Subgroups — C₁₃₇×#21060 #46870446

Order 35072.

1342 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#428×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#418×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#418×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#390×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	C₄×#117×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#1926×C₁₃₇	C₂	1	4	yes	maximal, complemented
7	#1925×C₁₃₇	C₂	1	4	yes	maximal, complemented
8	#1736×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1728×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
17	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
18	#428×C₁₃₇	—	2	4	no	—
19	C₂×#107×C₁₃₇	C₂²	1	2	yes	complemented
20	C₂×#106×C₁₃₇	C₂²	1	2	yes	complemented
21	#418×C₁₃₇	—	2	4	no	—
22	#418×C₁₃₇	C₄	1	8	yes	complemented
23	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
24	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
25	C₂×#102×C₁₃₇	C₂²	1	4	yes	—
26	#390×C₁₃₇	—	2	1	no	—
27	#390×C₁₃₇	—	2	1	no	—
28	#390×C₁₃₇	C₂²	1	4	yes	—
29	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	complemented
30	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	complemented
31	C₄×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
32	#376×C₁₃₇	—	2	1	no	—
33	C₄³×C₁₃₇	—	2	1	no	—
34	#340×C₁₃₇	C₂²	1	4	yes	complemented
35	#336×C₁₃₇	C₂²	1	4	yes	complemented
36	C₂⁵×C₁₃₇	—	2	1	no	—
37	C₂²×D₄×C₁₃₇	—	2	2	no	—
38	C₂²×D₄×C₁₃₇	—	2	1	no	—
39	C₂²×D₄×C₁₃₇	—	2	2	no	—
40	C₂²×D₄×C₁₃₇	—	2	2	no	—
41	C₂²×D₄×C₁₃₇	—	2	2	no	—
42	C₂²×D₄×C₁₃₇	—	2	2	no	—
43	C₂²×D₄×C₁₃₇	C₂×C₄	1	4	yes	—
44	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃₇	—	2	1	no	—
46	C₂³×C₄×C₁₃₇	D₄	1	2	yes	—
47	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₁₃₇	—	2	2	no	—
49	C₂×M₁₆×C₁₃₇	—	2	2	no	—
50	C₂×M₁₆×C₁₃₇	—	2	2	no	—
51	C₂×M₁₆×C₁₃₇	—	2	2	no	—
52	C₂×M₁₆×C₁₃₇	—	2	2	no	—
53	C₂×M₁₆×C₁₃₇	C₂×C₄	1	4	yes	—
54	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
56	#117×C₁₃₇	—	2	2	no	—
57	#117×C₁₃₇	—	2	2	no	—
58	#117×C₁₃₇	C₂×C₄	1	4	yes	—
59	#117×C₁₃₇	D₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₁₃₇	—	4	8	no	—
72	C₂×C₄²×C₁₃₇	—	2	1	no	—
73	C₂×C₄²×C₁₃₇	—	2	1	no	—
74	C₂×C₄²×C₁₃₇	—	2	2	no	—
75	C₂×C₄²×C₁₃₇	—	2	2	no	—
76	C₂×C₄²×C₁₃₇	—	2	2	no	—
77	C₂×C₄²×C₁₃₇	—	2	2	no	—
78	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
81	#107×C₁₃₇	—	2	4	no	—
82	#106×C₁₃₇	—	2	4	no	—
83	#102×C₁₃₇	—	2	4	no	—
84	#102×C₁₃₇	—	2	4	no	—
85	#102×C₁₃₇	C₂×C₄	1	16	yes	complemented
86	#95×C₁₃₇	—	2	2	no	—
87	#95×C₁₃₇	—	2	2	no	—
88	C₂⁴×C₁₃₇	—	2	4	no	—
89	C₂⁴×C₁₃₇	—	2	2	no	—
90	C₂⁴×C₁₃₇	—	4	4	no	—
91	C₂⁴×C₁₃₇	—	4	4	no	—
92	C₂⁴×C₁₃₇	—	4	2	no	—
93	C₂⁴×C₁₃₇	—	4	2	no	—
94	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
95	C₂×D₄×C₁₃₇	—	2	8	no	—
96	C₂×D₄×C₁₃₇	—	2	8	no	—
97	C₂×D₄×C₁₃₇	—	2	4	no	—
98	C₂×D₄×C₁₃₇	—	2	2	no	—
99	C₂×D₄×C₁₃₇	—	2	2	no	—
100	C₂×D₄×C₁₃₇	—	2	2	no	—
101	C₂×D₄×C₁₃₇	—	2	2	no	—
