Subgroups — C₂×#2499×C₁₃₇ #46884176

Order 35072.

2702 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2499×C₁₃₇	C₂	1	16	yes	maximal, direct product factor
4	C₂×#397×C₁₃₇	C₂	1	4	yes	maximal
5	C₂×#391×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#391×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#387×C₁₃₇	C₂	1	4	yes	maximal, complemented
8	C₂×#384×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#382×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×C₂²⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic
11	C₂³×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₁₃₇	—	2	8	no	—
14	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	8	yes	—
15	C₂×#117×C₁₃₇	—	2	8	no	—
16	C₂×#117×C₁₃₇	C₂²	1	8	yes	—
17	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	4	yes	—
20	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₃₇	C₂²	1	2	yes	—
28	#397×C₁₃₇	C₂²	1	32	yes	—
29	#391×C₁₃₇	C₂²	1	8	yes	complemented
30	#391×C₁₃₇	C₂²	1	8	yes	complemented
31	#387×C₁₃₇	C₂²	1	32	yes	complemented
32	#384×C₁₃₇	C₂²	1	8	yes	complemented
33	#382×C₁₃₇	C₂²	1	8	yes	complemented
34	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	8	yes	—
35	C₂×#95×C₁₃₇	C₂²	1	4	yes	—
36	C₂×#95×C₁₃₇	C₂²	1	2	yes	—
37	C₂×#95×C₁₃₇	C₂²	1	4	yes	—
38	C₂×#95×C₁₃₇	C₂²	1	4	yes	—
39	C₂⁵×C₁₃₇	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₁₃₇	—	2	4	no	—
41	C₂²×Q₈×C₁₃₇	—	2	4	no	—
42	C₂²×Q₈×C₁₃₇	—	2	4	no	—
43	C₂²×Q₈×C₁₃₇	C₂³	1	4	yes	—
44	C₂³×C₄×C₁₃₇	—	2	4	no	—
45	C₂³×C₄×C₁₃₇	—	2	4	no	—
46	C₂³×C₄×C₁₃₇	D₄	1	8	yes	—
47	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃₇	C₂³	1	4	yes	—
53	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
56	C₂²⋊Q₈×C₁₃₇	—	2	32	no	—
57	#117×C₁₃₇	—	2	32	no	—
58	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
60	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
61	C₂×C₄⋊C₄×C₁₃₇	—	2	8	no	—
62	C₂×C₄⋊C₄×C₁₃₇	—	2	16	no	—
63	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
64	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	16	yes	—
66	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	8	yes	—
68	C₂×C₂²⋊C₄×C₁₃₇	—	2	8	no	—
69	C₂×C₂²⋊C₄×C₁₃₇	—	2	8	no	—
70	C₂×C₂²⋊C₄×C₁₃₇	—	2	8	no	—
71	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
72	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
73	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
74	C₂×C₄²×C₁₃₇	—	2	8	no	—
75	C₂×C₄²×C₁₃₇	—	2	4	no	—
76	C₂×C₄²×C₁₃₇	—	2	4	no	—
77	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
78	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
79	C₂×C₄²×C₁₃₇	C₂³	1	8	yes	—
80	#95×C₁₃₇	C₂³	1	8	yes	—
81	#95×C₁₃₇	C₂³	1	16	yes	—
82	#95×C₁₃₇	C₂³	1	16	yes	—
83	#95×C₁₃₇	C₂³	1	16	yes	—
84	C₂⁴×C₁₃₇	—	2	4	no	—
85	C₂⁴×C₁₃₇	—	2	2	no	—
86	C₂⁴×C₁₃₇	—	2	2	no	—
87	C₂⁴×C₁₃₇	—	2	4	no	—
88	C₂⁴×C₁₃₇	C₂×D₄	1	4	yes	—
89	C₂⁴×C₁₃₇	C₂⁴	1	2	yes	—
