Subgroups — C₁₃₇×#19227 #46868613

Order 35072.

628 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3247×C₁₃₇	C₂	1	2	yes	maximal, complemented
2	#3169×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2966×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#1696×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1695×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#1688×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1687×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1678×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1677×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	C₂×#334×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1551×C₁₃₇	C₂	1	2	yes	maximal, complemented
12	#532×C₁₃₇	C₂²	1	2	yes	—
13	#529×C₁₃₇	C₂²	1	1	yes	characteristic
14	#500×C₁₃₇	C₂²	1	1	yes	characteristic
15	#493×C₁₃₇	C₂²	1	1	yes	characteristic
16	#486×C₁₃₇	C₂²	1	2	yes	—
17	#478×C₁₃₇	—	2	2	no	—
18	#477×C₁₃₇	C₂²	1	2	yes	—
19	#476×C₁₃₇	C₂²	1	2	yes	—
20	#466×C₁₃₇	—	2	1	no	—
21	#466×C₁₃₇	—	2	1	no	—
22	#466×C₁₃₇	—	2	2	no	—
23	#465×C₁₃₇	—	2	2	no	—
24	#463×C₁₃₇	—	2	2	no	—
25	#460×C₁₃₇	C₂²	1	2	yes	—
26	#459×C₁₃₇	C₂²	1	2	yes	—
27	#446×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₈×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
29	C₄×D₈×C₁₃₇	—	2	1	no	—
30	C₄×D₈×C₁₃₇	—	2	1	no	—
31	#436×C₁₃₇	C₂²	1	1	yes	characteristic
32	#435×C₁₃₇	—	2	1	no	—
33	C₈×D₄×C₁₃₇	—	2	1	no	—
34	C₈×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
35	#433×C₁₃₇	—	2	1	no	—
36	#432×C₁₃₇	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
38	#405×C₁₃₇	—	2	1	no	—
39	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
40	#334×C₁₃₇	C₂²	1	2	yes	—
41	#334×C₁₃₇	C₂²	1	1	yes	characteristic
42	#334×C₁₃₇	C₂²	1	1	yes	characteristic
43	#333×C₁₃₇	C₂²	1	2	yes	—
44	#333×C₁₃₇	C₂²	1	2	yes	—
45	#331×C₁₃₇	C₂²	1	2	yes	—
46	#331×C₁₃₇	C₂²	1	2	yes	—
47	C₂×#41×C₁₃₇	—	2	2	no	—
48	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
49	C₂×D₈×C₁₃₇	—	2	2	no	—
50	C₂×D₈×C₁₃₇	—	2	1	no	—
51	C₂×D₈×C₁₃₇	—	2	1	no	—
52	C₂×M₁₆×C₁₃₇	—	2	1	no	—
53	C₂²×C₈×C₁₃₇	—	2	2	no	—
54	C₂²×C₈×C₁₃₇	—	2	1	no	—
55	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
57	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
58	#127×C₁₃₇	C₂³	1	2	yes	—
59	#126×C₁₃₇	—	2	1	no	—
60	#125×C₁₃₇	D₄	1	1	yes	characteristic
61	#124×C₁₃₇	—	2	2	no	—
62	#124×C₁₃₇	D₄	1	1	yes	characteristic
63	#123×C₁₃₇	—	2	1	no	—
64	C₂²⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
65	#121×C₁₃₇	—	2	2	no	—
66	#121×C₁₃₇	—	2	2	no	—
67	#121×C₁₃₇	D₄	1	1	yes	characteristic
68	C₄×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₁₃₇	—	2	1	no	—
70	C₄×D₄×C₁₃₇	—	2	2	no	—
71	C₄×D₄×C₁₃₇	—	2	2	no	—
72	C₄×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
73	#117×C₁₃₇	—	2	1	no	—
74	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
75	#107×C₁₃₇	—	2	1	no	—
76	#107×C₁₃₇	—	2	1	no	—
77	#107×C₁₃₇	—	2	2	no	—
78	#106×C₁₃₇	—	2	2	no	—
79	C₄⋊C₈×C₁₃₇	—	2	1	no	—
80	C₄⋊C₈×C₁₃₇	—	2	1	no	—
81	C₄⋊C₈×C₁₃₇	—	2	2	no	—
82	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
83	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
84	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
85	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
86	#103×C₁₃₇	—	2	2	no	—
87	#102×C₁₃₇	—	2	2	no	—
