Subgroups — C₂×C₁₂₇×#1387 #44576241

Order 32512.

614 conjugacy classes of subgroups.

The subgroup lattice has 330 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	C₂²×#108×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#107×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1387	C₂	1	4	yes	maximal, direct product factor
5	C₂²×M₁₆×C₁₂₇	—	2	1	no	—
6	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
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	C₂×#108×C₁₂₇	—	2	1	no	—
14	C₂×#108×C₁₂₇	—	2	2	no	—
15	C₂×#108×C₁₂₇	C₄	1	4	yes	complemented
16	C₂×#108×C₁₂₇	C₂²	1	2	yes	—
17	C₂×#107×C₁₂₇	—	2	1	no	—
18	C₂×#107×C₁₂₇	—	2	1	no	—
19	C₂×#107×C₁₂₇	—	2	1	no	—
20	C₂×#107×C₁₂₇	C₄	1	2	yes	—
21	C₂×#107×C₁₂₇	C₄	1	2	yes	—
22	C₂×#107×C₁₂₇	C₂²	1	2	yes	—
23	C₂³×C₄×C₁₂₇	—	4	1	no	—
24	C₂³×C₄×C₁₂₇	D₄	1	1	yes	characteristic
25	C₂×M₁₆×C₁₂₇	—	2	4	no	—
26	C₂×M₁₆×C₁₂₇	—	2	2	no	—
27	C₂×M₁₆×C₁₂₇	—	4	1	no	—
28	C₂×M₁₆×C₁₂₇	—	4	2	no	—
29	C₂²×C₈×C₁₂₇	—	4	1	no	—
30	C₂²×C₈×C₁₂₇	C₂×C₄	1	2	yes	—
31	C₂²×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₂₇	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₁₂₇	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₂₇	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₂₇	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₂₇	D₄	1	2	yes	—
38	C₂²×C₈×C₁₂₇	Q₈	1	2	yes	—
39	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₂₇	—	4	1	no	—
44	C₂×C₄⋊C₄×C₁₂₇	—	4	1	no	—
45	C₂×C₄⋊C₄×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	#108×C₁₂₇	—	2	4	no	—
52	#108×C₁₂₇	—	2	2	no	—
53	#108×C₁₂₇	C₂×C₄	1	4	yes	complemented
54	#107×C₁₂₇	—	2	2	no	—
55	#107×C₁₂₇	—	2	2	no	—
56	#107×C₁₂₇	—	2	2	no	—
57	#107×C₁₂₇	C₂×C₄	1	4	yes	—
58	C₂⁴×C₁₂₇	SD₁₆	1	1	yes	characteristic
59	C₂²×C₄×C₁₂₇	—	4	2	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	D₈	1	1	yes	characteristic
69	C₂²×C₄×C₁₂₇	SD₁₆	1	1	yes	characteristic
70	C₂²×C₄×C₁₂₇	SD₁₆	1	2	yes	—
71	C₂²×C₄×C₁₂₇	Q₁₆	1	2	yes	—
72	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
73	M₁₆×C₁₂₇	—	2	4	no	—
74	M₁₆×C₁₂₇	—	4	4	no	—
75	M₁₆×C₁₂₇	—	4	2	no	—
76	C₂×C₈×C₁₂₇	—	4	4	no	—
77	C₂×C₈×C₁₂₇	—	4	2	no	—
78	C₂×C₈×C₁₂₇	C₄²	1	2	yes	—
79	C₂×C₈×C₁₂₇	C₄²	1	2	yes	—
