Subgroups — C₁₂₇×#19625 #44583298

Order 32512.

836 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₂₇×#3230	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₂₇×#3205	C₂	1	1	yes	maximal, characteristic
3	C₁₂₇×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#492×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₂₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₂₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₂₇×#1719	C₂	1	2	yes	maximal, complemented
8	C₁₂₇×#1717	C₂	1	2	yes	maximal, complemented
9	C₁₂₇×#1708	C₂	1	2	yes	maximal, complemented
10	C₁₂₇×#1706	C₂	1	2	yes	maximal, complemented
11	C₈×M₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₂₇	—	2	2	no	—
13	#533×C₁₂₇	C₂²	1	1	yes	characteristic
14	#532×C₁₂₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic
16	C₂×#127×C₁₂₇	C₂²	1	1	yes	characteristic
17	#500×C₁₂₇	C₂²	1	2	yes	complemented
18	#498×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
19	#493×C₁₂₇	C₂²	1	2	yes	—
20	#492×C₁₂₇	—	2	2	no	—
21	#492×C₁₂₇	C₂²	1	2	yes	—
22	#492×C₁₂₇	C₂²	1	2	yes	—
23	#492×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
24	#490×C₁₂₇	—	2	2	no	—
25	#489×C₁₂₇	—	2	2	no	—
26	#487×C₁₂₇	C₂²	1	2	yes	complemented
27	#487×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
28	#487×C₁₂₇	C₂²	1	2	yes	complemented
29	#486×C₁₂₇	C₂²	1	2	yes	—
30	#486×C₁₂₇	C₂²	1	2	yes	—
31	#486×C₁₂₇	C₂²	1	2	yes	—
32	#486×C₁₂₇	C₂²	1	2	yes	complemented
33	#486×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
34	#484×C₁₂₇	—	2	2	no	—
35	#477×C₁₂₇	—	2	2	no	—
36	#465×C₁₂₇	—	2	2	no	—
37	#459×C₁₂₇	—	2	2	no	—
38	#447×C₁₂₇	—	2	2	no	—
39	C₄×SD₁₆×C₁₂₇	—	2	2	no	—
40	#431×C₁₂₇	C₂²	1	1	yes	characteristic
41	#418×C₁₂₇	—	2	2	no	—
42	#417×C₁₂₇	—	2	2	no	—
43	C₄×M₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
45	#322×C₁₂₇	C₂²	1	2	yes	complemented
46	C₈²×C₁₂₇	C₂²	1	2	yes	complemented
47	C₂×#41×C₁₂₇	—	2	1	no	—
48	C₂²×Q₈×C₁₂₇	—	2	1	no	—
49	C₂²×D₄×C₁₂₇	—	2	1	no	—
50	C₂²×D₄×C₁₂₇	—	2	1	no	—
51	C₂²×D₄×C₁₂₇	—	2	1	no	—
52	C₂×SD₁₆×C₁₂₇	—	2	4	no	—
53	C₂×SD₁₆×C₁₂₇	—	2	4	no	—
54	C₂×SD₁₆×C₁₂₇	—	2	2	no	—
55	C₂×SD₁₆×C₁₂₇	—	4	8	no	—
56	C₂×D₈×C₁₂₇	—	2	4	no	—
57	C₂×M₁₆×C₁₂₇	D₄	1	2	yes	—
58	C₂²×C₈×C₁₂₇	D₄	1	2	yes	—
59	C₄⋊Q₈×C₁₂₇	—	2	1	no	—
60	C₄⋊Q₈×C₁₂₇	—	2	1	no	—
61	C₄⋊Q₈×C₁₂₇	—	2	1	no	—
62	C₄⋊Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
63	C₄⋊Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
