Subgroups — C₁₂₇×#21707 #44585380

Order 32512.

998 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	C₁₂₇×#3147	C₂	1	1	yes	maximal, characteristic
2	C₂×#444×C₁₂₇	C₂	1	2	yes	maximal, complemented
3	C₂×#443×C₁₂₇	C₂	1	2	yes	maximal, complemented
4	C₁₂₇×#2932	C₂	1	2	yes	maximal, complemented
5	C₁₂₇×#1975	C₂	1	2	yes	maximal, complemented
6	C₁₂₇×#1974	C₂	1	2	yes	maximal, complemented
7	C₁₂₇×#1963	C₂	1	2	yes	maximal, complemented
8	C₁₂₇×#1848	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₂₇×#1726	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#135×C₁₂₇	C₂²	1	2	yes	—
11	C₂×#135×C₁₂₇	C₂²	1	2	yes	—
12	C₂×#131×C₁₂₇	C₂²	1	4	yes	—
13	#532×C₁₂₇	C₂²	1	2	yes	—
14	#495×C₁₂₇	C₄	1	2	yes	complemented
15	#495×C₁₂₇	C₄	1	2	yes	complemented
16	#494×C₁₂₇	C₄	1	1	yes	characteristic, complemented
17	#493×C₁₂₇	C₄	1	1	yes	characteristic, complemented
18	#492×C₁₂₇	C₄	1	2	yes	complemented
19	#444×C₁₂₇	—	2	8	no	—
20	#443×C₁₂₇	—	2	8	no	—
21	#435×C₁₂₇	—	2	8	no	—
22	C₂×#108×C₁₂₇	C₂²	1	2	yes	—
23	C₂×#108×C₁₂₇	C₂²	1	2	yes	—
24	#423×C₁₂₇	C₂²	1	2	yes	—
25	C₂×#104×C₁₂₇	C₂²	1	4	yes	—
26	C₂×#104×C₁₂₇	C₂²	1	4	yes	—
27	#408×C₁₂₇	C₂²	1	4	yes	—
28	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
29	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
30	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
34	#376×C₁₂₇	C₂²	1	1	yes	characteristic
35	C₂×#41×C₁₂₇	C₂³	1	4	yes	—
36	#135×C₁₂₇	—	2	4	no	—
37	#135×C₁₂₇	—	2	4	no	—
38	#135×C₁₂₇	—	2	4	no	—
39	#135×C₁₂₇	—	2	4	no	—
40	C₂×Q₁₆×C₁₂₇	C₂×C₄	1	2	yes	—
41	C₂×Q₁₆×C₁₂₇	C₂×C₄	1	2	yes	—
42	C₂×SD₁₆×C₁₂₇	C₂×C₄	1	4	yes	—
43	C₂×SD₁₆×C₁₂₇	C₂×C₄	1	4	yes	—
44	C₂×D₈×C₁₂₇	C₂×C₄	1	2	yes	—
45	C₂×D₈×C₁₂₇	C₂×C₄	1	2	yes	—
46	#131×C₁₂₇	—	2	8	no	—
47	#131×C₁₂₇	—	2	8	no	—
48	C₂×M₁₆×C₁₂₇	—	2	4	no	—
49	C₂×M₁₆×C₁₂₇	C₂³	1	4	yes	—
50	C₂²×C₈×C₁₂₇	—	2	4	no	—
51	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
55	C₄⋊Q₈×C₁₂₇	C₂×C₄	1	2	yes	—
56	#127×C₁₂₇	C₂×C₄	1	2	yes	—
57	#124×C₁₂₇	C₂×C₄	1	4	yes	—
58	#121×C₁₂₇	—	2	4	no	—
59	C₄×D₄×C₁₂₇	—	2	4	no	—
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	#108×C₁₂₇	—	2	4	no	—
64	#108×C₁₂₇	—	2	4	no	—
65	C₄⋊C₈×C₁₂₇	—	2	4	no	—
66	#104×C₁₂₇	—	2	8	no	—
67	#104×C₁₂₇	—	2	8	no	—
68	C₂²⋊C₈×C₁₂₇	—	2	8	no	—
69	#97×C₁₂₇	—	2	2	no	—
70	#97×C₁₂₇	D₄	1	4	yes	—
71	#97×C₁₂₇	D₄	1	4	yes	complemented
72	C₄×C₈×C₁₂₇	—	2	2	no	—
73	C₄×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
74	C₄×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₁₂₇	D₄	1	4	yes	complemented
78	#95×C₁₂₇	—	2	2	no	—
79	#41×C₁₂₇	—	2	4	no	—
80	#41×C₁₂₇	—	2	4	no	—
81	#41×C₁₂₇	—	2	4	no	—
82	#41×C₁₂₇	—	2	4	no	—
83	C₂×Q₈×C₁₂₇	C₂²×C₄	1	4	yes	—
84	C₂×D₄×C₁₂₇	—	2	4	no	—
85	C₂×D₄×C₁₂₇	—	2	4	no	—
86	C₂×D₄×C₁₂₇	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₁₂₇	—	2	1	no	—
88	C₂²×C₄×C₁₂₇	—	2	1	no	—
89	C₂²×C₄×C₁₂₇	—	2	4	no	—
90	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
91	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
92	Q₁₆×C₁₂₇	—	2	4	no	—
93	Q₁₆×C₁₂₇	—	2	4	no	—
94	SD₁₆×C₁₂₇	—	2	8	no	—
95	SD₁₆×C₁₂₇	—	2	8	no	—
96	D₈×C₁₂₇	—	2	4	no	—
97	D₈×C₁₂₇	—	2	4	no	—
