Subgroups — C₁₃₇×#19228 #46868614

Order 35072.

584 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3248×C₁₃₇	C₂	1	2	yes	maximal
2	#3170×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2966×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1694×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1693×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#1690×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1689×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1680×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1679×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	C₂×#334×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1552×C₁₃₇	C₂	1	2	yes	maximal, complemented
12	#533×C₁₃₇	C₂²	1	2	yes	—
13	#529×C₁₃₇	C₂²	1	1	yes	characteristic
14	#500×C₁₃₇	C₂²	1	1	yes	characteristic
15	#494×C₁₃₇	C₂²	1	1	yes	characteristic
16	#487×C₁₃₇	C₂²	1	2	yes	—
17	#479×C₁₃₇	—	2	2	no	—
18	#475×C₁₃₇	C₂²	1	2	yes	—
19	#474×C₁₃₇	C₂²	1	2	yes	—
20	#467×C₁₃₇	—	2	1	no	—
21	#467×C₁₃₇	—	2	1	no	—
22	#467×C₁₃₇	—	2	2	no	—
23	#465×C₁₃₇	—	2	2	no	—
24	#464×C₁₃₇	—	2	2	no	—
25	#462×C₁₃₇	C₂²	1	2	yes	—
26	#461×C₁₃₇	C₂²	1	2	yes	—
27	#446×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₈×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
29	C₄×Q₁₆×C₁₃₇	—	2	1	no	—
30	C₄×Q₁₆×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	#332×C₁₃₇	C₂²	1	2	yes	—
44	#332×C₁₃₇	C₂²	1	2	yes	—
45	#332×C₁₃₇	C₂²	1	2	yes	—
46	#332×C₁₃₇	C₂²	1	2	yes	—
47	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
48	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
49	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
50	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
51	C₂×M₁₆×C₁₃₇	—	2	1	no	—
52	C₂²×C₈×C₁₃₇	—	2	2	no	—
53	C₂²×C₈×C₁₃₇	—	2	1	no	—
54	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
56	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
58	#126×C₁₃₇	—	2	1	no	—
59	#125×C₁₃₇	—	2	2	no	—
60	#125×C₁₃₇	D₄	1	1	yes	characteristic
61	#124×C₁₃₇	D₄	1	1	yes	characteristic
62	#123×C₁₃₇	—	2	1	no	—
63	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
64	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
65	C₂²⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
66	#121×C₁₃₇	D₄	1	1	yes	characteristic
67	C₄×Q₈×C₁₃₇	—	2	2	no	—
68	C₄×Q₈×C₁₃₇	—	2	2	no	—
69	C₄×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
70	C₄×D₄×C₁₃₇	—	2	1	no	—
71	C₄×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
72	#117×C₁₃₇	—	2	1	no	—
73	#117×C₁₃₇	—	2	2	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	#103×C₁₃₇	—	2	2	no	—
88	#103×C₁₃₇	—	2	2	no	—
89	#103×C₁₃₇	—	2	2	no	—
90	#103×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	C₂×Q₈×C₁₃₇	—	2	2	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	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₇	—	2	1	no	—
108	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
111	Q₁₆×C₁₃₇	—	4	2	no	—
