Subgroups — C₁₃₇×#21703 #46871089

Order 35072.

1062 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#497×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#441×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#440×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×Q₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×SD₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic
6	#2327×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#2326×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1973×C₁₃₇	C₂	1	1	yes	maximal, characteristic
9	#1971×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1969×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1968×C₁₃₇	C₂	1	1	yes	maximal, characteristic
12	#1958×C₁₃₇	C₂	1	1	yes	maximal, characteristic
13	#1956×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#1847×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
15	#1726×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
26	#497×C₁₃₇	C₄	1	8	yes	complemented
27	#441×C₁₃₇	—	2	4	no	—
28	#440×C₁₃₇	—	2	4	no	—
29	C₄×Q₁₆×C₁₃₇	—	2	4	no	—
30	C₄×SD₁₆×C₁₃₇	—	2	4	no	—
31	C₂×#107×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₂×#107×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₂×#106×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₂×#106×C₁₃₇	C₂²	1	1	yes	characteristic
35	C₂×#103×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₂×#103×C₁₃₇	C₂²	1	1	yes	characteristic
37	C₂×#103×C₁₃₇	C₂²	1	1	yes	characteristic
38	C₂×#103×C₁₃₇	C₂²	1	1	yes	characteristic
39	C₂×#103×C₁₃₇	C₂²	1	1	yes	characteristic
40	C₂×#103×C₁₃₇	C₂²	1	1	yes	characteristic
41	C₂×#102×C₁₃₇	C₂²	1	1	yes	characteristic
42	C₂×#102×C₁₃₇	C₂²	1	1	yes	characteristic
43	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
44	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
45	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
49	#391×C₁₃₇	C₂²	1	1	yes	characteristic
50	#391×C₁₃₇	C₂²	1	1	yes	characteristic
51	#391×C₁₃₇	C₂²	1	1	yes	characteristic
52	#390×C₁₃₇	C₂²	1	1	yes	characteristic
53	#388×C₁₃₇	—	2	2	no	—
54	#387×C₁₃₇	—	2	2	no	—
55	#387×C₁₃₇	—	2	2	no	—
56	#385×C₁₃₇	—	2	2	no	—
57	#384×C₁₃₇	C₂²	1	1	yes	characteristic
58	#382×C₁₃₇	C₂²	1	1	yes	characteristic
59	#376×C₁₃₇	C₂²	1	1	yes	characteristic
60	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃₇	—	2	1	no	—
65	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
66	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
67	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
68	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
69	C₂×Q₁₆×C₁₃₇	C₂×C₄	1	4	yes	complemented
70	C₂×Q₁₆×C₁₃₇	C₂×C₄	1	4	yes	complemented
71	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
