Subgroups — C₁₂₇×#11328 #44575001

Order 32512.

958 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#107×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#389×C₁₂₇	C₂	1	2	yes	maximal
3	C₂×#340×C₁₂₇	C₂	1	2	yes	maximal
4	C₂×#340×C₁₂₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#336×C₁₂₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₁₂₇	—	2	2	no	—
9	C₂²×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
12	C₂×#107×C₁₂₇	—	2	2	no	—
13	C₂×#107×C₁₂₇	—	2	4	no	—
14	#389×C₁₂₇	—	2	4	no	—
15	#389×C₁₂₇	—	2	4	no	—
16	C₂×#95×C₁₂₇	—	2	2	no	—
17	#340×C₁₂₇	—	2	4	no	—
18	#340×C₁₂₇	C₄	1	4	yes	complemented
19	#336×C₁₂₇	—	2	2	no	—
20	C₂³×C₄×C₁₂₇	—	2	2	no	—
21	C₂³×C₄×C₁₂₇	—	2	2	no	—
22	C₂³×C₄×C₁₂₇	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₂₇	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
25	C₂²×C₈×C₁₂₇	—	2	2	no	—
26	C₂²×C₈×C₁₂₇	—	2	2	no	—
27	C₂²×C₈×C₁₂₇	—	2	1	no	—
28	C₂²×C₈×C₁₂₇	—	2	2	no	—
29	C₂²×C₈×C₁₂₇	—	2	2	no	—
30	C₂²×C₈×C₁₂₇	—	2	1	no	—
31	C₂²×C₈×C₁₂₇	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₂₇	D₄	1	2	yes	—
33	C₂²×C₈×C₁₂₇	Q₈	1	2	yes	—
34	C₂²×C₈×C₁₂₇	Q₈	1	2	yes	—
35	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₂₇	—	2	8	no	—
43	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₂₇	—	4	4	no	—
45	C₂×C₄⋊C₄×C₁₂₇	—	4	4	no	—
46	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₁₂₇	D₄	1	4	yes	—
48	C₂×C₄⋊C₄×C₁₂₇	D₄	1	4	yes	—
49	C₂×C₄⋊C₄×C₁₂₇	Q₈	1	4	yes	—
50	C₂×C₄²×C₁₂₇	—	2	1	no	—
51	C₂×C₄²×C₁₂₇	—	2	2	no	—
52	C₂×C₄²×C₁₂₇	—	2	2	no	—
53	C₂×C₄²×C₁₂₇	—	2	1	no	—
54	#107×C₁₂₇	—	2	8	no	—
55	#95×C₁₂₇	—	2	8	no	—
56	C₂⁴×C₁₂₇	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₂₇	—	2	4	no	—
58	C₂²×C₄×C₁₂₇	—	2	2	no	—
59	C₂²×C₄×C₁₂₇	—	2	4	no	—
60	C₂²×C₄×C₁₂₇	—	2	2	no	—
61	C₂²×C₄×C₁₂₇	—	2	1	no	—
62	C₂²×C₄×C₁₂₇	—	2	1	no	—
63	C₂²×C₄×C₁₂₇	—	2	4	no	—
64	C₂²×C₄×C₁₂₇	—	2	1	no	—
65	C₂²×C₄×C₁₂₇	—	2	1	no	—
66	C₂²×C₄×C₁₂₇	—	2	2	no	—
67	C₂²×C₄×C₁₂₇	—	2	2	no	—
68	C₂²×C₄×C₁₂₇	—	2	4	no	—
69	C₂²×C₄×C₁₂₇	—	4	2	no	—
70	C₂²×C₄×C₁₂₇	—	4	2	no	—
71	C₂²×C₄×C₁₂₇	—	4	2	no	—
72	C₂²×C₄×C₁₂₇	—	4	2	no	—
73	C₂²×C₄×C₁₂₇	—	4	2	no	—
74	C₂²×C₄×C₁₂₇	—	4	2	no	—
75	C₂²×C₄×C₁₂₇	—	4	2	no	—
76	C₂²×C₄×C₁₂₇	—	4	2	no	—
77	C₂²×C₄×C₁₂₇	—	4	2	no	—
78	C₂²×C₄×C₁₂₇	—	4	2	no	—
79	C₂²×C₄×C₁₂₇	D₈	1	2	yes	—
80	C₂²×C₄×C₁₂₇	Q₁₆	1	2	yes	—
81	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₁₂₇	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₁₂₇	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₁₂₇	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
