Subgroups — C₁₃₇×#19195 #46868581

Order 35072.

638 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3246×C₁₃₇	C₂	1	2	yes	maximal
2	#3160×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2931×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1691×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	#1675×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1673×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	C₂×#335×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1550×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	C₂×#131×C₁₃₇	—	2	1	no	—
10	#533×C₁₃₇	C₂²	1	2	yes	—
11	#532×C₁₃₇	C₂²	1	1	yes	characteristic
12	#500×C₁₃₇	C₂²	1	1	yes	characteristic
13	#500×C₁₃₇	C₂²	1	1	yes	characteristic
14	#499×C₁₃₇	—	2	1	no	—
15	#499×C₁₃₇	—	2	1	no	—
16	#498×C₁₃₇	C₂²	1	2	yes	—
17	#476×C₁₃₇	C₂²	1	4	yes	—
18	#475×C₁₃₇	—	2	2	no	—
19	#465×C₁₃₇	—	2	4	no	—
20	#461×C₁₃₇	C₂²	1	4	yes	—
21	#460×C₁₃₇	—	2	2	no	—
22	#436×C₁₃₇	—	2	1	no	—
23	#436×C₁₃₇	C₂²	1	2	yes	—
24	C₈×D₄×C₁₃₇	—	2	1	no	—
25	C₈×D₄×C₁₃₇	C₂²	1	2	yes	—
26	#427×C₁₃₇	—	2	1	no	—
27	#427×C₁₃₇	—	2	1	no	—
28	#423×C₁₃₇	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
30	#408×C₁₃₇	—	2	1	no	—
31	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
32	#335×C₁₃₇	C₂²	1	2	yes	—
33	#335×C₁₃₇	C₂²	1	2	yes	—
34	#333×C₁₃₇	C₂²	1	4	yes	—
35	#332×C₁₃₇	C₂²	1	4	yes	—
36	C₂×#41×C₁₃₇	—	2	1	no	—
37	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
38	#131×C₁₃₇	—	4	4	no	—
39	C₂×M₁₆×C₁₃₇	—	2	1	no	—
40	C₂×M₁₆×C₁₃₇	—	2	2	no	—
41	C₂²×C₈×C₁₃₇	—	2	2	no	—
42	C₂²×C₈×C₁₃₇	—	2	2	no	—
43	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
45	C₄⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
46	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
47	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
48	#127×C₁₃₇	D₄	1	1	yes	characteristic
49	#125×C₁₃₇	—	2	2	no	—
50	#124×C₁₃₇	—	2	1	no	—
51	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
52	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
53	#121×C₁₃₇	—	2	1	no	—
54	#121×C₁₃₇	D₄	1	2	yes	—
55	C₄×Q₈×C₁₃₇	—	2	2	no	—
56	C₄×Q₈×C₁₃₇	—	2	2	no	—
57	C₄×D₄×C₁₃₇	—	2	1	no	—
58	C₄×D₄×C₁₃₇	C₂³	1	2	yes	—
59	#117×C₁₃₇	—	2	2	no	—
60	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
61	#107×C₁₃₇	—	2	1	no	—
62	#107×C₁₃₇	—	2	1	no	—
63	#107×C₁₃₇	—	2	1	no	—
64	#107×C₁₃₇	—	2	1	no	—
65	#106×C₁₃₇	—	2	2	no	—
66	#106×C₁₃₇	—	2	2	no	—
67	#106×C₁₃₇	—	2	4	no	—
68	C₄⋊C₈×C₁₃₇	—	2	2	no	—
69	C₄⋊C₈×C₁₃₇	—	2	1	no	—
70	C₄⋊C₈×C₁₃₇	C₂³	1	4	yes	—
71	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
72	#103×C₁₃₇	—	2	4	no	—
73	#102×C₁₃₇	—	2	4	no	—
74	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
75	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
76	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
77	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
78	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
80	#41×C₁₃₇	—	4	2	no	—
81	#41×C₁₃₇	—	4	2	no	—
82	C₂×Q₈×C₁₃₇	—	2	1	no	—
83	C₂×Q₈×C₁₃₇	—	2	2	no	—
