Subgroups — C₁₂₇×#11324 #44574997

Order 32512.

974 conjugacy classes of subgroups.

The subgroup lattice has 396 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	2	yes	maximal
2	C₂×#384×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#340×C₁₂₇	C₂	1	2	yes	maximal
4	C₂×#336×C₁₂₇	C₂	1	1	yes	maximal, characteristic
5	C₁₂₇×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₂₇	C₂²	1	2	yes	—
7	C₂²×C₄⋊C₄×C₁₂₇	—	2	2	no	—
8	C₂²×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
12	C₂×#107×C₁₂₇	—	2	4	no	—
13	C₂×#107×C₁₂₇	—	2	4	no	—
14	C₂×#107×C₁₂₇	—	2	4	no	—
15	#384×C₁₂₇	—	2	4	no	—
16	C₂×#95×C₁₂₇	—	2	2	no	—
17	#340×C₁₂₇	—	2	4	no	—
18	#336×C₁₂₇	C₄	1	4	yes	complemented
19	C₂³×C₄×C₁₂₇	—	2	2	no	—
20	C₂³×C₄×C₁₂₇	—	2	1	no	—
21	C₂³×C₄×C₁₂₇	—	2	1	no	—
22	C₂³×C₄×C₁₂₇	D₄	1	2	yes	—
23	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
24	C₂²×C₈×C₁₂₇	—	2	2	no	—
25	C₂²×C₈×C₁₂₇	—	2	2	no	—
26	C₂²×C₈×C₁₂₇	—	2	2	no	—
27	C₂²×C₈×C₁₂₇	—	2	2	no	—
28	C₂²×C₈×C₁₂₇	C₂×C₄	1	4	yes	—
29	C₂²×C₈×C₁₂₇	D₄	1	4	yes	—
30	C₂²×C₈×C₁₂₇	Q₈	1	4	yes	—
31	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
32	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
34	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
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	8	no	—
40	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₂₇	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₂₇	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₂₇	—	4	4	no	—
44	C₂×C₄⋊C₄×C₁₂₇	—	4	4	no	—
45	C₂×C₄⋊C₄×C₁₂₇	D₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₂₇	D₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₂₇	Q₈	1	2	yes	—
48	C₂×C₄²×C₁₂₇	—	2	2	no	—
49	C₂×C₄²×C₁₂₇	—	2	2	no	—
50	C₂×C₄²×C₁₂₇	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₂₇	Q₈	1	2	yes	—
52	#107×C₁₂₇	—	2	16	no	—
53	#95×C₁₂₇	—	4	4	no	—
54	C₂⁴×C₁₂₇	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₂₇	—	2	2	no	—
56	C₂²×C₄×C₁₂₇	—	2	2	no	—
57	C₂²×C₄×C₁₂₇	—	2	2	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	2	no	—
62	C₂²×C₄×C₁₂₇	—	4	1	no	—
63	C₂²×C₄×C₁₂₇	—	4	2	no	—
64	C₂²×C₄×C₁₂₇	—	4	1	no	—
65	C₂²×C₄×C₁₂₇	—	4	2	no	—
66	C₂²×C₄×C₁₂₇	—	4	1	no	—
67	C₂²×C₄×C₁₂₇	—	4	1	no	—
68	C₂²×C₄×C₁₂₇	—	4	2	no	—
69	C₂²×C₄×C₁₂₇	—	4	2	no	—
70	C₂²×C₄×C₁₂₇	—	4	4	no	—
71	C₂²×C₄×C₁₂₇	—	4	4	no	—
72	C₂²×C₄×C₁₂₇	—	4	2	no	—
73	C₂²×C₄×C₁₂₇	—	4	2	no	—
74	C₂²×C₄×C₁₂₇	C₄⋊C₄	1	4	yes	—
75	C₂²×C₄×C₁₂₇	D₈	1	4	yes	—
76	C₂²×C₄×C₁₂₇	Q₁₆	1	4	yes	—