89	C₂²×C₄×C₁₂₇	#41	1	1	yes	characteristic
90	C₂²×C₄×C₁₂₇	#41	1	1	yes	characteristic
91	C₂×C₈×C₁₂₇	—	2	4	no	—
92	C₂×C₈×C₁₂₇	—	2	2	no	—
93	C₂×C₈×C₁₂₇	—	2	4	no	—
94	C₂×C₈×C₁₂₇	—	2	2	no	—
95	C₂×C₈×C₁₂₇	—	2	4	no	—
96	C₂×C₈×C₁₂₇	—	2	2	no	—
97	C₂×C₈×C₁₂₇	—	4	1	no	—
98	C₂×C₈×C₁₂₇	—	4	2	no	—
99	C₂×C₈×C₁₂₇	—	4	1	no	—
100	C₂×C₈×C₁₂₇	C₄⋊C₄	1	4	yes	complemented
101	C₄⋊C₄×C₁₂₇	—	2	4	no	—
102	C₄⋊C₄×C₁₂₇	—	2	4	no	—
103	C₄⋊C₄×C₁₂₇	—	2	4	no	—
104	C₄⋊C₄×C₁₂₇	—	2	4	no	—
105	C₄⋊C₄×C₁₂₇	—	2	4	no	—
106	C₄⋊C₄×C₁₂₇	—	4	16	no	—
107	C₄⋊C₄×C₁₂₇	—	4	2	no	—
108	C₄⋊C₄×C₁₂₇	—	4	2	no	—
109	C₄⋊C₄×C₁₂₇	C₄⋊C₄	1	8	yes	complemented
110	C₄²×C₁₂₇	—	4	1	no	—
111	C₄²×C₁₂₇	—	4	2	no	—
112	C₄²×C₁₂₇	—	4	1	no	—
113	C₂³×C₁₂₇	C₄×D₄	1	1	yes	characteristic
114	C₂³×C₁₂₇	#120	1	2	yes	—
115	C₂³×C₁₂₇	#121	1	1	yes	characteristic
116	C₂³×C₁₂₇	C₂²⋊Q₈	1	2	yes	—
117	C₂³×C₁₂₇	C₄⋊Q₈	1	1	yes	characteristic
118	C₂³×C₁₂₇	C₂×D₈	1	1	yes	characteristic
119	C₂³×C₁₂₇	C₂×Q₁₆	1	1	yes	characteristic
120	C₂³×C₁₂₇	#135	1	1	yes	characteristic
121	C₂³×C₁₂₇	#135	1	1	yes	characteristic
122	C₂³×C₁₂₇	AGL(1,ℤ/8)	1	2	yes	—
123	C₂³×C₁₂₇	#137	1	2	yes	—
124	C₂×C₄×C₁₂₇	—	2	8	no	—
125	C₂×C₄×C₁₂₇	—	2	4	no	—
126	C₂×C₄×C₁₂₇	—	2	4	no	—
127	C₂×C₄×C₁₂₇	—	2	2	no	—
128	C₂×C₄×C₁₂₇	—	2	2	no	—
129	C₂×C₄×C₁₂₇	—	4	1	no	—
130	C₂×C₄×C₁₂₇	—	4	1	no	—
131	C₂×C₄×C₁₂₇	—	4	4	no	—
132	C₂×C₄×C₁₂₇	—	4	4	no	—
133	C₂×C₄×C₁₂₇	—	4	4	no	—
134	C₂×C₄×C₁₂₇	—	4	2	no	—
135	C₂×C₄×C₁₂₇	—	4	2	no	—
136	C₂×C₄×C₁₂₇	—	4	4	no	—
137	C₂×C₄×C₁₂₇	—	4	1	no	—
138	C₂×C₄×C₁₂₇	—	4	1	no	—
139	C₂×C₄×C₁₂₇	—	4	4	no	—
140	C₂×C₄×C₁₂₇	—	4	4	no	—
141	C₂×C₄×C₁₂₇	—	4	4	no	—
142	C₂×C₄×C₁₂₇	—	4	4	no	—
143	C₂×C₄×C₁₂₇	—	4	4	no	—
144	C₂×C₄×C₁₂₇	—	8	2	no	—
145	C₂×C₄×C₁₂₇	—	8	2	no	—
146	C₂×C₄×C₁₂₇	—	8	2	no	—
147	C₂×C₄×C₁₂₇	—	8	2	no	—
148	C₂×C₄×C₁₂₇	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₂₇	C₂×C₄⋊C₄	1	2	yes	—
150	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
151	C₂×C₄×C₁₂₇	C₄×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₁₂₇	#120	1	1	yes	characteristic
153	C₂×C₄×C₁₂₇	#121	1	2	yes	—
154	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	2	yes	—
155	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	2	yes	—
156	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₁₂₇	#123	1	1	yes	characteristic
159	C₂×C₄×C₁₂₇	#123	1	2	yes	—
160	C₂×C₄×C₁₂₇	#125	1	2	yes	—
161	C₂×C₄×C₁₂₇	#125	1	1	yes	characteristic
162	C₂×C₄×C₁₂₇	#127	1	1	yes	characteristic
163	C₂×C₄×C₁₂₇	C₄⋊Q₈	1	1	yes	characteristic
