Subgroups — C₁₃₇×#26490 #46875876

Order 35072.

906 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#498×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#442×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2452×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#2065×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2023×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1972×C₁₃₇	C₂	1	1	yes	maximal, characteristic
7	#1970×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1944×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1943×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1864×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	#1771×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	2	yes	—
14	C₂×C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
15	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
16	#498×C₁₃₇	—	2	4	no	—
17	#442×C₁₃₇	—	2	4	no	—
18	C₂×#107×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
20	C₂×#106×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×#106×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
24	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
25	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
26	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
29	#396×C₁₃₇	—	2	2	no	—
30	#393×C₁₃₇	—	2	2	no	—
31	#390×C₁₃₇	C₂²	1	2	yes	—
32	#390×C₁₃₇	C₂²	1	2	yes	—
33	#389×C₁₃₇	C₂²	1	2	yes	—
34	#389×C₁₃₇	C₂²	1	2	yes	—
35	#385×C₁₃₇	—	2	2	no	—
36	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
37	#340×C₁₃₇	C₂²	1	2	yes	—
38	#340×C₁₃₇	C₂²	1	2	yes	—
39	#336×C₁₃₇	C₂²	1	1	yes	characteristic
40	#336×C₁₃₇	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃₇	—	2	2	no	—
42	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃₇	—	2	2	no	—
44	C₂×D₈×C₁₃₇	—	2	2	no	—
45	C₂×D₈×C₁₃₇	—	2	2	no	—
46	C₂×D₈×C₁₃₇	Q₈	1	4	yes	complemented
47	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
51	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
52	C₄⋊Q₈×C₁₃₇	—	4	2	no	—
53	C₂²⋊Q₈×C₁₃₇	—	4	8	no	—
54	C₄×D₄×C₁₃₇	—	2	4	no	—
55	C₄×D₄×C₁₃₇	—	4	2	no	—
56	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
68	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
71	#107×C₁₃₇	—	2	2	no	—
72	#106×C₁₃₇	—	2	2	no	—
73	#106×C₁₃₇	—	2	4	no	—
74	#106×C₁₃₇	D₄	1	4	yes	—
75	C₄⋊C₈×C₁₃₇	—	2	2	no	—
76	#102×C₁₃₇	—	2	4	no	—
77	#102×C₁₃₇	—	2	4	no	—
78	#102×C₁₃₇	—	4	2	no	—
79	#97×C₁₃₇	—	2	2	no	—
80	#97×C₁₃₇	—	2	2	no	—
81	C₄×C₈×C₁₃₇	—	2	2	no	—
82	#95×C₁₃₇	—	2	2	no	—
83	#95×C₁₃₇	—	2	2	no	—
84	#95×C₁₃₇	D₄	1	2	yes	—
85	C₂⁴×C₁₃₇	—	2	2	no	—
86	C₂×Q₈×C₁₃₇	—	4	4	no	—
87	C₂×Q₈×C₁₃₇	—	4	4	no	—
88	C₂×Q₈×C₁₃₇	—	8	2	no	—
89	C₂×D₄×C₁₃₇	—	2	2	no	—
90	C₂×D₄×C₁₃₇	—	2	2	no	—
91	C₂×D₄×C₁₃₇	—	2	2	no	—
92	C₂×D₄×C₁₃₇	—	2	2	no	—
93	C₂×D₄×C₁₃₇	—	2	2	no	—
94	C₂×D₄×C₁₃₇	C₂×Q₈	1	4	yes	—
95	C₂²×C₄×C₁₃₇	—	2	2	no	—
96	C₂²×C₄×C₁₃₇	—	2	2	no	—
97	C₂²×C₄×C₁₃₇	—	2	2	no	—
98	C₂²×C₄×C₁₃₇	—	4	4	no	—
99	C₂²×C₄×C₁₃₇	—	4	4	no	—
100	C₂²×C₄×C₁₃₇	—	8	2	no	—
101	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
