Subgroups — C₁₃₇×#19244 #46868630

Order 35072.

594 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3246×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#3230×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#3141×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2962×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1704×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1698×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1684×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1678×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1565×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#333×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1540×C₁₃₇	C₂	1	1	yes	maximal, characteristic
12	#533×C₁₃₇	C₂²	1	1	yes	characteristic
13	#532×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
15	#500×C₁₃₇	—	2	1	no	—
16	#489×C₁₃₇	—	2	2	no	—
17	#487×C₁₃₇	—	2	1	no	—
18	#487×C₁₃₇	C₂²	1	2	yes	—
19	#486×C₁₃₇	C₂²	1	2	yes	—
20	#484×C₁₃₇	—	2	2	no	—
21	#477×C₁₃₇	C₂²	1	2	yes	—
22	#477×C₁₃₇	C₂²	1	2	yes	—
23	#476×C₁₃₇	—	2	1	no	—
24	#475×C₁₃₇	C₂²	1	2	yes	—
25	#465×C₁₃₇	—	2	2	no	—
26	#461×C₁₃₇	—	2	1	no	—
27	#460×C₁₃₇	C₂²	1	2	yes	—
28	#446×C₁₃₇	—	2	2	no	—
29	#446×C₁₃₇	C₂²	1	2	yes	—
30	C₈×Q₈×C₁₃₇	C₂²	1	2	yes	—
31	#431×C₁₃₇	C₂²	1	1	yes	characteristic
32	#424×C₁₃₇	—	2	1	no	—
33	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
35	#417×C₁₃₇	—	2	1	no	—
36	#417×C₁₃₇	—	2	1	no	—
37	#405×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	#333×C₁₃₇	C₂²	1	2	yes	—
42	#333×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	C₂²×Q₈×C₁₃₇	—	2	1	no	—
49	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
50	C₂×M₁₆×C₁₃₇	D₄	1	1	yes	characteristic
51	C₂×M₁₆×C₁₃₇	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃₇	—	2	1	no	—
53	C₂²×C₈×C₁₃₇	—	2	1	no	—
54	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
55	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
56	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
57	C₄⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
58	C₄⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
59	C₄⋊Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
60	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
61	#127×C₁₃₇	C₂³	1	1	yes	characteristic
62	#125×C₁₃₇	—	2	1	no	—
63	#124×C₁₃₇	—	2	1	no	—
64	C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
65	C₂²⋊Q₈×C₁₃₇	D₄	1	2	yes	—
66	#121×C₁₃₇	—	2	1	no	—
67	#121×C₁₃₇	—	2	1	no	—
68	C₄×Q₈×C₁₃₇	—	2	1	no	—
69	C₄×Q₈×C₁₃₇	C₂³	1	2	yes	—
70	C₄×D₄×C₁₃₇	—	2	1	no	—
71	C₄×D₄×C₁₃₇	—	2	1	no	—
72	#117×C₁₃₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
75	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
76	#107×C₁₃₇	—	2	2	no	—
77	#107×C₁₃₇	—	2	2	no	—
78	#106×C₁₃₇	—	2	2	no	—
79	C₄⋊C₈×C₁₃₇	—	2	2	no	—
80	C₄⋊C₈×C₁₃₇	—	2	2	no	—
81	C₄⋊C₈×C₁₃₇	—	2	1	no	—
82	C₄⋊C₈×C₁₃₇	—	2	1	no	—
83	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
85	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
86	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
88	#103×C₁₃₇	—	2	2	no	—
89	#103×C₁₃₇	—	2	2	no	—
90	#103×C₁₃₇	—	2	2	no	—
91	#103×C₁₃₇	—	2	2	no	—
92	#103×C₁₃₇	—	2	2	no	—
