Subgroups — C₂×#1866×C₁₃₇ #46870269

Order 35072.

1398 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#108×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#424×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#104×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#416×C₁₃₇	C₂	1	1	yes	maximal, characteristic
6	#1866×C₁₃₇	C₂	1	8	yes	maximal, direct product factor
7	C₂×#339×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#336×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₃₇	C₂²	1	1	yes	characteristic
10	C₂×#131×C₁₃₇	—	2	4	no	—
11	C₂×#131×C₁₃₇	—	2	4	no	—
12	C₂×#131×C₁₃₇	—	2	2	no	—
13	C₂×#131×C₁₃₇	C₂²	1	4	yes	—
14	C₂²×M₁₆×C₁₃₇	—	2	1	no	—
15	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₃₇	—	2	1	no	—
18	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×#108×C₁₃₇	—	2	4	no	—
23	C₂×#108×C₁₃₇	C₂²	1	4	yes	complemented
24	#424×C₁₃₇	—	2	2	no	—
25	#424×C₁₃₇	C₂²	1	4	yes	complemented
26	C₂×C₄⋊C₈×C₁₃₇	—	2	1	no	—
27	C₂×C₄⋊C₈×C₁₃₇	—	2	1	no	—
28	C₂×#104×C₁₃₇	—	2	4	no	—
29	C₂×#104×C₁₃₇	C₂²	1	4	yes	—
30	#416×C₁₃₇	C₄	1	4	yes	complemented
31	#416×C₁₃₇	C₂²	1	4	yes	—
32	C₂×#103×C₁₃₇	C₄	1	1	yes	characteristic, complemented
33	C₂×#103×C₁₃₇	C₄	1	1	yes	characteristic, complemented
34	C₂×#102×C₁₃₇	C₄	1	1	yes	characteristic, complemented
35	C₂×#102×C₁₃₇	C₄	1	1	yes	characteristic, complemented
36	#339×C₁₃₇	C₂²	1	4	yes	complemented
37	#336×C₁₃₇	C₂²	1	4	yes	complemented
38	C₂×#41×C₁₃₇	—	2	2	no	—
39	C₂×#41×C₁₃₇	—	2	1	no	—
40	C₂×#41×C₁₃₇	—	2	1	no	—
41	C₂×#41×C₁₃₇	—	2	2	no	—
42	C₂×#41×C₁₃₇	C₂×C₄	1	2	yes	—
43	C₂×#41×C₁₃₇	D₄	1	4	yes	—
44	C₂×#41×C₁₃₇	Q₈	1	4	yes	—
45	C₂×#41×C₁₃₇	C₂³	1	2	yes	—
46	C₂²×Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₃₇	—	2	1	no	—
48	C₂²×D₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃₇	—	2	1	no	—
50	C₂³×C₄×C₁₃₇	—	2	1	no	—
51	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
52	#131×C₁₃₇	—	2	16	no	—
53	#131×C₁₃₇	—	2	8	no	—
54	#131×C₁₃₇	—	2	8	no	—
55	C₂×M₁₆×C₁₃₇	—	2	8	no	—
56	C₂×M₁₆×C₁₃₇	—	2	2	no	—
57	C₂×M₁₆×C₁₃₇	—	2	1	no	—
58	C₂×M₁₆×C₁₃₇	—	2	1	no	—
59	C₂×M₁₆×C₁₃₇	—	2	4	no	—
60	C₂×M₁₆×C₁₃₇	—	2	2	no	—
61	C₂×M₁₆×C₁₃₇	—	2	2	no	—
62	C₂×M₁₆×C₁₃₇	D₄	1	4	yes	—
63	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
64	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
65	C₂²×C₈×C₁₃₇	—	2	8	no	—
66	C₂²×C₈×C₁₃₇	—	2	2	no	—
67	C₂²×C₈×C₁₃₇	—	2	2	no	—
68	C₂²×C₈×C₁₃₇	—	2	2	no	—
69	C₂²×C₈×C₁₃₇	—	2	1	no	—
70	C₂²×C₈×C₁₃₇	—	2	2	no	—
71	C₂²×C₈×C₁₃₇	—	2	4	no	—
72	C₂²×C₈×C₁₃₇	—	2	1	no	—
73	C₂²×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₈×C₁₃₇	C₂×C₄	1	2	yes	—
76	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
77	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
80	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
81	#117×C₁₃₇	—	2	1	no	—
82	#117×C₁₃₇	—	2	1	no	—
83	#117×C₁₃₇	C₂×C₄	1	2	yes	—
84	#117×C₁₃₇	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
88	C₂×C₄²×C₁₃₇	—	2	1	no	—
89	C₂×C₄²×C₁₃₇	—	2	2	no	—
90	C₂×C₄²×C₁₃₇	—	2	2	no	—
91	C₂×C₄²×C₁₃₇	—	2	1	no	—
92	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
