Subgroups — C₁₂₇×#21714 #44585387

Order 32512.

810 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#446×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊Q₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1984	C₂	1	1	yes	maximal, characteristic
5	C₁₂₇×#1984	C₂	1	1	yes	maximal, characteristic
6	C₁₂₇×#1940	C₂	1	4	yes	maximal
7	C₁₂₇×#1842	C₂	1	1	yes	maximal, characteristic
8	C₁₂₇×#1771	C₂	1	4	yes	maximal
9	C₄×#97×C₁₂₇	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄⋊Q₈×C₁₂₇	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic
13	#446×C₁₂₇	—	2	4	no	—
14	C₈×Q₈×C₁₂₇	—	2	4	no	—
15	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	4	yes	—
18	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
20	C₂×#97×C₁₂₇	C₂²	1	2	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	#391×C₁₂₇	C₄	1	1	yes	characteristic
28	#389×C₁₂₇	C₄	1	4	yes	—
29	#384×C₁₂₇	C₄	1	1	yes	characteristic
30	C₄×C₄⋊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×Q₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
41	C₄⋊Q₈×C₁₂₇	—	2	4	no	—
42	C₄×Q₈×C₁₂₇	—	2	2	no	—
43	C₄×Q₈×C₁₂₇	—	2	2	no	—
44	C₄×Q₈×C₁₂₇	—	2	2	no	—
45	C₄×Q₈×C₁₂₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
51	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
52	C₂×C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₂₇	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
56	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
57	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
59	C₄⋊C₈×C₁₂₇	—	2	4	no	—
60	C₄⋊C₈×C₁₂₇	—	2	4	no	—
61	C₄⋊C₈×C₁₂₇	—	2	2	no	—
62	C₄⋊C₈×C₁₂₇	—	2	2	no	—
63	C₄⋊C₈×C₁₂₇	—	2	8	no	—
64	#97×C₁₂₇	—	2	4	no	—
65	#97×C₁₂₇	—	2	4	no	—
66	#97×C₁₂₇	Q₈	1	8	yes	complemented
67	C₄×C₈×C₁₂₇	—	2	4	no	—
68	C₄×C₈×C₁₂₇	—	2	2	no	—
69	C₄×C₈×C₁₂₇	D₄	1	4	yes	—
70	#95×C₁₂₇	C₂×C₄	1	4	yes	—
71	#95×C₁₂₇	C₂×C₄	1	4	yes	—
72	C₂×Q₈×C₁₂₇	—	2	2	no	—
73	C₂×Q₈×C₁₂₇	—	2	2	no	—
74	C₂×Q₈×C₁₂₇	—	2	2	no	—
75	C₂×Q₈×C₁₂₇	—	2	2	no	—
76	C₂×Q₈×C₁₂₇	—	2	2	no	—
77	C₂×Q₈×C₁₂₇	M₁₆	1	4	yes	—
78	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
87	C₂×C₈×C₁₂₇	—	2	2	no	—
88	C₂×C₈×C₁₂₇	—	2	2	no	—
89	C₂×C₈×C₁₂₇	—	2	2	no	—
90	C₂×C₈×C₁₂₇	—	2	2	no	—
91	C₂×C₈×C₁₂₇	—	2	2	no	—
92	C₂×C₈×C₁₂₇	—	2	4	no	—
93	C₂×C₈×C₁₂₇	—	2	4	no	—
94	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
95	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
96	C₂×C₈×C₁₂₇	C₂×Q₈	1	4	yes	—
97	C₂×C₈×C₁₂₇	C₂×Q₈	1	4	yes	—
98	C₄⋊C₄×C₁₂₇	—	2	4	no	—
99	C₄⋊C₄×C₁₂₇	—	2	2	no	—
100	C₄⋊C₄×C₁₂₇	—	2	2	no	—
101	C₄⋊C₄×C₁₂₇	—	2	4	no	—
102	C₄⋊C₄×C₁₂₇	—	2	8	no	—
103	C₄⋊C₄×C₁₂₇	—	4	4	no	—
104	C₄²×C₁₂₇	—	2	2	no	—
105	C₄²×C₁₂₇	—	2	2	no	—
106	C₄²×C₁₂₇	—	2	2	no	—
107	C₄²×C₁₂₇	—	2	2	no	—
108	C₄²×C₁₂₇	—	2	2	no	—
