Subgroups — C₁₃₇×#28637 #46878023

Order 35072.

874 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#486×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2548×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2546×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2067×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1988×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1982×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1934×C₁₃₇	C₂	1	4	yes	maximal, complemented
9	C₄×#107×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄⋊Q₈×C₁₃₇	—	2	1	no	—
11	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#124×C₁₃₇	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
15	#486×C₁₃₇	—	2	4	no	—
16	C₈×Q₈×C₁₃₇	—	2	4	no	—
17	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
21	C₂×#102×C₁₃₇	C₂²	1	4	yes	—
22	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
25	#398×C₁₃₇	—	2	2	no	—
26	#394×C₁₃₇	—	2	2	no	—
27	#391×C₁₃₇	—	2	1	no	—
28	#390×C₁₃₇	—	2	1	no	—
29	#390×C₁₃₇	C₂²	1	4	yes	—
30	#389×C₁₃₇	C₂²	1	4	yes	—
31	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
33	#340×C₁₃₇	C₂²	1	2	yes	—
34	#340×C₁₃₇	C₂²	1	4	yes	—
35	C₂²×Q₈×C₁₃₇	—	2	1	no	—
36	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
37	C₂²×D₄×C₁₃₇	—	2	1	no	—
38	C₂²×D₄×C₁₃₇	—	2	1	no	—
39	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
43	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
44	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
45	C₄⋊Q₈×C₁₃₇	—	4	4	no	—
46	#127×C₁₃₇	—	2	2	no	—
47	#127×C₁₃₇	—	2	2	no	—
48	#124×C₁₃₇	—	4	4	no	—
49	C₄×Q₈×C₁₃₇	—	2	2	no	—
50	C₄×Q₈×C₁₃₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
60	C₂×C₄²×C₁₃₇	—	2	1	no	—
61	C₂×C₄²×C₁₃₇	—	2	1	no	—
62	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
64	#107×C₁₃₇	—	2	4	no	—
65	C₄⋊C₈×C₁₃₇	—	2	4	no	—
66	C₄⋊C₈×C₁₃₇	—	2	2	no	—
67	#102×C₁₃₇	—	2	4	no	—
68	#102×C₁₃₇	—	2	4	no	—
69	#102×C₁₃₇	—	2	8	no	—
70	C₄×C₈×C₁₃₇	—	2	4	no	—
71	C₄×C₈×C₁₃₇	D₄	1	4	yes	—
72	#95×C₁₃₇	—	2	1	no	—
73	#95×C₁₃₇	—	2	1	no	—
74	#95×C₁₃₇	—	2	4	no	—
75	C₂⁴×C₁₃₇	—	2	2	no	—
76	C₂×Q₈×C₁₃₇	—	2	2	no	—
77	C₂×Q₈×C₁₃₇	—	2	2	no	—
78	C₂×Q₈×C₁₃₇	—	4	2	no	—
79	C₂×Q₈×C₁₃₇	—	4	2	no	—
80	C₂×Q₈×C₁₃₇	—	4	2	no	—
81	C₂×Q₈×C₁₃₇	D₈	1	4	yes	—
82	C₂×D₄×C₁₃₇	—	2	2	no	—
83	C₂×D₄×C₁₃₇	—	2	4	no	—
84	C₂×D₄×C₁₃₇	—	2	2	no	—
85	C₂×D₄×C₁₃₇	—	2	4	no	—
86	C₂×D₄×C₁₃₇	—	4	2	no	—
87	C₂×D₄×C₁₃₇	—	4	2	no	—
88	C₂×D₄×C₁₃₇	—	4	2	no	—
89	C₂×D₄×C₁₃₇	—	4	2	no	—
90	C₂×D₄×C₁₃₇	—	8	2	no	—
91	C₂²×C₄×C₁₃₇	—	2	2	no	—
92	C₂²×C₄×C₁₃₇	—	2	2	no	—
93	C₂²×C₄×C₁₃₇	—	2	2	no	—
94	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₁₃₇	—	2	2	no	—
100	C₂×C₈×C₁₃₇	—	2	2	no	—
101	C₂×C₈×C₁₃₇	—	2	2	no	—
102	C₂×C₈×C₁₃₇	—	2	4	no	—
103	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
