Subgroups — C₁₃₇×#17945 #46867331

Order 35072.

670 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3106×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2965×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2931×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#1590×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1589×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1586×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1585×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1574×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1489×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1484×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#131×C₁₃₇	—	2	1	no	—
13	#532×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₄×#41×C₁₃₇	C₂²	1	1	yes	characteristic
15	#482×C₁₃₇	C₄	1	2	yes	—
16	#477×C₁₃₇	C₄	1	1	yes	characteristic
17	#476×C₁₃₇	C₄	1	1	yes	characteristic
18	#460×C₁₃₇	C₄	1	1	yes	characteristic
19	#459×C₁₃₇	C₄	1	1	yes	characteristic
20	#449×C₁₃₇	C₄	1	2	yes	—
21	#446×C₁₃₇	C₂²	1	1	yes	characteristic
22	#446×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₄×SD₁₆×C₁₃₇	C₂²	1	2	yes	—
24	C₄×D₈×C₁₃₇	C₂²	1	2	yes	—
25	#436×C₁₃₇	—	2	1	no	—
26	#436×C₁₃₇	C₂²	1	1	yes	characteristic
27	#436×C₁₃₇	C₂²	1	1	yes	characteristic
28	#436×C₁₃₇	C₂²	1	2	yes	—
29	#435×C₁₃₇	—	2	1	no	—
30	#435×C₁₃₇	—	2	1	no	—
31	C₈×D₄×C₁₃₇	—	2	1	no	—
32	C₈×D₄×C₁₃₇	C₂²	1	2	yes	—
33	#431×C₁₃₇	—	2	1	no	—
34	#431×C₁₃₇	C₂²	1	1	yes	characteristic
35	#431×C₁₃₇	C₂²	1	1	yes	characteristic
36	#423×C₁₃₇	C₂²	1	1	yes	characteristic
37	#408×C₁₃₇	—	2	1	no	—
38	C₄×M₁₆×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	D₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
45	D₄⋊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×#41×C₁₃₇	—	2	1	no	—
50	C₂×#41×C₁₃₇	C₂×C₄	1	1	yes	characteristic
51	C₂×SD₁₆×C₁₃₇	C₂×C₄	1	2	yes	—
52	C₂×D₈×C₁₃₇	C₂×C₄	1	2	yes	—
53	#131×C₁₃₇	—	4	4	no	—
54	C₂×M₁₆×C₁₃₇	—	2	1	no	—
55	C₂×M₁₆×C₁₃₇	—	2	1	no	—
56	C₂×M₁₆×C₁₃₇	—	2	1	no	—
57	C₂×M₁₆×C₁₃₇	—	2	1	no	—
58	C₂×M₁₆×C₁₃₇	—	2	2	no	—
59	C₂²×C₈×C₁₃₇	—	2	2	no	—
60	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
62	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
63	#127×C₁₃₇	C₂×C₄	1	1	yes	characteristic
64	#124×C₁₃₇	—	2	1	no	—
65	#121×C₁₃₇	—	2	1	no	—
66	#121×C₁₃₇	C₂×C₄	1	2	yes	—
67	C₄×Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
68	C₄×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₁₃₇	—	2	1	no	—
70	C₄×D₄×C₁₃₇	—	2	1	no	—
71	C₄×D₄×C₁₃₇	—	2	1	no	—
72	C₄×D₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
73	C₄×D₄×C₁₃₇	C₂³	1	2	yes	—
74	C₄×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
75	#117×C₁₃₇	—	2	1	no	—
76	#117×C₁₃₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃₇	—	2	1	no	—
78	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
79	#107×C₁₃₇	C₂×C₄	1	2	yes	—
80	#106×C₁₃₇	C₂×C₄	1	2	yes	—
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	C₂×C₄	1	1	yes	characteristic
85	C₄⋊C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
86	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
87	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
