Subgroups — C₁₃₇×#28767 #46878153

Order 35072.

728 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#497×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#3140×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#3139×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2961×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2047×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2046×C₁₃₇	C₂	1	2	yes	maximal
7	#1979×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1977×C₁₃₇	C₂	1	2	yes	maximal
9	#1967×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	#1966×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1778×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂²×SD₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
16	#533×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
19	#497×C₁₃₇	—	2	4	no	—
20	#491×C₁₃₇	—	2	2	no	—
21	#489×C₁₃₇	—	2	2	no	—
22	#488×C₁₃₇	—	2	2	no	—
23	#487×C₁₃₇	—	2	2	no	—
24	#446×C₁₃₇	—	2	4	no	—
25	C₂×#108×C₁₃₇	C₂²	1	2	yes	—
26	#424×C₁₃₇	C₂²	1	2	yes	—
27	#423×C₁₃₇	C₂²	1	1	yes	characteristic
28	#419×C₁₃₇	C₂²	1	2	yes	—
29	#419×C₁₃₇	C₂²	1	2	yes	—
30	#419×C₁₃₇	C₂²	1	2	yes	—
31	#418×C₁₃₇	C₂²	1	2	yes	—
32	C₂×#101×C₁₃₇	C₂²	1	2	yes	—
33	C₂×#101×C₁₃₇	C₂²	1	2	yes	—
34	C₂×#101×C₁₃₇	C₂²	1	2	yes	—
35	C₂×#100×C₁₃₇	C₂²	1	2	yes	—
36	#405×C₁₃₇	C₂²	1	2	yes	—
37	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
39	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
40	#341×C₁₃₇	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
42	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
45	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
46	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
47	C₂×Q₁₆×C₁₃₇	—	2	4	no	—
48	C₂×Q₁₆×C₁₃₇	—	4	2	no	—
49	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
50	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
51	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
52	C₂×SD₁₆×C₁₃₇	—	4	2	no	—
53	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
54	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
55	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
59	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
60	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
61	C₄⋊Q₈×C₁₃₇	D₄	1	2	yes	—
62	#125×C₁₃₇	D₄	1	2	yes	—
63	#124×C₁₃₇	—	2	1	no	—
64	#124×C₁₃₇	—	2	1	no	—
65	#124×C₁₃₇	—	2	2	no	—
66	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
67	C₄×Q₈×C₁₃₇	—	2	2	no	—
68	#117×C₁₃₇	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
71	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
72	#108×C₁₃₇	—	2	4	no	—
73	C₄⋊C₈×C₁₃₇	—	2	4	no	—
74	C₄⋊C₈×C₁₃₇	—	2	2	no	—
75	#103×C₁₃₇	—	2	4	no	—
76	#103×C₁₃₇	—	2	4	no	—
77	#103×C₁₃₇	—	2	4	no	—
78	#102×C₁₃₇	—	2	4	no	—
79	#101×C₁₃₇	—	4	2	no	—
80	#101×C₁₃₇	—	4	2	no	—
81	#101×C₁₃₇	—	4	2	no	—
82	#100×C₁₃₇	—	4	2	no	—
83	#97×C₁₃₇	—	2	2	no	—
