Subgroups — C₁₂₇×#19647 #44583320

Order 32512.

840 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₂₇×#3207	C₂	1	2	yes	maximal, complemented
2	C₁₂₇×#3184	C₂	1	2	yes	maximal, complemented
3	C₁₂₇×#3169	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₂₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₂₇×#1717	C₂	1	2	yes	maximal, complemented
6	C₁₂₇×#1715	C₂	1	2	yes	maximal, complemented
7	C₁₂₇×#1712	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₂₇×#1709	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₂₇×#1707	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₂₇×#1706	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₂₇	—	2	2	no	—
13	#532×C₁₂₇	C₂²	1	2	yes	—
14	#532×C₁₂₇	C₂²	1	2	yes	—
15	#500×C₁₂₇	C₂²	1	1	yes	characteristic
16	#498×C₁₂₇	C₂²	1	2	yes	—
17	#495×C₁₂₇	—	2	2	no	—
18	#494×C₁₂₇	C₂²	1	1	yes	characteristic
19	#493×C₁₂₇	C₂²	1	1	yes	characteristic
20	#493×C₁₂₇	C₂²	1	1	yes	characteristic
21	#493×C₁₂₇	C₂²	1	2	yes	—
22	#493×C₁₂₇	C₂²	1	2	yes	—
23	#492×C₁₂₇	C₂²	1	2	yes	—
24	#492×C₁₂₇	C₂²	1	2	yes	—
25	#487×C₁₂₇	C₂²	1	2	yes	—
26	#486×C₁₂₇	C₂²	1	2	yes	—
27	#486×C₁₂₇	C₂²	1	2	yes	—
28	#486×C₁₂₇	C₂²	1	2	yes	—
29	#486×C₁₂₇	C₂²	1	2	yes	—
30	#469×C₁₂₇	—	2	4	no	—
31	#466×C₁₂₇	—	2	2	no	—
32	#463×C₁₂₇	—	2	4	no	—
33	#449×C₁₂₇	—	2	4	no	—
34	#442×C₁₂₇	—	2	4	no	—
35	C₄×D₈×C₁₂₇	—	2	2	no	—
36	#431×C₁₂₇	C₂²	1	1	yes	characteristic
37	C₄×M₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
39	#322×C₁₂₇	C₂²	1	1	yes	characteristic
40	#322×C₁₂₇	C₂²	1	1	yes	characteristic
41	C₈²×C₁₂₇	C₂²	1	1	yes	characteristic
42	C₈²×C₁₂₇	C₂²	1	1	yes	characteristic
43	C₂×#41×C₁₂₇	—	2	2	no	—
44	C₂×#41×C₁₂₇	—	2	2	no	—
45	#135×C₁₂₇	—	4	8	no	—
46	C₂×Q₁₆×C₁₂₇	—	2	2	no	—
47	C₂×SD₁₆×C₁₂₇	—	2	4	no	—
48	C₂×SD₁₆×C₁₂₇	—	2	4	no	—
49	C₂×D₈×C₁₂₇	—	2	2	no	—
50	C₂×D₈×C₁₂₇	—	2	2	no	—
51	C₂×D₈×C₁₂₇	—	2	4	no	—
52	C₂×D₈×C₁₂₇	—	2	4	no	—
53	C₂×M₁₆×C₁₂₇	D₄	1	2	yes	—
54	C₂²×C₈×C₁₂₇	D₄	1	2	yes	—
55	C₄⋊Q₈×C₁₂₇	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₁₂₇	C₂³	1	2	yes	—
57	#127×C₁₂₇	C₂³	1	2	yes	—
58	#127×C₁₂₇	C₂³	1	2	yes	—
59	#124×C₁₂₇	—	2	2	no	—
60	#124×C₁₂₇	—	2	2	no	—
61	#121×C₁₂₇	—	2	2	no	—
62	#121×C₁₂₇	—	2	2	no	—
63	#121×C₁₂₇	—	2	2	no	—
64	#121×C₁₂₇	—	2	2	no	—
65	C₄×D₄×C₁₂₇	—	2	2	no	—
66	C₄×D₄×C₁₂₇	—	2	2	no	—
