Subgroups — C₁₃₇×#19255 #46868641

Order 35072.

798 conjugacy classes of subgroups.

The subgroup lattice has 398 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	#3036×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×D₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#1681×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	#1673×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1667×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1567×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1547×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	C₂×AGL(1,ℤ/8)×C₁₃₇	—	2	2	no	—
10	C₂³×C₈×C₁₃₇	—	2	1	no	—
11	#532×C₁₃₇	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
13	#500×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
14	#493×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
15	#486×C₁₃₇	C₂²	1	2	yes	complemented
16	#466×C₁₃₇	—	2	1	no	—
17	#466×C₁₃₇	—	2	1	no	—
18	#463×C₁₃₇	—	2	4	no	—
19	#461×C₁₃₇	C₂²	1	4	yes	—
20	#459×C₁₃₇	C₂²	1	4	yes	—
21	C₄×D₈×C₁₃₇	—	2	1	no	—
22	C₄×D₈×C₁₃₇	—	2	1	no	—
23	C₈×D₄×C₁₃₇	—	2	1	no	—
24	C₈×D₄×C₁₃₇	—	2	1	no	—
25	C₈×D₄×C₁₃₇	C₂²	1	2	yes	—
26	C₈×D₄×C₁₃₇	C₂²	1	2	yes	—
27	#423×C₁₃₇	C₂²	1	2	yes	—
28	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
29	#417×C₁₃₇	—	2	2	no	—
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	#335×C₁₃₇	C₂²	1	2	yes	complemented
34	#332×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	AGL(1,ℤ/8)×C₁₃₇	—	4	8	no	—
40	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
41	C₂×D₈×C₁₃₇	—	2	4	no	—
42	C₂×D₈×C₁₃₇	—	2	1	no	—
43	C₂×D₈×C₁₃₇	—	2	1	no	—
44	C₂×M₁₆×C₁₃₇	—	2	2	no	—
45	C₂²×C₈×C₁₃₇	—	2	1	no	—
46	C₂²×C₈×C₁₃₇	—	2	2	no	—
47	C₂²×C₈×C₁₃₇	—	2	2	no	—
48	C₂²×C₈×C₁₃₇	—	4	4	no	—
49	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
51	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
52	#127×C₁₃₇	C₂³	1	2	yes	—
53	#124×C₁₃₇	—	2	2	no	—
54	#121×C₁₃₇	—	2	2	no	—
55	#121×C₁₃₇	—	2	2	no	—
56	C₄×D₄×C₁₃₇	—	2	1	no	—
57	C₄×D₄×C₁₃₇	—	2	2	no	—
58	C₄×D₄×C₁₃₇	—	2	1	no	—
59	C₄×D₄×C₁₃₇	—	2	2	no	—
60	C₄×D₄×C₁₃₇	D₄	1	2	yes	—
61	C₄×D₄×C₁₃₇	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
64	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
65	#107×C₁₃₇	—	2	1	no	—
66	#107×C₁₃₇	—	2	1	no	—
67	C₄⋊C₈×C₁₃₇	—	2	1	no	—
68	C₄⋊C₈×C₁₃₇	—	2	2	no	—
69	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
70	C₄⋊C₈×C₁₃₇	C₂³	1	4	yes	—
71	#103×C₁₃₇	—	2	4	no	—
72	#102×C₁₃₇	—	2	2	no	—
73	#102×C₁₃₇	—	2	2	no	—
74	#102×C₁₃₇	—	2	4	no	—
75	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
76	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
77	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
78	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
81	C₂⁴×C₁₃₇	—	2	1	no	—
82	#41×C₁₃₇	—	4	4	no	—
83	#41×C₁₃₇	—	4	4	no	—
84	C₂×Q₈×C₁₃₇	—	2	2	no	—
85	C₂×D₄×C₁₃₇	—	2	1	no	—
86	C₂×D₄×C₁₃₇	—	2	2	no	—
87	C₂×D₄×C₁₃₇	—	2	2	no	—
88	C₂×D₄×C₁₃₇	—	2	2	no	—
89	C₂×D₄×C₁₃₇	—	2	2	no	—
90	C₂×D₄×C₁₃₇	—	4	2	no	—
91	C₂×D₄×C₁₃₇	D₈	1	4	yes	complemented
92	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃₇	—	2	1	no	—
94	C₂²×C₄×C₁₃₇	—	2	2	no	—
95	C₂²×C₄×C₁₃₇	—	2	2	no	—
