Subgroups — C₁₃₇×#11026 #46860412

Order 35072.

1278 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#421×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	C₂×#410×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#1735×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1729×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₁₃₇	C₂²	1	2	yes	—
7	C₂×#135×C₁₃₇	—	2	4	no	—
8	C₂×#135×C₁₃₇	—	2	4	no	—
9	C₂×#135×C₁₃₇	—	2	2	no	—
10	C₂×#135×C₁₃₇	—	2	2	no	—
11	C₂²×Q₁₆×C₁₃₇	C₄	1	1	yes	characteristic, complemented
12	C₂²×SD₁₆×C₁₃₇	C₄	1	2	yes	complemented
13	C₂²×D₈×C₁₃₇	C₄	1	1	yes	characteristic, complemented
14	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
17	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
18	#421×C₁₃₇	—	2	4	no	—
19	#421×C₁₃₇	—	2	4	no	—
20	C₂×#104×C₁₃₇	—	2	4	no	—
21	#410×C₁₃₇	—	2	4	no	—
22	#410×C₁₃₇	—	2	4	no	—
23	C₂×#99×C₁₃₇	—	2	4	no	—
24	#340×C₁₃₇	—	2	2	no	—
25	#336×C₁₃₇	—	2	2	no	—
26	C₂×#41×C₁₃₇	—	2	2	no	—
27	C₂×#41×C₁₃₇	—	2	2	no	—
28	C₂×#41×C₁₃₇	—	2	2	no	—
29	C₂×#41×C₁₃₇	—	2	2	no	—
30	C₂×#41×C₁₃₇	—	2	2	no	—
31	C₂×#41×C₁₃₇	—	2	2	no	—
32	C₂×#41×C₁₃₇	—	2	2	no	—
33	C₂×#41×C₁₃₇	—	2	2	no	—
34	C₂×#41×C₁₃₇	—	2	2	no	—
35	C₂×#41×C₁₃₇	—	2	2	no	—
36	C₂×#41×C₁₃₇	D₄	1	4	yes	—
37	C₂×#41×C₁₃₇	D₄	1	4	yes	—
38	C₂²×Q₈×C₁₃₇	C₂×C₄	1	2	yes	—
39	C₂²×D₄×C₁₃₇	—	2	2	no	—
40	C₂²×D₄×C₁₃₇	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₁₃₇	—	2	2	no	—
42	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
43	#135×C₁₃₇	—	2	8	no	—
44	#135×C₁₃₇	—	2	8	no	—
45	#135×C₁₃₇	—	2	16	no	—
46	C₂×Q₁₆×C₁₃₇	—	2	4	no	—
47	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
48	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
49	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
50	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
51	C₂×D₈×C₁₃₇	—	2	4	no	—
52	C₂×D₈×C₁₃₇	—	2	2	no	—
53	C₂×M₁₆×C₁₃₇	—	2	1	no	—
54	C₂×M₁₆×C₁₃₇	—	2	2	no	—
55	C₂×M₁₆×C₁₃₇	—	2	2	no	—
56	C₂×M₁₆×C₁₃₇	D₄	1	2	yes	—
57	C₂²×C₈×C₁₃₇	—	2	2	no	—
58	C₂²×C₈×C₁₃₇	—	2	2	no	—
59	C₂²×C₈×C₁₃₇	—	2	1	no	—
60	C₂²×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
63	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
64	#117×C₁₃₇	—	2	2	no	—
65	#117×C₁₃₇	—	2	2	no	—
66	#117×C₁₃₇	—	2	2	no	—
67	#117×C₁₃₇	—	2	2	no	—
68	#117×C₁₃₇	—	2	2	no	—
69	#117×C₁₃₇	D₄	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₃₇	D₄	1	2	yes	—
74	C₂×C₄²×C₁₃₇	—	2	2	no	—
75	C₂×C₄²×C₁₃₇	—	2	1	no	—
76	#104×C₁₃₇	—	2	16	no	—
77	#99×C₁₃₇	—	2	16	no	—
78	C₂⁴×C₁₃₇	—	2	2	no	—
79	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
80	#41×C₁₃₇	—	2	4	no	—
81	#41×C₁₃₇	—	2	4	no	—
82	#41×C₁₃₇	—	2	4	no	—
83	#41×C₁₃₇	—	2	4	no	—
84	#41×C₁₃₇	—	2	4	no	—
85	#41×C₁₃₇	—	2	4	no	—
86	#41×C₁₃₇	—	2	4	no	—