67	C₄×D₄×C₁₂₇	—	2	2	no	—
68	C₄×D₄×C₁₂₇	—	2	2	no	—
69	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
70	#107×C₁₂₇	—	2	2	no	—
71	#106×C₁₂₇	—	2	4	no	—
72	C₄⋊C₈×C₁₂₇	D₄	1	2	yes	—
73	#103×C₁₂₇	—	2	4	no	—
74	#102×C₁₂₇	—	2	4	no	—
75	#102×C₁₂₇	—	2	4	no	—
76	#102×C₁₂₇	—	2	4	no	—
77	#102×C₁₂₇	—	2	4	no	—
78	C₂²⋊C₈×C₁₂₇	D₄	1	2	yes	—
79	#97×C₁₂₇	D₄	1	2	yes	—
80	C₄×C₈×C₁₂₇	D₄	1	2	yes	—
81	C₄×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
82	C₄×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
83	C₄×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
84	C₄×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
87	#41×C₁₂₇	—	4	8	no	—
88	#41×C₁₂₇	—	8	4	no	—
89	C₂×Q₈×C₁₂₇	—	2	2	no	—
90	C₂×Q₈×C₁₂₇	—	2	2	no	—
91	C₂×D₄×C₁₂₇	—	2	2	no	—
92	C₂×D₄×C₁₂₇	—	2	2	no	—
93	C₂×D₄×C₁₂₇	—	2	2	no	—
94	C₂×D₄×C₁₂₇	—	2	2	no	—
95	C₂×D₄×C₁₂₇	—	2	2	no	—
96	C₂×D₄×C₁₂₇	—	2	2	no	—
97	C₂×D₄×C₁₂₇	—	4	2	no	—
98	C₂×D₄×C₁₂₇	—	4	2	no	—
99	C₂²×C₄×C₁₂₇	—	4	2	no	—
100	C₂²×C₄×C₁₂₇	—	4	2	no	—
101	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
104	Q₁₆×C₁₂₇	—	4	4	no	—
105	SD₁₆×C₁₂₇	—	4	8	no	—
106	SD₁₆×C₁₂₇	—	8	4	no	—
107	D₈×C₁₂₇	—	4	8	no	—
108	D₈×C₁₂₇	—	4	4	no	—
109	D₈×C₁₂₇	—	4	4	no	—
110	D₈×C₁₂₇	—	8	4	no	—
111	M₁₆×C₁₂₇	—	2	4	no	—
112	C₂×C₈×C₁₂₇	—	2	4	no	—
113	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
119	C₄⋊C₄×C₁₂₇	—	2	2	no	—
120	C₄⋊C₄×C₁₂₇	—	2	2	no	—
121	C₄⋊C₄×C₁₂₇	—	2	2	no	—
122	C₄⋊C₄×C₁₂₇	—	2	2	no	—
123	C₂²⋊C₄×C₁₂₇	—	4	2	no	—
124	C₂²⋊C₄×C₁₂₇	—	4	2	no	—
125	C₂²⋊C₄×C₁₂₇	—	4	2	no	—
126	C₂²⋊C₄×C₁₂₇	—	4	2	no	—
127	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₂₇	C₂⁴	1	1	yes	characteristic
131	C₂³×C₁₂₇	—	4	2	no	—
132	C₂³×C₁₂₇	—	4	2	no	—
133	C₂³×C₁₂₇	#127	1	1	yes	characteristic
134	Q₈×C₁₂₇	—	4	4	no	—
135	Q₈×C₁₂₇	—	4	4	no	—
136	D₄×C₁₂₇	—	4	4	no	—
137	D₄×C₁₂₇	—	4	4	no	—
138	D₄×C₁₂₇	—	4	4	no	—
139	D₄×C₁₂₇	—	4	4	no	—
140	D₄×C₁₂₇	—	4	4	no	—
141	D₄×C₁₂₇	—	4	4	no	—
142	D₄×C₁₂₇	—	8	4	no	—
143	D₄×C₁₂₇	—	8	4	no	—
144	C₂×C₄×C₁₂₇	—	2	2	no	—
145	C₂×C₄×C₁₂₇	—	2	2	no	—
146	C₂×C₄×C₁₂₇	—	2	2	no	—
147	C₂×C₄×C₁₂₇	—	4	2	no	—
148	C₂×C₄×C₁₂₇	—	4	2	no	—
149	C₂×C₄×C₁₂₇	—	8	4	no	—
150	C₂×C₄×C₁₂₇	—	8	4	no	—
151	C₂×C₄×C₁₂₇	#127	1	1	yes	characteristic
152	C₂×C₄×C₁₂₇	#127	1	1	yes	characteristic
153	C₂×C₄×C₁₂₇	#127	1	1	yes	characteristic
