Subgroups — C₁₃₇×#25831 #46875217

Order 35072.

946 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3504×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#3166×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#3080×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2859×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2061×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2060×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1998×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1994×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1860×C₁₃₇	C₂	1	2	yes	maximal
10	#1859×C₁₃₇	C₂	1	2	yes	maximal
11	C₄×#104×C₁₃₇	C₂	1	1	yes	maximal, characteristic
12	#557×C₁₃₇	—	2	2	no	—
13	#554×C₁₃₇	—	2	2	no	—
14	#554×C₁₃₇	—	2	4	no	—
15	#544×C₁₃₇	—	2	2	no	—
16	#544×C₁₃₇	C₂²	1	2	yes	—
17	#533×C₁₃₇	—	2	1	no	—
18	#533×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×#125×C₁₃₇	—	2	1	no	—
20	C₂×#125×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×#125×C₁₃₇	C₂²	1	1	yes	characteristic
22	#520×C₁₃₇	C₂²	1	2	yes	—
23	C₄×#41×C₁₃₇	C₂²	1	1	yes	characteristic
24	#501×C₁₃₇	—	2	2	no	—
25	#499×C₁₃₇	—	2	1	no	—
26	#499×C₁₃₇	—	2	1	no	—
27	#479×C₁₃₇	—	2	2	no	—
28	#478×C₁₃₇	—	2	2	no	—
29	#428×C₁₃₇	C₂²	1	2	yes	—
30	#428×C₁₃₇	C₂²	1	2	yes	—
31	#428×C₁₃₇	C₂²	1	2	yes	—
32	#423×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₂×#104×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₂×#104×C₁₃₇	C₂²	1	1	yes	characteristic
35	#417×C₁₃₇	C₂²	1	2	yes	—
36	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
37	#389×C₁₃₇	—	2	4	no	—
38	#384×C₁₃₇	C₂²	1	2	yes	—
39	#382×C₁₃₇	C₂²	1	2	yes	—
40	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
41	#343×C₁₃₇	C₂²	1	2	yes	—
42	#343×C₁₃₇	C₂²	1	2	yes	—
43	#339×C₁₃₇	C₂²	1	1	yes	characteristic
44	#339×C₁₃₇	C₂²	1	1	yes	characteristic
45	#339×C₁₃₇	C₂²	1	2	yes	—
46	#339×C₁₃₇	C₂²	1	2	yes	—
47	C₂×#41×C₁₃₇	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
49	C₂×M₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
51	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
52	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
53	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
54	C₄⋊Q₈×C₁₃₇	D₄	1	2	yes	—
55	#125×C₁₃₇	—	2	4	no	—
56	#125×C₁₃₇	—	2	4	no	—
57	#125×C₁₃₇	—	2	2	no	—
58	#125×C₁₃₇	—	2	2	no	—
59	#125×C₁₃₇	—	2	1	no	—
60	#125×C₁₃₇	—	2	1	no	—
61	#125×C₁₃₇	—	2	2	no	—
62	#125×C₁₃₇	—	2	2	no	—
63	#125×C₁₃₇	—	2	1	no	—
64	#125×C₁₃₇	—	2	1	no	—
65	#125×C₁₃₇	D₄	1	1	yes	characteristic
66	#125×C₁₃₇	D₄	1	1	yes	characteristic
67	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
68	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
69	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
70	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
71	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
72	C₄×Q₈×C₁₃₇	—	2	4	no	—
73	C₄×Q₈×C₁₃₇	—	2	2	no	—
