Subgroups — C₁₂₇×#14151 #44577824

Order 32512.

1630 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#389×C₁₂₇	C₂	1	4	yes	maximal
2	C₂×#384×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₁₂₇	C₂	1	2	yes	maximal
4	C₁₂₇×#1441	C₂	1	4	yes	maximal
5	C₁₂₇×C₄⋊#95	C₂	1	4	yes	maximal
6	C₂²×C₄⋊C₄×C₁₂₇	C₂²	1	4	yes	—
7	C₂²×C₄⋊C₄×C₁₂₇	C₂²	1	4	yes	—
8	C₂²×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₂₇	C₂²	1	4	yes	—
12	C₂²×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
13	#389×C₁₂₇	—	2	16	no	—
14	#384×C₁₂₇	C₄	1	8	yes	complemented
15	C₄×C₄⋊C₄×C₁₂₇	—	2	8	no	—
16	C₂×#95×C₁₂₇	C₂²	1	8	yes	—
17	C₂×#95×C₁₂₇	C₂²	1	4	yes	—
18	C₂×#95×C₁₂₇	C₂²	1	4	yes	—
19	C₂³×C₄×C₁₂₇	C₂³	1	4	yes	—
20	C₂³×C₄×C₁₂₇	C₂³	1	4	yes	—
21	C₂³×C₄×C₁₂₇	C₂³	1	4	yes	—
22	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
23	C₂³×C₄×C₁₂₇	C₂³	1	2	yes	—
24	C₂×C₄⋊C₄×C₁₂₇	—	2	4	no	—
25	C₂×C₄⋊C₄×C₁₂₇	—	2	4	no	—
26	C₂×C₄⋊C₄×C₁₂₇	—	2	8	no	—
27	C₂×C₄⋊C₄×C₁₂₇	—	2	8	no	—
28	C₂×C₄⋊C₄×C₁₂₇	—	2	4	no	—
29	C₂×C₄⋊C₄×C₁₂₇	—	2	4	no	—
30	C₂×C₄⋊C₄×C₁₂₇	—	2	16	no	—
31	C₂×C₄⋊C₄×C₁₂₇	—	4	2	no	—
32	C₂×C₄⋊C₄×C₁₂₇	—	4	2	no	—
33	C₂×C₄⋊C₄×C₁₂₇	—	4	4	no	—
34	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	16	yes	—
35	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	8	yes	—
36	C₂×C₄⋊C₄×C₁₂₇	D₄	1	8	yes	—
37	C₂×C₄⋊C₄×C₁₂₇	Q₈	1	8	yes	—
38	C₂×C₄²×C₁₂₇	—	2	8	no	—
39	C₂×C₄²×C₁₂₇	—	2	8	no	—
40	C₂×C₄²×C₁₂₇	—	2	8	no	—
41	C₂×C₄²×C₁₂₇	C₂×C₄	1	4	yes	—
42	C₂×C₄²×C₁₂₇	D₄	1	4	yes	—
43	C₂×C₄²×C₁₂₇	Q₈	1	4	yes	—
44	#95×C₁₂₇	—	2	8	no	—
45	#95×C₁₂₇	—	2	16	no	—
46	#95×C₁₂₇	—	4	4	no	—
47	C₂⁴×C₁₂₇	C₂⁴	1	1	yes	characteristic
48	C₂²×C₄×C₁₂₇	—	2	1	no	—
49	C₂²×C₄×C₁₂₇	—	2	1	no	—
50	C₂²×C₄×C₁₂₇	—	2	1	no	—
51	C₂²×C₄×C₁₂₇	—	2	1	no	—
52	C₂²×C₄×C₁₂₇	—	2	4	no	—
53	C₂²×C₄×C₁₂₇	—	2	4	no	—
54	C₂²×C₄×C₁₂₇	—	2	4	no	—
55	C₂²×C₄×C₁₂₇	—	2	8	no	—
56	C₂²×C₄×C₁₂₇	—	2	4	no	—
57	C₂²×C₄×C₁₂₇	—	2	4	no	—
58	C₂²×C₄×C₁₂₇	—	2	4	no	—
59	C₂²×C₄×C₁₂₇	—	2	8	no	—
