Subgroups — C₁₃₇×#18829 #46868215

Order 35072.

872 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3503×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#3237×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#3229×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#3116×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#1653×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1651×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1637×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1636×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1556×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1497×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1488×C₁₃₇	C₂	1	1	yes	maximal, characteristic
12	Q₈²×C₁₃₇	—	2	1	no	—
13	#557×C₁₃₇	C₂²	1	2	yes	—
14	#554×C₁₃₇	—	2	1	no	—
15	#554×C₁₃₇	—	2	2	no	—
16	D₄×Q₈×C₁₃₇	—	2	2	no	—
17	D₄×Q₈×C₁₃₇	C₂²	1	2	yes	—
18	#544×C₁₃₇	—	2	2	no	—
19	#544×C₁₃₇	—	2	1	no	—
20	#533×C₁₃₇	—	2	1	no	—
21	#533×C₁₃₇	C₂²	1	1	yes	characteristic
22	#533×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₁₃₇	—	2	1	no	—
24	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
25	#520×C₁₃₇	—	2	1	no	—
26	C₄×#41×C₁₃₇	C₂²	1	1	yes	characteristic
27	#501×C₁₃₇	—	2	1	no	—
28	#498×C₁₃₇	C₂²	1	2	yes	—
29	#491×C₁₃₇	—	2	1	no	—
30	#487×C₁₃₇	C₂²	1	2	yes	—
31	#485×C₁₃₇	—	2	2	no	—
32	#485×C₁₃₇	—	2	1	no	—
33	#483×C₁₃₇	—	2	2	no	—
34	#477×C₁₃₇	C₂²	1	1	yes	characteristic
35	#477×C₁₃₇	C₂²	1	2	yes	—
36	#476×C₁₃₇	C₂²	1	1	yes	characteristic
37	#475×C₁₃₇	—	2	2	no	—
38	#475×C₁₃₇	C₂²	1	2	yes	—
39	#462×C₁₃₇	C₂²	1	1	yes	characteristic
40	#461×C₁₃₇	C₂²	1	1	yes	characteristic
41	#452×C₁₃₇	—	2	1	no	—
42	#441×C₁₃₇	—	2	1	no	—
43	#440×C₁₃₇	—	2	1	no	—
44	#432×C₁₃₇	C₂²	1	1	yes	characteristic
45	#432×C₁₃₇	C₂²	1	1	yes	characteristic
46	#431×C₁₃₇	C₂²	1	1	yes	characteristic
47	#332×C₁₃₇	C₂²	1	2	yes	—
48	#332×C₁₃₇	C₂²	1	2	yes	—
49	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	—
50	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	—
51	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	—
52	D₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
53	C₂×#41×C₁₃₇	D₄	1	1	yes	characteristic
54	C₂²×Q₈×C₁₃₇	—	2	2	no	—
55	C₂²×Q₈×C₁₃₇	—	2	1	no	—
56	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
57	C₂×SD₁₆×C₁₃₇	—	2	1	no	—
58	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
59	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
60	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
61	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
62	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
63	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
64	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
65	C₄⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₁₃₇	D₄	1	2	yes	—
