Subgroups — C₁₃₇×#19225 #46868611

Order 35072.

630 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3212×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	#1694×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1693×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	#1682×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1681×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#1564×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1553×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	#495×C₁₃₇	—	2	2	no	—
16	#493×C₁₃₇	C₂²	1	1	yes	characteristic
17	#488×C₁₃₇	—	2	2	no	—
18	#486×C₁₃₇	C₂²	1	2	yes	—
19	#466×C₁₃₇	—	2	1	no	—
20	#466×C₁₃₇	—	2	1	no	—
21	#462×C₁₃₇	C₂²	1	2	yes	—
22	#461×C₁₃₇	C₂²	1	2	yes	—
23	#460×C₁₃₇	C₂²	1	2	yes	—
24	#459×C₁₃₇	C₂²	1	2	yes	—
25	#452×C₁₃₇	—	2	2	no	—
26	#449×C₁₃₇	—	2	2	no	—
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	#431×C₁₃₇	C₂²	1	2	yes	—
38	#405×C₁₃₇	—	2	1	no	—
39	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
40	#335×C₁₃₇	C₂²	1	2	yes	—
41	#334×C₁₃₇	C₂²	1	1	yes	characteristic
42	#334×C₁₃₇	C₂²	1	1	yes	characteristic
43	#332×C₁₃₇	C₂²	1	2	yes	—
44	#332×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×Q₁₆×C₁₃₇	—	2	2	no	—
49	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
50	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
51	C₂×D₈×C₁₃₇	—	2	2	no	—
52	C₂×D₈×C₁₃₇	—	2	1	no	—
53	C₂×D₈×C₁₃₇	—	2	1	no	—
54	C₂×M₁₆×C₁₃₇	—	2	1	no	—
55	C₂²×C₈×C₁₃₇	—	2	1	no	—
56	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
58	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
59	#127×C₁₃₇	C₂³	1	2	yes	—
60	#126×C₁₃₇	—	2	1	no	—
61	#125×C₁₃₇	D₄	1	1	yes	characteristic
62	#124×C₁₃₇	—	2	2	no	—
63	#124×C₁₃₇	D₄	1	1	yes	characteristic
64	#123×C₁₃₇	—	2	1	no	—
65	C₂²⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
66	#121×C₁₃₇	—	2	2	no	—
67	#121×C₁₃₇	—	2	2	no	—
68	#121×C₁₃₇	D₄	1	1	yes	characteristic
69	C₄×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
70	C₄×D₄×C₁₃₇	—	2	1	no	—
71	C₄×D₄×C₁₃₇	—	2	2	no	—
72	C₄×D₄×C₁₃₇	—	2	2	no	—
73	C₄×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
74	#117×C₁₃₇	—	2	1	no	—
75	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
76	#107×C₁₃₇	—	2	1	no	—
77	#107×C₁₃₇	—	2	1	no	—
78	C₄⋊C₈×C₁₃₇	—	2	1	no	—
79	C₄⋊C₈×C₁₃₇	—	2	1	no	—
80	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
81	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
82	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
84	#103×C₁₃₇	—	2	2	no	—
85	#103×C₁₃₇	—	2	2	no	—
86	#102×C₁₃₇	—	2	2	no	—
87	#102×C₁₃₇	—	2	2	no	—
88	#102×C₁₃₇	—	2	2	no	—
89	#102×C₁₃₇	—	2	2	no	—
90	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
91	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
92	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
93	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
94	#97×C₁₃₇	—	2	1	no	—
95	#97×C₁₃₇	—	2	1	no	—
96	C₄×C₈×C₁₃₇	—	2	1	no	—
97	C₄×C₈×C₁₃₇	—	2	2	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	2	no	—
103	#41×C₁₃₇	—	8	2	no	—
104	C₂×Q₈×C₁₃₇	—	2	2	no	—
105	C₂×Q₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₁₃₇	—	2	1	no	—
