Subgroups — C₁₃₇×#28716 #46878102

Order 35072.

1018 conjugacy classes of subgroups.

The subgroup lattice has 386 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	2	yes	maximal
2	#2868×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#127×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2071×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	#1990×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1802×C₁₃₇	C₂	1	4	yes	maximal, complemented
7	C₄×C₄⋊C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄⋊Q₈×C₁₃₇	—	2	1	no	—
9	C₂×C₄⋊Q₈×C₁₃₇	—	2	1	no	—
10	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	2	yes	—
11	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₃₇	—	2	1	no	—
13	C₂×C₄×D₄×C₁₃₇	—	2	1	no	—
14	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
15	#486×C₁₃₇	—	2	8	no	—
16	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
17	C₂×#102×C₁₃₇	C₂²	1	8	yes	—
18	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
19	#390×C₁₃₇	—	2	1	no	—
20	#390×C₁₃₇	—	2	1	no	—
21	#390×C₁₃₇	C₂²	1	2	yes	—
22	#384×C₁₃₇	—	2	1	no	—
23	#384×C₁₃₇	—	2	1	no	—
24	#384×C₁₃₇	C₂²	1	1	yes	characteristic
25	#384×C₁₃₇	C₂²	1	2	yes	—
26	#384×C₁₃₇	C₂²	1	2	yes	—
27	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
28	#340×C₁₃₇	C₂²	1	8	yes	—
29	#336×C₁₃₇	C₂²	1	2	yes	—
30	C₂²×Q₈×C₁₃₇	—	2	2	no	—
31	C₂²×D₄×C₁₃₇	—	2	1	no	—
32	C₂²×D₄×C₁₃₇	—	2	1	no	—
33	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₃₇	—	2	2	no	—
35	C₂²×C₈×C₁₃₇	C₂³	1	4	yes	—
36	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
37	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
38	C₄⋊Q₈×C₁₃₇	—	4	4	no	—
39	C₄⋊Q₈×C₁₃₇	—	4	4	no	—
40	#127×C₁₃₇	—	2	2	no	—
41	#127×C₁₃₇	D₄	1	4	yes	—
42	C₄×D₄×C₁₃₇	—	2	8	no	—
43	C₄×D₄×C₁₃₇	—	4	4	no	—
44	C₄×D₄×C₁₃₇	—	4	4	no	—
45	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
57	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
64	C₄⋊C₈×C₁₃₇	—	2	4	no	—
65	#102×C₁₃₇	—	2	16	no	—
66	C₄×C₈×C₁₃₇	—	2	4	no	—
67	C₂⁴×C₁₃₇	—	2	2	no	—
68	C₂×Q₈×C₁₃₇	—	4	4	no	—
69	C₂×Q₈×C₁₃₇	—	4	4	no	—
70	C₂×Q₈×C₁₃₇	—	4	4	no	—
71	C₂×D₄×C₁₃₇	—	2	4	no	—
72	C₂×D₄×C₁₃₇	—	2	4	no	—
73	C₂×D₄×C₁₃₇	—	2	4	no	—
74	C₂×D₄×C₁₃₇	—	2	2	no	—
75	C₂×D₄×C₁₃₇	—	2	4	no	—
76	C₂×D₄×C₁₃₇	—	4	2	no	—
77	C₂×D₄×C₁₃₇	—	4	2	no	—
78	C₂×D₄×C₁₃₇	—	4	2	no	—
79	C₂×D₄×C₁₃₇	—	4	2	no	—
80	C₂×D₄×C₁₃₇	C₂×D₄	1	4	yes	—
81	C₂²×C₄×C₁₃₇	—	2	2	no	—
82	C₂²×C₄×C₁₃₇	—	2	4	no	—
83	C₂²×C₄×C₁₃₇	—	4	4	no	—
84	C₂²×C₄×C₁₃₇	—	4	4	no	—
85	C₂²×C₄×C₁₃₇	—	4	4	no	—
86	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
93	C₂×C₈×C₁₃₇	—	2	4	no	—
94	C₂×C₈×C₁₃₇	—	2	4	no	—
95	C₂×C₈×C₁₃₇	—	2	4	no	—
96	C₄⋊C₄×C₁₃₇	—	2	4	no	—
97	C₄⋊C₄×C₁₃₇	—	2	4	no	—
98	C₄⋊C₄×C₁₃₇	—	2	4	no	—
99	C₄⋊C₄×C₁₃₇	—	4	4	no	—
100	C₄⋊C₄×C₁₃₇	—	4	4	no	—
101	C₄⋊C₄×C₁₃₇	—	4	4	no	—
102	C₄⋊C₄×C₁₃₇	—	4	2	no	—
103	C₄⋊C₄×C₁₃₇	—	4	4	no	—
104	C₄⋊C₄×C₁₃₇	—	4	4	no	—
105	C₄⋊C₄×C₁₃₇	—	4	2	no	—
