Subgroups — C₁₂₇×#17351 #44581024

Order 32512.

1278 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#520×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₁₂₇×#2972	C₂	1	2	yes	maximal, complemented
3	C₁₂₇×#1461	C₂	1	2	yes	maximal, complemented
4	C₁₂₇×#1459	C₂	1	4	yes	maximal, complemented
5	C₁₂₇×#1458	C₂	1	2	yes	maximal, complemented
6	C₂×#324×C₁₂₇	C₂	1	4	yes	maximal, complemented
7	C₂²×#41×C₁₂₇	C₄	1	1	yes	characteristic
8	#520×C₁₂₇	—	2	8	no	—
9	C₂×C₄×Q₈×C₁₂₇	C₄	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₂₇	C₄	1	2	yes	—
12	C₂×C₄×D₄×C₁₂₇	C₄	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₂₇	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₂₇	C₄	1	2	yes	—
16	C₂×#117×C₁₂₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₂₇	C₄	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
19	C₈×D₄×C₁₂₇	—	2	8	no	—
20	#431×C₁₂₇	C₂²	1	4	yes	—
21	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	8	yes	—
22	#324×C₁₂₇	C₂²	1	4	yes	—
23	#324×C₁₂₇	C₂²	1	8	yes	—
24	#323×C₁₂₇	C₂²	1	4	yes	—
25	C₂×#41×C₁₂₇	—	2	4	no	—
26	C₂×#41×C₁₂₇	—	2	4	no	—
27	C₂×#41×C₁₂₇	C₈	1	8	yes	complemented
28	C₂²×Q₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₂₇	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₂₇	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₂₇	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₂₇	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₂₇	C₂³	1	2	yes	—
36	C₂²×C₈×C₁₂₇	—	2	8	no	—
37	C₄×Q₈×C₁₂₇	—	2	4	no	—
38	C₄×Q₈×C₁₂₇	—	2	4	no	—
39	C₄×D₄×C₁₂₇	—	2	4	no	—
40	C₄×D₄×C₁₂₇	—	2	8	no	—
41	C₄×D₄×C₁₂₇	—	2	8	no	—
42	C₄×D₄×C₁₂₇	D₄	1	8	yes	—
43	#117×C₁₂₇	—	2	8	no	—
44	#117×C₁₂₇	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₂₇	—	2	8	no	—
46	C₂×C₄⋊C₄×C₁₂₇	—	2	4	no	—
47	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₁₂₇	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₁₂₇	C₂×C₄	1	2	yes	—
60	C₂×C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
62	C₄⋊C₈×C₁₂₇	—	2	4	no	—
63	C₂²⋊C₈×C₁₂₇	—	2	8	no	—
64	C₂²⋊C₈×C₁₂₇	C₂³	1	8	yes	—
65	C₄×C₈×C₁₂₇	—	2	4	no	—
66	C₂⁴×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
67	C₂⁴×C₁₂₇	C₂²×C₄	1	2	yes	—
68	#41×C₁₂₇	—	2	32	no	—
69	C₂×Q₈×C₁₂₇	—	2	2	no	—
70	C₂×Q₈×C₁₂₇	—	2	2	no	—
71	C₂×Q₈×C₁₂₇	C₂×C₈	1	4	yes	complemented
72	C₂×D₄×C₁₂₇	—	2	4	no	—
73	C₂×D₄×C₁₂₇	—	2	4	no	—
