Subgroups — C₄×#440×C₁₂₇ #44584174

Order 32512.

1206 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#440×C₁₂₇	C₂	1	2	yes	maximal
2	C₂×C₄×SD₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₄²×Q₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×D₄×C₁₂₇	C₂	1	1	yes	maximal, characteristic
5	C₁₂₇×#1776	C₂	1	2	yes	maximal, complemented
6	C₄×#107×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₂₇×#1763	C₂	1	2	yes	maximal, complemented
8	C₁₂₇×#1762	C₂	1	2	yes	maximal
9	C₄×#103×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#102×C₁₂₇	C₂	1	1	yes	maximal, characteristic
11	C₄×#97×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₂₇	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₂₇	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₂₇	—	2	1	no	—
18	#440×C₁₂₇	C₄	1	16	yes	direct product factor
19	C₄×SD₁₆×C₁₂₇	C₄	1	8	yes	complemented
20	C₂×#107×C₁₂₇	C₂²	1	2	yes	—
21	C₂×#106×C₁₂₇	C₂²	1	1	yes	characteristic
22	C₂×#103×C₁₂₇	C₂²	1	1	yes	characteristic
23	C₂×#103×C₁₂₇	C₂²	1	2	yes	—
24	C₂×#102×C₁₂₇	C₂²	1	1	yes	characteristic
25	C₂×#102×C₁₂₇	C₂²	1	2	yes	—
26	C₂×#97×C₁₂₇	C₂²	1	2	yes	—
27	C₂×#97×C₁₂₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₁₂₇	—	2	2	no	—
31	C₄×C₄⋊C₄×C₁₂₇	—	2	1	no	—
32	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
36	C₄×C₂²⋊C₄×C₁₂₇	—	2	2	no	—
37	C₄×C₂²⋊C₄×C₁₂₇	—	2	1	no	—
38	C₄³×C₁₂₇	—	2	1	no	—
39	C₄³×C₁₂₇	C₂²	1	1	yes	characteristic
40	#340×C₁₂₇	C₂²	1	2	yes	—
41	#340×C₁₂₇	C₂²	1	2	yes	—
42	#340×C₁₂₇	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₂₇	—	2	2	no	—
46	C₂³×C₄×C₁₂₇	—	2	1	no	—
47	C₂×SD₁₆×C₁₂₇	C₂×C₄	1	4	yes	—
48	C₂×SD₁₆×C₁₂₇	C₂×C₄	1	8	yes	—
49	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
52	C₄×Q₈×C₁₂₇	—	2	2	no	—
53	C₄×Q₈×C₁₂₇	—	2	4	no	—
54	C₄×Q₈×C₁₂₇	C₂×C₄	1	4	yes	complemented
55	C₄×Q₈×C₁₂₇	C₂×C₄	1	8	yes	complemented
56	C₄×D₄×C₁₂₇	—	2	2	no	—
57	C₄×D₄×C₁₂₇	—	2	4	no	—
58	C₄×D₄×C₁₂₇	C₂×C₄	1	4	yes	—
59	C₄×D₄×C₁₂₇	C₂×C₄	1	8	yes	—
60	C₂×C₄⋊C₄×C₁₂₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₂₇	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₂₇	—	2	2	no	—
68	C₂×C₄²×C₁₂₇	—	2	2	no	—
69	C₂×C₄²×C₁₂₇	—	2	1	no	—
70	C₂×C₄²×C₁₂₇	—	2	2	no	—
71	C₂×C₄²×C₁₂₇	—	2	2	no	—
72	C₂×C₄²×C₁₂₇	—	2	1	no	—
73	C₂×C₄²×C₁₂₇	—	2	1	no	—
74	C₂×C₄²×C₁₂₇	—	4	4	no	—
75	C₂×C₄²×C₁₂₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₂₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₂₇	D₄	1	2	yes	—
78	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