164	C₂×C₄×C₁₂₇	C₄⋊Q₈	1	2	yes	—
165	C₂×C₄×C₁₂₇	C₄⋊Q₈	1	2	yes	—
166	C₈×C₁₂₇	—	2	4	no	—
167	C₈×C₁₂₇	—	4	2	no	—
168	C₂²×C₁₂₇	#385	1	2	yes	—
169	C₂²×C₁₂₇	#389	1	1	yes	characteristic
170	C₂²×C₁₂₇	#392	1	1	yes	characteristic
171	C₂²×C₁₂₇	#395	1	2	yes	—
172	C₂²×C₁₂₇	#398	1	1	yes	characteristic
173	C₂²×C₁₂₇	C₄×D₈	1	1	yes	characteristic
174	C₂²×C₁₂₇	C₄×Q₁₆	1	1	yes	characteristic
175	C₂²×C₁₂₇	#440	1	2	yes	—
176	C₂²×C₁₂₇	#447	1	2	yes	—
177	C₂²×C₁₂₇	#449	1	2	yes	—
178	C₂²×C₁₂₇	#451	1	2	yes	—
179	C₂²×C₁₂₇	#452	1	2	yes	—
180	C₂²×C₁₂₇	#466	1	1	yes	characteristic
181	C₂²×C₁₂₇	#467	1	1	yes	characteristic
182	C₂²×C₁₂₇	#469	1	1	yes	characteristic
183	C₂²×C₁₂₇	#470	1	1	yes	characteristic
184	C₂²×C₁₂₇	#474	1	2	yes	—
185	C₂²×C₁₂₇	#477	1	2	yes	—
186	C₂²×C₁₂₇	#478	1	2	yes	—
187	C₂²×C₁₂₇	#479	1	2	yes	—
188	C₂²×C₁₂₇	#499	1	1	yes	characteristic
189	C₂²×C₁₂₇	#500	1	1	yes	characteristic
190	C₂²×C₁₂₇	#501	1	2	yes	—
191	C₄×C₁₂₇	—	4	8	no	—
192	C₄×C₁₂₇	—	4	2	no	—
193	C₄×C₁₂₇	—	4	2	no	—
194	C₄×C₁₂₇	—	8	4	no	—
195	C₄×C₁₂₇	#384	1	1	yes	characteristic
196	C₄×C₁₂₇	#385	1	1	yes	characteristic
197	C₄×C₁₂₇	#389	1	2	yes	—
198	C₄×C₁₂₇	#395	1	1	yes	characteristic
199	C₄×C₁₂₇	#398	1	2	yes	—
200	C₄×C₁₂₇	#399	1	1	yes	characteristic
201	#11328	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂×C₁₂₇	#1444	1	1	yes	characteristic
203	C₂×C₁₂₇	#1862	1	2	yes	—
204	C₂×C₁₂₇	#1863	1	2	yes	—
205	C₂×C₁₂₇	#1942	1	1	yes	characteristic
206	C₂×C₁₂₇	#1944	1	1	yes	characteristic
207	C₂×C₁₂₇	#1999	1	1	yes	characteristic
208	C₂×C₁₂₇	#2001	1	1	yes	characteristic
209	C₂×C₁₂₇	#2057	1	2	yes	—
210	C₂×C₁₂₇	#2059	1	2	yes	—
211	C₂×C₁₂₇	#2086	1	1	yes	characteristic
212	C₂×C₁₂₇	#2087	1	1	yes	characteristic
213	C₂²×#107	C₂×C₁₂₇	1	1	yes	characteristic
214	C₂×#389	C₂×C₁₂₇	1	2	yes	—
215	C₂×#340	C₂×C₁₂₇	1	2	yes	—
216	C₂×#340	C₂×C₁₂₇	1	1	yes	characteristic
217	C₂×#336	C₂×C₁₂₇	1	1	yes	characteristic
218	C₁₂₇	#11328	1	1	yes	characteristic, direct product factor, Sylow
219	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
220	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
221	C₂²×C₄⋊C₄	—	2	2	no	—
222	C₂²×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
223	C₂²×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
224	C₂²×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
225	C₂×#107	—	2	2	no	—
226	C₂×#107	—	2	4	no	—
227	#389	—	2	4	no	—
228	#389	—	2	4	no	—
229	C₂×#95	—	2	2	no	—
230	#340	—	2	4	no	—
231	#340	C₄×C₁₂₇	1	4	yes	complemented
232	#336	—	2	2	no	—
