Subgroups — C₁₃₇×#19646 #46869032

Order 35072.

732 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3210×C₁₃₇	C₂	1	2	yes	maximal, complemented
2	#3182×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#3169×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#3160×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1720×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1714×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1713×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1710×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1706×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1706×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#533×C₁₃₇	C₂²	1	2	yes	—
13	#532×C₁₃₇	C₂²	1	2	yes	—
14	#500×C₁₃₇	C₂²	1	1	yes	characteristic
15	#500×C₁₃₇	C₂²	1	1	yes	characteristic
16	#500×C₁₃₇	C₂²	1	1	yes	characteristic
17	#500×C₁₃₇	C₂²	1	2	yes	—
18	#499×C₁₃₇	—	2	2	no	—
19	#498×C₁₃₇	C₂²	1	2	yes	—
20	#494×C₁₃₇	C₂²	1	2	yes	—
21	#493×C₁₃₇	C₂²	1	1	yes	characteristic
22	#492×C₁₃₇	C₂²	1	2	yes	—
23	#492×C₁₃₇	C₂²	1	2	yes	—
24	#487×C₁₃₇	C₂²	1	2	yes	—
25	#487×C₁₃₇	C₂²	1	2	yes	—
26	#486×C₁₃₇	C₂²	1	2	yes	—
27	#486×C₁₃₇	C₂²	1	2	yes	—
28	#486×C₁₃₇	C₂²	1	2	yes	—
29	#468×C₁₃₇	—	2	4	no	—
30	#466×C₁₃₇	—	2	2	no	—
31	#464×C₁₃₇	—	2	4	no	—
32	#452×C₁₃₇	—	2	4	no	—
33	#440×C₁₃₇	—	2	4	no	—
34	C₄×D₈×C₁₃₇	—	2	2	no	—
35	#431×C₁₃₇	C₂²	1	1	yes	characteristic
36	#427×C₁₃₇	—	2	2	no	—
37	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
39	#322×C₁₃₇	C₂²	1	1	yes	characteristic
40	#322×C₁₃₇	C₂²	1	1	yes	characteristic
41	C₈²×C₁₃₇	C₂²	1	1	yes	characteristic
42	C₈²×C₁₃₇	C₂²	1	1	yes	characteristic
43	C₂×#41×C₁₃₇	—	2	2	no	—
44	C₂×Q₁₆×C₁₃₇	—	2	4	no	—
45	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
46	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
47	C₂×D₈×C₁₃₇	—	2	2	no	—
48	C₂×M₁₆×C₁₃₇	D₄	1	2	yes	—
49	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
50	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
53	#127×C₁₃₇	C₂³	1	2	yes	—
54	#125×C₁₃₇	—	2	2	no	—
55	#124×C₁₃₇	—	2	2	no	—
56	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
57	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
58	#121×C₁₃₇	—	2	2	no	—
59	#121×C₁₃₇	—	2	2	no	—
60	C₄×Q₈×C₁₃₇	—	2	2	no	—
61	C₄×Q₈×C₁₃₇	—	2	2	no	—
62	C₄×D₄×C₁₃₇	—	2	2	no	—
63	C₄×D₄×C₁₃₇	—	2	2	no	—
64	#117×C₁₃₇	—	2	2	no	—
65	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
66	#107×C₁₃₇	—	2	2	no	—
67	#107×C₁₃₇	—	2	2	no	—
68	#107×C₁₃₇	—	2	2	no	—
69	#107×C₁₃₇	—	2	4	no	—
70	#106×C₁₃₇	—	2	4	no	—
71	C₄⋊C₈×C₁₃₇	D₄	1	2	yes	—
72	#103×C₁₃₇	—	2	4	no	—
73	#103×C₁₃₇	—	2	4	no	—
74	#102×C₁₃₇	—	2	4	no	—
75	#102×C₁₃₇	—	2	4	no	—
76	#102×C₁₃₇	—	2	4	no	—
77	C₂²⋊C₈×C₁₃₇	D₄	1	2	yes	—
78	#97×C₁₃₇	D₄	1	2	yes	—
79	C₄×C₈×C₁₃₇	D₄	1	2	yes	—
80	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
82	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
