Subgroups — C₁₂₇×#18044 #44581717

Order 32512.

786 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₁₂₇	C₂	1	2	yes	maximal, complemented
3	C₁₂₇×#1594	C₂	1	2	yes	maximal, complemented
4	C₁₂₇×#1586	C₂	1	4	yes	maximal, complemented
5	C₁₂₇×#1580	C₂	1	2	yes	maximal, complemented
6	C₁₂₇×#1566	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₂₇×#1486	C₂	1	2	yes	maximal, complemented
8	C₁₂₇×#1451	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₁₂₇	C₄	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₂₇	—	2	2	no	—
11	C₂×C₄×D₄×C₁₂₇	C₂²	1	2	yes	—
12	C₄×D₈×C₁₂₇	C₄	1	2	yes	—
13	C₄×D₈×C₁₂₇	C₄	1	1	yes	characteristic
14	C₄×D₈×C₁₂₇	C₄	1	1	yes	characteristic
15	C₄×D₈×C₁₂₇	C₂²	1	1	yes	characteristic
16	C₄×D₈×C₁₂₇	C₂²	1	2	yes	—
17	C₄×D₈×C₁₂₇	C₂²	1	1	yes	characteristic
18	#436×C₁₂₇	C₂²	1	4	yes	complemented
19	#435×C₁₂₇	—	2	4	no	—
20	C₈×D₄×C₁₂₇	C₂²	1	4	yes	complemented
21	#431×C₁₂₇	C₂²	1	1	yes	characteristic
22	C₂×#107×C₁₂₇	C₄	1	1	yes	characteristic
23	#423×C₁₂₇	C₂²	1	2	yes	—
24	C₂×#102×C₁₂₇	C₄	1	2	yes	—
25	#407×C₁₂₇	—	2	2	no	—
26	C₄×M₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
28	#334×C₁₂₇	C₂²	1	2	yes	complemented
29	#334×C₁₂₇	C₂²	1	2	yes	complemented
30	D₄⋊C₈×C₁₂₇	C₂²	1	4	yes	complemented
31	D₄⋊C₈×C₁₂₇	C₂²	1	4	yes	complemented
32	#322×C₁₂₇	C₂²	1	2	yes	complemented
33	#322×C₁₂₇	C₂²	1	2	yes	complemented
34	C₂²×D₄×C₁₂₇	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₂₇	—	2	2	no	—
36	C₂×D₈×C₁₂₇	—	2	4	no	—
37	C₂×D₈×C₁₂₇	C₂×C₄	1	2	yes	—
38	C₂×D₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
39	C₂×D₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
40	C₂×M₁₆×C₁₂₇	—	2	2	no	—
41	C₂×M₁₆×C₁₂₇	—	2	4	no	—
42	C₂×M₁₆×C₁₂₇	—	4	8	no	—
43	C₂×M₁₆×C₁₂₇	D₄	1	2	yes	—
44	C₂²×C₈×C₁₂₇	—	2	4	no	—
45	C₂²×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
47	C₄×D₄×C₁₂₇	—	2	2	no	—
48	C₄×D₄×C₁₂₇	—	2	2	no	—
49	C₄×D₄×C₁₂₇	C₂×C₄	1	2	yes	—
50	C₄×D₄×C₁₂₇	C₂×C₄	1	2	yes	—
51	C₄×D₄×C₁₂₇	C₂³	1	2	yes	—
52	C₄×D₄×C₁₂₇	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₂₇	—	2	2	no	—
55	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
56	#107×C₁₂₇	C₂×C₄	1	2	yes	—
57	#107×C₁₂₇	C₂×C₄	1	1	yes	characteristic
58	#107×C₁₂₇	C₂×C₄	1	1	yes	characteristic
59	C₄⋊C₈×C₁₂₇	—	2	2	no	—
60	C₄⋊C₈×C₁₂₇	—	2	1	no	—
61	C₄⋊C₈×C₁₂₇	C₂³	1	4	yes	—
62	#102×C₁₂₇	C₂×C₄	1	2	yes	—
63	#102×C₁₂₇	C₂×C₄	1	2	yes	—
64	#102×C₁₂₇	C₂×C₄	1	2	yes	—
65	#102×C₁₂₇	C₂×C₄	1	2	yes	—
66	C₂²⋊C₈×C₁₂₇	—	2	1	no	—
67	C₂²⋊C₈×C₁₂₇	—	2	4	no	—
68	C₂²⋊C₈×C₁₂₇	—	2	4	no	—
69	#97×C₁₂₇	D₄	1	2	yes	—
