Subgroups — C₂×C₁₂₇×#1922 #44584713

Order 32512.

854 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#427×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#424×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#405×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1922	C₂	1	8	yes	maximal, direct product factor
5	C₂×#341×C₁₂₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#339×C₁₂₇	C₂	1	1	yes	maximal, characteristic
7	C₂×#339×C₁₂₇	C₂	1	1	yes	maximal, characteristic
8	C₂×#336×C₁₂₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×M₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂×#117×C₁₂₇	C₂²	1	1	yes	characteristic
14	C₂×#117×C₁₂₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
16	#427×C₁₂₇	C₄	1	4	yes	complemented
17	#427×C₁₂₇	C₂²	1	4	yes	—
18	C₂×#107×C₁₂₇	C₄	1	1	yes	characteristic, complemented
19	C₂×#107×C₁₂₇	C₄	1	1	yes	characteristic, complemented
20	C₂×#106×C₁₂₇	C₄	1	1	yes	characteristic, complemented
21	C₂×#106×C₁₂₇	C₄	1	1	yes	characteristic, complemented
22	#424×C₁₂₇	—	2	2	no	—
23	#424×C₁₂₇	C₂²	1	4	yes	—
24	C₂×C₄⋊C₈×C₁₂₇	—	2	1	no	—
25	C₂×C₄⋊C₈×C₁₂₇	—	2	1	no	—
26	#405×C₁₂₇	—	2	2	no	—
27	#405×C₁₂₇	C₂²	1	4	yes	—
28	C₂×#97×C₁₂₇	—	2	1	no	—
29	C₂×C₄×C₈×C₁₂₇	—	2	1	no	—
30	#341×C₁₂₇	C₂²	1	4	yes	—
31	#339×C₁₂₇	C₂²	1	4	yes	—
32	#339×C₁₂₇	C₂²	1	4	yes	—
33	#336×C₁₂₇	C₂²	1	4	yes	—
34	C₂³×C₄×C₁₂₇	—	2	1	no	—
35	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₁₂₇	—	2	1	no	—
37	C₂×M₁₆×C₁₂₇	—	2	2	no	—
38	C₂×M₁₆×C₁₂₇	—	2	1	no	—
39	C₂×M₁₆×C₁₂₇	—	2	2	no	—
40	C₂×M₁₆×C₁₂₇	—	2	2	no	—
41	C₂×M₁₆×C₁₂₇	Q₈	1	4	yes	—
42	C₂×M₁₆×C₁₂₇	C₂³	1	2	yes	—
43	C₂×M₁₆×C₁₂₇	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₂₇	—	2	1	no	—
45	C₂²×C₈×C₁₂₇	—	2	2	no	—
46	C₂²×C₈×C₁₂₇	—	2	2	no	—
47	C₂²×C₈×C₁₂₇	—	2	2	no	—
48	C₂²×C₈×C₁₂₇	—	2	2	no	—
49	C₂²×C₈×C₁₂₇	—	2	1	no	—
50	C₂²×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₂₇	C₂×C₄	1	2	yes	—
53	C₂²×C₈×C₁₂₇	D₄	1	2	yes	—
54	C₂²×C₈×C₁₂₇	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₂₇	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
58	#117×C₁₂₇	—	2	1	no	—
59	#117×C₁₂₇	—	2	1	no	—
60	#117×C₁₂₇	—	2	1	no	—
61	#117×C₁₂₇	—	2	1	no	—
62	#117×C₁₂₇	C₂×C₄	1	2	yes	—
63	#117×C₁₂₇	C₂×C₄	1	2	yes	—
64	#117×C₁₂₇	C₂³	1	2	yes	—
65	#117×C₁₂₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₁₂₇	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₁₂₇	—	2	1	no	—
72	C₂×C₄²×C₁₂₇	—	2	1	no	—
73	C₂×C₄²×C₁₂₇	—	2	1	no	—
74	C₂×C₄²×C₁₂₇	—	2	2	no	—
75	C₂×C₄²×C₁₂₇	—	2	2	no	—
76	C₂×C₄²×C₁₂₇	—	2	1	no	—
77	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
78	#107×C₁₂₇	C₂×C₄	1	4	yes	complemented
79	#107×C₁₂₇	C₂×C₄	1	4	yes	complemented
80	#106×C₁₂₇	C₂×C₄	1	4	yes	complemented
81	#106×C₁₂₇	C₂×C₄	1	4	yes	complemented
82	C₄⋊C₈×C₁₂₇	—	2	4	no	—
83	C₄⋊C₈×C₁₂₇	—	2	4	no	—
84	#97×C₁₂₇	—	2	4	no	—
