Subgroups — C₁₃₇×#28750 #46878136

Order 35072.

934 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#487×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#486×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2858×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₄×C₄⋊Q₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2042×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1983×C₁₃₇	C₂	1	4	yes	maximal, complemented
7	#1957×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1956×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₄⋊C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#124×C₁₃₇	C₂²	1	2	yes	—
14	C₂×#124×C₁₃₇	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₃₇	—	2	1	no	—
16	#487×C₁₃₇	—	2	4	no	—
17	#486×C₁₃₇	—	2	4	no	—
18	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
19	C₂×#103×C₁₃₇	C₂²	1	4	yes	—
20	C₂×#103×C₁₃₇	C₂²	1	4	yes	—
21	C₂×#102×C₁₃₇	C₂²	1	4	yes	—
22	C₂×#102×C₁₃₇	C₂²	1	4	yes	—
23	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
25	#391×C₁₃₇	—	2	1	no	—
26	#390×C₁₃₇	—	2	1	no	—
27	#390×C₁₃₇	—	2	1	no	—
28	#390×C₁₃₇	—	2	1	no	—
29	#390×C₁₃₇	—	2	1	no	—
30	#389×C₁₃₇	—	2	1	no	—
31	#389×C₁₃₇	C₂²	1	2	yes	—
32	#384×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₁₃₇	—	2	1	no	—
34	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
35	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
36	#336×C₁₃₇	C₂²	1	2	yes	—
37	C₂²×Q₈×C₁₃₇	—	2	1	no	—
38	C₂²×Q₈×C₁₃₇	C₂³	1	2	yes	—
39	C₂²×D₄×C₁₃₇	—	2	1	no	—
40	C₂²×D₄×C₁₃₇	—	2	1	no	—
41	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
44	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
45	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
46	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
47	C₄⋊Q₈×C₁₃₇	D₄	1	4	yes	—
48	#127×C₁₃₇	—	2	2	no	—
49	#127×C₁₃₇	—	2	2	no	—
50	#124×C₁₃₇	—	2	8	no	—
51	#124×C₁₃₇	—	4	4	no	—
52	C₄×Q₈×C₁₃₇	—	4	4	no	—
53	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
65	C₂×C₄²×C₁₃₇	—	2	2	no	—
66	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₁₃₇	—	2	4	no	—
74	#103×C₁₃₇	—	2	8	no	—
75	#103×C₁₃₇	—	4	4	no	—
76	#102×C₁₃₇	—	2	8	no	—
77	#102×C₁₃₇	—	4	4	no	—
78	C₄×C₈×C₁₃₇	—	2	2	no	—
79	C₄×C₈×C₁₃₇	—	2	2	no	—
80	#95×C₁₃₇	—	2	2	no	—
81	#95×C₁₃₇	—	2	2	no	—
82	C₂⁴×C₁₃₇	—	2	2	no	—
83	C₂×Q₈×C₁₃₇	—	2	4	no	—
84	C₂×Q₈×C₁₃₇	—	2	2	no	—
85	C₂×Q₈×C₁₃₇	—	2	4	no	—
86	C₂×Q₈×C₁₃₇	—	2	2	no	—
87	C₂×Q₈×C₁₃₇	—	2	4	no	—
88	C₂×Q₈×C₁₃₇	—	4	2	no	—
89	C₂×Q₈×C₁₃₇	—	4	2	no	—
90	C₂×D₄×C₁₃₇	—	2	2	no	—
91	C₂×D₄×C₁₃₇	—	2	4	no	—
92	C₂×D₄×C₁₃₇	—	2	2	no	—
93	C₂×D₄×C₁₃₇	—	2	4	no	—
94	C₂×D₄×C₁₃₇	—	4	2	no	—
95	C₂×D₄×C₁₃₇	—	4	2	no	—
96	C₂×D₄×C₁₃₇	—	4	2	no	—
97	C₂×D₄×C₁₃₇	—	4	2	no	—
98	C₂×D₄×C₁₃₇	—	4	2	no	—
99	C₂×D₄×C₁₃₇	—	4	2	no	—
100	C₂²×C₄×C₁₃₇	—	2	2	no	—
101	C₂²×C₄×C₁₃₇	—	2	2	no	—
102	C₂²×C₄×C₁₃₇	—	2	2	no	—
103	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₁₃₇	—	2	2	no	—
