Subgroups — C₂×C₁₂₇×#1481 #44581129

Order 32512.

1066 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄⋊C₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1481	C₂	1	8	yes	maximal, direct product factor
5	C₂×Q₈⋊C₈×C₁₂₇	C₂	1	4	yes	maximal, complemented
6	C₂³×C₈×C₁₂₇	—	2	1	no	—
7	#533×C₁₂₇	—	2	2	no	—
8	#533×C₁₂₇	—	2	2	no	—
9	#533×C₁₂₇	C₄	1	4	yes	—
10	#533×C₁₂₇	C₂²	1	4	yes	—
11	C₂×C₄⋊Q₈×C₁₂₇	C₄	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₁₂₇	C₄	1	1	yes	characteristic
13	C₂×#125×C₁₂₇	—	2	1	no	—
14	C₂×C₂²⋊Q₈×C₁₂₇	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₁₂₇	C₄	1	2	yes	—
16	C₂×C₄×Q₈×C₁₂₇	—	2	1	no	—
17	C₂×C₄×Q₈×C₁₂₇	C₂²	1	2	yes	—
18	C₂×#117×C₁₂₇	—	2	1	no	—
19	C₂²×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
20	#431×C₁₂₇	—	2	2	no	—
21	#431×C₁₂₇	C₂²	1	4	yes	—
22	C₂×C₄⋊C₈×C₁₂₇	—	2	2	no	—
23	C₂×C₄⋊C₈×C₁₂₇	—	2	1	no	—
24	C₂×C₄⋊C₈×C₁₂₇	—	2	1	no	—
25	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
26	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	4	yes	—
27	C₂×C₂²⋊C₈×C₁₂₇	—	2	1	no	—
28	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
29	Q₈⋊C₈×C₁₂₇	C₂²	1	16	yes	complemented
30	C₂²×Q₈×C₁₂₇	—	2	1	no	—
31	C₂²×Q₈×C₁₂₇	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₂₇	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₂₇	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₂₇	—	2	4	no	—
36	C₂²×C₈×C₁₂₇	—	2	2	no	—
37	C₂²×C₈×C₁₂₇	—	2	2	no	—
38	C₂²×C₈×C₁₂₇	—	4	4	no	—
39	C₄⋊Q₈×C₁₂₇	—	2	2	no	—
40	C₄⋊Q₈×C₁₂₇	—	2	2	no	—
41	C₄⋊Q₈×C₁₂₇	C₂×C₄	1	4	yes	—
42	C₄⋊Q₈×C₁₂₇	C₂×C₄	1	4	yes	—
43	#125×C₁₂₇	—	2	4	no	—
44	#125×C₁₂₇	—	2	4	no	—
45	C₂²⋊Q₈×C₁₂₇	—	2	4	no	—
46	C₂²⋊Q₈×C₁₂₇	—	2	4	no	—
47	C₂²⋊Q₈×C₁₂₇	—	2	4	no	—
48	C₂²⋊Q₈×C₁₂₇	C₂×C₄	1	8	yes	—
49	C₄×Q₈×C₁₂₇	—	2	4	no	—
50	C₄×Q₈×C₁₂₇	—	2	4	no	—
51	C₄×Q₈×C₁₂₇	—	2	2	no	—
52	C₄×Q₈×C₁₂₇	—	2	2	no	—
53	C₄×Q₈×C₁₂₇	C₂×C₄	1	4	yes	—
54	C₄×Q₈×C₁₂₇	C₂³	1	4	yes	—
55	#117×C₁₂₇	—	2	4	no	—
56	#117×C₁₂₇	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₂₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₂₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₂₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₂₇	—	2	2	no	—
64	C₂×C₄²×C₁₂₇	—	2	2	no	—
65	C₂×C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₂₇	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₂₇	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₂₇	D₄	1	2	yes	—