80	C₂×C₈×C₁₂₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₈×C₁₂₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₈×C₁₂₇	C₂²⋊C₄	1	2	yes	—
83	C₂×C₈×C₁₂₇	C₂²⋊C₄	1	2	yes	—
84	C₂×C₈×C₁₂₇	C₂²⋊C₄	1	2	yes	—
85	C₂×C₈×C₁₂₇	C₄⋊C₄	1	2	yes	—
86	C₂×C₈×C₁₂₇	C₄⋊C₄	1	2	yes	—
87	C₂×C₈×C₁₂₇	C₄⋊C₄	1	2	yes	—
88	C₂×C₈×C₁₂₇	C₄⋊C₄	1	2	yes	—
89	C₂×C₈×C₁₂₇	C₄⋊C₄	1	2	yes	—
90	C₂×C₈×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₈×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₈×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₈×C₁₂₇	C₂×D₄	1	1	yes	characteristic
94	C₂×C₈×C₁₂₇	C₂×D₄	1	1	yes	characteristic
95	C₂×C₈×C₁₂₇	C₂×Q₈	1	1	yes	characteristic
96	C₄⋊C₄×C₁₂₇	—	2	4	no	—
97	C₄⋊C₄×C₁₂₇	—	4	2	no	—
98	C₄⋊C₄×C₁₂₇	—	4	2	no	—
99	C₄⋊C₄×C₁₂₇	—	4	2	no	—
100	C₁₆×C₁₂₇	—	2	4	no	—
101	C₂³×C₁₂₇	—	2	2	no	—
102	C₂³×C₁₂₇	—	2	2	no	—
103	C₂³×C₁₂₇	#102	1	1	yes	characteristic
104	C₂³×C₁₂₇	#102	1	1	yes	characteristic
105	C₂³×C₁₂₇	#103	1	2	yes	—
106	C₂³×C₁₂₇	#106	1	2	yes	—
107	C₂³×C₁₂₇	C₂×SD₁₆	1	1	yes	characteristic
108	C₂×C₄×C₁₂₇	—	4	4	no	—
109	C₂×C₄×C₁₂₇	—	8	4	no	—
110	C₂×C₄×C₁₂₇	—	8	4	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	1	yes	characteristic
116	C₂×C₄×C₁₂₇	#102	1	2	yes	—
117	C₂×C₄×C₁₂₇	#102	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	#107	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×D₈	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	—	4	4	no	—
131	C₈×C₁₂₇	#95	1	2	yes	—
132	C₈×C₁₂₇	#95	1	2	yes	—
133	C₈×C₁₂₇	C₂×C₄²	1	1	yes	characteristic
134	C₈×C₁₂₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₈×C₁₂₇	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₈×C₁₂₇	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂²×C₁₂₇	—	2	1	no	—
138	C₂²×C₁₂₇	—	2	1	no	—
139	C₂²×C₁₂₇	—	2	1	no	—
140	C₂²×C₁₂₇	—	2	1	no	—
141	C₂²×C₁₂₇	—	2	4	no	—
142	C₂²×C₁₂₇	—	2	4	no	—
143	C₂²×C₁₂₇	#340	1	2	yes	—
144	C₂²×C₁₂₇	#340	1	2	yes	—
145	C₂²×C₁₂₇	#361	1	2	yes	—
146	C₂²×C₁₂₇	#362	1	2	yes	—
147	C₂²×C₁₂₇	C₂×#102	1	1	yes	characteristic
148	C₂²×C₁₂₇	C₂×#103	1	1	yes	characteristic
149	C₂²×C₁₂₇	C₂×#106	1	1	yes	characteristic
150	C₄×C₁₂₇	—	8	4	no	—
151	C₄×C₁₂₇	#340	1	2	yes	—
152	C₄×C₁₂₇	#340	1	2	yes	—
153	C₄×C₁₂₇	C₂×#95	1	1	yes	characteristic
154	C₄×C₁₂₇	C₂×#102	1	1	yes	characteristic
155	C₄×C₁₂₇	C₂×#103	1	1	yes	characteristic