67	C₄⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
68	C₄⋊Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
69	C₄⋊Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
70	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
71	#125×C₁₃₇	—	2	2	no	—
72	#125×C₁₃₇	—	2	4	no	—
73	#125×C₁₃₇	—	2	2	no	—
74	#125×C₁₃₇	—	2	1	no	—
75	#125×C₁₃₇	—	2	1	no	—
76	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
77	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
78	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
79	C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
80	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
81	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
82	C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
83	C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
84	C₂²⋊Q₈×C₁₃₇	D₄	1	2	yes	—
85	C₄×Q₈×C₁₃₇	—	2	2	no	—
86	C₄×Q₈×C₁₃₇	—	2	2	no	—
87	C₄×Q₈×C₁₃₇	—	2	2	no	—
88	C₄×Q₈×C₁₃₇	—	2	1	no	—
89	C₄×Q₈×C₁₃₇	—	2	1	no	—
90	C₄×Q₈×C₁₃₇	—	2	1	no	—
91	C₄×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
93	C₄×Q₈×C₁₃₇	C₂³	1	2	yes	—
94	C₄×D₄×C₁₃₇	—	2	4	no	—
95	C₄×D₄×C₁₃₇	—	2	2	no	—
96	C₄×D₄×C₁₃₇	—	2	1	no	—
97	C₄×D₄×C₁₃₇	—	2	1	no	—
98	C₄×D₄×C₁₃₇	D₄	1	1	yes	characteristic
99	C₄×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
100	#117×C₁₃₇	—	2	2	no	—
101	#117×C₁₃₇	—	2	1	no	—
102	#117×C₁₃₇	—	2	1	no	—
103	#117×C₁₃₇	—	2	1	no	—
104	#117×C₁₃₇	D₄	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
106	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
107	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
109	C₂×C₄²×C₁₃₇	—	2	1	no	—
110	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
111	#107×C₁₃₇	—	2	1	no	—
112	#107×C₁₃₇	—	2	2	no	—
113	#106×C₁₃₇	—	2	1	no	—
114	#106×C₁₃₇	—	2	4	no	—
115	#106×C₁₃₇	—	2	2	no	—
116	C₄⋊C₈×C₁₃₇	—	2	1	no	—
117	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
118	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
119	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
120	#103×C₁₃₇	—	2	1	no	—
121	#103×C₁₃₇	—	2	2	no	—
122	#103×C₁₃₇	—	2	2	no	—
123	#103×C₁₃₇	—	2	1	no	—
124	#103×C₁₃₇	—	2	1	no	—
125	#103×C₁₃₇	—	2	4	no	—
126	#102×C₁₃₇	—	2	1	no	—
127	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
128	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
129	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
130	#97×C₁₃₇	—	2	1	no	—
131	#97×C₁₃₇	—	2	1	no	—
132	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
133	#41×C₁₃₇	—	2	2	no	—
134	#41×C₁₃₇	—	2	2	no	—
135	C₂×Q₈×C₁₃₇	—	2	4	no	—
136	C₂×Q₈×C₁₃₇	—	2	1	no	—
137	C₂×Q₈×C₁₃₇	—	2	2	no	—
138	C₂×Q₈×C₁₃₇	—	2	2	no	—
139	C₂×Q₈×C₁₃₇	—	2	1	no	—
140	C₂×Q₈×C₁₃₇	—	2	1	no	—
141	C₂×Q₈×C₁₃₇	—	8	2	no	—
142	C₂×Q₈×C₁₃₇	—	8	4	no	—
143	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
