Subgroups — C₁₂₇×#21119 #44584792

Order 32512.

858 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₁₂₇×#2295	C₂	1	1	yes	maximal, characteristic
3	C₄²×Q₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1928	C₂	1	2	yes	maximal
5	C₁₂₇×#1921	C₂	1	2	yes	maximal
6	C₁₂₇×#1878	C₂	1	2	yes	maximal
7	C₁₂₇×#1863	C₂	1	2	yes	maximal
8	C₄×#107×C₁₂₇	C₂	1	1	yes	maximal, characteristic
9	C₄×#103×C₁₂₇	C₂	1	1	yes	maximal, characteristic
10	C₄×#103×C₁₂₇	C₂	1	1	yes	maximal, characteristic
11	C₁₂₇×#1744	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₂₇	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic
16	C₄×Q₁₆×C₁₂₇	C₄	1	8	yes	complemented
17	C₂×#107×C₁₂₇	C₂²	1	2	yes	—
18	C₂×#107×C₁₂₇	C₂²	1	1	yes	characteristic
19	C₂×#103×C₁₂₇	C₂²	1	2	yes	—
20	C₂×#103×C₁₂₇	C₂²	1	2	yes	—
21	C₂×#103×C₁₂₇	C₂²	1	1	yes	characteristic
22	C₂×#103×C₁₂₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
25	#391×C₁₂₇	C₂²	1	2	yes	—
26	#389×C₁₂₇	C₂²	1	2	yes	—
27	#387×C₁₂₇	—	2	2	no	—
28	C₄×C₄⋊C₄×C₁₂₇	—	2	2	no	—
29	C₄×C₄⋊C₄×C₁₂₇	—	2	1	no	—
30	C₄×C₄⋊C₄×C₁₂₇	—	2	1	no	—
31	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
32	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
34	#376×C₁₂₇	—	2	1	no	—
35	C₄³×C₁₂₇	—	2	1	no	—
36	C₄³×C₁₂₇	C₂²	1	1	yes	characteristic
37	#340×C₁₂₇	C₂²	1	2	yes	—
38	#340×C₁₂₇	C₂²	1	2	yes	—
39	#340×C₁₂₇	C₂²	1	2	yes	—
40	#336×C₁₂₇	C₂²	1	2	yes	—
41	#336×C₁₂₇	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆×C₁₂₇	—	2	4	no	—
45	C₂×Q₁₆×C₁₂₇	C₂×C₄	1	4	yes	—
46	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
49	C₄×Q₈×C₁₂₇	—	2	4	no	—
50	C₄×Q₈×C₁₂₇	—	2	4	no	—
51	C₄×Q₈×C₁₂₇	—	2	2	no	—
52	C₄×Q₈×C₁₂₇	—	2	2	no	—
53	C₄×Q₈×C₁₂₇	C₂×C₄	1	4	yes	—
54	C₄×Q₈×C₁₂₇	C₂×C₄	1	4	yes	—
55	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₂₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₂₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₂₇	—	2	2	no	—
64	C₂×C₄²×C₁₂₇	—	2	1	no	—
65	C₂×C₄²×C₁₂₇	—	2	1	no	—
66	C₂×C₄²×C₁₂₇	—	2	2	no	—
67	C₂×C₄²×C₁₂₇	—	2	1	no	—
68	C₂×C₄²×C₁₂₇	—	2	1	no	—
69	C₂×C₄²×C₁₂₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₂₇	D₄	1	2	yes	—
71	C₂×C₄²×C₁₂₇	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
73	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
74	#107×C₁₂₇	—	2	4	no	—