93	#108×C₁₃₇	—	2	8	no	—
94	C₄⋊C₈×C₁₃₇	—	2	4	no	—
95	C₄⋊C₈×C₁₃₇	—	2	4	no	—
96	#104×C₁₃₇	—	2	8	no	—
97	#103×C₁₃₇	C₂×C₄	1	4	yes	complemented
98	#103×C₁₃₇	C₂×C₄	1	4	yes	complemented
99	#102×C₁₃₇	C₂×C₄	1	4	yes	complemented
100	#102×C₁₃₇	C₂×C₄	1	4	yes	complemented
101	C₂⁴×C₁₃₇	—	2	1	no	—
102	C₂⁴×C₁₃₇	#41	1	1	yes	characteristic
103	#41×C₁₃₇	—	2	4	no	—
104	#41×C₁₃₇	—	2	4	no	—
105	#41×C₁₃₇	—	2	4	no	—
106	#41×C₁₃₇	—	2	4	no	—
107	#41×C₁₃₇	—	2	4	no	—
108	#41×C₁₃₇	—	2	2	no	—
109	#41×C₁₃₇	—	2	2	no	—
110	#41×C₁₃₇	C₄⋊C₄	1	8	yes	—
111	#41×C₁₃₇	C₂×D₄	1	4	yes	—
112	#41×C₁₃₇	C₂×Q₈	1	4	yes	—
113	C₂×Q₈×C₁₃₇	—	2	1	no	—
114	C₂×Q₈×C₁₃₇	—	2	2	no	—
115	C₂×Q₈×C₁₃₇	C₄⋊C₄	1	4	yes	—
116	C₂×Q₈×C₁₃₇	C₂²×C₄	1	2	yes	—
117	C₂×D₄×C₁₃₇	—	2	2	no	—
118	C₂×D₄×C₁₃₇	—	2	4	no	—
119	C₂×D₄×C₁₃₇	—	2	4	no	—
120	C₂×D₄×C₁₃₇	—	2	2	no	—
121	C₂×D₄×C₁₃₇	—	2	2	no	—
122	C₂×D₄×C₁₃₇	—	2	1	no	—
123	C₂×D₄×C₁₃₇	C₄⋊C₄	1	4	yes	—
124	C₂×D₄×C₁₃₇	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₁₃₇	—	2	1	no	—
126	C₂²×C₄×C₁₃₇	—	2	2	no	—
127	C₂²×C₄×C₁₃₇	—	2	4	no	—
128	C₂²×C₄×C₁₃₇	—	2	4	no	—
129	C₂²×C₄×C₁₃₇	—	2	2	no	—
130	C₂²×C₄×C₁₃₇	—	2	4	no	—
131	C₂²×C₄×C₁₃₇	—	2	1	no	—
132	C₂²×C₄×C₁₃₇	—	2	1	no	—
133	C₂²×C₄×C₁₃₇	—	2	2	no	—
134	C₂²×C₄×C₁₃₇	—	4	2	no	—
135	C₂²×C₄×C₁₃₇	—	4	2	no	—
136	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
143	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
144	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
145	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
146	M₁₆×C₁₃₇	—	2	16	no	—
147	M₁₆×C₁₃₇	—	2	4	no	—
148	M₁₆×C₁₃₇	—	2	2	no	—
149	M₁₆×C₁₃₇	—	2	2	no	—
150	M₁₆×C₁₃₇	—	2	2	no	—
151	M₁₆×C₁₃₇	—	4	2	no	—
152	M₁₆×C₁₃₇	C₂×D₄	1	4	yes	—
153	C₂×C₈×C₁₃₇	—	2	16	no	—
154	C₂×C₈×C₁₃₇	—	2	2	no	—
155	C₂×C₈×C₁₃₇	—	2	2	no	—
156	C₂×C₈×C₁₃₇	—	2	4	no	—
157	C₂×C₈×C₁₃₇	—	2	2	no	—
158	C₂×C₈×C₁₃₇	—	2	4	no	—
159	C₂×C₈×C₁₃₇	—	2	2	no	—
160	C₂×C₈×C₁₃₇	—	2	4	no	—
161	C₂×C₈×C₁₃₇	—	2	2	no	—
162	C₂×C₈×C₁₃₇	—	2	2	no	—
163	C₂×C₈×C₁₃₇	—	2	2	no	—
164	C₂×C₈×C₁₃₇	—	2	2	no	—
165	C₂×C₈×C₁₃₇	—	2	2	no	—
166	C₂×C₈×C₁₃₇	—	2	2	no	—
167	C₂×C₈×C₁₃₇	—	4	2	no	—
168	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
169	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
170	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
171	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
172	C₄⋊C₄×C₁₃₇	—	2	1	no	—
173	C₄⋊C₄×C₁₃₇	—	2	1	no	—
174	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
175	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
176	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
177	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
178	C₄²×C₁₃₇	—	2	2	no	—
179	C₄²×C₁₃₇	—	2	2	no	—
180	C₄²×C₁₃₇	—	2	2	no	—
181	C₄²×C₁₃₇	—	2	2	no	—
182	C₄²×C₁₃₇	—	4	2	no	—
183	C₂³×C₁₃₇	—	2	2	no	—
184	C₂³×C₁₃₇	—	2	2	no	—
185	C₂³×C₁₃₇	—	2	2	no	—
186	C₂³×C₁₃₇	—	2	4	no	—
187	C₂³×C₁₃₇	—	4	2	no	—
188	C₂³×C₁₃₇	—	4	2	no	—
189	C₂³×C₁₃₇	C₄×D₄	1	1	yes	characteristic
190	C₂³×C₁₃₇	C₄×D₄	1	1	yes	characteristic
191	C₂³×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
192	C₂³×C₁₃₇	#123	1	2	yes	—
