Subgroups — C₁₃₇×#10793 #46860179

Order 35072.

1164 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#568×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2896×C₁₃₇	C₂	1	2	yes	maximal
3	C₂×#344×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	C₂×#338×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×H(3,ℤ/4)×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₁₃₇	C₂²	1	1	yes	characteristic
7	#568×C₁₃₇	—	2	4	no	—
8	#568×C₁₃₇	—	2	4	no	—
9	C₂×#131×C₁₃₇	—	2	2	no	—
10	C₂×#131×C₁₃₇	C₄	1	4	yes	complemented
11	C₂²×M₁₆×C₁₃₇	—	2	2	no	—
12	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₃₇	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
16	#419×C₁₃₇	—	2	2	no	—
17	#418×C₁₃₇	—	2	2	no	—
18	#417×C₁₃₇	—	2	4	no	—
19	#416×C₁₃₇	C₄	1	8	yes	complemented
20	#344×C₁₃₇	—	2	4	no	—
21	#338×C₁₃₇	—	2	2	no	—
22	H(3,ℤ/4)×C₁₃₇	—	2	2	no	—
23	C₂×#41×C₁₃₇	—	2	1	no	—
24	C₂×#41×C₁₃₇	—	2	2	no	—
25	C₂×#41×C₁₃₇	—	2	2	no	—
26	C₂×#41×C₁₃₇	—	2	1	no	—
27	C₂×#41×C₁₃₇	C₂×C₄	1	4	yes	—
28	C₂×#41×C₁₃₇	C₂×C₄	1	2	yes	—
29	C₂×#41×C₁₃₇	D₄	1	4	yes	—
30	C₂×#41×C₁₃₇	Q₈	1	2	yes	—
31	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₃₇	—	2	1	no	—
33	C₂²×D₄×C₁₃₇	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃₇	—	2	1	no	—
35	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
36	#131×C₁₃₇	—	2	16	no	—
37	#131×C₁₃₇	—	2	8	no	—
38	#131×C₁₃₇	—	2	8	no	—
39	C₂×M₁₆×C₁₃₇	—	2	16	no	—
40	C₂×M₁₆×C₁₃₇	—	2	1	no	—
41	C₂×M₁₆×C₁₃₇	—	2	2	no	—
42	C₂×M₁₆×C₁₃₇	—	2	2	no	—
43	C₂×M₁₆×C₁₃₇	—	2	2	no	—
44	C₂×M₁₆×C₁₃₇	—	2	2	no	—
45	C₂×M₁₆×C₁₃₇	—	2	2	no	—
46	C₂×M₁₆×C₁₃₇	—	2	2	no	—
47	C₂×M₁₆×C₁₃₇	—	2	2	no	—
48	C₂×M₁₆×C₁₃₇	—	2	2	no	—
49	C₂×M₁₆×C₁₃₇	—	2	2	no	—
50	C₂×M₁₆×C₁₃₇	—	2	4	no	—
51	C₂×M₁₆×C₁₃₇	C₂×C₄	1	2	yes	—
52	C₂×M₁₆×C₁₃₇	D₄	1	4	yes	—
53	C₂×M₁₆×C₁₃₇	D₄	1	2	yes	—
54	C₂×M₁₆×C₁₃₇	D₄	1	2	yes	—
55	C₂²×C₈×C₁₃₇	—	2	1	no	—
56	C₂²×C₈×C₁₃₇	—	2	4	no	—
57	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
58	C₂²×C₈×C₁₃₇	C₂×C₄	1	2	yes	—
59	#117×C₁₃₇	—	2	2	no	—
60	#117×C₁₃₇	—	2	2	no	—
61	#117×C₁₃₇	—	2	2	no	—
62	#117×C₁₃₇	C₂×C₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
65	C₂×C₄²×C₁₃₇	—	2	2	no	—
66	#103×C₁₃₇	—	2	8	no	—
67	#102×C₁₃₇	—	2	8	no	—
68	C₂⁴×C₁₃₇	—	2	1	no	—
69	C₂⁴×C₁₃₇	#41	1	1	yes	characteristic
70	#41×C₁₃₇	—	2	2	no	—
71	#41×C₁₃₇	—	2	2	no	—
72	#41×C₁₃₇	—	2	4	no	—
73	#41×C₁₃₇	—	2	4	no	—
74	#41×C₁₃₇	—	2	4	no	—
75	#41×C₁₃₇	—	2	4	no	—