75	#107×C₁₂₇	C₂×C₄	1	4	yes	—
76	#103×C₁₂₇	—	2	4	no	—
77	#103×C₁₂₇	—	2	4	no	—
78	#103×C₁₂₇	C₂×C₄	1	4	yes	—
79	#103×C₁₂₇	C₂×C₄	1	4	yes	—
80	C₄×C₈×C₁₂₇	—	2	2	no	—
81	C₄×C₈×C₁₂₇	C₂×C₄	1	4	yes	—
82	#95×C₁₂₇	—	2	2	no	—
83	#95×C₁₂₇	—	2	2	no	—
84	#95×C₁₂₇	—	2	2	no	—
85	#95×C₁₂₇	—	2	1	no	—
86	#95×C₁₂₇	—	2	2	no	—
87	#95×C₁₂₇	—	2	1	no	—
88	C₂×Q₈×C₁₂₇	—	2	1	no	—
89	C₂×Q₈×C₁₂₇	—	2	2	no	—
90	C₂×Q₈×C₁₂₇	—	2	1	no	—
91	C₂×Q₈×C₁₂₇	—	2	2	no	—
92	C₂×Q₈×C₁₂₇	—	2	2	no	—
93	C₂×Q₈×C₁₂₇	C₂²×C₄	1	2	yes	—
94	C₂×Q₈×C₁₂₇	C₂²×C₄	1	2	yes	—
95	C₂×Q₈×C₁₂₇	#41	1	4	yes	—
96	C₂²×C₄×C₁₂₇	—	2	1	no	—
97	C₂²×C₄×C₁₂₇	—	2	1	no	—
98	C₂²×C₄×C₁₂₇	—	2	1	no	—
99	C₂²×C₄×C₁₂₇	—	2	2	no	—
100	C₂²×C₄×C₁₂₇	—	2	1	no	—
101	C₂²×C₄×C₁₂₇	—	2	2	no	—
102	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
107	Q₁₆×C₁₂₇	—	2	8	no	—
108	C₂×C₈×C₁₂₇	—	2	2	no	—
109	C₂×C₈×C₁₂₇	—	2	2	no	—
110	C₂×C₈×C₁₂₇	—	2	2	no	—
111	C₂×C₈×C₁₂₇	—	2	2	no	—
112	C₂×C₈×C₁₂₇	—	2	2	no	—
113	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
115	C₄⋊C₄×C₁₂₇	—	2	8	no	—
116	C₄⋊C₄×C₁₂₇	—	2	4	no	—
117	C₄⋊C₄×C₁₂₇	—	2	4	no	—
118	C₄⋊C₄×C₁₂₇	—	2	1	no	—
119	C₄⋊C₄×C₁₂₇	—	2	1	no	—
120	C₄⋊C₄×C₁₂₇	—	2	2	no	—
121	C₄⋊C₄×C₁₂₇	—	2	2	no	—
122	C₄⋊C₄×C₁₂₇	—	2	2	no	—
123	C₄⋊C₄×C₁₂₇	—	4	4	no	—
124	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
125	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
126	C₄⋊C₄×C₁₂₇	#41	1	4	yes	—
127	C₄²×C₁₂₇	—	2	8	no	—
128	C₄²×C₁₂₇	—	2	4	no	—
129	C₄²×C₁₂₇	—	2	4	no	—
130	C₄²×C₁₂₇	—	2	2	no	—
131	C₄²×C₁₂₇	—	2	2	no	—
132	C₄²×C₁₂₇	—	2	2	no	—
133	C₄²×C₁₂₇	—	4	2	no	—
134	C₄²×C₁₂₇	—	4	4	no	—
135	C₄²×C₁₂₇	—	4	2	no	—
136	C₄²×C₁₂₇	—	4	2	no	—
137	C₄²×C₁₂₇	Q₁₆	1	4	yes	complemented
138	C₄²×C₁₂₇	C₂²×C₄	1	2	yes	—
139	C₄²×C₁₂₇	#41	1	2	yes	—
140	C₂³×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₁₂₇	—	2	2	no	—
142	Q₈×C₁₂₇	—	2	4	no	—
143	Q₈×C₁₂₇	—	2	2	no	—
144	Q₈×C₁₂₇	—	2	2	no	—
145	Q₈×C₁₂₇	—	4	2	no	—
146	Q₈×C₁₂₇	#117	1	4	yes	—
147	C₂×C₄×C₁₂₇	—	2	2	no	—
148	C₂×C₄×C₁₂₇	—	2	2	no	—
149	C₂×C₄×C₁₂₇	—	2	4	no	—
150	C₂×C₄×C₁₂₇	—	2	2	no	—
151	C₂×C₄×C₁₂₇	—	2	2	no	—
152	C₂×C₄×C₁₂₇	—	2	2	no	—
153	C₂×C₄×C₁₂₇	—	2	2	no	—
154	C₂×C₄×C₁₂₇	—	2	2	no	—
155	C₂×C₄×C₁₂₇	—	2	2	no	—
156	C₂×C₄×C₁₂₇	—	2	4	no	—
157	C₂×C₄×C₁₂₇	—	2	2	no	—
158	C₂×C₄×C₁₂₇	—	2	2	no	—
159	C₂×C₄×C₁₂₇	—	4	2	no	—
160	C₂×C₄×C₁₂₇	—	4	2	no	—
