Subgroups — C₁₃₇×#20781 #46870167

Order 35072.

758 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#117×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#1839×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#1832×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#1817×C₁₃₇	C₂	1	2	yes	maximal
5	#1798×C₁₃₇	C₂	1	2	yes	maximal
6	#1767×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₄⋊C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1750×C₁₃₇	C₂	1	2	yes	maximal
9	#1746×C₁₃₇	C₂	1	2	yes	maximal, 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	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
14	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
15	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	4	yes	—
16	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
18	C₄×C₄⋊C₄×C₁₃₇	C₄	1	2	yes	—
19	C₄×C₄⋊C₄×C₁₃₇	C₄	1	2	yes	—
20	C₄×C₂²⋊C₄×C₁₃₇	C₄	1	2	yes	—
21	C₄×C₂²⋊C₄×C₁₃₇	C₄	1	2	yes	—
22	#376×C₁₃₇	C₂²	1	1	yes	characteristic
23	#376×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
25	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
26	#336×C₁₃₇	C₂²	1	2	yes	—
27	#336×C₁₃₇	C₂²	1	2	yes	—
28	#336×C₁₃₇	C₂²	1	4	yes	—
29	#336×C₁₃₇	C₂²	1	4	yes	—
30	#336×C₁₃₇	C₂²	1	4	yes	—
31	C₂³×C₄×C₁₃₇	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
33	C₂²×C₈×C₁₃₇	C₂³	1	4	yes	—
34	C₂²×C₈×C₁₃₇	C₂³	1	4	yes	—
35	#117×C₁₃₇	—	2	2	no	—
36	#117×C₁₃₇	—	2	2	no	—
37	#117×C₁₃₇	—	2	4	no	—
38	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
41	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₁₃₇	—	2	4	no	—
45	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
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	C₂³	1	1	yes	characteristic
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	C₄⋊C₈×C₁₃₇	—	2	4	no	—
57	C₄⋊C₈×C₁₃₇	—	2	4	no	—
58	C₂²⋊C₈×C₁₃₇	—	2	8	no	—
59	#97×C₁₃₇	—	2	4	no	—
60	C₄×C₈×C₁₃₇	—	2	4	no	—
61	#95×C₁₃₇	C₂×C₄	1	2	yes	—
62	#95×C₁₃₇	C₂×C₄	1	2	yes	—
63	#95×C₁₃₇	C₂×C₄	1	2	yes	—
64	#95×C₁₃₇	C₂×C₄	1	2	yes	—
65	C₂⁴×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₃₇	—	2	2	no	—
67	C₂²×C₄×C₁₃₇	—	2	1	no	—
68	C₂²×C₄×C₁₃₇	—	2	1	no	—
69	C₂²×C₄×C₁₃₇	—	2	4	no	—
70	C₂²×C₄×C₁₃₇	—	2	4	no	—
71	C₂²×C₄×C₁₃₇	—	4	2	no	—
72	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
73	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
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	2	yes	—
78	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
82	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
83	C₂×C₈×C₁₃₇	—	2	4	no	—
84	C₂×C₈×C₁₃₇	—	2	4	no	—
85	C₂×C₈×C₁₃₇	—	2	4	no	—
86	C₂×C₈×C₁₃₇	—	2	4	no	—
87	C₂×C₈×C₁₃₇	—	2	4	no	—
88	C₂×C₈×C₁₃₇	—	2	4	no	—
89	C₄⋊C₄×C₁₃₇	—	2	2	no	—
90	C₄⋊C₄×C₁₃₇	—	2	2	no	—
91	C₄⋊C₄×C₁₃₇	—	2	4	no	—
92	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
93	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
94	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
95	C₄²×C₁₃₇	—	2	4	no	—
96	C₄²×C₁₃₇	—	2	4	no	—
97	C₄²×C₁₃₇	—	2	4	no	—
98	C₄²×C₁₃₇	—	2	2	no	—
99	C₄²×C₁₃₇	—	2	2	no	—
100	C₄²×C₁₃₇	—	2	2	no	—
101	C₄²×C₁₃₇	—	2	1	no	—
102	C₄²×C₁₃₇	—	2	1	no	—
103	C₄²×C₁₃₇	—	4	2	no	—
104	C₄²×C₁₃₇	—	4	2	no	—
105	C₄²×C₁₃₇	#41	1	2	yes	—
106	C₄²×C₁₃₇	#41	1	2	yes	—
107	C₄²×C₁₃₇	#41	1	4	yes	—
108	C₂³×C₁₃₇	—	2	1	no	—
109	C₂³×C₁₃₇	—	2	1	no	—
110	C₂³×C₁₃₇	—	2	2	no	—
111	C₂³×C₁₃₇	—	2	2	no	—
112	C₂³×C₁₃₇	#117	1	2	yes	—
113	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
114	C₂×C₄×C₁₃₇	—	2	2	no	—
115	C₂×C₄×C₁₃₇	—	2	1	no	—
116	C₂×C₄×C₁₃₇	—	2	1	no	—
117	C₂×C₄×C₁₃₇	—	2	2	no	—
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	4	no	—
123	C₂×C₄×C₁₃₇	—	2	4	no	—
124	C₂×C₄×C₁₃₇	—	2	2	no	—
125	C₂×C₄×C₁₃₇	—	2	1	no	—
126	C₂×C₄×C₁₃₇	—	2	1	no	—
127	C₂×C₄×C₁₃₇	—	2	2	no	—
128	C₂×C₄×C₁₃₇	—	2	2	no	—
129	C₂×C₄×C₁₃₇	—	2	2	no	—
130	C₂×C₄×C₁₃₇	—	2	2	no	—
