Subgroups — C₁₃₇×#21138 #46870524

Order 35072.

772 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2943×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2922×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#131×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#1929×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1922×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1876×C₁₃₇	C₂	1	2	yes	maximal
7	#1866×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1778×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1759×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1759×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1746×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#131×C₁₃₇	C₂²	1	2	yes	—
14	C₄×#41×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₄×#41×C₁₃₇	C₂²	1	1	yes	characteristic
16	#442×C₁₃₇	C₄	1	2	yes	complemented
17	#441×C₁₃₇	C₄	1	2	yes	complemented
18	#440×C₁₃₇	C₄	1	2	yes	complemented
19	#440×C₁₃₇	C₄	1	2	yes	complemented
20	#433×C₁₃₇	—	2	1	no	—
21	#433×C₁₃₇	—	2	1	no	—
22	#431×C₁₃₇	—	2	2	no	—
23	C₂×#108×C₁₃₇	C₂²	1	2	yes	—
24	#427×C₁₃₇	C₂²	1	1	yes	characteristic
25	#424×C₁₃₇	C₂²	1	2	yes	—
26	C₂×#104×C₁₃₇	C₂²	1	2	yes	—
27	C₂×#104×C₁₃₇	C₂²	1	2	yes	—
28	#416×C₁₃₇	C₂²	1	1	yes	characteristic
29	#416×C₁₃₇	C₂²	1	1	yes	characteristic
30	#408×C₁₃₇	C₂²	1	2	yes	—
31	#405×C₁₃₇	—	2	2	no	—
32	#405×C₁₃₇	C₂²	1	2	yes	—
33	C₄×M₁₆×C₁₃₇	—	2	1	no	—
34	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
35	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₃₇	—	2	1	no	—
38	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
39	#376×C₁₃₇	C₂²	1	1	yes	characteristic
40	#341×C₁₃₇	C₂²	1	2	yes	—
41	#339×C₁₃₇	C₂²	1	2	yes	—
42	#339×C₁₃₇	C₂²	1	2	yes	—
43	#336×C₁₃₇	C₂²	1	2	yes	—
44	#336×C₁₃₇	C₂²	1	2	yes	—
45	C₂×#41×C₁₃₇	C₂³	1	1	yes	characteristic
46	C₂×#41×C₁₃₇	C₂³	1	1	yes	characteristic
47	#135×C₁₃₇	—	2	4	no	—
48	C₂×Q₁₆×C₁₃₇	C₂×C₄	1	1	yes	characteristic
49	C₂×SD₁₆×C₁₃₇	C₂×C₄	1	1	yes	characteristic
50	C₂×SD₁₆×C₁₃₇	C₂×C₄	1	1	yes	characteristic
51	C₂×D₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
52	#131×C₁₃₇	—	2	4	no	—
53	#131×C₁₃₇	—	2	4	no	—
54	C₂×M₁₆×C₁₃₇	—	2	2	no	—
55	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
56	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₃₇	—	2	2	no	—
58	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
61	C₄×Q₈×C₁₃₇	C₂×C₄	1	2	yes	—
62	C₄×Q₈×C₁₃₇	C₂×C₄	1	2	yes	—
63	C₄×D₄×C₁₃₇	—	2	2	no	—
64	C₄×D₄×C₁₃₇	—	2	2	no	—
65	C₄×D₄×C₁₃₇	C₂×C₄	1	2	yes	—
66	C₄×D₄×C₁₃₇	C₂×C₄	1	2	yes	—
67	#117×C₁₃₇	—	2	1	no	—
68	#117×C₁₃₇	—	2	1	no	—
69	#117×C₁₃₇	C₂³	1	1	yes	characteristic
70	#117×C₁₃₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃₇	—	2	1	no	—
72	C₂×C₄²×C₁₃₇	—	2	1	no	—