84	#97×C₁₃₇	—	2	1	no	—
85	#97×C₁₃₇	—	2	1	no	—
86	#97×C₁₃₇	D₄	1	4	yes	—
87	C₄×C₈×C₁₃₇	—	2	2	no	—
88	C₄×C₈×C₁₃₇	—	2	1	no	—
89	C₄×C₈×C₁₃₇	—	2	1	no	—
90	C₂⁴×C₁₃₇	—	2	1	no	—
91	C₂×Q₈×C₁₃₇	—	2	2	no	—
92	C₂×Q₈×C₁₃₇	—	2	1	no	—
93	C₂×Q₈×C₁₃₇	—	2	1	no	—
94	C₂×Q₈×C₁₃₇	—	2	1	no	—
95	C₂×Q₈×C₁₃₇	—	2	1	no	—
96	C₂×Q₈×C₁₃₇	—	2	1	no	—
97	C₂×Q₈×C₁₃₇	—	2	1	no	—
98	C₂×Q₈×C₁₃₇	—	2	2	no	—
99	C₂×Q₈×C₁₃₇	—	2	2	no	—
100	C₂×Q₈×C₁₃₇	—	2	2	no	—
101	C₂×Q₈×C₁₃₇	—	2	2	no	—
102	C₂×Q₈×C₁₃₇	—	2	2	no	—
103	C₂×Q₈×C₁₃₇	—	2	2	no	—
104	C₂×D₄×C₁₃₇	—	2	1	no	—
105	C₂×D₄×C₁₃₇	—	2	1	no	—
106	C₂×D₄×C₁₃₇	—	2	2	no	—
107	C₂×D₄×C₁₃₇	—	2	2	no	—
108	C₂²×C₄×C₁₃₇	—	2	1	no	—
109	C₂²×C₄×C₁₃₇	—	2	1	no	—
110	C₂²×C₄×C₁₃₇	—	2	1	no	—
111	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
112	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
113	Q₁₆×C₁₃₇	—	4	4	no	—
114	Q₁₆×C₁₃₇	—	4	4	no	—
115	SD₁₆×C₁₃₇	—	4	4	no	—
116	SD₁₆×C₁₃₇	—	4	4	no	—
117	M₁₆×C₁₃₇	—	2	2	no	—
118	M₁₆×C₁₃₇	—	2	2	no	—
119	M₁₆×C₁₃₇	—	2	2	no	—
120	M₁₆×C₁₃₇	—	2	2	no	—
121	M₁₆×C₁₃₇	—	2	2	no	—
122	M₁₆×C₁₃₇	—	2	2	no	—
123	C₂×C₈×C₁₃₇	—	2	2	no	—
124	C₂×C₈×C₁₃₇	—	2	2	no	—
125	C₂×C₈×C₁₃₇	—	2	2	no	—
126	C₂×C₈×C₁₃₇	—	2	2	no	—
127	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃₇	#41	1	4	yes	—
130	C₄⋊C₄×C₁₃₇	—	2	4	no	—
131	C₄⋊C₄×C₁₃₇	—	2	2	no	—
132	C₄⋊C₄×C₁₃₇	—	4	2	no	—
133	C₄⋊C₄×C₁₃₇	—	4	2	no	—
134	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
135	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
136	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
137	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
138	C₄²×C₁₃₇	—	2	2	no	—
139	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
142	C₂³×C₁₃₇	—	4	1	no	—
143	C₂³×C₁₃₇	—	4	2	no	—
144	C₂³×C₁₃₇	—	8	2	no	—
145	C₂³×C₁₃₇	C₂×#41	1	1	yes	characteristic
146	Q₈×C₁₃₇	—	4	1	no	—
147	Q₈×C₁₃₇	—	4	1	no	—
148	Q₈×C₁₃₇	—	4	1	no	—
149	Q₈×C₁₃₇	—	4	1	no	—
150	Q₈×C₁₃₇	—	4	1	no	—
151	Q₈×C₁₃₇	—	4	1	no	—
152	Q₈×C₁₃₇	—	4	2	no	—
153	Q₈×C₁₃₇	—	4	2	no	—
154	Q₈×C₁₃₇	—	4	2	no	—
155	Q₈×C₁₃₇	—	8	2	no	—
156	D₄×C₁₃₇	—	4	1	no	—
157	D₄×C₁₃₇	—	4	1	no	—
158	D₄×C₁₃₇	—	4	2	no	—
159	C₂×C₄×C₁₃₇	—	2	4	no	—
160	C₂×C₄×C₁₃₇	—	4	2	no	—
161	C₂×C₄×C₁₃₇	—	4	1	no	—
162	C₂×C₄×C₁₃₇	—	4	1	no	—
163	C₂×C₄×C₁₃₇	—	4	1	no	—
164	C₂×C₄×C₁₃₇	—	4	2	no	—
165	C₂×C₄×C₁₃₇	—	4	2	no	—
166	C₂×C₄×C₁₃₇	—	4	2	no	—
167	C₂×C₄×C₁₃₇	#121	1	2	yes	—
168	C₂×C₄×C₁₃₇	#121	1	2	yes	—
169	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
172	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
173	C₈×C₁₃₇	—	2	2	no	—
174	C₈×C₁₃₇	—	4	2	no	—
175	C₈×C₁₃₇	—	4	2	no	—
176	C₈×C₁₃₇	—	4	2	no	—
177	C₈×C₁₃₇	#124	1	4	yes	—
178	C₂²×C₁₃₇	—	2	2	no	—
179	C₂²×C₁₃₇	—	8	1	no	—
180	C₂²×C₁₃₇	—	8	2	no	—
181	C₂²×C₁₃₇	—	16	2	no	—
182	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
183	C₂²×C₁₃₇	#559	1	2	yes	—
184	C₄×C₁₃₇	—	2	2	no	—
185	C₄×C₁₃₇	—	2	2	no	—
186	C₄×C₁₃₇	—	4	4	no	—
