Subgroups — C₁₂₇×#21324 #44584997

Order 32512.

1382 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₁₂₇×#2285	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1993	C₂	1	4	yes	maximal, complemented
5	C₁₂₇×#1990	C₂	1	4	yes	maximal, complemented
6	C₁₂₇×#1736	C₂	1	4	yes	maximal
7	C₂³×Q₈×C₁₂₇	—	2	1	no	—
8	C₂²×M₁₆×C₁₂₇	C₂²	1	2	yes	—
9	C₂×C₄⋊Q₈×C₁₂₇	—	2	1	no	—
10	C₂×C₄⋊Q₈×C₁₂₇	—	2	1	no	—
11	C₂×C₄⋊Q₈×C₁₂₇	—	2	4	no	—
12	C₂×C₄⋊Q₈×C₁₂₇	C₄	1	8	yes	complemented
13	C₂×C₄⋊Q₈×C₁₂₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₁₂₇	C₂²	1	2	yes	—
15	C₂×#117×C₁₂₇	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₁₂₇	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
19	C₄×M₁₆×C₁₂₇	—	2	4	no	—
20	C₂×#97×C₁₂₇	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
22	#384×C₁₂₇	C₂²	1	2	yes	—
23	#382×C₁₂₇	C₂²	1	2	yes	—
24	#380×C₁₂₇	—	2	1	no	—
25	#380×C₁₂₇	—	2	1	no	—
26	C₄×C₄⋊C₄×C₁₂₇	—	2	1	no	—
27	C₄×C₄⋊C₄×C₁₂₇	—	2	1	no	—
28	#340×C₁₂₇	C₂²	1	16	yes	—
29	C₂²×Q₈×C₁₂₇	—	2	8	no	—
30	C₂²×Q₈×C₁₂₇	—	2	2	no	—
31	C₂²×Q₈×C₁₂₇	—	2	2	no	—
32	C₂²×Q₈×C₁₂₇	—	4	8	no	—
33	C₂³×C₄×C₁₂₇	—	2	2	no	—
34	C₂³×C₄×C₁₂₇	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₂₇	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
37	C₂×M₁₆×C₁₂₇	—	2	4	no	—
38	C₂×M₁₆×C₁₂₇	—	2	4	no	—
39	C₂×M₁₆×C₁₂₇	Q₈	1	8	yes	complemented
40	C₂²×C₈×C₁₂₇	C₂³	1	4	yes	—
41	C₄⋊Q₈×C₁₂₇	—	2	8	no	—
42	C₄⋊Q₈×C₁₂₇	—	2	8	no	—
43	C₄⋊Q₈×C₁₂₇	—	2	4	no	—
44	C₄⋊Q₈×C₁₂₇	—	2	4	no	—
45	C₄⋊Q₈×C₁₂₇	C₂×C₄	1	8	yes	—
46	C₄⋊Q₈×C₁₂₇	C₂×C₄	1	8	yes	—
47	#117×C₁₂₇	—	2	8	no	—
48	C₂×C₄⋊C₄×C₁₂₇	—	2	8	no	—
49	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₂₇	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	8	yes	—
56	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	4	yes	—
57	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	4	yes	—
58	C₂×C₂²⋊C₄×C₁₂₇	—	2	2	no	—
59	C₂×C₄²×C₁₂₇	—	2	2	no	—
60	C₂×C₄²×C₁₂₇	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₁₂₇	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₂₇	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₂₇	D₄	1	4	yes	—
64	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
66	#97×C₁₂₇	—	2	4	no	—
67	C₄×C₈×C₁₂₇	—	2	4	no	—
68	#95×C₁₂₇	—	2	2	no	—
69	#95×C₁₂₇	—	2	2	no	—
70	C₂⁴×C₁₂₇	C₂×D₄	1	1	yes	characteristic
71	C₂×Q₈×C₁₂₇	—	2	8	no	—
72	C₂×Q₈×C₁₂₇	—	2	8	no	—
73	C₂×Q₈×C₁₂₇	—	4	8	no	—
74	C₂×Q₈×C₁₂₇	—	4	32	no	—
75	C₂×Q₈×C₁₂₇	—	4	8	no	—
76	C₂²×C₄×C₁₂₇	—	2	4	no	—
77	C₂²×C₄×C₁₂₇	—	2	4	no	—
78	C₂²×C₄×C₁₂₇	—	2	8	no	—
79	C₂²×C₄×C₁₂₇	—	2	4	no	—
80	C₂²×C₄×C₁₂₇	—	2	4	no	—
81	C₂²×C₄×C₁₂₇	—	4	8	no	—
82	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	4	yes	—
83	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	4	yes	—
84	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₂₇	C₂×Q₈	1	4	yes	—
92	C₂²×C₄×C₁₂₇	#41	1	4	yes	—
93	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
94	M₁₆×C₁₂₇	—	2	16	no	—
95	C₂×C₈×C₁₂₇	—	2	4	no	—