107	C₂×D₄×C₁₃₇	—	2	2	no	—
108	C₂×D₄×C₁₃₇	—	2	2	no	—
109	C₂×D₄×C₁₃₇	—	2	2	no	—
110	C₂×D₄×C₁₃₇	—	4	2	no	—
111	C₂×D₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃₇	—	2	1	no	—
113	C₂²×C₄×C₁₃₇	—	4	2	no	—
114	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
117	Q₁₆×C₁₃₇	—	8	2	no	—
118	SD₁₆×C₁₃₇	—	8	2	no	—
119	SD₁₆×C₁₃₇	—	8	2	no	—
120	D₈×C₁₃₇	—	4	2	no	—
121	D₈×C₁₃₇	—	4	2	no	—
122	D₈×C₁₃₇	—	8	2	no	—
123	M₁₆×C₁₃₇	—	4	2	no	—
124	C₂×C₈×C₁₃₇	—	2	2	no	—
125	C₂×C₈×C₁₃₇	—	2	1	no	—
126	C₂×C₈×C₁₃₇	—	2	2	no	—
127	C₂×C₈×C₁₃₇	—	2	2	no	—
128	C₂×C₈×C₁₃₇	—	2	1	no	—
129	C₂×C₈×C₁₃₇	—	4	1	no	—
130	C₂×C₈×C₁₃₇	—	4	2	no	—
131	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
135	C₄⋊C₄×C₁₃₇	—	2	1	no	—
136	C₄⋊C₄×C₁₃₇	—	2	1	no	—
137	C₄⋊C₄×C₁₃₇	—	2	1	no	—
138	C₄⋊C₄×C₁₃₇	—	2	1	no	—
139	C₄⋊C₄×C₁₃₇	—	2	2	no	—
140	C₄⋊C₄×C₁₃₇	—	2	2	no	—
141	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
142	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
147	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
148	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
149	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
150	C₄²×C₁₃₇	—	2	1	no	—
151	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₁₃₇	#41	1	1	yes	characteristic
154	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
155	C₂³×C₁₃₇	—	2	1	no	—
156	C₂³×C₁₃₇	—	4	2	no	—
157	C₂³×C₁₃₇	#121	1	1	yes	characteristic
158	Q₈×C₁₃₇	—	2	2	no	—
159	Q₈×C₁₃₇	—	4	2	no	—
160	Q₈×C₁₃₇	—	4	2	no	—
161	D₄×C₁₃₇	—	2	2	no	—
162	D₄×C₁₃₇	—	4	2	no	—
163	D₄×C₁₃₇	—	4	2	no	—
164	D₄×C₁₃₇	—	4	2	no	—
165	D₄×C₁₃₇	—	4	2	no	—
166	D₄×C₁₃₇	—	4	2	no	—
167	D₄×C₁₃₇	—	8	2	no	—
168	D₄×C₁₃₇	—	8	4	no	—
169	C₂×C₄×C₁₃₇	—	2	1	no	—
170	C₂×C₄×C₁₃₇	—	2	1	no	—
171	C₂×C₄×C₁₃₇	—	2	2	no	—
172	C₂×C₄×C₁₃₇	—	2	1	no	—
173	C₂×C₄×C₁₃₇	—	2	1	no	—
174	C₂×C₄×C₁₃₇	—	2	1	no	—
175	C₂×C₄×C₁₃₇	—	4	1	no	—
176	C₂×C₄×C₁₃₇	—	4	1	no	—
177	C₂×C₄×C₁₃₇	—	4	1	no	—
178	C₂×C₄×C₁₃₇	—	4	2	no	—
179	C₂×C₄×C₁₃₇	—	8	4	no	—
180	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
183	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
186	C₈×C₁₃₇	—	2	1	no	—
187	C₈×C₁₃₇	—	2	1	no	—
188	C₈×C₁₃₇	—	2	1	no	—
189	C₈×C₁₃₇	—	4	1	no	—
190	C₈×C₁₃₇	—	4	1	no	—
191	C₈×C₁₃₇	—	4	2	no	—
192	C₈×C₁₃₇	—	4	2	no	—
193	C₈×C₁₃₇	#135	1	2	yes	—
194	C₂²×C₁₃₇	—	2	1	no	—
195	C₂²×C₁₃₇	—	2	1	no	—
196	C₂²×C₁₃₇	—	2	1	no	—
197	C₂²×C₁₃₇	—	4	1	no	—
198	C₂²×C₁₃₇	—	4	1	no	—
199	C₂²×C₁₃₇	—	4	1	no	—
200	C₂²×C₁₃₇	—	8	2	no	—
201	C₂²×C₁₃₇	—	8	2	no	—
202	C₂²×C₁₃₇	—	8	2	no	—
203	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
204	C₄×C₁₃₇	—	2	1	no	—
205	C₄×C₁₃₇	—	2	1	no	—
206	C₄×C₁₃₇	—	2	1	no	—
207	C₄×C₁₃₇	—	2	1	no	—
208	C₄×C₁₃₇	—	4	1	no	—
209	C₄×C₁₃₇	—	4	1	no	—
210	C₄×C₁₃₇	—	4	1	no	—
211	C₄×C₁₃₇	—	8	2	no	—
212	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
213	C₄×C₁₃₇	#575	1	1	yes	characteristic
214	C₄×C₁₃₇	#576	1	2	yes	—
215	C₂×C₁₃₇	—	4	1	no	—
216	C₂×C₁₃₇	—	8	1	no	—
217	C₂×C₁₃₇	—	16	2	no	—
218	C₂×C₁₃₇	#3035	1	1	yes	characteristic
219	C₂×C₁₃₇	#3058	1	1	yes	characteristic
220	C₂×C₁₃₇	#3067	1	1	yes	characteristic
221	#19225	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₁₃₇	#19225	1	1	yes	characteristic, direct product factor, Sylow