87	#41×C₁₃₇	—	2	4	no	—
88	#41×C₁₃₇	—	4	2	no	—
89	#41×C₁₃₇	—	4	2	no	—
90	#41×C₁₃₇	—	4	2	no	—
91	#41×C₁₃₇	—	4	2	no	—
92	#41×C₁₃₇	—	4	2	no	—
93	#41×C₁₃₇	—	4	2	no	—
94	#41×C₁₃₇	—	4	2	no	—
95	#41×C₁₃₇	—	4	2	no	—
96	C₂×Q₈×C₁₃₇	—	2	2	no	—
97	C₂×Q₈×C₁₃₇	—	2	2	no	—
98	C₂×Q₈×C₁₃₇	—	2	2	no	—
99	C₂×Q₈×C₁₃₇	—	2	2	no	—
100	C₂×Q₈×C₁₃₇	—	2	2	no	—
101	C₂×Q₈×C₁₃₇	C₂²⋊C₄	1	4	yes	—
102	C₂×D₄×C₁₃₇	—	2	4	no	—
103	C₂×D₄×C₁₃₇	—	2	4	no	—
104	C₂×D₄×C₁₃₇	—	2	2	no	—
105	C₂×D₄×C₁₃₇	—	2	2	no	—
106	C₂×D₄×C₁₃₇	—	2	2	no	—
107	C₂×D₄×C₁₃₇	—	2	2	no	—
108	C₂×D₄×C₁₃₇	—	2	2	no	—
109	C₂×D₄×C₁₃₇	—	4	2	no	—
110	C₂×D₄×C₁₃₇	—	4	2	no	—
111	C₂×D₄×C₁₃₇	—	4	2	no	—
112	C₂×D₄×C₁₃₇	—	4	2	no	—
113	C₂×D₄×C₁₃₇	C₂²⋊C₄	1	4	yes	—
114	C₂²×C₄×C₁₃₇	—	2	2	no	—
115	C₂²×C₄×C₁₃₇	—	2	4	no	—
116	C₂²×C₄×C₁₃₇	—	2	4	no	—
117	C₂²×C₄×C₁₃₇	—	2	2	no	—
118	C₂²×C₄×C₁₃₇	—	4	2	no	—
119	C₂²×C₄×C₁₃₇	—	4	2	no	—
120	C₂²×C₄×C₁₃₇	—	4	2	no	—
121	C₂²×C₄×C₁₃₇	—	4	2	no	—
122	C₂²×C₄×C₁₃₇	—	4	2	no	—
123	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
131	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
132	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
133	Q₁₆×C₁₃₇	—	2	8	no	—
134	SD₁₆×C₁₃₇	—	2	16	no	—
135	D₈×C₁₃₇	—	2	8	no	—
136	M₁₆×C₁₃₇	—	2	4	no	—
137	M₁₆×C₁₃₇	—	4	2	no	—
138	C₂×C₈×C₁₃₇	—	2	2	no	—
139	C₂×C₈×C₁₃₇	—	2	2	no	—
140	C₂×C₈×C₁₃₇	—	2	2	no	—
141	C₂×C₈×C₁₃₇	—	2	2	no	—
142	C₂×C₈×C₁₃₇	—	2	4	no	—
143	C₂×C₈×C₁₃₇	—	2	2	no	—
144	C₂×C₈×C₁₃₇	—	4	1	no	—
145	C₂×C₈×C₁₃₇	—	4	1	no	—
146	C₂×C₈×C₁₃₇	C₂²⋊C₄	1	2	yes	—
147	C₂×C₈×C₁₃₇	C₂²⋊C₄	1	2	yes	—
148	C₄⋊C₄×C₁₃₇	—	2	4	no	—
149	C₄⋊C₄×C₁₃₇	—	4	2	no	—
150	C₄⋊C₄×C₁₃₇	—	4	2	no	—
151	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
152	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
153	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
154	C₄²×C₁₃₇	—	2	4	no	—
155	C₄²×C₁₃₇	—	4	1	no	—
156	C₄²×C₁₃₇	—	4	2	no	—
157	C₄²×C₁₃₇	—	4	1	no	—
158	C₂³×C₁₃₇	—	2	4	no	—
159	C₂³×C₁₃₇	—	4	2	no	—
160	C₂³×C₁₃₇	—	4	2	no	—
161	C₂³×C₁₃₇	—	4	2	no	—
162	C₂³×C₁₃₇	—	8	4	no	—
163	C₂³×C₁₃₇	C₄×D₄	1	1	yes	characteristic
164	C₂³×C₁₃₇	#120	1	2	yes	—
165	C₂³×C₁₃₇	#121	1	1	yes	characteristic
166	C₂³×C₁₃₇	#121	1	2	yes	—
167	C₂³×C₁₃₇	#127	1	1	yes	characteristic
168	Q₈×C₁₃₇	—	2	4	no	—
169	Q₈×C₁₃₇	—	2	4	no	—
170	Q₈×C₁₃₇	—	4	2	no	—
171	Q₈×C₁₃₇	—	4	2	no	—
172	D₄×C₁₃₇	—	2	4	no	—
173	D₄×C₁₃₇	—	2	4	no	—
174	D₄×C₁₃₇	—	4	4	no	—
175	D₄×C₁₃₇	—	4	4	no	—
176	D₄×C₁₃₇	—	4	4	no	—
177	D₄×C₁₃₇	—	4	4	no	—
178	D₄×C₁₃₇	—	4	2	no	—
179	D₄×C₁₃₇	—	4	2	no	—
180	C₂×C₄×C₁₃₇	—	2	4	no	—
181	C₂×C₄×C₁₃₇	—	4	2	no	—
182	C₂×C₄×C₁₃₇	—	4	2	no	—
183	C₂×C₄×C₁₃₇	—	4	4	no	—
184	C₂×C₄×C₁₃₇	—	4	4	no	—
185	C₂×C₄×C₁₃₇	—	4	4	no	—
186	C₂×C₄×C₁₃₇	—	4	4	no	—
187	C₂×C₄×C₁₃₇	—	4	4	no	—
188	C₂×C₄×C₁₃₇	—	4	4	no	—
189	C₂×C₄×C₁₃₇	—	4	2	no	—
