Subgroups — C₁₃₇×#23734 #46873120

Order 35072.

1218 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#428×C₁₃₇	C₂	1	2	yes	maximal, complemented
2	C₂×#417×C₁₃₇	C₂	1	2	yes	maximal
3	#2297×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#384×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2096×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2095×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#2094×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#2093×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1728×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₃₇	C₂²	1	2	yes	—
12	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₃₇	—	2	2	no	—
14	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
16	#428×C₁₃₇	—	2	8	no	—
17	C₂×#107×C₁₃₇	C₂²	1	4	yes	—
18	C₂×#106×C₁₃₇	C₂²	1	4	yes	—
19	#417×C₁₃₇	—	2	8	no	—
20	C₂×#103×C₁₃₇	C₂²	1	4	yes	—
21	C₂×#102×C₁₃₇	C₂²	1	4	yes	—
22	#391×C₁₃₇	C₂²	1	1	yes	characteristic
23	#391×C₁₃₇	C₂²	1	1	yes	characteristic
24	#390×C₁₃₇	C₂²	1	1	yes	characteristic
25	#390×C₁₃₇	C₂²	1	1	yes	characteristic
26	#386×C₁₃₇	—	2	2	no	—
27	#384×C₁₃₇	—	2	2	no	—
28	#384×C₁₃₇	C₂²	1	2	yes	—
29	#384×C₁₃₇	C₂²	1	2	yes	—
30	C₄×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
31	#336×C₁₃₇	C₂²	1	2	yes	—
32	#336×C₁₃₇	C₂²	1	2	yes	—
33	C₂×#41×C₁₃₇	—	2	2	no	—
34	C₂×#41×C₁₃₇	—	2	4	no	—
35	C₂×#41×C₁₃₇	—	2	4	no	—
36	C₂×#41×C₁₃₇	Q₈	1	4	yes	—
37	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
38	C₂²×D₄×C₁₃₇	—	2	1	no	—
39	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₃₇	—	2	1	no	—
41	C₂³×C₄×C₁₃₇	—	2	2	no	—
42	C₂³×C₄×C₁₃₇	D₄	1	2	yes	—
43	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₁₃₇	—	2	4	no	—
45	C₂×M₁₆×C₁₃₇	—	2	4	no	—
46	C₂×M₁₆×C₁₃₇	D₄	1	8	yes	—
47	C₂²×C₈×C₁₃₇	C₂³	1	4	yes	—
48	#117×C₁₃₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₃₇	—	4	8	no	—
55	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
56	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
61	C₂×C₄²×C₁₃₇	—	2	4	no	—
62	C₂×C₄²×C₁₃₇	—	2	1	no	—
63	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
64	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
66	#107×C₁₃₇	—	2	8	no	—
67	#106×C₁₃₇	—	2	8	no	—
68	#103×C₁₃₇	—	2	8	no	—
69	#102×C₁₃₇	—	2	8	no	—
70	#95×C₁₃₇	—	2	2	no	—
71	#95×C₁₃₇	—	2	2	no	—
72	C₂⁴×C₁₃₇	—	2	1	no	—
73	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
74	#41×C₁₃₇	—	2	16	no	—
75	#41×C₁₃₇	—	4	8	no	—
76	C₂×Q₈×C₁₃₇	—	2	1	no	—
77	C₂×Q₈×C₁₃₇	—	2	2	no	—
78	C₂×Q₈×C₁₃₇	—	2	2	no	—
79	C₂×Q₈×C₁₃₇	C₂×Q₈	1	2	yes	—
80	C₂×D₄×C₁₃₇	—	2	4	no	—
81	C₂×D₄×C₁₃₇	—	2	2	no	—
82	C₂×D₄×C₁₃₇	—	2	2	no	—
83	C₂×D₄×C₁₃₇	—	2	1	no	—
84	C₂×D₄×C₁₃₇	—	4	2	no	—
85	C₂×D₄×C₁₃₇	—	4	2	no	—
86	C₂×D₄×C₁₃₇	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₁₃₇	—	2	4	no	—
88	C₂²×C₄×C₁₃₇	—	2	4	no	—
89	C₂²×C₄×C₁₃₇	—	2	4	no	—
90	C₂²×C₄×C₁₃₇	—	2	1	no	—
91	C₂²×C₄×C₁₃₇	—	2	4	no	—
92	C₂²×C₄×C₁₃₇	—	2	1	no	—
93	C₂²×C₄×C₁₃₇	—	2	1	no	—
94	C₂²×C₄×C₁₃₇	—	2	4	no	—
95	C₂²×C₄×C₁₃₇	—	4	2	no	—
96	C₂²×C₄×C₁₃₇	—	4	2	no	—
97	C₂²×C₄×C₁₃₇	—	4	8	no	—
