Subgroups — C₄×#492×C₁₂₇ #44585359

Order 32512.

1254 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#492×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₁₂₇	C₂	1	4	yes	maximal, complemented
3	C₄×C₄⋊Q₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#127×C₁₂₇	C₂	1	1	yes	maximal, characteristic
5	C₁₂₇×#1968	C₂	1	4	yes	maximal, complemented
6	C₁₂₇×#1957	C₂	1	1	yes	maximal, characteristic
7	C₁₂₇×#1956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₂₇×#1844	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄²×C₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₁₂₇	C₂²	1	4	yes	—
11	C₂×C₄⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic
12	C₂×#127×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₂₇	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₂₇	—	2	2	no	—
15	C₂×C₄×D₄×C₁₂₇	C₂²	1	2	yes	—
16	#492×C₁₂₇	C₄	1	8	yes	direct product factor
17	C₄×SD₁₆×C₁₂₇	—	2	16	no	—
18	C₂×#106×C₁₂₇	C₂²	1	4	yes	—
19	C₂×#103×C₁₂₇	C₂²	1	4	yes	—
20	C₂×#102×C₁₂₇	C₂²	1	4	yes	—
21	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
25	#391×C₁₂₇	C₂²	1	2	yes	—
26	#390×C₁₂₇	—	2	2	no	—
27	#390×C₁₂₇	C₂²	1	2	yes	—
28	#389×C₁₂₇	—	2	2	no	—
29	#384×C₁₂₇	C₂²	1	1	yes	characteristic
30	#384×C₁₂₇	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₁₂₇	—	2	2	no	—
32	C₄³×C₁₂₇	C₂²	1	1	yes	characteristic
33	C₂²×Q₈×C₁₂₇	C₂³	1	2	yes	—
34	C₂²×D₄×C₁₂₇	—	2	2	no	—
35	C₂²×D₄×C₁₂₇	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₂₇	—	2	2	no	—
37	C₂×SD₁₆×C₁₂₇	—	2	8	no	—
38	C₂×SD₁₆×C₁₂₇	—	2	8	no	—
39	C₂×SD₁₆×C₁₂₇	C₂×C₄	1	16	yes	complemented
40	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
42	C₄⋊Q₈×C₁₂₇	—	2	2	no	—
43	C₄⋊Q₈×C₁₂₇	C₂×C₄	1	4	yes	complemented
44	#127×C₁₂₇	—	2	2	no	—
45	#127×C₁₂₇	C₂×C₄	1	4	yes	—
46	C₄×Q₈×C₁₂₇	—	2	8	no	—
47	C₄×D₄×C₁₂₇	—	2	8	no	—
48	C₄×D₄×C₁₂₇	—	4	8	no	—
49	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₁₂₇	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₁₂₇	—	2	2	no	—
57	C₂×C₄²×C₁₂₇	—	2	2	no	—
58	C₂×C₄²×C₁₂₇	D₄	1	2	yes	—
59	C₂×C₄²×C₁₂₇	D₄	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	#106×C₁₂₇	—	2	8	no	—
64	#103×C₁₂₇	—	2	8	no	—
65	#102×C₁₂₇	—	2	8	no	—
66	C₄×C₈×C₁₂₇	—	2	4	no	—
67	C₄×C₈×C₁₂₇	—	2	2	no	—
68	C₄×C₈×C₁₂₇	C₂×C₄	1	4	yes	complemented
69	C₄×C₈×C₁₂₇	D₄	1	8	yes	complemented
70	#95×C₁₂₇	—	2	4	no	—
71	C₂⁴×C₁₂₇	—	2	2	no	—
72	C₂×Q₈×C₁₂₇	—	2	2	no	—
73	C₂×Q₈×C₁₂₇	—	2	4	no	—
74	C₂×Q₈×C₁₂₇	—	2	4	no	—