85	C₄×C₈×C₁₂₇	—	2	4	no	—
86	C₂⁴×C₁₂₇	#41	1	1	yes	characteristic
87	C₂²×C₄×C₁₂₇	—	2	4	no	—
88	C₂²×C₄×C₁₂₇	—	2	1	no	—
89	C₂²×C₄×C₁₂₇	—	2	1	no	—
90	C₂²×C₄×C₁₂₇	—	2	1	no	—
91	C₂²×C₄×C₁₂₇	—	2	1	no	—
92	C₂²×C₄×C₁₂₇	—	2	2	no	—
93	C₂²×C₄×C₁₂₇	—	4	2	no	—
94	C₂²×C₄×C₁₂₇	—	4	2	no	—
95	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₂₇	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
101	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
102	C₂²×C₄×C₁₂₇	#41	1	1	yes	characteristic
103	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
104	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
105	M₁₆×C₁₂₇	—	2	4	no	—
106	M₁₆×C₁₂₇	—	2	2	no	—
107	M₁₆×C₁₂₇	—	2	2	no	—
108	M₁₆×C₁₂₇	—	2	2	no	—
109	M₁₆×C₁₂₇	—	4	2	no	—
110	M₁₆×C₁₂₇	C₂×Q₈	1	4	yes	—
111	C₂×C₈×C₁₂₇	—	2	2	no	—
112	C₂×C₈×C₁₂₇	—	2	2	no	—
113	C₂×C₈×C₁₂₇	—	2	4	no	—
114	C₂×C₈×C₁₂₇	—	2	4	no	—
115	C₂×C₈×C₁₂₇	—	2	2	no	—
116	C₂×C₈×C₁₂₇	—	2	2	no	—
117	C₂×C₈×C₁₂₇	—	2	4	no	—
118	C₂×C₈×C₁₂₇	—	2	2	no	—
119	C₂×C₈×C₁₂₇	—	2	2	no	—
120	C₂×C₈×C₁₂₇	—	2	2	no	—
121	C₂×C₈×C₁₂₇	—	2	2	no	—
122	C₂×C₈×C₁₂₇	—	2	2	no	—
123	C₂×C₈×C₁₂₇	—	2	2	no	—
124	C₂×C₈×C₁₂₇	—	4	2	no	—
125	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₁₂₇	—	2	1	no	—
130	C₄⋊C₄×C₁₂₇	—	2	1	no	—
131	C₄⋊C₄×C₁₂₇	—	2	1	no	—
132	C₄⋊C₄×C₁₂₇	—	2	1	no	—
133	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
134	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
135	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
136	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
137	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
138	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
139	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
140	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
141	C₄²×C₁₂₇	—	2	2	no	—
142	C₄²×C₁₂₇	—	2	2	no	—
143	C₄²×C₁₂₇	—	2	2	no	—
144	C₄²×C₁₂₇	—	2	2	no	—
145	C₄²×C₁₂₇	—	2	2	no	—
146	C₄²×C₁₂₇	—	2	2	no	—
147	C₄²×C₁₂₇	—	4	2	no	—
148	C₂³×C₁₂₇	—	2	2	no	—
149	C₂³×C₁₂₇	—	2	2	no	—
150	C₂³×C₁₂₇	C₄×D₄	1	1	yes	characteristic
151	C₂³×C₁₂₇	C₄×D₄	1	1	yes	characteristic
152	C₂³×C₁₂₇	#125	1	2	yes	—
153	C₂³×C₁₂₇	#126	1	2	yes	—
154	C₂³×C₁₂₇	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₁₂₇	—	2	4	no	—
156	C₂×C₄×C₁₂₇	—	2	2	no	—
157	C₂×C₄×C₁₂₇	—	2	2	no	—
158	C₂×C₄×C₁₂₇	—	2	2	no	—
159	C₂×C₄×C₁₂₇	—	2	2	no	—
160	C₂×C₄×C₁₂₇	—	4	8	no	—
161	C₂×C₄×C₁₂₇	—	4	2	no	—
162	C₂×C₄×C₁₂₇	—	4	2	no	—
163	C₂×C₄×C₁₂₇	—	4	2	no	—
164	C₂×C₄×C₁₂₇	—	4	2	no	—
165	C₂×C₄×C₁₂₇	—	4	2	no	—
166	C₂×C₄×C₁₂₇	—	4	2	no	—
167	C₂×C₄×C₁₂₇	#117	1	2	yes	—
168	C₂×C₄×C₁₂₇	#117	1	2	yes	—
169	C₂×C₄×C₁₂₇	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₂₇	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₂₇	C₄×Q₈	1	2	yes	—
172	C₂×C₄×C₁₂₇	C₄×Q₈	1	2	yes	—
173	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	2	yes	—
174	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	2	yes	—
