Subgroups — C₁₃₇×#19355 #46868741

Order 35072.

678 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3251×C₁₃₇	C₂	1	2	yes	maximal, complemented
2	#3147×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2966×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#1690×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1689×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#1688×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1687×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1666×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1665×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#1566×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1557×C₁₃₇	C₂	1	2	yes	maximal, complemented
12	C₂×#135×C₁₃₇	—	2	1	no	—
13	C₂×#135×C₁₃₇	—	2	1	no	—
14	#532×C₁₃₇	C₂²	1	2	yes	—
15	#529×C₁₃₇	C₂²	1	1	yes	characteristic
16	#495×C₁₃₇	—	2	1	no	—
17	#495×C₁₃₇	—	2	1	no	—
18	#494×C₁₃₇	C₂²	1	1	yes	characteristic
19	#493×C₁₃₇	C₂²	1	1	yes	characteristic
20	#492×C₁₃₇	C₂²	1	2	yes	—
21	#478×C₁₃₇	—	2	2	no	—
22	#475×C₁₃₇	C₂²	1	2	yes	—
23	#474×C₁₃₇	C₂²	1	2	yes	—
24	#469×C₁₃₇	—	2	2	no	—
25	#468×C₁₃₇	—	2	2	no	—
26	#463×C₁₃₇	—	2	2	no	—
27	#460×C₁₃₇	C₂²	1	2	yes	—
28	#459×C₁₃₇	C₂²	1	2	yes	—
29	#446×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
31	#436×C₁₃₇	C₂²	1	1	yes	characteristic
32	#435×C₁₃₇	—	2	1	no	—
33	C₈×D₄×C₁₃₇	—	2	1	no	—
34	C₈×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
35	#433×C₁₃₇	—	2	1	no	—
36	#432×C₁₃₇	C₂²	1	1	yes	characteristic
37	#423×C₁₃₇	C₂²	1	2	yes	—
38	#405×C₁₃₇	—	2	1	no	—
39	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
40	#334×C₁₃₇	C₂²	1	2	yes	—
41	#334×C₁₃₇	C₂²	1	1	yes	characteristic
42	#334×C₁₃₇	C₂²	1	1	yes	characteristic
43	#332×C₁₃₇	C₂²	1	2	yes	—
44	#332×C₁₃₇	C₂²	1	2	yes	—
45	#331×C₁₃₇	C₂²	1	2	yes	—
46	#331×C₁₃₇	C₂²	1	2	yes	—
47	C₂×#41×C₁₃₇	—	2	2	no	—
48	#135×C₁₃₇	—	4	4	no	—
49	#135×C₁₃₇	—	4	4	no	—
50	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
51	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
52	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
53	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
54	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
55	C₂×D₈×C₁₃₇	—	2	2	no	—
56	C₂×D₈×C₁₃₇	—	2	1	no	—
57	C₂×D₈×C₁₃₇	—	2	1	no	—
58	C₂×M₁₆×C₁₃₇	—	2	2	no	—
59	C₂×M₁₆×C₁₃₇	—	2	1	no	—
60	C₂²×C₈×C₁₃₇	—	2	1	no	—
61	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
63	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
64	#127×C₁₃₇	C₂³	1	2	yes	—
65	#126×C₁₃₇	—	2	1	no	—
66	#125×C₁₃₇	D₄	1	1	yes	characteristic
67	#124×C₁₃₇	—	2	2	no	—
68	#124×C₁₃₇	D₄	1	1	yes	characteristic
69	#123×C₁₃₇	—	2	1	no	—
70	C₂²⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
71	#121×C₁₃₇	—	2	2	no	—
72	#121×C₁₃₇	—	2	2	no	—
73	#121×C₁₃₇	D₄	1	1	yes	characteristic
74	C₄×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
75	C₄×D₄×C₁₃₇	—	2	1	no	—
76	C₄×D₄×C₁₃₇	—	2	2	no	—
77	C₄×D₄×C₁₃₇	—	2	2	no	—
78	C₄×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
79	#117×C₁₃₇	—	2	1	no	—
80	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
81	#107×C₁₃₇	—	2	2	no	—
82	#106×C₁₃₇	—	2	2	no	—
83	C₄⋊C₈×C₁₃₇	—	2	1	no	—
84	C₄⋊C₈×C₁₃₇	—	2	1	no	—
85	C₄⋊C₈×C₁₃₇	—	2	2	no	—
86	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
87	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
88	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
90	#103×C₁₃₇	—	2	2	no	—
91	#102×C₁₃₇	—	2	2	no	—
92	#102×C₁₃₇	—	2	2	no	—
93	#102×C₁₃₇	—	2	2	no	—
94	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
