Subgroups — C₁₃₇×#19980 #46869366

Order 35072.

640 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	#3380×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#3335×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#3283×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1707×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1675×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#1671×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1670×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1643×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1635×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	C₈×SD₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₃₇	—	2	1	no	—
13	#554×C₁₃₇	C₂²	1	2	yes	—
14	#547×C₁₃₇	C₂²	1	2	yes	—
15	#500×C₁₃₇	C₂²	1	1	yes	characteristic
16	#499×C₁₃₇	—	2	1	no	—
17	#498×C₁₃₇	C₂²	1	2	yes	—
18	#494×C₁₃₇	C₂²	1	1	yes	characteristic
19	#487×C₁₃₇	C₂²	1	2	yes	—
20	#483×C₁₃₇	—	2	2	no	—
21	#481×C₁₃₇	—	2	2	no	—
22	#478×C₁₃₇	—	2	2	no	—
23	#476×C₁₃₇	C₂²	1	2	yes	—
24	#476×C₁₃₇	C₂²	1	2	yes	—
25	#475×C₁₃₇	C₂²	1	2	yes	—
26	#467×C₁₃₇	—	2	1	no	—
27	#465×C₁₃₇	—	2	2	no	—
28	#461×C₁₃₇	C₂²	1	2	yes	—
29	#452×C₁₃₇	—	2	2	no	—
30	C₈×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₄×SD₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₄×D₈×C₁₃₇	—	2	1	no	—
33	C₄×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₈×D₄×C₁₃₇	C₂²	1	2	yes	—
35	C₈×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₂×#106×C₁₃₇	—	2	2	no	—
37	#335×C₁₃₇	C₂²	1	1	yes	characteristic
38	#334×C₁₃₇	C₂²	1	1	yes	characteristic
39	#333×C₁₃₇	C₂²	1	2	yes	—
40	#332×C₁₃₇	C₂²	1	2	yes	—
41	Q₈⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
42	D₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
43	D₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
44	C₈²×C₁₃₇	C₂²	1	1	yes	characteristic
45	C₂×#41×C₁₃₇	—	2	2	no	—
46	#135×C₁₃₇	—	4	4	no	—
47	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
48	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
49	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
50	C₂×SD₁₆×C₁₃₇	D₄	1	1	yes	characteristic
51	C₂×D₈×C₁₃₇	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃₇	—	2	2	no	—
53	C₂²×C₈×C₁₃₇	—	2	1	no	—
54	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
56	#125×C₁₃₇	—	2	2	no	—
57	#123×C₁₃₇	—	4	2	no	—
58	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
59	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
60	C₂²⋊Q₈×C₁₃₇	—	4	2	no	—
61	#121×C₁₃₇	—	2	2	no	—
62	C₄×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₁₃₇	—	2	2	no	—
64	C₄×D₄×C₁₃₇	C₂³	1	2	yes	—
65	C₄×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
68	#107×C₁₃₇	—	2	1	no	—
69	#107×C₁₃₇	—	2	1	no	—
70	#107×C₁₃₇	D₄	1	1	yes	characteristic
71	#106×C₁₃₇	—	2	2	no	—
72	#106×C₁₃₇	—	2	2	no	—
73	#106×C₁₃₇	—	2	2	no	—
74	#106×C₁₃₇	—	2	2	no	—
75	#106×C₁₃₇	—	2	2	no	—
76	#106×C₁₃₇	D₄	1	1	yes	characteristic
77	C₄⋊C₈×C₁₃₇	—	2	1	no	—
78	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
80	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
81	#103×C₁₃₇	—	2	2	no	—
82	#103×C₁₃₇	—	2	2	no	—
83	#103×C₁₃₇	—	4	2	no	—
84	#103×C₁₃₇	D₄	1	1	yes	characteristic
85	#102×C₁₃₇	—	2	2	no	—