112	Q₁₆×C₁₃₇	—	4	2	no	—
113	Q₁₆×C₁₃₇	—	8	2	no	—
114	SD₁₆×C₁₃₇	—	8	2	no	—
115	M₁₆×C₁₃₇	—	4	2	no	—
116	C₂×C₈×C₁₃₇	—	2	2	no	—
117	C₂×C₈×C₁₃₇	—	2	1	no	—
118	C₂×C₈×C₁₃₇	—	2	1	no	—
119	C₂×C₈×C₁₃₇	—	2	2	no	—
120	C₂×C₈×C₁₃₇	—	2	2	no	—
121	C₂×C₈×C₁₃₇	—	4	1	no	—
122	C₂×C₈×C₁₃₇	—	4	2	no	—
123	C₂×C₈×C₁₃₇	—	8	2	no	—
124	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
128	C₄⋊C₄×C₁₃₇	—	2	1	no	—
129	C₄⋊C₄×C₁₃₇	—	2	1	no	—
130	C₄⋊C₄×C₁₃₇	—	2	1	no	—
131	C₄⋊C₄×C₁₃₇	—	2	1	no	—
132	C₄⋊C₄×C₁₃₇	—	2	2	no	—
133	C₄⋊C₄×C₁₃₇	—	2	2	no	—
134	C₄⋊C₄×C₁₃₇	—	2	2	no	—
135	C₄⋊C₄×C₁₃₇	—	2	2	no	—
136	C₄⋊C₄×C₁₃₇	—	4	2	no	—
137	C₄⋊C₄×C₁₃₇	—	4	2	no	—
138	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
139	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
140	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
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	—	4	2	no	—
146	C₄²×C₁₃₇	—	2	1	no	—
147	C₄²×C₁₃₇	—	4	2	no	—
148	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₃₇	#41	1	1	yes	characteristic
151	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
152	C₂³×C₁₃₇	—	2	1	no	—
153	C₂³×C₁₃₇	#121	1	1	yes	characteristic
154	Q₈×C₁₃₇	—	2	2	no	—
155	Q₈×C₁₃₇	—	4	2	no	—
156	Q₈×C₁₃₇	—	4	2	no	—
157	Q₈×C₁₃₇	—	4	2	no	—
158	Q₈×C₁₃₇	—	4	2	no	—
159	D₄×C₁₃₇	—	2	2	no	—
160	D₄×C₁₃₇	—	4	2	no	—
161	C₂×C₄×C₁₃₇	—	2	2	no	—
162	C₂×C₄×C₁₃₇	—	2	1	no	—
163	C₂×C₄×C₁₃₇	—	2	1	no	—
164	C₂×C₄×C₁₃₇	—	2	2	no	—
165	C₂×C₄×C₁₃₇	—	2	1	no	—
166	C₂×C₄×C₁₃₇	—	2	1	no	—
167	C₂×C₄×C₁₃₇	—	2	1	no	—
168	C₂×C₄×C₁₃₇	—	4	1	no	—
169	C₂×C₄×C₁₃₇	—	4	1	no	—
170	C₂×C₄×C₁₃₇	—	4	2	no	—
171	C₂×C₄×C₁₃₇	—	4	2	no	—
172	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
178	C₈×C₁₃₇	—	2	1	no	—
179	C₈×C₁₃₇	—	2	1	no	—
180	C₈×C₁₃₇	—	2	1	no	—
181	C₈×C₁₃₇	—	4	1	no	—
182	C₈×C₁₃₇	—	4	1	no	—
183	C₈×C₁₃₇	—	4	2	no	—
184	C₈×C₁₃₇	—	4	2	no	—
185	C₈×C₁₃₇	#135	1	2	yes	—
186	C₂²×C₁₃₇	—	2	1	no	—
187	C₂²×C₁₃₇	—	2	1	no	—
188	C₂²×C₁₃₇	—	4	1	no	—
189	C₂²×C₁₃₇	—	4	1	no	—
190	C₂²×C₁₃₇	—	4	1	no	—
191	C₂²×C₁₃₇	#473	1	2	yes	—
192	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
193	C₄×C₁₃₇	—	2	1	no	—
194	C₄×C₁₃₇	—	2	1	no	—
195	C₄×C₁₃₇	—	2	1	no	—
196	C₄×C₁₃₇	—	2	1	no	—
197	C₄×C₁₃₇	—	4	1	no	—
198	C₄×C₁₃₇	—	4	1	no	—
199	C₄×C₁₃₇	—	4	1	no	—
200	C₄×C₁₃₇	—	8	2	no	—
201	C₄×C₁₃₇	—	8	2	no	—
202	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
203	C₄×C₁₃₇	#575	1	1	yes	characteristic
204	C₄×C₁₃₇	#577	1	2	yes	—
205	C₂×C₁₃₇	—	2	2	no	—
206	C₂×C₁₃₇	—	8	1	no	—
207	C₂×C₁₃₇	#3035	1	1	yes	characteristic
208	C₂×C₁₃₇	#3060	1	1	yes	characteristic
209	C₂×C₁₃₇	C₂×#473	1	1	yes	characteristic
210	#19228	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₁₃₇	#19228	1	1	yes	characteristic, direct product factor, Sylow
212	#3248	C₂×C₁₃₇	1	2	yes	—
213	#3170	C₂×C₁₃₇	1	1	yes	characteristic, complemented
214	#2966	C₂×C₁₃₇	1	1	yes	characteristic
215	#1694	C₂×C₁₃₇	1	1	yes	characteristic, complemented
216	#1693	C₂×C₁₃₇	1	1	yes	characteristic, complemented
