Subgroups — C₁₃₇×#28745 #46878131

Order 35072.

898 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#492×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#446×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2568×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2548×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#2055×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1982×C₁₃₇	C₂	1	1	yes	maximal, characteristic
7	#1981×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1973×C₁₃₇	C₂	1	4	yes	maximal, complemented
9	C₄×#107×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₁₃₇	C₂²	1	2	yes	—
11	C₂²×SD₁₆×C₁₃₇	C₂²	1	2	yes	—
12	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×#124×C₁₃₇	—	2	1	no	—
15	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
16	#492×C₁₃₇	—	2	4	no	—
17	#446×C₁₃₇	—	2	4	no	—
18	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×#103×C₁₃₇	C₂²	1	4	yes	—
22	C₂×#102×C₁₃₇	C₂²	1	4	yes	—
23	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
25	#400×C₁₃₇	—	2	2	no	—
26	#394×C₁₃₇	—	2	2	no	—
27	#391×C₁₃₇	—	2	1	no	—
28	#391×C₁₃₇	C₂²	1	4	yes	—
29	#390×C₁₃₇	—	2	1	no	—
30	#390×C₁₃₇	C₂²	1	4	yes	—
31	#382×C₁₃₇	—	2	1	no	—
32	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
34	#340×C₁₃₇	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
36	C₂²×Q₈×C₁₃₇	C₂³	1	2	yes	—
37	C₂²×D₄×C₁₃₇	—	2	1	no	—
38	C₂²×D₄×C₁₃₇	—	2	1	no	—
39	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
40	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
41	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
42	C₂×SD₁₆×C₁₃₇	—	2	8	no	—
43	C₂×SD₁₆×C₁₃₇	—	4	4	no	—
44	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
47	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
48	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
49	#127×C₁₃₇	—	2	2	no	—
50	#127×C₁₃₇	—	2	2	no	—
51	#124×C₁₃₇	—	4	4	no	—
52	C₄×Q₈×C₁₃₇	—	2	2	no	—
53	C₄×Q₈×C₁₃₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
62	C₂×C₄²×C₁₃₇	—	2	1	no	—
63	C₂×C₄²×C₁₃₇	—	2	1	no	—
64	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
65	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
66	#107×C₁₃₇	—	2	4	no	—
67	C₄⋊C₈×C₁₃₇	—	2	4	no	—
68	C₄⋊C₈×C₁₃₇	—	2	2	no	—
69	#103×C₁₃₇	—	4	4	no	—
70	#102×C₁₃₇	—	4	4	no	—
71	#97×C₁₃₇	—	2	4	no	—
72	C₄×C₈×C₁₃₇	D₄	1	4	yes	—
73	#95×C₁₃₇	—	2	1	no	—
74	#95×C₁₃₇	—	2	1	no	—
75	#95×C₁₃₇	—	2	4	no	—
76	#95×C₁₃₇	—	2	4	no	—
77	C₂⁴×C₁₃₇	—	2	2	no	—
78	C₂×Q₈×C₁₃₇	—	2	2	no	—
79	C₂×Q₈×C₁₃₇	—	2	2	no	—
80	C₂×Q₈×C₁₃₇	—	2	2	no	—
81	C₂×Q₈×C₁₃₇	—	2	2	no	—
82	C₂×Q₈×C₁₃₇	—	2	2	no	—
83	C₂×Q₈×C₁₃₇	—	2	4	no	—
84	C₂×Q₈×C₁₃₇	—	2	4	no	—
85	C₂×D₄×C₁₃₇	—	2	2	no	—
86	C₂×D₄×C₁₃₇	—	2	2	no	—
87	C₂×D₄×C₁₃₇	—	2	4	no	—
88	C₂×D₄×C₁₃₇	—	2	4	no	—
89	C₂×D₄×C₁₃₇	—	4	2	no	—
90	C₂×D₄×C₁₃₇	—	4	2	no	—