109	C₄²×C₁₂₇	—	2	2	no	—
110	C₄²×C₁₂₇	—	4	2	no	—
111	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
112	C₄²×C₁₂₇	C₂×Q₈	1	4	yes	—
113	C₄²×C₁₂₇	#41	1	2	yes	—
114	C₄²×C₁₂₇	#41	1	4	yes	—
115	C₂³×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
116	Q₈×C₁₂₇	—	2	8	no	—
117	Q₈×C₁₂₇	—	4	4	no	—
118	C₂×C₄×C₁₂₇	—	2	2	no	—
119	C₂×C₄×C₁₂₇	—	2	2	no	—
120	C₂×C₄×C₁₂₇	—	2	2	no	—
121	C₂×C₄×C₁₂₇	—	2	2	no	—
122	C₂×C₄×C₁₂₇	—	2	2	no	—
123	C₂×C₄×C₁₂₇	—	2	2	no	—
124	C₂×C₄×C₁₂₇	—	2	2	no	—
125	C₂×C₄×C₁₂₇	—	2	2	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	4	no	—
131	C₂×C₄×C₁₂₇	—	2	4	no	—
132	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
133	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
134	C₂×C₄×C₁₂₇	C₄×Q₈	1	4	yes	—
135	C₂×C₄×C₁₂₇	C₄×Q₈	1	4	yes	—
136	C₂×C₄×C₁₂₇	C₂×M₁₆	1	4	yes	—
137	C₂×C₄×C₁₂₇	C₂×M₁₆	1	2	yes	—
138	C₂×C₄×C₁₂₇	#131	1	2	yes	—
139	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
140	C₂×C₄×C₁₂₇	C₂²×Q₈	1	2	yes	—
141	C₂×C₄×C₁₂₇	C₂×#41	1	2	yes	—
142	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
143	C₈×C₁₂₇	—	2	2	no	—
144	C₈×C₁₂₇	—	2	4	no	—
145	C₈×C₁₂₇	—	4	2	no	—
146	C₈×C₁₂₇	—	4	2	no	—
147	C₈×C₁₂₇	C₄⋊Q₈	1	4	yes	complemented
148	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
149	C₂²×C₁₂₇	C₂×C₄×Q₈	1	2	yes	—
150	C₂²×C₁₂₇	C₂²×M₁₆	1	1	yes	characteristic
151	C₂²×C₁₂₇	C₂×#131	1	1	yes	characteristic
152	C₂²×C₁₂₇	#568	1	2	yes	—
153	C₄×C₁₂₇	—	2	4	no	—
154	C₄×C₁₂₇	—	2	2	no	—
155	C₄×C₁₂₇	—	2	4	no	—
156	C₄×C₁₂₇	—	2	4	no	—
157	C₄×C₁₂₇	—	4	2	no	—
158	C₄×C₁₂₇	—	4	2	no	—
159	C₄×C₁₂₇	—	4	2	no	—
160	C₄×C₁₂₇	#435	1	4	yes	—
161	C₄×C₁₂₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
162	C₄×C₁₂₇	#532	1	1	yes	characteristic
163	C₄×C₁₂₇	#533	1	2	yes	—
164	#21714	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂×C₁₂₇	C₄×C₄⋊Q₈	1	1	yes	characteristic
166	C₂×C₁₂₇	C₂×#435	1	1	yes	characteristic
167	C₂×C₁₂₇	#2932	1	1	yes	characteristic
168	C₂×C₁₂₇	#2962	1	2	yes	—
169	C₂×C₁₂₇	Q₈×M₁₆	1	2	yes	—
170	C₂×#446	C₂×C₁₂₇	1	1	yes	characteristic
171	C₂×C₈×Q₈	C₂×C₁₂₇	1	1	yes	characteristic
172	C₄×C₄⋊Q₈	C₂×C₁₂₇	1	1	yes	characteristic
173	#1984	C₂×C₁₂₇	1	1	yes	characteristic
174	#1984	C₂×C₁₂₇	1	1	yes	characteristic
175	#1940	C₂×C₁₂₇	1	4	yes	—
176	#1842	C₂×C₁₂₇	1	1	yes	characteristic
177	#1771	C₂×C₁₂₇	1	4	yes	—
178	C₄×#97	C₂×C₁₂₇	1	1	yes	characteristic
179	C₁₂₇	#21714	1	1	yes	characteristic, direct product factor, Sylow
180	C₂×C₄⋊Q₈	C₄×C₁₂₇	1	1	yes	characteristic
181	C₂×C₄×Q₈	C₂²×C₁₂₇	1	1	yes	characteristic
182	C₂×C₄×Q₈	C₂²×C₁₂₇	1	1	yes	characteristic
183	#446	—	2	4	no	—
184	C₈×Q₈	—	2	4	no	—
185	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
186	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
