Subgroups — C₁₃₇×#19258 #46868644

Order 35072.

738 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3169×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#3109×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×D₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#1677×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	#1675×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1667×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1568×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1551×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	C₂³×C₈×C₁₃₇	—	2	1	no	—
10	#532×C₁₃₇	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
12	#500×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
13	#493×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
14	#486×C₁₃₇	C₂²	1	2	yes	complemented
15	#481×C₁₃₇	—	2	2	no	—
16	#476×C₁₃₇	C₂²	1	4	yes	—
17	#466×C₁₃₇	—	2	1	no	—
18	#466×C₁₃₇	—	2	1	no	—
19	#459×C₁₃₇	C₂²	1	4	yes	—
20	#447×C₁₃₇	—	2	2	no	—
21	#442×C₁₃₇	—	2	4	no	—
22	C₄×D₈×C₁₃₇	—	2	1	no	—
23	C₄×D₈×C₁₃₇	—	2	1	no	—
24	C₈×D₄×C₁₃₇	—	2	1	no	—
25	C₈×D₄×C₁₃₇	—	2	1	no	—
26	C₈×D₄×C₁₃₇	C₂²	1	2	yes	—
27	C₈×D₄×C₁₃₇	C₂²	1	2	yes	—
28	#432×C₁₃₇	C₂²	1	2	yes	—
29	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₁₃₇	—	2	1	no	—
31	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
32	#335×C₁₃₇	C₂²	1	2	yes	complemented
33	#334×C₁₃₇	C₂²	1	2	yes	complemented
34	#333×C₁₃₇	C₂²	1	4	yes	complemented
35	#331×C₁₃₇	C₂²	1	4	yes	complemented
36	C₂×#41×C₁₃₇	—	2	2	no	—
37	C₂²×D₄×C₁₃₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃₇	—	2	1	no	—
39	C₂×D₈×C₁₃₇	—	2	4	no	—
40	C₂×D₈×C₁₃₇	—	2	1	no	—
41	C₂×D₈×C₁₃₇	—	2	1	no	—
42	C₂²×C₈×C₁₃₇	—	2	1	no	—
43	C₂²×C₈×C₁₃₇	—	2	2	no	—
44	C₂²×C₈×C₁₃₇	—	2	2	no	—
45	C₂²×C₈×C₁₃₇	—	4	4	no	—
46	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
48	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
49	#127×C₁₃₇	C₂³	1	2	yes	—
50	#124×C₁₃₇	—	2	2	no	—
51	#121×C₁₃₇	—	2	2	no	—
52	#121×C₁₃₇	—	2	2	no	—
53	C₄×D₄×C₁₃₇	—	2	1	no	—
54	C₄×D₄×C₁₃₇	—	2	2	no	—
55	C₄×D₄×C₁₃₇	—	2	2	no	—
56	C₄×D₄×C₁₃₇	—	2	1	no	—
57	C₄×D₄×C₁₃₇	D₄	1	2	yes	—
58	C₄×D₄×C₁₃₇	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
61	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
62	#107×C₁₃₇	—	2	1	no	—
63	#107×C₁₃₇	—	2	1	no	—
64	#106×C₁₃₇	—	2	4	no	—
65	C₄⋊C₈×C₁₃₇	—	2	1	no	—
66	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
67	C₄⋊C₈×C₁₃₇	C₂³	1	4	yes	—
68	#102×C₁₃₇	—	2	4	no	—
69	#102×C₁₃₇	—	2	2	no	—
70	#102×C₁₃₇	—	2	2	no	—
71	#102×C₁₃₇	—	2	4	no	—
72	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
73	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
74	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
75	#97×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	C₂⁴×C₁₃₇	—	2	1	no	—
81	#41×C₁₃₇	—	8	4	no	—
82	C₂×Q₈×C₁₃₇	—	2	2	no	—
83	C₂×D₄×C₁₃₇	—	2	4	no	—
84	C₂×D₄×C₁₃₇	—	2	1	no	—
85	C₂×D₄×C₁₃₇	—	2	2	no	—
86	C₂×D₄×C₁₃₇	—	2	2	no	—
87	C₂×D₄×C₁₃₇	—	2	2	no	—
88	C₂×D₄×C₁₃₇	—	4	2	no	—
