Subgroups — C₁₃₇×#21279 #46870665

Order 35072.

874 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×SD₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2295×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2293×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1973×C₁₃₇	C₂	1	2	yes	maximal
5	#1944×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1936×C₁₃₇	C₂	1	2	yes	maximal
7	#1935×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	C₄×#107×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#103×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#102×C₁₃₇	C₂	1	1	yes	maximal, characteristic
11	C₄×#97×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₃₇	—	2	1	no	—
16	C₄×SD₁₆×C₁₃₇	C₄	1	8	yes	complemented
17	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
18	C₂×#106×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
20	C₂×#103×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#102×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
24	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
27	#391×C₁₃₇	C₂²	1	2	yes	—
28	#390×C₁₃₇	C₂²	1	2	yes	—
29	#389×C₁₃₇	C₂²	1	2	yes	—
30	#389×C₁₃₇	C₂²	1	2	yes	—
31	#388×C₁₃₇	—	2	2	no	—
32	#387×C₁₃₇	—	2	2	no	—
33	C₄×C₄⋊C₄×C₁₃₇	—	2	1	no	—
34	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
37	#376×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	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃₇	—	2	1	no	—
45	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
46	C₂×SD₁₆×C₁₃₇	C₂×C₄	1	4	yes	—
47	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
50	C₄×Q₈×C₁₃₇	—	2	2	no	—
51	C₄×Q₈×C₁₃₇	C₂×C₄	1	4	yes	—
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	2	no	—
57	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
65	C₂×C₄²×C₁₃₇	—	2	1	no	—
66	C₂×C₄²×C₁₃₇	—	2	1	no	—
67	C₂×C₄²×C₁₃₇	—	2	1	no	—
68	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
71	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
73	#107×C₁₃₇	—	2	4	no	—
74	#106×C₁₃₇	C₂×C₄	1	4	yes	—
75	#103×C₁₃₇	—	2	4	no	—
76	#103×C₁₃₇	C₂×C₄	1	4	yes	—
77	#102×C₁₃₇	—	2	4	no	—
78	#102×C₁₃₇	C₂×C₄	1	4	yes	—
79	#97×C₁₃₇	—	2	4	no	—
80	#97×C₁₃₇	—	2	4	no	—
81	C₄×C₈×C₁₃₇	—	2	2	no	—
82	C₄×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
83	#95×C₁₃₇	—	2	2	no	—
84	#95×C₁₃₇	—	2	2	no	—
85	#95×C₁₃₇	—	2	2	no	—
86	#95×C₁₃₇	—	2	2	no	—
87	#95×C₁₃₇	—	2	1	no	—
88	#95×C₁₃₇	—	2	1	no	—
89	C₂⁴×C₁₃₇	—	2	1	no	—
90	C₂×Q₈×C₁₃₇	—	2	1	no	—
91	C₂×Q₈×C₁₃₇	—	2	2	no	—
92	C₂×Q₈×C₁₃₇	—	2	2	no	—
93	C₂×Q₈×C₁₃₇	C₂²×C₄	1	2	yes	—
94	C₂×D₄×C₁₃₇	—	2	2	no	—
95	C₂×D₄×C₁₃₇	—	2	2	no	—
96	C₂×D₄×C₁₃₇	—	2	1	no	—
97	C₂×D₄×C₁₃₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₃₇	—	2	1	no	—
99	C₂²×C₄×C₁₃₇	—	2	1	no	—
100	C₂²×C₄×C₁₃₇	—	2	1	no	—
101	C₂²×C₄×C₁₃₇	—	2	4	no	—
102	C₂²×C₄×C₁₃₇	—	2	2	no	—
103	C₂²×C₄×C₁₃₇	—	2	2	no	—
104	C₂²×C₄×C₁₃₇	—	4	2	no	—
105	C₂²×C₄×C₁₃₇	—	4	2	no	—
106	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
111	SD₁₆×C₁₃₇	—	2	8	no	—
112	C₂×C₈×C₁₃₇	—	2	2	no	—
113	C₂×C₈×C₁₃₇	—	2	2	no	—
114	C₂×C₈×C₁₃₇	—	2	2	no	—
115	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₁₃₇	#41	1	4	yes	—