76	#41×C₁₃₇	—	2	4	no	—
77	#41×C₁₃₇	C₄²	1	4	yes	—
78	#41×C₁₃₇	C₂²⋊C₄	1	4	yes	—
79	#41×C₁₃₇	C₄⋊C₄	1	8	yes	—
80	C₂×Q₈×C₁₃₇	—	2	1	no	—
81	C₂×Q₈×C₁₃₇	—	2	2	no	—
82	C₂×Q₈×C₁₃₇	C₂²⋊C₄	1	4	yes	—
83	C₂×Q₈×C₁₃₇	C₄⋊C₄	1	2	yes	—
84	C₂×D₄×C₁₃₇	—	2	2	no	—
85	C₂×D₄×C₁₃₇	—	2	4	no	—
86	C₂×D₄×C₁₃₇	—	2	2	no	—
87	C₂×D₄×C₁₃₇	—	2	4	no	—
88	C₂×D₄×C₁₃₇	—	2	2	no	—
89	C₂×D₄×C₁₃₇	—	2	1	no	—
90	C₂×D₄×C₁₃₇	C₂²⋊C₄	1	4	yes	—
91	C₂×D₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
92	C₂²×C₄×C₁₃₇	—	2	1	no	—
93	C₂²×C₄×C₁₃₇	—	2	2	no	—
94	C₂²×C₄×C₁₃₇	—	2	4	no	—
95	C₂²×C₄×C₁₃₇	—	2	4	no	—
96	C₂²×C₄×C₁₃₇	—	2	2	no	—
97	C₂²×C₄×C₁₃₇	—	4	2	no	—
98	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
107	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
108	M₁₆×C₁₃₇	—	2	16	no	—
109	M₁₆×C₁₃₇	—	2	2	no	—
110	M₁₆×C₁₃₇	—	2	4	no	—
111	M₁₆×C₁₃₇	—	2	4	no	—
112	M₁₆×C₁₃₇	—	2	4	no	—
113	M₁₆×C₁₃₇	—	4	2	no	—
114	M₁₆×C₁₃₇	—	4	2	no	—
115	M₁₆×C₁₃₇	—	4	2	no	—
116	M₁₆×C₁₃₇	—	4	2	no	—
117	M₁₆×C₁₃₇	C₂²⋊C₄	1	4	yes	—
118	C₂×C₈×C₁₃₇	—	2	16	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	—	2	4	no	—
123	C₂×C₈×C₁₃₇	—	2	4	no	—
124	C₂×C₈×C₁₃₇	—	2	4	no	—
125	C₂×C₈×C₁₃₇	—	2	4	no	—
126	C₂×C₈×C₁₃₇	C₂²⋊C₄	1	4	yes	—
127	C₄⋊C₄×C₁₃₇	—	2	4	no	—
128	C₄⋊C₄×C₁₃₇	—	4	2	no	—
129	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
130	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
131	C₄²×C₁₃₇	—	2	4	no	—
132	C₄²×C₁₃₇	—	4	2	no	—
133	C₂³×C₁₃₇	—	2	2	no	—
134	C₂³×C₁₃₇	—	2	4	no	—
135	C₂³×C₁₃₇	—	8	1	no	—
136	C₂³×C₁₃₇	—	8	2	no	—
137	C₂³×C₁₃₇	#117	1	1	yes	characteristic
138	C₂³×C₁₃₇	C₄×D₄	1	2	yes	—
139	C₂³×C₁₃₇	#121	1	1	yes	characteristic
140	C₂³×C₁₃₇	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂³×C₁₃₇	#123	1	2	yes	—
142	Q₈×C₁₃₇	—	2	2	no	—
143	Q₈×C₁₃₇	—	2	4	no	—
144	Q₈×C₁₃₇	#95	1	4	yes	—
145	D₄×C₁₃₇	—	2	4	no	—
146	D₄×C₁₃₇	—	2	4	no	—
147	D₄×C₁₃₇	—	2	8	no	—
148	D₄×C₁₃₇	—	2	2	no	—
149	D₄×C₁₃₇	—	2	4	no	—
150	D₄×C₁₃₇	#95	1	4	yes	—
151	C₂×C₄×C₁₃₇	—	2	2	no	—
152	C₂×C₄×C₁₃₇	—	2	4	no	—
153	C₂×C₄×C₁₃₇	—	2	4	no	—
154	C₂×C₄×C₁₃₇	—	2	4	no	—
155	C₂×C₄×C₁₃₇	—	2	8	no	—
156	C₂×C₄×C₁₃₇	—	4	4	no	—
157	C₂×C₄×C₁₃₇	—	8	4	no	—
158	C₂×C₄×C₁₃₇	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₃₇	#117	1	1	yes	characteristic
166	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₁₃₇	#120	1	2	yes	—
170	C₂×C₄×C₁₃₇	#120	1	2	yes	—
171	C₂×C₄×C₁₃₇	#121	1	2	yes	—
