Subgroups — C₁₃₇×#10144 #46859530

Order 35072.

758 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3205×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#3151×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#493×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#1965×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1545×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#1492×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1278×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×AGL(1,ℤ/8)×C₁₃₇	—	2	2	no	—
9	C₂²×D₈×C₁₃₇	—	2	2	no	—
10	#532×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
13	#496×C₁₃₇	—	2	2	no	—
14	#493×C₁₃₇	—	2	2	no	—
15	#493×C₁₃₇	—	2	1	no	—
16	#493×C₁₃₇	—	2	1	no	—
17	#493×C₁₃₇	—	2	2	no	—
18	#492×C₁₃₇	—	2	1	no	—
19	#486×C₁₃₇	—	2	1	no	—
20	#459×C₁₃₇	—	2	2	no	—
21	#447×C₁₃₇	—	2	2	no	—
22	#431×C₁₃₇	C₂²	1	1	yes	characteristic
23	#423×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂×#100×C₁₃₇	—	2	2	no	—
25	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
27	#331×C₁₃₇	—	2	2	no	—
28	D₄⋊C₈×C₁₃₇	—	2	2	no	—
29	C₂×#41×C₁₃₇	—	2	1	no	—
30	C₂²×D₄×C₁₃₇	—	2	1	no	—
31	C₂²×D₄×C₁₃₇	—	2	1	no	—
32	C₂²×D₄×C₁₃₇	—	2	1	no	—
33	C₂²×D₄×C₁₃₇	—	2	1	no	—
34	C₂²×D₄×C₁₃₇	—	2	1	no	—
35	C₂²×D₄×C₁₃₇	D₄	1	2	yes	—
36	AGL(1,ℤ/8)×C₁₃₇	—	4	4	no	—
37	AGL(1,ℤ/8)×C₁₃₇	—	4	4	no	—
38	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
39	C₂×D₈×C₁₃₇	—	2	8	no	—
40	C₂×D₈×C₁₃₇	—	2	4	no	—
41	C₂×D₈×C₁₃₇	—	2	4	no	—
42	C₂×D₈×C₁₃₇	—	4	8	no	—
43	C₂×M₁₆×C₁₃₇	—	2	1	no	—
44	C₂×M₁₆×C₁₃₇	D₄	1	2	yes	—
45	C₂²×C₈×C₁₃₇	—	2	1	no	—
46	C₄⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
47	#127×C₁₃₇	—	2	1	no	—
48	#127×C₁₃₇	—	2	1	no	—
49	#127×C₁₃₇	—	2	1	no	—
50	#127×C₁₃₇	—	2	1	no	—
51	#127×C₁₃₇	—	2	1	no	—
52	#127×C₁₃₇	—	2	1	no	—
53	#127×C₁₃₇	—	2	1	no	—
54	#127×C₁₃₇	D₄	1	1	yes	characteristic
55	#127×C₁₃₇	D₄	1	2	yes	—
56	#124×C₁₃₇	—	2	1	no	—
57	#121×C₁₃₇	—	2	1	no	—
58	#121×C₁₃₇	—	2	1	no	—
59	C₄×D₄×C₁₃₇	—	2	1	no	—
60	C₄×D₄×C₁₃₇	—	2	1	no	—
61	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
62	C₄⋊C₈×C₁₃₇	—	2	1	no	—
63	C₄⋊C₈×C₁₃₇	—	2	1	no	—
64	C₄⋊C₈×C₁₃₇	D₄	1	2	yes	—
65	#102×C₁₃₇	—	2	4	no	—
66	#100×C₁₃₇	—	4	4	no	—
67	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
68	#97×C₁₃₇	—	2	1	no	—
69	C₄×C₈×C₁₃₇	—	2	1	no	—
70	C₄×C₈×C₁₃₇	—	2	1	no	—
71	C₄×C₈×C₁₃₇	—	2	1	no	—
72	C₄×C₈×C₁₃₇	D₄	1	2	yes	—
73	C₂⁴×C₁₃₇	—	2	2	no	—
74	C₂⁴×C₁₃₇	—	4	1	no	—
75	#41×C₁₃₇	—	4	2	no	—
76	#41×C₁₃₇	—	4	2	no	—
77	C₂×Q₈×C₁₃₇	—	2	1	no	—
78	C₂×D₄×C₁₃₇	—	2	2	no	—
79	C₂×D₄×C₁₃₇	—	2	1	no	—
80	C₂×D₄×C₁₃₇	—	2	1	no	—
81	C₂×D₄×C₁₃₇	—	2	2	no	—
82	C₂×D₄×C₁₃₇	—	2	2	no	—
83	C₂×D₄×C₁₃₇	—	2	2	no	—
84	C₂×D₄×C₁₃₇	—	2	1	no	—
85	C₂×D₄×C₁₃₇	—	2	2	no	—
86	C₂×D₄×C₁₃₇	—	4	4	no	—
87	C₂×D₄×C₁₃₇	—	4	4	no	—
88	C₂×D₄×C₁₃₇	—	4	1	no	—
89	C₂×D₄×C₁₃₇	—	4	1	no	—
90	C₂×D₄×C₁₃₇	—	4	1	no	—
91	C₂×D₄×C₁₃₇	—	4	1	no	—
92	C₂×D₄×C₁₃₇	—	4	1	no	—
93	C₂×D₄×C₁₃₇	—	4	1	no	—
94	C₂×D₄×C₁₃₇	—	4	1	no	—