86	#102×C₁₃₇	—	2	2	no	—
87	#102×C₁₃₇	D₄	1	2	yes	—
88	#102×C₁₃₇	D₄	1	1	yes	characteristic
89	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
90	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
91	C₄×C₈×C₁₃₇	—	2	1	no	—
92	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
95	#41×C₁₃₇	—	4	4	no	—
96	#41×C₁₃₇	—	8	2	no	—
97	C₂×Q₈×C₁₃₇	—	2	2	no	—
98	C₂×Q₈×C₁₃₇	—	2	2	no	—
99	C₂×Q₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
100	C₂×D₄×C₁₃₇	—	4	2	no	—
101	C₂×D₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃₇	—	2	2	no	—
104	C₂²×C₄×C₁₃₇	—	2	1	no	—
105	C₂²×C₄×C₁₃₇	—	4	2	no	—
106	C₂²×C₄×C₁₃₇	—	4	2	no	—
107	Q₁₆×C₁₃₇	—	4	2	no	—
108	Q₁₆×C₁₃₇	—	8	1	no	—
109	SD₁₆×C₁₃₇	—	2	2	no	—
110	SD₁₆×C₁₃₇	—	4	4	no	—
111	D₈×C₁₃₇	SD₁₆	1	4	yes	complemented
112	C₂×C₈×C₁₃₇	—	2	1	no	—
113	C₂×C₈×C₁₃₇	—	2	2	no	—
114	C₂×C₈×C₁₃₇	—	2	1	no	—
115	C₂×C₈×C₁₃₇	—	2	1	no	—
116	C₂×C₈×C₁₃₇	—	4	2	no	—
117	C₂×C₈×C₁₃₇	—	4	4	no	—
118	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
122	C₄⋊C₄×C₁₃₇	—	2	1	no	—
123	C₄⋊C₄×C₁₃₇	—	2	2	no	—
124	C₄⋊C₄×C₁₃₇	—	2	2	no	—
125	C₄⋊C₄×C₁₃₇	—	2	2	no	—
126	C₄⋊C₄×C₁₃₇	—	2	2	no	—
127	C₄⋊C₄×C₁₃₇	—	4	2	no	—
128	C₄⋊C₄×C₁₃₇	—	4	2	no	—
129	C₄⋊C₄×C₁₃₇	—	4	2	no	—
130	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
131	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
132	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
133	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
134	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
135	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
136	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
137	C₄²×C₁₃₇	—	2	1	no	—
138	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
139	C₂³×C₁₃₇	—	2	2	no	—
140	C₂³×C₁₃₇	—	2	1	no	—
141	Q₈×C₁₃₇	—	2	1	no	—
142	Q₈×C₁₃₇	—	2	1	no	—
143	Q₈×C₁₃₇	—	4	2	no	—
144	Q₈×C₁₃₇	—	4	2	no	—
145	Q₈×C₁₃₇	—	8	2	no	—
146	D₄×C₁₃₇	—	2	1	no	—
147	D₄×C₁₃₇	—	2	2	no	—
148	D₄×C₁₃₇	—	2	1	no	—
149	D₄×C₁₃₇	—	8	4	no	—
150	D₄×C₁₃₇	C₂×SD₁₆	1	4	yes	—
151	C₂×C₄×C₁₃₇	—	2	1	no	—
152	C₂×C₄×C₁₃₇	—	2	1	no	—
153	C₂×C₄×C₁₃₇	—	2	2	no	—
154	C₂×C₄×C₁₃₇	—	2	1	no	—
155	C₂×C₄×C₁₃₇	—	4	1	no	—
156	C₂×C₄×C₁₃₇	—	4	2	no	—
157	C₂×C₄×C₁₃₇	—	4	1	no	—
158	C₂×C₄×C₁₃₇	—	4	2	no	—
159	C₂×C₄×C₁₃₇	—	4	2	no	—
160	C₂×C₄×C₁₃₇	—	4	2	no	—
161	C₂×C₄×C₁₃₇	—	8	4	no	—
162	C₂×C₄×C₁₃₇	—	16	2	no	—
163	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
166	C₈×C₁₃₇	—	2	1	no	—
167	C₈×C₁₃₇	—	2	1	no	—
168	C₈×C₁₃₇	—	4	1	no	—
169	C₈×C₁₃₇	—	4	1	no	—
170	C₈×C₁₃₇	—	4	2	no	—
171	C₈×C₁₃₇	—	4	1	no	—
172	C₈×C₁₃₇	C₂×SD₁₆	1	2	yes	—
173	C₈×C₁₃₇	#135	1	2	yes	complemented
174	C₂²×C₁₃₇	—	2	4	no	—
175	C₂²×C₁₃₇	—	4	2	no	—
176	C₂²×C₁₃₇	—	4	2	no	—
177	C₂²×C₁₃₇	—	4	1	no	—
178	C₂²×C₁₃₇	—	4	1	no	—
179	C₂²×C₁₃₇	—	4	1	no	—
180	C₂²×C₁₃₇	D₄²	1	1	yes	characteristic
181	C₄×C₁₃₇	—	2	1	no	—
182	C₄×C₁₃₇	—	4	1	no	—
183	C₄×C₁₃₇	—	4	2	no	—
184	C₄×C₁₃₇	—	4	1	no	—
185	C₄×C₁₃₇	—	4	1	no	—
186	C₄×C₁₃₇	—	8	2	no	—
187	C₄×C₁₃₇	—	8	2	no	—
188	C₄×C₁₃₇	C₂²×SD₁₆	1	1	yes	characteristic
189	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
190	C₄×C₁₃₇	#577	1	1	yes	characteristic
191	C₄×C₁₃₇	#578	1	1	yes	characteristic
192	C₂×C₁₃₇	—	4	4	no	—
193	C₂×C₁₃₇	—	8	1	no	—
