Subgroups — C₁₃₇×#21200 #46870586

Order 35072.

1726 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#417×C₁₃₇	C₂	1	4	yes	maximal, complemented
3	C₂×C₄×M₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#384×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1959×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1957×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1956×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₁₃₇	C₂²	1	2	yes	—
9	C₂²×M₁₆×C₁₃₇	C₂²	1	2	yes	—
10	#532×C₁₃₇	—	2	4	no	—
11	#532×C₁₃₇	C₄	1	8	yes	complemented
12	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×#124×C₁₃₇	C₂²	1	2	yes	—
15	C₂×#121×C₁₃₇	—	2	2	no	—
16	C₂×C₄×D₄×C₁₃₇	—	2	2	no	—
17	C₂²×C₄⋊C₄×C₁₃₇	—	2	2	no	—
18	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
20	#417×C₁₃₇	—	2	16	no	—
21	C₂×#103×C₁₃₇	C₂²	1	8	yes	—
22	C₂×#102×C₁₃₇	C₂²	1	8	yes	—
23	C₄×M₁₆×C₁₃₇	—	2	4	no	—
24	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
26	#384×C₁₃₇	—	2	2	no	—
27	#384×C₁₃₇	C₂²	1	2	yes	—
28	#384×C₁₃₇	C₂²	1	2	yes	—
29	C₂×#41×C₁₃₇	—	2	4	no	—
30	C₂×#41×C₁₃₇	—	2	8	no	—
31	C₂×#41×C₁₃₇	—	2	8	no	—
32	C₂×#41×C₁₃₇	C₂×C₄	1	8	yes	—
33	C₂²×Q₈×C₁₃₇	C₂³	1	2	yes	—
34	C₂²×D₄×C₁₃₇	—	2	2	no	—
35	C₂²×D₄×C₁₃₇	—	2	2	no	—
36	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₃₇	—	2	2	no	—
38	C₂³×C₄×C₁₃₇	—	2	2	no	—
39	C₂³×C₄×C₁₃₇	D₄	1	2	yes	—
40	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
41	C₂×M₁₆×C₁₃₇	—	2	4	no	—
42	C₂×M₁₆×C₁₃₇	—	2	4	no	—
43	C₂×M₁₆×C₁₃₇	D₄	1	8	yes	complemented
44	C₂²×C₈×C₁₃₇	C₂³	1	4	yes	—
45	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
46	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	4	yes	complemented
47	#127×C₁₃₇	—	2	2	no	—
48	#127×C₁₃₇	C₂×C₄	1	4	yes	complemented
49	#124×C₁₃₇	—	2	4	no	—
50	#124×C₁₃₇	C₂×C₄	1	8	yes	complemented
51	#121×C₁₃₇	—	2	16	no	—
52	C₄×D₄×C₁₃₇	—	2	16	no	—
53	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₇	—	2	8	no	—
55	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
58	C₂×C₄⋊C₄×C₁₃₇	—	4	8	no	—
59	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
60	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
61	C₂×C₄²×C₁₃₇	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
63	C₂×C₄²×C₁₃₇	D₄	1	4	yes	—
64	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
66	#103×C₁₃₇	—	2	16	no	—
67	#102×C₁₃₇	—	2	16	no	—
68	#97×C₁₃₇	—	2	4	no	—
69	C₄×C₈×C₁₃₇	—	2	4	no	—
70	C₂⁴×C₁₃₇	—	2	2	no	—
71	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
72	#41×C₁₃₇	—	2	32	no	—
73	#41×C₁₃₇	—	4	16	no	—
74	C₂×Q₈×C₁₃₇	—	2	2	no	—
75	C₂×Q₈×C₁₃₇	—	2	4	no	—
76	C₂×Q₈×C₁₃₇	—	2	4	no	—
77	C₂×Q₈×C₁₃₇	C₂²×C₄	1	4	yes	—
