Subgroups — C₁₂₇×#21634 #44585307

Order 32512.

886 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Q₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#436×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₄×#124×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₂₇×#1954	C₂	1	1	yes	maximal, characteristic
6	C₁₂₇×#1924	C₂	1	4	yes	maximal, complemented
7	C₁₂₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₂₇×#1753	C₂	1	4	yes	maximal, complemented
9	C₄×#97×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×M₁₆×C₁₂₇	C₂²	1	2	yes	—
11	C₂×#124×C₁₂₇	C₄	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
14	C₈×Q₈×C₁₂₇	—	2	4	no	—
15	#436×C₁₂₇	—	2	4	no	—
16	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	4	yes	—
21	C₂×#97×C₁₂₇	C₂²	1	2	yes	—
22	C₂×#97×C₁₂₇	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
26	#391×C₁₂₇	C₄	1	1	yes	characteristic
27	#390×C₁₂₇	C₄	1	1	yes	characteristic
28	#388×C₁₂₇	C₄	1	4	yes	—
29	#382×C₁₂₇	C₄	1	1	yes	characteristic
30	C₄×C₂²⋊C₄×C₁₂₇	C₂²	1	4	yes	—
31	C₄³×C₁₂₇	C₂²	1	1	yes	characteristic
32	#336×C₁₂₇	C₂²	1	4	yes	—
33	#336×C₁₂₇	C₂²	1	4	yes	—
34	C₂²×Q₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₂₇	C₂³	1	2	yes	—
37	C₂×M₁₆×C₁₂₇	—	2	4	no	—
38	C₂×M₁₆×C₁₂₇	—	2	8	no	—
39	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
44	#124×C₁₂₇	—	2	4	no	—
45	C₄×Q₈×C₁₂₇	—	2	2	no	—
46	C₄×Q₈×C₁₂₇	—	2	2	no	—
47	C₄×D₄×C₁₂₇	—	2	2	no	—
48	C₄×D₄×C₁₂₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
54	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₂₇	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
59	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
60	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₁₂₇	—	2	4	no	—
62	C₄⋊C₈×C₁₂₇	—	2	2	no	—
63	C₄⋊C₈×C₁₂₇	—	2	2	no	—
64	C₂²⋊C₈×C₁₂₇	—	2	4	no	—
65	C₂²⋊C₈×C₁₂₇	—	2	8	no	—
66	#97×C₁₂₇	—	2	4	no	—
67	#97×C₁₂₇	—	2	4	no	—
68	C₄×C₈×C₁₂₇	—	2	4	no	—
69	C₄×C₈×C₁₂₇	—	2	2	no	—
70	C₄×C₈×C₁₂₇	D₄	1	4	yes	—
71	#95×C₁₂₇	C₂×C₄	1	4	yes	—
72	#95×C₁₂₇	C₂×C₄	1	4	yes	—
73	C₂⁴×C₁₂₇	C₂²×C₄	1	2	yes	—
74	C₂×Q₈×C₁₂₇	—	2	2	no	—
75	C₂×Q₈×C₁₂₇	—	2	2	no	—
76	C₂×Q₈×C₁₂₇	M₁₆	1	4	yes	complemented
77	C₂×D₄×C₁₂₇	—	2	2	no	—
78	C₂×D₄×C₁₂₇	—	2	2	no	—
79	C₂×D₄×C₁₂₇	—	2	2	no	—
80	C₂²×C₄×C₁₂₇	—	2	2	no	—
81	C₂²×C₄×C₁₂₇	—	2	4	no	—
82	C₂²×C₄×C₁₂₇	—	2	2	no	—
83	C₂²×C₄×C₁₂₇	—	2	4	no	—
84	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
92	M₁₆×C₁₂₇	—	4	8	no	—
93	C₂×C₈×C₁₂₇	—	2	2	no	—
94	C₂×C₈×C₁₂₇	—	2	2	no	—
95	C₂×C₈×C₁₂₇	—	2	2	no	—
96	C₂×C₈×C₁₂₇	—	2	2	no	—
97	C₂×C₈×C₁₂₇	—	2	2	no	—
98	C₂×C₈×C₁₂₇	—	2	4	no	—
99	C₂×C₈×C₁₂₇	—	2	4	no	—
100	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
101	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₁₂₇	#41	1	4	yes	—
103	C₂×C₈×C₁₂₇	#41	1	4	yes	—
104	C₄⋊C₄×C₁₂₇	—	2	2	no	—
105	C₄⋊C₄×C₁₂₇	—	2	4	no	—
106	C₄⋊C₄×C₁₂₇	—	2	2	no	—
107	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
