Subgroups — C₁₂₇×#20476 #44584149

Order 32512.

990 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#432×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₁₂₇×#2283	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1770	C₂	1	2	yes	maximal, complemented
5	C₈×C₄⋊C₄×C₁₂₇	C₂	1	2	yes	maximal, complemented
6	C₁₂₇×#1752	C₂	1	2	yes	maximal
7	C₈×C₂²⋊C₄×C₁₂₇	C₂	1	2	yes	maximal
8	C₁₂₇×#1746	C₂	1	2	yes	maximal, complemented
9	C₁₂₇×#1726	C₂	1	2	yes	maximal, complemented
10	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
13	#432×C₁₂₇	C₄	1	8	yes	complemented
14	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
15	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	—
16	C₂×#97×C₁₂₇	C₂²	1	4	yes	—
17	C₂×#97×C₁₂₇	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₂₇	C₄	1	8	yes	complemented
19	C₂×C₄×C₈×C₁₂₇	C₂²	1	4	yes	—
20	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
24	#383×C₁₂₇	C₄	1	2	yes	—
25	#382×C₁₂₇	C₄	1	2	yes	—
26	#381×C₁₂₇	C₄	1	2	yes	—
27	#380×C₁₂₇	C₄	1	2	yes	—
28	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₁₂₇	C₂²	1	2	yes	—
30	#376×C₁₂₇	C₂²	1	2	yes	—
31	#336×C₁₂₇	C₂²	1	4	yes	—
32	#336×C₁₂₇	C₂²	1	4	yes	—
33	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₂₇	—	2	4	no	—
37	C₂²×C₈×C₁₂₇	—	2	4	no	—
38	C₂²×C₈×C₁₂₇	C₂×C₄	1	4	yes	—
39	C₂²×C₈×C₁₂₇	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₂₇	C₂³	1	4	yes	—
43	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
46	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₂₇	C₂×C₄	1	4	yes	—
50	C₂×C₄²×C₁₂₇	C₂×C₄	1	4	yes	—
51	C₂×C₄²×C₁₂₇	C₂³	1	4	yes	—
52	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₁₂₇	C₂×C₄	1	8	yes	—
55	C₂²⋊C₈×C₁₂₇	C₂×C₄	1	8	yes	—
56	#97×C₁₂₇	—	2	8	no	—
57	#97×C₁₂₇	C₂×C₄	1	8	yes	—
58	C₄×C₈×C₁₂₇	—	2	8	no	—
59	C₄×C₈×C₁₂₇	C₂×C₄	1	4	yes	—
60	C₄×C₈×C₁₂₇	C₂×C₄	1	4	yes	—
61	C₄×C₈×C₁₂₇	C₂×C₄	1	4	yes	—
62	C₄×C₈×C₁₂₇	C₂×C₄	1	4	yes	—
63	#95×C₁₂₇	C₂×C₄	1	4	yes	—
64	#95×C₁₂₇	C₂×C₄	1	4	yes	—
65	#95×C₁₂₇	C₂×C₄	1	4	yes	—
66	#95×C₁₂₇	C₂×C₄	1	4	yes	—
67	C₂⁴×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₂₇	—	2	4	no	—
69	C₂²×C₄×C₁₂₇	—	2	4	no	—
70	C₂²×C₄×C₁₂₇	—	2	2	no	—
71	C₂²×C₄×C₁₂₇	—	2	2	no	—
72	C₂²×C₄×C₁₂₇	C₄²	1	4	yes	—
73	C₂²×C₄×C₁₂₇	C₄²	1	4	yes	—
74	C₂²×C₄×C₁₂₇	C₂²×C₄	1	8	yes	—
75	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
83	C₂×C₈×C₁₂₇	—	2	4	no	—
84	C₂×C₈×C₁₂₇	—	2	4	no	—
85	C₂×C₈×C₁₂₇	—	2	2	no	—
86	C₂×C₈×C₁₂₇	—	2	2	no	—
87	C₂×C₈×C₁₂₇	—	2	8	no	—
88	C₂×C₈×C₁₂₇	—	2	8	no	—
89	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
90	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
91	C₂×C₈×C₁₂₇	C₂²×C₄	1	8	yes	—
92	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
93	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
94	C₂×C₈×C₁₂₇	#41	1	4	yes	—
95	C₂×C₈×C₁₂₇	#41	1	4	yes	—
96	C₄⋊C₄×C₁₂₇	—	2	8	no	—
97	C₂²⋊C₄×C₁₂₇	—	2	8	no	—
