Subgroups — C₂×C₁₂₇×#1851 #44584506

Order 32512.

1702 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₈×C₁₂₇	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂²⋊C₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₂²⋊C₄×C₁₂₇	C₂	1	1	yes	maximal, characteristic
5	C₁₂₇×#1851	C₂	1	8	yes	maximal, direct product factor
6	C₂×#336×C₁₂₇	C₂	1	2	yes	maximal, complemented
7	C₂⁴×C₄×C₁₂₇	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₁₂₇	—	2	4	no	—
9	C₂²×M₁₆×C₁₂₇	—	2	8	no	—
10	C₂²×M₁₆×C₁₂₇	C₂²	1	4	yes	—
11	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₂₇	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₁₂₇	C₄	1	2	yes	—
15	C₂²×C₄²×C₁₂₇	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₁₂₇	—	2	8	no	—
17	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	8	yes	complemented
18	C₂×C₂²⋊C₈×C₁₂₇	—	2	4	no	—
19	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	4	yes	—
20	C₄×C₂²⋊C₄×C₁₂₇	C₄	1	4	yes	—
21	C₄×C₂²⋊C₄×C₁₂₇	C₂²	1	4	yes	—
22	C₂×#95×C₁₂₇	C₄	1	1	yes	characteristic
23	C₂×#95×C₁₂₇	C₄	1	1	yes	characteristic
24	#336×C₁₂₇	C₂²	1	8	yes	complemented
25	C₂⁵×C₁₂₇	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₂₇	—	2	4	no	—
27	C₂³×C₄×C₁₂₇	—	2	4	no	—
28	C₂³×C₄×C₁₂₇	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₂₇	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₁₂₇	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₁₂₇	D₄	1	4	yes	—
33	C₂³×C₄×C₁₂₇	Q₈	1	4	yes	—
34	C₂³×C₄×C₁₂₇	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₁₂₇	—	2	32	no	—
37	C₂×M₁₆×C₁₂₇	—	2	8	no	—
38	C₂×M₁₆×C₁₂₇	—	2	16	no	—
39	C₂²×C₈×C₁₂₇	—	2	4	no	—
40	C₂²×C₈×C₁₂₇	—	2	4	no	—
41	C₂²×C₈×C₁₂₇	—	2	2	no	—
42	C₂²×C₈×C₁₂₇	—	2	2	no	—
43	C₂²×C₈×C₁₂₇	—	2	4	no	—
44	C₂²×C₈×C₁₂₇	—	2	4	no	—
45	C₂²×C₈×C₁₂₇	D₄	1	8	yes	—
46	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₂₇	C₂³	1	4	yes	—
49	C₂×C₂²⋊C₄×C₁₂₇	—	2	8	no	—
50	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	8	yes	—
51	C₂×C₄²×C₁₂₇	—	2	4	no	—
52	C₂×C₄²×C₁₂₇	—	2	4	no	—
53	C₂×C₄²×C₁₂₇	C₂×C₄	1	4	yes	—
54	C₂×C₄²×C₁₂₇	C₂³	1	4	yes	—
55	C₄⋊C₈×C₁₂₇	—	2	16	no	—
56	C₂²⋊C₈×C₁₂₇	—	2	8	no	—
57	#95×C₁₂₇	C₂×C₄	1	4	yes	—
58	#95×C₁₂₇	C₂×C₄	1	4	yes	—
59	C₂⁴×C₁₂₇	—	2	4	no	—
60	C₂⁴×C₁₂₇	—	2	4	no	—
61	C₂⁴×C₁₂₇	—	2	2	no	—
62	C₂⁴×C₁₂₇	—	2	2	no	—
63	C₂⁴×C₁₂₇	C₄⋊C₄	1	4	yes	—
64	C₂⁴×C₁₂₇	C₂²×C₄	1	2	yes	—
65	C₂⁴×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₂₇	—	2	4	no	—
67	C₂²×C₄×C₁₂₇	—	2	4	no	—
68	C₂²×C₄×C₁₂₇	—	2	4	no	—