96	C₂×C₈×C₁₂₇	—	2	4	no	—
97	C₂×C₈×C₁₂₇	C₂×Q₈	1	8	yes	complemented
98	C₄⋊C₄×C₁₂₇	—	2	8	no	—
99	C₄⋊C₄×C₁₂₇	—	2	8	no	—
100	C₄⋊C₄×C₁₂₇	—	2	8	no	—
101	C₄⋊C₄×C₁₂₇	—	2	4	no	—
102	C₄⋊C₄×C₁₂₇	—	2	8	no	—
103	C₄⋊C₄×C₁₂₇	—	4	4	no	—
104	C₄⋊C₄×C₁₂₇	—	4	4	no	—
105	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	8	yes	—
106	C₂²⋊C₄×C₁₂₇	—	4	4	no	—
107	C₄²×C₁₂₇	—	4	4	no	—
108	C₄²×C₁₂₇	C₂²⋊C₄	1	4	yes	—
109	C₄²×C₁₂₇	C₂²⋊C₄	1	4	yes	—
110	C₄²×C₁₂₇	C₂²×C₄	1	2	yes	—
111	C₄²×C₁₂₇	C₂²×C₄	1	2	yes	—
112	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
113	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
114	C₂³×C₁₂₇	—	2	2	no	—
115	C₂³×C₁₂₇	—	2	2	no	—
116	C₂³×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
117	C₂³×C₁₂₇	#124	1	2	yes	—
118	C₂³×C₁₂₇	C₄⋊Q₈	1	2	yes	—
119	C₂³×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
120	Q₈×C₁₂₇	—	4	16	no	—
121	Q₈×C₁₂₇	—	4	16	no	—
122	C₂×C₄×C₁₂₇	—	2	2	no	—
123	C₂×C₄×C₁₂₇	—	2	2	no	—
124	C₂×C₄×C₁₂₇	—	2	8	no	—
125	C₂×C₄×C₁₂₇	—	2	8	no	—
126	C₂×C₄×C₁₂₇	—	2	8	no	—
127	C₂×C₄×C₁₂₇	—	4	16	no	—
128	C₂×C₄×C₁₂₇	—	4	8	no	—
129	C₂×C₄×C₁₂₇	—	4	4	no	—
130	C₂×C₄×C₁₂₇	—	4	4	no	—
131	C₂×C₄×C₁₂₇	—	4	4	no	—
132	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
133	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
135	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
136	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
137	C₂×C₄×C₁₂₇	C₄×Q₈	1	8	yes	—
138	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	8	yes	—
139	C₂×C₄×C₁₂₇	#124	1	2	yes	—
140	C₂×C₄×C₁₂₇	C₄⋊Q₈	1	2	yes	—
141	C₂×C₄×C₁₂₇	AGL(1,ℤ/8)	1	4	yes	—
142	C₂×C₄×C₁₂₇	#137	1	4	yes	—
143	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₂₇	C₂²×Q₈	1	2	yes	—
146	C₂×C₄×C₁₂₇	C₂×#41	1	2	yes	—
147	C₈×C₁₂₇	—	2	8	no	—
148	C₂²×C₁₂₇	—	2	4	no	—
149	C₂²×C₁₂₇	—	2	2	no	—
150	C₂²×C₁₂₇	—	2	2	no	—
151	C₂²×C₁₂₇	—	2	4	no	—
152	C₂²×C₁₂₇	#391	1	4	yes	—
153	C₂²×C₁₂₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₁₂₇	C₂×#124	1	1	yes	characteristic
155	C₂²×C₁₂₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
156	C₂²×C₁₂₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
157	C₂²×C₁₂₇	C₂×#137	1	2	yes	—
158	C₄×C₁₂₇	—	2	2	no	—
159	C₄×C₁₂₇	—	2	2	no	—
160	C₄×C₁₂₇	—	4	8	no	—
161	C₄×C₁₂₇	—	8	4	no	—
162	C₄×C₁₂₇	#391	1	4	yes	—
163	C₄×C₁₂₇	#418	1	4	yes	—
164	C₄×C₁₂₇	#419	1	4	yes	—
165	C₄×C₁₂₇	C₂×C₄×Q₈	1	2	yes	—
166	C₄×C₁₂₇	C₂×C₂²⋊Q₈	1	2	yes	—
167	#21324	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂×C₁₂₇	—	2	4	no	—
169	C₂×C₁₂₇	C₂×#391	1	1	yes	characteristic
170	C₂×C₁₂₇	C₂×#418	1	1	yes	characteristic
171	C₂×C₁₂₇	C₂×#419	1	1	yes	characteristic
172	C₂×C₁₂₇	#3141	1	2	yes	—
173	C₂×C₁₂₇	#3165	1	2	yes	—
174	C₂²×C₄⋊Q₈	C₂×C₁₂₇	1	1	yes	characteristic
175	C₂×C₄×M₁₆	C₂×C₁₂₇	1	1	yes	characteristic
176	#2285	C₂×C₁₂₇	1	1	yes	characteristic
177	#1993	C₂×C₁₂₇	1	4	yes	complemented
178	#1990	C₂×C₁₂₇	1	4	yes	complemented
179	#1736	C₂×C₁₂₇	1	4	yes	—