91	C₂×D₄×C₁₃₇	—	4	2	no	—
92	C₂×D₄×C₁₃₇	—	4	2	no	—
93	C₂×D₄×C₁₃₇	—	8	2	no	—
94	C₂²×C₄×C₁₃₇	—	2	2	no	—
95	C₂²×C₄×C₁₃₇	—	2	2	no	—
96	C₂²×C₄×C₁₃₇	—	2	2	no	—
97	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
102	SD₁₆×C₁₃₇	—	4	8	no	—
103	SD₁₆×C₁₃₇	—	4	8	no	—
104	C₂×C₈×C₁₃₇	—	2	2	no	—
105	C₂×C₈×C₁₃₇	—	2	2	no	—
106	C₂×C₈×C₁₃₇	—	2	4	no	—
107	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₁₃₇	#41	1	4	yes	—
110	C₄⋊C₄×C₁₃₇	—	2	2	no	—
111	C₄⋊C₄×C₁₃₇	—	2	4	no	—
112	C₄⋊C₄×C₁₃₇	—	2	2	no	—
113	C₄⋊C₄×C₁₃₇	—	2	2	no	—
114	C₄⋊C₄×C₁₃₇	—	2	2	no	—
115	C₄⋊C₄×C₁₃₇	—	2	2	no	—
116	C₄⋊C₄×C₁₃₇	—	4	2	no	—
117	C₄⋊C₄×C₁₃₇	—	4	2	no	—
118	C₂²⋊C₄×C₁₃₇	—	4	8	no	—
119	C₂²⋊C₄×C₁₃₇	—	8	4	no	—
120	C₄²×C₁₃₇	—	2	2	no	—
121	C₄²×C₁₃₇	—	2	2	no	—
122	C₄²×C₁₃₇	—	4	2	no	—
123	C₄²×C₁₃₇	—	4	2	no	—
124	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
125	C₄²×C₁₃₇	#41	1	2	yes	—
126	C₂³×C₁₃₇	—	4	2	no	—
127	C₂³×C₁₃₇	—	4	4	no	—
128	C₂³×C₁₃₇	—	4	2	no	—
129	C₂³×C₁₃₇	—	4	2	no	—
130	C₂³×C₁₃₇	—	4	4	no	—
131	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
132	Q₈×C₁₃₇	—	4	4	no	—
133	Q₈×C₁₃₇	—	4	2	no	—
134	Q₈×C₁₃₇	—	4	2	no	—
135	Q₈×C₁₃₇	—	4	4	no	—
136	D₄×C₁₃₇	—	4	2	no	—
137	D₄×C₁₃₇	—	4	2	no	—
138	D₄×C₁₃₇	—	4	4	no	—
139	D₄×C₁₃₇	—	8	4	no	—
140	D₄×C₁₃₇	—	8	4	no	—
141	C₂×C₄×C₁₃₇	—	2	2	no	—
142	C₂×C₄×C₁₃₇	—	2	2	no	—
143	C₂×C₄×C₁₃₇	—	2	2	no	—
144	C₂×C₄×C₁₃₇	—	2	2	no	—
145	C₂×C₄×C₁₃₇	—	2	2	no	—
146	C₂×C₄×C₁₃₇	—	2	4	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	—	4	4	no	—
151	C₂×C₄×C₁₃₇	—	4	2	no	—
152	C₂×C₄×C₁₃₇	—	4	2	no	—
153	C₂×C₄×C₁₃₇	—	4	2	no	—
154	C₂×C₄×C₁₃₇	—	4	2	no	—
155	C₂×C₄×C₁₃₇	#121	1	2	yes	—
156	C₂×C₄×C₁₃₇	#121	1	2	yes	—
157	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
158	C₂×C₄×C₁₃₇	#137	1	2	yes	—
159	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
161	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
163	C₈×C₁₃₇	—	2	2	no	—
164	C₈×C₁₃₇	—	4	2	no	—
165	C₈×C₁₃₇	#124	1	4	yes	complemented
166	C₂²×C₁₃₇	—	8	4	no	—
167	C₂²×C₁₃₇	—	8	4	no	—
168	C₂²×C₁₃₇	—	8	2	no	—
169	C₂²×C₁₃₇	—	8	2	no	—
170	C₂²×C₁₃₇	—	8	2	no	—
171	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
172	C₂²×C₁₃₇	#550	1	2	yes	—
173	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₂²×C₁₃₇	C₂×#137	1	1	yes	characteristic
175	C₂²×C₁₃₇	#577	1	2	yes	—
176	C₄×C₁₃₇	—	2	2	no	—
177	C₄×C₁₃₇	—	4	2	no	—
178	C₄×C₁₃₇	—	4	2	no	—
179	C₄×C₁₃₇	—	8	2	no	—
180	C₄×C₁₃₇	—	8	2	no	—
181	C₄×C₁₃₇	—	8	2	no	—
182	C₄×C₁₃₇	#468	1	4	yes	—
183	C₄×C₁₃₇	C₂×#124	1	1	yes	characteristic
184	C₄×C₁₃₇	#535	1	1	yes	characteristic
185	C₄×C₁₃₇	#559	1	2	yes	—
186	C₂×C₁₃₇	—	16	2	no	—
187	C₂×C₁₃₇	#2548	1	1	yes	characteristic
188	C₂×C₁₃₇	C₂×#468	1	1	yes	characteristic
189	C₂×C₁₃₇	#3057	1	1	yes	characteristic
190	C₂×C₁₃₇	#3397	1	2	yes	—
191	C₂×C₁₃₇	#3400	1	2	yes	—