60	C₂²×C₄×C₁₂₇	—	2	4	no	—
61	C₂²×C₄×C₁₂₇	—	2	4	no	—
62	C₂²×C₄×C₁₂₇	—	2	4	no	—
63	C₂²×C₄×C₁₂₇	—	2	4	no	—
64	C₂²×C₄×C₁₂₇	—	2	4	no	—
65	C₂²×C₄×C₁₂₇	—	2	4	no	—
66	C₂²×C₄×C₁₂₇	—	2	4	no	—
67	C₂²×C₄×C₁₂₇	—	2	4	no	—
68	C₂²×C₄×C₁₂₇	C₂²×C₄	1	8	yes	—
69	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
70	C₂²×C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
71	C₂²×C₄×C₁₂₇	C₂×D₄	1	8	yes	—
72	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
73	C₂²×C₄×C₁₂₇	C₂×D₄	1	4	yes	—
74	C₂²×C₄×C₁₂₇	C₂×D₄	1	4	yes	—
75	C₂²×C₄×C₁₂₇	C₂×Q₈	1	8	yes	—
76	C₂²×C₄×C₁₂₇	C₂×Q₈	1	2	yes	—
77	C₂²×C₄×C₁₂₇	C₂×Q₈	1	4	yes	—
78	C₂²×C₄×C₁₂₇	C₂×Q₈	1	4	yes	—
79	C₂²×C₄×C₁₂₇	#41	1	4	yes	—
80	C₂²×C₄×C₁₂₇	#41	1	4	yes	—
81	C₄⋊C₄×C₁₂₇	—	2	32	no	—
82	C₄⋊C₄×C₁₂₇	—	2	16	no	—
83	C₄⋊C₄×C₁₂₇	—	2	16	no	—
84	C₄⋊C₄×C₁₂₇	—	4	8	no	—
85	C₄⋊C₄×C₁₂₇	—	4	16	no	—
86	C₄²×C₁₂₇	—	4	16	no	—
87	C₄²×C₁₂₇	C₄⋊C₄	1	16	yes	complemented
88	C₂³×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
89	C₂³×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
90	C₂³×C₁₂₇	C₂²×D₄	1	2	yes	—
91	C₂³×C₁₂₇	C₂²×Q₈	1	1	yes	characteristic
92	C₂³×C₁₂₇	C₂²×Q₈	1	2	yes	—
93	C₂³×C₁₂₇	C₂×#41	1	2	yes	—
94	C₂³×C₁₂₇	C₂×#41	1	2	yes	—
95	C₂³×C₁₂₇	H(5,𝔽₂)	1	1	yes	characteristic
96	C₂³×C₁₂₇	H(5,𝔽₂)	1	1	yes	characteristic
97	C₂³×C₁₂₇	2₋¹⁺⁴	1	1	yes	characteristic
98	C₂³×C₁₂₇	2₋¹⁺⁴	1	1	yes	characteristic
99	C₂×C₄×C₁₂₇	—	2	2	no	—
100	C₂×C₄×C₁₂₇	—	2	2	no	—
101	C₂×C₄×C₁₂₇	—	2	2	no	—
102	C₂×C₄×C₁₂₇	—	2	2	no	—
103	C₂×C₄×C₁₂₇	—	2	2	no	—
104	C₂×C₄×C₁₂₇	—	2	2	no	—
105	C₂×C₄×C₁₂₇	—	2	16	no	—
106	C₂×C₄×C₁₂₇	—	2	8	no	—
107	C₂×C₄×C₁₂₇	—	2	8	no	—
108	C₂×C₄×C₁₂₇	—	2	8	no	—
109	C₂×C₄×C₁₂₇	—	2	8	no	—
110	C₂×C₄×C₁₂₇	—	2	8	no	—
111	C₂×C₄×C₁₂₇	—	2	8	no	—
112	C₂×C₄×C₁₂₇	—	2	8	no	—
113	C₂×C₄×C₁₂₇	—	4	4	no	—
114	C₂×C₄×C₁₂₇	—	4	4	no	—
115	C₂×C₄×C₁₂₇	—	4	4	no	—
116	C₂×C₄×C₁₂₇	—	4	4	no	—
117	C₂×C₄×C₁₂₇	—	4	4	no	—
118	C₂×C₄×C₁₂₇	—	4	4	no	—
119	C₂×C₄×C₁₂₇	—	4	8	no	—
120	C₂×C₄×C₁₂₇	—	4	4	no	—