70	C₄×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₁₂₇	C₂³	1	2	yes	—
73	C₄×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₁₂₇	C₂³	1	2	yes	—
76	C₂⁴×C₁₂₇	—	2	2	no	—
77	C₂×D₄×C₁₂₇	—	2	4	no	—
78	C₂×D₄×C₁₂₇	—	2	2	no	—
79	C₂×D₄×C₁₂₇	—	4	2	no	—
80	C₂×D₄×C₁₂₇	C₂²×C₄	1	2	yes	—
81	C₂×D₄×C₁₂₇	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₂₇	—	2	2	no	—
83	C₂²×C₄×C₁₂₇	—	2	2	no	—
84	C₂²×C₄×C₁₂₇	—	2	2	no	—
85	C₂²×C₄×C₁₂₇	—	2	2	no	—
86	C₂²×C₄×C₁₂₇	—	2	2	no	—
87	C₂²×C₄×C₁₂₇	—	4	4	no	—
88	C₂²×C₄×C₁₂₇	—	4	4	no	—
89	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₂₇	#41	1	1	yes	characteristic
92	D₈×C₁₂₇	—	2	4	no	—
93	D₈×C₁₂₇	—	2	2	no	—
94	D₈×C₁₂₇	M₁₆	1	4	yes	complemented
95	M₁₆×C₁₂₇	—	2	4	no	—
96	M₁₆×C₁₂₇	—	4	8	no	—
97	M₁₆×C₁₂₇	—	4	4	no	—
98	C₂×C₈×C₁₂₇	—	2	2	no	—
99	C₂×C₈×C₁₂₇	—	2	4	no	—
100	C₂×C₈×C₁₂₇	—	2	2	no	—
101	C₂×C₈×C₁₂₇	—	4	1	no	—
102	C₂×C₈×C₁₂₇	—	4	8	no	—
103	C₂×C₈×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₁₂₇	C₂×D₄	1	4	yes	—
108	C₄⋊C₄×C₁₂₇	—	2	2	no	—
109	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
110	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
111	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
112	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
113	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
114	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
115	C₄²×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₁₂₇	#41	1	1	yes	characteristic
118	C₄²×C₁₂₇	C₂⁴	1	1	yes	characteristic
119	C₂³×C₁₂₇	—	2	2	no	—
120	C₂³×C₁₂₇	—	2	2	no	—
121	C₂³×C₁₂₇	—	4	4	no	—
122	C₂³×C₁₂₇	—	4	4	no	—
123	C₂³×C₁₂₇	—	8	2	no	—
124	C₂³×C₁₂₇	C₄×D₄	1	1	yes	characteristic
125	D₄×C₁₂₇	—	2	2	no	—
126	D₄×C₁₂₇	—	2	2	no	—
127	D₄×C₁₂₇	—	2	2	no	—
128	D₄×C₁₂₇	—	4	4	no	—
129	D₄×C₁₂₇	C₂×M₁₆	1	4	yes	complemented
130	C₂×C₄×C₁₂₇	—	2	1	no	—
131	C₂×C₄×C₁₂₇	—	2	1	no	—
132	C₂×C₄×C₁₂₇	—	2	2	no	—
133	C₂×C₄×C₁₂₇	—	2	2	no	—
134	C₂×C₄×C₁₂₇	—	4	1	no	—
135	C₂×C₄×C₁₂₇	—	4	4	no	—
136	C₂×C₄×C₁₂₇	—	4	2	no	—
137	C₂×C₄×C₁₂₇	—	4	2	no	—
138	C₂×C₄×C₁₂₇	—	4	2	no	—
139	C₂×C₄×C₁₂₇	—	4	2	no	—
140	C₂×C₄×C₁₂₇	—	4	4	no	—
141	C₂×C₄×C₁₂₇	—	4	4	no	—
142	C₂×C₄×C₁₂₇	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₂₇	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₂₇	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₂₇	AGL(1,ℤ/8)	1	4	yes	—
146	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
149	C₈×C₁₂₇	—	2	1	no	—
150	C₈×C₁₂₇	—	2	1	no	—
151	C₈×C₁₂₇	—	2	1	no	—
152	C₈×C₁₂₇	—	2	4	no	—
153	C₈×C₁₂₇	—	4	2	no	—
154	C₈×C₁₂₇	—	4	4	no	—
155	C₈×C₁₂₇	C₂×M₁₆	1	2	yes	complemented
