Subgroups — C₁₂₇×#21567 #44585240

Order 32512.

886 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#405×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₂₇×#2395	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1923	C₂	1	2	yes	maximal, complemented
5	C₁₂₇×#1916	C₂	1	2	yes	maximal, complemented
6	C₁₂₇×#1870	C₂	1	1	yes	maximal, characteristic
7	C₁₂₇×#1851	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₂₇×#1818	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₂₇×#1771	C₂	1	2	yes	maximal, complemented
10	C₁₂₇×#1752	C₂	1	2	yes	maximal, complemented
11	C₁₂₇×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×M₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₁₂₇	C₂²	1	1	yes	characteristic
17	C₈×D₄×C₁₂₇	—	2	4	no	—
18	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
24	#405×C₁₂₇	—	2	4	no	—
25	C₂×#97×C₁₂₇	C₂²	1	2	yes	—
26	C₂×#97×C₁₂₇	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
29	#400×C₁₂₇	C₄	1	1	yes	characteristic
30	#399×C₁₂₇	C₄	1	1	yes	characteristic
31	#398×C₁₂₇	C₄	1	1	yes	characteristic
32	#397×C₁₂₇	C₄	1	2	yes	—
33	#397×C₁₂₇	C₄	1	1	yes	characteristic
34	#394×C₁₂₇	C₄	1	2	yes	—
35	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
36	C₄×C₂²⋊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×D₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₁₂₇	—	2	2	no	—
47	C₂×M₁₆×C₁₂₇	—	2	4	no	—
48	C₂²×C₈×C₁₂₇	—	2	4	no	—
49	C₂²×C₈×C₁₂₇	—	2	2	no	—
50	C₂²×C₈×C₁₂₇	—	2	4	no	—
51	C₂²×C₈×C₁₂₇	D₄	1	4	yes	—
52	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
58	C₄×D₄×C₁₂₇	—	2	2	no	—
59	C₄×D₄×C₁₂₇	—	2	2	no	—
60	#117×C₁₂₇	—	2	2	no	—
61	#117×C₁₂₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
68	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
72	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
76	C₄⋊C₈×C₁₂₇	—	2	2	no	—
77	C₄⋊C₈×C₁₂₇	—	2	4	no	—
78	C₂²⋊C₈×C₁₂₇	—	2	2	no	—
79	C₂²⋊C₈×C₁₂₇	—	2	2	no	—
80	C₂²⋊C₈×C₁₂₇	—	2	2	no	—
81	C₂²⋊C₈×C₁₂₇	—	2	4	no	—
82	#97×C₁₂₇	—	2	4	no	—
83	#97×C₁₂₇	—	2	4	no	—
84	C₄×C₈×C₁₂₇	—	2	4	no	—
85	C₄×C₈×C₁₂₇	—	2	2	no	—
86	#95×C₁₂₇	C₂×C₄	1	2	yes	—
87	#95×C₁₂₇	C₂×C₄	1	1	yes	characteristic
88	#95×C₁₂₇	C₂×C₄	1	2	yes	—
89	#95×C₁₂₇	C₂×C₄	1	1	yes	characteristic
90	#95×C₁₂₇	C₂×C₄	1	2	yes	—
91	#95×C₁₂₇	C₂×C₄	1	2	yes	—
92	C₂⁴×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
93	C₂⁴×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
94	C₂×D₄×C₁₂₇	—	2	2	no	—
95	C₂×D₄×C₁₂₇	—	2	2	no	—
96	C₂×D₄×C₁₂₇	—	2	2	no	—
97	C₂²×C₄×C₁₂₇	—	2	2	no	—
98	C₂²×C₄×C₁₂₇	—	2	2	no	—
99	C₂²×C₄×C₁₂₇	—	2	1	no	—
100	C₂²×C₄×C₁₂₇	—	2	2	no	—
101	C₂²×C₄×C₁₂₇	—	2	1	no	—
102	C₂²×C₄×C₁₂₇	—	2	2	no	—
103	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
113	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
114	M₁₆×C₁₂₇	—	2	8	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	—	2	8	no	—
119	C₂×C₈×C₁₂₇	—	2	1	no	—
120	C₂×C₈×C₁₂₇	—	2	1	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	—	2	2	no	—
125	C₂×C₈×C₁₂₇	—	2	2	no	—
126	C₂×C₈×C₁₂₇	—	4	4	no	—
127	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₂₇	#41	1	4	yes	—