154	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
157	C₈×C₁₂₇	—	2	2	no	—
158	C₈×C₁₂₇	—	2	2	no	—
159	C₈×C₁₂₇	—	2	2	no	—
160	C₈×C₁₂₇	—	2	2	no	—
161	C₈×C₁₂₇	#135	1	4	yes	complemented
162	C₈×C₁₂₇	AGL(1,ℤ/8)	1	4	yes	—
163	C₂²×C₁₂₇	—	2	1	no	—
164	C₂²×C₁₂₇	—	2	1	no	—
165	C₂²×C₁₂₇	—	2	1	no	—
166	C₂²×C₁₂₇	—	8	2	no	—
167	C₂²×C₁₂₇	—	8	2	no	—
168	C₂²×C₁₂₇	—	8	2	no	—
169	C₂²×C₁₂₇	—	8	2	no	—
170	C₂²×C₁₂₇	—	8	2	no	—
171	C₂²×C₁₂₇	—	8	2	no	—
172	C₂²×C₁₂₇	C₂×#127	1	1	yes	characteristic
173	C₄×C₁₂₇	—	2	1	no	—
174	C₄×C₁₂₇	—	2	1	no	—
175	C₄×C₁₂₇	—	2	1	no	—
176	C₄×C₁₂₇	—	8	2	no	—
177	C₄×C₁₂₇	—	8	2	no	—
178	C₄×C₁₂₇	C₂×#135	1	2	yes	—
179	C₄×C₁₂₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
180	C₄×C₁₂₇	#576	1	2	yes	—
181	#19647	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂×C₁₂₇	—	4	1	no	—
183	C₂×C₁₂₇	—	16	2	no	—
184	C₂×C₁₂₇	—	16	2	no	—
185	C₂×C₁₂₇	#3147	1	1	yes	characteristic
186	C₂×C₁₂₇	#3151	1	1	yes	characteristic
187	C₂×C₁₂₇	#3155	1	1	yes	characteristic
188	#3207	C₂×C₁₂₇	1	2	yes	complemented
189	#3184	C₂×C₁₂₇	1	2	yes	complemented
190	#3169	C₂×C₁₂₇	1	1	yes	characteristic, complemented
191	#3147	C₂×C₁₂₇	1	1	yes	characteristic, complemented
192	#1717	C₂×C₁₂₇	1	2	yes	complemented
193	#1715	C₂×C₁₂₇	1	2	yes	complemented
194	#1712	C₂×C₁₂₇	1	1	yes	characteristic, complemented
195	#1709	C₂×C₁₂₇	1	1	yes	characteristic, complemented
196	#1707	C₂×C₁₂₇	1	1	yes	characteristic, complemented
197	#1706	C₂×C₁₂₇	1	1	yes	characteristic, complemented
198	C₈×M₁₆	C₂×C₁₂₇	1	1	yes	characteristic, complemented
199	C₁₂₇	#19647	1	1	yes	characteristic, direct product factor, Sylow
200	C₂×#135	—	2	2	no	—
201	#532	C₂²×C₁₂₇	1	2	yes	—
202	#532	C₂²×C₁₂₇	1	2	yes	—
203	#500	C₂²×C₁₂₇	1	1	yes	characteristic
204	#498	C₂²×C₁₂₇	1	2	yes	—
205	#495	—	2	2	no	—
206	#494	C₂²×C₁₂₇	1	1	yes	characteristic
207	#493	C₂²×C₁₂₇	1	1	yes	characteristic
208	#493	C₂²×C₁₂₇	1	1	yes	characteristic
209	#493	C₂²×C₁₂₇	1	2	yes	—
210	#493	C₂²×C₁₂₇	1	2	yes	—
211	#492	C₂²×C₁₂₇	1	2	yes	—
212	#492	C₂²×C₁₂₇	1	2	yes	—
213	#487	C₂²×C₁₂₇	1	2	yes	—
214	#486	C₂²×C₁₂₇	1	2	yes	—
215	#486	C₂²×C₁₂₇	1	2	yes	—
216	#486	C₂²×C₁₂₇	1	2	yes	—
217	#486	C₂²×C₁₂₇	1	2	yes	—
218	#469	—	2	4	no	—
219	#466	—	2	2	no	—
220	#463	—	2	4	no	—
221	#449	—	2	4	no	—
222	#442	—	2	4	no	—