144	C₂×Q₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
145	C₂×D₄×C₁₃₇	—	2	1	no	—
146	C₂×D₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃₇	—	2	1	no	—
148	C₂²×C₄×C₁₃₇	—	2	4	no	—
149	C₂²×C₄×C₁₃₇	—	2	2	no	—
150	C₂²×C₄×C₁₃₇	—	2	1	no	—
151	C₂²×C₄×C₁₃₇	—	2	1	no	—
152	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
155	Q₁₆×C₁₃₇	—	4	2	no	—
156	SD₁₆×C₁₃₇	—	4	2	no	—
157	C₂×C₈×C₁₃₇	—	2	2	no	—
158	C₂×C₈×C₁₃₇	—	2	1	no	—
159	C₂×C₈×C₁₃₇	—	2	2	no	—
160	C₂×C₈×C₁₃₇	—	2	1	no	—
161	C₄⋊C₄×C₁₃₇	—	2	4	no	—
162	C₄⋊C₄×C₁₃₇	—	2	4	no	—
163	C₄⋊C₄×C₁₃₇	—	2	4	no	—
164	C₄⋊C₄×C₁₃₇	—	2	4	no	—
165	C₄⋊C₄×C₁₃₇	—	2	1	no	—
166	C₄⋊C₄×C₁₃₇	—	2	2	no	—
167	C₄⋊C₄×C₁₃₇	—	2	1	no	—
168	C₄⋊C₄×C₁₃₇	—	2	2	no	—
169	C₄⋊C₄×C₁₃₇	—	2	1	no	—
170	C₄⋊C₄×C₁₃₇	—	2	1	no	—
171	C₄⋊C₄×C₁₃₇	—	2	2	no	—
172	C₄⋊C₄×C₁₃₇	—	2	2	no	—
173	C₄⋊C₄×C₁₃₇	—	2	1	no	—
174	C₄⋊C₄×C₁₃₇	—	2	2	no	—
175	C₄⋊C₄×C₁₃₇	—	2	1	no	—
176	C₄⋊C₄×C₁₃₇	—	2	1	no	—
177	C₄⋊C₄×C₁₃₇	—	2	1	no	—
178	C₄⋊C₄×C₁₃₇	—	2	1	no	—
179	C₄⋊C₄×C₁₃₇	—	4	1	no	—
180	C₄⋊C₄×C₁₃₇	—	4	1	no	—
181	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
182	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
183	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
184	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
185	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
186	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
187	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
188	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
189	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
190	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
191	C₄²×C₁₃₇	—	2	4	no	—
192	C₄²×C₁₃₇	—	2	1	no	—
193	C₄²×C₁₃₇	—	2	1	no	—
194	C₄²×C₁₃₇	—	2	1	no	—
195	C₄²×C₁₃₇	—	2	2	no	—
196	C₄²×C₁₃₇	—	4	1	no	—
197	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
201	C₂³×C₁₃₇	—	2	1	no	—
202	C₂³×C₁₃₇	#120	1	1	yes	characteristic
203	Q₈×C₁₃₇	—	2	1	no	—
204	Q₈×C₁₃₇	—	2	4	no	—
205	Q₈×C₁₃₇	—	4	2	no	—
206	Q₈×C₁₃₇	—	4	2	no	—
207	Q₈×C₁₃₇	—	4	4	no	—
208	Q₈×C₁₃₇	—	4	1	no	—
209	Q₈×C₁₃₇	—	4	1	no	—
210	Q₈×C₁₃₇	—	8	2	no	—
211	Q₈×C₁₃₇	—	8	4	no	—
212	Q₈×C₁₃₇	#137	1	2	yes	—
213	D₄×C₁₃₇	—	2	4	no	—
214	D₄×C₁₃₇	—	2	1	no	—
215	D₄×C₁₃₇	#137	1	2	yes	—
216	C₂×C₄×C₁₃₇	—	2	4	no	—
217	C₂×C₄×C₁₃₇	—	2	1	no	—
218	C₂×C₄×C₁₃₇	—	2	1	no	—
219	C₂×C₄×C₁₃₇	—	2	1	no	—
220	C₂×C₄×C₁₃₇	—	2	2	no	—
221	C₂×C₄×C₁₃₇	—	2	2	no	—
222	C₂×C₄×C₁₃₇	—	2	1	no	—
223	C₂×C₄×C₁₃₇	—	2	1	no	—
224	C₂×C₄×C₁₃₇	—	2	2	no	—
225	C₂×C₄×C₁₃₇	—	2	4	no	—
226	C₂×C₄×C₁₃₇	—	4	1	no	—
227	C₂×C₄×C₁₃₇	—	4	2	no	—
228	C₂×C₄×C₁₃₇	—	4	2	no	—
229	C₂×C₄×C₁₃₇	—	4	1	no	—
230	C₂×C₄×C₁₃₇	—	4	1	no	—
231	C₂×C₄×C₁₃₇	—	8	2	no	—
232	C₂×C₄×C₁₃₇	—	8	4	no	—
233	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
234	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
235	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
