Subgroups — C₁₃₇×#7974 #46857360

Order 35072.

648 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2920×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2283×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1288×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₁₃₇	—	2	1	no	—
6	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
7	#432×C₁₃₇	C₄	1	2	yes	complemented
8	#432×C₁₃₇	C₂²	1	2	yes	—
9	#431×C₁₃₇	—	2	1	no	—
10	#431×C₁₃₇	—	2	1	no	—
11	#423×C₁₃₇	—	2	1	no	—
12	#407×C₁₃₇	—	2	1	no	—
13	C₄×M₁₆×C₁₃₇	—	2	1	no	—
14	C₄×M₁₆×C₁₃₇	—	2	1	no	—
15	C₄×M₁₆×C₁₃₇	C₄	1	2	yes	complemented
16	C₄×M₁₆×C₁₃₇	C₄	1	2	yes	complemented
17	C₄×M₁₆×C₁₃₇	C₂²	1	2	yes	—
18	C₂×#97×C₁₃₇	—	2	1	no	—
19	C₂×C₄×C₈×C₁₃₇	C₄	1	2	yes	complemented
20	#383×C₁₃₇	C₂²	1	2	yes	—
21	#382×C₁₃₇	C₄	1	2	yes	—
22	#381×C₁₃₇	—	2	1	no	—
23	#380×C₁₃₇	—	2	1	no	—
24	C₄×C₄⋊C₄×C₁₃₇	—	2	1	no	—
25	C₄×C₂²⋊C₄×C₁₃₇	C₄	1	2	yes	—
26	#376×C₁₃₇	—	2	1	no	—
27	C₂³×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₁₃₇	—	2	8	no	—
31	C₂×M₁₆×C₁₃₇	—	2	2	no	—
32	C₂×M₁₆×C₁₃₇	—	2	2	no	—
33	C₂×M₁₆×C₁₃₇	—	2	2	no	—
34	C₂²×C₈×C₁₃₇	—	2	2	no	—
35	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
36	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
37	C₂×C₄²×C₁₃₇	—	2	2	no	—
38	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃₇	Q₈	1	1	yes	characteristic
48	C₂×C₄²×C₁₃₇	Q₈	1	1	yes	characteristic
49	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
50	C₄⋊C₈×C₁₃₇	—	2	2	no	—
51	C₄⋊C₈×C₁₃₇	—	2	2	no	—
52	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
53	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
54	#97×C₁₃₇	—	2	2	no	—
55	#97×C₁₃₇	—	2	2	no	—
56	#97×C₁₃₇	C₂×C₄	1	4	yes	—
57	C₄×C₈×C₁₃₇	—	2	2	no	—
58	C₄×C₈×C₁₃₇	—	2	2	no	—
59	C₄×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
60	#95×C₁₃₇	—	2	2	no	—
61	#95×C₁₃₇	—	2	2	no	—
62	#95×C₁₃₇	—	2	2	no	—
63	#95×C₁₃₇	C₂×C₄	1	4	yes	—
64	C₂⁴×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₃₇	—	2	4	no	—
66	C₂²×C₄×C₁₃₇	—	2	4	no	—
67	C₂²×C₄×C₁₃₇	—	4	2	no	—
68	C₂²×C₄×C₁₃₇	—	4	2	no	—
69	C₂²×C₄×C₁₃₇	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₁₃₇	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
87	M₁₆×C₁₃₇	—	2	8	no	—
88	M₁₆×C₁₃₇	—	2	8	no	—
89	M₁₆×C₁₃₇	—	4	4	no	—
90	C₂×C₈×C₁₃₇	—	2	8	no	—
91	C₂×C₈×C₁₃₇	—	2	4	no	—
92	C₂×C₈×C₁₃₇	—	2	4	no	—
93	C₄⋊C₄×C₁₃₇	—	4	4	no	—
94	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
95	C₄²×C₁₃₇	—	4	4	no	—
96	C₄²×C₁₃₇	C₄²	1	1	yes	characteristic
97	C₄²×C₁₃₇	C₄²	1	1	yes	characteristic
98	C₄²×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
112	C₂³×C₁₃₇	—	2	2	no	—
113	C₂³×C₁₃₇	—	2	2	no	—
114	C₂³×C₁₃₇	—	4	1	no	—
115	C₂³×C₁₃₇	#95	1	1	yes	characteristic
116	C₂³×C₁₃₇	#95	1	1	yes	characteristic