75	C₂×Q₈×C₁₂₇	C₂²×C₄	1	4	yes	—
76	C₂×D₄×C₁₂₇	—	2	8	no	—
77	C₂×D₄×C₁₂₇	—	2	4	no	—
78	C₂×D₄×C₁₂₇	—	2	4	no	—
79	C₂×D₄×C₁₂₇	—	2	2	no	—
80	C₂×D₄×C₁₂₇	—	4	4	no	—
81	C₂×D₄×C₁₂₇	—	4	4	no	—
82	C₂×D₄×C₁₂₇	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₁₂₇	—	2	2	no	—
84	C₂²×C₄×C₁₂₇	—	2	2	no	—
85	C₂²×C₄×C₁₂₇	—	2	2	no	—
86	C₂²×C₄×C₁₂₇	—	4	4	no	—
87	C₂²×C₄×C₁₂₇	—	4	8	no	—
88	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
93	SD₁₆×C₁₂₇	—	2	32	no	—
94	C₂×C₈×C₁₂₇	—	2	2	no	—
95	C₂×C₈×C₁₂₇	—	2	2	no	—
96	C₂×C₈×C₁₂₇	C₂²×C₄	1	4	yes	—
97	C₂×C₈×C₁₂₇	C₂×D₄	1	4	yes	—
98	C₂×C₈×C₁₂₇	C₂×D₄	1	4	yes	—
99	C₂×C₈×C₁₂₇	#41	1	4	yes	—
100	C₄⋊C₄×C₁₂₇	—	2	8	no	—
101	C₄⋊C₄×C₁₂₇	—	2	4	no	—
102	C₄⋊C₄×C₁₂₇	—	2	4	no	—
103	C₄⋊C₄×C₁₂₇	—	4	4	no	—
104	C₄⋊C₄×C₁₂₇	—	4	4	no	—
105	C₄⋊C₄×C₁₂₇	—	4	4	no	—
106	C₂²⋊C₄×C₁₂₇	—	4	4	no	—
107	C₂²⋊C₄×C₁₂₇	—	4	8	no	—
108	C₄²×C₁₂₇	—	2	4	no	—
109	C₄²×C₁₂₇	—	2	2	no	—
110	C₄²×C₁₂₇	—	4	4	no	—
111	C₄²×C₁₂₇	SD₁₆	1	8	yes	complemented
112	C₄²×C₁₂₇	C₂²×C₄	1	2	yes	—
113	C₄²×C₁₂₇	C₂×D₄	1	4	yes	—
114	C₄²×C₁₂₇	#41	1	2	yes	—
115	C₂³×C₁₂₇	—	2	4	no	—
116	C₂³×C₁₂₇	—	4	2	no	—
117	C₂³×C₁₂₇	—	4	2	no	—
118	C₂³×C₁₂₇	—	4	4	no	—
119	C₂³×C₁₂₇	—	4	4	no	—
120	C₂³×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
121	Q₈×C₁₂₇	—	2	8	no	—
122	Q₈×C₁₂₇	—	4	4	no	—
123	D₄×C₁₂₇	—	2	8	no	—
124	D₄×C₁₂₇	—	4	4	no	—
125	D₄×C₁₂₇	—	4	16	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	4	no	—
130	C₂×C₄×C₁₂₇	—	4	2	no	—
131	C₂×C₄×C₁₂₇	—	4	2	no	—
132	C₂×C₄×C₁₂₇	—	4	2	no	—
133	C₂×C₄×C₁₂₇	—	4	2	no	—
134	C₂×C₄×C₁₂₇	—	4	4	no	—
135	C₂×C₄×C₁₂₇	—	4	4	no	—
136	C₂×C₄×C₁₂₇	—	8	8	no	—
137	C₂×C₄×C₁₂₇	C₄×D₄	1	4	yes	—
138	C₂×C₄×C₁₂₇	#127	1	2	yes	—
139	C₂×C₄×C₁₂₇	#127	1	2	yes	—
140	C₂×C₄×C₁₂₇	C₂×SD₁₆	1	4	yes	—
141	C₂×C₄×C₁₂₇	C₂×SD₁₆	1	4	yes	—
142	C₂×C₄×C₁₂₇	C₂×SD₁₆	1	4	yes	—
143	C₂×C₄×C₁₂₇	#135	1	4	yes	—
144	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₂₇	C₂²×D₄	1	2	yes	—
146	C₂×C₄×C₁₂₇	C₂×#41	1	2	yes	—
147	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
148	C₈×C₁₂₇	—	2	4	no	—
149	C₈×C₁₂₇	C₄×D₄	1	8	yes	complemented
150	C₂²×C₁₂₇	—	4	4	no	—
151	C₂²×C₁₂₇	—	4	8	no	—
152	C₂²×C₁₂₇	—	8	2	no	—
153	C₂²×C₁₂₇	—	8	2	no	—
154	C₂²×C₁₂₇	—	8	4	no	—
155	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
156	C₂²×C₁₂₇	C₂×#127	1	1	yes	characteristic
157	C₂²×C₁₂₇	#532	1	1	yes	characteristic
158	C₂²×C₁₂₇	C₂²×SD₁₆	1	2	yes	—
159	C₂²×C₁₂₇	C₂×#135	1	2	yes	—
160	C₄×C₁₂₇	—	2	2	no	—
161	C₄×C₁₂₇	—	2	4	no	—