98	C₄²×C₁₂₇	—	2	4	no	—
99	C₄²×C₁₂₇	—	2	4	no	—
100	C₄²×C₁₂₇	C₄²	1	4	yes	—
101	C₄²×C₁₂₇	C₄²	1	4	yes	—
102	C₄²×C₁₂₇	C₂²×C₄	1	2	yes	—
103	C₄²×C₁₂₇	C₂²×C₄	1	2	yes	—
104	C₄²×C₁₂₇	C₂²×C₄	1	2	yes	—
105	C₄²×C₁₂₇	C₂²×C₄	1	2	yes	—
106	C₂³×C₁₂₇	—	2	2	no	—
107	C₂³×C₁₂₇	—	2	2	no	—
108	C₂³×C₁₂₇	C₂×C₄²	1	2	yes	—
109	C₂³×C₁₂₇	#131	1	4	yes	—
110	C₂³×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
111	C₂×C₄×C₁₂₇	—	2	2	no	—
112	C₂×C₄×C₁₂₇	—	2	2	no	—
113	C₂×C₄×C₁₂₇	—	2	2	no	—
114	C₂×C₄×C₁₂₇	—	2	2	no	—
115	C₂×C₄×C₁₂₇	—	2	8	no	—
116	C₂×C₄×C₁₂₇	—	2	2	no	—
117	C₂×C₄×C₁₂₇	—	2	2	no	—
118	C₂×C₄×C₁₂₇	—	2	4	no	—
119	C₂×C₄×C₁₂₇	—	2	8	no	—
120	C₂×C₄×C₁₂₇	—	2	8	no	—
121	C₂×C₄×C₁₂₇	—	2	8	no	—
122	C₂×C₄×C₁₂₇	—	2	8	no	—
123	C₂×C₄×C₁₂₇	C₂×C₄²	1	2	yes	—
124	C₂×C₄×C₁₂₇	C₂×C₄²	1	2	yes	—
125	C₂×C₄×C₁₂₇	C₂×C₄²	1	2	yes	—
126	C₂×C₄×C₁₂₇	C₂×C₄²	1	2	yes	—
127	C₂×C₄×C₁₂₇	C₂×C₄²	1	2	yes	—
128	C₂×C₄×C₁₂₇	#131	1	4	yes	—
129	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₂₇	C₂×#41	1	2	yes	—
132	C₂×C₄×C₁₂₇	C₂×#41	1	2	yes	—
133	C₈×C₁₂₇	—	2	2	no	—
134	C₈×C₁₂₇	—	2	2	no	—
135	C₈×C₁₂₇	—	2	8	no	—
136	C₈×C₁₂₇	#117	1	4	yes	—
137	C₈×C₁₂₇	#117	1	4	yes	—
138	C₂²×C₁₂₇	—	2	2	no	—
139	C₂²×C₁₂₇	—	2	8	no	—
140	C₂²×C₁₂₇	—	2	2	no	—
141	C₂²×C₁₂₇	#405	1	4	yes	—
142	C₂²×C₁₂₇	C₂²×C₄²	1	1	yes	characteristic
143	C₂²×C₁₂₇	C₄×#41	1	2	yes	—
144	C₂²×C₁₂₇	C₂×#131	1	2	yes	—
145	C₂²×C₁₂₇	C₂×#131	1	2	yes	—
146	C₄×C₁₂₇	—	2	2	no	—
147	C₄×C₁₂₇	—	2	2	no	—
148	C₄×C₁₂₇	—	2	2	no	—
149	C₄×C₁₂₇	—	2	2	no	—
150	C₄×C₁₂₇	—	4	8	no	—
151	C₄×C₁₂₇	#405	1	4	yes	—
152	C₄×C₁₂₇	C₂×#117	1	1	yes	characteristic
153	C₄×C₁₂₇	C₂×#117	1	1	yes	characteristic
154	C₄×C₁₂₇	C₄×#41	1	2	yes	—
155	#20476	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂×C₁₂₇	—	2	4	no	—
157	C₂×C₁₂₇	C₄×#117	1	1	yes	characteristic
158	C₂×C₁₂₇	C₂×#405	1	1	yes	characteristic
159	C₂×C₁₂₇	C₂×#405	1	1	yes	characteristic
160	C₂×C₁₂₇	#2966	1	4	yes	—
161	C₂×#432	C₂×C₁₂₇	1	1	yes	characteristic
162	C₂²×C₄×C₈	C₂×C₁₂₇	1	1	yes	characteristic
163	#2283	C₂×C₁₂₇	1	1	yes	characteristic
164	#1770	C₂×C₁₂₇	1	2	yes	complemented
165	C₈×C₄⋊C₄	C₂×C₁₂₇	1	2	yes	complemented
166	#1752	C₂×C₁₂₇	1	2	yes	—
167	C₈×C₂²⋊C₄	C₂×C₁₂₇	1	2	yes	—
168	#1746	C₂×C₁₂₇	1	2	yes	complemented
169	#1726	C₂×C₁₂₇	1	2	yes	complemented
170	C₁₂₇	#20476	1	1	yes	characteristic, direct product factor, Sylow
171	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
172	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
173	C₂²×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
174	#432	C₄×C₁₂₇	1	8	yes	complemented
175	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
176	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	—
177	C₂×#97	C₂²×C₁₂₇	1	4	yes	—
178	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
179	C₂×C₄×C₈	C₄×C₁₂₇	1	8	yes	complemented
180	C₂×C₄×C₈	C₂²×C₁₂₇	1	4	yes	—
