Subgroups — C₂×C₁₂₇×#1687 #44582804

Order 32512.

926 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#493×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#459×C₁₂₇	C₂	1	2	yes	maximal, complemented
3	C₂×#436×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₂₇×#1687	C₂	1	8	yes	maximal, direct product factor
5	C₂×#334×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#331×C₁₂₇	C₂	1	2	yes	maximal, complemented
7	C₂²×D₈×C₁₂₇	—	2	2	no	—
8	C₂²×D₈×C₁₂₇	—	2	1	no	—
9	C₂²×D₈×C₁₂₇	—	2	1	no	—
10	C₂²×M₁₆×C₁₂₇	—	2	1	no	—
11	C₂×#127×C₁₂₇	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
13	#493×C₁₂₇	—	2	2	no	—
14	#493×C₁₂₇	C₂²	1	4	yes	complemented
15	#459×C₁₂₇	—	2	4	no	—
16	#459×C₁₂₇	C₂²	1	8	yes	complemented
17	#436×C₁₂₇	—	2	2	no	—
18	#436×C₁₂₇	C₂²	1	4	yes	complemented
19	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
21	C₂×#102×C₁₂₇	—	2	2	no	—
22	C₂×C₂²⋊C₈×C₁₂₇	—	2	1	no	—
23	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
24	#334×C₁₂₇	C₂²	1	4	yes	complemented
25	#331×C₁₂₇	C₂²	1	8	yes	complemented
26	C₂²×D₄×C₁₂₇	—	2	2	no	—
27	C₂²×D₄×C₁₂₇	—	2	2	no	—
28	C₂²×D₄×C₁₂₇	—	2	2	no	—
29	C₂²×D₄×C₁₂₇	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₂₇	—	2	1	no	—
31	C₂×D₈×C₁₂₇	—	2	8	no	—
32	C₂×D₈×C₁₂₇	—	2	4	no	—
33	C₂×D₈×C₁₂₇	—	2	4	no	—
34	C₂×D₈×C₁₂₇	—	4	4	no	—
35	C₂×D₈×C₁₂₇	—	4	8	no	—
36	C₂×D₈×C₁₂₇	—	4	4	no	—
37	C₂×M₁₆×C₁₂₇	—	2	4	no	—
38	C₂×M₁₆×C₁₂₇	—	4	4	no	—
39	C₂²×C₈×C₁₂₇	—	2	1	no	—
40	C₂²×C₈×C₁₂₇	—	2	2	no	—
41	C₂²×C₈×C₁₂₇	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₂₇	D₄	1	1	yes	characteristic
43	#127×C₁₂₇	—	2	2	no	—
44	#127×C₁₂₇	—	2	2	no	—
45	#127×C₁₂₇	—	2	2	no	—
46	#127×C₁₂₇	C₂³	1	4	yes	—
47	C₄×D₄×C₁₂₇	—	2	1	no	—
48	C₄×D₄×C₁₂₇	—	2	1	no	—
49	C₄×D₄×C₁₂₇	D₄	1	2	yes	—
50	C₄×D₄×C₁₂₇	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₂₇	D₄	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₁₂₇	—	2	1	no	—
53	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₁₂₇	—	2	1	no	—
55	C₄⋊C₈×C₁₂₇	—	2	2	no	—
56	C₄⋊C₈×C₁₂₇	C₂³	1	2	yes	—
57	C₄⋊C₈×C₁₂₇	C₂³	1	4	yes	—
58	#102×C₁₂₇	—	2	8	no	—
59	C₂²⋊C₈×C₁₂₇	—	2	4	no	—
60	C₄×C₈×C₁₂₇	D₄	1	2	yes	—
61	C₄×C₈×C₁₂₇	C₂³	1	2	yes	—
62	C₂⁴×C₁₂₇	—	2	1	no	—
63	C₂⁴×C₁₂₇	—	4	2	no	—
64	C₂×D₄×C₁₂₇	—	2	1	no	—
65	C₂×D₄×C₁₂₇	—	2	4	no	—
66	C₂×D₄×C₁₂₇	—	2	4	no	—
67	C₂×D₄×C₁₂₇	—	2	4	no	—
68	C₂×D₄×C₁₂₇	—	2	4	no	—
