Subgroups — C₂×C₁₂₇×#1386 #44576239

Order 32512.

630 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×M₃₂×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#427×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#106×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1386	C₂	1	4	yes	maximal, direct product factor
5	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
6	C₂×#117×C₁₂₇	—	2	1	no	—
7	C₂²×C₄⋊C₄×C₁₂₇	—	2	1	no	—
8	C₂×M₃₂×C₁₂₇	—	2	2	no	—
9	C₂×M₃₂×C₁₂₇	—	2	1	no	—
10	C₂×M₃₂×C₁₂₇	C₄	1	4	yes	complemented
11	C₂×M₃₂×C₁₂₇	C₂²	1	2	yes	—
12	C₂²×C₁₆×C₁₂₇	—	2	1	no	—
13	#427×C₁₂₇	—	2	1	no	—
14	#427×C₁₂₇	—	2	1	no	—
15	#427×C₁₂₇	C₄	1	2	yes	complemented
16	#427×C₁₂₇	C₂²	1	2	yes	—
17	C₂×#107×C₁₂₇	C₄	1	2	yes	complemented
18	C₂×#106×C₁₂₇	—	2	1	no	—
19	C₂×#106×C₁₂₇	—	2	2	no	—
20	C₂×#106×C₁₂₇	—	2	1	no	—
21	C₂×#106×C₁₂₇	C₄	1	4	yes	complemented
22	C₂×#106×C₁₂₇	C₂²	1	2	yes	—
23	C₂³×C₄×C₁₂₇	—	4	1	no	—
24	C₂³×C₄×C₁₂₇	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₂₇	C₂×C₄	1	2	yes	—
26	C₂²×C₈×C₁₂₇	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₂₇	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₂₇	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₂₇	D₄	1	2	yes	—
32	C₂²×C₈×C₁₂₇	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₂₇	Q₈	1	2	yes	—
34	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
35	#117×C₁₂₇	—	2	2	no	—
36	#117×C₁₂₇	—	2	2	no	—
37	#117×C₁₂₇	—	4	1	no	—
38	#117×C₁₂₇	—	4	1	no	—
39	C₂×C₄⋊C₄×C₁₂₇	—	2	4	no	—
40	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₂₇	—	4	1	no	—
43	C₂×C₄⋊C₄×C₁₂₇	—	4	2	no	—
44	C₂×C₂²⋊C₄×C₁₂₇	—	4	1	no	—
45	C₂×C₄²×C₁₂₇	—	4	1	no	—
46	M₃₂×C₁₂₇	—	2	4	no	—
47	M₃₂×C₁₂₇	—	2	2	no	—
48	M₃₂×C₁₂₇	C₂×C₄	1	4	yes	complemented
49	C₂×C₁₆×C₁₂₇	—	2	4	no	—
50	C₂×C₁₆×C₁₂₇	—	2	2	no	—
51	#107×C₁₂₇	—	2	2	no	—
52	#107×C₁₂₇	C₂×C₄	1	4	yes	complemented
53	#106×C₁₂₇	—	2	4	no	—
54	#106×C₁₂₇	—	2	2	no	—
55	#106×C₁₂₇	—	2	2	no	—
56	#106×C₁₂₇	—	2	2	no	—
57	#106×C₁₂₇	C₂×C₄	1	4	yes	complemented
58	C₂⁴×C₁₂₇	D₈	1	1	yes	characteristic
59	C₂²×C₄×C₁₂₇	—	4	4	no	—
60	C₂²×C₄×C₁₂₇	—	4	2	no	—
61	C₂²×C₄×C₁₂₇	—	4	2	no	—
62	C₂²×C₄×C₁₂₇	—	8	4	no	—
63	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₂₇	C₄⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₂₇	D₈	1	1	yes	characteristic
68	C₂²×C₄×C₁₂₇	SD₁₆	1	2	yes	—
69	C₂²×C₄×C₁₂₇	SD₁₆	1	1	yes	characteristic
70	C₂²×C₄×C₁₂₇	SD₁₆	1	1	yes	characteristic
71	C₂²×C₄×C₁₂₇	Q₁₆	1	2	yes	—