181	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
182	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
183	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
184	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
185	#383	C₄×C₁₂₇	1	2	yes	—
186	#382	C₄×C₁₂₇	1	2	yes	—
187	#381	C₄×C₁₂₇	1	2	yes	—
188	#380	C₄×C₁₂₇	1	2	yes	—
189	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
190	C₄×C₂²⋊C₄	C₂²×C₁₂₇	1	2	yes	—
191	#376	C₂²×C₁₂₇	1	2	yes	—
192	#336	C₂²×C₁₂₇	1	4	yes	—
193	#336	C₂²×C₁₂₇	1	4	yes	—
194	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
195	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
196	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
197	C₂²×C₈	—	2	4	no	—
198	C₂²×C₈	—	2	4	no	—
199	C₂²×C₈	C₂×C₄×C₁₂₇	1	4	yes	—
200	C₂²×C₈	C₂×C₄×C₁₂₇	1	4	yes	—
201	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
202	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
203	C₂²×C₈	C₂³×C₁₂₇	1	4	yes	—
204	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
205	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
207	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
208	C₂×C₄²	C₂×C₄×C₁₂₇	1	1	yes	characteristic
209	C₂×C₄²	C₂×C₄×C₁₂₇	1	1	yes	characteristic
210	C₂×C₄²	C₂×C₄×C₁₂₇	1	4	yes	—
211	C₂×C₄²	C₂×C₄×C₁₂₇	1	4	yes	—
212	C₂×C₄²	C₂³×C₁₂₇	1	4	yes	—
213	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
214	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
215	C₄⋊C₈	C₂×C₄×C₁₂₇	1	8	yes	—
216	C₂²⋊C₈	C₂×C₄×C₁₂₇	1	8	yes	—
217	#97	—	2	8	no	—
218	#97	C₂×C₄×C₁₂₇	1	8	yes	—
219	C₄×C₈	—	2	8	no	—
220	C₄×C₈	C₂×C₄×C₁₂₇	1	4	yes	—
221	C₄×C₈	C₂×C₄×C₁₂₇	1	4	yes	—
222	C₄×C₈	C₂×C₄×C₁₂₇	1	4	yes	—
223	C₄×C₈	C₂×C₄×C₁₂₇	1	4	yes	—
224	#95	C₂×C₄×C₁₂₇	1	4	yes	—
225	#95	C₂×C₄×C₁₂₇	1	4	yes	—
226	#95	C₂×C₄×C₁₂₇	1	4	yes	—
227	#95	C₂×C₄×C₁₂₇	1	4	yes	—
228	C₂⁴	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
229	C₂²×C₄	—	2	4	no	—
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	C₄²×C₁₂₇	1	4	yes	—
234	C₂²×C₄	C₄²×C₁₂₇	1	4	yes	—
235	C₂²×C₄	C₂²×C₄×C₁₂₇	1	8	yes	—
236	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
237	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
238	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
239	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
240	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
241	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
242	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
243	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
244	C₂×C₈	—	2	4	no	—
245	C₂×C₈	—	2	4	no	—
246	C₂×C₈	—	2	2	no	—
247	C₂×C₈	—	2	2	no	—
248	C₂×C₈	—	2	8	no	—
249	C₂×C₈	—	2	8	no	—
250	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
251	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
252	C₂×C₈	C₂²×C₄×C₁₂₇	1	8	yes	—
253	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