121	C₂×C₄×C₁₂₇	—	4	4	no	—
122	C₂×C₄×C₁₂₇	—	4	4	no	—
123	C₂×C₄×C₁₂₇	—	4	4	no	—
124	C₂×C₄×C₁₂₇	C₂×C₄⋊C₄	1	4	yes	—
125	C₂×C₄×C₁₂₇	C₂×C₄⋊C₄	1	8	yes	—
126	C₂×C₄×C₁₂₇	C₄×D₄	1	8	yes	—
127	C₂×C₄×C₁₂₇	C₄×Q₈	1	8	yes	—
128	C₂×C₄×C₁₂₇	#121	1	8	yes	—
129	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	8	yes	—
130	C₂×C₄×C₁₂₇	#125	1	8	yes	—
131	C₂×C₄×C₁₂₇	C₄⋊Q₈	1	8	yes	—
132	C₂²×C₁₂₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
133	C₂²×C₁₂₇	C₂×C₄×D₄	1	2	yes	—
134	C₂²×C₁₂₇	C₂×C₄×Q₈	1	2	yes	—
135	C₂²×C₁₂₇	#518	1	1	yes	characteristic
136	C₂²×C₁₂₇	#519	1	1	yes	characteristic
137	C₂²×C₁₂₇	C₂×#121	1	2	yes	—
138	C₂²×C₁₂₇	C₂×C₂²⋊Q₈	1	2	yes	—
139	C₂²×C₁₂₇	C₂×#125	1	2	yes	—
140	C₂²×C₁₂₇	C₂×C₄⋊Q₈	1	2	yes	—
141	C₂²×C₁₂₇	#537	1	1	yes	characteristic
142	C₂²×C₁₂₇	#537	1	1	yes	characteristic
143	C₂²×C₁₂₇	#544	1	1	yes	characteristic
144	C₂²×C₁₂₇	#544	1	1	yes	characteristic
145	C₂²×C₁₂₇	D₄²	1	1	yes	characteristic
146	C₂²×C₁₂₇	#547	1	2	yes	—
147	C₂²×C₁₂₇	D₄×Q₈	1	2	yes	—
148	C₂²×C₁₂₇	#550	1	2	yes	—
149	C₂²×C₁₂₇	#554	1	2	yes	—
150	C₂²×C₁₂₇	#555	1	1	yes	characteristic
151	C₂²×C₁₂₇	#556	1	2	yes	—
152	C₂²×C₁₂₇	#557	1	2	yes	—
153	C₂²×C₁₂₇	Q₈²	1	1	yes	characteristic
154	C₂²×C₁₂₇	#559	1	1	yes	characteristic
155	C₄×C₁₂₇	—	2	4	no	—
156	C₄×C₁₂₇	—	4	8	no	—
157	C₄×C₁₂₇	—	4	8	no	—
158	C₄×C₁₂₇	—	4	8	no	—
159	C₄×C₁₂₇	#389	1	16	yes	complemented
160	#14151	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂×C₁₂₇	C₂×#389	1	2	yes	—
162	C₂×C₁₂₇	#2316	1	1	yes	characteristic
163	C₂×C₁₂₇	#2365	1	2	yes	—
164	C₂×C₁₂₇	#2366	1	1	yes	characteristic
165	C₂×C₁₂₇	#2369	1	1	yes	characteristic
166	C₂×C₁₂₇	#2537	1	1	yes	characteristic
167	C₂×C₁₂₇	#2538	1	2	yes	—
168	C₂×C₁₂₇	#2551	1	1	yes	characteristic
169	C₂×C₁₂₇	#2552	1	2	yes	—
170	C₂×C₁₂₇	#2571	1	1	yes	characteristic
171	C₂×C₁₂₇	#2582	1	1	yes	characteristic
172	C₂×#389	C₂×C₁₂₇	1	4	yes	—
173	C₂×#384	C₂×C₁₂₇	1	1	yes	characteristic
174	C₂×C₄×C₄⋊C₄	C₂×C₁₂₇	1	2	yes	—