98	M₁₆×C₁₂₇	—	2	4	no	—
99	M₁₆×C₁₂₇	—	2	4	no	—
100	M₁₆×C₁₂₇	—	4	8	no	—
101	C₂×C₈×C₁₂₇	—	2	1	no	—
102	C₂×C₈×C₁₂₇	—	2	1	no	—
103	C₂×C₈×C₁₂₇	—	2	4	no	—
104	C₂×C₈×C₁₂₇	—	4	8	no	—
105	C₂×C₈×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₁₂₇	#41	1	2	yes	—
116	C₂×C₈×C₁₂₇	#41	1	2	yes	—
117	C₄⋊C₄×C₁₂₇	—	2	4	no	—
118	C₂²⋊C₄×C₁₂₇	—	2	8	no	—
119	C₄²×C₁₂₇	—	2	1	no	—
120	C₄²×C₁₂₇	—	2	1	no	—
121	C₄²×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
124	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
125	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
126	C₂³×C₁₂₇	—	2	4	no	—
127	C₂³×C₁₂₇	C₂×#41	1	1	yes	characteristic
128	Q₈×C₁₂₇	—	2	4	no	—
129	Q₈×C₁₂₇	—	2	4	no	—
130	D₄×C₁₂₇	—	2	4	no	—
131	D₄×C₁₂₇	—	2	4	no	—
132	D₄×C₁₂₇	—	4	4	no	—
133	D₄×C₁₂₇	—	4	4	no	—
134	D₄×C₁₂₇	—	8	4	no	—
135	C₂×C₄×C₁₂₇	—	2	4	no	—
136	C₂×C₄×C₁₂₇	—	2	2	no	—
137	C₂×C₄×C₁₂₇	—	2	2	no	—
138	C₂×C₄×C₁₂₇	—	4	2	no	—
139	C₂×C₄×C₁₂₇	—	4	2	no	—
140	C₂×C₄×C₁₂₇	—	4	2	no	—
141	C₂×C₄×C₁₂₇	—	4	4	no	—
142	C₂×C₄×C₁₂₇	—	4	4	no	—
143	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
144	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
145	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
151	C₈×C₁₂₇	—	2	2	no	—
152	C₈×C₁₂₇	—	4	4	no	—
153	C₈×C₁₂₇	C₄×D₄	1	2	yes	—
154	C₈×C₁₂₇	C₄×D₄	1	2	yes	—
155	C₈×C₁₂₇	C₄×D₄	1	2	yes	—
156	C₈×C₁₂₇	C₄×D₄	1	2	yes	—
157	C₈×C₁₂₇	#127	1	4	yes	—
158	C₂²×C₁₂₇	—	2	2	no	—
159	C₂²×C₁₂₇	—	4	4	no	—
160	C₂²×C₁₂₇	—	4	8	no	—
161	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
162	C₂²×C₁₂₇	#532	1	1	yes	characteristic
163	C₂²×C₁₂₇	#532	1	1	yes	characteristic
164	C₄×C₁₂₇	—	2	2	no	—
165	C₄×C₁₂₇	—	2	2	no	—
166	C₄×C₁₂₇	—	4	2	no	—
167	C₄×C₁₂₇	—	4	2	no	—
168	C₄×C₁₂₇	—	4	4	no	—
169	C₄×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
170	C₄×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
171	C₄×C₁₂₇	C₂×#127	1	1	yes	characteristic
172	C₄×C₁₂₇	#532	1	1	yes	characteristic
173	#21707	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂×C₁₂₇	—	2	1	no	—
175	C₂×C₁₂₇	—	2	1	no	—
176	C₂×C₁₂₇	—	8	4	no	—
177	C₂×C₁₂₇	C₄×#127	1	1	yes	characteristic
178	C₂×C₁₂₇	#2957	1	2	yes	—
179	#3147	C₂×C₁₂₇	1	1	yes	characteristic
180	C₂×#444	C₂×C₁₂₇	1	2	yes	complemented
181	C₂×#443	C₂×C₁₂₇	1	2	yes	complemented
182	#2932	C₂×C₁₂₇	1	2	yes	complemented
183	#1975	C₂×C₁₂₇	1	2	yes	complemented
184	#1974	C₂×C₁₂₇	1	2	yes	complemented
185	#1963	C₂×C₁₂₇	1	2	yes	complemented
186	#1848	C₂×C₁₂₇	1	1	yes	characteristic, complemented
187	#1726	C₂×C₁₂₇	1	1	yes	characteristic, complemented
188	C₁₂₇	#21707	1	1	yes	characteristic, direct product factor, Sylow
189	C₂×#135	C₂²×C₁₂₇	1	2	yes	—
190	C₂×#135	C₂²×C₁₂₇	1	2	yes	—
191	C₂×#131	C₂²×C₁₂₇	1	4	yes	—
192	#532	C₂²×C₁₂₇	1	2	yes	—
193	#495	C₄×C₁₂₇	1	2	yes	complemented
194	#495	C₄×C₁₂₇	1	2	yes	complemented
195	#494	C₄×C₁₂₇	1	1	yes	characteristic, complemented
196	#493	C₄×C₁₂₇	1	1	yes	characteristic, complemented
197	#492	C₄×C₁₂₇	1	2	yes	complemented
198	#444	—	2	8	no	—
199	#443	—	2	8	no	—
200	#435	—	2	8	no	—
201	C₂×#108	C₂²×C₁₂₇	1	2	yes	—
202	C₂×#108	C₂²×C₁₂₇	1	2	yes	—