73	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
75	#108×C₁₃₇	—	2	4	no	—
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	#104×C₁₃₇	—	2	4	no	—
81	#104×C₁₃₇	—	2	4	no	—
82	#103×C₁₃₇	C₂×C₄	1	2	yes	—
83	#103×C₁₃₇	C₂×C₄	1	2	yes	—
84	#102×C₁₃₇	C₂×C₄	1	2	yes	—
85	#102×C₁₃₇	C₂×C₄	1	2	yes	—
86	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
87	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
88	#97×C₁₃₇	—	2	2	no	—
89	#97×C₁₃₇	—	2	1	no	—
90	#97×C₁₃₇	—	2	1	no	—
91	#97×C₁₃₇	C₂×C₄	1	2	yes	—
92	#97×C₁₃₇	C₂×C₄	1	2	yes	—
93	C₄×C₈×C₁₃₇	—	2	2	no	—
94	C₄×C₈×C₁₃₇	—	2	1	no	—
95	C₄×C₈×C₁₃₇	—	2	1	no	—
96	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
97	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
98	C₄×C₈×C₁₃₇	D₄	1	2	yes	—
99	#95×C₁₃₇	—	2	2	no	—
100	#41×C₁₃₇	—	2	2	no	—
101	#41×C₁₃₇	—	2	2	no	—
102	#41×C₁₃₇	—	2	2	no	—
103	#41×C₁₃₇	#41	1	4	yes	—
104	C₂×Q₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
105	C₂×Q₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×D₄×C₁₃₇	—	2	1	no	—
107	C₂×D₄×C₁₃₇	—	2	1	no	—
108	C₂×D₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×D₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₇	—	2	1	no	—
111	C₂²×C₄×C₁₃₇	—	2	2	no	—
112	C₂²×C₄×C₁₃₇	—	2	2	no	—
113	C₂²×C₄×C₁₃₇	—	2	1	no	—
114	C₂²×C₄×C₁₃₇	—	2	2	no	—
115	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
116	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
117	Q₁₆×C₁₃₇	—	2	2	no	—
118	SD₁₆×C₁₃₇	—	2	2	no	—
119	SD₁₆×C₁₃₇	—	2	2	no	—
120	D₈×C₁₃₇	—	2	2	no	—
121	M₁₆×C₁₃₇	—	2	8	no	—
122	M₁₆×C₁₃₇	—	2	2	no	—
123	M₁₆×C₁₃₇	—	2	2	no	—
124	M₁₆×C₁₃₇	—	2	2	no	—
125	M₁₆×C₁₃₇	#41	1	4	yes	—
126	C₂×C₈×C₁₃₇	—	2	8	no	—
127	C₂×C₈×C₁₃₇	—	2	2	no	—
128	C₂×C₈×C₁₃₇	—	2	2	no	—
129	C₂×C₈×C₁₃₇	—	2	2	no	—
130	C₂×C₈×C₁₃₇	—	2	2	no	—
131	C₂×C₈×C₁₃₇	—	2	2	no	—
132	C₂×C₈×C₁₃₇	—	2	2	no	—
133	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₁₃₇	—	2	2	no	—
139	C₄⋊C₄×C₁₃₇	—	2	2	no	—
140	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
141	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
142	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
143	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
144	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
145	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
146	C₄²×C₁₃₇	—	2	2	no	—
147	C₄²×C₁₃₇	—	2	2	no	—
148	C₄²×C₁₃₇	—	2	1	no	—
149	C₄²×C₁₃₇	—	2	1	no	—
150	C₄²×C₁₃₇	—	2	2	no	—
151	C₄²×C₁₃₇	—	2	2	no	—
152	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
153	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
155	C₂³×C₁₃₇	—	2	1	no	—
156	C₂³×C₁₃₇	—	2	1	no	—
157	C₂³×C₁₃₇	C₂×#41	1	1	yes	characteristic
158	Q₈×C₁₃₇	—	2	1	no	—
159	Q₈×C₁₃₇	—	2	1	no	—
160	Q₈×C₁₃₇	—	2	1	no	—
161	Q₈×C₁₃₇	#117	1	2	yes	—
162	D₄×C₁₃₇	—	2	4	no	—
163	D₄×C₁₃₇	—	2	1	no	—