89	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₃₇	—	2	1	no	—
91	C₂²×C₄×C₁₃₇	—	2	2	no	—
92	C₂²×C₄×C₁₃₇	—	2	2	no	—
93	C₂²×C₄×C₁₃₇	—	4	2	no	—
94	C₂²×C₄×C₁₃₇	—	4	2	no	—
95	C₂²×C₄×C₁₃₇	—	4	2	no	—
96	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
99	D₈×C₁₃₇	—	4	2	no	—
100	D₈×C₁₃₇	—	4	8	no	—
101	D₈×C₁₃₇	—	4	2	no	—
102	C₂×C₈×C₁₃₇	—	2	2	no	—
103	C₂×C₈×C₁₃₇	—	2	4	no	—
104	C₂×C₈×C₁₃₇	—	2	2	no	—
105	C₂×C₈×C₁₃₇	—	4	1	no	—
106	C₂×C₈×C₁₃₇	—	4	4	no	—
107	C₂×C₈×C₁₃₇	—	4	2	no	—
108	C₂×C₈×C₁₃₇	—	4	4	no	—
109	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
113	C₄⋊C₄×C₁₃₇	—	2	1	no	—
114	C₄⋊C₄×C₁₃₇	—	2	2	no	—
115	C₄⋊C₄×C₁₃₇	—	2	2	no	—
116	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
117	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
118	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
119	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
120	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
121	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₃₇	#41	1	1	yes	characteristic
124	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
125	C₂³×C₁₃₇	—	2	4	no	—
126	C₂³×C₁₃₇	—	2	2	no	—
127	C₂³×C₁₃₇	—	4	2	no	—
128	C₂³×C₁₃₇	—	4	2	no	—
129	C₂³×C₁₃₇	—	4	2	no	—
130	C₂³×C₁₃₇	#121	1	1	yes	characteristic
131	Q₈×C₁₃₇	—	8	2	no	—
132	D₄×C₁₃₇	—	2	4	no	—
133	D₄×C₁₃₇	—	2	2	no	—
134	D₄×C₁₃₇	—	4	4	no	—
135	D₄×C₁₃₇	—	4	2	no	—
136	D₄×C₁₃₇	—	4	2	no	—
137	D₄×C₁₃₇	—	8	2	no	—
138	D₄×C₁₃₇	—	8	4	no	—
139	D₄×C₁₃₇	#135	1	4	yes	—
140	C₂×C₄×C₁₃₇	—	2	2	no	—
141	C₂×C₄×C₁₃₇	—	2	2	no	—
142	C₂×C₄×C₁₃₇	—	2	1	no	—
143	C₂×C₄×C₁₃₇	—	2	1	no	—
144	C₂×C₄×C₁₃₇	—	2	2	no	—
145	C₂×C₄×C₁₃₇	—	4	4	no	—
146	C₂×C₄×C₁₃₇	—	4	2	no	—
147	C₂×C₄×C₁₃₇	—	4	2	no	—
148	C₂×C₄×C₁₃₇	—	4	2	no	—
149	C₂×C₄×C₁₃₇	—	4	2	no	—
150	C₂×C₄×C₁₃₇	—	8	4	no	—
151	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
153	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
154	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
157	C₈×C₁₃₇	—	2	1	no	—
158	C₈×C₁₃₇	—	2	1	no	—
159	C₈×C₁₃₇	—	2	1	no	—
160	C₈×C₁₃₇	—	4	4	no	—
161	C₈×C₁₃₇	—	4	2	no	—
162	C₈×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
163	C₂²×C₁₃₇	—	2	1	no	—
164	C₂²×C₁₃₇	—	2	1	no	—
165	C₂²×C₁₃₇	—	2	4	no	—
166	C₂²×C₁₃₇	—	4	8	no	—
167	C₂²×C₁₃₇	—	4	2	no	—
168	C₂²×C₁₃₇	—	4	2	no	—
169	C₂²×C₁₃₇	—	8	2	no	—
170	C₂²×C₁₃₇	—	8	2	no	—
171	C₂²×C₁₃₇	—	8	2	no	—
172	C₂²×C₁₃₇	#472	1	2	yes	—
173	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
174	C₄×C₁₃₇	—	2	1	no	—
175	C₄×C₁₃₇	—	2	1	no	—
176	C₄×C₁₃₇	—	2	1	no	—
177	C₄×C₁₃₇	—	2	1	no	—
178	C₄×C₁₃₇	—	4	2	no	—
179	C₄×C₁₃₇	—	8	2	no	—
180	C₄×C₁₃₇	C₂×#135	1	2	yes	—
181	C₄×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₄×C₁₃₇	#575	1	1	yes	characteristic
183	C₂×C₁₃₇	—	2	2	no	—
184	C₂×C₁₃₇	—	4	4	no	—
185	C₂×C₁₃₇	—	16	2	no	—
186	C₂×C₁₃₇	#3036	1	1	yes	characteristic
187	C₂×C₁₃₇	#3050	1	1	yes	characteristic
188	C₂×C₁₃₇	C₂×#472	1	1	yes	characteristic
189	#19258	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₁₃₇	#19258	1	1	yes	characteristic, direct product factor, Sylow