93	#102×C₁₃₇	—	2	2	no	—
94	#102×C₁₃₇	—	2	2	no	—
95	#102×C₁₃₇	—	2	2	no	—
96	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
97	#97×C₁₃₇	—	2	2	no	—
98	#97×C₁₃₇	D₄	1	2	yes	—
99	C₄×C₈×C₁₃₇	—	2	2	no	—
100	C₄×C₈×C₁₃₇	—	2	1	no	—
101	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
102	#41×C₁₃₇	—	4	2	no	—
103	#41×C₁₃₇	—	4	2	no	—
104	C₂×Q₈×C₁₃₇	—	2	1	no	—
105	C₂×Q₈×C₁₃₇	—	2	1	no	—
106	C₂×Q₈×C₁₃₇	—	2	2	no	—
107	C₂×Q₈×C₁₃₇	—	4	1	no	—
108	C₂×Q₈×C₁₃₇	—	8	2	no	—
109	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₁₃₇	—	2	1	no	—
111	C₂×D₄×C₁₃₇	—	2	1	no	—
112	C₂×D₄×C₁₃₇	—	2	1	no	—
113	C₂×D₄×C₁₃₇	—	4	1	no	—
114	C₂²×C₄×C₁₃₇	—	4	1	no	—
115	C₂²×C₄×C₁₃₇	—	4	1	no	—
116	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
119	SD₁₆×C₁₃₇	—	8	2	no	—
120	M₁₆×C₁₃₇	—	2	2	no	—
121	M₁₆×C₁₃₇	—	2	2	no	—
122	C₂×C₈×C₁₃₇	—	2	1	no	—
123	C₂×C₈×C₁₃₇	—	2	1	no	—
124	C₂×C₈×C₁₃₇	—	2	1	no	—
125	C₂×C₈×C₁₃₇	—	2	1	no	—
126	C₂×C₈×C₁₃₇	—	2	2	no	—
127	C₂×C₈×C₁₃₇	—	4	2	no	—
128	C₂×C₈×C₁₃₇	—	8	1	no	—
129	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
131	C₄⋊C₄×C₁₃₇	—	2	1	no	—
132	C₄⋊C₄×C₁₃₇	—	2	1	no	—
133	C₄⋊C₄×C₁₃₇	—	2	1	no	—
134	C₄⋊C₄×C₁₃₇	—	2	2	no	—
135	C₄⋊C₄×C₁₃₇	—	2	2	no	—
136	C₄⋊C₄×C₁₃₇	—	2	2	no	—
137	C₄⋊C₄×C₁₃₇	—	2	1	no	—
138	C₄⋊C₄×C₁₃₇	—	2	2	no	—
139	C₄⋊C₄×C₁₃₇	—	2	1	no	—
140	C₄⋊C₄×C₁₃₇	—	4	1	no	—
141	C₄⋊C₄×C₁₃₇	—	4	1	no	—
142	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
143	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
144	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
145	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
146	C₄²×C₁₃₇	—	2	2	no	—
147	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₃₇	#41	1	1	yes	characteristic
150	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
151	C₂³×C₁₃₇	—	4	1	no	—
152	C₂³×C₁₃₇	#121	1	1	yes	characteristic
153	Q₈×C₁₃₇	—	2	2	no	—
154	Q₈×C₁₃₇	—	2	2	no	—
155	Q₈×C₁₃₇	—	4	1	no	—
156	Q₈×C₁₃₇	—	4	1	no	—
157	Q₈×C₁₃₇	—	8	1	no	—
158	Q₈×C₁₃₇	—	8	2	no	—
159	Q₈×C₁₃₇	—	8	2	no	—
160	D₄×C₁₃₇	—	4	1	no	—
161	D₄×C₁₃₇	—	4	1	no	—
162	D₄×C₁₃₇	—	4	1	no	—
163	D₄×C₁₃₇	—	4	1	no	—
164	D₄×C₁₃₇	—	8	1	no	—
165	D₄×C₁₃₇	—	8	2	no	—
166	C₂×C₄×C₁₃₇	—	2	1	no	—
167	C₂×C₄×C₁₃₇	—	2	1	no	—
168	C₂×C₄×C₁₃₇	—	2	2	no	—
169	C₂×C₄×C₁₃₇	—	2	2	no	—
170	C₂×C₄×C₁₃₇	—	4	1	no	—
171	C₂×C₄×C₁₃₇	—	4	1	no	—
172	C₂×C₄×C₁₃₇	—	4	2	no	—
173	C₂×C₄×C₁₃₇	—	8	2	no	—
174	C₂×C₄×C₁₃₇	—	8	2	no	—
175	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₃₇	#135	1	2	yes	—
179	C₂×C₄×C₁₃₇	#137	1	2	yes	—
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	2	no	—
184	C₈×C₁₃₇	—	2	2	no	—
185	C₈×C₁₃₇	—	4	1	no	—
186	C₈×C₁₃₇	—	4	1	no	—
187	C₈×C₁₃₇	—	4	1	no	—
188	C₈×C₁₃₇	—	4	2	no	—
189	C₈×C₁₃₇	—	4	1	no	—
190	C₂²×C₁₃₇	—	2	1	no	—
191	C₂²×C₁₃₇	—	2	1	no	—
192	C₂²×C₁₃₇	—	8	1	no	—
193	C₂²×C₁₃₇	—	8	1	no	—
194	C₂²×C₁₃₇	—	8	1	no	—
195	C₂²×C₁₃₇	#464	1	2	yes	—
196	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
197	C₄×C₁₃₇	—	2	1	no	—
198	C₄×C₁₃₇	—	2	1	no	—
199	C₄×C₁₃₇	—	2	1	no	—
200	C₄×C₁₃₇	—	4	2	no	—
201	C₄×C₁₃₇	—	4	2	no	—
202	C₄×C₁₃₇	—	8	1	no	—
203	C₄×C₁₃₇	—	8	2	no	—
204	C₄×C₁₃₇	#464	1	2	yes	—
205	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