69	C₂×C₄²×C₁₂₇	D₄	1	2	yes	—
70	C₂×C₄²×C₁₂₇	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₁₂₇	—	2	2	no	—
74	C₄⋊C₈×C₁₂₇	—	2	4	no	—
75	C₄⋊C₈×C₁₂₇	—	2	4	no	—
76	C₄⋊C₈×C₁₂₇	C₂³	1	4	yes	—
77	C₂²⋊C₈×C₁₂₇	—	2	4	no	—
78	C₄×C₈×C₁₂₇	—	2	2	no	—
79	C₄×C₈×C₁₂₇	C₂³	1	4	yes	—
80	C₂⁴×C₁₂₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×Q₈×C₁₂₇	—	2	2	no	—
82	C₂×Q₈×C₁₂₇	—	2	4	no	—
83	C₂×Q₈×C₁₂₇	—	2	8	no	—
84	C₂×Q₈×C₁₂₇	—	4	4	no	—
85	C₂×Q₈×C₁₂₇	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₁₂₇	—	2	4	no	—
87	C₂²×C₄×C₁₂₇	—	2	2	no	—
88	C₂²×C₄×C₁₂₇	—	2	2	no	—
89	C₂²×C₄×C₁₂₇	—	4	2	no	—
90	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	2	yes	—
94	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₁₂₇	SD₁₆	1	4	yes	—
97	C₂²×C₄×C₁₂₇	Q₁₆	1	4	yes	—
98	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
104	C₂×C₈×C₁₂₇	—	2	4	no	—
105	C₂×C₈×C₁₂₇	—	2	4	no	—
106	C₂×C₈×C₁₂₇	—	4	4	no	—
107	C₂×C₈×C₁₂₇	—	4	8	no	—
108	C₂×C₈×C₁₂₇	—	4	4	no	—
109	C₄⋊C₄×C₁₂₇	—	2	4	no	—
110	C₄⋊C₄×C₁₂₇	—	2	4	no	—
111	C₄⋊C₄×C₁₂₇	—	2	4	no	—
112	C₄⋊C₄×C₁₂₇	—	2	8	no	—
113	C₄⋊C₄×C₁₂₇	—	2	4	no	—
114	C₄⋊C₄×C₁₂₇	—	2	2	no	—
115	C₄⋊C₄×C₁₂₇	—	2	4	no	—
116	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
117	C₂²⋊C₄×C₁₂₇	—	2	8	no	—
118	C₄²×C₁₂₇	—	2	4	no	—
119	C₄²×C₁₂₇	—	2	4	no	—
120	C₄²×C₁₂₇	C₂²⋊C₄	1	2	yes	—
121	C₄²×C₁₂₇	C₂²⋊C₄	1	2	yes	—
122	C₄²×C₁₂₇	C₂²⋊C₄	1	2	yes	—
123	C₄²×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₂₇	C₂²×C₄	1	2	yes	—
125	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
128	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
129	C₄²×C₁₂₇	C₂⁴	1	1	yes	characteristic
130	C₂³×C₁₂₇	—	2	2	no	—
131	C₂³×C₁₂₇	—	2	2	no	—
132	C₂³×C₁₂₇	#103	1	4	yes	—
133	C₂³×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂³×C₁₂₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	Q₈×C₁₂₇	—	2	8	no	—
136	Q₈×C₁₂₇	—	4	8	no	—
137	Q₈×C₁₂₇	—	4	4	no	—
138	C₂×C₄×C₁₂₇	—	2	2	no	—
139	C₂×C₄×C₁₂₇	—	2	2	no	—
140	C₂×C₄×C₁₂₇	—	2	2	no	—
141	C₂×C₄×C₁₂₇	—	2	4	no	—
142	C₂×C₄×C₁₂₇	—	2	4	no	—
143	C₂×C₄×C₁₂₇	—	2	4	no	—
144	C₂×C₄×C₁₂₇	—	2	4	no	—
145	C₂×C₄×C₁₂₇	—	4	2	no	—
146	C₂×C₄×C₁₂₇	—	4	2	no	—
147	C₂×C₄×C₁₂₇	—	4	4	no	—
148	C₂×C₄×C₁₂₇	—	4	4	no	—
149	C₂×C₄×C₁₂₇	#103	1	8	yes	—
150	C₂×C₄×C₁₂₇	#103	1	4	yes	—
151	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₁₂₇	#131	1	4	yes	—
158	C₂×C₄×C₁₂₇	C₂×SD₁₆	1	4	yes	—