156	C₄×C₁₂₇	C₂×#107	1	1	yes	characteristic
157	C₂×#1387	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂×C₁₂₇	—	2	2	no	—
159	C₂×C₁₂₇	—	2	1	no	—
160	C₂×C₁₂₇	—	2	1	no	—
161	C₂×C₁₂₇	#1387	1	4	yes	direct product factor
162	C₂×C₁₂₇	C₂×#340	1	1	yes	characteristic
163	C₂×C₁₂₇	C₂×#361	1	1	yes	characteristic
164	C₂×C₁₂₇	C₂×#362	1	1	yes	characteristic
165	C₂²×M₃₂	C₂×C₁₂₇	1	1	yes	characteristic
166	C₂²×#108	C₂×C₁₂₇	1	1	yes	characteristic
167	C₂²×#107	C₂×C₁₂₇	1	1	yes	characteristic
168	#1387	C₂×C₁₂₇	1	4	yes	direct product factor
169	C₁₂₇	C₂×#1387	1	1	yes	characteristic, direct product factor, Sylow
170	C₂²×M₁₆	—	2	1	no	—
171	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
172	C₂²×C₄⋊C₄	—	2	1	no	—
173	C₂×M₃₂	—	2	2	no	—
174	C₂×M₃₂	—	2	1	no	—
175	C₂×M₃₂	C₄×C₁₂₇	1	4	yes	complemented
176	C₂×M₃₂	C₂²×C₁₂₇	1	2	yes	—
177	C₂²×C₁₆	—	2	1	no	—
178	C₂×#108	—	2	1	no	—
179	C₂×#108	—	2	2	no	—
180	C₂×#108	C₄×C₁₂₇	1	4	yes	complemented
181	C₂×#108	C₂²×C₁₂₇	1	2	yes	—
182	C₂×#107	—	2	1	no	—
183	C₂×#107	—	2	1	no	—
184	C₂×#107	—	2	1	no	—
185	C₂×#107	C₄×C₁₂₇	1	2	yes	—
186	C₂×#107	C₄×C₁₂₇	1	2	yes	—
187	C₂×#107	C₂²×C₁₂₇	1	2	yes	—
188	C₂³×C₄	—	4	1	no	—
189	C₂³×C₄	D₄×C₁₂₇	1	1	yes	characteristic
190	C₂×M₁₆	—	2	4	no	—
191	C₂×M₁₆	—	2	2	no	—
192	C₂×M₁₆	—	4	1	no	—
193	C₂×M₁₆	—	4	2	no	—
194	C₂²×C₈	—	4	1	no	—
195	C₂²×C₈	C₂×C₄×C₁₂₇	1	2	yes	—
196	C₂²×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
197	C₂²×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
198	C₂²×C₈	C₂×C₄×C₁₂₇	1	2	yes	—
199	C₂²×C₈	D₄×C₁₂₇	1	1	yes	characteristic
200	C₂²×C₈	D₄×C₁₂₇	1	1	yes	characteristic
201	C₂²×C₈	D₄×C₁₂₇	1	1	yes	characteristic
202	C₂²×C₈	D₄×C₁₂₇	1	2	yes	—
203	C₂²×C₈	Q₈×C₁₂₇	1	2	yes	—
204	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
205	C₂×C₄⋊C₄	—	2	2	no	—
206	C₂×C₄⋊C₄	—	2	2	no	—
207	C₂×C₄⋊C₄	—	2	2	no	—
208	C₂×C₄⋊C₄	—	4	1	no	—
209	C₂×C₄⋊C₄	—	4	1	no	—
210	C₂×C₄⋊C₄	—	4	1	no	—
211	M₃₂	—	2	4	no	—
212	M₃₂	—	2	2	no	—
213	M₃₂	C₂×C₄×C₁₂₇	1	4	yes	complemented
214	C₂×C₁₆	—	2	4	no	—
215	C₂×C₁₆	—	2	2	no	—
216	#108	—	2	4	no	—
217	#108	—	2	2	no	—
218	#108	C₂×C₄×C₁₂₇	1	4	yes	complemented
219	#107	—	2	2	no	—
220	#107	—	2	2	no	—
221	#107	—	2	2	no	—
222	#107	C₂×C₄×C₁₂₇	1	4	yes	—
223	C₂⁴	SD₁₆×C₁₂₇	1	1	yes	characteristic
224	C₂²×C₄	—	4	2	no	—