233	C₂³×C₄	—	2	2	no	—
234	C₂³×C₄	—	2	2	no	—
235	C₂³×C₄	D₄×C₁₂₇	1	1	yes	characteristic
236	C₂³×C₄	D₄×C₁₂₇	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	C₂×C₄×C₁₂₇	1	2	yes	—
245	C₂²×C₈	D₄×C₁₂₇	1	2	yes	—
246	C₂²×C₈	Q₈×C₁₂₇	1	2	yes	—
247	C₂²×C₈	Q₈×C₁₂₇	1	2	yes	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	8	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	4	4	no	—
258	C₂×C₄⋊C₄	—	4	4	no	—
259	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
260	C₂×C₄⋊C₄	D₄×C₁₂₇	1	4	yes	—
261	C₂×C₄⋊C₄	D₄×C₁₂₇	1	4	yes	—
262	C₂×C₄⋊C₄	Q₈×C₁₂₇	1	4	yes	—
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	1	no	—
267	#107	—	2	8	no	—
268	#95	—	2	8	no	—
269	C₂⁴	C₂×D₄×C₁₂₇	1	1	yes	characteristic
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	D₈×C₁₂₇	1	2	yes	—
293	C₂²×C₄	Q₁₆×C₁₂₇	1	2	yes	—
294	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
298	C₂²×C₄	C₂×Q₈×C₁₂₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×Q₈×C₁₂₇	1	2	yes	—
300	C₂²×C₄	C₂×Q₈×C₁₂₇	1	1	yes	characteristic
301	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
302	C₂²×C₄	#41×C₁₂₇	1	1	yes	characteristic
303	C₂²×C₄	#41×C₁₂₇	1	1	yes	characteristic
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	—	4	2	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	C₄⋊C₄×C₁₂₇	1	4	yes	complemented
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	4	16	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	C₄⋊C₄×C₁₂₇	1	8	yes	complemented
323	C₄²	—	4	1	no	—
324	C₄²	—	4	2	no	—
325	C₄²	—	4	1	no	—
326	C₂³	C₄×D₄×C₁₂₇	1	1	yes	characteristic
327	C₂³	#120×C₁₂₇	1	2	yes	—
328	C₂³	#121×C₁₂₇	1	1	yes	characteristic
329	C₂³	C₂²⋊Q₈×C₁₂₇	1	2	yes	—
330	C₂³	C₄⋊Q₈×C₁₂₇	1	1	yes	characteristic
331	C₂³	C₂×D₈×C₁₂₇	1	1	yes	characteristic
332	C₂³	C₂×Q₁₆×C₁₂₇	1	1	yes	characteristic
333	C₂³	#135×C₁₂₇	1	1	yes	characteristic
334	C₂³	#135×C₁₂₇	1	1	yes	characteristic
335	C₂³	AGL(1,ℤ/8)×C₁₂₇	1	2	yes	—
336	C₂³	#137×C₁₂₇	1	2	yes	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	8	2	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	—	8	2	no	—
361	C₂×C₄	C₂×C₄⋊C₄×C₁₂₇	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄⋊C₄×C₁₂₇	1	2	yes	—
363	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
364	C₂×C₄	C₄×Q₈×C₁₂₇	1	1	yes	characteristic
365	C₂×C₄	#120×C₁₂₇	1	1	yes	characteristic
366	C₂×C₄	#121×C₁₂₇	1	2	yes	—
367	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	2	yes	—
368	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	2	yes	—
