Subgroups — C₁₃₇×#22117 #46871503

Order 35072.

836 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#476×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊Q₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2293×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1987×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1947×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#1944×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1936×C₁₃₇	C₂	1	2	yes	maximal
8	#1925×C₁₃₇	C₂	1	2	yes	maximal
9	#1920×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#1802×C₁₃₇	C₂	1	1	yes	maximal, characteristic
11	#1767×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃₇	—	2	1	no	—
14	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₃₇	—	2	1	no	—
16	#476×C₁₃₇	C₄	1	8	yes	complemented
17	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
18	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
23	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
24	#391×C₁₃₇	—	2	1	no	—
25	#390×C₁₃₇	C₂²	1	1	yes	characteristic
26	#390×C₁₃₇	C₂²	1	1	yes	characteristic
27	#389×C₁₃₇	—	2	1	no	—
28	#389×C₁₃₇	C₂²	1	1	yes	characteristic
29	#389×C₁₃₇	C₂²	1	1	yes	characteristic
30	#389×C₁₃₇	C₂²	1	2	yes	—
31	#388×C₁₃₇	—	2	1	no	—
32	#388×C₁₃₇	—	2	1	no	—
33	#384×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₁₃₇	—	2	1	no	—
35	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
38	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
39	#340×C₁₃₇	C₂²	1	2	yes	—
40	#340×C₁₃₇	C₂²	1	2	yes	—
41	#340×C₁₃₇	C₂²	1	2	yes	—
42	#340×C₁₃₇	C₂²	1	2	yes	—
43	#336×C₁₃₇	C₂²	1	2	yes	—
44	C₂²×Q₈×C₁₃₇	—	2	1	no	—
45	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃₇	—	2	1	no	—
47	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
50	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	4	yes	—
51	C₄×Q₈×C₁₃₇	—	4	4	no	—
52	C₄×D₄×C₁₃₇	—	2	2	no	—
53	C₄×D₄×C₁₃₇	C₂×C₄	1	4	yes	—
54	#117×C₁₃₇	—	4	4	no	—
55	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
71	C₂×C₄²×C₁₃₇	—	2	1	no	—
72	C₂×C₄²×C₁₃₇	—	2	2	no	—
73	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
80	#107×C₁₃₇	—	4	2	no	—
81	#106×C₁₃₇	C₂×C₄	1	8	yes	—
82	C₄⋊C₈×C₁₃₇	—	2	2	no	—
83	C₄⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
84	#102×C₁₃₇	—	4	2	no	—
85	#102×C₁₃₇	C₂×C₄	1	8	yes	—
86	#97×C₁₃₇	—	4	2	no	—
87	#95×C₁₃₇	—	2	1	no	—
88	#95×C₁₃₇	—	2	1	no	—
89	#95×C₁₃₇	—	2	2	no	—
90	#95×C₁₃₇	—	2	1	no	—
91	#95×C₁₃₇	—	2	2	no	—
92	C₂⁴×C₁₃₇	—	2	1	no	—
93	C₂×Q₈×C₁₃₇	—	2	4	no	—
94	C₂×Q₈×C₁₃₇	—	4	2	no	—
95	C₂×Q₈×C₁₃₇	—	4	2	no	—
96	C₂×D₄×C₁₃₇	—	2	1	no	—
97	C₂×D₄×C₁₃₇	—	2	1	no	—
98	C₂×D₄×C₁₃₇	—	2	1	no	—
99	C₂×D₄×C₁₃₇	—	2	1	no	—
100	C₂×D₄×C₁₃₇	—	2	1	no	—
101	C₂×D₄×C₁₃₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₃₇	—	2	2	no	—
103	C₂²×C₄×C₁₃₇	—	2	1	no	—
104	C₂²×C₄×C₁₃₇	—	2	4	no	—
105	C₂²×C₄×C₁₃₇	—	2	1	no	—
106	C₂²×C₄×C₁₃₇	—	2	1	no	—
107	C₂²×C₄×C₁₃₇	—	2	2	no	—
108	C₂²×C₄×C₁₃₇	—	4	2	no	—
109	C₂²×C₄×C₁₃₇	—	4	2	no	—
110	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
117	C₂×C₈×C₁₃₇	—	2	2	no	—
118	C₂×C₈×C₁₃₇	—	2	2	no	—
119	C₂×C₈×C₁₃₇	—	2	2	no	—
120	C₂×C₈×C₁₃₇	—	2	2	no	—
121	C₂×C₈×C₁₃₇	—	2	2	no	—
122	C₂×C₈×C₁₃₇	C₂²×C₄	1	4	yes	—
123	C₄⋊C₄×C₁₃₇	—	2	4	no	—
124	C₄⋊C₄×C₁₃₇	—	2	1	no	—
125	C₄⋊C₄×C₁₃₇	—	2	2	no	—
126	C₄⋊C₄×C₁₃₇	—	2	2	no	—
127	C₄⋊C₄×C₁₃₇	—	2	1	no	—
128	C₄⋊C₄×C₁₃₇	—	2	1	no	—
129	C₄⋊C₄×C₁₃₇	—	2	1	no	—
130	C₄⋊C₄×C₁₃₇	—	2	2	no	—