69	C₂²×C₄×C₁₂₇	—	2	8	no	—
70	C₂²×C₄×C₁₂₇	—	2	8	no	—
71	C₂²×C₄×C₁₂₇	—	2	16	no	—
72	C₂²×C₄×C₁₂₇	—	2	8	no	—
73	C₂²×C₄×C₁₂₇	—	2	4	no	—
74	C₂²×C₄×C₁₂₇	—	2	4	no	—
75	C₂²×C₄×C₁₂₇	—	2	4	no	—
76	C₂²×C₄×C₁₂₇	—	2	4	no	—
77	C₂²×C₄×C₁₂₇	—	2	4	no	—
78	C₂²×C₄×C₁₂₇	C₄⋊C₄	1	4	yes	—
79	C₂²×C₄×C₁₂₇	C₄⋊C₄	1	8	yes	—
80	C₂²×C₄×C₁₂₇	M₁₆	1	8	yes	complemented
81	C₂²×C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₂₇	C₂×D₄	1	4	yes	—
86	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₂₇	C₂×D₄	1	4	yes	—
88	C₂²×C₄×C₁₂₇	C₂×Q₈	1	4	yes	—
89	C₂²×C₄×C₁₂₇	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₁₂₇	#41	1	4	yes	—
91	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
92	M₁₆×C₁₂₇	—	2	32	no	—
93	C₂×C₈×C₁₂₇	—	2	16	no	—
94	C₂×C₈×C₁₂₇	—	2	4	no	—
95	C₂×C₈×C₁₂₇	—	2	4	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	—	4	4	no	—
101	C₂×C₈×C₁₂₇	—	4	4	no	—
102	C₂×C₈×C₁₂₇	C₂×D₄	1	8	yes	—
103	C₂²⋊C₄×C₁₂₇	—	2	16	no	—
104	C₄²×C₁₂₇	—	2	8	no	—
105	C₄²×C₁₂₇	—	2	4	no	—
106	C₄²×C₁₂₇	—	2	4	no	—
107	C₂³×C₁₂₇	—	2	4	no	—
108	C₂³×C₁₂₇	—	2	4	no	—
109	C₂³×C₁₂₇	—	2	2	no	—
110	C₂³×C₁₂₇	—	2	2	no	—
111	C₂³×C₁₂₇	—	2	8	no	—
112	C₂³×C₁₂₇	—	2	8	no	—
113	C₂³×C₁₂₇	—	2	8	no	—
114	C₂³×C₁₂₇	—	4	8	no	—
115	C₂³×C₁₂₇	—	4	8	no	—
116	C₂³×C₁₂₇	C₂×C₄⋊C₄	1	4	yes	—
117	C₂³×C₁₂₇	C₂×C₄⋊C₄	1	2	yes	—
118	C₂³×C₁₂₇	C₄×D₄	1	4	yes	—
119	C₂³×C₁₂₇	C₂×M₁₆	1	4	yes	—
120	C₂³×C₁₂₇	#131	1	2	yes	—
121	C₂³×C₁₂₇	#131	1	2	yes	—
122	C₂³×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
123	C₂×C₄×C₁₂₇	—	2	4	no	—
124	C₂×C₄×C₁₂₇	—	2	4	no	—
125	C₂×C₄×C₁₂₇	—	2	4	no	—
126	C₂×C₄×C₁₂₇	—	2	8	no	—
127	C₂×C₄×C₁₂₇	—	2	16	no	—
128	C₂×C₄×C₁₂₇	—	2	4	no	—
129	C₂×C₄×C₁₂₇	—	2	8	no	—
130	C₂×C₄×C₁₂₇	—	2	4	no	—
131	C₂×C₄×C₁₂₇	—	2	16	no	—
132	C₂×C₄×C₁₂₇	—	2	4	no	—
133	C₂×C₄×C₁₂₇	—	2	4	no	—
134	C₂×C₄×C₁₂₇	—	2	4	no	—
135	C₂×C₄×C₁₂₇	—	4	8	no	—
136	C₂×C₄×C₁₂₇	C₂×C₄⋊C₄	1	4	yes	—
137	C₂×C₄×C₁₂₇	C₂×C₄⋊C₄	1	2	yes	—
138	C₂×C₄×C₁₂₇	C₄×D₄	1	4	yes	—
139	C₂×C₄×C₁₂₇	#120	1	4	yes	—
140	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	8	yes	—
141	C₂×C₄×C₁₂₇	#123	1	4	yes	—
142	C₂×C₄×C₁₂₇	C₂×M₁₆	1	8	yes	complemented
143	C₂×C₄×C₁₂₇	C₂²×D₄	1	2	yes	—
144	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₂₇	C₂²×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₁₂₇	C₂×#41	1	2	yes	—
147	C₈×C₁₂₇	—	2	8	no	—
148	C₈×C₁₂₇	—	4	2	no	—
149	C₈×C₁₂₇	—	4	2	no	—
150	C₂²×C₁₂₇	—	2	4	no	—
151	C₂²×C₁₂₇	—	2	4	no	—
152	C₂²×C₁₂₇	—	2	4	no	—
153	C₂²×C₁₂₇	—	4	16	no	—