89	#103×C₁₃₇	C₂×C₄	1	2	yes	—
90	#102×C₁₃₇	C₂×C₄	1	2	yes	—
91	#102×C₁₃₇	C₂×C₄	1	2	yes	—
92	#102×C₁₃₇	C₂×C₄	1	2	yes	—
93	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
94	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
95	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
96	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
97	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
98	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	2	yes	—
99	#97×C₁₃₇	—	2	1	no	—
100	#97×C₁₃₇	—	2	1	no	—
101	#97×C₁₃₇	—	2	1	no	—
102	C₄×C₈×C₁₃₇	—	2	1	no	—
103	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
104	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
105	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
106	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
107	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
109	#41×C₁₃₇	—	4	1	no	—
110	#41×C₁₃₇	—	4	1	no	—
111	#41×C₁₃₇	—	4	2	no	—
112	#41×C₁₃₇	—	4	2	no	—
113	C₂×Q₈×C₁₃₇	—	2	1	no	—
114	C₂×Q₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×D₄×C₁₃₇	—	2	1	no	—
116	C₂×D₄×C₁₃₇	—	2	2	no	—
117	C₂×D₄×C₁₃₇	—	2	1	no	—
118	C₂×D₄×C₁₃₇	—	2	1	no	—
119	C₂×D₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
120	C₂×D₄×C₁₃₇	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₁₃₇	—	2	1	no	—
122	C₂²×C₄×C₁₃₇	—	2	1	no	—
123	C₂²×C₄×C₁₃₇	—	2	1	no	—
124	C₂²×C₄×C₁₃₇	—	2	2	no	—
125	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
128	SD₁₆×C₁₃₇	—	4	2	no	—
129	D₈×C₁₃₇	—	4	2	no	—
130	M₁₆×C₁₃₇	—	2	4	no	—
131	M₁₆×C₁₃₇	—	4	2	no	—
132	M₁₆×C₁₃₇	—	4	2	no	—
133	M₁₆×C₁₃₇	—	4	2	no	—
134	M₁₆×C₁₃₇	—	4	4	no	—
135	C₂×C₈×C₁₃₇	—	2	2	no	—
136	C₂×C₈×C₁₃₇	—	2	2	no	—
137	C₂×C₈×C₁₃₇	—	2	1	no	—
138	C₂×C₈×C₁₃₇	—	2	1	no	—
139	C₂×C₈×C₁₃₇	—	2	2	no	—
140	C₂×C₈×C₁₃₇	—	4	1	no	—
141	C₂×C₈×C₁₃₇	—	4	4	no	—
142	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
148	C₄⋊C₄×C₁₃₇	—	2	1	no	—
149	C₄⋊C₄×C₁₃₇	—	2	1	no	—
150	C₄⋊C₄×C₁₃₇	—	2	1	no	—
151	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
152	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
153	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
154	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
155	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
156	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
157	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
158	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
159	C₄²×C₁₃₇	—	2	1	no	—
160	C₄²×C₁₃₇	—	2	1	no	—
161	C₄²×C₁₃₇	—	2	1	no	—
162	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₃₇	#41	1	1	yes	characteristic
165	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
166	C₂³×C₁₃₇	—	2	1	no	—
167	C₂³×C₁₃₇	—	2	2	no	—
168	C₂³×C₁₃₇	C₄×D₄	1	1	yes	characteristic
169	Q₈×C₁₃₇	—	2	1	no	—
170	Q₈×C₁₃₇	—	2	1	no	—
171	Q₈×C₁₃₇	—	4	2	no	—
172	D₄×C₁₃₇	—	2	1	no	—
173	D₄×C₁₃₇	—	2	2	no	—
174	D₄×C₁₃₇	—	2	2	no	—
175	D₄×C₁₃₇	—	2	1	no	—
176	D₄×C₁₃₇	—	4	2	no	—
177	D₄×C₁₃₇	—	4	2	no	—
178	D₄×C₁₃₇	—	4	4	no	—
179	D₄×C₁₃₇	—	4	2	no	—
180	C₂×C₄×C₁₃₇	—	2	1	no	—
181	C₂×C₄×C₁₃₇	—	2	1	no	—
182	C₂×C₄×C₁₃₇	—	2	1	no	—
183	C₂×C₄×C₁₃₇	—	2	1	no	—
184	C₂×C₄×C₁₃₇	—	2	2	no	—