104	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
105	C₄⋊C₄×C₁₃₇	—	2	4	no	—
106	C₄⋊C₄×C₁₃₇	—	2	2	no	—
107	C₄⋊C₄×C₁₃₇	—	2	2	no	—
108	C₄⋊C₄×C₁₃₇	—	2	2	no	—
109	C₄⋊C₄×C₁₃₇	—	2	2	no	—
110	C₄⋊C₄×C₁₃₇	—	2	2	no	—
111	C₄⋊C₄×C₁₃₇	—	2	2	no	—
112	C₄⋊C₄×C₁₃₇	—	4	2	no	—
113	C₄⋊C₄×C₁₃₇	—	4	8	no	—
114	C₄⋊C₄×C₁₃₇	#41	1	4	yes	—
115	C₂²⋊C₄×C₁₃₇	—	4	8	no	—
116	C₂²⋊C₄×C₁₃₇	—	8	4	no	—
117	C₄²×C₁₃₇	—	2	2	no	—
118	C₄²×C₁₃₇	—	2	2	no	—
119	C₄²×C₁₃₇	—	4	2	no	—
120	C₄²×C₁₃₇	—	4	2	no	—
121	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
122	C₄²×C₁₃₇	#41	1	2	yes	—
123	C₂³×C₁₃₇	—	4	2	no	—
124	C₂³×C₁₃₇	—	4	4	no	—
125	C₂³×C₁₃₇	—	4	2	no	—
126	C₂³×C₁₃₇	—	4	2	no	—
127	C₂³×C₁₃₇	—	4	4	no	—
128	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
129	Q₈×C₁₃₇	—	2	8	no	—
130	Q₈×C₁₃₇	—	8	4	no	—
131	D₄×C₁₃₇	—	4	2	no	—
132	D₄×C₁₃₇	—	4	2	no	—
133	D₄×C₁₃₇	—	4	4	no	—
134	D₄×C₁₃₇	—	8	4	no	—
135	D₄×C₁₃₇	—	8	4	no	—
136	C₂×C₄×C₁₃₇	—	2	2	no	—
137	C₂×C₄×C₁₃₇	—	2	2	no	—
138	C₂×C₄×C₁₃₇	—	2	2	no	—
139	C₂×C₄×C₁₃₇	—	2	2	no	—
140	C₂×C₄×C₁₃₇	—	2	4	no	—
141	C₂×C₄×C₁₃₇	—	2	4	no	—
142	C₂×C₄×C₁₃₇	—	4	2	no	—
143	C₂×C₄×C₁₃₇	—	4	2	no	—
144	C₂×C₄×C₁₃₇	—	4	2	no	—
145	C₂×C₄×C₁₃₇	—	4	2	no	—
146	C₂×C₄×C₁₃₇	—	4	2	no	—
147	C₂×C₄×C₁₃₇	—	4	2	no	—
148	C₂×C₄×C₁₃₇	—	4	2	no	—
149	C₂×C₄×C₁₃₇	—	4	2	no	—
150	C₂×C₄×C₁₃₇	#121	1	2	yes	—
151	C₂×C₄×C₁₃₇	#121	1	2	yes	—
152	C₂×C₄×C₁₃₇	C₂×D₈	1	4	yes	—
153	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
154	C₂×C₄×C₁₃₇	#135	1	2	yes	—
155	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
157	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
159	C₈×C₁₃₇	—	2	2	no	—
160	C₈×C₁₃₇	—	2	2	no	—
161	C₈×C₁₃₇	—	4	2	no	—
162	C₂²×C₁₃₇	—	8	4	no	—
163	C₂²×C₁₃₇	—	8	4	no	—
164	C₂²×C₁₃₇	—	8	2	no	—
165	C₂²×C₁₃₇	—	8	2	no	—
166	C₂²×C₁₃₇	—	8	2	no	—
167	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
168	C₂²×C₁₃₇	#548	1	2	yes	—
169	C₂²×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
170	C₂²×C₁₃₇	C₂×#135	1	1	yes	characteristic
171	C₂²×C₁₃₇	#577	1	2	yes	—
172	C₄×C₁₃₇	—	2	4	no	—
173	C₄×C₁₃₇	—	2	2	no	—
174	C₄×C₁₃₇	—	4	4	no	—
175	C₄×C₁₃₇	—	4	2	no	—
176	C₄×C₁₃₇	—	8	2	no	—
177	C₄×C₁₃₇	—	8	2	no	—
178	C₄×C₁₃₇	#466	1	4	yes	—
179	C₄×C₁₃₇	#532	1	1	yes	characteristic
180	C₄×C₁₃₇	#536	1	1	yes	characteristic
181	C₄×C₁₃₇	#556	1	2	yes	—
182	C₂×C₁₃₇	—	16	2	no	—
183	C₂×C₁₃₇	#2545	1	1	yes	characteristic
184	C₂×C₁₃₇	C₂×#466	1	1	yes	characteristic
185	C₂×C₁₃₇	#3057	1	1	yes	characteristic
186	C₂×C₁₃₇	#3358	1	2	yes	—
187	C₂×C₁₃₇	#3365	1	2	yes	—
188	#28637	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₁₃₇	#28637	1	1	yes	characteristic, direct product factor, Sylow
190	C₂×#486	C₂×C₁₃₇	1	1	yes	characteristic
191	C₂×C₈×Q₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