164	D₄×C₁₃₇	—	2	1	no	—
165	D₄×C₁₃₇	—	2	1	no	—
166	D₄×C₁₃₇	—	4	2	no	—
167	D₄×C₁₃₇	#117	1	2	yes	—
168	C₂×C₄×C₁₃₇	—	2	1	no	—
169	C₂×C₄×C₁₃₇	—	2	4	no	—
170	C₂×C₄×C₁₃₇	—	2	2	no	—
171	C₂×C₄×C₁₃₇	—	2	2	no	—
172	C₂×C₄×C₁₃₇	—	2	1	no	—
173	C₂×C₄×C₁₃₇	—	4	2	no	—
174	C₂×C₄×C₁₃₇	—	4	4	no	—
175	C₂×C₄×C₁₃₇	—	4	4	no	—
176	C₂×C₄×C₁₃₇	—	4	2	no	—
177	C₂×C₄×C₁₃₇	—	4	4	no	—
178	C₂×C₄×C₁₃₇	—	4	2	no	—
179	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
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	2	yes	—
184	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
185	C₈×C₁₃₇	—	2	1	no	—
186	C₈×C₁₃₇	—	2	1	no	—
187	C₈×C₁₃₇	—	2	2	no	—
188	C₈×C₁₃₇	—	2	2	no	—
189	C₈×C₁₃₇	—	2	4	no	—
190	C₈×C₁₃₇	—	2	2	no	—
191	C₈×C₁₃₇	—	4	2	no	—
192	C₂²×C₁₃₇	—	2	2	no	—
193	C₂²×C₁₃₇	—	2	2	no	—
194	C₂²×C₁₃₇	—	4	2	no	—
195	C₂²×C₁₃₇	—	4	2	no	—
196	C₂²×C₁₃₇	—	4	1	no	—
197	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₁₃₇	#529	1	2	yes	—
199	C₄×C₁₃₇	—	2	2	no	—
200	C₄×C₁₃₇	—	2	2	no	—
201	C₄×C₁₃₇	—	2	2	no	—
202	C₄×C₁₃₇	—	4	2	no	—
203	C₄×C₁₃₇	—	4	2	no	—
204	C₄×C₁₃₇	—	4	1	no	—
205	C₄×C₁₃₇	—	8	2	no	—
206	C₄×C₁₃₇	C₂×#117	1	1	yes	characteristic
207	C₄×C₁₃₇	C₄×#41	1	1	yes	characteristic
208	C₄×C₁₃₇	#525	1	2	yes	—
209	C₂×C₁₃₇	—	2	2	no	—
210	C₂×C₁₃₇	—	4	2	no	—
211	C₂×C₁₃₇	—	8	1	no	—
212	C₂×C₁₃₇	#2290	1	1	yes	characteristic
213	C₂×C₁₃₇	#2955	1	2	yes	—
214	#21138	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₁₃₇	#21138	1	1	yes	characteristic, direct product factor, Sylow
216	#2943	C₂×C₁₃₇	1	1	yes	characteristic
217	#2922	C₂×C₁₃₇	1	1	yes	characteristic, complemented
218	C₄×#131	C₂×C₁₃₇	1	1	yes	characteristic, complemented
219	#1929	C₂×C₁₃₇	1	2	yes	complemented
220	#1922	C₂×C₁₃₇	1	2	yes	complemented
221	#1876	C₂×C₁₃₇	1	2	yes	—
222	#1866	C₂×C₁₃₇	1	2	yes	complemented
223	#1778	C₂×C₁₃₇	1	1	yes	characteristic, complemented
224	#1759	C₂×C₁₃₇	1	1	yes	characteristic, complemented
225	#1759	C₂×C₁₃₇	1	1	yes	characteristic, complemented
226	#1746	C₂×C₁₃₇	1	1	yes	characteristic, complemented
227	C₂×#135	C₂²×C₁₃₇	1	1	yes	characteristic
228	C₂×#131	C₂²×C₁₃₇	1	2	yes	—
229	C₄×#41	C₂²×C₁₃₇	1	1	yes	characteristic
230	C₄×#41	C₂²×C₁₃₇	1	1	yes	characteristic
231	#442	C₄×C₁₃₇	1	2	yes	complemented
232	#441	C₄×C₁₃₇	1	2	yes	complemented
233	#440	C₄×C₁₃₇	1	2	yes	complemented
234	#440	C₄×C₁₃₇	1	2	yes	complemented
235	#433	—	2	1	no	—
236	#433	—	2	1	no	—
237	#431	—	2	2	no	—
238	C₂×#108	C₂²×C₁₃₇	1	2	yes	—
239	#427	C₂²×C₁₃₇	1	1	yes	characteristic
240	#424	C₂²×C₁₃₇	1	2	yes	—
241	C₂×#104	C₂²×C₁₃₇	1	2	yes	—
242	C₂×#104	C₂²×C₁₃₇	1	2	yes	—
243	#416	C₂²×C₁₃₇	1	1	yes	characteristic
244	#416	C₂²×C₁₃₇	1	1	yes	characteristic
245	#408	C₂²×C₁₃₇	1	2	yes	—
246	#405	—	2	2	no	—
247	#405	C₂²×C₁₃₇	1	2	yes	—
248	C₄×M₁₆	—	2	1	no	—