185	C₂×C₄×C₁₃₇	—	2	1	no	—
186	C₂×C₄×C₁₃₇	—	2	1	no	—
187	C₂×C₄×C₁₃₇	—	2	1	no	—
188	C₂×C₄×C₁₃₇	—	2	2	no	—
189	C₂×C₄×C₁₃₇	—	4	2	no	—
190	C₂×C₄×C₁₃₇	—	4	2	no	—
191	C₂×C₄×C₁₃₇	—	4	1	no	—
192	C₂×C₄×C₁₃₇	—	4	1	no	—
193	C₂×C₄×C₁₃₇	—	4	2	no	—
194	C₂×C₄×C₁₃₇	—	4	2	no	—
195	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
201	C₈×C₁₃₇	—	2	4	no	—
202	C₈×C₁₃₇	—	2	2	no	—
203	C₈×C₁₃₇	—	2	2	no	—
204	C₈×C₁₃₇	—	2	1	no	—
205	C₈×C₁₃₇	—	2	1	no	—
206	C₈×C₁₃₇	—	2	1	no	—
207	C₈×C₁₃₇	—	4	2	no	—
208	C₈×C₁₃₇	—	4	1	no	—
209	C₈×C₁₃₇	—	4	1	no	—
210	C₈×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
211	C₂²×C₁₃₇	—	2	1	no	—
212	C₂²×C₁₃₇	—	2	1	no	—
213	C₂²×C₁₃₇	—	2	1	no	—
214	C₂²×C₁₃₇	—	4	1	no	—
215	C₂²×C₁₃₇	—	4	2	no	—
216	C₂²×C₁₃₇	—	4	2	no	—
217	C₂²×C₁₃₇	—	4	1	no	—
218	C₂²×C₁₃₇	—	4	1	no	—
219	C₂²×C₁₃₇	—	4	2	no	—
220	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
221	C₄×C₁₃₇	—	2	1	no	—
222	C₄×C₁₃₇	—	2	1	no	—
223	C₄×C₁₃₇	—	2	1	no	—
224	C₄×C₁₃₇	—	4	1	no	—
225	C₄×C₁₃₇	—	4	1	no	—
226	C₄×C₁₃₇	—	4	2	no	—
227	C₄×C₁₃₇	—	4	1	no	—
228	C₄×C₁₃₇	#443	1	2	yes	—
229	C₄×C₁₃₇	#568	1	1	yes	characteristic
230	C₄×C₁₃₇	#568	1	1	yes	characteristic
231	C₄×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
232	C₄×C₁₃₇	#575	1	1	yes	characteristic
233	C₂×C₁₃₇	—	4	1	no	—
234	C₂×C₁₃₇	—	8	1	no	—
235	C₂×C₁₃₇	—	8	2	no	—
236	C₂×C₁₃₇	#2930	1	1	yes	characteristic
237	C₂×C₁₃₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
238	C₂×C₁₃₇	C₂×#443	1	1	yes	characteristic
239	#17945	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₁₃₇	#17945	1	1	yes	characteristic, direct product factor, Sylow
241	#3106	C₂×C₁₃₇	1	1	yes	characteristic
242	#2965	C₂×C₁₃₇	1	1	yes	characteristic, complemented
243	#2931	C₂×C₁₃₇	1	1	yes	characteristic, complemented
244	#1590	C₂×C₁₃₇	1	2	yes	complemented
245	#1589	C₂×C₁₃₇	1	2	yes	complemented
246	#1586	C₂×C₁₃₇	1	2	yes	complemented
247	#1585	C₂×C₁₃₇	1	2	yes	complemented
248	#1574	C₂×C₁₃₇	1	1	yes	characteristic, complemented
249	#1489	C₂×C₁₃₇	1	1	yes	characteristic, complemented
250	#1484	C₂×C₁₃₇	1	1	yes	characteristic, complemented
251	C₈×M₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
252	C₂×#131	—	2	1	no	—
253	#532	C₂²×C₁₃₇	1	1	yes	characteristic
254	C₄×#41	C₂²×C₁₃₇	1	1	yes	characteristic
255	#482	C₄×C₁₃₇	1	2	yes	—
256	#477	C₄×C₁₃₇	1	1	yes	characteristic
257	#476	C₄×C₁₃₇	1	1	yes	characteristic
258	#460	C₄×C₁₃₇	1	1	yes	characteristic
259	#459	C₄×C₁₃₇	1	1	yes	characteristic
260	#449	C₄×C₁₃₇	1	2	yes	—
261	#446	C₂²×C₁₃₇	1	1	yes	characteristic
262	#446	C₂²×C₁₃₇	1	1	yes	characteristic
263	C₄×SD₁₆	C₂²×C₁₃₇	1	2	yes	—
264	C₄×D₈	C₂²×C₁₃₇	1	2	yes	—
265	#436	—	2	1	no	—
266	#436	C₂²×C₁₃₇	1	1	yes	characteristic
267	#436	C₂²×C₁₃₇	1	1	yes	characteristic
268	#436	C₂²×C₁₃₇	1	2	yes	—
269	#435	—	2	1	no	—
270	#435	—	2	1	no	—
271	C₈×D₄	—	2	1	no	—
272	C₈×D₄	C₂²×C₁₃₇	1	2	yes	—
273	#431	—	2	1	no	—
274	#431	C₂²×C₁₃₇	1	1	yes	characteristic
275	#431	C₂²×C₁₃₇	1	1	yes	characteristic
276	#423	C₂²×C₁₃₇	1	1	yes	characteristic
277	#408	—	2	1	no	—
278	C₄×M₁₆	—	2	1	no	—
279	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
280	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
