Subgroups — C₁₃₇×#19126 #46868512

Order 35072.

618 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3170×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#3076×C₁₃₇	C₂	1	2	yes	maximal
3	C₈×#41×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1684×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1683×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1676×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1675×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1670×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1669×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#335×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1542×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	#494×C₁₃₇	C₂²	1	1	yes	characteristic
16	#487×C₁₃₇	C₂²	1	2	yes	—
17	#479×C₁₃₇	—	2	2	no	—
18	#478×C₁₃₇	—	2	2	no	—
19	#477×C₁₃₇	C₂²	1	2	yes	—
20	#476×C₁₃₇	C₂²	1	2	yes	—
21	#475×C₁₃₇	C₂²	1	2	yes	—
22	#474×C₁₃₇	C₂²	1	2	yes	—
23	#467×C₁₃₇	—	2	1	no	—
24	#467×C₁₃₇	—	2	1	no	—
25	C₈×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
26	C₈×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₄×Q₁₆×C₁₃₇	—	2	1	no	—
28	C₄×Q₁₆×C₁₃₇	—	2	1	no	—
29	C₈×D₄×C₁₃₇	—	2	1	no	—
30	C₈×D₄×C₁₃₇	—	2	1	no	—
31	C₈×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₈×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
33	#431×C₁₃₇	—	2	1	no	—
34	#431×C₁₃₇	C₂²	1	1	yes	characteristic
35	#427×C₁₃₇	—	2	2	no	—
36	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
37	#416×C₁₃₇	—	2	2	no	—
38	C₂×C₄×C₈×C₁₃₇	—	2	1	no	—
39	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
40	#335×C₁₃₇	C₂²	1	1	yes	characteristic
41	#335×C₁₃₇	C₂²	1	1	yes	characteristic
42	#335×C₁₃₇	C₂²	1	2	yes	—
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	1	no	—
49	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
50	C₂²×C₈×C₁₃₇	—	2	2	no	—
51	C₂²×C₈×C₁₃₇	—	2	1	no	—
52	C₂²×C₈×C₁₃₇	—	2	1	no	—
53	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
57	#125×C₁₃₇	—	2	2	no	—
58	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
59	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
60	C₄×Q₈×C₁₃₇	—	2	2	no	—
61	C₄×Q₈×C₁₃₇	—	2	2	no	—
62	C₄×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
63	C₄×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₁₃₇	—	2	1	no	—
65	C₄×D₄×C₁₃₇	—	2	1	no	—
66	C₄×D₄×C₁₃₇	D₄	1	1	yes	characteristic
67	C₄×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
68	#117×C₁₃₇	—	2	1	no	—
69	#117×C₁₃₇	—	2	2	no	—
70	#117×C₁₃₇	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃₇	—	2	1	no	—
72	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
73	#107×C₁₃₇	—	2	1	no	—
74	#107×C₁₃₇	—	2	1	no	—
75	#107×C₁₃₇	—	2	2	no	—
76	#107×C₁₃₇	—	2	2	no	—
77	#106×C₁₃₇	—	2	2	no	—
78	#106×C₁₃₇	—	2	2	no	—
79	C₄⋊C₈×C₁₃₇	—	2	1	no	—
80	C₄⋊C₈×C₁₃₇	—	2	1	no	—
81	C₄⋊C₈×C₁₃₇	—	2	2	no	—
82	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
83	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
84	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
85	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
86	#103×C₁₃₇	—	2	2	no	—
87	#103×C₁₃₇	—	2	2	no	—
88	#103×C₁₃₇	—	2	2	no	—
89	#103×C₁₃₇	—	2	2	no	—
90	#102×C₁₃₇	—	2	2	no	—
91	#102×C₁₃₇	—	2	2	no	—
92	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
93	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
94	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
