Subgroups — C₁₂₇×#19629 #44583302

Order 32512.

1050 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₂₇×#3205	C₂	1	2	yes	maximal, complemented
2	C₁₂₇×#3169	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₂₇×#3151	C₂	1	2	yes	maximal, complemented
4	C₂×#493×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₂₇×#1721	C₂	1	4	yes	maximal, complemented
6	C₁₂₇×#1712	C₂	1	2	yes	maximal, complemented
7	C₁₂₇×#1706	C₂	1	2	yes	maximal, complemented
8	C₈×M₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×AGL(1,ℤ/8)×C₁₂₇	—	2	4	no	—
10	C₂²×D₈×C₁₂₇	—	2	2	no	—
11	#532×C₁₂₇	C₂²	1	2	yes	—
12	C₂×#127×C₁₂₇	C₂²	1	2	yes	—
13	#500×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
14	#496×C₁₂₇	—	2	4	no	—
15	#493×C₁₂₇	—	2	2	no	—
16	#493×C₁₂₇	C₂²	1	2	yes	—
17	#493×C₁₂₇	C₂²	1	2	yes	—
18	#493×C₁₂₇	C₂²	1	4	yes	complemented
19	#493×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
20	#493×C₁₂₇	C₂²	1	4	yes	complemented
21	#492×C₁₂₇	C₂²	1	4	yes	complemented
22	#486×C₁₂₇	C₂²	1	2	yes	complemented
23	#486×C₁₂₇	C₂²	1	4	yes	complemented
24	#466×C₁₂₇	—	2	2	no	—
25	#459×C₁₂₇	—	2	4	no	—
26	#447×C₁₂₇	—	2	4	no	—
27	C₄×D₈×C₁₂₇	—	2	2	no	—
28	#431×C₁₂₇	C₂²	1	1	yes	characteristic
29	C₄×M₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
31	#322×C₁₂₇	C₂²	1	2	yes	complemented
32	C₈²×C₁₂₇	C₂²	1	2	yes	complemented
33	C₂×#41×C₁₂₇	—	2	2	no	—
34	C₂²×D₄×C₁₂₇	—	2	2	no	—
35	C₂²×D₄×C₁₂₇	—	2	2	no	—
36	C₂²×D₄×C₁₂₇	—	2	2	no	—
37	AGL(1,ℤ/8)×C₁₂₇	—	4	16	no	—
38	C₂×SD₁₆×C₁₂₇	—	2	8	no	—
39	C₂×D₈×C₁₂₇	—	2	8	no	—
40	C₂×D₈×C₁₂₇	—	2	4	no	—
41	C₂×D₈×C₁₂₇	—	2	4	no	—
42	C₂×D₈×C₁₂₇	—	2	2	no	—
43	C₂×D₈×C₁₂₇	—	2	8	no	—
44	C₂×D₈×C₁₂₇	—	4	8	no	—
45	C₂×M₁₆×C₁₂₇	D₄	1	2	yes	—
46	C₂²×C₈×C₁₂₇	D₄	1	2	yes	—
47	C₄⋊Q₈×C₁₂₇	C₂³	1	2	yes	—
48	#127×C₁₂₇	—	2	2	no	—
49	#127×C₁₂₇	—	2	2	no	—
50	#127×C₁₂₇	—	2	2	no	—
51	#127×C₁₂₇	C₂³	1	4	yes	—
52	#127×C₁₂₇	C₂³	1	2	yes	—
53	#124×C₁₂₇	—	2	2	no	—
54	#121×C₁₂₇	—	2	2	no	—
55	#121×C₁₂₇	—	2	2	no	—
56	C₄×D₄×C₁₂₇	—	2	2	no	—
57	C₄×D₄×C₁₂₇	—	2	2	no	—
58	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
59	#107×C₁₂₇	—	2	2	no	—
60	C₄⋊C₈×C₁₂₇	D₄	1	2	yes	—
61	#102×C₁₂₇	—	2	4	no	—
62	#102×C₁₂₇	—	2	8	no	—
63	C₂²⋊C₈×C₁₂₇	D₄	1	2	yes	—
64	#97×C₁₂₇	D₄	1	2	yes	—
65	C₄×C₈×C₁₂₇	D₄	1	2	yes	—
66	C₄×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
67	C₄×C₈×C₁₂₇	C₂³	1	2	yes	—
68	C₄×C₈×C₁₂₇	C₂³	1	2	yes	—
