Subgroups — C₁₃₇×#25274 #46874660

Order 35072.

986 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#486×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#476×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2541×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2369×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2065×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2041×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1982×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1982×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1939×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1926×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	C₄×#102×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×#127×C₁₃₇	C₂²	1	2	yes	—
15	C₂×#121×C₁₃₇	—	2	1	no	—
16	C₂×#121×C₁₃₇	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
18	#486×C₁₃₇	—	2	4	no	—
19	#476×C₁₃₇	—	2	4	no	—
20	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
23	C₂×#102×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂×#102×C₁₃₇	C₂²	1	1	yes	characteristic
25	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
26	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
27	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
28	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
29	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
31	#392×C₁₃₇	—	2	2	no	—
32	#391×C₁₃₇	—	2	2	no	—
33	#390×C₁₃₇	C₂²	1	2	yes	—
34	#389×C₁₃₇	—	2	1	no	—
35	#389×C₁₃₇	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₁₃₇	—	2	1	no	—
37	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
40	#340×C₁₃₇	C₂²	1	1	yes	characteristic
41	#340×C₁₃₇	C₂²	1	1	yes	characteristic
42	#336×C₁₃₇	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃₇	—	2	1	no	—
44	C₂²×D₄×C₁₃₇	—	2	1	no	—
45	C₂²×D₄×C₁₃₇	—	2	2	no	—
46	C₂²×D₄×C₁₃₇	—	2	2	no	—
47	C₂²×D₄×C₁₃₇	—	2	1	no	—
48	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
49	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃₇	—	2	1	no	—
51	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
55	C₄⋊Q₈×C₁₃₇	D₄	1	4	yes	complemented
56	#127×C₁₃₇	—	2	4	no	—
57	#127×C₁₃₇	—	2	2	no	—
58	#127×C₁₃₇	—	2	2	no	—
59	#127×C₁₃₇	—	4	2	no	—
60	#121×C₁₃₇	—	4	4	no	—
61	#121×C₁₃₇	—	4	4	no	—
62	C₄×D₄×C₁₃₇	—	2	2	no	—
63	C₄×D₄×C₁₃₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
75	C₂×C₄²×C₁₃₇	—	2	1	no	—
76	C₂×C₄²×C₁₃₇	—	2	2	no	—
77	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
78	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
79	#106×C₁₃₇	—	2	4	no	—
80	C₄⋊C₈×C₁₃₇	—	2	2	no	—
81	C₄⋊C₈×C₁₃₇	—	4	2	no	—
82	#102×C₁₃₇	—	2	2	no	—
83	#102×C₁₃₇	—	2	4	no	—
84	#102×C₁₃₇	—	2	4	no	—
85	#102×C₁₃₇	—	2	4	no	—
86	#102×C₁₃₇	—	2	2	no	—
87	#102×C₁₃₇	—	2	4	no	—
88	#102×C₁₃₇	—	4	2	no	—
89	C₄×C₈×C₁₃₇	—	2	2	no	—
90	#95×C₁₃₇	—	2	2	no	—
91	#95×C₁₃₇	—	2	2	no	—
92	#95×C₁₃₇	—	2	1	no	—
93	#95×C₁₃₇	D₄	1	2	yes	—
94	C₂⁴×C₁₃₇	—	2	1	no	—
95	C₂⁴×C₁₃₇	—	2	2	no	—
96	C₂×Q₈×C₁₃₇	—	2	4	no	—
97	C₂×Q₈×C₁₃₇	—	8	1	no	—
98	C₂×Q₈×C₁₃₇	—	8	1	no	—
