Subgroups — C₂×C₁₂₇×#1917 #44584692

Order 32512.

1070 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#97×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1917	C₂	1	8	yes	maximal, direct product factor
5	C₂×#336×C₁₂₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#336×C₁₂₇	C₂	1	1	yes	maximal, characteristic
7	C₂×#336×C₁₂₇	C₂	1	1	yes	maximal, characteristic
8	C₂×#336×C₁₂₇	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
10	C₂³×C₈×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	C₂²×C₄⋊C₄×C₁₂₇	C₄	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₂₇	C₄	1	1	yes	characteristic
15	C₂²×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₁₂₇	—	2	4	no	—
19	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	4	yes	—
20	C₂×#97×C₁₂₇	—	2	4	no	—
21	C₂×#97×C₁₂₇	C₂²	1	4	yes	—
22	C₄×C₄⋊C₄×C₁₂₇	C₄	1	4	yes	—
23	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	4	yes	—
24	C₂×#95×C₁₂₇	C₄	1	1	yes	characteristic
25	C₂×#95×C₁₂₇	C₄	1	1	yes	characteristic
26	#336×C₁₂₇	C₂²	1	4	yes	—
27	#336×C₁₂₇	C₂²	1	4	yes	—
28	#336×C₁₂₇	C₂²	1	4	yes	—
29	#336×C₁₂₇	C₂²	1	4	yes	—
30	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₂₇	—	2	2	no	—
38	C₂²×C₈×C₁₂₇	—	2	2	no	—
39	C₂²×C₈×C₁₂₇	—	2	2	no	—
40	C₂²×C₈×C₁₂₇	—	2	2	no	—
41	C₂²×C₈×C₁₂₇	—	2	2	no	—
42	C₂²×C₈×C₁₂₇	—	2	2	no	—
43	C₂²×C₈×C₁₂₇	—	2	2	no	—
44	C₂²×C₈×C₁₂₇	—	2	2	no	—
45	C₂²×C₈×C₁₂₇	—	2	2	no	—
46	C₂²×C₈×C₁₂₇	—	2	2	no	—
47	C₂²×C₈×C₁₂₇	D₄	1	4	yes	—
48	C₂²×C₈×C₁₂₇	Q₈	1	4	yes	—
49	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₂₇	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₂₇	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
57	C₂×C₄²×C₁₂₇	—	2	2	no	—
58	C₂×C₄²×C₁₂₇	—	2	2	no	—
59	C₂×C₄²×C₁₂₇	—	2	2	no	—
60	C₂×C₄²×C₁₂₇	—	2	2	no	—
61	C₂×C₄²×C₁₂₇	—	2	2	no	—
62	C₂×C₄²×C₁₂₇	—	2	2	no	—
63	C₂×C₄²×C₁₂₇	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₂₇	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₁₂₇	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
67	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
69	C₄⋊C₈×C₁₂₇	—	2	8	no	—
70	#97×C₁₂₇	—	2	8	no	—
71	#95×C₁₂₇	C₂×C₄	1	4	yes	—
72	#95×C₁₂₇	C₂×C₄	1	4	yes	—
73	C₂⁴×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₂₇	—	2	2	no	—
75	C₂²×C₄×C₁₂₇	—	2	2	no	—
76	C₂²×C₄×C₁₂₇	—	2	2	no	—
77	C₂²×C₄×C₁₂₇	—	2	2	no	—
78	C₂²×C₄×C₁₂₇	—	2	2	no	—
79	C₂²×C₄×C₁₂₇	—	2	2	no	—
80	C₂²×C₄×C₁₂₇	—	2	2	no	—
81	C₂²×C₄×C₁₂₇	—	2	2	no	—
82	C₂²×C₄×C₁₂₇	—	2	2	no	—
83	C₂²×C₄×C₁₂₇	—	2	2	no	—
84	C₂²×C₄×C₁₂₇	—	2	2	no	—
85	C₂²×C₄×C₁₂₇	—	2	2	no	—
86	C₂²×C₄×C₁₂₇	—	2	2	no	—
87	C₂²×C₄×C₁₂₇	—	2	2	no	—