159	C₂×C₄×C₁₂₇	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₁₂₇	C₂×Q₁₆	1	4	yes	—
161	C₂×C₄×C₁₂₇	C₂×Q₁₆	1	2	yes	—
162	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
165	C₈×C₁₂₇	—	4	4	no	—
166	C₈×C₁₂₇	—	4	4	no	—
167	C₂²×C₁₂₇	—	2	2	no	—
168	C₂²×C₁₂₇	—	2	2	no	—
169	C₂²×C₁₂₇	—	2	8	no	—
170	C₂²×C₁₂₇	#408	1	2	yes	—
171	C₂²×C₁₂₇	C₂×#103	1	4	yes	—
172	C₂²×C₁₂₇	C₂×#103	1	2	yes	—
173	C₂²×C₁₂₇	#421	1	2	yes	—
174	C₂²×C₁₂₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
175	C₄×C₁₂₇	—	2	2	no	—
176	C₄×C₁₂₇	—	2	1	no	—
177	C₄×C₁₂₇	—	2	1	no	—
178	C₄×C₁₂₇	—	2	2	no	—
179	C₄×C₁₂₇	—	4	4	no	—
180	C₄×C₁₂₇	—	4	4	no	—
181	C₄×C₁₂₇	#408	1	2	yes	—
182	C₄×C₁₂₇	C₂×#103	1	2	yes	—
183	C₄×C₁₂₇	C₂×#103	1	4	yes	—
184	C₄×C₁₂₇	C₂×#131	1	2	yes	—
185	C₄×C₁₂₇	C₂²×SD₁₆	1	1	yes	characteristic
186	C₄×C₁₂₇	C₂²×Q₁₆	1	1	yes	characteristic
187	C₂×#1481	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂×C₁₂₇	—	2	4	no	—
189	C₂×C₁₂₇	#1481	1	4	yes	direct product factor
190	C₂×C₁₂₇	C₂×#408	1	1	yes	characteristic
191	C₂×C₁₂₇	C₂²×#103	1	1	yes	characteristic
192	C₂×C₁₂₇	C₂×#421	1	1	yes	characteristic
193	C₂×#533	C₂×C₁₂₇	1	1	yes	characteristic
194	C₂×#431	C₂×C₁₂₇	1	1	yes	characteristic
195	C₂²×C₄⋊C₈	C₂×C₁₂₇	1	1	yes	characteristic
196	#1481	C₂×C₁₂₇	1	8	yes	direct product factor
197	C₂×Q₈⋊C₈	C₂×C₁₂₇	1	4	yes	complemented
198	C₁₂₇	C₂×#1481	1	1	yes	characteristic, direct product factor, Sylow
199	C₂³×C₈	—	2	1	no	—
200	#533	—	2	2	no	—
201	#533	—	2	2	no	—
202	#533	C₄×C₁₂₇	1	4	yes	—
203	#533	C₂²×C₁₂₇	1	4	yes	—
204	C₂×C₄⋊Q₈	C₄×C₁₂₇	1	1	yes	characteristic
205	C₂×C₄⋊Q₈	C₄×C₁₂₇	1	1	yes	characteristic
206	C₂×#125	—	2	1	no	—
207	C₂×C₂²⋊Q₈	—	2	1	no	—
208	C₂×C₂²⋊Q₈	C₄×C₁₂₇	1	2	yes	—
209	C₂×C₄×Q₈	—	2	1	no	—
210	C₂×C₄×Q₈	C₂²×C₁₂₇	1	2	yes	—
211	C₂×#117	—	2	1	no	—
212	C₂²×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
213	#431	—	2	2	no	—
214	#431	C₂²×C₁₂₇	1	4	yes	—
215	C₂×C₄⋊C₈	—	2	1	no	—
216	C₂×C₄⋊C₈	—	2	2	no	—
217	C₂×C₄⋊C₈	—	2	1	no	—
218	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
219	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	4	yes	—
220	C₂×C₂²⋊C₈	—	2	1	no	—
221	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
222	Q₈⋊C₈	C₂²×C₁₂₇	1	16	yes	complemented
223	C₂²×Q₈	—	2	1	no	—
224	C₂²×Q₈	C₂×C₄×C₁₂₇	1	2	yes	—
225	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
226	C₂³×C₄	D₄×C₁₂₇	1	1	yes	characteristic
227	C₂³×C₄	D₄×C₁₂₇	1	1	yes	characteristic