72	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
73	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
74	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
75	C₂×SD₁₆×C₁₃₇	C₂×C₄	1	4	yes	—
76	C₂×SD₁₆×C₁₃₇	C₂×C₄	1	4	yes	—
77	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
81	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
82	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	4	yes	complemented
83	#124×C₁₃₇	—	2	2	no	—
84	#124×C₁₃₇	C₂×C₄	1	4	yes	—
85	C₄×Q₈×C₁₃₇	—	2	2	no	—
86	C₄×Q₈×C₁₃₇	—	2	2	no	—
87	C₄×Q₈×C₁₃₇	—	2	2	no	—
88	C₄×Q₈×C₁₃₇	—	2	2	no	—
89	C₄×Q₈×C₁₃₇	—	2	2	no	—
90	C₄×Q₈×C₁₃₇	—	2	2	no	—
91	C₄×D₄×C₁₃₇	—	2	2	no	—
92	C₄×D₄×C₁₃₇	—	2	2	no	—
93	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
94	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
98	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
103	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
105	C₂×C₄²×C₁₃₇	—	2	1	no	—
106	C₂×C₄²×C₁₃₇	—	2	1	no	—
107	C₂×C₄²×C₁₃₇	—	2	1	no	—
108	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
111	#107×C₁₃₇	—	2	2	no	—
112	#107×C₁₃₇	—	2	2	no	—
113	#106×C₁₃₇	—	2	2	no	—
114	#106×C₁₃₇	—	2	2	no	—
115	#103×C₁₃₇	—	2	2	no	—
116	#103×C₁₃₇	—	2	2	no	—
117	#103×C₁₃₇	—	2	2	no	—
118	#103×C₁₃₇	—	2	2	no	—
119	#103×C₁₃₇	—	2	2	no	—
120	#103×C₁₃₇	—	2	2	no	—
121	#102×C₁₃₇	—	2	2	no	—
122	#102×C₁₃₇	—	2	2	no	—
123	#97×C₁₃₇	—	2	2	no	—
124	#97×C₁₃₇	C₂×C₄	1	4	yes	complemented
125	#97×C₁₃₇	D₄	1	4	yes	—
126	C₄×C₈×C₁₃₇	—	2	2	no	—
127	C₄×C₈×C₁₃₇	—	2	2	no	—
128	C₄×C₈×C₁₃₇	D₄	1	4	yes	—
129	#95×C₁₃₇	—	2	2	no	—
130	#95×C₁₃₇	—	2	2	no	—
131	#95×C₁₃₇	—	2	2	no	—
132	#95×C₁₃₇	—	2	2	no	—
133	#95×C₁₃₇	D₄	1	2	yes	—
134	#95×C₁₃₇	D₄	1	2	yes	—
135	C₂⁴×C₁₃₇	—	2	1	no	—
136	C₂×Q₈×C₁₃₇	—	2	1	no	—
137	C₂×Q₈×C₁₃₇	—	2	1	no	—
138	C₂×Q₈×C₁₃₇	—	2	1	no	—
139	C₂×Q₈×C₁₃₇	—	2	1	no	—
140	C₂×Q₈×C₁₃₇	—	2	1	no	—
141	C₂×Q₈×C₁₃₇	—	2	1	no	—
142	C₂×Q₈×C₁₃₇	—	2	1	no	—
143	C₂×Q₈×C₁₃₇	—	2	1	no	—
144	C₂×Q₈×C₁₃₇	—	2	1	no	—
145	C₂×Q₈×C₁₃₇	—	2	1	no	—
146	C₂×Q₈×C₁₃₇	—	2	1	no	—
147	C₂×Q₈×C₁₃₇	—	2	1	no	—
148	C₂×Q₈×C₁₃₇	—	2	1	no	—
149	C₂×Q₈×C₁₃₇	—	2	1	no	—
150	C₂×Q₈×C₁₃₇	—	2	1	no	—
151	C₂×Q₈×C₁₃₇	C₂²×C₄	1	2	yes	—
152	C₂×Q₈×C₁₃₇	C₂²×C₄	1	2	yes	—
153	C₂×Q₈×C₁₃₇	C₂²×C₄	1	2	yes	—
154	C₂×D₄×C₁₃₇	—	2	1	no	—
155	C₂×D₄×C₁₃₇	—	2	1	no	—
156	C₂×D₄×C₁₃₇	—	2	1	no	—
157	C₂×D₄×C₁₃₇	—	2	1	no	—
158	C₂×D₄×C₁₃₇	—	2	1	no	—
159	C₂×D₄×C₁₃₇	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₁₃₇	—	2	1	no	—
161	C₂²×C₄×C₁₃₇	—	2	1	no	—
162	C₂²×C₄×C₁₃₇	—	2	1	no	—
163	C₂²×C₄×C₁₃₇	—	2	1	no	—
164	C₂²×C₄×C₁₃₇	—	2	1	no	—
165	C₂²×C₄×C₁₃₇	—	2	1	no	—
166	C₂²×C₄×C₁₃₇	—	2	1	no	—
167	C₂²×C₄×C₁₃₇	—	4	2	no	—
168	C₂²×C₄×C₁₃₇	—	8	2	no	—
169	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