74	C₄×Q₈×C₁₃₇	—	2	2	no	—
75	C₄×Q₈×C₁₃₇	D₄	1	2	yes	—
76	C₄×D₄×C₁₃₇	—	2	2	no	—
77	C₄×D₄×C₁₃₇	—	2	2	no	—
78	C₄×D₄×C₁₃₇	—	2	4	no	—
79	C₄×D₄×C₁₃₇	D₄	1	2	yes	—
80	#117×C₁₃₇	—	2	2	no	—
81	#117×C₁₃₇	—	2	1	no	—
82	#117×C₁₃₇	C₂³	1	1	yes	characteristic
83	#117×C₁₃₇	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
85	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
86	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
87	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
88	C₂×C₄⋊C₄×C₁₃₇	D₄	1	4	yes	—
89	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
91	C₂×C₄²×C₁₃₇	—	2	1	no	—
92	C₂×C₄²×C₁₃₇	—	2	2	no	—
93	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
96	#107×C₁₃₇	—	2	2	no	—
97	#107×C₁₃₇	—	2	2	no	—
98	#107×C₁₃₇	—	2	2	no	—
99	#106×C₁₃₇	—	2	2	no	—
100	#106×C₁₃₇	—	2	2	no	—
101	#106×C₁₃₇	—	2	2	no	—
102	C₄⋊C₈×C₁₃₇	—	2	2	no	—
103	#104×C₁₃₇	Q₈	1	4	yes	complemented
104	#104×C₁₃₇	Q₈	1	4	yes	complemented
105	#103×C₁₃₇	—	2	2	no	—
106	#102×C₁₃₇	—	2	2	no	—
107	#97×C₁₃₇	—	2	1	no	—
108	C₄×C₈×C₁₃₇	—	2	1	no	—
109	#95×C₁₃₇	—	2	4	no	—
110	#41×C₁₃₇	—	2	1	no	—
111	#41×C₁₃₇	—	2	1	no	—
112	#41×C₁₃₇	C₂×Q₈	1	2	yes	—
113	#41×C₁₃₇	C₂×Q₈	1	2	yes	—
114	C₂×Q₈×C₁₃₇	—	2	4	no	—
115	C₂×Q₈×C₁₃₇	—	2	2	no	—
116	C₂×Q₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
117	C₂×D₄×C₁₃₇	—	2	1	no	—
118	C₂×D₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃₇	—	2	1	no	—
120	C₂²×C₄×C₁₃₇	—	2	1	no	—
121	C₂²×C₄×C₁₃₇	—	2	1	no	—
122	C₂²×C₄×C₁₃₇	—	2	4	no	—
123	C₂²×C₄×C₁₃₇	—	2	2	no	—
124	C₂²×C₄×C₁₃₇	—	2	2	no	—
125	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
128	M₁₆×C₁₃₇	—	2	1	no	—
129	M₁₆×C₁₃₇	—	2	1	no	—
130	M₁₆×C₁₃₇	—	2	2	no	—
131	M₁₆×C₁₃₇	—	2	2	no	—
132	M₁₆×C₁₃₇	C₂×Q₈	1	2	yes	—
133	M₁₆×C₁₃₇	C₂×Q₈	1	2	yes	—
134	C₂×C₈×C₁₃₇	—	2	1	no	—
135	C₂×C₈×C₁₃₇	—	2	1	no	—
136	C₂×C₈×C₁₃₇	—	2	2	no	—
137	C₄⋊C₄×C₁₃₇	—	2	4	no	—
138	C₄⋊C₄×C₁₃₇	—	2	4	no	—
139	C₄⋊C₄×C₁₃₇	—	2	4	no	—
140	C₄⋊C₄×C₁₃₇	—	2	4	no	—
141	C₄⋊C₄×C₁₃₇	—	2	2	no	—
142	C₄⋊C₄×C₁₃₇	—	2	4	no	—
143	C₄⋊C₄×C₁₃₇	—	2	4	no	—
144	C₄⋊C₄×C₁₃₇	—	2	2	no	—
145	C₄⋊C₄×C₁₃₇	—	2	2	no	—
146	C₄⋊C₄×C₁₃₇	—	2	2	no	—
147	C₄⋊C₄×C₁₃₇	—	2	2	no	—
148	C₄⋊C₄×C₁₃₇	—	2	2	no	—
149	C₄⋊C₄×C₁₃₇	—	2	2	no	—
150	C₄⋊C₄×C₁₃₇	—	2	2	no	—
151	C₄⋊C₄×C₁₃₇	—	4	8	no	—
152	C₄⋊C₄×C₁₃₇	—	4	2	no	—
153	C₄⋊C₄×C₁₃₇	—	4	2	no	—
154	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
155	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
156	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
157	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
158	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
159	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
160	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
161	C₄²×C₁₃₇	—	2	4	no	—
162	C₄²×C₁₃₇	—	2	2	no	—
163	C₄²×C₁₃₇	—	2	1	no	—
164	C₄²×C₁₃₇	—	2	2	no	—
165	C₄²×C₁₃₇	—	2	1	no	—
166	C₄²×C₁₃₇	—	2	1	no	—
167	C₄²×C₁₃₇	—	4	4	no	—