175	#1441	C₂×C₁₂₇	1	4	yes	—
176	C₄⋊#95	C₂×C₁₂₇	1	4	yes	—
177	C₁₂₇	#14151	1	1	yes	characteristic, direct product factor, Sylow
178	C₂²×C₄⋊C₄	C₂²×C₁₂₇	1	4	yes	—
179	C₂²×C₄⋊C₄	C₂²×C₁₂₇	1	4	yes	—
180	C₂²×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
181	C₂²×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
182	C₂²×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
183	C₂²×C₄²	C₂²×C₁₂₇	1	4	yes	—
184	C₂²×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
185	#389	—	2	16	no	—
186	#384	C₄×C₁₂₇	1	8	yes	complemented
187	C₄×C₄⋊C₄	—	2	8	no	—
188	C₂×#95	C₂²×C₁₂₇	1	8	yes	—
189	C₂×#95	C₂²×C₁₂₇	1	4	yes	—
190	C₂×#95	C₂²×C₁₂₇	1	4	yes	—
191	C₂³×C₄	C₂³×C₁₂₇	1	4	yes	—
192	C₂³×C₄	C₂³×C₁₂₇	1	4	yes	—
193	C₂³×C₄	C₂³×C₁₂₇	1	4	yes	—
194	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
195	C₂³×C₄	C₂³×C₁₂₇	1	2	yes	—
196	C₂×C₄⋊C₄	—	2	4	no	—
197	C₂×C₄⋊C₄	—	2	4	no	—
198	C₂×C₄⋊C₄	—	2	8	no	—
199	C₂×C₄⋊C₄	—	2	8	no	—
200	C₂×C₄⋊C₄	—	2	4	no	—
201	C₂×C₄⋊C₄	—	2	4	no	—
202	C₂×C₄⋊C₄	—	2	16	no	—
203	C₂×C₄⋊C₄	—	4	2	no	—
204	C₂×C₄⋊C₄	—	4	2	no	—
205	C₂×C₄⋊C₄	—	4	4	no	—
206	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	16	yes	—
207	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	8	yes	—
208	C₂×C₄⋊C₄	D₄×C₁₂₇	1	8	yes	—
209	C₂×C₄⋊C₄	Q₈×C₁₂₇	1	8	yes	—
210	C₂×C₄²	—	2	8	no	—
211	C₂×C₄²	—	2	8	no	—
212	C₂×C₄²	—	2	8	no	—
213	C₂×C₄²	C₂×C₄×C₁₂₇	1	4	yes	—
214	C₂×C₄²	D₄×C₁₂₇	1	4	yes	—
215	C₂×C₄²	Q₈×C₁₂₇	1	4	yes	—
216	#95	—	2	8	no	—
217	#95	—	2	16	no	—
218	#95	—	4	4	no	—
219	C₂⁴	C₂⁴×C₁₂₇	1	1	yes	characteristic
220	C₂²×C₄	—	2	1	no	—
221	C₂²×C₄	—	2	1	no	—
222	C₂²×C₄	—	2	1	no	—
223	C₂²×C₄	—	2	1	no	—
224	C₂²×C₄	—	2	4	no	—
225	C₂²×C₄	—	2	4	no	—
226	C₂²×C₄	—	2	4	no	—
227	C₂²×C₄	—	2	8	no	—
228	C₂²×C₄	—	2	4	no	—
229	C₂²×C₄	—	2	4	no	—
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	2	8	no	—
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	—	2	4	no	—
234	C₂²×C₄	—	2	4	no	—