154	C₂²×C₁₂₇	—	4	4	no	—
155	C₂²×C₁₂₇	—	4	4	no	—
156	C₂²×C₁₂₇	#385	1	4	yes	—
157	C₂²×C₁₂₇	#423	1	4	yes	—
158	C₂²×C₁₂₇	#424	1	4	yes	—
159	C₂²×C₁₂₇	#435	1	8	yes	—
160	C₂²×C₁₂₇	#436	1	8	yes	—
161	C₂²×C₁₂₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
162	C₂²×C₁₂₇	C₂×C₄×D₄	1	2	yes	—
163	C₂²×C₁₂₇	C₂²×M₁₆	1	2	yes	—
164	C₂²×C₁₂₇	C₂×#131	1	1	yes	characteristic
165	C₂²×C₁₂₇	C₂×#131	1	1	yes	characteristic
166	C₄×C₁₂₇	—	2	8	no	—
167	C₄×C₁₂₇	—	2	4	no	—
168	C₄×C₁₂₇	—	4	4	no	—
169	C₄×C₁₂₇	#385	1	4	yes	—
170	C₄×C₁₂₇	C₂×#120	1	1	yes	characteristic
171	C₄×C₁₂₇	C₂×C₂²⋊Q₈	1	2	yes	—
172	C₄×C₁₂₇	C₂×#123	1	1	yes	characteristic
173	C₂×#1851	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂×C₁₂₇	—	4	4	no	—
175	C₂×C₁₂₇	#1851	1	8	yes	direct product factor
176	C₂×C₁₂₇	C₂×#385	1	1	yes	characteristic
177	C₂×C₁₂₇	C₂×#423	1	1	yes	characteristic
178	C₂×C₁₂₇	C₂×#424	1	1	yes	characteristic
179	C₂×C₁₂₇	C₂×#435	1	2	yes	—
180	C₂×C₁₂₇	C₂×#436	1	2	yes	—
181	C₂³×M₁₆	C₂×C₁₂₇	1	1	yes	characteristic
182	C₂²×C₄⋊C₈	C₂×C₁₂₇	1	2	yes	complemented
183	C₂²×C₂²⋊C₈	C₂×C₁₂₇	1	1	yes	characteristic
184	C₂×C₄×C₂²⋊C₄	C₂×C₁₂₇	1	1	yes	characteristic
185	#1851	C₂×C₁₂₇	1	8	yes	direct product factor
186	C₂×#336	C₂×C₁₂₇	1	2	yes	complemented
187	C₁₂₇	C₂×#1851	1	1	yes	characteristic, direct product factor, Sylow
188	C₂⁴×C₄	C₂²×C₁₂₇	1	1	yes	characteristic
189	C₂²×M₁₆	—	2	4	no	—
190	C₂²×M₁₆	—	2	8	no	—
191	C₂²×M₁₆	C₂²×C₁₂₇	1	4	yes	—
192	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
193	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
194	C₂³×C₈	C₂²×C₁₂₇	1	2	yes	—
195	C₂²×C₂²⋊C₄	C₄×C₁₂₇	1	2	yes	—
196	C₂²×C₄²	C₂²×C₁₂₇	1	2	yes	—
197	C₂×C₄⋊C₈	—	2	8	no	—
198	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	8	yes	complemented
199	C₂×C₂²⋊C₈	—	2	4	no	—
200	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	4	yes	—
201	C₄×C₂²⋊C₄	C₄×C₁₂₇	1	4	yes	—
202	C₄×C₂²⋊C₄	C₂²×C₁₂₇	1	4	yes	—
203	C₂×#95	C₄×C₁₂₇	1	1	yes	characteristic
204	C₂×#95	C₄×C₁₂₇	1	1	yes	characteristic
205	#336	C₂²×C₁₂₇	1	8	yes	complemented
206	C₂⁵	C₂×C₄×C₁₂₇	1	1	yes	characteristic
207	C₂³×C₄	—	2	4	no	—
208	C₂³×C₄	—	2	4	no	—
209	C₂³×C₄	C₂×C₄×C₁₂₇	1	2	yes	—
210	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
211	C₂³×C₄	C₂×C₄×C₁₂₇	1	2	yes	—
212	C₂³×C₄	C₂×C₄×C₁₂₇	1	2	yes	—
213	C₂³×C₄	D₄×C₁₂₇	1	4	yes	—
214	C₂³×C₄	Q₈×C₁₂₇	1	4	yes	—
215	C₂³×C₄	C₂³×C₁₂₇	1	2	yes	—
216	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