69	C₄×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
70	C₂⁴×C₁₂₇	—	4	2	no	—
71	#41×C₁₂₇	—	4	8	no	—
72	C₂×Q₈×C₁₂₇	—	2	2	no	—
73	C₂×D₄×C₁₂₇	—	2	2	no	—
74	C₂×D₄×C₁₂₇	—	2	4	no	—
75	C₂×D₄×C₁₂₇	—	2	2	no	—
76	C₂×D₄×C₁₂₇	—	2	2	no	—
77	C₂×D₄×C₁₂₇	—	2	4	no	—
78	C₂×D₄×C₁₂₇	—	2	4	no	—
79	C₂×D₄×C₁₂₇	—	4	8	no	—
80	C₂×D₄×C₁₂₇	—	4	2	no	—
81	C₂×D₄×C₁₂₇	—	4	2	no	—
82	C₂×D₄×C₁₂₇	—	4	2	no	—
83	C₂×D₄×C₁₂₇	—	4	2	no	—
84	C₂×D₄×C₁₂₇	—	4	8	no	—
85	C₂×D₄×C₁₂₇	—	8	4	no	—
86	C₂²×C₄×C₁₂₇	—	4	2	no	—
87	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
90	SD₁₆×C₁₂₇	—	4	16	no	—
91	D₈×C₁₂₇	—	4	8	no	—
92	D₈×C₁₂₇	—	4	16	no	—
93	D₈×C₁₂₇	—	4	4	no	—
94	D₈×C₁₂₇	—	4	8	no	—
95	D₈×C₁₂₇	—	8	8	no	—
96	M₁₆×C₁₂₇	D₈	1	8	yes	complemented
97	C₂×C₈×C₁₂₇	—	2	4	no	—
98	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
99	C₂×C₈×C₁₂₇	C₂×D₄	1	4	yes	—
100	C₂×C₈×C₁₂₇	C₂×D₄	1	4	yes	—
101	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
102	C₄⋊C₄×C₁₂₇	—	2	2	no	—
103	C₄⋊C₄×C₁₂₇	—	2	2	no	—
104	C₂²⋊C₄×C₁₂₇	—	4	2	no	—
105	C₂²⋊C₄×C₁₂₇	—	4	2	no	—
106	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₂₇	C₂⁴	1	1	yes	characteristic
110	C₂³×C₁₂₇	—	4	2	no	—
111	C₂³×C₁₂₇	—	4	4	no	—
112	C₂³×C₁₂₇	—	8	4	no	—
113	C₂³×C₁₂₇	—	8	4	no	—
114	C₂³×C₁₂₇	—	8	4	no	—
115	C₂³×C₁₂₇	#127	1	1	yes	characteristic
116	Q₈×C₁₂₇	—	4	4	no	—
117	D₄×C₁₂₇	—	4	4	no	—
118	D₄×C₁₂₇	—	4	8	no	—
119	D₄×C₁₂₇	—	4	8	no	—
120	D₄×C₁₂₇	—	4	4	no	—
121	D₄×C₁₂₇	—	4	4	no	—
122	D₄×C₁₂₇	—	4	8	no	—
123	D₄×C₁₂₇	—	8	4	no	—
124	D₄×C₁₂₇	—	8	4	no	—
125	D₄×C₁₂₇	—	8	4	no	—
126	D₄×C₁₂₇	—	8	4	no	—
127	C₂×C₄×C₁₂₇	—	2	2	no	—
128	C₂×C₄×C₁₂₇	—	2	2	no	—
129	C₂×C₄×C₁₂₇	—	4	2	no	—
130	C₂×C₄×C₁₂₇	—	8	4	no	—
131	C₂×C₄×C₁₂₇	#127	1	1	yes	characteristic
132	C₂×C₄×C₁₂₇	#127	1	1	yes	characteristic
133	C₂×C₄×C₁₂₇	#127	1	1	yes	characteristic
134	C₂×C₄×C₁₂₇	C₂×D₈	1	4	yes	—
135	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
136	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
138	C₈×C₁₂₇	—	2	2	no	—
139	C₈×C₁₂₇	—	2	4	no	—
140	C₈×C₁₂₇	C₂×D₈	1	8	yes	complemented
141	C₈×C₁₂₇	AGL(1,ℤ/8)	1	4	yes	complemented
142	C₂²×C₁₂₇	—	2	1	no	—
143	C₂²×C₁₂₇	—	2	1	no	—
144	C₂²×C₁₂₇	—	8	2	no	—
145	C₂²×C₁₂₇	—	8	4	no	—
146	C₂²×C₁₂₇	—	8	4	no	—
147	C₂²×C₁₂₇	—	8	2	no	—
148	C₂²×C₁₂₇	—	8	4	no	—
149	C₂²×C₁₂₇	—	8	2	no	—
150	C₂²×C₁₂₇	—	16	8	no	—
151	C₂²×C₁₂₇	#493	1	2	yes	—
152	C₂²×C₁₂₇	C₂×#127	1	1	yes	characteristic
153	C₄×C₁₂₇	—	2	1	no	—