130	C₂×C₈×C₁₂₇	#41	1	4	yes	—
131	C₄⋊C₄×C₁₂₇	—	2	2	no	—
132	C₄⋊C₄×C₁₂₇	—	2	2	no	—
133	C₄⋊C₄×C₁₂₇	—	2	2	no	—
134	C₄⋊C₄×C₁₂₇	—	2	4	no	—
135	C₄⋊C₄×C₁₂₇	—	4	2	no	—
136	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
137	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
138	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
139	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
140	C₂²⋊C₄×C₁₂₇	—	4	2	no	—
141	C₂²⋊C₄×C₁₂₇	—	4	2	no	—
142	C₄²×C₁₂₇	—	2	2	no	—
143	C₄²×C₁₂₇	—	2	1	no	—
144	C₄²×C₁₂₇	—	2	2	no	—
145	C₄²×C₁₂₇	—	2	2	no	—
146	C₄²×C₁₂₇	—	2	2	no	—
147	C₄²×C₁₂₇	—	2	1	no	—
148	C₂³×C₁₂₇	—	2	1	no	—
149	C₂³×C₁₂₇	—	2	2	no	—
150	C₂³×C₁₂₇	—	2	2	no	—
151	C₂³×C₁₂₇	—	2	1	no	—
152	C₂³×C₁₂₇	—	2	1	no	—
153	C₂³×C₁₂₇	—	2	1	no	—
154	C₂³×C₁₂₇	—	2	2	no	—
155	C₂³×C₁₂₇	—	2	2	no	—
156	C₂³×C₁₂₇	C₄×D₄	1	2	yes	—
157	C₂³×C₁₂₇	#131	1	2	yes	—
158	C₂³×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
159	D₄×C₁₂₇	—	2	8	no	—
160	C₂×C₄×C₁₂₇	—	2	1	no	—
161	C₂×C₄×C₁₂₇	—	2	2	no	—
162	C₂×C₄×C₁₂₇	—	2	1	no	—
163	C₂×C₄×C₁₂₇	—	2	2	no	—
164	C₂×C₄×C₁₂₇	—	2	2	no	—
165	C₂×C₄×C₁₂₇	—	2	4	no	—
166	C₂×C₄×C₁₂₇	—	2	1	no	—
167	C₂×C₄×C₁₂₇	—	2	2	no	—
168	C₂×C₄×C₁₂₇	—	2	2	no	—
169	C₂×C₄×C₁₂₇	—	2	1	no	—
170	C₂×C₄×C₁₂₇	—	2	2	no	—
171	C₂×C₄×C₁₂₇	—	2	2	no	—
172	C₂×C₄×C₁₂₇	—	2	2	no	—
173	C₂×C₄×C₁₂₇	—	2	2	no	—
174	C₂×C₄×C₁₂₇	—	2	2	no	—
175	C₂×C₄×C₁₂₇	—	2	2	no	—
176	C₂×C₄×C₁₂₇	—	2	2	no	—
177	C₂×C₄×C₁₂₇	—	2	2	no	—
178	C₂×C₄×C₁₂₇	—	2	2	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	—	4	1	no	—
183	C₂×C₄×C₁₂₇	—	4	1	no	—
184	C₂×C₄×C₁₂₇	—	4	2	no	—
185	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₁₂₇	#131	1	2	yes	—
187	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₂₇	C₂×#41	1	2	yes	—
189	C₂×C₄×C₁₂₇	C₂×#41	1	2	yes	—
190	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
191	C₈×C₁₂₇	—	2	2	no	—
192	C₈×C₁₂₇	—	2	4	no	—
193	C₈×C₁₂₇	—	4	1	no	—
194	C₈×C₁₂₇	—	4	1	no	—
195	C₈×C₁₂₇	—	4	2	no	—
196	C₈×C₁₂₇	#123	1	4	yes	—
197	C₂²×C₁₂₇	—	2	2	no	—
198	C₂²×C₁₂₇	—	2	2	no	—
199	C₂²×C₁₂₇	—	2	2	no	—
200	C₂²×C₁₂₇	—	2	4	no	—
201	C₂²×C₁₂₇	—	2	2	no	—
202	C₂²×C₁₂₇	—	4	1	no	—
203	C₂²×C₁₂₇	—	4	2	no	—
204	C₂²×C₁₂₇	—	4	2	no	—
205	C₂²×C₁₂₇	—	4	2	no	—
206	C₂²×C₁₂₇	—	4	1	no	—
207	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂²×C₁₂₇	C₄×#41	1	2	yes	—
209	C₂²×C₁₂₇	C₂×#131	1	1	yes	characteristic
210	C₂²×C₁₂₇	C₂×#131	1	1	yes	characteristic
211	C₂²×C₁₂₇	#568	1	2	yes	—
212	C₄×C₁₂₇	—	2	2	no	—
213	C₄×C₁₂₇	—	2	2	no	—
214	C₄×C₁₂₇	—	4	2	no	—
215	C₄×C₁₂₇	—	4	1	no	—
216	C₄×C₁₂₇	—	4	2	no	—
217	C₄×C₁₂₇	—	4	2	no	—
218	C₄×C₁₂₇	—	4	2	no	—
219	C₄×C₁₂₇	—	4	1	no	—
220	C₄×C₁₂₇	C₂×#123	1	1	yes	characteristic
221	C₄×C₁₂₇	#525	1	1	yes	characteristic
222	C₄×C₁₂₇	#529	1	2	yes	—
223	#21567	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂×C₁₂₇	—	4	2	no	—
225	C₂×C₁₂₇	—	4	2	no	—
226	C₂×C₁₂₇	C₄×#123	1	1	yes	characteristic
227	C₂×C₁₂₇	#2929	1	1	yes	characteristic
228	C₂×C₁₂₇	#2932	1	1	yes	characteristic
229	C₂×C₁₂₇	#2968	1	2	yes	—
230	C₂×C₁₂₇	#2969	1	2	yes	—
231	C₂×C₈×D₄	C₂×C₁₂₇	1	1	yes	characteristic
232	C₂×#405	C₂×C₁₂₇	1	1	yes	characteristic, complemented
