Subgroups — C₁₃₇×#19298 #46868684

Order 35072.

586 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3160×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#3116×C₁₃₇	C₂	1	2	yes	maximal
3	#2965×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1696×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1695×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#1694×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1693×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1692×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1691×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#1568×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1554×C₁₃₇	C₂	1	2	yes	maximal, complemented
12	#533×C₁₃₇	C₂²	1	2	yes	—
13	C₄×#41×C₁₃₇	C₂²	1	1	yes	characteristic
14	#500×C₁₃₇	C₂²	1	1	yes	characteristic
15	#500×C₁₃₇	C₂²	1	1	yes	characteristic
16	#499×C₁₃₇	—	2	1	no	—
17	#499×C₁₃₇	—	2	1	no	—
18	#498×C₁₃₇	C₂²	1	2	yes	—
19	#485×C₁₃₇	—	2	2	no	—
20	#477×C₁₃₇	C₂²	1	2	yes	—
21	#476×C₁₃₇	C₂²	1	2	yes	—
22	#462×C₁₃₇	C₂²	1	2	yes	—
23	#461×C₁₃₇	C₂²	1	2	yes	—
24	#452×C₁₃₇	—	2	2	no	—
25	#446×C₁₃₇	C₂²	1	1	yes	characteristic
26	#446×C₁₃₇	C₂²	1	1	yes	characteristic
27	#441×C₁₃₇	—	2	2	no	—
28	#440×C₁₃₇	—	2	2	no	—
29	#436×C₁₃₇	C₂²	1	1	yes	characteristic
30	#436×C₁₃₇	C₂²	1	1	yes	characteristic
31	#435×C₁₃₇	—	2	1	no	—
32	#435×C₁₃₇	—	2	1	no	—
33	#432×C₁₃₇	C₂²	1	2	yes	—
34	#431×C₁₃₇	—	2	1	no	—
35	#431×C₁₃₇	C₂²	1	1	yes	characteristic
36	#427×C₁₃₇	—	2	1	no	—
37	#427×C₁₃₇	—	2	1	no	—
38	C₄×M₁₆×C₁₃₇	—	2	1	no	—
39	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
40	#335×C₁₃₇	C₂²	1	2	yes	—
41	#334×C₁₃₇	C₂²	1	1	yes	characteristic
42	#334×C₁₃₇	C₂²	1	1	yes	characteristic
43	#333×C₁₃₇	C₂²	1	2	yes	—
44	#333×C₁₃₇	C₂²	1	2	yes	—
45	#332×C₁₃₇	C₂²	1	2	yes	—
46	#332×C₁₃₇	C₂²	1	2	yes	—
47	C₂×#41×C₁₃₇	D₄	1	1	yes	characteristic
48	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
49	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
50	C₂×M₁₆×C₁₃₇	—	2	1	no	—
51	C₂×M₁₆×C₁₃₇	—	2	1	no	—
52	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
54	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
56	#125×C₁₃₇	—	2	2	no	—
57	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
58	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
59	C₄×Q₈×C₁₃₇	—	2	2	no	—
60	C₄×Q₈×C₁₃₇	—	2	2	no	—
61	C₄×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
62	C₄×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₁₃₇	—	2	1	no	—
64	C₄×D₄×C₁₃₇	—	2	1	no	—
65	C₄×D₄×C₁₃₇	D₄	1	1	yes	characteristic
66	C₄×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
67	#117×C₁₃₇	—	2	1	no	—
68	#117×C₁₃₇	—	2	2	no	—
69	#117×C₁₃₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₇	—	2	1	no	—
71	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
72	#107×C₁₃₇	—	2	1	no	—
73	#107×C₁₃₇	—	2	1	no	—
74	#107×C₁₃₇	—	2	1	no	—
75	#107×C₁₃₇	—	2	1	no	—
76	#107×C₁₃₇	—	2	2	no	—
77	#106×C₁₃₇	—	2	2	no	—
78	#106×C₁₃₇	—	2	2	no	—
79	#106×C₁₃₇	—	2	2	no	—
80	C₄⋊C₈×C₁₃₇	—	2	1	no	—
81	C₄⋊C₈×C₁₃₇	—	2	1	no	—
82	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
85	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
86	#103×C₁₃₇	—	2	2	no	—
87	#103×C₁₃₇	—	2	2	no	—
88	#103×C₁₃₇	—	2	2	no	—
89	#102×C₁₃₇	—	2	2	no	—
