Subgroups — C₁₂₇×#21685 #44585358

Order 32512.

1194 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#436×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#435×C₁₂₇	C₂	1	4	yes	maximal, complemented
3	C₂×C₈×D₄×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₂₇×#2397	C₂	1	1	yes	maximal, characteristic
5	C₁₂₇×#1955	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₂₇×#1955	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₂₇×#1954	C₂	1	4	yes	maximal, complemented
8	C₁₂₇×#1843	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₂₇×#1726	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×M₁₆×C₁₂₇	C₂²	1	2	yes	—
11	C₂³×C₈×C₁₂₇	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₂₇	C₂²	1	4	yes	—
14	C₂×C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
15	#436×C₁₂₇	—	2	4	no	—
16	#435×C₁₂₇	—	2	16	no	—
17	C₈×D₄×C₁₂₇	—	2	4	no	—
18	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	4	yes	—
20	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	4	yes	—
23	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	4	yes	—
24	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	—
25	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
26	C₂×#97×C₁₂₇	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
29	#399×C₁₂₇	C₄	1	2	yes	—
30	#399×C₁₂₇	C₄	1	2	yes	—
31	#392×C₁₂₇	C₄	1	2	yes	—
32	#392×C₁₂₇	C₄	1	2	yes	—
33	#376×C₁₂₇	C₂²	1	1	yes	characteristic
34	C₂²×D₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₂₇	C₂×C₄	1	4	yes	—
36	C₂²×D₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₂₇	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₂₇	C₂³	1	2	yes	—
39	C₂×M₁₆×C₁₂₇	—	2	8	no	—
40	C₂×M₁₆×C₁₂₇	—	2	4	no	—
41	C₂²×C₈×C₁₂₇	—	2	4	no	—
42	C₂²×C₈×C₁₂₇	—	2	8	no	—
43	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
48	C₄×D₄×C₁₂₇	—	2	2	no	—
49	C₄×D₄×C₁₂₇	—	2	8	no	—
50	C₄×D₄×C₁₂₇	—	2	2	no	—
51	C₄×D₄×C₁₂₇	—	2	8	no	—
52	C₄×D₄×C₁₂₇	—	2	2	no	—
53	C₄×D₄×C₁₂₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
58	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
63	C₄⋊C₈×C₁₂₇	—	2	2	no	—
64	C₄⋊C₈×C₁₂₇	—	2	8	no	—
65	C₄⋊C₈×C₁₂₇	—	2	2	no	—
66	C₂²⋊C₈×C₁₂₇	—	2	4	no	—
67	C₂²⋊C₈×C₁₂₇	—	2	8	no	—
68	C₂²⋊C₈×C₁₂₇	—	2	8	no	—
69	C₂²⋊C₈×C₁₂₇	—	2	4	no	—
70	#97×C₁₂₇	—	2	2	no	—
71	#97×C₁₂₇	D₄	1	8	yes	complemented
72	C₄×C₈×C₁₂₇	—	2	4	no	—
73	C₄×C₈×C₁₂₇	D₄	1	4	yes	complemented
74	#95×C₁₂₇	C₂×C₄	1	2	yes	—
75	#95×C₁₂₇	C₂×C₄	1	2	yes	—
76	C₂⁴×C₁₂₇	C₂²×C₄	1	2	yes	—
77	C₂⁴×C₁₂₇	C₂²×C₄	1	2	yes	—
78	C₂×D₄×C₁₂₇	—	2	4	no	—
79	C₂×D₄×C₁₂₇	—	2	8	no	—
80	C₂×D₄×C₁₂₇	—	2	2	no	—
81	C₂×D₄×C₁₂₇	—	2	8	no	—
82	C₂×D₄×C₁₂₇	—	2	2	no	—
83	C₂×D₄×C₁₂₇	—	4	4	no	—
84	C₂×D₄×C₁₂₇	—	4	2	no	—
85	C₂²×C₄×C₁₂₇	—	2	2	no	—
86	C₂²×C₄×C₁₂₇	—	2	4	no	—
87	C₂²×C₄×C₁₂₇	—	2	4	no	—
88	C₂²×C₄×C₁₂₇	—	2	2	no	—
89	C₂²×C₄×C₁₂₇	—	2	2	no	—
90	C₂²×C₄×C₁₂₇	—	2	4	no	—
91	C₂²×C₄×C₁₂₇	—	2	2	no	—
92	C₂²×C₄×C₁₂₇	—	2	4	no	—
93	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
99	M₁₆×C₁₂₇	—	4	8	no	—
100	C₂×C₈×C₁₂₇	—	2	2	no	—
101	C₂×C₈×C₁₂₇	—	2	2	no	—
102	C₂×C₈×C₁₂₇	—	2	2	no	—
103	C₂×C₈×C₁₂₇	—	2	2	no	—
