Subgroups — C₈×C₂²⋊Q₈×C₁₂₇ #44585268

Order 32512.

990 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Q₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂²⋊Q₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₂₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₂₇×#1916	C₂	1	2	yes	maximal, complemented
7	C₁₂₇×#1850	C₂	1	2	yes	maximal
8	C₁₂₇×#1797	C₂	1	1	yes	maximal, characteristic
9	C₈×C₄⋊C₄×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₄⋊C₄×C₁₂₇	C₂	1	2	yes	maximal, complemented
11	C₈×C₂²⋊C₄×C₁₂₇	C₂	1	2	yes	maximal
12	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₁₂₇	C₄	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
17	C₈×Q₈×C₁₂₇	—	2	4	no	—
18	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₂₇	—	2	4	no	—
24	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
30	#391×C₁₂₇	C₄	1	1	yes	characteristic
31	#389×C₁₂₇	C₄	1	1	yes	characteristic
32	#387×C₁₂₇	C₄	1	2	yes	—
33	#385×C₁₂₇	C₄	1	2	yes	—
34	#380×C₁₂₇	C₄	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₁₂₇	C₂²	1	2	yes	—
38	#336×C₁₂₇	C₂²	1	2	yes	—
39	#336×C₁₂₇	C₂²	1	2	yes	—
40	#336×C₁₂₇	C₂²	1	2	yes	—
41	#336×C₁₂₇	C₂²	1	2	yes	—
42	#336×C₁₂₇	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₂₇	—	2	2	no	—
48	C₂²×C₈×C₁₂₇	—	2	2	no	—
49	C₂²×C₈×C₁₂₇	—	2	2	no	—
50	C₂²×C₈×C₁₂₇	—	2	2	no	—
51	C₂²×C₈×C₁₂₇	—	2	2	no	—
52	C₂²×C₈×C₁₂₇	Q₈	1	4	yes	complemented
53	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
59	C₂²⋊Q₈×C₁₂₇	C₈	1	8	yes	direct product factor
60	C₄×Q₈×C₁₂₇	—	2	2	no	—
61	C₄×Q₈×C₁₂₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₁₂₇	—	2	2	no	—
71	C₂×C₄²×C₁₂₇	—	2	2	no	—
72	C₂×C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
76	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₁₂₇	—	2	4	no	—
79	C₄⋊C₈×C₁₂₇	—	2	4	no	—
80	C₄⋊C₈×C₁₂₇	—	2	2	no	—
81	C₄⋊C₈×C₁₂₇	—	2	2	no	—
82	C₂²⋊C₈×C₁₂₇	—	2	4	no	—
83	C₄×C₈×C₁₂₇	—	2	2	no	—
84	C₄×C₈×C₁₂₇	—	2	2	no	—
85	C₄×C₈×C₁₂₇	—	2	4	no	—
86	C₄×C₈×C₁₂₇	—	2	4	no	—
87	C₄×C₈×C₁₂₇	—	2	2	no	—
88	C₄×C₈×C₁₂₇	D₄	1	4	yes	—
89	#95×C₁₂₇	C₂×C₄	1	2	yes	—
90	#95×C₁₂₇	C₂×C₄	1	2	yes	—
91	#95×C₁₂₇	C₂×C₄	1	2	yes	—
92	#95×C₁₂₇	C₂×C₄	1	2	yes	—
93	#95×C₁₂₇	C₂×C₄	1	2	yes	—
94	C₂⁴×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
95	C₂×Q₈×C₁₂₇	—	2	2	no	—
96	C₂×Q₈×C₁₂₇	—	2	2	no	—
97	C₂×Q₈×C₁₂₇	C₂×C₈	1	4	yes	complemented
98	C₂²×C₄×C₁₂₇	—	2	2	no	—
99	C₂²×C₄×C₁₂₇	—	2	2	no	—
100	C₂²×C₄×C₁₂₇	—	2	2	no	—
101	C₂²×C₄×C₁₂₇	—	2	2	no	—
102	C₂²×C₄×C₁₂₇	—	2	2	no	—
103	C₂²×C₄×C₁₂₇	—	2	1	no	—
104	C₂²×C₄×C₁₂₇	—	2	1	no	—