193	C₂³×C₁₃₇	C₂×#41	1	1	yes	characteristic
194	Q₈×C₁₃₇	—	2	2	no	—
195	Q₈×C₁₃₇	—	2	4	no	—
196	Q₈×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
197	D₄×C₁₃₇	—	2	4	no	—
198	D₄×C₁₃₇	—	2	4	no	—
199	D₄×C₁₃₇	—	2	8	no	—
200	D₄×C₁₃₇	—	2	2	no	—
201	D₄×C₁₃₇	—	2	4	no	—
202	D₄×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
203	C₂×C₄×C₁₃₇	—	2	2	no	—
204	C₂×C₄×C₁₃₇	—	2	4	no	—
205	C₂×C₄×C₁₃₇	—	2	4	no	—
206	C₂×C₄×C₁₃₇	—	2	4	no	—
207	C₂×C₄×C₁₃₇	—	2	8	no	—
208	C₂×C₄×C₁₃₇	—	2	4	no	—
209	C₂×C₄×C₁₃₇	—	2	2	no	—
210	C₂×C₄×C₁₃₇	—	2	2	no	—
211	C₂×C₄×C₁₃₇	—	4	8	no	—
212	C₂×C₄×C₁₃₇	—	4	2	no	—
213	C₂×C₄×C₁₃₇	—	4	2	no	—
214	C₂×C₄×C₁₃₇	—	4	2	no	—
215	C₂×C₄×C₁₃₇	—	4	2	no	—
216	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
217	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
218	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
219	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
220	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃₇	#120	1	2	yes	—
223	C₂×C₄×C₁₃₇	#120	1	2	yes	—
224	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
225	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
226	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
227	C₂×C₄×C₁₃₇	#123	1	2	yes	—
228	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
233	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
234	C₈×C₁₃₇	—	2	2	no	—
235	C₈×C₁₃₇	—	2	2	no	—
236	C₈×C₁₃₇	—	2	2	no	—
237	C₈×C₁₃₇	—	2	4	no	—
238	C₈×C₁₃₇	—	2	2	no	—
239	C₈×C₁₃₇	—	4	2	no	—
240	C₂²×C₁₃₇	—	2	4	no	—
241	C₂²×C₁₃₇	—	2	4	no	—
242	C₂²×C₁₃₇	—	2	1	no	—
243	C₂²×C₁₃₇	—	2	1	no	—
244	C₂²×C₁₃₇	—	2	1	no	—
245	C₂²×C₁₃₇	—	2	1	no	—
246	C₂²×C₁₃₇	—	2	4	no	—
247	C₂²×C₁₃₇	—	4	8	no	—
248	C₂²×C₁₃₇	—	4	2	no	—
249	C₂²×C₁₃₇	—	4	2	no	—
250	C₂²×C₁₃₇	#385	1	2	yes	—
251	C₂²×C₁₃₇	#385	1	2	yes	—
252	C₂²×C₁₃₇	#443	1	2	yes	—
253	C₂²×C₁₃₇	#444	1	2	yes	—
254	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
255	C₂²×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
256	C₂²×C₁₃₇	C₂×#123	1	1	yes	characteristic
257	C₄×C₁₃₇	—	2	4	no	—
258	C₄×C₁₃₇	—	4	4	no	—
259	C₄×C₁₃₇	—	4	2	no	—
260	C₄×C₁₃₇	—	4	2	no	—
261	C₄×C₁₃₇	#385	1	2	yes	—
262	C₄×C₁₃₇	#385	1	2	yes	—
263	C₄×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
264	C₄×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
265	C₄×C₁₃₇	C₂×#120	1	1	yes	characteristic
266	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
267	C₂×C₁₃₇	—	2	1	no	—
268	C₂×C₁₃₇	—	2	1	no	—
269	C₂×C₁₃₇	—	2	2	no	—
270	C₂×C₁₃₇	—	4	4	no	—
271	C₂×C₁₃₇	#1866	1	4	yes	direct product factor
272	C₂×C₁₃₇	C₂×#385	1	1	yes	characteristic
273	C₂×C₁₃₇	C₂×#443	1	1	yes	characteristic
274	C₂×C₁₃₇	C₂×#444	1	1	yes	characteristic
275	C₂×#1866	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₁₃₇	C₂×#1866	1	1	yes	characteristic, direct product factor, Sylow
277	C₂²×#131	C₂×C₁₃₇	1	1	yes	characteristic
278	C₂²×#108	C₂×C₁₃₇	1	1	yes	characteristic, complemented
279	C₂×#424	C₂×C₁₃₇	1	1	yes	characteristic, complemented
280	C₂²×#104	C₂×C₁₃₇	1	1	yes	characteristic
281	C₂×#416	C₂×C₁₃₇	1	1	yes	characteristic