117	C₂³×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₃₇	—	2	2	no	—
119	C₂×C₄×C₁₃₇	—	2	2	no	—
120	C₂×C₄×C₁₃₇	—	2	2	no	—
121	C₂×C₄×C₁₃₇	—	2	2	no	—
122	C₂×C₄×C₁₃₇	—	2	2	no	—
123	C₂×C₄×C₁₃₇	—	2	2	no	—
124	C₂×C₄×C₁₃₇	—	2	2	no	—
125	C₂×C₄×C₁₃₇	—	2	2	no	—
126	C₂×C₄×C₁₃₇	—	2	2	no	—
127	C₂×C₄×C₁₃₇	—	2	2	no	—
128	C₂×C₄×C₁₃₇	—	4	1	no	—
129	C₂×C₄×C₁₃₇	—	4	1	no	—
130	C₂×C₄×C₁₃₇	—	4	1	no	—
131	C₂×C₄×C₁₃₇	—	4	1	no	—
132	C₂×C₄×C₁₃₇	—	4	1	no	—
133	C₂×C₄×C₁₃₇	—	4	1	no	—
134	C₂×C₄×C₁₃₇	—	4	1	no	—
135	C₂×C₄×C₁₃₇	—	4	4	no	—
136	C₂×C₄×C₁₃₇	—	4	4	no	—
137	C₂×C₄×C₁₃₇	—	4	4	no	—
138	C₂×C₄×C₁₃₇	#95	1	1	yes	characteristic
139	C₂×C₄×C₁₃₇	#95	1	1	yes	characteristic
140	C₂×C₄×C₁₃₇	#95	1	1	yes	characteristic
141	C₂×C₄×C₁₃₇	#95	1	1	yes	characteristic
142	C₂×C₄×C₁₃₇	#95	1	1	yes	characteristic
143	C₂×C₄×C₁₃₇	#95	1	1	yes	characteristic
144	C₂×C₄×C₁₃₇	#104	1	4	yes	—
145	C₂×C₄×C₁₃₇	C₂×C₄²	1	1	yes	characteristic
146	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₈×C₁₃₇	—	2	8	no	—
152	C₈×C₁₃₇	—	4	4	no	—
153	C₂²×C₁₃₇	—	2	1	no	—
154	C₂²×C₁₃₇	—	2	1	no	—
155	C₂²×C₁₃₇	—	2	1	no	—
156	C₂²×C₁₃₇	—	2	1	no	—
157	C₂²×C₁₃₇	—	2	1	no	—
158	C₂²×C₁₃₇	—	2	1	no	—
159	C₂²×C₁₃₇	—	2	1	no	—
160	C₂²×C₁₃₇	—	4	4	no	—
161	C₂²×C₁₃₇	H(3,ℤ/4)	1	2	yes	—
162	C₂²×C₁₃₇	C₂×#95	1	1	yes	characteristic
163	C₂²×C₁₃₇	C₂×#104	1	2	yes	—
164	C₄×C₁₃₇	—	2	1	no	—
165	C₄×C₁₃₇	—	2	1	no	—
166	C₄×C₁₃₇	—	2	1	no	—
167	C₄×C₁₃₇	—	2	1	no	—
168	C₄×C₁₃₇	—	2	1	no	—
169	C₄×C₁₃₇	—	2	1	no	—
170	C₄×C₁₃₇	—	2	1	no	—
171	C₄×C₁₃₇	—	2	1	no	—
172	C₄×C₁₃₇	—	2	1	no	—
173	C₄×C₁₃₇	—	8	4	no	—
174	C₄×C₁₃₇	#339	1	2	yes	—
175	C₄×C₁₃₇	#339	1	2	yes	—
176	C₄×C₁₃₇	#344	1	2	yes	—
177	C₂×C₁₃₇	—	2	2	no	—
178	C₂×C₁₃₇	—	2	2	no	—
179	C₂×C₁₃₇	—	4	1	no	—
180	C₂×C₁₃₇	C₂×H(3,ℤ/4)	1	1	yes	characteristic
181	C₂×C₁₃₇	C₂×#339	1	1	yes	characteristic
182	C₂×C₁₃₇	C₂×#344	1	1	yes	characteristic
183	#7974	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₁₃₇	#7974	1	1	yes	characteristic, direct product factor, Sylow
185	#2920	C₂×C₁₃₇	1	1	yes	characteristic
186	C₂×C₄×M₁₆	C₂×C₁₃₇	1	1	yes	characteristic
187	#2283	C₂×C₁₃₇	1	1	yes	characteristic
188	#1288	C₂×C₁₃₇	1	4	yes	complemented
189	C₂²×M₁₆	—	2	1	no	—
190	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
191	#432	C₄×C₁₃₇	1	2	yes	complemented
192	#432	C₂²×C₁₃₇	1	2	yes	—
193	#431	—	2	1	no	—
194	#431	—	2	1	no	—
195	#423	—	2	1	no	—
196	#407	—	2	1	no	—
197	C₄×M₁₆	—	2	1	no	—
198	C₄×M₁₆	—	2	1	no	—
199	C₄×M₁₆	C₄×C₁₃₇	1	2	yes	complemented
200	C₄×M₁₆	C₄×C₁₃₇	1	2	yes	complemented
201	C₄×M₁₆	C₂²×C₁₃₇	1	2	yes	—
202	C₂×#97	—	2	1	no	—
203	C₂×C₄×C₈	C₄×C₁₃₇	1	2	yes	complemented
204	#383	C₂²×C₁₃₇	1	2	yes	—
205	#382	C₄×C₁₃₇	1	2	yes	—
206	#381	—	2	1	no	—
207	#380	—	2	1	no	—