95	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
96	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
97	#97×C₁₃₇	—	2	1	no	—
98	#97×C₁₃₇	—	2	1	no	—
99	C₄×C₈×C₁₃₇	—	2	1	no	—
100	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
101	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
102	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
104	#41×C₁₃₇	—	4	4	no	—
105	#41×C₁₃₇	—	4	4	no	—
106	C₂×Q₈×C₁₃₇	—	2	2	no	—
107	C₂×Q₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
108	C₂×D₄×C₁₃₇	—	2	1	no	—
109	C₂×D₄×C₁₃₇	—	2	2	no	—
110	C₂×D₄×C₁₃₇	—	2	2	no	—
111	C₂×D₄×C₁₃₇	—	2	2	no	—
112	C₂×D₄×C₁₃₇	—	4	2	no	—
113	C₂×D₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₇	—	2	1	no	—
115	C₂²×C₄×C₁₃₇	—	4	2	no	—
116	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
119	Q₁₆×C₁₃₇	—	4	2	no	—
120	Q₁₆×C₁₃₇	—	4	2	no	—
121	SD₁₆×C₁₃₇	—	4	4	no	—
122	SD₁₆×C₁₃₇	—	4	4	no	—
123	SD₁₆×C₁₃₇	—	8	2	no	—
124	D₈×C₁₃₇	—	4	2	no	—
125	D₈×C₁₃₇	—	4	2	no	—
126	D₈×C₁₃₇	—	8	2	no	—
127	M₁₆×C₁₃₇	—	4	2	no	—
128	M₁₆×C₁₃₇	—	8	2	no	—
129	C₂×C₈×C₁₃₇	—	2	2	no	—
130	C₂×C₈×C₁₃₇	—	2	2	no	—
131	C₂×C₈×C₁₃₇	—	2	1	no	—
132	C₂×C₈×C₁₃₇	—	2	1	no	—
133	C₂×C₈×C₁₃₇	—	2	2	no	—
134	C₂×C₈×C₁₃₇	—	2	2	no	—
135	C₂×C₈×C₁₃₇	—	4	2	no	—
136	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
140	C₄⋊C₄×C₁₃₇	—	2	1	no	—
141	C₄⋊C₄×C₁₃₇	—	2	1	no	—
142	C₄⋊C₄×C₁₃₇	—	2	1	no	—
143	C₄⋊C₄×C₁₃₇	—	2	1	no	—
144	C₄⋊C₄×C₁₃₇	—	2	2	no	—
145	C₄⋊C₄×C₁₃₇	—	2	2	no	—
146	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
147	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
148	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
149	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
150	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
151	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
152	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
153	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
154	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
155	C₄²×C₁₃₇	—	2	1	no	—
156	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₁₃₇	#41	1	1	yes	characteristic
159	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
160	C₂³×C₁₃₇	—	2	1	no	—
161	C₂³×C₁₃₇	—	4	2	no	—
162	C₂³×C₁₃₇	#121	1	1	yes	characteristic
163	Q₈×C₁₃₇	—	2	2	no	—
164	Q₈×C₁₃₇	—	4	2	no	—
165	Q₈×C₁₃₇	—	4	2	no	—
166	D₄×C₁₃₇	—	2	2	no	—
167	D₄×C₁₃₇	—	4	2	no	—
168	D₄×C₁₃₇	—	4	2	no	—
169	D₄×C₁₃₇	—	4	2	no	—
170	D₄×C₁₃₇	—	4	2	no	—
171	D₄×C₁₃₇	—	4	2	no	—
172	D₄×C₁₃₇	—	8	2	no	—
173	D₄×C₁₃₇	—	8	4	no	—
174	C₂×C₄×C₁₃₇	—	2	1	no	—
175	C₂×C₄×C₁₃₇	—	2	1	no	—
176	C₂×C₄×C₁₃₇	—	2	2	no	—
177	C₂×C₄×C₁₃₇	—	2	1	no	—
178	C₂×C₄×C₁₃₇	—	2	1	no	—
179	C₂×C₄×C₁₃₇	—	2	1	no	—
180	C₂×C₄×C₁₃₇	—	4	1	no	—
181	C₂×C₄×C₁₃₇	—	4	1	no	—
182	C₂×C₄×C₁₃₇	—	4	1	no	—
183	C₂×C₄×C₁₃₇	—	4	2	no	—
184	C₂×C₄×C₁₃₇	—	8	4	no	—
185	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
188	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
191	C₈×C₁₃₇	—	2	1	no	—
192	C₈×C₁₃₇	—	2	1	no	—
193	C₈×C₁₃₇	—	4	1	no	—
194	C₈×C₁₃₇	—	4	1	no	—
195	C₈×C₁₃₇	—	4	2	no	—
196	C₈×C₁₃₇	—	4	2	no	—
197	C₈×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
198	C₈×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
199	C₂²×C₁₃₇	—	2	1	no	—
200	C₂²×C₁₃₇	—	2	1	no	—
201	C₂²×C₁₃₇	—	2	1	no	—
202	C₂²×C₁₃₇	—	4	1	no	—
203	C₂²×C₁₃₇	—	4	1	no	—
204	C₂²×C₁₃₇	—	4	1	no	—
205	C₂²×C₁₃₇	—	8	2	no	—
206	C₂²×C₁₃₇	—	8	2	no	—
207	C₂²×C₁₃₇	—	8	2	no	—
208	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
209	C₄×C₁₃₇	—	2	1	no	—
210	C₄×C₁₃₇	—	2	1	no	—
211	C₄×C₁₃₇	—	2	1	no	—