223	#3212	C₂×C₁₃₇	1	2	yes	complemented
224	#3169	C₂×C₁₃₇	1	1	yes	characteristic, complemented
225	#2966	C₂×C₁₃₇	1	1	yes	characteristic, complemented
226	#1694	C₂×C₁₃₇	1	1	yes	characteristic, complemented
227	#1693	C₂×C₁₃₇	1	1	yes	characteristic, complemented
228	#1688	C₂×C₁₃₇	1	1	yes	characteristic, complemented
229	#1687	C₂×C₁₃₇	1	1	yes	characteristic, complemented
230	#1682	C₂×C₁₃₇	1	2	yes	complemented
231	#1681	C₂×C₁₃₇	1	2	yes	complemented
232	#1564	C₂×C₁₃₇	1	1	yes	characteristic, complemented
233	#1553	C₂×C₁₃₇	1	2	yes	complemented
234	#532	C₂²×C₁₃₇	1	2	yes	—
235	#529	C₂²×C₁₃₇	1	1	yes	characteristic
236	#500	C₂²×C₁₃₇	1	1	yes	characteristic
237	#495	—	2	2	no	—
238	#493	C₂²×C₁₃₇	1	1	yes	characteristic
239	#488	—	2	2	no	—
240	#486	C₂²×C₁₃₇	1	2	yes	—
241	#466	—	2	1	no	—
242	#466	—	2	1	no	—
243	#462	C₂²×C₁₃₇	1	2	yes	—
244	#461	C₂²×C₁₃₇	1	2	yes	—
245	#460	C₂²×C₁₃₇	1	2	yes	—
246	#459	C₂²×C₁₃₇	1	2	yes	—
247	#452	—	2	2	no	—
248	#449	—	2	2	no	—
249	#446	C₂²×C₁₃₇	1	1	yes	characteristic
250	C₈×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
251	C₄×D₈	—	2	1	no	—
252	C₄×D₈	—	2	1	no	—
253	#436	C₂²×C₁₃₇	1	1	yes	characteristic
254	#435	—	2	1	no	—
255	C₈×D₄	—	2	1	no	—
256	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
257	#433	—	2	1	no	—
258	#432	C₂²×C₁₃₇	1	1	yes	characteristic
259	#431	C₂²×C₁₃₇	1	2	yes	—
260	#405	—	2	1	no	—
261	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
262	#335	C₂²×C₁₃₇	1	2	yes	—
263	#334	C₂²×C₁₃₇	1	1	yes	characteristic
264	#334	C₂²×C₁₃₇	1	1	yes	characteristic
265	#332	C₂²×C₁₃₇	1	2	yes	—
266	#332	C₂²×C₁₃₇	1	2	yes	—
267	#331	C₂²×C₁₃₇	1	2	yes	—
268	#331	C₂²×C₁₃₇	1	2	yes	—
269	C₂×#41	—	2	2	no	—
270	C₂×Q₁₆	—	2	2	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂×SD₁₆	—	2	2	no	—
273	C₂×D₈	—	2	2	no	—
274	C₂×D₈	—	2	1	no	—
275	C₂×D₈	—	2	1	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
279	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
280	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
281	#127	C₂³×C₁₃₇	1	2	yes	—
282	#126	—	2	1	no	—
283	#125	D₄×C₁₃₇	1	1	yes	characteristic
284	#124	—	2	2	no	—
285	#124	D₄×C₁₃₇	1	1	yes	characteristic
286	#123	—	2	1	no	—
287	C₂²⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
288	#121	—	2	2	no	—
289	#121	—	2	2	no	—
290	#121	D₄×C₁₃₇	1	1	yes	characteristic
291	C₄×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
296	#117	—	2	1	no	—
297	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
298	#107	—	2	1	no	—
299	#107	—	2	1	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
303	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
304	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
305	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
306	#103	—	2	2	no	—
307	#103	—	2	2	no	—
308	#102	—	2	2	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	#102	—	2	2	no	—
312	C₂²⋊C₈	—	2	2	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	2	1	no	—
316	#97	—	2	1	no	—
317	#97	—	2	1	no	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	—	2	2	no	—
320	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
321	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