104	C₂×C₈×C₁₂₇	—	2	4	no	—
105	C₂×C₈×C₁₂₇	—	2	4	no	—
106	C₂×C₈×C₁₂₇	—	2	2	no	—
107	C₂×C₈×C₁₂₇	—	4	8	no	—
108	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₁₂₇	C₂×D₄	1	4	yes	—
110	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₁₂₇	C₂×D₄	1	4	yes	—
112	C₄⋊C₄×C₁₂₇	—	2	2	no	—
113	C₄⋊C₄×C₁₂₇	—	2	8	no	—
114	C₄⋊C₄×C₁₂₇	—	2	2	no	—
115	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
116	C₂²⋊C₄×C₁₂₇	—	2	8	no	—
117	C₂²⋊C₄×C₁₂₇	—	2	8	no	—
118	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
119	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
120	C₄²×C₁₂₇	C₂×D₄	1	4	yes	—
121	C₄²×C₁₂₇	#41	1	4	yes	—
122	C₄²×C₁₂₇	#41	1	2	yes	—
123	C₂³×C₁₂₇	—	2	2	no	—
124	C₂³×C₁₂₇	—	2	4	no	—
125	C₂³×C₁₂₇	—	2	2	no	—
126	C₂³×C₁₂₇	—	2	4	no	—
127	C₂³×C₁₂₇	—	2	2	no	—
128	C₂³×C₁₂₇	—	2	4	no	—
129	C₂³×C₁₂₇	—	2	4	no	—
130	C₂³×C₁₂₇	—	2	2	no	—
131	C₂³×C₁₂₇	—	2	2	no	—
132	C₂³×C₁₂₇	#131	1	4	yes	—
133	C₂³×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
134	D₄×C₁₂₇	—	2	8	no	—
135	D₄×C₁₂₇	—	4	16	no	—
136	D₄×C₁₂₇	—	4	4	no	—
137	C₂×C₄×C₁₂₇	—	2	2	no	—
138	C₂×C₄×C₁₂₇	—	2	4	no	—
139	C₂×C₄×C₁₂₇	—	2	2	no	—
140	C₂×C₄×C₁₂₇	—	2	4	no	—
141	C₂×C₄×C₁₂₇	—	2	2	no	—
142	C₂×C₄×C₁₂₇	—	2	2	no	—
143	C₂×C₄×C₁₂₇	—	2	4	no	—
144	C₂×C₄×C₁₂₇	—	2	4	no	—
145	C₂×C₄×C₁₂₇	—	4	2	no	—
146	C₂×C₄×C₁₂₇	—	4	2	no	—
147	C₂×C₄×C₁₂₇	—	4	2	no	—
148	C₂×C₄×C₁₂₇	—	4	4	no	—
149	C₂×C₄×C₁₂₇	—	4	4	no	—
150	C₂×C₄×C₁₂₇	—	4	2	no	—
151	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₁₂₇	C₄×D₄	1	8	yes	—
154	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₂₇	C₂²×D₄	1	2	yes	—
156	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₁₂₇	C₂×#41	1	2	yes	—
158	C₈×C₁₂₇	—	2	2	no	—
159	C₈×C₁₂₇	—	2	4	no	—
160	C₈×C₁₂₇	—	4	2	no	—
161	C₈×C₁₂₇	—	4	2	no	—
162	C₈×C₁₂₇	#127	1	4	yes	—
163	C₂²×C₁₂₇	—	2	4	no	—
164	C₂²×C₁₂₇	—	2	8	no	—
165	C₂²×C₁₂₇	—	4	2	no	—
166	C₂²×C₁₂₇	—	4	2	no	—
167	C₂²×C₁₂₇	—	4	4	no	—
168	C₂²×C₁₂₇	—	4	2	no	—
169	C₂²×C₁₂₇	—	4	2	no	—
170	C₂²×C₁₂₇	—	4	2	no	—
171	C₂²×C₁₂₇	—	4	4	no	—
172	C₂²×C₁₂₇	—	4	4	no	—
173	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
174	C₂²×C₁₂₇	C₂×C₄×D₄	1	2	yes	—
175	C₂²×C₁₂₇	C₂×#131	1	2	yes	—
176	C₂²×C₁₂₇	#568	1	2	yes	—
177	C₄×C₁₂₇	—	2	2	no	—
178	C₄×C₁₂₇	—	2	2	no	—
179	C₄×C₁₂₇	—	2	8	no	—
180	C₄×C₁₂₇	—	4	2	no	—
181	C₄×C₁₂₇	—	4	2	no	—
182	C₄×C₁₂₇	C₂×#127	1	1	yes	characteristic
183	C₄×C₁₂₇	#532	1	1	yes	characteristic
184	C₄×C₁₂₇	#532	1	2	yes	—
185	#21685	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂×C₁₂₇	—	4	4	no	—
187	C₂×C₁₂₇	—	8	2	no	—
188	C₂×C₁₂₇	C₄×#127	1	1	yes	characteristic
189	C₂×C₁₂₇	#2929	1	1	yes	characteristic
190	C₂×C₁₂₇	#2930	1	1	yes	characteristic
191	C₂×C₁₂₇	#2933	1	4	yes	—
192	C₂×#436	C₂×C₁₂₇	1	1	yes	characteristic, complemented
193	C₂×#435	C₂×C₁₂₇	1	4	yes	complemented
194	C₂×C₈×D₄	C₂×C₁₂₇	1	1	yes	characteristic, complemented
195	#2397	C₂×C₁₂₇	1	1	yes	characteristic
196	#1955	C₂×C₁₂₇	1	1	yes	characteristic, complemented
197	#1955	C₂×C₁₂₇	1	1	yes	characteristic, complemented
198	#1954	C₂×C₁₂₇	1	4	yes	complemented
199	#1843	C₂×C₁₂₇	1	1	yes	characteristic, complemented