83	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
84	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
86	#41×C₁₃₇	—	8	4	no	—
87	C₂×Q₈×C₁₃₇	—	2	2	no	—
88	C₂×Q₈×C₁₃₇	—	2	2	no	—
89	C₂×Q₈×C₁₃₇	—	2	2	no	—
90	C₂×D₄×C₁₃₇	—	2	2	no	—
91	C₂×D₄×C₁₃₇	—	2	2	no	—
92	C₂×D₄×C₁₃₇	—	2	2	no	—
93	C₂×D₄×C₁₃₇	—	4	2	no	—
94	C₂²×C₄×C₁₃₇	—	4	2	no	—
95	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
98	Q₁₆×C₁₃₇	—	8	4	no	—
99	SD₁₆×C₁₃₇	—	4	8	no	—
100	SD₁₆×C₁₃₇	—	8	4	no	—
101	D₈×C₁₃₇	—	4	4	no	—
102	M₁₆×C₁₃₇	—	2	4	no	—
103	C₂×C₈×C₁₃₇	—	2	4	no	—
104	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
105	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
110	C₄⋊C₄×C₁₃₇	—	2	2	no	—
111	C₄⋊C₄×C₁₃₇	—	2	2	no	—
112	C₄⋊C₄×C₁₃₇	—	2	2	no	—
113	C₄⋊C₄×C₁₃₇	—	2	2	no	—
114	C₄⋊C₄×C₁₃₇	—	2	2	no	—
115	C₄⋊C₄×C₁₃₇	—	2	2	no	—
116	C₄⋊C₄×C₁₃₇	—	4	2	no	—
117	C₄⋊C₄×C₁₃₇	—	4	2	no	—
118	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
119	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
120	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
121	C₄²×C₁₃₇	—	4	2	no	—
122	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
126	C₂³×C₁₃₇	—	4	2	no	—
127	C₂³×C₁₃₇	#127	1	1	yes	characteristic
128	Q₈×C₁₃₇	—	4	4	no	—
129	Q₈×C₁₃₇	—	4	4	no	—
130	Q₈×C₁₃₇	—	4	4	no	—
131	D₄×C₁₃₇	—	4	4	no	—
132	D₄×C₁₃₇	—	4	4	no	—
133	D₄×C₁₃₇	—	4	4	no	—
134	D₄×C₁₃₇	—	8	4	no	—
135	C₂×C₄×C₁₃₇	—	2	2	no	—
136	C₂×C₄×C₁₃₇	—	2	2	no	—
137	C₂×C₄×C₁₃₇	—	2	2	no	—
138	C₂×C₄×C₁₃₇	—	4	2	no	—
139	C₂×C₄×C₁₃₇	—	4	2	no	—
140	C₂×C₄×C₁₃₇	—	4	2	no	—
141	C₂×C₄×C₁₃₇	—	8	4	no	—
142	C₂×C₄×C₁₃₇	#127	1	1	yes	characteristic
143	C₂×C₄×C₁₃₇	#127	1	1	yes	characteristic
144	C₂×C₄×C₁₃₇	#127	1	1	yes	characteristic
145	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
148	C₈×C₁₃₇	—	2	2	no	—
149	C₈×C₁₃₇	—	2	2	no	—
150	C₈×C₁₃₇	—	2	2	no	—
151	C₈×C₁₃₇	—	2	2	no	—
152	C₈×C₁₃₇	#135	1	4	yes	—
153	C₈×C₁₃₇	#137	1	4	yes	—
154	C₂²×C₁₃₇	—	2	1	no	—
155	C₂²×C₁₃₇	—	2	1	no	—
156	C₂²×C₁₃₇	—	2	1	no	—
157	C₂²×C₁₃₇	—	8	2	no	—
158	C₂²×C₁₃₇	—	8	2	no	—
159	C₂²×C₁₃₇	—	8	2	no	—
160	C₂²×C₁₃₇	C₂×#127	1	1	yes	characteristic
161	C₄×C₁₃₇	—	2	1	no	—
162	C₄×C₁₃₇	—	2	1	no	—
163	C₄×C₁₃₇	—	2	1	no	—
164	C₄×C₁₃₇	—	8	2	no	—
165	C₄×C₁₃₇	—	8	2	no	—
166	C₄×C₁₃₇	—	8	2	no	—
167	C₄×C₁₃₇	C₂×#135	1	2	yes	—
168	C₄×C₁₃₇	C₂×#137	1	2	yes	—
169	C₄×C₁₃₇	#576	1	2	yes	—
170	C₂×C₁₃₇	—	4	1	no	—
171	C₂×C₁₃₇	—	16	2	no	—
172	C₂×C₁₃₇	#3147	1	1	yes	characteristic
173	C₂×C₁₃₇	#3152	1	1	yes	characteristic
174	C₂×C₁₃₇	#3155	1	1	yes	characteristic
175	#19646	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₁₃₇	#19646	1	1	yes	characteristic, direct product factor, Sylow
177	#3210	C₂×C₁₃₇	1	2	yes	complemented
178	#3182	C₂×C₁₃₇	1	2	yes	complemented
179	#3169	C₂×C₁₃₇	1	1	yes	characteristic
180	#3160	C₂×C₁₃₇	1	1	yes	characteristic, complemented
181	#1720	C₂×C₁₃₇	1	2	yes	complemented
182	#1714	C₂×C₁₃₇	1	2	yes	complemented