84	C₂×Q₈×C₁₃₇	—	2	2	no	—
85	C₂×D₄×C₁₃₇	—	2	2	no	—
86	C₂×D₄×C₁₃₇	—	2	1	no	—
87	C₂×D₄×C₁₃₇	—	2	1	no	—
88	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₃₇	—	2	2	no	—
90	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
93	SD₁₆×C₁₃₇	—	8	4	no	—
94	M₁₆×C₁₃₇	—	4	2	no	—
95	M₁₆×C₁₃₇	—	4	4	no	—
96	C₂×C₈×C₁₃₇	—	2	2	no	—
97	C₂×C₈×C₁₃₇	—	2	2	no	—
98	C₂×C₈×C₁₃₇	—	2	4	no	—
99	C₂×C₈×C₁₃₇	—	4	4	no	—
100	C₂×C₈×C₁₃₇	—	8	2	no	—
101	C₂×C₈×C₁₃₇	SD₁₆	1	4	yes	complemented
102	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
103	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
104	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
105	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
106	C₄⋊C₄×C₁₃₇	—	2	1	no	—
107	C₄⋊C₄×C₁₃₇	—	2	2	no	—
108	C₄⋊C₄×C₁₃₇	—	2	2	no	—
109	C₄⋊C₄×C₁₃₇	—	2	2	no	—
110	C₄⋊C₄×C₁₃₇	—	2	2	no	—
111	C₄⋊C₄×C₁₃₇	—	4	2	no	—
112	C₄⋊C₄×C₁₃₇	—	4	2	no	—
113	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
114	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
115	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
116	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
117	C₄²×C₁₃₇	—	4	2	no	—
118	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₁₃₇	#41	1	1	yes	characteristic
121	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
122	C₂³×C₁₃₇	—	2	2	no	—
123	C₂³×C₁₃₇	#121	1	1	yes	characteristic
124	Q₈×C₁₃₇	—	4	2	no	—
125	Q₈×C₁₃₇	—	4	2	no	—
126	Q₈×C₁₃₇	—	4	2	no	—
127	Q₈×C₁₃₇	—	8	2	no	—
128	D₄×C₁₃₇	—	2	2	no	—
129	D₄×C₁₃₇	—	2	2	no	—
130	D₄×C₁₃₇	—	4	2	no	—
131	D₄×C₁₃₇	—	4	4	no	—
132	D₄×C₁₃₇	—	4	2	no	—
133	C₂×C₄×C₁₃₇	—	2	1	no	—
134	C₂×C₄×C₁₃₇	—	2	1	no	—
135	C₂×C₄×C₁₃₇	—	2	2	no	—
136	C₂×C₄×C₁₃₇	—	4	1	no	—
137	C₂×C₄×C₁₃₇	—	4	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	#121	1	1	yes	characteristic
142	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
143	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
144	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	2	yes	—
145	C₂×C₄×C₁₃₇	#137	1	2	yes	—
146	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
149	C₈×C₁₃₇	—	2	1	no	—
150	C₈×C₁₃₇	—	2	1	no	—
151	C₈×C₁₃₇	—	4	2	no	—
152	C₈×C₁₃₇	—	4	4	no	—
153	C₈×C₁₃₇	C₂×SD₁₆	1	2	yes	—
154	C₈×C₁₃₇	C₂×SD₁₆	1	2	yes	—
155	C₂²×C₁₃₇	—	2	1	no	—
156	C₂²×C₁₃₇	—	2	1	no	—
157	C₂²×C₁₃₇	—	4	2	no	—
158	C₂²×C₁₃₇	—	4	2	no	—
159	C₂²×C₁₃₇	—	4	2	no	—
160	C₂²×C₁₃₇	#461	1	2	yes	—
161	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
162	C₄×C₁₃₇	—	2	1	no	—
163	C₄×C₁₃₇	—	2	1	no	—
164	C₄×C₁₃₇	—	2	1	no	—
165	C₄×C₁₃₇	—	4	2	no	—
166	C₄×C₁₃₇	—	8	2	no	—
167	C₄×C₁₃₇	—	8	2	no	—
168	C₄×C₁₃₇	#461	1	2	yes	—
169	C₄×C₁₃₇	C₂²×SD₁₆	1	1	yes	characteristic
170	C₄×C₁₃₇	C₂×#137	1	1	yes	characteristic
171	C₄×C₁₃₇	#576	1	1	yes	characteristic
172	C₄×C₁₃₇	#578	1	1	yes	characteristic
173	C₂×C₁₃₇	—	2	2	no	—
174	C₂×C₁₃₇	—	8	2	no	—
175	C₂×C₁₃₇	C₂×#461	1	1	yes	characteristic
176	C₂×C₁₃₇	#3061	1	1	yes	characteristic
177	C₂×C₁₃₇	#3067	1	1	yes	characteristic