187	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	4	yes	—
188	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
189	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
190	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
191	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
192	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
193	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
194	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
195	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
196	#391	C₄×C₁₂₇	1	1	yes	characteristic
197	#391	C₄×C₁₂₇	1	1	yes	characteristic
198	#389	C₄×C₁₂₇	1	4	yes	—
199	#384	C₄×C₁₂₇	1	1	yes	characteristic
200	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	4	yes	—
201	C₄³	C₂²×C₁₂₇	1	1	yes	characteristic
202	#336	C₂²×C₁₂₇	1	4	yes	—
203	#336	C₂²×C₁₂₇	1	4	yes	—
204	C₂²×Q₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
205	C₂²×Q₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
206	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
207	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
208	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
209	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
210	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
211	C₄⋊Q₈	—	2	4	no	—
212	C₄×Q₈	—	2	2	no	—
213	C₄×Q₈	—	2	2	no	—
214	C₄×Q₈	—	2	2	no	—
215	C₄×Q₈	—	2	2	no	—
216	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
218	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
219	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
220	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
221	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
222	C₂×C₄²	C₂×C₄×C₁₂₇	1	1	yes	characteristic
223	C₂×C₄²	C₂×C₄×C₁₂₇	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₄×C₁₂₇	1	2	yes	—
225	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
226	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
227	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
229	C₄⋊C₈	—	2	4	no	—
230	C₄⋊C₈	—	2	4	no	—
231	C₄⋊C₈	—	2	2	no	—
232	C₄⋊C₈	—	2	2	no	—
233	C₄⋊C₈	—	2	8	no	—
234	#97	—	2	4	no	—
235	#97	—	2	4	no	—
236	#97	Q₈×C₁₂₇	1	8	yes	complemented
237	C₄×C₈	—	2	4	no	—
238	C₄×C₈	—	2	2	no	—
239	C₄×C₈	D₄×C₁₂₇	1	4	yes	—
240	#95	C₂×C₄×C₁₂₇	1	4	yes	—
241	#95	C₂×C₄×C₁₂₇	1	4	yes	—
242	C₂×Q₈	—	2	2	no	—
243	C₂×Q₈	—	2	2	no	—
244	C₂×Q₈	—	2	2	no	—
245	C₂×Q₈	—	2	2	no	—
246	C₂×Q₈	—	2	2	no	—
247	C₂×Q₈	M₁₆×C₁₂₇	1	4	yes	—
248	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
249	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
250	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
251	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