172	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
174	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃₇	#123	1	2	yes	—
176	C₈×C₁₃₇	—	2	4	no	—
177	C₈×C₁₃₇	—	2	4	no	—
178	C₈×C₁₃₇	—	4	4	no	—
179	C₂²×C₁₃₇	—	2	4	no	—
180	C₂²×C₁₃₇	—	4	2	no	—
181	C₂²×C₁₃₇	—	4	1	no	—
182	C₂²×C₁₃₇	—	4	1	no	—
183	C₂²×C₁₃₇	—	4	2	no	—
184	C₂²×C₁₃₇	—	4	1	no	—
185	C₂²×C₁₃₇	—	4	4	no	—
186	C₂²×C₁₃₇	—	8	4	no	—
187	C₂²×C₁₃₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
188	C₂²×C₁₃₇	#380	1	1	yes	characteristic
189	C₂²×C₁₃₇	#381	1	1	yes	characteristic
190	C₂²×C₁₃₇	#385	1	2	yes	—
191	C₂²×C₁₃₇	#386	1	2	yes	—
192	C₄×C₁₃₇	—	2	4	no	—
193	C₄×C₁₃₇	—	8	4	no	—
194	C₄×C₁₃₇	C₂×#95	1	1	yes	characteristic
195	C₄×C₁₃₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
196	C₄×C₁₃₇	#379	1	1	yes	characteristic
197	C₄×C₁₃₇	#380	1	1	yes	characteristic
198	C₄×C₁₃₇	#385	1	2	yes	—
199	C₄×C₁₃₇	#386	1	2	yes	—
200	C₂×C₁₃₇	—	2	2	no	—
201	C₂×C₁₃₇	—	2	1	no	—
202	C₂×C₁₃₇	—	2	1	no	—
203	C₂×C₁₃₇	—	2	1	no	—
204	C₂×C₁₃₇	—	2	2	no	—
205	C₂×C₁₃₇	—	4	4	no	—
206	C₂×C₁₃₇	C₂²⋊#95	1	1	yes	characteristic
207	#10793	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₁₃₇	#10793	1	1	yes	characteristic, direct product factor, Sylow
209	C₂×#568	C₂×C₁₃₇	1	1	yes	characteristic
210	#2896	C₂×C₁₃₇	1	2	yes	—
211	C₂×#344	C₂×C₁₃₇	1	2	yes	complemented
212	C₂×#338	C₂×C₁₃₇	1	1	yes	characteristic, complemented
213	C₂×H(3,ℤ/4)	C₂×C₁₃₇	1	1	yes	characteristic, complemented
214	C₂²×#41	C₂²×C₁₃₇	1	1	yes	characteristic
215	#568	—	2	4	no	—
216	#568	—	2	4	no	—
217	C₂×#131	—	2	2	no	—
218	C₂×#131	C₄×C₁₃₇	1	4	yes	complemented
219	C₂²×M₁₆	—	2	2	no	—
220	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
221	C₂²×M₁₆	C₂²×C₁₃₇	1	2	yes	—
222	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
223	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
224	#419	—	2	2	no	—
225	#418	—	2	2	no	—
226	#417	—	2	4	no	—
227	#416	C₄×C₁₃₇	1	8	yes	complemented
228	#344	—	2	4	no	—
229	#338	—	2	2	no	—
230	H(3,ℤ/4)	—	2	2	no	—
231	C₂×#41	—	2	1	no	—
232	C₂×#41	—	2	2	no	—
233	C₂×#41	—	2	2	no	—
234	C₂×#41	—	2	1	no	—
235	C₂×#41	C₂×C₄×C₁₃₇	1	4	yes	—
236	C₂×#41	C₂×C₄×C₁₃₇	1	2	yes	—
237	C₂×#41	D₄×C₁₃₇	1	4	yes	—
238	C₂×#41	Q₈×C₁₃₇	1	2	yes	—
239	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	D₄×C₁₃₇	1	1	yes	characteristic
242	C₂³×C₄	—	2	1	no	—
243	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
244	#131	—	2	16	no	—