162	C₄×C₁₂₇	—	4	4	no	—
163	C₄×C₁₂₇	—	8	2	no	—
164	C₄×C₁₂₇	—	8	2	no	—
165	C₄×C₁₂₇	C₄×SD₁₆	1	8	yes	complemented
166	C₄×C₁₂₇	#492	1	4	yes	direct product factor
167	C₄×C₁₂₇	C₂×C₄×D₄	1	2	yes	—
168	C₄×C₁₂₇	#532	1	2	yes	—
169	C₄×#492	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂×C₁₂₇	—	8	4	no	—
171	C₂×C₁₂₇	C₄×#127	1	1	yes	characteristic
172	C₂×C₁₂₇	C₂×C₄×SD₁₆	1	2	yes	—
173	C₂×C₁₂₇	C₂×#492	1	1	yes	characteristic
174	C₂×C₁₂₇	#3147	1	1	yes	characteristic
175	C₂×C₁₂₇	#3167	1	2	yes	—
176	C₂×#492	C₂×C₁₂₇	1	1	yes	characteristic
177	C₂×C₄×SD₁₆	C₂×C₁₂₇	1	4	yes	complemented
178	C₄×C₄⋊Q₈	C₂×C₁₂₇	1	1	yes	characteristic, complemented
179	C₄×#127	C₂×C₁₂₇	1	1	yes	characteristic
180	#1968	C₂×C₁₂₇	1	4	yes	complemented
181	#1957	C₂×C₁₂₇	1	1	yes	characteristic
182	#1956	C₂×C₁₂₇	1	1	yes	characteristic, complemented
183	#1844	C₂×C₁₂₇	1	1	yes	characteristic, complemented
184	C₄²×C₈	C₂×C₁₂₇	1	1	yes	characteristic, complemented
185	C₁₂₇	C₄×#492	1	1	yes	characteristic, direct product factor, Sylow
186	C₂²×SD₁₆	C₂²×C₁₂₇	1	4	yes	—
187	C₂×C₄⋊Q₈	C₂²×C₁₂₇	1	1	yes	characteristic
188	C₂×#127	C₂²×C₁₂₇	1	1	yes	characteristic
189	C₂×C₄×Q₈	C₂²×C₁₂₇	1	2	yes	—
190	C₂×C₄×D₄	—	2	2	no	—
191	C₂×C₄×D₄	C₂²×C₁₂₇	1	2	yes	—
192	#492	C₄×C₁₂₇	1	8	yes	direct product factor
193	C₄×SD₁₆	—	2	16	no	—
194	C₂×#106	C₂²×C₁₂₇	1	4	yes	—
195	C₂×#103	C₂²×C₁₂₇	1	4	yes	—
196	C₂×#102	C₂²×C₁₂₇	1	4	yes	—
197	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
198	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
199	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
200	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
201	#391	C₂²×C₁₂₇	1	2	yes	—
202	#390	—	2	2	no	—
203	#390	C₂²×C₁₂₇	1	2	yes	—
204	#389	—	2	2	no	—
205	#384	C₂²×C₁₂₇	1	1	yes	characteristic
206	#384	C₂²×C₁₂₇	1	1	yes	characteristic
207	C₄×C₄⋊C₄	—	2	2	no	—
208	C₄³	C₂²×C₁₂₇	1	1	yes	characteristic
209	C₂²×Q₈	C₂³×C₁₂₇	1	2	yes	—
210	C₂²×D₄	—	2	2	no	—
211	C₂²×D₄	C₂³×C₁₂₇	1	2	yes	—
212	C₂³×C₄	—	2	2	no	—
213	C₂×SD₁₆	—	2	8	no	—
214	C₂×SD₁₆	—	2	8	no	—
215	C₂×SD₁₆	C₂×C₄×C₁₂₇	1	16	yes	complemented
216	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
217	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
218	C₄⋊Q₈	—	2	2	no	—
219	C₄⋊Q₈	C₂×C₄×C₁₂₇	1	4	yes	complemented
220	#127	—	2	2	no	—
221	#127	C₂×C₄×C₁₂₇	1	4	yes	—
222	C₄×Q₈	—	2	8	no	—
223	C₄×D₄	—	2	8	no	—
224	C₄×D₄	—	4	8	no	—
225	C₂×C₄⋊C₄	—	2	2	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	2	yes	—