88	C₂²×C₄×C₁₂₇	—	2	2	no	—
89	C₂²×C₄×C₁₂₇	—	2	2	no	—
90	C₂²×C₄×C₁₂₇	M₁₆	1	4	yes	—
91	C₂²×C₄×C₁₂₇	M₁₆	1	4	yes	—
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	2	yes	—
95	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₂₇	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
102	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
103	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
104	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
105	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
106	C₂×C₈×C₁₂₇	—	2	8	no	—
107	C₂×C₈×C₁₂₇	—	2	8	no	—
108	C₂×C₈×C₁₂₇	—	2	2	no	—
109	C₂×C₈×C₁₂₇	—	2	2	no	—
110	C₂×C₈×C₁₂₇	—	2	2	no	—
111	C₂×C₈×C₁₂₇	—	2	2	no	—
112	C₂×C₈×C₁₂₇	—	2	2	no	—
113	C₂×C₈×C₁₂₇	—	2	2	no	—
114	C₂×C₈×C₁₂₇	—	2	2	no	—
115	C₂×C₈×C₁₂₇	—	2	2	no	—
116	C₂×C₈×C₁₂₇	—	2	2	no	—
117	C₂×C₈×C₁₂₇	—	2	2	no	—
118	C₂×C₈×C₁₂₇	—	4	4	no	—
119	C₂×C₈×C₁₂₇	—	4	4	no	—
120	C₂×C₈×C₁₂₇	C₂×D₄	1	4	yes	—
121	C₂×C₈×C₁₂₇	C₂×Q₈	1	4	yes	—
122	C₄⋊C₄×C₁₂₇	—	2	8	no	—
123	C₄⋊C₄×C₁₂₇	—	2	8	no	—
124	C₄²×C₁₂₇	—	2	4	no	—
125	C₄²×C₁₂₇	—	2	4	no	—
126	C₄²×C₁₂₇	—	2	4	no	—
127	C₄²×C₁₂₇	—	2	2	no	—
128	C₄²×C₁₂₇	—	2	2	no	—
129	C₄²×C₁₂₇	—	2	2	no	—
130	C₄²×C₁₂₇	—	2	2	no	—
131	C₄²×C₁₂₇	—	2	2	no	—
132	C₄²×C₁₂₇	—	2	2	no	—
133	C₂³×C₁₂₇	#117	1	2	yes	—
134	C₂³×C₁₂₇	C₄×D₄	1	2	yes	—
135	C₂³×C₁₂₇	C₄×Q₈	1	2	yes	—
136	C₂³×C₁₂₇	C₂×M₁₆	1	2	yes	—
137	C₂³×C₁₂₇	C₂×M₁₆	1	2	yes	—
138	C₂³×C₁₂₇	#131	1	2	yes	—
139	C₂³×C₁₂₇	#131	1	2	yes	—
140	C₂³×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₂₇	—	2	2	no	—
142	C₂×C₄×C₁₂₇	—	2	2	no	—
143	C₂×C₄×C₁₂₇	—	2	2	no	—
144	C₂×C₄×C₁₂₇	—	2	2	no	—
145	C₂×C₄×C₁₂₇	—	2	8	no	—
146	C₂×C₄×C₁₂₇	—	2	8	no	—
147	C₂×C₄×C₁₂₇	—	2	2	no	—
148	C₂×C₄×C₁₂₇	—	2	2	no	—
149	C₂×C₄×C₁₂₇	—	2	2	no	—
150	C₂×C₄×C₁₂₇	—	2	2	no	—
151	C₂×C₄×C₁₂₇	—	2	2	no	—
152	C₂×C₄×C₁₂₇	—	2	2	no	—
153	C₂×C₄×C₁₂₇	—	2	2	no	—
154	C₂×C₄×C₁₂₇	—	2	2	no	—
155	C₂×C₄×C₁₂₇	—	2	2	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	—	4	4	no	—
160	C₂×C₄×C₁₂₇	—	4	4	no	—
161	C₂×C₄×C₁₂₇	—	4	4	no	—
162	C₂×C₄×C₁₂₇	—	4	4	no	—
163	C₂×C₄×C₁₂₇	#117	1	2	yes	—
164	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₁₂₇	C₄×Q₈	1	2	yes	—
166	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	4	yes	—
167	C₂×C₄×C₁₂₇	#123	1	4	yes	—
168	C₂×C₄×C₁₂₇	#125	1	4	yes	—
169	C₂×C₄×C₁₂₇	#126	1	4	yes	—
170	C₂×C₄×C₁₂₇	C₂×M₁₆	1	4	yes	—
171	C₂×C₄×C₁₂₇	C₂×M₁₆	1	4	yes	—
172	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₂₇	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
178	C₈×C₁₂₇	—	2	4	no	—
179	C₈×C₁₂₇	—	2	4	no	—
180	C₈×C₁₂₇	—	4	2	no	—
181	C₈×C₁₂₇	—	4	2	no	—
182	C₂²×C₁₂₇	#387	1	4	yes	—