77	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
81	C₂²×C₄×C₁₂₇	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₁₂₇	C₂×Q₈	1	1	yes	characteristic
83	C₂²×C₄×C₁₂₇	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
85	C₂²×C₄×C₁₂₇	#41	1	1	yes	characteristic
86	C₂²×C₄×C₁₂₇	#41	1	1	yes	characteristic
87	C₂×C₈×C₁₂₇	—	2	4	no	—
88	C₂×C₈×C₁₂₇	—	2	4	no	—
89	C₂×C₈×C₁₂₇	—	2	4	no	—
90	C₂×C₈×C₁₂₇	—	2	4	no	—
91	C₂×C₈×C₁₂₇	—	2	4	no	—
92	C₂×C₈×C₁₂₇	—	2	4	no	—
93	C₂×C₈×C₁₂₇	C₄⋊C₄	1	8	yes	complemented
94	C₄⋊C₄×C₁₂₇	—	2	4	no	—
95	C₄⋊C₄×C₁₂₇	—	2	4	no	—
96	C₄⋊C₄×C₁₂₇	—	2	4	no	—
97	C₄⋊C₄×C₁₂₇	—	2	4	no	—
98	C₄⋊C₄×C₁₂₇	—	4	16	no	—
99	C₄⋊C₄×C₁₂₇	—	4	2	no	—
100	C₄⋊C₄×C₁₂₇	—	4	2	no	—
101	C₄⋊C₄×C₁₂₇	—	4	2	no	—
102	C₄⋊C₄×C₁₂₇	—	4	2	no	—
103	C₄²×C₁₂₇	—	2	4	no	—
104	C₄²×C₁₂₇	—	2	4	no	—
105	C₂³×C₁₂₇	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂³×C₁₂₇	#120	1	1	yes	characteristic
107	C₂³×C₁₂₇	#121	1	1	yes	characteristic
108	C₂³×C₁₂₇	C₂²⋊Q₈	1	1	yes	characteristic
109	C₂³×C₁₂₇	#123	1	1	yes	characteristic
110	C₂³×C₁₂₇	#127	1	1	yes	characteristic
111	C₂³×C₁₂₇	C₄⋊Q₈	1	1	yes	characteristic
112	C₂³×C₁₂₇	C₂×D₈	1	2	yes	—
113	C₂³×C₁₂₇	C₂×Q₁₆	1	2	yes	—
114	C₂³×C₁₂₇	AGL(1,ℤ/8)	1	2	yes	—
115	C₂³×C₁₂₇	#137	1	2	yes	—
116	C₂×C₄×C₁₂₇	—	2	4	no	—
117	C₂×C₄×C₁₂₇	—	2	4	no	—
118	C₂×C₄×C₁₂₇	—	2	4	no	—
119	C₂×C₄×C₁₂₇	—	2	4	no	—
120	C₂×C₄×C₁₂₇	—	2	4	no	—
121	C₂×C₄×C₁₂₇	—	2	4	no	—
122	C₂×C₄×C₁₂₇	—	4	2	no	—
123	C₂×C₄×C₁₂₇	—	4	4	no	—
124	C₂×C₄×C₁₂₇	—	4	2	no	—
125	C₂×C₄×C₁₂₇	—	4	8	no	—
126	C₂×C₄×C₁₂₇	—	4	4	no	—
127	C₂×C₄×C₁₂₇	—	4	4	no	—
128	C₂×C₄×C₁₂₇	—	8	2	no	—
129	C₂×C₄×C₁₂₇	—	8	4	no	—
130	C₂×C₄×C₁₂₇	—	8	2	no	—
131	C₂×C₄×C₁₂₇	—	8	1	no	—
132	C₂×C₄×C₁₂₇	—	8	1	no	—
133	C₂×C₄×C₁₂₇	—	8	2	no	—
134	C₂×C₄×C₁₂₇	—	8	2	no	—
135	C₂×C₄×C₁₂₇	—	8	1	no	—
136	C₂×C₄×C₁₂₇	—	8	1	no	—
137	C₂×C₄×C₁₂₇	#107	1	8	yes	complemented
138	C₂×C₄×C₁₂₇	C₂×C₄⋊C₄	1	2	yes	—
139	C₂×C₄×C₁₂₇	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
141	C₂×C₄×C₁₂₇	C₄×Q₈	1	1	yes	characteristic
142	C₂×C₄×C₁₂₇	#120	1	2	yes	—
143	C₂×C₄×C₁₂₇	#121	1	2	yes	—
144	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	2	yes	—
145	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	2	yes	—
146	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	2	yes	—
147	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	2	yes	—
148	C₂×C₄×C₁₂₇	#123	1	2	yes	—
149	C₂×C₄×C₁₂₇	#125	1	2	yes	—
150	C₂×C₄×C₁₂₇	#125	1	1	yes	characteristic
151	C₂×C₄×C₁₂₇	C₄⋊Q₈	1	2	yes	—
