Subgroups — C₂×#1738×C₁₃₇ #46869736

Order 35072.

2110 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₁₃₇	C₂	1	2	yes	maximal
2	C₂³×M₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#1738×C₁₃₇	C₂	1	8	yes	maximal, direct product factor
4	C₂×#341×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₁₃₇	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₁₃₇	—	2	8	no	—
7	C₂²×M₁₆×C₁₃₇	—	2	4	no	—
8	C₂²×M₁₆×C₁₃₇	—	2	8	no	—
9	C₂²×M₁₆×C₁₃₇	—	2	2	no	—
10	C₂²×M₁₆×C₁₃₇	C₄	1	16	yes	—
11	C₂²×M₁₆×C₁₃₇	C₄	1	4	yes	—
12	C₂²×M₁₆×C₁₃₇	C₄	1	4	yes	—
13	C₂²×M₁₆×C₁₃₇	C₂²	1	4	yes	—
14	C₂²×M₁₆×C₁₃₇	C₂²	1	8	yes	—
15	C₂²×M₁₆×C₁₃₇	C₂²	1	4	yes	—
16	C₂³×C₈×C₁₃₇	—	2	2	no	—
17	C₂³×C₈×C₁₃₇	C₂²	1	2	yes	—
18	#341×C₁₃₇	C₂²	1	16	yes	complemented
19	C₂⁵×C₁₃₇	Q₈	1	1	yes	characteristic
20	C₂³×C₄×C₁₃₇	C₂×C₄	1	8	yes	—
21	C₂³×C₄×C₁₃₇	C₂×C₄	1	2	yes	—
22	C₂³×C₄×C₁₃₇	C₂×C₄	1	2	yes	—
23	C₂³×C₄×C₁₃₇	D₄	1	8	yes	—
24	C₂³×C₄×C₁₃₇	D₄	1	2	yes	—
25	C₂³×C₄×C₁₃₇	D₄	1	2	yes	—
26	C₂³×C₄×C₁₃₇	Q₈	1	1	yes	characteristic
27	C₂³×C₄×C₁₃₇	Q₈	1	2	yes	—
28	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
29	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
30	C₂×M₁₆×C₁₃₇	—	2	32	no	—
31	C₂×M₁₆×C₁₃₇	—	2	16	no	—
32	C₂×M₁₆×C₁₃₇	—	2	16	no	—
33	C₂×M₁₆×C₁₃₇	—	2	16	no	—
34	C₂×M₁₆×C₁₃₇	—	2	8	no	—
35	C₂×M₁₆×C₁₃₇	—	2	16	no	—
36	C₂×M₁₆×C₁₃₇	—	2	8	no	—
37	C₂×M₁₆×C₁₃₇	—	2	4	no	—
38	C₂×M₁₆×C₁₃₇	—	2	16	no	—
39	C₂×M₁₆×C₁₃₇	C₂×C₄	1	16	yes	—
40	C₂×M₁₆×C₁₃₇	C₂×C₄	1	32	yes	—
41	C₂×M₁₆×C₁₃₇	C₂×C₄	1	16	yes	—
42	C₂×M₁₆×C₁₃₇	C₂³	1	8	yes	—
43	C₂²×C₈×C₁₃₇	—	2	16	no	—
44	C₂²×C₈×C₁₃₇	—	2	8	no	—
45	C₂²×C₈×C₁₃₇	—	2	8	no	—
46	C₂²×C₈×C₁₃₇	—	2	4	no	—
47	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
48	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
49	C₂²×C₈×C₁₃₇	C₂³	1	4	yes	—
50	C₂⁴×C₁₃₇	—	4	4	no	—
51	C₂⁴×C₁₃₇	C₄⋊C₄	1	2	yes	—
52	C₂⁴×C₁₃₇	C₄⋊C₄	1	8	yes	—
53	C₂⁴×C₁₃₇	C₄⋊C₄	1	2	yes	—
54	C₂⁴×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
55	C₂⁴×C₁₃₇	C₂×Q₈	1	2	yes	—
56	C₂²×C₄×C₁₃₇	C₄²	1	8	yes	—
57	C₂²×C₄×C₁₃₇	C₄²	1	8	yes	—
58	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	8	yes	—
59	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	8	yes	—
60	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	8	yes	—
61	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	16	yes	—
62	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	8	yes	—
63	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	4	yes	—
64	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
65	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	8	yes	—
66	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	16	yes	—
67	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
68	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	4	yes	—
69	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
72	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
73	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
74	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
75	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
76	C₂²×C₄×C₁₃₇	C₂×D₄	1	8	yes	—
77	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
80	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
82	M₁₆×C₁₃₇	—	2	16	no	—
83	M₁₆×C₁₃₇	—	2	32	no	—
84	M₁₆×C₁₃₇	—	2	32	no	—
85	M₁₆×C₁₃₇	—	2	8	no	—