90	C₂⁴×C₁₃₇	C₂⁴	1	1	yes	characteristic
91	C₂×Q₈×C₁₃₇	—	2	8	no	—
92	C₂×Q₈×C₁₃₇	—	2	8	no	—
93	C₂×Q₈×C₁₃₇	—	2	8	no	—
94	C₂×Q₈×C₁₃₇	—	4	16	no	—
95	C₂²×C₄×C₁₃₇	—	2	4	no	—
96	C₂²×C₄×C₁₃₇	—	2	2	no	—
97	C₂²×C₄×C₁₃₇	—	2	2	no	—
98	C₂²×C₄×C₁₃₇	—	2	4	no	—
99	C₂²×C₄×C₁₃₇	—	2	32	no	—
100	C₂²×C₄×C₁₃₇	—	2	8	no	—
101	C₂²×C₄×C₁₃₇	—	2	8	no	—
102	C₂²×C₄×C₁₃₇	—	2	4	no	—
103	C₂²×C₄×C₁₃₇	—	2	4	no	—
104	C₂²×C₄×C₁₃₇	—	2	4	no	—
105	C₂²×C₄×C₁₃₇	—	2	4	no	—
106	C₂²×C₄×C₁₃₇	—	2	4	no	—
107	C₂²×C₄×C₁₃₇	—	2	4	no	—
108	C₂²×C₄×C₁₃₇	—	2	8	no	—
109	C₂²×C₄×C₁₃₇	—	2	8	no	—
110	C₂²×C₄×C₁₃₇	—	2	4	no	—
111	C₂²×C₄×C₁₃₇	—	2	4	no	—
112	C₂²×C₄×C₁₃₇	—	2	8	no	—
113	C₂²×C₄×C₁₃₇	—	2	4	no	—
114	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₁₃₇	C₂×D₄	1	16	yes	—
116	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₁₃₇	#41	1	8	yes	—
118	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
119	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
120	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
126	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
128	C₄⋊C₄×C₁₃₇	—	2	8	no	—
129	C₄⋊C₄×C₁₃₇	—	2	8	no	—
130	C₄⋊C₄×C₁₃₇	—	2	8	no	—
131	C₄⋊C₄×C₁₃₇	—	2	16	no	—
132	C₄⋊C₄×C₁₃₇	—	2	32	no	—
133	C₂²⋊C₄×C₁₃₇	—	2	16	no	—
134	C₂²⋊C₄×C₁₃₇	—	2	16	no	—
135	C₂²⋊C₄×C₁₃₇	—	2	16	no	—
136	C₄²×C₁₃₇	—	2	16	no	—
137	C₄²×C₁₃₇	—	2	8	no	—
138	C₄²×C₁₃₇	—	2	8	no	—
139	C₂³×C₁₃₇	—	2	8	no	—
140	C₂³×C₁₃₇	—	2	8	no	—
141	C₂³×C₁₃₇	—	2	8	no	—
142	C₂³×C₁₃₇	—	2	4	no	—
143	C₂³×C₁₃₇	—	2	2	no	—
144	C₂³×C₁₃₇	—	2	2	no	—
145	C₂³×C₁₃₇	—	2	4	no	—
146	C₂³×C₁₃₇	—	4	8	no	—
147	C₂³×C₁₃₇	—	4	8	no	—
148	C₂³×C₁₃₇	C₂²×D₄	1	4	yes	—
149	C₂³×C₁₃₇	C₂²×D₄	1	2	yes	—
150	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
151	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
152	C₂³×C₁₃₇	C₂×#41	1	4	yes	—
153	C₂³×C₁₃₇	2₋¹⁺⁴	1	4	yes	—
154	C₂³×C₁₃₇	C₂⁵	1	1	yes	characteristic
155	Q₈×C₁₃₇	—	4	16	no	—
156	C₂×C₄×C₁₃₇	—	2	8	no	—
157	C₂×C₄×C₁₃₇	—	2	16	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	4	no	—
162	C₂×C₄×C₁₃₇	—	2	32	no	—
163	C₂×C₄×C₁₃₇	—	2	4	no	—
164	C₂×C₄×C₁₃₇	—	2	4	no	—
165	C₂×C₄×C₁₃₇	—	2	4	no	—
166	C₂×C₄×C₁₃₇	—	2	4	no	—
167	C₂×C₄×C₁₃₇	—	2	4	no	—
168	C₂×C₄×C₁₃₇	—	2	4	no	—
169	C₂×C₄×C₁₃₇	—	2	8	no	—
170	C₂×C₄×C₁₃₇	—	2	8	no	—
171	C₂×C₄×C₁₃₇	—	2	4	no	—
172	C₂×C₄×C₁₃₇	—	2	4	no	—
173	C₂×C₄×C₁₃₇	—	2	8	no	—
174	C₂×C₄×C₁₃₇	—	2	4	no	—
175	C₂×C₄×C₁₃₇	—	4	8	no	—
176	C₂×C₄×C₁₃₇	—	4	8	no	—
177	C₂×C₄×C₁₃₇	—	4	8	no	—
178	C₂×C₄×C₁₃₇	—	4	8	no	—
179	C₂×C₄×C₁₃₇	—	4	8	no	—
180	C₂×C₄×C₁₃₇	#123	1	16	yes	—
181	C₂×C₄×C₁₃₇	C₂²×D₄	1	4	yes	—
182	C₂×C₄×C₁₃₇	C₂²×D₄	1	4	yes	—
183	C₂×C₄×C₁₃₇	C₂×#41	1	8	yes	—
184	C₂×C₄×C₁₃₇	C₂×#41	1	4	yes	—
185	C₂×C₄×C₁₃₇	C₂×#41	1	4	yes	—
186	C₂²×C₁₃₇	—	2	4	no	—
187	C₂²×C₁₃₇	—	2	4	no	—
188	C₂²×C₁₃₇	—	2	4	no	—
189	C₂²×C₁₃₇	—	4	4	no	—
190	C₂²×C₁₃₇	—	4	4	no	—
191	C₂²×C₁₃₇	—	4	16	no	—
192	C₂²×C₁₃₇	C₂×#123	1	4	yes	—