72	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₁₂₇	C₄²	1	2	yes	—
74	C₂×C₈×C₁₂₇	C₄²	1	2	yes	—
75	C₂×C₈×C₁₂₇	C₂²⋊C₄	1	2	yes	—
76	C₂×C₈×C₁₂₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₈×C₁₂₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₈×C₁₂₇	C₂²⋊C₄	1	2	yes	—
79	C₂×C₈×C₁₂₇	C₂²⋊C₄	1	2	yes	—
80	C₂×C₈×C₁₂₇	C₄⋊C₄	1	2	yes	—
81	C₂×C₈×C₁₂₇	C₄⋊C₄	1	2	yes	—
82	C₂×C₈×C₁₂₇	C₄⋊C₄	1	2	yes	—
83	C₂×C₈×C₁₂₇	C₄⋊C₄	1	2	yes	—
84	C₂×C₈×C₁₂₇	C₄⋊C₄	1	2	yes	—
85	C₂×C₈×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₈×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₈×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₈×C₁₂₇	C₂×D₄	1	1	yes	characteristic
89	C₂×C₈×C₁₂₇	C₂×D₄	1	1	yes	characteristic
90	C₂×C₈×C₁₂₇	C₂×Q₈	1	1	yes	characteristic
91	C₄⋊C₄×C₁₂₇	—	2	4	no	—
92	C₄⋊C₄×C₁₂₇	—	2	4	no	—
93	C₄⋊C₄×C₁₂₇	—	4	4	no	—
94	C₄⋊C₄×C₁₂₇	—	4	2	no	—
95	C₄⋊C₄×C₁₂₇	—	4	2	no	—
96	C₂²⋊C₄×C₁₂₇	—	4	2	no	—
97	C₂²⋊C₄×C₁₂₇	—	4	2	no	—
98	C₄²×C₁₂₇	—	4	2	no	—
99	C₄²×C₁₂₇	—	4	2	no	—
100	C₁₆×C₁₂₇	—	2	4	no	—
101	C₂³×C₁₂₇	—	2	4	no	—
102	C₂³×C₁₂₇	#102	1	1	yes	characteristic
103	C₂³×C₁₂₇	#102	1	2	yes	—
104	C₂³×C₁₂₇	#102	1	1	yes	characteristic
105	C₂³×C₁₂₇	#107	1	2	yes	—
106	C₂³×C₁₂₇	C₂×D₈	1	1	yes	characteristic
107	C₂×C₄×C₁₂₇	—	4	4	no	—
108	C₂×C₄×C₁₂₇	—	4	4	no	—
109	C₂×C₄×C₁₂₇	—	8	4	no	—
110	C₂×C₄×C₁₂₇	—	8	8	no	—
111	C₂×C₄×C₁₂₇	—	8	4	no	—
112	C₂×C₄×C₁₂₇	#95	1	2	yes	—
113	C₂×C₄×C₁₂₇	#95	1	2	yes	—
114	C₂×C₄×C₁₂₇	#102	1	1	yes	characteristic
115	C₂×C₄×C₁₂₇	#102	1	2	yes	—
116	C₂×C₄×C₁₂₇	#102	1	1	yes	characteristic
117	C₂×C₄×C₁₂₇	#103	1	2	yes	—
118	C₂×C₄×C₁₂₇	#103	1	2	yes	—
119	C₂×C₄×C₁₂₇	#103	1	2	yes	—
120	C₂×C₄×C₁₂₇	#103	1	2	yes	—
121	C₂×C₄×C₁₂₇	#106	1	2	yes	—
122	C₂×C₄×C₁₂₇	#106	1	2	yes	—
123	C₂×C₄×C₁₂₇	#107	1	2	yes	—
124	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₁₂₇	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₁₂₇	C₂×SD₁₆	1	1	yes	characteristic
128	C₂×C₄×C₁₂₇	C₂×SD₁₆	1	1	yes	characteristic
129	C₂×C₄×C₁₂₇	C₂×Q₁₆	1	1	yes	characteristic
130	C₈×C₁₂₇	#95	1	2	yes	—
131	C₈×C₁₂₇	#95	1	2	yes	—
132	C₈×C₁₂₇	C₂×C₄²	1	1	yes	characteristic
133	C₈×C₁₂₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₈×C₁₂₇	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₈×C₁₂₇	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂²×C₁₂₇	—	2	2	no	—
137	C₂²×C₁₂₇	—	2	2	no	—
138	C₂²×C₁₂₇	—	2	4	no	—
139	C₂²×C₁₂₇	—	2	4	no	—
140	C₂²×C₁₂₇	#340	1	2	yes	—
141	C₂²×C₁₂₇	#340	1	2	yes	—