212	C₄×C₁₃₇	—	2	1	no	—
213	C₄×C₁₃₇	—	4	1	no	—
214	C₄×C₁₃₇	—	4	1	no	—
215	C₄×C₁₃₇	—	4	1	no	—
216	C₄×C₁₃₇	—	8	2	no	—
217	C₄×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₄×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
219	C₄×C₁₃₇	#577	1	2	yes	—
220	C₂×C₁₃₇	—	4	1	no	—
221	C₂×C₁₃₇	—	8	1	no	—
222	C₂×C₁₃₇	—	16	2	no	—
223	C₂×C₁₃₇	#3038	1	1	yes	characteristic
224	C₂×C₁₃₇	#3060	1	1	yes	characteristic
225	C₂×C₁₃₇	#3067	1	1	yes	characteristic
226	#19355	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₁₃₇	#19355	1	1	yes	characteristic, direct product factor, Sylow
228	#3251	C₂×C₁₃₇	1	2	yes	complemented
229	#3147	C₂×C₁₃₇	1	1	yes	characteristic, complemented
230	#2966	C₂×C₁₃₇	1	1	yes	characteristic, complemented
231	#1690	C₂×C₁₃₇	1	1	yes	characteristic, complemented
232	#1689	C₂×C₁₃₇	1	1	yes	characteristic, complemented
233	#1688	C₂×C₁₃₇	1	1	yes	characteristic, complemented
234	#1687	C₂×C₁₃₇	1	1	yes	characteristic, complemented
235	#1666	C₂×C₁₃₇	1	2	yes	complemented
236	#1665	C₂×C₁₃₇	1	2	yes	complemented
237	#1566	C₂×C₁₃₇	1	1	yes	characteristic, complemented
238	#1557	C₂×C₁₃₇	1	2	yes	complemented
239	C₂×#135	—	2	1	no	—
240	C₂×#135	—	2	1	no	—
241	#532	C₂²×C₁₃₇	1	2	yes	—
242	#529	C₂²×C₁₃₇	1	1	yes	characteristic
243	#495	—	2	1	no	—
244	#495	—	2	1	no	—
245	#494	C₂²×C₁₃₇	1	1	yes	characteristic
246	#493	C₂²×C₁₃₇	1	1	yes	characteristic
247	#492	C₂²×C₁₃₇	1	2	yes	—
248	#478	—	2	2	no	—
249	#475	C₂²×C₁₃₇	1	2	yes	—
250	#474	C₂²×C₁₃₇	1	2	yes	—
251	#469	—	2	2	no	—
252	#468	—	2	2	no	—
253	#463	—	2	2	no	—
254	#460	C₂²×C₁₃₇	1	2	yes	—
255	#459	C₂²×C₁₃₇	1	2	yes	—
256	#446	C₂²×C₁₃₇	1	1	yes	characteristic
257	C₈×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
258	#436	C₂²×C₁₃₇	1	1	yes	characteristic
259	#435	—	2	1	no	—
260	C₈×D₄	—	2	1	no	—
261	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
262	#433	—	2	1	no	—
263	#432	C₂²×C₁₃₇	1	1	yes	characteristic
264	#423	C₂²×C₁₃₇	1	2	yes	—
265	#405	—	2	1	no	—
266	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
267	#334	C₂²×C₁₃₇	1	2	yes	—
268	#334	C₂²×C₁₃₇	1	1	yes	characteristic
269	#334	C₂²×C₁₃₇	1	1	yes	characteristic
270	#332	C₂²×C₁₃₇	1	2	yes	—
271	#332	C₂²×C₁₃₇	1	2	yes	—
272	#331	C₂²×C₁₃₇	1	2	yes	—
273	#331	C₂²×C₁₃₇	1	2	yes	—
274	C₂×#41	—	2	2	no	—
275	#135	—	4	4	no	—
276	#135	—	4	4	no	—
277	C₂×Q₁₆	—	2	1	no	—
278	C₂×Q₁₆	—	2	1	no	—
279	C₂×SD₁₆	—	2	2	no	—
280	C₂×SD₁₆	—	2	2	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	C₂×D₈	—	2	2	no	—
283	C₂×D₈	—	2	1	no	—
284	C₂×D₈	—	2	1	no	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	2	1	no	—
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
289	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
290	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
291	#127	C₂³×C₁₃₇	1	2	yes	—
292	#126	—	2	1	no	—
293	#125	D₄×C₁₃₇	1	1	yes	characteristic
294	#124	—	2	2	no	—
295	#124	D₄×C₁₃₇	1	1	yes	characteristic
296	#123	—	2	1	no	—
297	C₂²⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
298	#121	—	2	2	no	—
299	#121	—	2	2	no	—
300	#121	D₄×C₁₃₇	1	1	yes	characteristic
301	C₄×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
306	#117	—	2	1	no	—
307	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
308	#107	—	2	2	no	—
309	#106	—	2	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	2	2	no	—
313	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
314	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
315	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
316	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