183	#1713	C₂×C₁₃₇	1	1	yes	characteristic, complemented
184	#1710	C₂×C₁₃₇	1	1	yes	characteristic, complemented
185	#1706	C₂×C₁₃₇	1	1	yes	characteristic, complemented
186	#1706	C₂×C₁₃₇	1	1	yes	characteristic, complemented
187	C₈×M₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
188	#533	C₂²×C₁₃₇	1	2	yes	—
189	#532	C₂²×C₁₃₇	1	2	yes	—
190	#500	C₂²×C₁₃₇	1	1	yes	characteristic
191	#500	C₂²×C₁₃₇	1	1	yes	characteristic
192	#500	C₂²×C₁₃₇	1	1	yes	characteristic
193	#500	C₂²×C₁₃₇	1	2	yes	—
194	#499	—	2	2	no	—
195	#498	C₂²×C₁₃₇	1	2	yes	—
196	#494	C₂²×C₁₃₇	1	2	yes	—
197	#493	C₂²×C₁₃₇	1	1	yes	characteristic
198	#492	C₂²×C₁₃₇	1	2	yes	—
199	#492	C₂²×C₁₃₇	1	2	yes	—
200	#487	C₂²×C₁₃₇	1	2	yes	—
201	#487	C₂²×C₁₃₇	1	2	yes	—
202	#486	C₂²×C₁₃₇	1	2	yes	—
203	#486	C₂²×C₁₃₇	1	2	yes	—
204	#486	C₂²×C₁₃₇	1	2	yes	—
205	#468	—	2	4	no	—
206	#466	—	2	2	no	—
207	#464	—	2	4	no	—
208	#452	—	2	4	no	—
209	#440	—	2	4	no	—
210	C₄×D₈	—	2	2	no	—
211	#431	C₂²×C₁₃₇	1	1	yes	characteristic
212	#427	—	2	2	no	—
213	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
214	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
215	#322	C₂²×C₁₃₇	1	1	yes	characteristic
216	#322	C₂²×C₁₃₇	1	1	yes	characteristic
217	C₈²	C₂²×C₁₃₇	1	1	yes	characteristic
218	C₈²	C₂²×C₁₃₇	1	1	yes	characteristic
219	C₂×#41	—	2	2	no	—
220	C₂×Q₁₆	—	2	4	no	—
221	C₂×SD₁₆	—	2	4	no	—
222	C₂×SD₁₆	—	2	4	no	—
223	C₂×D₈	—	2	2	no	—
224	C₂×M₁₆	D₄×C₁₃₇	1	2	yes	—
225	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
226	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
227	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
228	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
229	#127	C₂³×C₁₃₇	1	2	yes	—
230	#125	—	2	2	no	—
231	#124	—	2	2	no	—
232	C₂²⋊Q₈	—	2	2	no	—
233	C₂²⋊Q₈	—	2	2	no	—
234	#121	—	2	2	no	—
235	#121	—	2	2	no	—
236	C₄×Q₈	—	2	2	no	—
237	C₄×Q₈	—	2	2	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	—	2	2	no	—
240	#117	—	2	2	no	—
241	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
242	#107	—	2	2	no	—
243	#107	—	2	2	no	—
244	#107	—	2	2	no	—
245	#107	—	2	4	no	—
246	#106	—	2	4	no	—
247	C₄⋊C₈	D₄×C₁₃₇	1	2	yes	—
248	#103	—	2	4	no	—
249	#103	—	2	4	no	—
250	#102	—	2	4	no	—
251	#102	—	2	4	no	—
252	#102	—	2	4	no	—
253	C₂²⋊C₈	D₄×C₁₃₇	1	2	yes	—
254	#97	D₄×C₁₃₇	1	2	yes	—
255	C₄×C₈	D₄×C₁₃₇	1	2	yes	—
256	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
257	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
258	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
259	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
260	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
261	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
262	#41	—	8	4	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
274	Q₁₆	—	8	4	no	—
275	SD₁₆	—	4	8	no	—
276	SD₁₆	—	8	4	no	—
277	D₈	—	4	4	no	—
278	M₁₆	—	2	4	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
