Subgroups — C₁₃₇×#19231 #46868617

Order 35072.

726 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3245×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#3226×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#3152×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2935×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1689×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1685×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1669×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1665×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1565×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1540×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#332×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₁₃₇	—	2	1	no	—
13	C₂×#137×C₁₃₇	—	2	1	no	—
14	C₂×#131×C₁₃₇	—	2	1	no	—
15	#532×C₁₃₇	C₂²	1	1	yes	characteristic
16	#532×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
18	#500×C₁₃₇	—	2	1	no	—
19	#497×C₁₃₇	—	2	2	no	—
20	#494×C₁₃₇	C₂²	1	2	yes	—
21	#492×C₁₃₇	C₂²	1	2	yes	—
22	#486×C₁₃₇	—	2	1	no	—
23	#480×C₁₃₇	—	2	2	no	—
24	#474×C₁₃₇	—	2	1	no	—
25	#474×C₁₃₇	C₂²	1	2	yes	—
26	#474×C₁₃₇	C₂²	1	2	yes	—
27	#474×C₁₃₇	C₂²	1	2	yes	—
28	#466×C₁₃₇	—	2	2	no	—
29	#459×C₁₃₇	—	2	1	no	—
30	#459×C₁₃₇	C₂²	1	2	yes	—
31	#436×C₁₃₇	C₂²	1	2	yes	—
32	#435×C₁₃₇	—	2	2	no	—
33	C₈×D₄×C₁₃₇	C₂²	1	2	yes	—
34	#431×C₁₃₇	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
37	#408×C₁₃₇	—	2	1	no	—
38	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
39	#335×C₁₃₇	C₂²	1	2	yes	—
40	#334×C₁₃₇	C₂²	1	2	yes	—
41	#332×C₁₃₇	C₂²	1	2	yes	—
42	#332×C₁₃₇	C₂²	1	2	yes	—
43	#332×C₁₃₇	C₂²	1	1	yes	characteristic
44	#332×C₁₃₇	C₂²	1	1	yes	characteristic
45	#331×C₁₃₇	C₂²	1	1	yes	characteristic
46	#331×C₁₃₇	C₂²	1	1	yes	characteristic
47	C₂×#41×C₁₃₇	—	2	1	no	—
48	C₂×#41×C₁₃₇	—	2	1	no	—
49	C₂²×Q₈×C₁₃₇	—	2	1	no	—
50	#137×C₁₃₇	—	4	4	no	—
51	#137×C₁₃₇	—	4	4	no	—
52	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
53	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
54	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
55	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
56	C₂×D₈×C₁₃₇	—	2	2	no	—
57	#131×C₁₃₇	—	4	4	no	—
58	C₂×M₁₆×C₁₃₇	—	2	2	no	—
59	C₂×M₁₆×C₁₃₇	D₄	1	1	yes	characteristic
60	C₂×M₁₆×C₁₃₇	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₃₇	—	2	1	no	—
62	C₂²×C₈×C₁₃₇	—	2	1	no	—
63	C₂²×C₈×C₁₃₇	—	2	2	no	—
64	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
65	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
66	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
67	C₄⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
68	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
69	C₄⋊Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
70	#127×C₁₃₇	D₄	1	1	yes	characteristic
71	#127×C₁₃₇	C₂³	1	1	yes	characteristic
72	#124×C₁₃₇	—	2	1	no	—
73	#124×C₁₃₇	—	2	1	no	—
74	#121×C₁₃₇	—	2	1	no	—
75	#121×C₁₃₇	—	2	1	no	—
76	#121×C₁₃₇	—	2	1	no	—