105	C₂²×C₄×C₁₂₇	—	2	1	no	—
106	C₂²×C₄×C₁₂₇	—	2	1	no	—
107	C₂²×C₄×C₁₂₇	C₂×C₈	1	4	yes	—
108	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₂₇	C₂×Q₈	1	2	yes	—
118	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
119	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₁₂₇	—	2	8	no	—
121	C₂×C₈×C₁₂₇	—	2	1	no	—
122	C₂×C₈×C₁₂₇	—	2	1	no	—
123	C₂×C₈×C₁₂₇	—	2	1	no	—
124	C₂×C₈×C₁₂₇	—	2	1	no	—
125	C₂×C₈×C₁₂₇	—	2	1	no	—
126	C₂×C₈×C₁₂₇	—	2	1	no	—
127	C₂×C₈×C₁₂₇	—	2	8	no	—
128	C₂×C₈×C₁₂₇	—	2	2	no	—
129	C₂×C₈×C₁₂₇	—	2	2	no	—
130	C₂×C₈×C₁₂₇	—	2	2	no	—
131	C₂×C₈×C₁₂₇	—	2	2	no	—
132	C₂×C₈×C₁₂₇	—	2	2	no	—
133	C₂×C₈×C₁₂₇	—	2	2	no	—
134	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₁₂₇	C₂×Q₈	1	2	yes	—
137	C₂×C₈×C₁₂₇	C₂×Q₈	1	2	yes	—
138	C₂×C₈×C₁₂₇	#41	1	2	yes	—
139	C₂×C₈×C₁₂₇	#41	1	2	yes	—
140	C₄⋊C₄×C₁₂₇	—	2	4	no	—
141	C₄⋊C₄×C₁₂₇	—	2	2	no	—
142	C₄⋊C₄×C₁₂₇	—	2	4	no	—
143	C₄⋊C₄×C₁₂₇	—	2	2	no	—
144	C₄⋊C₄×C₁₂₇	C₂×C₈	1	4	yes	complemented
145	C₄⋊C₄×C₁₂₇	C₂×C₈	1	8	yes	complemented
146	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
147	C₂²⋊C₄×C₁₂₇	C₂×C₈	1	8	yes	—
148	C₄²×C₁₂₇	—	2	2	no	—
149	C₄²×C₁₂₇	—	2	2	no	—
150	C₄²×C₁₂₇	—	2	1	no	—
151	C₄²×C₁₂₇	—	2	2	no	—
152	C₄²×C₁₂₇	—	2	2	no	—
153	C₄²×C₁₂₇	—	2	2	no	—
154	C₄²×C₁₂₇	—	2	1	no	—
155	C₄²×C₁₂₇	—	2	2	no	—
156	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
157	C₄²×C₁₂₇	#41	1	2	yes	—
158	C₂³×C₁₂₇	—	2	1	no	—
159	C₂³×C₁₂₇	—	2	1	no	—
160	C₂³×C₁₂₇	—	2	1	no	—
161	C₂³×C₁₂₇	—	2	1	no	—
162	C₂³×C₁₂₇	C₄×Q₈	1	2	yes	—
163	C₂³×C₁₂₇	C₂²×C₈	1	2	yes	—
164	C₂³×C₁₂₇	#131	1	2	yes	—
165	C₂³×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
166	Q₈×C₁₂₇	—	2	8	no	—
167	C₂×C₄×C₁₂₇	—	2	8	no	—
168	C₂×C₄×C₁₂₇	—	2	1	no	—
169	C₂×C₄×C₁₂₇	—	2	1	no	—
170	C₂×C₄×C₁₂₇	—	2	1	no	—
171	C₂×C₄×C₁₂₇	—	2	2	no	—
172	C₂×C₄×C₁₂₇	—	2	2	no	—
173	C₂×C₄×C₁₂₇	—	2	1	no	—
174	C₂×C₄×C₁₂₇	—	2	2	no	—
175	C₂×C₄×C₁₂₇	—	2	1	no	—
176	C₂×C₄×C₁₂₇	—	2	1	no	—
177	C₂×C₄×C₁₂₇	—	2	1	no	—
178	C₂×C₄×C₁₂₇	—	2	1	no	—
179	C₂×C₄×C₁₂₇	—	2	2	no	—
180	C₂×C₄×C₁₂₇	—	2	2	no	—
181	C₂×C₄×C₁₂₇	—	2	2	no	—
182	C₂×C₄×C₁₂₇	—	2	2	no	—
183	C₂×C₄×C₁₂₇	—	2	2	no	—
184	C₂×C₄×C₁₂₇	—	2	8	no	—
185	C₂×C₄×C₁₂₇	—	2	2	no	—
186	C₂×C₄×C₁₂₇	—	2	2	no	—
187	C₂×C₄×C₁₂₇	—	2	2	no	—
188	C₂×C₄×C₁₂₇	—	2	2	no	—
189	C₂×C₄×C₁₂₇	—	2	2	no	—
190	C₂×C₄×C₁₂₇	—	2	2	no	—
191	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
193	C₂×C₄×C₁₂₇	C₄×Q₈	1	2	yes	—
194	C₂×C₄×C₁₂₇	C₂²×C₈	1	4	yes	—
195	C₂×C₄×C₁₂₇	C₂²×C₈	1	4	yes	—
196	C₂×C₄×C₁₂₇	C₂²×C₈	1	2	yes	—