217	C₂×M₁₆	—	2	32	no	—
218	C₂×M₁₆	—	2	8	no	—
219	C₂×M₁₆	—	2	16	no	—
220	C₂²×C₈	—	2	4	no	—
221	C₂²×C₈	—	2	4	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	2	4	no	—
225	C₂²×C₈	—	2	4	no	—
226	C₂²×C₈	D₄×C₁₂₇	1	8	yes	—
227	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
228	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
229	C₂²×C₈	C₂³×C₁₂₇	1	4	yes	—
230	C₂×C₂²⋊C₄	—	2	8	no	—
231	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	8	yes	—
232	C₂×C₄²	—	2	4	no	—
233	C₂×C₄²	—	2	4	no	—
234	C₂×C₄²	C₂×C₄×C₁₂₇	1	4	yes	—
235	C₂×C₄²	C₂³×C₁₂₇	1	4	yes	—
236	C₄⋊C₈	—	2	16	no	—
237	C₂²⋊C₈	—	2	8	no	—
238	#95	C₂×C₄×C₁₂₇	1	4	yes	—
239	#95	C₂×C₄×C₁₂₇	1	4	yes	—
240	C₂⁴	—	2	4	no	—
241	C₂⁴	—	2	4	no	—
242	C₂⁴	—	2	2	no	—
243	C₂⁴	—	2	2	no	—
244	C₂⁴	C₄⋊C₄×C₁₂₇	1	4	yes	—
245	C₂⁴	C₂²×C₄×C₁₂₇	1	2	yes	—
246	C₂⁴	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	8	no	—
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	—	2	16	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	C₄⋊C₄×C₁₂₇	1	4	yes	—
260	C₂²×C₄	C₄⋊C₄×C₁₂₇	1	8	yes	—
261	C₂²×C₄	M₁₆×C₁₂₇	1	8	yes	complemented
262	C₂²×C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
263	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
264	C₂²×C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
265	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₁₂₇	1	4	yes	—
267	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
268	C₂²×C₄	C₂×D₄×C₁₂₇	1	4	yes	—
269	C₂²×C₄	C₂×Q₈×C₁₂₇	1	4	yes	—
270	C₂²×C₄	C₂×Q₈×C₁₂₇	1	2	yes	—
271	C₂²×C₄	#41×C₁₂₇	1	4	yes	—
272	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
273	M₁₆	—	2	32	no	—
274	C₂×C₈	—	2	16	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	4	4	no	—
282	C₂×C₈	—	4	4	no	—
283	C₂×C₈	C₂×D₄×C₁₂₇	1	8	yes	—
284	C₂²⋊C₄	—	2	16	no	—
285	C₄²	—	2	8	no	—
286	C₄²	—	2	4	no	—
287	C₄²	—	2	4	no	—
288	C₂³	—	2	4	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	8	no	—
293	C₂³	—	2	8	no	—
294	C₂³	—	2	8	no	—
295	C₂³	—	4	8	no	—
296	C₂³	—	4	8	no	—
297	C₂³	C₂×C₄⋊C₄×C₁₂₇	1	4	yes	—
298	C₂³	C₂×C₄⋊C₄×C₁₂₇	1	2	yes	—
299	C₂³	C₄×D₄×C₁₂₇	1	4	yes	—
300	C₂³	C₂×M₁₆×C₁₂₇	1	4	yes	—
301	C₂³	#131×C₁₂₇	1	2	yes	—
302	C₂³	#131×C₁₂₇	1	2	yes	—
303	C₂³	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	16	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	16	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	4	8	no	—
317	C₂×C₄	C₂×C₄⋊C₄×C₁₂₇	1	4	yes	—
318	C₂×C₄	C₂×C₄⋊C₄×C₁₂₇	1	2	yes	—
