Subgroups — C₁₂₇×#20492 #44584165

Order 32512.

1122 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#435×C₁₂₇	C₂	1	2	yes	maximal
2	C₂×#405×C₁₂₇	C₂	1	2	yes	maximal, complemented
3	C₁₂₇×#2293	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1771	C₂	1	2	yes	maximal, complemented
5	C₄×C₄⋊C₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₂₇×#1753	C₂	1	2	yes	maximal, complemented
7	C₈×C₂²⋊C₄×C₁₂₇	C₂	1	2	yes	maximal, complemented
8	C₁₂₇×#1750	C₂	1	2	yes	maximal, complemented
9	C₄×#97×C₁₂₇	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×#117×C₁₂₇	C₂²	1	2	yes	—
14	#435×C₁₂₇	C₄	1	16	yes	complemented
15	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	—
18	#405×C₁₂₇	—	2	8	no	—
19	C₂×#97×C₁₂₇	C₂²	1	2	yes	—
20	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
21	C₂×#97×C₁₂₇	C₂²	1	2	yes	—
22	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
26	#390×C₁₂₇	C₄	1	2	yes	—
27	#389×C₁₂₇	C₄	1	2	yes	—
28	#388×C₁₂₇	C₄	1	4	yes	—
29	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
30	C₄×C₂²⋊C₄×C₁₂₇	C₂²	1	2	yes	—
31	C₄³×C₁₂₇	C₂²	1	1	yes	characteristic
32	#336×C₁₂₇	C₂²	1	2	yes	—
33	#336×C₁₂₇	C₂²	1	2	yes	—
34	#336×C₁₂₇	C₂²	1	1	yes	characteristic
35	#336×C₁₂₇	C₂²	1	1	yes	characteristic
36	C₂²×D₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₂₇	C₂³	1	2	yes	—
38	C₂×M₁₆×C₁₂₇	—	2	4	no	—
39	C₂×M₁₆×C₁₂₇	—	2	4	no	—
40	C₂×M₁₆×C₁₂₇	C₂×C₄	1	8	yes	—
41	C₂²×C₈×C₁₂₇	—	2	4	no	—
42	C₂²×C₈×C₁₂₇	—	2	4	no	—
43	C₂²×C₈×C₁₂₇	C₂×C₄	1	8	yes	—
44	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
48	C₄×D₄×C₁₂₇	C₂×C₄	1	8	yes	—
49	#117×C₁₂₇	—	2	4	no	—
50	#117×C₁₂₇	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
55	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
56	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₁₂₇	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₂₇	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
60	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₁₂₇	C₂×C₄	1	8	yes	—
64	C₂²⋊C₈×C₁₂₇	C₂×C₄	1	8	yes	—
65	C₂²⋊C₈×C₁₂₇	C₂×C₄	1	8	yes	—
66	#97×C₁₂₇	—	2	4	no	—
67	#97×C₁₂₇	—	2	2	no	—
68	#97×C₁₂₇	C₂×C₄	1	8	yes	—
69	#97×C₁₂₇	D₄	1	4	yes	complemented
70	C₄×C₈×C₁₂₇	—	2	4	no	—
71	C₄×C₈×C₁₂₇	—	2	4	no	—
72	C₄×C₈×C₁₂₇	—	2	4	no	—
73	#95×C₁₂₇	C₂×C₄	1	4	yes	—
74	#95×C₁₂₇	C₂×C₄	1	2	yes	—
75	C₂⁴×C₁₂₇	C₂²×C₄	1	2	yes	—
76	C₂×D₄×C₁₂₇	—	4	2	no	—
77	C₂×D₄×C₁₂₇	C₄²	1	4	yes	—
78	C₂²×C₄×C₁₂₇	—	2	2	no	—
79	C₂²×C₄×C₁₂₇	—	2	2	no	—
80	C₂²×C₄×C₁₂₇	—	2	2	no	—
81	C₂²×C₄×C₁₂₇	—	2	2	no	—
82	C₂²×C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
91	M₁₆×C₁₂₇	—	2	16	no	—
92	C₂×C₈×C₁₂₇	—	2	2	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	16	no	—
99	C₂×C₈×C₁₂₇	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₁₂₇	C₂²×C₄	1	4	yes	—
101	C₂×C₈×C₁₂₇	C₂²×C₄	1	4	yes	—
102	C₂×C₈×C₁₂₇	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₁₂₇	C₂×D₄	1	4	yes	—