118	C₂×C₈×C₁₃₇	#41	1	4	yes	—
119	C₄⋊C₄×C₁₃₇	—	2	4	no	—
120	C₄⋊C₄×C₁₃₇	—	2	1	no	—
121	C₄⋊C₄×C₁₃₇	—	2	1	no	—
122	C₄⋊C₄×C₁₃₇	—	2	2	no	—
123	C₄⋊C₄×C₁₃₇	—	2	2	no	—
124	C₄⋊C₄×C₁₃₇	—	2	2	no	—
125	C₄⋊C₄×C₁₃₇	—	2	2	no	—
126	C₄⋊C₄×C₁₃₇	—	4	4	no	—
127	C₄⋊C₄×C₁₃₇	—	4	4	no	—
128	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
129	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
130	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
131	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
132	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
133	C₄²×C₁₃₇	—	2	4	no	—
134	C₄²×C₁₃₇	—	2	2	no	—
135	C₄²×C₁₃₇	—	2	2	no	—
136	C₄²×C₁₃₇	—	2	2	no	—
137	C₄²×C₁₃₇	—	2	2	no	—
138	C₄²×C₁₃₇	—	4	2	no	—
139	C₄²×C₁₃₇	—	4	2	no	—
140	C₄²×C₁₃₇	—	4	2	no	—
141	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
142	C₄²×C₁₃₇	#41	1	2	yes	—
143	C₂³×C₁₃₇	—	2	2	no	—
144	C₂³×C₁₃₇	—	4	2	no	—
145	C₂³×C₁₃₇	—	4	1	no	—
146	C₂³×C₁₃₇	—	4	1	no	—
147	C₂³×C₁₃₇	—	4	2	no	—
148	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₁₃₇	—	2	2	no	—
150	Q₈×C₁₃₇	—	2	2	no	—
151	Q₈×C₁₃₇	—	4	2	no	—
152	D₄×C₁₃₇	—	2	2	no	—
153	D₄×C₁₃₇	—	2	2	no	—
154	D₄×C₁₃₇	—	4	2	no	—
155	C₂×C₄×C₁₃₇	—	2	2	no	—
156	C₂×C₄×C₁₃₇	—	2	2	no	—
157	C₂×C₄×C₁₃₇	—	2	2	no	—
158	C₂×C₄×C₁₃₇	—	2	2	no	—
159	C₂×C₄×C₁₃₇	—	2	2	no	—
160	C₂×C₄×C₁₃₇	—	2	2	no	—
161	C₂×C₄×C₁₃₇	—	2	2	no	—
162	C₂×C₄×C₁₃₇	—	2	2	no	—
163	C₂×C₄×C₁₃₇	—	2	2	no	—
164	C₂×C₄×C₁₃₇	—	2	2	no	—
165	C₂×C₄×C₁₃₇	—	4	2	no	—
166	C₂×C₄×C₁₃₇	—	4	1	no	—
167	C₂×C₄×C₁₃₇	—	4	1	no	—
168	C₂×C₄×C₁₃₇	—	4	2	no	—
169	C₂×C₄×C₁₃₇	—	4	8	no	—
170	C₂×C₄×C₁₃₇	—	4	2	no	—
171	C₂×C₄×C₁₃₇	—	4	2	no	—
172	C₂×C₄×C₁₃₇	—	4	2	no	—
173	C₂×C₄×C₁₃₇	—	4	2	no	—
174	C₂×C₄×C₁₃₇	—	4	2	no	—
175	C₂×C₄×C₁₃₇	—	4	2	no	—
176	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
179	C₂×C₄×C₁₃₇	#137	1	2	yes	—
180	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
182	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
183	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
184	C₈×C₁₃₇	—	2	2	no	—
185	C₈×C₁₃₇	—	2	4	no	—
186	C₈×C₁₃₇	#117	1	4	yes	complemented
187	C₂²×C₁₃₇	—	4	2	no	—
188	C₂²×C₁₃₇	—	4	2	no	—
189	C₂²×C₁₃₇	—	4	2	no	—
190	C₂²×C₁₃₇	—	8	2	no	—
191	C₂²×C₁₃₇	—	8	2	no	—
192	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₂²×C₁₃₇	#532	1	2	yes	—
194	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂²×C₁₃₇	C₂×#137	1	1	yes	characteristic
196	C₂²×C₁₃₇	#575	1	2	yes	—
197	C₄×C₁₃₇	—	2	2	no	—
198	C₄×C₁₃₇	—	4	2	no	—
199	C₄×C₁₃₇	—	4	2	no	—
200	C₄×C₁₃₇	—	4	2	no	—
201	C₄×C₁₃₇	—	4	2	no	—
202	C₄×C₁₃₇	—	4	2	no	—
203	C₄×C₁₃₇	—	8	2	no	—
204	C₄×C₁₃₇	—	8	2	no	—
205	C₄×C₁₃₇	#440	1	4	yes	—
206	C₄×C₁₃₇	C₂×#117	1	1	yes	characteristic
207	C₄×C₁₃₇	C₄×#41	1	1	yes	characteristic
208	C₄×C₁₃₇	#529	1	2	yes	—
209	C₂×C₁₃₇	—	8	2	no	—
210	C₂×C₁₃₇	#2293	1	1	yes	characteristic
211	C₂×C₁₃₇	C₂×#440	1	1	yes	characteristic
212	C₂×C₁₃₇	#2943	1	1	yes	characteristic
213	C₂×C₁₃₇	#3171	1	2	yes	—
214	C₂×C₁₃₇	#3172	1	2	yes	—
215	#21279	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₁₃₇	#21279	1	1	yes	characteristic, direct product factor, Sylow
217	C₂×C₄×SD₁₆	C₂×C₁₃₇	1	1	yes	characteristic
218	#2295	C₂×C₁₃₇	1	1	yes	characteristic, complemented