69	C₂×D₄×C₁₂₇	—	4	2	no	—
70	C₂×D₄×C₁₂₇	—	4	2	no	—
71	C₂×D₄×C₁₂₇	—	4	2	no	—
72	C₂×D₄×C₁₂₇	—	4	4	no	—
73	C₂×D₄×C₁₂₇	—	4	4	no	—
74	C₂×D₄×C₁₂₇	—	4	4	no	—
75	C₂×D₄×C₁₂₇	—	4	4	no	—
76	C₂×D₄×C₁₂₇	—	8	4	no	—
77	C₂×D₄×C₁₂₇	C₂×D₄	1	2	yes	—
78	C₂²×C₄×C₁₂₇	—	2	1	no	—
79	C₂²×C₄×C₁₂₇	—	2	2	no	—
80	C₂²×C₄×C₁₂₇	—	2	2	no	—
81	C₂²×C₄×C₁₂₇	—	4	2	no	—
82	C₂²×C₄×C₁₂₇	—	4	2	no	—
83	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₂₇	#41	1	1	yes	characteristic
86	D₈×C₁₂₇	—	4	8	no	—
87	D₈×C₁₂₇	—	4	16	no	—
88	D₈×C₁₂₇	—	4	8	no	—
89	M₁₆×C₁₂₇	—	4	8	no	—
90	C₂×C₈×C₁₂₇	—	2	2	no	—
91	C₂×C₈×C₁₂₇	—	2	2	no	—
92	C₂×C₈×C₁₂₇	—	2	4	no	—
93	C₂×C₈×C₁₂₇	—	4	2	no	—
94	C₂×C₈×C₁₂₇	—	4	4	no	—
95	C₂×C₈×C₁₂₇	D₈	1	4	yes	complemented
96	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
97	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
98	C₄⋊C₄×C₁₂₇	—	2	1	no	—
99	C₄⋊C₄×C₁₂₇	C₂×D₄	1	2	yes	—
100	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
101	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
102	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₁₂₇	#41	1	1	yes	characteristic
105	C₄²×C₁₂₇	C₂⁴	1	1	yes	characteristic
106	C₂³×C₁₂₇	—	2	2	no	—
107	C₂³×C₁₂₇	—	4	2	no	—
108	C₂³×C₁₂₇	—	4	2	no	—
109	C₂³×C₁₂₇	—	4	2	no	—
110	C₂³×C₁₂₇	—	4	4	no	—
111	C₂³×C₁₂₇	—	8	4	no	—
112	C₂³×C₁₂₇	—	8	4	no	—
113	C₂³×C₁₂₇	—	8	4	no	—
114	C₂³×C₁₂₇	#121	1	1	yes	characteristic
115	D₄×C₁₂₇	—	2	4	no	—
116	D₄×C₁₂₇	—	4	4	no	—
117	D₄×C₁₂₇	—	4	4	no	—
118	D₄×C₁₂₇	—	4	4	no	—
119	D₄×C₁₂₇	—	4	4	no	—
120	D₄×C₁₂₇	—	4	2	no	—
121	D₄×C₁₂₇	—	8	4	no	—
122	D₄×C₁₂₇	—	8	4	no	—
123	D₄×C₁₂₇	—	8	4	no	—
124	D₄×C₁₂₇	—	8	4	no	—
125	C₂×C₄×C₁₂₇	—	2	2	no	—
126	C₂×C₄×C₁₂₇	—	2	2	no	—
127	C₂×C₄×C₁₂₇	—	4	2	no	—
128	C₂×C₄×C₁₂₇	—	4	2	no	—
129	C₂×C₄×C₁₂₇	—	4	2	no	—
130	C₂×C₄×C₁₂₇	—	4	4	no	—
131	C₂×C₄×C₁₂₇	#121	1	1	yes	characteristic
132	C₂×C₄×C₁₂₇	#121	1	1	yes	characteristic
133	C₂×C₄×C₁₂₇	#121	1	1	yes	characteristic
134	C₂×C₄×C₁₂₇	C₂×D₈	1	2	yes	—
135	C₂×C₄×C₁₂₇	AGL(1,ℤ/8)	1	2	yes	—
136	C₂×C₄×C₁₂₇	AGL(1,ℤ/8)	1	4	yes	—
137	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
140	C₈×C₁₂₇	—	2	2	no	—
141	C₈×C₁₂₇	—	4	2	no	—
142	C₈×C₁₂₇	—	4	4	no	—
143	C₈×C₁₂₇	C₂×D₈	1	4	yes	complemented
144	C₂²×C₁₂₇	—	4	2	no	—
145	C₂²×C₁₂₇	—	4	2	no	—
146	C₂²×C₁₂₇	—	4	2	no	—
147	C₂²×C₁₂₇	—	8	4	no	—
148	C₂²×C₁₂₇	—	8	4	no	—
149	C₂²×C₁₂₇	—	8	4	no	—
150	C₂²×C₁₂₇	—	8	4	no	—
