Subgroups — C₁₂₇×#18074 #44581747

Order 32512.

592 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₂₇×#3168	C₂	1	1	yes	maximal, characteristic
2	C₁₂₇×#2969	C₂	1	2	yes	maximal, complemented
3	C₁₂₇×#1592	C₂	1	2	yes	maximal, complemented
4	C₁₂₇×#1587	C₂	1	2	yes	maximal, complemented
5	C₁₂₇×#1586	C₂	1	2	yes	maximal, complemented
6	C₁₂₇×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₁₂₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₂₇×#1482	C₂	1	2	yes	maximal, complemented
9	C₁₂₇×#1451	C₂	1	1	yes	maximal, characteristic, complemented
10	#529×C₁₂₇	C₂²	1	2	yes	—
11	#499×C₁₂₇	C₄	1	1	yes	characteristic
12	#495×C₁₂₇	C₄	1	1	yes	characteristic
13	#488×C₁₂₇	C₄	1	2	yes	—
14	#467×C₁₂₇	C₄	1	1	yes	characteristic
15	#466×C₁₂₇	C₄	1	1	yes	characteristic
16	#465×C₁₂₇	C₄	1	2	yes	—
17	#446×C₁₂₇	C₂²	1	2	yes	—
18	C₈×Q₈×C₁₂₇	C₂²	1	2	yes	—
19	C₄×Q₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
20	C₄×SD₁₆×C₁₂₇	C₂²	1	2	yes	—
21	C₄×D₈×C₁₂₇	C₂²	1	1	yes	characteristic
22	#436×C₁₂₇	—	2	2	no	—
23	#436×C₁₂₇	C₂²	1	2	yes	—
24	#435×C₁₂₇	—	2	2	no	—
25	C₈×D₄×C₁₂₇	C₂²	1	2	yes	—
26	#433×C₁₂₇	—	2	2	no	—
27	#431×C₁₂₇	C₂²	1	2	yes	—
28	#431×C₁₂₇	C₂²	1	1	yes	characteristic
29	#405×C₁₂₇	—	2	2	no	—
30	C₄×M₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
32	#335×C₁₂₇	C₂²	1	1	yes	characteristic
33	#335×C₁₂₇	C₂²	1	1	yes	characteristic
34	#334×C₁₂₇	C₂²	1	2	yes	—
35	Q₈⋊C₈×C₁₂₇	C₂²	1	2	yes	—
36	Q₈⋊C₈×C₁₂₇	C₂²	1	2	yes	—
37	D₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
38	D₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
39	#322×C₁₂₇	C₂²	1	2	yes	—
40	#322×C₁₂₇	C₂²	1	2	yes	—
41	C₂×Q₁₆×C₁₂₇	C₂×C₄	1	1	yes	characteristic
42	C₂×SD₁₆×C₁₂₇	C₂×C₄	1	2	yes	—
43	C₂×D₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
44	C₂×M₁₆×C₁₂₇	—	2	2	no	—
45	C₂×M₁₆×C₁₂₇	D₄	1	1	yes	characteristic
46	C₂×M₁₆×C₁₂₇	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₂₇	—	2	2	no	—
48	C₂²×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
50	#126×C₁₂₇	—	2	2	no	—
51	#125×C₁₂₇	C₂×C₄	1	2	yes	—
52	#124×C₁₂₇	C₂×C₄	1	2	yes	—
53	#123×C₁₂₇	—	2	2	no	—
54	C₂²⋊Q₈×C₁₂₇	C₂×C₄	1	2	yes	—
55	#121×C₁₂₇	C₂×C₄	1	2	yes	—
56	C₄×Q₈×C₁₂₇	C₂³	1	2	yes	—
57	C₄×D₄×C₁₂₇	—	2	2	no	—
58	C₄×D₄×C₁₂₇	C₂³	1	2	yes	—
59	#117×C₁₂₇	—	2	2	no	—
60	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
61	#107×C₁₂₇	C₂×C₄	1	1	yes	characteristic
62	#107×C₁₂₇	C₂×C₄	1	1	yes	characteristic
63	#106×C₁₂₇	C₂×C₄	1	2	yes	—
64	C₄⋊C₈×C₁₂₇	—	2	2	no	—
65	C₄⋊C₈×C₁₂₇	—	2	2	no	—
66	C₄⋊C₈×C₁₂₇	—	2	1	no	—