104	C₂×C₈×C₁₂₇	#41	1	4	yes	—
105	C₄⋊C₄×C₁₂₇	—	2	8	no	—
106	C₄⋊C₄×C₁₂₇	—	4	2	no	—
107	C₄⋊C₄×C₁₂₇	C₄²	1	4	yes	—
108	C₂²⋊C₄×C₁₂₇	—	2	8	no	—
109	C₂²⋊C₄×C₁₂₇	—	2	8	no	—
110	C₂²⋊C₄×C₁₂₇	C₄²	1	8	yes	—
111	C₄²×C₁₂₇	—	2	4	no	—
112	C₄²×C₁₂₇	—	2	2	no	—
113	C₄²×C₁₂₇	—	2	2	no	—
114	C₄²×C₁₂₇	—	2	2	no	—
115	C₄²×C₁₂₇	—	4	2	no	—
116	C₄²×C₁₂₇	C₂²×C₄	1	4	yes	—
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	2	no	—
121	C₂³×C₁₂₇	—	2	4	no	—
122	C₂³×C₁₂₇	—	2	4	no	—
123	C₂³×C₁₂₇	C₂×C₄²	1	4	yes	—
124	C₂³×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
125	D₄×C₁₂₇	—	4	4	no	—
126	C₂×C₄×C₁₂₇	—	2	2	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	4	no	—
136	C₂×C₄×C₁₂₇	—	2	4	no	—
137	C₂×C₄×C₁₂₇	—	2	4	no	—
138	C₂×C₄×C₁₂₇	—	2	4	no	—
139	C₂×C₄×C₁₂₇	—	2	4	no	—
140	C₂×C₄×C₁₂₇	—	2	4	no	—
141	C₂×C₄×C₁₂₇	C₂×C₄²	1	2	yes	—
142	C₂×C₄×C₁₂₇	C₂×C₄²	1	2	yes	—
143	C₂×C₄×C₁₂₇	C₂×C₄²	1	4	yes	—
144	C₂×C₄×C₁₂₇	C₄×D₄	1	4	yes	—
145	C₂×C₄×C₁₂₇	#131	1	4	yes	—
146	C₂×C₄×C₁₂₇	C₂³×C₄	1	2	yes	—
147	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₂₇	C₂×#41	1	2	yes	—
149	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
150	C₈×C₁₂₇	—	2	4	no	—
151	C₈×C₁₂₇	—	2	4	no	—
152	C₈×C₁₂₇	—	2	4	no	—
153	C₈×C₁₂₇	C₄×D₄	1	8	yes	—
154	C₂²×C₁₂₇	—	2	4	no	—
155	C₂²×C₁₂₇	—	2	4	no	—
156	C₂²×C₁₂₇	—	2	4	no	—
157	C₂²×C₁₂₇	—	4	4	no	—
158	C₂²×C₁₂₇	—	4	4	no	—
159	C₂²×C₁₂₇	C₂²×C₄²	1	1	yes	characteristic
160	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
161	C₂²×C₁₂₇	C₄×#41	1	1	yes	characteristic
162	C₂²×C₁₂₇	C₂×#131	1	2	yes	—
163	C₂²×C₁₂₇	#568	1	2	yes	—
164	C₄×C₁₂₇	—	2	2	no	—
165	C₄×C₁₂₇	—	2	2	no	—
166	C₄×C₁₂₇	—	2	4	no	—
167	C₄×C₁₂₇	—	2	4	no	—
168	C₄×C₁₂₇	—	2	4	no	—
169	C₄×C₁₂₇	—	4	4	no	—
170	C₄×C₁₂₇	C₂×C₄×D₄	1	2	yes	—
171	C₄×C₁₂₇	C₄×#41	1	2	yes	—
172	#20492	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂×C₁₂₇	—	4	4	no	—
174	C₂×C₁₂₇	C₄²×D₄	1	1	yes	characteristic
175	C₂×C₁₂₇	#2873	1	1	yes	characteristic
176	C₂×C₁₂₇	C₄×#131	1	1	yes	characteristic
177	C₂×C₁₂₇	#2935	1	2	yes	—
178	C₂×C₁₂₇	#2968	1	2	yes	—
179	C₂×#435	C₂×C₁₂₇	1	2	yes	—
180	C₂×#405	C₂×C₁₂₇	1	2	yes	complemented
181	#2293	C₂×C₁₂₇	1	1	yes	characteristic
182	#1771	C₂×C₁₂₇	1	2	yes	complemented
183	C₄×C₄⋊C₈	C₂×C₁₂₇	1	1	yes	characteristic, complemented
184	#1753	C₂×C₁₂₇	1	2	yes	complemented
185	C₈×C₂²⋊C₄	C₂×C₁₂₇	1	2	yes	complemented
186	#1750	C₂×C₁₂₇	1	2	yes	complemented
187	C₄×#97	C₂×C₁₂₇	1	1	yes	characteristic, complemented
188	C₁₂₇	#20492	1	1	yes	characteristic, direct product factor, Sylow
189	C₂²×M₁₆	C₂²×C₁₂₇	1	2	yes	—
190	C₂³×C₈	C₂²×C₁₂₇	1	2	yes	—
191	C₂×C₄×D₄	C₂²×C₁₂₇	1	1	yes	characteristic
192	C₂×#117	C₂²×C₁₂₇	1	2	yes	—
193	#435	C₄×C₁₂₇	1	16	yes	complemented
194	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
195	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	—