90	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
91	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
92	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
93	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
94	#97×C₁₃₇	—	2	1	no	—
95	#97×C₁₃₇	—	2	1	no	—
96	#97×C₁₃₇	—	2	2	no	—
97	C₄×C₈×C₁₃₇	—	2	1	no	—
98	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
99	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
102	#41×C₁₃₇	—	4	2	no	—
103	C₂×Q₈×C₁₃₇	—	2	2	no	—
104	C₂×Q₈×C₁₃₇	—	2	2	no	—
105	C₂×Q₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₁₃₇	—	2	1	no	—
107	C₂×D₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
114	Q₁₆×C₁₃₇	—	4	4	no	—
115	SD₁₆×C₁₃₇	—	4	4	no	—
116	M₁₆×C₁₃₇	—	4	2	no	—
117	M₁₆×C₁₃₇	—	4	2	no	—
118	C₂×C₈×C₁₃₇	—	2	2	no	—
119	C₂×C₈×C₁₃₇	—	2	2	no	—
120	C₂×C₈×C₁₃₇	—	2	1	no	—
121	C₂×C₈×C₁₃₇	—	2	1	no	—
122	C₂×C₈×C₁₃₇	—	2	2	no	—
123	C₂×C₈×C₁₃₇	—	2	2	no	—
124	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
128	C₄⋊C₄×C₁₃₇	—	2	1	no	—
129	C₄⋊C₄×C₁₃₇	—	2	1	no	—
130	C₄⋊C₄×C₁₃₇	—	2	2	no	—
131	C₄⋊C₄×C₁₃₇	—	2	2	no	—
132	C₄⋊C₄×C₁₃₇	—	2	2	no	—
133	C₄⋊C₄×C₁₃₇	—	2	2	no	—
134	C₄⋊C₄×C₁₃₇	—	4	2	no	—
135	C₄⋊C₄×C₁₃₇	—	4	2	no	—
136	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
137	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
138	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
139	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
140	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
141	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
142	C₄²×C₁₃₇	—	2	1	no	—
143	C₄²×C₁₃₇	—	2	1	no	—
144	C₄²×C₁₃₇	—	2	1	no	—
145	C₄²×C₁₃₇	—	4	2	no	—
146	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₁₃₇	#41	1	1	yes	characteristic
149	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
150	C₂³×C₁₃₇	—	2	1	no	—
151	C₂³×C₁₃₇	#121	1	1	yes	characteristic
152	Q₈×C₁₃₇	—	2	2	no	—
153	Q₈×C₁₃₇	—	4	2	no	—
154	Q₈×C₁₃₇	—	4	2	no	—
155	Q₈×C₁₃₇	—	8	2	no	—
156	D₄×C₁₃₇	—	2	2	no	—
157	D₄×C₁₃₇	—	4	2	no	—
158	C₂×C₄×C₁₃₇	—	2	1	no	—
159	C₂×C₄×C₁₃₇	—	2	1	no	—
160	C₂×C₄×C₁₃₇	—	2	2	no	—
161	C₂×C₄×C₁₃₇	—	2	1	no	—
162	C₂×C₄×C₁₃₇	—	2	1	no	—
163	C₂×C₄×C₁₃₇	—	2	1	no	—
164	C₂×C₄×C₁₃₇	—	4	1	no	—
165	C₂×C₄×C₁₃₇	—	4	2	no	—
166	C₂×C₄×C₁₃₇	—	4	2	no	—
167	C₂×C₄×C₁₃₇	—	4	1	no	—
168	C₂×C₄×C₁₃₇	—	4	1	no	—
169	C₂×C₄×C₁₃₇	—	4	2	no	—
170	C₂×C₄×C₁₃₇	—	4	2	no	—
171	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
177	C₈×C₁₃₇	—	2	1	no	—
178	C₈×C₁₃₇	—	2	1	no	—
179	C₈×C₁₃₇	—	4	1	no	—
180	C₈×C₁₃₇	—	4	1	no	—
181	C₈×C₁₃₇	—	4	2	no	—
182	C₈×C₁₃₇	—	4	2	no	—
183	C₈×C₁₃₇	#137	1	2	yes	—
184	C₈×C₁₃₇	#137	1	2	yes	—
185	C₂²×C₁₃₇	—	2	1	no	—
186	C₂²×C₁₃₇	—	2	1	no	—
187	C₂²×C₁₃₇	—	2	1	no	—
188	C₂²×C₁₃₇	—	4	1	no	—
189	C₂²×C₁₃₇	—	4	1	no	—
190	C₂²×C₁₃₇	—	4	1	no	—
191	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
192	C₄×C₁₃₇	—	2	1	no	—
193	C₄×C₁₃₇	—	2	1	no	—
194	C₄×C₁₃₇	—	2	1	no	—
195	C₄×C₁₃₇	—	2	1	no	—
196	C₄×C₁₃₇	—	4	1	no	—
197	C₄×C₁₃₇	—	4	1	no	—
198	C₄×C₁₃₇	—	4	1	no	—
199	C₄×C₁₃₇	—	8	2	no	—
200	C₄×C₁₃₇	—	8	2	no	—
201	C₄×C₁₃₇	C₂×#137	1	1	yes	characteristic
202	C₄×C₁₃₇	C₂×#137	1	1	yes	characteristic
203	C₄×C₁₃₇	#575	1	2	yes	—
204	C₂×C₁₃₇	—	4	1	no	—
205	C₂×C₁₃₇	—	8	1	no	—
206	C₂×C₁₃₇	#3039	1	1	yes	characteristic