99	C₂×D₄×C₁₃₇	—	2	1	no	—
100	C₂×D₄×C₁₃₇	—	2	2	no	—
101	C₂×D₄×C₁₃₇	—	2	1	no	—
102	C₂×D₄×C₁₃₇	—	2	1	no	—
103	C₂×D₄×C₁₃₇	—	2	2	no	—
104	C₂×D₄×C₁₃₇	—	2	2	no	—
105	C₂×D₄×C₁₃₇	—	2	2	no	—
106	C₂×D₄×C₁₃₇	—	2	1	no	—
107	C₂×D₄×C₁₃₇	—	2	2	no	—
108	C₂×D₄×C₁₃₇	—	2	1	no	—
109	C₂×D₄×C₁₃₇	—	2	2	no	—
110	C₂×D₄×C₁₃₇	—	4	4	no	—
111	C₂×D₄×C₁₃₇	—	4	4	no	—
112	C₂×D₄×C₁₃₇	—	4	4	no	—
113	C₂×D₄×C₁₃₇	—	4	2	no	—
114	C₂×D₄×C₁₃₇	—	4	2	no	—
115	C₂×D₄×C₁₃₇	—	4	4	no	—
116	C₂×D₄×C₁₃₇	—	4	2	no	—
117	C₂×D₄×C₁₃₇	—	4	2	no	—
118	C₂×D₄×C₁₃₇	—	8	2	no	—
119	C₂×D₄×C₁₃₇	—	8	1	no	—
120	C₂×D₄×C₁₃₇	—	8	1	no	—
121	C₂×D₄×C₁₃₇	—	8	2	no	—
122	C₂×D₄×C₁₃₇	#41	1	2	yes	—
123	C₂²×C₄×C₁₃₇	—	2	1	no	—
124	C₂²×C₄×C₁₃₇	—	2	2	no	—
125	C₂²×C₄×C₁₃₇	—	2	1	no	—
126	C₂²×C₄×C₁₃₇	—	2	1	no	—
127	C₂²×C₄×C₁₃₇	—	4	2	no	—
128	C₂²×C₄×C₁₃₇	—	4	2	no	—
129	C₂²×C₄×C₁₃₇	—	4	2	no	—
130	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
135	C₂×C₈×C₁₃₇	—	2	1	no	—
136	C₂×C₈×C₁₃₇	—	2	1	no	—
137	C₂×C₈×C₁₃₇	—	2	2	no	—
138	C₂×C₈×C₁₃₇	—	2	1	no	—
139	C₂×C₈×C₁₃₇	—	2	1	no	—
140	C₂×C₈×C₁₃₇	—	2	2	no	—
141	C₂×C₈×C₁₃₇	—	2	2	no	—
142	C₂×C₈×C₁₃₇	—	2	1	no	—
143	C₂×C₈×C₁₃₇	—	2	1	no	—
144	C₄⋊C₄×C₁₃₇	—	2	4	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	1	no	—
150	C₄⋊C₄×C₁₃₇	—	2	1	no	—
151	C₄⋊C₄×C₁₃₇	—	2	1	no	—
152	C₄⋊C₄×C₁₃₇	—	8	2	no	—
153	C₄⋊C₄×C₁₃₇	SD₁₆	1	4	yes	—
154	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
155	C₄⋊C₄×C₁₃₇	#41	1	2	yes	—
156	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
157	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
158	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
159	C₄²×C₁₃₇	—	2	2	no	—
160	C₄²×C₁₃₇	—	2	2	no	—
161	C₄²×C₁₃₇	—	4	2	no	—
162	C₄²×C₁₃₇	—	8	2	no	—
163	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
164	C₄²×C₁₃₇	#41	1	2	yes	—
165	C₂³×C₁₃₇	—	2	2	no	—
166	C₂³×C₁₃₇	—	4	1	no	—
167	C₂³×C₁₃₇	—	4	1	no	—
168	C₂³×C₁₃₇	—	4	1	no	—
169	C₂³×C₁₃₇	—	4	1	no	—
170	C₂³×C₁₃₇	—	4	1	no	—
171	C₂³×C₁₃₇	—	4	1	no	—
172	C₂³×C₁₃₇	—	4	2	no	—
173	C₂³×C₁₃₇	—	4	2	no	—
174	C₂³×C₁₃₇	—	4	2	no	—
175	C₂³×C₁₃₇	—	4	2	no	—
176	C₂³×C₁₃₇	—	4	2	no	—
177	C₂³×C₁₃₇	—	4	2	no	—
178	C₂³×C₁₃₇	—	4	2	no	—
179	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₁₃₇	—	8	4	no	—
181	D₄×C₁₃₇	—	2	2	no	—
182	D₄×C₁₃₇	—	2	2	no	—
183	D₄×C₁₃₇	—	4	2	no	—
184	D₄×C₁₃₇	—	4	1	no	—
185	D₄×C₁₃₇	—	4	2	no	—
186	D₄×C₁₃₇	—	4	2	no	—
187	D₄×C₁₃₇	—	4	1	no	—
188	D₄×C₁₃₇	—	4	2	no	—
189	D₄×C₁₃₇	—	8	8	no	—
190	D₄×C₁₃₇	—	8	4	no	—
191	D₄×C₁₃₇	—	8	8	no	—
192	D₄×C₁₃₇	—	8	4	no	—
193	C₂×C₄×C₁₃₇	—	2	2	no	—
194	C₂×C₄×C₁₃₇	—	2	2	no	—
195	C₂×C₄×C₁₃₇	—	2	1	no	—
196	C₂×C₄×C₁₃₇	—	2	1	no	—
197	C₂×C₄×C₁₃₇	—	2	4	no	—
198	C₂×C₄×C₁₃₇	—	2	2	no	—
199	C₂×C₄×C₁₃₇	—	2	2	no	—
200	C₂×C₄×C₁₃₇	—	2	2	no	—
201	C₂×C₄×C₁₃₇	—	2	2	no	—
202	C₂×C₄×C₁₃₇	—	4	1	no	—
203	C₂×C₄×C₁₃₇	—	4	1	no	—
204	C₂×C₄×C₁₃₇	—	4	2	no	—
205	C₂×C₄×C₁₃₇	—	4	2	no	—
206	C₂×C₄×C₁₃₇	—	4	1	no	—
207	C₂×C₄×C₁₃₇	—	4	1	no	—
208	C₂×C₄×C₁₃₇	—	4	1	no	—
209	C₂×C₄×C₁₃₇	—	4	1	no	—
210	C₂×C₄×C₁₃₇	—	4	1	no	—
211	C₂×C₄×C₁₃₇	—	4	1	no	—
212	C₂×C₄×C₁₃₇	—	8	4	no	—
213	C₂×C₄×C₁₃₇	#121	1	2	yes	—