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	—	2	2	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	4	4	no	—
232	C₄⋊Q₈	—	2	2	no	—
233	C₄⋊Q₈	—	2	2	no	—
234	C₄⋊Q₈	C₂×C₄×C₁₂₇	1	4	yes	—
235	C₄⋊Q₈	C₂×C₄×C₁₂₇	1	4	yes	—
236	#125	—	2	4	no	—
237	#125	—	2	4	no	—
238	C₂²⋊Q₈	—	2	4	no	—
239	C₂²⋊Q₈	—	2	4	no	—
240	C₂²⋊Q₈	—	2	4	no	—
241	C₂²⋊Q₈	C₂×C₄×C₁₂₇	1	8	yes	—
242	C₄×Q₈	—	2	4	no	—
243	C₄×Q₈	—	2	4	no	—
244	C₄×Q₈	—	2	2	no	—
245	C₄×Q₈	—	2	2	no	—
246	C₄×Q₈	C₂×C₄×C₁₂₇	1	4	yes	—
247	C₄×Q₈	C₂³×C₁₂₇	1	4	yes	—
248	#117	—	2	4	no	—
249	#117	—	2	4	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	C₂×C₄×C₁₂₇	1	1	yes	characteristic
259	C₂×C₄²	C₂×C₄×C₁₂₇	1	2	yes	—
260	C₂×C₄²	D₄×C₁₂₇	1	1	yes	characteristic
261	C₂×C₄²	D₄×C₁₂₇	1	1	yes	characteristic
262	C₂×C₄²	D₄×C₁₂₇	1	2	yes	—
263	C₂×C₄²	D₄×C₁₂₇	1	2	yes	—
264	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	2	4	no	—
268	C₄⋊C₈	—	2	4	no	—
269	C₄⋊C₈	C₂³×C₁₂₇	1	4	yes	—
270	C₂²⋊C₈	—	2	4	no	—
271	C₄×C₈	—	2	2	no	—
272	C₄×C₈	C₂³×C₁₂₇	1	4	yes	—
273	C₂⁴	C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	2	8	no	—
277	C₂×Q₈	—	4	4	no	—
278	C₂×Q₈	C₂²×C₄×C₁₂₇	1	4	yes	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
284	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
285	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	2	yes	—
286	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	2	yes	—
287	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
288	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	2	yes	—
289	C₂²×C₄	SD₁₆×C₁₂₇	1	4	yes	—
290	C₂²×C₄	Q₁₆×C₁₂₇	1	4	yes	—
291	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
292	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	4	4	no	—
300	C₂×C₈	—	4	8	no	—
301	C₂×C₈	—	4	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
310	C₂²⋊C₄	—	2	8	no	—
311	C₄²	—	2	4	no	—
312	C₄²	—	2	4	no	—
313	C₄²	C₂²⋊C₄×C₁₂₇	1	2	yes	—
314	C₄²	C₂²⋊C₄×C₁₂₇	1	2	yes	—
315	C₄²	C₂²⋊C₄×C₁₂₇	1	2	yes	—
316	C₄²	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
317	C₄²	C₂²×C₄×C₁₂₇	1	2	yes	—
318	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
319	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
320	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
321	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
322	C₄²	C₂⁴×C₁₂₇	1	1	yes	characteristic
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	#103×C₁₂₇	1	4	yes	—