151	C₂²×C₁₂₇	—	16	8	no	—
152	C₂²×C₁₂₇	#459	1	2	yes	—
153	C₂²×C₁₂₇	#469	1	2	yes	—
154	C₂²×C₁₂₇	#472	1	2	yes	—
155	C₂²×C₁₂₇	C₂×#121	1	1	yes	characteristic
156	C₄×C₁₂₇	—	2	1	no	—
157	C₄×C₁₂₇	—	2	1	no	—
158	C₄×C₁₂₇	—	4	2	no	—
159	C₄×C₁₂₇	#459	1	2	yes	—
160	C₄×C₁₂₇	#469	1	2	yes	—
161	C₄×C₁₂₇	C₂²×D₈	1	1	yes	characteristic
162	C₄×C₁₂₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₄×C₁₂₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
164	C₂×#1687	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂×C₁₂₇	—	8	2	no	—
166	C₂×C₁₂₇	—	16	4	no	—
167	C₂×C₁₂₇	#1687	1	4	yes	direct product factor
168	C₂×C₁₂₇	C₂×#459	1	1	yes	characteristic
169	C₂×C₁₂₇	C₂×#469	1	1	yes	characteristic
170	C₂×C₁₂₇	C₂×#472	1	1	yes	characteristic
171	C₂×#493	C₂×C₁₂₇	1	1	yes	characteristic, complemented
172	C₂×#459	C₂×C₁₂₇	1	2	yes	complemented
173	C₂×#436	C₂×C₁₂₇	1	1	yes	characteristic, complemented
174	#1687	C₂×C₁₂₇	1	8	yes	direct product factor
175	C₂×#334	C₂×C₁₂₇	1	1	yes	characteristic, complemented
176	C₂×#331	C₂×C₁₂₇	1	2	yes	complemented
177	C₁₂₇	C₂×#1687	1	1	yes	characteristic, direct product factor, Sylow
178	C₂²×D₈	—	2	2	no	—
179	C₂²×D₈	—	2	1	no	—
180	C₂²×D₈	—	2	1	no	—
181	C₂²×M₁₆	—	2	1	no	—
182	C₂×#127	C₂²×C₁₂₇	1	2	yes	—
183	C₂×C₄×D₄	C₂²×C₁₂₇	1	1	yes	characteristic
184	#493	—	2	2	no	—
185	#493	C₂²×C₁₂₇	1	4	yes	complemented
186	#459	—	2	4	no	—
187	#459	C₂²×C₁₂₇	1	8	yes	complemented
188	#436	—	2	2	no	—
189	#436	C₂²×C₁₂₇	1	4	yes	complemented
190	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
191	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
192	C₂×#102	—	2	2	no	—
193	C₂×C₂²⋊C₈	—	2	1	no	—
194	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
195	#334	C₂²×C₁₂₇	1	4	yes	complemented
196	#331	C₂²×C₁₂₇	1	8	yes	complemented
197	C₂²×D₄	—	2	2	no	—
198	C₂²×D₄	—	2	2	no	—
199	C₂²×D₄	—	2	2	no	—
200	C₂²×D₄	D₄×C₁₂₇	1	1	yes	characteristic
201	C₂³×C₄	—	2	1	no	—
202	C₂×D₈	—	2	8	no	—
203	C₂×D₈	—	2	4	no	—
204	C₂×D₈	—	2	4	no	—
205	C₂×D₈	—	4	4	no	—
206	C₂×D₈	—	4	8	no	—
207	C₂×D₈	—	4	4	no	—
208	C₂×M₁₆	—	2	4	no	—
209	C₂×M₁₆	—	4	4	no	—
210	C₂²×C₈	—	2	1	no	—
211	C₂²×C₈	—	2	2	no	—
212	C₂²×C₈	D₄×C₁₂₇	1	1	yes	characteristic
213	C₂²×C₈	D₄×C₁₂₇	1	1	yes	characteristic
214	#127	—	2	2	no	—
215	#127	—	2	2	no	—
216	#127	—	2	2	no	—
217	#127	C₂³×C₁₂₇	1	4	yes	—
218	C₄×D₄	—	2	1	no	—
219	C₄×D₄	—	2	1	no	—