200	#1726	C₂×C₁₂₇	1	1	yes	characteristic, complemented
201	C₁₂₇	#21685	1	1	yes	characteristic, direct product factor, Sylow
202	C₂²×M₁₆	C₂²×C₁₂₇	1	2	yes	—
203	C₂³×C₈	C₂²×C₁₂₇	1	2	yes	—
204	C₂×C₄×D₄	C₂²×C₁₂₇	1	1	yes	characteristic
205	C₂×C₄×D₄	C₂²×C₁₂₇	1	4	yes	—
206	C₂×C₄×D₄	C₂²×C₁₂₇	1	1	yes	characteristic
207	#436	—	2	4	no	—
208	#435	—	2	16	no	—
209	C₈×D₄	—	2	4	no	—
210	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	4	yes	—
212	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
213	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	—
214	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	4	yes	—
215	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	4	yes	—
216	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	—
217	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
218	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
219	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
220	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
221	#399	C₄×C₁₂₇	1	2	yes	—
222	#399	C₄×C₁₂₇	1	2	yes	—
223	#392	C₄×C₁₂₇	1	2	yes	—
224	#392	C₄×C₁₂₇	1	2	yes	—
225	#376	C₂²×C₁₂₇	1	1	yes	characteristic
226	C₂²×D₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
227	C₂²×D₄	C₂×C₄×C₁₂₇	1	4	yes	—
228	C₂²×D₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₁₂₇	1	2	yes	—
230	C₂³×C₄	C₂³×C₁₂₇	1	2	yes	—
231	C₂×M₁₆	—	2	8	no	—
232	C₂×M₁₆	—	2	4	no	—
233	C₂²×C₈	—	2	4	no	—
234	C₂²×C₈	—	2	8	no	—
235	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
236	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
237	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
239	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	2	8	no	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	—	2	8	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	2	2	no	—
246	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
248	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
250	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
251	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
252	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
253	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
254	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	2	8	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₂²⋊C₈	—	2	4	no	—
259	C₂²⋊C₈	—	2	8	no	—
260	C₂²⋊C₈	—	2	8	no	—
261	C₂²⋊C₈	—	2	4	no	—
262	#97	—	2	2	no	—
263	#97	D₄×C₁₂₇	1	8	yes	complemented
264	C₄×C₈	—	2	4	no	—
265	C₄×C₈	D₄×C₁₂₇	1	4	yes	complemented
266	#95	C₂×C₄×C₁₂₇	1	2	yes	—
267	#95	C₂×C₄×C₁₂₇	1	2	yes	—
268	C₂⁴	C₂²×C₄×C₁₂₇	1	2	yes	—
269	C₂⁴	C₂²×C₄×C₁₂₇	1	2	yes	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	2	8	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	8	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	4	4	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
286	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
289	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
290	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