77	#121×C₁₃₇	D₄	1	2	yes	—
78	C₄×D₄×C₁₃₇	—	2	1	no	—
79	C₄×D₄×C₁₃₇	—	2	1	no	—
80	C₄×D₄×C₁₃₇	—	2	1	no	—
81	C₄×D₄×C₁₃₇	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
84	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
85	#107×C₁₃₇	—	2	2	no	—
86	#107×C₁₃₇	—	2	2	no	—
87	#107×C₁₃₇	—	2	2	no	—
88	C₄⋊C₈×C₁₃₇	—	2	1	no	—
89	C₄⋊C₈×C₁₃₇	—	2	1	no	—
90	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
93	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
95	#102×C₁₃₇	—	2	2	no	—
96	#102×C₁₃₇	—	2	2	no	—
97	#102×C₁₃₇	—	2	2	no	—
98	#102×C₁₃₇	—	2	2	no	—
99	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
100	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
101	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
102	#97×C₁₃₇	D₄	1	2	yes	—
103	C₄×C₈×C₁₃₇	—	2	1	no	—
104	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
105	#41×C₁₃₇	—	4	2	no	—
106	#41×C₁₃₇	—	4	2	no	—
107	#41×C₁₃₇	—	4	2	no	—
108	#41×C₁₃₇	—	4	2	no	—
109	C₂×Q₈×C₁₃₇	—	2	1	no	—
110	C₂×Q₈×C₁₃₇	—	2	1	no	—
111	C₂×Q₈×C₁₃₇	—	2	2	no	—
112	C₂×Q₈×C₁₃₇	—	4	1	no	—
113	C₂×Q₈×C₁₃₇	—	4	2	no	—
114	C₂×Q₈×C₁₃₇	—	4	2	no	—
115	C₂×D₄×C₁₃₇	—	2	2	no	—
116	C₂×D₄×C₁₃₇	—	2	1	no	—
117	C₂×D₄×C₁₃₇	—	2	1	no	—
118	C₂×D₄×C₁₃₇	—	2	1	no	—
119	C₂×D₄×C₁₃₇	—	2	1	no	—
120	C₂×D₄×C₁₃₇	—	2	1	no	—
121	C₂×D₄×C₁₃₇	—	4	1	no	—
122	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₃₇	—	2	2	no	—
124	C₂²×C₄×C₁₃₇	—	4	1	no	—
125	C₂²×C₄×C₁₃₇	—	4	1	no	—
126	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
129	Q₁₆×C₁₃₇	—	4	4	no	—
130	Q₁₆×C₁₃₇	—	4	4	no	—
131	SD₁₆×C₁₃₇	—	4	4	no	—
132	SD₁₆×C₁₃₇	—	4	4	no	—
133	D₈×C₁₃₇	—	8	2	no	—
134	M₁₆×C₁₃₇	—	2	2	no	—
135	M₁₆×C₁₃₇	—	4	4	no	—
136	M₁₆×C₁₃₇	D₈	1	4	yes	complemented
137	C₂×C₈×C₁₃₇	—	2	1	no	—
138	C₂×C₈×C₁₃₇	—	2	1	no	—
139	C₂×C₈×C₁₃₇	—	2	1	no	—
140	C₂×C₈×C₁₃₇	—	2	1	no	—
141	C₂×C₈×C₁₃₇	—	2	2	no	—
142	C₂×C₈×C₁₃₇	—	4	2	no	—
143	C₂×C₈×C₁₃₇	—	4	4	no	—
144	C₂×C₈×C₁₃₇	—	8	1	no	—
145	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₁₃₇	—	2	1	no	—
148	C₄⋊C₄×C₁₃₇	—	2	2	no	—
149	C₄⋊C₄×C₁₃₇	—	2	1	no	—
150	C₄⋊C₄×C₁₃₇	—	2	2	no	—
151	C₄⋊C₄×C₁₃₇	—	2	1	no	—
152	C₄⋊C₄×C₁₃₇	—	4	1	no	—
153	C₄⋊C₄×C₁₃₇	—	4	1	no	—
154	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
155	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
156	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
157	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
158	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
159	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₁₃₇	#41	1	1	yes	characteristic
162	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
163	C₂³×C₁₃₇	—	2	2	no	—
164	C₂³×C₁₃₇	—	4	1	no	—
165	C₂³×C₁₃₇	#121	1	1	yes	characteristic
166	Q₈×C₁₃₇	—	4	2	no	—
167	Q₈×C₁₃₇	—	4	2	no	—
168	Q₈×C₁₃₇	—	4	1	no	—
169	Q₈×C₁₃₇	—	4	2	no	—
170	Q₈×C₁₃₇	—	4	1	no	—
171	Q₈×C₁₃₇	—	8	2	no	—
172	D₄×C₁₃₇	—	2	2	no	—
173	D₄×C₁₃₇	—	2	2	no	—
174	D₄×C₁₃₇	—	4	4	no	—
175	D₄×C₁₃₇	—	4	1	no	—
176	D₄×C₁₃₇	—	4	1	no	—
177	D₄×C₁₃₇	—	4	1	no	—
178	D₄×C₁₃₇	—	4	1	no	—