142	C₂²×C₁₂₇	#360	1	4	yes	—
143	C₂²×C₁₂₇	C₂×#102	1	1	yes	characteristic
144	C₂²×C₁₂₇	C₂×#102	1	1	yes	characteristic
145	C₂²×C₁₂₇	C₂×#107	1	1	yes	characteristic
146	C₄×C₁₂₇	—	8	4	no	—
147	C₄×C₁₂₇	—	8	4	no	—
148	C₄×C₁₂₇	#340	1	2	yes	—
149	C₄×C₁₂₇	#340	1	2	yes	—
150	C₄×C₁₂₇	C₂×#95	1	1	yes	characteristic
151	C₄×C₁₂₇	C₂×#103	1	1	yes	characteristic
152	C₄×C₁₂₇	C₂×#103	1	1	yes	characteristic
153	C₄×C₁₂₇	C₂×#106	1	1	yes	characteristic
154	C₂×#1386	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂×C₁₂₇	—	2	1	no	—
156	C₂×C₁₂₇	—	2	2	no	—
157	C₂×C₁₂₇	—	2	1	no	—
158	C₂×C₁₂₇	#1386	1	4	yes	direct product factor
159	C₂×C₁₂₇	C₂×#340	1	1	yes	characteristic
160	C₂×C₁₂₇	C₂×#360	1	2	yes	—
161	C₂²×M₃₂	C₂×C₁₂₇	1	1	yes	characteristic
162	C₂×#427	C₂×C₁₂₇	1	1	yes	characteristic
163	C₂²×#106	C₂×C₁₂₇	1	1	yes	characteristic
164	#1386	C₂×C₁₂₇	1	4	yes	direct product factor
165	C₁₂₇	C₂×#1386	1	1	yes	characteristic, direct product factor, Sylow
166	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
167	C₂×#117	—	2	1	no	—
168	C₂²×C₄⋊C₄	—	2	1	no	—
169	C₂×M₃₂	—	2	2	no	—
170	C₂×M₃₂	—	2	1	no	—
171	C₂×M₃₂	C₄×C₁₂₇	1	4	yes	complemented
172	C₂×M₃₂	C₂²×C₁₂₇	1	2	yes	—
173	C₂²×C₁₆	—	2	1	no	—
174	#427	—	2	1	no	—
175	#427	—	2	1	no	—
176	#427	C₄×C₁₂₇	1	2	yes	complemented
177	#427	C₂²×C₁₂₇	1	2	yes	—
178	C₂×#107	C₄×C₁₂₇	1	2	yes	complemented
179	C₂×#106	—	2	1	no	—
180	C₂×#106	—	2	2	no	—
181	C₂×#106	—	2	1	no	—
182	C₂×#106	C₄×C₁₂₇	1	4	yes	complemented
183	C₂×#106	C₂²×C₁₂₇	1	2	yes	—
184	C₂³×C₄	—	4	1	no	—
185	C₂³×C₄	D₄×C₁₂₇	1	1	yes	characteristic
186	C₂²×C₈	C₂×C₄×C₁₂₇	1	2	yes	—
187	C₂²×C₈	C₂×C₄×C₁₂₇	1	2	yes	—
188	C₂²×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
189	C₂²×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
190	C₂²×C₈	D₄×C₁₂₇	1	1	yes	characteristic
191	C₂²×C₈	D₄×C₁₂₇	1	1	yes	characteristic
192	C₂²×C₈	D₄×C₁₂₇	1	2	yes	—
193	C₂²×C₈	D₄×C₁₂₇	1	1	yes	characteristic
194	C₂²×C₈	Q₈×C₁₂₇	1	2	yes	—
195	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
196	#117	—	2	2	no	—
197	#117	—	2	2	no	—
198	#117	—	4	1	no	—
199	#117	—	4	1	no	—
200	C₂×C₄⋊C₄	—	2	4	no	—
201	C₂×C₄⋊C₄	—	2	2	no	—
202	C₂×C₄⋊C₄	—	2	2	no	—
203	C₂×C₄⋊C₄	—	4	1	no	—
204	C₂×C₄⋊C₄	—	4	2	no	—
205	C₂×C₂²⋊C₄	—	4	1	no	—
206	C₂×C₄²	—	4	1	no	—
207	M₃₂	—	2	4	no	—
208	M₃₂	—	2	2	no	—
209	M₃₂	C₂×C₄×C₁₂₇	1	4	yes	complemented
210	C₂×C₁₆	—	2	4	no	—
211	C₂×C₁₆	—	2	2	no	—
212	#107	—	2	2	no	—
213	#107	C₂×C₄×C₁₂₇	1	4	yes	complemented