156	C₂²×C₁₂₇	—	2	1	no	—
157	C₂²×C₁₂₇	—	2	1	no	—
158	C₂²×C₁₂₇	—	2	4	no	—
159	C₂²×C₁₂₇	—	4	2	no	—
160	C₂²×C₁₂₇	—	4	2	no	—
161	C₂²×C₁₂₇	—	4	2	no	—
162	C₂²×C₁₂₇	—	4	2	no	—
163	C₂²×C₁₂₇	—	4	2	no	—
164	C₂²×C₁₂₇	—	8	8	no	—
165	C₂²×C₁₂₇	#442	1	2	yes	—
166	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
167	C₄×C₁₂₇	—	2	1	no	—
168	C₄×C₁₂₇	—	2	1	no	—
169	C₄×C₁₂₇	—	2	1	no	—
170	C₄×C₁₂₇	—	4	2	no	—
171	C₄×C₁₂₇	—	4	2	no	—
172	C₄×C₁₂₇	#442	1	2	yes	—
173	C₄×C₁₂₇	C₂²×M₁₆	1	1	yes	characteristic
174	C₄×C₁₂₇	#568	1	1	yes	characteristic
175	C₄×C₁₂₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
176	#18044	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂×C₁₂₇	—	2	2	no	—
178	C₂×C₁₂₇	—	4	4	no	—
179	C₂×C₁₂₇	—	8	2	no	—
180	C₂×C₁₂₇	D₄×M₁₆	1	1	yes	characteristic
181	C₂×C₁₂₇	C₂×#442	1	1	yes	characteristic
182	C₂×C₁₂₇	#2957	1	1	yes	characteristic
183	C₂×C₄×D₈	C₂×C₁₂₇	1	1	yes	characteristic
184	D₄×M₁₆	C₂×C₁₂₇	1	2	yes	complemented
185	#1594	C₂×C₁₂₇	1	2	yes	complemented
186	#1586	C₂×C₁₂₇	1	4	yes	complemented
187	#1580	C₂×C₁₂₇	1	2	yes	complemented
188	#1566	C₂×C₁₂₇	1	1	yes	characteristic, complemented
189	#1486	C₂×C₁₂₇	1	2	yes	complemented
190	#1451	C₂×C₁₂₇	1	1	yes	characteristic, complemented
191	C₁₂₇	#18044	1	1	yes	characteristic, direct product factor, Sylow
192	C₂²×D₈	C₄×C₁₂₇	1	1	yes	characteristic
193	C₂²×M₁₆	—	2	2	no	—
194	C₂×C₄×D₄	C₂²×C₁₂₇	1	2	yes	—
195	C₄×D₈	C₄×C₁₂₇	1	2	yes	—
196	C₄×D₈	C₄×C₁₂₇	1	1	yes	characteristic
197	C₄×D₈	C₄×C₁₂₇	1	1	yes	characteristic
198	C₄×D₈	C₂²×C₁₂₇	1	1	yes	characteristic
199	C₄×D₈	C₂²×C₁₂₇	1	2	yes	—
200	C₄×D₈	C₂²×C₁₂₇	1	1	yes	characteristic
201	#436	C₂²×C₁₂₇	1	4	yes	complemented
202	#435	—	2	4	no	—
203	C₈×D₄	C₂²×C₁₂₇	1	4	yes	complemented
204	#431	C₂²×C₁₂₇	1	1	yes	characteristic
205	C₂×#107	C₄×C₁₂₇	1	1	yes	characteristic
206	#423	C₂²×C₁₂₇	1	2	yes	—
207	C₂×#102	C₄×C₁₂₇	1	2	yes	—
208	#407	—	2	2	no	—
209	C₄×M₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
211	#334	C₂²×C₁₂₇	1	2	yes	complemented
212	#334	C₂²×C₁₂₇	1	2	yes	complemented
213	D₄⋊C₈	C₂²×C₁₂₇	1	4	yes	complemented
214	D₄⋊C₈	C₂²×C₁₂₇	1	4	yes	complemented
215	#322	C₂²×C₁₂₇	1	2	yes	complemented
216	#322	C₂²×C₁₂₇	1	2	yes	complemented
217	C₂²×D₄	C₂×C₄×C₁₂₇	1	2	yes	—
218	C₂³×C₄	—	2	2	no	—
219	C₂×D₈	—	2	4	no	—
220	C₂×D₈	C₂×C₄×C₁₂₇	1	2	yes	—
221	C₂×D₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
222	C₂×D₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	4	no	—
225	C₂×M₁₆	—	4	8	no	—
226	C₂×M₁₆	D₄×C₁₂₇	1	2	yes	—
227	C₂²×C₈	—	2	4	no	—
228	C₂²×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