233	#2395	C₂×C₁₂₇	1	1	yes	characteristic
234	#1923	C₂×C₁₂₇	1	2	yes	complemented
235	#1916	C₂×C₁₂₇	1	2	yes	complemented
236	#1870	C₂×C₁₂₇	1	1	yes	characteristic
237	#1851	C₂×C₁₂₇	1	1	yes	characteristic, complemented
238	#1818	C₂×C₁₂₇	1	1	yes	characteristic, complemented
239	#1771	C₂×C₁₂₇	1	2	yes	complemented
240	#1752	C₂×C₁₂₇	1	2	yes	complemented
241	#1752	C₂×C₁₂₇	1	1	yes	characteristic, complemented
242	C₁₂₇	#21567	1	1	yes	characteristic, direct product factor, Sylow
243	C₂²×M₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
244	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
245	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
246	C₂×C₄×D₄	C₂²×C₁₂₇	1	1	yes	characteristic
247	C₂×#117	C₂²×C₁₂₇	1	1	yes	characteristic
248	C₈×D₄	—	2	4	no	—
249	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
250	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
251	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
252	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
253	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	—
254	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
255	#405	—	2	4	no	—
256	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
257	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
258	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
259	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
260	#400	C₄×C₁₂₇	1	1	yes	characteristic
261	#399	C₄×C₁₂₇	1	1	yes	characteristic
262	#398	C₄×C₁₂₇	1	1	yes	characteristic
263	#397	C₄×C₁₂₇	1	2	yes	—
264	#397	C₄×C₁₂₇	1	1	yes	characteristic
265	#394	C₄×C₁₂₇	1	2	yes	—
266	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
267	C₄×C₂²⋊C₄	C₂²×C₁₂₇	1	1	yes	characteristic
268	C₄×C₂²⋊C₄	C₂²×C₁₂₇	1	2	yes	—
269	#336	C₂²×C₁₂₇	1	2	yes	—
270	#336	C₂²×C₁₂₇	1	2	yes	—
271	#336	C₂²×C₁₂₇	1	2	yes	—
272	#336	C₂²×C₁₂₇	1	2	yes	—
273	#336	C₂²×C₁₂₇	1	2	yes	—
274	C₂²×D₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
275	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	4	no	—
279	C₂²×C₈	—	2	4	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	4	no	—
282	C₂²×C₈	D₄×C₁₂₇	1	4	yes	—
283	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
285	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
288	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	2	no	—
291	#117	—	2	2	no	—
292	#117	—	2	2	no	—
293	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
297	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
299	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
302	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
303	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
304	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
305	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
307	C₄⋊C₈	—	2	2	no	—
308	C₄⋊C₈	—	2	4	no	—
309	C₂²⋊C₈	—	2	2	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	C₂²⋊C₈	—	2	4	no	—
313	#97	—	2	4	no	—
314	#97	—	2	4	no	—
315	C₄×C₈	—	2	4	no	—
316	C₄×C₈	—	2	2	no	—
317	#95	C₂×C₄×C₁₂₇	1	2	yes	—
318	#95	C₂×C₄×C₁₂₇	1	1	yes	characteristic