214	#106	—	2	4	no	—
215	#106	—	2	2	no	—
216	#106	—	2	2	no	—
217	#106	—	2	2	no	—
218	#106	C₂×C₄×C₁₂₇	1	4	yes	complemented
219	C₂⁴	D₈×C₁₂₇	1	1	yes	characteristic
220	C₂²×C₄	—	4	2	no	—
221	C₂²×C₄	—	4	4	no	—
222	C₂²×C₄	—	4	2	no	—
223	C₂²×C₄	—	8	4	no	—
224	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	2	yes	—
225	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
226	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
227	C₂²×C₄	C₄⋊C₄×C₁₂₇	1	2	yes	—
228	C₂²×C₄	D₈×C₁₂₇	1	1	yes	characteristic
229	C₂²×C₄	SD₁₆×C₁₂₇	1	1	yes	characteristic
230	C₂²×C₄	SD₁₆×C₁₂₇	1	2	yes	—
231	C₂²×C₄	SD₁₆×C₁₂₇	1	1	yes	characteristic
232	C₂²×C₄	Q₁₆×C₁₂₇	1	2	yes	—
233	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
234	C₂×C₈	C₄²×C₁₂₇	1	2	yes	—
235	C₂×C₈	C₄²×C₁₂₇	1	2	yes	—
236	C₂×C₈	C₂²⋊C₄×C₁₂₇	1	2	yes	—
237	C₂×C₈	C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
238	C₂×C₈	C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
239	C₂×C₈	C₂²⋊C₄×C₁₂₇	1	2	yes	—
240	C₂×C₈	C₂²⋊C₄×C₁₂₇	1	2	yes	—
241	C₂×C₈	C₄⋊C₄×C₁₂₇	1	2	yes	—
242	C₂×C₈	C₄⋊C₄×C₁₂₇	1	2	yes	—
243	C₂×C₈	C₄⋊C₄×C₁₂₇	1	2	yes	—
244	C₂×C₈	C₄⋊C₄×C₁₂₇	1	2	yes	—
245	C₂×C₈	C₄⋊C₄×C₁₂₇	1	2	yes	—
246	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
247	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
248	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
249	C₂×C₈	C₂×D₄×C₁₂₇	1	1	yes	characteristic
250	C₂×C₈	C₂×D₄×C₁₂₇	1	1	yes	characteristic
251	C₂×C₈	C₂×Q₈×C₁₂₇	1	1	yes	characteristic
252	C₄⋊C₄	—	2	4	no	—
253	C₄⋊C₄	—	2	4	no	—
254	C₄⋊C₄	—	4	4	no	—
255	C₄⋊C₄	—	4	2	no	—
256	C₄⋊C₄	—	4	2	no	—
257	C₂²⋊C₄	—	4	2	no	—
258	C₂²⋊C₄	—	4	2	no	—
259	C₄²	—	4	2	no	—
260	C₄²	—	4	2	no	—
261	C₁₆	—	2	4	no	—
262	C₂³	—	2	4	no	—
263	C₂³	#102×C₁₂₇	1	1	yes	characteristic
264	C₂³	#102×C₁₂₇	1	2	yes	—
265	C₂³	#102×C₁₂₇	1	1	yes	characteristic
266	C₂³	#107×C₁₂₇	1	2	yes	—
267	C₂³	C₂×D₈×C₁₂₇	1	1	yes	characteristic
268	C₂×C₄	—	4	4	no	—
269	C₂×C₄	—	4	4	no	—
270	C₂×C₄	—	8	4	no	—
271	C₂×C₄	—	8	8	no	—
272	C₂×C₄	—	8	4	no	—
273	C₂×C₄	#95×C₁₂₇	1	2	yes	—
274	C₂×C₄	#95×C₁₂₇	1	2	yes	—
275	C₂×C₄	#102×C₁₂₇	1	1	yes	characteristic
276	C₂×C₄	#102×C₁₂₇	1	2	yes	—
277	C₂×C₄	#102×C₁₂₇	1	1	yes	characteristic
278	C₂×C₄	#103×C₁₂₇	1	2	yes	—
279	C₂×C₄	#103×C₁₂₇	1	2	yes	—
280	C₂×C₄	#103×C₁₂₇	1	2	yes	—
281	C₂×C₄	#103×C₁₂₇	1	2	yes	—
282	C₂×C₄	#106×C₁₂₇	1	2	yes	—
283	C₂×C₄	#106×C₁₂₇	1	2	yes	—
284	C₂×C₄	#107×C₁₂₇	1	2	yes	—