236	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
239	C₈×C₁₃₇	—	4	2	no	—
240	C₈×C₁₃₇	—	4	1	no	—
241	C₈×C₁₃₇	—	4	1	no	—
242	C₈×C₁₃₇	—	4	2	no	—
243	C₂²×C₁₃₇	—	2	1	no	—
244	C₂²×C₁₃₇	—	2	2	no	—
245	C₂²×C₁₃₇	—	2	1	no	—
246	C₂²×C₁₃₇	—	2	1	no	—
247	C₂²×C₁₃₇	—	4	1	no	—
248	C₂²×C₁₃₇	—	4	1	no	—
249	C₂²×C₁₃₇	C₂×#120	1	1	yes	characteristic
250	C₄×C₁₃₇	—	2	1	no	—
251	C₄×C₁₃₇	—	2	2	no	—
252	C₄×C₁₃₇	—	2	1	no	—
253	C₄×C₁₃₇	—	2	1	no	—
254	C₄×C₁₃₇	—	2	1	no	—
255	C₄×C₁₃₇	—	4	1	no	—
256	C₄×C₁₃₇	—	4	2	no	—
257	C₄×C₁₃₇	—	4	4	no	—
258	C₄×C₁₃₇	—	4	1	no	—
259	C₄×C₁₃₇	—	4	2	no	—
260	C₄×C₁₃₇	—	8	1	no	—
261	C₄×C₁₃₇	—	8	1	no	—
262	C₄×C₁₃₇	C₂×#137	1	1	yes	characteristic
263	C₄×C₁₃₇	C₂×#137	1	1	yes	characteristic
264	C₄×C₁₃₇	#577	1	2	yes	—
265	C₂×C₁₃₇	—	4	1	no	—
266	C₂×C₁₃₇	—	4	2	no	—
267	C₂×C₁₃₇	#3004	1	1	yes	characteristic
268	C₂×C₁₃₇	#3009	1	1	yes	characteristic
269	C₂×C₁₃₇	#3020	1	1	yes	characteristic
270	#18829	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₁₃₇	#18829	1	1	yes	characteristic, direct product factor, Sylow
272	#3503	C₂×C₁₃₇	1	1	yes	characteristic
273	#3237	C₂×C₁₃₇	1	1	yes	characteristic, complemented
274	#3229	C₂×C₁₃₇	1	1	yes	characteristic, complemented
275	#3116	C₂×C₁₃₇	1	1	yes	characteristic
276	#1653	C₂×C₁₃₇	1	2	yes	complemented
277	#1651	C₂×C₁₃₇	1	2	yes	complemented
278	#1637	C₂×C₁₃₇	1	2	yes	complemented
279	#1636	C₂×C₁₃₇	1	2	yes	complemented
280	#1556	C₂×C₁₃₇	1	1	yes	characteristic, complemented
281	#1497	C₂×C₁₃₇	1	1	yes	characteristic, complemented
282	#1488	C₂×C₁₃₇	1	1	yes	characteristic
283	Q₈²	—	2	1	no	—
284	#557	C₂²×C₁₃₇	1	2	yes	—
285	#554	—	2	1	no	—
286	#554	—	2	2	no	—
287	D₄×Q₈	—	2	2	no	—
288	D₄×Q₈	C₂²×C₁₃₇	1	2	yes	—
289	#544	—	2	2	no	—
290	#544	—	2	1	no	—
291	#533	—	2	1	no	—
292	#533	C₂²×C₁₃₇	1	1	yes	characteristic
293	#533	C₂²×C₁₃₇	1	1	yes	characteristic
294	C₂×C₄⋊Q₈	—	2	1	no	—
295	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
296	#520	—	2	1	no	—
297	C₄×#41	C₂²×C₁₃₇	1	1	yes	characteristic
298	#501	—	2	1	no	—
299	#498	C₂²×C₁₃₇	1	2	yes	—
300	#491	—	2	1	no	—
301	#487	C₂²×C₁₃₇	1	2	yes	—
302	#485	—	2	2	no	—
303	#485	—	2	1	no	—
304	#483	—	2	2	no	—
305	#477	C₂²×C₁₃₇	1	1	yes	characteristic
306	#477	C₂²×C₁₃₇	1	2	yes	—
307	#476	C₂²×C₁₃₇	1	1	yes	characteristic
308	#475	—	2	2	no	—
309	#475	C₂²×C₁₃₇	1	2	yes	—
310	#462	C₂²×C₁₃₇	1	1	yes	characteristic
311	#461	C₂²×C₁₃₇	1	1	yes	characteristic
312	#452	—	2	1	no	—
313	#441	—	2	1	no	—
314	#440	—	2	1	no	—
315	#432	C₂²×C₁₃₇	1	1	yes	characteristic
316	#432	C₂²×C₁₃₇	1	1	yes	characteristic
317	#431	C₂²×C₁₃₇	1	1	yes	characteristic
318	#332	C₂²×C₁₃₇	1	2	yes	—
319	#332	C₂²×C₁₃₇	1	2	yes	—
320	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	—
321	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	—
322	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	—