180	C₁₂₇	#21324	1	1	yes	characteristic, direct product factor, Sylow
181	C₂³×Q₈	—	2	1	no	—
182	C₂²×M₁₆	C₂²×C₁₂₇	1	2	yes	—
183	C₂×C₄⋊Q₈	—	2	1	no	—
184	C₂×C₄⋊Q₈	—	2	1	no	—
185	C₂×C₄⋊Q₈	—	2	4	no	—
186	C₂×C₄⋊Q₈	C₄×C₁₂₇	1	8	yes	complemented
187	C₂×C₄⋊Q₈	C₂²×C₁₂₇	1	2	yes	—
188	C₂×C₄⋊Q₈	C₂²×C₁₂₇	1	2	yes	—
189	C₂×#117	C₂²×C₁₂₇	1	2	yes	—
190	C₂²×C₄⋊C₄	—	2	1	no	—
191	C₂²×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
192	C₂²×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
193	C₄×M₁₆	—	2	4	no	—
194	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
195	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
196	#384	C₂²×C₁₂₇	1	2	yes	—
197	#382	C₂²×C₁₂₇	1	2	yes	—
198	#380	—	2	1	no	—
199	#380	—	2	1	no	—
200	C₄×C₄⋊C₄	—	2	1	no	—
201	C₄×C₄⋊C₄	—	2	1	no	—
202	#340	C₂²×C₁₂₇	1	16	yes	—
203	C₂²×Q₈	—	2	8	no	—
204	C₂²×Q₈	—	2	2	no	—
205	C₂²×Q₈	—	2	2	no	—
206	C₂²×Q₈	—	4	8	no	—
207	C₂³×C₄	—	2	2	no	—
208	C₂³×C₄	D₄×C₁₂₇	1	1	yes	characteristic
209	C₂³×C₄	D₄×C₁₂₇	1	1	yes	characteristic
210	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
211	C₂×M₁₆	—	2	4	no	—
212	C₂×M₁₆	—	2	4	no	—
213	C₂×M₁₆	Q₈×C₁₂₇	1	8	yes	complemented
214	C₂²×C₈	C₂³×C₁₂₇	1	4	yes	—
215	C₄⋊Q₈	—	2	8	no	—
216	C₄⋊Q₈	—	2	8	no	—
217	C₄⋊Q₈	—	2	4	no	—
218	C₄⋊Q₈	—	2	4	no	—
219	C₄⋊Q₈	C₂×C₄×C₁₂₇	1	8	yes	—
220	C₄⋊Q₈	C₂×C₄×C₁₂₇	1	8	yes	—
221	#117	—	2	8	no	—
222	C₂×C₄⋊C₄	—	2	8	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	2	no	—
226	C₂×C₄⋊C₄	—	2	4	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	8	yes	—
230	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	4	yes	—
231	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	4	yes	—
232	C₂×C₂²⋊C₄	—	2	2	no	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	C₂×C₄×C₁₂₇	1	4	yes	—
235	C₂×C₄²	D₄×C₁₂₇	1	1	yes	characteristic
236	C₂×C₄²	D₄×C₁₂₇	1	1	yes	characteristic
237	C₂×C₄²	D₄×C₁₂₇	1	4	yes	—
238	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
240	#97	—	2	4	no	—
241	C₄×C₈	—	2	4	no	—
242	#95	—	2	2	no	—
243	#95	—	2	2	no	—
244	C₂⁴	C₂×D₄×C₁₂₇	1	1	yes	characteristic
245	C₂×Q₈	—	2	8	no	—
246	C₂×Q₈	—	2	8	no	—
247	C₂×Q₈	—	4	8	no	—
248	C₂×Q₈	—	4	32	no	—
249	C₂×Q₈	—	4	8	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	4	8	no	—
256	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	4	yes	—
257	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	4	yes	—
258	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
259	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
260	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
261	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
265	C₂²×C₄	C₂×Q₈×C₁₂₇	1	4	yes	—
266	C₂²×C₄	#41×C₁₂₇	1	4	yes	—
267	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
268	M₁₆	—	2	16	no	—
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	2	4	no	—
271	C₂×C₈	C₂×Q₈×C₁₂₇	1	8	yes	complemented
272	C₄⋊C₄	—	2	8	no	—
273	C₄⋊C₄	—	2	8	no	—
274	C₄⋊C₄	—	2	8	no	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	—	2	8	no	—