223	C₄×D₈	—	2	2	no	—
224	#431	C₂²×C₁₂₇	1	1	yes	characteristic
225	C₄×M₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
226	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
227	#322	C₂²×C₁₂₇	1	1	yes	characteristic
228	#322	C₂²×C₁₂₇	1	1	yes	characteristic
229	C₈²	C₂²×C₁₂₇	1	1	yes	characteristic
230	C₈²	C₂²×C₁₂₇	1	1	yes	characteristic
231	C₂×#41	—	2	2	no	—
232	C₂×#41	—	2	2	no	—
233	#135	—	4	8	no	—
234	C₂×Q₁₆	—	2	2	no	—
235	C₂×SD₁₆	—	2	4	no	—
236	C₂×SD₁₆	—	2	4	no	—
237	C₂×D₈	—	2	2	no	—
238	C₂×D₈	—	2	2	no	—
239	C₂×D₈	—	2	4	no	—
240	C₂×D₈	—	2	4	no	—
241	C₂×M₁₆	D₄×C₁₂₇	1	2	yes	—
242	C₂²×C₈	D₄×C₁₂₇	1	2	yes	—
243	C₄⋊Q₈	C₂³×C₁₂₇	1	2	yes	—
244	C₄⋊Q₈	C₂³×C₁₂₇	1	2	yes	—
245	#127	C₂³×C₁₂₇	1	2	yes	—
246	#127	C₂³×C₁₂₇	1	2	yes	—
247	#124	—	2	2	no	—
248	#124	—	2	2	no	—
249	#121	—	2	2	no	—
250	#121	—	2	2	no	—
251	#121	—	2	2	no	—
252	#121	—	2	2	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	—	2	2	no	—
257	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
258	#107	—	2	2	no	—
259	#106	—	2	4	no	—
260	C₄⋊C₈	D₄×C₁₂₇	1	2	yes	—
261	#103	—	2	4	no	—
262	#102	—	2	4	no	—
263	#102	—	2	4	no	—
264	#102	—	2	4	no	—
265	#102	—	2	4	no	—
266	C₂²⋊C₈	D₄×C₁₂₇	1	2	yes	—
267	#97	D₄×C₁₂₇	1	2	yes	—
268	C₄×C₈	D₄×C₁₂₇	1	2	yes	—
269	C₄×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
270	C₄×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
271	C₄×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
272	C₄×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
275	#41	—	4	8	no	—
276	#41	—	8	4	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
292	Q₁₆	—	4	4	no	—
293	SD₁₆	—	4	8	no	—
294	SD₁₆	—	8	4	no	—
295	D₈	—	4	8	no	—
296	D₈	—	4	4	no	—
297	D₈	—	4	4	no	—
298	D₈	—	8	4	no	—
299	M₁₆	—	2	4	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
302	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
303	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
304	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
305	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
306	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
316	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
317	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
318	C₄²	C₂⁴×C₁₂₇	1	1	yes	characteristic
319	C₂³	—	4	2	no	—