197	C₂×C₄×C₁₂₇	C₂²×C₈	1	2	yes	—
198	C₂×C₄×C₁₂₇	#131	1	2	yes	—
199	C₂×C₄×C₁₂₇	#131	1	2	yes	—
200	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₂₇	C₂²×Q₈	1	1	yes	characteristic
202	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
206	C₈×C₁₂₇	—	2	2	no	—
207	C₈×C₁₂₇	—	2	2	no	—
208	C₈×C₁₂₇	—	2	2	no	—
209	C₈×C₁₂₇	—	4	2	no	—
210	C₈×C₁₂₇	—	4	2	no	—
211	C₈×C₁₂₇	C₂²⋊Q₈	1	4	yes	direct product factor
212	C₂²×C₁₂₇	—	2	2	no	—
213	C₂²×C₁₂₇	—	2	2	no	—
214	C₂²×C₁₂₇	—	2	2	no	—
215	C₂²×C₁₂₇	—	2	2	no	—
216	C₂²×C₁₂₇	—	2	2	no	—
217	C₂²×C₁₂₇	—	2	2	no	—
218	C₂²×C₁₂₇	C₈×Q₈	1	4	yes	complemented
219	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
220	C₂²×C₁₂₇	C₂×C₄×Q₈	1	1	yes	characteristic
221	C₂²×C₁₂₇	C₄×#41	1	1	yes	characteristic
222	C₂²×C₁₂₇	C₂³×C₈	1	1	yes	characteristic
223	C₂²×C₁₂₇	C₂×#131	1	1	yes	characteristic
224	C₂²×C₁₂₇	C₂×#131	1	1	yes	characteristic
225	C₂²×C₁₂₇	C₂×#131	1	1	yes	characteristic
226	C₄×C₁₂₇	—	2	2	no	—
227	C₄×C₁₂₇	—	2	4	no	—
228	C₄×C₁₂₇	—	2	2	no	—
229	C₄×C₁₂₇	—	2	2	no	—
230	C₄×C₁₂₇	—	2	4	no	—
231	C₄×C₁₂₇	—	2	2	no	—
232	C₄×C₁₂₇	—	4	2	no	—
233	C₄×C₁₂₇	—	4	2	no	—
234	C₄×C₁₂₇	C₈×D₄	1	4	yes	—
235	C₄×C₁₂₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
236	C₄×C₁₂₇	#525	1	1	yes	characteristic
237	C₄×C₁₂₇	#529	1	1	yes	characteristic
238	C₄×C₁₂₇	#533	1	1	yes	characteristic
239	C₈×C₂²⋊Q₈	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂×C₁₂₇	—	2	4	no	—
241	C₂×C₁₂₇	C₄×C₂²⋊Q₈	1	1	yes	characteristic
242	C₂×C₁₂₇	C₂×C₈×D₄	1	1	yes	characteristic
243	C₂×C₁₂₇	#2929	1	1	yes	characteristic
244	C₂×C₁₂₇	C₂×C₈×Q₈	1	1	yes	characteristic
245	C₂×C₁₂₇	#2960	1	1	yes	characteristic
246	C₂×C₁₂₇	C₈×#41	1	1	yes	characteristic
247	C₂×C₁₂₇	#2966	1	1	yes	characteristic
248	C₂×C₈×Q₈	C₂×C₁₂₇	1	1	yes	characteristic, complemented
249	C₂²×C₄×C₈	C₂×C₁₂₇	1	1	yes	characteristic
250	C₄×C₂²⋊Q₈	C₂×C₁₂₇	1	1	yes	characteristic
251	#1984	C₂×C₁₂₇	1	1	yes	characteristic, complemented
252	#1939	C₂×C₁₂₇	1	1	yes	characteristic, complemented
253	#1916	C₂×C₁₂₇	1	2	yes	complemented
254	#1850	C₂×C₁₂₇	1	2	yes	—
255	#1797	C₂×C₁₂₇	1	1	yes	characteristic
256	C₈×C₄⋊C₄	C₂×C₁₂₇	1	2	yes	complemented
257	C₈×C₄⋊C₄	C₂×C₁₂₇	1	1	yes	characteristic, complemented
258	C₈×C₂²⋊C₄	C₂×C₁₂₇	1	2	yes	—
259	C₁₂₇	C₈×C₂²⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
260	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
261	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
262	C₂×C₂²⋊Q₈	C₄×C₁₂₇	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂²×C₁₂₇	1	1	yes	characteristic