98	C₂²×C₄×C₁₃₇	—	4	4	no	—
99	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
105	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
106	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
107	M₁₆×C₁₃₇	—	2	16	no	—
108	C₂×C₈×C₁₃₇	—	2	4	no	—
109	C₂×C₈×C₁₃₇	—	2	4	no	—
110	C₂×C₈×C₁₃₇	C₂×D₄	1	8	yes	—
111	C₄⋊C₄×C₁₃₇	—	2	4	no	—
112	C₄⋊C₄×C₁₃₇	—	2	2	no	—
113	C₄⋊C₄×C₁₃₇	—	2	4	no	—
114	C₄⋊C₄×C₁₃₇	—	2	2	no	—
115	C₄⋊C₄×C₁₃₇	—	4	8	no	—
116	C₄⋊C₄×C₁₃₇	—	4	4	no	—
117	C₄⋊C₄×C₁₃₇	—	4	8	no	—
118	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
119	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
120	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
121	C₄²×C₁₃₇	—	2	4	no	—
122	C₄²×C₁₃₇	—	2	2	no	—
123	C₄²×C₁₃₇	—	2	2	no	—
124	C₄²×C₁₃₇	—	4	2	no	—
125	C₂³×C₁₃₇	—	2	2	no	—
126	C₂³×C₁₃₇	—	2	2	no	—
127	C₂³×C₁₃₇	—	2	2	no	—
128	C₂³×C₁₃₇	—	4	1	no	—
129	C₂³×C₁₃₇	—	4	1	no	—
130	C₂³×C₁₃₇	—	4	2	no	—
131	C₂³×C₁₃₇	—	4	2	no	—
132	C₂³×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
133	C₂³×C₁₃₇	#123	1	2	yes	—
134	C₂³×C₁₃₇	#127	1	2	yes	—
135	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₁₃₇	—	2	4	no	—
137	Q₈×C₁₃₇	—	4	2	no	—
138	D₄×C₁₃₇	—	2	4	no	—
139	D₄×C₁₃₇	—	4	8	no	—
140	D₄×C₁₃₇	—	4	2	no	—
141	C₂×C₄×C₁₃₇	—	2	16	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	2	no	—
147	C₂×C₄×C₁₃₇	—	4	1	no	—
148	C₂×C₄×C₁₃₇	—	4	1	no	—
149	C₂×C₄×C₁₃₇	—	4	8	no	—
150	C₂×C₄×C₁₃₇	—	4	1	no	—
151	C₂×C₄×C₁₃₇	—	4	1	no	—
152	C₂×C₄×C₁₃₇	—	4	4	no	—
153	C₂×C₄×C₁₃₇	—	4	2	no	—
154	C₂×C₄×C₁₃₇	—	4	8	no	—
155	C₂×C₄×C₁₃₇	—	4	2	no	—
156	C₂×C₄×C₁₃₇	—	8	8	no	—
157	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	8	yes	—
158	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
159	C₂×C₄×C₁₃₇	#123	1	8	yes	—
160	C₂×C₄×C₁₃₇	#123	1	2	yes	—
161	C₂×C₄×C₁₃₇	#127	1	2	yes	—
162	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	4	yes	—
163	C₂×C₄×C₁₃₇	#137	1	4	yes	—
164	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
165	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
166	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
167	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
168	C₈×C₁₃₇	—	2	8	no	—
169	C₂²×C₁₃₇	—	2	4	no	—
170	C₂²×C₁₃₇	—	2	4	no	—
171	C₂²×C₁₃₇	—	2	2	no	—
172	C₂²×C₁₃₇	—	2	2	no	—
173	C₂²×C₁₃₇	—	4	4	no	—
174	C₂²×C₁₃₇	—	4	2	no	—
175	C₂²×C₁₃₇	—	8	2	no	—
176	C₂²×C₁₃₇	—	8	1	no	—
177	C₂²×C₁₃₇	—	8	1	no	—
178	C₂²×C₁₃₇	#399	1	4	yes	—
179	C₂²×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
180	C₂²×C₁₃₇	C₂×#123	1	1	yes	characteristic
181	C₂²×C₁₃₇	C₂×#127	1	1	yes	characteristic
182	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
183	C₂²×C₁₃₇	C₂×#137	1	2	yes	—
184	C₄×C₁₃₇	—	2	4	no	—
185	C₄×C₁₃₇	—	2	4	no	—
186	C₄×C₁₃₇	—	4	2	no	—
187	C₄×C₁₃₇	—	8	1	no	—
188	C₄×C₁₃₇	—	8	4	no	—
189	C₄×C₁₃₇	—	8	1	no	—
190	C₄×C₁₃₇	#399	1	4	yes	—
191	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	2	yes	—
192	C₄×C₁₃₇	C₂×#123	1	2	yes	—
193	C₂×C₁₃₇	—	2	4	no	—
194	C₂×C₁₃₇	—	8	2	no	—
195	C₂×C₁₃₇	C₂×#399	1	1	yes	characteristic
196	C₂×C₁₃₇	#3079	1	2	yes	—