203	#423	C₂²×C₁₂₇	1	2	yes	—
204	C₂×#104	C₂²×C₁₂₇	1	4	yes	—
205	C₂×#104	C₂²×C₁₂₇	1	4	yes	—
206	#408	C₂²×C₁₂₇	1	4	yes	—
207	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
208	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
209	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
211	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
212	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
213	#376	C₂²×C₁₂₇	1	1	yes	characteristic
214	C₂×#41	C₂³×C₁₂₇	1	4	yes	—
215	#135	—	2	4	no	—
216	#135	—	2	4	no	—
217	#135	—	2	4	no	—
218	#135	—	2	4	no	—
219	C₂×Q₁₆	C₂×C₄×C₁₂₇	1	2	yes	—
220	C₂×Q₁₆	C₂×C₄×C₁₂₇	1	2	yes	—
221	C₂×SD₁₆	C₂×C₄×C₁₂₇	1	4	yes	—
222	C₂×SD₁₆	C₂×C₄×C₁₂₇	1	4	yes	—
223	C₂×D₈	C₂×C₄×C₁₂₇	1	2	yes	—
224	C₂×D₈	C₂×C₄×C₁₂₇	1	2	yes	—
225	#131	—	2	8	no	—
226	#131	—	2	8	no	—
227	C₂×M₁₆	—	2	4	no	—
228	C₂×M₁₆	C₂³×C₁₂₇	1	4	yes	—
229	C₂²×C₈	—	2	4	no	—
230	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
234	C₄⋊Q₈	C₂×C₄×C₁₂₇	1	2	yes	—
235	#127	C₂×C₄×C₁₂₇	1	2	yes	—
236	#124	C₂×C₄×C₁₂₇	1	4	yes	—
237	#121	—	2	4	no	—
238	C₄×D₄	—	2	4	no	—
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	#108	—	2	4	no	—
243	#108	—	2	4	no	—
244	C₄⋊C₈	—	2	4	no	—
245	#104	—	2	8	no	—
246	#104	—	2	8	no	—
247	C₂²⋊C₈	—	2	8	no	—
248	#97	—	2	2	no	—
249	#97	D₄×C₁₂₇	1	4	yes	—
250	#97	D₄×C₁₂₇	1	4	yes	complemented
251	C₄×C₈	—	2	2	no	—
252	C₄×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
253	C₄×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
254	C₄×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
255	C₄×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
256	C₄×C₈	D₄×C₁₂₇	1	4	yes	complemented
257	#95	—	2	2	no	—
258	#41	—	2	4	no	—
259	#41	—	2	4	no	—
260	#41	—	2	4	no	—
261	#41	—	2	4	no	—
262	C₂×Q₈	C₂²×C₄×C₁₂₇	1	4	yes	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	C₂²×C₄×C₁₂₇	1	4	yes	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
270	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
271	Q₁₆	—	2	4	no	—
272	Q₁₆	—	2	4	no	—
273	SD₁₆	—	2	8	no	—
274	SD₁₆	—	2	8	no	—
275	D₈	—	2	4	no	—
276	D₈	—	2	4	no	—
277	M₁₆	—	2	4	no	—
278	M₁₆	—	2	4	no	—
279	M₁₆	—	4	8	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	4	8	no	—
284	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
285	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
286	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
287	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
288	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
289	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
290	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
291	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
292	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
293	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
294	C₂×C₈	#41×C₁₂₇	1	2	yes	—
295	C₂×C₈	#41×C₁₂₇	1	2	yes	—
296	C₄⋊C₄	—	2	4	no	—
297	C₂²⋊C₄	—	2	8	no	—
298	C₄²	—	2	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
301	C₄²	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
302	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