183	C₂²×C₁₂₇	#432	1	4	yes	—
184	C₂²×C₁₂₇	#433	1	4	yes	—
185	C₂²×C₁₂₇	#435	1	4	yes	—
186	C₂²×C₁₂₇	#436	1	4	yes	—
187	C₂²×C₁₂₇	#446	1	4	yes	—
188	C₂²×C₁₂₇	#446	1	4	yes	—
189	C₂²×C₁₂₇	C₂×#117	1	1	yes	characteristic
190	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
191	C₂²×C₁₂₇	C₂×C₄×Q₈	1	1	yes	characteristic
192	C₂²×C₁₂₇	C₂²×M₁₆	1	1	yes	characteristic
193	C₂²×C₁₂₇	C₂²×M₁₆	1	1	yes	characteristic
194	C₂²×C₁₂₇	C₂×#131	1	1	yes	characteristic
195	C₂²×C₁₂₇	C₂×#131	1	1	yes	characteristic
196	C₄×C₁₂₇	—	2	4	no	—
197	C₄×C₁₂₇	—	2	4	no	—
198	C₄×C₁₂₇	—	4	2	no	—
199	C₄×C₁₂₇	—	4	2	no	—
200	C₄×C₁₂₇	—	4	2	no	—
201	C₄×C₁₂₇	—	4	2	no	—
202	C₄×C₁₂₇	#387	1	4	yes	—
203	C₄×C₁₂₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
204	C₄×C₁₂₇	C₂×#123	1	1	yes	characteristic
205	C₄×C₁₂₇	C₂×#125	1	1	yes	characteristic
206	C₄×C₁₂₇	C₂×#126	1	1	yes	characteristic
207	C₂×#1917	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂×C₁₂₇	#1917	1	8	yes	direct product factor
209	C₂×C₁₂₇	C₂×#387	1	1	yes	characteristic
210	C₂×C₁₂₇	C₂×#432	1	1	yes	characteristic
211	C₂×C₁₂₇	C₂×#433	1	1	yes	characteristic
212	C₂×C₁₂₇	C₂×#435	1	1	yes	characteristic
213	C₂×C₁₂₇	C₂×#436	1	1	yes	characteristic
214	C₂×C₁₂₇	C₂×#446	1	1	yes	characteristic
215	C₂×C₁₂₇	C₂×#446	1	1	yes	characteristic
216	C₂²×C₄⋊C₈	C₂×C₁₂₇	1	1	yes	characteristic
217	C₂²×#97	C₂×C₁₂₇	1	1	yes	characteristic
218	C₂×C₄×C₄⋊C₄	C₂×C₁₂₇	1	1	yes	characteristic
219	#1917	C₂×C₁₂₇	1	8	yes	direct product factor
220	C₂×#336	C₂×C₁₂₇	1	1	yes	characteristic
221	C₂×#336	C₂×C₁₂₇	1	1	yes	characteristic
222	C₂×#336	C₂×C₁₂₇	1	1	yes	characteristic
223	C₂×#336	C₂×C₁₂₇	1	1	yes	characteristic
224	C₁₂₇	C₂×#1917	1	1	yes	characteristic, direct product factor, Sylow
225	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
226	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
227	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
228	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₄×C₁₂₇	1	1	yes	characteristic
230	C₂²×C₄⋊C₄	C₄×C₁₂₇	1	1	yes	characteristic
231	C₂²×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
232	C₂²×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
233	C₂²×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
234	C₂×C₄⋊C₈	—	2	4	no	—
235	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	4	yes	—
236	C₂×#97	—	2	4	no	—
237	C₂×#97	C₂²×C₁₂₇	1	4	yes	—
238	C₄×C₄⋊C₄	C₄×C₁₂₇	1	4	yes	—
239	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	4	yes	—
240	C₂×#95	C₄×C₁₂₇	1	1	yes	characteristic
241	C₂×#95	C₄×C₁₂₇	1	1	yes	characteristic
242	#336	C₂²×C₁₂₇	1	4	yes	—