78	C₂×D₄×C₁₃₇	—	2	8	no	—
79	C₂×D₄×C₁₃₇	—	2	8	no	—
80	C₂×D₄×C₁₃₇	—	2	4	no	—
81	C₂×D₄×C₁₃₇	—	2	2	no	—
82	C₂×D₄×C₁₃₇	—	2	4	no	—
83	C₂×D₄×C₁₃₇	—	4	4	no	—
84	C₂×D₄×C₁₃₇	—	4	4	no	—
85	C₂×D₄×C₁₃₇	—	4	4	no	—
86	C₂×D₄×C₁₃₇	—	4	4	no	—
87	C₂×D₄×C₁₃₇	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₁₃₇	—	2	4	no	—
89	C₂²×C₄×C₁₃₇	—	2	4	no	—
90	C₂²×C₄×C₁₃₇	—	2	2	no	—
91	C₂²×C₄×C₁₃₇	—	2	8	no	—
92	C₂²×C₄×C₁₃₇	—	2	4	no	—
93	C₂²×C₄×C₁₃₇	—	4	4	no	—
94	C₂²×C₄×C₁₃₇	—	4	4	no	—
95	C₂²×C₄×C₁₃₇	—	4	8	no	—
96	C₂²×C₄×C₁₃₇	—	4	4	no	—
97	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	8	yes	—
98	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
105	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
106	M₁₆×C₁₃₇	—	2	16	no	—
107	C₂×C₈×C₁₃₇	—	2	4	no	—
108	C₂×C₈×C₁₃₇	—	2	4	no	—
109	C₂×C₈×C₁₃₇	C₂×D₄	1	8	yes	—
110	C₄⋊C₄×C₁₃₇	—	2	8	no	—
111	C₄⋊C₄×C₁₃₇	—	2	8	no	—
112	C₄⋊C₄×C₁₃₇	—	4	8	no	—
113	C₄⋊C₄×C₁₃₇	—	4	4	no	—
114	C₄⋊C₄×C₁₃₇	—	4	8	no	—
115	C₂²⋊C₄×C₁₃₇	—	2	16	no	—
116	C₄²×C₁₃₇	C₂²⋊C₄	1	8	yes	—
117	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
118	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
119	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
120	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
121	C₂³×C₁₃₇	—	2	2	no	—
122	C₂³×C₁₃₇	—	2	2	no	—
123	C₂³×C₁₃₇	—	2	4	no	—
124	C₂³×C₁₃₇	—	4	2	no	—
125	C₂³×C₁₃₇	—	4	2	no	—
126	C₂³×C₁₃₇	—	4	4	no	—
127	C₂³×C₁₃₇	—	4	4	no	—
128	C₂³×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
129	C₂³×C₁₃₇	#124	1	2	yes	—
130	C₂³×C₁₃₇	#127	1	2	yes	—
131	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
132	Q₈×C₁₃₇	—	2	8	no	—
133	Q₈×C₁₃₇	—	4	4	no	—
134	D₄×C₁₃₇	—	2	8	no	—
135	D₄×C₁₃₇	—	4	16	no	—
136	D₄×C₁₃₇	—	4	4	no	—
137	D₄×C₁₃₇	—	4	16	no	—
138	C₂×C₄×C₁₃₇	—	2	2	no	—
139	C₂×C₄×C₁₃₇	—	2	2	no	—
140	C₂×C₄×C₁₃₇	—	2	16	no	—
141	C₂×C₄×C₁₃₇	—	2	4	no	—
142	C₂×C₄×C₁₃₇	—	4	2	no	—
143	C₂×C₄×C₁₃₇	—	4	2	no	—
144	C₂×C₄×C₁₃₇	—	4	16	no	—
145	C₂×C₄×C₁₃₇	—	4	4	no	—
146	C₂×C₄×C₁₃₇	—	4	8	no	—
147	C₂×C₄×C₁₃₇	—	8	8	no	—
148	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	4	yes	—
149	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	4	yes	—
151	C₂×C₄×C₁₃₇	C₄×D₄	1	8	yes	—
152	C₂×C₄×C₁₃₇	#121	1	8	yes	—
153	C₂×C₄×C₁₃₇	#124	1	2	yes	—
154	C₂×C₄×C₁₃₇	#127	1	2	yes	—
155	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	4	yes	—
156	C₂×C₄×C₁₃₇	#137	1	4	yes	—
157	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
159	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
161	C₈×C₁₃₇	—	2	8	no	—
162	C₂²×C₁₃₇	—	2	4	no	—
163	C₂²×C₁₃₇	—	2	4	no	—
164	C₂²×C₁₃₇	—	2	2	no	—
165	C₂²×C₁₃₇	—	2	2	no	—
166	C₂²×C₁₃₇	—	4	8	no	—
