Subgroups — C₂×C₁₂₇×#1815 #44584349

Order 32512.

1374 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#108×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#106×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#417×C₁₂₇	C₂	1	2	yes	maximal
5	C₁₂₇×#1815	C₂	1	8	yes	maximal, direct product factor
6	C₂×#343×C₁₂₇	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₂₇	C₂²	1	1	yes	characteristic
8	C₂×#131×C₁₂₇	—	2	4	no	—
9	C₂×#131×C₁₂₇	—	2	2	no	—
10	C₂×#131×C₁₂₇	C₄	1	8	yes	complemented
11	C₂×#131×C₁₂₇	C₂²	1	4	yes	—
12	C₂²×M₁₆×C₁₂₇	—	2	1	no	—
13	C₂²×M₁₆×C₁₂₇	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₂₇	—	2	1	no	—
16	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
18	C₂×#108×C₁₂₇	—	2	4	no	—
19	C₂×#108×C₁₂₇	C₂²	1	4	yes	complemented
20	C₂×#106×C₁₂₇	—	2	1	no	—
21	C₂×#106×C₁₂₇	—	2	1	no	—
22	C₂×#106×C₁₂₇	—	2	2	no	—
23	C₂×#106×C₁₂₇	C₂²	1	4	yes	complemented
24	#417×C₁₂₇	—	2	4	no	—
25	#417×C₁₂₇	C₂²	1	8	yes	—
26	C₂×#103×C₁₂₇	—	2	2	no	—
27	C₂×#102×C₁₂₇	—	2	2	no	—
28	#343×C₁₂₇	C₂²	1	8	yes	complemented
29	C₂×#41×C₁₂₇	—	2	2	no	—
30	C₂×#41×C₁₂₇	—	2	1	no	—
31	C₂×#41×C₁₂₇	—	2	1	no	—
32	C₂×#41×C₁₂₇	—	2	2	no	—
33	C₂×#41×C₁₂₇	C₂×C₄	1	4	yes	—
34	C₂×#41×C₁₂₇	D₄	1	2	yes	—
35	C₂×#41×C₁₂₇	Q₈	1	4	yes	—
36	C₂×#41×C₁₂₇	C₂³	1	2	yes	—
37	C₂²×Q₈×C₁₂₇	D₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₂₇	—	2	1	no	—
39	C₂²×D₄×C₁₂₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₂₇	—	2	1	no	—
41	C₂³×C₄×C₁₂₇	—	2	2	no	—
42	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
43	#131×C₁₂₇	—	2	16	no	—
44	#131×C₁₂₇	—	2	8	no	—
45	#131×C₁₂₇	C₂×C₄	1	16	yes	complemented
46	C₂×M₁₆×C₁₂₇	—	2	2	no	—
47	C₂×M₁₆×C₁₂₇	—	2	1	no	—
48	C₂×M₁₆×C₁₂₇	—	2	2	no	—
49	C₂×M₁₆×C₁₂₇	—	2	8	no	—
50	C₂×M₁₆×C₁₂₇	—	2	4	no	—
51	C₂×M₁₆×C₁₂₇	—	2	4	no	—
52	C₂×M₁₆×C₁₂₇	—	2	4	no	—
53	C₂×M₁₆×C₁₂₇	C₂×C₄	1	4	yes	—
54	C₂×M₁₆×C₁₂₇	C₂³	1	4	yes	—
55	C₂×M₁₆×C₁₂₇	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₂₇	—	2	1	no	—
57	C₂²×C₈×C₁₂₇	—	2	8	no	—
58	C₂²×C₈×C₁₂₇	—	2	4	no	—
59	C₂²×C₈×C₁₂₇	—	2	2	no	—
60	C₂²×C₈×C₁₂₇	C₂×C₄	1	4	yes	—
61	C₂²×C₈×C₁₂₇	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₂₇	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₁₂₇	D₄	1	2	yes	—
64	C₂²×C₈×C₁₂₇	D₄	1	4	yes	—
65	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	4	yes	—
72	#108×C₁₂₇	—	2	8	no	—
73	#106×C₁₂₇	—	2	4	no	—