323	D₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
324	C₂×#41	D₄×C₁₃₇	1	1	yes	characteristic
325	C₂²×Q₈	—	2	2	no	—
326	C₂²×Q₈	—	2	1	no	—
327	C₂×Q₁₆	—	2	1	no	—
328	C₂×SD₁₆	—	2	1	no	—
329	C₄⋊Q₈	—	2	2	no	—
330	C₄⋊Q₈	—	2	2	no	—
331	C₄⋊Q₈	—	2	4	no	—
332	C₄⋊Q₈	—	2	2	no	—
333	C₄⋊Q₈	—	2	2	no	—
334	C₄⋊Q₈	—	2	1	no	—
335	C₄⋊Q₈	—	2	1	no	—
336	C₄⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
337	C₄⋊Q₈	D₄×C₁₃₇	1	2	yes	—
338	C₄⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
339	C₄⋊Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
340	C₄⋊Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
341	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
342	#125	—	2	2	no	—
343	#125	—	2	4	no	—
344	#125	—	2	2	no	—
345	#125	—	2	1	no	—
346	#125	—	2	1	no	—
347	C₂²⋊Q₈	—	2	2	no	—
348	C₂²⋊Q₈	—	2	4	no	—
349	C₂²⋊Q₈	—	2	4	no	—
350	C₂²⋊Q₈	—	2	1	no	—
351	C₂²⋊Q₈	—	2	2	no	—
352	C₂²⋊Q₈	—	2	4	no	—
353	C₂²⋊Q₈	—	2	1	no	—
354	C₂²⋊Q₈	—	2	1	no	—
355	C₂²⋊Q₈	D₄×C₁₃₇	1	2	yes	—
356	C₄×Q₈	—	2	2	no	—
357	C₄×Q₈	—	2	2	no	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	—	2	1	no	—
361	C₄×Q₈	—	2	1	no	—
362	C₄×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
363	C₄×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
364	C₄×Q₈	C₂³×C₁₃₇	1	2	yes	—
365	C₄×D₄	—	2	4	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	D₄×C₁₃₇	1	1	yes	characteristic
370	C₄×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
371	#117	—	2	2	no	—
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	—	2	1	no	—
375	#117	D₄×C₁₃₇	1	1	yes	characteristic
376	C₂×C₄⋊C₄	—	2	2	no	—
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
382	#107	—	2	1	no	—
383	#107	—	2	2	no	—
384	#106	—	2	1	no	—
385	#106	—	2	4	no	—
386	#106	—	2	2	no	—
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
389	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
390	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
391	#103	—	2	1	no	—
392	#103	—	2	2	no	—
393	#103	—	2	2	no	—
394	#103	—	2	1	no	—
395	#103	—	2	1	no	—
396	#103	—	2	4	no	—
397	#102	—	2	1	no	—
398	C₂²⋊C₈	—	2	1	no	—
399	C₂²⋊C₈	—	2	1	no	—
400	C₂²⋊C₈	—	2	1	no	—
401	#97	—	2	1	no	—
402	#97	—	2	1	no	—
403	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	C₂×Q₈	—	2	4	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	8	2	no	—
413	C₂×Q₈	—	8	4	no	—
414	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
415	C₂×Q₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
426	Q₁₆	—	4	2	no	—
427	SD₁₆	—	4	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	1	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	4	1	no	—
451	C₄⋊C₄	—	4	1	no	—
452	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
453	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
