Subgroups — C₁₃₇×#17965 #46867351

Order 35072.

594 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3172×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2966×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2960×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#1593×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1592×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	C₈×Q₁₆×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	C₈×SD₁₆×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1569×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1497×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1495×C₁₃₇	C₂	1	1	yes	maximal, characteristic
11	C₈×M₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#533×C₁₃₇	C₂²	1	1	yes	characteristic
13	#529×C₁₃₇	C₂²	1	1	yes	characteristic
14	#501×C₁₃₇	C₄	1	1	yes	characteristic
15	#497×C₁₃₇	C₄	1	1	yes	characteristic
16	#491×C₁₃₇	C₄	1	1	yes	characteristic
17	#489×C₁₃₇	C₄	1	1	yes	characteristic
18	#470×C₁₃₇	C₄	1	2	yes	—
19	#468×C₁₃₇	C₄	1	2	yes	—
20	#446×C₁₃₇	—	2	1	no	—
21	#446×C₁₃₇	C₂²	1	2	yes	—
22	#446×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₈×Q₈×C₁₃₇	—	2	1	no	—
24	C₈×Q₈×C₁₃₇	C₂²	1	2	yes	—
25	C₈×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
26	C₄×Q₁₆×C₁₃₇	C₂²	1	2	yes	—
27	C₄×SD₁₆×C₁₃₇	C₂²	1	2	yes	—
28	#436×C₁₃₇	C₂²	1	1	yes	characteristic
29	#435×C₁₃₇	—	2	1	no	—
30	C₈×D₄×C₁₃₇	—	2	1	no	—
31	C₈×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
32	#433×C₁₃₇	—	2	1	no	—
33	#432×C₁₃₇	C₂²	1	1	yes	characteristic
34	#431×C₁₃₇	C₂²	1	1	yes	characteristic
35	#424×C₁₃₇	—	2	1	no	—
36	#423×C₁₃₇	C₂²	1	1	yes	characteristic
37	#405×C₁₃₇	—	2	1	no	—
38	#405×C₁₃₇	—	2	1	no	—
39	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
41	#335×C₁₃₇	C₂²	1	2	yes	—
42	#334×C₁₃₇	C₂²	1	2	yes	—
43	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	—
44	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	—
45	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	—
46	D₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
47	#322×C₁₃₇	C₂²	1	2	yes	—
48	C₈²×C₁₃₇	C₂²	1	2	yes	—
49	C₂×Q₁₆×C₁₃₇	C₂×C₄	1	2	yes	—
50	C₂×SD₁₆×C₁₃₇	C₂×C₄	1	2	yes	—
51	C₂×M₁₆×C₁₃₇	—	2	1	no	—
52	C₂×M₁₆×C₁₃₇	—	2	1	no	—
53	C₂×M₁₆×C₁₃₇	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₁₃₇	—	2	1	no	—
55	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
57	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
58	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
59	#126×C₁₃₇	—	2	1	no	—
60	#125×C₁₃₇	—	2	1	no	—
61	#125×C₁₃₇	C₂×C₄	1	1	yes	characteristic
62	#124×C₁₃₇	C₂×C₄	1	1	yes	characteristic
63	#123×C₁₃₇	—	2	1	no	—
64	C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
65	C₂²⋊Q₈×C₁₃₇	C₂×C₄	1	2	yes	—
66	C₂²⋊Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
67	#121×C₁₃₇	C₂×C₄	1	1	yes	characteristic
68	C₄×Q₈×C₁₃₇	—	2	1	no	—
69	C₄×Q₈×C₁₃₇	C₂³	1	2	yes	—
70	C₄×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
71	C₄×D₄×C₁₃₇	—	2	1	no	—
72	C₄×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
73	#117×C₁₃₇	—	2	1	no	—
74	#117×C₁₃₇	—	2	1	no	—
75	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
76	#107×C₁₃₇	C₂×C₄	1	2	yes	—
77	#106×C₁₃₇	C₂×C₄	1	2	yes	—
78	C₄⋊C₈×C₁₃₇	—	2	2	no	—
79	C₄⋊C₈×C₁₃₇	—	2	2	no	—
80	C₄⋊C₈×C₁₃₇	—	2	1	no	—
81	C₄⋊C₈×C₁₃₇	—	2	1	no	—
82	C₄⋊C₈×C₁₃₇	—	2	1	no	—
83	C₄⋊C₈×C₁₃₇	—	2	1	no	—
84	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
85	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
87	#103×C₁₃₇	C₂×C₄	1	2	yes	—
88	#103×C₁₃₇	C₂×C₄	1	2	yes	—