154	C₄×C₁₂₇	—	2	1	no	—
155	C₄×C₁₂₇	—	8	2	no	—
156	C₄×C₁₂₇	#493	1	2	yes	—
157	C₄×C₁₂₇	C₂²×D₈	1	2	yes	—
158	C₄×C₁₂₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
159	C₄×C₁₂₇	#576	1	2	yes	—
160	#19629	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂×C₁₂₇	—	2	2	no	—
162	C₂×C₁₂₇	—	16	2	no	—
163	C₂×C₁₂₇	—	16	4	no	—
164	C₂×C₁₂₇	C₂×#493	1	1	yes	characteristic
165	C₂×C₁₂₇	#3151	1	1	yes	characteristic
166	C₂×C₁₂₇	#3155	1	1	yes	characteristic
167	#3205	C₂×C₁₂₇	1	2	yes	complemented
168	#3169	C₂×C₁₂₇	1	1	yes	characteristic, complemented
169	#3151	C₂×C₁₂₇	1	2	yes	complemented
170	C₂×#493	C₂×C₁₂₇	1	1	yes	characteristic, complemented
171	#1721	C₂×C₁₂₇	1	4	yes	complemented
172	#1712	C₂×C₁₂₇	1	2	yes	complemented
173	#1706	C₂×C₁₂₇	1	2	yes	complemented
174	C₈×M₁₆	C₂×C₁₂₇	1	1	yes	characteristic, complemented
175	C₁₂₇	#19629	1	1	yes	characteristic, direct product factor, Sylow
176	C₂×AGL(1,ℤ/8)	—	2	4	no	—
177	C₂²×D₈	—	2	2	no	—
178	#532	C₂²×C₁₂₇	1	2	yes	—
179	C₂×#127	C₂²×C₁₂₇	1	2	yes	—
180	#500	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
181	#496	—	2	4	no	—
182	#493	—	2	2	no	—
183	#493	C₂²×C₁₂₇	1	2	yes	—
184	#493	C₂²×C₁₂₇	1	2	yes	—
185	#493	C₂²×C₁₂₇	1	4	yes	complemented
186	#493	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
187	#493	C₂²×C₁₂₇	1	4	yes	complemented
188	#492	C₂²×C₁₂₇	1	4	yes	complemented
189	#486	C₂²×C₁₂₇	1	2	yes	complemented
190	#486	C₂²×C₁₂₇	1	4	yes	complemented
191	#466	—	2	2	no	—
192	#459	—	2	4	no	—
193	#447	—	2	4	no	—
194	C₄×D₈	—	2	2	no	—
195	#431	C₂²×C₁₂₇	1	1	yes	characteristic
196	C₄×M₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
197	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
198	#322	C₂²×C₁₂₇	1	2	yes	complemented
199	C₈²	C₂²×C₁₂₇	1	2	yes	complemented
200	C₂×#41	—	2	2	no	—
201	C₂²×D₄	—	2	2	no	—
202	C₂²×D₄	—	2	2	no	—
203	C₂²×D₄	—	2	2	no	—
204	AGL(1,ℤ/8)	—	4	16	no	—
205	C₂×SD₁₆	—	2	8	no	—
206	C₂×D₈	—	2	4	no	—
207	C₂×D₈	—	2	4	no	—
208	C₂×D₈	—	2	8	no	—
209	C₂×D₈	—	2	2	no	—
210	C₂×D₈	—	2	8	no	—
211	C₂×D₈	—	4	8	no	—
212	C₂×M₁₆	D₄×C₁₂₇	1	2	yes	—
213	C₂²×C₈	D₄×C₁₂₇	1	2	yes	—
214	C₄⋊Q₈	C₂³×C₁₂₇	1	2	yes	—
215	#127	—	2	2	no	—
216	#127	—	2	2	no	—
217	#127	—	2	2	no	—
218	#127	C₂³×C₁₂₇	1	4	yes	—
219	#127	C₂³×C₁₂₇	1	2	yes	—
220	#124	—	2	2	no	—
221	#121	—	2	2	no	—
222	#121	—	2	2	no	—
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	2	no	—