152	C₂×C₄×C₁₂₇	C₄⋊Q₈	1	1	yes	characteristic
153	C₂×C₄×C₁₂₇	C₄⋊Q₈	1	2	yes	—
154	C₈×C₁₂₇	—	2	8	no	—
155	C₂²×C₁₂₇	#384	1	1	yes	characteristic
156	C₂²×C₁₂₇	#385	1	1	yes	characteristic
157	C₂²×C₁₂₇	#389	1	1	yes	characteristic
158	C₂²×C₁₂₇	#392	1	1	yes	characteristic
159	C₂²×C₁₂₇	#395	1	1	yes	characteristic
160	C₂²×C₁₂₇	#398	1	1	yes	characteristic
161	C₂²×C₁₂₇	#399	1	1	yes	characteristic
162	C₂²×C₁₂₇	C₂×#107	1	2	yes	—
163	C₂²×C₁₂₇	#428	1	2	yes	—
164	C₂²×C₁₂₇	#447	1	2	yes	—
165	C₂²×C₁₂₇	#451	1	2	yes	—
166	C₂²×C₁₂₇	#459	1	2	yes	—
167	C₂²×C₁₂₇	#462	1	2	yes	—
168	C₂²×C₁₂₇	#474	1	2	yes	—
169	C₂²×C₁₂₇	#477	1	2	yes	—
170	C₂²×C₁₂₇	#480	1	2	yes	—
171	C₂²×C₁₂₇	#484	1	2	yes	—
172	C₂²×C₁₂₇	#493	1	1	yes	characteristic
173	C₂²×C₁₂₇	#494	1	1	yes	characteristic
174	C₂²×C₁₂₇	#496	1	1	yes	characteristic
175	C₂²×C₁₂₇	#497	1	1	yes	characteristic
176	C₂²×C₁₂₇	#500	1	2	yes	—
177	C₂²×C₁₂₇	#501	1	2	yes	—
178	C₄×C₁₂₇	—	2	8	no	—
179	C₄×C₁₂₇	—	8	2	no	—
180	C₄×C₁₂₇	—	8	4	no	—
181	C₄×C₁₂₇	—	8	2	no	—
182	C₄×C₁₂₇	#385	1	2	yes	—
183	C₄×C₁₂₇	#389	1	2	yes	—
184	C₄×C₁₂₇	#395	1	2	yes	—
185	C₄×C₁₂₇	#398	1	2	yes	—
186	#11324	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂×C₁₂₇	#1444	1	1	yes	characteristic
188	C₂×C₁₂₇	#1845	1	1	yes	characteristic
189	C₂×C₁₂₇	#1847	1	1	yes	characteristic
190	C₂×C₁₂₇	#1852	1	2	yes	—
191	C₂×C₁₂₇	#1947	1	2	yes	—
192	C₂×C₁₂₇	#2011	1	1	yes	characteristic
193	C₂×C₁₂₇	#2016	1	1	yes	characteristic
194	C₂×C₁₂₇	#2057	1	2	yes	—
195	C₂×C₁₂₇	#2083	1	2	yes	—
196	C₂×C₁₂₇	#2093	1	1	yes	characteristic
197	C₂×C₁₂₇	#2095	1	1	yes	characteristic
198	C₂²×#107	C₂×C₁₂₇	1	2	yes	—
199	C₂×#384	C₂×C₁₂₇	1	1	yes	characteristic
200	C₂×#340	C₂×C₁₂₇	1	2	yes	—
201	C₂×#336	C₂×C₁₂₇	1	1	yes	characteristic
202	C₄⋊#95	C₂×C₁₂₇	1	1	yes	characteristic
203	C₁₂₇	#11324	1	1	yes	characteristic, direct product factor, Sylow
204	C₂³×C₈	C₂²×C₁₂₇	1	2	yes	—
205	C₂²×C₄⋊C₄	—	2	2	no	—
206	C₂²×C₄⋊C₄	C₂²×C₁₂₇	1	1	yes	characteristic
207	C₂²×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
208	C₂²×C₄⋊C₄	C₂²×C₁₂₇	1	1	yes	characteristic
209	C₂²×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
210	C₂×#107	—	2	4	no	—
211	C₂×#107	—	2	4	no	—
212	C₂×#107	—	2	4	no	—
213	#384	—	2	4	no	—
214	C₂×#95	—	2	2	no	—
215	#340	—	2	4	no	—
216	#336	C₄×C₁₂₇	1	4	yes	complemented
217	C₂³×C₄	—	2	2	no	—
218	C₂³×C₄	—	2	1	no	—
219	C₂³×C₄	—	2	1	no	—
220	C₂³×C₄	D₄×C₁₂₇	1	2	yes	—
221	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	C₂×C₄×C₁₂₇	1	4	yes	—
