Subgroups — C₁₃₇×#18540 #46867926

Order 35072.

1146 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#3165×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#3113×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#3110×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#1651×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1649×C₁₃₇	C₂	1	4	yes	maximal, complemented
7	#1556×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1491×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1490×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₃₇	—	2	1	no	—
11	D₄×Q₈×C₁₃₇	—	2	2	no	—
12	D₄×Q₈×C₁₃₇	—	2	2	no	—
13	D₄×Q₈×C₁₃₇	—	2	2	no	—
14	D₄×Q₈×C₁₃₇	C₂²	1	4	yes	—
15	#533×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₁₃₇	—	2	1	no	—
17	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
19	C₂×C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
20	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃₇	—	2	1	no	—
22	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
23	#501×C₁₃₇	—	2	2	no	—
24	#500×C₁₃₇	C₂²	1	2	yes	complemented
25	#498×C₁₃₇	C₂²	1	2	yes	complemented
26	#484×C₁₃₇	—	2	1	no	—
27	#483×C₁₃₇	—	2	1	no	—
28	#475×C₁₃₇	C₂²	1	2	yes	complemented
29	#474×C₁₃₇	C₂²	1	2	yes	—
30	#462×C₁₃₇	C₂²	1	2	yes	complemented
31	#461×C₁₃₇	C₂²	1	2	yes	—
32	#451×C₁₃₇	—	2	1	no	—
33	#450×C₁₃₇	—	2	1	no	—
34	#441×C₁₃₇	—	2	2	no	—
35	#440×C₁₃₇	—	2	2	no	—
36	#432×C₁₃₇	C₂²	1	1	yes	characteristic
37	#432×C₁₃₇	C₂²	1	1	yes	characteristic
38	#428×C₁₃₇	—	2	2	no	—
39	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
40	#332×C₁₃₇	C₂²	1	4	yes	complemented
41	Q₈⋊C₈×C₁₃₇	C₂²	1	4	yes	complemented
42	D₄⋊C₈×C₁₃₇	C₂²	1	4	yes	—
43	C₂²×Q₈×C₁₃₇	—	2	2	no	—
44	C₂²×Q₈×C₁₃₇	—	2	4	no	—
45	C₂²×Q₈×C₁₃₇	—	2	4	no	—
46	C₂²×Q₈×C₁₃₇	—	2	1	no	—
47	C₂²×Q₈×C₁₃₇	—	4	8	no	—
48	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₃₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₃₇	—	2	2	no	—
51	C₂³×C₄×C₁₃₇	—	2	1	no	—
52	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
53	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
54	C₂×M₁₆×C₁₃₇	—	2	1	no	—
55	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
56	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
57	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
58	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
59	C₄⋊Q₈×C₁₃₇	D₄	1	2	yes	—
60	C₄⋊Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
63	#125×C₁₃₇	—	2	1	no	—
64	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
65	C₂²⋊Q₈×C₁₃₇	—	2	8	no	—
66	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
67	C₂²⋊Q₈×C₁₃₇	—	2	8	no	—
68	C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
69	C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
70	C₄×Q₈×C₁₃₇	—	2	1	no	—
71	C₄×Q₈×C₁₃₇	—	2	1	no	—
72	C₄×Q₈×C₁₃₇	—	2	1	no	—
73	C₄×Q₈×C₁₃₇	—	2	1	no	—
