Subgroups — C₁₃₇×#20813 #46870199

Order 35072.

854 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#433×C₁₃₇	C₂	1	2	yes	maximal
2	C₄×#117×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#1843×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#1831×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1798×C₁₃₇	C₂	1	2	yes	maximal
6	#1797×C₁₃₇	C₂	1	2	yes	maximal
7	#1768×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1767×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₄⋊C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
13	#433×C₁₃₇	—	2	8	no	—
14	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	4	yes	—
17	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	4	yes	—
18	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	4	yes	—
19	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
21	C₄×C₄⋊C₄×C₁₃₇	C₄	1	2	yes	—
22	C₄×C₄⋊C₄×C₁₃₇	C₄	1	2	yes	—
23	C₄×C₂²⋊C₄×C₁₃₇	C₄	1	2	yes	—
24	C₄×C₂²⋊C₄×C₁₃₇	C₄	1	2	yes	—
25	#376×C₁₃₇	C₂²	1	1	yes	characteristic
26	#376×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
29	#336×C₁₃₇	C₂²	1	2	yes	—
30	#336×C₁₃₇	C₂²	1	2	yes	—
31	#336×C₁₃₇	C₂²	1	4	yes	—
32	C₂³×C₄×C₁₃₇	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
34	C₂²×C₈×C₁₃₇	C₂³	1	4	yes	—
35	C₂²×C₈×C₁₃₇	C₂³	1	4	yes	—
36	#117×C₁₃₇	—	2	4	no	—
37	#117×C₁₃₇	D₄	1	4	yes	—
38	#117×C₁₃₇	Q₈	1	4	yes	—
39	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
42	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₁₃₇	—	2	4	no	—
46	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
57	C₄⋊C₈×C₁₃₇	—	2	8	no	—
58	C₄⋊C₈×C₁₃₇	—	2	8	no	—
59	C₄⋊C₈×C₁₃₇	—	2	4	no	—
60	C₄⋊C₈×C₁₃₇	—	2	4	no	—
61	C₂²⋊C₈×C₁₃₇	—	2	8	no	—
62	#97×C₁₃₇	—	2	4	no	—
63	C₄×C₈×C₁₃₇	—	2	4	no	—
64	#95×C₁₃₇	C₂×C₄	1	2	yes	—
65	#95×C₁₃₇	C₂×C₄	1	2	yes	—
66	#95×C₁₃₇	C₂×C₄	1	2	yes	—
67	#95×C₁₃₇	C₂×C₄	1	2	yes	—
68	C₂⁴×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃₇	—	2	2	no	—
70	C₂²×C₄×C₁₃₇	—	2	2	no	—
71	C₂²×C₄×C₁₃₇	—	2	4	no	—
72	C₂²×C₄×C₁₃₇	—	2	4	no	—
73	C₂²×C₄×C₁₃₇	—	4	2	no	—
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	2	yes	—
77	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
85	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
86	C₂×C₈×C₁₃₇	—	2	4	no	—
87	C₂×C₈×C₁₃₇	—	2	4	no	—
88	C₂×C₈×C₁₃₇	—	2	4	no	—
89	C₂×C₈×C₁₃₇	—	2	4	no	—
90	C₂×C₈×C₁₃₇	—	2	4	no	—
91	C₂×C₈×C₁₃₇	—	2	4	no	—
92	C₄⋊C₄×C₁₃₇	—	2	2	no	—
93	C₄⋊C₄×C₁₃₇	—	2	2	no	—
94	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	8	yes	—
95	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
96	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
97	C₂²⋊C₄×C₁₃₇	C₄⋊C₄	1	8	yes	—
98	C₄²×C₁₃₇	—	2	4	no	—
99	C₄²×C₁₃₇	—	2	4	no	—
100	C₄²×C₁₃₇	—	2	4	no	—
101	C₄²×C₁₃₇	—	2	2	no	—
102	C₄²×C₁₃₇	—	2	2	no	—
103	C₄²×C₁₃₇	—	4	2	no	—
104	C₄²×C₁₃₇	—	4	2	no	—
105	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
106	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
107	C₄²×C₁₃₇	C₂×Q₈	1	2	yes	—
108	C₄²×C₁₃₇	C₂×Q₈	1	2	yes	—
109	C₄²×C₁₃₇	#41	1	4	yes	—
110	C₄²×C₁₃₇	#41	1	4	yes	—
111	C₂³×C₁₃₇	—	2	1	no	—
112	C₂³×C₁₃₇	—	2	1	no	—
113	C₂³×C₁₃₇	—	2	2	no	—
114	C₂³×C₁₃₇	—	2	2	no	—
115	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
116	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
117	C₂×C₄×C₁₃₇	—	2	2	no	—
118	C₂×C₄×C₁₃₇	—	2	1	no	—
119	C₂×C₄×C₁₃₇	—	2	1	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	—	2	2	no	—
129	C₂×C₄×C₁₃₇	—	2	4	no	—
130	C₂×C₄×C₁₃₇	—	2	4	no	—
131	C₂×C₄×C₁₃₇	—	2	1	no	—
132	C₂×C₄×C₁₃₇	—	2	1	no	—
133	C₂×C₄×C₁₃₇	—	2	2	no	—
134	C₂×C₄×C₁₃₇	—	2	2	no	—
135	C₂×C₄×C₁₃₇	—	4	8	no	—
136	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
137	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
138	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
139	C₂×C₄×C₁₃₇	#117	1	4	yes	—