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	C₂²×C₄×C₁₂₇	1	8	yes	—
241	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
242	C₂²×C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
243	C₂²×C₄	C₂×D₄×C₁₂₇	1	8	yes	—
244	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
245	C₂²×C₄	C₂×D₄×C₁₂₇	1	4	yes	—
246	C₂²×C₄	C₂×D₄×C₁₂₇	1	4	yes	—
247	C₂²×C₄	C₂×Q₈×C₁₂₇	1	8	yes	—
248	C₂²×C₄	C₂×Q₈×C₁₂₇	1	2	yes	—
249	C₂²×C₄	C₂×Q₈×C₁₂₇	1	4	yes	—
250	C₂²×C₄	C₂×Q₈×C₁₂₇	1	4	yes	—
251	C₂²×C₄	#41×C₁₂₇	1	4	yes	—
252	C₂²×C₄	#41×C₁₂₇	1	4	yes	—
253	C₄⋊C₄	—	2	32	no	—
254	C₄⋊C₄	—	2	16	no	—
255	C₄⋊C₄	—	2	16	no	—
256	C₄⋊C₄	—	4	8	no	—
257	C₄⋊C₄	—	4	16	no	—
258	C₄²	—	4	16	no	—
259	C₄²	C₄⋊C₄×C₁₂₇	1	16	yes	complemented
260	C₂³	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
261	C₂³	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
262	C₂³	C₂²×D₄×C₁₂₇	1	2	yes	—
263	C₂³	C₂²×Q₈×C₁₂₇	1	1	yes	characteristic
264	C₂³	C₂²×Q₈×C₁₂₇	1	2	yes	—
265	C₂³	C₂×#41×C₁₂₇	1	2	yes	—
266	C₂³	C₂×#41×C₁₂₇	1	2	yes	—
267	C₂³	H(5,𝔽₂)×C₁₂₇	1	1	yes	characteristic
268	C₂³	H(5,𝔽₂)×C₁₂₇	1	1	yes	characteristic
269	C₂³	2₋¹⁺⁴×C₁₂₇	1	1	yes	characteristic
270	C₂³	2₋¹⁺⁴×C₁₂₇	1	1	yes	characteristic
271	C₂×C₄	—	2	2	no	—
272	C₂×C₄	—	2	2	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	16	no	—
278	C₂×C₄	—	2	8	no	—
279	C₂×C₄	—	2	8	no	—
280	C₂×C₄	—	2	8	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	8	no	—
283	C₂×C₄	—	2	8	no	—
284	C₂×C₄	—	2	8	no	—
285	C₂×C₄	—	4	4	no	—
286	C₂×C₄	—	4	4	no	—
287	C₂×C₄	—	4	4	no	—
288	C₂×C₄	—	4	4	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	—	4	4	no	—
291	C₂×C₄	—	4	8	no	—
292	C₂×C₄	—	4	4	no	—
293	C₂×C₄	—	4	4	no	—
294	C₂×C₄	—	4	4	no	—
295	C₂×C₄	—	4	4	no	—
296	C₂×C₄	C₂×C₄⋊C₄×C₁₂₇	1	4	yes	—
297	C₂×C₄	C₂×C₄⋊C₄×C₁₂₇	1	8	yes	—
298	C₂×C₄	C₄×D₄×C₁₂₇	1	8	yes	—
299	C₂×C₄	C₄×Q₈×C₁₂₇	1	8	yes	—
300	C₂×C₄	#121×C₁₂₇	1	8	yes	—
301	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	8	yes	—