88	#102×C₁₃₇	—	2	2	no	—
89	#102×C₁₃₇	—	2	2	no	—
90	#102×C₁₃₇	—	2	2	no	—
91	#102×C₁₃₇	—	2	2	no	—
92	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
93	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
94	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
95	#97×C₁₃₇	—	2	1	no	—
96	#97×C₁₃₇	—	2	1	no	—
97	C₄×C₈×C₁₃₇	—	2	1	no	—
98	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
99	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
102	#41×C₁₃₇	—	8	4	no	—
103	C₂×Q₈×C₁₃₇	—	2	2	no	—
104	C₂×Q₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₁₃₇	—	2	1	no	—
106	C₂×D₄×C₁₃₇	—	2	2	no	—
107	C₂×D₄×C₁₃₇	—	2	2	no	—
108	C₂×D₄×C₁₃₇	—	2	2	no	—
109	C₂×D₄×C₁₃₇	—	4	2	no	—
110	C₂×D₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₇	—	2	1	no	—
112	C₂²×C₄×C₁₃₇	—	4	2	no	—
113	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
116	SD₁₆×C₁₃₇	—	8	2	no	—
117	D₈×C₁₃₇	—	4	2	no	—
118	D₈×C₁₃₇	—	4	2	no	—
119	D₈×C₁₃₇	—	8	2	no	—
120	M₁₆×C₁₃₇	—	4	2	no	—
121	C₂×C₈×C₁₃₇	—	2	2	no	—
122	C₂×C₈×C₁₃₇	—	2	1	no	—
123	C₂×C₈×C₁₃₇	—	2	1	no	—
124	C₂×C₈×C₁₃₇	—	2	2	no	—
125	C₂×C₈×C₁₃₇	—	2	2	no	—
126	C₂×C₈×C₁₃₇	—	4	1	no	—
127	C₂×C₈×C₁₃₇	—	4	2	no	—
128	C₂×C₈×C₁₃₇	—	8	2	no	—
129	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
133	C₄⋊C₄×C₁₃₇	—	2	1	no	—
134	C₄⋊C₄×C₁₃₇	—	2	1	no	—
135	C₄⋊C₄×C₁₃₇	—	2	1	no	—
136	C₄⋊C₄×C₁₃₇	—	2	1	no	—
137	C₄⋊C₄×C₁₃₇	—	2	2	no	—
138	C₄⋊C₄×C₁₃₇	—	2	2	no	—
139	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
140	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
141	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
142	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
143	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
144	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
145	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
146	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
147	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
148	C₄²×C₁₃₇	—	2	1	no	—
149	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₃₇	#41	1	1	yes	characteristic
152	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
153	C₂³×C₁₃₇	—	2	1	no	—
154	C₂³×C₁₃₇	—	4	2	no	—
155	C₂³×C₁₃₇	#121	1	1	yes	characteristic
156	Q₈×C₁₃₇	—	2	2	no	—
157	Q₈×C₁₃₇	—	8	2	no	—
158	D₄×C₁₃₇	—	2	2	no	—
159	D₄×C₁₃₇	—	4	2	no	—
160	D₄×C₁₃₇	—	4	2	no	—
161	D₄×C₁₃₇	—	4	2	no	—
162	D₄×C₁₃₇	—	4	2	no	—
163	D₄×C₁₃₇	—	4	2	no	—
164	D₄×C₁₃₇	—	8	2	no	—
165	D₄×C₁₃₇	—	8	4	no	—
166	C₂×C₄×C₁₃₇	—	2	2	no	—
167	C₂×C₄×C₁₃₇	—	2	1	no	—
168	C₂×C₄×C₁₃₇	—	2	1	no	—
169	C₂×C₄×C₁₃₇	—	2	2	no	—
170	C₂×C₄×C₁₃₇	—	2	1	no	—
171	C₂×C₄×C₁₃₇	—	2	1	no	—
172	C₂×C₄×C₁₃₇	—	2	1	no	—
173	C₂×C₄×C₁₃₇	—	4	1	no	—
174	C₂×C₄×C₁₃₇	—	4	1	no	—
175	C₂×C₄×C₁₃₇	—	4	2	no	—
176	C₂×C₄×C₁₃₇	—	8	4	no	—
177	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
183	C₈×C₁₃₇	—	2	1	no	—
184	C₈×C₁₃₇	—	2	1	no	—
185	C₈×C₁₃₇	—	2	1	no	—
186	C₈×C₁₃₇	—	4	1	no	—
187	C₈×C₁₃₇	—	4	1	no	—
188	C₈×C₁₃₇	—	4	2	no	—
189	C₈×C₁₃₇	—	4	2	no	—
190	C₈×C₁₃₇	#135	1	2	yes	—
191	C₂²×C₁₃₇	—	2	1	no	—
192	C₂²×C₁₃₇	—	2	1	no	—
193	C₂²×C₁₃₇	—	4	1	no	—
194	C₂²×C₁₃₇	—	4	1	no	—
195	C₂²×C₁₃₇	—	4	1	no	—
196	C₂²×C₁₃₇	—	8	2	no	—
197	C₂²×C₁₃₇	—	8	2	no	—
198	C₂²×C₁₃₇	—	8	2	no	—
199	C₂²×C₁₃₇	#472	1	2	yes	—
200	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
201	C₄×C₁₃₇	—	2	1	no	—
202	C₄×C₁₃₇	—	2	1	no	—