140	C₂×C₄×C₁₃₇	#117	1	2	yes	—
141	C₂×C₄×C₁₃₇	#117	1	2	yes	—
142	C₂×C₄×C₁₃₇	#131	1	4	yes	—
143	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
146	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
147	C₈×C₁₃₇	—	4	4	no	—
148	C₈×C₁₃₇	—	4	4	no	—
149	C₂²×C₁₃₇	—	2	4	no	—
150	C₂²×C₁₃₇	—	2	2	no	—
151	C₂²×C₁₃₇	—	4	1	no	—
152	C₂²×C₁₃₇	—	4	1	no	—
153	C₂²×C₁₃₇	—	4	2	no	—
154	C₂²×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
155	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
156	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
157	C₂²×C₁₃₇	C₂×#131	1	2	yes	—
158	C₂²×C₁₃₇	#568	1	2	yes	—
159	C₄×C₁₃₇	—	2	4	no	—
160	C₄×C₁₃₇	—	2	4	no	—
161	C₄×C₁₃₇	—	2	2	no	—
162	C₄×C₁₃₇	—	2	2	no	—
163	C₄×C₁₃₇	—	2	4	no	—
164	C₄×C₁₃₇	—	2	4	no	—
165	C₄×C₁₃₇	—	2	2	no	—
166	C₄×C₁₃₇	—	4	1	no	—
167	C₄×C₁₃₇	—	4	1	no	—
168	C₄×C₁₃₇	#532	1	2	yes	—
169	C₄×C₁₃₇	#533	1	2	yes	—
170	C₂×C₁₃₇	—	4	2	no	—
171	C₂×C₁₃₇	#2285	1	1	yes	characteristic
172	C₂×C₁₃₇	#2906	1	2	yes	—
173	C₂×C₁₃₇	#2922	1	1	yes	characteristic
174	C₂×C₁₃₇	#2923	1	1	yes	characteristic
175	C₂×C₁₃₇	#2924	1	2	yes	—
176	#20813	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₁₃₇	#20813	1	1	yes	characteristic, direct product factor, Sylow
178	C₂×#433	C₂×C₁₃₇	1	2	yes	—
179	C₄×#117	C₂×C₁₃₇	1	1	yes	characteristic
180	#1843	C₂×C₁₃₇	1	2	yes	complemented
181	#1831	C₂×C₁₃₇	1	2	yes	complemented
182	#1798	C₂×C₁₃₇	1	2	yes	—
183	#1797	C₂×C₁₃₇	1	2	yes	—
184	#1768	C₂×C₁₃₇	1	2	yes	complemented
185	#1767	C₂×C₁₃₇	1	1	yes	characteristic, complemented
186	C₄×C₄⋊C₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
187	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
188	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
189	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
190	#433	—	2	8	no	—
191	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	4	yes	—
192	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
193	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
194	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	4	yes	—
195	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	4	yes	—
196	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
197	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
198	C₄×C₄⋊C₄	C₄×C₁₃₇	1	2	yes	—
199	C₄×C₄⋊C₄	C₄×C₁₃₇	1	2	yes	—
200	C₄×C₂²⋊C₄	C₄×C₁₃₇	1	2	yes	—
201	C₄×C₂²⋊C₄	C₄×C₁₃₇	1	2	yes	—
202	#376	C₂²×C₁₃₇	1	1	yes	characteristic
203	#376	C₂²×C₁₃₇	1	1	yes	characteristic
204	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
205	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
206	#336	C₂²×C₁₃₇	1	2	yes	—
207	#336	C₂²×C₁₃₇	1	2	yes	—
208	#336	C₂²×C₁₃₇	1	4	yes	—
209	C₂³×C₄	C₂×C₄×C₁₃₇	1	2	yes	—
210	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
211	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
212	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
213	#117	—	2	4	no	—
214	#117	D₄×C₁₃₇	1	4	yes	—
215	#117	Q₈×C₁₃₇	1	4	yes	—
216	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
218	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
219	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
220	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
221	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
222	C₂×C₄²	—	2	4	no	—
223	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
224	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
225	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
226	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
227	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
228	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
231	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
232	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
233	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