208	C₄×C₄⋊C₄	—	2	1	no	—
209	C₄×C₂²⋊C₄	C₄×C₁₃₇	1	2	yes	—
210	#376	—	2	1	no	—
211	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
212	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
213	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
214	C₂×M₁₆	—	2	8	no	—
215	C₂×M₁₆	—	2	2	no	—
216	C₂×M₁₆	—	2	2	no	—
217	C₂×M₁₆	—	2	2	no	—
218	C₂²×C₈	—	2	2	no	—
219	C₂×C₄⋊C₄	—	2	2	no	—
220	C₂×C₂²⋊C₄	—	2	2	no	—
221	C₂×C₄²	—	2	2	no	—
222	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
223	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
225	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
226	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
227	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
228	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
229	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
230	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
231	C₂×C₄²	Q₈×C₁₃₇	1	1	yes	characteristic
232	C₂×C₄²	Q₈×C₁₃₇	1	1	yes	characteristic
233	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
234	C₄⋊C₈	—	2	2	no	—
235	C₄⋊C₈	—	2	2	no	—
236	C₂²⋊C₈	—	2	2	no	—
237	C₂²⋊C₈	—	2	2	no	—
238	#97	—	2	2	no	—
239	#97	—	2	2	no	—
240	#97	C₂×C₄×C₁₃₇	1	4	yes	—
241	C₄×C₈	—	2	2	no	—
242	C₄×C₈	—	2	2	no	—
243	C₄×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
244	#95	—	2	2	no	—
245	#95	—	2	2	no	—
246	#95	—	2	2	no	—
247	#95	C₂×C₄×C₁₃₇	1	4	yes	—
248	C₂⁴	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	4	2	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	C₄²×C₁₃₇	1	1	yes	characteristic
254	C₂²×C₄	C₄²×C₁₃₇	1	1	yes	characteristic
255	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
256	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
257	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
258	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
259	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
261	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
262	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
263	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
264	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
271	M₁₆	—	2	8	no	—
272	M₁₆	—	2	8	no	—
273	M₁₆	—	4	4	no	—
274	C₂×C₈	—	2	8	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	4	no	—
277	C₄⋊C₄	—	4	4	no	—
278	C₂²⋊C₄	—	4	4	no	—
279	C₄²	—	4	4	no	—
280	C₄²	C₄²×C₁₃₇	1	1	yes	characteristic
281	C₄²	C₄²×C₁₃₇	1	1	yes	characteristic
282	C₄²	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
283	C₄²	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
284	C₄²	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
285	C₄²	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
286	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