281	#335	C₂²×C₁₃₇	1	2	yes	—
282	#334	C₂²×C₁₃₇	1	2	yes	—
283	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	—
284	D₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
285	D₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
286	D₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
287	#322	C₂²×C₁₃₇	1	2	yes	—
288	C₈²	C₂²×C₁₃₇	1	2	yes	—
289	C₂×#41	—	2	1	no	—
290	C₂×#41	C₂×C₄×C₁₃₇	1	1	yes	characteristic
291	C₂×SD₁₆	C₂×C₄×C₁₃₇	1	2	yes	—
292	C₂×D₈	C₂×C₄×C₁₃₇	1	2	yes	—
293	#131	—	4	4	no	—
294	C₂×M₁₆	—	2	1	no	—
295	C₂×M₁₆	—	2	1	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	2	1	no	—
298	C₂×M₁₆	—	2	1	no	—
299	C₂²×C₈	—	2	2	no	—
300	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
301	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
302	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
303	#127	C₂×C₄×C₁₃₇	1	1	yes	characteristic
304	#124	—	2	1	no	—
305	#121	—	2	1	no	—
306	#121	C₂×C₄×C₁₃₇	1	2	yes	—
307	C₄×Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
308	C₄×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
313	C₄×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
314	C₄×D₄	C₂³×C₁₃₇	1	2	yes	—
315	#117	—	2	1	no	—
316	#117	C₂×C₄×C₁₃₇	1	1	yes	characteristic
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
319	#107	C₂×C₄×C₁₃₇	1	2	yes	—
320	#106	C₂×C₄×C₁₃₇	1	2	yes	—
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	—	2	1	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
325	C₄⋊C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
326	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
327	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
328	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
329	#103	C₂×C₄×C₁₃₇	1	2	yes	—
330	#102	C₂×C₄×C₁₃₇	1	2	yes	—
331	#102	C₂×C₄×C₁₃₇	1	2	yes	—
332	#102	C₂×C₄×C₁₃₇	1	2	yes	—
333	C₂²⋊C₈	—	2	1	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	C₂²⋊C₈	—	2	2	no	—
336	C₂²⋊C₈	—	2	1	no	—
337	C₂²⋊C₈	—	2	1	no	—
338	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
339	#97	—	2	1	no	—
340	#97	—	2	1	no	—
341	#97	—	2	1	no	—
342	C₄×C₈	—	2	1	no	—
343	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
344	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
345	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
346	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
347	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
348	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
349	#41	—	4	1	no	—
350	#41	—	4	1	no	—
351	#41	—	4	2	no	—
352	#41	—	4	2	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
360	C₂×D₄	C₂²×C₄×C₁₃₇	1	2	yes	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
367	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
368	SD₁₆	—	4	2	no	—
369	D₈	—	4	2	no	—
370	M₁₆	—	2	4	no	—
371	M₁₆	—	4	2	no	—
372	M₁₆	—	4	2	no	—
373	M₁₆	—	4	2	no	—
374	M₁₆	—	4	4	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	4	1	no	—
381	C₂×C₈	—	4	4	no	—
382	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
383	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
384	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
