Subgroups — C₁₃₇×#36716 #46886102

Order 35072.

2406 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#538×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊Q₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2849×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#2700×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	#2698×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#2681×C₁₃₇	C₂	1	4	yes	maximal, complemented
7	#2680×C₁₃₇	C₂	1	4	yes	maximal, complemented
8	#2622×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#2591×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#2583×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#2579×C₁₃₇	C₂	1	2	yes	maximal, complemented
12	#2504×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#2502×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#2409×C₁₃₇	C₂	1	2	yes	maximal, complemented
15	#2312×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃₇	C₂²	1	1	yes	characteristic
18	#538×C₁₃₇	—	2	8	no	—
19	C₂×#126×C₁₃₇	C₂²	1	2	yes	—
20	C₂×#124×C₁₃₇	C₂²	1	2	yes	—
21	C₂×#123×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₇	C₂²	1	4	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₇	—	2	8	no	—
24	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	4	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	4	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	4	yes	complemented
28	C₂×#121×C₁₃₇	C₂²	1	1	yes	characteristic
29	C₂×#121×C₁₃₇	C₂²	1	2	yes	—
30	C₂×#120×C₁₃₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
32	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
37	#400×C₁₃₇	C₂²	1	2	yes	complemented
38	#398×C₁₃₇	C₂²	1	4	yes	complemented
39	#398×C₁₃₇	C₂²	1	2	yes	complemented
40	#398×C₁₃₇	C₂²	1	4	yes	complemented
41	#397×C₁₃₇	C₂²	1	4	yes	—
42	#397×C₁₃₇	C₂²	1	4	yes	—
43	#397×C₁₃₇	C₂²	1	4	yes	complemented
44	#396×C₁₃₇	C₂²	1	4	yes	complemented
45	#395×C₁₃₇	C₂²	1	2	yes	complemented
46	#395×C₁₃₇	C₂²	1	4	yes	complemented
47	#394×C₁₃₇	C₂²	1	4	yes	—
48	#394×C₁₃₇	C₂²	1	4	yes	—
49	#394×C₁₃₇	C₂²	1	2	yes	complemented
50	#393×C₁₃₇	C₂²	1	4	yes	complemented
51	#391×C₁₃₇	C₂²	1	4	yes	complemented
52	#391×C₁₃₇	C₂²	1	2	yes	complemented
53	#390×C₁₃₇	C₂²	1	2	yes	complemented
54	#389×C₁₃₇	C₂²	1	4	yes	complemented
55	#388×C₁₃₇	C₂²	1	4	yes	—
56	#388×C₁₃₇	C₂²	1	4	yes	—
57	#388×C₁₃₇	C₂²	1	4	yes	complemented
58	#387×C₁₃₇	C₂²	1	4	yes	complemented
59	#386×C₁₃₇	C₂²	1	2	yes	—
60	#386×C₁₃₇	C₂²	1	2	yes	—
61	#386×C₁₃₇	C₂²	1	2	yes	—
62	#386×C₁₃₇	C₂²	1	4	yes	—
63	#386×C₁₃₇	C₂²	1	2	yes	—
64	#385×C₁₃₇	C₂²	1	2	yes	—
65	#385×C₁₃₇	C₂²	1	2	yes	—
66	#385×C₁₃₇	C₂²	1	2	yes	—
67	#385×C₁₃₇	C₂²	1	4	yes	—