320	C₂³	—	4	2	no	—
321	C₂³	#127×C₁₂₇	1	1	yes	characteristic
322	Q₈	—	4	4	no	—
323	Q₈	—	4	4	no	—
324	D₄	—	4	4	no	—
325	D₄	—	4	4	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	4	no	—
328	D₄	—	4	4	no	—
329	D₄	—	4	4	no	—
330	D₄	—	8	4	no	—
331	D₄	—	8	4	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	8	4	no	—
338	C₂×C₄	—	8	4	no	—
339	C₂×C₄	#127×C₁₂₇	1	1	yes	characteristic
340	C₂×C₄	#127×C₁₂₇	1	1	yes	characteristic
341	C₂×C₄	#127×C₁₂₇	1	1	yes	characteristic
342	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
345	C₈	—	2	2	no	—
346	C₈	—	2	2	no	—
347	C₈	—	2	2	no	—
348	C₈	—	2	2	no	—
349	C₈	#135×C₁₂₇	1	4	yes	complemented
350	C₈	AGL(1,ℤ/8)×C₁₂₇	1	4	yes	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	8	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	8	2	no	—
360	C₂²	C₂×#127×C₁₂₇	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	8	2	no	—
365	C₄	—	8	2	no	—
366	C₄	C₂×#135×C₁₂₇	1	2	yes	—
367	C₄	C₂×AGL(1,ℤ/8)×C₁₂₇	1	2	yes	—
368	C₄	#576×C₁₂₇	1	2	yes	—
369	C₂	—	4	1	no	—
370	C₂	—	16	2	no	—
371	C₂	—	16	2	no	—
372	C₂	C₁₂₇×#3147	1	1	yes	characteristic
373	C₂	C₁₂₇×#3151	1	1	yes	characteristic
374	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×#3207	C₂	semidirect
2. C₁₂₇×#3184	C₂	semidirect
3. C₁₂₇×#3169	C₂	semidirect
4. C₁₂₇×#3147	C₂	semidirect
5. C₁₂₇×#1717	C₂	semidirect
6. C₁₂₇×#1715	C₂	semidirect
7. C₁₂₇×#1712	C₂	semidirect
8. C₁₂₇×#1709	C₂	semidirect
9. C₁₂₇×#1707	C₂	semidirect
10. C₁₂₇×#1706	C₂	semidirect
11. C₈×M₁₆×C₁₂₇	C₂	semidirect
161. C₈×C₁₂₇	#135	semidirect
181. #19647	C₁₂₇	direct (N × H)
188. #3207	C₂×C₁₂₇	semidirect
189. #3184	C₂×C₁₂₇	semidirect
190. #3169	C₂×C₁₂₇	semidirect
191. #3147	C₂×C₁₂₇	semidirect
192. #1717	C₂×C₁₂₇	semidirect
193. #1715	C₂×C₁₂₇	semidirect
194. #1712	C₂×C₁₂₇	semidirect
195. #1709	C₂×C₁₂₇	semidirect
196. #1707	C₂×C₁₂₇	semidirect
197. #1706	C₂×C₁₂₇	semidirect
198. C₈×M₁₆	C₂×C₁₂₇	semidirect
199. C₁₂₇	#19647	direct (N × H)
349. C₈	#135×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₂₇×#3207	2
C₁₂₇×#3184	2
C₁₂₇×#3169	2
C₁₂₇×#3147	2
C₁₂₇×#1717	2
C₁₂₇×#1715	2
C₁₂₇×#1712	2
C₁₂₇×#1709	2
C₁₂₇×#1707	2
C₁₂₇×#1706	2
C₈×M₁₆×C₁₂₇	2
#19647	127

Subgroups — C127×#19647 #44583320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#19647 #44583320