225	C₂²×C₄	—	4	2	no	—
226	C₂²×C₄	—	4	2	no	—
227	C₂²×C₄	—	8	4	no	—
228	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	2	yes	—
229	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
230	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
231	C₂²×C₄	C₄⋊C₄×C₁₂₇	1	2	yes	—
232	C₂²×C₄	D₈×C₁₂₇	1	1	yes	characteristic
233	C₂²×C₄	D₈×C₁₂₇	1	1	yes	characteristic
234	C₂²×C₄	SD₁₆×C₁₂₇	1	1	yes	characteristic
235	C₂²×C₄	SD₁₆×C₁₂₇	1	2	yes	—
236	C₂²×C₄	Q₁₆×C₁₂₇	1	2	yes	—
237	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
238	M₁₆	—	2	4	no	—
239	M₁₆	—	4	4	no	—
240	M₁₆	—	4	2	no	—
241	C₂×C₈	—	4	4	no	—
242	C₂×C₈	—	4	2	no	—
243	C₂×C₈	C₄²×C₁₂₇	1	2	yes	—
244	C₂×C₈	C₄²×C₁₂₇	1	2	yes	—
245	C₂×C₈	C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
246	C₂×C₈	C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
247	C₂×C₈	C₂²⋊C₄×C₁₂₇	1	2	yes	—
248	C₂×C₈	C₂²⋊C₄×C₁₂₇	1	2	yes	—
249	C₂×C₈	C₂²⋊C₄×C₁₂₇	1	2	yes	—
250	C₂×C₈	C₄⋊C₄×C₁₂₇	1	2	yes	—
251	C₂×C₈	C₄⋊C₄×C₁₂₇	1	2	yes	—
252	C₂×C₈	C₄⋊C₄×C₁₂₇	1	2	yes	—
253	C₂×C₈	C₄⋊C₄×C₁₂₇	1	2	yes	—
254	C₂×C₈	C₄⋊C₄×C₁₂₇	1	2	yes	—
255	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
256	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
257	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
258	C₂×C₈	C₂×D₄×C₁₂₇	1	1	yes	characteristic
259	C₂×C₈	C₂×D₄×C₁₂₇	1	1	yes	characteristic
260	C₂×C₈	C₂×Q₈×C₁₂₇	1	1	yes	characteristic
261	C₄⋊C₄	—	2	4	no	—
262	C₄⋊C₄	—	4	2	no	—
263	C₄⋊C₄	—	4	2	no	—
264	C₄⋊C₄	—	4	2	no	—
265	C₁₆	—	2	4	no	—
266	C₂³	—	2	2	no	—
267	C₂³	—	2	2	no	—
268	C₂³	#102×C₁₂₇	1	1	yes	characteristic
269	C₂³	#102×C₁₂₇	1	1	yes	characteristic
270	C₂³	#103×C₁₂₇	1	2	yes	—
271	C₂³	#106×C₁₂₇	1	2	yes	—
272	C₂³	C₂×SD₁₆×C₁₂₇	1	1	yes	characteristic
273	C₂×C₄	—	4	4	no	—
274	C₂×C₄	—	8	4	no	—
275	C₂×C₄	—	8	4	no	—
276	C₂×C₄	—	8	4	no	—
277	C₂×C₄	#95×C₁₂₇	1	2	yes	—
278	C₂×C₄	#95×C₁₂₇	1	2	yes	—
279	C₂×C₄	#102×C₁₂₇	1	1	yes	characteristic
280	C₂×C₄	#102×C₁₂₇	1	1	yes	characteristic
281	C₂×C₄	#102×C₁₂₇	1	2	yes	—
282	C₂×C₄	#102×C₁₂₇	1	2	yes	—
283	C₂×C₄	#103×C₁₂₇	1	2	yes	—
284	C₂×C₄	#103×C₁₂₇	1	2	yes	—
285	C₂×C₄	#103×C₁₂₇	1	2	yes	—
286	C₂×C₄	#106×C₁₂₇	1	2	yes	—
287	C₂×C₄	#107×C₁₂₇	1	2	yes	—
288	C₂×C₄	#107×C₁₂₇	1	2	yes	—
289	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