193	C₂²×C₁₃₇	#532	1	4	yes	—
194	C₂²×C₁₃₇	#536	1	4	yes	—
195	C₂²×C₁₃₇	#552	1	8	yes	—
196	C₂²×C₁₃₇	#556	1	8	yes	—
197	C₂²×C₁₃₇	C₂³×D₄	1	1	yes	characteristic
198	C₂²×C₁₃₇	C₂²×#41	1	1	yes	characteristic
199	C₂²×C₁₃₇	C₂²×#41	1	1	yes	characteristic
200	C₂²×C₁₃₇	C₂²×#41	1	2	yes	—
201	C₂²×C₁₃₇	C₂×2₋¹⁺⁴	1	2	yes	—
202	C₄×C₁₃₇	—	2	4	no	—
203	C₄×C₁₃₇	—	2	8	no	—
204	C₄×C₁₃₇	—	4	4	no	—
205	C₄×C₁₃₇	—	4	4	no	—
206	C₄×C₁₃₇	—	4	4	no	—
207	C₄×C₁₃₇	—	4	4	no	—
208	C₄×C₁₃₇	—	4	4	no	—
209	C₄×C₁₃₇	C₂×#123	1	8	yes	—
210	C₂×C₁₃₇	—	4	4	no	—
211	C₂×C₁₃₇	#2499	1	8	yes	direct product factor
212	C₂×C₁₃₇	C₂²×#123	1	1	yes	characteristic
213	C₂×C₁₃₇	C₂×#532	1	1	yes	characteristic
214	C₂×C₁₃₇	C₂×#536	1	1	yes	characteristic
215	C₂×C₁₃₇	C₂×#552	1	2	yes	—
216	C₂×C₁₃₇	C₂×#556	1	2	yes	—
217	C₂×#2499	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₁₃₇	C₂×#2499	1	1	yes	characteristic, direct product factor, Sylow
219	C₂²×C₂²⋊Q₈	C₂×C₁₃₇	1	1	yes	characteristic
220	C₂²×#117	C₂×C₁₃₇	1	1	yes	characteristic
221	#2499	C₂×C₁₃₇	1	16	yes	direct product factor
222	C₂×#397	C₂×C₁₃₇	1	4	yes	—
223	C₂×#391	C₂×C₁₃₇	1	1	yes	characteristic, complemented
224	C₂×#391	C₂×C₁₃₇	1	1	yes	characteristic, complemented
225	C₂×#387	C₂×C₁₃₇	1	4	yes	complemented
226	C₂×#384	C₂×C₁₃₇	1	1	yes	characteristic, complemented
227	C₂×#382	C₂×C₁₃₇	1	1	yes	characteristic, complemented
228	C₂×C₄×C₂²⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic
229	C₂³×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
230	C₂⁴×C₄	C₂²×C₁₃₇	1	1	yes	characteristic
231	C₂×C₂²⋊Q₈	—	2	8	no	—
232	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	8	yes	—
233	C₂×#117	—	2	8	no	—
234	C₂×#117	C₂²×C₁₃₇	1	8	yes	—
235	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	4	yes	—
236	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
238	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
240	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
241	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
242	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
243	C₂²×C₄²	C₂²×C₁₃₇	1	2	yes	—
244	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
245	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
246	#397	C₂²×C₁₃₇	1	32	yes	—
247	#391	C₂²×C₁₃₇	1	8	yes	complemented
248	#391	C₂²×C₁₃₇	1	8	yes	complemented
249	#387	C₂²×C₁₃₇	1	32	yes	complemented
250	#384	C₂²×C₁₃₇	1	8	yes	complemented
251	#382	C₂²×C₁₃₇	1	8	yes	complemented
252	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	8	yes	—
253	C₂×#95	C₂²×C₁₃₇	1	4	yes	—
254	C₂×#95	C₂²×C₁₃₇	1	4	yes	—
255	C₂×#95	C₂²×C₁₃₇	1	4	yes	—
256	C₂×#95	C₂²×C₁₃₇	1	2	yes	—
257	C₂⁵	C₂³×C₁₃₇	1	1	yes	characteristic
258	C₂²×Q₈	—	2	4	no	—
259	C₂²×Q₈	—	2	4	no	—
260	C₂²×Q₈	—	2	4	no	—
261	C₂²×Q₈	C₂³×C₁₃₇	1	4	yes	—
262	C₂³×C₄	—	2	4	no	—
263	C₂³×C₄	—	2	4	no	—
264	C₂³×C₄	D₄×C₁₃₇	1	8	yes	—