206	C₄×C₁₃₇	C₂×#137	1	1	yes	characteristic
207	C₄×C₁₃₇	#577	1	1	yes	characteristic
208	C₄×C₁₃₇	#578	1	1	yes	characteristic
209	C₂×C₁₃₇	—	2	2	no	—
210	C₂×C₁₃₇	—	16	1	no	—
211	C₂×C₁₃₇	C₂×#464	1	1	yes	characteristic
212	C₂×C₁₃₇	#3063	1	1	yes	characteristic
213	C₂×C₁₃₇	#3068	1	1	yes	characteristic
214	#19244	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₁₃₇	#19244	1	1	yes	characteristic, direct product factor, Sylow
216	#3246	C₂×C₁₃₇	1	1	yes	characteristic
217	#3230	C₂×C₁₃₇	1	1	yes	characteristic, complemented
218	#3141	C₂×C₁₃₇	1	1	yes	characteristic
219	#2962	C₂×C₁₃₇	1	1	yes	characteristic, complemented
220	#1704	C₂×C₁₃₇	1	2	yes	complemented
221	#1698	C₂×C₁₃₇	1	2	yes	complemented
222	#1684	C₂×C₁₃₇	1	2	yes	complemented
223	#1678	C₂×C₁₃₇	1	2	yes	complemented
224	#1565	C₂×C₁₃₇	1	1	yes	characteristic, complemented
225	C₂×#333	C₂×C₁₃₇	1	1	yes	characteristic, complemented
226	#1540	C₂×C₁₃₇	1	1	yes	characteristic
227	#533	C₂²×C₁₃₇	1	1	yes	characteristic
228	#532	C₂²×C₁₃₇	1	1	yes	characteristic
229	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
230	#500	—	2	1	no	—
231	#489	—	2	2	no	—
232	#487	—	2	1	no	—
233	#487	C₂²×C₁₃₇	1	2	yes	—
234	#486	C₂²×C₁₃₇	1	2	yes	—
235	#484	—	2	2	no	—
236	#477	C₂²×C₁₃₇	1	2	yes	—
237	#477	C₂²×C₁₃₇	1	2	yes	—
238	#476	—	2	1	no	—
239	#475	C₂²×C₁₃₇	1	2	yes	—
240	#465	—	2	2	no	—
241	#461	—	2	1	no	—
242	#460	C₂²×C₁₃₇	1	2	yes	—
243	#446	—	2	2	no	—
244	#446	C₂²×C₁₃₇	1	2	yes	—
245	C₈×Q₈	C₂²×C₁₃₇	1	2	yes	—
246	#431	C₂²×C₁₃₇	1	1	yes	characteristic
247	#424	—	2	1	no	—
248	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
249	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
250	#417	—	2	1	no	—
251	#417	—	2	1	no	—
252	#405	—	2	1	no	—
253	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
254	#335	C₂²×C₁₃₇	1	2	yes	—
255	#334	C₂²×C₁₃₇	1	2	yes	—
256	#333	C₂²×C₁₃₇	1	2	yes	—
257	#333	C₂²×C₁₃₇	1	2	yes	—
258	#332	C₂²×C₁₃₇	1	1	yes	characteristic
259	#332	C₂²×C₁₃₇	1	1	yes	characteristic
260	#331	C₂²×C₁₃₇	1	1	yes	characteristic
261	#331	C₂²×C₁₃₇	1	1	yes	characteristic
262	C₂×#41	—	2	1	no	—
263	C₂²×Q₈	—	2	1	no	—
264	C₂×SD₁₆	—	2	2	no	—
265	C₂×M₁₆	D₄×C₁₃₇	1	1	yes	characteristic
266	C₂×M₁₆	D₄×C₁₃₇	1	1	yes	characteristic
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	—	2	1	no	—
271	C₄⋊Q₈	—	2	1	no	—
272	C₄⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
273	C₄⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
274	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
275	C₄⋊Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
276	#127	C₂³×C₁₃₇	1	1	yes	characteristic
277	#125	—	2	1	no	—
278	#124	—	2	1	no	—
279	C₂²⋊Q₈	—	2	1	no	—
280	C₂²⋊Q₈	D₄×C₁₃₇	1	2	yes	—
281	#121	—	2	1	no	—
282	#121	—	2	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	C₂³×C₁₃₇	1	2	yes	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	#117	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
291	#107	—	2	2	no	—
292	#107	—	2	2	no	—
293	#106	—	2	2	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
299	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
300	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
301	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