287	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
288	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
289	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
290	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
291	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
292	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
293	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
294	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
295	C₄²	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
296	C₂³	—	2	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	—	4	1	no	—
299	C₂³	#95×C₁₃₇	1	1	yes	characteristic
300	C₂³	#95×C₁₃₇	1	1	yes	characteristic
301	C₂³	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	#95×C₁₃₇	1	1	yes	characteristic
323	C₂×C₄	#95×C₁₃₇	1	1	yes	characteristic
324	C₂×C₄	#95×C₁₃₇	1	1	yes	characteristic
325	C₂×C₄	#95×C₁₃₇	1	1	yes	characteristic
326	C₂×C₄	#95×C₁₃₇	1	1	yes	characteristic
327	C₂×C₄	#95×C₁₃₇	1	1	yes	characteristic
328	C₂×C₄	#104×C₁₃₇	1	4	yes	—
329	C₂×C₄	C₂×C₄²×C₁₃₇	1	1	yes	characteristic
330	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
331	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
332	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
333	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
335	C₈	—	2	8	no	—
336	C₈	—	4	4	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	4	4	no	—
345	C₂²	H(3,ℤ/4)×C₁₃₇	1	2	yes	—
346	C₂²	C₂×#95×C₁₃₇	1	1	yes	characteristic
347	C₂²	C₂×#104×C₁₃₇	1	2	yes	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	8	4	no	—
358	C₄	#339×C₁₃₇	1	2	yes	—
359	C₄	#339×C₁₃₇	1	2	yes	—
360	C₄	#344×C₁₃₇	1	2	yes	—
361	C₂	—	2	2	no	—
362	C₂	—	2	2	no	—
363	C₂	—	4	1	no	—
364	C₂	C₂×H(3,ℤ/4)×C₁₃₇	1	1	yes	characteristic
365	C₂	C₂×#339×C₁₃₇	1	1	yes	characteristic
366	C₂	C₂×#344×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₇	#95
commutator	C₂×C₄	C₂×C₄²×C₁₃₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₇
socle	C₂²×C₁₃₇	C₂×#95
prime radical	C₂⁴×C₁₃₇	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₇ ◁ C₂²×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1288×C₁₃₇	C₂	semidirect
7. #432×C₁₃₇	C₄	semidirect
15. C₄×M₁₆×C₁₃₇	C₄	semidirect
16. C₄×M₁₆×C₁₃₇	C₄	semidirect
19. C₂×C₄×C₈×C₁₃₇	C₄	semidirect
183. #7974	C₁₃₇	direct (N × H)
184. C₁₃₇	#7974	direct (N × H)
188. #1288	C₂×C₁₃₇	semidirect
191. #432	C₄×C₁₃₇	semidirect
199. C₄×M₁₆	C₄×C₁₃₇	semidirect
200. C₄×M₁₆	C₄×C₁₃₇	semidirect
203. C₂×C₄×C₈	C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#2920×C₁₃₇	2
C₂×C₄×M₁₆×C₁₃₇	2
#2283×C₁₃₇	2
#1288×C₁₃₇	2
#7974	137

Subgroups — C137×#7974 #46857360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#7974 #46857360