285	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
286	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
287	C₂×C₄	C₂×C₄⋊C₄×C₁₂₇	1	1	yes	characteristic
288	C₂×C₄	C₂×SD₁₆×C₁₂₇	1	1	yes	characteristic
289	C₂×C₄	C₂×SD₁₆×C₁₂₇	1	1	yes	characteristic
290	C₂×C₄	C₂×Q₁₆×C₁₂₇	1	1	yes	characteristic
291	C₈	#95×C₁₂₇	1	2	yes	—
292	C₈	#95×C₁₂₇	1	2	yes	—
293	C₈	C₂×C₄²×C₁₂₇	1	1	yes	characteristic
294	C₈	C₂×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
295	C₈	C₂×C₄⋊C₄×C₁₂₇	1	1	yes	characteristic
296	C₈	C₂×C₄⋊C₄×C₁₂₇	1	1	yes	characteristic
297	C₂²	—	2	2	no	—
298	C₂²	—	2	2	no	—
299	C₂²	—	2	4	no	—
300	C₂²	—	2	4	no	—
301	C₂²	#340×C₁₂₇	1	2	yes	—
302	C₂²	#340×C₁₂₇	1	2	yes	—
303	C₂²	#360×C₁₂₇	1	4	yes	—
304	C₂²	C₂×#102×C₁₂₇	1	1	yes	characteristic
305	C₂²	C₂×#102×C₁₂₇	1	1	yes	characteristic
306	C₂²	C₂×#107×C₁₂₇	1	1	yes	characteristic
307	C₄	—	8	4	no	—
308	C₄	—	8	4	no	—
309	C₄	#340×C₁₂₇	1	2	yes	—
310	C₄	#340×C₁₂₇	1	2	yes	—
311	C₄	C₂×#95×C₁₂₇	1	1	yes	characteristic
312	C₄	C₂×#103×C₁₂₇	1	1	yes	characteristic
313	C₄	C₂×#103×C₁₂₇	1	1	yes	characteristic
314	C₄	C₂×#106×C₁₂₇	1	1	yes	characteristic
315	C₂	—	2	1	no	—
316	C₂	—	2	2	no	—
317	C₂	—	2	1	no	—
318	C₂	C₁₂₇×#1386	1	4	yes	direct product factor
319	C₂	C₂×#340×C₁₂₇	1	1	yes	characteristic
320	C₂	C₂×#360×C₁₂₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₂₇	#102
commutator	C₈	C₂×C₄²×C₁₂₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₂₇
prime radical	C₂⁴×C₁₂₇	D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₂₇ ◁ C₂³×C₄×C₁₂₇ ◁ C₂³×C₈×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₂₇×#1386	C₂	direct (N × H)
10. C₂×M₃₂×C₁₂₇	C₄	semidirect
15. #427×C₁₂₇	C₄	semidirect
17. C₂×#107×C₁₂₇	C₄	semidirect
21. C₂×#106×C₁₂₇	C₄	semidirect
48. M₃₂×C₁₂₇	C₂×C₄	semidirect
52. #107×C₁₂₇	C₂×C₄	semidirect
57. #106×C₁₂₇	C₂×C₄	semidirect
154. C₂×#1386	C₁₂₇	direct (N × H)
158. C₂×C₁₂₇	#1386	direct (N × H)
164. #1386	C₂×C₁₂₇	direct (N × H)
165. C₁₂₇	C₂×#1386	direct (N × H)
171. C₂×M₃₂	C₄×C₁₂₇	semidirect
176. #427	C₄×C₁₂₇	semidirect
178. C₂×#107	C₄×C₁₂₇	semidirect
182. C₂×#106	C₄×C₁₂₇	semidirect
209. M₃₂	C₂×C₄×C₁₂₇	semidirect
213. #107	C₂×C₄×C₁₂₇	semidirect
218. #106	C₂×C₄×C₁₂₇	semidirect
318. C₂	C₁₂₇×#1386	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×M₃₂×C₁₂₇	2
C₂×#427×C₁₂₇	2
C₂²×#106×C₁₂₇	2
C₁₂₇×#1386	2
C₂×#1386	127

Subgroups — C2×C127×#1386 #44576239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₂₇×#1386 #44576239