74	C₂×D₄×C₁₂₇	C₂²⋊C₄	1	4	yes	—
75	C₂×D₄×C₁₂₇	C₂×C₈	1	4	yes	—
76	C₂×D₄×C₁₂₇	C₂×C₈	1	8	yes	complemented
77	C₂×D₄×C₁₂₇	M₁₆	1	4	yes	—
78	C₂²×C₄×C₁₂₇	—	2	4	no	—
79	C₂²×C₄×C₁₂₇	—	2	4	no	—
80	C₂²×C₄×C₁₂₇	—	2	2	no	—
81	C₂²×C₄×C₁₂₇	—	2	2	no	—
82	C₂²×C₄×C₁₂₇	—	2	4	no	—
83	C₂²×C₄×C₁₂₇	—	2	4	no	—
84	C₂²×C₄×C₁₂₇	—	8	2	no	—
85	C₂²×C₄×C₁₂₇	—	8	2	no	—
86	C₂²×C₄×C₁₂₇	—	8	2	no	—
87	C₂²×C₄×C₁₂₇	C₂×C₈	1	8	yes	complemented
88	C₂²×C₄×C₁₂₇	C₂×C₈	1	4	yes	complemented
89	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
94	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₂₇	C₂×D₄	1	8	yes	—
98	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₁₂₇	—	2	8	no	—
100	C₂×C₈×C₁₂₇	—	8	8	no	—
101	C₄⋊C₄×C₁₂₇	—	2	4	no	—
102	C₄⋊C₄×C₁₂₇	—	2	4	no	—
103	C₄⋊C₄×C₁₂₇	—	2	2	no	—
104	C₄⋊C₄×C₁₂₇	—	2	2	no	—
105	C₄⋊C₄×C₁₂₇	—	2	2	no	—
106	C₄⋊C₄×C₁₂₇	—	2	4	no	—
107	C₄⋊C₄×C₁₂₇	C₂²⋊C₄	1	4	yes	—
108	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
109	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
110	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
111	C₂²⋊C₄×C₁₂₇	C₂²⋊C₄	1	8	yes	—
112	C₄²×C₁₂₇	—	2	4	no	—
113	C₄²×C₁₂₇	—	2	4	no	—
114	C₄²×C₁₂₇	—	2	2	no	—
115	C₄²×C₁₂₇	C₂×D₄	1	4	yes	—
116	C₂³×C₁₂₇	—	2	1	no	—
117	C₂³×C₁₂₇	—	2	1	no	—
118	C₂³×C₁₂₇	—	4	2	no	—
119	C₂³×C₁₂₇	—	4	2	no	—
120	C₂³×C₁₂₇	—	4	1	no	—
121	C₂³×C₁₂₇	—	4	1	no	—
122	C₂³×C₁₂₇	C₂×C₂²⋊C₄	1	4	yes	—
123	C₂³×C₁₂₇	C₂²×C₈	1	2	yes	—
124	C₂³×C₁₂₇	C₂²×C₈	1	4	yes	—
125	C₂³×C₁₂₇	C₂×M₁₆	1	4	yes	—
126	C₂³×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
127	Q₈×C₁₂₇	—	2	8	no	—
128	D₄×C₁₂₇	—	2	16	no	—
129	D₄×C₁₂₇	C₂²⋊C₈	1	16	yes	—
130	C₂×C₄×C₁₂₇	—	2	2	no	—
131	C₂×C₄×C₁₂₇	—	2	1	no	—
132	C₂×C₄×C₁₂₇	—	2	1	no	—
133	C₂×C₄×C₁₂₇	—	2	2	no	—
134	C₂×C₄×C₁₂₇	—	2	16	no	—
135	C₂×C₄×C₁₂₇	—	2	8	no	—
136	C₂×C₄×C₁₂₇	—	2	1	no	—
137	C₂×C₄×C₁₂₇	—	2	2	no	—
138	C₂×C₄×C₁₂₇	—	2	1	no	—
139	C₂×C₄×C₁₂₇	—	4	8	no	—
140	C₂×C₄×C₁₂₇	—	4	2	no	—
141	C₂×C₄×C₁₂₇	—	4	1	no	—
142	C₂×C₄×C₁₂₇	—	4	1	no	—
143	C₂×C₄×C₁₂₇	—	4	2	no	—
144	C₂×C₄×C₁₂₇	—	4	1	no	—
145	C₂×C₄×C₁₂₇	—	4	1	no	—
146	C₂×C₄×C₁₂₇	—	8	4	no	—
147	C₂×C₄×C₁₂₇	—	8	4	no	—
148	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	4	yes	—
150	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₁₂₇	C₂²×C₈	1	2	yes	—
152	C₂×C₄×C₁₂₇	C₂²×C₈	1	4	yes	—
153	C₂×C₄×C₁₂₇	C₂²×C₈	1	2	yes	—