167	C₂²×C₁₃₇	—	4	4	no	—
168	C₂²×C₁₃₇	—	8	4	no	—
169	C₂²×C₁₃₇	—	8	2	no	—
170	C₂²×C₁₃₇	—	8	2	no	—
171	C₂²×C₁₃₇	#390	1	4	yes	—
172	C₂²×C₁₃₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
173	C₂²×C₁₃₇	C₂×#124	1	1	yes	characteristic
174	C₂²×C₁₃₇	C₂×#127	1	1	yes	characteristic
175	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
176	C₂²×C₁₃₇	C₂×#137	1	2	yes	—
177	C₄×C₁₃₇	—	2	4	no	—
178	C₄×C₁₃₇	—	4	4	no	—
179	C₄×C₁₃₇	—	8	4	no	—
180	C₄×C₁₃₇	#390	1	4	yes	—
181	C₄×C₁₃₇	#417	1	8	yes	complemented
182	C₄×C₁₃₇	C₂×C₄×D₄	1	2	yes	—
183	C₄×C₁₃₇	C₂×#121	1	2	yes	—
184	C₂×C₁₃₇	—	2	4	no	—
185	C₂×C₁₃₇	—	8	4	no	—
186	C₂×C₁₃₇	C₂×#390	1	1	yes	characteristic
187	C₂×C₁₃₇	C₂×#417	1	2	yes	—
188	C₂×C₁₃₇	#3141	1	2	yes	—
189	C₂×C₁₃₇	#3151	1	1	yes	characteristic
190	C₂×C₁₃₇	#3152	1	1	yes	characteristic
191	#21200	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₁₃₇	#21200	1	1	yes	characteristic, direct product factor, Sylow
193	C₂×#532	C₂×C₁₃₇	1	1	yes	characteristic
194	C₂×#417	C₂×C₁₃₇	1	4	yes	complemented
195	C₂×C₄×M₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
196	C₂×#384	C₂×C₁₃₇	1	1	yes	characteristic, complemented
197	#1959	C₂×C₁₃₇	1	4	yes	complemented
198	#1957	C₂×C₁₃₇	1	2	yes	complemented
199	#1956	C₂×C₁₃₇	1	2	yes	complemented
200	C₂²×#41	C₂²×C₁₃₇	1	2	yes	—
201	C₂²×M₁₆	C₂²×C₁₃₇	1	2	yes	—
202	#532	—	2	4	no	—
203	#532	C₄×C₁₃₇	1	8	yes	complemented
204	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
205	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
206	C₂×#124	C₂²×C₁₃₇	1	2	yes	—
207	C₂×#121	—	2	2	no	—
208	C₂×C₄×D₄	—	2	2	no	—
209	C₂²×C₄⋊C₄	—	2	2	no	—
210	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
211	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
212	#417	—	2	16	no	—
213	C₂×#103	C₂²×C₁₃₇	1	8	yes	—
214	C₂×#102	C₂²×C₁₃₇	1	8	yes	—
215	C₄×M₁₆	—	2	4	no	—
216	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
217	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
218	#384	—	2	2	no	—
219	#384	C₂²×C₁₃₇	1	2	yes	—
220	#384	C₂²×C₁₃₇	1	2	yes	—
221	C₂×#41	—	2	4	no	—
222	C₂×#41	—	2	8	no	—
223	C₂×#41	—	2	8	no	—
224	C₂×#41	C₂×C₄×C₁₃₇	1	8	yes	—
225	C₂²×Q₈	C₂³×C₁₃₇	1	2	yes	—
226	C₂²×D₄	—	2	2	no	—
227	C₂²×D₄	—	2	2	no	—
228	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
229	C₂³×C₄	—	2	2	no	—
230	C₂³×C₄	—	2	2	no	—
231	C₂³×C₄	D₄×C₁₃₇	1	2	yes	—
232	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
233	C₂×M₁₆	—	2	4	no	—
234	C₂×M₁₆	—	2	4	no	—
235	C₂×M₁₆	D₄×C₁₃₇	1	8	yes	complemented
236	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
237	C₄⋊Q₈	—	2	2	no	—
238	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	4	yes	complemented