227	C₂²×C₈	D₄×C₁₂₇	1	4	yes	—
228	C₂²×C₈	Q₈×C₁₂₇	1	4	yes	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	8	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	4	4	no	—
242	C₂×C₄⋊C₄	—	4	4	no	—
243	C₂×C₄⋊C₄	D₄×C₁₂₇	1	4	yes	—
244	C₂×C₄⋊C₄	D₄×C₁₂₇	1	2	yes	—
245	C₂×C₄⋊C₄	Q₈×C₁₂₇	1	2	yes	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	C₂×C₄×C₁₂₇	1	2	yes	—
249	C₂×C₄²	Q₈×C₁₂₇	1	2	yes	—
250	#107	—	2	16	no	—
251	#95	—	4	4	no	—
252	C₂⁴	C₂×D₄×C₁₂₇	1	1	yes	characteristic
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	4	1	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	4	1	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	1	no	—
265	C₂²×C₄	—	4	1	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	4	4	no	—
269	C₂²×C₄	—	4	4	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	C₄⋊C₄×C₁₂₇	1	4	yes	—
273	C₂²×C₄	D₈×C₁₂₇	1	4	yes	—
274	C₂²×C₄	Q₁₆×C₁₂₇	1	4	yes	—
275	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
279	C₂²×C₄	C₂×Q₈×C₁₂₇	1	2	yes	—
280	C₂²×C₄	C₂×Q₈×C₁₂₇	1	1	yes	characteristic
281	C₂²×C₄	C₂×Q₈×C₁₂₇	1	1	yes	characteristic
282	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
283	C₂²×C₄	#41×C₁₂₇	1	1	yes	characteristic
284	C₂²×C₄	#41×C₁₂₇	1	1	yes	characteristic
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	C₄⋊C₄×C₁₂₇	1	8	yes	complemented
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	4	16	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₄⋊C₄	—	4	2	no	—
300	C₄⋊C₄	—	4	2	no	—
301	C₄²	—	2	4	no	—
302	C₄²	—	2	4	no	—
303	C₂³	C₂×C₄⋊C₄×C₁₂₇	1	1	yes	characteristic
304	C₂³	#120×C₁₂₇	1	1	yes	characteristic
305	C₂³	#121×C₁₂₇	1	1	yes	characteristic
306	C₂³	C₂²⋊Q₈×C₁₂₇	1	1	yes	characteristic
307	C₂³	#123×C₁₂₇	1	1	yes	characteristic
308	C₂³	#127×C₁₂₇	1	1	yes	characteristic
309	C₂³	C₄⋊Q₈×C₁₂₇	1	1	yes	characteristic
310	C₂³	C₂×D₈×C₁₂₇	1	2	yes	—
311	C₂³	C₂×Q₁₆×C₁₂₇	1	2	yes	—
312	C₂³	AGL(1,ℤ/8)×C₁₂₇	1	2	yes	—
313	C₂³	#137×C₁₂₇	1	2	yes	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	8	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	8	2	no	—
327	C₂×C₄	—	8	1	no	—
328	C₂×C₄	—	8	1	no	—
329	C₂×C₄	—	8	2	no	—
330	C₂×C₄	—	8	4	no	—
331	C₂×C₄	—	8	2	no	—
332	C₂×C₄	—	8	1	no	—
333	C₂×C₄	—	8	1	no	—
334	C₂×C₄	—	8	2	no	—
335	C₂×C₄	#107×C₁₂₇	1	8	yes	complemented
336	C₂×C₄	C₂×C₄⋊C₄×C₁₂₇	1	2	yes	—
337	C₂×C₄	C₄×D₄×C₁₂₇	1	1	yes	characteristic
338	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
339	C₂×C₄	C₄×Q₈×C₁₂₇	1	1	yes	characteristic