225	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
226	#107	—	2	2	no	—
227	C₄⋊C₈	D₄×C₁₂₇	1	2	yes	—
228	#102	—	2	4	no	—
229	#102	—	2	8	no	—
230	C₂²⋊C₈	D₄×C₁₂₇	1	2	yes	—
231	#97	D₄×C₁₂₇	1	2	yes	—
232	C₄×C₈	D₄×C₁₂₇	1	2	yes	—
233	C₄×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
234	C₄×C₈	C₂³×C₁₂₇	1	2	yes	—
235	C₄×C₈	C₂³×C₁₂₇	1	2	yes	—
236	C₄×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
237	C₂⁴	—	4	2	no	—
238	#41	—	4	8	no	—
239	C₂×Q₈	—	2	2	no	—
240	C₂×D₄	—	2	2	no	—
241	C₂×D₄	—	2	4	no	—
242	C₂×D₄	—	2	2	no	—
243	C₂×D₄	—	2	2	no	—
244	C₂×D₄	—	2	4	no	—
245	C₂×D₄	—	2	4	no	—
246	C₂×D₄	—	4	8	no	—
247	C₂×D₄	—	4	2	no	—
248	C₂×D₄	—	4	2	no	—
249	C₂×D₄	—	4	2	no	—
250	C₂×D₄	—	4	2	no	—
251	C₂×D₄	—	4	8	no	—
252	C₂×D₄	—	8	4	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
255	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
256	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
257	SD₁₆	—	4	16	no	—
258	D₈	—	4	8	no	—
259	D₈	—	4	16	no	—
260	D₈	—	4	4	no	—
261	D₈	—	4	8	no	—
262	D₈	—	8	8	no	—
263	M₁₆	D₈×C₁₂₇	1	8	yes	complemented
264	C₂×C₈	—	2	4	no	—
265	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
266	C₂×C₈	C₂×D₄×C₁₂₇	1	4	yes	—
267	C₂×C₈	C₂×D₄×C₁₂₇	1	4	yes	—
268	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₂²⋊C₄	—	4	2	no	—
272	C₂²⋊C₄	—	4	2	no	—
273	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
274	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
275	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
276	C₄²	C₂⁴×C₁₂₇	1	1	yes	characteristic
277	C₂³	—	4	2	no	—
278	C₂³	—	4	4	no	—
279	C₂³	—	8	4	no	—
280	C₂³	—	8	4	no	—
281	C₂³	—	8	4	no	—
282	C₂³	#127×C₁₂₇	1	1	yes	characteristic
283	Q₈	—	4	4	no	—
284	D₄	—	4	4	no	—
285	D₄	—	4	8	no	—
286	D₄	—	4	8	no	—
287	D₄	—	4	4	no	—
288	D₄	—	4	4	no	—
289	D₄	—	4	8	no	—
290	D₄	—	8	4	no	—
291	D₄	—	8	4	no	—
292	D₄	—	8	4	no	—
293	D₄	—	8	4	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	4	2	no	—
297	C₂×C₄	—	8	4	no	—
298	C₂×C₄	#127×C₁₂₇	1	1	yes	characteristic
299	C₂×C₄	#127×C₁₂₇	1	1	yes	characteristic
300	C₂×C₄	#127×C₁₂₇	1	1	yes	characteristic
301	C₂×C₄	C₂×D₈×C₁₂₇	1	4	yes	—
302	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
303	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
304	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
305	C₈	—	2	2	no	—
306	C₈	—	2	4	no	—
307	C₈	C₂×D₈×C₁₂₇	1	8	yes	complemented