96	C₂²×C₄×C₁₃₇	—	4	2	no	—
97	C₂²×C₄×C₁₃₇	—	4	2	no	—
98	C₂²×C₄×C₁₃₇	—	4	2	no	—
99	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
102	SD₁₆×C₁₃₇	—	4	8	no	—
103	D₈×C₁₃₇	—	4	2	no	—
104	D₈×C₁₃₇	—	4	8	no	—
105	D₈×C₁₃₇	—	4	2	no	—
106	M₁₆×C₁₃₇	—	4	4	no	—
107	C₂×C₈×C₁₃₇	—	2	2	no	—
108	C₂×C₈×C₁₃₇	—	2	2	no	—
109	C₂×C₈×C₁₃₇	—	2	4	no	—
110	C₂×C₈×C₁₃₇	—	4	1	no	—
111	C₂×C₈×C₁₃₇	—	4	4	no	—
112	C₂×C₈×C₁₃₇	—	4	2	no	—
113	C₂×C₈×C₁₃₇	—	4	4	no	—
114	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
118	C₄⋊C₄×C₁₃₇	—	2	1	no	—
119	C₄⋊C₄×C₁₃₇	—	2	2	no	—
120	C₄⋊C₄×C₁₃₇	—	2	2	no	—
121	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
122	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
123	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
124	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
125	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
126	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₃₇	#41	1	1	yes	characteristic
129	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
130	C₂³×C₁₃₇	—	2	2	no	—
131	C₂³×C₁₃₇	—	2	4	no	—
132	C₂³×C₁₃₇	—	4	2	no	—
133	C₂³×C₁₃₇	—	4	2	no	—
134	C₂³×C₁₃₇	—	4	2	no	—
135	C₂³×C₁₃₇	#121	1	1	yes	characteristic
136	Q₈×C₁₃₇	—	4	2	no	—
137	Q₈×C₁₃₇	—	4	2	no	—
138	D₄×C₁₃₇	—	2	2	no	—
139	D₄×C₁₃₇	—	2	4	no	—
140	D₄×C₁₃₇	—	4	2	no	—
141	D₄×C₁₃₇	—	4	2	no	—
142	D₄×C₁₃₇	—	4	2	no	—
143	D₄×C₁₃₇	—	4	2	no	—
144	D₄×C₁₃₇	—	8	2	no	—
145	D₄×C₁₃₇	—	8	4	no	—
146	D₄×C₁₃₇	C₂×D₈	1	4	yes	—
147	C₂×C₄×C₁₃₇	—	2	1	no	—
148	C₂×C₄×C₁₃₇	—	2	1	no	—
149	C₂×C₄×C₁₃₇	—	2	2	no	—
150	C₂×C₄×C₁₃₇	—	4	1	no	—
151	C₂×C₄×C₁₃₇	—	4	4	no	—
152	C₂×C₄×C₁₃₇	—	4	2	no	—
153	C₂×C₄×C₁₃₇	—	4	2	no	—
154	C₂×C₄×C₁₃₇	—	4	2	no	—
155	C₂×C₄×C₁₃₇	—	4	2	no	—
156	C₂×C₄×C₁₃₇	—	8	4	no	—
157	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
158	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
159	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
160	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
161	C₂×C₄×C₁₃₇	#135	1	2	yes	—
162	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
165	C₈×C₁₃₇	—	2	1	no	—
166	C₈×C₁₃₇	—	2	1	no	—
167	C₈×C₁₃₇	—	2	1	no	—
168	C₈×C₁₃₇	—	4	4	no	—
169	C₈×C₁₃₇	—	4	2	no	—
170	C₈×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	complemented
171	C₂²×C₁₃₇	—	2	1	no	—
172	C₂²×C₁₃₇	—	2	1	no	—
173	C₂²×C₁₃₇	—	2	4	no	—
174	C₂²×C₁₃₇	—	4	8	no	—
175	C₂²×C₁₃₇	—	4	2	no	—
176	C₂²×C₁₃₇	—	4	2	no	—
177	C₂²×C₁₃₇	—	8	2	no	—
178	C₂²×C₁₃₇	—	8	2	no	—
179	C₂²×C₁₃₇	—	8	2	no	—
180	C₂²×C₁₃₇	#466	1	2	yes	—
181	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
182	C₄×C₁₃₇	—	2	1	no	—
183	C₄×C₁₃₇	—	2	1	no	—
184	C₄×C₁₃₇	—	2	1	no	—
185	C₄×C₁₃₇	—	4	2	no	—
186	C₄×C₁₃₇	—	8	2	no	—
187	C₄×C₁₃₇	#466	1	2	yes	—
188	C₄×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
189	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
190	C₄×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₄×C₁₃₇	#575	1	1	yes	characteristic
192	C₂×C₁₃₇	—	2	2	no	—
193	C₂×C₁₃₇	—	4	4	no	—
194	C₂×C₁₃₇	—	16	2	no	—
195	C₂×C₁₃₇	#3036	1	1	yes	characteristic
196	C₂×C₁₃₇	C₂×#466	1	1	yes	characteristic
197	C₂×C₁₃₇	#3067	1	1	yes	characteristic