106	D₈×C₁₃₇	—	2	8	no	—
107	C₂×C₈×C₁₃₇	—	2	1	no	—
108	C₂×C₈×C₁₃₇	—	2	1	no	—
109	C₂×C₈×C₁₃₇	—	2	1	no	—
110	C₂×C₈×C₁₃₇	—	2	1	no	—
111	C₂×C₈×C₁₃₇	—	2	1	no	—
112	C₂×C₈×C₁₃₇	—	2	1	no	—
113	C₂×C₈×C₁₃₇	—	2	1	no	—
114	C₂×C₈×C₁₃₇	—	2	1	no	—
115	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₁₃₇	C₂×Q₈	1	2	yes	—
117	C₂×C₈×C₁₃₇	#41	1	2	yes	—
118	C₂×C₈×C₁₃₇	#41	1	2	yes	—
119	C₄⋊C₄×C₁₃₇	—	2	4	no	—
120	C₄⋊C₄×C₁₃₇	—	2	2	no	—
121	C₄⋊C₄×C₁₃₇	—	2	2	no	—
122	C₄⋊C₄×C₁₃₇	—	2	2	no	—
123	C₄⋊C₄×C₁₃₇	—	2	2	no	—
124	C₄⋊C₄×C₁₃₇	—	2	2	no	—
125	C₄⋊C₄×C₁₃₇	—	4	4	no	—
126	C₄⋊C₄×C₁₃₇	—	4	4	no	—
127	C₄⋊C₄×C₁₃₇	—	4	4	no	—
128	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
129	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
130	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
131	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
132	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
133	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
134	C₄²×C₁₃₇	—	2	1	no	—
135	C₄²×C₁₃₇	—	2	1	no	—
136	C₄²×C₁₃₇	—	2	1	no	—
137	C₄²×C₁₃₇	—	2	1	no	—
138	C₄²×C₁₃₇	—	2	1	no	—
139	C₄²×C₁₃₇	—	2	1	no	—
140	C₂³×C₁₃₇	—	2	4	no	—
141	C₂³×C₁₃₇	—	4	2	no	—
142	C₂³×C₁₃₇	—	4	2	no	—
143	C₂³×C₁₃₇	—	4	2	no	—
144	C₂³×C₁₃₇	—	4	2	no	—
145	C₂³×C₁₃₇	—	4	2	no	—
146	C₂³×C₁₃₇	—	4	2	no	—
147	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₁₃₇	—	8	8	no	—
149	D₄×C₁₃₇	—	2	4	no	—
150	D₄×C₁₃₇	—	2	4	no	—
151	D₄×C₁₃₇	—	4	2	no	—
152	D₄×C₁₃₇	—	4	2	no	—
153	C₂×C₄×C₁₃₇	—	2	2	no	—
154	C₂×C₄×C₁₃₇	—	2	2	no	—
155	C₂×C₄×C₁₃₇	—	2	1	no	—
156	C₂×C₄×C₁₃₇	—	2	1	no	—
157	C₂×C₄×C₁₃₇	—	2	2	no	—
158	C₂×C₄×C₁₃₇	—	2	4	no	—
159	C₂×C₄×C₁₃₇	—	2	2	no	—
160	C₂×C₄×C₁₃₇	—	2	2	no	—
161	C₂×C₄×C₁₃₇	—	2	2	no	—
162	C₂×C₄×C₁₃₇	—	2	2	no	—
163	C₂×C₄×C₁₃₇	—	4	2	no	—
164	C₂×C₄×C₁₃₇	—	4	2	no	—
165	C₂×C₄×C₁₃₇	—	4	2	no	—
166	C₂×C₄×C₁₃₇	—	4	2	no	—
167	C₂×C₄×C₁₃₇	—	4	2	no	—
168	C₂×C₄×C₁₃₇	—	4	2	no	—
169	C₂×C₄×C₁₃₇	—	4	2	no	—
170	C₂×C₄×C₁₃₇	—	4	2	no	—
171	C₂×C₄×C₁₃₇	—	8	8	no	—
172	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	4	yes	—
173	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
179	C₈×C₁₃₇	—	2	2	no	—
180	C₈×C₁₃₇	—	4	1	no	—
181	C₈×C₁₃₇	—	4	1	no	—
182	C₈×C₁₃₇	C₂²⋊Q₈	1	4	yes	complemented
183	C₂²×C₁₃₇	—	4	4	no	—
184	C₂²×C₁₃₇	—	4	4	no	—
185	C₂²×C₁₃₇	—	4	4	no	—
186	C₂²×C₁₃₇	—	8	2	no	—
187	C₂²×C₁₃₇	—	8	2	no	—
188	C₂²×C₁₃₇	—	8	2	no	—
189	C₂²×C₁₃₇	—	8	2	no	—
190	C₂²×C₁₃₇	#532	1	1	yes	characteristic
191	C₂²×C₁₃₇	D₄²	1	1	yes	characteristic
192	C₂²×C₁₃₇	D₄×Q₈	1	1	yes	characteristic
193	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
194	C₂²×C₁₃₇	#577	1	2	yes	—
195	C₄×C₁₃₇	—	2	4	no	—
196	C₄×C₁₃₇	—	4	1	no	—
197	C₄×C₁₃₇	—	4	1	no	—
198	C₄×C₁₃₇	—	4	2	no	—
199	C₄×C₁₃₇	—	4	4	no	—
200	C₄×C₁₃₇	—	8	2	no	—
201	C₄×C₁₃₇	—	8	2	no	—
202	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
203	C₄×C₁₃₇	#542	1	1	yes	characteristic
204	C₄×C₁₃₇	#548	1	1	yes	characteristic
205	C₄×C₁₃₇	#554	1	1	yes	characteristic
206	C₂×C₁₃₇	—	8	4	no	—
207	C₂×C₁₃₇	#2452	1	1	yes	characteristic
208	C₂×C₁₃₇	#3173	1	1	yes	characteristic