74	#106×C₁₂₇	—	2	4	no	—
75	#103×C₁₂₇	—	2	8	no	—
76	#102×C₁₂₇	—	2	8	no	—
77	C₂⁴×C₁₂₇	—	2	1	no	—
78	C₂⁴×C₁₂₇	#41	1	1	yes	characteristic
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	#41×C₁₂₇	—	2	4	no	—
84	#41×C₁₂₇	—	2	2	no	—
85	#41×C₁₂₇	—	2	2	no	—
86	#41×C₁₂₇	C₄⋊C₄	1	8	yes	—
87	#41×C₁₂₇	C₂²×C₄	1	4	yes	—
88	#41×C₁₂₇	C₂×Q₈	1	4	yes	—
89	C₂×Q₈×C₁₂₇	—	2	1	no	—
90	C₂×Q₈×C₁₂₇	—	2	2	no	—
91	C₂×Q₈×C₁₂₇	C₄⋊C₄	1	4	yes	—
92	C₂×Q₈×C₁₂₇	C₂×D₄	1	2	yes	—
93	C₂×D₄×C₁₂₇	—	2	4	no	—
94	C₂×D₄×C₁₂₇	—	2	2	no	—
95	C₂×D₄×C₁₂₇	—	2	4	no	—
96	C₂×D₄×C₁₂₇	—	2	2	no	—
97	C₂×D₄×C₁₂₇	—	2	2	no	—
98	C₂×D₄×C₁₂₇	—	2	1	no	—
99	C₂×D₄×C₁₂₇	C₄⋊C₄	1	4	yes	—
100	C₂×D₄×C₁₂₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₂₇	—	2	1	no	—
102	C₂²×C₄×C₁₂₇	—	2	4	no	—
103	C₂²×C₄×C₁₂₇	—	2	2	no	—
104	C₂²×C₄×C₁₂₇	—	2	4	no	—
105	C₂²×C₄×C₁₂₇	—	2	2	no	—
106	C₂²×C₄×C₁₂₇	—	2	4	no	—
107	C₂²×C₄×C₁₂₇	—	4	2	no	—
108	C₂²×C₄×C₁₂₇	—	4	2	no	—
109	C₂²×C₄×C₁₂₇	—	8	4	no	—
110	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₂₇	C₂×Q₈	1	2	yes	—
117	C₂²×C₄×C₁₂₇	#41	1	1	yes	characteristic
118	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
119	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
120	M₁₆×C₁₂₇	—	2	4	no	—
121	M₁₆×C₁₂₇	—	2	2	no	—
122	M₁₆×C₁₂₇	—	2	16	no	—
123	M₁₆×C₁₂₇	—	2	4	no	—
124	M₁₆×C₁₂₇	—	2	4	no	—
125	M₁₆×C₁₂₇	—	4	4	no	—
126	M₁₆×C₁₂₇	C₂²×C₄	1	4	yes	—
127	C₂×C₈×C₁₂₇	—	2	4	no	—
128	C₂×C₈×C₁₂₇	—	2	2	no	—
129	C₂×C₈×C₁₂₇	—	2	16	no	—
130	C₂×C₈×C₁₂₇	—	2	4	no	—
131	C₂×C₈×C₁₂₇	—	4	4	no	—
132	C₂×C₈×C₁₂₇	C₂²⋊C₄	1	4	yes	—
133	C₂×C₈×C₁₂₇	C₂²⋊C₄	1	4	yes	—
134	C₂×C₈×C₁₂₇	C₂²⋊C₄	1	8	yes	—
135	C₂×C₈×C₁₂₇	C₂²×C₄	1	4	yes	—
136	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₁₂₇	C₂×D₄	1	4	yes	—
139	C₄⋊C₄×C₁₂₇	—	2	4	no	—
140	C₄⋊C₄×C₁₂₇	—	2	4	no	—
141	C₄⋊C₄×C₁₂₇	—	4	2	no	—
142	C₄⋊C₄×C₁₂₇	—	4	2	no	—
143	C₂³×C₁₂₇	—	2	4	no	—
144	C₂³×C₁₂₇	—	2	2	no	—
145	C₂³×C₁₂₇	—	2	4	no	—
146	C₂³×C₁₂₇	—	4	4	no	—
147	C₂³×C₁₂₇	#117	1	2	yes	—
148	C₂³×C₁₂₇	#121	1	1	yes	characteristic
149	C₂³×C₁₂₇	#121	1	1	yes	characteristic
150	C₂³×C₁₂₇	C₂²⋊Q₈	1	2	yes	—
151	C₂³×C₁₂₇	C₂×#41	1	1	yes	characteristic
152	Q₈×C₁₂₇	—	2	2	no	—
153	Q₈×C₁₂₇	—	2	4	no	—
154	Q₈×C₁₂₇	C₂×C₄⋊C₄	1	4	yes	—
155	D₄×C₁₂₇	—	2	4	no	—
156	D₄×C₁₂₇	—	2	4	no	—
157	D₄×C₁₂₇	—	2	8	no	—
158	D₄×C₁₂₇	—	2	2	no	—
159	D₄×C₁₂₇	—	2	4	no	—
160	D₄×C₁₂₇	C₂×C₄⋊C₄	1	4	yes	—