68	#385×C₁₃₇	C₂²	1	2	yes	—
69	#385×C₁₃₇	C₂²	1	4	yes	complemented
70	#384×C₁₃₇	C₂²	1	2	yes	complemented
71	#382×C₁₃₇	C₂²	1	2	yes	complemented
72	#381×C₁₃₇	C₂²	1	4	yes	—
73	#380×C₁₃₇	C₂²	1	2	yes	—
74	#379×C₁₃₇	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
77	C₂⁵×C₁₃₇	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₃₇	—	2	4	no	—
79	C₂²×Q₈×C₁₃₇	—	4	4	no	—
80	C₂²×Q₈×C₁₃₇	C₂³	1	4	yes	—
81	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
83	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
84	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₃₇	—	2	4	no	—
87	C₂³×C₄×C₁₃₇	—	4	4	no	—
88	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃₇	C₂³	1	4	yes	—
90	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
96	#126×C₁₃₇	—	2	8	no	—
97	#124×C₁₃₇	—	2	8	no	—
98	#123×C₁₃₇	—	2	8	no	—
99	#123×C₁₃₇	—	4	8	no	—
100	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
101	C₂²⋊Q₈×C₁₃₇	—	2	16	no	—
102	C₂²⋊Q₈×C₁₃₇	—	2	16	no	—
103	C₂²⋊Q₈×C₁₃₇	—	4	8	no	—
104	#121×C₁₃₇	—	2	4	no	—
105	#121×C₁₃₇	—	2	8	no	—
106	#120×C₁₃₇	—	2	8	no	—
107	C₄×D₄×C₁₃₇	—	2	8	no	—
108	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
109	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
110	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
111	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
126	C₂×C₂²⋊C₄×C₁₃₇	D₄	1	8	yes	—
127	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
143	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
146	#95×C₁₃₇	C₂³	1	2	yes	—
147	#95×C₁₃₇	C₂³	1	2	yes	—
148	#95×C₁₃₇	C₂³	1	4	yes	—
149	#95×C₁₃₇	C₂³	1	4	yes	—
150	#95×C₁₃₇	C₂³	1	4	yes	—
151	#95×C₁₃₇	C₂³	1	4	yes	—
152	#95×C₁₃₇	C₂³	1	4	yes	—
153	#95×C₁₃₇	C₂³	1	4	yes	—
154	#95×C₁₃₇	C₂³	1	4	yes	—
155	#95×C₁₃₇	C₂³	1	4	yes	—
156	#95×C₁₃₇	C₂³	1	4	yes	—
157	C₂⁴×C₁₃₇	—	2	4	no	—
158	C₂⁴×C₁₃₇	—	4	2	no	—
159	C₂⁴×C₁₃₇	—	4	2	no	—
160	C₂⁴×C₁₃₇	C₂×D₄	1	4	yes	—
161	C₂⁴×C₁₃₇	C₂⁴	1	2	yes	—
162	C₂⁴×C₁₃₇	C₂⁴	1	2	yes	—
163	C₂⁴×C₁₃₇	C₂⁴	1	1	yes	characteristic
164	C₂×Q₈×C₁₃₇	—	2	8	no	—
165	C₂×Q₈×C₁₃₇	—	2	2	no	—
166	C₂×Q₈×C₁₃₇	—	2	8	no	—
167	C₂×Q₈×C₁₃₇	—	4	4	no	—
168	C₂×Q₈×C₁₃₇	—	4	2	no	—
169	C₂×Q₈×C₁₃₇	—	4	16	no	—
170	C₂×D₄×C₁₃₇	—	2	4	no	—
171	C₂×D₄×C₁₃₇	—	2	8	no	—
172	C₂×D₄×C₁₃₇	—	2	4	no	—
173	C₂×D₄×C₁₃₇	—	2	4	no	—
174	C₂×D₄×C₁₃₇	—	2	2	no	—
175	C₂×D₄×C₁₃₇	—	4	4	no	—
176	C₂×D₄×C₁₃₇	—	4	2	no	—
177	C₂×D₄×C₁₃₇	—	4	4	no	—
178	C₂²×C₄×C₁₃₇	—	2	2	no	—
179	C₂²×C₄×C₁₃₇	—	2	4	no	—
180	C₂²×C₄×C₁₃₇	—	2	2	no	—
181	C₂²×C₄×C₁₃₇	—	2	2	no	—
182	C₂²×C₄×C₁₃₇	—	2	2	no	—
183	C₂²×C₄×C₁₃₇	—	2	8	no	—
184	C₂²×C₄×C₁₃₇	—	2	8	no	—
185	C₂²×C₄×C₁₃₇	—	2	4	no	—
186	C₂²×C₄×C₁₃₇	—	4	4	no	—
187	C₂²×C₄×C₁₃₇	—	4	2	no	—