79	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
80	#107×C₁₂₇	C₂×C₄	1	8	yes	complemented
81	#106×C₁₂₇	C₂×C₄	1	4	yes	complemented
82	#103×C₁₂₇	C₂×C₄	1	4	yes	complemented
83	#103×C₁₂₇	C₂×C₄	1	8	yes	complemented
84	#102×C₁₂₇	C₂×C₄	1	4	yes	—
85	#102×C₁₂₇	C₂×C₄	1	8	yes	—
86	#97×C₁₂₇	—	2	4	no	—
87	#97×C₁₂₇	C₂×C₄	1	8	yes	complemented
88	C₄×C₈×C₁₂₇	—	2	2	no	—
89	C₄×C₈×C₁₂₇	C₂×C₄	1	4	yes	complemented
90	#95×C₁₂₇	—	2	1	no	—
91	#95×C₁₂₇	—	2	2	no	—
92	#95×C₁₂₇	—	2	1	no	—
93	#95×C₁₂₇	—	2	2	no	—
94	C₂⁴×C₁₂₇	—	2	1	no	—
95	C₂×Q₈×C₁₂₇	—	2	1	no	—
96	C₂×Q₈×C₁₂₇	—	2	2	no	—
97	C₂×Q₈×C₁₂₇	C₂²×C₄	1	2	yes	—
98	C₂×Q₈×C₁₂₇	C₂²×C₄	1	4	yes	—
99	C₂×D₄×C₁₂₇	—	2	1	no	—
100	C₂×D₄×C₁₂₇	—	2	2	no	—
101	C₂×D₄×C₁₂₇	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₁₂₇	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₁₂₇	—	2	1	no	—
104	C₂²×C₄×C₁₂₇	—	2	2	no	—
105	C₂²×C₄×C₁₂₇	—	2	1	no	—
106	C₂²×C₄×C₁₂₇	—	2	1	no	—
107	C₂²×C₄×C₁₂₇	—	2	2	no	—
108	C₂²×C₄×C₁₂₇	—	2	8	no	—
109	C₂²×C₄×C₁₂₇	—	2	4	no	—
110	C₂²×C₄×C₁₂₇	—	4	4	no	—
111	C₂²×C₄×C₁₂₇	—	4	4	no	—
112	C₂²×C₄×C₁₂₇	—	4	2	no	—
113	C₂²×C₄×C₁₂₇	—	4	2	no	—
114	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
119	SD₁₆×C₁₂₇	C₄²	1	16	yes	complemented
120	C₂×C₈×C₁₂₇	—	2	2	no	—
121	C₂×C₈×C₁₂₇	—	2	2	no	—
122	C₂×C₈×C₁₂₇	—	2	2	no	—
123	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₁₂₇	C₂²×C₄	1	4	yes	—
125	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₁₂₇	C₂²×C₄	1	4	yes	—
127	C₄⋊C₄×C₁₂₇	—	2	4	no	—
128	C₄⋊C₄×C₁₂₇	—	2	8	no	—
129	C₄⋊C₄×C₁₂₇	—	2	1	no	—
130	C₄⋊C₄×C₁₂₇	—	2	2	no	—
131	C₄⋊C₄×C₁₂₇	—	2	1	no	—
132	C₄⋊C₄×C₁₂₇	—	2	2	no	—
133	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
134	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
135	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
136	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
137	C₂²⋊C₄×C₁₂₇	—	2	8	no	—
138	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
139	C₄²×C₁₂₇	—	2	8	no	—
140	C₄²×C₁₂₇	—	2	4	no	—
141	C₄²×C₁₂₇	—	2	2	no	—
142	C₄²×C₁₂₇	—	2	2	no	—
143	C₄²×C₁₂₇	—	4	2	no	—
144	C₄²×C₁₂₇	—	4	4	no	—
145	C₄²×C₁₂₇	—	4	4	no	—
146	C₄²×C₁₂₇	—	4	2	no	—
147	C₄²×C₁₂₇	—	4	2	no	—
148	C₄²×C₁₂₇	C₂²×C₄	1	2	yes	—
149	C₄²×C₁₂₇	C₂²×C₄	1	4	yes	—
150	C₄²×C₁₂₇	#41	1	2	yes	—
151	C₄²×C₁₂₇	#41	1	4	yes	—
152	C₂³×C₁₂₇	—	2	2	no	—
153	C₂³×C₁₂₇	—	2	4	no	—
154	C₂³×C₁₂₇	—	4	1	no	—
155	C₂³×C₁₂₇	—	4	1	no	—
156	C₂³×C₁₂₇	—	4	2	no	—
157	C₂³×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₁₂₇	—	2	2	no	—