65	C₄⋊Q₈×C₁₂₇	C₂³	1	2	yes	—
66	#127×C₁₂₇	—	2	1	no	—
67	#127×C₁₂₇	—	2	1	no	—
68	#127×C₁₂₇	—	2	1	no	—
69	#127×C₁₂₇	C₂³	1	2	yes	—
70	#127×C₁₂₇	C₂³	1	1	yes	characteristic
71	#125×C₁₂₇	—	2	1	no	—
72	#124×C₁₂₇	—	2	1	no	—
73	C₂²⋊Q₈×C₁₂₇	—	2	1	no	—
74	C₂²⋊Q₈×C₁₂₇	—	2	1	no	—
75	#121×C₁₂₇	—	2	1	no	—
76	#121×C₁₂₇	—	2	1	no	—
77	C₄×Q₈×C₁₂₇	—	2	1	no	—
78	C₄×Q₈×C₁₂₇	—	2	1	no	—
79	C₄×D₄×C₁₂₇	—	2	1	no	—
80	C₄×D₄×C₁₂₇	—	2	1	no	—
81	#117×C₁₂₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₂₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₂₇	—	2	1	no	—
84	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
85	#107×C₁₂₇	—	2	4	no	—
86	#106×C₁₂₇	—	2	2	no	—
87	C₄⋊C₈×C₁₂₇	D₄	1	2	yes	—
88	#103×C₁₂₇	—	2	4	no	—
89	#103×C₁₂₇	—	2	2	no	—
90	#103×C₁₂₇	—	2	4	no	—
91	#102×C₁₂₇	—	2	4	no	—
92	#102×C₁₂₇	—	2	4	no	—
93	#102×C₁₂₇	—	2	4	no	—
94	#102×C₁₂₇	—	2	2	no	—
95	#102×C₁₂₇	—	2	4	no	—
96	C₂²⋊C₈×C₁₂₇	D₄	1	2	yes	—
97	#97×C₁₂₇	D₄	1	2	yes	—
98	C₄×C₈×C₁₂₇	D₄	1	2	yes	—
99	C₄×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₂₇	C₂³	1	2	yes	—
101	C₄×C₈×C₁₂₇	C₂³	1	2	yes	—
102	C₄×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
103	C₂⁴×C₁₂₇	—	4	1	no	—
104	#41×C₁₂₇	—	4	4	no	—
105	C₂×Q₈×C₁₂₇	—	2	1	no	—
106	C₂×Q₈×C₁₂₇	—	2	1	no	—
107	C₂×Q₈×C₁₂₇	—	2	1	no	—
108	C₂×Q₈×C₁₂₇	—	2	2	no	—
109	C₂×Q₈×C₁₂₇	—	4	4	no	—
110	C₂×Q₈×C₁₂₇	—	4	1	no	—
111	C₂×D₄×C₁₂₇	—	2	1	no	—
112	C₂×D₄×C₁₂₇	—	2	2	no	—
113	C₂×D₄×C₁₂₇	—	2	1	no	—
114	C₂×D₄×C₁₂₇	—	2	2	no	—
115	C₂×D₄×C₁₂₇	—	2	1	no	—
116	C₂×D₄×C₁₂₇	—	2	2	no	—
117	C₂×D₄×C₁₂₇	—	4	4	no	—
118	C₂×D₄×C₁₂₇	—	4	1	no	—
119	C₂×D₄×C₁₂₇	—	4	1	no	—
120	C₂×D₄×C₁₂₇	—	4	1	no	—
121	C₂×D₄×C₁₂₇	—	4	1	no	—
122	C₂×D₄×C₁₂₇	—	4	4	no	—
123	C₂×D₄×C₁₂₇	—	8	2	no	—
124	C₂²×C₄×C₁₂₇	—	4	1	no	—
125	C₂²×C₄×C₁₂₇	—	4	1	no	—
126	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
129	SD₁₆×C₁₂₇	—	4	8	no	—
130	SD₁₆×C₁₂₇	—	4	4	no	—
131	SD₁₆×C₁₂₇	—	4	8	no	—
132	D₈×C₁₂₇	—	8	4	no	—
133	M₁₆×C₁₂₇	—	2	4	no	—
134	C₂×C₈×C₁₂₇	—	2	4	no	—
135	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₁₂₇	C₂×D₄	1	4	yes	—
137	C₂×C₈×C₁₂₇	C₂×D₄	1	4	yes	—
138	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₁₂₇	—	2	1	no	—
140	C₄⋊C₄×C₁₂₇	—	2	1	no	—
141	C₄⋊C₄×C₁₂₇	—	2	1	no	—
142	C₄⋊C₄×C₁₂₇	—	2	2	no	—
143	C₄⋊C₄×C₁₂₇	—	2	1	no	—
144	C₄⋊C₄×C₁₂₇	—	2	1	no	—
145	C₄⋊C₄×C₁₂₇	—	2	2	no	—
146	C₄⋊C₄×C₁₂₇	—	2	1	no	—
147	C₄⋊C₄×C₁₂₇	—	4	1	no	—
148	C₄⋊C₄×C₁₂₇	—	4	1	no	—
149	C₄⋊C₄×C₁₂₇	—	4	1	no	—