214	C₂×C₄×C₁₃₇	#121	1	2	yes	—
215	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	4	yes	—
216	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	2	yes	—
217	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
218	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
224	C₈×C₁₃₇	—	4	1	no	—
225	C₈×C₁₃₇	—	4	1	no	—
226	C₈×C₁₃₇	—	4	2	no	—
227	C₂²×C₁₃₇	—	4	2	no	—
228	C₂²×C₁₃₇	—	4	2	no	—
229	C₂²×C₁₃₇	—	4	2	no	—
230	C₂²×C₁₃₇	—	8	1	no	—
231	C₂²×C₁₃₇	—	8	1	no	—
232	C₂²×C₁₃₇	—	8	1	no	—
233	C₂²×C₁₃₇	—	8	1	no	—
234	C₂²×C₁₃₇	—	8	2	no	—
235	C₂²×C₁₃₇	—	8	2	no	—
236	C₂²×C₁₃₇	—	8	2	no	—
237	C₂²×C₁₃₇	—	8	2	no	—
238	C₂²×C₁₃₇	—	8	2	no	—
239	C₂²×C₁₃₇	—	8	2	no	—
240	C₂²×C₁₃₇	—	8	2	no	—
241	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
242	C₂²×C₁₃₇	#546	1	1	yes	characteristic
243	C₂²×C₁₃₇	#548	1	1	yes	characteristic
244	C₂²×C₁₃₇	C₂²×SD₁₆	1	1	yes	characteristic
245	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
246	C₂²×C₁₃₇	#576	1	1	yes	characteristic
247	C₂²×C₁₃₇	#576	1	1	yes	characteristic
248	C₄×C₁₃₇	—	2	4	no	—
249	C₄×C₁₃₇	—	2	2	no	—
250	C₄×C₁₃₇	—	4	2	no	—
251	C₄×C₁₃₇	—	4	4	no	—
252	C₄×C₁₃₇	—	4	2	no	—
253	C₄×C₁₃₇	—	8	1	no	—
254	C₄×C₁₃₇	—	8	1	no	—
255	C₄×C₁₃₇	#460	1	4	yes	—
256	C₄×C₁₃₇	#529	1	1	yes	characteristic
257	C₄×C₁₃₇	#542	1	1	yes	characteristic
258	C₄×C₁₃₇	#548	1	1	yes	characteristic
259	C₄×C₁₃₇	#550	1	1	yes	characteristic
260	C₂×C₁₃₇	—	8	2	no	—
261	C₂×C₁₃₇	—	16	2	no	—
262	C₂×C₁₃₇	#2426	1	1	yes	characteristic
263	C₂×C₁₃₇	C₂×#460	1	1	yes	characteristic
264	C₂×C₁₃₇	#3041	1	1	yes	characteristic
265	C₂×C₁₃₇	#3295	1	1	yes	characteristic
266	C₂×C₁₃₇	#3325	1	1	yes	characteristic
267	C₂×C₁₃₇	#3362	1	1	yes	characteristic
268	C₂×C₁₃₇	#3366	1	1	yes	characteristic
269	#25274	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
270	C₁₃₇	#25274	1	1	yes	characteristic, direct product factor, Sylow
271	C₂×#486	C₂×C₁₃₇	1	1	yes	characteristic, complemented
272	C₂×#476	C₂×C₁₃₇	1	1	yes	characteristic, complemented
273	#2541	C₂×C₁₃₇	1	1	yes	characteristic
274	#2369	C₂×C₁₃₇	1	1	yes	characteristic, complemented
275	#2065	C₂×C₁₃₇	1	2	yes	complemented
276	#2041	C₂×C₁₃₇	1	2	yes	complemented
277	#1982	C₂×C₁₃₇	1	1	yes	characteristic, complemented
278	#1982	C₂×C₁₃₇	1	2	yes	complemented
279	#1939	C₂×C₁₃₇	1	1	yes	characteristic, complemented
280	#1926	C₂×C₁₃₇	1	2	yes	complemented
281	C₄×#102	C₂×C₁₃₇	1	1	yes	characteristic, complemented
282	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
283	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
284	C₂×#127	C₂²×C₁₃₇	1	2	yes	—
285	C₂×#121	—	2	1	no	—
286	C₂×#121	—	2	1	no	—
287	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
288	#486	—	2	4	no	—
289	#476	—	2	4	no	—
290	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
291	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
292	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
293	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
294	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