131	C₂×C₄×C₁₃₇	—	2	2	no	—
132	C₂×C₄×C₁₃₇	—	2	2	no	—
133	C₂×C₄×C₁₃₇	—	2	2	no	—
134	C₂×C₄×C₁₃₇	—	4	8	no	—
135	C₂×C₄×C₁₃₇	#117	1	2	yes	—
136	C₂×C₄×C₁₃₇	#117	1	2	yes	—
137	C₂×C₄×C₁₃₇	#117	1	2	yes	—
138	C₂×C₄×C₁₃₇	#117	1	4	yes	—
139	C₂×C₄×C₁₃₇	#131	1	4	yes	—
140	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
141	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
142	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
143	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
144	C₈×C₁₃₇	—	4	4	no	—
145	C₈×C₁₃₇	—	4	4	no	—
146	C₂²×C₁₃₇	—	2	4	no	—
147	C₂²×C₁₃₇	—	2	2	no	—
148	C₂²×C₁₃₇	—	4	1	no	—
149	C₂²×C₁₃₇	—	4	1	no	—
150	C₂²×C₁₃₇	—	4	2	no	—
151	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
152	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
153	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
154	C₂²×C₁₃₇	C₂×#131	1	2	yes	—
155	C₂²×C₁₃₇	#568	1	2	yes	—
156	C₄×C₁₃₇	—	2	2	no	—
157	C₄×C₁₃₇	—	2	2	no	—
158	C₄×C₁₃₇	—	2	4	no	—
159	C₄×C₁₃₇	—	2	4	no	—
160	C₄×C₁₃₇	—	2	2	no	—
161	C₄×C₁₃₇	—	4	1	no	—
162	C₄×C₁₃₇	—	4	1	no	—
163	C₄×C₁₃₇	—	4	2	no	—
164	C₄×C₁₃₇	—	4	2	no	—
165	C₄×C₁₃₇	#529	1	2	yes	—
166	C₄×C₁₃₇	#529	1	2	yes	—
167	C₂×C₁₃₇	—	4	2	no	—
168	C₂×C₁₃₇	#2283	1	1	yes	characteristic
169	C₂×C₁₃₇	#2922	1	1	yes	characteristic
170	C₂×C₁₃₇	#2923	1	1	yes	characteristic
171	C₂×C₁₃₇	#2924	1	2	yes	—
172	C₂×C₁₃₇	#2925	1	2	yes	—
173	#20781	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₁₃₇	#20781	1	1	yes	characteristic, direct product factor, Sylow
175	C₄×#117	C₂×C₁₃₇	1	1	yes	characteristic
176	#1839	C₂×C₁₃₇	1	2	yes	complemented
177	#1832	C₂×C₁₃₇	1	2	yes	complemented
178	#1817	C₂×C₁₃₇	1	2	yes	—
179	#1798	C₂×C₁₃₇	1	2	yes	—
180	#1767	C₂×C₁₃₇	1	1	yes	characteristic, complemented
181	C₄×C₄⋊C₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
182	#1750	C₂×C₁₃₇	1	2	yes	—
183	#1746	C₂×C₁₃₇	1	2	yes	complemented
184	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
185	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
186	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
187	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
188	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
189	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	4	yes	—
190	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
191	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
192	C₄×C₄⋊C₄	C₄×C₁₃₇	1	2	yes	—
193	C₄×C₄⋊C₄	C₄×C₁₃₇	1	2	yes	—
194	C₄×C₂²⋊C₄	C₄×C₁₃₇	1	2	yes	—
195	C₄×C₂²⋊C₄	C₄×C₁₃₇	1	2	yes	—
196	#376	C₂²×C₁₃₇	1	1	yes	characteristic
197	#376	C₂²×C₁₃₇	1	1	yes	characteristic
198	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
199	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
200	#336	C₂²×C₁₃₇	1	4	yes	—
201	#336	C₂²×C₁₃₇	1	4	yes	—
202	#336	C₂²×C₁₃₇	1	2	yes	—
203	#336	C₂²×C₁₃₇	1	2	yes	—
204	#336	C₂²×C₁₃₇	1	4	yes	—
205	C₂³×C₄	C₂×C₄×C₁₃₇	1	2	yes	—
206	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
207	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
208	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
209	#117	—	2	2	no	—
210	#117	—	2	2	no	—
211	#117	—	2	4	no	—
212	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
213	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
215	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
216	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
217	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
218	C₂×C₄²	—	2	4	no	—
219	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
220	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
221	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
222	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
223	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
224	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
225	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