245	#131	—	2	8	no	—
246	#131	—	2	8	no	—
247	C₂×M₁₆	—	2	16	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	—	2	4	no	—
259	C₂×M₁₆	C₂×C₄×C₁₃₇	1	2	yes	—
260	C₂×M₁₆	D₄×C₁₃₇	1	4	yes	—
261	C₂×M₁₆	D₄×C₁₃₇	1	2	yes	—
262	C₂×M₁₆	D₄×C₁₃₇	1	2	yes	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	2	4	no	—
265	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
266	C₂²×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
267	#117	—	2	2	no	—
268	#117	—	2	2	no	—
269	#117	—	2	2	no	—
270	#117	C₂×C₄×C₁₃₇	1	4	yes	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₄²	—	2	2	no	—
274	#103	—	2	8	no	—
275	#102	—	2	8	no	—
276	C₂⁴	—	2	1	no	—
277	C₂⁴	#41×C₁₃₇	1	1	yes	characteristic
278	#41	—	2	2	no	—
279	#41	—	2	2	no	—
280	#41	—	2	4	no	—
281	#41	—	2	4	no	—
282	#41	—	2	4	no	—
283	#41	—	2	4	no	—
284	#41	—	2	4	no	—
285	#41	C₄²×C₁₃₇	1	4	yes	—
286	#41	C₂²⋊C₄×C₁₃₇	1	4	yes	—
287	#41	C₄⋊C₄×C₁₃₇	1	8	yes	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	C₂²⋊C₄×C₁₃₇	1	4	yes	—
291	C₂×Q₈	C₄⋊C₄×C₁₃₇	1	2	yes	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	C₂²⋊C₄×C₁₃₇	1	4	yes	—
299	C₂×D₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
313	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
314	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
315	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
316	M₁₆	—	2	16	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	4	no	—
319	M₁₆	—	2	4	no	—
320	M₁₆	—	2	4	no	—
321	M₁₆	—	4	2	no	—
322	M₁₆	—	4	2	no	—
323	M₁₆	—	4	2	no	—
324	M₁₆	—	4	2	no	—
325	M₁₆	C₂²⋊C₄×C₁₃₇	1	4	yes	—
326	C₂×C₈	—	2	16	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	4	no	—
331	C₂×C₈	—	2	4	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	4	no	—
334	C₂×C₈	C₂²⋊C₄×C₁₃₇	1	4	yes	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₄²	—	2	4	no	—
340	C₄²	—	4	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	8	1	no	—
344	C₂³	—	8	2	no	—
345	C₂³	#117×C₁₃₇	1	1	yes	characteristic
346	C₂³	C₄×D₄×C₁₃₇	1	2	yes	—
347	C₂³	#121×C₁₃₇	1	1	yes	characteristic
348	C₂³	C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
349	C₂³	#123×C₁₃₇	1	2	yes	—
350	Q₈	—	2	2	no	—
351	Q₈	—	2	4	no	—
352	Q₈	#95×C₁₃₇	1	4	yes	—
353	D₄	—	2	4	no	—
354	D₄	—	2	4	no	—
355	D₄	—	2	8	no	—
356	D₄	—	2	2	no	—
357	D₄	—	2	4	no	—
358	D₄	#95×C₁₃₇	1	4	yes	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	8	4	no	—
366	C₂×C₄	C₂×C₄²×C₁₃₇	1	1	yes	characteristic