131	C₄⋊C₄×C₁₃₇	—	2	1	no	—
132	C₄⋊C₄×C₁₃₇	—	4	2	no	—
133	C₄⋊C₄×C₁₃₇	—	4	2	no	—
134	C₄⋊C₄×C₁₃₇	—	4	2	no	—
135	C₄⋊C₄×C₁₃₇	—	4	4	no	—
136	C₄⋊C₄×C₁₃₇	—	4	2	no	—
137	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
138	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
139	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
140	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
141	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
142	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
143	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
144	C₄²×C₁₃₇	—	2	2	no	—
145	C₄²×C₁₃₇	—	2	2	no	—
146	C₄²×C₁₃₇	—	2	2	no	—
147	C₄²×C₁₃₇	—	2	1	no	—
148	C₄²×C₁₃₇	—	2	1	no	—
149	C₄²×C₁₃₇	—	2	1	no	—
150	C₄²×C₁₃₇	—	2	1	no	—
151	C₄²×C₁₃₇	—	4	1	no	—
152	C₄²×C₁₃₇	—	4	2	no	—
153	C₄²×C₁₃₇	—	4	4	no	—
154	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
155	C₄²×C₁₃₇	#41	1	2	yes	—
156	C₂³×C₁₃₇	—	2	2	no	—
157	C₂³×C₁₃₇	—	4	1	no	—
158	C₂³×C₁₃₇	—	4	1	no	—
159	C₂³×C₁₃₇	—	4	1	no	—
160	C₂³×C₁₃₇	—	4	1	no	—
161	C₂³×C₁₃₇	—	4	1	no	—
162	C₂³×C₁₃₇	—	4	1	no	—
163	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₁₃₇	—	4	8	no	—
165	D₄×C₁₃₇	—	2	2	no	—
166	D₄×C₁₃₇	—	2	2	no	—
167	D₄×C₁₃₇	—	4	1	no	—
168	D₄×C₁₃₇	—	4	1	no	—
169	C₂×C₄×C₁₃₇	—	2	1	no	—
170	C₂×C₄×C₁₃₇	—	2	1	no	—
171	C₂×C₄×C₁₃₇	—	2	1	no	—
172	C₂×C₄×C₁₃₇	—	2	1	no	—
173	C₂×C₄×C₁₃₇	—	2	2	no	—
174	C₂×C₄×C₁₃₇	—	2	4	no	—
175	C₂×C₄×C₁₃₇	—	2	1	no	—
176	C₂×C₄×C₁₃₇	—	2	1	no	—
177	C₂×C₄×C₁₃₇	—	2	1	no	—
178	C₂×C₄×C₁₃₇	—	2	1	no	—
179	C₂×C₄×C₁₃₇	—	2	1	no	—
180	C₂×C₄×C₁₃₇	—	2	1	no	—
181	C₂×C₄×C₁₃₇	—	2	1	no	—
182	C₂×C₄×C₁₃₇	—	2	1	no	—
183	C₂×C₄×C₁₃₇	—	2	1	no	—
184	C₂×C₄×C₁₃₇	—	4	2	no	—
185	C₂×C₄×C₁₃₇	—	4	1	no	—
186	C₂×C₄×C₁₃₇	—	4	1	no	—
187	C₂×C₄×C₁₃₇	—	4	2	no	—
188	C₂×C₄×C₁₃₇	—	4	8	no	—
189	C₂×C₄×C₁₃₇	—	4	1	no	—
190	C₂×C₄×C₁₃₇	—	4	2	no	—
191	C₂×C₄×C₁₃₇	—	4	1	no	—
192	C₂×C₄×C₁₃₇	—	4	1	no	—
193	C₂×C₄×C₁₃₇	—	4	1	no	—
194	C₂×C₄×C₁₃₇	—	4	2	no	—
195	C₂×C₄×C₁₃₇	—	4	1	no	—
196	C₂×C₄×C₁₃₇	—	4	2	no	—
197	C₂×C₄×C₁₃₇	—	4	1	no	—
198	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
199	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
201	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
202	C₂×C₄×C₁₃₇	#137	1	2	yes	—
203	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
206	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
207	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
208	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
209	C₈×C₁₃₇	—	2	4	no	—
210	C₈×C₁₃₇	—	4	2	no	—
211	C₂²×C₁₃₇	—	4	2	no	—
212	C₂²×C₁₃₇	—	4	2	no	—
213	C₂²×C₁₃₇	—	4	2	no	—
214	C₂²×C₁₃₇	—	8	1	no	—
215	C₂²×C₁₃₇	—	8	1	no	—
216	C₂²×C₁₃₇	—	8	1	no	—
217	C₂²×C₁₃₇	—	8	1	no	—
218	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
219	C₂²×C₁₃₇	#536	1	1	yes	characteristic
220	C₂²×C₁₃₇	#537	1	1	yes	characteristic
221	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
222	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₂²×C₁₃₇	C₂×#137	1	1	yes	characteristic
224	C₂²×C₁₃₇	#575	1	1	yes	characteristic
225	C₄×C₁₃₇	—	2	2	no	—
226	C₄×C₁₃₇	—	2	2	no	—
227	C₄×C₁₃₇	—	4	2	no	—
228	C₄×C₁₃₇	—	4	4	no	—
229	C₄×C₁₃₇	—	4	1	no	—
230	C₄×C₁₃₇	—	4	1	no	—
231	C₄×C₁₃₇	—	4	1	no	—
232	C₄×C₁₃₇	—	8	1	no	—
233	C₄×C₁₃₇	—	8	1	no	—
234	C₄×C₁₃₇	—	8	2	no	—
235	C₄×C₁₃₇	#440	1	4	yes	—
236	C₄×C₁₃₇	#519	1	1	yes	characteristic
237	C₄×C₁₃₇	#520	1	1	yes	characteristic