243	#336	C₂²×C₁₂₇	1	4	yes	—
244	#336	C₂²×C₁₂₇	1	4	yes	—
245	#336	C₂²×C₁₂₇	1	4	yes	—
246	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
247	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
248	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
249	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
250	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
251	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
252	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	—	2	2	no	—
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	—	2	2	no	—
259	C₂²×C₈	—	2	2	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	D₄×C₁₂₇	1	4	yes	—
264	C₂²×C₈	Q₈×C₁₂₇	1	4	yes	—
265	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
266	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
267	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
268	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
269	C₂×C₄⋊C₄	—	2	4	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
272	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	C₂×C₄×C₁₂₇	1	2	yes	—
280	C₂×C₄²	C₂×C₄×C₁₂₇	1	2	yes	—
281	C₂×C₄²	C₂×C₄×C₁₂₇	1	2	yes	—
282	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
283	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
284	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
285	C₄⋊C₈	—	2	8	no	—
286	#97	—	2	8	no	—
287	#95	C₂×C₄×C₁₂₇	1	4	yes	—
288	#95	C₂×C₄×C₁₂₇	1	4	yes	—
289	C₂⁴	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	M₁₆×C₁₂₇	1	4	yes	—
307	C₂²×C₄	M₁₆×C₁₂₇	1	4	yes	—
308	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
309	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
310	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
312	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
314	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
316	C₂²×C₄	C₂×Q₈×C₁₂₇	1	2	yes	—
317	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
318	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
319	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
320	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
321	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
322	C₂×C₈	—	2	8	no	—
323	C₂×C₈	—	2	8	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	4	4	no	—
335	C₂×C₈	—	4	4	no	—
336	C₂×C₈	C₂×D₄×C₁₂₇	1	4	yes	—
337	C₂×C₈	C₂×Q₈×C₁₂₇	1	4	yes	—
338	C₄⋊C₄	—	2	8	no	—
339	C₄⋊C₄	—	2	8	no	—
340	C₄²	—	2	4	no	—
341	C₄²	—	2	4	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₂³	#117×C₁₂₇	1	2	yes	—
350	C₂³	C₄×D₄×C₁₂₇	1	2	yes	—
351	C₂³	C₄×Q₈×C₁₂₇	1	2	yes	—
352	C₂³	C₂×M₁₆×C₁₂₇	1	2	yes	—