150	C₄⋊C₄×C₁₂₇	—	4	1	no	—
151	C₂²⋊C₄×C₁₂₇	—	4	1	no	—
152	C₂²⋊C₄×C₁₂₇	—	4	1	no	—
153	C₂²⋊C₄×C₁₂₇	—	4	1	no	—
154	C₄²×C₁₂₇	—	4	1	no	—
155	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₁₂₇	C₂⁴	1	1	yes	characteristic
159	C₂³×C₁₂₇	—	4	1	no	—
160	C₂³×C₁₂₇	—	4	2	no	—
161	C₂³×C₁₂₇	—	8	2	no	—
162	C₂³×C₁₂₇	—	8	2	no	—
163	C₂³×C₁₂₇	—	8	2	no	—
164	C₂³×C₁₂₇	#127	1	1	yes	characteristic
165	Q₈×C₁₂₇	—	4	2	no	—
166	Q₈×C₁₂₇	—	4	4	no	—
167	Q₈×C₁₂₇	—	4	2	no	—
168	Q₈×C₁₂₇	—	4	2	no	—
169	Q₈×C₁₂₇	—	8	2	no	—
170	D₄×C₁₂₇	—	4	4	no	—
171	D₄×C₁₂₇	—	4	2	no	—
172	D₄×C₁₂₇	—	4	4	no	—
173	D₄×C₁₂₇	—	4	2	no	—
174	D₄×C₁₂₇	—	4	2	no	—
175	D₄×C₁₂₇	—	4	4	no	—
176	D₄×C₁₂₇	—	8	2	no	—
177	D₄×C₁₂₇	—	8	2	no	—
178	D₄×C₁₂₇	—	8	2	no	—
179	D₄×C₁₂₇	—	8	2	no	—
180	C₂×C₄×C₁₂₇	—	2	2	no	—
181	C₂×C₄×C₁₂₇	—	2	2	no	—
182	C₂×C₄×C₁₂₇	—	4	1	no	—
183	C₂×C₄×C₁₂₇	—	4	1	no	—
184	C₂×C₄×C₁₂₇	—	4	1	no	—
185	C₂×C₄×C₁₂₇	—	4	2	no	—
186	C₂×C₄×C₁₂₇	—	8	2	no	—
187	C₂×C₄×C₁₂₇	—	8	2	no	—
188	C₂×C₄×C₁₂₇	#127	1	1	yes	characteristic
189	C₂×C₄×C₁₂₇	#127	1	1	yes	characteristic
190	C₂×C₄×C₁₂₇	#127	1	1	yes	characteristic
191	C₂×C₄×C₁₂₇	#135	1	4	yes	—
192	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
195	C₈×C₁₂₇	—	2	4	no	—
196	C₈×C₁₂₇	—	2	2	no	—
197	C₈×C₁₂₇	—	2	4	no	—
198	C₈×C₁₂₇	AGL(1,ℤ/8)	1	4	yes	—
199	C₂²×C₁₂₇	—	2	1	no	—
200	C₂²×C₁₂₇	—	2	1	no	—
201	C₂²×C₁₂₇	—	8	1	no	—
202	C₂²×C₁₂₇	—	8	2	no	—
203	C₂²×C₁₂₇	—	8	2	no	—
204	C₂²×C₁₂₇	—	8	1	no	—
205	C₂²×C₁₂₇	—	8	2	no	—
206	C₂²×C₁₂₇	—	8	1	no	—
207	C₂²×C₁₂₇	—	16	4	no	—
208	C₂²×C₁₂₇	#495	1	2	yes	—
209	C₂²×C₁₂₇	C₂×#127	1	1	yes	characteristic
210	C₄×C₁₂₇	—	2	1	no	—
211	C₄×C₁₂₇	—	2	1	no	—
212	C₄×C₁₂₇	—	8	1	no	—
213	C₄×C₁₂₇	—	8	2	no	—
214	C₄×C₁₂₇	—	8	1	no	—
215	C₄×C₁₂₇	—	8	1	no	—
216	C₄×C₁₂₇	#495	1	2	yes	—
217	C₄×C₁₂₇	C₂×#135	1	2	yes	—
218	C₄×C₁₂₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
219	C₄×C₁₂₇	#577	1	2	yes	—
220	#19625	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂×C₁₂₇	—	2	2	no	—
222	C₂×C₁₂₇	—	16	1	no	—
223	C₂×C₁₂₇	—	16	2	no	—
224	C₂×C₁₂₇	C₂×#495	1	1	yes	characteristic
225	C₂×C₁₂₇	#3151	1	1	yes	characteristic
226	C₂×C₁₂₇	#3154	1	1	yes	characteristic
227	#3230	C₂×C₁₂₇	1	1	yes	characteristic, complemented
228	#3205	C₂×C₁₂₇	1	1	yes	characteristic
229	#3167	C₂×C₁₂₇	1	1	yes	characteristic, complemented
230	C₂×#492	C₂×C₁₂₇	1	1	yes	characteristic, complemented
231	#3141	C₂×C₁₂₇	1	1	yes	characteristic, complemented
232	#3138	C₂×C₁₂₇	1	1	yes	characteristic, complemented