187	C₄×C₁₃₇	—	8	1	no	—
188	C₄×C₁₃₇	—	8	1	no	—
189	C₄×C₁₃₇	—	8	1	no	—
190	C₄×C₁₃₇	C₂×#124	1	1	yes	characteristic
191	C₄×C₁₃₇	#535	1	1	yes	characteristic
192	C₄×C₁₃₇	#550	1	2	yes	—
193	C₂×C₁₃₇	—	2	2	no	—
194	C₂×C₁₃₇	—	16	1	no	—
195	C₂×C₁₃₇	#2548	1	1	yes	characteristic
196	C₂×C₁₃₇	#3069	1	2	yes	—
197	#28767	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₁₃₇	#28767	1	1	yes	characteristic, direct product factor, Sylow
199	C₂×#497	C₂×C₁₃₇	1	1	yes	characteristic
200	#3140	C₂×C₁₃₇	1	1	yes	characteristic
201	#3139	C₂×C₁₃₇	1	1	yes	characteristic, complemented
202	#2961	C₂×C₁₃₇	1	1	yes	characteristic, complemented
203	#2047	C₂×C₁₃₇	1	2	yes	complemented
204	#2046	C₂×C₁₃₇	1	2	yes	—
205	#1979	C₂×C₁₃₇	1	2	yes	complemented
206	#1977	C₂×C₁₃₇	1	2	yes	—
207	#1967	C₂×C₁₃₇	1	1	yes	characteristic
208	#1966	C₂×C₁₃₇	1	1	yes	characteristic, complemented
209	#1778	C₂×C₁₃₇	1	1	yes	characteristic, complemented
210	C₂²×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
211	C₂²×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
212	C₂²×SD₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
213	C₂²×SD₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
214	#533	C₂²×C₁₃₇	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
216	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
217	#497	—	2	4	no	—
218	#491	—	2	2	no	—
219	#489	—	2	2	no	—
220	#488	—	2	2	no	—
221	#487	—	2	2	no	—
222	#446	—	2	4	no	—
223	C₂×#108	C₂²×C₁₃₇	1	2	yes	—
224	#424	C₂²×C₁₃₇	1	2	yes	—
225	#423	C₂²×C₁₃₇	1	1	yes	characteristic
226	#419	C₂²×C₁₃₇	1	2	yes	—
227	#419	C₂²×C₁₃₇	1	2	yes	—
228	#419	C₂²×C₁₃₇	1	2	yes	—
229	#418	C₂²×C₁₃₇	1	2	yes	—
230	C₂×#101	C₂²×C₁₃₇	1	2	yes	—
231	C₂×#101	C₂²×C₁₃₇	1	2	yes	—
232	C₂×#101	C₂²×C₁₃₇	1	2	yes	—
233	C₂×#100	C₂²×C₁₃₇	1	2	yes	—
234	#405	C₂²×C₁₃₇	1	2	yes	—
235	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
236	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
237	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
238	#341	C₂²×C₁₃₇	1	2	yes	—
239	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
240	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
241	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
242	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
243	C₂×Q₁₆	—	2	2	no	—
244	C₂×Q₁₆	—	2	2	no	—
245	C₂×Q₁₆	—	2	4	no	—
246	C₂×Q₁₆	—	4	2	no	—
247	C₂×SD₁₆	—	2	2	no	—
248	C₂×SD₁₆	—	2	2	no	—
249	C₂×SD₁₆	—	2	4	no	—
250	C₂×SD₁₆	—	4	2	no	—
251	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
252	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
253	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
254	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	—	2	2	no	—
259	C₄⋊Q₈	D₄×C₁₃₇	1	2	yes	—
260	#125	D₄×C₁₃₇	1	2	yes	—
261	#124	—	2	1	no	—
262	#124	—	2	1	no	—
263	#124	—	2	2	no	—
264	C₂²⋊Q₈	—	2	2	no	—
265	C₄×Q₈	—	2	2	no	—
266	#117	C₂³×C₁₃₇	1	2	yes	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