322	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
323	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
324	#41	—	8	2	no	—
325	#41	—	8	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
338	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
339	Q₁₆	—	8	2	no	—
340	SD₁₆	—	8	2	no	—
341	SD₁₆	—	8	2	no	—
342	D₈	—	4	2	no	—
343	D₈	—	4	2	no	—
344	D₈	—	8	2	no	—
345	M₁₆	—	4	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	4	2	no	—
353	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
354	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
355	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
356	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
364	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	4	2	no	—
371	C₂²⋊C₄	—	4	2	no	—
372	C₄²	—	2	1	no	—
373	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
374	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
375	C₄²	#41×C₁₃₇	1	1	yes	characteristic
376	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
377	C₂³	—	2	1	no	—
378	C₂³	—	4	2	no	—
379	C₂³	#121×C₁₃₇	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	4	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	8	4	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	8	4	no	—
402	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
403	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
404	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
405	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
407	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
408	C₈	—	2	1	no	—
409	C₈	—	2	1	no	—
410	C₈	—	2	1	no	—
411	C₈	—	4	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	4	2	no	—
414	C₈	—	4	2	no	—
415	C₈	#135×C₁₃₇	1	2	yes	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	8	2	no	—
434	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
435	C₄	#575×C₁₃₇	1	1	yes	characteristic
436	C₄	#576×C₁₃₇	1	2	yes	—
437	C₂	—	4	1	no	—
438	C₂	—	8	1	no	—
439	C₂	—	16	2	no	—
440	C₂	#3035×C₁₃₇	1	1	yes	characteristic
441	C₂	#3058×C₁₃₇	1	1	yes	characteristic
442	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. #3212×C₁₃₇	C₂	semidirect
2. #3169×C₁₃₇	C₂	semidirect
3. #2966×C₁₃₇	C₂	semidirect
4. #1694×C₁₃₇	C₂	semidirect
5. #1693×C₁₃₇	C₂	semidirect
6. #1688×C₁₃₇	C₂	semidirect
7. #1687×C₁₃₇	C₂	semidirect
8. #1682×C₁₃₇	C₂	semidirect
9. #1681×C₁₃₇	C₂	semidirect
10. #1564×C₁₃₇	C₂	semidirect
11. #1553×C₁₃₇	C₂	semidirect
221. #19225	C₁₃₇	direct (N × H)
222. C₁₃₇	#19225	direct (N × H)
223. #3212	C₂×C₁₃₇	semidirect
224. #3169	C₂×C₁₃₇	semidirect
225. #2966	C₂×C₁₃₇	semidirect
226. #1694	C₂×C₁₃₇	semidirect
227. #1693	C₂×C₁₃₇	semidirect
228. #1688	C₂×C₁₃₇	semidirect
229. #1687	C₂×C₁₃₇	semidirect
230. #1682	C₂×C₁₃₇	semidirect
231. #1681	C₂×C₁₃₇	semidirect
232. #1564	C₂×C₁₃₇	semidirect
233. #1553	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3212×C₁₃₇	2
#3169×C₁₃₇	2
#2966×C₁₃₇	2
#1694×C₁₃₇	2
#1693×C₁₃₇	2
#1688×C₁₃₇	2
#1687×C₁₃₇	2
#1682×C₁₃₇	2
#1681×C₁₃₇	2
#1564×C₁₃₇	2
#1553×C₁₃₇	2
#19225	137

Subgroups — C137×#19225 #46868611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19225 #46868611