203	C₄×C₁₃₇	—	2	1	no	—
204	C₄×C₁₃₇	—	2	1	no	—
205	C₄×C₁₃₇	—	4	1	no	—
206	C₄×C₁₃₇	—	4	1	no	—
207	C₄×C₁₃₇	—	4	1	no	—
208	C₄×C₁₃₇	—	8	2	no	—
209	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
210	C₄×C₁₃₇	#575	1	1	yes	characteristic
211	C₄×C₁₃₇	#577	1	2	yes	—
212	C₂×C₁₃₇	—	2	2	no	—
213	C₂×C₁₃₇	—	8	1	no	—
214	C₂×C₁₃₇	—	16	2	no	—
215	C₂×C₁₃₇	#3035	1	1	yes	characteristic
216	C₂×C₁₃₇	#3060	1	1	yes	characteristic
217	C₂×C₁₃₇	C₂×#472	1	1	yes	characteristic
218	#19227	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₁₃₇	#19227	1	1	yes	characteristic, direct product factor, Sylow
220	#3247	C₂×C₁₃₇	1	2	yes	complemented
221	#3169	C₂×C₁₃₇	1	1	yes	characteristic, complemented
222	#2966	C₂×C₁₃₇	1	1	yes	characteristic, complemented
223	#1696	C₂×C₁₃₇	1	1	yes	characteristic, complemented
224	#1695	C₂×C₁₃₇	1	1	yes	characteristic, complemented
225	#1688	C₂×C₁₃₇	1	1	yes	characteristic, complemented
226	#1687	C₂×C₁₃₇	1	1	yes	characteristic, complemented
227	#1678	C₂×C₁₃₇	1	2	yes	complemented
228	#1677	C₂×C₁₃₇	1	2	yes	complemented
229	C₂×#334	C₂×C₁₃₇	1	1	yes	characteristic, complemented
230	#1551	C₂×C₁₃₇	1	2	yes	complemented
231	#532	C₂²×C₁₃₇	1	2	yes	—
232	#529	C₂²×C₁₃₇	1	1	yes	characteristic
233	#500	C₂²×C₁₃₇	1	1	yes	characteristic
234	#493	C₂²×C₁₃₇	1	1	yes	characteristic
235	#486	C₂²×C₁₃₇	1	2	yes	—
236	#478	—	2	2	no	—
237	#477	C₂²×C₁₃₇	1	2	yes	—
238	#476	C₂²×C₁₃₇	1	2	yes	—
239	#466	—	2	1	no	—
240	#466	—	2	1	no	—
241	#466	—	2	2	no	—
242	#465	—	2	2	no	—
243	#463	—	2	2	no	—
244	#460	C₂²×C₁₃₇	1	2	yes	—
245	#459	C₂²×C₁₃₇	1	2	yes	—
246	#446	C₂²×C₁₃₇	1	1	yes	characteristic
247	C₈×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
248	C₄×D₈	—	2	1	no	—
249	C₄×D₈	—	2	1	no	—
250	#436	C₂²×C₁₃₇	1	1	yes	characteristic
251	#435	—	2	1	no	—
252	C₈×D₄	—	2	1	no	—
253	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
254	#433	—	2	1	no	—
255	#432	C₂²×C₁₃₇	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
257	#405	—	2	1	no	—
258	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
259	#334	C₂²×C₁₃₇	1	2	yes	—
260	#334	C₂²×C₁₃₇	1	1	yes	characteristic
261	#334	C₂²×C₁₃₇	1	1	yes	characteristic
262	#333	C₂²×C₁₃₇	1	2	yes	—
263	#333	C₂²×C₁₃₇	1	2	yes	—
264	#331	C₂²×C₁₃₇	1	2	yes	—
265	#331	C₂²×C₁₃₇	1	2	yes	—
266	C₂×#41	—	2	2	no	—
267	C₂×SD₁₆	—	2	2	no	—
268	C₂×D₈	—	2	2	no	—
269	C₂×D₈	—	2	1	no	—
270	C₂×D₈	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
275	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
276	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
277	#127	C₂³×C₁₃₇	1	2	yes	—
278	#126	—	2	1	no	—
279	#125	D₄×C₁₃₇	1	1	yes	characteristic
280	#124	—	2	2	no	—
281	#124	D₄×C₁₃₇	1	1	yes	characteristic
282	#123	—	2	1	no	—
283	C₂²⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
284	#121	—	2	2	no	—
285	#121	—	2	2	no	—
286	#121	D₄×C₁₃₇	1	1	yes	characteristic
287	C₄×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
292	#117	—	2	1	no	—
293	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
294	#107	—	2	1	no	—
295	#107	—	2	1	no	—
296	#107	—	2	2	no	—
297	#106	—	2	2	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
302	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
303	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
304	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