217	#1690	C₂×C₁₃₇	1	1	yes	characteristic, complemented
218	#1689	C₂×C₁₃₇	1	1	yes	characteristic, complemented
219	#1680	C₂×C₁₃₇	1	2	yes	complemented
220	#1679	C₂×C₁₃₇	1	2	yes	complemented
221	C₂×#334	C₂×C₁₃₇	1	1	yes	characteristic, complemented
222	#1552	C₂×C₁₃₇	1	2	yes	complemented
223	#533	C₂²×C₁₃₇	1	2	yes	—
224	#529	C₂²×C₁₃₇	1	1	yes	characteristic
225	#500	C₂²×C₁₃₇	1	1	yes	characteristic
226	#494	C₂²×C₁₃₇	1	1	yes	characteristic
227	#487	C₂²×C₁₃₇	1	2	yes	—
228	#479	—	2	2	no	—
229	#475	C₂²×C₁₃₇	1	2	yes	—
230	#474	C₂²×C₁₃₇	1	2	yes	—
231	#467	—	2	1	no	—
232	#467	—	2	1	no	—
233	#467	—	2	2	no	—
234	#465	—	2	2	no	—
235	#464	—	2	2	no	—
236	#462	C₂²×C₁₃₇	1	2	yes	—
237	#461	C₂²×C₁₃₇	1	2	yes	—
238	#446	C₂²×C₁₃₇	1	1	yes	characteristic
239	C₈×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
240	C₄×Q₁₆	—	2	1	no	—
241	C₄×Q₁₆	—	2	1	no	—
242	#436	C₂²×C₁₃₇	1	1	yes	characteristic
243	#435	—	2	1	no	—
244	C₈×D₄	—	2	1	no	—
245	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
246	#433	—	2	1	no	—
247	#432	C₂²×C₁₃₇	1	1	yes	characteristic
248	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
249	#405	—	2	1	no	—
250	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
251	#334	C₂²×C₁₃₇	1	2	yes	—
252	#334	C₂²×C₁₃₇	1	1	yes	characteristic
253	#334	C₂²×C₁₃₇	1	1	yes	characteristic
254	#332	C₂²×C₁₃₇	1	2	yes	—
255	#332	C₂²×C₁₃₇	1	2	yes	—
256	#332	C₂²×C₁₃₇	1	2	yes	—
257	#332	C₂²×C₁₃₇	1	2	yes	—
258	C₂×Q₁₆	—	2	2	no	—
259	C₂×Q₁₆	—	2	1	no	—
260	C₂×Q₁₆	—	2	1	no	—
261	C₂×SD₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	1	no	—
263	C₂²×C₈	—	2	2	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
266	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
267	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
268	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
269	#126	—	2	1	no	—
270	#125	—	2	2	no	—
271	#125	D₄×C₁₃₇	1	1	yes	characteristic
272	#124	D₄×C₁₃₇	1	1	yes	characteristic
273	#123	—	2	1	no	—
274	C₂²⋊Q₈	—	2	2	no	—
275	C₂²⋊Q₈	—	2	2	no	—
276	C₂²⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
277	#121	D₄×C₁₃₇	1	1	yes	characteristic
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
283	#117	—	2	1	no	—
284	#117	—	2	2	no	—
285	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
286	#107	—	2	1	no	—
287	#107	—	2	1	no	—
288	#107	—	2	2	no	—
289	#106	—	2	2	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
294	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
295	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
296	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
297	#103	—	2	2	no	—
298	#103	—	2	2	no	—
299	#103	—	2	2	no	—
300	#103	—	2	2	no	—
301	#103	—	2	2	no	—
302	#102	—	2	2	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	#97	—	2	1	no	—
307	#97	—	2	1	no	—
308	C₄×C₈	—	2	1	no	—
309	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
310	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