111	C₂×C₈×C₁₃₇	—	2	2	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	—	2	2	no	—
116	C₄⋊C₄×C₁₃₇	—	2	4	no	—
117	C₄⋊C₄×C₁₃₇	—	2	2	no	—
118	C₄⋊C₄×C₁₃₇	—	2	4	no	—
119	C₄⋊C₄×C₁₃₇	—	4	4	no	—
120	C₄⋊C₄×C₁₃₇	—	4	2	no	—
121	C₄⋊C₄×C₁₃₇	—	4	2	no	—
122	C₄⋊C₄×C₁₃₇	—	4	2	no	—
123	C₄⋊C₄×C₁₃₇	—	4	2	no	—
124	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
125	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
126	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
127	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
128	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
129	C₄²×C₁₃₇	—	2	2	no	—
130	C₄²×C₁₃₇	—	2	2	no	—
131	C₄²×C₁₃₇	—	2	2	no	—
132	C₄²×C₁₃₇	—	2	2	no	—
133	C₄²×C₁₃₇	—	2	2	no	—
134	C₄²×C₁₃₇	—	4	4	no	—
135	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
136	C₄²×C₁₃₇	#41	1	2	yes	—
137	C₄²×C₁₃₇	#41	1	4	yes	—
138	C₂³×C₁₃₇	—	4	2	no	—
139	C₂³×C₁₃₇	—	4	2	no	—
140	C₂³×C₁₃₇	—	4	2	no	—
141	C₂³×C₁₃₇	—	4	2	no	—
142	C₂³×C₁₃₇	—	4	2	no	—
143	C₂³×C₁₃₇	—	4	2	no	—
144	C₂³×C₁₃₇	—	4	2	no	—
145	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₁₃₇	—	4	8	no	—
147	Q₈×C₁₃₇	—	4	4	no	—
148	Q₈×C₁₃₇	—	4	4	no	—
149	D₄×C₁₃₇	—	4	4	no	—
150	D₄×C₁₃₇	—	4	4	no	—
151	D₄×C₁₃₇	—	8	4	no	—
152	D₄×C₁₃₇	—	8	4	no	—
153	C₂×C₄×C₁₃₇	—	2	1	no	—
154	C₂×C₄×C₁₃₇	—	2	1	no	—
155	C₂×C₄×C₁₃₇	—	2	1	no	—
156	C₂×C₄×C₁₃₇	—	2	1	no	—
157	C₂×C₄×C₁₃₇	—	2	4	no	—
158	C₂×C₄×C₁₃₇	—	2	1	no	—
159	C₂×C₄×C₁₃₇	—	2	1	no	—
160	C₂×C₄×C₁₃₇	—	2	1	no	—
161	C₂×C₄×C₁₃₇	—	2	1	no	—
162	C₂×C₄×C₁₃₇	—	2	1	no	—
163	C₂×C₄×C₁₃₇	—	2	1	no	—
164	C₂×C₄×C₁₃₇	—	4	2	no	—
165	C₂×C₄×C₁₃₇	—	4	2	no	—
166	C₂×C₄×C₁₃₇	—	4	2	no	—
167	C₂×C₄×C₁₃₇	—	4	2	no	—
168	C₂×C₄×C₁₃₇	—	4	2	no	—
169	C₂×C₄×C₁₃₇	—	4	2	no	—
170	C₂×C₄×C₁₃₇	—	4	2	no	—
171	C₂×C₄×C₁₃₇	—	4	2	no	—
172	C₂×C₄×C₁₃₇	#121	1	2	yes	—
173	C₂×C₄×C₁₃₇	#121	1	2	yes	—
174	C₂×C₄×C₁₃₇	#124	1	2	yes	—
175	C₂×C₄×C₁₃₇	#124	1	2	yes	—
176	C₂×C₄×C₁₃₇	#135	1	2	yes	—
177	C₂×C₄×C₁₃₇	#135	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	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
182	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
184	C₈×C₁₃₇	—	4	2	no	—
185	C₈×C₁₃₇	—	4	2	no	—
186	C₂²×C₁₃₇	—	8	2	no	—
187	C₂²×C₁₃₇	—	8	2	no	—
188	C₂²×C₁₃₇	—	8	2	no	—
189	C₂²×C₁₃₇	—	8	2	no	—
190	C₂²×C₁₃₇	—	8	2	no	—
191	C₂²×C₁₃₇	—	8	2	no	—
192	C₂²×C₁₃₇	—	8	2	no	—
193	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
194	C₂²×C₁₃₇	C₂×#124	1	1	yes	characteristic
195	C₂²×C₁₃₇	#535	1	1	yes	characteristic
196	C₂²×C₁₃₇	C₂×#135	1	1	yes	characteristic
197	C₂²×C₁₃₇	C₂×#135	1	1	yes	characteristic
198	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₂²×C₁₃₇	C₂×#137	1	1	yes	characteristic
200	C₄×C₁₃₇	—	2	2	no	—
201	C₄×C₁₃₇	—	2	2	no	—
202	C₄×C₁₃₇	—	4	1	no	—
203	C₄×C₁₃₇	—	4	1	no	—
204	C₄×C₁₃₇	—	4	4	no	—
205	C₄×C₁₃₇	—	8	2	no	—
206	C₄×C₁₃₇	—	8	2	no	—
207	C₄×C₁₃₇	#463	1	4	yes	—
208	C₄×C₁₃₇	#464	1	4	yes	—
209	C₄×C₁₃₇	#550	1	2	yes	—
210	C₄×C₁₃₇	#559	1	2	yes	—
211	C₂×C₁₃₇	—	16	2	no	—