234	C₄⋊C₈	—	2	8	no	—
235	C₄⋊C₈	—	2	8	no	—
236	C₄⋊C₈	—	2	4	no	—
237	C₄⋊C₈	—	2	4	no	—
238	C₂²⋊C₈	—	2	8	no	—
239	#97	—	2	4	no	—
240	C₄×C₈	—	2	4	no	—
241	#95	C₂×C₄×C₁₃₇	1	2	yes	—
242	#95	C₂×C₄×C₁₃₇	1	2	yes	—
243	#95	C₂×C₄×C₁₃₇	1	2	yes	—
244	#95	C₂×C₄×C₁₃₇	1	2	yes	—
245	C₂⁴	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
252	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
253	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
256	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
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	2	yes	—
260	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
261	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
262	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
263	C₂×C₈	—	2	4	no	—
264	C₂×C₈	—	2	4	no	—
265	C₂×C₈	—	2	4	no	—
266	C₂×C₈	—	2	4	no	—
267	C₂×C₈	—	2	4	no	—
268	C₂×C₈	—	2	4	no	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	8	yes	—
272	C₂²⋊C₄	—	2	2	no	—
273	C₂²⋊C₄	—	2	2	no	—
274	C₂²⋊C₄	C₄⋊C₄×C₁₃₇	1	8	yes	—
275	C₄²	—	2	4	no	—
276	C₄²	—	2	4	no	—
277	C₄²	—	2	4	no	—
278	C₄²	—	2	2	no	—
279	C₄²	—	2	2	no	—
280	C₄²	—	4	2	no	—
281	C₄²	—	4	2	no	—
282	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
283	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
284	C₄²	C₂×Q₈×C₁₃₇	1	2	yes	—
285	C₄²	C₂×Q₈×C₁₃₇	1	2	yes	—
286	C₄²	#41×C₁₃₇	1	4	yes	—
287	C₄²	#41×C₁₃₇	1	4	yes	—
288	C₂³	—	2	1	no	—
289	C₂³	—	2	1	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	2	no	—
292	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
293	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
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	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	4	8	no	—
313	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
314	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
315	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
316	C₂×C₄	#117×C₁₃₇	1	4	yes	—
317	C₂×C₄	#117×C₁₃₇	1	2	yes	—
318	C₂×C₄	#117×C₁₃₇	1	2	yes	—
319	C₂×C₄	#131×C₁₃₇	1	4	yes	—
320	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
321	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
322	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
323	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
324	C₈	—	4	4	no	—
325	C₈	—	4	4	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	2	4	no	—
328	C₂²	—	4	1	no	—
329	C₂²	—	4	1	no	—
330	C₂²	—	4	2	no	—
331	C₂²	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
332	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
333	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
334	C₂²	C₂×#131×C₁₃₇	1	2	yes	—
335	C₂²	#568×C₁₃₇	1	2	yes	—
336	C₄	—	2	2	no	—
337	C₄	—	2	4	no	—
338	C₄	—	2	4	no	—
339	C₄	—	2	2	no	—
340	C₄	—	2	2	no	—
341	C₄	—	2	4	no	—
342	C₄	—	2	4	no	—
343	C₄	—	4	1	no	—
344	C₄	—	4	1	no	—
345	C₄	#532×C₁₃₇	1	2	yes	—
346	C₄	#533×C₁₃₇	1	2	yes	—
347	C₂	—	4	2	no	—
348	C₂	#2285×C₁₃₇	1	1	yes	characteristic
349	C₂	#2906×C₁₃₇	1	2	yes	—
350	C₂	#2922×C₁₃₇	1	1	yes	characteristic
351	C₂	#2923×C₁₃₇	1	1	yes	characteristic
352	C₂	#2924×C₁₃₇	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. #1843×C₁₃₇	C₂	semidirect
4. #1831×C₁₃₇	C₂	semidirect
7. #1768×C₁₃₇	C₂	semidirect
8. #1767×C₁₃₇	C₂	semidirect
9. C₄×C₄⋊C₈×C₁₃₇	C₂	semidirect
176. #20813	C₁₃₇	direct (N × H)
177. C₁₃₇	#20813	direct (N × H)
180. #1843	C₂×C₁₃₇	semidirect
181. #1831	C₂×C₁₃₇	semidirect
184. #1768	C₂×C₁₃₇	semidirect
185. #1767	C₂×C₁₃₇	semidirect
186. C₄×C₄⋊C₈	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#433×C₁₃₇	2
C₄×#117×C₁₃₇	2
#1843×C₁₃₇	2
#1831×C₁₃₇	2
#1798×C₁₃₇	2
#1797×C₁₃₇	2
#1768×C₁₃₇	2
#1767×C₁₃₇	2
C₄×C₄⋊C₈×C₁₃₇	2
#20813	137

Subgroups — C137×#20813 #46870199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#20813 #46870199