Subgroups — C₁₂₇×#21024 #44584697

Order 32512.

914 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#405×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₁₂₇×#2296	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1917	C₂	1	4	yes	maximal, complemented
5	C₁₂₇×#1916	C₂	1	4	yes	maximal, complemented
6	C₁₂₇×#1729	C₂	1	1	yes	maximal, characteristic
7	C₁₂₇×#1729	C₂	1	1	yes	maximal, characteristic
8	C₁₂₇×#1729	C₂	1	1	yes	maximal, characteristic
9	C₁₂₇×#1728	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
14	C₂×#117×C₁₂₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₂₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₁₂₇	—	2	4	no	—
18	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
20	#405×C₁₂₇	—	2	4	no	—
21	C₂×#97×C₁₂₇	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
23	#389×C₁₂₇	C₄	1	2	yes	—
24	#389×C₁₂₇	C₄	1	2	yes	—
25	#385×C₁₂₇	C₄	1	2	yes	—
26	#385×C₁₂₇	C₄	1	2	yes	—
27	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	4	yes	—
28	#336×C₁₂₇	C₂²	1	2	yes	—
29	#336×C₁₂₇	C₂²	1	4	yes	—
30	#336×C₁₂₇	C₂²	1	4	yes	—
31	#336×C₁₂₇	C₂²	1	4	yes	—
32	#336×C₁₂₇	C₂²	1	2	yes	—
33	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₁₂₇	—	2	2	no	—
37	C₂×M₁₆×C₁₂₇	—	2	2	no	—
38	C₂×M₁₆×C₁₂₇	—	2	2	no	—
39	C₂×M₁₆×C₁₂₇	—	2	2	no	—
40	C₂×M₁₆×C₁₂₇	—	2	2	no	—
41	C₂×M₁₆×C₁₂₇	Q₈	1	4	yes	—
42	C₂²×C₈×C₁₂₇	—	2	2	no	—
43	C₂²×C₈×C₁₂₇	—	2	2	no	—
44	C₂²×C₈×C₁₂₇	—	2	2	no	—
45	C₂²×C₈×C₁₂₇	—	2	2	no	—
46	C₂²×C₈×C₁₂₇	—	2	2	no	—
47	C₂²×C₈×C₁₂₇	D₄	1	4	yes	—
48	C₂²×C₈×C₁₂₇	C₂³	1	2	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	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
53	#117×C₁₂₇	—	2	2	no	—
54	#117×C₁₂₇	—	2	2	no	—
55	#117×C₁₂₇	—	2	2	no	—
56	#117×C₁₂₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
62	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₂₇	—	2	2	no	—
65	C₂×C₄²×C₁₂₇	—	2	2	no	—
66	C₂×C₄²×C₁₂₇	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
70	C₄⋊C₈×C₁₂₇	—	2	4	no	—
71	C₄⋊C₈×C₁₂₇	—	2	4	no	—
72	#97×C₁₂₇	—	2	4	no	—
73	C₄×C₈×C₁₂₇	—	2	4	no	—
74	#95×C₁₂₇	C₂×C₄	1	4	yes	—
75	#95×C₁₂₇	C₂×C₄	1	4	yes	—
76	C₂⁴×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₂₇	—	2	2	no	—
78	C₂²×C₄×C₁₂₇	—	2	4	no	—
79	C₂²×C₄×C₁₂₇	—	2	2	no	—
80	C₂²×C₄×C₁₂₇	—	4	2	no	—
81	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₂₇	C₂×Q₈	1	2	yes	—
89	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
90	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
91	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
92	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
93	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
94	M₁₆×C₁₂₇	—	2	8	no	—
95	M₁₆×C₁₂₇	—	4	4	no	—
96	C₂×C₈×C₁₂₇	—	2	8	no	—
97	C₂×C₈×C₁₂₇	—	2	2	no	—
98	C₂×C₈×C₁₂₇	—	2	1	no	—
99	C₂×C₈×C₁₂₇	—	2	1	no	—
100	C₂×C₈×C₁₂₇	—	2	1	no	—
101	C₂×C₈×C₁₂₇	—	2	1	no	—
102	C₂×C₈×C₁₂₇	—	2	2	no	—
103	C₂×C₈×C₁₂₇	—	2	2	no	—