108	C₂²⋊C₄×C₁₂₇	—	2	8	no	—
109	C₂²⋊C₄×C₁₂₇	—	4	4	no	—
110	C₄²×C₁₂₇	—	2	2	no	—
111	C₄²×C₁₂₇	—	2	2	no	—
112	C₄²×C₁₂₇	—	2	2	no	—
113	C₄²×C₁₂₇	—	2	2	no	—
114	C₄²×C₁₂₇	—	2	2	no	—
115	C₄²×C₁₂₇	—	2	2	no	—
116	C₄²×C₁₂₇	—	4	2	no	—
117	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
118	C₄²×C₁₂₇	#41	1	2	yes	—
119	C₂³×C₁₂₇	—	2	2	no	—
120	C₂³×C₁₂₇	—	2	4	no	—
121	C₂³×C₁₂₇	—	2	2	no	—
122	C₂³×C₁₂₇	—	2	2	no	—
123	C₂³×C₁₂₇	—	2	4	no	—
124	C₂³×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
125	Q₈×C₁₂₇	—	2	8	no	—
126	D₄×C₁₂₇	—	4	4	no	—
127	C₂×C₄×C₁₂₇	—	2	2	no	—
128	C₂×C₄×C₁₂₇	—	2	2	no	—
129	C₂×C₄×C₁₂₇	—	2	2	no	—
130	C₂×C₄×C₁₂₇	—	2	2	no	—
131	C₂×C₄×C₁₂₇	—	2	2	no	—
132	C₂×C₄×C₁₂₇	—	2	2	no	—
133	C₂×C₄×C₁₂₇	—	2	2	no	—
134	C₂×C₄×C₁₂₇	—	2	4	no	—
135	C₂×C₄×C₁₂₇	—	2	2	no	—
136	C₂×C₄×C₁₂₇	—	2	2	no	—
137	C₂×C₄×C₁₂₇	—	2	2	no	—
138	C₂×C₄×C₁₂₇	—	2	2	no	—
139	C₂×C₄×C₁₂₇	—	2	4	no	—
140	C₂×C₄×C₁₂₇	—	4	2	no	—
141	C₂×C₄×C₁₂₇	—	4	4	no	—
142	C₂×C₄×C₁₂₇	—	4	2	no	—
143	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
144	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
145	C₂×C₄×C₁₂₇	C₂×M₁₆	1	4	yes	—
146	C₂×C₄×C₁₂₇	C₂×M₁₆	1	2	yes	—
147	C₂×C₄×C₁₂₇	#131	1	2	yes	—
148	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₂₇	C₂×#41	1	2	yes	—
150	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₁₂₇	C₂×#41	1	2	yes	—
152	C₈×C₁₂₇	—	2	4	no	—
153	C₈×C₁₂₇	—	2	2	no	—
154	C₈×C₁₂₇	—	4	2	no	—
155	C₈×C₁₂₇	—	4	2	no	—
156	C₈×C₁₂₇	#124	1	4	yes	complemented
157	C₂²×C₁₂₇	—	4	2	no	—
158	C₂²×C₁₂₇	—	4	2	no	—
159	C₂²×C₁₂₇	—	4	4	no	—
160	C₂²×C₁₂₇	—	4	4	no	—
161	C₂²×C₁₂₇	—	4	2	no	—
162	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
163	C₂²×C₁₂₇	C₄×#41	1	2	yes	—
164	C₂²×C₁₂₇	C₂²×M₁₆	1	1	yes	characteristic
165	C₂²×C₁₂₇	C₂×#131	1	1	yes	characteristic
166	C₂²×C₁₂₇	#568	1	2	yes	—
167	C₄×C₁₂₇	—	2	4	no	—
168	C₄×C₁₂₇	—	2	2	no	—
169	C₄×C₁₂₇	—	4	2	no	—
170	C₄×C₁₂₇	—	4	2	no	—
171	C₄×C₁₂₇	—	4	2	no	—
172	C₄×C₁₂₇	—	4	2	no	—
173	C₄×C₁₂₇	#435	1	4	yes	—
174	C₄×C₁₂₇	C₂×#124	1	1	yes	characteristic
175	C₄×C₁₂₇	#529	1	2	yes	—
176	C₄×C₁₂₇	#532	1	1	yes	characteristic
177	#21634	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂×C₁₂₇	—	8	2	no	—
179	C₂×C₁₂₇	C₄×#124	1	1	yes	characteristic
180	C₂×C₁₂₇	C₂×#435	1	1	yes	characteristic
181	C₂×C₁₂₇	#2932	1	1	yes	characteristic
182	C₂×C₁₂₇	#2969	1	2	yes	—
183	C₂×C₁₂₇	#2971	1	2	yes	—
184	C₂×C₈×Q₈	C₂×C₁₂₇	1	1	yes	characteristic, complemented
185	C₂×#436	C₂×C₁₂₇	1	1	yes	characteristic
186	C₄×#124	C₂×C₁₂₇	1	1	yes	characteristic
187	#1984	C₂×C₁₂₇	1	1	yes	characteristic, complemented
188	#1954	C₂×C₁₂₇	1	1	yes	characteristic
189	#1924	C₂×C₁₂₇	1	4	yes	complemented
190	#1831	C₂×C₁₂₇	1	1	yes	characteristic, complemented
191	#1753	C₂×C₁₂₇	1	4	yes	complemented
192	C₄×#97	C₂×C₁₂₇	1	1	yes	characteristic, complemented
193	C₁₂₇	#21634	1	1	yes	characteristic, direct product factor, Sylow