238	C₄×C₁₃₇	#541	1	1	yes	characteristic
239	C₄×C₁₃₇	#542	1	1	yes	characteristic
240	C₂×C₁₃₇	—	8	2	no	—
241	C₂×C₁₃₇	#2323	1	1	yes	characteristic
242	C₂×C₁₃₇	C₂×#440	1	1	yes	characteristic
243	C₂×C₁₃₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
244	C₂×C₁₃₇	#3235	1	1	yes	characteristic
245	C₂×C₁₃₇	#3238	1	1	yes	characteristic
246	C₂×C₁₃₇	#3252	1	1	yes	characteristic
247	C₂×C₁₃₇	#3253	1	1	yes	characteristic
248	#22117	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
249	C₁₃₇	#22117	1	1	yes	characteristic, direct product factor, Sylow
250	C₂×#476	C₂×C₁₃₇	1	1	yes	characteristic
251	C₄×C₄⋊Q₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
252	#2293	C₂×C₁₃₇	1	1	yes	characteristic
253	#1987	C₂×C₁₃₇	1	1	yes	characteristic, complemented
254	#1947	C₂×C₁₃₇	1	1	yes	characteristic, complemented
255	#1944	C₂×C₁₃₇	1	2	yes	complemented
256	#1936	C₂×C₁₃₇	1	2	yes	—
257	#1925	C₂×C₁₃₇	1	2	yes	—
258	#1920	C₂×C₁₃₇	1	2	yes	complemented
259	#1802	C₂×C₁₃₇	1	1	yes	characteristic
260	#1767	C₂×C₁₃₇	1	1	yes	characteristic, complemented
261	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
262	C₂×C₄×Q₈	—	2	1	no	—
263	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
264	C₂×#117	—	2	1	no	—
265	#476	C₄×C₁₃₇	1	8	yes	complemented
266	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
267	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
268	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
270	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
271	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
272	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
273	#391	—	2	1	no	—
274	#390	C₂²×C₁₃₇	1	1	yes	characteristic
275	#390	C₂²×C₁₃₇	1	1	yes	characteristic
276	#389	—	2	1	no	—
277	#389	C₂²×C₁₃₇	1	2	yes	—
278	#389	C₂²×C₁₃₇	1	1	yes	characteristic
279	#389	C₂²×C₁₃₇	1	1	yes	characteristic
280	#388	—	2	1	no	—
281	#388	—	2	1	no	—
282	#384	C₂²×C₁₃₇	1	1	yes	characteristic
283	C₄×C₄⋊C₄	—	2	1	no	—
284	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
285	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
286	C₄×C₂²⋊C₄	—	2	1	no	—
287	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
288	#340	C₂²×C₁₃₇	1	2	yes	—
289	#340	C₂²×C₁₃₇	1	2	yes	—
290	#340	C₂²×C₁₃₇	1	2	yes	—
291	#340	C₂²×C₁₃₇	1	2	yes	—
292	#336	C₂²×C₁₃₇	1	2	yes	—
293	C₂²×Q₈	—	2	1	no	—
294	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
295	C₂³×C₄	—	2	1	no	—
296	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
297	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
298	C₄⋊Q₈	—	2	2	no	—
299	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	4	yes	—
300	C₄×Q₈	—	4	4	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	C₂×C₄×C₁₃₇	1	4	yes	—
303	#117	—	4	4	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
323	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
324	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
325	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
329	#107	—	4	2	no	—
330	#106	C₂×C₄×C₁₃₇	1	8	yes	—
331	C₄⋊C₈	—	2	2	no	—
332	C₄⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
333	#102	—	4	2	no	—
334	#102	C₂×C₄×C₁₃₇	1	8	yes	—
335	#97	—	4	2	no	—
336	#95	—	2	1	no	—
337	#95	—	2	1	no	—
338	#95	—	2	2	no	—
339	#95	—	2	1	no	—
340	#95	—	2	2	no	—
341	C₂⁴	—	2	1	no	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×Q₈	—	4	2	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	C₂²×C₄×C₁₃₇	1	2	yes	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