179	D₄×C₁₃₇	—	4	2	no	—
180	D₄×C₁₃₇	—	8	1	no	—
181	D₄×C₁₃₇	—	8	1	no	—
182	D₄×C₁₃₇	—	8	2	no	—
183	C₂×C₄×C₁₃₇	—	2	1	no	—
184	C₂×C₄×C₁₃₇	—	2	1	no	—
185	C₂×C₄×C₁₃₇	—	2	2	no	—
186	C₂×C₄×C₁₃₇	—	4	1	no	—
187	C₂×C₄×C₁₃₇	—	4	2	no	—
188	C₂×C₄×C₁₃₇	—	4	2	no	—
189	C₂×C₄×C₁₃₇	—	4	1	no	—
190	C₂×C₄×C₁₃₇	—	4	2	no	—
191	C₂×C₄×C₁₃₇	—	8	2	no	—
192	C₂×C₄×C₁₃₇	—	8	2	no	—
193	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
195	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
196	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
197	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
198	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
201	C₈×C₁₃₇	—	2	2	no	—
202	C₈×C₁₃₇	—	4	1	no	—
203	C₈×C₁₃₇	—	4	1	no	—
204	C₈×C₁₃₇	—	4	1	no	—
205	C₈×C₁₃₇	—	4	2	no	—
206	C₈×C₁₃₇	—	4	1	no	—
207	C₈×C₁₃₇	C₂×D₈	1	4	yes	—
208	C₂²×C₁₃₇	—	2	1	no	—
209	C₂²×C₁₃₇	—	2	1	no	—
210	C₂²×C₁₃₇	—	4	2	no	—
211	C₂²×C₁₃₇	—	4	2	no	—
212	C₂²×C₁₃₇	—	4	2	no	—
213	C₂²×C₁₃₇	—	8	1	no	—
214	C₂²×C₁₃₇	—	8	1	no	—
215	C₂²×C₁₃₇	—	8	1	no	—
216	C₂²×C₁₃₇	#459	1	2	yes	—
217	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
218	C₄×C₁₃₇	—	2	1	no	—
219	C₄×C₁₃₇	—	2	1	no	—
220	C₄×C₁₃₇	—	2	1	no	—
221	C₄×C₁₃₇	—	4	2	no	—
222	C₄×C₁₃₇	—	8	1	no	—
223	C₄×C₁₃₇	—	8	2	no	—
224	C₄×C₁₃₇	#459	1	2	yes	—
225	C₄×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
226	C₄×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₄×C₁₃₇	#577	1	1	yes	characteristic
228	C₄×C₁₃₇	#578	1	1	yes	characteristic
229	C₂×C₁₃₇	—	2	2	no	—
230	C₂×C₁₃₇	—	8	2	no	—
231	C₂×C₁₃₇	—	16	1	no	—
232	C₂×C₁₃₇	C₂×#459	1	1	yes	characteristic
233	C₂×C₁₃₇	#3063	1	1	yes	characteristic
234	C₂×C₁₃₇	#3069	1	1	yes	characteristic
235	#19231	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₁₃₇	#19231	1	1	yes	characteristic, direct product factor, Sylow
237	#3245	C₂×C₁₃₇	1	1	yes	characteristic
238	#3226	C₂×C₁₃₇	1	1	yes	characteristic, complemented
239	#3152	C₂×C₁₃₇	1	1	yes	characteristic, complemented
240	#2935	C₂×C₁₃₇	1	1	yes	characteristic, complemented
241	#1689	C₂×C₁₃₇	1	2	yes	complemented
242	#1685	C₂×C₁₃₇	1	2	yes	complemented
243	#1669	C₂×C₁₃₇	1	2	yes	complemented
244	#1665	C₂×C₁₃₇	1	2	yes	complemented
245	#1565	C₂×C₁₃₇	1	1	yes	characteristic, complemented
246	#1540	C₂×C₁₃₇	1	1	yes	characteristic, complemented
247	C₂×#332	C₂×C₁₃₇	1	1	yes	characteristic, complemented
248	C₂×#137	—	2	1	no	—
249	C₂×#137	—	2	1	no	—
250	C₂×#131	—	2	1	no	—
251	#532	C₂²×C₁₃₇	1	1	yes	characteristic
252	#532	C₂²×C₁₃₇	1	1	yes	characteristic
253	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
254	#500	—	2	1	no	—
255	#497	—	2	2	no	—
256	#494	C₂²×C₁₃₇	1	2	yes	—
257	#492	C₂²×C₁₃₇	1	2	yes	—
258	#486	—	2	1	no	—
259	#480	—	2	2	no	—
260	#474	—	2	1	no	—
261	#474	C₂²×C₁₃₇	1	2	yes	—
262	#474	C₂²×C₁₃₇	1	2	yes	—
263	#474	C₂²×C₁₃₇	1	2	yes	—
264	#466	—	2	2	no	—
265	#459	—	2	1	no	—
266	#459	C₂²×C₁₃₇	1	2	yes	—
267	#436	C₂²×C₁₃₇	1	2	yes	—
268	#435	—	2	2	no	—
269	C₈×D₄	C₂²×C₁₃₇	1	2	yes	—