265	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
266	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
267	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
268	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
269	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
270	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
271	C₂³×C₄	C₂³×C₁₃₇	1	4	yes	—
272	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
273	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
274	C₂²⋊Q₈	—	2	32	no	—
275	#117	—	2	32	no	—
276	C₂×C₄⋊C₄	—	2	4	no	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	4	no	—
279	C₂×C₄⋊C₄	—	2	8	no	—
280	C₂×C₄⋊C₄	—	2	16	no	—
281	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	8	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	16	yes	—
286	C₂×C₂²⋊C₄	—	2	8	no	—
287	C₂×C₂²⋊C₄	—	2	8	no	—
288	C₂×C₂²⋊C₄	—	2	8	no	—
289	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
292	C₂×C₄²	—	2	8	no	—
293	C₂×C₄²	—	2	4	no	—
294	C₂×C₄²	—	2	4	no	—
295	C₂×C₄²	C₂³×C₁₃₇	1	8	yes	—
296	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
297	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
298	#95	C₂³×C₁₃₇	1	8	yes	—
299	#95	C₂³×C₁₃₇	1	16	yes	—
300	#95	C₂³×C₁₃₇	1	16	yes	—
301	#95	C₂³×C₁₃₇	1	16	yes	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	—	2	2	no	—
304	C₂⁴	—	2	2	no	—
305	C₂⁴	—	2	4	no	—
306	C₂⁴	C₂×D₄×C₁₃₇	1	4	yes	—
307	C₂⁴	C₂⁴×C₁₃₇	1	2	yes	—
308	C₂⁴	C₂⁴×C₁₃₇	1	1	yes	characteristic
309	C₂×Q₈	—	2	8	no	—
310	C₂×Q₈	—	2	8	no	—
311	C₂×Q₈	—	2	8	no	—
312	C₂×Q₈	—	4	16	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	32	no	—
318	C₂²×C₄	—	2	8	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
333	C₂²×C₄	C₂×D₄×C₁₃₇	1	16	yes	—
334	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
335	C₂²×C₄	#41×C₁₃₇	1	8	yes	—
336	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
337	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
338	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
339	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
340	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
341	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
342	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
343	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
344	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
345	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	8	no	—
348	C₄⋊C₄	—	2	8	no	—
349	C₄⋊C₄	—	2	16	no	—
350	C₄⋊C₄	—	2	32	no	—
351	C₂²⋊C₄	—	2	16	no	—
352	C₂²⋊C₄	—	2	16	no	—
353	C₂²⋊C₄	—	2	16	no	—
354	C₄²	—	2	16	no	—
355	C₄²	—	2	8	no	—
356	C₄²	—	2	8	no	—
357	C₂³	—	2	8	no	—
358	C₂³	—	2	8	no	—
359	C₂³	—	2	8	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	4	8	no	—
365	C₂³	—	4	8	no	—
366	C₂³	C₂²×D₄×C₁₃₇	1	4	yes	—
367	C₂³	C₂²×D₄×C₁₃₇	1	2	yes	—
368	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