197	C₂×C₁₃₇	#3092	1	2	yes	—
198	C₂×C₁₃₇	#3151	1	1	yes	characteristic
199	C₂×C₁₃₇	#3152	1	1	yes	characteristic
200	#23734	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₁₃₇	#23734	1	1	yes	characteristic, direct product factor, Sylow
202	C₂×#428	C₂×C₁₃₇	1	2	yes	complemented
203	C₂×#417	C₂×C₁₃₇	1	2	yes	—
204	#2297	C₂×C₁₃₇	1	1	yes	characteristic
205	C₂×#384	C₂×C₁₃₇	1	1	yes	characteristic, complemented
206	#2096	C₂×C₁₃₇	1	2	yes	complemented
207	#2095	C₂×C₁₃₇	1	2	yes	complemented
208	#2094	C₂×C₁₃₇	1	2	yes	complemented
209	#2093	C₂×C₁₃₇	1	2	yes	complemented
210	#1728	C₂×C₁₃₇	1	1	yes	characteristic, complemented
211	C₂²×#41	C₂²×C₁₃₇	1	1	yes	characteristic
212	C₂²×M₁₆	C₂²×C₁₃₇	1	2	yes	—
213	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
214	C₂²×C₄⋊C₄	—	2	2	no	—
215	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
216	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
217	#428	—	2	8	no	—
218	C₂×#107	C₂²×C₁₃₇	1	4	yes	—
219	C₂×#106	C₂²×C₁₃₇	1	4	yes	—
220	#417	—	2	8	no	—
221	C₂×#103	C₂²×C₁₃₇	1	4	yes	—
222	C₂×#102	C₂²×C₁₃₇	1	4	yes	—
223	#391	C₂²×C₁₃₇	1	1	yes	characteristic
224	#391	C₂²×C₁₃₇	1	1	yes	characteristic
225	#390	C₂²×C₁₃₇	1	1	yes	characteristic
226	#390	C₂²×C₁₃₇	1	1	yes	characteristic
227	#386	—	2	2	no	—
228	#384	—	2	2	no	—
229	#384	C₂²×C₁₃₇	1	2	yes	—
230	#384	C₂²×C₁₃₇	1	2	yes	—
231	C₄×C₂²⋊C₄	—	2	2	no	—
232	#336	C₂²×C₁₃₇	1	2	yes	—
233	#336	C₂²×C₁₃₇	1	2	yes	—
234	C₂×#41	—	2	2	no	—
235	C₂×#41	—	2	4	no	—
236	C₂×#41	—	2	4	no	—
237	C₂×#41	Q₈×C₁₃₇	1	4	yes	—
238	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
241	C₂³×C₄	—	2	1	no	—
242	C₂³×C₄	—	2	2	no	—
243	C₂³×C₄	D₄×C₁₃₇	1	2	yes	—
244	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
245	C₂×M₁₆	—	2	4	no	—
246	C₂×M₁₆	—	2	4	no	—
247	C₂×M₁₆	D₄×C₁₃₇	1	8	yes	—
248	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
249	#117	—	2	4	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	4	no	—
253	C₂×C₄⋊C₄	—	2	4	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	4	8	no	—
256	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
257	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₄²	—	2	4	no	—
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
265	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
267	#107	—	2	8	no	—
268	#106	—	2	8	no	—
269	#103	—	2	8	no	—
270	#102	—	2	8	no	—
271	#95	—	2	2	no	—
272	#95	—	2	2	no	—
273	C₂⁴	—	2	1	no	—
274	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
275	#41	—	2	16	no	—
276	#41	—	4	8	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	C₂×Q₈×C₁₃₇	1	2	yes	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	C₂×Q₈×C₁₃₇	1	2	yes	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	8	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
304	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
305	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
306	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
307	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
