Subgroups — C₁₂₇×#21679 #44585352

Order 32512.

638 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₂₇×#2402	C₂	1	1	yes	maximal, characteristic
2	C₁₂₇×#1940	C₂	1	1	yes	maximal, characteristic
3	C₁₂₇×#1940	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1916	C₂	1	2	yes	maximal
5	C₁₂₇×#1916	C₂	1	2	yes	maximal
6	C₁₂₇×#1832	C₂	1	1	yes	maximal, characteristic
7	C₁₂₇×#1771	C₂	1	2	yes	maximal
8	C₁₂₇×#1770	C₂	1	2	yes	maximal
9	C₁₂₇×#1770	C₂	1	1	yes	maximal, characteristic
10	C₈×C₄⋊C₄×C₁₂₇	C₂	1	1	yes	maximal, characteristic
11	C₁₂₇×#1726	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
16	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
17	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
18	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
19	C₂×#97×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×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
24	#400×C₁₂₇	C₄	1	2	yes	—
25	#400×C₁₂₇	C₄	1	2	yes	—
26	#398×C₁₂₇	C₄	1	2	yes	—
27	#398×C₁₂₇	C₄	1	2	yes	—
28	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
32	#376×C₁₂₇	C₂²	1	1	yes	characteristic
33	#336×C₁₂₇	C₂²	1	2	yes	—
34	#336×C₁₂₇	C₂²	1	2	yes	—
35	#336×C₁₂₇	C₂²	1	2	yes	—
36	#336×C₁₂₇	C₂²	1	2	yes	—
37	#336×C₁₂₇	C₂²	1	2	yes	—
38	#336×C₁₂₇	C₂²	1	2	yes	—
39	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
46	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
54	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
56	C₄⋊C₈×C₁₂₇	—	2	4	no	—
57	C₄⋊C₈×C₁₂₇	—	2	4	no	—
58	C₄⋊C₈×C₁₂₇	—	2	2	no	—
59	C₄⋊C₈×C₁₂₇	—	2	2	no	—
60	#97×C₁₂₇	—	2	2	no	—
61	#97×C₁₂₇	—	2	2	no	—
62	#97×C₁₂₇	—	2	4	no	—
63	#97×C₁₂₇	—	2	2	no	—
64	C₄×C₈×C₁₂₇	—	2	2	no	—
65	C₄×C₈×C₁₂₇	—	2	2	no	—
66	C₄×C₈×C₁₂₇	—	2	4	no	—
67	C₄×C₈×C₁₂₇	Q₈	1	4	yes	—
68	#95×C₁₂₇	C₂×C₄	1	2	yes	—
69	#95×C₁₂₇	C₂×C₄	1	2	yes	—
70	#95×C₁₂₇	C₂×C₄	1	1	yes	characteristic
71	#95×C₁₂₇	C₂×C₄	1	1	yes	characteristic
72	#95×C₁₂₇	C₂×C₄	1	2	yes	—
73	#95×C₁₂₇	C₂×C₄	1	2	yes	—
74	#95×C₁₂₇	C₂×C₄	1	2	yes	—
75	#95×C₁₂₇	C₂×C₄	1	2	yes	—
76	#95×C₁₂₇	C₂×C₄	1	1	yes	characteristic
77	#95×C₁₂₇	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
87	C₂×C₈×C₁₂₇	—	2	1	no	—
88	C₂×C₈×C₁₂₇	—	2	1	no	—
89	C₂×C₈×C₁₂₇	—	2	1	no	—
90	C₂×C₈×C₁₂₇	—	2	1	no	—
91	C₂×C₈×C₁₂₇	—	2	1	no	—
92	C₂×C₈×C₁₂₇	—	2	1	no	—
93	C₂×C₈×C₁₂₇	—	2	2	no	—
94	C₂×C₈×C₁₂₇	—	2	2	no	—
95	C₂×C₈×C₁₂₇	—	2	2	no	—
96	C₂×C₈×C₁₂₇	—	2	2	no	—
97	C₂×C₈×C₁₂₇	—	2	2	no	—
98	C₂×C₈×C₁₂₇	—	2	2	no	—
99	C₂×C₈×C₁₂₇	C₂×Q₈	1	2	yes	—
100	C₂×C₈×C₁₂₇	C₂×Q₈	1	2	yes	—
101	C₂×C₈×C₁₂₇	#41	1	2	yes	—
102	C₂×C₈×C₁₂₇	#41	1	2	yes	—
103	C₂×C₈×C₁₂₇	#41	1	2	yes	—
104	C₂×C₈×C₁₂₇	#41	1	2	yes	—
105	C₄⋊C₄×C₁₂₇	—	2	4	no	—