233	#1719	C₂×C₁₂₇	1	2	yes	complemented
234	#1717	C₂×C₁₂₇	1	2	yes	complemented
235	#1708	C₂×C₁₂₇	1	2	yes	complemented
236	#1706	C₂×C₁₂₇	1	2	yes	complemented
237	C₈×M₁₆	C₂×C₁₂₇	1	1	yes	characteristic, complemented
238	C₁₂₇	#19625	1	1	yes	characteristic, direct product factor, Sylow
239	C₂²×SD₁₆	—	2	2	no	—
240	#533	C₂²×C₁₂₇	1	1	yes	characteristic
241	#532	C₂²×C₁₂₇	1	1	yes	characteristic
242	C₂×C₄⋊Q₈	C₂²×C₁₂₇	1	1	yes	characteristic
243	C₂×#127	C₂²×C₁₂₇	1	1	yes	characteristic
244	#500	C₂²×C₁₂₇	1	2	yes	complemented
245	#498	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
246	#493	C₂²×C₁₂₇	1	2	yes	—
247	#492	—	2	2	no	—
248	#492	C₂²×C₁₂₇	1	2	yes	—
249	#492	C₂²×C₁₂₇	1	2	yes	—
250	#492	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
251	#490	—	2	2	no	—
252	#489	—	2	2	no	—
253	#487	C₂²×C₁₂₇	1	2	yes	complemented
254	#487	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
255	#487	C₂²×C₁₂₇	1	2	yes	complemented
256	#486	C₂²×C₁₂₇	1	2	yes	—
257	#486	C₂²×C₁₂₇	1	2	yes	—
258	#486	C₂²×C₁₂₇	1	2	yes	—
259	#486	C₂²×C₁₂₇	1	2	yes	complemented
260	#486	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
261	#484	—	2	2	no	—
262	#477	—	2	2	no	—
263	#465	—	2	2	no	—
264	#459	—	2	2	no	—
265	#447	—	2	2	no	—
266	C₄×SD₁₆	—	2	2	no	—
267	#431	C₂²×C₁₂₇	1	1	yes	characteristic
268	#418	—	2	2	no	—
269	#417	—	2	2	no	—
270	C₄×M₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
271	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
272	#322	C₂²×C₁₂₇	1	2	yes	complemented
273	C₈²	C₂²×C₁₂₇	1	2	yes	complemented
274	C₂×#41	—	2	1	no	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	—	2	1	no	—
278	C₂²×D₄	—	2	1	no	—
279	C₂×SD₁₆	—	2	4	no	—
280	C₂×SD₁₆	—	2	4	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	C₂×SD₁₆	—	4	8	no	—
283	C₂×D₈	—	2	4	no	—
284	C₂×M₁₆	D₄×C₁₂₇	1	2	yes	—
285	C₂²×C₈	D₄×C₁₂₇	1	2	yes	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	—	2	1	no	—
289	C₄⋊Q₈	C₂³×C₁₂₇	1	2	yes	—
290	C₄⋊Q₈	C₂³×C₁₂₇	1	1	yes	characteristic
291	C₄⋊Q₈	C₂³×C₁₂₇	1	1	yes	characteristic
292	C₄⋊Q₈	C₂³×C₁₂₇	1	1	yes	characteristic
293	#127	—	2	1	no	—
294	#127	—	2	1	no	—
295	#127	—	2	1	no	—
296	#127	C₂³×C₁₂₇	1	2	yes	—
297	#127	C₂³×C₁₂₇	1	1	yes	characteristic
298	#125	—	2	1	no	—
299	#124	—	2	1	no	—
300	C₂²⋊Q₈	—	2	1	no	—
301	C₂²⋊Q₈	—	2	1	no	—
302	#121	—	2	1	no	—
303	#121	—	2	1	no	—
304	C₄×Q₈	—	2	1	no	—