302	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
303	#103	—	2	2	no	—
304	#103	—	2	2	no	—
305	#103	—	2	2	no	—
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	C₂²⋊C₈	—	2	1	no	—
312	#97	—	2	2	no	—
313	#97	D₄×C₁₃₇	1	2	yes	—
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	4	1	no	—
323	C₂×Q₈	—	8	2	no	—
324	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
333	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
334	SD₁₆	—	8	2	no	—
335	M₁₆	—	2	2	no	—
336	M₁₆	—	2	2	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	—	8	1	no	—
344	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
345	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₄²	—	2	2	no	—
362	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
363	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
364	C₄²	#41×C₁₃₇	1	1	yes	characteristic
365	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
366	C₂³	—	4	1	no	—
367	C₂³	#121×C₁₃₇	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	1	no	—
371	Q₈	—	4	1	no	—
372	Q₈	—	8	1	no	—
373	Q₈	—	8	2	no	—
374	Q₈	—	8	2	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	1	no	—
377	D₄	—	4	1	no	—
378	D₄	—	4	1	no	—
379	D₄	—	8	1	no	—
380	D₄	—	8	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
391	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
392	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
393	C₂×C₄	#135×C₁₃₇	1	2	yes	—
394	C₂×C₄	#137×C₁₃₇	1	2	yes	—
395	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
397	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	2	2	no	—
400	C₈	—	4	1	no	—
401	C₈	—	4	1	no	—
402	C₈	—	4	2	no	—
403	C₈	—	4	1	no	—
404	C₈	—	4	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	8	1	no	—
410	C₂²	#464×C₁₃₇	1	2	yes	—
411	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	8	2	no	—
418	C₄	—	8	1	no	—
419	C₄	#464×C₁₃₇	1	2	yes	—
420	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
421	C₄	C₂×#137×C₁₃₇	1	1	yes	characteristic
422	C₄	#577×C₁₃₇	1	1	yes	characteristic
423	C₄	#578×C₁₃₇	1	1	yes	characteristic
424	C₂	—	2	2	no	—
425	C₂	—	16	1	no	—
426	C₂	C₂×#464×C₁₃₇	1	1	yes	characteristic
427	C₂	#3063×C₁₃₇	1	1	yes	characteristic
428	C₂	#3068×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	#532×C₁₃₇	C₂²
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. #3230×C₁₃₇	C₂	semidirect
4. #2962×C₁₃₇	C₂	semidirect
5. #1704×C₁₃₇	C₂	semidirect
6. #1698×C₁₃₇	C₂	semidirect
7. #1684×C₁₃₇	C₂	semidirect
8. #1678×C₁₃₇	C₂	semidirect
9. #1565×C₁₃₇	C₂	semidirect
10. C₂×#333×C₁₃₇	C₂	semidirect
214. #19244	C₁₃₇	direct (N × H)
215. C₁₃₇	#19244	direct (N × H)
217. #3230	C₂×C₁₃₇	semidirect
219. #2962	C₂×C₁₃₇	semidirect
220. #1704	C₂×C₁₃₇	semidirect
221. #1698	C₂×C₁₃₇	semidirect
222. #1684	C₂×C₁₃₇	semidirect
223. #1678	C₂×C₁₃₇	semidirect
224. #1565	C₂×C₁₃₇	semidirect
225. C₂×#333	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3246×C₁₃₇	2
#3230×C₁₃₇	2
#3141×C₁₃₇	2
#2962×C₁₃₇	2
#1704×C₁₃₇	2
#1698×C₁₃₇	2
#1684×C₁₃₇	2
#1678×C₁₃₇	2
#1565×C₁₃₇	2
C₂×#333×C₁₃₇	2
#1540×C₁₃₇	2
#19244	137

Subgroups — C137×#19244 #46868630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19244 #46868630