305	#103	—	2	2	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	2	2	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	#97	—	2	1	no	—
315	#97	—	2	1	no	—
316	C₄×C₈	—	2	1	no	—
317	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
318	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
319	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
320	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
321	#41	—	8	4	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
334	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
335	SD₁₆	—	8	2	no	—
336	D₈	—	4	2	no	—
337	D₈	—	4	2	no	—
338	D₈	—	8	2	no	—
339	M₁₆	—	4	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	—	8	2	no	—
348	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
349	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
350	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
351	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
359	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₄²	—	2	1	no	—
368	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
369	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
370	C₄²	#41×C₁₃₇	1	1	yes	characteristic
371	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
372	C₂³	—	2	1	no	—
373	C₂³	—	4	2	no	—
374	C₂³	#121×C₁₃₇	1	1	yes	characteristic
375	Q₈	—	2	2	no	—
376	Q₈	—	8	2	no	—
377	D₄	—	2	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	8	2	no	—
384	D₄	—	8	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	8	4	no	—
396	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
397	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
398	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
401	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	4	1	no	—
407	C₈	—	4	2	no	—
408	C₈	—	4	2	no	—
409	C₈	#135×C₁₃₇	1	2	yes	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	#472×C₁₃₇	1	2	yes	—
419	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	8	2	no	—
428	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
429	C₄	#575×C₁₃₇	1	1	yes	characteristic
430	C₄	#577×C₁₃₇	1	2	yes	—
431	C₂	—	2	2	no	—
432	C₂	—	8	1	no	—
433	C₂	—	16	2	no	—
434	C₂	#3035×C₁₃₇	1	1	yes	characteristic
435	C₂	#3060×C₁₃₇	1	1	yes	characteristic
436	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. #3247×C₁₃₇	C₂	semidirect
2. #3169×C₁₃₇	C₂	semidirect
3. #2966×C₁₃₇	C₂	semidirect
4. #1696×C₁₃₇	C₂	semidirect
5. #1695×C₁₃₇	C₂	semidirect
6. #1688×C₁₃₇	C₂	semidirect
7. #1687×C₁₃₇	C₂	semidirect
8. #1678×C₁₃₇	C₂	semidirect
9. #1677×C₁₃₇	C₂	semidirect
10. C₂×#334×C₁₃₇	C₂	semidirect
11. #1551×C₁₃₇	C₂	semidirect
218. #19227	C₁₃₇	direct (N × H)
219. C₁₃₇	#19227	direct (N × H)
220. #3247	C₂×C₁₃₇	semidirect
221. #3169	C₂×C₁₃₇	semidirect
222. #2966	C₂×C₁₃₇	semidirect
223. #1696	C₂×C₁₃₇	semidirect
224. #1695	C₂×C₁₃₇	semidirect
225. #1688	C₂×C₁₃₇	semidirect
226. #1687	C₂×C₁₃₇	semidirect
227. #1678	C₂×C₁₃₇	semidirect
228. #1677	C₂×C₁₃₇	semidirect
229. C₂×#334	C₂×C₁₃₇	semidirect
230. #1551	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3247×C₁₃₇	2
#3169×C₁₃₇	2
#2966×C₁₃₇	2
#1696×C₁₃₇	2
#1695×C₁₃₇	2
#1688×C₁₃₇	2
#1687×C₁₃₇	2
#1678×C₁₃₇	2
#1677×C₁₃₇	2
C₂×#334×C₁₃₇	2
#1551×C₁₃₇	2
#19227	137

Subgroups — C137×#19227 #46868613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19227 #46868613