168	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
171	C₄²×C₁₃₇	C₂×Q₈	1	2	yes	—
172	C₄²×C₁₃₇	C₂×Q₈	1	2	yes	—
173	C₂³×C₁₃₇	—	2	1	no	—
174	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₁₃₇	—	2	1	no	—
176	Q₈×C₁₃₇	—	8	2	no	—
177	Q₈×C₁₃₇	—	8	4	no	—
178	Q₈×C₁₃₇	C₄⋊Q₈	1	2	yes	—
179	D₄×C₁₃₇	—	2	2	no	—
180	D₄×C₁₃₇	—	2	2	no	—
181	D₄×C₁₃₇	—	2	1	no	—
182	D₄×C₁₃₇	C₄⋊Q₈	1	2	yes	—
183	C₂×C₄×C₁₃₇	—	2	4	no	—
184	C₂×C₄×C₁₃₇	—	2	1	no	—
185	C₂×C₄×C₁₃₇	—	2	2	no	—
186	C₂×C₄×C₁₃₇	—	2	2	no	—
187	C₂×C₄×C₁₃₇	—	2	2	no	—
188	C₂×C₄×C₁₃₇	—	2	2	no	—
189	C₂×C₄×C₁₃₇	—	2	2	no	—
190	C₂×C₄×C₁₃₇	—	2	4	no	—
191	C₂×C₄×C₁₃₇	—	2	2	no	—
192	C₂×C₄×C₁₃₇	—	2	2	no	—
193	C₂×C₄×C₁₃₇	—	4	2	no	—
194	C₂×C₄×C₁₃₇	—	4	2	no	—
195	C₂×C₄×C₁₃₇	—	4	4	no	—
196	C₂×C₄×C₁₃₇	—	4	4	no	—
197	C₂×C₄×C₁₃₇	—	4	2	no	—
198	C₂×C₄×C₁₃₇	—	8	2	no	—
199	C₂×C₄×C₁₃₇	—	8	4	no	—
200	C₂×C₄×C₁₃₇	#120	1	2	yes	—
201	C₂×C₄×C₁₃₇	#120	1	2	yes	—
202	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
205	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
206	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
207	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
208	C₈×C₁₃₇	—	2	2	no	—
209	C₈×C₁₃₇	—	2	2	no	—
210	C₈×C₁₃₇	—	4	2	no	—
211	C₂²×C₁₃₇	—	2	2	no	—
212	C₂²×C₁₃₇	—	2	2	no	—
213	C₂²×C₁₃₇	—	4	2	no	—
214	C₂²×C₁₃₇	C₂×#120	1	1	yes	characteristic
215	C₂²×C₁₃₇	D₄×Q₈	1	1	yes	characteristic
216	C₂²×C₁₃₇	D₄×Q₈	1	1	yes	characteristic
217	C₄×C₁₃₇	—	2	4	no	—
218	C₄×C₁₃₇	—	2	2	no	—
219	C₄×C₁₃₇	—	2	2	no	—
220	C₄×C₁₃₇	—	2	2	no	—
221	C₄×C₁₃₇	—	4	2	no	—
222	C₄×C₁₃₇	—	4	4	no	—
223	C₄×C₁₃₇	—	4	2	no	—
224	C₄×C₁₃₇	—	4	2	no	—
225	C₄×C₁₃₇	—	4	2	no	—
226	C₄×C₁₃₇	—	8	2	no	—
227	C₄×C₁₃₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
228	C₄×C₁₃₇	#536	1	1	yes	characteristic
229	C₄×C₁₃₇	D₄×Q₈	1	1	yes	characteristic
230	C₄×C₁₃₇	D₄×Q₈	1	1	yes	characteristic
231	C₂×C₁₃₇	—	2	1	no	—
232	C₂×C₁₃₇	—	2	1	no	—
233	C₂×C₁₃₇	—	4	2	no	—
234	C₂×C₁₃₇	#2434	1	1	yes	characteristic
235	C₂×C₁₃₇	#3018	1	2	yes	—
236	#25831	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₁₃₇	#25831	1	1	yes	characteristic, direct product factor, Sylow
238	#3504	C₂×C₁₃₇	1	1	yes	characteristic
239	#3166	C₂×C₁₃₇	1	1	yes	characteristic, complemented
240	#3080	C₂×C₁₃₇	1	1	yes	characteristic
241	#2859	C₂×C₁₃₇	1	1	yes	characteristic, complemented
242	#2061	C₂×C₁₃₇	1	2	yes	complemented
243	#2060	C₂×C₁₃₇	1	2	yes	complemented
244	#1998	C₂×C₁₃₇	1	1	yes	characteristic, complemented
245	#1994	C₂×C₁₃₇	1	1	yes	characteristic, complemented
246	#1860	C₂×C₁₃₇	1	2	yes	—
247	#1859	C₂×C₁₃₇	1	2	yes	—
248	C₄×#104	C₂×C₁₃₇	1	1	yes	characteristic
249	#557	—	2	2	no	—
250	#554	—	2	2	no	—
251	#554	—	2	4	no	—
252	#544	—	2	2	no	—
253	#544	C₂²×C₁₃₇	1	2	yes	—
254	#533	—	2	1	no	—
255	#533	C₂²×C₁₃₇	1	1	yes	characteristic
256	C₂×#125	—	2	1	no	—
257	C₂×#125	C₂²×C₁₃₇	1	1	yes	characteristic
258	C₂×#125	C₂²×C₁₃₇	1	1	yes	characteristic