308	C₈	AGL(1,ℤ/8)×C₁₂₇	1	4	yes	complemented
309	C₂²	—	2	1	no	—
310	C₂²	—	2	1	no	—
311	C₂²	—	8	2	no	—
312	C₂²	—	8	4	no	—
313	C₂²	—	8	4	no	—
314	C₂²	—	8	2	no	—
315	C₂²	—	8	4	no	—
316	C₂²	—	8	2	no	—
317	C₂²	—	16	8	no	—
318	C₂²	#493×C₁₂₇	1	2	yes	—
319	C₂²	C₂×#127×C₁₂₇	1	1	yes	characteristic
320	C₄	—	2	1	no	—
321	C₄	—	2	1	no	—
322	C₄	—	8	2	no	—
323	C₄	#493×C₁₂₇	1	2	yes	—
324	C₄	C₂²×D₈×C₁₂₇	1	2	yes	—
325	C₄	C₂×AGL(1,ℤ/8)×C₁₂₇	1	2	yes	—
326	C₄	#576×C₁₂₇	1	2	yes	—
327	C₂	—	2	2	no	—
328	C₂	—	16	4	no	—
329	C₂	—	16	2	no	—
330	C₂	C₂×#493×C₁₂₇	1	1	yes	characteristic
331	C₂	C₁₂₇×#3151	1	1	yes	characteristic
332	C₂	C₁₂₇×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₂₇	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₂₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₂₇ ◁ C₂×C₄²×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₂₇×#3205	C₂	semidirect
2. C₁₂₇×#3169	C₂	semidirect
3. C₁₂₇×#3151	C₂	semidirect
4. C₂×#493×C₁₂₇	C₂	semidirect
5. C₁₂₇×#1721	C₂	semidirect
6. C₁₂₇×#1712	C₂	semidirect
7. C₁₂₇×#1706	C₂	semidirect
8. C₈×M₁₆×C₁₂₇	C₂	semidirect
13. #500×C₁₂₇	C₂²	semidirect
18. #493×C₁₂₇	C₂²	semidirect
19. #493×C₁₂₇	C₂²	semidirect
20. #493×C₁₂₇	C₂²	semidirect
21. #492×C₁₂₇	C₂²	semidirect
22. #486×C₁₂₇	C₂²	semidirect
23. #486×C₁₂₇	C₂²	semidirect
31. #322×C₁₂₇	C₂²	semidirect
32. C₈²×C₁₂₇	C₂²	semidirect
96. M₁₆×C₁₂₇	D₈	semidirect
140. C₈×C₁₂₇	C₂×D₈	semidirect
141. C₈×C₁₂₇	AGL(1,ℤ/8)	semidirect
160. #19629	C₁₂₇	direct (N × H)
167. #3205	C₂×C₁₂₇	semidirect
168. #3169	C₂×C₁₂₇	semidirect
169. #3151	C₂×C₁₂₇	semidirect
170. C₂×#493	C₂×C₁₂₇	semidirect
171. #1721	C₂×C₁₂₇	semidirect
172. #1712	C₂×C₁₂₇	semidirect
173. #1706	C₂×C₁₂₇	semidirect
174. C₈×M₁₆	C₂×C₁₂₇	semidirect
175. C₁₂₇	#19629	direct (N × H)
180. #500	C₂²×C₁₂₇	semidirect
185. #493	C₂²×C₁₂₇	semidirect
186. #493	C₂²×C₁₂₇	semidirect
187. #493	C₂²×C₁₂₇	semidirect
188. #492	C₂²×C₁₂₇	semidirect
189. #486	C₂²×C₁₂₇	semidirect
190. #486	C₂²×C₁₂₇	semidirect
198. #322	C₂²×C₁₂₇	semidirect
199. C₈²	C₂²×C₁₂₇	semidirect
263. M₁₆	D₈×C₁₂₇	semidirect
307. C₈	C₂×D₈×C₁₂₇	semidirect
308. C₈	AGL(1,ℤ/8)×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₂₇×#3205	2
C₁₂₇×#3169	2
C₁₂₇×#3151	2
C₂×#493×C₁₂₇	2
C₁₂₇×#1721	2
C₁₂₇×#1712	2
C₁₂₇×#1706	2
C₈×M₁₆×C₁₂₇	2
#19629	127

Subgroups — C127×#19629 #44583302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#19629 #44583302