190	C₂×C₄×C₁₃₇	—	8	4	no	—
191	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
196	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
197	C₂×C₄×C₁₃₇	#120	1	2	yes	—
198	C₂×C₄×C₁₃₇	#120	1	2	yes	—
199	C₂×C₄×C₁₃₇	#121	1	2	yes	—
200	C₂×C₄×C₁₃₇	#121	1	2	yes	—
201	C₂×C₄×C₁₃₇	#121	1	2	yes	—
202	C₂×C₄×C₁₃₇	#121	1	2	yes	—
203	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
204	C₂×C₄×C₁₃₇	#123	1	2	yes	—
205	C₂×C₄×C₁₃₇	#123	1	2	yes	—
206	C₂×C₄×C₁₃₇	#124	1	1	yes	characteristic
207	C₂×C₄×C₁₃₇	#124	1	1	yes	characteristic
208	C₂×C₄×C₁₃₇	#127	1	1	yes	characteristic
209	C₈×C₁₃₇	—	2	2	no	—
210	C₈×C₁₃₇	—	2	2	no	—
211	C₈×C₁₃₇	—	4	2	no	—
212	C₂²×C₁₃₇	—	2	2	no	—
213	C₂²×C₁₃₇	—	2	2	no	—
214	C₂²×C₁₃₇	—	2	2	no	—
215	C₂²×C₁₃₇	—	4	2	no	—
216	C₂²×C₁₃₇	—	4	2	no	—
217	C₂²×C₁₃₇	—	4	4	no	—
218	C₂²×C₁₃₇	—	8	4	no	—
219	C₂²×C₁₃₇	—	8	4	no	—
220	C₂²×C₁₃₇	—	8	4	no	—
221	C₂²×C₁₃₇	#386	1	2	yes	—
222	C₂²×C₁₃₇	#390	1	1	yes	characteristic
223	C₂²×C₁₃₇	#392	1	2	yes	—
224	C₂²×C₁₃₇	#392	1	1	yes	characteristic
225	C₂²×C₁₃₇	#394	1	1	yes	characteristic
226	C₄×C₁₃₇	—	4	4	no	—
227	C₄×C₁₃₇	—	8	2	no	—
228	C₄×C₁₃₇	—	8	4	no	—
229	C₄×C₁₃₇	#379	1	1	yes	characteristic
230	C₄×C₁₃₇	#386	1	2	yes	—
231	C₄×C₁₃₇	#390	1	1	yes	characteristic
232	C₄×C₁₃₇	#392	1	1	yes	characteristic
233	C₄×C₁₃₇	#394	1	2	yes	—
234	C₄×C₁₃₇	#394	1	1	yes	characteristic
235	C₂×C₁₃₇	—	2	1	no	—
236	C₂×C₁₃₇	—	2	2	no	—
237	C₂×C₁₃₇	—	2	2	no	—
238	C₂×C₁₃₇	—	2	1	no	—
239	C₂×C₁₃₇	—	8	4	no	—
240	C₂×C₁₃₇	#1438	1	1	yes	characteristic
241	C₂×C₁₃₇	#1976	1	2	yes	—
242	#11026	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₁₃₇	#11026	1	1	yes	characteristic, direct product factor, Sylow
244	C₂²×#135	C₂×C₁₃₇	1	1	yes	characteristic
245	C₂×#421	C₂×C₁₃₇	1	2	yes	complemented
246	C₂×#410	C₂×C₁₃₇	1	2	yes	complemented
247	#1735	C₂×C₁₃₇	1	1	yes	characteristic, complemented
248	#1729	C₂×C₁₃₇	1	1	yes	characteristic, complemented
249	C₂²×#41	C₂²×C₁₃₇	1	2	yes	—
250	C₂×#135	—	2	4	no	—
251	C₂×#135	—	2	4	no	—
252	C₂×#135	—	2	2	no	—
253	C₂×#135	—	2	2	no	—
254	C₂²×Q₁₆	C₄×C₁₃₇	1	1	yes	characteristic, complemented
255	C₂²×SD₁₆	C₄×C₁₃₇	1	2	yes	complemented
256	C₂²×D₈	C₄×C₁₃₇	1	1	yes	characteristic, complemented
257	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
258	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
259	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
260	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
261	#421	—	2	4	no	—
262	#421	—	2	4	no	—
263	C₂×#104	—	2	4	no	—
264	#410	—	2	4	no	—
265	#410	—	2	4	no	—
266	C₂×#99	—	2	4	no	—
267	#340	—	2	2	no	—
268	#336	—	2	2	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	2	2	no	—
274	C₂×#41	—	2	2	no	—
275	C₂×#41	—	2	2	no	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	2	2	no	—