295	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
296	C₂×#102	C₂²×C₁₃₇	1	1	yes	characteristic
297	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
298	C₂×#102	C₂²×C₁₃₇	1	1	yes	characteristic
299	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
300	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
301	#392	—	2	2	no	—
302	#391	—	2	2	no	—
303	#390	C₂²×C₁₃₇	1	2	yes	—
304	#389	—	2	1	no	—
305	#389	C₂²×C₁₃₇	1	2	yes	—
306	C₄×C₄⋊C₄	—	2	1	no	—
307	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
308	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
309	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
310	#340	C₂²×C₁₃₇	1	1	yes	characteristic
311	#340	C₂²×C₁₃₇	1	1	yes	characteristic
312	#336	C₂²×C₁₃₇	1	2	yes	—
313	C₂²×Q₈	—	2	1	no	—
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
319	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
320	C₂³×C₄	—	2	1	no	—
321	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
322	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
323	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
324	C₄⋊Q₈	—	2	2	no	—
325	C₄⋊Q₈	D₄×C₁₃₇	1	4	yes	complemented
326	#127	—	2	4	no	—
327	#127	—	2	2	no	—
328	#127	—	2	2	no	—
329	#127	—	4	2	no	—
330	#121	—	4	4	no	—
331	#121	—	4	4	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
337	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₄²	—	2	1	no	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
348	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
349	#106	—	2	4	no	—
350	C₄⋊C₈	—	2	2	no	—
351	C₄⋊C₈	—	4	2	no	—
352	#102	—	2	2	no	—
353	#102	—	2	4	no	—
354	#102	—	2	4	no	—
355	#102	—	2	4	no	—
356	#102	—	2	2	no	—
357	#102	—	2	4	no	—
358	#102	—	4	2	no	—
359	C₄×C₈	—	2	2	no	—
360	#95	—	2	2	no	—
361	#95	—	2	2	no	—
362	#95	—	2	1	no	—
363	#95	D₄×C₁₃₇	1	2	yes	—
364	C₂⁴	—	2	1	no	—
365	C₂⁴	—	2	2	no	—
366	C₂×Q₈	—	2	4	no	—
367	C₂×Q₈	—	8	1	no	—
368	C₂×Q₈	—	8	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	4	4	no	—
381	C₂×D₄	—	4	4	no	—
382	C₂×D₄	—	4	4	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	4	4	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	4	2	no	—
388	C₂×D₄	—	8	2	no	—
389	C₂×D₄	—	8	1	no	—
390	C₂×D₄	—	8	1	no	—
391	C₂×D₄	—	8	2	no	—
392	C₂×D₄	#41×C₁₃₇	1	2	yes	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
401	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
403	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	8	2	no	—
423	C₄⋊C₄	SD₁₆×C₁₃₇	1	4	yes	—
424	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
425	C₄⋊C₄	#41×C₁₃₇	1	2	yes	—
426	C₂²⋊C₄	—	4	4	no	—
427	C₂²⋊C₄	—	4	2	no	—
428	C₂²⋊C₄	—	4	4	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	4	2	no	—
432	C₄²	—	8	2	no	—
433	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
434	C₄²	#41×C₁₃₇	1	2	yes	—
435	C₂³	—	2	2	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	4	1	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
450	Q₈	—	8	4	no	—
451	D₄	—	2	2	no	—
452	D₄	—	2	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	1	no	—