249	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
250	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
251	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
252	C₂×C₄×C₈	—	2	1	no	—
253	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
254	#376	C₂²×C₁₃₇	1	1	yes	characteristic
255	#341	C₂²×C₁₃₇	1	2	yes	—
256	#339	C₂²×C₁₃₇	1	2	yes	—
257	#339	C₂²×C₁₃₇	1	2	yes	—
258	#336	C₂²×C₁₃₇	1	2	yes	—
259	#336	C₂²×C₁₃₇	1	2	yes	—
260	C₂×#41	C₂³×C₁₃₇	1	1	yes	characteristic
261	C₂×#41	C₂³×C₁₃₇	1	1	yes	characteristic
262	#135	—	2	4	no	—
263	C₂×Q₁₆	C₂×C₄×C₁₃₇	1	1	yes	characteristic
264	C₂×SD₁₆	C₂×C₄×C₁₃₇	1	1	yes	characteristic
265	C₂×SD₁₆	C₂×C₄×C₁₃₇	1	1	yes	characteristic
266	C₂×D₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
267	#131	—	2	4	no	—
268	#131	—	2	4	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
271	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
276	C₄×Q₈	C₂×C₄×C₁₃₇	1	2	yes	—
277	C₄×Q₈	C₂×C₄×C₁₃₇	1	2	yes	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	—	2	2	no	—
280	C₄×D₄	C₂×C₄×C₁₃₇	1	2	yes	—
281	C₄×D₄	C₂×C₄×C₁₃₇	1	2	yes	—
282	#117	—	2	1	no	—
283	#117	—	2	1	no	—
284	#117	C₂³×C₁₃₇	1	1	yes	characteristic
285	#117	C₂³×C₁₃₇	1	1	yes	characteristic
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
289	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
290	#108	—	2	4	no	—
291	#107	C₂×C₄×C₁₃₇	1	2	yes	—
292	#106	C₂×C₄×C₁₃₇	1	2	yes	—
293	C₄⋊C₈	—	2	2	no	—
294	C₄⋊C₈	—	2	2	no	—
295	#104	—	2	4	no	—
296	#104	—	2	4	no	—
297	#103	C₂×C₄×C₁₃₇	1	2	yes	—
298	#103	C₂×C₄×C₁₃₇	1	2	yes	—
299	#102	C₂×C₄×C₁₃₇	1	2	yes	—
300	#102	C₂×C₄×C₁₃₇	1	2	yes	—
301	C₂²⋊C₈	—	2	2	no	—
302	C₂²⋊C₈	—	2	2	no	—
303	#97	—	2	2	no	—
304	#97	—	2	1	no	—
305	#97	—	2	1	no	—
306	#97	C₂×C₄×C₁₃₇	1	2	yes	—
307	#97	C₂×C₄×C₁₃₇	1	2	yes	—
308	C₄×C₈	—	2	2	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	—	2	1	no	—
311	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
312	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
313	C₄×C₈	D₄×C₁₃₇	1	2	yes	—
314	#95	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	#41	#41×C₁₃₇	1	4	yes	—
319	C₂×Q₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
320	C₂×Q₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
324	C₂×D₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
331	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
332	Q₁₆	—	2	2	no	—
333	SD₁₆	—	2	2	no	—
334	SD₁₆	—	2	2	no	—
335	D₈	—	2	2	no	—
336	M₁₆	—	2	8	no	—
337	M₁₆	—	2	2	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	#41×C₁₃₇	1	4	yes	—
341	C₂×C₈	—	2	8	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
349	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
350	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
351	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