159	Q₈×C₁₂₇	—	2	4	no	—
160	Q₈×C₁₂₇	C₂×C₄²	1	4	yes	complemented
161	D₄×C₁₂₇	—	2	2	no	—
162	D₄×C₁₂₇	—	2	4	no	—
163	D₄×C₁₂₇	C₂×C₄²	1	4	yes	—
164	C₂×C₄×C₁₂₇	—	2	2	no	—
165	C₂×C₄×C₁₂₇	—	2	4	no	—
166	C₂×C₄×C₁₂₇	—	2	2	no	—
167	C₂×C₄×C₁₂₇	—	2	2	no	—
168	C₂×C₄×C₁₂₇	—	2	2	no	—
169	C₂×C₄×C₁₂₇	—	2	2	no	—
170	C₂×C₄×C₁₂₇	—	2	2	no	—
171	C₂×C₄×C₁₂₇	—	2	2	no	—
172	C₂×C₄×C₁₂₇	—	2	4	no	—
173	C₂×C₄×C₁₂₇	—	2	2	no	—
174	C₂×C₄×C₁₂₇	—	2	4	no	—
175	C₂×C₄×C₁₂₇	—	4	16	no	—
176	C₂×C₄×C₁₂₇	—	4	1	no	—
177	C₂×C₄×C₁₂₇	—	4	2	no	—
178	C₂×C₄×C₁₂₇	—	4	2	no	—
179	C₂×C₄×C₁₂₇	—	4	1	no	—
180	C₂×C₄×C₁₂₇	—	4	2	no	—
181	C₂×C₄×C₁₂₇	—	4	2	no	—
182	C₂×C₄×C₁₂₇	—	4	2	no	—
183	C₂×C₄×C₁₂₇	—	4	8	no	—
184	C₂×C₄×C₁₂₇	C₄×D₄	1	4	yes	—
185	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₁₂₇	C₄×D₄	1	4	yes	—
187	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₁₂₇	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×C₄×C₁₂₇	#137	1	2	yes	—
190	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₂₇	C₂³×C₄	1	2	yes	—
192	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₁₂₇	C₂×#41	1	2	yes	—
194	C₈×C₁₂₇	—	2	4	no	—
195	C₈×C₁₂₇	—	2	2	no	—
196	C₈×C₁₂₇	C₂×C₄²	1	4	yes	complemented
197	C₂²×C₁₂₇	—	2	4	no	—
198	C₂²×C₁₂₇	—	4	2	no	—
199	C₂²×C₁₂₇	—	4	2	no	—
200	C₂²×C₁₂₇	—	4	4	no	—
201	C₂²×C₁₂₇	—	4	4	no	—
202	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂²×C₁₂₇	C₂×C₄×D₄	1	2	yes	—
204	C₂²×C₁₂₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
205	C₂²×C₁₂₇	C₂×#137	1	1	yes	characteristic
206	C₂²×C₁₂₇	#575	1	2	yes	—
207	C₄×C₁₂₇	—	2	2	no	—
208	C₄×C₁₂₇	—	2	4	no	—
209	C₄×C₁₂₇	—	2	4	no	—
210	C₄×C₁₂₇	—	2	4	no	—
211	C₄×C₁₂₇	—	4	2	no	—
212	C₄×C₁₂₇	—	4	2	no	—
213	C₄×C₁₂₇	—	4	4	no	—
214	C₄×C₁₂₇	—	4	4	no	—
215	C₄×C₁₂₇	#440	1	4	yes	direct product factor
216	C₄×C₁₂₇	C₂²×C₄²	1	1	yes	characteristic
217	C₄×C₁₂₇	C₄×#41	1	2	yes	—
218	C₄×C₁₂₇	C₄×#41	1	1	yes	characteristic
219	C₄×#440	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂×C₁₂₇	—	4	4	no	—
221	C₂×C₁₂₇	C₄²×D₄	1	1	yes	characteristic
222	C₂×C₁₂₇	C₂×#440	1	1	yes	characteristic
223	C₂×C₁₂₇	#2943	1	1	yes	characteristic
224	C₂×C₁₂₇	C₄×AGL(1,ℤ/8)	1	2	yes	—
225	C₂×C₁₂₇	C₄×#137	1	2	yes	—
226	C₂×#440	C₂×C₁₂₇	1	2	yes	—
227	C₂×C₄×SD₁₆	C₂×C₁₂₇	1	1	yes	characteristic
228	C₄²×Q₈	C₂×C₁₂₇	1	1	yes	characteristic, complemented
229	C₄²×D₄	C₂×C₁₂₇	1	1	yes	characteristic
230	#1776	C₂×C₁₂₇	1	2	yes	complemented
231	C₄×#107	C₂×C₁₂₇	1	1	yes	characteristic, complemented
232	#1763	C₂×C₁₂₇	1	2	yes	complemented
233	#1762	C₂×C₁₂₇	1	2	yes	—