192	#2548	C₂×C₁₃₇	1	1	yes	characteristic
193	#2546	C₂×C₁₃₇	1	1	yes	characteristic, complemented
194	#2067	C₂×C₁₃₇	1	4	yes	complemented
195	#1988	C₂×C₁₃₇	1	1	yes	characteristic, complemented
196	#1982	C₂×C₁₃₇	1	1	yes	characteristic
197	#1934	C₂×C₁₃₇	1	4	yes	complemented
198	C₄×#107	C₂×C₁₃₇	1	1	yes	characteristic, complemented
199	C₂×C₄⋊Q₈	—	2	1	no	—
200	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
201	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
202	C₂×#124	—	2	1	no	—
203	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
204	#486	—	2	4	no	—
205	C₈×Q₈	—	2	4	no	—
206	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
207	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
208	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
209	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
210	C₂×#102	C₂²×C₁₃₇	1	4	yes	—
211	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
212	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
213	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
214	#398	—	2	2	no	—
215	#394	—	2	2	no	—
216	#391	—	2	1	no	—
217	#390	—	2	1	no	—
218	#390	C₂²×C₁₃₇	1	4	yes	—
219	#389	C₂²×C₁₃₇	1	4	yes	—
220	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
221	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
222	#340	C₂²×C₁₃₇	1	4	yes	—
223	#340	C₂²×C₁₃₇	1	2	yes	—
224	C₂²×Q₈	—	2	1	no	—
225	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
226	C₂²×D₄	—	2	1	no	—
227	C₂²×D₄	—	2	1	no	—
228	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
229	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
230	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
232	C₄⋊Q₈	—	2	2	no	—
233	C₄⋊Q₈	—	2	2	no	—
234	C₄⋊Q₈	—	4	4	no	—
235	#127	—	2	2	no	—
236	#127	—	2	2	no	—
237	#124	—	4	4	no	—
238	C₄×Q₈	—	2	2	no	—
239	C₄×Q₈	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
243	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
244	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
247	C₂×C₂²⋊C₄	—	2	4	no	—
248	C₂×C₂²⋊C₄	—	2	4	no	—
249	C₂×C₄²	—	2	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
252	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
253	#107	—	2	4	no	—
254	C₄⋊C₈	—	2	4	no	—
255	C₄⋊C₈	—	2	2	no	—
256	#102	—	2	4	no	—
257	#102	—	2	4	no	—
258	#102	—	2	8	no	—
259	C₄×C₈	—	2	4	no	—
260	C₄×C₈	D₄×C₁₃₇	1	4	yes	—
261	#95	—	2	1	no	—
262	#95	—	2	1	no	—
263	#95	—	2	4	no	—
264	C₂⁴	—	2	2	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	4	2	no	—
268	C₂×Q₈	—	4	2	no	—
269	C₂×Q₈	—	4	2	no	—
270	C₂×Q₈	D₈×C₁₃₇	1	4	yes	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	8	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
284	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