264	C₂²×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
265	C₈×Q₈	—	2	4	no	—
266	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
269	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
270	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	—
271	C₂×C₄×C₈	—	2	4	no	—
272	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
273	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
274	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
275	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
276	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
277	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
278	#391	C₄×C₁₂₇	1	1	yes	characteristic
279	#389	C₄×C₁₂₇	1	1	yes	characteristic
280	#387	C₄×C₁₂₇	1	2	yes	—
281	#385	C₄×C₁₂₇	1	2	yes	—
282	#380	C₄×C₁₂₇	1	1	yes	characteristic
283	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
284	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	1	yes	characteristic
285	C₄×C₂²⋊C₄	C₂²×C₁₂₇	1	2	yes	—
286	#336	C₂²×C₁₂₇	1	2	yes	—
287	#336	C₂²×C₁₂₇	1	2	yes	—
288	#336	C₂²×C₁₂₇	1	2	yes	—
289	#336	C₂²×C₁₂₇	1	2	yes	—
290	#336	C₂²×C₁₂₇	1	2	yes	—
291	C₂²×Q₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
292	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
293	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
295	C₂²×C₈	—	2	2	no	—
296	C₂²×C₈	—	2	2	no	—
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	2	2	no	—
299	C₂²×C₈	—	2	2	no	—
300	C₂²×C₈	Q₈×C₁₂₇	1	4	yes	complemented
301	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
302	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
303	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
307	C₂²⋊Q₈	C₈×C₁₂₇	1	8	yes	direct product factor
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
312	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
314	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
315	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
317	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	C₂×C₄×C₁₂₇	1	1	yes	characteristic
321	C₂×C₄²	C₂×C₄×C₁₂₇	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
323	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
324	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
326	C₄⋊C₈	—	2	4	no	—
327	C₄⋊C₈	—	2	4	no	—
328	C₄⋊C₈	—	2	2	no	—
329	C₄⋊C₈	—	2	2	no	—
330	C₂²⋊C₈	—	2	4	no	—
331	C₄×C₈	—	2	2	no	—
332	C₄×C₈	—	2	2	no	—
333	C₄×C₈	—	2	4	no	—
334	C₄×C₈	—	2	4	no	—
335	C₄×C₈	—	2	2	no	—
336	C₄×C₈	D₄×C₁₂₇	1	4	yes	—