319	C₂×C₄	C₄×D₄×C₁₂₇	1	4	yes	—
320	C₂×C₄	#120×C₁₂₇	1	4	yes	—
321	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	8	yes	—
322	C₂×C₄	#123×C₁₂₇	1	4	yes	—
323	C₂×C₄	C₂×M₁₆×C₁₂₇	1	8	yes	complemented
324	C₂×C₄	C₂²×D₄×C₁₂₇	1	2	yes	—
325	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
326	C₂×C₄	C₂²×Q₈×C₁₂₇	1	1	yes	characteristic
327	C₂×C₄	C₂×#41×C₁₂₇	1	2	yes	—
328	C₈	—	2	8	no	—
329	C₈	—	4	2	no	—
330	C₈	—	4	2	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	4	no	—
333	C₂²	—	2	4	no	—
334	C₂²	—	4	16	no	—
335	C₂²	—	4	4	no	—
336	C₂²	—	4	4	no	—
337	C₂²	#385×C₁₂₇	1	4	yes	—
338	C₂²	#423×C₁₂₇	1	4	yes	—
339	C₂²	#424×C₁₂₇	1	4	yes	—
340	C₂²	#435×C₁₂₇	1	8	yes	—
341	C₂²	#436×C₁₂₇	1	8	yes	—
342	C₂²	C₂²×C₄⋊C₄×C₁₂₇	1	1	yes	characteristic
343	C₂²	C₂×C₄×D₄×C₁₂₇	1	2	yes	—
344	C₂²	C₂²×M₁₆×C₁₂₇	1	2	yes	—
345	C₂²	C₂×#131×C₁₂₇	1	1	yes	characteristic
346	C₂²	C₂×#131×C₁₂₇	1	1	yes	characteristic
347	C₄	—	2	8	no	—
348	C₄	—	2	4	no	—
349	C₄	—	4	4	no	—
350	C₄	#385×C₁₂₇	1	4	yes	—
351	C₄	C₂×#120×C₁₂₇	1	1	yes	characteristic
352	C₄	C₂×C₂²⋊Q₈×C₁₂₇	1	2	yes	—
353	C₄	C₂×#123×C₁₂₇	1	1	yes	characteristic
354	C₂	—	4	4	no	—
355	C₂	C₁₂₇×#1851	1	8	yes	direct product factor
356	C₂	C₂×#385×C₁₂₇	1	1	yes	characteristic
357	C₂	C₂×#423×C₁₂₇	1	1	yes	characteristic
358	C₂	C₂×#424×C₁₂₇	1	1	yes	characteristic
359	C₂	C₂×#435×C₁₂₇	1	2	yes	—
360	C₂	C₂×#436×C₁₂₇	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₂₇	C₂³
commutator	C₂³	C₂³×C₄×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₂₇
socle	C₂⁴×C₁₂₇	C₂²×C₄
prime radical	C₂⁵×C₁₂₇	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊C₈×C₁₂₇	C₂	semidirect
5. C₁₂₇×#1851	C₂	direct (N × H)
6. C₂×#336×C₁₂₇	C₂	semidirect
17. C₂×C₄⋊C₈×C₁₂₇	C₂²	semidirect
24. #336×C₁₂₇	C₂²	semidirect
80. C₂²×C₄×C₁₂₇	M₁₆	semidirect
142. C₂×C₄×C₁₂₇	C₂×M₁₆	semidirect
173. C₂×#1851	C₁₂₇	direct (N × H)
175. C₂×C₁₂₇	#1851	direct (N × H)
182. C₂²×C₄⋊C₈	C₂×C₁₂₇	semidirect
185. #1851	C₂×C₁₂₇	direct (N × H)
186. C₂×#336	C₂×C₁₂₇	semidirect
187. C₁₂₇	C₂×#1851	direct (N × H)
198. C₂×C₄⋊C₈	C₂²×C₁₂₇	semidirect
205. #336	C₂²×C₁₂₇	semidirect
261. C₂²×C₄	M₁₆×C₁₂₇	semidirect
323. C₂×C₄	C₂×M₁₆×C₁₂₇	semidirect
355. C₂	C₁₂₇×#1851	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₁₂₇	2
C₂²×C₄⋊C₈×C₁₂₇	2
C₂²×C₂²⋊C₈×C₁₂₇	2
C₂×C₄×C₂²⋊C₄×C₁₂₇	2
C₁₂₇×#1851	2
C₂×#336×C₁₂₇	2
C₂×#1851	127

Subgroups — C2×C127×#1851 #44584506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₂₇×#1851 #44584506