191	#3169	C₂×C₁₃₇	1	1	yes	characteristic, complemented
192	#3109	C₂×C₁₃₇	1	2	yes	complemented
193	C₂×C₈×D₄	C₂×C₁₃₇	1	1	yes	characteristic, complemented
194	#1677	C₂×C₁₃₇	1	4	yes	complemented
195	#1675	C₂×C₁₃₇	1	2	yes	complemented
196	#1667	C₂×C₁₃₇	1	2	yes	complemented
197	#1568	C₂×C₁₃₇	1	1	yes	characteristic, complemented
198	#1551	C₂×C₁₃₇	1	2	yes	complemented
199	C₂³×C₈	—	2	1	no	—
200	#532	C₂²×C₁₃₇	1	2	yes	—
201	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
202	#500	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
203	#493	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
204	#486	C₂²×C₁₃₇	1	2	yes	complemented
205	#481	—	2	2	no	—
206	#476	C₂²×C₁₃₇	1	4	yes	—
207	#466	—	2	1	no	—
208	#466	—	2	1	no	—
209	#459	C₂²×C₁₃₇	1	4	yes	—
210	#447	—	2	2	no	—
211	#442	—	2	4	no	—
212	C₄×D₈	—	2	1	no	—
213	C₄×D₈	—	2	1	no	—
214	C₈×D₄	—	2	1	no	—
215	C₈×D₄	—	2	1	no	—
216	C₈×D₄	C₂²×C₁₃₇	1	2	yes	—
217	C₈×D₄	C₂²×C₁₃₇	1	2	yes	—
218	#432	C₂²×C₁₃₇	1	2	yes	—
219	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
220	C₂×C₂²⋊C₈	—	2	1	no	—
221	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
222	#335	C₂²×C₁₃₇	1	2	yes	complemented
223	#334	C₂²×C₁₃₇	1	2	yes	complemented
224	#333	C₂²×C₁₃₇	1	4	yes	complemented
225	#331	C₂²×C₁₃₇	1	4	yes	complemented
226	C₂×#41	—	2	2	no	—
227	C₂²×D₄	D₄×C₁₃₇	1	1	yes	characteristic
228	C₂³×C₄	—	2	1	no	—
229	C₂×D₈	—	2	4	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×D₈	—	2	1	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	2	2	no	—
234	C₂²×C₈	—	2	2	no	—
235	C₂²×C₈	—	4	4	no	—
236	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
237	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
238	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
239	#127	C₂³×C₁₃₇	1	2	yes	—
240	#124	—	2	2	no	—
241	#121	—	2	2	no	—
242	#121	—	2	2	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	2	2	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	D₄×C₁₃₇	1	2	yes	—
248	C₄×D₄	C₂³×C₁₃₇	1	2	yes	—
249	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	—	2	1	no	—
251	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
252	#107	—	2	1	no	—
253	#107	—	2	1	no	—
254	#106	—	2	4	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
257	C₄⋊C₈	C₂³×C₁₃₇	1	4	yes	—
258	#102	—	2	4	no	—
259	#102	—	2	2	no	—
260	#102	—	2	2	no	—
261	#102	—	2	4	no	—
262	C₂²⋊C₈	—	2	2	no	—
263	C₂²⋊C₈	—	2	2	no	—
264	C₂²⋊C₈	—	2	2	no	—
265	#97	—	2	2	no	—
266	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
267	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
268	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
269	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
270	C₂⁴	—	2	1	no	—
271	#41	—	8	4	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
288	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
289	D₈	—	4	2	no	—
290	D₈	—	4	8	no	—
291	D₈	—	4	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	4	4	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	4	4	no	—
299	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