67	C₄⋊C₈×C₁₂₇	C₂³	1	2	yes	—
68	C₄⋊C₈×C₁₂₇	C₂³	1	2	yes	—
69	#103×C₁₂₇	C₂×C₄	1	2	yes	—
70	#103×C₁₂₇	C₂×C₄	1	2	yes	—
71	#102×C₁₂₇	C₂×C₄	1	2	yes	—
72	#102×C₁₂₇	C₂×C₄	1	2	yes	—
73	C₂²⋊C₈×C₁₂₇	—	2	2	no	—
74	C₂²⋊C₈×C₁₂₇	—	2	1	no	—
75	C₂²⋊C₈×C₁₂₇	—	2	2	no	—
76	C₂²⋊C₈×C₁₂₇	—	2	2	no	—
77	#97×C₁₂₇	—	2	2	no	—
78	#97×C₁₂₇	D₄	1	2	yes	—
79	C₄×C₈×C₁₂₇	—	2	2	no	—
80	C₄×C₈×C₁₂₇	—	2	2	no	—
81	C₄×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₁₂₇	C₂³	1	2	yes	—
84	C₄×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₁₂₇	C₂³	1	2	yes	—
87	C₂×Q₈×C₁₂₇	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₁₂₇	—	2	2	no	—
89	C₂×D₄×C₁₂₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₂₇	—	2	2	no	—
91	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₂₇	#41	1	1	yes	characteristic
94	Q₁₆×C₁₂₇	—	4	1	no	—
95	SD₁₆×C₁₂₇	—	2	4	no	—
96	D₈×C₁₂₇	—	4	1	no	—
97	M₁₆×C₁₂₇	—	4	1	no	—
98	M₁₆×C₁₂₇	—	4	1	no	—
99	M₁₆×C₁₂₇	—	4	4	no	—
100	C₂×C₈×C₁₂₇	—	2	2	no	—
101	C₂×C₈×C₁₂₇	—	2	2	no	—
102	C₂×C₈×C₁₂₇	—	2	2	no	—
103	C₂×C₈×C₁₂₇	—	2	2	no	—
104	C₂×C₈×C₁₂₇	—	4	1	no	—
105	C₂×C₈×C₁₂₇	—	4	4	no	—
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	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
112	C₄⋊C₄×C₁₂₇	—	2	2	no	—
113	C₄⋊C₄×C₁₂₇	—	2	2	no	—
114	C₄⋊C₄×C₁₂₇	—	2	2	no	—
115	C₄⋊C₄×C₁₂₇	—	2	2	no	—
116	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
117	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
118	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
119	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
120	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
121	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
122	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
123	C₄²×C₁₂₇	—	2	2	no	—
124	C₄²×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₂₇	#41	1	1	yes	characteristic
127	C₄²×C₁₂₇	C₂⁴	1	1	yes	characteristic
128	C₂³×C₁₂₇	—	2	2	no	—
129	C₂³×C₁₂₇	C₄×D₄	1	1	yes	characteristic
130	Q₈×C₁₂₇	—	2	2	no	—
131	Q₈×C₁₂₇	—	2	2	no	—
132	D₄×C₁₂₇	—	2	2	no	—
133	D₄×C₁₂₇	—	2	2	no	—
134	D₄×C₁₂₇	—	8	2	no	—
135	C₂×C₄×C₁₂₇	—	2	1	no	—
136	C₂×C₄×C₁₂₇	—	2	1	no	—
137	C₂×C₄×C₁₂₇	—	2	1	no	—
138	C₂×C₄×C₁₂₇	—	2	1	no	—
139	C₂×C₄×C₁₂₇	—	2	2	no	—
140	C₂×C₄×C₁₂₇	—	2	2	no	—
141	C₂×C₄×C₁₂₇	—	2	2	no	—
142	C₂×C₄×C₁₂₇	—	4	1	no	—
143	C₂×C₄×C₁₂₇	—	4	2	no	—
144	C₂×C₄×C₁₂₇	—	4	2	no	—
145	C₂×C₄×C₁₂₇	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₂₇	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₂₇	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