234	C₄×#103	C₂×C₁₂₇	1	1	yes	characteristic, complemented
235	C₄×#102	C₂×C₁₂₇	1	1	yes	characteristic
236	C₄×#97	C₂×C₁₂₇	1	1	yes	characteristic, complemented
237	C₁₂₇	C₄×#440	1	1	yes	characteristic, direct product factor, Sylow
238	C₂²×SD₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
239	C₂×C₄×Q₈	C₂²×C₁₂₇	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂²×C₁₂₇	1	2	yes	—
241	C₂×C₄×D₄	C₂²×C₁₂₇	1	1	yes	characteristic
242	C₂×C₄×D₄	C₂²×C₁₂₇	1	2	yes	—
243	C₂²×C₄²	—	2	1	no	—
244	#440	C₄×C₁₂₇	1	16	yes	direct product factor
245	C₄×SD₁₆	C₄×C₁₂₇	1	8	yes	complemented
246	C₂×#107	C₂²×C₁₂₇	1	2	yes	—
247	C₂×#106	C₂²×C₁₂₇	1	1	yes	characteristic
248	C₂×#103	C₂²×C₁₂₇	1	1	yes	characteristic
249	C₂×#103	C₂²×C₁₂₇	1	2	yes	—
250	C₂×#102	C₂²×C₁₂₇	1	1	yes	characteristic
251	C₂×#102	C₂²×C₁₂₇	1	2	yes	—
252	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
253	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
254	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
255	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
256	C₄×C₄⋊C₄	—	2	1	no	—
257	C₄×C₄⋊C₄	—	2	2	no	—
258	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	1	yes	characteristic
259	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
260	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	1	yes	characteristic
261	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
262	C₄×C₂²⋊C₄	—	2	1	no	—
263	C₄×C₂²⋊C₄	—	2	2	no	—
264	C₄³	—	2	1	no	—
265	C₄³	C₂²×C₁₂₇	1	1	yes	characteristic
266	#340	C₂²×C₁₂₇	1	2	yes	—
267	#340	C₂²×C₁₂₇	1	2	yes	—
268	#340	C₂²×C₁₂₇	1	2	yes	—
269	C₂²×Q₈	C₂³×C₁₂₇	1	1	yes	characteristic
270	C₂²×D₄	C₂³×C₁₂₇	1	1	yes	characteristic
271	C₂³×C₄	—	2	2	no	—
272	C₂³×C₄	—	2	1	no	—
273	C₂×SD₁₆	C₂×C₄×C₁₂₇	1	4	yes	—
274	C₂×SD₁₆	C₂×C₄×C₁₂₇	1	8	yes	—
275	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
276	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	4	no	—
280	C₄×Q₈	C₂×C₄×C₁₂₇	1	4	yes	complemented
281	C₄×Q₈	C₂×C₄×C₁₂₇	1	8	yes	complemented
282	C₄×D₄	—	2	2	no	—
283	C₄×D₄	—	2	4	no	—
284	C₄×D₄	C₂×C₄×C₁₂₇	1	4	yes	—
285	C₄×D₄	C₂×C₄×C₁₂₇	1	8	yes	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	2	yes	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	4	4	no	—
301	C₂×C₄²	D₄×C₁₂₇	1	1	yes	characteristic
302	C₂×C₄²	D₄×C₁₂₇	1	1	yes	characteristic
303	C₂×C₄²	D₄×C₁₂₇	1	2	yes	—
304	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
306	#107	C₂×C₄×C₁₂₇	1	8	yes	complemented
307	#106	C₂×C₄×C₁₂₇	1	4	yes	complemented