161	C₂×C₄×C₁₂₇	—	2	2	no	—
162	C₂×C₄×C₁₂₇	—	2	4	no	—
163	C₂×C₄×C₁₂₇	—	2	4	no	—
164	C₂×C₄×C₁₂₇	—	2	4	no	—
165	C₂×C₄×C₁₂₇	—	2	8	no	—
166	C₂×C₄×C₁₂₇	—	4	4	no	—
167	C₂×C₄×C₁₂₇	—	8	4	no	—
168	C₂×C₄×C₁₂₇	—	8	4	no	—
169	C₂×C₄×C₁₂₇	—	8	4	no	—
170	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₂₇	C₂×C₄⋊C₄	1	2	yes	—
173	C₂×C₄×C₁₂₇	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×C₄×C₁₂₇	#117	1	2	yes	—
175	C₂×C₄×C₁₂₇	#121	1	2	yes	—
176	C₂×C₄×C₁₂₇	#121	1	2	yes	—
177	C₂×C₄×C₁₂₇	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₂₇	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	2	yes	—
180	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	2	yes	—
181	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	2	yes	—
182	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₂₇	C₂²×Q₈	1	1	yes	characteristic
187	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
188	C₈×C₁₂₇	—	2	4	no	—
189	C₈×C₁₂₇	—	4	4	no	—
190	C₈×C₁₂₇	C₂×C₂²⋊C₄	1	4	yes	—
191	C₈×C₁₂₇	C₂×C₂²⋊C₄	1	4	yes	—
192	C₂²×C₁₂₇	—	2	4	no	—
193	C₂²×C₁₂₇	—	2	4	no	—
194	C₂²×C₁₂₇	—	2	2	no	—
195	C₂²×C₁₂₇	—	2	2	no	—
196	C₂²×C₁₂₇	—	2	4	no	—
197	C₂²×C₁₂₇	—	4	8	no	—
198	C₂²×C₁₂₇	—	4	4	no	—
199	C₂²×C₁₂₇	#380	1	2	yes	—
200	C₂²×C₁₂₇	#380	1	2	yes	—
201	C₂²×C₁₂₇	#471	1	4	yes	—
202	C₂²×C₁₂₇	C₂×#117	1	1	yes	characteristic
203	C₂²×C₁₂₇	C₂×#121	1	1	yes	characteristic
204	C₂²×C₁₂₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
205	C₄×C₁₂₇	—	2	4	no	—
206	C₄×C₁₂₇	—	8	4	no	—
207	C₄×C₁₂₇	#380	1	2	yes	—
208	C₄×C₁₂₇	#380	1	2	yes	—
209	C₄×C₁₂₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
210	C₄×C₁₂₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
211	C₄×C₁₂₇	C₂×#121	1	1	yes	characteristic
212	C₄×C₁₂₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
213	C₂×#1815	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂×C₁₂₇	—	2	1	no	—
215	C₂×C₁₂₇	—	2	1	no	—
216	C₂×C₁₂₇	—	2	2	no	—
217	C₂×C₁₂₇	—	4	4	no	—
218	C₂×C₁₂₇	#1815	1	4	yes	direct product factor
219	C₂×C₁₂₇	C₂×#380	1	1	yes	characteristic
220	C₂×C₁₂₇	C₂×#471	1	2	yes	—
221	C₂²×#131	C₂×C₁₂₇	1	1	yes	characteristic
222	C₂²×#108	C₂×C₁₂₇	1	1	yes	characteristic, complemented
223	C₂²×#106	C₂×C₁₂₇	1	1	yes	characteristic, complemented
224	C₂×#417	C₂×C₁₂₇	1	2	yes	—
225	#1815	C₂×C₁₂₇	1	8	yes	direct product factor
226	C₂×#343	C₂×C₁₂₇	1	2	yes	complemented