326	C₂³	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
327	C₂³	C₂×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
328	Q₈	—	2	8	no	—
329	Q₈	—	4	8	no	—
330	Q₈	—	4	4	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	#103×C₁₂₇	1	8	yes	—
343	C₂×C₄	#103×C₁₂₇	1	4	yes	—
344	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
345	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
346	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
347	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
348	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
349	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
350	C₂×C₄	#131×C₁₂₇	1	4	yes	—
351	C₂×C₄	C₂×SD₁₆×C₁₂₇	1	4	yes	—
352	C₂×C₄	C₂×SD₁₆×C₁₂₇	1	2	yes	—
353	C₂×C₄	C₂×Q₁₆×C₁₂₇	1	4	yes	—
354	C₂×C₄	C₂×Q₁₆×C₁₂₇	1	2	yes	—
355	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
356	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
357	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
358	C₈	—	4	4	no	—
359	C₈	—	4	4	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	8	no	—
363	C₂²	#408×C₁₂₇	1	2	yes	—
364	C₂²	C₂×#103×C₁₂₇	1	4	yes	—
365	C₂²	C₂×#103×C₁₂₇	1	2	yes	—
366	C₂²	#421×C₁₂₇	1	2	yes	—
367	C₂²	C₂²×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
368	C₄	—	2	2	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	2	no	—
371	C₄	—	2	1	no	—
372	C₄	—	4	4	no	—
373	C₄	—	4	4	no	—
374	C₄	#408×C₁₂₇	1	2	yes	—
375	C₄	C₂×#103×C₁₂₇	1	2	yes	—
376	C₄	C₂×#103×C₁₂₇	1	4	yes	—
377	C₄	C₂×#131×C₁₂₇	1	2	yes	—
378	C₄	C₂²×SD₁₆×C₁₂₇	1	1	yes	characteristic
379	C₄	C₂²×Q₁₆×C₁₂₇	1	1	yes	characteristic
380	C₂	—	2	4	no	—
381	C₂	C₁₂₇×#1481	1	4	yes	direct product factor
382	C₂	C₂×#408×C₁₂₇	1	1	yes	characteristic
383	C₂	C₂²×#103×C₁₂₇	1	1	yes	characteristic
384	C₂	C₂×#421×C₁₂₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₁₂₇×#1481	C₂	direct (N × H)
5. C₂×Q₈⋊C₈×C₁₂₇	C₂	semidirect
29. Q₈⋊C₈×C₁₂₇	C₂²	semidirect
187. C₂×#1481	C₁₂₇	direct (N × H)
189. C₂×C₁₂₇	#1481	direct (N × H)
196. #1481	C₂×C₁₂₇	direct (N × H)
197. C₂×Q₈⋊C₈	C₂×C₁₂₇	semidirect
198. C₁₂₇	C₂×#1481	direct (N × H)
222. Q₈⋊C₈	C₂²×C₁₂₇	semidirect
381. C₂	C₁₂₇×#1481	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×#533×C₁₂₇	2
C₂×#431×C₁₂₇	2
C₂²×C₄⋊C₈×C₁₂₇	2
C₁₂₇×#1481	2
C₂×Q₈⋊C₈×C₁₂₇	2
C₂×#1481	127

Subgroups — C2×C127×#1481 #44581129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₂₇×#1481 #44581129