161	C₂×C₄×C₁₂₇	—	4	2	no	—
162	C₂×C₄×C₁₂₇	—	4	2	no	—
163	C₂×C₄×C₁₂₇	—	4	2	no	—
164	C₂×C₄×C₁₂₇	—	4	2	no	—
165	C₂×C₄×C₁₂₇	—	4	2	no	—
166	C₂×C₄×C₁₂₇	—	4	2	no	—
167	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₁₂₇	C₂×Q₁₆	1	4	yes	—
170	C₂×C₄×C₁₂₇	C₂×Q₁₆	1	2	yes	—
171	C₂×C₄×C₁₂₇	#135	1	2	yes	—
172	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₂₇	C₂×#41	1	2	yes	—
174	C₂×C₄×C₁₂₇	C₂×#41	1	2	yes	—
175	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
176	C₈×C₁₂₇	—	2	2	no	—
177	C₈×C₁₂₇	—	2	2	no	—
178	C₈×C₁₂₇	—	4	2	no	—
179	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
180	C₂²×C₁₂₇	#525	1	2	yes	—
181	C₂²×C₁₂₇	C₂²×Q₁₆	1	1	yes	characteristic
182	C₂²×C₁₂₇	C₂×#135	1	1	yes	characteristic
183	C₂²×C₁₂₇	#575	1	2	yes	—
184	C₄×C₁₂₇	—	2	4	no	—
185	C₄×C₁₂₇	—	2	2	no	—
186	C₄×C₁₂₇	—	2	4	no	—
187	C₄×C₁₂₇	—	4	2	no	—
188	C₄×C₁₂₇	—	4	4	no	—
189	C₄×C₁₂₇	—	4	2	no	—
190	C₄×C₁₂₇	—	4	2	no	—
191	C₄×C₁₂₇	—	4	2	no	—
192	C₄×C₁₂₇	—	8	2	no	—
193	C₄×C₁₂₇	C₄×Q₁₆	1	4	yes	—
194	C₄×C₁₂₇	C₂×#117	1	1	yes	characteristic
195	C₄×C₁₂₇	C₄×#41	1	1	yes	characteristic
196	C₄×C₁₂₇	#529	1	2	yes	—
197	#21119	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂×C₁₂₇	#2290	1	1	yes	characteristic
199	C₂×C₁₂₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
200	C₂×C₁₂₇	#2943	1	1	yes	characteristic
201	C₂×C₁₂₇	#3102	1	2	yes	—
202	C₂×C₁₂₇	#3104	1	2	yes	—
203	C₂×C₄×Q₁₆	C₂×C₁₂₇	1	1	yes	characteristic
204	#2295	C₂×C₁₂₇	1	1	yes	characteristic
205	C₄²×Q₈	C₂×C₁₂₇	1	1	yes	characteristic
206	#1928	C₂×C₁₂₇	1	2	yes	—
207	#1921	C₂×C₁₂₇	1	2	yes	—
208	#1878	C₂×C₁₂₇	1	2	yes	—
209	#1863	C₂×C₁₂₇	1	2	yes	—
210	C₄×#107	C₂×C₁₂₇	1	1	yes	characteristic
211	C₄×#103	C₂×C₁₂₇	1	1	yes	characteristic
212	C₄×#103	C₂×C₁₂₇	1	1	yes	characteristic
213	#1744	C₂×C₁₂₇	1	1	yes	characteristic
214	C₁₂₇	#21119	1	1	yes	characteristic, direct product factor, Sylow
215	C₂²×Q₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
216	C₂×C₄×Q₈	C₂²×C₁₂₇	1	2	yes	—
217	C₂×C₄×Q₈	C₂²×C₁₂₇	1	1	yes	characteristic
218	C₂×C₄×Q₈	C₂²×C₁₂₇	1	1	yes	characteristic
219	C₄×Q₁₆	C₄×C₁₂₇	1	8	yes	complemented
220	C₂×#107	C₂²×C₁₂₇	1	2	yes	—
221	C₂×#107	C₂²×C₁₂₇	1	1	yes	characteristic
222	C₂×#103	C₂²×C₁₂₇	1	2	yes	—
223	C₂×#103	C₂²×C₁₂₇	1	2	yes	—
224	C₂×#103	C₂²×C₁₂₇	1	1	yes	characteristic