198	#19255	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₁₃₇	#19255	1	1	yes	characteristic, direct product factor, Sylow
200	#3169	C₂×C₁₃₇	1	1	yes	characteristic, complemented
201	#3036	C₂×C₁₃₇	1	2	yes	complemented
202	C₂×C₈×D₄	C₂×C₁₃₇	1	1	yes	characteristic, complemented
203	#1681	C₂×C₁₃₇	1	4	yes	complemented
204	#1673	C₂×C₁₃₇	1	2	yes	complemented
205	#1667	C₂×C₁₃₇	1	2	yes	complemented
206	#1567	C₂×C₁₃₇	1	1	yes	characteristic, complemented
207	#1547	C₂×C₁₃₇	1	2	yes	complemented
208	C₂×AGL(1,ℤ/8)	—	2	2	no	—
209	C₂³×C₈	—	2	1	no	—
210	#532	C₂²×C₁₃₇	1	2	yes	—
211	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
212	#500	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
213	#493	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
214	#486	C₂²×C₁₃₇	1	2	yes	complemented
215	#466	—	2	1	no	—
216	#466	—	2	1	no	—
217	#463	—	2	4	no	—
218	#461	C₂²×C₁₃₇	1	4	yes	—
219	#459	C₂²×C₁₃₇	1	4	yes	—
220	C₄×D₈	—	2	1	no	—
221	C₄×D₈	—	2	1	no	—
222	C₈×D₄	—	2	1	no	—
223	C₈×D₄	—	2	1	no	—
224	C₈×D₄	C₂²×C₁₃₇	1	2	yes	—
225	C₈×D₄	C₂²×C₁₃₇	1	2	yes	—
226	#423	C₂²×C₁₃₇	1	2	yes	—
227	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
228	#417	—	2	2	no	—
229	C₂×C₂²⋊C₈	—	2	1	no	—
230	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
231	#335	C₂²×C₁₃₇	1	2	yes	complemented
232	#335	C₂²×C₁₃₇	1	2	yes	complemented
233	#332	C₂²×C₁₃₇	1	4	yes	complemented
234	#331	C₂²×C₁₃₇	1	4	yes	complemented
235	C₂×#41	—	2	2	no	—
236	C₂²×D₄	D₄×C₁₃₇	1	1	yes	characteristic
237	C₂³×C₄	—	2	1	no	—
238	AGL(1,ℤ/8)	—	4	8	no	—
239	C₂×SD₁₆	—	2	4	no	—
240	C₂×D₈	—	2	4	no	—
241	C₂×D₈	—	2	1	no	—
242	C₂×D₈	—	2	1	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	—	4	4	no	—
248	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
249	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
250	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
251	#127	C₂³×C₁₃₇	1	2	yes	—
252	#124	—	2	2	no	—
253	#121	—	2	2	no	—
254	#121	—	2	2	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	2	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	D₄×C₁₃₇	1	2	yes	—
260	C₄×D₄	C₂³×C₁₃₇	1	2	yes	—
261	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
264	#107	—	2	1	no	—
265	#107	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
269	C₄⋊C₈	C₂³×C₁₃₇	1	4	yes	—
270	#103	—	2	4	no	—
271	#102	—	2	2	no	—
272	#102	—	2	2	no	—
273	#102	—	2	4	no	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₂²⋊C₈	—	2	2	no	—
276	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
277	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
280	C₂⁴	—	2	1	no	—
281	#41	—	4	4	no	—
282	#41	—	4	4	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	D₈×C₁₃₇	1	4	yes	complemented
291	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
300	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
301	SD₁₆	—	4	8	no	—
302	D₈	—	4	2	no	—
303	D₈	—	4	8	no	—
304	D₈	—	4	2	no	—
305	M₁₆	—	4	4	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	4	4	no	—
311	C₂×C₈	—	4	2	no	—
312	C₂×C₈	—	4	4	no	—
313	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
314	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
315	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