151	C₈×C₁₂₇	—	2	1	no	—
152	C₈×C₁₂₇	—	2	1	no	—
153	C₈×C₁₂₇	—	2	1	no	—
154	C₈×C₁₂₇	—	2	2	no	—
155	C₈×C₁₂₇	—	2	2	no	—
156	C₈×C₁₂₇	—	4	2	no	—
157	C₈×C₁₂₇	—	4	2	no	—
158	C₈×C₁₂₇	—	4	2	no	—
159	C₈×C₁₂₇	#131	1	2	yes	—
160	C₂²×C₁₂₇	—	2	1	no	—
161	C₂²×C₁₂₇	—	2	1	no	—
162	C₂²×C₁₂₇	—	2	1	no	—
163	C₂²×C₁₂₇	—	4	2	no	—
164	C₂²×C₁₂₇	—	4	2	no	—
165	C₂²×C₁₂₇	—	4	2	no	—
166	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
167	C₄×C₁₂₇	—	2	1	no	—
168	C₄×C₁₂₇	—	2	1	no	—
169	C₄×C₁₂₇	—	2	1	no	—
170	C₄×C₁₂₇	—	2	1	no	—
171	C₄×C₁₂₇	—	4	2	no	—
172	C₄×C₁₂₇	—	4	2	no	—
173	C₄×C₁₂₇	—	4	2	no	—
174	C₄×C₁₂₇	C₂×#131	1	1	yes	characteristic
175	C₄×C₁₂₇	#568	1	1	yes	characteristic
176	C₄×C₁₂₇	#575	1	1	yes	characteristic
177	C₄×C₁₂₇	#575	1	1	yes	characteristic
178	#18074	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂×C₁₂₇	—	4	1	no	—
180	C₂×C₁₂₇	—	8	2	no	—
181	C₂×C₁₂₇	#2935	1	1	yes	characteristic
182	C₂×C₁₂₇	#2943	1	1	yes	characteristic
183	C₂×C₁₂₇	#2957	1	1	yes	characteristic
184	#3168	C₂×C₁₂₇	1	1	yes	characteristic
185	#2969	C₂×C₁₂₇	1	2	yes	complemented
186	#1592	C₂×C₁₂₇	1	2	yes	complemented
187	#1587	C₂×C₁₂₇	1	2	yes	complemented
188	#1586	C₂×C₁₂₇	1	2	yes	complemented
189	SD₁₆⋊C₈	C₂×C₁₂₇	1	2	yes	complemented
190	#1564	C₂×C₁₂₇	1	1	yes	characteristic, complemented
191	#1482	C₂×C₁₂₇	1	2	yes	complemented
192	#1451	C₂×C₁₂₇	1	1	yes	characteristic, complemented
193	C₁₂₇	#18074	1	1	yes	characteristic, direct product factor, Sylow
194	#529	C₂²×C₁₂₇	1	2	yes	—
195	#499	C₄×C₁₂₇	1	1	yes	characteristic
196	#495	C₄×C₁₂₇	1	1	yes	characteristic
197	#488	C₄×C₁₂₇	1	2	yes	—
198	#467	C₄×C₁₂₇	1	1	yes	characteristic
199	#466	C₄×C₁₂₇	1	1	yes	characteristic
200	#465	C₄×C₁₂₇	1	2	yes	—
201	#446	C₂²×C₁₂₇	1	2	yes	—
202	C₈×Q₈	C₂²×C₁₂₇	1	2	yes	—
203	C₄×Q₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
204	C₄×SD₁₆	C₂²×C₁₂₇	1	2	yes	—
205	C₄×D₈	C₂²×C₁₂₇	1	1	yes	characteristic
206	#436	—	2	2	no	—
207	#436	C₂²×C₁₂₇	1	2	yes	—
208	#435	—	2	2	no	—
209	C₈×D₄	C₂²×C₁₂₇	1	2	yes	—
210	#433	—	2	2	no	—
211	#431	C₂²×C₁₂₇	1	2	yes	—
212	#431	C₂²×C₁₂₇	1	1	yes	characteristic
213	#405	—	2	2	no	—
214	C₄×M₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
215	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
216	#335	C₂²×C₁₂₇	1	1	yes	characteristic
217	#335	C₂²×C₁₂₇	1	1	yes	characteristic
218	#334	C₂²×C₁₂₇	1	2	yes	—
219	Q₈⋊C₈	C₂²×C₁₂₇	1	2	yes	—
220	Q₈⋊C₈	C₂²×C₁₂₇	1	2	yes	—
221	D₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