95	C₄×C₈×C₁₃₇	—	2	1	no	—
96	C₄×C₈×C₁₃₇	—	2	1	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	—	2	2	no	—
103	#41×C₁₃₇	Q₁₆	1	4	yes	complemented
104	C₂×Q₈×C₁₃₇	—	2	2	no	—
105	C₂×Q₈×C₁₃₇	—	2	2	no	—
106	C₂×Q₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
107	C₂×D₄×C₁₃₇	—	2	1	no	—
108	C₂×D₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₇	—	2	1	no	—
110	C₂²×C₄×C₁₃₇	—	2	1	no	—
111	C₂²×C₄×C₁₃₇	—	2	1	no	—
112	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
115	Q₁₆×C₁₃₇	—	4	2	no	—
116	Q₁₆×C₁₃₇	—	4	2	no	—
117	C₂×C₈×C₁₃₇	—	2	2	no	—
118	C₂×C₈×C₁₃₇	—	2	1	no	—
119	C₂×C₈×C₁₃₇	—	2	1	no	—
120	C₂×C₈×C₁₃₇	—	2	2	no	—
121	C₂×C₈×C₁₃₇	—	2	2	no	—
122	C₂×C₈×C₁₃₇	—	4	1	no	—
123	C₂×C₈×C₁₃₇	—	4	2	no	—
124	C₂×C₈×C₁₃₇	—	4	4	no	—
125	C₂×C₈×C₁₃₇	—	4	2	no	—
126	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
130	C₄⋊C₄×C₁₃₇	—	2	1	no	—
131	C₄⋊C₄×C₁₃₇	—	2	1	no	—
132	C₄⋊C₄×C₁₃₇	—	2	2	no	—
133	C₄⋊C₄×C₁₃₇	—	2	2	no	—
134	C₄⋊C₄×C₁₃₇	—	2	2	no	—
135	C₄⋊C₄×C₁₃₇	—	2	2	no	—
136	C₄⋊C₄×C₁₃₇	—	4	2	no	—
137	C₄⋊C₄×C₁₃₇	—	4	2	no	—
138	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
139	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
140	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
141	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
142	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
143	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
144	C₄²×C₁₃₇	—	2	1	no	—
145	C₄²×C₁₃₇	—	2	1	no	—
146	C₄²×C₁₃₇	—	2	1	no	—
147	C₄²×C₁₃₇	—	4	2	no	—
148	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₃₇	#41	1	1	yes	characteristic
151	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
152	C₂³×C₁₃₇	—	2	1	no	—
153	C₂³×C₁₃₇	#121	1	1	yes	characteristic
154	Q₈×C₁₃₇	—	2	1	no	—
155	Q₈×C₁₃₇	—	4	2	no	—
156	Q₈×C₁₃₇	—	4	2	no	—
157	Q₈×C₁₃₇	—	8	2	no	—
158	Q₈×C₁₃₇	C₂×Q₁₆	1	2	yes	—
159	D₄×C₁₃₇	—	2	4	no	—
160	D₄×C₁₃₇	—	2	1	no	—
161	D₄×C₁₃₇	C₂×Q₁₆	1	2	yes	—
162	C₂×C₄×C₁₃₇	—	2	1	no	—
163	C₂×C₄×C₁₃₇	—	2	1	no	—
164	C₂×C₄×C₁₃₇	—	2	1	no	—
165	C₂×C₄×C₁₃₇	—	2	4	no	—
166	C₂×C₄×C₁₃₇	—	2	1	no	—
167	C₂×C₄×C₁₃₇	—	2	1	no	—
168	C₂×C₄×C₁₃₇	—	4	1	no	—
169	C₂×C₄×C₁₃₇	—	4	2	no	—
170	C₂×C₄×C₁₃₇	—	4	1	no	—
171	C₂×C₄×C₁₃₇	—	4	1	no	—
172	C₂×C₄×C₁₃₇	—	4	2	no	—
173	C₂×C₄×C₁₃₇	—	4	2	no	—
174	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₃₇	C₂×Q₁₆	1	2	yes	—
178	C₂×C₄×C₁₃₇	#135	1	2	yes	—
179	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
182	C₈×C₁₃₇	—	2	1	no	—
183	C₈×C₁₃₇	—	2	1	no	—
184	C₈×C₁₃₇	—	2	1	no	—
185	C₈×C₁₃₇	—	4	1	no	—
186	C₈×C₁₃₇	—	4	2	no	—
187	C₈×C₁₃₇	—	4	2	no	—
188	C₈×C₁₃₇	—	4	1	no	—
189	C₈×C₁₃₇	#135	1	2	yes	—
190	C₂²×C₁₃₇	—	2	1	no	—
191	C₂²×C₁₃₇	—	2	1	no	—
192	C₂²×C₁₃₇	—	2	2	no	—
193	C₂²×C₁₃₇	—	4	1	no	—
194	C₂²×C₁₃₇	—	4	1	no	—
195	C₂²×C₁₃₇	#467	1	2	yes	—
196	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
197	C₄×C₁₃₇	—	2	1	no	—
198	C₄×C₁₃₇	—	2	2	no	—
199	C₄×C₁₃₇	—	2	1	no	—
200	C₄×C₁₃₇	—	2	1	no	—
201	C₄×C₁₃₇	—	4	1	no	—
202	C₄×C₁₃₇	—	4	1	no	—
203	C₄×C₁₃₇	—	8	2	no	—
204	C₄×C₁₃₇	—	8	2	no	—
205	C₄×C₁₃₇	#467	1	2	yes	—
206	C₄×C₁₃₇	C₂²×Q₁₆	1	1	yes	characteristic
207	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
208	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
209	C₄×C₁₃₇	#575	1	1	yes	characteristic
210	C₂×C₁₃₇	—	2	2	no	—
211	C₂×C₁₃₇	—	4	2	no	—
212	C₂×C₁₃₇	#3035	1	1	yes	characteristic
213	C₂×C₁₃₇	C₂×#467	1	1	yes	characteristic
214	C₂×C₁₃₇	#3067	1	1	yes	characteristic