178	#19195	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₁₃₇	#19195	1	1	yes	characteristic, direct product factor, Sylow
180	#3246	C₂×C₁₃₇	1	2	yes	—
181	#3160	C₂×C₁₃₇	1	1	yes	characteristic, complemented
182	#2931	C₂×C₁₃₇	1	1	yes	characteristic
183	#1691	C₂×C₁₃₇	1	4	yes	complemented
184	#1675	C₂×C₁₃₇	1	2	yes	complemented
185	#1673	C₂×C₁₃₇	1	2	yes	complemented
186	C₂×#335	C₂×C₁₃₇	1	1	yes	characteristic, complemented
187	#1550	C₂×C₁₃₇	1	2	yes	complemented
188	C₂×#131	—	2	1	no	—
189	#533	C₂²×C₁₃₇	1	2	yes	—
190	#532	C₂²×C₁₃₇	1	1	yes	characteristic
191	#500	C₂²×C₁₃₇	1	1	yes	characteristic
192	#500	C₂²×C₁₃₇	1	1	yes	characteristic
193	#499	—	2	1	no	—
194	#499	—	2	1	no	—
195	#498	C₂²×C₁₃₇	1	2	yes	—
196	#476	C₂²×C₁₃₇	1	4	yes	—
197	#475	—	2	2	no	—
198	#465	—	2	4	no	—
199	#461	C₂²×C₁₃₇	1	4	yes	—
200	#460	—	2	2	no	—
201	#436	—	2	1	no	—
202	#436	C₂²×C₁₃₇	1	2	yes	—
203	C₈×D₄	—	2	1	no	—
204	C₈×D₄	C₂²×C₁₃₇	1	2	yes	—
205	#427	—	2	1	no	—
206	#427	—	2	1	no	—
207	#423	C₂²×C₁₃₇	1	1	yes	characteristic
208	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
209	#408	—	2	1	no	—
210	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
211	#335	C₂²×C₁₃₇	1	2	yes	—
212	#335	C₂²×C₁₃₇	1	2	yes	—
213	#333	C₂²×C₁₃₇	1	4	yes	—
214	#332	C₂²×C₁₃₇	1	4	yes	—
215	C₂×#41	—	2	1	no	—
216	C₂×SD₁₆	—	2	4	no	—
217	#131	—	4	4	no	—
218	C₂×M₁₆	—	2	1	no	—
219	C₂×M₁₆	—	2	2	no	—
220	C₂²×C₈	—	2	2	no	—
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
223	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
224	C₄⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
225	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
226	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
227	#127	D₄×C₁₃₇	1	1	yes	characteristic
228	#125	—	2	2	no	—
229	#124	—	2	1	no	—
230	C₂²⋊Q₈	—	2	2	no	—
231	C₂²⋊Q₈	—	2	2	no	—
232	#121	—	2	1	no	—
233	#121	D₄×C₁₃₇	1	2	yes	—
234	C₄×Q₈	—	2	2	no	—
235	C₄×Q₈	—	2	2	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	C₂³×C₁₃₇	1	2	yes	—
238	#117	—	2	2	no	—
239	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
240	#107	—	2	1	no	—
241	#107	—	2	1	no	—
242	#107	—	2	1	no	—
243	#107	—	2	1	no	—
244	#106	—	2	2	no	—
245	#106	—	2	2	no	—
246	#106	—	2	4	no	—
247	C₄⋊C₈	—	2	2	no	—
248	C₄⋊C₈	—	2	1	no	—
249	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
250	C₄⋊C₈	C₂³×C₁₃₇	1	4	yes	—
251	#103	—	2	4	no	—
252	#102	—	2	4	no	—
253	C₂²⋊C₈	—	2	2	no	—
254	C₂²⋊C₈	—	2	2	no	—
255	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
256	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
257	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
258	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
259	#41	—	4	2	no	—
260	#41	—	4	2	no	—
261	C₂×Q₈	—	2	1	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	2	1	no	—
266	C₂×D₄	—	2	1	no	—
267	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
271	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
272	SD₁₆	—	8	4	no	—
273	M₁₆	—	4	2	no	—
274	M₁₆	—	4	4	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	4	4	no	—
279	C₂×C₈	—	8	2	no	—