270	#431	C₂²×C₁₃₇	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
273	#408	—	2	1	no	—
274	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
275	#335	C₂²×C₁₃₇	1	2	yes	—
276	#334	C₂²×C₁₃₇	1	2	yes	—
277	#332	C₂²×C₁₃₇	1	2	yes	—
278	#332	C₂²×C₁₃₇	1	2	yes	—
279	#332	C₂²×C₁₃₇	1	1	yes	characteristic
280	#332	C₂²×C₁₃₇	1	1	yes	characteristic
281	#331	C₂²×C₁₃₇	1	1	yes	characteristic
282	#331	C₂²×C₁₃₇	1	1	yes	characteristic
283	C₂×#41	—	2	1	no	—
284	C₂×#41	—	2	1	no	—
285	C₂²×Q₈	—	2	1	no	—
286	#137	—	4	4	no	—
287	#137	—	4	4	no	—
288	C₂×Q₁₆	—	2	2	no	—
289	C₂×Q₁₆	—	2	2	no	—
290	C₂×SD₁₆	—	2	2	no	—
291	C₂×SD₁₆	—	2	2	no	—
292	C₂×D₈	—	2	2	no	—
293	#131	—	4	4	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	D₄×C₁₃₇	1	1	yes	characteristic
296	C₂×M₁₆	D₄×C₁₃₇	1	1	yes	characteristic
297	C₂²×C₈	—	2	1	no	—
298	C₂²×C₈	—	2	1	no	—
299	C₂²×C₈	—	2	2	no	—
300	C₄⋊Q₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
304	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
305	C₄⋊Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
306	#127	D₄×C₁₃₇	1	1	yes	characteristic
307	#127	C₂³×C₁₃₇	1	1	yes	characteristic
308	#124	—	2	1	no	—
309	#124	—	2	1	no	—
310	#121	—	2	1	no	—
311	#121	—	2	1	no	—
312	#121	—	2	1	no	—
313	#121	D₄×C₁₃₇	1	2	yes	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	C₂³×C₁₃₇	1	2	yes	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
321	#107	—	2	2	no	—
322	#107	—	2	2	no	—
323	#107	—	2	2	no	—
324	C₄⋊C₈	—	2	1	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
327	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
328	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
329	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
330	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
331	#102	—	2	2	no	—
332	#102	—	2	2	no	—
333	#102	—	2	2	no	—
334	#102	—	2	2	no	—
335	C₂²⋊C₈	—	2	1	no	—
336	C₂²⋊C₈	—	2	2	no	—
337	C₂²⋊C₈	—	2	2	no	—
338	#97	D₄×C₁₃₇	1	2	yes	—
339	C₄×C₈	—	2	1	no	—
340	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
341	#41	—	4	2	no	—
342	#41	—	4	2	no	—
343	#41	—	4	2	no	—
344	#41	—	4	2	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	4	1	no	—
349	C₂×Q₈	—	4	2	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	4	1	no	—
358	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	—	4	1	no	—
362	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
364	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
365	Q₁₆	—	4	4	no	—
366	Q₁₆	—	4	4	no	—
367	SD₁₆	—	4	4	no	—
368	SD₁₆	—	4	4	no	—
369	D₈	—	8	2	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	4	4	no	—
372	M₁₆	D₈×C₁₃₇	1	4	yes	complemented
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	4	2	no	—
379	C₂×C₈	—	4	4	no	—
380	C₂×C₈	—	8	1	no	—
381	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
382	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₄⋊C₄	—	4	1	no	—
390	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
396	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