226	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
227	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
230	C₄⋊C₈	—	2	4	no	—
231	C₄⋊C₈	—	2	4	no	—
232	C₂²⋊C₈	—	2	8	no	—
233	#97	—	2	4	no	—
234	C₄×C₈	—	2	4	no	—
235	#95	C₂×C₄×C₁₃₇	1	2	yes	—
236	#95	C₂×C₄×C₁₃₇	1	2	yes	—
237	#95	C₂×C₄×C₁₃₇	1	2	yes	—
238	#95	C₂×C₄×C₁₃₇	1	2	yes	—
239	C₂⁴	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	1	no	—
242	C₂²×C₄	—	2	1	no	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	4	2	no	—
246	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
247	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
248	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
249	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
251	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
252	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
253	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
254	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
255	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
256	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
257	C₂×C₈	—	2	4	no	—
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	4	no	—
263	C₄⋊C₄	—	2	2	no	—
264	C₄⋊C₄	—	2	2	no	—
265	C₄⋊C₄	—	2	4	no	—
266	C₂²⋊C₄	—	2	2	no	—
267	C₂²⋊C₄	—	2	2	no	—
268	C₂²⋊C₄	—	2	4	no	—
269	C₄²	—	2	4	no	—
270	C₄²	—	2	4	no	—
271	C₄²	—	2	4	no	—
272	C₄²	—	2	2	no	—
273	C₄²	—	2	2	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	1	no	—
276	C₄²	—	2	1	no	—
277	C₄²	—	4	2	no	—
278	C₄²	—	4	2	no	—
279	C₄²	#41×C₁₃₇	1	2	yes	—
280	C₄²	#41×C₁₃₇	1	2	yes	—
281	C₄²	#41×C₁₃₇	1	4	yes	—
282	C₂³	—	2	1	no	—
283	C₂³	—	2	1	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	2	no	—
286	C₂³	#117×C₁₃₇	1	2	yes	—
287	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	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	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	4	8	no	—
309	C₂×C₄	#117×C₁₃₇	1	2	yes	—
310	C₂×C₄	#117×C₁₃₇	1	2	yes	—
311	C₂×C₄	#117×C₁₃₇	1	2	yes	—
312	C₂×C₄	#117×C₁₃₇	1	4	yes	—
313	C₂×C₄	#131×C₁₃₇	1	4	yes	—
314	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
315	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
316	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
317	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
318	C₈	—	4	4	no	—
319	C₈	—	4	4	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	4	no	—
322	C₂²	—	4	1	no	—
323	C₂²	—	4	1	no	—
324	C₂²	—	4	2	no	—
325	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
326	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
327	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
328	C₂²	C₂×#131×C₁₃₇	1	2	yes	—
329	C₂²	#568×C₁₃₇	1	2	yes	—
330	C₄	—	2	2	no	—
331	C₄	—	2	2	no	—
332	C₄	—	2	2	no	—
333	C₄	—	2	4	no	—
334	C₄	—	2	4	no	—
335	C₄	—	4	1	no	—
336	C₄	—	4	1	no	—
337	C₄	—	4	2	no	—
338	C₄	—	4	2	no	—
339	C₄	#529×C₁₃₇	1	2	yes	—
340	C₄	#529×C₁₃₇	1	2	yes	—
341	C₂	—	4	2	no	—
342	C₂	#2283×C₁₃₇	1	1	yes	characteristic
343	C₂	#2922×C₁₃₇	1	1	yes	characteristic
344	C₂	#2923×C₁₃₇	1	1	yes	characteristic
345	C₂	#2924×C₁₃₇	1	2	yes	—
346	C₂	#2925×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
2. #1839×C₁₃₇	C₂	semidirect
3. #1832×C₁₃₇	C₂	semidirect
6. #1767×C₁₃₇	C₂	semidirect
7. C₄×C₄⋊C₈×C₁₃₇	C₂	semidirect
9. #1746×C₁₃₇	C₂	semidirect
173. #20781	C₁₃₇	direct (N × H)
174. C₁₃₇	#20781	direct (N × H)
176. #1839	C₂×C₁₃₇	semidirect
177. #1832	C₂×C₁₃₇	semidirect
180. #1767	C₂×C₁₃₇	semidirect
181. C₄×C₄⋊C₈	C₂×C₁₃₇	semidirect
183. #1746	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×#117×C₁₃₇	2
#1839×C₁₃₇	2
#1832×C₁₃₇	2
#1817×C₁₃₇	2
#1798×C₁₃₇	2
#1767×C₁₃₇	2
C₄×C₄⋊C₈×C₁₃₇	2
#1750×C₁₃₇	2
#1746×C₁₃₇	2
#20781	137

Subgroups — C137×#20781 #46870167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#20781 #46870167