174	Q₁₆×C₁₃₇	—	2	8	no	—
175	Q₁₆×C₁₃₇	—	2	8	no	—
176	SD₁₆×C₁₃₇	—	2	8	no	—
177	SD₁₆×C₁₃₇	—	2	8	no	—
178	C₂×C₈×C₁₃₇	—	2	1	no	—
179	C₂×C₈×C₁₃₇	—	2	1	no	—
180	C₂×C₈×C₁₃₇	—	2	1	no	—
181	C₂×C₈×C₁₃₇	—	2	1	no	—
182	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
183	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
184	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
185	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
186	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
187	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
188	C₂×C₈×C₁₃₇	#41	1	2	yes	—
189	C₂×C₈×C₁₃₇	#41	1	2	yes	—
190	C₄⋊C₄×C₁₃₇	—	2	8	no	—
191	C₄⋊C₄×C₁₃₇	—	2	1	no	—
192	C₄⋊C₄×C₁₃₇	—	2	1	no	—
193	C₄⋊C₄×C₁₃₇	—	2	1	no	—
194	C₄⋊C₄×C₁₃₇	—	2	1	no	—
195	C₄⋊C₄×C₁₃₇	—	2	1	no	—
196	C₄⋊C₄×C₁₃₇	—	2	1	no	—
197	C₄⋊C₄×C₁₃₇	—	2	1	no	—
198	C₄⋊C₄×C₁₃₇	—	2	1	no	—
199	C₄⋊C₄×C₁₃₇	—	4	2	no	—
200	C₄⋊C₄×C₁₃₇	—	4	2	no	—
201	C₄⋊C₄×C₁₃₇	—	4	2	no	—
202	C₄⋊C₄×C₁₃₇	—	8	2	no	—
203	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
204	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
205	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
206	C₄²×C₁₃₇	—	2	1	no	—
207	C₄²×C₁₃₇	—	2	1	no	—
208	C₄²×C₁₃₇	—	4	2	no	—
209	C₄²×C₁₃₇	—	4	2	no	—
210	C₄²×C₁₃₇	—	4	2	no	—
211	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
212	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
213	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
214	C₄²×C₁₃₇	#41	1	2	yes	—
215	C₂³×C₁₃₇	—	2	2	no	—
216	C₂³×C₁₃₇	—	4	1	no	—
217	C₂³×C₁₃₇	—	4	1	no	—
218	C₂³×C₁₃₇	—	4	2	no	—
219	C₂³×C₁₃₇	—	4	2	no	—
220	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
221	Q₈×C₁₃₇	—	2	2	no	—
222	Q₈×C₁₃₇	—	2	2	no	—
223	Q₈×C₁₃₇	—	2	2	no	—
224	Q₈×C₁₃₇	—	2	2	no	—
225	Q₈×C₁₃₇	—	2	2	no	—
226	Q₈×C₁₃₇	—	2	2	no	—
227	Q₈×C₁₃₇	—	4	1	no	—
228	Q₈×C₁₃₇	—	4	1	no	—
229	Q₈×C₁₃₇	—	4	1	no	—
230	Q₈×C₁₃₇	—	4	1	no	—
231	Q₈×C₁₃₇	—	4	1	no	—
232	Q₈×C₁₃₇	—	4	1	no	—
233	D₄×C₁₃₇	—	2	2	no	—
234	D₄×C₁₃₇	—	2	2	no	—
235	D₄×C₁₃₇	—	4	1	no	—
236	D₄×C₁₃₇	—	4	1	no	—
237	C₂×C₄×C₁₃₇	—	2	2	no	—
238	C₂×C₄×C₁₃₇	—	2	2	no	—
239	C₂×C₄×C₁₃₇	—	2	2	no	—
240	C₂×C₄×C₁₃₇	—	2	2	no	—
241	C₂×C₄×C₁₃₇	—	2	2	no	—
242	C₂×C₄×C₁₃₇	—	2	2	no	—
243	C₂×C₄×C₁₃₇	—	2	2	no	—
244	C₂×C₄×C₁₃₇	—	2	2	no	—
245	C₂×C₄×C₁₃₇	—	2	2	no	—
246	C₂×C₄×C₁₃₇	—	2	2	no	—
247	C₂×C₄×C₁₃₇	—	4	1	no	—
248	C₂×C₄×C₁₃₇	—	4	1	no	—
249	C₂×C₄×C₁₃₇	—	4	1	no	—
250	C₂×C₄×C₁₃₇	—	4	1	no	—
251	C₂×C₄×C₁₃₇	—	4	1	no	—
252	C₂×C₄×C₁₃₇	—	4	1	no	—
253	C₂×C₄×C₁₃₇	—	4	1	no	—
254	C₂×C₄×C₁₃₇	—	4	1	no	—
255	C₂×C₄×C₁₃₇	—	4	1	no	—
256	C₂×C₄×C₁₃₇	—	4	1	no	—
257	C₂×C₄×C₁₃₇	—	4	2	no	—
258	C₂×C₄×C₁₃₇	—	4	2	no	—
259	C₂×C₄×C₁₃₇	—	4	2	no	—
260	C₂×C₄×C₁₃₇	—	4	2	no	—
261	C₂×C₄×C₁₃₇	—	8	4	no	—
262	C₂×C₄×C₁₃₇	C₄×D₄	1	4	yes	—