102	C₂×D₄×C₁₃₇	—	2	2	no	—
103	C₂×D₄×C₁₃₇	—	4	2	no	—
104	C₂×D₄×C₁₃₇	—	4	2	no	—
105	C₂×D₄×C₁₃₇	—	4	4	no	—
106	C₂×D₄×C₁₃₇	—	4	4	no	—
107	C₂×D₄×C₁₃₇	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₁₃₇	—	2	4	no	—
109	C₂²×C₄×C₁₃₇	—	2	2	no	—
110	C₂²×C₄×C₁₃₇	—	2	1	no	—
111	C₂²×C₄×C₁₃₇	—	2	1	no	—
112	C₂²×C₄×C₁₃₇	—	2	4	no	—
113	C₂²×C₄×C₁₃₇	—	2	2	no	—
114	C₂²×C₄×C₁₃₇	—	4	2	no	—
115	C₂²×C₄×C₁₃₇	—	4	4	no	—
116	C₂²×C₄×C₁₃₇	—	4	2	no	—
117	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
123	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
124	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
125	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
126	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
127	M₁₆×C₁₃₇	—	2	8	no	—
128	M₁₆×C₁₃₇	—	4	4	no	—
129	C₂×C₈×C₁₃₇	—	2	2	no	—
130	C₂×C₈×C₁₃₇	—	2	2	no	—
131	C₂×C₈×C₁₃₇	—	2	2	no	—
132	C₂×C₈×C₁₃₇	—	2	2	no	—
133	C₂×C₈×C₁₃₇	—	2	2	no	—
134	C₂×C₈×C₁₃₇	C₂²×C₄	1	4	yes	—
135	C₄⋊C₄×C₁₃₇	—	2	2	no	—
136	C₄⋊C₄×C₁₃₇	—	2	1	no	—
137	C₄⋊C₄×C₁₃₇	—	2	1	no	—
138	C₄⋊C₄×C₁₃₇	—	2	2	no	—
139	C₄⋊C₄×C₁₃₇	—	2	2	no	—
140	C₄⋊C₄×C₁₃₇	—	4	2	no	—
141	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
142	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
143	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
144	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
145	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
146	C₂²⋊C₄×C₁₃₇	—	4	8	no	—
147	C₂²⋊C₄×C₁₃₇	—	4	8	no	—
148	C₄²×C₁₃₇	—	2	4	no	—
149	C₄²×C₁₃₇	—	2	4	no	—
150	C₄²×C₁₃₇	—	2	2	no	—
151	C₄²×C₁₃₇	—	2	2	no	—
152	C₄²×C₁₃₇	—	2	2	no	—
153	C₄²×C₁₃₇	—	2	2	no	—
154	C₄²×C₁₃₇	—	4	4	no	—
155	C₄²×C₁₃₇	—	4	4	no	—
156	C₂³×C₁₃₇	—	2	2	no	—
157	C₂³×C₁₃₇	—	2	2	no	—
158	C₂³×C₁₃₇	—	2	4	no	—
159	C₂³×C₁₃₇	—	4	16	no	—
160	C₂³×C₁₃₇	—	4	2	no	—
161	C₂³×C₁₃₇	—	4	2	no	—
162	C₂³×C₁₃₇	—	4	4	no	—
163	C₂³×C₁₃₇	—	4	4	no	—
164	C₂³×C₁₃₇	—	4	8	no	—
165	C₂³×C₁₃₇	—	8	8	no	—
166	C₂³×C₁₃₇	—	8	4	no	—
167	C₂³×C₁₃₇	—	8	4	no	—
168	C₂³×C₁₃₇	C₄×D₄	1	2	yes	—
169	C₂³×C₁₃₇	#121	1	2	yes	—
170	C₂³×C₁₃₇	#123	1	2	yes	—
171	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
172	D₄×C₁₃₇	—	2	4	no	—
173	D₄×C₁₃₇	—	2	4	no	—
174	D₄×C₁₃₇	—	4	2	no	—
175	D₄×C₁₃₇	—	4	2	no	—
176	D₄×C₁₃₇	—	4	8	no	—
177	C₂×C₄×C₁₃₇	—	2	2	no	—
178	C₂×C₄×C₁₃₇	—	2	2	no	—
179	C₂×C₄×C₁₃₇	—	2	4	no	—
180	C₂×C₄×C₁₃₇	—	2	2	no	—
181	C₂×C₄×C₁₃₇	—	2	2	no	—
182	C₂×C₄×C₁₃₇	—	2	2	no	—
183	C₂×C₄×C₁₃₇	—	2	2	no	—
184	C₂×C₄×C₁₃₇	—	2	2	no	—
185	C₂×C₄×C₁₃₇	—	4	8	no	—
186	C₂×C₄×C₁₃₇	—	4	2	no	—
187	C₂×C₄×C₁₃₇	—	4	2	no	—
188	C₂×C₄×C₁₃₇	—	4	2	no	—
189	C₂×C₄×C₁₃₇	—	4	2	no	—
190	C₂×C₄×C₁₃₇	—	4	2	no	—
191	C₂×C₄×C₁₃₇	—	4	4	no	—
192	C₂×C₄×C₁₃₇	—	8	4	no	—
193	C₂×C₄×C₁₃₇	#117	1	4	yes	—
194	C₂×C₄×C₁₃₇	C₄×D₄	1	4	yes	—
195	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
196	C₂×C₄×C₁₃₇	#121	1	2	yes	—
197	C₂×C₄×C₁₃₇	#123	1	2	yes	—
198	C₂×C₄×C₁₃₇	#124	1	4	yes	—
199	C₂×C₄×C₁₃₇	#126	1	4	yes	—
200	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	4	yes	—
