁₃₇	C₂×#103	1	4	yes	—
176	C₄×C₁₃₇	C₂×#103	1	4	yes	—
177	C₄×C₁₃₇	#416	1	4	yes	—
178	C₄×C₁₃₇	C₄×#41	1	2	yes	—
179	C₄×C₁₃₇	#525	1	2	yes	—
180	C₂×C₁₃₇	—	2	4	no	—
181	C₂×C₁₃₇	#2297	1	1	yes	characteristic
182	C₂×C₁₃₇	C₂²×#103	1	1	yes	characteristic
183	C₂×C₁₃₇	C₂×#416	1	1	yes	characteristic
184	C₂×C₁₃₇	#3167	1	2	yes	—
185	C₂×C₁₃₇	#3170	1	2	yes	—
186	#21400	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₁₃₇	#21400	1	1	yes	characteristic, direct product factor, Sylow
188	C₂×#533	C₂×C₁₃₇	1	1	yes	characteristic
189	C₂²×C₄×C₈	C₂×C₁₃₇	1	1	yes	characteristic
190	#2285	C₂×C₁₃₇	1	1	yes	characteristic
191	#1990	C₂×C₁₃₇	1	2	yes	complemented
192	#1956	C₂×C₁₃₇	1	2	yes	complemented
193	#1892	C₂×C₁₃₇	1	4	yes	—
194	C₄×#103	C₂×C₁₃₇	1	4	yes	complemented
195	C₂³×C₈	C₂²×C₁₃₇	1	2	yes	—
196	#533	—	2	4	no	—
197	#533	C₄×C₁₃₇	1	8	yes	complemented
198	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
199	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
200	C₂×#125	—	2	1	no	—
201	C₂×C₂²⋊Q₈	—	2	1	no	—
202	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
203	C₂×C₄×Q₈	—	2	1	no	—
204	C₂×C₄×Q₈	C₂²×C₁₃₇	1	2	yes	—
205	C₂×#117	—	2	1	no	—
206	C₂×#117	—	2	1	no	—
207	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
208	C₂×#103	C₂²×C₁₃₇	1	8	yes	—
209	C₂×C₄×C₈	—	2	4	no	—
210	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
211	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
212	#384	C₂²×C₁₃₇	1	2	yes	—
213	#382	—	2	1	no	—
214	#380	—	2	1	no	—
215	#380	C₂²×C₁₃₇	1	2	yes	—
216	C₄×C₄⋊C₄	—	2	1	no	—
217	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
218	#340	C₂²×C₁₃₇	1	8	yes	—
219	C₂²×Q₈	—	2	1	no	—
220	C₂²×Q₈	C₂³×C₁₃₇	1	2	yes	—
221	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
222	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
223	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
224	C₂²×C₈	—	2	4	no	—
225	C₂²×C₈	—	2	8	no	—
226	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
227	C₄⋊Q₈	—	2	2	no	—
228	C₄⋊Q₈	—	2	2	no	—
229	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	4	yes	—
230	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	4	yes	—
231	#125	—	2	8	no	—
232	C₂²⋊Q₈	—	2	8	no	—
233	C₂²⋊Q₈	—	2	4	no	—
234	C₂²⋊Q₈	C₂×C₄×C₁₃₇	1	8	yes	—
235	C₄×Q₈	—	2	8	no	—
236	C₄×Q₈	—	2	4	no	—
237	C₄×Q₈	C₂×C₄×C₁₃₇	1	8	yes	—
238	#117	—	2	8	no	—
239	#117	—	4	4	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
248	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	C₂×C₄×C₁₃₇	1	4	yes	—
254	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
255	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
256	C₂×C₄²	D₄×C₁₃₇	1	4	yes	—
257	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
259	#103	—	2	16	no	—
260	C₄×C₈	—	2	4	no	—
261	C₄×C₈	—	2	4	no	—
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	8	no	—
268	C₂×Q₈	—	4	4	no	—
269	C₂×Q₈	C₂²×C₄×C₁₃₇	1	4	yes	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	4	yes	—
276	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	4	yes	—
277	C₂²×C₄	SD₁₆×C₁₃₇	1	4	yes	—