225	C₂×#103	C₂²×C₁₂₇	1	1	yes	characteristic
226	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
227	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
228	#391	C₂²×C₁₂₇	1	2	yes	—
229	#389	C₂²×C₁₂₇	1	2	yes	—
230	#387	—	2	2	no	—
231	C₄×C₄⋊C₄	—	2	1	no	—
232	C₄×C₄⋊C₄	—	2	2	no	—
233	C₄×C₄⋊C₄	—	2	1	no	—
234	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
235	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	1	yes	characteristic
236	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	1	yes	characteristic
237	#376	—	2	1	no	—
238	C₄³	—	2	1	no	—
239	C₄³	C₂²×C₁₂₇	1	1	yes	characteristic
240	#340	C₂²×C₁₂₇	1	2	yes	—
241	#340	C₂²×C₁₂₇	1	2	yes	—
242	#340	C₂²×C₁₂₇	1	2	yes	—
243	#336	C₂²×C₁₂₇	1	2	yes	—
244	#336	C₂²×C₁₂₇	1	2	yes	—
245	C₂²×Q₈	C₂³×C₁₂₇	1	1	yes	characteristic
246	C₂²×Q₈	C₂³×C₁₂₇	1	1	yes	characteristic
247	C₂×Q₁₆	—	2	4	no	—
248	C₂×Q₁₆	C₂×C₄×C₁₂₇	1	4	yes	—
249	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
250	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
252	C₄×Q₈	—	2	4	no	—
253	C₄×Q₈	—	2	4	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	C₂×C₄×C₁₂₇	1	4	yes	—
257	C₄×Q₈	C₂×C₄×C₁₂₇	1	4	yes	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	2	yes	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	D₄×C₁₂₇	1	1	yes	characteristic
273	C₂×C₄²	D₄×C₁₂₇	1	2	yes	—
274	C₂×C₄²	D₄×C₁₂₇	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
276	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
277	#107	—	2	4	no	—
278	#107	C₂×C₄×C₁₂₇	1	4	yes	—
279	#103	—	2	4	no	—
280	#103	—	2	4	no	—
281	#103	C₂×C₄×C₁₂₇	1	4	yes	—
282	#103	C₂×C₄×C₁₂₇	1	4	yes	—
283	C₄×C₈	—	2	2	no	—
284	C₄×C₈	C₂×C₄×C₁₂₇	1	4	yes	—
285	#95	—	2	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	—	2	1	no	—
289	#95	—	2	2	no	—
290	#95	—	2	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	C₂²×C₄×C₁₂₇	1	2	yes	—
297	C₂×Q₈	C₂²×C₄×C₁₂₇	1	2	yes	—
298	C₂×Q₈	#41×C₁₂₇	1	4	yes	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
309	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
310	Q₁₆	—	2	8	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
317	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	4	4	no	—
327	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
328	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