365	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	C₂²×C₄×C₁₃₇	1	4	yes	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	4	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
387	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₂²⋊C₄	—	4	2	no	—
392	C₂²⋊C₄	—	4	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	4	1	no	—
401	C₄²	—	4	2	no	—
402	C₄²	—	4	4	no	—
403	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
404	C₄²	#41×C₁₃₇	1	2	yes	—
405	C₂³	—	2	2	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
413	Q₈	—	4	8	no	—
414	D₄	—	2	2	no	—
415	D₄	—	2	2	no	—
416	D₄	—	4	1	no	—
417	D₄	—	4	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	8	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
448	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
449	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
450	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
451	C₂×C₄	#137×C₁₃₇	1	2	yes	—
452	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
454	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
455	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
456	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
457	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
458	C₈	—	2	4	no	—
459	C₈	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	8	1	no	—
464	C₂²	—	8	1	no	—
465	C₂²	—	8	1	no	—
466	C₂²	—	8	1	no	—
467	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
468	C₂²	#536×C₁₃₇	1	1	yes	characteristic
469	C₂²	#537×C₁₃₇	1	1	yes	characteristic
470	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
471	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
472	C₂²	C₂×#137×C₁₃₇	1	1	yes	characteristic
473	C₂²	#575×C₁₃₇	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	4	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	8	1	no	—
482	C₄	—	8	1	no	—
483	C₄	—	8	2	no	—
484	C₄	#440×C₁₃₇	1	4	yes	—
485	C₄	#519×C₁₃₇	1	1	yes	characteristic
486	C₄	#520×C₁₃₇	1	1	yes	characteristic
487	C₄	#541×C₁₃₇	1	1	yes	characteristic
488	C₄	#542×C₁₃₇	1	1	yes	characteristic
489	C₂	—	8	2	no	—
490	C₂	#2323×C₁₃₇	1	1	yes	characteristic
491	C₂	C₂×#440×C₁₃₇	1	1	yes	characteristic
492	C₂	C₄×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
493	C₂	#3235×C₁₃₇	1	1	yes	characteristic
494	C₂	#3238×C₁₃₇	1	1	yes	characteristic
495	C₂	#3252×C₁₃₇	1	1	yes	characteristic
496	C₂	#3253×C₁₃₇	1	1	yes	characteristic

	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 ◁ C₄³×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₄⋊Q₈×C₁₃₇	C₂	semidirect
4. #1987×C₁₃₇	C₂	semidirect
5. #1947×C₁₃₇	C₂	semidirect
6. #1944×C₁₃₇	C₂	semidirect
9. #1920×C₁₃₇	C₂	semidirect
11. #1767×C₁₃₇	C₂	semidirect
16. #476×C₁₃₇	C₄	semidirect
248. #22117	C₁₃₇	direct (N × H)
249. C₁₃₇	#22117	direct (N × H)
251. C₄×C₄⋊Q₈	C₂×C₁₃₇	semidirect
253. #1987	C₂×C₁₃₇	semidirect
254. #1947	C₂×C₁₃₇	semidirect
255. #1944	C₂×C₁₃₇	semidirect
258. #1920	C₂×C₁₃₇	semidirect
260. #1767	C₂×C₁₃₇	semidirect
265. #476	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×#476×C₁₃₇	2
C₄×C₄⋊Q₈×C₁₃₇	2
#2293×C₁₃₇	2
#1987×C₁₃₇	2
#1947×C₁₃₇	2
#1944×C₁₃₇	2
#1936×C₁₃₇	2
#1925×C₁₃₇	2
#1920×C₁₃₇	2
#1802×C₁₃₇	2
#1767×C₁₃₇	2
#22117	137

Subgroups — C137×#22117 #46871503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#22117 #46871503