86	M₁₆×C₁₃₇	C₂²×C₄	1	16	yes	—
87	C₂×C₈×C₁₃₇	—	2	32	no	—
88	C₂×C₈×C₁₃₇	—	2	16	no	—
89	C₂×C₈×C₁₃₇	—	2	8	no	—
90	C₂×C₈×C₁₃₇	—	2	8	no	—
91	C₂×C₈×C₁₃₇	—	2	8	no	—
92	C₂×C₈×C₁₃₇	—	2	8	no	—
93	C₂×C₈×C₁₃₇	C₂²×C₄	1	8	yes	—
94	C₂³×C₁₃₇	—	2	8	no	—
95	C₂³×C₁₃₇	—	2	4	no	—
96	C₂³×C₁₃₇	—	4	4	no	—
97	C₂³×C₁₃₇	—	4	16	no	—
98	C₂³×C₁₃₇	—	4	4	no	—
99	C₂³×C₁₃₇	#95	1	8	yes	—
100	C₂³×C₁₃₇	#95	1	8	yes	—
101	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
102	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
103	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
104	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	8	yes	—
105	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂³×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
107	C₂×C₄×C₁₃₇	#95	1	16	yes	—
108	C₂×C₄×C₁₃₇	#95	1	16	yes	—
109	C₂×C₄×C₁₃₇	#95	1	8	yes	—
110	C₂×C₄×C₁₃₇	#95	1	8	yes	—
111	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
112	C₂×C₄×C₁₃₇	C₂×C₄²	1	8	yes	—
113	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
114	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	8	yes	—
115	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
116	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
117	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	4	yes	—
118	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	8	yes	—
119	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	4	yes	—
120	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	8	yes	—
121	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
122	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	8	yes	—
123	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
125	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
127	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
128	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
129	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
130	C₈×C₁₃₇	—	2	16	no	—
131	C₈×C₁₃₇	—	2	8	no	—
132	C₂²×C₁₃₇	—	2	8	no	—
133	C₂²×C₁₃₇	—	2	2	no	—
134	C₂²×C₁₃₇	—	2	2	no	—
135	C₂²×C₁₃₇	—	2	16	no	—
136	C₂²×C₁₃₇	—	2	8	no	—
137	C₂²×C₁₃₇	—	4	8	no	—
138	C₂²×C₁₃₇	—	4	8	no	—
139	C₂²×C₁₃₇	C₂×#95	1	8	yes	—
140	C₂²×C₁₃₇	C₂×#95	1	2	yes	—
141	C₂²×C₁₃₇	C₂×#95	1	2	yes	—
142	C₂²×C₁₃₇	#430	1	4	yes	—
143	C₂²×C₁₃₇	C₂²×C₄⋊C₄	1	2	yes	—
144	C₂²×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
145	C₄×C₁₃₇	C₂×#95	1	2	yes	—
146	C₄×C₁₃₇	C₂×#95	1	8	yes	—
147	C₄×C₁₃₇	C₂×#95	1	2	yes	—
148	C₄×C₁₃₇	C₂²×C₄²	1	1	yes	characteristic
149	C₄×C₁₃₇	C₂²×C₂²⋊C₄	1	2	yes	—
150	C₄×C₁₃₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₁₃₇	—	2	2	no	—
152	C₂×C₁₃₇	—	2	8	no	—
153	C₂×C₁₃₇	—	2	2	no	—
154	C₂×C₁₃₇	#1738	1	4	yes	direct product factor
155	C₂×C₁₃₇	C₂²×#95	1	1	yes	characteristic
156	C₂×C₁₃₇	C₂×#430	1	2	yes	—
157	C₂×#1738	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₁₃₇	C₂×#1738	1	1	yes	characteristic, direct product factor, Sylow
159	C₂³×M₁₆	C₂×C₁₃₇	1	2	yes	—
160	C₂³×M₁₆	C₂×C₁₃₇	1	1	yes	characteristic
161	#1738	C₂×C₁₃₇	1	8	yes	direct product factor
162	C₂×#341	C₂×C₁₃₇	1	4	yes	complemented
163	C₂⁴×C₄	C₂²×C₁₃₇	1	1	yes	characteristic
164	C₂²×M₁₆	—	2	8	no	—
165	C₂²×M₁₆	—	2	2	no	—
166	C₂²×M₁₆	—	2	4	no	—
167	C₂²×M₁₆	—	2	8	no	—
168	C₂²×M₁₆	C₄×C₁₃₇	1	16	yes	—
169	C₂²×M₁₆	C₄×C₁₃₇	1	4	yes	—
170	C₂²×M₁₆	C₄×C₁₃₇	1	4	yes	—
171	C₂²×M₁₆	C₂²×C₁₃₇	1	4	yes	—