201	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
207	C₈×C₁₃₇	—	2	4	no	—
208	C₈×C₁₃₇	—	4	2	no	—
209	C₂²×C₁₃₇	—	2	4	no	—
210	C₂²×C₁₃₇	—	2	4	no	—
211	C₂²×C₁₃₇	—	2	2	no	—
212	C₂²×C₁₃₇	—	2	2	no	—
213	C₂²×C₁₃₇	—	4	8	no	—
214	C₂²×C₁₃₇	—	4	4	no	—
215	C₂²×C₁₃₇	—	8	16	no	—
216	C₂²×C₁₃₇	—	8	4	no	—
217	C₂²×C₁₃₇	—	8	2	no	—
218	C₂²×C₁₃₇	—	8	2	no	—
219	C₂²×C₁₃₇	#388	1	4	yes	—
220	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
221	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
222	C₂²×C₁₃₇	C₂×#123	1	1	yes	characteristic
223	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
224	C₂²×C₁₃₇	#575	1	2	yes	—
225	C₄×C₁₃₇	—	2	4	no	—
226	C₄×C₁₃₇	—	4	2	no	—
227	C₄×C₁₃₇	—	4	4	no	—
228	C₄×C₁₃₇	—	4	2	no	—
229	C₄×C₁₃₇	—	4	2	no	—
230	C₄×C₁₃₇	—	8	2	no	—
231	C₄×C₁₃₇	#388	1	4	yes	—
232	C₄×C₁₃₇	C₂×#117	1	1	yes	characteristic
233	C₄×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
234	C₄×C₁₃₇	C₂×#124	1	1	yes	characteristic
235	C₄×C₁₃₇	C₂×#126	1	1	yes	characteristic
236	C₂×C₁₃₇	—	2	4	no	—
237	C₂×C₁₃₇	—	8	4	no	—
238	C₂×C₁₃₇	C₂×#388	1	1	yes	characteristic
239	C₂×C₁₃₇	C₄×AGL(1,ℤ/8)	1	2	yes	—
240	C₂×C₁₃₇	#3038	1	1	yes	characteristic
241	C₂×C₁₃₇	#3040	1	1	yes	characteristic
242	C₂×C₁₃₇	#3094	1	2	yes	—
243	#21060	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₁₃₇	#21060	1	1	yes	characteristic, direct product factor, Sylow
245	C₂×#428	C₂×C₁₃₇	1	1	yes	characteristic, complemented
246	C₂×#418	C₂×C₁₃₇	1	1	yes	characteristic
247	C₂×#418	C₂×C₁₃₇	1	1	yes	characteristic
248	C₂×#390	C₂×C₁₃₇	1	1	yes	characteristic
249	C₄×#117	C₂×C₁₃₇	1	1	yes	characteristic, complemented
250	#1926	C₂×C₁₃₇	1	4	yes	complemented
251	#1925	C₂×C₁₃₇	1	4	yes	complemented
252	#1736	C₂×C₁₃₇	1	1	yes	characteristic, complemented
253	#1728	C₂×C₁₃₇	1	1	yes	characteristic, complemented
254	C₂³×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
255	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
256	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
257	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
258	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
259	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
260	C₂²×C₂²⋊C₄	—	2	2	no	—
261	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
262	#428	—	2	4	no	—
263	C₂×#107	C₂²×C₁₃₇	1	2	yes	complemented
264	C₂×#106	C₂²×C₁₃₇	1	2	yes	complemented
265	#418	—	2	4	no	—
266	#418	C₄×C₁₃₇	1	8	yes	complemented
267	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
268	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
269	C₂×#102	C₂²×C₁₃₇	1	4	yes	—
270	#390	—	2	1	no	—
271	#390	—	2	1	no	—
272	#390	C₂²×C₁₃₇	1	4	yes	—
273	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	complemented
274	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	complemented
275	C₄×C₂²⋊C₄	—	2	2	no	—
276	#376	—	2	1	no	—
277	C₄³	—	2	1	no	—
278	#340	C₂²×C₁₃₇	1	4	yes	complemented