74	C₄×Q₈×C₁₃₇	D₄	1	2	yes	—
75	C₄×Q₈×C₁₃₇	C₂³	1	2	yes	—
76	C₄×D₄×C₁₃₇	—	2	4	no	—
77	C₄×D₄×C₁₃₇	—	2	4	no	—
78	C₄×D₄×C₁₃₇	—	2	1	no	—
79	C₄×D₄×C₁₃₇	—	2	1	no	—
80	C₄×D₄×C₁₃₇	D₄	1	2	yes	—
81	C₄×D₄×C₁₃₇	C₂³	1	2	yes	—
82	#117×C₁₃₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
91	C₂×C₄²×C₁₃₇	—	2	1	no	—
92	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
93	#107×C₁₃₇	—	2	4	no	—
94	#107×C₁₃₇	—	2	2	no	—
95	#106×C₁₃₇	—	2	4	no	—
96	#106×C₁₃₇	—	2	2	no	—
97	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
98	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
99	#103×C₁₃₇	—	2	2	no	—
100	#103×C₁₃₇	—	2	2	no	—
101	#103×C₁₃₇	—	2	2	no	—
102	#102×C₁₃₇	—	2	2	no	—
103	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
104	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
105	#97×C₁₃₇	—	2	1	no	—
106	#97×C₁₃₇	—	2	1	no	—
107	#97×C₁₃₇	—	2	1	no	—
108	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
109	C₂⁴×C₁₃₇	—	2	1	no	—
110	C₂×Q₈×C₁₃₇	—	2	4	no	—
111	C₂×Q₈×C₁₃₇	—	2	8	no	—
112	C₂×Q₈×C₁₃₇	—	2	1	no	—
113	C₂×Q₈×C₁₃₇	—	2	2	no	—
114	C₂×Q₈×C₁₃₇	—	2	2	no	—
115	C₂×Q₈×C₁₃₇	—	2	1	no	—
116	C₂×Q₈×C₁₃₇	—	2	1	no	—
117	C₂×Q₈×C₁₃₇	—	4	8	no	—
118	C₂×Q₈×C₁₃₇	—	4	4	no	—
119	C₂×Q₈×C₁₃₇	—	4	16	no	—
120	C₂×Q₈×C₁₃₇	—	4	8	no	—
121	C₂×Q₈×C₁₃₇	—	4	8	no	—
122	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₁₃₇	—	2	4	no	—
124	C₂×D₄×C₁₃₇	—	2	1	no	—
125	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₃₇	—	2	1	no	—
127	C₂²×C₄×C₁₃₇	—	2	8	no	—
128	C₂²×C₄×C₁₃₇	—	2	1	no	—
129	C₂²×C₄×C₁₃₇	—	2	2	no	—
130	C₂²×C₄×C₁₃₇	—	2	1	no	—
131	C₂²×C₄×C₁₃₇	—	2	2	no	—
132	C₂²×C₄×C₁₃₇	—	2	2	no	—
133	C₂²×C₄×C₁₃₇	—	4	8	no	—
134	C₂²×C₄×C₁₃₇	—	4	4	no	—
135	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
138	Q₁₆×C₁₃₇	—	4	4	no	—
139	SD₁₆×C₁₃₇	—	4	4	no	—
140	M₁₆×C₁₃₇	—	2	4	no	—
141	C₂×C₈×C₁₃₇	—	2	2	no	—
142	C₂×C₈×C₁₃₇	—	2	2	no	—
143	C₂×C₈×C₁₃₇	—	2	2	no	—
144	C₄⋊C₄×C₁₃₇	—	2	8	no	—
145	C₄⋊C₄×C₁₃₇	—	2	2	no	—
146	C₄⋊C₄×C₁₃₇	—	2	2	no	—
147	C₄⋊C₄×C₁₃₇	—	2	1	no	—
148	C₄⋊C₄×C₁₃₇	—	2	1	no	—
149	C₄⋊C₄×C₁₃₇	—	2	2	no	—
150	C₄⋊C₄×C₁₃₇	—	2	2	no	—
151	C₄⋊C₄×C₁₃₇	—	2	2	no	—
152	C₄⋊C₄×C₁₃₇	—	2	1	no	—
153	C₄⋊C₄×C₁₃₇	—	2	1	no	—
154	C₄⋊C₄×C₁₃₇	—	2	1	no	—
155	C₄⋊C₄×C₁₃₇	—	2	1	no	—
156	C₄⋊C₄×C₁₃₇	—	4	1	no	—
157	C₄⋊C₄×C₁₃₇	—	4	1	no	—
158	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
161	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
162	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
163	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
164	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
165	C₄²×C₁₃₇	—	2	2	no	—
166	C₄²×C₁₃₇	—	2	2	no	—
167	C₄²×C₁₃₇	—	4	1	no	—
168	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
172	C₂³×C₁₃₇	—	2	4	no	—
173	C₂³×C₁₃₇	—	2	2	no	—
174	C₂³×C₁₃₇	—	4	2	no	—
175	C₂³×C₁₃₇	—	4	2	no	—
176	C₂³×C₁₃₇	#120	1	1	yes	characteristic