104	C₂×C₈×C₁₂₇	—	2	2	no	—
105	C₂×C₈×C₁₂₇	—	2	2	no	—
106	C₂×C₈×C₁₂₇	—	2	2	no	—
107	C₂×C₈×C₁₂₇	—	2	2	no	—
108	C₂×C₈×C₁₂₇	—	2	2	no	—
109	C₂×C₈×C₁₂₇	—	4	4	no	—
110	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₁₂₇	C₂×Q₈	1	4	yes	—
113	C₄⋊C₄×C₁₂₇	—	2	4	no	—
114	C₄⋊C₄×C₁₂₇	—	2	2	no	—
115	C₄⋊C₄×C₁₂₇	—	2	2	no	—
116	C₄⋊C₄×C₁₂₇	—	2	8	no	—
117	C₄⋊C₄×C₁₂₇	—	4	4	no	—
118	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
119	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
120	C₄²×C₁₂₇	—	2	4	no	—
121	C₄²×C₁₂₇	—	2	2	no	—
122	C₄²×C₁₂₇	—	2	2	no	—
123	C₄²×C₁₂₇	—	2	2	no	—
124	C₄²×C₁₂₇	—	2	2	no	—
125	C₄²×C₁₂₇	—	2	2	no	—
126	C₄²×C₁₂₇	—	2	2	no	—
127	C₂³×C₁₂₇	—	2	2	no	—
128	C₂³×C₁₂₇	—	2	2	no	—
129	C₂³×C₁₂₇	#117	1	2	yes	—
130	C₂³×C₁₂₇	C₄×D₄	1	2	yes	—
131	C₂³×C₁₂₇	C₄×Q₈	1	2	yes	—
132	C₂³×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₂₇	—	2	8	no	—
134	C₂×C₄×C₁₂₇	—	2	2	no	—
135	C₂×C₄×C₁₂₇	—	2	2	no	—
136	C₂×C₄×C₁₂₇	—	2	4	no	—
137	C₂×C₄×C₁₂₇	—	2	2	no	—
138	C₂×C₄×C₁₂₇	—	2	2	no	—
139	C₂×C₄×C₁₂₇	—	2	2	no	—
140	C₂×C₄×C₁₂₇	—	2	4	no	—
141	C₂×C₄×C₁₂₇	—	2	4	no	—
142	C₂×C₄×C₁₂₇	—	2	2	no	—
143	C₂×C₄×C₁₂₇	—	2	4	no	—
144	C₂×C₄×C₁₂₇	—	2	4	no	—
145	C₂×C₄×C₁₂₇	—	2	2	no	—
146	C₂×C₄×C₁₂₇	—	4	4	no	—
147	C₂×C₄×C₁₂₇	#117	1	2	yes	—
148	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₁₂₇	C₄×Q₈	1	2	yes	—
150	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	4	yes	—
151	C₂×C₄×C₁₂₇	#123	1	4	yes	—
152	C₂×C₄×C₁₂₇	#125	1	4	yes	—
153	C₂×C₄×C₁₂₇	#126	1	4	yes	—
154	C₂×C₄×C₁₂₇	#131	1	4	yes	—
155	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₂₇	C₂²×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
161	C₈×C₁₂₇	—	2	4	no	—
162	C₈×C₁₂₇	—	2	2	no	—
163	C₈×C₁₂₇	—	2	2	no	—
164	C₈×C₁₂₇	—	4	2	no	—
165	C₈×C₁₂₇	—	4	2	no	—
166	C₂²×C₁₂₇	—	2	4	no	—
167	C₂²×C₁₂₇	—	2	2	no	—
168	C₂²×C₁₂₇	—	2	2	no	—
169	C₂²×C₁₂₇	—	2	4	no	—
170	C₂²×C₁₂₇	#387	1	4	yes	—
171	C₂²×C₁₂₇	C₂×#117	1	1	yes	characteristic
172	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
173	C₂²×C₁₂₇	C₂×C₄×Q₈	1	1	yes	characteristic
174	C₂²×C₁₂₇	C₂×#131	1	2	yes	—
175	C₂²×C₁₂₇	#568	1	2	yes	—
176	C₄×C₁₂₇	—	2	4	no	—
177	C₄×C₁₂₇	—	4	4	no	—
178	C₄×C₁₂₇	—	4	2	no	—
179	C₄×C₁₂₇	—	4	2	no	—
180	C₄×C₁₂₇	—	4	2	no	—
181	C₄×C₁₂₇	#387	1	4	yes	—
182	C₄×C₁₂₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
183	C₄×C₁₂₇	C₂×#123	1	1	yes	characteristic
184	C₄×C₁₂₇	C₂×#125	1	1	yes	characteristic
185	C₄×C₁₂₇	C₂×#126	1	1	yes	characteristic
186	#21024	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂×C₁₂₇	—	2	4	no	—
188	C₂×C₁₂₇	C₂×#387	1	1	yes	characteristic
189	C₂×C₁₂₇	#2925	1	2	yes	—
190	C₂×C₁₂₇	#2929	1	1	yes	characteristic
191	C₂×C₁₂₇	#2930	1	1	yes	characteristic
192	C₂×C₁₂₇	#2962	1	2	yes	—
193	C₂²×C₄⋊C₈	C₂×C₁₂₇	1	1	yes	characteristic
194	C₂×#405	C₂×C₁₂₇	1	1	yes	characteristic
195	#2296	C₂×C₁₂₇	1	1	yes	characteristic
196	#1917	C₂×C₁₂₇	1	4	yes	complemented