290	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
291	C₂×C₄	C₂×C₄⋊C₄×C₁₂₇	1	1	yes	characteristic
292	C₂×C₄	C₂×D₈×C₁₂₇	1	1	yes	characteristic
293	C₂×C₄	C₂×SD₁₆×C₁₂₇	1	1	yes	characteristic
294	C₂×C₄	C₂×Q₁₆×C₁₂₇	1	1	yes	characteristic
295	C₈	—	4	4	no	—
296	C₈	#95×C₁₂₇	1	2	yes	—
297	C₈	#95×C₁₂₇	1	2	yes	—
298	C₈	C₂×C₄²×C₁₂₇	1	1	yes	characteristic
299	C₈	C₂×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
300	C₈	C₂×C₄⋊C₄×C₁₂₇	1	1	yes	characteristic
301	C₈	C₂×C₄⋊C₄×C₁₂₇	1	1	yes	characteristic
302	C₂²	—	2	1	no	—
303	C₂²	—	2	1	no	—
304	C₂²	—	2	1	no	—
305	C₂²	—	2	1	no	—
306	C₂²	—	2	4	no	—
307	C₂²	—	2	4	no	—
308	C₂²	#340×C₁₂₇	1	2	yes	—
309	C₂²	#340×C₁₂₇	1	2	yes	—
310	C₂²	#361×C₁₂₇	1	2	yes	—
311	C₂²	#362×C₁₂₇	1	2	yes	—
312	C₂²	C₂×#102×C₁₂₇	1	1	yes	characteristic
313	C₂²	C₂×#103×C₁₂₇	1	1	yes	characteristic
314	C₂²	C₂×#106×C₁₂₇	1	1	yes	characteristic
315	C₄	—	8	4	no	—
316	C₄	#340×C₁₂₇	1	2	yes	—
317	C₄	#340×C₁₂₇	1	2	yes	—
318	C₄	C₂×#95×C₁₂₇	1	1	yes	characteristic
319	C₄	C₂×#102×C₁₂₇	1	1	yes	characteristic
320	C₄	C₂×#103×C₁₂₇	1	1	yes	characteristic
321	C₄	C₂×#107×C₁₂₇	1	1	yes	characteristic
322	C₂	—	2	2	no	—
323	C₂	—	2	1	no	—
324	C₂	—	2	1	no	—
325	C₂	C₁₂₇×#1387	1	4	yes	direct product factor
326	C₂	C₂×#340×C₁₂₇	1	1	yes	characteristic
327	C₂	C₂×#361×C₁₂₇	1	1	yes	characteristic
328	C₂	C₂×#362×C₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₂₇	#102
commutator	C₈	C₂×C₄²×C₁₂₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₂₇
prime radical	C₂⁴×C₁₂₇	SD₁₆
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×#1387	C₂	direct (N × H)
10. C₂×M₃₂×C₁₂₇	C₄	semidirect
15. C₂×#108×C₁₂₇	C₄	semidirect
48. M₃₂×C₁₂₇	C₂×C₄	semidirect
53. #108×C₁₂₇	C₂×C₄	semidirect
157. C₂×#1387	C₁₂₇	direct (N × H)
161. C₂×C₁₂₇	#1387	direct (N × H)
168. #1387	C₂×C₁₂₇	direct (N × H)
169. C₁₂₇	C₂×#1387	direct (N × H)
175. C₂×M₃₂	C₄×C₁₂₇	semidirect
180. C₂×#108	C₄×C₁₂₇	semidirect
213. M₃₂	C₂×C₄×C₁₂₇	semidirect
218. #108	C₂×C₄×C₁₂₇	semidirect
325. C₂	C₁₂₇×#1387	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
C₂²×#108×C₁₂₇	2
C₂²×#107×C₁₂₇	2
C₁₂₇×#1387	2
C₂×#1387	127

Subgroups — C2×C127×#1387 #44576241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₂₇×#1387 #44576241