263	C₂×C₄×C₁₃₇	#127	1	2	yes	—
264	C₂×C₄×C₁₃₇	#127	1	2	yes	—
265	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
271	C₈×C₁₃₇	—	2	2	no	—
272	C₈×C₁₃₇	—	2	2	no	—
273	C₈×C₁₃₇	C₄×D₄	1	4	yes	—
274	C₈×C₁₃₇	C₄×D₄	1	4	yes	—
275	C₂²×C₁₃₇	—	4	2	no	—
276	C₂²×C₁₃₇	—	4	4	no	—
277	C₂²×C₁₃₇	—	8	1	no	—
278	C₂²×C₁₃₇	—	8	1	no	—
279	C₂²×C₁₃₇	—	8	2	no	—
280	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
281	C₂²×C₁₃₇	C₂×#127	1	1	yes	characteristic
282	C₂²×C₁₃₇	#532	1	1	yes	characteristic
283	C₂²×C₁₃₇	#577	1	2	yes	—
284	C₂²×C₁₃₇	#578	1	2	yes	—
285	C₄×C₁₃₇	—	2	2	no	—
286	C₄×C₁₃₇	—	2	2	no	—
287	C₄×C₁₃₇	—	2	4	no	—
288	C₄×C₁₃₇	—	4	2	no	—
289	C₄×C₁₃₇	—	4	2	no	—
290	C₄×C₁₃₇	—	4	2	no	—
291	C₄×C₁₃₇	—	4	2	no	—
292	C₄×C₁₃₇	—	8	1	no	—
293	C₄×C₁₃₇	—	8	1	no	—
294	C₄×C₁₃₇	—	8	1	no	—
295	C₄×C₁₃₇	—	8	1	no	—
296	C₄×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
297	C₄×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
298	C₄×C₁₃₇	#532	1	1	yes	characteristic
299	C₄×C₁₃₇	#532	1	1	yes	characteristic
300	C₂×C₁₃₇	—	8	2	no	—
301	C₂×C₁₃₇	C₄×#127	1	1	yes	characteristic
302	C₂×C₁₃₇	#2947	1	2	yes	—
303	C₂×C₁₃₇	#3154	1	1	yes	characteristic
304	C₂×C₁₃₇	#3156	1	1	yes	characteristic
305	C₂×C₁₃₇	#3178	1	2	yes	—
306	#21703	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
307	C₁₃₇	#21703	1	1	yes	characteristic, direct product factor, Sylow
308	C₂×#497	C₂×C₁₃₇	1	1	yes	characteristic
309	C₂×#441	C₂×C₁₃₇	1	1	yes	characteristic, complemented
310	C₂×#440	C₂×C₁₃₇	1	1	yes	characteristic
311	C₂×C₄×Q₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
312	C₂×C₄×SD₁₆	C₂×C₁₃₇	1	1	yes	characteristic
313	#2327	C₂×C₁₃₇	1	1	yes	characteristic, complemented
314	#2326	C₂×C₁₃₇	1	1	yes	characteristic
315	#1973	C₂×C₁₃₇	1	1	yes	characteristic
316	#1971	C₂×C₁₃₇	1	1	yes	characteristic, complemented
317	#1969	C₂×C₁₃₇	1	1	yes	characteristic, complemented
318	#1968	C₂×C₁₃₇	1	1	yes	characteristic
319	#1958	C₂×C₁₃₇	1	1	yes	characteristic
320	#1956	C₂×C₁₃₇	1	1	yes	characteristic, complemented
321	#1847	C₂×C₁₃₇	1	1	yes	characteristic, complemented
322	#1726	C₂×C₁₃₇	1	1	yes	characteristic, complemented
323	C₂²×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
324	C₂²×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
325	C₂²×SD₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
326	C₂²×SD₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
327	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
328	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
329	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
330	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
331	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
332	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