197	#1916	C₂×C₁₂₇	1	4	yes	complemented
198	#1729	C₂×C₁₂₇	1	1	yes	characteristic
199	#1729	C₂×C₁₂₇	1	1	yes	characteristic
200	#1729	C₂×C₁₂₇	1	1	yes	characteristic
201	#1728	C₂×C₁₂₇	1	1	yes	characteristic
202	C₁₂₇	#21024	1	1	yes	characteristic, direct product factor, Sylow
203	C₂²×M₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
204	C₂²×M₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
205	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
206	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
207	C₂×#117	C₂²×C₁₂₇	1	1	yes	characteristic
208	C₂×#117	C₂²×C₁₂₇	1	1	yes	characteristic
209	C₂²×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
210	C₂×C₄⋊C₈	—	2	4	no	—
211	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
212	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
213	#405	—	2	4	no	—
214	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
215	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
216	#389	C₄×C₁₂₇	1	2	yes	—
217	#389	C₄×C₁₂₇	1	2	yes	—
218	#385	C₄×C₁₂₇	1	2	yes	—
219	#385	C₄×C₁₂₇	1	2	yes	—
220	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	4	yes	—
221	#336	C₂²×C₁₂₇	1	2	yes	—
222	#336	C₂²×C₁₂₇	1	4	yes	—
223	#336	C₂²×C₁₂₇	1	4	yes	—
224	#336	C₂²×C₁₂₇	1	4	yes	—
225	#336	C₂²×C₁₂₇	1	2	yes	—
226	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
227	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
228	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	Q₈×C₁₂₇	1	4	yes	—
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	—	2	2	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	D₄×C₁₂₇	1	4	yes	—
241	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
242	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
243	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
246	#117	—	2	2	no	—
247	#117	—	2	2	no	—
248	#117	—	2	2	no	—
249	#117	—	2	2	no	—
250	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
251	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
254	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
255	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
256	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	C₂×C₄×C₁₂₇	1	2	yes	—
260	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
261	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
262	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
263	C₄⋊C₈	—	2	4	no	—
264	C₄⋊C₈	—	2	4	no	—
265	#97	—	2	4	no	—
266	C₄×C₈	—	2	4	no	—
267	#95	C₂×C₄×C₁₂₇	1	4	yes	—
268	#95	C₂×C₄×C₁₂₇	1	4	yes	—
269	C₂⁴	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
276	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
277	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
278	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
279	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
281	C₂²×C₄	C₂×Q₈×C₁₂₇	1	2	yes	—
282	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