282	#1866	C₂×C₁₃₇	1	8	yes	direct product factor
283	C₂×#339	C₂×C₁₃₇	1	1	yes	characteristic, complemented
284	C₂×#336	C₂×C₁₃₇	1	1	yes	characteristic, complemented
285	C₂²×#41	C₂²×C₁₃₇	1	1	yes	characteristic
286	C₂×#131	—	2	4	no	—
287	C₂×#131	—	2	4	no	—
288	C₂×#131	—	2	2	no	—
289	C₂×#131	C₂²×C₁₃₇	1	4	yes	—
290	C₂²×M₁₆	—	2	1	no	—
291	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
292	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
293	C₂³×C₈	—	2	1	no	—
294	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
295	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
296	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
297	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
298	C₂×#108	—	2	4	no	—
299	C₂×#108	C₂²×C₁₃₇	1	4	yes	complemented
300	#424	—	2	2	no	—
301	#424	C₂²×C₁₃₇	1	4	yes	complemented
302	C₂×C₄⋊C₈	—	2	1	no	—
303	C₂×C₄⋊C₈	—	2	1	no	—
304	C₂×#104	—	2	4	no	—
305	C₂×#104	C₂²×C₁₃₇	1	4	yes	—
306	#416	C₄×C₁₃₇	1	4	yes	complemented
307	#416	C₂²×C₁₃₇	1	4	yes	—
308	C₂×#103	C₄×C₁₃₇	1	1	yes	characteristic, complemented
309	C₂×#103	C₄×C₁₃₇	1	1	yes	characteristic, complemented
310	C₂×#102	C₄×C₁₃₇	1	1	yes	characteristic, complemented
311	C₂×#102	C₄×C₁₃₇	1	1	yes	characteristic, complemented
312	#339	C₂²×C₁₃₇	1	4	yes	complemented
313	#336	C₂²×C₁₃₇	1	4	yes	complemented
314	C₂×#41	—	2	2	no	—
315	C₂×#41	—	2	1	no	—
316	C₂×#41	—	2	1	no	—
317	C₂×#41	—	2	2	no	—
318	C₂×#41	C₂×C₄×C₁₃₇	1	2	yes	—
319	C₂×#41	D₄×C₁₃₇	1	4	yes	—
320	C₂×#41	Q₈×C₁₃₇	1	4	yes	—
321	C₂×#41	C₂³×C₁₃₇	1	2	yes	—
322	C₂²×Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
323	C₂²×D₄	—	2	1	no	—
324	C₂²×D₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
325	C₂³×C₄	—	2	1	no	—
326	C₂³×C₄	—	2	1	no	—
327	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
328	#131	—	2	16	no	—
329	#131	—	2	8	no	—
330	#131	—	2	8	no	—
331	C₂×M₁₆	—	2	8	no	—
332	C₂×M₁₆	—	2	2	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	2	1	no	—
335	C₂×M₁₆	—	2	4	no	—
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	—	2	2	no	—
338	C₂×M₁₆	D₄×C₁₃₇	1	4	yes	—
339	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
340	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
341	C₂²×C₈	—	2	8	no	—
342	C₂²×C₈	—	2	1	no	—
343	C₂²×C₈	—	2	2	no	—
344	C₂²×C₈	—	2	2	no	—
345	C₂²×C₈	—	2	2	no	—
346	C₂²×C₈	—	2	2	no	—
347	C₂²×C₈	—	2	4	no	—
348	C₂²×C₈	—	2	1	no	—
349	C₂²×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
350	C₂²×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
351	C₂²×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
352	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
353	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
354	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
355	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
356	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
357	#117	—	2	1	no	—
358	#117	—	2	1	no	—
359	#117	C₂×C₄×C₁₃₇	1	2	yes	—
360	#117	C₂³×C₁₃₇	1	2	yes	—
361	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	2	2	no	—
366	C₂×C₄²	—	2	2	no	—
367	C₂×C₄²	—	2	1	no	—