192	#28745	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₁₃₇	#28745	1	1	yes	characteristic, direct product factor, Sylow
194	C₂×#492	C₂×C₁₃₇	1	1	yes	characteristic
195	C₂×#446	C₂×C₁₃₇	1	1	yes	characteristic, complemented
196	#2568	C₂×C₁₃₇	1	1	yes	characteristic, complemented
197	#2548	C₂×C₁₃₇	1	1	yes	characteristic
198	#2055	C₂×C₁₃₇	1	4	yes	complemented
199	#1982	C₂×C₁₃₇	1	1	yes	characteristic
200	#1981	C₂×C₁₃₇	1	1	yes	characteristic, complemented
201	#1973	C₂×C₁₃₇	1	4	yes	complemented
202	C₄×#107	C₂×C₁₃₇	1	1	yes	characteristic, complemented
203	C₂²×SD₁₆	C₂²×C₁₃₇	1	2	yes	—
204	C₂²×SD₁₆	C₂²×C₁₃₇	1	2	yes	—
205	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
206	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
207	C₂×#124	—	2	1	no	—
208	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
209	#492	—	2	4	no	—
210	#446	—	2	4	no	—
211	C₂×#107	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	C₂×#103	C₂²×C₁₃₇	1	4	yes	—
215	C₂×#102	C₂²×C₁₃₇	1	4	yes	—
216	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
217	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
218	#400	—	2	2	no	—
219	#394	—	2	2	no	—
220	#391	—	2	1	no	—
221	#391	C₂²×C₁₃₇	1	4	yes	—
222	#390	—	2	1	no	—
223	#390	C₂²×C₁₃₇	1	4	yes	—
224	#382	—	2	1	no	—
225	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
226	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
227	#340	C₂²×C₁₃₇	1	2	yes	—
228	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
229	C₂²×Q₈	C₂³×C₁₃₇	1	2	yes	—
230	C₂²×D₄	—	2	1	no	—
231	C₂²×D₄	—	2	1	no	—
232	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
233	C₂×SD₁₆	—	2	4	no	—
234	C₂×SD₁₆	—	2	4	no	—
235	C₂×SD₁₆	—	2	8	no	—
236	C₂×SD₁₆	—	4	4	no	—
237	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
238	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
240	C₄⋊Q₈	—	2	2	no	—
241	C₄⋊Q₈	—	2	2	no	—
242	#127	—	2	2	no	—
243	#127	—	2	2	no	—
244	#124	—	4	4	no	—
245	C₄×Q₈	—	2	2	no	—
246	C₄×Q₈	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
250	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
253	C₂×C₂²⋊C₄	—	2	4	no	—
254	C₂×C₂²⋊C₄	—	2	4	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
258	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
259	#107	—	2	4	no	—
260	C₄⋊C₈	—	2	4	no	—
261	C₄⋊C₈	—	2	2	no	—
262	#103	—	4	4	no	—
263	#102	—	4	4	no	—
264	#97	—	2	4	no	—
265	C₄×C₈	D₄×C₁₃₇	1	4	yes	—
266	#95	—	2	1	no	—
267	#95	—	2	1	no	—
268	#95	—	2	4	no	—
269	#95	—	2	4	no	—
270	C₂⁴	—	2	2	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	—	4	2	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	8	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
294	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
295	SD₁₆	—	4	8	no	—
296	SD₁₆	—	4	8	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