333	#497	C₄×C₁₃₇	1	8	yes	complemented
334	#441	—	2	4	no	—
335	#440	—	2	4	no	—
336	C₄×Q₁₆	—	2	4	no	—
337	C₄×SD₁₆	—	2	4	no	—
338	C₂×#107	C₂²×C₁₃₇	1	1	yes	characteristic
339	C₂×#107	C₂²×C₁₃₇	1	1	yes	characteristic
340	C₂×#106	C₂²×C₁₃₇	1	1	yes	characteristic
341	C₂×#106	C₂²×C₁₃₇	1	1	yes	characteristic
342	C₂×#103	C₂²×C₁₃₇	1	1	yes	characteristic
343	C₂×#103	C₂²×C₁₃₇	1	1	yes	characteristic
344	C₂×#103	C₂²×C₁₃₇	1	1	yes	characteristic
345	C₂×#103	C₂²×C₁₃₇	1	1	yes	characteristic
346	C₂×#103	C₂²×C₁₃₇	1	1	yes	characteristic
347	C₂×#103	C₂²×C₁₃₇	1	1	yes	characteristic
348	C₂×#102	C₂²×C₁₃₇	1	1	yes	characteristic
349	C₂×#102	C₂²×C₁₃₇	1	1	yes	characteristic
350	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
351	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
352	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
353	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
354	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
355	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
356	#391	C₂²×C₁₃₇	1	1	yes	characteristic
357	#391	C₂²×C₁₃₇	1	1	yes	characteristic
358	#391	C₂²×C₁₃₇	1	1	yes	characteristic
359	#390	C₂²×C₁₃₇	1	1	yes	characteristic
360	#388	—	2	2	no	—
361	#387	—	2	2	no	—
362	#387	—	2	2	no	—
363	#385	—	2	2	no	—
364	#384	C₂²×C₁₃₇	1	1	yes	characteristic
365	#382	C₂²×C₁₃₇	1	1	yes	characteristic
366	#376	C₂²×C₁₃₇	1	1	yes	characteristic
367	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
368	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
369	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
370	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
371	C₂³×C₄	—	2	1	no	—
372	C₂×Q₁₆	—	2	2	no	—
373	C₂×Q₁₆	—	2	2	no	—
374	C₂×Q₁₆	—	2	2	no	—
375	C₂×Q₁₆	—	2	2	no	—
376	C₂×Q₁₆	C₂×C₄×C₁₃₇	1	4	yes	complemented
377	C₂×Q₁₆	C₂×C₄×C₁₃₇	1	4	yes	complemented
378	C₂×SD₁₆	—	2	2	no	—
379	C₂×SD₁₆	—	2	2	no	—
380	C₂×SD₁₆	—	2	2	no	—
381	C₂×SD₁₆	—	2	2	no	—
382	C₂×SD₁₆	C₂×C₄×C₁₃₇	1	4	yes	—
383	C₂×SD₁₆	C₂×C₄×C₁₃₇	1	4	yes	—
384	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
385	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
386	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
387	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
388	C₄⋊Q₈	—	2	2	no	—
389	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	4	yes	complemented
390	#124	—	2	2	no	—
391	#124	C₂×C₄×C₁₃₇	1	4	yes	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	—	2	2	no	—
396	C₄×Q₈	—	2	2	no	—
397	C₄×Q₈	—	2	2	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	2	no	—
400	C₂×C₄⋊C₄	—	2	2	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	2	no	—
405	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	—	2	2	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	2	no	—