209	C₂×C₁₃₇	#3184	1	1	yes	characteristic
210	C₂×C₁₃₇	#3265	1	2	yes	—
211	C₂×C₁₃₇	#3384	1	2	yes	—
212	#26490	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₁₃₇	#26490	1	1	yes	characteristic, direct product factor, Sylow
214	C₂×#498	C₂×C₁₃₇	1	1	yes	characteristic, complemented
215	C₂×#442	C₂×C₁₃₇	1	1	yes	characteristic
216	#2452	C₂×C₁₃₇	1	2	yes	complemented
217	#2065	C₂×C₁₃₇	1	2	yes	complemented
218	#2023	C₂×C₁₃₇	1	2	yes	complemented
219	#1972	C₂×C₁₃₇	1	1	yes	characteristic
220	#1970	C₂×C₁₃₇	1	1	yes	characteristic
221	#1944	C₂×C₁₃₇	1	1	yes	characteristic, complemented
222	#1943	C₂×C₁₃₇	1	1	yes	characteristic, complemented
223	#1864	C₂×C₁₃₇	1	2	yes	complemented
224	#1771	C₂×C₁₃₇	1	1	yes	characteristic, complemented
225	C₂²×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
226	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
227	C₂×C₂²⋊Q₈	—	2	2	no	—
228	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
229	#498	—	2	4	no	—
230	#442	—	2	4	no	—
231	C₂×#107	C₂²×C₁₃₇	1	1	yes	characteristic
232	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
233	C₂×#106	C₂²×C₁₃₇	1	1	yes	characteristic
234	C₂×#106	C₂²×C₁₃₇	1	1	yes	characteristic
235	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
236	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
237	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
238	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
239	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
240	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
241	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
242	#396	—	2	2	no	—
243	#393	—	2	2	no	—
244	#390	C₂²×C₁₃₇	1	2	yes	—
245	#390	C₂²×C₁₃₇	1	2	yes	—
246	#389	C₂²×C₁₃₇	1	2	yes	—
247	#389	C₂²×C₁₃₇	1	2	yes	—
248	#385	—	2	2	no	—
249	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
250	#340	C₂²×C₁₃₇	1	2	yes	—
251	#340	C₂²×C₁₃₇	1	2	yes	—
252	#336	C₂²×C₁₃₇	1	1	yes	characteristic
253	#336	C₂²×C₁₃₇	1	1	yes	characteristic
254	C₂²×Q₈	—	2	2	no	—
255	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
256	C₂³×C₄	—	2	2	no	—
257	C₂×D₈	—	2	2	no	—
258	C₂×D₈	—	2	2	no	—
259	C₂×D₈	Q₈×C₁₃₇	1	4	yes	complemented
260	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
264	C₄⋊Q₈	—	2	4	no	—
265	C₄⋊Q₈	—	4	2	no	—
266	C₂²⋊Q₈	—	4	8	no	—
267	C₄×D₄	—	2	4	no	—
268	C₄×D₄	—	4	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
284	#107	—	2	2	no	—
285	#106	—	2	2	no	—
286	#106	—	2	4	no	—
287	#106	D₄×C₁₃₇	1	4	yes	—
288	C₄⋊C₈	—	2	2	no	—
289	#102	—	2	4	no	—
290	#102	—	2	4	no	—
291	#102	—	4	2	no	—
292	#97	—	2	2	no	—
293	#97	—	2	2	no	—
294	C₄×C₈	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	D₄×C₁₃₇	1	2	yes	—
298	C₂⁴	—	2	2	no	—
299	C₂×Q₈	—	4	4	no	—
300	C₂×Q₈	—	4	4	no	—
301	C₂×Q₈	—	8	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	C₂×Q₈×C₁₃₇	1	4	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	4	4	no	—
312	C₂²×C₄	—	4	4	no	—
313	C₂²×C₄	—	8	2	no	—
314	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
318	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