303	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
304	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
305	C₂³	—	2	4	no	—
306	C₂³	C₂×#41×C₁₂₇	1	1	yes	characteristic
307	Q₈	—	2	4	no	—
308	Q₈	—	2	4	no	—
309	D₄	—	2	4	no	—
310	D₄	—	2	4	no	—
311	D₄	—	4	4	no	—
312	D₄	—	4	4	no	—
313	D₄	—	8	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
323	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
324	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
325	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
326	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
327	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
328	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
329	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
330	C₈	—	2	2	no	—
331	C₈	—	4	4	no	—
332	C₈	C₄×D₄×C₁₂₇	1	2	yes	—
333	C₈	C₄×D₄×C₁₂₇	1	2	yes	—
334	C₈	C₄×D₄×C₁₂₇	1	2	yes	—
335	C₈	C₄×D₄×C₁₂₇	1	2	yes	—
336	C₈	#127×C₁₂₇	1	4	yes	—
337	C₂²	—	2	2	no	—
338	C₂²	—	4	8	no	—
339	C₂²	—	4	4	no	—
340	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
341	C₂²	#532×C₁₂₇	1	1	yes	characteristic
342	C₂²	#532×C₁₂₇	1	1	yes	characteristic
343	C₄	—	2	2	no	—
344	C₄	—	2	2	no	—
345	C₄	—	4	2	no	—
346	C₄	—	4	2	no	—
347	C₄	—	4	4	no	—
348	C₄	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
349	C₄	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
350	C₄	C₂×#127×C₁₂₇	1	1	yes	characteristic
351	C₄	#532×C₁₂₇	1	1	yes	characteristic
352	C₂	—	2	1	no	—
353	C₂	—	2	1	no	—
354	C₂	—	8	4	no	—
355	C₂	C₄×#127×C₁₂₇	1	1	yes	characteristic
356	C₂	C₁₂₇×#2957	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₂₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₂₇
socle	C₂²×C₁₂₇	C₂×C₄×D₄
prime radical	C₁₂₇×#3147	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₂₇ ◁ C₂×#97×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#444×C₁₂₇	C₂	semidirect
3. C₂×#443×C₁₂₇	C₂	semidirect
4. C₁₂₇×#2932	C₂	semidirect
5. C₁₂₇×#1975	C₂	semidirect
6. C₁₂₇×#1974	C₂	semidirect
7. C₁₂₇×#1963	C₂	semidirect
8. C₁₂₇×#1848	C₂	semidirect
9. C₁₂₇×#1726	C₂	semidirect
14. #495×C₁₂₇	C₄	semidirect
15. #495×C₁₂₇	C₄	semidirect
16. #494×C₁₂₇	C₄	semidirect
17. #493×C₁₂₇	C₄	semidirect
18. #492×C₁₂₇	C₄	semidirect
71. #97×C₁₂₇	D₄	semidirect
77. C₄×C₈×C₁₂₇	D₄	semidirect
173. #21707	C₁₂₇	direct (N × H)
180. C₂×#444	C₂×C₁₂₇	semidirect
181. C₂×#443	C₂×C₁₂₇	semidirect
182. #2932	C₂×C₁₂₇	semidirect
183. #1975	C₂×C₁₂₇	semidirect
184. #1974	C₂×C₁₂₇	semidirect
185. #1963	C₂×C₁₂₇	semidirect
186. #1848	C₂×C₁₂₇	semidirect
187. #1726	C₂×C₁₂₇	semidirect
188. C₁₂₇	#21707	direct (N × H)
193. #495	C₄×C₁₂₇	semidirect
194. #495	C₄×C₁₂₇	semidirect
195. #494	C₄×C₁₂₇	semidirect
196. #493	C₄×C₁₂₇	semidirect
197. #492	C₄×C₁₂₇	semidirect
250. #97	D₄×C₁₂₇	semidirect
256. 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
C₁₂₇×#3147	2
C₂×#444×C₁₂₇	2
C₂×#443×C₁₂₇	2
C₁₂₇×#2932	2
C₁₂₇×#1975	2
C₁₂₇×#1974	2
C₁₂₇×#1963	2
C₁₂₇×#1848	2
C₁₂₇×#1726	2
#21707	127

Subgroups — C127×#21707 #44585380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#21707 #44585380