95	C₂×D₄×C₁₃₇	—	4	1	no	—
96	C₂×D₄×C₁₃₇	—	4	2	no	—
97	C₂×D₄×C₁₃₇	—	4	2	no	—
98	C₂×D₄×C₁₃₇	—	4	2	no	—
99	C₂×D₄×C₁₃₇	—	4	2	no	—
100	C₂×D₄×C₁₃₇	—	8	2	no	—
101	C₂×D₄×C₁₃₇	—	8	2	no	—
102	C₂²×C₄×C₁₃₇	—	4	1	no	—
103	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
106	SD₁₆×C₁₃₇	—	4	8	no	—
107	D₈×C₁₃₇	—	4	16	no	—
108	D₈×C₁₃₇	—	4	8	no	—
109	D₈×C₁₃₇	—	8	4	no	—
110	M₁₆×C₁₃₇	—	2	2	no	—
111	M₁₆×C₁₃₇	—	4	2	no	—
112	M₁₆×C₁₃₇	D₈	1	4	yes	complemented
113	C₂×C₈×C₁₃₇	—	2	4	no	—
114	C₂×C₈×C₁₃₇	—	2	2	no	—
115	C₂×C₈×C₁₃₇	—	2	2	no	—
116	C₂×C₈×C₁₃₇	—	2	2	no	—
117	C₂×C₈×C₁₃₇	—	4	1	no	—
118	C₄⋊C₄×C₁₃₇	—	2	1	no	—
119	C₄⋊C₄×C₁₃₇	—	2	1	no	—
120	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
121	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
122	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
126	C₂³×C₁₃₇	—	4	1	no	—
127	C₂³×C₁₃₇	—	4	2	no	—
128	C₂³×C₁₃₇	—	4	2	no	—
129	C₂³×C₁₃₇	—	4	4	no	—
130	C₂³×C₁₃₇	—	8	2	no	—
131	C₂³×C₁₃₇	—	8	2	no	—
132	C₂³×C₁₃₇	—	8	2	no	—
133	C₂³×C₁₃₇	—	8	2	no	—
134	C₂³×C₁₃₇	—	8	2	no	—
135	C₂³×C₁₃₇	#121	1	1	yes	characteristic
136	Q₈×C₁₃₇	—	4	2	no	—
137	D₄×C₁₃₇	—	4	4	no	—
138	D₄×C₁₃₇	—	4	4	no	—
139	D₄×C₁₃₇	—	4	2	no	—
140	D₄×C₁₃₇	—	4	4	no	—
141	D₄×C₁₃₇	—	4	2	no	—
142	D₄×C₁₃₇	—	4	4	no	—
143	D₄×C₁₃₇	—	4	2	no	—
144	D₄×C₁₃₇	—	8	2	no	—
145	D₄×C₁₃₇	—	8	2	no	—
146	D₄×C₁₃₇	—	8	2	no	—
147	D₄×C₁₃₇	—	8	2	no	—
148	D₄×C₁₃₇	—	8	2	no	—
149	D₄×C₁₃₇	—	8	2	no	—
150	D₄×C₁₃₇	—	8	2	no	—
151	D₄×C₁₃₇	—	8	1	no	—
152	D₄×C₁₃₇	—	8	1	no	—
153	D₄×C₁₃₇	—	8	1	no	—
154	D₄×C₁₃₇	—	8	1	no	—
155	C₂×C₄×C₁₃₇	—	2	2	no	—
156	C₂×C₄×C₁₃₇	—	2	2	no	—
157	C₂×C₄×C₁₃₇	—	4	1	no	—
158	C₂×C₄×C₁₃₇	—	8	1	no	—
159	C₂×C₄×C₁₃₇	—	8	1	no	—
160	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
161	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
162	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
163	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
164	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
165	C₂×C₄×C₁₃₇	#127	1	1	yes	characteristic
166	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
167	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
168	C₈×C₁₃₇	—	2	4	no	—
169	C₈×C₁₃₇	—	2	4	no	—
170	C₈×C₁₃₇	—	4	2	no	—
171	C₈×C₁₃₇	—	8	1	no	—
172	C₂²×C₁₃₇	—	2	1	no	—
173	C₂²×C₁₃₇	—	2	1	no	—
174	C₂²×C₁₃₇	—	8	2	no	—
175	C₂²×C₁₃₇	—	8	2	no	—
176	C₂²×C₁₃₇	—	8	1	no	—
177	C₂²×C₁₃₇	—	8	1	no	—
178	C₂²×C₁₃₇	—	8	2	no	—
179	C₂²×C₁₃₇	—	8	2	no	—
180	C₂²×C₁₃₇	—	8	1	no	—
181	C₂²×C₁₃₇	—	8	2	no	—
182	C₂²×C₁₃₇	—	8	2	no	—
183	C₂²×C₁₃₇	—	16	4	no	—
184	C₂²×C₁₃₇	—	16	4	no	—
185	C₂²×C₁₃₇	#392	1	1	yes	characteristic
186	C₂²×C₁₃₇	#459	1	2	yes	—
187	C₄×C₁₃₇	—	2	1	no	—
188	C₄×C₁₃₇	—	2	1	no	—
189	C₄×C₁₃₇	—	8	1	no	—
190	C₄×C₁₃₇	#447	1	2	yes	—
191	C₄×C₁₃₇	#453	1	2	yes	—
192	C₄×C₁₃₇	#472	1	2	yes	—
193	C₄×C₁₃₇	#493	1	1	yes	characteristic
194	C₄×C₁₃₇	#496	1	1	yes	characteristic
195	C₂×C₁₃₇	—	2	2	no	—
196	C₂×C₁₃₇	—	16	1	no	—
197	C₂×C₁₃₇	—	16	2	no	—
198	C₂×C₁₃₇	—	16	2	no	—
199	C₂×C₁₃₇	#2002	1	1	yes	characteristic