317	#103	—	2	2	no	—
318	#102	—	2	2	no	—
319	#102	—	2	2	no	—
320	#102	—	2	2	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	2	1	no	—
323	C₂²⋊C₈	—	2	1	no	—
324	#97	—	2	1	no	—
325	#97	—	2	1	no	—
326	C₄×C₈	—	2	1	no	—
327	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
328	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
329	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
330	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
331	#41	—	4	4	no	—
332	#41	—	4	4	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
345	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
346	Q₁₆	—	4	2	no	—
347	Q₁₆	—	4	2	no	—
348	SD₁₆	—	4	4	no	—
349	SD₁₆	—	4	4	no	—
350	SD₁₆	—	8	2	no	—
351	D₈	—	4	2	no	—
352	D₈	—	4	2	no	—
353	D₈	—	8	2	no	—
354	M₁₆	—	4	2	no	—
355	M₁₆	—	8	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	4	2	no	—
363	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
364	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
365	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
366	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
374	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	2	1	no	—
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	2	1	no	—
379	C₂²⋊C₄	—	2	1	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
384	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
385	C₄²	#41×C₁₃₇	1	1	yes	characteristic
386	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
387	C₂³	—	2	1	no	—
388	C₂³	—	4	2	no	—
389	C₂³	#121×C₁₃₇	1	1	yes	characteristic
390	Q₈	—	2	2	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	8	2	no	—
400	D₄	—	8	4	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	8	4	no	—
412	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
413	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
414	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
415	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	4	1	no	—
421	C₈	—	4	1	no	—
422	C₈	—	4	2	no	—
423	C₈	—	4	2	no	—
424	C₈	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
425	C₈	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	1	no	—
443	C₄	—	8	2	no	—
444	C₄	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
445	C₄	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
446	C₄	#577×C₁₃₇	1	2	yes	—
447	C₂	—	4	1	no	—
448	C₂	—	8	1	no	—
449	C₂	—	16	2	no	—
450	C₂	#3038×C₁₃₇	1	1	yes	characteristic
451	C₂	#3060×C₁₃₇	1	1	yes	characteristic
452	C₂	#3067×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3251×C₁₃₇	C₂	semidirect
2. #3147×C₁₃₇	C₂	semidirect
3. #2966×C₁₃₇	C₂	semidirect
4. #1690×C₁₃₇	C₂	semidirect
5. #1689×C₁₃₇	C₂	semidirect
6. #1688×C₁₃₇	C₂	semidirect
7. #1687×C₁₃₇	C₂	semidirect
8. #1666×C₁₃₇	C₂	semidirect
9. #1665×C₁₃₇	C₂	semidirect
10. #1566×C₁₃₇	C₂	semidirect
11. #1557×C₁₃₇	C₂	semidirect
226. #19355	C₁₃₇	direct (N × H)
227. C₁₃₇	#19355	direct (N × H)
228. #3251	C₂×C₁₃₇	semidirect
229. #3147	C₂×C₁₃₇	semidirect
230. #2966	C₂×C₁₃₇	semidirect
231. #1690	C₂×C₁₃₇	semidirect
232. #1689	C₂×C₁₃₇	semidirect
233. #1688	C₂×C₁₃₇	semidirect
234. #1687	C₂×C₁₃₇	semidirect
235. #1666	C₂×C₁₃₇	semidirect
236. #1665	C₂×C₁₃₇	semidirect
237. #1566	C₂×C₁₃₇	semidirect
238. #1557	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3251×C₁₃₇	2
#3147×C₁₃₇	2
#2966×C₁₃₇	2
#1690×C₁₃₇	2
#1689×C₁₃₇	2
#1688×C₁₃₇	2
#1687×C₁₃₇	2
#1666×C₁₃₇	2
#1665×C₁₃₇	2
#1566×C₁₃₇	2
#1557×C₁₃₇	2
#19355	137

Subgroups — C137×#19355 #46868741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19355 #46868741