316	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
326	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
327	C₄²	#41×C₁₃₇	1	1	yes	characteristic
328	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
329	C₂³	—	2	4	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	#121×C₁₃₇	1	1	yes	characteristic
335	Q₈	—	4	2	no	—
336	Q₈	—	4	2	no	—
337	D₄	—	2	4	no	—
338	D₄	—	2	2	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	8	2	no	—
344	D₄	—	8	4	no	—
345	D₄	C₂×D₈×C₁₃₇	1	4	yes	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	8	4	no	—
356	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
357	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
358	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
359	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
360	C₂×C₄	#135×C₁₃₇	1	2	yes	—
361	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
362	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
363	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	2	1	no	—
367	C₈	—	4	4	no	—
368	C₈	—	4	2	no	—
369	C₈	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	complemented
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	4	8	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	#466×C₁₃₇	1	2	yes	—
380	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	4	2	no	—
385	C₄	—	8	2	no	—
386	C₄	#466×C₁₃₇	1	2	yes	—
387	C₄	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
388	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
389	C₄	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
390	C₄	#575×C₁₃₇	1	1	yes	characteristic
391	C₂	—	2	2	no	—
392	C₂	—	4	4	no	—
393	C₂	—	16	2	no	—
394	C₂	#3036×C₁₃₇	1	1	yes	characteristic
395	C₂	C₂×#466×C₁₃₇	1	1	yes	characteristic
396	C₂	#3067×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. #3036×C₁₃₇	C₂	semidirect
3. C₂×C₈×D₄×C₁₃₇	C₂	semidirect
4. #1681×C₁₃₇	C₂	semidirect
5. #1673×C₁₃₇	C₂	semidirect
6. #1667×C₁₃₇	C₂	semidirect
7. #1567×C₁₃₇	C₂	semidirect
8. #1547×C₁₃₇	C₂	semidirect
13. #500×C₁₃₇	C₂²	semidirect
14. #493×C₁₃₇	C₂²	semidirect
15. #486×C₁₃₇	C₂²	semidirect
32. #335×C₁₃₇	C₂²	semidirect
33. #335×C₁₃₇	C₂²	semidirect
34. #332×C₁₃₇	C₂²	semidirect
35. #331×C₁₃₇	C₂²	semidirect
91. C₂×D₄×C₁₃₇	D₈	semidirect
170. C₈×C₁₃₇	AGL(1,ℤ/8)	semidirect
198. #19255	C₁₃₇	direct (N × H)
199. C₁₃₇	#19255	direct (N × H)
200. #3169	C₂×C₁₃₇	semidirect
201. #3036	C₂×C₁₃₇	semidirect
202. C₂×C₈×D₄	C₂×C₁₃₇	semidirect
203. #1681	C₂×C₁₃₇	semidirect
204. #1673	C₂×C₁₃₇	semidirect
205. #1667	C₂×C₁₃₇	semidirect
206. #1567	C₂×C₁₃₇	semidirect
207. #1547	C₂×C₁₃₇	semidirect
212. #500	C₂²×C₁₃₇	semidirect
213. #493	C₂²×C₁₃₇	semidirect
214. #486	C₂²×C₁₃₇	semidirect
231. #335	C₂²×C₁₃₇	semidirect
232. #335	C₂²×C₁₃₇	semidirect
233. #332	C₂²×C₁₃₇	semidirect
234. #331	C₂²×C₁₃₇	semidirect
290. C₂×D₄	D₈×C₁₃₇	semidirect
369. C₈	AGL(1,ℤ/8)×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
#3036×C₁₃₇	2
C₂×C₈×D₄×C₁₃₇	2
#1681×C₁₃₇	2
#1673×C₁₃₇	2
#1667×C₁₃₇	2
#1567×C₁₃₇	2
#1547×C₁₃₇	2
#19255	137

Subgroups — C137×#19255 #46868641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19255 #46868641