337	#95	C₂×C₄×C₁₂₇	1	2	yes	—
338	#95	C₂×C₄×C₁₂₇	1	2	yes	—
339	#95	C₂×C₄×C₁₂₇	1	2	yes	—
340	#95	C₂×C₄×C₁₂₇	1	2	yes	—
341	#95	C₂×C₄×C₁₂₇	1	2	yes	—
342	C₂⁴	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	C₂×C₈×C₁₂₇	1	4	yes	complemented
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	C₂×C₈×C₁₂₇	1	4	yes	—
356	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
357	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
358	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
359	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
360	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
361	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
362	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
363	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
364	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
365	C₂²×C₄	C₂×Q₈×C₁₂₇	1	2	yes	—
366	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
368	C₂×C₈	—	2	8	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	8	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
383	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
384	C₂×C₈	C₂×Q₈×C₁₂₇	1	2	yes	—
385	C₂×C₈	C₂×Q₈×C₁₂₇	1	2	yes	—
386	C₂×C₈	#41×C₁₂₇	1	2	yes	—
387	C₂×C₈	#41×C₁₂₇	1	2	yes	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	C₂×C₈×C₁₂₇	1	4	yes	complemented
393	C₄⋊C₄	C₂×C₈×C₁₂₇	1	8	yes	complemented
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	C₂×C₈×C₁₂₇	1	8	yes	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	2	no	—
404	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
405	C₄²	#41×C₁₂₇	1	2	yes	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	C₄×Q₈×C₁₂₇	1	2	yes	—
411	C₂³	C₂²×C₈×C₁₂₇	1	2	yes	—
412	C₂³	#131×C₁₂₇	1	2	yes	—
413	C₂³	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
414	Q₈	—	2	8	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
440	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
441	C₂×C₄	C₄×Q₈×C₁₂₇	1	2	yes	—
442	C₂×C₄	C₂²×C₈×C₁₂₇	1	4	yes	—
443	C₂×C₄	C₂²×C₈×C₁₂₇	1	4	yes	—
444	C₂×C₄	C₂²×C₈×C₁₂₇	1	2	yes	—
445	C₂×C₄	C₂²×C₈×C₁₂₇	1	2	yes	—
446	C₂×C₄	#131×C₁₂₇	1	2	yes	—
447	C₂×C₄	#131×C₁₂₇	1	2	yes	—
448	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
449	C₂×C₄	C₂²×Q₈×C₁₂₇	1	1	yes	characteristic
450	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
451	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₈	—	2	2	no	—
457	C₈	—	4	2	no	—
458	C₈	—	4	2	no	—
459	C₈	C₂²⋊Q₈×C₁₂₇	1	4	yes	direct product factor