281	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
282	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
283	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
284	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
285	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	4	2	no	—
293	C₄⋊C₄	—	4	2	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₂²⋊C₄	—	4	2	no	—
296	C₂²⋊C₄	—	4	2	no	—
297	C₄²	—	4	2	no	—
298	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
299	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
300	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
301	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
302	C₂³	—	4	2	no	—
303	C₂³	#127×C₁₃₇	1	1	yes	characteristic
304	Q₈	—	4	4	no	—
305	Q₈	—	4	4	no	—
306	Q₈	—	4	4	no	—
307	D₄	—	4	4	no	—
308	D₄	—	4	4	no	—
309	D₄	—	4	4	no	—
310	D₄	—	8	4	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	8	4	no	—
318	C₂×C₄	#127×C₁₃₇	1	1	yes	characteristic
319	C₂×C₄	#127×C₁₃₇	1	1	yes	characteristic
320	C₂×C₄	#127×C₁₃₇	1	1	yes	characteristic
321	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
322	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
323	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
324	C₈	—	2	2	no	—
325	C₈	—	2	2	no	—
326	C₈	—	2	2	no	—
327	C₈	—	2	2	no	—
328	C₈	#135×C₁₃₇	1	4	yes	—
329	C₈	#137×C₁₃₇	1	4	yes	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	1	no	—
333	C₂²	—	8	2	no	—
334	C₂²	—	8	2	no	—
335	C₂²	—	8	2	no	—
336	C₂²	C₂×#127×C₁₃₇	1	1	yes	characteristic
337	C₄	—	2	1	no	—
338	C₄	—	2	1	no	—
339	C₄	—	2	1	no	—
340	C₄	—	8	2	no	—
341	C₄	—	8	2	no	—
342	C₄	—	8	2	no	—
343	C₄	C₂×#135×C₁₃₇	1	2	yes	—
344	C₄	C₂×#137×C₁₃₇	1	2	yes	—
345	C₄	#576×C₁₃₇	1	2	yes	—
346	C₂	—	4	1	no	—
347	C₂	—	16	2	no	—
348	C₂	#3147×C₁₃₇	1	1	yes	characteristic
349	C₂	#3152×C₁₃₇	1	1	yes	characteristic
350	C₂	#3155×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	#3169×C₁₃₇	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3210×C₁₃₇	C₂	semidirect
2. #3182×C₁₃₇	C₂	semidirect
4. #3160×C₁₃₇	C₂	semidirect
5. #1720×C₁₃₇	C₂	semidirect
6. #1714×C₁₃₇	C₂	semidirect
7. #1713×C₁₃₇	C₂	semidirect
8. #1710×C₁₃₇	C₂	semidirect
9. #1706×C₁₃₇	C₂	semidirect
10. #1706×C₁₃₇	C₂	semidirect
11. C₈×M₁₆×C₁₃₇	C₂	semidirect
175. #19646	C₁₃₇	direct (N × H)
176. C₁₃₇	#19646	direct (N × H)
177. #3210	C₂×C₁₃₇	semidirect
178. #3182	C₂×C₁₃₇	semidirect
180. #3160	C₂×C₁₃₇	semidirect
181. #1720	C₂×C₁₃₇	semidirect
182. #1714	C₂×C₁₃₇	semidirect
183. #1713	C₂×C₁₃₇	semidirect
184. #1710	C₂×C₁₃₇	semidirect
185. #1706	C₂×C₁₃₇	semidirect
186. #1706	C₂×C₁₃₇	semidirect
187. C₈×M₁₆	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3210×C₁₃₇	2
#3182×C₁₃₇	2
#3169×C₁₃₇	2
#3160×C₁₃₇	2
#1720×C₁₃₇	2
#1714×C₁₃₇	2
#1713×C₁₃₇	2
#1710×C₁₃₇	2
#1706×C₁₃₇	2
C₈×M₁₆×C₁₃₇	2
#19646	137

Subgroups — C137×#19646 #46869032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19646 #46869032