177	Q₈×C₁₃₇	—	2	4	no	—
178	Q₈×C₁₃₇	—	2	2	no	—
179	Q₈×C₁₃₇	—	4	16	no	—
180	Q₈×C₁₃₇	—	4	4	no	—
181	Q₈×C₁₃₇	—	4	4	no	—
182	Q₈×C₁₃₇	—	4	2	no	—
183	Q₈×C₁₃₇	—	4	2	no	—
184	Q₈×C₁₃₇	AGL(1,ℤ/8)	1	4	yes	—
185	D₄×C₁₃₇	—	2	4	no	—
186	D₄×C₁₃₇	—	2	2	no	—
187	D₄×C₁₃₇	#137	1	4	yes	—
188	C₂×C₄×C₁₃₇	—	2	4	no	—
189	C₂×C₄×C₁₃₇	—	2	2	no	—
190	C₂×C₄×C₁₃₇	—	2	2	no	—
191	C₂×C₄×C₁₃₇	—	2	2	no	—
192	C₂×C₄×C₁₃₇	—	2	2	no	—
193	C₂×C₄×C₁₃₇	—	2	2	no	—
194	C₂×C₄×C₁₃₇	—	2	4	no	—
195	C₂×C₄×C₁₃₇	—	2	2	no	—
196	C₂×C₄×C₁₃₇	—	4	16	no	—
197	C₂×C₄×C₁₃₇	—	4	4	no	—
198	C₂×C₄×C₁₃₇	—	4	4	no	—
199	C₂×C₄×C₁₃₇	—	4	2	no	—
200	C₂×C₄×C₁₃₇	—	4	2	no	—
201	C₂×C₄×C₁₃₇	—	4	4	no	—
202	C₂×C₄×C₁₃₇	—	4	1	no	—
203	C₂×C₄×C₁₃₇	—	4	1	no	—
204	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
205	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
206	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
207	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
210	C₈×C₁₃₇	—	2	4	no	—
211	C₈×C₁₃₇	—	4	2	no	—
212	C₈×C₁₃₇	—	4	2	no	—
213	C₂²×C₁₃₇	—	2	1	no	—
214	C₂²×C₁₃₇	—	2	1	no	—
215	C₂²×C₁₃₇	—	2	4	no	—
216	C₂²×C₁₃₇	—	4	8	no	—
217	C₂²×C₁₃₇	—	4	2	no	—
218	C₂²×C₁₃₇	—	4	2	no	—
219	C₂²×C₁₃₇	#456	1	2	yes	—
220	C₂²×C₁₃₇	C₂×#120	1	1	yes	characteristic
221	C₄×C₁₃₇	—	2	4	no	—
222	C₄×C₁₃₇	—	2	1	no	—
223	C₄×C₁₃₇	—	2	1	no	—
224	C₄×C₁₃₇	—	2	1	no	—
225	C₄×C₁₃₇	—	2	1	no	—
226	C₄×C₁₃₇	—	4	4	no	—
227	C₄×C₁₃₇	—	4	2	no	—
228	C₄×C₁₃₇	—	4	2	no	—
229	C₄×C₁₃₇	—	8	1	no	—
230	C₄×C₁₃₇	—	8	1	no	—
231	C₄×C₁₃₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
232	C₄×C₁₃₇	C₂×#137	1	2	yes	—
233	C₂×C₁₃₇	—	2	2	no	—
234	C₂×C₁₃₇	—	4	4	no	—
235	C₂×C₁₃₇	#3003	1	1	yes	characteristic
236	C₂×C₁₃₇	#3004	1	1	yes	characteristic
237	C₂×C₁₃₇	C₂×#456	1	1	yes	characteristic
238	#18540	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₁₃₇	#18540	1	1	yes	characteristic, direct product factor, Sylow
240	C₂×D₄×Q₈	C₂×C₁₃₇	1	1	yes	characteristic
241	#3165	C₂×C₁₃₇	1	1	yes	characteristic, complemented
242	#3113	C₂×C₁₃₇	1	1	yes	characteristic, complemented
243	#3110	C₂×C₁₃₇	1	1	yes	characteristic
244	#1651	C₂×C₁₃₇	1	4	yes	complemented
245	#1649	C₂×C₁₃₇	1	4	yes	complemented
246	#1556	C₂×C₁₃₇	1	1	yes	characteristic, complemented
247	#1491	C₂×C₁₃₇	1	1	yes	characteristic, complemented
248	#1490	C₂×C₁₃₇	1	1	yes	characteristic
249	C₂³×Q₈	—	2	1	no	—
250	D₄×Q₈	—	2	2	no	—
251	D₄×Q₈	—	2	2	no	—
252	D₄×Q₈	—	2	2	no	—
253	D₄×Q₈	C₂²×C₁₃₇	1	4	yes	—
254	#533	C₂²×C₁₃₇	1	1	yes	characteristic
255	C₂×C₄⋊Q₈	—	2	1	no	—
256	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
257	C₂×C₂²⋊Q₈	—	2	1	no	—
258	C₂×C₂²⋊Q₈	—	2	2	no	—
259	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
260	C₂×C₄×D₄	—	2	1	no	—
261	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
262	#501	—	2	2	no	—
263	#500	C₂²×C₁₃₇	1	2	yes	complemented
264	#498	C₂²×C₁₃₇	1	2	yes	complemented