311	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
312	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
321	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
322	Q₁₆	—	4	2	no	—
323	Q₁₆	—	4	2	no	—
324	Q₁₆	—	8	2	no	—
325	SD₁₆	—	8	2	no	—
326	M₁₆	—	4	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	2	no	—
334	C₂×C₈	—	8	2	no	—
335	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
336	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
337	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
338	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
350	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	4	2	no	—
359	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
360	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
361	C₄²	#41×C₁₃₇	1	1	yes	characteristic
362	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
363	C₂³	—	2	1	no	—
364	C₂³	#121×C₁₃₇	1	1	yes	characteristic
365	Q₈	—	2	2	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	D₄	—	2	2	no	—
371	D₄	—	4	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
384	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
385	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
386	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
388	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
389	C₈	—	2	1	no	—
390	C₈	—	2	1	no	—
391	C₈	—	2	1	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	1	no	—
394	C₈	—	4	2	no	—
395	C₈	—	4	2	no	—
396	C₈	#135×C₁₃₇	1	2	yes	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	#473×C₁₃₇	1	2	yes	—
403	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	8	2	no	—
412	C₄	—	8	2	no	—
413	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
414	C₄	#575×C₁₃₇	1	1	yes	characteristic
415	C₄	#577×C₁₃₇	1	2	yes	—
416	C₂	—	2	2	no	—
417	C₂	—	8	1	no	—
418	C₂	#3035×C₁₃₇	1	1	yes	characteristic
419	C₂	#3060×C₁₃₇	1	1	yes	characteristic
420	C₂	C₂×#473×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	#121×C₁₃₇	D₄
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. #3170×C₁₃₇	C₂	semidirect
4. #1694×C₁₃₇	C₂	semidirect
5. #1693×C₁₃₇	C₂	semidirect
6. #1690×C₁₃₇	C₂	semidirect
7. #1689×C₁₃₇	C₂	semidirect
8. #1680×C₁₃₇	C₂	semidirect
9. #1679×C₁₃₇	C₂	semidirect
10. C₂×#334×C₁₃₇	C₂	semidirect
11. #1552×C₁₃₇	C₂	semidirect
210. #19228	C₁₃₇	direct (N × H)
211. C₁₃₇	#19228	direct (N × H)
213. #3170	C₂×C₁₃₇	semidirect
215. #1694	C₂×C₁₃₇	semidirect
216. #1693	C₂×C₁₃₇	semidirect
217. #1690	C₂×C₁₃₇	semidirect
218. #1689	C₂×C₁₃₇	semidirect
219. #1680	C₂×C₁₃₇	semidirect
220. #1679	C₂×C₁₃₇	semidirect
221. C₂×#334	C₂×C₁₃₇	semidirect
222. #1552	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3248×C₁₃₇	2
#3170×C₁₃₇	2
#2966×C₁₃₇	2
#1694×C₁₃₇	2
#1693×C₁₃₇	2
#1690×C₁₃₇	2
#1689×C₁₃₇	2
#1680×C₁₃₇	2
#1679×C₁₃₇	2
C₂×#334×C₁₃₇	2
#1552×C₁₃₇	2
#19228	137

Subgroups — C137×#19228 #46868614

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19228 #46868614