219	#2293	C₂×C₁₃₇	1	1	yes	characteristic
220	#1973	C₂×C₁₃₇	1	2	yes	—
221	#1944	C₂×C₁₃₇	1	2	yes	complemented
222	#1936	C₂×C₁₃₇	1	2	yes	—
223	#1935	C₂×C₁₃₇	1	2	yes	complemented
224	C₄×#107	C₂×C₁₃₇	1	1	yes	characteristic, complemented
225	C₄×#103	C₂×C₁₃₇	1	1	yes	characteristic, complemented
226	C₄×#102	C₂×C₁₃₇	1	1	yes	characteristic
227	C₄×#97	C₂×C₁₃₇	1	1	yes	characteristic, complemented
228	C₂²×SD₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
229	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
230	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
231	C₂×#117	—	2	1	no	—
232	C₄×SD₁₆	C₄×C₁₃₇	1	8	yes	complemented
233	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
234	C₂×#106	C₂²×C₁₃₇	1	1	yes	characteristic
235	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
236	C₂×#103	C₂²×C₁₃₇	1	1	yes	characteristic
237	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
238	C₂×#102	C₂²×C₁₃₇	1	1	yes	characteristic
239	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
240	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
241	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
242	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
243	#391	C₂²×C₁₃₇	1	2	yes	—
244	#390	C₂²×C₁₃₇	1	2	yes	—
245	#389	C₂²×C₁₃₇	1	2	yes	—
246	#389	C₂²×C₁₃₇	1	2	yes	—
247	#388	—	2	2	no	—
248	#387	—	2	2	no	—
249	C₄×C₄⋊C₄	—	2	1	no	—
250	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
251	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
252	C₄×C₂²⋊C₄	—	2	1	no	—
253	#376	—	2	1	no	—
254	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
255	#340	C₂²×C₁₃₇	1	2	yes	—
256	#340	C₂²×C₁₃₇	1	2	yes	—
257	#340	C₂²×C₁₃₇	1	2	yes	—
258	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
259	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
260	C₂³×C₄	—	2	1	no	—
261	C₂×SD₁₆	—	2	4	no	—
262	C₂×SD₁₆	C₂×C₄×C₁₃₇	1	4	yes	—
263	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
265	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
266	C₄×Q₈	—	2	2	no	—
267	C₄×Q₈	C₂×C₄×C₁₃₇	1	4	yes	—
268	C₄×D₄	—	2	2	no	—
269	C₄×D₄	C₂×C₄×C₁₃₇	1	4	yes	—
270	#117	—	4	4	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
285	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
286	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
287	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
288	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
289	#107	—	2	4	no	—
290	#106	C₂×C₄×C₁₃₇	1	4	yes	—
291	#103	—	2	4	no	—
292	#103	C₂×C₄×C₁₃₇	1	4	yes	—
293	#102	—	2	4	no	—
294	#102	C₂×C₄×C₁₃₇	1	4	yes	—
295	#97	—	2	4	no	—
296	#97	—	2	4	no	—
297	C₄×C₈	—	2	2	no	—
298	C₄×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
299	#95	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	1	no	—
304	#95	—	2	1	no	—
305	C₂⁴	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	C₂²×C₄×C₁₃₇	1	2	yes	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	C₂²×C₄×C₁₃₇	1	2	yes	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
323	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
327	SD₁₆	—	2	8	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