329	C₄⋊C₄	#41×C₁₂₇	1	4	yes	—
330	C₄²	—	2	8	no	—
331	C₄²	—	2	4	no	—
332	C₄²	—	2	4	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	4	2	no	—
337	C₄²	—	4	4	no	—
338	C₄²	—	4	2	no	—
339	C₄²	—	4	2	no	—
340	C₄²	Q₁₆×C₁₂₇	1	4	yes	complemented
341	C₄²	C₂²×C₄×C₁₂₇	1	2	yes	—
342	C₄²	#41×C₁₂₇	1	2	yes	—
343	C₂³	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
344	Q₈	—	2	2	no	—
345	Q₈	—	2	4	no	—
346	Q₈	—	2	2	no	—
347	Q₈	—	2	2	no	—
348	Q₈	—	4	2	no	—
349	Q₈	#117×C₁₂₇	1	4	yes	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
371	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
372	C₂×C₄	C₂×Q₁₆×C₁₂₇	1	4	yes	—
373	C₂×C₄	C₂×Q₁₆×C₁₂₇	1	2	yes	—
374	C₂×C₄	#135×C₁₂₇	1	2	yes	—
375	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
376	C₂×C₄	C₂×#41×C₁₂₇	1	2	yes	—
377	C₂×C₄	C₂×#41×C₁₂₇	1	2	yes	—
378	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
379	C₈	—	2	2	no	—
380	C₈	—	2	2	no	—
381	C₈	—	4	2	no	—
382	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
383	C₂²	#525×C₁₂₇	1	2	yes	—
384	C₂²	C₂²×Q₁₆×C₁₂₇	1	1	yes	characteristic
385	C₂²	C₂×#135×C₁₂₇	1	1	yes	characteristic
386	C₂²	#575×C₁₂₇	1	2	yes	—
387	C₄	—	2	4	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	4	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	4	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	2	no	—
395	C₄	—	8	2	no	—
396	C₄	C₄×Q₁₆×C₁₂₇	1	4	yes	—
397	C₄	C₂×#117×C₁₂₇	1	1	yes	characteristic
398	C₄	C₄×#41×C₁₂₇	1	1	yes	characteristic
399	C₄	#529×C₁₂₇	1	2	yes	—
400	C₂	C₁₂₇×#2290	1	1	yes	characteristic
401	C₂	C₂×C₄×Q₁₆×C₁₂₇	1	1	yes	characteristic
402	C₂	C₁₂₇×#2943	1	1	yes	characteristic
403	C₂	C₁₂₇×#3102	1	2	yes	—
404	C₂	C₁₂₇×#3104	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, prime radical	C₂³×C₁₂₇	C₂²×D₄
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
16. C₄×Q₁₆×C₁₂₇	C₄	semidirect
137. C₄²×C₁₂₇	Q₁₆	semidirect
197. #21119	C₁₂₇	direct (N × H)
214. C₁₂₇	#21119	direct (N × H)
219. C₄×Q₁₆	C₄×C₁₂₇	semidirect
340. C₄²	Q₁₆×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Q₁₆×C₁₂₇	2
C₁₂₇×#2295	2
C₄²×Q₈×C₁₂₇	2
C₁₂₇×#1928	2
C₁₂₇×#1921	2
C₁₂₇×#1878	2
C₁₂₇×#1863	2
C₄×#107×C₁₂₇	2
C₄×#103×C₁₂₇	2
C₁₂₇×#1744	2
#21119	127

Subgroups — C127×#21119 #44584792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#21119 #44584792