369	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	2	yes	—
370	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	1	yes	characteristic
371	C₂×C₄	#123×C₁₂₇	1	1	yes	characteristic
372	C₂×C₄	#123×C₁₂₇	1	2	yes	—
373	C₂×C₄	#125×C₁₂₇	1	2	yes	—
374	C₂×C₄	#125×C₁₂₇	1	1	yes	characteristic
375	C₂×C₄	#127×C₁₂₇	1	1	yes	characteristic
376	C₂×C₄	C₄⋊Q₈×C₁₂₇	1	1	yes	characteristic
377	C₂×C₄	C₄⋊Q₈×C₁₂₇	1	2	yes	—
378	C₂×C₄	C₄⋊Q₈×C₁₂₇	1	2	yes	—
379	C₈	—	2	4	no	—
380	C₈	—	4	2	no	—
381	C₂²	#385×C₁₂₇	1	2	yes	—
382	C₂²	#389×C₁₂₇	1	1	yes	characteristic
383	C₂²	#392×C₁₂₇	1	1	yes	characteristic
384	C₂²	#395×C₁₂₇	1	2	yes	—
385	C₂²	#398×C₁₂₇	1	1	yes	characteristic
386	C₂²	C₄×D₈×C₁₂₇	1	1	yes	characteristic
387	C₂²	C₄×Q₁₆×C₁₂₇	1	1	yes	characteristic
388	C₂²	#440×C₁₂₇	1	2	yes	—
389	C₂²	#447×C₁₂₇	1	2	yes	—
390	C₂²	#449×C₁₂₇	1	2	yes	—
391	C₂²	#451×C₁₂₇	1	2	yes	—
392	C₂²	#452×C₁₂₇	1	2	yes	—
393	C₂²	#466×C₁₂₇	1	1	yes	characteristic
394	C₂²	#467×C₁₂₇	1	1	yes	characteristic
395	C₂²	#469×C₁₂₇	1	1	yes	characteristic
396	C₂²	#470×C₁₂₇	1	1	yes	characteristic
397	C₂²	#474×C₁₂₇	1	2	yes	—
398	C₂²	#477×C₁₂₇	1	2	yes	—
399	C₂²	#478×C₁₂₇	1	2	yes	—
400	C₂²	#479×C₁₂₇	1	2	yes	—
401	C₂²	#499×C₁₂₇	1	1	yes	characteristic
402	C₂²	#500×C₁₂₇	1	1	yes	characteristic
403	C₂²	#501×C₁₂₇	1	2	yes	—
404	C₄	—	4	8	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	8	4	no	—
408	C₄	#384×C₁₂₇	1	1	yes	characteristic
409	C₄	#385×C₁₂₇	1	1	yes	characteristic
410	C₄	#389×C₁₂₇	1	2	yes	—
411	C₄	#395×C₁₂₇	1	1	yes	characteristic
412	C₄	#398×C₁₂₇	1	2	yes	—
413	C₄	#399×C₁₂₇	1	1	yes	characteristic
414	C₂	C₁₂₇×#1444	1	1	yes	characteristic
415	C₂	C₁₂₇×#1862	1	2	yes	—
416	C₂	C₁₂₇×#1863	1	2	yes	—
417	C₂	C₁₂₇×#1942	1	1	yes	characteristic
418	C₂	C₁₂₇×#1944	1	1	yes	characteristic
419	C₂	C₁₂₇×#1999	1	1	yes	characteristic
420	C₂	C₁₂₇×#2001	1	1	yes	characteristic
421	C₂	C₁₂₇×#2057	1	2	yes	—
422	C₂	C₁₂₇×#2059	1	2	yes	—
423	C₂	C₁₂₇×#2086	1	1	yes	characteristic
424	C₂	C₁₂₇×#2087	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
18. #340×C₁₂₇	C₄	semidirect
100. C₂×C₈×C₁₂₇	C₄⋊C₄	semidirect
109. C₄⋊C₄×C₁₂₇	C₄⋊C₄	semidirect
201. #11328	C₁₂₇	direct (N × H)
218. C₁₂₇	#11328	direct (N × H)
231. #340	C₄×C₁₂₇	semidirect
313. C₂×C₈	C₄⋊C₄×C₁₂₇	semidirect
322. C₄⋊C₄	C₄⋊C₄×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#107×C₁₂₇	2
C₂×#389×C₁₂₇	2
C₂×#340×C₁₂₇	2
C₂×#336×C₁₂₇	2
#11328	127

Subgroups — C127×#11328 #44575001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#11328 #44575001