188	C₂²×C₄×C₁₃₇	—	4	2	no	—
189	C₂²×C₄×C₁₃₇	—	4	2	no	—
190	C₂²×C₄×C₁₃₇	—	4	2	no	—
191	C₂²×C₄×C₁₃₇	—	4	2	no	—
192	C₂²×C₄×C₁₃₇	—	4	4	no	—
193	C₂²×C₄×C₁₃₇	—	4	16	no	—
194	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
195	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
196	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
208	C₄⋊C₄×C₁₃₇	—	2	4	no	—
209	C₄⋊C₄×C₁₃₇	—	2	4	no	—
210	C₄⋊C₄×C₁₃₇	—	2	8	no	—
211	C₄⋊C₄×C₁₃₇	—	2	4	no	—
212	C₄⋊C₄×C₁₃₇	—	2	4	no	—
213	C₄⋊C₄×C₁₃₇	—	2	4	no	—
214	C₄⋊C₄×C₁₃₇	—	2	4	no	—
215	C₄⋊C₄×C₁₃₇	—	2	2	no	—
216	C₄⋊C₄×C₁₃₇	—	2	2	no	—
217	C₄⋊C₄×C₁₃₇	—	2	8	no	—
218	C₄⋊C₄×C₁₃₇	—	4	4	no	—
219	C₄⋊C₄×C₁₃₇	—	4	4	no	—
220	C₄⋊C₄×C₁₃₇	—	4	4	no	—
221	C₄⋊C₄×C₁₃₇	—	4	4	no	—
222	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
223	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
224	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
225	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
226	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
227	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
228	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
229	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
230	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
231	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
232	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
233	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
234	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
235	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
236	C₂²⋊C₄×C₁₃₇	C₂×D₄	1	8	yes	—
237	C₂²⋊C₄×C₁₃₇	C₂×D₄	1	8	yes	—
238	C₄²×C₁₃₇	—	2	4	no	—
239	C₄²×C₁₃₇	—	4	2	no	—
240	C₄²×C₁₃₇	—	4	2	no	—
241	C₂³×C₁₃₇	—	2	2	no	—
242	C₂³×C₁₃₇	—	2	2	no	—
243	C₂³×C₁₃₇	—	2	8	no	—
244	C₂³×C₁₃₇	—	2	4	no	—
245	C₂³×C₁₃₇	—	2	4	no	—
246	C₂³×C₁₃₇	—	2	4	no	—
247	C₂³×C₁₃₇	—	2	2	no	—
248	C₂³×C₁₃₇	—	2	4	no	—
249	C₂³×C₁₃₇	—	2	4	no	—
250	C₂³×C₁₃₇	—	2	4	no	—
251	C₂³×C₁₃₇	—	4	4	no	—
252	C₂³×C₁₃₇	—	4	4	no	—
253	C₂³×C₁₃₇	—	4	16	no	—
254	C₂³×C₁₃₇	C₂²×D₄	1	4	yes	—
255	C₂³×C₁₃₇	C₂²×D₄	1	2	yes	—
256	C₂³×C₁₃₇	2₋¹⁺⁴	1	4	yes	—
257	C₂³×C₁₃₇	C₂⁵	1	1	yes	characteristic
258	Q₈×C₁₃₇	—	4	16	no	—
259	Q₈×C₁₃₇	—	8	2	no	—
260	D₄×C₁₃₇	—	4	8	no	—
261	D₄×C₁₃₇	—	8	2	no	—
262	D₄×C₁₃₇	—	8	4	no	—
263	D₄×C₁₃₇	—	8	4	no	—
264	C₂×C₄×C₁₃₇	—	2	8	no	—
265	C₂×C₄×C₁₃₇	—	2	2	no	—
266	C₂×C₄×C₁₃₇	—	2	4	no	—
267	C₂×C₄×C₁₃₇	—	2	2	no	—
268	C₂×C₄×C₁₃₇	—	2	2	no	—
269	C₂×C₄×C₁₃₇	—	2	2	no	—
270	C₂×C₄×C₁₃₇	—	2	2	no	—
271	C₂×C₄×C₁₃₇	—	2	2	no	—
272	C₂×C₄×C₁₃₇	—	2	2	no	—
273	C₂×C₄×C₁₃₇	—	2	2	no	—
274	C₂×C₄×C₁₃₇	—	2	2	no	—
275	C₂×C₄×C₁₃₇	—	2	2	no	—
276	C₂×C₄×C₁₃₇	—	2	4	no	—
277	C₂×C₄×C₁₃₇	—	2	4	no	—