305	C₄×Q₈	—	2	1	no	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	2	1	no	—
308	#117	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
312	#107	—	2	4	no	—
313	#106	—	2	2	no	—
314	C₄⋊C₈	D₄×C₁₂₇	1	2	yes	—
315	#103	—	2	4	no	—
316	#103	—	2	2	no	—
317	#103	—	2	4	no	—
318	#102	—	2	4	no	—
319	#102	—	2	4	no	—
320	#102	—	2	4	no	—
321	#102	—	2	2	no	—
322	#102	—	2	4	no	—
323	C₂²⋊C₈	D₄×C₁₂₇	1	2	yes	—
324	#97	D₄×C₁₂₇	1	2	yes	—
325	C₄×C₈	D₄×C₁₂₇	1	2	yes	—
326	C₄×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
327	C₄×C₈	C₂³×C₁₂₇	1	2	yes	—
328	C₄×C₈	C₂³×C₁₂₇	1	2	yes	—
329	C₄×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
330	C₂⁴	—	4	1	no	—
331	#41	—	4	4	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	4	4	no	—
337	C₂×Q₈	—	4	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	4	4	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	4	4	no	—
350	C₂×D₄	—	8	2	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
356	SD₁₆	—	4	8	no	—
357	SD₁₆	—	4	4	no	—
358	SD₁₆	—	4	8	no	—
359	D₈	—	8	4	no	—
360	M₁₆	—	2	4	no	—
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
363	C₂×C₈	C₂×D₄×C₁₂₇	1	4	yes	—
364	C₂×C₈	C₂×D₄×C₁₂₇	1	4	yes	—
365	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₂²⋊C₄	—	4	1	no	—
379	C₂²⋊C₄	—	4	1	no	—
380	C₂²⋊C₄	—	4	1	no	—
381	C₄²	—	4	1	no	—
382	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
383	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
384	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
385	C₄²	C₂⁴×C₁₂₇	1	1	yes	characteristic
386	C₂³	—	4	1	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	8	2	no	—
389	C₂³	—	8	2	no	—
390	C₂³	—	8	2	no	—
391	C₂³	#127×C₁₂₇	1	1	yes	characteristic
392	Q₈	—	4	2	no	—
393	Q₈	—	4	4	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	8	2	no	—
397	D₄	—	4	4	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	4	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	4	no	—
403	D₄	—	8	2	no	—
404	D₄	—	8	2	no	—
405	D₄	—	8	2	no	—
406	D₄	—	8	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	8	2	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	#127×C₁₂₇	1	1	yes	characteristic
416	C₂×C₄	#127×C₁₂₇	1	1	yes	characteristic
417	C₂×C₄	#127×C₁₂₇	1	1	yes	characteristic
418	C₂×C₄	#135×C₁₂₇	1	4	yes	—
419	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
420	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
421	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
422	C₈	—	2	4	no	—
423	C₈	—	2	2	no	—