220	C₄×D₄	D₄×C₁₂₇	1	2	yes	—
221	C₄×D₄	C₂³×C₁₂₇	1	2	yes	—
222	C₂×C₄⋊C₄	D₄×C₁₂₇	1	1	yes	characteristic
223	C₂×C₂²⋊C₄	—	2	1	no	—
224	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
225	C₄⋊C₈	—	2	1	no	—
226	C₄⋊C₈	—	2	2	no	—
227	C₄⋊C₈	C₂³×C₁₂₇	1	2	yes	—
228	C₄⋊C₈	C₂³×C₁₂₇	1	4	yes	—
229	#102	—	2	8	no	—
230	C₂²⋊C₈	—	2	4	no	—
231	C₄×C₈	D₄×C₁₂₇	1	2	yes	—
232	C₄×C₈	C₂³×C₁₂₇	1	2	yes	—
233	C₂⁴	—	2	1	no	—
234	C₂⁴	—	4	2	no	—
235	C₂×D₄	—	2	1	no	—
236	C₂×D₄	—	2	4	no	—
237	C₂×D₄	—	2	4	no	—
238	C₂×D₄	—	2	4	no	—
239	C₂×D₄	—	2	4	no	—
240	C₂×D₄	—	4	2	no	—
241	C₂×D₄	—	4	2	no	—
242	C₂×D₄	—	4	2	no	—
243	C₂×D₄	—	4	4	no	—
244	C₂×D₄	—	4	4	no	—
245	C₂×D₄	—	4	4	no	—
246	C₂×D₄	—	4	4	no	—
247	C₂×D₄	—	8	4	no	—
248	C₂×D₄	C₂×D₄×C₁₂₇	1	2	yes	—
249	C₂²×C₄	—	2	1	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
255	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
256	C₂²×C₄	#41×C₁₂₇	1	1	yes	characteristic
257	D₈	—	4	8	no	—
258	D₈	—	4	16	no	—
259	D₈	—	4	8	no	—
260	M₁₆	—	4	8	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	4	no	—
264	C₂×C₈	—	4	2	no	—
265	C₂×C₈	—	4	4	no	—
266	C₂×C₈	D₈×C₁₂₇	1	4	yes	complemented
267	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
268	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
269	C₄⋊C₄	—	2	1	no	—
270	C₄⋊C₄	C₂×D₄×C₁₂₇	1	2	yes	—
271	C₂²⋊C₄	—	2	2	no	—
272	C₂²⋊C₄	—	2	2	no	—
273	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
274	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
275	C₄²	#41×C₁₂₇	1	1	yes	characteristic
276	C₄²	C₂⁴×C₁₂₇	1	1	yes	characteristic
277	C₂³	—	2	2	no	—
278	C₂³	—	4	2	no	—
279	C₂³	—	4	2	no	—
280	C₂³	—	4	2	no	—
281	C₂³	—	4	4	no	—
282	C₂³	—	8	4	no	—
283	C₂³	—	8	4	no	—
284	C₂³	—	8	4	no	—
285	C₂³	#121×C₁₂₇	1	1	yes	characteristic
286	D₄	—	2	4	no	—
287	D₄	—	4	4	no	—
288	D₄	—	4	4	no	—
289	D₄	—	4	4	no	—
290	D₄	—	4	4	no	—
291	D₄	—	4	2	no	—
292	D₄	—	8	4	no	—
293	D₄	—	8	4	no	—
294	D₄	—	8	4	no	—
295	D₄	—	8	4	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	4	2	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	#121×C₁₂₇	1	1	yes	characteristic
303	C₂×C₄	#121×C₁₂₇	1	1	yes	characteristic
304	C₂×C₄	#121×C₁₂₇	1	1	yes	characteristic
305	C₂×C₄	C₂×D₈×C₁₂₇	1	2	yes	—
306	C₂×C₄	AGL(1,ℤ/8)×C₁₂₇	1	2	yes	—
307	C₂×C₄	AGL(1,ℤ/8)×C₁₂₇	1	4	yes	—
308	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