222	D₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
223	#322	C₂²×C₁₂₇	1	2	yes	—
224	#322	C₂²×C₁₂₇	1	2	yes	—
225	C₂×Q₁₆	C₂×C₄×C₁₂₇	1	1	yes	characteristic
226	C₂×SD₁₆	C₂×C₄×C₁₂₇	1	2	yes	—
227	C₂×D₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
228	C₂×M₁₆	—	2	2	no	—
229	C₂×M₁₆	D₄×C₁₂₇	1	1	yes	characteristic
230	C₂×M₁₆	D₄×C₁₂₇	1	1	yes	characteristic
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
233	C₂²×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
234	#126	—	2	2	no	—
235	#125	C₂×C₄×C₁₂₇	1	2	yes	—
236	#124	C₂×C₄×C₁₂₇	1	2	yes	—
237	#123	—	2	2	no	—
238	C₂²⋊Q₈	C₂×C₄×C₁₂₇	1	2	yes	—
239	#121	C₂×C₄×C₁₂₇	1	2	yes	—
240	C₄×Q₈	C₂³×C₁₂₇	1	2	yes	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	C₂³×C₁₂₇	1	2	yes	—
243	#117	—	2	2	no	—
244	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
245	#107	C₂×C₄×C₁₂₇	1	1	yes	characteristic
246	#107	C₂×C₄×C₁₂₇	1	1	yes	characteristic
247	#106	C₂×C₄×C₁₂₇	1	2	yes	—
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	1	no	—
251	C₄⋊C₈	C₂³×C₁₂₇	1	2	yes	—
252	C₄⋊C₈	C₂³×C₁₂₇	1	2	yes	—
253	#103	C₂×C₄×C₁₂₇	1	2	yes	—
254	#103	C₂×C₄×C₁₂₇	1	2	yes	—
255	#102	C₂×C₄×C₁₂₇	1	2	yes	—
256	#102	C₂×C₄×C₁₂₇	1	2	yes	—
257	C₂²⋊C₈	—	2	2	no	—
258	C₂²⋊C₈	—	2	1	no	—
259	C₂²⋊C₈	—	2	2	no	—
260	C₂²⋊C₈	—	2	2	no	—
261	#97	—	2	2	no	—
262	#97	D₄×C₁₂₇	1	2	yes	—
263	C₄×C₈	—	2	2	no	—
264	C₄×C₈	—	2	2	no	—
265	C₄×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
266	C₄×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
267	C₄×C₈	C₂³×C₁₂₇	1	2	yes	—
268	C₄×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
269	C₄×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
270	C₄×C₈	C₂³×C₁₂₇	1	2	yes	—
271	C₂×Q₈	C₂²×C₄×C₁₂₇	1	2	yes	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	C₂²×C₄×C₁₂₇	1	2	yes	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
277	C₂²×C₄	#41×C₁₂₇	1	1	yes	characteristic
278	Q₁₆	—	4	1	no	—
279	SD₁₆	—	2	4	no	—
280	D₈	—	4	1	no	—
281	M₁₆	—	4	1	no	—
282	M₁₆	—	4	1	no	—
283	M₁₆	—	4	4	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	4	1	no	—
289	C₂×C₈	—	4	4	no	—
290	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
291	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
292	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
293	C₂×C₈	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
294	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
295	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
301	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