277	C₄⋊C₄	—	4	4	no	—
278	C₄⋊C₄	—	4	4	no	—
279	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	8	yes	—
280	C₂²⋊C₄	—	4	4	no	—
281	C₄²	—	4	4	no	—
282	C₄²	C₂²⋊C₄×C₁₂₇	1	4	yes	—
283	C₄²	C₂²⋊C₄×C₁₂₇	1	4	yes	—
284	C₄²	C₂²×C₄×C₁₂₇	1	2	yes	—
285	C₄²	C₂²×C₄×C₁₂₇	1	2	yes	—
286	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
287	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	2	no	—
290	C₂³	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
291	C₂³	#124×C₁₂₇	1	2	yes	—
292	C₂³	C₄⋊Q₈×C₁₂₇	1	2	yes	—
293	C₂³	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
294	Q₈	—	4	16	no	—
295	Q₈	—	4	16	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	4	16	no	—
302	C₂×C₄	—	4	8	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	—	4	4	no	—
305	C₂×C₄	—	4	4	no	—
306	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
307	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
308	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
309	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
310	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
311	C₂×C₄	C₄×Q₈×C₁₂₇	1	8	yes	—
312	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	8	yes	—
313	C₂×C₄	#124×C₁₂₇	1	2	yes	—
314	C₂×C₄	C₄⋊Q₈×C₁₂₇	1	2	yes	—
315	C₂×C₄	AGL(1,ℤ/8)×C₁₂₇	1	4	yes	—
316	C₂×C₄	#137×C₁₂₇	1	4	yes	—
317	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
318	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
319	C₂×C₄	C₂²×Q₈×C₁₂₇	1	2	yes	—
320	C₂×C₄	C₂×#41×C₁₂₇	1	2	yes	—
321	C₈	—	2	8	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	2	4	no	—
326	C₂²	#391×C₁₂₇	1	4	yes	—
327	C₂²	C₂²×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
328	C₂²	C₂×#124×C₁₂₇	1	1	yes	characteristic
329	C₂²	C₂×C₄⋊Q₈×C₁₂₇	1	1	yes	characteristic
330	C₂²	C₂×AGL(1,ℤ/8)×C₁₂₇	1	2	yes	—
331	C₂²	C₂×#137×C₁₂₇	1	2	yes	—
332	C₄	—	2	2	no	—
333	C₄	—	2	2	no	—
334	C₄	—	4	8	no	—
335	C₄	—	8	4	no	—
336	C₄	#391×C₁₂₇	1	4	yes	—
337	C₄	#418×C₁₂₇	1	4	yes	—
338	C₄	#419×C₁₂₇	1	4	yes	—
339	C₄	C₂×C₄×Q₈×C₁₂₇	1	2	yes	—
340	C₄	C₂×C₂²⋊Q₈×C₁₂₇	1	2	yes	—
341	C₂	—	2	4	no	—
342	C₂	C₂×#391×C₁₂₇	1	1	yes	characteristic
343	C₂	C₂×#418×C₁₂₇	1	1	yes	characteristic
344	C₂	C₂×#419×C₁₂₇	1	1	yes	characteristic
345	C₂	C₁₂₇×#3141	1	2	yes	—
346	C₂	C₁₂₇×#3165	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₁₂₇×#1993	C₂	semidirect
5. C₁₂₇×#1990	C₂	semidirect
12. C₂×C₄⋊Q₈×C₁₂₇	C₄	semidirect
39. C₂×M₁₆×C₁₂₇	Q₈	semidirect
97. C₂×C₈×C₁₂₇	C₂×Q₈	semidirect
167. #21324	C₁₂₇	direct (N × H)
177. #1993	C₂×C₁₂₇	semidirect
178. #1990	C₂×C₁₂₇	semidirect
180. C₁₂₇	#21324	direct (N × H)
186. C₂×C₄⋊Q₈	C₄×C₁₂₇	semidirect
213. C₂×M₁₆	Q₈×C₁₂₇	semidirect
271. C₂×C₈	C₂×Q₈×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₁₂₇	2
C₂×C₄×M₁₆×C₁₂₇	2
C₁₂₇×#2285	2
C₁₂₇×#1993	2
C₁₂₇×#1990	2
C₁₂₇×#1736	2
#21324	127

Subgroups — C127×#21324 #44584997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#21324 #44584997