230	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	2	yes	—
231	C₂×C₂²⋊C₄	—	2	4	no	—
232	C₂×C₂²⋊C₄	—	2	2	no	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	D₄×C₁₂₇	1	2	yes	—
235	C₂×C₄²	D₄×C₁₂₇	1	2	yes	—
236	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
239	#106	—	2	8	no	—
240	#103	—	2	8	no	—
241	#102	—	2	8	no	—
242	C₄×C₈	—	2	4	no	—
243	C₄×C₈	—	2	2	no	—
244	C₄×C₈	C₂×C₄×C₁₂₇	1	4	yes	complemented
245	C₄×C₈	D₄×C₁₂₇	1	8	yes	complemented
246	#95	—	2	4	no	—
247	C₂⁴	—	2	2	no	—
248	C₂×Q₈	—	2	2	no	—
249	C₂×Q₈	—	2	4	no	—
250	C₂×Q₈	—	2	4	no	—
251	C₂×Q₈	C₂²×C₄×C₁₂₇	1	4	yes	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	—	2	4	no	—
254	C₂×D₄	—	2	4	no	—
255	C₂×D₄	—	2	2	no	—
256	C₂×D₄	—	4	4	no	—
257	C₂×D₄	—	4	4	no	—
258	C₂×D₄	C₂²×C₄×C₁₂₇	1	4	yes	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	4	4	no	—
263	C₂²×C₄	—	4	8	no	—
264	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
266	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
267	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
268	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
269	SD₁₆	—	2	32	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	C₂²×C₄×C₁₂₇	1	4	yes	—
273	C₂×C₈	C₂×D₄×C₁₂₇	1	4	yes	—
274	C₂×C₈	C₂×D₄×C₁₂₇	1	4	yes	—
275	C₂×C₈	#41×C₁₂₇	1	4	yes	—
276	C₄⋊C₄	—	2	8	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	4	4	no	—
280	C₄⋊C₄	—	4	4	no	—
281	C₄⋊C₄	—	4	4	no	—
282	C₂²⋊C₄	—	4	4	no	—
283	C₂²⋊C₄	—	4	8	no	—
284	C₄²	—	2	4	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	4	4	no	—
287	C₄²	SD₁₆×C₁₂₇	1	8	yes	complemented
288	C₄²	C₂²×C₄×C₁₂₇	1	2	yes	—
289	C₄²	C₂×D₄×C₁₂₇	1	4	yes	—
290	C₄²	#41×C₁₂₇	1	2	yes	—
291	C₂³	—	2	4	no	—
292	C₂³	—	4	2	no	—
293	C₂³	—	4	2	no	—
294	C₂³	—	4	4	no	—
295	C₂³	—	4	4	no	—
296	C₂³	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
297	Q₈	—	2	8	no	—
298	Q₈	—	4	4	no	—
299	D₄	—	2	8	no	—
300	D₄	—	4	4	no	—
301	D₄	—	4	16	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	4	4	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	8	8	no	—
313	C₂×C₄	C₄×D₄×C₁₂₇	1	4	yes	—
314	C₂×C₄	#127×C₁₂₇	1	2	yes	—
315	C₂×C₄	#127×C₁₂₇	1	2	yes	—
316	C₂×C₄	C₂×SD₁₆×C₁₂₇	1	4	yes	—
317	C₂×C₄	C₂×SD₁₆×C₁₂₇	1	4	yes	—
318	C₂×C₄	C₂×SD₁₆×C₁₂₇	1	4	yes	—
319	C₂×C₄	#135×C₁₂₇	1	4	yes	—
320	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
321	C₂×C₄	C₂²×D₄×C₁₂₇	1	2	yes	—
322	C₂×C₄	C₂×#41×C₁₂₇	1	2	yes	—