283	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
284	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
285	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
286	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
287	M₁₆	—	2	8	no	—
288	M₁₆	—	4	4	no	—
289	C₂×C₈	—	2	8	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	4	4	no	—
303	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
304	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
305	C₂×C₈	C₂×Q₈×C₁₂₇	1	4	yes	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	—	4	4	no	—
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	—	2	4	no	—
313	C₄²	—	2	4	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	#117×C₁₂₇	1	2	yes	—
323	C₂³	C₄×D₄×C₁₂₇	1	2	yes	—
324	C₂³	C₄×Q₈×C₁₂₇	1	2	yes	—
325	C₂³	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	#117×C₁₂₇	1	2	yes	—
341	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
342	C₂×C₄	C₄×Q₈×C₁₂₇	1	2	yes	—
343	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	4	yes	—
344	C₂×C₄	#123×C₁₂₇	1	4	yes	—
345	C₂×C₄	#125×C₁₂₇	1	4	yes	—
346	C₂×C₄	#126×C₁₂₇	1	4	yes	—
347	C₂×C₄	#131×C₁₂₇	1	4	yes	—
348	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
349	C₂×C₄	C₂²×Q₈×C₁₂₇	1	1	yes	characteristic
350	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
351	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
352	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
353	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
354	C₈	—	2	4	no	—
355	C₈	—	2	2	no	—
356	C₈	—	2	2	no	—
357	C₈	—	4	2	no	—
358	C₈	—	4	2	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	4	no	—
363	C₂²	#387×C₁₂₇	1	4	yes	—
364	C₂²	C₂×#117×C₁₂₇	1	1	yes	characteristic
365	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
366	C₂²	C₂×C₄×Q₈×C₁₂₇	1	1	yes	characteristic
367	C₂²	C₂×#131×C₁₂₇	1	2	yes	—
368	C₂²	#568×C₁₂₇	1	2	yes	—
369	C₄	—	2	4	no	—
370	C₄	—	4	4	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	2	no	—
374	C₄	#387×C₁₂₇	1	4	yes	—
375	C₄	C₂×C₂²⋊Q₈×C₁₂₇	1	1	yes	characteristic
376	C₄	C₂×#123×C₁₂₇	1	1	yes	characteristic
377	C₄	C₂×#125×C₁₂₇	1	1	yes	characteristic
378	C₄	C₂×#126×C₁₂₇	1	1	yes	characteristic
379	C₂	—	2	4	no	—
380	C₂	C₂×#387×C₁₂₇	1	1	yes	characteristic
381	C₂	C₁₂₇×#2925	1	2	yes	—
382	C₂	C₁₂₇×#2929	1	1	yes	characteristic
383	C₂	C₁₂₇×#2930	1	1	yes	characteristic
384	C₂	C₁₂₇×#2962	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₁₂₇×#1917	C₂	semidirect
5. C₁₂₇×#1916	C₂	semidirect
186. #21024	C₁₂₇	direct (N × H)
196. #1917	C₂×C₁₂₇	semidirect
197. #1916	C₂×C₁₂₇	semidirect
202. C₁₂₇	#21024	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×C₄⋊C₈×C₁₂₇	2
C₂×#405×C₁₂₇	2
C₁₂₇×#2296	2
C₁₂₇×#1917	2
C₁₂₇×#1916	2
C₁₂₇×#1729	2
C₁₂₇×#1728	2
#21024	127

Subgroups — C127×#21024 #44584697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#21024 #44584697