215	#19126	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₁₃₇	#19126	1	1	yes	characteristic, direct product factor, Sylow
217	#3170	C₂×C₁₃₇	1	1	yes	characteristic, complemented
218	#3076	C₂×C₁₃₇	1	2	yes	—
219	C₈×#41	C₂×C₁₃₇	1	1	yes	characteristic
220	#1684	C₂×C₁₃₇	1	2	yes	complemented
221	#1683	C₂×C₁₃₇	1	2	yes	complemented
222	#1676	C₂×C₁₃₇	1	1	yes	characteristic, complemented
223	#1675	C₂×C₁₃₇	1	1	yes	characteristic, complemented
224	#1670	C₂×C₁₃₇	1	1	yes	characteristic, complemented
225	#1669	C₂×C₁₃₇	1	1	yes	characteristic, complemented
226	C₂×#335	C₂×C₁₃₇	1	1	yes	characteristic, complemented
227	#1542	C₂×C₁₃₇	1	2	yes	complemented
228	#533	C₂²×C₁₃₇	1	2	yes	—
229	C₄×#41	C₂²×C₁₃₇	1	1	yes	characteristic
230	#500	C₂²×C₁₃₇	1	1	yes	characteristic
231	#494	C₂²×C₁₃₇	1	1	yes	characteristic
232	#487	C₂²×C₁₃₇	1	2	yes	—
233	#479	—	2	2	no	—
234	#478	—	2	2	no	—
235	#477	C₂²×C₁₃₇	1	2	yes	—
236	#476	C₂²×C₁₃₇	1	2	yes	—
237	#475	C₂²×C₁₃₇	1	2	yes	—
238	#474	C₂²×C₁₃₇	1	2	yes	—
239	#467	—	2	1	no	—
240	#467	—	2	1	no	—
241	C₈×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
242	C₈×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
243	C₄×Q₁₆	—	2	1	no	—
244	C₄×Q₁₆	—	2	1	no	—
245	C₈×D₄	—	2	1	no	—
246	C₈×D₄	—	2	1	no	—
247	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
248	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
249	#431	—	2	1	no	—
250	#431	C₂²×C₁₃₇	1	1	yes	characteristic
251	#427	—	2	2	no	—
252	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
253	#416	—	2	2	no	—
254	C₂×C₄×C₈	—	2	1	no	—
255	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
256	#335	C₂²×C₁₃₇	1	1	yes	characteristic
257	#335	C₂²×C₁₃₇	1	1	yes	characteristic
258	#335	C₂²×C₁₃₇	1	2	yes	—
259	#333	C₂²×C₁₃₇	1	2	yes	—
260	#333	C₂²×C₁₃₇	1	2	yes	—
261	#332	C₂²×C₁₃₇	1	2	yes	—
262	#332	C₂²×C₁₃₇	1	2	yes	—
263	C₂×#41	D₄×C₁₃₇	1	1	yes	characteristic
264	C₂×Q₁₆	—	2	1	no	—
265	C₂×Q₁₆	—	2	1	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
270	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
271	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
272	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
273	#125	—	2	2	no	—
274	C₂²⋊Q₈	—	2	2	no	—
275	C₂²⋊Q₈	—	2	2	no	—
276	C₄×Q₈	—	2	2	no	—
277	C₄×Q₈	—	2	2	no	—
278	C₄×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
279	C₄×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	D₄×C₁₃₇	1	1	yes	characteristic
283	C₄×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
284	#117	—	2	1	no	—
285	#117	—	2	2	no	—
286	#117	D₄×C₁₃₇	1	1	yes	characteristic
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
289	#107	—	2	1	no	—
290	#107	—	2	1	no	—
291	#107	—	2	2	no	—
292	#107	—	2	2	no	—
293	#106	—	2	2	no	—
294	#106	—	2	2	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
299	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
300	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
301	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
302	#103	—	2	2	no	—
303	#103	—	2	2	no	—
304	#103	—	2	2	no	—
305	#103	—	2	2	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	—	2	1	no	—
310	C₂²⋊C₈	—	2	1	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	—	2	1	no	—
314	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
315	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
316	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
317	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