229	C₂²×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	C₂×C₄×C₁₂₇	1	2	yes	—
233	C₄×D₄	C₂×C₄×C₁₂₇	1	2	yes	—
234	C₄×D₄	C₂³×C₁₂₇	1	2	yes	—
235	C₄×D₄	C₂³×C₁₂₇	1	2	yes	—
236	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
239	#107	C₂×C₄×C₁₂₇	1	2	yes	—
240	#107	C₂×C₄×C₁₂₇	1	1	yes	characteristic
241	#107	C₂×C₄×C₁₂₇	1	1	yes	characteristic
242	C₄⋊C₈	—	2	2	no	—
243	C₄⋊C₈	—	2	1	no	—
244	C₄⋊C₈	C₂³×C₁₂₇	1	4	yes	—
245	#102	C₂×C₄×C₁₂₇	1	2	yes	—
246	#102	C₂×C₄×C₁₂₇	1	2	yes	—
247	#102	C₂×C₄×C₁₂₇	1	2	yes	—
248	#102	C₂×C₄×C₁₂₇	1	2	yes	—
249	C₂²⋊C₈	—	2	1	no	—
250	C₂²⋊C₈	—	2	4	no	—
251	C₂²⋊C₈	—	2	4	no	—
252	#97	D₄×C₁₂₇	1	2	yes	—
253	C₄×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
254	C₄×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
255	C₄×C₈	C₂³×C₁₂₇	1	2	yes	—
256	C₄×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
257	C₄×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
258	C₄×C₈	C₂³×C₁₂₇	1	2	yes	—
259	C₂⁴	—	2	2	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	4	2	no	—
263	C₂×D₄	C₂²×C₄×C₁₂₇	1	2	yes	—
264	C₂×D₄	C₂²×C₄×C₁₂₇	1	2	yes	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	4	4	no	—
271	C₂²×C₄	—	4	4	no	—
272	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
274	C₂²×C₄	#41×C₁₂₇	1	1	yes	characteristic
275	D₈	—	2	4	no	—
276	D₈	—	2	2	no	—
277	D₈	M₁₆×C₁₂₇	1	4	yes	complemented
278	M₁₆	—	2	4	no	—
279	M₁₆	—	4	8	no	—
280	M₁₆	—	4	4	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	4	1	no	—
285	C₂×C₈	—	4	8	no	—
286	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
287	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
288	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
289	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
290	C₂×C₈	C₂×D₄×C₁₂₇	1	4	yes	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
293	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	2	no	—
297	C₂²⋊C₄	—	2	2	no	—
298	C₄²	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
299	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
300	C₄²	#41×C₁₂₇	1	1	yes	characteristic
301	C₄²	C₂⁴×C₁₂₇	1	1	yes	characteristic
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	4	4	no	—
305	C₂³	—	4	4	no	—
306	C₂³	—	8	2	no	—
307	C₂³	C₄×D₄×C₁₂₇	1	1	yes	characteristic
308	D₄	—	2	2	no	—
309	D₄	—	2	2	no	—
310	D₄	—	2	2	no	—
311	D₄	—	4	4	no	—
312	D₄	C₂×M₁₆×C₁₂₇	1	4	yes	complemented
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	C₄×D₄×C₁₂₇	1	1	yes	characteristic
326	C₂×C₄	C₄×D₄×C₁₂₇	1	1	yes	characteristic
327	C₂×C₄	C₄×D₄×C₁₂₇	1	1	yes	characteristic