200	C₂×C₁₃₇	#2011	1	1	yes	characteristic
201	C₂×C₁₃₇	#2018	1	1	yes	characteristic
202	#10144	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₁₃₇	#10144	1	1	yes	characteristic, direct product factor, Sylow
204	#3205	C₂×C₁₃₇	1	1	yes	characteristic, complemented
205	#3151	C₂×C₁₃₇	1	1	yes	characteristic, complemented
206	C₂×#493	C₂×C₁₃₇	1	1	yes	characteristic, complemented
207	#1965	C₂×C₁₃₇	1	1	yes	characteristic, complemented
208	#1545	C₂×C₁₃₇	1	1	yes	characteristic, complemented
209	#1492	C₂×C₁₃₇	1	1	yes	characteristic, complemented
210	#1278	C₂×C₁₃₇	1	1	yes	characteristic, complemented
211	C₂×AGL(1,ℤ/8)	—	2	2	no	—
212	C₂²×D₈	—	2	2	no	—
213	#532	C₂²×C₁₃₇	1	1	yes	characteristic
214	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
215	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
216	#496	—	2	2	no	—
217	#493	—	2	2	no	—
218	#493	—	2	1	no	—
219	#493	—	2	1	no	—
220	#493	—	2	2	no	—
221	#492	—	2	1	no	—
222	#486	—	2	1	no	—
223	#459	—	2	2	no	—
224	#447	—	2	2	no	—
225	#431	C₂²×C₁₃₇	1	1	yes	characteristic
226	#423	C₂²×C₁₃₇	1	1	yes	characteristic
227	C₂×#100	—	2	2	no	—
228	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
230	#331	—	2	2	no	—
231	D₄⋊C₈	—	2	2	no	—
232	C₂×#41	—	2	1	no	—
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	—	2	1	no	—
235	C₂²×D₄	—	2	1	no	—
236	C₂²×D₄	—	2	1	no	—
237	C₂²×D₄	—	2	1	no	—
238	C₂²×D₄	D₄×C₁₃₇	1	2	yes	—
239	AGL(1,ℤ/8)	—	4	4	no	—
240	AGL(1,ℤ/8)	—	4	4	no	—
241	C₂×SD₁₆	—	2	4	no	—
242	C₂×D₈	—	2	8	no	—
243	C₂×D₈	—	2	4	no	—
244	C₂×D₈	—	2	4	no	—
245	C₂×D₈	—	4	8	no	—
246	C₂×M₁₆	—	2	1	no	—
247	C₂×M₁₆	D₄×C₁₃₇	1	2	yes	—
248	C₂²×C₈	—	2	1	no	—
249	C₄⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
250	#127	—	2	1	no	—
251	#127	—	2	1	no	—
252	#127	—	2	1	no	—
253	#127	—	2	1	no	—
254	#127	—	2	1	no	—
255	#127	—	2	1	no	—
256	#127	—	2	1	no	—
257	#127	D₄×C₁₃₇	1	2	yes	—
258	#127	D₄×C₁₃₇	1	1	yes	characteristic
259	#124	—	2	1	no	—
260	#121	—	2	1	no	—
261	#121	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	D₄×C₁₃₇	1	2	yes	—
268	#102	—	2	4	no	—
269	#100	—	4	4	no	—
270	C₂²⋊C₈	—	2	1	no	—
271	#97	—	2	1	no	—
272	C₄×C₈	—	2	1	no	—
273	C₄×C₈	—	2	1	no	—
274	C₄×C₈	—	2	1	no	—
275	C₄×C₈	D₄×C₁₃₇	1	2	yes	—
276	C₂⁴	—	2	2	no	—
277	C₂⁴	—	4	1	no	—
278	#41	—	4	2	no	—
279	#41	—	4	2	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	4	4	no	—
290	C₂×D₄	—	4	4	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	8	2	no	—
304	C₂×D₄	—	8	2	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
308	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
309	SD₁₆	—	4	8	no	—
310	D₈	—	4	16	no	—
311	D₈	—	4	8	no	—
312	D₈	—	8	4	no	—
313	M₁₆	—	2	2	no	—
314	M₁₆	—	4	2	no	—
315	M₁₆	D₈×C₁₃₇	1	4	yes	complemented
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	4	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₂²⋊C₄	—	4	1	no	—
324	C₂²⋊C₄	—	4	1	no	—
325	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