194	C₂²×M₁₆	C₂²×C₁₂₇	1	2	yes	—
195	C₂×#124	C₄×C₁₂₇	1	1	yes	characteristic
196	C₂×C₄×Q₈	C₂²×C₁₂₇	1	1	yes	characteristic
197	C₂×C₄×D₄	C₂²×C₁₂₇	1	1	yes	characteristic
198	C₈×Q₈	—	2	4	no	—
199	#436	—	2	4	no	—
200	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
201	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
202	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
203	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	—
204	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	4	yes	—
205	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
206	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
207	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
208	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
209	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
210	#391	C₄×C₁₂₇	1	1	yes	characteristic
211	#390	C₄×C₁₂₇	1	1	yes	characteristic
212	#388	C₄×C₁₂₇	1	4	yes	—
213	#382	C₄×C₁₂₇	1	1	yes	characteristic
214	C₄×C₂²⋊C₄	C₂²×C₁₂₇	1	4	yes	—
215	C₄³	C₂²×C₁₂₇	1	1	yes	characteristic
216	#336	C₂²×C₁₂₇	1	4	yes	—
217	#336	C₂²×C₁₂₇	1	4	yes	—
218	C₂²×Q₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
219	C₂²×D₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
220	C₂³×C₄	C₂³×C₁₂₇	1	2	yes	—
221	C₂×M₁₆	—	2	4	no	—
222	C₂×M₁₆	—	2	8	no	—
223	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
224	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
225	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
227	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
228	#124	—	2	4	no	—
229	C₄×Q₈	—	2	2	no	—
230	C₄×Q₈	—	2	2	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	—	2	2	no	—
233	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
236	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
237	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
238	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
239	C₂×C₄²	C₂×C₄×C₁₂₇	1	1	yes	characteristic
240	C₂×C₄²	C₂×C₄×C₁₂₇	1	1	yes	characteristic
241	C₂×C₄²	C₂×C₄×C₁₂₇	1	2	yes	—
242	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
243	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
244	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
245	C₄⋊C₈	—	2	4	no	—
246	C₄⋊C₈	—	2	2	no	—
247	C₄⋊C₈	—	2	2	no	—
248	C₂²⋊C₈	—	2	4	no	—
249	C₂²⋊C₈	—	2	8	no	—
250	#97	—	2	4	no	—
251	#97	—	2	4	no	—
252	C₄×C₈	—	2	4	no	—
253	C₄×C₈	—	2	2	no	—
254	C₄×C₈	D₄×C₁₂₇	1	4	yes	—
255	#95	C₂×C₄×C₁₂₇	1	4	yes	—
256	#95	C₂×C₄×C₁₂₇	1	4	yes	—
257	C₂⁴	C₂²×C₄×C₁₂₇	1	2	yes	—
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	M₁₆×C₁₂₇	1	4	yes	complemented
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
269	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
270	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
272	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