278	C₂×C₄×C₁₃₇	—	2	4	no	—
279	C₂×C₄×C₁₃₇	—	2	4	no	—
280	C₂×C₄×C₁₃₇	—	2	4	no	—
281	C₂×C₄×C₁₃₇	—	2	4	no	—
282	C₂×C₄×C₁₃₇	—	2	4	no	—
283	C₂×C₄×C₁₃₇	—	2	4	no	—
284	C₂×C₄×C₁₃₇	—	2	4	no	—
285	C₂×C₄×C₁₃₇	—	2	4	no	—
286	C₂×C₄×C₁₃₇	—	2	4	no	—
287	C₂×C₄×C₁₃₇	—	2	4	no	—
288	C₂×C₄×C₁₃₇	—	4	4	no	—
289	C₂×C₄×C₁₃₇	—	4	4	no	—
290	C₂×C₄×C₁₃₇	—	4	16	no	—
291	C₂×C₄×C₁₃₇	—	4	4	no	—
292	C₂×C₄×C₁₃₇	—	4	4	no	—
293	C₂×C₄×C₁₃₇	—	4	4	no	—
294	C₂×C₄×C₁₃₇	—	8	4	no	—
295	C₂×C₄×C₁₃₇	C₂²×D₄	1	4	yes	—
296	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
297	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
298	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	4	yes	—
299	C₂²×C₁₃₇	—	2	2	no	—
300	C₂²×C₁₃₇	—	2	2	no	—
301	C₂²×C₁₃₇	—	2	8	no	—
302	C₂²×C₁₃₇	—	2	4	no	—
303	C₂²×C₁₃₇	—	2	4	no	—
304	C₂²×C₁₃₇	—	2	4	no	—
305	C₂²×C₁₃₇	—	4	16	no	—
306	C₂²×C₁₃₇	—	4	8	no	—
307	C₂²×C₁₃₇	—	4	2	no	—
308	C₂²×C₁₃₇	—	4	2	no	—
309	C₂²×C₁₃₇	—	4	2	no	—
310	C₂²×C₁₃₇	—	4	8	no	—
311	C₂²×C₁₃₇	#536	1	4	yes	—
312	C₂²×C₁₃₇	C₂³×D₄	1	1	yes	characteristic
313	C₂²×C₁₃₇	C₂×H(5,𝔽₂)	1	2	yes	—
314	C₂²×C₁₃₇	C₂×2₋¹⁺⁴	1	2	yes	—
315	C₂²×C₁₃₇	#585	1	2	yes	—
316	C₄×C₁₃₇	—	2	4	no	—
317	C₄×C₁₃₇	—	2	4	no	—
318	C₄×C₁₃₇	—	2	2	no	—
319	C₄×C₁₃₇	—	2	2	no	—
320	C₄×C₁₃₇	—	4	2	no	—
321	C₄×C₁₃₇	—	4	2	no	—
322	C₄×C₁₃₇	—	4	2	no	—
323	C₄×C₁₃₇	—	4	2	no	—
324	C₄×C₁₃₇	—	4	2	no	—
325	C₄×C₁₃₇	—	4	2	no	—
326	C₄×C₁₃₇	—	4	4	no	—
327	C₄×C₁₃₇	—	4	4	no	—
328	C₂×C₁₃₇	—	2	4	no	—
329	C₂×C₁₃₇	—	4	4	no	—
330	C₂×C₁₃₇	—	8	2	no	—
331	C₂×C₁₃₇	C₂×#536	1	1	yes	characteristic
332	C₂×C₁₃₇	#3484	1	1	yes	characteristic
333	C₂×C₁₃₇	#3485	1	1	yes	characteristic
334	C₂×C₁₃₇	#3541	1	4	yes	—
335	#36716	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₁₃₇	#36716	1	1	yes	characteristic, direct product factor, Sylow
337	C₂×#538	C₂×C₁₃₇	1	1	yes	characteristic
338	C₂²×C₂²⋊Q₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
339	#2849	C₂×C₁₃₇	1	2	yes	complemented
340	#2700	C₂×C₁₃₇	1	4	yes	complemented
341	#2698	C₂×C₁₃₇	1	4	yes	complemented
342	#2681	C₂×C₁₃₇	1	4	yes	complemented
343	#2680	C₂×C₁₃₇	1	4	yes	complemented
344	#2622	C₂×C₁₃₇	1	2	yes	complemented
345	#2591	C₂×C₁₃₇	1	1	yes	characteristic, complemented
346	#2583	C₂×C₁₃₇	1	1	yes	characteristic, complemented
347	#2579	C₂×C₁₃₇	1	2	yes	complemented
348	#2504	C₂×C₁₃₇	1	1	yes	characteristic, complemented
349	#2502	C₂×C₁₃₇	1	1	yes	characteristic, complemented
350	#2409	C₂×C₁₃₇	1	2	yes	complemented
351	#2312	C₂×C₁₃₇	1	1	yes	characteristic, complemented
352	C₂³×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
353	C₂⁴×C₄	C₂²×C₁₃₇	1	1	yes	characteristic
354	#538	—	2	8	no	—
355	C₂×#126	C₂²×C₁₃₇	1	2	yes	—