412	C₂×C₄²	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
418	#107	—	2	2	no	—
419	#107	—	2	2	no	—
420	#106	—	2	2	no	—
421	#106	—	2	2	no	—
422	#103	—	2	2	no	—
423	#103	—	2	2	no	—
424	#103	—	2	2	no	—
425	#103	—	2	2	no	—
426	#103	—	2	2	no	—
427	#103	—	2	2	no	—
428	#102	—	2	2	no	—
429	#102	—	2	2	no	—
430	#97	—	2	2	no	—
431	#97	C₂×C₄×C₁₃₇	1	4	yes	complemented
432	#97	D₄×C₁₃₇	1	4	yes	—
433	C₄×C₈	—	2	2	no	—
434	C₄×C₈	—	2	2	no	—
435	C₄×C₈	D₄×C₁₃₇	1	4	yes	—
436	#95	—	2	2	no	—
437	#95	—	2	2	no	—
438	#95	—	2	2	no	—
439	#95	—	2	2	no	—
440	#95	D₄×C₁₃₇	1	2	yes	—
441	#95	D₄×C₁₃₇	1	2	yes	—
442	C₂⁴	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	C₂²×C₄×C₁₃₇	1	2	yes	—
459	C₂×Q₈	C₂²×C₄×C₁₃₇	1	2	yes	—
460	C₂×Q₈	C₂²×C₄×C₁₃₇	1	2	yes	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	C₂²×C₄×C₁₃₇	1	2	yes	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	8	2	no	—
476	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
477	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
478	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
481	Q₁₆	—	2	8	no	—
482	Q₁₆	—	2	8	no	—
483	SD₁₆	—	2	8	no	—
484	SD₁₆	—	2	8	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
490	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
491	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
492	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
493	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
494	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
495	C₂×C₈	#41×C₁₃₇	1	2	yes	—
496	C₂×C₈	#41×C₁₃₇	1	2	yes	—
497	C₄⋊C₄	—	2	8	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	4	2	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	—	4	2	no	—
509	C₄⋊C₄	—	8	2	no	—
510	C₂²⋊C₄	—	2	8	no	—
511	C₂²⋊C₄	—	4	2	no	—
512	C₂²⋊C₄	—	8	2	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	4	2	no	—
516	C₄²	—	4	2	no	—
517	C₄²	—	4	2	no	—
518	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
519	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
520	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
521	C₄²	#41×C₁₃₇	1	2	yes	—
522	C₂³	—	2	2	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	4	1	no	—
525	C₂³	—	4	2	no	—
526	C₂³	—	4	2	no	—
527	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
528	Q₈	—	2	2	no	—
529	Q₈	—	2	2	no	—
530	Q₈	—	2	2	no	—
531	Q₈	—	2	2	no	—
532	Q₈	—	2	2	no	—
533	Q₈	—	2	2	no	—
534	Q₈	—	4	1	no	—
535	Q₈	—	4	1	no	—
536	Q₈	—	4	1	no	—
537	Q₈	—	4	1	no	—
538	Q₈	—	4	1	no	—
539	Q₈	—	4	1	no	—
540	D₄	—	2	2	no	—
541	D₄	—	2	2	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	1	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	8	4	no	—
569	C₂×C₄	C₄×D₄×C₁₃₇	1	4	yes	—
570	C₂×C₄	#127×C₁₃₇	1	2	yes	—