212	C₂×C₁₃₇	#2548	1	1	yes	characteristic
213	C₂×C₁₃₇	C₂×#463	1	1	yes	characteristic
214	C₂×C₁₃₇	C₂×#464	1	1	yes	characteristic
215	C₂×C₁₃₇	#3131	1	1	yes	characteristic
216	C₂×C₁₃₇	#3141	1	1	yes	characteristic
217	C₂×C₁₃₇	#3207	1	1	yes	characteristic
218	C₂×C₁₃₇	#3210	1	1	yes	characteristic
219	#28750	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₁₃₇	#28750	1	1	yes	characteristic, direct product factor, Sylow
221	C₂×#487	C₂×C₁₃₇	1	1	yes	characteristic, complemented
222	C₂×#486	C₂×C₁₃₇	1	1	yes	characteristic
223	#2858	C₂×C₁₃₇	1	1	yes	characteristic
224	C₄×C₄⋊Q₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
225	#2042	C₂×C₁₃₇	1	4	yes	complemented
226	#1983	C₂×C₁₃₇	1	4	yes	complemented
227	#1957	C₂×C₁₃₇	1	1	yes	characteristic
228	#1956	C₂×C₁₃₇	1	1	yes	characteristic, complemented
229	C₄×C₄⋊C₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
230	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
231	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
232	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
233	C₂×#124	C₂²×C₁₃₇	1	2	yes	—
234	C₂×#124	C₂²×C₁₃₇	1	2	yes	—
235	C₂×C₄×Q₈	—	2	1	no	—
236	#487	—	2	4	no	—
237	#486	—	2	4	no	—
238	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
239	C₂×#103	C₂²×C₁₃₇	1	4	yes	—
240	C₂×#103	C₂²×C₁₃₇	1	4	yes	—
241	C₂×#102	C₂²×C₁₃₇	1	4	yes	—
242	C₂×#102	C₂²×C₁₃₇	1	4	yes	—
243	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
244	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
245	#391	—	2	1	no	—
246	#390	—	2	1	no	—
247	#390	—	2	1	no	—
248	#390	—	2	1	no	—
249	#390	—	2	1	no	—
250	#389	—	2	1	no	—
251	#389	C₂²×C₁₃₇	1	2	yes	—
252	#384	C₂²×C₁₃₇	1	1	yes	characteristic
253	C₄×C₄⋊C₄	—	2	1	no	—
254	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
255	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
256	#336	C₂²×C₁₃₇	1	2	yes	—
257	C₂²×Q₈	—	2	1	no	—
258	C₂²×Q₈	C₂³×C₁₃₇	1	2	yes	—
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	—	2	1	no	—
261	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
262	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
263	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
264	C₄⋊Q₈	—	2	2	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	C₄⋊Q₈	—	2	2	no	—
267	C₄⋊Q₈	D₄×C₁₃₇	1	4	yes	—
268	#127	—	2	2	no	—
269	#127	—	2	2	no	—
270	#124	—	2	8	no	—
271	#124	—	4	4	no	—
272	C₄×Q₈	—	4	4	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
287	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
288	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
289	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
293	C₄⋊C₈	—	2	4	no	—
294	#103	—	2	8	no	—
295	#103	—	4	4	no	—
296	#102	—	2	8	no	—
297	#102	—	4	4	no	—
298	C₄×C₈	—	2	2	no	—
299	C₄×C₈	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	C₂⁴	—	2	2	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	—	4	2	no	—
309	C₂×Q₈	—	4	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