265	#484	—	2	1	no	—
266	#483	—	2	1	no	—
267	#475	C₂²×C₁₃₇	1	2	yes	complemented
268	#474	C₂²×C₁₃₇	1	2	yes	—
269	#462	C₂²×C₁₃₇	1	2	yes	complemented
270	#461	C₂²×C₁₃₇	1	2	yes	—
271	#451	—	2	1	no	—
272	#450	—	2	1	no	—
273	#441	—	2	2	no	—
274	#440	—	2	2	no	—
275	#432	C₂²×C₁₃₇	1	1	yes	characteristic
276	#432	C₂²×C₁₃₇	1	1	yes	characteristic
277	#428	—	2	2	no	—
278	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
279	#332	C₂²×C₁₃₇	1	4	yes	complemented
280	Q₈⋊C₈	C₂²×C₁₃₇	1	4	yes	complemented
281	D₄⋊C₈	C₂²×C₁₃₇	1	4	yes	—
282	C₂²×Q₈	—	2	2	no	—
283	C₂²×Q₈	—	2	4	no	—
284	C₂²×Q₈	—	2	4	no	—
285	C₂²×Q₈	—	2	1	no	—
286	C₂²×Q₈	—	4	8	no	—
287	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
288	C₂²×D₄	D₄×C₁₃₇	1	1	yes	characteristic
289	C₂³×C₄	—	2	2	no	—
290	C₂³×C₄	—	2	1	no	—
291	C₂×Q₁₆	—	2	2	no	—
292	C₂×SD₁₆	—	2	2	no	—
293	C₂×M₁₆	—	2	1	no	—
294	C₄⋊Q₈	—	2	4	no	—
295	C₄⋊Q₈	—	2	4	no	—
296	C₄⋊Q₈	—	2	1	no	—
297	C₄⋊Q₈	—	2	1	no	—
298	C₄⋊Q₈	D₄×C₁₃₇	1	2	yes	—
299	C₄⋊Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
300	C₄⋊Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
301	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
302	#125	—	2	1	no	—
303	C₂²⋊Q₈	—	2	4	no	—
304	C₂²⋊Q₈	—	2	8	no	—
305	C₂²⋊Q₈	—	2	4	no	—
306	C₂²⋊Q₈	—	2	8	no	—
307	C₂²⋊Q₈	—	2	1	no	—
308	C₂²⋊Q₈	—	2	1	no	—
309	C₄×Q₈	—	2	1	no	—
310	C₄×Q₈	—	2	1	no	—
311	C₄×Q₈	—	2	1	no	—
312	C₄×Q₈	—	2	1	no	—
313	C₄×Q₈	D₄×C₁₃₇	1	2	yes	—
314	C₄×Q₈	C₂³×C₁₃₇	1	2	yes	—
315	C₄×D₄	—	2	4	no	—
316	C₄×D₄	—	2	4	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	2	1	no	—
319	C₄×D₄	D₄×C₁₃₇	1	2	yes	—
320	C₄×D₄	C₂³×C₁₃₇	1	2	yes	—
321	#117	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
326	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
327	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
332	#107	—	2	4	no	—
333	#107	—	2	2	no	—
334	#106	—	2	4	no	—
335	#106	—	2	2	no	—
336	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
337	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
338	#103	—	2	2	no	—
339	#103	—	2	2	no	—
340	#103	—	2	2	no	—
341	#102	—	2	2	no	—
342	C₂²⋊C₈	—	2	1	no	—
343	C₂²⋊C₈	—	2	1	no	—
344	#97	—	2	1	no	—
345	#97	—	2	1	no	—
346	#97	—	2	1	no	—
347	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
348	C₂⁴	—	2	1	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	2	8	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	4	8	no	—
357	C₂×Q₈	—	4	4	no	—
358	C₂×Q₈	—	4	16	no	—
359	C₂×Q₈	—	4	8	no	—
360	C₂×Q₈	—	4	8	no	—
361	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	8	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	4	8	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
377	Q₁₆	—	4	4	no	—
378	SD₁₆	—	4	4	no	—
379	M₁₆	—	2	4	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	4	1	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