340	C₂×C₄	#120×C₁₂₇	1	2	yes	—
341	C₂×C₄	#121×C₁₂₇	1	2	yes	—
342	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	2	yes	—
343	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	2	yes	—
344	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	2	yes	—
345	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	2	yes	—
346	C₂×C₄	#123×C₁₂₇	1	2	yes	—
347	C₂×C₄	#125×C₁₂₇	1	2	yes	—
348	C₂×C₄	#125×C₁₂₇	1	1	yes	characteristic
349	C₂×C₄	C₄⋊Q₈×C₁₂₇	1	2	yes	—
350	C₂×C₄	C₄⋊Q₈×C₁₂₇	1	1	yes	characteristic
351	C₂×C₄	C₄⋊Q₈×C₁₂₇	1	2	yes	—
352	C₈	—	2	8	no	—
353	C₂²	#384×C₁₂₇	1	1	yes	characteristic
354	C₂²	#385×C₁₂₇	1	1	yes	characteristic
355	C₂²	#389×C₁₂₇	1	1	yes	characteristic
356	C₂²	#392×C₁₂₇	1	1	yes	characteristic
357	C₂²	#395×C₁₂₇	1	1	yes	characteristic
358	C₂²	#398×C₁₂₇	1	1	yes	characteristic
359	C₂²	#399×C₁₂₇	1	1	yes	characteristic
360	C₂²	C₂×#107×C₁₂₇	1	2	yes	—
361	C₂²	#428×C₁₂₇	1	2	yes	—
362	C₂²	#447×C₁₂₇	1	2	yes	—
363	C₂²	#451×C₁₂₇	1	2	yes	—
364	C₂²	#459×C₁₂₇	1	2	yes	—
365	C₂²	#462×C₁₂₇	1	2	yes	—
366	C₂²	#474×C₁₂₇	1	2	yes	—
367	C₂²	#477×C₁₂₇	1	2	yes	—
368	C₂²	#480×C₁₂₇	1	2	yes	—
369	C₂²	#484×C₁₂₇	1	2	yes	—
370	C₂²	#493×C₁₂₇	1	1	yes	characteristic
371	C₂²	#494×C₁₂₇	1	1	yes	characteristic
372	C₂²	#496×C₁₂₇	1	1	yes	characteristic
373	C₂²	#497×C₁₂₇	1	1	yes	characteristic
374	C₂²	#500×C₁₂₇	1	2	yes	—
375	C₂²	#501×C₁₂₇	1	2	yes	—
376	C₄	—	2	8	no	—
377	C₄	—	8	2	no	—
378	C₄	—	8	4	no	—
379	C₄	—	8	2	no	—
380	C₄	#385×C₁₂₇	1	2	yes	—
381	C₄	#389×C₁₂₇	1	2	yes	—
382	C₄	#395×C₁₂₇	1	2	yes	—
383	C₄	#398×C₁₂₇	1	2	yes	—
384	C₂	C₁₂₇×#1444	1	1	yes	characteristic
385	C₂	C₁₂₇×#1845	1	1	yes	characteristic
386	C₂	C₁₂₇×#1847	1	1	yes	characteristic
387	C₂	C₁₂₇×#1852	1	2	yes	—
388	C₂	C₁₂₇×#1947	1	2	yes	—
389	C₂	C₁₂₇×#2011	1	1	yes	characteristic
390	C₂	C₁₂₇×#2016	1	1	yes	characteristic
391	C₂	C₁₂₇×#2057	1	2	yes	—
392	C₂	C₁₂₇×#2083	1	2	yes	—
393	C₂	C₁₂₇×#2093	1	1	yes	characteristic
394	C₂	C₁₂₇×#2095	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. #336×C₁₂₇	C₄	semidirect
93. C₂×C₈×C₁₂₇	C₄⋊C₄	semidirect
137. C₂×C₄×C₁₂₇	#107	semidirect
186. #11324	C₁₂₇	direct (N × H)
203. C₁₂₇	#11324	direct (N × H)
216. #336	C₄×C₁₂₇	semidirect
291. C₂×C₈	C₄⋊C₄×C₁₂₇	semidirect
335. C₂×C₄	#107×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×#384×C₁₂₇	2
C₂×#340×C₁₂₇	2
C₂×#336×C₁₂₇	2
C₁₂₇×C₄⋊#95	2
#11324	127

Subgroups — C127×#11324 #44574997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#11324 #44574997