369	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
370	C₂³	C₂×#41×C₁₃₇	1	4	yes	—
371	C₂³	2₋¹⁺⁴×C₁₃₇	1	4	yes	—
372	C₂³	C₂⁵×C₁₃₇	1	1	yes	characteristic
373	Q₈	—	4	16	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	16	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	32	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	8	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	4	8	no	—
394	C₂×C₄	—	4	8	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	—	4	8	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	#123×C₁₃₇	1	16	yes	—
399	C₂×C₄	C₂²×D₄×C₁₃₇	1	4	yes	—
400	C₂×C₄	C₂²×D₄×C₁₃₇	1	4	yes	—
401	C₂×C₄	C₂×#41×C₁₃₇	1	8	yes	—
402	C₂×C₄	C₂×#41×C₁₃₇	1	4	yes	—
403	C₂×C₄	C₂×#41×C₁₃₇	1	4	yes	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	16	no	—
410	C₂²	C₂×#123×C₁₃₇	1	4	yes	—
411	C₂²	#532×C₁₃₇	1	4	yes	—
412	C₂²	#536×C₁₃₇	1	4	yes	—
413	C₂²	#552×C₁₃₇	1	8	yes	—
414	C₂²	#556×C₁₃₇	1	8	yes	—
415	C₂²	C₂³×D₄×C₁₃₇	1	1	yes	characteristic
416	C₂²	C₂²×#41×C₁₃₇	1	1	yes	characteristic
417	C₂²	C₂²×#41×C₁₃₇	1	1	yes	characteristic
418	C₂²	C₂²×#41×C₁₃₇	1	2	yes	—
419	C₂²	C₂×2₋¹⁺⁴×C₁₃₇	1	2	yes	—
420	C₄	—	2	4	no	—
421	C₄	—	2	8	no	—
422	C₄	—	4	4	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	4	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	4	no	—
427	C₄	C₂×#123×C₁₃₇	1	8	yes	—
428	C₂	—	4	4	no	—
429	C₂	#2499×C₁₃₇	1	8	yes	direct product factor
430	C₂	C₂²×#123×C₁₃₇	1	1	yes	characteristic
431	C₂	C₂×#532×C₁₃₇	1	1	yes	characteristic
432	C₂	C₂×#536×C₁₃₇	1	1	yes	characteristic
433	C₂	C₂×#552×C₁₃₇	1	2	yes	—
434	C₂	C₂×#556×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₇
prime radical	C₂⁵×C₁₃₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. #2499×C₁₃₇	C₂	direct (N × H)
5. C₂×#391×C₁₃₇	C₂	semidirect
6. C₂×#391×C₁₃₇	C₂	semidirect
7. C₂×#387×C₁₃₇	C₂	semidirect
8. C₂×#384×C₁₃₇	C₂	semidirect
9. C₂×#382×C₁₃₇	C₂	semidirect
29. #391×C₁₃₇	C₂²	semidirect
30. #391×C₁₃₇	C₂²	semidirect
31. #387×C₁₃₇	C₂²	semidirect
32. #384×C₁₃₇	C₂²	semidirect
33. #382×C₁₃₇	C₂²	semidirect
211. C₂×C₁₃₇	#2499	direct (N × H)
217. C₂×#2499	C₁₃₇	direct (N × H)
218. C₁₃₇	C₂×#2499	direct (N × H)
221. #2499	C₂×C₁₃₇	direct (N × H)
223. C₂×#391	C₂×C₁₃₇	semidirect
224. C₂×#391	C₂×C₁₃₇	semidirect
225. C₂×#387	C₂×C₁₃₇	semidirect
226. C₂×#384	C₂×C₁₃₇	semidirect
227. C₂×#382	C₂×C₁₃₇	semidirect
247. #391	C₂²×C₁₃₇	semidirect
248. #391	C₂²×C₁₃₇	semidirect
249. #387	C₂²×C₁₃₇	semidirect
250. #384	C₂²×C₁₃₇	semidirect
251. #382	C₂²×C₁₃₇	semidirect
429. C₂	#2499×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×C₂²⋊Q₈×C₁₃₇	2
C₂²×#117×C₁₃₇	2
#2499×C₁₃₇	2
C₂×#397×C₁₃₇	2
C₂×#391×C₁₃₇	2
C₂×#387×C₁₃₇	2
C₂×#384×C₁₃₇	2
C₂×#382×C₁₃₇	2
C₂×C₄×C₂²⋊C₄×C₁₃₇	2
C₂×#2499	137

Subgroups — C2×#2499×C137 #46884176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2499×C₁₃₇ #46884176