Subgroups — C₁₃₇×#20786 #46870172

Order 35072.

758 conjugacy classes of subgroups.

The subgroup lattice has 350 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	#1840×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#1831×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#1818×C₁₃₇	C₂	1	2	yes	maximal
5	#1797×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	1	yes	characteristic
32	C₂³×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
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	—	2	2	no	—
38	#117×C₁₃₇	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
41	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
42	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
43	C₂×C₄²×C₁₃₇	—	2	4	no	—
44	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
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	2	no	—
70	C₂²×C₄×C₁₃₇	—	2	2	no	—
71	C₂²×C₄×C₁₃₇	—	2	4	no	—
72	C₂²×C₄×C₁₃₇	—	4	2	no	—
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	2	yes	—
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	2	yes	—
79	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
83	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
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	C₂×C₈×C₁₃₇	—	2	4	no	—
90	C₄⋊C₄×C₁₃₇	—	2	4	no	—
91	C₄⋊C₄×C₁₃₇	—	2	4	no	—
92	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
93	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
94	C₄²×C₁₃₇	—	2	2	no	—
95	C₄²×C₁₃₇	—	2	2	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	1	no	—
115	C₂×C₄×C₁₃₇	—	2	1	no	—
116	C₂×C₄×C₁₃₇	—	2	2	no	—
117	C₂×C₄×C₁₃₇	—	2	2	no	—
118	C₂×C₄×C₁₃₇	—	2	2	no	—
119	C₂×C₄×C₁₃₇	—	2	4	no	—
120	C₂×C₄×C₁₃₇	—	2	4	no	—
121	C₂×C₄×C₁₃₇	—	2	1	no	—
122	C₂×C₄×C₁₃₇	—	2	1	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	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	4	no	—
135	C₂×C₄×C₁₃₇	—	4	4	no	—
136	C₂×C₄×C₁₃₇	#117	1	2	yes	—
137	C₂×C₄×C₁₃₇	#117	1	4	yes	—
138	C₂×C₄×C₁₃₇	#117	1	2	yes	—
139	C₂×C₄×C₁₃₇	#117	1	2	yes	—
140	C₂×C₄×C₁₃₇	#131	1	4	yes	—
141	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
142	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
143	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
144	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
145	C₈×C₁₃₇	—	4	4	no	—
146	C₈×C₁₃₇	—	4	4	no	—
147	C₂²×C₁₃₇	—	2	4	no	—
148	C₂²×C₁₃₇	—	2	2	no	—
149	C₂²×C₁₃₇	—	4	1	no	—
150	C₂²×C₁₃₇	—	4	1	no	—
151	C₂²×C₁₃₇	—	4	2	no	—
152	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
153	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
154	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
155	C₂²×C₁₃₇	C₂×#131	1	2	yes	—
156	C₂²×C₁₃₇	#568	1	2	yes	—
157	C₄×C₁₃₇	—	2	2	no	—
158	C₄×C₁₃₇	—	2	4	no	—
159	C₄×C₁₃₇	—	2	2	no	—
160	C₄×C₁₃₇	—	4	1	no	—
161	C₄×C₁₃₇	—	4	1	no	—
162	C₄×C₁₃₇	—	4	2	no	—
163	C₄×C₁₃₇	—	4	2	no	—
164	C₄×C₁₃₇	—	4	2	no	—
165	C₄×C₁₃₇	#433	1	4	yes	—
166	C₄×C₁₃₇	#529	1	2	yes	—
167	C₄×C₁₃₇	#529	1	2	yes	—
168	C₂×C₁₃₇	—	4	2	no	—
169	C₂×C₁₃₇	#2283	1	1	yes	characteristic
170	C₂×C₁₃₇	C₂×#433	1	1	yes	characteristic
171	C₂×C₁₃₇	#2921	1	1	yes	characteristic
172	C₂×C₁₃₇	#2925	1	2	yes	—
173	C₂×C₁₃₇	#2925	1	2	yes	—
174	#20786	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₁₃₇	#20786	1	1	yes	characteristic, direct product factor, Sylow
176	C₄×#117	C₂×C₁₃₇	1	1	yes	characteristic
177	#1840	C₂×C₁₃₇	1	2	yes	complemented
178	#1831	C₂×C₁₃₇	1	2	yes	complemented
179	#1818	C₂×C₁₃₇	1	2	yes	—
180	#1797	C₂×C₁₃₇	1	2	yes	—
181	#1767	C₂×C₁₃₇	1	1	yes	characteristic, complemented
182	C₄×C₄⋊C₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
183	#1750	C₂×C₁₃₇	1	2	yes	—
184	#1746	C₂×C₁₃₇	1	2	yes	complemented
185	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
186	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
187	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
188	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
189	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
190	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	4	yes	—
191	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
192	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
193	C₄×C₄⋊C₄	C₄×C₁₃₇	1	2	yes	—
194	C₄×C₄⋊C₄	C₄×C₁₃₇	1	2	yes	—
195	C₄×C₂²⋊C₄	C₄×C₁₃₇	1	2	yes	—
196	C₄×C₂²⋊C₄	C₄×C₁₃₇	1	2	yes	—
197	#376	C₂²×C₁₃₇	1	1	yes	characteristic
198	#376	C₂²×C₁₃₇	1	1	yes	characteristic
199	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
200	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