279	#336	C₂²×C₁₃₇	1	4	yes	complemented
280	C₂⁵	—	2	1	no	—
281	C₂²×D₄	—	2	2	no	—
282	C₂²×D₄	—	2	1	no	—
283	C₂²×D₄	—	2	2	no	—
284	C₂²×D₄	—	2	2	no	—
285	C₂²×D₄	—	2	2	no	—
286	C₂²×D₄	—	2	2	no	—
287	C₂²×D₄	C₂×C₄×C₁₃₇	1	4	yes	—
288	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
289	C₂³×C₄	—	2	1	no	—
290	C₂³×C₄	D₄×C₁₃₇	1	2	yes	—
291	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
292	C₂×M₁₆	—	2	2	no	—
293	C₂×M₁₆	—	2	2	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	C₂×C₄×C₁₃₇	1	4	yes	—
298	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
299	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
300	#117	—	2	2	no	—
301	#117	—	2	2	no	—
302	#117	C₂×C₄×C₁₃₇	1	4	yes	—
303	#117	D₄×C₁₃₇	1	4	yes	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	4	no	—
314	C₂×C₂²⋊C₄	—	2	4	no	—
315	C₂×C₂²⋊C₄	—	4	8	no	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
323	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
325	#107	—	2	4	no	—
326	#106	—	2	4	no	—
327	#102	—	2	4	no	—
328	#102	—	2	4	no	—
329	#102	C₂×C₄×C₁₃₇	1	16	yes	complemented
330	#95	—	2	2	no	—
331	#95	—	2	2	no	—
332	C₂⁴	—	2	4	no	—
333	C₂⁴	—	2	2	no	—
334	C₂⁴	—	4	4	no	—
335	C₂⁴	—	4	4	no	—
336	C₂⁴	—	4	2	no	—
337	C₂⁴	—	4	2	no	—
338	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	8	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	4	4	no	—
350	C₂×D₄	—	4	4	no	—
351	C₂×D₄	C₂²×C₄×C₁₃₇	1	4	yes	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	4	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
366	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
367	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
368	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
369	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
370	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
371	M₁₆	—	2	8	no	—
372	M₁₆	—	4	4	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	C₂²×C₄×C₁₃₇	1	4	yes	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
386	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
387	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	4	8	no	—
391	C₂²⋊C₄	—	4	8	no	—
392	C₄²	—	2	4	no	—
393	C₄²	—	2	4	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	4	4	no	—
399	C₄²	—	4	4	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	4	16	no	—
404	C₂³	—	4	8	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	4	no	—
408	C₂³	—	4	4	no	—
409	C₂³	—	8	4	no	—
410	C₂³	—	8	4	no	—
411	C₂³	—	8	8	no	—
412	C₂³	C₄×D₄×C₁₃₇	1	2	yes	—
413	C₂³	#121×C₁₃₇	1	2	yes	—
414	C₂³	#123×C₁₃₇	1	2	yes	—
415	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
416	D₄	—	2	4	no	—
417	D₄	—	2	4	no	—
418	D₄	—	4	8	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	8	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	8	4	no	—
437	C₂×C₄	#117×C₁₃₇	1	4	yes	—
438	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
439	C₂×C₄	C₄×D₄×C₁₃₇	1	4	yes	—
440	C₂×C₄	#121×C₁₃₇	1	2	yes	—