154	C₂×C₄×C₁₂₇	C₂×M₁₆	1	2	yes	—
155	C₂×C₄×C₁₂₇	C₂²×D₄	1	2	yes	—
156	C₈×C₁₂₇	—	4	8	no	—
157	C₂²×C₁₂₇	—	2	1	no	—
158	C₂²×C₁₂₇	—	2	4	no	—
159	C₂²×C₁₂₇	—	2	1	no	—
160	C₂²×C₁₂₇	—	2	4	no	—
161	C₂²×C₁₂₇	—	2	2	no	—
162	C₂²×C₁₂₇	—	4	4	no	—
163	C₂²×C₁₂₇	—	4	4	no	—
164	C₂²×C₁₂₇	—	4	2	no	—
165	C₂²×C₁₂₇	—	4	2	no	—
166	C₂²×C₁₂₇	—	4	1	no	—
167	C₂²×C₁₂₇	—	4	1	no	—
168	C₂²×C₁₂₇	C₂×C₂²⋊C₈	1	8	yes	—
169	C₂²×C₁₂₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
170	C₂²×C₁₂₇	C₂³×C₈	1	1	yes	characteristic
171	C₂²×C₁₂₇	C₂²×M₁₆	1	1	yes	characteristic
172	C₄×C₁₂₇	—	2	2	no	—
173	C₄×C₁₂₇	—	2	4	no	—
174	C₄×C₁₂₇	—	2	2	no	—
175	C₄×C₁₂₇	—	2	4	no	—
176	C₄×C₁₂₇	—	2	2	no	—
177	C₄×C₁₂₇	—	4	2	no	—
178	C₄×C₁₂₇	—	4	1	no	—
179	C₄×C₁₂₇	—	4	1	no	—
180	C₄×C₁₂₇	C₂×C₂²⋊C₈	1	4	yes	—
181	#17351	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂×C₁₂₇	—	2	1	no	—
183	C₂×C₁₂₇	—	2	1	no	—
184	C₂×C₁₂₇	—	2	8	no	—
185	C₂×C₁₂₇	—	4	2	no	—
186	C₂×C₁₂₇	C₂²×C₂²⋊C₈	1	1	yes	characteristic
187	C₂×C₁₂₇	#2883	1	1	yes	characteristic
188	C₂×C₁₂₇	#2889	1	1	yes	characteristic
189	C₂×#520	C₂×C₁₂₇	1	1	yes	characteristic
190	#2972	C₂×C₁₂₇	1	2	yes	complemented
191	#1461	C₂×C₁₂₇	1	2	yes	complemented
192	#1459	C₂×C₁₂₇	1	4	yes	complemented
193	#1458	C₂×C₁₂₇	1	2	yes	complemented
194	C₂×#324	C₂×C₁₂₇	1	4	yes	complemented
195	C₁₂₇	#17351	1	1	yes	characteristic, direct product factor, Sylow
196	C₂²×#41	C₄×C₁₂₇	1	1	yes	characteristic
197	#520	—	2	8	no	—
198	C₂×C₄×Q₈	C₄×C₁₂₇	1	1	yes	characteristic
199	C₂×C₄×Q₈	C₂²×C₁₂₇	1	1	yes	characteristic
200	C₂×C₄×D₄	C₄×C₁₂₇	1	2	yes	—
201	C₂×C₄×D₄	C₄×C₁₂₇	1	1	yes	characteristic
202	C₂×C₄×D₄	C₂²×C₁₂₇	1	2	yes	—
203	C₂×C₄×D₄	C₂²×C₁₂₇	1	1	yes	characteristic
204	C₂×#117	C₄×C₁₂₇	1	2	yes	—
205	C₂×#117	C₂²×C₁₂₇	1	1	yes	characteristic
206	C₂²×C₄⋊C₄	C₄×C₁₂₇	1	1	yes	characteristic
207	C₂²×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
208	C₈×D₄	—	2	8	no	—
209	#431	C₂²×C₁₂₇	1	4	yes	—
210	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	8	yes	—
211	#324	C₂²×C₁₂₇	1	4	yes	—
212	#324	C₂²×C₁₂₇	1	8	yes	—
213	#323	C₂²×C₁₂₇	1	4	yes	—
214	C₂×#41	—	2	4	no	—
215	C₂×#41	—	2	4	no	—
216	C₂×#41	C₈×C₁₂₇	1	8	yes	complemented
217	C₂²×Q₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
218	C₂²×D₄	C₂×C₄×C₁₂₇	1	2	yes	—
219	C₂²×D₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