328	C₂×C₄	AGL(1,ℤ/8)×C₁₂₇	1	4	yes	—
329	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
330	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
331	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
332	C₈	—	2	1	no	—
333	C₈	—	2	1	no	—
334	C₈	—	2	1	no	—
335	C₈	—	2	4	no	—
336	C₈	—	4	2	no	—
337	C₈	—	4	4	no	—
338	C₈	C₂×M₁₆×C₁₂₇	1	2	yes	complemented
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	8	8	no	—
348	C₂²	#442×C₁₂₇	1	2	yes	—
349	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	#442×C₁₂₇	1	2	yes	—
356	C₄	C₂²×M₁₆×C₁₂₇	1	1	yes	characteristic
357	C₄	#568×C₁₂₇	1	1	yes	characteristic
358	C₄	C₂×AGL(1,ℤ/8)×C₁₂₇	1	2	yes	—
359	C₂	—	2	2	no	—
360	C₂	—	4	4	no	—
361	C₂	—	8	2	no	—
362	C₂	D₄×M₁₆×C₁₂₇	1	1	yes	characteristic
363	C₂	C₂×#442×C₁₂₇	1	1	yes	characteristic
364	C₂	C₁₂₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₂₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₂₇
Frattini, cosocle	C₄²	C₂⁴×C₁₂₇
socle	C₂²×C₁₂₇	C₂×C₄×D₄
prime radical	C₂²×D₈×C₁₂₇	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₂₇ ◁ C₄×M₁₆×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×M₁₆×C₁₂₇	C₂	semidirect
3. C₁₂₇×#1594	C₂	semidirect
4. C₁₂₇×#1586	C₂	semidirect
5. C₁₂₇×#1580	C₂	semidirect
6. C₁₂₇×#1566	C₂	semidirect
7. C₁₂₇×#1486	C₂	semidirect
8. C₁₂₇×#1451	C₂	semidirect
18. #436×C₁₂₇	C₂²	semidirect
20. C₈×D₄×C₁₂₇	C₂²	semidirect
28. #334×C₁₂₇	C₂²	semidirect
29. #334×C₁₂₇	C₂²	semidirect
30. D₄⋊C₈×C₁₂₇	C₂²	semidirect
31. D₄⋊C₈×C₁₂₇	C₂²	semidirect
32. #322×C₁₂₇	C₂²	semidirect
33. #322×C₁₂₇	C₂²	semidirect
94. D₈×C₁₂₇	M₁₆	semidirect
129. D₄×C₁₂₇	C₂×M₁₆	semidirect
155. C₈×C₁₂₇	C₂×M₁₆	semidirect
176. #18044	C₁₂₇	direct (N × H)
184. D₄×M₁₆	C₂×C₁₂₇	semidirect
185. #1594	C₂×C₁₂₇	semidirect
186. #1586	C₂×C₁₂₇	semidirect
187. #1580	C₂×C₁₂₇	semidirect
188. #1566	C₂×C₁₂₇	semidirect
189. #1486	C₂×C₁₂₇	semidirect
190. #1451	C₂×C₁₂₇	semidirect
191. C₁₂₇	#18044	direct (N × H)
201. #436	C₂²×C₁₂₇	semidirect
203. C₈×D₄	C₂²×C₁₂₇	semidirect
211. #334	C₂²×C₁₂₇	semidirect
212. #334	C₂²×C₁₂₇	semidirect
213. D₄⋊C₈	C₂²×C₁₂₇	semidirect
214. D₄⋊C₈	C₂²×C₁₂₇	semidirect
215. #322	C₂²×C₁₂₇	semidirect
216. #322	C₂²×C₁₂₇	semidirect
277. D₈	M₁₆×C₁₂₇	semidirect
312. D₄	C₂×M₁₆×C₁₂₇	semidirect
338. C₈	C₂×M₁₆×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₈×C₁₂₇	2
D₄×M₁₆×C₁₂₇	2
C₁₂₇×#1594	2
C₁₂₇×#1586	2
C₁₂₇×#1580	2
C₁₂₇×#1566	2
C₁₂₇×#1486	2
C₁₂₇×#1451	2
#18044	127

Subgroups — C127×#18044 #44581717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#18044 #44581717