356	C₂×#124	C₂²×C₁₃₇	1	2	yes	—
357	C₂×#123	C₂²×C₁₃₇	1	2	yes	—
358	C₂×#123	C₂²×C₁₃₇	1	4	yes	—
359	C₂×C₂²⋊Q₈	—	2	8	no	—
360	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
361	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	4	yes	—
362	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	4	yes	—
363	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	4	yes	complemented
364	C₂×#121	C₂²×C₁₃₇	1	1	yes	characteristic
365	C₂×#121	C₂²×C₁₃₇	1	2	yes	—
366	C₂×#120	C₂²×C₁₃₇	1	2	yes	—
367	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
368	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
369	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
370	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
371	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
372	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
373	#400	C₂²×C₁₃₇	1	2	yes	complemented
374	#398	C₂²×C₁₃₇	1	4	yes	complemented
375	#398	C₂²×C₁₃₇	1	2	yes	complemented
376	#398	C₂²×C₁₃₇	1	4	yes	complemented
377	#397	C₂²×C₁₃₇	1	4	yes	—
378	#397	C₂²×C₁₃₇	1	4	yes	—
379	#397	C₂²×C₁₃₇	1	4	yes	complemented
380	#396	C₂²×C₁₃₇	1	4	yes	complemented
381	#395	C₂²×C₁₃₇	1	2	yes	complemented
382	#395	C₂²×C₁₃₇	1	4	yes	complemented
383	#394	C₂²×C₁₃₇	1	4	yes	—
384	#394	C₂²×C₁₃₇	1	4	yes	—
385	#394	C₂²×C₁₃₇	1	2	yes	complemented
386	#393	C₂²×C₁₃₇	1	4	yes	complemented
387	#391	C₂²×C₁₃₇	1	4	yes	complemented
388	#391	C₂²×C₁₃₇	1	2	yes	complemented
389	#390	C₂²×C₁₃₇	1	2	yes	complemented
390	#389	C₂²×C₁₃₇	1	4	yes	complemented
391	#388	C₂²×C₁₃₇	1	4	yes	—
392	#388	C₂²×C₁₃₇	1	4	yes	—
393	#388	C₂²×C₁₃₇	1	4	yes	complemented
394	#387	C₂²×C₁₃₇	1	4	yes	complemented
395	#386	C₂²×C₁₃₇	1	2	yes	—
396	#386	C₂²×C₁₃₇	1	2	yes	—
397	#386	C₂²×C₁₃₇	1	2	yes	—
398	#386	C₂²×C₁₃₇	1	4	yes	—
399	#386	C₂²×C₁₃₇	1	2	yes	—
400	#385	C₂²×C₁₃₇	1	2	yes	—
401	#385	C₂²×C₁₃₇	1	2	yes	—
402	#385	C₂²×C₁₃₇	1	2	yes	—
403	#385	C₂²×C₁₃₇	1	4	yes	—
404	#385	C₂²×C₁₃₇	1	2	yes	—
405	#385	C₂²×C₁₃₇	1	4	yes	complemented
406	#384	C₂²×C₁₃₇	1	2	yes	complemented
407	#382	C₂²×C₁₃₇	1	2	yes	complemented
408	#381	C₂²×C₁₃₇	1	4	yes	—
409	#380	C₂²×C₁₃₇	1	2	yes	—
410	#379	C₂²×C₁₃₇	1	2	yes	—
411	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
412	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
413	C₂⁵	C₂³×C₁₃₇	1	1	yes	characteristic
414	C₂²×Q₈	—	2	4	no	—
415	C₂²×Q₈	—	4	4	no	—
416	C₂²×Q₈	C₂³×C₁₃₇	1	4	yes	—
417	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
418	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
419	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
420	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