106	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
107	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
108	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
109	C₄²×C₁₃₇	—	2	2	no	—
110	C₄²×C₁₃₇	—	2	2	no	—
111	C₄²×C₁₃₇	—	2	2	no	—
112	C₄²×C₁₃₇	D₈	1	4	yes	—
113	C₄²×C₁₃₇	SD₁₆	1	4	yes	—
114	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
115	C₄²×C₁₃₇	#41	1	2	yes	—
116	C₄²×C₁₃₇	#41	1	4	yes	—
117	C₂³×C₁₃₇	—	2	4	no	—
118	C₂³×C₁₃₇	—	4	2	no	—
119	C₂³×C₁₃₇	—	4	2	no	—
120	C₂³×C₁₃₇	—	4	2	no	—
121	C₂³×C₁₃₇	—	4	2	no	—
122	C₂³×C₁₃₇	—	4	2	no	—
123	C₂³×C₁₃₇	—	4	2	no	—
124	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
125	Q₈×C₁₃₇	—	8	8	no	—
126	D₄×C₁₃₇	—	2	8	no	—
127	D₄×C₁₃₇	—	4	4	no	—
128	D₄×C₁₃₇	—	4	8	no	—
129	D₄×C₁₃₇	—	4	8	no	—
130	C₂×C₄×C₁₃₇	—	2	1	no	—
131	C₂×C₄×C₁₃₇	—	2	1	no	—
132	C₂×C₄×C₁₃₇	—	2	1	no	—
133	C₂×C₄×C₁₃₇	—	2	1	no	—
134	C₂×C₄×C₁₃₇	—	2	1	no	—
135	C₂×C₄×C₁₃₇	—	2	1	no	—
136	C₂×C₄×C₁₃₇	—	4	4	no	—
137	C₂×C₄×C₁₃₇	—	4	2	no	—
138	C₂×C₄×C₁₃₇	—	4	2	no	—
139	C₂×C₄×C₁₃₇	—	4	4	no	—
140	C₂×C₄×C₁₃₇	—	4	2	no	—
141	C₂×C₄×C₁₃₇	—	4	4	no	—
142	C₂×C₄×C₁₃₇	—	8	8	no	—
143	C₂×C₄×C₁₃₇	#121	1	2	yes	—
144	C₂×C₄×C₁₃₇	#121	1	2	yes	—
145	C₂×C₄×C₁₃₇	#124	1	2	yes	—
146	C₂×C₄×C₁₃₇	#124	1	2	yes	—
147	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
148	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
149	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
150	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	2	yes	—
151	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	2	yes	—
152	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	2	yes	—
153	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
154	C₂×C₄×C₁₃₇	#137	1	2	yes	—
155	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
157	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
159	C₈×C₁₃₇	—	4	4	no	—
160	C₂²×C₁₃₇	—	4	4	no	—
161	C₂²×C₁₃₇	—	4	4	no	—
162	C₂²×C₁₃₇	—	4	4	no	—
163	C₂²×C₁₃₇	—	8	2	no	—
164	C₂²×C₁₃₇	—	8	2	no	—
165	C₂²×C₁₃₇	—	8	2	no	—
166	C₂²×C₁₃₇	—	8	2	no	—
167	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
168	C₂²×C₁₃₇	C₂×#124	1	1	yes	characteristic
169	C₂²×C₁₃₇	#536	1	1	yes	characteristic
170	C₂²×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
171	C₂²×C₁₃₇	C₂²×SD₁₆	1	1	yes	characteristic
172	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₂²×C₁₃₇	C₂×#137	1	1	yes	characteristic
174	C₄×C₁₃₇	—	2	2	no	—
175	C₄×C₁₃₇	—	2	2	no	—
176	C₄×C₁₃₇	—	2	2	no	—
177	C₄×C₁₃₇	—	8	2	no	—
178	C₄×C₁₃₇	—	8	4	no	—
179	C₄×C₁₃₇	#459	1	4	yes	—
180	C₄×C₁₃₇	#461	1	4	yes	—
181	C₄×C₁₃₇	#486	1	4	yes	complemented
182	C₄×C₁₃₇	#547	1	2	yes	—
183	C₄×C₁₃₇	#556	1	2	yes	—
184	C₂×C₁₃₇	—	8	4	no	—
185	C₂×C₁₃₇	#2547	1	1	yes	characteristic
186	C₂×C₁₃₇	C₂×#459	1	1	yes	characteristic
187	C₂×C₁₃₇	C₂×#461	1	1	yes	characteristic
188	C₂×C₁₃₇	C₂×#486	1	1	yes	characteristic
189	C₂×C₁₃₇	#3141	1	1	yes	characteristic
190	C₂×C₁₃₇	#3226	1	1	yes	characteristic