270	#108	—	2	4	no	—
271	C₄⋊C₈	—	2	4	no	—
272	C₄⋊C₈	—	2	2	no	—
273	#103	—	2	4	no	—
274	#103	—	2	4	no	—
275	#103	—	2	4	no	—
276	#102	—	2	4	no	—
277	#101	—	4	2	no	—
278	#101	—	4	2	no	—
279	#101	—	4	2	no	—
280	#100	—	4	2	no	—
281	#97	—	2	2	no	—
282	#97	—	2	1	no	—
283	#97	—	2	1	no	—
284	#97	D₄×C₁₃₇	1	4	yes	—
285	C₄×C₈	—	2	2	no	—
286	C₄×C₈	—	2	1	no	—
287	C₄×C₈	—	2	1	no	—
288	C₂⁴	—	2	1	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
311	Q₁₆	—	4	4	no	—
312	Q₁₆	—	4	4	no	—
313	SD₁₆	—	4	4	no	—
314	SD₁₆	—	4	4	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
326	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
327	C₂×C₈	#41×C₁₃₇	1	4	yes	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
338	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
340	C₂³	—	4	1	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	8	2	no	—
343	C₂³	C₂×#41×C₁₃₇	1	1	yes	characteristic
344	Q₈	—	4	1	no	—
345	Q₈	—	4	1	no	—
346	Q₈	—	4	1	no	—
347	Q₈	—	4	1	no	—
348	Q₈	—	4	1	no	—
349	Q₈	—	4	1	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	8	2	no	—
354	D₄	—	4	1	no	—
355	D₄	—	4	1	no	—
356	D₄	—	4	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	#121×C₁₃₇	1	2	yes	—
366	C₂×C₄	#121×C₁₃₇	1	2	yes	—
367	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
369	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
370	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
371	C₈	—	2	2	no	—
372	C₈	—	4	2	no	—
373	C₈	—	4	2	no	—
374	C₈	—	4	2	no	—
375	C₈	#124×C₁₃₇	1	4	yes	—
376	C₂²	—	2	2	no	—
377	C₂²	—	8	1	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	16	2	no	—
380	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
381	C₂²	#559×C₁₃₇	1	2	yes	—
382	C₄	—	2	2	no	—
383	C₄	—	2	2	no	—
384	C₄	—	4	4	no	—
385	C₄	—	8	1	no	—
386	C₄	—	8	1	no	—
387	C₄	—	8	1	no	—
388	C₄	C₂×#124×C₁₃₇	1	1	yes	characteristic
389	C₄	#535×C₁₃₇	1	1	yes	characteristic
390	C₄	#550×C₁₃₇	1	2	yes	—
391	C₂	—	2	2	no	—
392	C₂	—	16	1	no	—
393	C₂	#2548×C₁₃₇	1	1	yes	characteristic
394	C₂	#3069×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂²×D₄×C₁₃₇	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. #3139×C₁₃₇	C₂	semidirect
4. #2961×C₁₃₇	C₂	semidirect
5. #2047×C₁₃₇	C₂	semidirect
7. #1979×C₁₃₇	C₂	semidirect
10. #1966×C₁₃₇	C₂	semidirect
11. #1778×C₁₃₇	C₂	semidirect
197. #28767	C₁₃₇	direct (N × H)
198. C₁₃₇	#28767	direct (N × H)
201. #3139	C₂×C₁₃₇	semidirect
202. #2961	C₂×C₁₃₇	semidirect
203. #2047	C₂×C₁₃₇	semidirect
205. #1979	C₂×C₁₃₇	semidirect
208. #1966	C₂×C₁₃₇	semidirect
209. #1778	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×#497×C₁₃₇	2
#3140×C₁₃₇	2
#3139×C₁₃₇	2
#2961×C₁₃₇	2
#2047×C₁₃₇	2
#2046×C₁₃₇	2
#1979×C₁₃₇	2
#1977×C₁₃₇	2
#1967×C₁₃₇	2
#1966×C₁₃₇	2
#1778×C₁₃₇	2
#28767	137

Subgroups — C137×#28767 #46878153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28767 #46878153