220	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
221	C₂³×C₄	C₂×C₄×C₁₂₇	1	2	yes	—
222	C₂³×C₄	C₂×C₄×C₁₂₇	1	2	yes	—
223	C₂³×C₄	C₂×C₄×C₁₂₇	1	2	yes	—
224	C₂³×C₄	C₂³×C₁₂₇	1	2	yes	—
225	C₂²×C₈	—	2	8	no	—
226	C₄×Q₈	—	2	4	no	—
227	C₄×Q₈	—	2	4	no	—
228	C₄×D₄	—	2	4	no	—
229	C₄×D₄	—	2	8	no	—
230	C₄×D₄	—	2	8	no	—
231	C₄×D₄	D₄×C₁₂₇	1	8	yes	—
232	#117	—	2	8	no	—
233	#117	—	2	4	no	—
234	C₂×C₄⋊C₄	—	2	8	no	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
239	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	2	yes	—
243	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
244	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
246	C₂×C₂²⋊C₄	C₂³×C₁₂₇	1	1	yes	characteristic
247	C₂×C₄²	C₂×C₄×C₁₂₇	1	2	yes	—
248	C₂×C₄²	C₂×C₄×C₁₂₇	1	2	yes	—
249	C₂×C₄²	C₂×C₄×C₁₂₇	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
251	C₄⋊C₈	—	2	4	no	—
252	C₂²⋊C₈	—	2	8	no	—
253	C₂²⋊C₈	C₂³×C₁₂₇	1	8	yes	—
254	C₄×C₈	—	2	4	no	—
255	C₂⁴	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
256	C₂⁴	C₂²×C₄×C₁₂₇	1	2	yes	—
257	#41	—	2	32	no	—
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	C₂×C₈×C₁₂₇	1	4	yes	complemented
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	C₂²⋊C₄×C₁₂₇	1	4	yes	—
264	C₂×D₄	C₂×C₈×C₁₂₇	1	4	yes	—
265	C₂×D₄	C₂×C₈×C₁₂₇	1	8	yes	complemented
266	C₂×D₄	M₁₆×C₁₂₇	1	4	yes	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	8	2	no	—
274	C₂²×C₄	—	8	2	no	—
275	C₂²×C₄	—	8	2	no	—
276	C₂²×C₄	C₂×C₈×C₁₂₇	1	8	yes	complemented
277	C₂²×C₄	C₂×C₈×C₁₂₇	1	4	yes	complemented
278	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
279	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
282	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₁₂₇	1	8	yes	—
287	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
288	C₂×C₈	—	2	8	no	—
289	C₂×C₈	—	8	8	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	C₂²⋊C₄×C₁₂₇	1	4	yes	—
297	C₂²⋊C₄	—	2	4	no	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	2	2	no	—
300	C₂²⋊C₄	C₂²⋊C₄×C₁₂₇	1	8	yes	—
301	C₄²	—	2	4	no	—
302	C₄²	—	2	4	no	—
303	C₄²	—	2	2	no	—
304	C₄²	C₂×D₄×C₁₂₇	1	4	yes	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	2	no	—
309	C₂³	—	4	1	no	—
310	C₂³	—	4	1	no	—
311	C₂³	C₂×C₂²⋊C₄×C₁₂₇	1	4	yes	—
312	C₂³	C₂²×C₈×C₁₂₇	1	2	yes	—
313	C₂³	C₂²×C₈×C₁₂₇	1	4	yes	—
314	C₂³	C₂×M₁₆×C₁₂₇	1	4	yes	—