175	C₂×C₄×C₁₂₇	#123	1	2	yes	—
176	C₂×C₄×C₁₂₇	#123	1	2	yes	—
177	C₂×C₄×C₁₂₇	#125	1	2	yes	—
178	C₂×C₄×C₁₂₇	#126	1	2	yes	—
179	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₂₇	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
185	C₈×C₁₂₇	—	2	2	no	—
186	C₈×C₁₂₇	—	2	2	no	—
187	C₈×C₁₂₇	—	2	4	no	—
188	C₈×C₁₂₇	—	2	2	no	—
189	C₈×C₁₂₇	—	2	2	no	—
190	C₈×C₁₂₇	—	4	2	no	—
191	C₂²×C₁₂₇	—	2	4	no	—
192	C₂²×C₁₂₇	—	2	4	no	—
193	C₂²×C₁₂₇	—	2	1	no	—
194	C₂²×C₁₂₇	—	2	1	no	—
195	C₂²×C₁₂₇	—	2	1	no	—
196	C₂²×C₁₂₇	—	2	1	no	—
197	C₂²×C₁₂₇	#387	1	2	yes	—
198	C₂²×C₁₂₇	#387	1	2	yes	—
199	C₂²×C₁₂₇	#443	1	2	yes	—
200	C₂²×C₁₂₇	#444	1	2	yes	—
201	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
202	C₂²×C₁₂₇	C₂×#125	1	1	yes	characteristic
203	C₂²×C₁₂₇	C₂×#126	1	1	yes	characteristic
204	C₄×C₁₂₇	—	4	4	no	—
205	C₄×C₁₂₇	—	4	2	no	—
206	C₄×C₁₂₇	—	4	2	no	—
207	C₄×C₁₂₇	—	4	2	no	—
208	C₄×C₁₂₇	—	4	2	no	—
209	C₄×C₁₂₇	#387	1	2	yes	—
210	C₄×C₁₂₇	#387	1	2	yes	—
211	C₄×C₁₂₇	C₂×#117	1	1	yes	characteristic
212	C₄×C₁₂₇	C₂×C₄×Q₈	1	1	yes	characteristic
213	C₄×C₁₂₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
214	C₄×C₁₂₇	C₂×#123	1	1	yes	characteristic
215	C₂×#1922	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂×C₁₂₇	—	2	1	no	—
217	C₂×C₁₂₇	—	2	1	no	—
218	C₂×C₁₂₇	—	2	2	no	—
219	C₂×C₁₂₇	#1922	1	4	yes	direct product factor
220	C₂×C₁₂₇	C₂×#387	1	1	yes	characteristic
221	C₂×C₁₂₇	C₂×#443	1	1	yes	characteristic
222	C₂×C₁₂₇	C₂×#444	1	1	yes	characteristic
223	C₂×#427	C₂×C₁₂₇	1	1	yes	characteristic
224	C₂×#424	C₂×C₁₂₇	1	1	yes	characteristic
225	C₂×#405	C₂×C₁₂₇	1	1	yes	characteristic
226	#1922	C₂×C₁₂₇	1	8	yes	direct product factor
227	C₂×#341	C₂×C₁₂₇	1	1	yes	characteristic
228	C₂×#339	C₂×C₁₂₇	1	1	yes	characteristic
229	C₂×#339	C₂×C₁₂₇	1	1	yes	characteristic
230	C₂×#336	C₂×C₁₂₇	1	1	yes	characteristic
231	C₁₂₇	C₂×#1922	1	1	yes	characteristic, direct product factor, Sylow
232	C₂²×M₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
233	C₂²×M₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
234	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
235	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
236	C₂×#117	C₂²×C₁₂₇	1	1	yes	characteristic
237	C₂×#117	C₂²×C₁₂₇	1	1	yes	characteristic
238	C₂²×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
239	#427	C₄×C₁₂₇	1	4	yes	complemented
240	#427	C₂²×C₁₂₇	1	4	yes	—
241	C₂×#107	C₄×C₁₂₇	1	1	yes	characteristic, complemented
242	C₂×#107	C₄×C₁₂₇	1	1	yes	characteristic, complemented
243	C₂×#106	C₄×C₁₂₇	1	1	yes	characteristic, complemented
244	C₂×#106	C₄×C₁₂₇	1	1	yes	characteristic, complemented
245	#424	—	2	2	no	—
246	#424	C₂²×C₁₂₇	1	4	yes	—
247	C₂×C₄⋊C₈	—	2	1	no	—
248	C₂×C₄⋊C₈	—	2	1	no	—
249	#405	—	2	2	no	—
250	#405	C₂²×C₁₂₇	1	4	yes	—
251	C₂×#97	—	2	1	no	—
252	C₂×C₄×C₈	—	2	1	no	—