254	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
255	C₂×C₈	#41×C₁₂₇	1	4	yes	—
256	C₂×C₈	#41×C₁₂₇	1	4	yes	—
257	C₄⋊C₄	—	2	8	no	—
258	C₂²⋊C₄	—	2	8	no	—
259	C₄²	—	2	4	no	—
260	C₄²	—	2	4	no	—
261	C₄²	C₄²×C₁₂₇	1	4	yes	—
262	C₄²	C₄²×C₁₂₇	1	4	yes	—
263	C₄²	C₂²×C₄×C₁₂₇	1	2	yes	—
264	C₄²	C₂²×C₄×C₁₂₇	1	2	yes	—
265	C₄²	C₂²×C₄×C₁₂₇	1	2	yes	—
266	C₄²	C₂²×C₄×C₁₂₇	1	2	yes	—
267	C₂³	—	2	2	no	—
268	C₂³	—	2	2	no	—
269	C₂³	C₂×C₄²×C₁₂₇	1	2	yes	—
270	C₂³	#131×C₁₂₇	1	4	yes	—
271	C₂³	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
272	C₂×C₄	—	2	2	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	8	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	8	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	8	no	—
283	C₂×C₄	—	2	8	no	—
284	C₂×C₄	C₂×C₄²×C₁₂₇	1	2	yes	—
285	C₂×C₄	C₂×C₄²×C₁₂₇	1	2	yes	—
286	C₂×C₄	C₂×C₄²×C₁₂₇	1	2	yes	—
287	C₂×C₄	C₂×C₄²×C₁₂₇	1	2	yes	—
288	C₂×C₄	C₂×C₄²×C₁₂₇	1	2	yes	—
289	C₂×C₄	#131×C₁₂₇	1	4	yes	—
290	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
291	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
292	C₂×C₄	C₂×#41×C₁₂₇	1	2	yes	—
293	C₂×C₄	C₂×#41×C₁₂₇	1	2	yes	—
294	C₈	—	2	2	no	—
295	C₈	—	2	2	no	—
296	C₈	—	2	8	no	—
297	C₈	#117×C₁₂₇	1	4	yes	—
298	C₈	#117×C₁₂₇	1	4	yes	—
299	C₂²	—	2	2	no	—
300	C₂²	—	2	8	no	—
301	C₂²	—	2	2	no	—
302	C₂²	#405×C₁₂₇	1	4	yes	—
303	C₂²	C₂²×C₄²×C₁₂₇	1	1	yes	characteristic
304	C₂²	C₄×#41×C₁₂₇	1	2	yes	—
305	C₂²	C₂×#131×C₁₂₇	1	2	yes	—
306	C₂²	C₂×#131×C₁₂₇	1	2	yes	—
307	C₄	—	2	2	no	—
308	C₄	—	2	2	no	—
309	C₄	—	2	2	no	—
310	C₄	—	2	2	no	—
311	C₄	—	4	8	no	—
312	C₄	#405×C₁₂₇	1	4	yes	—
313	C₄	C₂×#117×C₁₂₇	1	1	yes	characteristic
314	C₄	C₂×#117×C₁₂₇	1	1	yes	characteristic
315	C₄	C₄×#41×C₁₂₇	1	2	yes	—
316	C₂	—	2	4	no	—
317	C₂	C₄×#117×C₁₂₇	1	1	yes	characteristic
318	C₂	C₂×#405×C₁₂₇	1	1	yes	characteristic
319	C₂	C₂×#405×C₁₂₇	1	1	yes	characteristic
320	C₂	C₁₂₇×#2966	1	4	yes	—

	subgroup	G/H
center	C₂²×C₈×C₁₂₇	C₂³
commutator	C₂²	C₂²×C₄²×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₂₇
socle	C₂³×C₁₂₇	C₂³×C₄
prime radical	C₂⁴×C₁₂₇	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₂₇×#1770	C₂	semidirect
5. C₈×C₄⋊C₄×C₁₂₇	C₂	semidirect
8. C₁₂₇×#1746	C₂	semidirect
9. C₁₂₇×#1726	C₂	semidirect
13. #432×C₁₂₇	C₄	semidirect
18. C₂×C₄×C₈×C₁₂₇	C₄	semidirect
155. #20476	C₁₂₇	direct (N × H)
164. #1770	C₂×C₁₂₇	semidirect
165. C₈×C₄⋊C₄	C₂×C₁₂₇	semidirect
168. #1746	C₂×C₁₂₇	semidirect
169. #1726	C₂×C₁₂₇	semidirect
170. C₁₂₇	#20476	direct (N × H)
174. #432	C₄×C₁₂₇	semidirect
179. C₂×C₄×C₈	C₄×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#432×C₁₂₇	2
C₂²×C₄×C₈×C₁₂₇	2
C₁₂₇×#2283	2
C₁₂₇×#1770	2
C₈×C₄⋊C₄×C₁₂₇	2
C₁₂₇×#1752	2
C₈×C₂²⋊C₄×C₁₂₇	2
C₁₂₇×#1746	2
C₁₂₇×#1726	2
#20476	127

Subgroups — C127×#20476 #44584149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#20476 #44584149