259	#520	C₂²×C₁₃₇	1	2	yes	—
260	C₄×#41	C₂²×C₁₃₇	1	1	yes	characteristic
261	#501	—	2	2	no	—
262	#499	—	2	1	no	—
263	#499	—	2	1	no	—
264	#479	—	2	2	no	—
265	#478	—	2	2	no	—
266	#428	C₂²×C₁₃₇	1	2	yes	—
267	#428	C₂²×C₁₃₇	1	2	yes	—
268	#428	C₂²×C₁₃₇	1	2	yes	—
269	#423	C₂²×C₁₃₇	1	1	yes	characteristic
270	C₂×#104	C₂²×C₁₃₇	1	1	yes	characteristic
271	C₂×#104	C₂²×C₁₃₇	1	1	yes	characteristic
272	#417	C₂²×C₁₃₇	1	2	yes	—
273	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
274	#389	—	2	4	no	—
275	#384	C₂²×C₁₃₇	1	2	yes	—
276	#382	C₂²×C₁₃₇	1	2	yes	—
277	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
278	#343	C₂²×C₁₃₇	1	2	yes	—
279	#343	C₂²×C₁₃₇	1	2	yes	—
280	#339	C₂²×C₁₃₇	1	1	yes	characteristic
281	#339	C₂²×C₁₃₇	1	2	yes	—
282	#339	C₂²×C₁₃₇	1	1	yes	characteristic
283	#339	C₂²×C₁₃₇	1	2	yes	—
284	C₂×#41	C₂³×C₁₃₇	1	1	yes	characteristic
285	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
286	C₂×M₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
287	C₂×M₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
288	C₄⋊Q₈	—	2	4	no	—
289	C₄⋊Q₈	—	2	2	no	—
290	C₄⋊Q₈	—	2	2	no	—
291	C₄⋊Q₈	D₄×C₁₃₇	1	2	yes	—
292	#125	—	2	4	no	—
293	#125	—	2	4	no	—
294	#125	—	2	2	no	—
295	#125	—	2	2	no	—
296	#125	—	2	1	no	—
297	#125	—	2	1	no	—
298	#125	—	2	2	no	—
299	#125	—	2	2	no	—
300	#125	—	2	1	no	—
301	#125	—	2	1	no	—
302	#125	D₄×C₁₃₇	1	1	yes	characteristic
303	#125	D₄×C₁₃₇	1	1	yes	characteristic
304	C₂²⋊Q₈	—	2	4	no	—
305	C₂²⋊Q₈	—	2	4	no	—
306	C₂²⋊Q₈	—	2	4	no	—
307	C₂²⋊Q₈	—	2	2	no	—
308	C₂²⋊Q₈	—	2	4	no	—
309	C₄×Q₈	—	2	4	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	—	2	2	no	—
312	C₄×Q₈	D₄×C₁₃₇	1	2	yes	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	2	2	no	—
315	C₄×D₄	—	2	4	no	—
316	C₄×D₄	D₄×C₁₃₇	1	2	yes	—
317	#117	—	2	2	no	—
318	#117	—	2	1	no	—
319	#117	C₂³×C₁₃₇	1	1	yes	characteristic
320	#117	C₂³×C₁₃₇	1	2	yes	—
321	C₂×C₄⋊C₄	—	2	4	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	4	no	—
325	C₂×C₄⋊C₄	D₄×C₁₃₇	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
333	#107	—	2	2	no	—
334	#107	—	2	2	no	—
335	#107	—	2	2	no	—
336	#106	—	2	2	no	—
337	#106	—	2	2	no	—
338	#106	—	2	2	no	—
339	C₄⋊C₈	—	2	2	no	—
340	#104	Q₈×C₁₃₇	1	4	yes	complemented
341	#104	Q₈×C₁₃₇	1	4	yes	complemented
342	#103	—	2	2	no	—
343	#102	—	2	2	no	—
344	#97	—	2	1	no	—
345	C₄×C₈	—	2	1	no	—
346	#95	—	2	4	no	—
347	#41	—	2	1	no	—
348	#41	—	2	1	no	—
349	#41	C₂×Q₈×C₁₃₇	1	2	yes	—
350	#41	C₂×Q₈×C₁₃₇	1	2	yes	—
351	C₂×Q₈	—	2	4	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
363	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
365	M₁₆	—	2	1	no	—
366	M₁₆	—	2	1	no	—
367	M₁₆	—	2	2	no	—
368	M₁₆	—	2	2	no	—
369	M₁₆	C₂×Q₈×C₁₃₇	1	2	yes	—
370	M₁₆	C₂×Q₈×C₁₃₇	1	2	yes	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	2	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	4	8	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