253	#341	C₂²×C₁₂₇	1	4	yes	—
254	#339	C₂²×C₁₂₇	1	4	yes	—
255	#339	C₂²×C₁₂₇	1	4	yes	—
256	#336	C₂²×C₁₂₇	1	4	yes	—
257	C₂³×C₄	—	2	1	no	—
258	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	Q₈×C₁₂₇	1	4	yes	—
265	C₂×M₁₆	C₂³×C₁₂₇	1	2	yes	—
266	C₂×M₁₆	C₂³×C₁₂₇	1	2	yes	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₂²×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
274	C₂²×C₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
275	C₂²×C₈	C₂×C₄×C₁₂₇	1	2	yes	—
276	C₂²×C₈	D₄×C₁₂₇	1	1	yes	characteristic
277	C₂²×C₈	D₄×C₁₂₇	1	1	yes	characteristic
278	C₂²×C₈	D₄×C₁₂₇	1	2	yes	—
279	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
280	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
281	#117	—	2	1	no	—
282	#117	—	2	1	no	—
283	#117	—	2	1	no	—
284	#117	—	2	1	no	—
285	#117	C₂×C₄×C₁₂₇	1	2	yes	—
286	#117	C₂×C₄×C₁₂₇	1	2	yes	—
287	#117	C₂³×C₁₂₇	1	2	yes	—
288	#117	C₂³×C₁₂₇	1	2	yes	—
289	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
301	#107	C₂×C₄×C₁₂₇	1	4	yes	complemented
302	#107	C₂×C₄×C₁₂₇	1	4	yes	complemented
303	#106	C₂×C₄×C₁₂₇	1	4	yes	complemented
304	#106	C₂×C₄×C₁₂₇	1	4	yes	complemented
305	C₄⋊C₈	—	2	4	no	—
306	C₄⋊C₈	—	2	4	no	—
307	#97	—	2	4	no	—
308	C₄×C₈	—	2	4	no	—
309	C₂⁴	#41×C₁₂₇	1	1	yes	characteristic
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
319	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
322	C₂²×C₄	C₂×Q₈×C₁₂₇	1	2	yes	—
323	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
324	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
325	C₂²×C₄	#41×C₁₂₇	1	1	yes	characteristic
326	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
327	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
328	M₁₆	—	2	4	no	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	4	2	no	—
333	M₁₆	C₂×Q₈×C₁₂₇	1	4	yes	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	2	4	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	4	2	no	—
348	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
349	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
350	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
351	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
357	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
358	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
359	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	4	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	C₄×D₄×C₁₂₇	1	1	yes	characteristic
374	C₂³	C₄×D₄×C₁₂₇	1	1	yes	characteristic
375	C₂³	#125×C₁₂₇	1	2	yes	—
376	C₂³	#126×C₁₂₇	1	2	yes	—
377	C₂³	C₂×#41×C₁₂₇	1	1	yes	characteristic
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	8	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	#117×C₁₂₇	1	2	yes	—
391	C₂×C₄	#117×C₁₂₇	1	2	yes	—
392	C₂×C₄	C₄×D₄×C₁₂₇	1	1	yes	characteristic
393	C₂×C₄	C₄×D₄×C₁₂₇	1	1	yes	characteristic