278	C₂×#41	—	2	2	no	—
279	C₂×#41	D₄×C₁₃₇	1	4	yes	—
280	C₂×#41	D₄×C₁₃₇	1	4	yes	—
281	C₂²×Q₈	C₂×C₄×C₁₃₇	1	2	yes	—
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	C₂×C₄×C₁₃₇	1	2	yes	—
284	C₂³×C₄	—	2	2	no	—
285	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
286	#135	—	2	8	no	—
287	#135	—	2	8	no	—
288	#135	—	2	16	no	—
289	C₂×Q₁₆	—	2	4	no	—
290	C₂×Q₁₆	—	2	2	no	—
291	C₂×SD₁₆	—	2	4	no	—
292	C₂×SD₁₆	—	2	4	no	—
293	C₂×SD₁₆	—	2	4	no	—
294	C₂×D₈	—	2	4	no	—
295	C₂×D₈	—	2	2	no	—
296	C₂×M₁₆	—	2	1	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	D₄×C₁₃₇	1	2	yes	—
300	C₂²×C₈	—	2	2	no	—
301	C₂²×C₈	—	2	2	no	—
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
304	C₂²×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
305	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
306	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
307	#117	—	2	2	no	—
308	#117	—	2	2	no	—
309	#117	—	2	2	no	—
310	#117	—	2	2	no	—
311	#117	—	2	2	no	—
312	#117	D₄×C₁₃₇	1	4	yes	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	D₄×C₁₃₇	1	2	yes	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	1	no	—
319	#104	—	2	16	no	—
320	#99	—	2	16	no	—
321	C₂⁴	—	2	2	no	—
322	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
323	#41	—	2	4	no	—
324	#41	—	2	4	no	—
325	#41	—	2	4	no	—
326	#41	—	2	4	no	—
327	#41	—	2	4	no	—
328	#41	—	2	4	no	—
329	#41	—	2	4	no	—
330	#41	—	2	4	no	—
331	#41	—	4	2	no	—
332	#41	—	4	2	no	—
333	#41	—	4	2	no	—
334	#41	—	4	2	no	—
335	#41	—	4	2	no	—
336	#41	—	4	2	no	—
337	#41	—	4	2	no	—
338	#41	—	4	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	C₂²⋊C₄×C₁₃₇	1	4	yes	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	4	2	no	—
355	C₂×D₄	—	4	2	no	—
356	C₂×D₄	C₂²⋊C₄×C₁₃₇	1	4	yes	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
373	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
374	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
375	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
376	Q₁₆	—	2	8	no	—
377	SD₁₆	—	2	16	no	—
378	D₈	—	2	8	no	—
379	M₁₆	—	2	4	no	—
380	M₁₆	—	4	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	4	1	no	—
388	C₂×C₈	—	4	1	no	—
389	C₂×C₈	C₂²⋊C₄×C₁₃₇	1	2	yes	—
390	C₂×C₈	C₂²⋊C₄×C₁₃₇	1	2	yes	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₄²	—	2	4	no	—
398	C₄²	—	4	1	no	—
399	C₄²	—	4	2	no	—
400	C₄²	—	4	1	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	8	4	no	—
406	C₂³	C₄×D₄×C₁₃₇	1	1	yes	characteristic
407	C₂³	#120×C₁₃₇	1	2	yes	—
408	C₂³	#121×C₁₃₇	1	1	yes	characteristic
409	C₂³	#121×C₁₃₇	1	2	yes	—
410	C₂³	#127×C₁₃₇	1	1	yes	characteristic
411	Q₈	—	2	4	no	—
412	Q₈	—	2	4	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	D₄	—	2	4	no	—