191	C₂×C₁₃₇	#3227	1	1	yes	characteristic
192	#28716	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₁₃₇	#28716	1	1	yes	characteristic, direct product factor, Sylow
194	C₂×#486	C₂×C₁₃₇	1	2	yes	—
195	#2868	C₂×C₁₃₇	1	1	yes	characteristic, complemented
196	C₄×#127	C₂×C₁₃₇	1	1	yes	characteristic
197	#2071	C₂×C₁₃₇	1	4	yes	complemented
198	#1990	C₂×C₁₃₇	1	2	yes	complemented
199	#1802	C₂×C₁₃₇	1	4	yes	complemented
200	C₄×C₄⋊C₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
201	C₂×C₄⋊Q₈	—	2	1	no	—
202	C₂×C₄⋊Q₈	—	2	1	no	—
203	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
204	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
205	C₂×C₄×D₄	—	2	1	no	—
206	C₂×C₄×D₄	—	2	1	no	—
207	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
208	#486	—	2	8	no	—
209	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
210	C₂×#102	C₂²×C₁₃₇	1	8	yes	—
211	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
212	#390	—	2	1	no	—
213	#390	—	2	1	no	—
214	#390	C₂²×C₁₃₇	1	2	yes	—
215	#384	—	2	1	no	—
216	#384	—	2	1	no	—
217	#384	C₂²×C₁₃₇	1	1	yes	characteristic
218	#384	C₂²×C₁₃₇	1	2	yes	—
219	#384	C₂²×C₁₃₇	1	2	yes	—
220	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
221	#340	C₂²×C₁₃₇	1	8	yes	—
222	#336	C₂²×C₁₃₇	1	2	yes	—
223	C₂²×Q₈	—	2	2	no	—
224	C₂²×D₄	—	2	1	no	—
225	C₂²×D₄	—	2	1	no	—
226	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
227	C₂³×C₄	—	2	2	no	—
228	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
229	C₄⋊Q₈	—	2	4	no	—
230	C₄⋊Q₈	—	2	4	no	—
231	C₄⋊Q₈	—	4	4	no	—
232	C₄⋊Q₈	—	4	4	no	—
233	#127	—	2	2	no	—
234	#127	D₄×C₁₃₇	1	4	yes	—
235	C₄×D₄	—	2	8	no	—
236	C₄×D₄	—	4	4	no	—
237	C₄×D₄	—	4	4	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
251	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
252	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
253	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
254	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
257	C₄⋊C₈	—	2	4	no	—
258	#102	—	2	16	no	—
259	C₄×C₈	—	2	4	no	—
260	C₂⁴	—	2	2	no	—
261	C₂×Q₈	—	4	4	no	—
262	C₂×Q₈	—	4	4	no	—
263	C₂×Q₈	—	4	4	no	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	—	2	4	no	—
266	C₂×D₄	—	2	4	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	—	4	2	no	—
273	C₂×D₄	C₂×D₄×C₁₃₇	1	4	yes	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	4	4	no	—
279	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
285	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	4	4	no	—
293	C₄⋊C₄	—	4	4	no	—
294	C₄⋊C₄	—	4	4	no	—
295	C₄⋊C₄	—	4	2	no	—
296	C₄⋊C₄	—	4	4	no	—
297	C₄⋊C₄	—	4	4	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₂²⋊C₄	—	4	4	no	—
300	C₂²⋊C₄	—	4	4	no	—
301	C₂²⋊C₄	—	4	4	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	D₈×C₁₃₇	1	4	yes	—
306	C₄²	SD₁₆×C₁₃₇	1	4	yes	—
307	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
308	C₄²	#41×C₁₃₇	1	2	yes	—
309	C₄²	#41×C₁₃₇	1	4	yes	—