329	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	4	4	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
345	C₂²⋊C₄	—	4	4	no	—
346	C₂²⋊C₄	—	4	4	no	—
347	C₂²⋊C₄	—	4	4	no	—
348	C₂²⋊C₄	—	4	4	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	4	4	no	—
355	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
356	C₄²	#41×C₁₃₇	1	2	yes	—
357	C₄²	#41×C₁₃₇	1	4	yes	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
366	Q₈	—	4	8	no	—
367	Q₈	—	4	4	no	—
368	Q₈	—	4	4	no	—
369	D₄	—	4	4	no	—
370	D₄	—	4	4	no	—
371	D₄	—	8	4	no	—
372	D₄	—	8	4	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	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	#121×C₁₃₇	1	2	yes	—
393	C₂×C₄	#121×C₁₃₇	1	2	yes	—
394	C₂×C₄	#124×C₁₃₇	1	2	yes	—
395	C₂×C₄	#124×C₁₃₇	1	2	yes	—
396	C₂×C₄	#135×C₁₃₇	1	2	yes	—
397	C₂×C₄	#135×C₁₃₇	1	2	yes	—
398	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
399	C₂×C₄	#137×C₁₃₇	1	2	yes	—
400	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
401	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
402	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
403	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
404	C₈	—	4	2	no	—
405	C₈	—	4	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	2	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
414	C₂²	C₂×#124×C₁₃₇	1	1	yes	characteristic
415	C₂²	#535×C₁₃₇	1	1	yes	characteristic
416	C₂²	C₂×#135×C₁₃₇	1	1	yes	characteristic
417	C₂²	C₂×#135×C₁₃₇	1	1	yes	characteristic
418	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
419	C₂²	C₂×#137×C₁₃₇	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	4	no	—
425	C₄	—	8	2	no	—
426	C₄	—	8	2	no	—
427	C₄	#463×C₁₃₇	1	4	yes	—
428	C₄	#464×C₁₃₇	1	4	yes	—
429	C₄	#550×C₁₃₇	1	2	yes	—
430	C₄	#559×C₁₃₇	1	2	yes	—
431	C₂	—	16	2	no	—
432	C₂	#2548×C₁₃₇	1	1	yes	characteristic
433	C₂	C₂×#463×C₁₃₇	1	1	yes	characteristic
434	C₂	C₂×#464×C₁₃₇	1	1	yes	characteristic
435	C₂	#3131×C₁₃₇	1	1	yes	characteristic
436	C₂	#3141×C₁₃₇	1	1	yes	characteristic
437	C₂	#3207×C₁₃₇	1	1	yes	characteristic
438	C₂	#3210×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂×#127×C₁₃₇	C₂²
LCS	G ▷ C₂²×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
1. C₂×#487×C₁₃₇	C₂	semidirect
4. C₄×C₄⋊Q₈×C₁₃₇	C₂	semidirect
5. #2042×C₁₃₇	C₂	semidirect
6. #1983×C₁₃₇	C₂	semidirect
8. #1956×C₁₃₇	C₂	semidirect
9. C₄×C₄⋊C₈×C₁₃₇	C₂	semidirect
219. #28750	C₁₃₇	direct (N × H)
220. C₁₃₇	#28750	direct (N × H)
221. C₂×#487	C₂×C₁₃₇	semidirect
224. C₄×C₄⋊Q₈	C₂×C₁₃₇	semidirect
225. #2042	C₂×C₁₃₇	semidirect
226. #1983	C₂×C₁₃₇	semidirect
228. #1956	C₂×C₁₃₇	semidirect
229. C₄×C₄⋊C₈	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#487×C₁₃₇	2
C₂×#486×C₁₃₇	2
#2858×C₁₃₇	2
C₄×C₄⋊Q₈×C₁₃₇	2
#2042×C₁₃₇	2
#1983×C₁₃₇	2
#1957×C₁₃₇	2
#1956×C₁₃₇	2
C₄×C₄⋊C₈×C₁₃₇	2
#28750	137

Subgroups — C137×#28750 #46878136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28750 #46878136