291	M₁₆	—	4	8	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	4	8	no	—
300	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
301	C₂×C₈	C₂×D₄×C₁₂₇	1	4	yes	—
302	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
303	C₂×C₈	C₂×D₄×C₁₂₇	1	4	yes	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	4	no	—
308	C₂²⋊C₄	—	2	8	no	—
309	C₂²⋊C₄	—	2	8	no	—
310	C₂²⋊C₄	—	2	4	no	—
311	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
312	C₄²	C₂×D₄×C₁₂₇	1	4	yes	—
313	C₄²	#41×C₁₂₇	1	4	yes	—
314	C₄²	#41×C₁₂₇	1	2	yes	—
315	C₂³	—	2	2	no	—
316	C₂³	—	2	4	no	—
317	C₂³	—	2	2	no	—
318	C₂³	—	2	4	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	#131×C₁₂₇	1	4	yes	—
325	C₂³	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
326	D₄	—	2	8	no	—
327	D₄	—	4	16	no	—
328	D₄	—	4	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
344	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
345	C₂×C₄	C₄×D₄×C₁₂₇	1	8	yes	—
346	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
347	C₂×C₄	C₂²×D₄×C₁₂₇	1	2	yes	—
348	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
349	C₂×C₄	C₂×#41×C₁₂₇	1	2	yes	—
350	C₈	—	2	2	no	—
351	C₈	—	2	4	no	—
352	C₈	—	4	2	no	—
353	C₈	—	4	2	no	—
354	C₈	#127×C₁₂₇	1	4	yes	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	8	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	4	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	4	no	—
363	C₂²	—	4	4	no	—
364	C₂²	—	4	2	no	—
365	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
366	C₂²	C₂×C₄×D₄×C₁₂₇	1	2	yes	—
367	C₂²	C₂×#131×C₁₂₇	1	2	yes	—
368	C₂²	#568×C₁₂₇	1	2	yes	—
369	C₄	—	2	2	no	—
370	C₄	—	2	2	no	—
371	C₄	—	2	8	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	2	no	—
374	C₄	C₂×#127×C₁₂₇	1	1	yes	characteristic
375	C₄	#532×C₁₂₇	1	1	yes	characteristic
376	C₄	#532×C₁₂₇	1	2	yes	—
377	C₂	—	4	4	no	—
378	C₂	—	8	2	no	—
379	C₂	C₄×#127×C₁₂₇	1	1	yes	characteristic
380	C₂	C₁₂₇×#2929	1	1	yes	characteristic
381	C₂	C₁₂₇×#2930	1	1	yes	characteristic
382	C₂	C₁₂₇×#2933	1	4	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	C₁₂₇×#2397	C₂
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×#436×C₁₂₇	C₂	semidirect
2. C₂×#435×C₁₂₇	C₂	semidirect
3. C₂×C₈×D₄×C₁₂₇	C₂	semidirect
5. C₁₂₇×#1955	C₂	semidirect
6. C₁₂₇×#1955	C₂	semidirect
7. C₁₂₇×#1954	C₂	semidirect
8. C₁₂₇×#1843	C₂	semidirect
9. C₁₂₇×#1726	C₂	semidirect
71. #97×C₁₂₇	D₄	semidirect
73. C₄×C₈×C₁₂₇	D₄	semidirect
185. #21685	C₁₂₇	direct (N × H)
192. C₂×#436	C₂×C₁₂₇	semidirect
193. C₂×#435	C₂×C₁₂₇	semidirect
194. C₂×C₈×D₄	C₂×C₁₂₇	semidirect
196. #1955	C₂×C₁₂₇	semidirect
197. #1955	C₂×C₁₂₇	semidirect
198. #1954	C₂×C₁₂₇	semidirect
199. #1843	C₂×C₁₂₇	semidirect
200. #1726	C₂×C₁₂₇	semidirect
201. C₁₂₇	#21685	direct (N × H)
263. #97	D₄×C₁₂₇	semidirect
265. C₄×C₈	D₄×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#436×C₁₂₇	2
C₂×#435×C₁₂₇	2
C₂×C₈×D₄×C₁₂₇	2
C₁₂₇×#2397	2
C₁₂₇×#1955	2
C₁₂₇×#1954	2
C₁₂₇×#1843	2
C₁₂₇×#1726	2
#21685	127

Subgroups — C127×#21685 #44585358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#21685 #44585358