301	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
302	C₂×C₈	#41×C₁₃₇	1	4	yes	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	4	8	no	—
312	C₂²⋊C₄	—	8	4	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	4	2	no	—
316	C₄²	—	4	2	no	—
317	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
318	C₄²	#41×C₁₃₇	1	2	yes	—
319	C₂³	—	4	2	no	—
320	C₂³	—	4	4	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	4	4	no	—
324	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
325	Q₈	—	4	4	no	—
326	Q₈	—	4	2	no	—
327	Q₈	—	4	2	no	—
328	Q₈	—	4	4	no	—
329	D₄	—	4	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	4	no	—
332	D₄	—	8	4	no	—
333	D₄	—	8	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	#121×C₁₃₇	1	2	yes	—
349	C₂×C₄	#121×C₁₃₇	1	2	yes	—
350	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
351	C₂×C₄	#137×C₁₃₇	1	2	yes	—
352	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
353	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
354	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
355	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
356	C₈	—	2	2	no	—
357	C₈	—	4	2	no	—
358	C₈	#124×C₁₃₇	1	4	yes	complemented
359	C₂²	—	8	2	no	—
360	C₂²	—	8	2	no	—
361	C₂²	—	8	2	no	—
362	C₂²	—	8	4	no	—
363	C₂²	—	8	4	no	—
364	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
365	C₂²	#550×C₁₃₇	1	2	yes	—
366	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
367	C₂²	C₂×#137×C₁₃₇	1	1	yes	characteristic
368	C₂²	#577×C₁₃₇	1	2	yes	—
369	C₄	—	2	2	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	2	no	—
372	C₄	—	8	2	no	—
373	C₄	—	8	2	no	—
374	C₄	—	8	2	no	—
375	C₄	#468×C₁₃₇	1	4	yes	—
376	C₄	C₂×#124×C₁₃₇	1	1	yes	characteristic
377	C₄	#535×C₁₃₇	1	1	yes	characteristic
378	C₄	#559×C₁₃₇	1	2	yes	—
379	C₂	—	16	2	no	—
380	C₂	#2548×C₁₃₇	1	1	yes	characteristic
381	C₂	C₂×#468×C₁₃₇	1	1	yes	characteristic
382	C₂	#3057×C₁₃₇	1	1	yes	characteristic
383	C₂	#3397×C₁₃₇	1	2	yes	—
384	C₂	#3400×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×#446×C₁₃₇	C₂	semidirect
3. #2568×C₁₃₇	C₂	semidirect
5. #2055×C₁₃₇	C₂	semidirect
7. #1981×C₁₃₇	C₂	semidirect
8. #1973×C₁₃₇	C₂	semidirect
9. C₄×#107×C₁₃₇	C₂	semidirect
165. C₈×C₁₃₇	#124	semidirect
192. #28745	C₁₃₇	direct (N × H)
193. C₁₃₇	#28745	direct (N × H)
195. C₂×#446	C₂×C₁₃₇	semidirect
196. #2568	C₂×C₁₃₇	semidirect
198. #2055	C₂×C₁₃₇	semidirect
200. #1981	C₂×C₁₃₇	semidirect
201. #1973	C₂×C₁₃₇	semidirect
202. C₄×#107	C₂×C₁₃₇	semidirect
358. C₈	#124×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#492×C₁₃₇	2
C₂×#446×C₁₃₇	2
#2568×C₁₃₇	2
#2548×C₁₃₇	2
#2055×C₁₃₇	2
#1982×C₁₃₇	2
#1981×C₁₃₇	2
#1973×C₁₃₇	2
C₄×#107×C₁₃₇	2
#28745	137

Subgroups — C137×#28745 #46878131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28745 #46878131