421	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
422	C₂³×C₄	—	2	4	no	—
423	C₂³×C₄	—	4	4	no	—
424	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₁₃₇	1	4	yes	—
426	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
430	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
432	#126	—	2	8	no	—
433	#124	—	2	8	no	—
434	#123	—	2	8	no	—
435	#123	—	4	8	no	—
436	C₂²⋊Q₈	—	2	4	no	—
437	C₂²⋊Q₈	—	2	16	no	—
438	C₂²⋊Q₈	—	2	16	no	—
439	C₂²⋊Q₈	—	4	8	no	—
440	#121	—	2	4	no	—
441	#121	—	2	8	no	—
442	#120	—	2	8	no	—
443	C₄×D₄	—	2	8	no	—
444	C₂×C₄⋊C₄	—	2	4	no	—
445	C₂×C₄⋊C₄	—	2	4	no	—
446	C₂×C₄⋊C₄	—	2	4	no	—
447	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
450	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
457	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
459	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
460	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
461	C₂×C₂²⋊C₄	—	2	4	no	—
462	C₂×C₂²⋊C₄	D₄×C₁₃₇	1	8	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
479	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
480	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
481	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
482	#95	C₂³×C₁₃₇	1	2	yes	—
483	#95	C₂³×C₁₃₇	1	2	yes	—
484	#95	C₂³×C₁₃₇	1	4	yes	—
485	#95	C₂³×C₁₃₇	1	4	yes	—
486	#95	C₂³×C₁₃₇	1	4	yes	—
487	#95	C₂³×C₁₃₇	1	4	yes	—
488	#95	C₂³×C₁₃₇	1	4	yes	—
489	#95	C₂³×C₁₃₇	1	4	yes	—
490	#95	C₂³×C₁₃₇	1	4	yes	—
491	#95	C₂³×C₁₃₇	1	4	yes	—
492	#95	C₂³×C₁₃₇	1	4	yes	—
493	C₂⁴	—	2	4	no	—
494	C₂⁴	—	4	2	no	—
495	C₂⁴	—	4	2	no	—
496	C₂⁴	C₂×D₄×C₁₃₇	1	4	yes	—
497	C₂⁴	C₂⁴×C₁₃₇	1	2	yes	—
498	C₂⁴	C₂⁴×C₁₃₇	1	2	yes	—
499	C₂⁴	C₂⁴×C₁₃₇	1	1	yes	characteristic
500	C₂×Q₈	—	2	8	no	—
501	C₂×Q₈	—	2	2	no	—
502	C₂×Q₈	—	2	8	no	—
503	C₂×Q₈	—	4	4	no	—
504	C₂×Q₈	—	4	2	no	—
505	C₂×Q₈	—	4	16	no	—
506	C₂×D₄	—	2	4	no	—
507	C₂×D₄	—	2	8	no	—
508	C₂×D₄	—	2	4	no	—
509	C₂×D₄	—	2	4	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	4	4	no	—
512	C₂×D₄	—	4	2	no	—
513	C₂×D₄	—	4	4	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	8	no	—
520	C₂²×C₄	—	2	8	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	4	4	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	—	4	2	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	4	2	no	—
528	C₂²×C₄	—	4	4	no	—
529	C₂²×C₄	—	4	16	no	—
530	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
531	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
532	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
534	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
535	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
537	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