172	C₂²×M₁₆	C₂²×C₁₃₇	1	8	yes	—
173	C₂²×M₁₆	C₂²×C₁₃₇	1	4	yes	—
174	C₂³×C₈	—	2	2	no	—
175	C₂³×C₈	C₂²×C₁₃₇	1	2	yes	—
176	#341	C₂²×C₁₃₇	1	16	yes	complemented
177	C₂⁵	Q₈×C₁₃₇	1	1	yes	characteristic
178	C₂³×C₄	C₂×C₄×C₁₃₇	1	8	yes	—
179	C₂³×C₄	C₂×C₄×C₁₃₇	1	2	yes	—
180	C₂³×C₄	C₂×C₄×C₁₃₇	1	2	yes	—
181	C₂³×C₄	D₄×C₁₃₇	1	2	yes	—
182	C₂³×C₄	D₄×C₁₃₇	1	8	yes	—
183	C₂³×C₄	D₄×C₁₃₇	1	2	yes	—
184	C₂³×C₄	Q₈×C₁₃₇	1	1	yes	characteristic
185	C₂³×C₄	Q₈×C₁₃₇	1	2	yes	—
186	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
187	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
188	C₂×M₁₆	—	2	16	no	—
189	C₂×M₁₆	—	2	32	no	—
190	C₂×M₁₆	—	2	16	no	—
191	C₂×M₁₆	—	2	16	no	—
192	C₂×M₁₆	—	2	8	no	—
193	C₂×M₁₆	—	2	16	no	—
194	C₂×M₁₆	—	2	8	no	—
195	C₂×M₁₆	—	2	4	no	—
196	C₂×M₁₆	—	2	16	no	—
197	C₂×M₁₆	C₂×C₄×C₁₃₇	1	16	yes	—
198	C₂×M₁₆	C₂×C₄×C₁₃₇	1	32	yes	—
199	C₂×M₁₆	C₂×C₄×C₁₃₇	1	16	yes	—
200	C₂×M₁₆	C₂³×C₁₃₇	1	8	yes	—
201	C₂²×C₈	—	2	16	no	—
202	C₂²×C₈	—	2	8	no	—
203	C₂²×C₈	—	2	4	no	—
204	C₂²×C₈	—	2	8	no	—
205	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
206	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
207	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
208	C₂⁴	—	4	4	no	—
209	C₂⁴	C₄⋊C₄×C₁₃₇	1	2	yes	—
210	C₂⁴	C₄⋊C₄×C₁₃₇	1	8	yes	—
211	C₂⁴	C₄⋊C₄×C₁₃₇	1	2	yes	—
212	C₂⁴	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
213	C₂⁴	C₂×Q₈×C₁₃₇	1	2	yes	—
214	C₂²×C₄	C₄²×C₁₃₇	1	8	yes	—
215	C₂²×C₄	C₄²×C₁₃₇	1	8	yes	—
216	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	8	yes	—
217	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	8	yes	—
218	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	8	yes	—
219	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	8	yes	—
220	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	16	yes	—
221	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	4	yes	—
222	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	4	yes	—
223	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
224	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	8	yes	—
225	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	16	yes	—
226	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
227	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
228	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
229	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
230	C₂²×C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
231	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
232	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
233	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
234	C₂²×C₄	C₂×D₄×C₁₃₇	1	8	yes	—
235	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
236	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
237	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
238	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
239	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
240	M₁₆	—	2	16	no	—
241	M₁₆	—	2	32	no	—
242	M₁₆	—	2	32	no	—
243	M₁₆	—	2	8	no	—
244	M₁₆	C₂²×C₄×C₁₃₇	1	16	yes	—
245	C₂×C₈	—	2	32	no	—
246	C₂×C₈	—	2	16	no	—
247	C₂×C₈	—	2	8	no	—
248	C₂×C₈	—	2	8	no	—
249	C₂×C₈	—	2	8	no	—
250	C₂×C₈	—	2	8	no	—
251	C₂×C₈	C₂²×C₄×C₁₃₇	1	8	yes	—
252	C₂³	—	2	8	no	—
253	C₂³	—	2	4	no	—
254	C₂³	—	4	4	no	—
255	C₂³	—	4	16	no	—
256	C₂³	—	4	4	no	—