308	#103	C₂×C₄×C₁₂₇	1	4	yes	complemented
309	#103	C₂×C₄×C₁₂₇	1	8	yes	complemented
310	#102	C₂×C₄×C₁₂₇	1	4	yes	—
311	#102	C₂×C₄×C₁₂₇	1	8	yes	—
312	#97	—	2	4	no	—
313	#97	C₂×C₄×C₁₂₇	1	8	yes	complemented
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	C₂×C₄×C₁₂₇	1	4	yes	complemented
316	#95	—	2	1	no	—
317	#95	—	2	2	no	—
318	#95	—	2	1	no	—
319	#95	—	2	2	no	—
320	C₂⁴	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	C₂²×C₄×C₁₂₇	1	2	yes	—
324	C₂×Q₈	C₂²×C₄×C₁₂₇	1	4	yes	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	C₂²×C₄×C₁₂₇	1	2	yes	—
328	C₂×D₄	C₂²×C₄×C₁₂₇	1	4	yes	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
345	SD₁₆	C₄²×C₁₂₇	1	16	yes	complemented
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
350	C₂×C₈	C₂²×C₄×C₁₂₇	1	4	yes	—
351	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
352	C₂×C₈	C₂²×C₄×C₁₂₇	1	4	yes	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	8	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
360	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
361	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
362	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₄²	—	2	8	no	—
366	C₄²	—	2	4	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	4	2	no	—
370	C₄²	—	4	4	no	—
371	C₄²	—	4	4	no	—
372	C₄²	—	4	2	no	—
373	C₄²	—	4	2	no	—
374	C₄²	C₂²×C₄×C₁₂₇	1	2	yes	—
375	C₄²	C₂²×C₄×C₁₂₇	1	4	yes	—
376	C₄²	#41×C₁₂₇	1	2	yes	—
377	C₄²	#41×C₁₂₇	1	4	yes	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	2	no	—
383	C₂³	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
384	Q₈	—	2	2	no	—
385	Q₈	—	2	4	no	—
386	Q₈	C₂×C₄²×C₁₂₇	1	4	yes	complemented
387	D₄	—	2	2	no	—
388	D₄	—	2	4	no	—
389	D₄	C₂×C₄²×C₁₂₇	1	4	yes	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	4	16	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	8	no	—
410	C₂×C₄	C₄×D₄×C₁₂₇	1	4	yes	—
411	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
412	C₂×C₄	C₄×D₄×C₁₂₇	1	4	yes	—
413	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
414	C₂×C₄	AGL(1,ℤ/8)×C₁₂₇	1	2	yes	—
415	C₂×C₄	#137×C₁₂₇	1	2	yes	—
416	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
417	C₂×C₄	C₂³×C₄×C₁₂₇	1	2	yes	—
418	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₁₂₇	1	2	yes	—
420	C₈	—	2	4	no	—
421	C₈	—	2	2	no	—
422	C₈	C₂×C₄²×C₁₂₇	1	4	yes	complemented
423	C₂²	—	2	4	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
429	C₂²	C₂×C₄×D₄×C₁₂₇	1	2	yes	—
430	C₂²	C₂×AGL(1,ℤ/8)×C₁₂₇	1	1	yes	characteristic