315	C₂³	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
316	Q₈	—	2	8	no	—
317	D₄	—	2	16	no	—
318	D₄	C₂²⋊C₈×C₁₂₇	1	16	yes	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	16	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	4	8	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	8	4	no	—
336	C₂×C₄	—	8	4	no	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	4	yes	—
339	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
340	C₂×C₄	C₂²×C₈×C₁₂₇	1	2	yes	—
341	C₂×C₄	C₂²×C₈×C₁₂₇	1	4	yes	—
342	C₂×C₄	C₂²×C₈×C₁₂₇	1	2	yes	—
343	C₂×C₄	C₂×M₁₆×C₁₂₇	1	2	yes	—
344	C₂×C₄	C₂²×D₄×C₁₂₇	1	2	yes	—
345	C₈	—	4	8	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	4	4	no	—
352	C₂²	—	4	4	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	C₂×C₂²⋊C₈×C₁₂₇	1	8	yes	—
358	C₂²	C₂²×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
359	C₂²	C₂³×C₈×C₁₂₇	1	1	yes	characteristic
360	C₂²	C₂²×M₁₆×C₁₂₇	1	1	yes	characteristic
361	C₄	—	2	2	no	—
362	C₄	—	2	4	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	4	no	—
365	C₄	—	2	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	1	no	—
369	C₄	C₂×C₂²⋊C₈×C₁₂₇	1	4	yes	—
370	C₂	—	2	1	no	—
371	C₂	—	2	1	no	—
372	C₂	—	2	8	no	—
373	C₂	—	4	2	no	—
374	C₂	C₂²×C₂²⋊C₈×C₁₂₇	1	1	yes	characteristic
375	C₂	C₁₂₇×#2883	1	1	yes	characteristic
376	C₂	C₁₂₇×#2889	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₂₇×#2972	C₂	semidirect
3. C₁₂₇×#1461	C₂	semidirect
4. C₁₂₇×#1459	C₂	semidirect
5. C₁₂₇×#1458	C₂	semidirect
6. C₂×#324×C₁₂₇	C₂	semidirect
27. C₂×#41×C₁₂₇	C₈	semidirect
71. C₂×Q₈×C₁₂₇	C₂×C₈	semidirect
76. C₂×D₄×C₁₂₇	C₂×C₈	semidirect
87. C₂²×C₄×C₁₂₇	C₂×C₈	semidirect
88. C₂²×C₄×C₁₂₇	C₂×C₈	semidirect
181. #17351	C₁₂₇	direct (N × H)
190. #2972	C₂×C₁₂₇	semidirect
191. #1461	C₂×C₁₂₇	semidirect
192. #1459	C₂×C₁₂₇	semidirect
193. #1458	C₂×C₁₂₇	semidirect
194. C₂×#324	C₂×C₁₂₇	semidirect
195. C₁₂₇	#17351	direct (N × H)
216. C₂×#41	C₈×C₁₂₇	semidirect
260. C₂×Q₈	C₂×C₈×C₁₂₇	semidirect
265. C₂×D₄	C₂×C₈×C₁₂₇	semidirect
276. C₂²×C₄	C₂×C₈×C₁₂₇	semidirect
277. C₂²×C₄	C₂×C₈×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#520×C₁₂₇	2
C₁₂₇×#2972	2
C₁₂₇×#1461	2
C₁₂₇×#1459	2
C₁₂₇×#1458	2
C₂×#324×C₁₂₇	2
#17351	127

Subgroups — C127×#17351 #44581024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#17351 #44581024