194	C₂×C₁₃₇	D₄×SD₁₆	1	1	yes	characteristic
195	C₂×C₁₃₇	#3283	1	1	yes	characteristic
196	C₂×C₁₃₇	#3290	1	1	yes	characteristic
197	#19980	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₁₃₇	#19980	1	1	yes	characteristic, direct product factor, Sylow
199	#3380	C₂×C₁₃₇	1	1	yes	characteristic, complemented
200	#3335	C₂×C₁₃₇	1	2	yes	complemented
201	#3283	C₂×C₁₃₇	1	1	yes	characteristic
202	#1707	C₂×C₁₃₇	1	1	yes	characteristic, complemented
203	#1675	C₂×C₁₃₇	1	1	yes	characteristic, complemented
204	#1671	C₂×C₁₃₇	1	2	yes	complemented
205	#1670	C₂×C₁₃₇	1	1	yes	characteristic, complemented
206	#1643	C₂×C₁₃₇	1	2	yes	complemented
207	#1635	C₂×C₁₃₇	1	2	yes	complemented
208	C₈×SD₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
209	C₈×D₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
210	C₂×#135	—	2	1	no	—
211	#554	C₂²×C₁₃₇	1	2	yes	—
212	#547	C₂²×C₁₃₇	1	2	yes	—
213	#500	C₂²×C₁₃₇	1	1	yes	characteristic
214	#499	—	2	1	no	—
215	#498	C₂²×C₁₃₇	1	2	yes	—
216	#494	C₂²×C₁₃₇	1	1	yes	characteristic
217	#487	C₂²×C₁₃₇	1	2	yes	—
218	#483	—	2	2	no	—
219	#481	—	2	2	no	—
220	#478	—	2	2	no	—
221	#476	C₂²×C₁₃₇	1	2	yes	—
222	#476	C₂²×C₁₃₇	1	2	yes	—
223	#475	C₂²×C₁₃₇	1	2	yes	—
224	#467	—	2	1	no	—
225	#465	—	2	2	no	—
226	#461	C₂²×C₁₃₇	1	2	yes	—
227	#452	—	2	2	no	—
228	C₈×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
229	C₄×SD₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
230	C₄×D₈	—	2	1	no	—
231	C₄×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
232	C₈×D₄	C₂²×C₁₃₇	1	2	yes	—
233	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
234	C₂×#106	—	2	2	no	—
235	#335	C₂²×C₁₃₇	1	1	yes	characteristic
236	#334	C₂²×C₁₃₇	1	1	yes	characteristic
237	#333	C₂²×C₁₃₇	1	2	yes	—
238	#332	C₂²×C₁₃₇	1	2	yes	—
239	Q₈⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
240	D₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
241	D₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
242	C₈²	C₂²×C₁₃₇	1	1	yes	characteristic
243	C₂×#41	—	2	2	no	—
244	#135	—	4	4	no	—
245	C₂×Q₁₆	—	2	1	no	—
246	C₂×Q₁₆	—	2	1	no	—
247	C₂×SD₁₆	—	2	2	no	—
248	C₂×SD₁₆	D₄×C₁₃₇	1	1	yes	characteristic
249	C₂×D₈	D₄×C₁₃₇	1	1	yes	characteristic
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
253	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
254	#125	—	2	2	no	—
255	#123	—	4	2	no	—
256	C₂²⋊Q₈	—	2	2	no	—
257	C₂²⋊Q₈	—	2	2	no	—
258	C₂²⋊Q₈	—	4	2	no	—
259	#121	—	2	2	no	—
260	C₄×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
263	C₄×D₄	C₂³×C₁₃₇	1	2	yes	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	#107	—	2	1	no	—
267	#107	—	2	1	no	—
268	#107	D₄×C₁₃₇	1	1	yes	characteristic
269	#106	—	2	2	no	—
270	#106	—	2	2	no	—
271	#106	—	2	2	no	—
272	#106	—	2	2	no	—
273	#106	—	2	2	no	—
274	#106	D₄×C₁₃₇	1	1	yes	characteristic
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
277	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
278	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
279	#103	—	2	2	no	—
280	#103	—	2	2	no	—
281	#103	—	4	2	no	—
282	#103	D₄×C₁₃₇	1	1	yes	characteristic
283	#102	—	2	2	no	—
284	#102	—	2	2	no	—
285	#102	D₄×C₁₃₇	1	2	yes	—
286	#102	D₄×C₁₃₇	1	1	yes	characteristic
287	C₂²⋊C₈	—	2	1	no	—