227	C₁₂₇	C₂×#1815	1	1	yes	characteristic, direct product factor, Sylow
228	C₂²×#41	C₂²×C₁₂₇	1	1	yes	characteristic
229	C₂×#131	—	2	4	no	—
230	C₂×#131	—	2	2	no	—
231	C₂×#131	C₄×C₁₂₇	1	8	yes	complemented
232	C₂×#131	C₂²×C₁₂₇	1	4	yes	—
233	C₂²×M₁₆	—	2	1	no	—
234	C₂²×M₁₆	C₂²×C₁₂₇	1	2	yes	—
235	C₂²×M₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
236	C₂³×C₈	—	2	1	no	—
237	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
238	C₂²×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
239	C₂×#108	—	2	4	no	—
240	C₂×#108	C₂²×C₁₂₇	1	4	yes	complemented
241	C₂×#106	—	2	1	no	—
242	C₂×#106	—	2	1	no	—
243	C₂×#106	—	2	2	no	—
244	C₂×#106	C₂²×C₁₂₇	1	4	yes	complemented
245	#417	—	2	4	no	—
246	#417	C₂²×C₁₂₇	1	8	yes	—
247	C₂×#103	—	2	2	no	—
248	C₂×#102	—	2	2	no	—
249	#343	C₂²×C₁₂₇	1	8	yes	complemented
250	C₂×#41	—	2	2	no	—
251	C₂×#41	—	2	1	no	—
252	C₂×#41	—	2	1	no	—
253	C₂×#41	—	2	2	no	—
254	C₂×#41	C₂×C₄×C₁₂₇	1	4	yes	—
255	C₂×#41	D₄×C₁₂₇	1	2	yes	—
256	C₂×#41	Q₈×C₁₂₇	1	4	yes	—
257	C₂×#41	C₂³×C₁₂₇	1	2	yes	—
258	C₂²×Q₈	D₄×C₁₂₇	1	1	yes	characteristic
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	D₄×C₁₂₇	1	1	yes	characteristic
261	C₂³×C₄	—	2	1	no	—
262	C₂³×C₄	—	2	2	no	—
263	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
264	#131	—	2	16	no	—
265	#131	—	2	8	no	—
266	#131	C₂×C₄×C₁₂₇	1	16	yes	complemented
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	2	8	no	—
271	C₂×M₁₆	—	2	4	no	—
272	C₂×M₁₆	—	2	4	no	—
273	C₂×M₁₆	—	2	4	no	—
274	C₂×M₁₆	C₂×C₄×C₁₂₇	1	4	yes	—
275	C₂×M₁₆	C₂³×C₁₂₇	1	4	yes	—
276	C₂×M₁₆	C₂³×C₁₂₇	1	2	yes	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	8	no	—
279	C₂²×C₈	—	2	4	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	C₂×C₄×C₁₂₇	1	4	yes	—
282	C₂²×C₈	D₄×C₁₂₇	1	1	yes	characteristic
283	C₂²×C₈	D₄×C₁₂₇	1	1	yes	characteristic
284	C₂²×C₈	D₄×C₁₂₇	1	2	yes	—
285	C₂²×C₈	D₄×C₁₂₇	1	4	yes	—
286	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	4	yes	—
293	#108	—	2	8	no	—
294	#106	—	2	4	no	—
295	#106	—	2	4	no	—
296	#103	—	2	8	no	—
297	#102	—	2	8	no	—
298	C₂⁴	—	2	1	no	—
299	C₂⁴	#41×C₁₂₇	1	1	yes	characteristic
300	#41	—	2	4	no	—
301	#41	—	2	4	no	—
302	#41	—	2	4	no	—
303	#41	—	2	4	no	—
304	#41	—	2	4	no	—
305	#41	—	2	2	no	—
306	#41	—	2	2	no	—
307	#41	C₄⋊C₄×C₁₂₇	1	8	yes	—
308	#41	C₂²×C₄×C₁₂₇	1	4	yes	—
309	#41	C₂×Q₈×C₁₂₇	1	4	yes	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	C₄⋊C₄×C₁₂₇	1	4	yes	—