239	#127	—	2	2	no	—
240	#127	C₂×C₄×C₁₃₇	1	4	yes	complemented
241	#124	—	2	4	no	—
242	#124	C₂×C₄×C₁₃₇	1	8	yes	complemented
243	#121	—	2	16	no	—
244	C₄×D₄	—	2	16	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	8	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	4	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	4	8	no	—
251	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
252	C₂×C₂²⋊C₄	—	2	4	no	—
253	C₂×C₄²	C₂×C₄×C₁₃₇	1	4	yes	—
254	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
255	C₂×C₄²	D₄×C₁₃₇	1	4	yes	—
256	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
257	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
258	#103	—	2	16	no	—
259	#102	—	2	16	no	—
260	#97	—	2	4	no	—
261	C₄×C₈	—	2	4	no	—
262	C₂⁴	—	2	2	no	—
263	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
264	#41	—	2	32	no	—
265	#41	—	4	16	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	C₂²×C₄×C₁₃₇	1	4	yes	—
270	C₂×D₄	—	2	8	no	—
271	C₂×D₄	—	2	8	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	4	4	no	—
276	C₂×D₄	—	4	4	no	—
277	C₂×D₄	—	4	4	no	—
278	C₂×D₄	—	4	4	no	—
279	C₂×D₄	C₂²×C₄×C₁₃₇	1	4	yes	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	4	4	no	—
286	C₂²×C₄	—	4	4	no	—
287	C₂²×C₄	—	4	8	no	—
288	C₂²×C₄	—	4	4	no	—
289	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	8	yes	—
290	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
296	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
297	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
298	M₁₆	—	2	16	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	C₂×D₄×C₁₃₇	1	8	yes	—
302	C₄⋊C₄	—	2	8	no	—
303	C₄⋊C₄	—	2	8	no	—
304	C₄⋊C₄	—	4	8	no	—
305	C₄⋊C₄	—	4	4	no	—
306	C₄⋊C₄	—	4	8	no	—
307	C₂²⋊C₄	—	2	16	no	—
308	C₄²	C₂²⋊C₄×C₁₃₇	1	8	yes	—
309	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
310	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
311	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
312	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	4	no	—
319	C₂³	—	4	4	no	—
320	C₂³	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
321	C₂³	#124×C₁₃₇	1	2	yes	—
322	C₂³	#127×C₁₃₇	1	2	yes	—
323	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
324	Q₈	—	2	8	no	—
325	Q₈	—	4	4	no	—
326	D₄	—	2	8	no	—
327	D₄	—	4	16	no	—
328	D₄	—	4	16	no	—
329	D₄	—	4	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	16	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	16	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	8	no	—
339	C₂×C₄	—	8	8	no	—
340	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	4	yes	—