368	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
369	#108	—	2	8	no	—
370	C₄⋊C₈	—	2	4	no	—
371	C₄⋊C₈	—	2	4	no	—
372	#104	—	2	8	no	—
373	#103	C₂×C₄×C₁₃₇	1	4	yes	complemented
374	#103	C₂×C₄×C₁₃₇	1	4	yes	complemented
375	#102	C₂×C₄×C₁₃₇	1	4	yes	complemented
376	#102	C₂×C₄×C₁₃₇	1	4	yes	complemented
377	C₂⁴	—	2	1	no	—
378	C₂⁴	#41×C₁₃₇	1	1	yes	characteristic
379	#41	—	2	4	no	—
380	#41	—	2	4	no	—
381	#41	—	2	4	no	—
382	#41	—	2	4	no	—
383	#41	—	2	4	no	—
384	#41	—	2	2	no	—
385	#41	—	2	2	no	—
386	#41	C₄⋊C₄×C₁₃₇	1	8	yes	—
387	#41	C₂×D₄×C₁₃₇	1	4	yes	—
388	#41	C₂×Q₈×C₁₃₇	1	4	yes	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	C₄⋊C₄×C₁₃₇	1	4	yes	—
392	C₂×Q₈	C₂²×C₄×C₁₃₇	1	2	yes	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	C₄⋊C₄×C₁₃₇	1	4	yes	—
400	C₂×D₄	C₂²×C₄×C₁₃₇	1	2	yes	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
413	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
415	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
416	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
418	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
419	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
420	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
421	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
422	M₁₆	—	2	16	no	—
423	M₁₆	—	2	4	no	—
424	M₁₆	—	2	2	no	—
425	M₁₆	—	2	2	no	—
426	M₁₆	—	2	2	no	—
427	M₁₆	—	4	2	no	—
428	M₁₆	C₂×D₄×C₁₃₇	1	4	yes	—
429	C₂×C₈	—	2	16	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	4	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	4	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	4	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	4	2	no	—
444	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
445	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
446	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
447	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
451	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	4	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	C₄×D₄×C₁₃₇	1	1	yes	characteristic
466	C₂³	C₄×D₄×C₁₃₇	1	1	yes	characteristic
467	C₂³	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
468	C₂³	#123×C₁₃₇	1	2	yes	—
469	C₂³	C₂×#41×C₁₃₇	1	1	yes	characteristic
470	Q₈	—	2	4	no	—
471	Q₈	—	2	2	no	—
472	Q₈	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
473	D₄	—	2	8	no	—
474	D₄	—	2	4	no	—
475	D₄	—	2	4	no	—
476	D₄	—	2	4	no	—
477	D₄	—	2	2	no	—
478	D₄	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	4	8	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
493	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
494	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
495	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
496	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
497	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
498	C₂×C₄	#120×C₁₃₇	1	2	yes	—
499	C₂×C₄	#120×C₁₃₇	1	2	yes	—
500	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
501	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
502	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