318	#41	—	2	2	no	—
319	#41	Q₁₆×C₁₃₇	1	4	yes	complemented
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
330	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
331	Q₁₆	—	4	2	no	—
332	Q₁₆	—	4	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	2	no	—
340	C₂×C₈	—	4	4	no	—
341	C₂×C₈	—	4	2	no	—
342	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
343	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
344	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
345	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
355	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
356	C₂²⋊C₄	—	2	1	no	—
357	C₂²⋊C₄	—	2	1	no	—
358	C₂²⋊C₄	—	2	1	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	4	2	no	—
364	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
365	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
366	C₄²	#41×C₁₃₇	1	1	yes	characteristic
367	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
368	C₂³	—	2	1	no	—
369	C₂³	#121×C₁₃₇	1	1	yes	characteristic
370	Q₈	—	2	1	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	8	2	no	—
374	Q₈	C₂×Q₁₆×C₁₃₇	1	2	yes	—
375	D₄	—	2	4	no	—
376	D₄	—	2	1	no	—
377	D₄	C₂×Q₁₆×C₁₃₇	1	2	yes	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
391	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
392	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
393	C₂×C₄	C₂×Q₁₆×C₁₃₇	1	2	yes	—
394	C₂×C₄	#135×C₁₃₇	1	2	yes	—
395	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
397	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
398	C₈	—	2	1	no	—
399	C₈	—	2	1	no	—
400	C₈	—	2	1	no	—
401	C₈	—	4	2	no	—
402	C₈	—	4	2	no	—
403	C₈	—	4	1	no	—
404	C₈	—	4	1	no	—
405	C₈	#135×C₁₃₇	1	2	yes	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	#467×C₁₃₇	1	2	yes	—
412	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	8	2	no	—
420	C₄	—	8	2	no	—
421	C₄	#467×C₁₃₇	1	2	yes	—
422	C₄	C₂²×Q₁₆×C₁₃₇	1	1	yes	characteristic
423	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
424	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
425	C₄	#575×C₁₃₇	1	1	yes	characteristic
426	C₂	—	2	2	no	—
427	C₂	—	4	2	no	—
428	C₂	#3035×C₁₃₇	1	1	yes	characteristic
429	C₂	C₂×#467×C₁₃₇	1	1	yes	characteristic
430	C₂	#3067×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₇	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
socle	C₂²×C₁₃₇	C₂×#121
prime radical	C₂×#41×C₁₃₇	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3170×C₁₃₇	C₂	semidirect
4. #1684×C₁₃₇	C₂	semidirect
5. #1683×C₁₃₇	C₂	semidirect
6. #1676×C₁₃₇	C₂	semidirect
7. #1675×C₁₃₇	C₂	semidirect
8. #1670×C₁₃₇	C₂	semidirect
9. #1669×C₁₃₇	C₂	semidirect
10. C₂×#335×C₁₃₇	C₂	semidirect
11. #1542×C₁₃₇	C₂	semidirect
103. #41×C₁₃₇	Q₁₆	semidirect
215. #19126	C₁₃₇	direct (N × H)
216. C₁₃₇	#19126	direct (N × H)
217. #3170	C₂×C₁₃₇	semidirect
220. #1684	C₂×C₁₃₇	semidirect
221. #1683	C₂×C₁₃₇	semidirect
222. #1676	C₂×C₁₃₇	semidirect
223. #1675	C₂×C₁₃₇	semidirect
224. #1670	C₂×C₁₃₇	semidirect
225. #1669	C₂×C₁₃₇	semidirect
226. C₂×#335	C₂×C₁₃₇	semidirect
227. #1542	C₂×C₁₃₇	semidirect
319. #41	Q₁₆×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3170×C₁₃₇	2
#3076×C₁₃₇	2
C₈×#41×C₁₃₇	2
#1684×C₁₃₇	2
#1683×C₁₃₇	2
#1676×C₁₃₇	2
#1675×C₁₃₇	2
#1670×C₁₃₇	2
#1669×C₁₃₇	2
C₂×#335×C₁₃₇	2
#1542×C₁₃₇	2
#19126	137

Subgroups — C137×#19126 #46868512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19126 #46868512