89	#103×C₁₃₇	C₂×C₄	1	2	yes	—
90	#102×C₁₃₇	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
92	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
93	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
94	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
95	#97×C₁₃₇	—	2	1	no	—
96	#97×C₁₃₇	—	2	2	no	—
97	#97×C₁₃₇	—	2	1	no	—
98	#97×C₁₃₇	C₂×C₄	1	1	yes	characteristic
99	#97×C₁₃₇	C₂×C₄	1	1	yes	characteristic
100	C₄×C₈×C₁₃₇	—	2	1	no	—
101	C₄×C₈×C₁₃₇	—	2	2	no	—
102	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
103	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
104	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
105	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
106	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₁₃₇	—	2	1	no	—
109	C₂×Q₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
110	C₂×Q₈×C₁₃₇	C₂²×C₄	1	2	yes	—
111	C₂×D₄×C₁₃₇	—	2	1	no	—
112	C₂×D₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₇	—	2	1	no	—
114	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
117	Q₁₆×C₁₃₇	—	2	4	no	—
118	SD₁₆×C₁₃₇	—	2	4	no	—
119	M₁₆×C₁₃₇	—	2	4	no	—
120	M₁₆×C₁₃₇	—	4	2	no	—
121	M₁₆×C₁₃₇	—	4	2	no	—
122	C₂×C₈×C₁₃₇	—	2	2	no	—
123	C₂×C₈×C₁₃₇	—	2	1	no	—
124	C₂×C₈×C₁₃₇	—	2	2	no	—
125	C₂×C₈×C₁₃₇	—	2	1	no	—
126	C₂×C₈×C₁₃₇	—	2	2	no	—
127	C₂×C₈×C₁₃₇	—	4	1	no	—
128	C₂×C₈×C₁₃₇	—	4	2	no	—
129	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
135	C₄⋊C₄×C₁₃₇	—	2	1	no	—
136	C₄⋊C₄×C₁₃₇	—	2	1	no	—
137	C₄⋊C₄×C₁₃₇	—	2	1	no	—
138	C₄⋊C₄×C₁₃₇	—	2	1	no	—
139	C₄⋊C₄×C₁₃₇	—	2	1	no	—
140	C₄⋊C₄×C₁₃₇	—	2	1	no	—
141	C₄⋊C₄×C₁₃₇	—	2	2	no	—
142	C₄⋊C₄×C₁₃₇	—	2	2	no	—
143	C₄⋊C₄×C₁₃₇	—	2	1	no	—
144	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
145	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
146	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
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	C₄²×C₁₃₇	—	2	1	no	—
154	C₄²×C₁₃₇	—	2	2	no	—
155	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₁₃₇	#41	1	1	yes	characteristic
158	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
159	C₂³×C₁₃₇	—	2	1	no	—
160	C₂³×C₁₃₇	C₄×D₄	1	1	yes	characteristic
161	Q₈×C₁₃₇	—	2	2	no	—
162	Q₈×C₁₃₇	—	2	2	no	—
163	Q₈×C₁₃₇	—	2	2	no	—
164	Q₈×C₁₃₇	—	4	2	no	—
165	D₄×C₁₃₇	—	2	2	no	—
166	D₄×C₁₃₇	—	4	2	no	—
167	C₂×C₄×C₁₃₇	—	2	2	no	—
168	C₂×C₄×C₁₃₇	—	2	1	no	—
169	C₂×C₄×C₁₃₇	—	2	1	no	—
170	C₂×C₄×C₁₃₇	—	2	1	no	—
171	C₂×C₄×C₁₃₇	—	2	2	no	—
172	C₂×C₄×C₁₃₇	—	2	1	no	—
173	C₂×C₄×C₁₃₇	—	2	2	no	—
174	C₂×C₄×C₁₃₇	—	2	1	no	—
175	C₂×C₄×C₁₃₇	—	4	1	no	—
176	C₂×C₄×C₁₃₇	—	4	1	no	—
177	C₂×C₄×C₁₃₇	—	4	1	no	—
178	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
184	C₈×C₁₃₇	—	2	2	no	—
185	C₈×C₁₃₇	—	2	1	no	—
186	C₈×C₁₃₇	—	2	1	no	—
187	C₈×C₁₃₇	—	2	1	no	—
188	C₈×C₁₃₇	—	4	2	no	—
189	C₈×C₁₃₇	—	4	1	no	—
190	C₈×C₁₃₇	—	4	1	no	—
191	C₈×C₁₃₇	—	4	2	no	—
192	C₈×C₁₃₇	#131	1	4	yes	—
193	C₈×C₁₃₇	#137	1	2	yes	—
194	C₂²×C₁₃₇	—	2	1	no	—
195	C₂²×C₁₃₇	—	2	1	no	—
196	C₂²×C₁₃₇	—	2	1	no	—
197	C₂²×C₁₃₇	—	4	1	no	—
198	C₂²×C₁₃₇	—	4	1	no	—
199	C₂²×C₁₃₇	—	4	1	no	—
200	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
201	C₄×C₁₃₇	—	2	1	no	—
202	C₄×C₁₃₇	—	2	1	no	—
203	C₄×C₁₃₇	—	2	1	no	—
204	C₄×C₁₃₇	—	2	1	no	—
205	C₄×C₁₃₇	—	4	1	no	—
206	C₄×C₁₃₇	—	4	2	no	—
207	C₄×C₁₃₇	—	4	1	no	—
208	C₄×C₁₃₇	—	4	1	no	—
209	C₄×C₁₃₇	—	4	2	no	—
210	C₄×C₁₃₇	C₂×#131	1	2	yes	—
211	C₄×C₁₃₇	C₂×#137	1	1	yes	characteristic
212	C₄×C₁₃₇	#575	1	1	yes	characteristic
213	C₂×C₁₃₇	—	4	1	no	—
214	C₂×C₁₃₇	—	8	1	no	—
215	C₂×C₁₃₇	#2931	1	1	yes	characteristic