302	C₂²⋊C₄	—	2	2	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
309	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
310	C₄²	#41×C₁₂₇	1	1	yes	characteristic
311	C₄²	C₂⁴×C₁₂₇	1	1	yes	characteristic
312	C₂³	—	2	2	no	—
313	C₂³	C₄×D₄×C₁₂₇	1	1	yes	characteristic
314	Q₈	—	2	2	no	—
315	Q₈	—	2	2	no	—
316	D₄	—	2	2	no	—
317	D₄	—	2	2	no	—
318	D₄	—	8	2	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	C₄×D₄×C₁₂₇	1	1	yes	characteristic
330	C₂×C₄	C₄×D₄×C₁₂₇	1	1	yes	characteristic
331	C₂×C₄	C₄×D₄×C₁₂₇	1	1	yes	characteristic
332	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
333	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
334	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
335	C₈	—	2	1	no	—
336	C₈	—	2	1	no	—
337	C₈	—	2	1	no	—
338	C₈	—	2	2	no	—
339	C₈	—	2	2	no	—
340	C₈	—	4	2	no	—
341	C₈	—	4	2	no	—
342	C₈	—	4	2	no	—
343	C₈	#131×C₁₂₇	1	2	yes	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	4	2	no	—
348	C₂²	—	4	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	4	2	no	—
356	C₄	—	4	2	no	—
357	C₄	—	4	2	no	—
358	C₄	C₂×#131×C₁₂₇	1	1	yes	characteristic
359	C₄	#568×C₁₂₇	1	1	yes	characteristic
360	C₄	#575×C₁₂₇	1	1	yes	characteristic
361	C₄	#575×C₁₂₇	1	1	yes	characteristic
362	C₂	—	4	1	no	—
363	C₂	—	8	2	no	—
364	C₂	C₁₂₇×#2935	1	1	yes	characteristic
365	C₂	C₁₂₇×#2943	1	1	yes	characteristic
366	C₂	C₁₂₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₂₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₂₇
Frattini, cosocle	C₄²	C₂⁴×C₁₂₇
socle	C₂²×C₁₂₇	C₂×C₄×D₄
prime radical	#466×C₁₂₇	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₂₇ ◁ C₄×M₁₆×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₂₇×#2969	C₂	semidirect
3. C₁₂₇×#1592	C₂	semidirect
4. C₁₂₇×#1587	C₂	semidirect
5. C₁₂₇×#1586	C₂	semidirect
6. C₁₂₇×SD₁₆⋊C₈	C₂	semidirect
7. C₁₂₇×#1564	C₂	semidirect
8. C₁₂₇×#1482	C₂	semidirect
9. C₁₂₇×#1451	C₂	semidirect
178. #18074	C₁₂₇	direct (N × H)
185. #2969	C₂×C₁₂₇	semidirect
186. #1592	C₂×C₁₂₇	semidirect
187. #1587	C₂×C₁₂₇	semidirect
188. #1586	C₂×C₁₂₇	semidirect
189. SD₁₆⋊C₈	C₂×C₁₂₇	semidirect
190. #1564	C₂×C₁₂₇	semidirect
191. #1482	C₂×C₁₂₇	semidirect
192. #1451	C₂×C₁₂₇	semidirect
193. C₁₂₇	#18074	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₂₇×#3168	2
C₁₂₇×#2969	2
C₁₂₇×#1592	2
C₁₂₇×#1587	2
C₁₂₇×#1586	2
C₁₂₇×SD₁₆⋊C₈	2
C₁₂₇×#1564	2
C₁₂₇×#1482	2
C₁₂₇×#1451	2
#18074	127

Subgroups — C127×#18074 #44581747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#18074 #44581747