201	#336	C₂²×C₁₃₇	1	4	yes	—
202	#336	C₂²×C₁₃₇	1	4	yes	—
203	#336	C₂²×C₁₃₇	1	2	yes	—
204	#336	C₂²×C₁₃₇	1	2	yes	—
205	#336	C₂²×C₁₃₇	1	4	yes	—
206	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
207	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
208	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
209	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
210	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
211	#117	—	2	4	no	—
212	#117	—	2	2	no	—
213	#117	—	2	2	no	—
214	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
215	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
216	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
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	1	yes	characteristic
222	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
223	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
224	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
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	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
231	C₄⋊C₈	—	2	4	no	—
232	C₄⋊C₈	—	2	4	no	—
233	C₂²⋊C₈	—	2	8	no	—
234	#97	—	2	4	no	—
235	C₄×C₈	—	2	4	no	—
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	#95	C₂×C₄×C₁₃₇	1	2	yes	—
240	C₂⁴	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	1	no	—
243	C₂²×C₄	—	2	1	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	4	2	no	—
248	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
249	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
251	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
252	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×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	#41×C₁₃₇	1	4	yes	—
258	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
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	C₂×C₈	—	2	4	no	—
264	C₂×C₈	—	2	4	no	—
265	C₄⋊C₄	—	2	4	no	—
266	C₄⋊C₄	—	2	4	no	—
267	C₂²⋊C₄	—	2	4	no	—
268	C₂²⋊C₄	—	2	4	no	—
269	C₄²	—	2	2	no	—
270	C₄²	—	2	2	no	—
271	C₄²	—	2	4	no	—
272	C₄²	—	2	4	no	—
273	C₄²	—	2	2	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	2	no	—
276	C₄²	—	2	1	no	—
277	C₄²	—	2	1	no	—
278	C₄²	—	4	2	no	—
279	C₄²	—	4	2	no	—
280	C₄²	#41×C₁₃₇	1	2	yes	—
281	C₄²	#41×C₁₃₇	1	2	yes	—
282	C₄²	#41×C₁₃₇	1	4	yes	—
283	C₂³	—	2	1	no	—
284	C₂³	—	2	1	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	2	no	—
287	C₂³	#117×C₁₃₇	1	2	yes	—
288	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
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	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	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	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	—	4	4	no	—
311	C₂×C₄	#117×C₁₃₇	1	2	yes	—
312	C₂×C₄	#117×C₁₃₇	1	4	yes	—
313	C₂×C₄	#117×C₁₃₇	1	2	yes	—
314	C₂×C₄	#117×C₁₃₇	1	2	yes	—
315	C₂×C₄	#131×C₁₃₇	1	4	yes	—
316	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
317	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
318	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
319	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
320	C₈	—	4	4	no	—
321	C₈	—	4	4	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	4	no	—
324	C₂²	—	4	1	no	—
325	C₂²	—	4	1	no	—
326	C₂²	—	4	2	no	—
327	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
328	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
329	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
330	C₂²	C₂×#131×C₁₃₇	1	2	yes	—
331	C₂²	#568×C₁₃₇	1	2	yes	—
332	C₄	—	2	2	no	—
333	C₄	—	2	2	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	—	4	2	no	—
340	C₄	#433×C₁₃₇	1	4	yes	—
341	C₄	#529×C₁₃₇	1	2	yes	—
342	C₄	#529×C₁₃₇	1	2	yes	—
343	C₂	—	4	2	no	—
344	C₂	#2283×C₁₃₇	1	1	yes	characteristic
345	C₂	C₂×#433×C₁₃₇	1	1	yes	characteristic
346	C₂	#2921×C₁₃₇	1	1	yes	characteristic
347	C₂	#2925×C₁₃₇	1	2	yes	—
348	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. #1840×C₁₃₇	C₂	semidirect
3. #1831×C₁₃₇	C₂	semidirect
6. #1767×C₁₃₇	C₂	semidirect
7. C₄×C₄⋊C₈×C₁₃₇	C₂	semidirect
9. #1746×C₁₃₇	C₂	semidirect
174. #20786	C₁₃₇	direct (N × H)
175. C₁₃₇	#20786	direct (N × H)
177. #1840	C₂×C₁₃₇	semidirect
178. #1831	C₂×C₁₃₇	semidirect
181. #1767	C₂×C₁₃₇	semidirect
182. C₄×C₄⋊C₈	C₂×C₁₃₇	semidirect
184. #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
#1840×C₁₃₇	2
#1831×C₁₃₇	2
#1818×C₁₃₇	2
#1797×C₁₃₇	2
#1767×C₁₃₇	2
C₄×C₄⋊C₈×C₁₃₇	2
#1750×C₁₃₇	2
#1746×C₁₃₇	2
#20786	137

Subgroups — C137×#20786 #46870172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#20786 #46870172