503	C₂×C₄	#123×C₁₃₇	1	2	yes	—
504	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
508	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
509	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
510	C₈	—	2	2	no	—
511	C₈	—	2	2	no	—
512	C₈	—	2	2	no	—
513	C₈	—	2	4	no	—
514	C₈	—	2	2	no	—
515	C₈	—	4	2	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	4	8	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	#385×C₁₃₇	1	2	yes	—
527	C₂²	#385×C₁₃₇	1	2	yes	—
528	C₂²	#443×C₁₃₇	1	2	yes	—
529	C₂²	#444×C₁₃₇	1	2	yes	—
530	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
531	C₂²	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
532	C₂²	C₂×#123×C₁₃₇	1	1	yes	characteristic
533	C₄	—	2	4	no	—
534	C₄	—	4	4	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	#385×C₁₃₇	1	2	yes	—
538	C₄	#385×C₁₃₇	1	2	yes	—
539	C₄	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
540	C₄	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
541	C₄	C₂×#120×C₁₃₇	1	1	yes	characteristic
542	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
543	C₂	—	2	1	no	—
544	C₂	—	2	2	no	—
545	C₂	—	2	1	no	—
546	C₂	—	4	4	no	—
547	C₂	#1866×C₁₃₇	1	4	yes	direct product factor
548	C₂	C₂×#385×C₁₃₇	1	1	yes	characteristic
549	C₂	C₂×#443×C₁₃₇	1	1	yes	characteristic
550	C₂	C₂×#444×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle	C₂³×C₁₃₇	C₄×D₄
prime radical	C₂²×#41×C₁₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₇ ◁ C₂³×C₈×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#108×C₁₃₇	C₂	semidirect
3. C₂×#424×C₁₃₇	C₂	semidirect
6. #1866×C₁₃₇	C₂	direct (N × H)
7. C₂×#339×C₁₃₇	C₂	semidirect
8. C₂×#336×C₁₃₇	C₂	semidirect
23. C₂×#108×C₁₃₇	C₂²	semidirect
25. #424×C₁₃₇	C₂²	semidirect
30. #416×C₁₃₇	C₄	semidirect
32. C₂×#103×C₁₃₇	C₄	semidirect
33. C₂×#103×C₁₃₇	C₄	semidirect
34. C₂×#102×C₁₃₇	C₄	semidirect
35. C₂×#102×C₁₃₇	C₄	semidirect
36. #339×C₁₃₇	C₂²	semidirect
37. #336×C₁₃₇	C₂²	semidirect
97. #103×C₁₃₇	C₂×C₄	semidirect
98. #103×C₁₃₇	C₂×C₄	semidirect
99. #102×C₁₃₇	C₂×C₄	semidirect
100. #102×C₁₃₇	C₂×C₄	semidirect
271. C₂×C₁₃₇	#1866	direct (N × H)
275. C₂×#1866	C₁₃₇	direct (N × H)
276. C₁₃₇	C₂×#1866	direct (N × H)
278. C₂²×#108	C₂×C₁₃₇	semidirect
279. C₂×#424	C₂×C₁₃₇	semidirect
282. #1866	C₂×C₁₃₇	direct (N × H)
283. C₂×#339	C₂×C₁₃₇	semidirect
284. C₂×#336	C₂×C₁₃₇	semidirect
299. C₂×#108	C₂²×C₁₃₇	semidirect
301. #424	C₂²×C₁₃₇	semidirect
306. #416	C₄×C₁₃₇	semidirect
308. C₂×#103	C₄×C₁₃₇	semidirect
309. C₂×#103	C₄×C₁₃₇	semidirect
310. C₂×#102	C₄×C₁₃₇	semidirect
311. C₂×#102	C₄×C₁₃₇	semidirect
312. #339	C₂²×C₁₃₇	semidirect
313. #336	C₂²×C₁₃₇	semidirect
373. #103	C₂×C₄×C₁₃₇	semidirect
374. #103	C₂×C₄×C₁₃₇	semidirect
375. #102	C₂×C₄×C₁₃₇	semidirect
376. #102	C₂×C₄×C₁₃₇	semidirect
547. C₂	#1866×C₁₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#131×C₁₃₇	2
C₂²×#108×C₁₃₇	2
C₂×#424×C₁₃₇	2
C₂²×#104×C₁₃₇	2
C₂×#416×C₁₃₇	2
#1866×C₁₃₇	2
C₂×#339×C₁₃₇	2
C₂×#336×C₁₃₇	2
C₂×#1866	137

Subgroups — C2×#1866×C137 #46870269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1866×C₁₃₇ #46870269