106	C₄⋊C₄×C₁₂₇	—	2	4	no	—
107	C₄⋊C₄×C₁₂₇	—	2	4	no	—
108	C₄⋊C₄×C₁₂₇	—	4	2	no	—
109	C₄⋊C₄×C₁₂₇	—	4	2	no	—
110	C₄⋊C₄×C₁₂₇	—	4	2	no	—
111	C₄²×C₁₂₇	—	2	2	no	—
112	C₄²×C₁₂₇	—	2	1	no	—
113	C₄²×C₁₂₇	—	2	1	no	—
114	C₄²×C₁₂₇	—	2	1	no	—
115	C₄²×C₁₂₇	—	2	1	no	—
116	C₄²×C₁₂₇	—	2	2	no	—
117	C₄²×C₁₂₇	—	2	2	no	—
118	C₄²×C₁₂₇	—	2	2	no	—
119	C₄²×C₁₂₇	C₂×Q₈	1	2	yes	—
120	C₄²×C₁₂₇	#41	1	2	yes	—
121	C₂³×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₂₇	—	2	2	no	—
123	C₂×C₄×C₁₂₇	—	2	2	no	—
124	C₂×C₄×C₁₂₇	—	2	2	no	—
125	C₂×C₄×C₁₂₇	—	2	2	no	—
126	C₂×C₄×C₁₂₇	—	2	2	no	—
127	C₂×C₄×C₁₂₇	—	2	2	no	—
128	C₂×C₄×C₁₂₇	—	2	2	no	—
129	C₂×C₄×C₁₂₇	—	2	2	no	—
130	C₂×C₄×C₁₂₇	—	2	2	no	—
131	C₂×C₄×C₁₂₇	—	2	2	no	—
132	C₂×C₄×C₁₂₇	—	2	2	no	—
133	C₂×C₄×C₁₂₇	—	2	2	no	—
134	C₂×C₄×C₁₂₇	—	2	2	no	—
135	C₂×C₄×C₁₂₇	—	2	2	no	—
136	C₂×C₄×C₁₂₇	—	2	2	no	—
137	C₂×C₄×C₁₂₇	—	2	2	no	—
138	C₂×C₄×C₁₂₇	—	2	2	no	—
139	C₂×C₄×C₁₂₇	—	2	2	no	—
140	C₂×C₄×C₁₂₇	—	2	2	no	—
141	C₂×C₄×C₁₂₇	C₄×Q₈	1	2	yes	—
142	C₂×C₄×C₁₂₇	C₄×Q₈	1	2	yes	—
143	C₂×C₄×C₁₂₇	#131	1	4	yes	—
144	C₂×C₄×C₁₂₇	C₂²×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
146	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
147	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
148	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
149	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
150	C₈×C₁₂₇	—	2	2	no	—
151	C₈×C₁₂₇	—	2	2	no	—
152	C₈×C₁₂₇	—	2	2	no	—
153	C₈×C₁₂₇	—	4	2	no	—
154	C₈×C₁₂₇	—	4	2	no	—
155	C₈×C₁₂₇	#125	1	4	yes	—
156	C₂²×C₁₂₇	C₂×C₄×Q₈	1	1	yes	characteristic
157	C₂²×C₁₂₇	C₄×#41	1	1	yes	characteristic
158	C₂²×C₁₂₇	C₄×#41	1	1	yes	characteristic
159	C₂²×C₁₂₇	C₂×#131	1	2	yes	—
160	C₂²×C₁₂₇	#568	1	2	yes	—
161	C₄×C₁₂₇	—	2	2	no	—
162	C₄×C₁₂₇	—	2	2	no	—
163	C₄×C₁₂₇	—	2	4	no	—
164	C₄×C₁₂₇	—	4	2	no	—
165	C₄×C₁₂₇	—	4	2	no	—
166	C₄×C₁₂₇	—	4	2	no	—
167	C₄×C₁₂₇	—	4	2	no	—
168	C₄×C₁₂₇	—	4	2	no	—
169	C₄×C₁₂₇	C₂×#125	1	1	yes	characteristic
170	C₄×C₁₂₇	#529	1	1	yes	characteristic
171	C₄×C₁₂₇	#529	1	1	yes	characteristic
172	C₄×C₁₂₇	#533	1	1	yes	characteristic
173	#21679	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂×C₁₂₇	C₄×#125	1	1	yes	characteristic
175	C₂×C₁₂₇	#2960	1	1	yes	characteristic
176	C₂×C₁₂₇	#2961	1	1	yes	characteristic
177	C₂×C₁₂₇	#2968	1	2	yes	—
178	C₂×C₁₂₇	#2969	1	2	yes	—
179	#2402	C₂×C₁₂₇	1	1	yes	characteristic
180	#1940	C₂×C₁₂₇	1	1	yes	characteristic
181	#1940	C₂×C₁₂₇	1	1	yes	characteristic
182	#1916	C₂×C₁₂₇	1	2	yes	—
183	#1916	C₂×C₁₂₇	1	2	yes	—
184	#1832	C₂×C₁₂₇	1	1	yes	characteristic
185	#1771	C₂×C₁₂₇	1	2	yes	—
186	#1770	C₂×C₁₂₇	1	2	yes	—
187	#1770	C₂×C₁₂₇	1	1	yes	characteristic
188	C₈×C₄⋊C₄	C₂×C₁₂₇	1	1	yes	characteristic