367	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
368	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
370	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
373	C₂×C₄	#117×C₁₃₇	1	1	yes	characteristic
374	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
375	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
376	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
377	C₂×C₄	#120×C₁₃₇	1	2	yes	—
378	C₂×C₄	#120×C₁₃₇	1	2	yes	—
379	C₂×C₄	#121×C₁₃₇	1	2	yes	—
380	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
381	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
382	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
383	C₂×C₄	#123×C₁₃₇	1	2	yes	—
384	C₈	—	2	4	no	—
385	C₈	—	2	4	no	—
386	C₈	—	4	4	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	8	4	no	—
395	C₂²	C₄×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
396	C₂²	#380×C₁₃₇	1	1	yes	characteristic
397	C₂²	#381×C₁₃₇	1	1	yes	characteristic
398	C₂²	#385×C₁₃₇	1	2	yes	—
399	C₂²	#386×C₁₃₇	1	2	yes	—
400	C₄	—	2	4	no	—
401	C₄	—	8	4	no	—
402	C₄	C₂×#95×C₁₃₇	1	1	yes	characteristic
403	C₄	C₄×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
404	C₄	#379×C₁₃₇	1	1	yes	characteristic
405	C₄	#380×C₁₃₇	1	1	yes	characteristic
406	C₄	#385×C₁₃₇	1	2	yes	—
407	C₄	#386×C₁₃₇	1	2	yes	—
408	C₂	—	2	2	no	—
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	2	no	—
413	C₂	—	4	4	no	—
414	C₂	C₂²⋊#95×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃₇	C₄×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₁₃₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₇
socle	C₂×C₁₃₇	C₂²⋊#95
prime radical	C₂²×#41×C₁₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃₇ ◁ C₂²×M₁₆×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×#344×C₁₃₇	C₂	semidirect
4. C₂×#338×C₁₃₇	C₂	semidirect
5. C₂×H(3,ℤ/4)×C₁₃₇	C₂	semidirect
10. C₂×#131×C₁₃₇	C₄	semidirect
19. #416×C₁₃₇	C₄	semidirect
207. #10793	C₁₃₇	direct (N × H)
208. C₁₃₇	#10793	direct (N × H)
211. C₂×#344	C₂×C₁₃₇	semidirect
212. C₂×#338	C₂×C₁₃₇	semidirect
213. C₂×H(3,ℤ/4)	C₂×C₁₃₇	semidirect
218. C₂×#131	C₄×C₁₃₇	semidirect
227. #416	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×#568×C₁₃₇	2
#2896×C₁₃₇	2
C₂×#344×C₁₃₇	2
C₂×#338×C₁₃₇	2
C₂×H(3,ℤ/4)×C₁₃₇	2
#10793	137

Subgroups — C137×#10793 #46860179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#10793 #46860179