431	C₂²	C₂×#137×C₁₂₇	1	1	yes	characteristic
432	C₂²	#575×C₁₂₇	1	2	yes	—
433	C₄	—	2	2	no	—
434	C₄	—	2	4	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	4	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	4	no	—
441	C₄	#440×C₁₂₇	1	4	yes	direct product factor
442	C₄	C₂²×C₄²×C₁₂₇	1	1	yes	characteristic
443	C₄	C₄×#41×C₁₂₇	1	2	yes	—
444	C₄	C₄×#41×C₁₂₇	1	1	yes	characteristic
445	C₂	—	4	4	no	—
446	C₂	C₄²×D₄×C₁₂₇	1	1	yes	characteristic
447	C₂	C₂×#440×C₁₂₇	1	1	yes	characteristic
448	C₂	C₁₂₇×#2943	1	1	yes	characteristic
449	C₂	C₄×AGL(1,ℤ/8)×C₁₂₇	1	2	yes	—
450	C₂	C₄×#137×C₁₂₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₂₇	C₂×D₄
commutator	C₄	C₂²×C₄²×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₂₇
socle	C₂³×C₁₂₇	C₂²×D₄
prime radical	C₂²×D₄×C₁₂₇	C₂³
LCS	G ▷ 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
3. C₄²×Q₈×C₁₂₇	C₂	semidirect
5. C₁₂₇×#1776	C₂	semidirect
6. C₄×#107×C₁₂₇	C₂	semidirect
7. C₁₂₇×#1763	C₂	semidirect
9. C₄×#103×C₁₂₇	C₂	semidirect
11. C₄×#97×C₁₂₇	C₂	semidirect
18. #440×C₁₂₇	C₄	direct (N × H)
19. C₄×SD₁₆×C₁₂₇	C₄	semidirect
54. C₄×Q₈×C₁₂₇	C₂×C₄	semidirect
55. C₄×Q₈×C₁₂₇	C₂×C₄	semidirect
80. #107×C₁₂₇	C₂×C₄	semidirect
81. #106×C₁₂₇	C₂×C₄	semidirect
82. #103×C₁₂₇	C₂×C₄	semidirect
83. #103×C₁₂₇	C₂×C₄	semidirect
87. #97×C₁₂₇	C₂×C₄	semidirect
89. C₄×C₈×C₁₂₇	C₂×C₄	semidirect
119. SD₁₆×C₁₂₇	C₄²	semidirect
160. Q₈×C₁₂₇	C₂×C₄²	semidirect
196. C₈×C₁₂₇	C₂×C₄²	semidirect
215. C₄×C₁₂₇	#440	direct (N × H)
219. C₄×#440	C₁₂₇	direct (N × H)
228. C₄²×Q₈	C₂×C₁₂₇	semidirect
230. #1776	C₂×C₁₂₇	semidirect
231. C₄×#107	C₂×C₁₂₇	semidirect
232. #1763	C₂×C₁₂₇	semidirect
234. C₄×#103	C₂×C₁₂₇	semidirect
236. C₄×#97	C₂×C₁₂₇	semidirect
237. C₁₂₇	C₄×#440	direct (N × H)
244. #440	C₄×C₁₂₇	direct (N × H)
245. C₄×SD₁₆	C₄×C₁₂₇	semidirect
280. C₄×Q₈	C₂×C₄×C₁₂₇	semidirect
281. C₄×Q₈	C₂×C₄×C₁₂₇	semidirect
306. #107	C₂×C₄×C₁₂₇	semidirect
307. #106	C₂×C₄×C₁₂₇	semidirect
308. #103	C₂×C₄×C₁₂₇	semidirect
309. #103	C₂×C₄×C₁₂₇	semidirect
313. #97	C₂×C₄×C₁₂₇	semidirect
315. C₄×C₈	C₂×C₄×C₁₂₇	semidirect
345. SD₁₆	C₄²×C₁₂₇	semidirect
386. Q₈	C₂×C₄²×C₁₂₇	semidirect
422. C₈	C₂×C₄²×C₁₂₇	semidirect
441. C₄	#440×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×#440×C₁₂₇	2
C₂×C₄×SD₁₆×C₁₂₇	2
C₄²×Q₈×C₁₂₇	2
C₄²×D₄×C₁₂₇	2
C₁₂₇×#1776	2
C₄×#107×C₁₂₇	2
C₁₂₇×#1763	2
C₁₂₇×#1762	2
C₄×#103×C₁₂₇	2
C₄×#102×C₁₂₇	2
C₄×#97×C₁₂₇	2
C₄×#440	127

Subgroups — C4×#440×C127 #44584174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#440×C₁₂₇ #44584174