326	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
327	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
328	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
329	C₂³	—	4	1	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	4	no	—
333	C₂³	—	8	2	no	—
334	C₂³	—	8	2	no	—
335	C₂³	—	8	2	no	—
336	C₂³	—	8	2	no	—
337	C₂³	—	8	2	no	—
338	C₂³	#121×C₁₃₇	1	1	yes	characteristic
339	Q₈	—	4	2	no	—
340	D₄	—	4	4	no	—
341	D₄	—	4	4	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	4	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	4	no	—
346	D₄	—	4	2	no	—
347	D₄	—	8	2	no	—
348	D₄	—	8	2	no	—
349	D₄	—	8	2	no	—
350	D₄	—	8	2	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	1	no	—
355	D₄	—	8	1	no	—
356	D₄	—	8	1	no	—
357	D₄	—	8	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	8	1	no	—
362	C₂×C₄	—	8	1	no	—
363	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
364	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
365	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
366	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
367	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
368	C₂×C₄	#127×C₁₃₇	1	1	yes	characteristic
369	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
370	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
371	C₈	—	2	4	no	—
372	C₈	—	2	4	no	—
373	C₈	—	4	2	no	—
374	C₈	—	8	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	8	1	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	1	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	16	4	no	—
387	C₂²	—	16	4	no	—
388	C₂²	#392×C₁₃₇	1	1	yes	characteristic
389	C₂²	#459×C₁₃₇	1	2	yes	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	8	1	no	—
393	C₄	#447×C₁₃₇	1	2	yes	—
394	C₄	#453×C₁₃₇	1	2	yes	—
395	C₄	#472×C₁₃₇	1	2	yes	—
396	C₄	#493×C₁₃₇	1	1	yes	characteristic
397	C₄	#496×C₁₃₇	1	1	yes	characteristic
398	C₂	—	2	2	no	—
399	C₂	—	16	2	no	—
400	C₂	—	16	2	no	—
401	C₂	—	16	1	no	—
402	C₂	#2002×C₁₃₇	1	1	yes	characteristic
403	C₂	#2011×C₁₃₇	1	1	yes	characteristic
404	C₂	#2018×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₇
LCS	G ▷ C₂×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. #3205×C₁₃₇	C₂	semidirect
2. #3151×C₁₃₇	C₂	semidirect
3. C₂×#493×C₁₃₇	C₂	semidirect
4. #1965×C₁₃₇	C₂	semidirect
5. #1545×C₁₃₇	C₂	semidirect
6. #1492×C₁₃₇	C₂	semidirect
7. #1278×C₁₃₇	C₂	semidirect
112. M₁₆×C₁₃₇	D₈	semidirect
202. #10144	C₁₃₇	direct (N × H)
203. C₁₃₇	#10144	direct (N × H)
204. #3205	C₂×C₁₃₇	semidirect
205. #3151	C₂×C₁₃₇	semidirect
206. C₂×#493	C₂×C₁₃₇	semidirect
207. #1965	C₂×C₁₃₇	semidirect
208. #1545	C₂×C₁₃₇	semidirect
209. #1492	C₂×C₁₃₇	semidirect
210. #1278	C₂×C₁₃₇	semidirect
315. M₁₆	D₈×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3205×C₁₃₇	2
#3151×C₁₃₇	2
C₂×#493×C₁₃₇	2
#1965×C₁₃₇	2
#1545×C₁₃₇	2
#1492×C₁₃₇	2
#1278×C₁₃₇	2
#10144	137

Subgroups — C137×#10144 #46859530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#10144 #46859530