323	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
324	C₈	—	2	4	no	—
325	C₈	C₄×D₄×C₁₂₇	1	8	yes	complemented
326	C₂²	—	4	8	no	—
327	C₂²	—	4	4	no	—
328	C₂²	—	8	2	no	—
329	C₂²	—	8	2	no	—
330	C₂²	—	8	4	no	—
331	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
332	C₂²	C₂×#127×C₁₂₇	1	1	yes	characteristic
333	C₂²	#532×C₁₂₇	1	1	yes	characteristic
334	C₂²	C₂²×SD₁₆×C₁₂₇	1	2	yes	—
335	C₂²	C₂×#135×C₁₂₇	1	2	yes	—
336	C₄	—	2	2	no	—
337	C₄	—	2	4	no	—
338	C₄	—	4	4	no	—
339	C₄	—	8	2	no	—
340	C₄	—	8	2	no	—
341	C₄	C₄×SD₁₆×C₁₂₇	1	8	yes	complemented
342	C₄	#492×C₁₂₇	1	4	yes	direct product factor
343	C₄	C₂×C₄×D₄×C₁₂₇	1	2	yes	—
344	C₄	#532×C₁₂₇	1	2	yes	—
345	C₂	—	8	4	no	—
346	C₂	C₄×#127×C₁₂₇	1	1	yes	characteristic
347	C₂	C₂×C₄×SD₁₆×C₁₂₇	1	2	yes	—
348	C₂	C₂×#492×C₁₂₇	1	1	yes	characteristic
349	C₂	C₁₂₇×#3147	1	1	yes	characteristic
350	C₂	C₁₂₇×#3167	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₂₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₂₇
socle	C₂³×C₁₂₇	C₂²×D₄
prime radical	C₂×#127×C₁₂₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₂₇ ◁ C₄³×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×SD₁₆×C₁₂₇	C₂	semidirect
3. C₄×C₄⋊Q₈×C₁₂₇	C₂	semidirect
5. C₁₂₇×#1968	C₂	semidirect
7. C₁₂₇×#1956	C₂	semidirect
8. C₁₂₇×#1844	C₂	semidirect
9. C₄²×C₈×C₁₂₇	C₂	semidirect
16. #492×C₁₂₇	C₄	direct (N × H)
39. C₂×SD₁₆×C₁₂₇	C₂×C₄	semidirect
43. C₄⋊Q₈×C₁₂₇	C₂×C₄	semidirect
68. C₄×C₈×C₁₂₇	C₂×C₄	semidirect
69. C₄×C₈×C₁₂₇	D₄	semidirect
111. C₄²×C₁₂₇	SD₁₆	semidirect
149. C₈×C₁₂₇	C₄×D₄	semidirect
165. C₄×C₁₂₇	C₄×SD₁₆	semidirect
166. C₄×C₁₂₇	#492	direct (N × H)
169. C₄×#492	C₁₂₇	direct (N × H)
177. C₂×C₄×SD₁₆	C₂×C₁₂₇	semidirect
178. C₄×C₄⋊Q₈	C₂×C₁₂₇	semidirect
180. #1968	C₂×C₁₂₇	semidirect
182. #1956	C₂×C₁₂₇	semidirect
183. #1844	C₂×C₁₂₇	semidirect
184. C₄²×C₈	C₂×C₁₂₇	semidirect
185. C₁₂₇	C₄×#492	direct (N × H)
192. #492	C₄×C₁₂₇	direct (N × H)
215. C₂×SD₁₆	C₂×C₄×C₁₂₇	semidirect
219. C₄⋊Q₈	C₂×C₄×C₁₂₇	semidirect
244. C₄×C₈	C₂×C₄×C₁₂₇	semidirect
245. C₄×C₈	D₄×C₁₂₇	semidirect
287. C₄²	SD₁₆×C₁₂₇	semidirect
325. C₈	C₄×D₄×C₁₂₇	semidirect
341. C₄	C₄×SD₁₆×C₁₂₇	semidirect
342. C₄	#492×C₁₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#492×C₁₂₇	2
C₂×C₄×SD₁₆×C₁₂₇	2
C₄×C₄⋊Q₈×C₁₂₇	2
C₄×#127×C₁₂₇	2
C₁₂₇×#1968	2
C₁₂₇×#1957	2
C₁₂₇×#1956	2
C₁₂₇×#1844	2
C₄²×C₈×C₁₂₇	2
C₄×#492	127

Subgroups — C4×#492×C127 #44585359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#492×C₁₂₇ #44585359