539	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
541	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
542	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	8	no	—
547	C₄⋊C₄	—	2	4	no	—
548	C₄⋊C₄	—	2	4	no	—
549	C₄⋊C₄	—	2	4	no	—
550	C₄⋊C₄	—	2	4	no	—
551	C₄⋊C₄	—	2	2	no	—
552	C₄⋊C₄	—	2	2	no	—
553	C₄⋊C₄	—	2	8	no	—
554	C₄⋊C₄	—	4	4	no	—
555	C₄⋊C₄	—	4	4	no	—
556	C₄⋊C₄	—	4	4	no	—
557	C₄⋊C₄	—	4	4	no	—
558	C₂²⋊C₄	—	2	8	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	2	4	no	—
563	C₂²⋊C₄	—	2	4	no	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	4	no	—
566	C₂²⋊C₄	—	2	8	no	—
567	C₂²⋊C₄	—	4	4	no	—
568	C₂²⋊C₄	—	4	4	no	—
569	C₂²⋊C₄	—	4	4	no	—
570	C₂²⋊C₄	—	4	4	no	—
571	C₂²⋊C₄	—	4	4	no	—
572	C₂²⋊C₄	C₂×D₄×C₁₃₇	1	8	yes	—
573	C₂²⋊C₄	C₂×D₄×C₁₃₇	1	8	yes	—
574	C₄²	—	2	4	no	—
575	C₄²	—	4	2	no	—
576	C₄²	—	4	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	8	no	—
580	C₂³	—	2	4	no	—
581	C₂³	—	2	4	no	—
582	C₂³	—	2	4	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	4	no	—
585	C₂³	—	2	4	no	—
586	C₂³	—	2	4	no	—
587	C₂³	—	4	4	no	—
588	C₂³	—	4	4	no	—
589	C₂³	—	4	16	no	—
590	C₂³	C₂²×D₄×C₁₃₇	1	4	yes	—
591	C₂³	C₂²×D₄×C₁₃₇	1	2	yes	—
592	C₂³	2₋¹⁺⁴×C₁₃₇	1	4	yes	—
593	C₂³	C₂⁵×C₁₃₇	1	1	yes	characteristic
594	Q₈	—	4	16	no	—
595	Q₈	—	8	2	no	—
596	D₄	—	4	8	no	—
597	D₄	—	8	2	no	—
598	D₄	—	8	4	no	—
599	D₄	—	8	4	no	—
600	C₂×C₄	—	2	8	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	4	4	no	—
625	C₂×C₄	—	4	4	no	—
626	C₂×C₄	—	4	16	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	—	4	4	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	—	8	4	no	—
631	C₂×C₄	C₂²×D₄×C₁₃₇	1	4	yes	—
632	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
633	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
634	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	4	yes	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	8	no	—
638	C₂²	—	2	4	no	—
639	C₂²	—	2	4	no	—
640	C₂²	—	2	4	no	—
641	C₂²	—	4	16	no	—
642	C₂²	—	4	8	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	4	2	no	—
645	C₂²	—	4	2	no	—
646	C₂²	—	4	8	no	—
647	C₂²	#536×C₁₃₇	1	4	yes	—
648	C₂²	C₂³×D₄×C₁₃₇	1	1	yes	characteristic
649	C₂²	C₂×H(5,𝔽₂)×C₁₃₇	1	2	yes	—
650	C₂²	C₂×2₋¹⁺⁴×C₁₃₇	1	2	yes	—
651	C₂²	#585×C₁₃₇	1	2	yes	—
652	C₄	—	2	4	no	—
653	C₄	—	2	4	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	4	2	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	2	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	4	no	—
663	C₄	—	4	4	no	—
664	C₂	—	2	4	no	—
665	C₂	—	4	4	no	—
666	C₂	—	8	2	no	—
667	C₂	C₂×#536×C₁₃₇	1	1	yes	characteristic
668	C₂	#3484×C₁₃₇	1	1	yes	characteristic
669	C₂	#3485×C₁₃₇	1	1	yes	characteristic