394	C₂×C₄	C₄×Q₈×C₁₂₇	1	2	yes	—
395	C₂×C₄	C₄×Q₈×C₁₂₇	1	2	yes	—
396	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	2	yes	—
397	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	2	yes	—
398	C₂×C₄	#123×C₁₂₇	1	2	yes	—
399	C₂×C₄	#123×C₁₂₇	1	2	yes	—
400	C₂×C₄	#125×C₁₂₇	1	2	yes	—
401	C₂×C₄	#126×C₁₂₇	1	2	yes	—
402	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
403	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
404	C₂×C₄	C₂²×Q₈×C₁₂₇	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
406	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
407	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	2	2	no	—
410	C₈	—	2	4	no	—
411	C₈	—	2	2	no	—
412	C₈	—	2	2	no	—
413	C₈	—	4	2	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	#387×C₁₂₇	1	2	yes	—
421	C₂²	#387×C₁₂₇	1	2	yes	—
422	C₂²	#443×C₁₂₇	1	2	yes	—
423	C₂²	#444×C₁₂₇	1	2	yes	—
424	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
425	C₂²	C₂×#125×C₁₂₇	1	1	yes	characteristic
426	C₂²	C₂×#126×C₁₂₇	1	1	yes	characteristic
427	C₄	—	4	4	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	#387×C₁₂₇	1	2	yes	—
433	C₄	#387×C₁₂₇	1	2	yes	—
434	C₄	C₂×#117×C₁₂₇	1	1	yes	characteristic
435	C₄	C₂×C₄×Q₈×C₁₂₇	1	1	yes	characteristic
436	C₄	C₂×C₂²⋊Q₈×C₁₂₇	1	1	yes	characteristic
437	C₄	C₂×#123×C₁₂₇	1	1	yes	characteristic
438	C₂	—	2	1	no	—
439	C₂	—	2	1	no	—
440	C₂	—	2	2	no	—
441	C₂	C₁₂₇×#1922	1	4	yes	direct product factor
442	C₂	C₂×#387×C₁₂₇	1	1	yes	characteristic
443	C₂	C₂×#443×C₁₂₇	1	1	yes	characteristic
444	C₂	C₂×#444×C₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₂₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₂₇
socle	C₂³×C₁₂₇	C₄×D₄
prime radical	C₂⁴×C₁₂₇	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₂₇ ◁ C₂³×C₈×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₂₇×#1922	C₂	direct (N × H)
16. #427×C₁₂₇	C₄	semidirect
18. C₂×#107×C₁₂₇	C₄	semidirect
19. C₂×#107×C₁₂₇	C₄	semidirect
20. C₂×#106×C₁₂₇	C₄	semidirect
21. C₂×#106×C₁₂₇	C₄	semidirect
78. #107×C₁₂₇	C₂×C₄	semidirect
79. #107×C₁₂₇	C₂×C₄	semidirect
80. #106×C₁₂₇	C₂×C₄	semidirect
81. #106×C₁₂₇	C₂×C₄	semidirect
215. C₂×#1922	C₁₂₇	direct (N × H)
219. C₂×C₁₂₇	#1922	direct (N × H)
226. #1922	C₂×C₁₂₇	direct (N × H)
231. C₁₂₇	C₂×#1922	direct (N × H)
239. #427	C₄×C₁₂₇	semidirect
241. C₂×#107	C₄×C₁₂₇	semidirect
242. C₂×#107	C₄×C₁₂₇	semidirect
243. C₂×#106	C₄×C₁₂₇	semidirect
244. C₂×#106	C₄×C₁₂₇	semidirect
301. #107	C₂×C₄×C₁₂₇	semidirect
302. #107	C₂×C₄×C₁₂₇	semidirect
303. #106	C₂×C₄×C₁₂₇	semidirect
304. #106	C₂×C₄×C₁₂₇	semidirect
441. C₂	C₁₂₇×#1922	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×#427×C₁₂₇	2
C₂×#424×C₁₂₇	2
C₂×#405×C₁₂₇	2
C₁₂₇×#1922	2
C₂×#341×C₁₂₇	2
C₂×#339×C₁₂₇	2
C₂×#336×C₁₂₇	2
C₂×#1922	127

Subgroups — C2×C127×#1922 #44584713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₂₇×#1922 #44584713