313	C₂×Q₈	C₂×D₄×C₁₂₇	1	2	yes	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	C₄⋊C₄×C₁₂₇	1	4	yes	—
321	C₂×D₄	C₂×D₄×C₁₂₇	1	2	yes	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	8	4	no	—
331	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
337	C₂²×C₄	C₂×Q₈×C₁₂₇	1	2	yes	—
338	C₂²×C₄	#41×C₁₂₇	1	1	yes	characteristic
339	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
340	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
341	M₁₆	—	2	4	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	2	16	no	—
344	M₁₆	—	2	4	no	—
345	M₁₆	—	2	4	no	—
346	M₁₆	—	4	4	no	—
347	M₁₆	C₂²×C₄×C₁₂₇	1	4	yes	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	16	no	—
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	4	4	no	—
353	C₂×C₈	C₂²⋊C₄×C₁₂₇	1	4	yes	—
354	C₂×C₈	C₂²⋊C₄×C₁₂₇	1	4	yes	—
355	C₂×C₈	C₂²⋊C₄×C₁₂₇	1	8	yes	—
356	C₂×C₈	C₂²×C₄×C₁₂₇	1	4	yes	—
357	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
358	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
359	C₂×C₈	C₂×D₄×C₁₂₇	1	4	yes	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	4	no	—
367	C₂³	—	4	4	no	—
368	C₂³	#117×C₁₂₇	1	2	yes	—
369	C₂³	#121×C₁₂₇	1	1	yes	characteristic
370	C₂³	#121×C₁₂₇	1	1	yes	characteristic
371	C₂³	C₂²⋊Q₈×C₁₂₇	1	2	yes	—
372	C₂³	C₂×#41×C₁₂₇	1	1	yes	characteristic
373	Q₈	—	2	2	no	—
374	Q₈	—	2	4	no	—
375	Q₈	C₂×C₄⋊C₄×C₁₂₇	1	4	yes	—
376	D₄	—	2	4	no	—
377	D₄	—	2	4	no	—
378	D₄	—	2	8	no	—
379	D₄	—	2	2	no	—
380	D₄	—	2	4	no	—
381	D₄	C₂×C₄⋊C₄×C₁₂₇	1	4	yes	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	8	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	8	4	no	—
389	C₂×C₄	—	8	4	no	—
390	C₂×C₄	—	8	4	no	—
391	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
392	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
393	C₂×C₄	C₂×C₄⋊C₄×C₁₂₇	1	2	yes	—
394	C₂×C₄	C₂×C₄⋊C₄×C₁₂₇	1	2	yes	—
395	C₂×C₄	#117×C₁₂₇	1	2	yes	—
396	C₂×C₄	#121×C₁₂₇	1	2	yes	—
397	C₂×C₄	#121×C₁₂₇	1	2	yes	—
398	C₂×C₄	#121×C₁₂₇	1	1	yes	characteristic
399	C₂×C₄	#121×C₁₂₇	1	1	yes	characteristic
400	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	2	yes	—
401	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	2	yes	—
402	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	2	yes	—
403	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