196	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	—
197	#405	—	2	8	no	—
198	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
199	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
200	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
201	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
202	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
203	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
204	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
205	#390	C₄×C₁₂₇	1	2	yes	—
206	#389	C₄×C₁₂₇	1	2	yes	—
207	#388	C₄×C₁₂₇	1	4	yes	—
208	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	1	yes	characteristic
209	C₄×C₂²⋊C₄	C₂²×C₁₂₇	1	2	yes	—
210	C₄³	C₂²×C₁₂₇	1	1	yes	characteristic
211	#336	C₂²×C₁₂₇	1	2	yes	—
212	#336	C₂²×C₁₂₇	1	2	yes	—
213	#336	C₂²×C₁₂₇	1	1	yes	characteristic
214	#336	C₂²×C₁₂₇	1	1	yes	characteristic
215	C₂²×D₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
216	C₂³×C₄	C₂³×C₁₂₇	1	2	yes	—
217	C₂×M₁₆	—	2	4	no	—
218	C₂×M₁₆	—	2	4	no	—
219	C₂×M₁₆	C₂×C₄×C₁₂₇	1	8	yes	—
220	C₂²×C₈	—	2	4	no	—
221	C₂²×C₈	—	2	4	no	—
222	C₂²×C₈	C₂×C₄×C₁₂₇	1	8	yes	—
223	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
224	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
225	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
226	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
227	C₄×D₄	C₂×C₄×C₁₂₇	1	8	yes	—
228	#117	—	2	4	no	—
229	#117	—	2	4	no	—
230	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
232	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
233	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
234	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
235	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
236	C₂×C₄²	C₂×C₄×C₁₂₇	1	2	yes	—
237	C₂×C₄²	C₂×C₄×C₁₂₇	1	2	yes	—
238	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
239	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
240	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
242	C₄⋊C₈	C₂×C₄×C₁₂₇	1	8	yes	—
243	C₂²⋊C₈	C₂×C₄×C₁₂₇	1	8	yes	—
244	C₂²⋊C₈	C₂×C₄×C₁₂₇	1	8	yes	—
245	#97	—	2	4	no	—
246	#97	—	2	2	no	—
247	#97	C₂×C₄×C₁₂₇	1	8	yes	—
248	#97	D₄×C₁₂₇	1	4	yes	complemented
249	C₄×C₈	—	2	4	no	—
250	C₄×C₈	—	2	4	no	—
251	C₄×C₈	—	2	4	no	—
252	#95	C₂×C₄×C₁₂₇	1	4	yes	—
253	#95	C₂×C₄×C₁₂₇	1	2	yes	—
254	C₂⁴	C₂²×C₄×C₁₂₇	1	2	yes	—
255	C₂×D₄	—	4	2	no	—
256	C₂×D₄	C₄²×C₁₂₇	1	4	yes	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
262	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
263	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
264	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
266	C₂²×C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
267	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
269	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
270	M₁₆	—	2	16	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	16	no	—