309	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
310	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
311	C₈	—	2	2	no	—
312	C₈	—	4	2	no	—
313	C₈	—	4	4	no	—
314	C₈	C₂×D₈×C₁₂₇	1	4	yes	complemented
315	C₂²	—	4	2	no	—
316	C₂²	—	4	2	no	—
317	C₂²	—	4	2	no	—
318	C₂²	—	8	4	no	—
319	C₂²	—	8	4	no	—
320	C₂²	—	8	4	no	—
321	C₂²	—	8	4	no	—
322	C₂²	—	16	8	no	—
323	C₂²	#459×C₁₂₇	1	2	yes	—
324	C₂²	#469×C₁₂₇	1	2	yes	—
325	C₂²	#472×C₁₂₇	1	2	yes	—
326	C₂²	C₂×#121×C₁₂₇	1	1	yes	characteristic
327	C₄	—	2	1	no	—
328	C₄	—	2	1	no	—
329	C₄	—	4	2	no	—
330	C₄	#459×C₁₂₇	1	2	yes	—
331	C₄	#469×C₁₂₇	1	2	yes	—
332	C₄	C₂²×D₈×C₁₂₇	1	1	yes	characteristic
333	C₄	C₂×AGL(1,ℤ/8)×C₁₂₇	1	1	yes	characteristic
334	C₄	C₂×AGL(1,ℤ/8)×C₁₂₇	1	2	yes	—
335	C₂	—	8	2	no	—
336	C₂	—	16	4	no	—
337	C₂	C₁₂₇×#1687	1	4	yes	direct product factor
338	C₂	C₂×#459×C₁₂₇	1	1	yes	characteristic
339	C₂	C₂×#469×C₁₂₇	1	1	yes	characteristic
340	C₂	C₂×#472×C₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₂₇	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₂₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₂₇ ◁ C₂×C₄²×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#493×C₁₂₇	C₂	semidirect
2. C₂×#459×C₁₂₇	C₂	semidirect
3. C₂×#436×C₁₂₇	C₂	semidirect
4. C₁₂₇×#1687	C₂	direct (N × H)
5. C₂×#334×C₁₂₇	C₂	semidirect
6. C₂×#331×C₁₂₇	C₂	semidirect
14. #493×C₁₂₇	C₂²	semidirect
16. #459×C₁₂₇	C₂²	semidirect
18. #436×C₁₂₇	C₂²	semidirect
24. #334×C₁₂₇	C₂²	semidirect
25. #331×C₁₂₇	C₂²	semidirect
95. C₂×C₈×C₁₂₇	D₈	semidirect
143. C₈×C₁₂₇	C₂×D₈	semidirect
164. C₂×#1687	C₁₂₇	direct (N × H)
167. C₂×C₁₂₇	#1687	direct (N × H)
171. C₂×#493	C₂×C₁₂₇	semidirect
172. C₂×#459	C₂×C₁₂₇	semidirect
173. C₂×#436	C₂×C₁₂₇	semidirect
174. #1687	C₂×C₁₂₇	direct (N × H)
175. C₂×#334	C₂×C₁₂₇	semidirect
176. C₂×#331	C₂×C₁₂₇	semidirect
177. C₁₂₇	C₂×#1687	direct (N × H)
185. #493	C₂²×C₁₂₇	semidirect
187. #459	C₂²×C₁₂₇	semidirect
189. #436	C₂²×C₁₂₇	semidirect
195. #334	C₂²×C₁₂₇	semidirect
196. #331	C₂²×C₁₂₇	semidirect
266. C₂×C₈	D₈×C₁₂₇	semidirect
314. C₈	C₂×D₈×C₁₂₇	semidirect
337. C₂	C₁₂₇×#1687	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#493×C₁₂₇	2
C₂×#459×C₁₂₇	2
C₂×#436×C₁₂₇	2
C₁₂₇×#1687	2
C₂×#334×C₁₂₇	2
C₂×#331×C₁₂₇	2
C₂×#1687	127

Subgroups — C2×C127×#1687 #44582804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₂₇×#1687 #44582804