385	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
386	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
387	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
392	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
393	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
394	C₂²⋊C₄	—	2	1	no	—
395	C₂²⋊C₄	—	2	1	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	2	1	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	2	1	no	—
402	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
403	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
404	C₄²	#41×C₁₃₇	1	1	yes	characteristic
405	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
406	C₂³	—	2	1	no	—
407	C₂³	—	2	2	no	—
408	C₂³	C₄×D₄×C₁₃₇	1	1	yes	characteristic
409	Q₈	—	2	1	no	—
410	Q₈	—	2	1	no	—
411	Q₈	—	4	2	no	—
412	D₄	—	2	1	no	—
413	D₄	—	2	2	no	—
414	D₄	—	2	2	no	—
415	D₄	—	2	1	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	4	no	—
419	D₄	—	4	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
436	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
437	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
438	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
440	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
441	C₈	—	2	4	no	—
442	C₈	—	2	2	no	—
443	C₈	—	2	2	no	—
444	C₈	—	2	1	no	—
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	4	2	no	—
448	C₈	—	4	1	no	—
449	C₈	—	4	1	no	—
450	C₈	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	4	2	no	—
460	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	1	no	—
468	C₄	#443×C₁₃₇	1	2	yes	—
469	C₄	#568×C₁₃₇	1	1	yes	characteristic
470	C₄	#568×C₁₃₇	1	1	yes	characteristic
471	C₄	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
472	C₄	#575×C₁₃₇	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	8	1	no	—
475	C₂	—	8	2	no	—
476	C₂	#2930×C₁₃₇	1	1	yes	characteristic
477	C₂	C₄×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
478	C₂	C₂×#443×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
socle	C₂²×C₁₃₇	C₂×C₄×D₄
prime radical	#3106×C₁₃₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₇ ◁ C₂×C₄×C₈×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2965×C₁₃₇	C₂	semidirect
3. #2931×C₁₃₇	C₂	semidirect
4. #1590×C₁₃₇	C₂	semidirect
5. #1589×C₁₃₇	C₂	semidirect
6. #1586×C₁₃₇	C₂	semidirect
7. #1585×C₁₃₇	C₂	semidirect
8. #1574×C₁₃₇	C₂	semidirect
9. #1489×C₁₃₇	C₂	semidirect
10. #1484×C₁₃₇	C₂	semidirect
11. C₈×M₁₆×C₁₃₇	C₂	semidirect
239. #17945	C₁₃₇	direct (N × H)
240. C₁₃₇	#17945	direct (N × H)
242. #2965	C₂×C₁₃₇	semidirect
243. #2931	C₂×C₁₃₇	semidirect
244. #1590	C₂×C₁₃₇	semidirect
245. #1589	C₂×C₁₃₇	semidirect
246. #1586	C₂×C₁₃₇	semidirect
247. #1585	C₂×C₁₃₇	semidirect
248. #1574	C₂×C₁₃₇	semidirect
249. #1489	C₂×C₁₃₇	semidirect
250. #1484	C₂×C₁₃₇	semidirect
251. 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
#3106×C₁₃₇	2
#2965×C₁₃₇	2
#2931×C₁₃₇	2
#1590×C₁₃₇	2
#1589×C₁₃₇	2
#1586×C₁₃₇	2
#1585×C₁₃₇	2
#1574×C₁₃₇	2
#1489×C₁₃₇	2
#1484×C₁₃₇	2
C₈×M₁₆×C₁₃₇	2
#17945	137

Subgroups — C137×#17945 #46867331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#17945 #46867331