207	C₂×C₁₃₇	#3054	1	1	yes	characteristic
208	C₂×C₁₃₇	#3067	1	1	yes	characteristic
209	#19298	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₁₃₇	#19298	1	1	yes	characteristic, direct product factor, Sylow
211	#3160	C₂×C₁₃₇	1	1	yes	characteristic, complemented
212	#3116	C₂×C₁₃₇	1	2	yes	—
213	#2965	C₂×C₁₃₇	1	1	yes	characteristic
214	#1696	C₂×C₁₃₇	1	1	yes	characteristic, complemented
215	#1695	C₂×C₁₃₇	1	1	yes	characteristic, complemented
216	#1694	C₂×C₁₃₇	1	1	yes	characteristic, complemented
217	#1693	C₂×C₁₃₇	1	1	yes	characteristic, complemented
218	#1692	C₂×C₁₃₇	1	2	yes	complemented
219	#1691	C₂×C₁₃₇	1	2	yes	complemented
220	#1568	C₂×C₁₃₇	1	1	yes	characteristic, complemented
221	#1554	C₂×C₁₃₇	1	2	yes	complemented
222	#533	C₂²×C₁₃₇	1	2	yes	—
223	C₄×#41	C₂²×C₁₃₇	1	1	yes	characteristic
224	#500	C₂²×C₁₃₇	1	1	yes	characteristic
225	#500	C₂²×C₁₃₇	1	1	yes	characteristic
226	#499	—	2	1	no	—
227	#499	—	2	1	no	—
228	#498	C₂²×C₁₃₇	1	2	yes	—
229	#485	—	2	2	no	—
230	#477	C₂²×C₁₃₇	1	2	yes	—
231	#476	C₂²×C₁₃₇	1	2	yes	—
232	#462	C₂²×C₁₃₇	1	2	yes	—
233	#461	C₂²×C₁₃₇	1	2	yes	—
234	#452	—	2	2	no	—
235	#446	C₂²×C₁₃₇	1	1	yes	characteristic
236	#446	C₂²×C₁₃₇	1	1	yes	characteristic
237	#441	—	2	2	no	—
238	#440	—	2	2	no	—
239	#436	C₂²×C₁₃₇	1	1	yes	characteristic
240	#436	C₂²×C₁₃₇	1	1	yes	characteristic
241	#435	—	2	1	no	—
242	#435	—	2	1	no	—
243	#432	C₂²×C₁₃₇	1	2	yes	—
244	#431	—	2	1	no	—
245	#431	C₂²×C₁₃₇	1	1	yes	characteristic
246	#427	—	2	1	no	—
247	#427	—	2	1	no	—
248	C₄×M₁₆	—	2	1	no	—
249	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
250	#335	C₂²×C₁₃₇	1	2	yes	—
251	#334	C₂²×C₁₃₇	1	1	yes	characteristic
252	#334	C₂²×C₁₃₇	1	1	yes	characteristic
253	#333	C₂²×C₁₃₇	1	2	yes	—
254	#333	C₂²×C₁₃₇	1	2	yes	—
255	#332	C₂²×C₁₃₇	1	2	yes	—
256	#332	C₂²×C₁₃₇	1	2	yes	—
257	C₂×#41	D₄×C₁₃₇	1	1	yes	characteristic
258	C₂×Q₁₆	—	2	2	no	—
259	C₂×SD₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
263	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
264	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
265	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
266	#125	—	2	2	no	—
267	C₂²⋊Q₈	—	2	2	no	—
268	C₂²⋊Q₈	—	2	2	no	—
269	C₄×Q₈	—	2	2	no	—
270	C₄×Q₈	—	2	2	no	—
271	C₄×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
272	C₄×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	D₄×C₁₃₇	1	1	yes	characteristic
276	C₄×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
277	#117	—	2	1	no	—
278	#117	—	2	2	no	—
279	#117	D₄×C₁₃₇	1	1	yes	characteristic
280	C₂×C₄²	—	2	1	no	—
281	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
282	#107	—	2	1	no	—
283	#107	—	2	1	no	—
284	#107	—	2	1	no	—
285	#107	—	2	1	no	—
286	#107	—	2	2	no	—
287	#106	—	2	2	no	—
288	#106	—	2	2	no	—
289	#106	—	2	2	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
293	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
294	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
295	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
296	#103	—	2	2	no	—
297	#103	—	2	2	no	—
298	#103	—	2	2	no	—
299	#102	—	2	2	no	—
300	C₂²⋊C₈	—	2	1	no	—
301	C₂²⋊C₈	—	2	2	no	—
302	C₂²⋊C₈	—	2	1	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	#97	—	2	1	no	—
305	#97	—	2	1	no	—