398	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
399	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
400	C₂²⋊C₄	—	2	8	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	4	1	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	4	1	no	—
407	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
408	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
409	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
410	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
411	C₂³	—	2	4	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	#120×C₁₃₇	1	1	yes	characteristic
416	Q₈	—	2	4	no	—
417	Q₈	—	2	2	no	—
418	Q₈	—	4	16	no	—
419	Q₈	—	4	4	no	—
420	Q₈	—	4	4	no	—
421	Q₈	—	4	2	no	—
422	Q₈	—	4	2	no	—
423	Q₈	AGL(1,ℤ/8)×C₁₃₇	1	4	yes	—
424	D₄	—	2	4	no	—
425	D₄	—	2	2	no	—
426	D₄	#137×C₁₃₇	1	4	yes	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	16	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
444	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
445	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
449	C₈	—	2	4	no	—
450	C₈	—	4	2	no	—
451	C₈	—	4	2	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	4	8	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	#456×C₁₃₇	1	2	yes	—
459	C₂²	C₂×#120×C₁₃₇	1	1	yes	characteristic
460	C₄	—	2	4	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	4	4	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	8	1	no	—
469	C₄	—	8	1	no	—
470	C₄	C₂×AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
471	C₄	C₂×#137×C₁₃₇	1	2	yes	—
472	C₂	—	2	2	no	—
473	C₂	—	4	4	no	—
474	C₂	#3003×C₁₃₇	1	1	yes	characteristic
475	C₂	#3004×C₁₃₇	1	1	yes	characteristic
476	C₂	C₂×#456×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	C₂²×D₄×C₁₃₇	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #3165×C₁₃₇	C₂	semidirect
3. #3113×C₁₃₇	C₂	semidirect
5. #1651×C₁₃₇	C₂	semidirect
6. #1649×C₁₃₇	C₂	semidirect
7. #1556×C₁₃₇	C₂	semidirect
8. #1491×C₁₃₇	C₂	semidirect
24. #500×C₁₃₇	C₂²	semidirect
25. #498×C₁₃₇	C₂²	semidirect
28. #475×C₁₃₇	C₂²	semidirect
30. #462×C₁₃₇	C₂²	semidirect
40. #332×C₁₃₇	C₂²	semidirect
41. Q₈⋊C₈×C₁₃₇	C₂²	semidirect
238. #18540	C₁₃₇	direct (N × H)
239. C₁₃₇	#18540	direct (N × H)
241. #3165	C₂×C₁₃₇	semidirect
242. #3113	C₂×C₁₃₇	semidirect
244. #1651	C₂×C₁₃₇	semidirect
245. #1649	C₂×C₁₃₇	semidirect
246. #1556	C₂×C₁₃₇	semidirect
247. #1491	C₂×C₁₃₇	semidirect
263. #500	C₂²×C₁₃₇	semidirect
264. #498	C₂²×C₁₃₇	semidirect
267. #475	C₂²×C₁₃₇	semidirect
269. #462	C₂²×C₁₃₇	semidirect
279. #332	C₂²×C₁₃₇	semidirect
280. Q₈⋊C₈	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×D₄×Q₈×C₁₃₇	2
#3165×C₁₃₇	2
#3113×C₁₃₇	2
#3110×C₁₃₇	2
#1651×C₁₃₇	2
#1649×C₁₃₇	2
#1556×C₁₃₇	2
#1491×C₁₃₇	2
#1490×C₁₃₇	2
#18540	137

Subgroups — C137×#18540 #46867926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#18540 #46867926