274	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
275	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
276	M₁₆	—	4	8	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
285	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
286	C₂×C₈	#41×C₁₂₇	1	4	yes	—
287	C₂×C₈	#41×C₁₂₇	1	4	yes	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₂²⋊C₄	—	2	4	no	—
292	C₂²⋊C₄	—	2	8	no	—
293	C₂²⋊C₄	—	4	4	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	4	2	no	—
301	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
302	C₄²	#41×C₁₂₇	1	2	yes	—
303	C₂³	—	2	2	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	4	no	—
308	C₂³	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
309	Q₈	—	2	8	no	—
310	D₄	—	4	4	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
328	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
329	C₂×C₄	C₂×M₁₆×C₁₂₇	1	4	yes	—
330	C₂×C₄	C₂×M₁₆×C₁₂₇	1	2	yes	—
331	C₂×C₄	#131×C₁₂₇	1	2	yes	—
332	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
333	C₂×C₄	C₂×#41×C₁₂₇	1	2	yes	—
334	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
335	C₂×C₄	C₂×#41×C₁₂₇	1	2	yes	—
336	C₈	—	2	4	no	—
337	C₈	—	2	2	no	—
338	C₈	—	4	2	no	—
339	C₈	—	4	2	no	—
340	C₈	#124×C₁₂₇	1	4	yes	complemented
341	C₂²	—	4	2	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	4	no	—
344	C₂²	—	4	4	no	—
345	C₂²	—	4	2	no	—
346	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
347	C₂²	C₄×#41×C₁₂₇	1	2	yes	—
348	C₂²	C₂²×M₁₆×C₁₂₇	1	1	yes	characteristic
349	C₂²	C₂×#131×C₁₂₇	1	1	yes	characteristic
350	C₂²	#568×C₁₂₇	1	2	yes	—
351	C₄	—	2	4	no	—
352	C₄	—	2	2	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	—	4	2	no	—
356	C₄	—	4	2	no	—
357	C₄	#435×C₁₂₇	1	4	yes	—
358	C₄	C₂×#124×C₁₂₇	1	1	yes	characteristic
359	C₄	#529×C₁₂₇	1	2	yes	—
360	C₄	#532×C₁₂₇	1	1	yes	characteristic
361	C₂	—	8	2	no	—
362	C₂	C₄×#124×C₁₂₇	1	1	yes	characteristic
363	C₂	C₂×#435×C₁₂₇	1	1	yes	characteristic
364	C₂	C₁₂₇×#2932	1	1	yes	characteristic
365	C₂	C₁₂₇×#2969	1	2	yes	—
366	C₂	C₁₂₇×#2971	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×Q₈×C₁₂₇	C₂	semidirect
4. C₁₂₇×#1984	C₂	semidirect
6. C₁₂₇×#1924	C₂	semidirect
7. C₁₂₇×#1831	C₂	semidirect
8. C₁₂₇×#1753	C₂	semidirect
9. C₄×#97×C₁₂₇	C₂	semidirect
76. C₂×Q₈×C₁₂₇	M₁₆	semidirect
156. C₈×C₁₂₇	#124	semidirect
177. #21634	C₁₂₇	direct (N × H)
184. C₂×C₈×Q₈	C₂×C₁₂₇	semidirect
187. #1984	C₂×C₁₂₇	semidirect
189. #1924	C₂×C₁₂₇	semidirect
190. #1831	C₂×C₁₂₇	semidirect
191. #1753	C₂×C₁₂₇	semidirect
192. C₄×#97	C₂×C₁₂₇	semidirect
193. C₁₂₇	#21634	direct (N × H)
260. C₂×Q₈	M₁₆×C₁₂₇	semidirect
340. C₈	#124×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×Q₈×C₁₂₇	2
C₂×#436×C₁₂₇	2
C₄×#124×C₁₂₇	2
C₁₂₇×#1984	2
C₁₂₇×#1954	2
C₁₂₇×#1924	2
C₁₂₇×#1831	2
C₁₂₇×#1753	2
C₄×#97×C₁₂₇	2
#21634	127

Subgroups — C127×#21634 #44585307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#21634 #44585307