302	C₂×C₄	#125×C₁₂₇	1	8	yes	—
303	C₂×C₄	C₄⋊Q₈×C₁₂₇	1	8	yes	—
304	C₂²	C₂²×C₄⋊C₄×C₁₂₇	1	1	yes	characteristic
305	C₂²	C₂×C₄×D₄×C₁₂₇	1	2	yes	—
306	C₂²	C₂×C₄×Q₈×C₁₂₇	1	2	yes	—
307	C₂²	#518×C₁₂₇	1	1	yes	characteristic
308	C₂²	#519×C₁₂₇	1	1	yes	characteristic
309	C₂²	C₂×#121×C₁₂₇	1	2	yes	—
310	C₂²	C₂×C₂²⋊Q₈×C₁₂₇	1	2	yes	—
311	C₂²	C₂×#125×C₁₂₇	1	2	yes	—
312	C₂²	C₂×C₄⋊Q₈×C₁₂₇	1	2	yes	—
313	C₂²	#537×C₁₂₇	1	1	yes	characteristic
314	C₂²	#537×C₁₂₇	1	1	yes	characteristic
315	C₂²	#544×C₁₂₇	1	1	yes	characteristic
316	C₂²	#544×C₁₂₇	1	1	yes	characteristic
317	C₂²	D₄²×C₁₂₇	1	1	yes	characteristic
318	C₂²	#547×C₁₂₇	1	2	yes	—
319	C₂²	D₄×Q₈×C₁₂₇	1	2	yes	—
320	C₂²	#550×C₁₂₇	1	2	yes	—
321	C₂²	#554×C₁₂₇	1	2	yes	—
322	C₂²	#555×C₁₂₇	1	1	yes	characteristic
323	C₂²	#556×C₁₂₇	1	2	yes	—
324	C₂²	#557×C₁₂₇	1	2	yes	—
325	C₂²	Q₈²×C₁₂₇	1	1	yes	characteristic
326	C₂²	#559×C₁₂₇	1	1	yes	characteristic
327	C₄	—	2	4	no	—
328	C₄	—	4	8	no	—
329	C₄	—	4	8	no	—
330	C₄	—	4	8	no	—
331	C₄	#389×C₁₂₇	1	16	yes	complemented
332	C₂	C₂×#389×C₁₂₇	1	2	yes	—
333	C₂	C₁₂₇×#2316	1	1	yes	characteristic
334	C₂	C₁₂₇×#2365	1	2	yes	—
335	C₂	C₁₂₇×#2366	1	1	yes	characteristic
336	C₂	C₁₂₇×#2369	1	1	yes	characteristic
337	C₂	C₁₂₇×#2537	1	1	yes	characteristic
338	C₂	C₁₂₇×#2538	1	2	yes	—
339	C₂	C₁₂₇×#2551	1	1	yes	characteristic
340	C₂	C₁₂₇×#2552	1	2	yes	—
341	C₂	C₁₂₇×#2571	1	1	yes	characteristic
342	C₂	C₁₂₇×#2582	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
14. #384×C₁₂₇	C₄	semidirect
87. C₄²×C₁₂₇	C₄⋊C₄	semidirect
159. C₄×C₁₂₇	#389	semidirect
160. #14151	C₁₂₇	direct (N × H)
177. C₁₂₇	#14151	direct (N × H)
186. #384	C₄×C₁₂₇	semidirect
259. C₄²	C₄⋊C₄×C₁₂₇	semidirect
331. C₄	#389×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#389×C₁₂₇	2
C₂×#384×C₁₂₇	2
C₂×C₄×C₄⋊C₄×C₁₂₇	2
C₁₂₇×#1441	2
C₁₂₇×C₄⋊#95	2
#14151	127

Subgroups — C127×#14151 #44577824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#14151 #44577824