571	C₂×C₄	#127×C₁₃₇	1	2	yes	—
572	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
574	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
575	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
576	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
577	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
578	C₈	—	2	2	no	—
579	C₈	—	2	2	no	—
580	C₈	C₄×D₄×C₁₃₇	1	4	yes	—
581	C₈	C₄×D₄×C₁₃₇	1	4	yes	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	8	1	no	—
585	C₂²	—	8	1	no	—
586	C₂²	—	8	2	no	—
587	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
588	C₂²	C₂×#127×C₁₃₇	1	1	yes	characteristic
589	C₂²	#532×C₁₃₇	1	1	yes	characteristic
590	C₂²	#577×C₁₃₇	1	2	yes	—
591	C₂²	#578×C₁₃₇	1	2	yes	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	4	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	2	no	—
599	C₄	—	8	1	no	—
600	C₄	—	8	1	no	—
601	C₄	—	8	1	no	—
602	C₄	—	8	1	no	—
603	C₄	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
604	C₄	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
605	C₄	#532×C₁₃₇	1	1	yes	characteristic
606	C₄	#532×C₁₃₇	1	1	yes	characteristic
607	C₂	—	8	2	no	—
608	C₂	C₄×#127×C₁₃₇	1	1	yes	characteristic
609	C₂	#2947×C₁₃₇	1	2	yes	—
610	C₂	#3154×C₁₃₇	1	1	yes	characteristic
611	C₂	#3156×C₁₃₇	1	1	yes	characteristic
612	C₂	#3178×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	C₂²×D₄×C₁₃₇	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ #376×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#441×C₁₃₇	C₂	semidirect
4. C₂×C₄×Q₁₆×C₁₃₇	C₂	semidirect
6. #2327×C₁₃₇	C₂	semidirect
9. #1971×C₁₃₇	C₂	semidirect
10. #1969×C₁₃₇	C₂	semidirect
13. #1956×C₁₃₇	C₂	semidirect
14. #1847×C₁₃₇	C₂	semidirect
15. #1726×C₁₃₇	C₂	semidirect
26. #497×C₁₃₇	C₄	semidirect
69. C₂×Q₁₆×C₁₃₇	C₂×C₄	semidirect
70. C₂×Q₁₆×C₁₃₇	C₂×C₄	semidirect
82. C₄⋊Q₈×C₁₃₇	C₂×C₄	semidirect
124. #97×C₁₃₇	C₂×C₄	semidirect
306. #21703	C₁₃₇	direct (N × H)
307. C₁₃₇	#21703	direct (N × H)
309. C₂×#441	C₂×C₁₃₇	semidirect
311. C₂×C₄×Q₁₆	C₂×C₁₃₇	semidirect
313. #2327	C₂×C₁₃₇	semidirect
316. #1971	C₂×C₁₃₇	semidirect
317. #1969	C₂×C₁₃₇	semidirect
320. #1956	C₂×C₁₃₇	semidirect
321. #1847	C₂×C₁₃₇	semidirect
322. #1726	C₂×C₁₃₇	semidirect
333. #497	C₄×C₁₃₇	semidirect
376. C₂×Q₁₆	C₂×C₄×C₁₃₇	semidirect
377. C₂×Q₁₆	C₂×C₄×C₁₃₇	semidirect
389. C₄⋊Q₈	C₂×C₄×C₁₃₇	semidirect
431. #97	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×#497×C₁₃₇	2
C₂×#441×C₁₃₇	2
C₂×#440×C₁₃₇	2
C₂×C₄×Q₁₆×C₁₃₇	2
C₂×C₄×SD₁₆×C₁₃₇	2
#2327×C₁₃₇	2
#2326×C₁₃₇	2
#1973×C₁₃₇	2
#1971×C₁₃₇	2
#1969×C₁₃₇	2
#1968×C₁₃₇	2
#1958×C₁₃₇	2
#1956×C₁₃₇	2
#1847×C₁₃₇	2
#1726×C₁₃₇	2
#21703	137

Subgroups — C137×#21703 #46871089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21703 #46871089