278	C₂²×C₄	Q₁₆×C₁₃₇	1	4	yes	—
279	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
280	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
286	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
287	C₂×C₈	—	2	16	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	#41×C₁₃₇	1	8	yes	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	8	no	—
298	C₄⋊C₄	—	4	4	no	—
299	C₄⋊C₄	—	4	4	no	—
300	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
301	C₂²⋊C₄	—	2	8	no	—
302	C₂²⋊C₄	—	4	4	no	—
303	C₄²	—	2	8	no	—
304	C₄²	—	4	4	no	—
305	C₄²	C₂²⋊C₄×C₁₃₇	1	4	yes	—
306	C₄²	C₂²⋊C₄×C₁₃₇	1	4	yes	—
307	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
308	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
309	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
310	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
314	C₂³	C₂×SD₁₆×C₁₃₇	1	2	yes	—
315	C₂³	C₂×Q₁₆×C₁₃₇	1	2	yes	—
316	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
317	Q₈	—	2	8	no	—
318	Q₈	—	4	8	no	—
319	Q₈	—	4	4	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	#103×C₁₃₇	1	16	yes	complemented
333	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
334	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
335	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
338	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	2	yes	—
339	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	2	yes	—
340	C₂×C₄	C₂×Q₁₆×C₁₃₇	1	2	yes	—
341	C₂×C₄	C₂×Q₁₆×C₁₃₇	1	2	yes	—
342	C₂×C₄	#135×C₁₃₇	1	4	yes	—
343	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
345	C₂×C₄	C₂×#41×C₁₃₇	1	4	yes	—
346	C₈	—	2	8	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	2	4	no	—
351	C₂²	C₂×#103×C₁₃₇	1	4	yes	—
352	C₂²	C₂²×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
353	C₂²	#532×C₁₃₇	1	2	yes	—
354	C₂²	C₂²×SD₁₆×C₁₃₇	1	1	yes	characteristic
355	C₂²	C₂²×Q₁₆×C₁₃₇	1	1	yes	characteristic
356	C₂²	C₂×#135×C₁₃₇	1	2	yes	—
357	C₄	—	2	2	no	—
358	C₄	—	2	2	no	—
359	C₄	—	4	4	no	—
360	C₄	—	4	4	no	—
361	C₄	—	8	4	no	—
362	C₄	C₂×#103×C₁₃₇	1	4	yes	—
363	C₄	C₂×#103×C₁₃₇	1	4	yes	—
364	C₄	#416×C₁₃₇	1	4	yes	—
365	C₄	C₄×#41×C₁₃₇	1	2	yes	—
366	C₄	#525×C₁₃₇	1	2	yes	—
367	C₂	—	2	4	no	—
368	C₂	#2297×C₁₃₇	1	1	yes	characteristic
369	C₂	C₂²×#103×C₁₃₇	1	1	yes	characteristic
370	C₂	C₂×#416×C₁₃₇	1	1	yes	characteristic
371	C₂	#3167×C₁₃₇	1	2	yes	—
372	C₂	#3170×C₁₃₇	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. #1990×C₁₃₇	C₂	semidirect
5. #1956×C₁₃₇	C₂	semidirect
7. C₄×#103×C₁₃₇	C₂	semidirect
10. #533×C₁₃₇	C₄	semidirect
145. C₂×C₄×C₁₃₇	#103	semidirect
186. #21400	C₁₃₇	direct (N × H)
187. C₁₃₇	#21400	direct (N × H)
191. #1990	C₂×C₁₃₇	semidirect
192. #1956	C₂×C₁₃₇	semidirect
194. C₄×#103	C₂×C₁₃₇	semidirect
197. #533	C₄×C₁₃₇	semidirect
332. C₂×C₄	#103×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₁₃₇	2
C₂²×C₄×C₈×C₁₃₇	2
#2285×C₁₃₇	2
#1990×C₁₃₇	2
#1956×C₁₃₇	2
#1892×C₁₃₇	2
C₄×#103×C₁₃₇	2
#21400	137

Subgroups — C137×#21400 #46870786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21400 #46870786