670	C₂	#3541×C₁₃₇	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₇
prime radical	C₂×#538×C₁₃₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₂²⋊Q₈×C₁₃₇	C₂	semidirect
3. #2849×C₁₃₇	C₂	semidirect
4. #2700×C₁₃₇	C₂	semidirect
5. #2698×C₁₃₇	C₂	semidirect
6. #2681×C₁₃₇	C₂	semidirect
7. #2680×C₁₃₇	C₂	semidirect
8. #2622×C₁₃₇	C₂	semidirect
9. #2591×C₁₃₇	C₂	semidirect
10. #2583×C₁₃₇	C₂	semidirect
11. #2579×C₁₃₇	C₂	semidirect
12. #2504×C₁₃₇	C₂	semidirect
13. #2502×C₁₃₇	C₂	semidirect
14. #2409×C₁₃₇	C₂	semidirect
15. #2312×C₁₃₇	C₂	semidirect
27. C₂×C₂²⋊Q₈×C₁₃₇	C₂²	semidirect
37. #400×C₁₃₇	C₂²	semidirect
38. #398×C₁₃₇	C₂²	semidirect
39. #398×C₁₃₇	C₂²	semidirect
40. #398×C₁₃₇	C₂²	semidirect
43. #397×C₁₃₇	C₂²	semidirect
44. #396×C₁₃₇	C₂²	semidirect
45. #395×C₁₃₇	C₂²	semidirect
46. #395×C₁₃₇	C₂²	semidirect
49. #394×C₁₃₇	C₂²	semidirect
50. #393×C₁₃₇	C₂²	semidirect
51. #391×C₁₃₇	C₂²	semidirect
52. #391×C₁₃₇	C₂²	semidirect
53. #390×C₁₃₇	C₂²	semidirect
54. #389×C₁₃₇	C₂²	semidirect
57. #388×C₁₃₇	C₂²	semidirect
58. #387×C₁₃₇	C₂²	semidirect
69. #385×C₁₃₇	C₂²	semidirect
70. #384×C₁₃₇	C₂²	semidirect
71. #382×C₁₃₇	C₂²	semidirect
335. #36716	C₁₃₇	direct (N × H)
336. C₁₃₇	#36716	direct (N × H)
338. C₂²×C₂²⋊Q₈	C₂×C₁₃₇	semidirect
339. #2849	C₂×C₁₃₇	semidirect
340. #2700	C₂×C₁₃₇	semidirect
341. #2698	C₂×C₁₃₇	semidirect
342. #2681	C₂×C₁₃₇	semidirect
343. #2680	C₂×C₁₃₇	semidirect
344. #2622	C₂×C₁₃₇	semidirect
345. #2591	C₂×C₁₃₇	semidirect
346. #2583	C₂×C₁₃₇	semidirect
347. #2579	C₂×C₁₃₇	semidirect
348. #2504	C₂×C₁₃₇	semidirect
349. #2502	C₂×C₁₃₇	semidirect
350. #2409	C₂×C₁₃₇	semidirect
351. #2312	C₂×C₁₃₇	semidirect
363. C₂×C₂²⋊Q₈	C₂²×C₁₃₇	semidirect
373. #400	C₂²×C₁₃₇	semidirect
374. #398	C₂²×C₁₃₇	semidirect
375. #398	C₂²×C₁₃₇	semidirect
376. #398	C₂²×C₁₃₇	semidirect
379. #397	C₂²×C₁₃₇	semidirect
380. #396	C₂²×C₁₃₇	semidirect
381. #395	C₂²×C₁₃₇	semidirect
382. #395	C₂²×C₁₃₇	semidirect
385. #394	C₂²×C₁₃₇	semidirect
386. #393	C₂²×C₁₃₇	semidirect
387. #391	C₂²×C₁₃₇	semidirect
388. #391	C₂²×C₁₃₇	semidirect
389. #390	C₂²×C₁₃₇	semidirect
390. #389	C₂²×C₁₃₇	semidirect
393. #388	C₂²×C₁₃₇	semidirect
394. #387	C₂²×C₁₃₇	semidirect
405. #385	C₂²×C₁₃₇	semidirect
406. #384	C₂²×C₁₃₇	semidirect
407. #382	C₂²×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#538×C₁₃₇	2
C₂²×C₂²⋊Q₈×C₁₃₇	2
#2849×C₁₃₇	2
#2700×C₁₃₇	2
#2698×C₁₃₇	2
#2681×C₁₃₇	2
#2680×C₁₃₇	2
#2622×C₁₃₇	2
#2591×C₁₃₇	2
#2583×C₁₃₇	2
#2579×C₁₃₇	2
#2504×C₁₃₇	2
#2502×C₁₃₇	2
#2409×C₁₃₇	2
#2312×C₁₃₇	2
#36716	137

Subgroups — C137×#36716 #46886102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#36716 #46886102