252	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
256	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	2	4	no	—
264	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
265	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
266	C₂×C₈	C₂×Q₈×C₁₂₇	1	4	yes	—
267	C₂×C₈	C₂×Q₈×C₁₂₇	1	4	yes	—
268	C₄⋊C₄	—	2	4	no	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	—	2	4	no	—
272	C₄⋊C₄	—	2	8	no	—
273	C₄⋊C₄	—	4	4	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	2	no	—
276	C₄²	—	2	2	no	—
277	C₄²	—	2	2	no	—
278	C₄²	—	2	2	no	—
279	C₄²	—	2	2	no	—
280	C₄²	—	4	2	no	—
281	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
282	C₄²	C₂×Q₈×C₁₂₇	1	4	yes	—
283	C₄²	#41×C₁₂₇	1	2	yes	—
284	C₄²	#41×C₁₂₇	1	4	yes	—
285	C₂³	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
286	Q₈	—	2	8	no	—
287	Q₈	—	4	4	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
303	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
304	C₂×C₄	C₄×Q₈×C₁₂₇	1	4	yes	—
305	C₂×C₄	C₄×Q₈×C₁₂₇	1	4	yes	—
306	C₂×C₄	C₂×M₁₆×C₁₂₇	1	4	yes	—
307	C₂×C₄	C₂×M₁₆×C₁₂₇	1	2	yes	—
308	C₂×C₄	#131×C₁₂₇	1	2	yes	—
309	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
310	C₂×C₄	C₂²×Q₈×C₁₂₇	1	2	yes	—
311	C₂×C₄	C₂×#41×C₁₂₇	1	2	yes	—
312	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
313	C₈	—	2	2	no	—
314	C₈	—	2	4	no	—
315	C₈	—	4	2	no	—
316	C₈	—	4	2	no	—
317	C₈	C₄⋊Q₈×C₁₂₇	1	4	yes	complemented
318	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
319	C₂²	C₂×C₄×Q₈×C₁₂₇	1	2	yes	—
320	C₂²	C₂²×M₁₆×C₁₂₇	1	1	yes	characteristic
321	C₂²	C₂×#131×C₁₂₇	1	1	yes	characteristic
322	C₂²	#568×C₁₂₇	1	2	yes	—
323	C₄	—	2	4	no	—
324	C₄	—	2	2	no	—
325	C₄	—	2	4	no	—
326	C₄	—	2	4	no	—
327	C₄	—	4	2	no	—
328	C₄	—	4	2	no	—
329	C₄	—	4	2	no	—
330	C₄	#435×C₁₂₇	1	4	yes	—
331	C₄	C₂×C₄⋊Q₈×C₁₂₇	1	1	yes	characteristic
332	C₄	#532×C₁₂₇	1	1	yes	characteristic
333	C₄	#533×C₁₂₇	1	2	yes	—
334	C₂	C₄×C₄⋊Q₈×C₁₂₇	1	1	yes	characteristic
335	C₂	C₂×#435×C₁₂₇	1	1	yes	characteristic
336	C₂	C₁₂₇×#2932	1	1	yes	characteristic
337	C₂	C₁₂₇×#2962	1	2	yes	—
338	C₂	Q₈×M₁₆×C₁₂₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₂₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₂₇
socle, prime radical	C₂³×C₁₂₇	C₂³×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
66. #97×C₁₂₇	Q₈	semidirect
147. C₈×C₁₂₇	C₄⋊Q₈	semidirect
164. #21714	C₁₂₇	direct (N × H)
179. C₁₂₇	#21714	direct (N × H)
236. #97	Q₈×C₁₂₇	semidirect
317. C₈	C₄⋊Q₈×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#446×C₁₂₇	2
C₂×C₈×Q₈×C₁₂₇	2
C₄×C₄⋊Q₈×C₁₂₇	2
C₁₂₇×#1984	2
C₁₂₇×#1940	2
C₁₂₇×#1842	2
C₁₂₇×#1771	2
C₄×#97×C₁₂₇	2
#21714	127

Subgroups — C127×#21714 #44585387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#21714 #44585387