341	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
342	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	4	yes	—
343	C₂×C₄	C₄×D₄×C₁₃₇	1	8	yes	—
344	C₂×C₄	#121×C₁₃₇	1	8	yes	—
345	C₂×C₄	#124×C₁₃₇	1	2	yes	—
346	C₂×C₄	#127×C₁₃₇	1	2	yes	—
347	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	4	yes	—
348	C₂×C₄	#137×C₁₃₇	1	4	yes	—
349	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
350	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
351	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
352	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
353	C₈	—	2	8	no	—
354	C₂²	—	2	4	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	4	4	no	—
359	C₂²	—	4	8	no	—
360	C₂²	—	8	4	no	—
361	C₂²	—	8	2	no	—
362	C₂²	—	8	2	no	—
363	C₂²	#390×C₁₃₇	1	4	yes	—
364	C₂²	C₂²×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
365	C₂²	C₂×#124×C₁₃₇	1	1	yes	characteristic
366	C₂²	C₂×#127×C₁₃₇	1	1	yes	characteristic
367	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
368	C₂²	C₂×#137×C₁₃₇	1	2	yes	—
369	C₄	—	2	4	no	—
370	C₄	—	4	4	no	—
371	C₄	—	8	4	no	—
372	C₄	#390×C₁₃₇	1	4	yes	—
373	C₄	#417×C₁₃₇	1	8	yes	complemented
374	C₄	C₂×C₄×D₄×C₁₃₇	1	2	yes	—
375	C₄	C₂×#121×C₁₃₇	1	2	yes	—
376	C₂	—	2	4	no	—
377	C₂	—	8	4	no	—
378	C₂	C₂×#390×C₁₃₇	1	1	yes	characteristic
379	C₂	C₂×#417×C₁₃₇	1	2	yes	—
380	C₂	#3141×C₁₃₇	1	2	yes	—
381	C₂	#3151×C₁₃₇	1	1	yes	characteristic
382	C₂	#3152×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	C₂×#532×C₁₃₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂²×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#417×C₁₃₇	C₂	semidirect
3. C₂×C₄×M₁₆×C₁₃₇	C₂	semidirect
4. C₂×#384×C₁₃₇	C₂	semidirect
5. #1959×C₁₃₇	C₂	semidirect
6. #1957×C₁₃₇	C₂	semidirect
7. #1956×C₁₃₇	C₂	semidirect
11. #532×C₁₃₇	C₄	semidirect
43. C₂×M₁₆×C₁₃₇	D₄	semidirect
46. C₄⋊Q₈×C₁₃₇	C₂×C₄	semidirect
48. #127×C₁₃₇	C₂×C₄	semidirect
50. #124×C₁₃₇	C₂×C₄	semidirect
181. C₄×C₁₃₇	#417	semidirect
191. #21200	C₁₃₇	direct (N × H)
192. C₁₃₇	#21200	direct (N × H)
194. C₂×#417	C₂×C₁₃₇	semidirect
195. C₂×C₄×M₁₆	C₂×C₁₃₇	semidirect
196. C₂×#384	C₂×C₁₃₇	semidirect
197. #1959	C₂×C₁₃₇	semidirect
198. #1957	C₂×C₁₃₇	semidirect
199. #1956	C₂×C₁₃₇	semidirect
203. #532	C₄×C₁₃₇	semidirect
235. C₂×M₁₆	D₄×C₁₃₇	semidirect
238. C₄⋊Q₈	C₂×C₄×C₁₃₇	semidirect
240. #127	C₂×C₄×C₁₃₇	semidirect
242. #124	C₂×C₄×C₁₃₇	semidirect
373. C₄	#417×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₁₃₇	2
C₂×#417×C₁₃₇	2
C₂×C₄×M₁₆×C₁₃₇	2
C₂×#384×C₁₃₇	2
#1959×C₁₃₇	2
#1957×C₁₃₇	2
#1956×C₁₃₇	2
#21200	137

Subgroups — C137×#21200 #46870586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21200 #46870586