352	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
356	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
357	C₂²⋊C₄	—	2	1	no	—
358	C₂²⋊C₄	—	2	1	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
368	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
369	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	C₂×#41×C₁₃₇	1	1	yes	characteristic
373	Q₈	—	2	1	no	—
374	Q₈	—	2	1	no	—
375	Q₈	—	2	1	no	—
376	Q₈	#117×C₁₃₇	1	2	yes	—
377	D₄	—	2	4	no	—
378	D₄	—	2	1	no	—
379	D₄	—	2	1	no	—
380	D₄	—	2	1	no	—
381	D₄	—	4	2	no	—
382	D₄	#117×C₁₃₇	1	2	yes	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
395	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
396	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
397	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
398	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
399	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
400	C₈	—	2	1	no	—
401	C₈	—	2	1	no	—
402	C₈	—	2	2	no	—
403	C₈	—	2	2	no	—
404	C₈	—	2	4	no	—
405	C₈	—	2	2	no	—
406	C₈	—	4	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	2	no	—
412	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
413	C₂²	#529×C₁₃₇	1	2	yes	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	8	2	no	—
421	C₄	C₂×#117×C₁₃₇	1	1	yes	characteristic
422	C₄	C₄×#41×C₁₃₇	1	1	yes	characteristic
423	C₄	#525×C₁₃₇	1	2	yes	—
424	C₂	—	2	2	no	—
425	C₂	—	4	2	no	—
426	C₂	—	8	1	no	—
427	C₂	#2290×C₁₃₇	1	1	yes	characteristic
428	C₂	#2955×C₁₃₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle	C₂²×C₁₃₇	C₂×C₄×D₄
prime radical	C₂×#135×C₁₃₇	C₂²
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. #2922×C₁₃₇	C₂	semidirect
3. C₄×#131×C₁₃₇	C₂	semidirect
4. #1929×C₁₃₇	C₂	semidirect
5. #1922×C₁₃₇	C₂	semidirect
7. #1866×C₁₃₇	C₂	semidirect
8. #1778×C₁₃₇	C₂	semidirect
9. #1759×C₁₃₇	C₂	semidirect
10. #1759×C₁₃₇	C₂	semidirect
11. #1746×C₁₃₇	C₂	semidirect
16. #442×C₁₃₇	C₄	semidirect
17. #441×C₁₃₇	C₄	semidirect
18. #440×C₁₃₇	C₄	semidirect
19. #440×C₁₃₇	C₄	semidirect
214. #21138	C₁₃₇	direct (N × H)
215. C₁₃₇	#21138	direct (N × H)
217. #2922	C₂×C₁₃₇	semidirect
218. C₄×#131	C₂×C₁₃₇	semidirect
219. #1929	C₂×C₁₃₇	semidirect
220. #1922	C₂×C₁₃₇	semidirect
222. #1866	C₂×C₁₃₇	semidirect
223. #1778	C₂×C₁₃₇	semidirect
224. #1759	C₂×C₁₃₇	semidirect
225. #1759	C₂×C₁₃₇	semidirect
226. #1746	C₂×C₁₃₇	semidirect
231. #442	C₄×C₁₃₇	semidirect
232. #441	C₄×C₁₃₇	semidirect
233. #440	C₄×C₁₃₇	semidirect
234. #440	C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#2943×C₁₃₇	2
#2922×C₁₃₇	2
C₄×#131×C₁₃₇	2
#1929×C₁₃₇	2
#1922×C₁₃₇	2
#1876×C₁₃₇	2
#1866×C₁₃₇	2
#1778×C₁₃₇	2
#1759×C₁₃₇	2
#1746×C₁₃₇	2
#21138	137

Subgroups — C137×#21138 #46870524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21138 #46870524