293	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₄⋊C₄	—	4	8	no	—
303	C₄⋊C₄	#41×C₁₃₇	1	4	yes	—
304	C₂²⋊C₄	—	4	8	no	—
305	C₂²⋊C₄	—	8	4	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	4	2	no	—
309	C₄²	—	4	2	no	—
310	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
311	C₄²	#41×C₁₃₇	1	2	yes	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	4	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	4	no	—
317	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
318	Q₈	—	2	8	no	—
319	Q₈	—	8	4	no	—
320	D₄	—	4	2	no	—
321	D₄	—	4	2	no	—
322	D₄	—	4	4	no	—
323	D₄	—	8	4	no	—
324	D₄	—	8	4	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	#121×C₁₃₇	1	2	yes	—
340	C₂×C₄	#121×C₁₃₇	1	2	yes	—
341	C₂×C₄	C₂×D₈×C₁₃₇	1	4	yes	—
342	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
343	C₂×C₄	#135×C₁₃₇	1	2	yes	—
344	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
345	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
346	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
347	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
348	C₈	—	2	2	no	—
349	C₈	—	2	2	no	—
350	C₈	—	4	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	8	2	no	—
353	C₂²	—	8	2	no	—
354	C₂²	—	8	4	no	—
355	C₂²	—	8	4	no	—
356	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
357	C₂²	#548×C₁₃₇	1	2	yes	—
358	C₂²	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
359	C₂²	C₂×#135×C₁₃₇	1	1	yes	characteristic
360	C₂²	#577×C₁₃₇	1	2	yes	—
361	C₄	—	2	4	no	—
362	C₄	—	2	2	no	—
363	C₄	—	4	2	no	—
364	C₄	—	4	4	no	—
365	C₄	—	8	2	no	—
366	C₄	—	8	2	no	—
367	C₄	#466×C₁₃₇	1	4	yes	—
368	C₄	#532×C₁₃₇	1	1	yes	characteristic
369	C₄	#536×C₁₃₇	1	1	yes	characteristic
370	C₄	#556×C₁₃₇	1	2	yes	—
371	C₂	—	16	2	no	—
372	C₂	#2545×C₁₃₇	1	1	yes	characteristic
373	C₂	C₂×#466×C₁₃₇	1	1	yes	characteristic
374	C₂	#3057×C₁₃₇	1	1	yes	characteristic
375	C₂	#3358×C₁₃₇	1	2	yes	—
376	C₂	#3365×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂×#127×C₁₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂×C₄×Q₈×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×Q₈×C₁₃₇	C₂	semidirect
4. #2546×C₁₃₇	C₂	semidirect
5. #2067×C₁₃₇	C₂	semidirect
6. #1988×C₁₃₇	C₂	semidirect
8. #1934×C₁₃₇	C₂	semidirect
9. C₄×#107×C₁₃₇	C₂	semidirect
188. #28637	C₁₃₇	direct (N × H)
189. C₁₃₇	#28637	direct (N × H)
191. C₂×C₈×Q₈	C₂×C₁₃₇	semidirect
193. #2546	C₂×C₁₃₇	semidirect
194. #2067	C₂×C₁₃₇	semidirect
195. #1988	C₂×C₁₃₇	semidirect
197. #1934	C₂×C₁₃₇	semidirect
198. C₄×#107	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#486×C₁₃₇	2
C₂×C₈×Q₈×C₁₃₇	2
#2548×C₁₃₇	2
#2546×C₁₃₇	2
#2067×C₁₃₇	2
#1988×C₁₃₇	2
#1982×C₁₃₇	2
#1934×C₁₃₇	2
C₄×#107×C₁₃₇	2
#28637	137

Subgroups — C137×#28637 #46878023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28637 #46878023