416	D₄	—	2	4	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	4	no	—
419	D₄	—	4	4	no	—
420	D₄	—	4	4	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	8	4	no	—
434	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
435	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
436	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
437	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
438	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
439	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
440	C₂×C₄	#120×C₁₃₇	1	2	yes	—
441	C₂×C₄	#120×C₁₃₇	1	2	yes	—
442	C₂×C₄	#121×C₁₃₇	1	2	yes	—
443	C₂×C₄	#121×C₁₃₇	1	2	yes	—
444	C₂×C₄	#121×C₁₃₇	1	2	yes	—
445	C₂×C₄	#121×C₁₃₇	1	2	yes	—
446	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
447	C₂×C₄	#123×C₁₃₇	1	2	yes	—
448	C₂×C₄	#123×C₁₃₇	1	2	yes	—
449	C₂×C₄	#124×C₁₃₇	1	1	yes	characteristic
450	C₂×C₄	#124×C₁₃₇	1	1	yes	characteristic
451	C₂×C₄	#127×C₁₃₇	1	1	yes	characteristic
452	C₈	—	2	2	no	—
453	C₈	—	2	2	no	—
454	C₈	—	4	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	8	4	no	—
462	C₂²	—	8	4	no	—
463	C₂²	—	8	4	no	—
464	C₂²	#386×C₁₃₇	1	2	yes	—
465	C₂²	#390×C₁₃₇	1	1	yes	characteristic
466	C₂²	#392×C₁₃₇	1	2	yes	—
467	C₂²	#392×C₁₃₇	1	1	yes	characteristic
468	C₂²	#394×C₁₃₇	1	1	yes	characteristic
469	C₄	—	4	4	no	—
470	C₄	—	8	2	no	—
471	C₄	—	8	4	no	—
472	C₄	#379×C₁₃₇	1	1	yes	characteristic
473	C₄	#386×C₁₃₇	1	2	yes	—
474	C₄	#390×C₁₃₇	1	1	yes	characteristic
475	C₄	#392×C₁₃₇	1	1	yes	characteristic
476	C₄	#394×C₁₃₇	1	1	yes	characteristic
477	C₄	#394×C₁₃₇	1	2	yes	—
478	C₂	—	2	1	no	—
479	C₂	—	2	2	no	—
480	C₂	—	2	2	no	—
481	C₂	—	2	1	no	—
482	C₂	—	8	4	no	—
483	C₂	#1438×C₁₃₇	1	1	yes	characteristic
484	C₂	#1976×C₁₃₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃₇	#121
commutator	C₂²×C₄	C₂²×C₄×C₁₃₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₇
socle	C₂²×C₁₃₇	#390
prime radical	C₂²×#135×C₁₃₇	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₇ ◁ C₂³×C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#421×C₁₃₇	C₂	semidirect
3. C₂×#410×C₁₃₇	C₂	semidirect
4. #1735×C₁₃₇	C₂	semidirect
5. #1729×C₁₃₇	C₂	semidirect
11. C₂²×Q₁₆×C₁₃₇	C₄	semidirect
12. C₂²×SD₁₆×C₁₃₇	C₄	semidirect
13. C₂²×D₈×C₁₃₇	C₄	semidirect
242. #11026	C₁₃₇	direct (N × H)
243. C₁₃₇	#11026	direct (N × H)
245. C₂×#421	C₂×C₁₃₇	semidirect
246. C₂×#410	C₂×C₁₃₇	semidirect
247. #1735	C₂×C₁₃₇	semidirect
248. #1729	C₂×C₁₃₇	semidirect
254. C₂²×Q₁₆	C₄×C₁₃₇	semidirect
255. C₂²×SD₁₆	C₄×C₁₃₇	semidirect
256. C₂²×D₈	C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#135×C₁₃₇	2
C₂×#421×C₁₃₇	2
C₂×#410×C₁₃₇	2
#1735×C₁₃₇	2
#1729×C₁₃₇	2
#11026	137

Subgroups — C137×#11026 #46860412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#11026 #46860412