319	#95	C₂×C₄×C₁₂₇	1	2	yes	—
320	#95	C₂×C₄×C₁₂₇	1	1	yes	characteristic
321	#95	C₂×C₄×C₁₂₇	1	2	yes	—
322	#95	C₂×C₄×C₁₂₇	1	2	yes	—
323	C₂⁴	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
324	C₂⁴	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
335	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
336	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
338	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
339	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
340	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
343	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
344	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
345	M₁₆	—	2	8	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	8	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	4	no	—
358	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
359	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
360	C₂×C₈	#41×C₁₂₇	1	4	yes	—
361	C₂×C₈	#41×C₁₂₇	1	4	yes	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	4	2	no	—
372	C₂²⋊C₄	—	4	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	C₄×D₄×C₁₂₇	1	2	yes	—
388	C₂³	#131×C₁₂₇	1	2	yes	—
389	C₂³	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
390	D₄	—	2	8	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
417	C₂×C₄	#131×C₁₂₇	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₁₂₇	1	2	yes	—
420	C₂×C₄	C₂×#41×C₁₂₇	1	2	yes	—
421	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
422	C₈	—	2	2	no	—
423	C₈	—	2	4	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	1	no	—
426	C₈	—	4	2	no	—
427	C₈	#123×C₁₂₇	1	4	yes	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
439	C₂²	C₄×#41×C₁₂₇	1	2	yes	—
440	C₂²	C₂×#131×C₁₂₇	1	1	yes	characteristic
441	C₂²	C₂×#131×C₁₂₇	1	1	yes	characteristic
442	C₂²	#568×C₁₂₇	1	2	yes	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	1	no	—
451	C₄	C₂×#123×C₁₂₇	1	1	yes	characteristic
452	C₄	#525×C₁₂₇	1	1	yes	characteristic
453	C₄	#529×C₁₂₇	1	2	yes	—
454	C₂	—	4	2	no	—
455	C₂	—	4	2	no	—
456	C₂	C₄×#123×C₁₂₇	1	1	yes	characteristic
457	C₂	C₁₂₇×#2929	1	1	yes	characteristic
458	C₂	C₁₂₇×#2932	1	1	yes	characteristic
459	C₂	C₁₂₇×#2968	1	2	yes	—
460	C₂	C₁₂₇×#2969	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×#405×C₁₂₇	C₂	semidirect
4. C₁₂₇×#1923	C₂	semidirect
5. C₁₂₇×#1916	C₂	semidirect
7. C₁₂₇×#1851	C₂	semidirect
8. C₁₂₇×#1818	C₂	semidirect
9. C₁₂₇×#1771	C₂	semidirect
10. C₁₂₇×#1752	C₂	semidirect
11. C₁₂₇×#1752	C₂	semidirect
223. #21567	C₁₂₇	direct (N × H)
232. C₂×#405	C₂×C₁₂₇	semidirect
234. #1923	C₂×C₁₂₇	semidirect
235. #1916	C₂×C₁₂₇	semidirect
237. #1851	C₂×C₁₂₇	semidirect
238. #1818	C₂×C₁₂₇	semidirect
239. #1771	C₂×C₁₂₇	semidirect
240. #1752	C₂×C₁₂₇	semidirect
241. #1752	C₂×C₁₂₇	semidirect
242. C₁₂₇	#21567	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×C₈×D₄×C₁₂₇	2
C₂×#405×C₁₂₇	2
C₁₂₇×#2395	2
C₁₂₇×#1923	2
C₁₂₇×#1916	2
C₁₂₇×#1870	2
C₁₂₇×#1851	2
C₁₂₇×#1818	2
C₁₂₇×#1771	2
C₁₂₇×#1752	2
#21567	127

Subgroups — C127×#21567 #44585240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#21567 #44585240