441	C₂×C₄	#123×C₁₃₇	1	2	yes	—
442	C₂×C₄	#124×C₁₃₇	1	4	yes	—
443	C₂×C₄	#126×C₁₃₇	1	4	yes	—
444	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	4	yes	—
445	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
447	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
448	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
449	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
450	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
451	C₈	—	2	4	no	—
452	C₈	—	4	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	8	no	—
459	C₂²	—	8	16	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	4	no	—
463	C₂²	#388×C₁₃₇	1	4	yes	—
464	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
465	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
466	C₂²	C₂×#123×C₁₃₇	1	1	yes	characteristic
467	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
468	C₂²	#575×C₁₃₇	1	2	yes	—
469	C₄	—	2	4	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	4	no	—
474	C₄	—	8	2	no	—
475	C₄	#388×C₁₃₇	1	4	yes	—
476	C₄	C₂×#117×C₁₃₇	1	1	yes	characteristic
477	C₄	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
478	C₄	C₂×#124×C₁₃₇	1	1	yes	characteristic
479	C₄	C₂×#126×C₁₃₇	1	1	yes	characteristic
480	C₂	—	2	4	no	—
481	C₂	—	8	4	no	—
482	C₂	C₂×#388×C₁₃₇	1	1	yes	characteristic
483	C₂	C₄×AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
484	C₂	#3038×C₁₃₇	1	1	yes	characteristic
485	C₂	#3040×C₁₃₇	1	1	yes	characteristic
486	C₂	#3094×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂³×D₄×C₁₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂²×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#428×C₁₃₇	C₂	semidirect
5. C₄×#117×C₁₃₇	C₂	semidirect
6. #1926×C₁₃₇	C₂	semidirect
7. #1925×C₁₃₇	C₂	semidirect
8. #1736×C₁₃₇	C₂	semidirect
9. #1728×C₁₃₇	C₂	semidirect
19. C₂×#107×C₁₃₇	C₂²	semidirect
20. C₂×#106×C₁₃₇	C₂²	semidirect
22. #418×C₁₃₇	C₄	semidirect
29. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
30. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
34. #340×C₁₃₇	C₂²	semidirect
35. #336×C₁₃₇	C₂²	semidirect
85. #102×C₁₃₇	C₂×C₄	semidirect
243. #21060	C₁₃₇	direct (N × H)
244. C₁₃₇	#21060	direct (N × H)
245. C₂×#428	C₂×C₁₃₇	semidirect
249. C₄×#117	C₂×C₁₃₇	semidirect
250. #1926	C₂×C₁₃₇	semidirect
251. #1925	C₂×C₁₃₇	semidirect
252. #1736	C₂×C₁₃₇	semidirect
253. #1728	C₂×C₁₃₇	semidirect
263. C₂×#107	C₂²×C₁₃₇	semidirect
264. C₂×#106	C₂²×C₁₃₇	semidirect
266. #418	C₄×C₁₃₇	semidirect
273. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
274. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
278. #340	C₂²×C₁₃₇	semidirect
279. #336	C₂²×C₁₃₇	semidirect
329. #102	C₂×C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#428×C₁₃₇	2
C₂×#418×C₁₃₇	2
C₂×#390×C₁₃₇	2
C₄×#117×C₁₃₇	2
#1926×C₁₃₇	2
#1925×C₁₃₇	2
#1736×C₁₃₇	2
#1728×C₁₃₇	2
#21060	137

Subgroups — C137×#21060 #46870446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21060 #46870446