454	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
455	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	4	1	no	—
462	C₄²	—	2	4	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	2	no	—
467	C₄²	—	4	1	no	—
468	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
469	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
470	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
471	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
472	C₂³	—	2	1	no	—
473	C₂³	#120×C₁₃₇	1	1	yes	characteristic
474	Q₈	—	2	1	no	—
475	Q₈	—	2	4	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	4	2	no	—
478	Q₈	—	4	4	no	—
479	Q₈	—	4	1	no	—
480	Q₈	—	4	1	no	—
481	Q₈	—	8	2	no	—
482	Q₈	—	8	4	no	—
483	Q₈	#137×C₁₃₇	1	2	yes	—
484	D₄	—	2	4	no	—
485	D₄	—	2	1	no	—
486	D₄	#137×C₁₃₇	1	2	yes	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	8	2	no	—
503	C₂×C₄	—	8	4	no	—
504	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
505	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
506	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
508	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
509	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
510	C₈	—	4	2	no	—
511	C₈	—	4	1	no	—
512	C₈	—	4	1	no	—
513	C₈	—	4	2	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	2	1	no	—
518	C₂²	—	4	1	no	—
519	C₂²	—	4	1	no	—
520	C₂²	C₂×#120×C₁₃₇	1	1	yes	characteristic
521	C₄	—	2	1	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	2	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	4	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	2	no	—
531	C₄	—	8	1	no	—
532	C₄	—	8	1	no	—
533	C₄	C₂×#137×C₁₃₇	1	1	yes	characteristic
534	C₄	C₂×#137×C₁₃₇	1	1	yes	characteristic
535	C₄	#577×C₁₃₇	1	2	yes	—
536	C₂	—	4	1	no	—
537	C₂	—	4	2	no	—
538	C₂	#3004×C₁₃₇	1	1	yes	characteristic
539	C₂	#3009×C₁₃₇	1	1	yes	characteristic
540	C₂	#3020×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	C₂×#41×C₁₃₇	D₄
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
2. #3237×C₁₃₇	C₂	semidirect
3. #3229×C₁₃₇	C₂	semidirect
5. #1653×C₁₃₇	C₂	semidirect
6. #1651×C₁₃₇	C₂	semidirect
7. #1637×C₁₃₇	C₂	semidirect
8. #1636×C₁₃₇	C₂	semidirect
9. #1556×C₁₃₇	C₂	semidirect
10. #1497×C₁₃₇	C₂	semidirect
270. #18829	C₁₃₇	direct (N × H)
271. C₁₃₇	#18829	direct (N × H)
273. #3237	C₂×C₁₃₇	semidirect
274. #3229	C₂×C₁₃₇	semidirect
276. #1653	C₂×C₁₃₇	semidirect
277. #1651	C₂×C₁₃₇	semidirect
278. #1637	C₂×C₁₃₇	semidirect
279. #1636	C₂×C₁₃₇	semidirect
280. #1556	C₂×C₁₃₇	semidirect
281. #1497	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3503×C₁₃₇	2
#3237×C₁₃₇	2
#3229×C₁₃₇	2
#3116×C₁₃₇	2
#1653×C₁₃₇	2
#1651×C₁₃₇	2
#1637×C₁₃₇	2
#1636×C₁₃₇	2
#1556×C₁₃₇	2
#1497×C₁₃₇	2
#1488×C₁₃₇	2
#18829	137

Subgroups — C137×#18829 #46868215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#18829 #46868215