353	C₂³	C₂×M₁₆×C₁₂₇	1	2	yes	—
354	C₂³	#131×C₁₂₇	1	2	yes	—
355	C₂³	#131×C₁₂₇	1	2	yes	—
356	C₂³	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	8	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	#117×C₁₂₇	1	2	yes	—
380	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
381	C₂×C₄	C₄×Q₈×C₁₂₇	1	2	yes	—
382	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	4	yes	—
383	C₂×C₄	#123×C₁₂₇	1	4	yes	—
384	C₂×C₄	#125×C₁₂₇	1	4	yes	—
385	C₂×C₄	#126×C₁₂₇	1	4	yes	—
386	C₂×C₄	C₂×M₁₆×C₁₂₇	1	4	yes	—
387	C₂×C₄	C₂×M₁₆×C₁₂₇	1	4	yes	—
388	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
389	C₂×C₄	C₂²×Q₈×C₁₂₇	1	1	yes	characteristic
390	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
391	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
392	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
393	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
394	C₈	—	2	4	no	—
395	C₈	—	2	4	no	—
396	C₈	—	4	2	no	—
397	C₈	—	4	2	no	—
398	C₂²	#387×C₁₂₇	1	4	yes	—
399	C₂²	#432×C₁₂₇	1	4	yes	—
400	C₂²	#433×C₁₂₇	1	4	yes	—
401	C₂²	#435×C₁₂₇	1	4	yes	—
402	C₂²	#436×C₁₂₇	1	4	yes	—
403	C₂²	#446×C₁₂₇	1	4	yes	—
404	C₂²	#446×C₁₂₇	1	4	yes	—
405	C₂²	C₂×#117×C₁₂₇	1	1	yes	characteristic
406	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
407	C₂²	C₂×C₄×Q₈×C₁₂₇	1	1	yes	characteristic
408	C₂²	C₂²×M₁₆×C₁₂₇	1	1	yes	characteristic
409	C₂²	C₂²×M₁₆×C₁₂₇	1	1	yes	characteristic
410	C₂²	C₂×#131×C₁₂₇	1	1	yes	characteristic
411	C₂²	C₂×#131×C₁₂₇	1	1	yes	characteristic
412	C₄	—	2	4	no	—
413	C₄	—	2	4	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	#387×C₁₂₇	1	4	yes	—
419	C₄	C₂×C₂²⋊Q₈×C₁₂₇	1	1	yes	characteristic
420	C₄	C₂×#123×C₁₂₇	1	1	yes	characteristic
421	C₄	C₂×#125×C₁₂₇	1	1	yes	characteristic
422	C₄	C₂×#126×C₁₂₇	1	1	yes	characteristic
423	C₂	C₁₂₇×#1917	1	8	yes	direct product factor
424	C₂	C₂×#387×C₁₂₇	1	1	yes	characteristic
425	C₂	C₂×#432×C₁₂₇	1	1	yes	characteristic
426	C₂	C₂×#433×C₁₂₇	1	1	yes	characteristic
427	C₂	C₂×#435×C₁₂₇	1	1	yes	characteristic
428	C₂	C₂×#436×C₁₂₇	1	1	yes	characteristic
429	C₂	C₂×#446×C₁₂₇	1	1	yes	characteristic
430	C₂	C₂×#446×C₁₂₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₁₂₇×#1917	C₂	direct (N × H)
207. C₂×#1917	C₁₂₇	direct (N × H)
208. C₂×C₁₂₇	#1917	direct (N × H)
219. #1917	C₂×C₁₂₇	direct (N × H)
224. C₁₂₇	C₂×#1917	direct (N × H)
423. C₂	C₁₂₇×#1917	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊C₈×C₁₂₇	2
C₂²×#97×C₁₂₇	2
C₂×C₄×C₄⋊C₄×C₁₂₇	2
C₁₂₇×#1917	2
C₂×#336×C₁₂₇	2
C₂×#1917	127

Subgroups — C2×C127×#1917 #44584692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₂₇×#1917 #44584692