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	C₈×Q₈×C₁₂₇	1	4	yes	complemented
467	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
468	C₂²	C₂×C₄×Q₈×C₁₂₇	1	1	yes	characteristic
469	C₂²	C₄×#41×C₁₂₇	1	1	yes	characteristic
470	C₂²	C₂³×C₈×C₁₂₇	1	1	yes	characteristic
471	C₂²	C₂×#131×C₁₂₇	1	1	yes	characteristic
472	C₂²	C₂×#131×C₁₂₇	1	1	yes	characteristic
473	C₂²	C₂×#131×C₁₂₇	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	4	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	4	no	—
479	C₄	—	2	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	C₈×D₄×C₁₂₇	1	4	yes	—
483	C₄	C₂×C₂²⋊Q₈×C₁₂₇	1	1	yes	characteristic
484	C₄	#525×C₁₂₇	1	1	yes	characteristic
485	C₄	#529×C₁₂₇	1	1	yes	characteristic
486	C₄	#533×C₁₂₇	1	1	yes	characteristic
487	C₂	—	2	4	no	—
488	C₂	C₄×C₂²⋊Q₈×C₁₂₇	1	1	yes	characteristic
489	C₂	C₂×C₈×D₄×C₁₂₇	1	1	yes	characteristic
490	C₂	C₁₂₇×#2929	1	1	yes	characteristic
491	C₂	C₂×C₈×Q₈×C₁₂₇	1	1	yes	characteristic
492	C₂	C₁₂₇×#2960	1	1	yes	characteristic
493	C₂	C₈×#41×C₁₂₇	1	1	yes	characteristic
494	C₂	C₁₂₇×#2966	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈×C₁₂₇	C₂³
commutator	C₂²	C₂³×C₈×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₂₇
socle	C₂³×C₁₂₇	C₂³×C₄
prime radical	C₂⁴×C₁₂₇	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×Q₈×C₁₂₇	C₂	semidirect
4. C₁₂₇×#1984	C₂	semidirect
5. C₁₂₇×#1939	C₂	semidirect
6. C₁₂₇×#1916	C₂	semidirect
9. C₈×C₄⋊C₄×C₁₂₇	C₂	semidirect
10. C₈×C₄⋊C₄×C₁₂₇	C₂	semidirect
52. C₂²×C₈×C₁₂₇	Q₈	semidirect
59. C₂²⋊Q₈×C₁₂₇	C₈	direct (N × H)
97. C₂×Q₈×C₁₂₇	C₂×C₈	semidirect
144. C₄⋊C₄×C₁₂₇	C₂×C₈	semidirect
145. C₄⋊C₄×C₁₂₇	C₂×C₈	semidirect
211. C₈×C₁₂₇	C₂²⋊Q₈	direct (N × H)
218. C₂²×C₁₂₇	C₈×Q₈	semidirect
239. C₈×C₂²⋊Q₈	C₁₂₇	direct (N × H)
248. C₂×C₈×Q₈	C₂×C₁₂₇	semidirect
251. #1984	C₂×C₁₂₇	semidirect
252. #1939	C₂×C₁₂₇	semidirect
253. #1916	C₂×C₁₂₇	semidirect
256. C₈×C₄⋊C₄	C₂×C₁₂₇	semidirect
257. C₈×C₄⋊C₄	C₂×C₁₂₇	semidirect
259. C₁₂₇	C₈×C₂²⋊Q₈	direct (N × H)
300. C₂²×C₈	Q₈×C₁₂₇	semidirect
307. C₂²⋊Q₈	C₈×C₁₂₇	direct (N × H)
345. C₂×Q₈	C₂×C₈×C₁₂₇	semidirect
392. C₄⋊C₄	C₂×C₈×C₁₂₇	semidirect
393. C₄⋊C₄	C₂×C₈×C₁₂₇	semidirect
459. C₈	C₂²⋊Q₈×C₁₂₇	direct (N × H)
466. C₂²	C₈×Q₈×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×Q₈×C₁₂₇	2
C₂²×C₄×C₈×C₁₂₇	2
C₄×C₂²⋊Q₈×C₁₂₇	2
C₁₂₇×#1984	2
C₁₂₇×#1939	2
C₁₂₇×#1916	2
C₁₂₇×#1850	2
C₁₂₇×#1797	2
C₈×C₄⋊C₄×C₁₂₇	2
C₈×C₂²⋊C₄×C₁₂₇	2
C₈×C₂²⋊Q₈	127

Subgroups — C8×C22⋊Q8×C127 #44585268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₂²⋊Q₈×C₁₂₇ #44585268