278	C₂×C₈	C₂²×C₄×C₁₂₇	1	4	yes	—
279	C₂×C₈	C₂²×C₄×C₁₂₇	1	4	yes	—
280	C₂×C₈	C₂²×C₄×C₁₂₇	1	4	yes	—
281	C₂×C₈	C₂²×C₄×C₁₂₇	1	4	yes	—
282	C₂×C₈	C₂×D₄×C₁₂₇	1	4	yes	—
283	C₂×C₈	#41×C₁₂₇	1	4	yes	—
284	C₄⋊C₄	—	2	8	no	—
285	C₄⋊C₄	—	4	2	no	—
286	C₄⋊C₄	C₄²×C₁₂₇	1	4	yes	—
287	C₂²⋊C₄	—	2	8	no	—
288	C₂²⋊C₄	—	2	8	no	—
289	C₂²⋊C₄	C₄²×C₁₂₇	1	8	yes	—
290	C₄²	—	2	4	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	4	2	no	—
295	C₄²	C₂²×C₄×C₁₂₇	1	4	yes	—
296	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
297	C₄²	#41×C₁₂₇	1	2	yes	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	2	no	—
300	C₂³	—	2	4	no	—
301	C₂³	—	2	4	no	—
302	C₂³	C₂×C₄²×C₁₂₇	1	4	yes	—
303	C₂³	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
304	D₄	—	4	4	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	C₂×C₄²×C₁₂₇	1	2	yes	—
321	C₂×C₄	C₂×C₄²×C₁₂₇	1	2	yes	—
322	C₂×C₄	C₂×C₄²×C₁₂₇	1	4	yes	—
323	C₂×C₄	C₄×D₄×C₁₂₇	1	4	yes	—
324	C₂×C₄	#131×C₁₂₇	1	4	yes	—
325	C₂×C₄	C₂³×C₄×C₁₂₇	1	2	yes	—
326	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
327	C₂×C₄	C₂×#41×C₁₂₇	1	2	yes	—
328	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
329	C₈	—	2	4	no	—
330	C₈	—	2	4	no	—
331	C₈	—	2	4	no	—
332	C₈	C₄×D₄×C₁₂₇	1	8	yes	—
333	C₂²	—	2	4	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	4	4	no	—
337	C₂²	—	4	4	no	—
338	C₂²	C₂²×C₄²×C₁₂₇	1	1	yes	characteristic
339	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
340	C₂²	C₄×#41×C₁₂₇	1	1	yes	characteristic
341	C₂²	C₂×#131×C₁₂₇	1	2	yes	—
342	C₂²	#568×C₁₂₇	1	2	yes	—
343	C₄	—	2	2	no	—
344	C₄	—	2	2	no	—
345	C₄	—	2	4	no	—
346	C₄	—	2	4	no	—
347	C₄	—	2	4	no	—
348	C₄	—	4	4	no	—
349	C₄	C₂×C₄×D₄×C₁₂₇	1	2	yes	—
350	C₄	C₄×#41×C₁₂₇	1	2	yes	—
351	C₂	—	4	4	no	—
352	C₂	C₄²×D₄×C₁₂₇	1	1	yes	characteristic
353	C₂	C₁₂₇×#2873	1	1	yes	characteristic
354	C₂	C₄×#131×C₁₂₇	1	1	yes	characteristic
355	C₂	C₁₂₇×#2935	1	2	yes	—
356	C₂	C₁₂₇×#2968	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×#405×C₁₂₇	C₂	semidirect
4. C₁₂₇×#1771	C₂	semidirect
5. C₄×C₄⋊C₈×C₁₂₇	C₂	semidirect
6. C₁₂₇×#1753	C₂	semidirect
7. C₈×C₂²⋊C₄×C₁₂₇	C₂	semidirect
8. C₁₂₇×#1750	C₂	semidirect
9. C₄×#97×C₁₂₇	C₂	semidirect
14. #435×C₁₂₇	C₄	semidirect
69. #97×C₁₂₇	D₄	semidirect
172. #20492	C₁₂₇	direct (N × H)
180. C₂×#405	C₂×C₁₂₇	semidirect
182. #1771	C₂×C₁₂₇	semidirect
183. C₄×C₄⋊C₈	C₂×C₁₂₇	semidirect
184. #1753	C₂×C₁₂₇	semidirect
185. C₈×C₂²⋊C₄	C₂×C₁₂₇	semidirect
186. #1750	C₂×C₁₂₇	semidirect
187. C₄×#97	C₂×C₁₂₇	semidirect
188. C₁₂₇	#20492	direct (N × H)
193. #435	C₄×C₁₂₇	semidirect
248. #97	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×#435×C₁₂₇	2
C₂×#405×C₁₂₇	2
C₁₂₇×#2293	2
C₁₂₇×#1771	2
C₄×C₄⋊C₈×C₁₂₇	2
C₁₂₇×#1753	2
C₈×C₂²⋊C₄×C₁₂₇	2
C₁₂₇×#1750	2
C₄×#97×C₁₂₇	2
#20492	127

Subgroups — C127×#20492 #44584165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#20492 #44584165