257	C₂³	#95×C₁₃₇	1	8	yes	—
258	C₂³	#95×C₁₃₇	1	8	yes	—
259	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
260	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
261	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
262	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	8	yes	—
263	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
264	C₂³	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
265	C₂×C₄	#95×C₁₃₇	1	16	yes	—
266	C₂×C₄	#95×C₁₃₇	1	16	yes	—
267	C₂×C₄	#95×C₁₃₇	1	8	yes	—
268	C₂×C₄	#95×C₁₃₇	1	8	yes	—
269	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
270	C₂×C₄	C₂×C₄²×C₁₃₇	1	8	yes	—
271	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
272	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	8	yes	—
273	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
274	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	4	yes	—
275	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
276	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	8	yes	—
277	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	4	yes	—
278	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	8	yes	—
279	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
280	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	8	yes	—
281	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
282	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
283	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
284	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
285	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
286	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
287	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
288	C₈	—	2	16	no	—
289	C₈	—	2	8	no	—
290	C₂²	—	2	8	no	—
291	C₂²	—	2	2	no	—
292	C₂²	—	2	2	no	—
293	C₂²	—	2	16	no	—
294	C₂²	—	2	8	no	—
295	C₂²	—	4	8	no	—
296	C₂²	—	4	8	no	—
297	C₂²	C₂×#95×C₁₃₇	1	8	yes	—
298	C₂²	C₂×#95×C₁₃₇	1	2	yes	—
299	C₂²	C₂×#95×C₁₃₇	1	2	yes	—
300	C₂²	#430×C₁₃₇	1	4	yes	—
301	C₂²	C₂²×C₄⋊C₄×C₁₃₇	1	2	yes	—
302	C₂²	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
303	C₄	C₂×#95×C₁₃₇	1	2	yes	—
304	C₄	C₂×#95×C₁₃₇	1	8	yes	—
305	C₄	C₂×#95×C₁₃₇	1	2	yes	—
306	C₄	C₂²×C₄²×C₁₃₇	1	1	yes	characteristic
307	C₄	C₂²×C₂²⋊C₄×C₁₃₇	1	2	yes	—
308	C₄	C₂²×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
309	C₂	—	2	8	no	—
310	C₂	—	2	2	no	—
311	C₂	—	2	2	no	—
312	C₂	#1738×C₁₃₇	1	4	yes	direct product factor
313	C₂	C₂²×#95×C₁₃₇	1	1	yes	characteristic
314	C₂	C₂×#430×C₁₃₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₇	C₂×D₄
commutator	C₄	C₂²×C₄²×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle	C₂³×C₁₃₇	C₂×C₄⋊C₄
prime radical	C₂⁵×C₁₃₇	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₇ ◁ C₂⁴×C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1738×C₁₃₇	C₂	direct (N × H)
4. C₂×#341×C₁₃₇	C₂	semidirect
18. #341×C₁₃₇	C₂²	semidirect
154. C₂×C₁₃₇	#1738	direct (N × H)
157. C₂×#1738	C₁₃₇	direct (N × H)
158. C₁₃₇	C₂×#1738	direct (N × H)
161. #1738	C₂×C₁₃₇	direct (N × H)
162. C₂×#341	C₂×C₁₃₇	semidirect
176. #341	C₂²×C₁₃₇	semidirect
312. C₂	#1738×C₁₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₁₃₇	2
#1738×C₁₃₇	2
C₂×#341×C₁₃₇	2
C₂×#1738	137

Subgroups — C2×#1738×C137 #46869736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1738×C₁₃₇ #46869736