216	C₂×C₁₃₇	C₄×#137	1	1	yes	characteristic
217	C₂×C₁₃₇	#2955	1	1	yes	characteristic
218	#17965	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₁₃₇	#17965	1	1	yes	characteristic, direct product factor, Sylow
220	#3172	C₂×C₁₃₇	1	1	yes	characteristic
221	#2966	C₂×C₁₃₇	1	1	yes	characteristic
222	#2960	C₂×C₁₃₇	1	1	yes	characteristic, complemented
223	#1593	C₂×C₁₃₇	1	2	yes	complemented
224	#1592	C₂×C₁₃₇	1	2	yes	complemented
225	C₈×Q₁₆	C₂×C₁₃₇	1	2	yes	complemented
226	C₈×SD₁₆	C₂×C₁₃₇	1	2	yes	complemented
227	#1569	C₂×C₁₃₇	1	1	yes	characteristic, complemented
228	#1497	C₂×C₁₃₇	1	1	yes	characteristic, complemented
229	#1495	C₂×C₁₃₇	1	1	yes	characteristic
230	C₈×M₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
231	#533	C₂²×C₁₃₇	1	1	yes	characteristic
232	#529	C₂²×C₁₃₇	1	1	yes	characteristic
233	#501	C₄×C₁₃₇	1	1	yes	characteristic
234	#497	C₄×C₁₃₇	1	1	yes	characteristic
235	#491	C₄×C₁₃₇	1	1	yes	characteristic
236	#489	C₄×C₁₃₇	1	1	yes	characteristic
237	#470	C₄×C₁₃₇	1	2	yes	—
238	#468	C₄×C₁₃₇	1	2	yes	—
239	#446	—	2	1	no	—
240	#446	C₂²×C₁₃₇	1	2	yes	—
241	#446	C₂²×C₁₃₇	1	1	yes	characteristic
242	C₈×Q₈	—	2	1	no	—
243	C₈×Q₈	C₂²×C₁₃₇	1	2	yes	—
244	C₈×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
245	C₄×Q₁₆	C₂²×C₁₃₇	1	2	yes	—
246	C₄×SD₁₆	C₂²×C₁₃₇	1	2	yes	—
247	#436	C₂²×C₁₃₇	1	1	yes	characteristic
248	#435	—	2	1	no	—
249	C₈×D₄	—	2	1	no	—
250	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
251	#433	—	2	1	no	—
252	#432	C₂²×C₁₃₇	1	1	yes	characteristic
253	#431	C₂²×C₁₃₇	1	1	yes	characteristic
254	#424	—	2	1	no	—
255	#423	C₂²×C₁₃₇	1	1	yes	characteristic
256	#405	—	2	1	no	—
257	#405	—	2	1	no	—
258	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
260	#335	C₂²×C₁₃₇	1	2	yes	—
261	#334	C₂²×C₁₃₇	1	2	yes	—
262	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	—
263	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	—
264	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	—
265	D₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
266	#322	C₂²×C₁₃₇	1	2	yes	—
267	C₈²	C₂²×C₁₃₇	1	2	yes	—
268	C₂×Q₁₆	C₂×C₄×C₁₃₇	1	2	yes	—
269	C₂×SD₁₆	C₂×C₄×C₁₃₇	1	2	yes	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	C₂×C₄×C₁₃₇	1	2	yes	—
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
275	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
276	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
277	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
278	#126	—	2	1	no	—
279	#125	—	2	1	no	—
280	#125	C₂×C₄×C₁₃₇	1	1	yes	characteristic
281	#124	C₂×C₄×C₁₃₇	1	1	yes	characteristic
282	#123	—	2	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	C₂²⋊Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
285	C₂²⋊Q₈	C₂×C₄×C₁₃₇	1	2	yes	—
286	#121	C₂×C₄×C₁₃₇	1	1	yes	characteristic
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
289	C₄×Q₈	C₂³×C₁₃₇	1	2	yes	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
292	#117	—	2	1	no	—
293	#117	—	2	1	no	—
294	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
295	#107	C₂×C₄×C₁₃₇	1	2	yes	—
296	#106	C₂×C₄×C₁₃₇	1	2	yes	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	—	2	2	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
304	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
305	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
306	#103	C₂×C₄×C₁₃₇	1	2	yes	—
307	#103	C₂×C₄×C₁₃₇	1	2	yes	—
308	#103	C₂×C₄×C₁₃₇	1	2	yes	—
309	#102	C₂×C₄×C₁₃₇	1	2	yes	—
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	#97	—	2	1	no	—
315	#97	—	2	2	no	—
316	#97	—	2	1	no	—