306	#97	—	2	2	no	—
307	C₄×C₈	—	2	1	no	—
308	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
309	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
310	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
311	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
312	#41	—	4	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
323	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
324	Q₁₆	—	4	4	no	—
325	SD₁₆	—	4	4	no	—
326	M₁₆	—	4	2	no	—
327	M₁₆	—	4	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
335	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
336	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
337	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
347	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
348	C₂²⋊C₄	—	2	1	no	—
349	C₂²⋊C₄	—	2	1	no	—
350	C₂²⋊C₄	—	2	1	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	4	2	no	—
356	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
357	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
358	C₄²	#41×C₁₃₇	1	1	yes	characteristic
359	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
360	C₂³	—	2	1	no	—
361	C₂³	#121×C₁₃₇	1	1	yes	characteristic
362	Q₈	—	2	2	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	8	2	no	—
366	D₄	—	2	2	no	—
367	D₄	—	4	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
382	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
383	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
384	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
385	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
386	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
387	C₈	—	2	1	no	—
388	C₈	—	2	1	no	—
389	C₈	—	4	1	no	—
390	C₈	—	4	1	no	—
391	C₈	—	4	2	no	—
392	C₈	—	4	2	no	—
393	C₈	#137×C₁₃₇	1	2	yes	—
394	C₈	#137×C₁₃₇	1	2	yes	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	4	1	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	2	no	—
411	C₄	C₂×#137×C₁₃₇	1	1	yes	characteristic
412	C₄	C₂×#137×C₁₃₇	1	1	yes	characteristic
413	C₄	#575×C₁₃₇	1	2	yes	—
414	C₂	—	4	1	no	—
415	C₂	—	8	1	no	—
416	C₂	#3039×C₁₃₇	1	1	yes	characteristic
417	C₂	#3054×C₁₃₇	1	1	yes	characteristic
418	C₂	#3067×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	C₂×#41×C₁₃₇	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ 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
1. #3160×C₁₃₇	C₂	semidirect
4. #1696×C₁₃₇	C₂	semidirect
5. #1695×C₁₃₇	C₂	semidirect
6. #1694×C₁₃₇	C₂	semidirect
7. #1693×C₁₃₇	C₂	semidirect
8. #1692×C₁₃₇	C₂	semidirect
9. #1691×C₁₃₇	C₂	semidirect
10. #1568×C₁₃₇	C₂	semidirect
11. #1554×C₁₃₇	C₂	semidirect
209. #19298	C₁₃₇	direct (N × H)
210. C₁₃₇	#19298	direct (N × H)
211. #3160	C₂×C₁₃₇	semidirect
214. #1696	C₂×C₁₃₇	semidirect
215. #1695	C₂×C₁₃₇	semidirect
216. #1694	C₂×C₁₃₇	semidirect
217. #1693	C₂×C₁₃₇	semidirect
218. #1692	C₂×C₁₃₇	semidirect
219. #1691	C₂×C₁₃₇	semidirect
220. #1568	C₂×C₁₃₇	semidirect
221. #1554	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3160×C₁₃₇	2
#3116×C₁₃₇	2
#2965×C₁₃₇	2
#1696×C₁₃₇	2
#1695×C₁₃₇	2
#1694×C₁₃₇	2
#1693×C₁₃₇	2
#1692×C₁₃₇	2
#1691×C₁₃₇	2
#1568×C₁₃₇	2
#1554×C₁₃₇	2
#19298	137

Subgroups — C137×#19298 #46868684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19298 #46868684