280	C₂×C₈	SD₁₆×C₁₃₇	1	4	yes	complemented
281	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
282	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
283	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
284	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
285	C₄⋊C₄	—	2	1	no	—
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	—	4	2	no	—
291	C₄⋊C₄	—	4	2	no	—
292	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₂²⋊C₄	—	4	2	no	—
296	C₄²	—	4	2	no	—
297	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
298	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
299	C₄²	#41×C₁₃₇	1	1	yes	characteristic
300	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
301	C₂³	—	2	2	no	—
302	C₂³	#121×C₁₃₇	1	1	yes	characteristic
303	Q₈	—	4	2	no	—
304	Q₈	—	4	2	no	—
305	Q₈	—	4	2	no	—
306	Q₈	—	8	2	no	—
307	D₄	—	2	2	no	—
308	D₄	—	2	2	no	—
309	D₄	—	4	2	no	—
310	D₄	—	4	4	no	—
311	D₄	—	4	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
321	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
322	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
323	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	2	yes	—
324	C₂×C₄	#137×C₁₃₇	1	2	yes	—
325	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
326	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
327	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
328	C₈	—	2	1	no	—
329	C₈	—	2	1	no	—
330	C₈	—	4	2	no	—
331	C₈	—	4	4	no	—
332	C₈	C₂×SD₁₆×C₁₃₇	1	2	yes	—
333	C₈	C₂×SD₁₆×C₁₃₇	1	2	yes	—
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	4	2	no	—
338	C₂²	—	4	2	no	—
339	C₂²	#461×C₁₃₇	1	2	yes	—
340	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
341	C₄	—	2	1	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	4	2	no	—
345	C₄	—	8	2	no	—
346	C₄	—	8	2	no	—
347	C₄	#461×C₁₃₇	1	2	yes	—
348	C₄	C₂²×SD₁₆×C₁₃₇	1	1	yes	characteristic
349	C₄	C₂×#137×C₁₃₇	1	1	yes	characteristic
350	C₄	#576×C₁₃₇	1	1	yes	characteristic
351	C₄	#578×C₁₃₇	1	1	yes	characteristic
352	C₂	—	2	2	no	—
353	C₂	—	8	2	no	—
354	C₂	C₂×#461×C₁₃₇	1	1	yes	characteristic
355	C₂	#3061×C₁₃₇	1	1	yes	characteristic
356	C₂	#3067×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	#532×C₁₃₇	C₂²
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
2. #3160×C₁₃₇	C₂	semidirect
4. #1691×C₁₃₇	C₂	semidirect
5. #1675×C₁₃₇	C₂	semidirect
6. #1673×C₁₃₇	C₂	semidirect
7. C₂×#335×C₁₃₇	C₂	semidirect
8. #1550×C₁₃₇	C₂	semidirect
101. C₂×C₈×C₁₃₇	SD₁₆	semidirect
178. #19195	C₁₃₇	direct (N × H)
179. C₁₃₇	#19195	direct (N × H)
181. #3160	C₂×C₁₃₇	semidirect
183. #1691	C₂×C₁₃₇	semidirect
184. #1675	C₂×C₁₃₇	semidirect
185. #1673	C₂×C₁₃₇	semidirect
186. C₂×#335	C₂×C₁₃₇	semidirect
187. #1550	C₂×C₁₃₇	semidirect
280. C₂×C₈	SD₁₆×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3246×C₁₃₇	2
#3160×C₁₃₇	2
#2931×C₁₃₇	2
#1691×C₁₃₇	2
#1675×C₁₃₇	2
#1673×C₁₃₇	2
C₂×#335×C₁₃₇	2
#1550×C₁₃₇	2
#19195	137

Subgroups — C137×#19195 #46868581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19195 #46868581