424	C₈	—	2	4	no	—
425	C₈	AGL(1,ℤ/8)×C₁₂₇	1	4	yes	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	1	no	—
434	C₂²	—	16	4	no	—
435	C₂²	#495×C₁₂₇	1	2	yes	—
436	C₂²	C₂×#127×C₁₂₇	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	8	1	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	1	no	—
443	C₄	#495×C₁₂₇	1	2	yes	—
444	C₄	C₂×#135×C₁₂₇	1	2	yes	—
445	C₄	C₂×AGL(1,ℤ/8)×C₁₂₇	1	2	yes	—
446	C₄	#577×C₁₂₇	1	2	yes	—
447	C₂	—	2	2	no	—
448	C₂	—	16	2	no	—
449	C₂	—	16	1	no	—
450	C₂	C₂×#495×C₁₂₇	1	1	yes	characteristic
451	C₂	C₁₂₇×#3151	1	1	yes	characteristic
452	C₂	C₁₂₇×#3154	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₂₇	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₂₇
prime radical	C₁₂₇×#3205	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₂₇ ◁ C₂×C₄²×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₂₇×#3230	C₂	semidirect
3. C₁₂₇×#3167	C₂	semidirect
4. C₂×#492×C₁₂₇	C₂	semidirect
5. C₁₂₇×#3141	C₂	semidirect
6. C₁₂₇×#3138	C₂	semidirect
7. C₁₂₇×#1719	C₂	semidirect
8. C₁₂₇×#1717	C₂	semidirect
9. C₁₂₇×#1708	C₂	semidirect
10. C₁₂₇×#1706	C₂	semidirect
11. C₈×M₁₆×C₁₂₇	C₂	semidirect
17. #500×C₁₂₇	C₂²	semidirect
18. #498×C₁₂₇	C₂²	semidirect
23. #492×C₁₂₇	C₂²	semidirect
26. #487×C₁₂₇	C₂²	semidirect
27. #487×C₁₂₇	C₂²	semidirect
28. #487×C₁₂₇	C₂²	semidirect
32. #486×C₁₂₇	C₂²	semidirect
33. #486×C₁₂₇	C₂²	semidirect
45. #322×C₁₂₇	C₂²	semidirect
46. C₈²×C₁₂₇	C₂²	semidirect
220. #19625	C₁₂₇	direct (N × H)
227. #3230	C₂×C₁₂₇	semidirect
229. #3167	C₂×C₁₂₇	semidirect
230. C₂×#492	C₂×C₁₂₇	semidirect
231. #3141	C₂×C₁₂₇	semidirect
232. #3138	C₂×C₁₂₇	semidirect
233. #1719	C₂×C₁₂₇	semidirect
234. #1717	C₂×C₁₂₇	semidirect
235. #1708	C₂×C₁₂₇	semidirect
236. #1706	C₂×C₁₂₇	semidirect
237. C₈×M₁₆	C₂×C₁₂₇	semidirect
238. C₁₂₇	#19625	direct (N × H)
244. #500	C₂²×C₁₂₇	semidirect
245. #498	C₂²×C₁₂₇	semidirect
250. #492	C₂²×C₁₂₇	semidirect
253. #487	C₂²×C₁₂₇	semidirect
254. #487	C₂²×C₁₂₇	semidirect
255. #487	C₂²×C₁₂₇	semidirect
259. #486	C₂²×C₁₂₇	semidirect
260. #486	C₂²×C₁₂₇	semidirect
272. #322	C₂²×C₁₂₇	semidirect
273. C₈²	C₂²×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₂₇×#3230	2
C₁₂₇×#3205	2
C₁₂₇×#3167	2
C₂×#492×C₁₂₇	2
C₁₂₇×#3141	2
C₁₂₇×#3138	2
C₁₂₇×#1719	2
C₁₂₇×#1717	2
C₁₂₇×#1708	2
C₁₂₇×#1706	2
C₈×M₁₆×C₁₂₇	2
#19625	127

Subgroups — C127×#19625 #44583298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#19625 #44583298