332	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
333	C₂×C₈	#41×C₁₃₇	1	4	yes	—
334	C₂×C₈	#41×C₁₃₇	1	4	yes	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	4	4	no	—
343	C₄⋊C₄	—	4	4	no	—
344	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
345	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
346	C₂²⋊C₄	—	2	4	no	—
347	C₂²⋊C₄	—	4	4	no	—
348	C₂²⋊C₄	—	4	4	no	—
349	C₄²	—	2	4	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	4	2	no	—
355	C₄²	—	4	2	no	—
356	C₄²	—	4	2	no	—
357	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
358	C₄²	#41×C₁₃₇	1	2	yes	—
359	C₂³	—	2	2	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	2	no	—
364	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
365	Q₈	—	2	2	no	—
366	Q₈	—	2	2	no	—
367	Q₈	—	4	2	no	—
368	D₄	—	2	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	4	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	8	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
393	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
394	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
395	C₂×C₄	#137×C₁₃₇	1	2	yes	—
396	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
397	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
398	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
399	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	2	4	no	—
402	C₈	#117×C₁₃₇	1	4	yes	complemented
403	C₂²	—	4	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
409	C₂²	#532×C₁₃₇	1	2	yes	—
410	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
411	C₂²	C₂×#137×C₁₃₇	1	1	yes	characteristic
412	C₂²	#575×C₁₃₇	1	2	yes	—
413	C₄	—	2	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	8	2	no	—
420	C₄	—	8	2	no	—
421	C₄	#440×C₁₃₇	1	4	yes	—
422	C₄	C₂×#117×C₁₃₇	1	1	yes	characteristic
423	C₄	C₄×#41×C₁₃₇	1	1	yes	characteristic
424	C₄	#529×C₁₃₇	1	2	yes	—
425	C₂	—	8	2	no	—
426	C₂	#2293×C₁₃₇	1	1	yes	characteristic
427	C₂	C₂×#440×C₁₃₇	1	1	yes	characteristic
428	C₂	#2943×C₁₃₇	1	1	yes	characteristic
429	C₂	#3171×C₁₃₇	1	2	yes	—
430	C₂	#3172×C₁₃₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle	C₂³×C₁₃₇	C₂²×D₄
prime radical	C₂²×D₄×C₁₃₇	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₇ ◁ C₄³×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2295×C₁₃₇	C₂	semidirect
5. #1944×C₁₃₇	C₂	semidirect
7. #1935×C₁₃₇	C₂	semidirect
8. C₄×#107×C₁₃₇	C₂	semidirect
9. C₄×#103×C₁₃₇	C₂	semidirect
11. C₄×#97×C₁₃₇	C₂	semidirect
16. C₄×SD₁₆×C₁₃₇	C₄	semidirect
186. C₈×C₁₃₇	#117	semidirect
215. #21279	C₁₃₇	direct (N × H)
216. C₁₃₇	#21279	direct (N × H)
218. #2295	C₂×C₁₃₇	semidirect
221. #1944	C₂×C₁₃₇	semidirect
223. #1935	C₂×C₁₃₇	semidirect
224. C₄×#107	C₂×C₁₃₇	semidirect
225. C₄×#103	C₂×C₁₃₇	semidirect
227. C₄×#97	C₂×C₁₃₇	semidirect
232. C₄×SD₁₆	C₄×C₁₃₇	semidirect
402. C₈	#117×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×SD₁₆×C₁₃₇	2
#2295×C₁₃₇	2
#2293×C₁₃₇	2
#1973×C₁₃₇	2
#1944×C₁₃₇	2
#1936×C₁₃₇	2
#1935×C₁₃₇	2
C₄×#107×C₁₃₇	2
C₄×#103×C₁₃₇	2
C₄×#102×C₁₃₇	2
C₄×#97×C₁₃₇	2
#21279	137

Subgroups — C137×#21279 #46870665

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21279 #46870665