397	C₄²	#41×C₁₃₇	1	1	yes	characteristic
398	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
399	C₂³	—	2	2	no	—
400	C₂³	—	4	1	no	—
401	C₂³	#121×C₁₃₇	1	1	yes	characteristic
402	Q₈	—	4	2	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	4	1	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	1	no	—
407	Q₈	—	8	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	2	no	—
410	D₄	—	4	4	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	1	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	1	no	—
415	D₄	—	4	1	no	—
416	D₄	—	8	1	no	—
417	D₄	—	8	1	no	—
418	D₄	—	8	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
430	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
431	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
432	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
433	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
434	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
436	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
437	C₈	—	2	2	no	—
438	C₈	—	4	1	no	—
439	C₈	—	4	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	1	no	—
442	C₈	—	4	1	no	—
443	C₈	C₂×D₈×C₁₃₇	1	4	yes	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	8	1	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	#459×C₁₃₇	1	2	yes	—
453	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	4	2	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	2	no	—
460	C₄	#459×C₁₃₇	1	2	yes	—
461	C₄	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
462	C₄	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
463	C₄	#577×C₁₃₇	1	1	yes	characteristic
464	C₄	#578×C₁₃₇	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	8	2	no	—
467	C₂	—	16	1	no	—
468	C₂	C₂×#459×C₁₃₇	1	1	yes	characteristic
469	C₂	#3063×C₁₃₇	1	1	yes	characteristic
470	C₂	#3069×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	#3245×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
2. #3226×C₁₃₇	C₂	semidirect
3. #3152×C₁₃₇	C₂	semidirect
4. #2935×C₁₃₇	C₂	semidirect
5. #1689×C₁₃₇	C₂	semidirect
6. #1685×C₁₃₇	C₂	semidirect
7. #1669×C₁₃₇	C₂	semidirect
8. #1665×C₁₃₇	C₂	semidirect
9. #1565×C₁₃₇	C₂	semidirect
10. #1540×C₁₃₇	C₂	semidirect
11. C₂×#332×C₁₃₇	C₂	semidirect
136. M₁₆×C₁₃₇	D₈	semidirect
235. #19231	C₁₃₇	direct (N × H)
236. C₁₃₇	#19231	direct (N × H)
238. #3226	C₂×C₁₃₇	semidirect
239. #3152	C₂×C₁₃₇	semidirect
240. #2935	C₂×C₁₃₇	semidirect
241. #1689	C₂×C₁₃₇	semidirect
242. #1685	C₂×C₁₃₇	semidirect
243. #1669	C₂×C₁₃₇	semidirect
244. #1665	C₂×C₁₃₇	semidirect
245. #1565	C₂×C₁₃₇	semidirect
246. #1540	C₂×C₁₃₇	semidirect
247. C₂×#332	C₂×C₁₃₇	semidirect
372. M₁₆	D₈×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3245×C₁₃₇	2
#3226×C₁₃₇	2
#3152×C₁₃₇	2
#2935×C₁₃₇	2
#1689×C₁₃₇	2
#1685×C₁₃₇	2
#1669×C₁₃₇	2
#1665×C₁₃₇	2
#1565×C₁₃₇	2
#1540×C₁₃₇	2
C₂×#332×C₁₃₇	2
#19231	137

Subgroups — C137×#19231 #46868617

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19231 #46868617