300	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
301	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
302	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
312	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
313	C₄²	#41×C₁₃₇	1	1	yes	characteristic
314	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
315	C₂³	—	2	4	no	—
316	C₂³	—	2	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	#121×C₁₃₇	1	1	yes	characteristic
321	Q₈	—	8	2	no	—
322	D₄	—	2	4	no	—
323	D₄	—	2	2	no	—
324	D₄	—	4	4	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	2	no	—
327	D₄	—	8	2	no	—
328	D₄	—	8	4	no	—
329	D₄	#135×C₁₃₇	1	4	yes	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	8	4	no	—
341	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
342	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
343	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
345	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
346	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
347	C₈	—	2	1	no	—
348	C₈	—	2	1	no	—
349	C₈	—	2	1	no	—
350	C₈	—	4	4	no	—
351	C₈	—	4	2	no	—
352	C₈	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	4	8	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	8	2	no	—
360	C₂²	—	8	2	no	—
361	C₂²	—	8	2	no	—
362	C₂²	#472×C₁₃₇	1	2	yes	—
363	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	4	2	no	—
369	C₄	—	8	2	no	—
370	C₄	C₂×#135×C₁₃₇	1	2	yes	—
371	C₄	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
372	C₄	#575×C₁₃₇	1	1	yes	characteristic
373	C₂	—	2	2	no	—
374	C₂	—	4	4	no	—
375	C₂	—	16	2	no	—
376	C₂	#3036×C₁₃₇	1	1	yes	characteristic
377	C₂	#3050×C₁₃₇	1	1	yes	characteristic
378	C₂	C₂×#472×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
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. #3169×C₁₃₇	C₂	semidirect
2. #3109×C₁₃₇	C₂	semidirect
3. C₂×C₈×D₄×C₁₃₇	C₂	semidirect
4. #1677×C₁₃₇	C₂	semidirect
5. #1675×C₁₃₇	C₂	semidirect
6. #1667×C₁₃₇	C₂	semidirect
7. #1568×C₁₃₇	C₂	semidirect
8. #1551×C₁₃₇	C₂	semidirect
12. #500×C₁₃₇	C₂²	semidirect
13. #493×C₁₃₇	C₂²	semidirect
14. #486×C₁₃₇	C₂²	semidirect
32. #335×C₁₃₇	C₂²	semidirect
33. #334×C₁₃₇	C₂²	semidirect
34. #333×C₁₃₇	C₂²	semidirect
35. #331×C₁₃₇	C₂²	semidirect
189. #19258	C₁₃₇	direct (N × H)
190. C₁₃₇	#19258	direct (N × H)
191. #3169	C₂×C₁₃₇	semidirect
192. #3109	C₂×C₁₃₇	semidirect
193. C₂×C₈×D₄	C₂×C₁₃₇	semidirect
194. #1677	C₂×C₁₃₇	semidirect
195. #1675	C₂×C₁₃₇	semidirect
196. #1667	C₂×C₁₃₇	semidirect
197. #1568	C₂×C₁₃₇	semidirect
198. #1551	C₂×C₁₃₇	semidirect
202. #500	C₂²×C₁₃₇	semidirect
203. #493	C₂²×C₁₃₇	semidirect
204. #486	C₂²×C₁₃₇	semidirect
222. #335	C₂²×C₁₃₇	semidirect
223. #334	C₂²×C₁₃₇	semidirect
224. #333	C₂²×C₁₃₇	semidirect
225. #331	C₂²×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3169×C₁₃₇	2
#3109×C₁₃₇	2
C₂×C₈×D₄×C₁₃₇	2
#1677×C₁₃₇	2
#1675×C₁₃₇	2
#1667×C₁₃₇	2
#1568×C₁₃₇	2
#1551×C₁₃₇	2
#19258	137

Subgroups — C137×#19258 #46868644

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19258 #46868644