308	M₁₆	—	2	16	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	C₂×D₄×C₁₃₇	1	8	yes	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	8	no	—
317	C₄⋊C₄	—	4	4	no	—
318	C₄⋊C₄	—	4	8	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₂²⋊C₄	—	4	4	no	—
322	C₄²	—	2	4	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	4	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	4	1	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
334	C₂³	#123×C₁₃₇	1	2	yes	—
335	C₂³	#127×C₁₃₇	1	2	yes	—
336	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
337	Q₈	—	2	4	no	—
338	Q₈	—	4	2	no	—
339	D₄	—	2	4	no	—
340	D₄	—	4	8	no	—
341	D₄	—	4	2	no	—
342	C₂×C₄	—	2	16	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	8	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	8	8	no	—
358	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
359	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	8	yes	—
360	C₂×C₄	#123×C₁₃₇	1	2	yes	—
361	C₂×C₄	#123×C₁₃₇	1	8	yes	—
362	C₂×C₄	#127×C₁₃₇	1	2	yes	—
363	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	4	yes	—
364	C₂×C₄	#137×C₁₃₇	1	4	yes	—
365	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
366	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
367	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
368	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
369	C₈	—	2	8	no	—
370	C₂²	—	2	4	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	1	no	—
378	C₂²	—	8	1	no	—
379	C₂²	#399×C₁₃₇	1	4	yes	—
380	C₂²	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
381	C₂²	C₂×#123×C₁₃₇	1	1	yes	characteristic
382	C₂²	C₂×#127×C₁₃₇	1	1	yes	characteristic
383	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
384	C₂²	C₂×#137×C₁₃₇	1	2	yes	—
385	C₄	—	2	4	no	—
386	C₄	—	2	4	no	—
387	C₄	—	4	2	no	—
388	C₄	—	8	4	no	—
389	C₄	—	8	1	no	—
390	C₄	—	8	1	no	—
391	C₄	#399×C₁₃₇	1	4	yes	—
392	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	2	yes	—
393	C₄	C₂×#123×C₁₃₇	1	2	yes	—
394	C₂	—	2	4	no	—
395	C₂	—	8	2	no	—
396	C₂	C₂×#399×C₁₃₇	1	1	yes	characteristic
397	C₂	#3079×C₁₃₇	1	2	yes	—
398	C₂	#3092×C₁₃₇	1	2	yes	—
399	C₂	#3151×C₁₃₇	1	1	yes	characteristic
400	C₂	#3152×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂²×#41×C₁₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂²×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#428×C₁₃₇	C₂	semidirect
4. C₂×#384×C₁₃₇	C₂	semidirect
5. #2096×C₁₃₇	C₂	semidirect
6. #2095×C₁₃₇	C₂	semidirect
7. #2094×C₁₃₇	C₂	semidirect
8. #2093×C₁₃₇	C₂	semidirect
9. #1728×C₁₃₇	C₂	semidirect
200. #23734	C₁₃₇	direct (N × H)
201. C₁₃₇	#23734	direct (N × H)
202. C₂×#428	C₂×C₁₃₇	semidirect
205. C₂×#384	C₂×C₁₃₇	semidirect
206. #2096	C₂×C₁₃₇	semidirect
207. #2095	C₂×C₁₃₇	semidirect
208. #2094	C₂×C₁₃₇	semidirect
209. #2093	C₂×C₁₃₇	semidirect
210. #1728	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×#428×C₁₃₇	2
C₂×#417×C₁₃₇	2
#2297×C₁₃₇	2
C₂×#384×C₁₃₇	2
#2096×C₁₃₇	2
#2095×C₁₃₇	2
#2094×C₁₃₇	2
#2093×C₁₃₇	2
#1728×C₁₃₇	2
#23734	137

Subgroups — C137×#23734 #46873120

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#23734 #46873120