288	C₂²⋊C₈	—	2	2	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
291	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
292	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
293	#41	—	4	4	no	—
294	#41	—	8	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
300	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	2	no	—
305	Q₁₆	—	4	2	no	—
306	Q₁₆	—	8	1	no	—
307	SD₁₆	—	2	2	no	—
308	SD₁₆	—	4	4	no	—
309	D₈	SD₁₆×C₁₃₇	1	4	yes	complemented
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	—	4	4	no	—
316	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
317	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
329	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
330	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₄²	—	2	1	no	—
336	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
337	C₂³	—	2	2	no	—
338	C₂³	—	2	1	no	—
339	Q₈	—	2	1	no	—
340	Q₈	—	2	1	no	—
341	Q₈	—	4	2	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	8	2	no	—
344	D₄	—	2	1	no	—
345	D₄	—	2	2	no	—
346	D₄	—	2	1	no	—
347	D₄	—	8	4	no	—
348	D₄	C₂×SD₁₆×C₁₃₇	1	4	yes	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	8	4	no	—
360	C₂×C₄	—	16	2	no	—
361	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
362	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
363	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	4	1	no	—
367	C₈	—	4	1	no	—
368	C₈	—	4	2	no	—
369	C₈	—	4	1	no	—
370	C₈	C₂×SD₁₆×C₁₃₇	1	2	yes	—
371	C₈	#135×C₁₃₇	1	2	yes	complemented
372	C₂²	—	2	4	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	D₄²×C₁₃₇	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	1	no	—
383	C₄	—	4	1	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	2	no	—
386	C₄	C₂²×SD₁₆×C₁₃₇	1	1	yes	characteristic
387	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
388	C₄	#577×C₁₃₇	1	1	yes	characteristic
389	C₄	#578×C₁₃₇	1	1	yes	characteristic
390	C₂	—	4	4	no	—
391	C₂	—	8	1	no	—
392	C₂	D₄×SD₁₆×C₁₃₇	1	1	yes	characteristic
393	C₂	#3283×C₁₃₇	1	1	yes	characteristic
394	C₂	#3290×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	#3283×C₁₃₇	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3380×C₁₃₇	C₂	semidirect
2. #3335×C₁₃₇	C₂	semidirect
4. #1707×C₁₃₇	C₂	semidirect
5. #1675×C₁₃₇	C₂	semidirect
6. #1671×C₁₃₇	C₂	semidirect
7. #1670×C₁₃₇	C₂	semidirect
8. #1643×C₁₃₇	C₂	semidirect
9. #1635×C₁₃₇	C₂	semidirect
10. C₈×SD₁₆×C₁₃₇	C₂	semidirect
11. C₈×D₈×C₁₃₇	C₂	semidirect
111. D₈×C₁₃₇	SD₁₆	semidirect
173. C₈×C₁₃₇	#135	semidirect
197. #19980	C₁₃₇	direct (N × H)
198. C₁₃₇	#19980	direct (N × H)
199. #3380	C₂×C₁₃₇	semidirect
200. #3335	C₂×C₁₃₇	semidirect
202. #1707	C₂×C₁₃₇	semidirect
203. #1675	C₂×C₁₃₇	semidirect
204. #1671	C₂×C₁₃₇	semidirect
205. #1670	C₂×C₁₃₇	semidirect
206. #1643	C₂×C₁₃₇	semidirect
207. #1635	C₂×C₁₃₇	semidirect
208. C₈×SD₁₆	C₂×C₁₃₇	semidirect
209. C₈×D₈	C₂×C₁₃₇	semidirect
309. D₈	SD₁₆×C₁₃₇	semidirect
371. C₈	#135×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3380×C₁₃₇	2
#3335×C₁₃₇	2
#3283×C₁₃₇	2
#1707×C₁₃₇	2
#1675×C₁₃₇	2
#1671×C₁₃₇	2
#1670×C₁₃₇	2
#1643×C₁₃₇	2
#1635×C₁₃₇	2
C₈×SD₁₆×C₁₃₇	2
C₈×D₈×C₁₃₇	2
#19980	137

Subgroups — C137×#19980 #46869366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19980 #46869366