319	D₈	—	2	8	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
329	C₂×C₈	C₂×Q₈×C₁₃₇	1	2	yes	—
330	C₂×C₈	#41×C₁₃₇	1	2	yes	—
331	C₂×C₈	#41×C₁₃₇	1	2	yes	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	—	4	4	no	—
340	C₄⋊C₄	—	4	4	no	—
341	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	4	4	no	—
344	C₂²⋊C₄	—	4	4	no	—
345	C₂²⋊C₄	—	4	4	no	—
346	C₂²⋊C₄	—	8	2	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	1	no	—
353	C₂³	—	2	4	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
361	Q₈	—	8	8	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	4	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	8	8	no	—
385	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	4	yes	—
386	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
387	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
388	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
389	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
390	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
391	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
392	C₈	—	2	2	no	—
393	C₈	—	4	1	no	—
394	C₈	—	4	1	no	—
395	C₈	C₂²⋊Q₈×C₁₃₇	1	4	yes	complemented
396	C₂²	—	4	4	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	#532×C₁₃₇	1	1	yes	characteristic
404	C₂²	D₄²×C₁₃₇	1	1	yes	characteristic
405	C₂²	D₄×Q₈×C₁₃₇	1	1	yes	characteristic
406	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
407	C₂²	#577×C₁₃₇	1	2	yes	—
408	C₄	—	2	4	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	4	no	—
413	C₄	—	8	2	no	—
414	C₄	—	8	2	no	—
415	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
416	C₄	#542×C₁₃₇	1	1	yes	characteristic
417	C₄	#548×C₁₃₇	1	1	yes	characteristic
418	C₄	#554×C₁₃₇	1	1	yes	characteristic
419	C₂	—	8	4	no	—
420	C₂	#2452×C₁₃₇	1	1	yes	characteristic
421	C₂	#3173×C₁₃₇	1	1	yes	characteristic
422	C₂	#3184×C₁₃₇	1	1	yes	characteristic
423	C₂	#3265×C₁₃₇	1	2	yes	—
424	C₂	#3384×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂²×D₈×C₁₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₄×C₄⋊C₄×C₁₃₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#498×C₁₃₇	C₂	semidirect
3. #2452×C₁₃₇	C₂	semidirect
4. #2065×C₁₃₇	C₂	semidirect
5. #2023×C₁₃₇	C₂	semidirect
8. #1944×C₁₃₇	C₂	semidirect
9. #1943×C₁₃₇	C₂	semidirect
10. #1864×C₁₃₇	C₂	semidirect
11. #1771×C₁₃₇	C₂	semidirect
46. C₂×D₈×C₁₃₇	Q₈	semidirect
182. C₈×C₁₃₇	C₂²⋊Q₈	semidirect
212. #26490	C₁₃₇	direct (N × H)
213. C₁₃₇	#26490	direct (N × H)
214. C₂×#498	C₂×C₁₃₇	semidirect
216. #2452	C₂×C₁₃₇	semidirect
217. #2065	C₂×C₁₃₇	semidirect
218. #2023	C₂×C₁₃₇	semidirect
221. #1944	C₂×C₁₃₇	semidirect
222. #1943	C₂×C₁₃₇	semidirect
223. #1864	C₂×C₁₃₇	semidirect
224. #1771	C₂×C₁₃₇	semidirect
259. C₂×D₈	Q₈×C₁₃₇	semidirect
395. C₈	C₂²⋊Q₈×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#498×C₁₃₇	2
C₂×#442×C₁₃₇	2
#2452×C₁₃₇	2
#2065×C₁₃₇	2
#2023×C₁₃₇	2
#1972×C₁₃₇	2
#1970×C₁₃₇	2
#1944×C₁₃₇	2
#1943×C₁₃₇	2
#1864×C₁₃₇	2
#1771×C₁₃₇	2
#26490	137

Subgroups — C137×#26490 #46875876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#26490 #46875876