310	C₂³	—	2	4	no	—
311	C₂³	—	4	2	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	2	no	—
317	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
318	Q₈	—	8	8	no	—
319	D₄	—	2	8	no	—
320	D₄	—	4	8	no	—
321	D₄	—	4	8	no	—
322	D₄	—	4	4	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	8	8	no	—
336	C₂×C₄	#121×C₁₃₇	1	2	yes	—
337	C₂×C₄	#121×C₁₃₇	1	2	yes	—
338	C₂×C₄	#124×C₁₃₇	1	2	yes	—
339	C₂×C₄	#124×C₁₃₇	1	2	yes	—
340	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
341	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
342	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
343	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	2	yes	—
344	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	2	yes	—
345	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	2	yes	—
346	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
347	C₂×C₄	#137×C₁₃₇	1	2	yes	—
348	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
349	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
350	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
351	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
352	C₈	—	4	4	no	—
353	C₂²	—	4	4	no	—
354	C₂²	—	4	4	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	8	2	no	—
360	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
361	C₂²	C₂×#124×C₁₃₇	1	1	yes	characteristic
362	C₂²	#536×C₁₃₇	1	1	yes	characteristic
363	C₂²	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
364	C₂²	C₂²×SD₁₆×C₁₃₇	1	1	yes	characteristic
365	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
366	C₂²	C₂×#137×C₁₃₇	1	1	yes	characteristic
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	2	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	4	no	—
372	C₄	#459×C₁₃₇	1	4	yes	—
373	C₄	#461×C₁₃₇	1	4	yes	—
374	C₄	#486×C₁₃₇	1	4	yes	complemented
375	C₄	#547×C₁₃₇	1	2	yes	—
376	C₄	#556×C₁₃₇	1	2	yes	—
377	C₂	—	8	4	no	—
378	C₂	#2547×C₁₃₇	1	1	yes	characteristic
379	C₂	C₂×#459×C₁₃₇	1	1	yes	characteristic
380	C₂	C₂×#461×C₁₃₇	1	1	yes	characteristic
381	C₂	C₂×#486×C₁₃₇	1	1	yes	characteristic
382	C₂	#3141×C₁₃₇	1	1	yes	characteristic
383	C₂	#3226×C₁₃₇	1	1	yes	characteristic
384	C₂	#3227×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
2. #2868×C₁₃₇	C₂	semidirect
4. #2071×C₁₃₇	C₂	semidirect
5. #1990×C₁₃₇	C₂	semidirect
6. #1802×C₁₃₇	C₂	semidirect
7. C₄×C₄⋊C₈×C₁₃₇	C₂	semidirect
181. C₄×C₁₃₇	#486	semidirect
192. #28716	C₁₃₇	direct (N × H)
193. C₁₃₇	#28716	direct (N × H)
195. #2868	C₂×C₁₃₇	semidirect
197. #2071	C₂×C₁₃₇	semidirect
198. #1990	C₂×C₁₃₇	semidirect
199. #1802	C₂×C₁₃₇	semidirect
200. C₄×C₄⋊C₈	C₂×C₁₃₇	semidirect
374. C₄	#486×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
#2868×C₁₃₇	2
C₄×#127×C₁₃₇	2
#2071×C₁₃₇	2
#1990×C₁₃₇	2
#1802×C₁₃₇	2
C₄×C₄⋊C₈×C₁₃₇	2
#28716	137

Subgroups — C137×#28716 #46878102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28716 #46878102