404	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
405	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
407	C₂×C₄	C₂²×Q₈×C₁₂₇	1	1	yes	characteristic
408	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
409	C₈	—	2	4	no	—
410	C₈	—	4	4	no	—
411	C₈	C₂×C₂²⋊C₄×C₁₂₇	1	4	yes	—
412	C₈	C₂×C₂²⋊C₄×C₁₂₇	1	4	yes	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	4	8	no	—
419	C₂²	—	4	4	no	—
420	C₂²	#380×C₁₂₇	1	2	yes	—
421	C₂²	#380×C₁₂₇	1	2	yes	—
422	C₂²	#471×C₁₂₇	1	4	yes	—
423	C₂²	C₂×#117×C₁₂₇	1	1	yes	characteristic
424	C₂²	C₂×#121×C₁₂₇	1	1	yes	characteristic
425	C₂²	C₂×C₂²⋊Q₈×C₁₂₇	1	1	yes	characteristic
426	C₄	—	2	4	no	—
427	C₄	—	8	4	no	—
428	C₄	#380×C₁₂₇	1	2	yes	—
429	C₄	#380×C₁₂₇	1	2	yes	—
430	C₄	C₂²×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
431	C₄	C₂²×C₄⋊C₄×C₁₂₇	1	1	yes	characteristic
432	C₄	C₂×#121×C₁₂₇	1	1	yes	characteristic
433	C₄	C₂×C₂²⋊Q₈×C₁₂₇	1	1	yes	characteristic
434	C₂	—	2	1	no	—
435	C₂	—	2	1	no	—
436	C₂	—	2	2	no	—
437	C₂	—	4	4	no	—
438	C₂	C₁₂₇×#1815	1	4	yes	direct product factor
439	C₂	C₂×#380×C₁₂₇	1	1	yes	characteristic
440	C₂	C₂×#471×C₁₂₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₂₇	#121
commutator	C₂×C₄	C₂³×C₄×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₂₇
prime radical	C₂²×#41×C₁₂₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₂₇ ◁ C₂³×C₄×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#108×C₁₂₇	C₂	semidirect
3. C₂²×#106×C₁₂₇	C₂	semidirect
5. C₁₂₇×#1815	C₂	direct (N × H)
6. C₂×#343×C₁₂₇	C₂	semidirect
10. C₂×#131×C₁₂₇	C₄	semidirect
19. C₂×#108×C₁₂₇	C₂²	semidirect
23. C₂×#106×C₁₂₇	C₂²	semidirect
28. #343×C₁₂₇	C₂²	semidirect
45. #131×C₁₂₇	C₂×C₄	semidirect
213. C₂×#1815	C₁₂₇	direct (N × H)
218. C₂×C₁₂₇	#1815	direct (N × H)
222. C₂²×#108	C₂×C₁₂₇	semidirect
223. C₂²×#106	C₂×C₁₂₇	semidirect
225. #1815	C₂×C₁₂₇	direct (N × H)
226. C₂×#343	C₂×C₁₂₇	semidirect
227. C₁₂₇	C₂×#1815	direct (N × H)
231. C₂×#131	C₄×C₁₂₇	semidirect
240. C₂×#108	C₂²×C₁₂₇	semidirect
244. C₂×#106	C₂²×C₁₂₇	semidirect
249. #343	C₂²×C₁₂₇	semidirect
266. #131	C₂×C₄×C₁₂₇	semidirect
438. C₂	C₁₂₇×#1815	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#131×C₁₂₇	2
C₂²×#108×C₁₂₇	2
C₂²×#106×C₁₂₇	2
C₂×#417×C₁₂₇	2
C₁₂₇×#1815	2
C₂×#343×C₁₂₇	2
C₂×#1815	127

Subgroups — C2×C127×#1815 #44584349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₂₇×#1815 #44584349