458	D₄	—	4	2	no	—
459	D₄	—	8	8	no	—
460	D₄	—	8	4	no	—
461	D₄	—	8	8	no	—
462	D₄	—	8	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	8	4	no	—
483	C₂×C₄	#121×C₁₃₇	1	2	yes	—
484	C₂×C₄	#121×C₁₃₇	1	2	yes	—
485	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	4	yes	—
486	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	2	yes	—
487	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
488	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
489	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
490	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
491	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
492	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
493	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
494	C₈	—	4	1	no	—
495	C₈	—	4	1	no	—
496	C₈	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	2	no	—
506	C₂²	—	8	2	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
512	C₂²	#546×C₁₃₇	1	1	yes	characteristic
513	C₂²	#548×C₁₃₇	1	1	yes	characteristic
514	C₂²	C₂²×SD₁₆×C₁₃₇	1	1	yes	characteristic
515	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
516	C₂²	#576×C₁₃₇	1	1	yes	characteristic
517	C₂²	#576×C₁₃₇	1	1	yes	characteristic
518	C₄	—	2	4	no	—
519	C₄	—	2	2	no	—
520	C₄	—	4	4	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	8	1	no	—
524	C₄	—	8	1	no	—
525	C₄	#460×C₁₃₇	1	4	yes	—
526	C₄	#529×C₁₃₇	1	1	yes	characteristic
527	C₄	#542×C₁₃₇	1	1	yes	characteristic
528	C₄	#548×C₁₃₇	1	1	yes	characteristic
529	C₄	#550×C₁₃₇	1	1	yes	characteristic
530	C₂	—	8	2	no	—
531	C₂	—	16	2	no	—
532	C₂	#2426×C₁₃₇	1	1	yes	characteristic
533	C₂	C₂×#460×C₁₃₇	1	1	yes	characteristic
534	C₂	#3041×C₁₃₇	1	1	yes	characteristic
535	C₂	#3295×C₁₃₇	1	1	yes	characteristic
536	C₂	#3325×C₁₃₇	1	1	yes	characteristic
537	C₂	#3362×C₁₃₇	1	1	yes	characteristic
538	C₂	#3366×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	#2541×C₁₃₇	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₄×C₄⋊C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#486×C₁₃₇	C₂	semidirect
2. C₂×#476×C₁₃₇	C₂	semidirect
4. #2369×C₁₃₇	C₂	semidirect
5. #2065×C₁₃₇	C₂	semidirect
6. #2041×C₁₃₇	C₂	semidirect
7. #1982×C₁₃₇	C₂	semidirect
8. #1982×C₁₃₇	C₂	semidirect
9. #1939×C₁₃₇	C₂	semidirect
10. #1926×C₁₃₇	C₂	semidirect
11. C₄×#102×C₁₃₇	C₂	semidirect
55. C₄⋊Q₈×C₁₃₇	D₄	semidirect
269. #25274	C₁₃₇	direct (N × H)
270. C₁₃₇	#25274	direct (N × H)
271. C₂×#486	C₂×C₁₃₇	semidirect
272. C₂×#476	C₂×C₁₃₇	semidirect
274. #2369	C₂×C₁₃₇	semidirect
275. #2065	C₂×C₁₃₇	semidirect
276. #2041	C₂×C₁₃₇	semidirect
277. #1982	C₂×C₁₃₇	semidirect
278. #1982	C₂×C₁₃₇	semidirect
279. #1939	C₂×C₁₃₇	semidirect
280. #1926	C₂×C₁₃₇	semidirect
281. C₄×#102	C₂×C₁₃₇	semidirect
325. C₄⋊Q₈	D₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#486×C₁₃₇	2
C₂×#476×C₁₃₇	2
#2541×C₁₃₇	2
#2369×C₁₃₇	2
#2065×C₁₃₇	2
#2041×C₁₃₇	2
#1982×C₁₃₇	2
#1939×C₁₃₇	2
#1926×C₁₃₇	2
C₄×#102×C₁₃₇	2
#25274	137

Subgroups — C137×#25274 #46874660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#25274 #46874660