317	#97	C₂×C₄×C₁₃₇	1	1	yes	characteristic
318	#97	C₂×C₄×C₁₃₇	1	1	yes	characteristic
319	C₄×C₈	—	2	1	no	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
322	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
323	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
324	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
325	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
326	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
329	C₂×Q₈	C₂²×C₄×C₁₃₇	1	2	yes	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
335	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
336	Q₁₆	—	2	4	no	—
337	SD₁₆	—	2	4	no	—
338	M₁₆	—	2	4	no	—
339	M₁₆	—	4	2	no	—
340	M₁₆	—	4	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	4	1	no	—
347	C₂×C₈	—	4	2	no	—
348	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
349	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
350	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
351	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
352	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
353	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
364	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
365	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	2	no	—
374	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
375	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
376	C₄²	#41×C₁₃₇	1	1	yes	characteristic
377	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
378	C₂³	—	2	1	no	—
379	C₂³	C₄×D₄×C₁₃₇	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	2	2	no	—
383	Q₈	—	4	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	4	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
398	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
399	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
400	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
402	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	2	1	no	—
407	C₈	—	4	2	no	—
408	C₈	—	4	1	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	2	no	—
411	C₈	#131×C₁₃₇	1	4	yes	—
412	C₈	#137×C₁₃₇	1	2	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	2	no	—
429	C₄	C₂×#131×C₁₃₇	1	2	yes	—
430	C₄	C₂×#137×C₁₃₇	1	1	yes	characteristic
431	C₄	#575×C₁₃₇	1	1	yes	characteristic
432	C₂	—	4	1	no	—
433	C₂	—	8	1	no	—
434	C₂	#2931×C₁₃₇	1	1	yes	characteristic
435	C₂	C₄×#137×C₁₃₇	1	1	yes	characteristic
436	C₂	#2955×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₃₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
socle	C₂²×C₁₃₇	C₂×C₄×D₄
prime radical	#121×C₁₃₇	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃₇ ◁ C₂×C₄×C₈×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. #2960×C₁₃₇	C₂	semidirect
4. #1593×C₁₃₇	C₂	semidirect
5. #1592×C₁₃₇	C₂	semidirect
6. C₈×Q₁₆×C₁₃₇	C₂	semidirect
7. C₈×SD₁₆×C₁₃₇	C₂	semidirect
8. #1569×C₁₃₇	C₂	semidirect
9. #1497×C₁₃₇	C₂	semidirect
11. C₈×M₁₆×C₁₃₇	C₂	semidirect
218. #17965	C₁₃₇	direct (N × H)
219. C₁₃₇	#17965	direct (N × H)
222. #2960	C₂×C₁₃₇	semidirect
223. #1593	C₂×C₁₃₇	semidirect
224. #1592	C₂×C₁₃₇	semidirect
225. C₈×Q₁₆	C₂×C₁₃₇	semidirect
226. C₈×SD₁₆	C₂×C₁₃₇	semidirect
227. #1569	C₂×C₁₃₇	semidirect
228. #1497	C₂×C₁₃₇	semidirect
230. C₈×M₁₆	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3172×C₁₃₇	2
#2966×C₁₃₇	2
#2960×C₁₃₇	2
#1593×C₁₃₇	2
#1592×C₁₃₇	2
C₈×Q₁₆×C₁₃₇	2
C₈×SD₁₆×C₁₃₇	2
#1569×C₁₃₇	2
#1497×C₁₃₇	2
#1495×C₁₃₇	2
C₈×M₁₆×C₁₃₇	2
#17965	137

Subgroups — C137×#17965 #46867351

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#17965 #46867351