392	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
393	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	2	1	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₄²	—	2	4	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	4	4	no	—
405	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
406	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
407	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
408	C₄²	C₂×Q₈×C₁₃₇	1	2	yes	—
409	C₄²	C₂×Q₈×C₁₃₇	1	2	yes	—
410	C₂³	—	2	1	no	—
411	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
412	Q₈	—	2	1	no	—
413	Q₈	—	8	2	no	—
414	Q₈	—	8	4	no	—
415	Q₈	C₄⋊Q₈×C₁₃₇	1	2	yes	—
416	D₄	—	2	2	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	1	no	—
419	D₄	C₄⋊Q₈×C₁₃₇	1	2	yes	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	8	2	no	—
436	C₂×C₄	—	8	4	no	—
437	C₂×C₄	#120×C₁₃₇	1	2	yes	—
438	C₂×C₄	#120×C₁₃₇	1	2	yes	—
439	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
441	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
442	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
443	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
444	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
445	C₈	—	2	2	no	—
446	C₈	—	2	2	no	—
447	C₈	—	4	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	C₂×#120×C₁₃₇	1	1	yes	characteristic
452	C₂²	D₄×Q₈×C₁₃₇	1	1	yes	characteristic
453	C₂²	D₄×Q₈×C₁₃₇	1	1	yes	characteristic
454	C₄	—	2	4	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	4	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	8	2	no	—
464	C₄	C₂×C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
465	C₄	#536×C₁₃₇	1	1	yes	characteristic
466	C₄	D₄×Q₈×C₁₃₇	1	1	yes	characteristic
467	C₄	D₄×Q₈×C₁₃₇	1	1	yes	characteristic
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	—	4	2	no	—
471	C₂	#2434×C₁₃₇	1	1	yes	characteristic
472	C₂	#3018×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂×#41×C₁₃₇	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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. #3166×C₁₃₇	C₂	semidirect
4. #2859×C₁₃₇	C₂	semidirect
5. #2061×C₁₃₇	C₂	semidirect
6. #2060×C₁₃₇	C₂	semidirect
7. #1998×C₁₃₇	C₂	semidirect
8. #1994×C₁₃₇	C₂	semidirect
103. #104×C₁₃₇	Q₈	semidirect
104. #104×C₁₃₇	Q₈	semidirect
236. #25831	C₁₃₇	direct (N × H)
237. C₁₃₇	#25831	direct (N × H)
239. #3166	C₂×C₁₃₇	semidirect
241. #2859	C₂×C₁₃₇	semidirect
242. #2061	C₂×C₁₃₇	semidirect
243. #2060	C₂×C₁₃₇	semidirect
244. #1998	C₂×C₁₃₇	semidirect
245. #1994	C₂×C₁₃₇	semidirect
340. #104	Q₈×C₁₃₇	semidirect
341. #104	Q₈×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3504×C₁₃₇	2
#3166×C₁₃₇	2
#3080×C₁₃₇	2
#2859×C₁₃₇	2
#2061×C₁₃₇	2
#2060×C₁₃₇	2
#1998×C₁₃₇	2
#1994×C₁₃₇	2
#1860×C₁₃₇	2
#1859×C₁₃₇	2
C₄×#104×C₁₃₇	2
#25831	137

Subgroups — C137×#25831 #46875217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#25831 #46875217