189	#1726	C₂×C₁₂₇	1	1	yes	characteristic
190	C₁₂₇	#21679	1	1	yes	characteristic, direct product factor, Sylow
191	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
192	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
193	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
194	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
195	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
196	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
197	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
198	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
199	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
200	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
201	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
202	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
203	#400	C₄×C₁₂₇	1	2	yes	—
204	#400	C₄×C₁₂₇	1	2	yes	—
205	#398	C₄×C₁₂₇	1	2	yes	—
206	#398	C₄×C₁₂₇	1	2	yes	—
207	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
208	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
209	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	1	yes	characteristic
210	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	1	yes	characteristic
211	#376	C₂²×C₁₂₇	1	1	yes	characteristic
212	#336	C₂²×C₁₂₇	1	2	yes	—
213	#336	C₂²×C₁₂₇	1	2	yes	—
214	#336	C₂²×C₁₂₇	1	2	yes	—
215	#336	C₂²×C₁₂₇	1	2	yes	—
216	#336	C₂²×C₁₂₇	1	2	yes	—
217	#336	C₂²×C₁₂₇	1	2	yes	—
218	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
219	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
220	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
222	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
225	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
226	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
227	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
228	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
229	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
230	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
231	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
232	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
233	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
234	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
235	C₄⋊C₈	—	2	4	no	—
236	C₄⋊C₈	—	2	4	no	—
237	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	—	2	2	no	—
239	#97	—	2	2	no	—
240	#97	—	2	2	no	—
241	#97	—	2	4	no	—
242	#97	—	2	2	no	—
243	C₄×C₈	—	2	2	no	—
244	C₄×C₈	—	2	2	no	—
245	C₄×C₈	—	2	4	no	—
246	C₄×C₈	Q₈×C₁₂₇	1	4	yes	—
247	#95	C₂×C₄×C₁₂₇	1	2	yes	—
248	#95	C₂×C₄×C₁₂₇	1	2	yes	—
249	#95	C₂×C₄×C₁₂₇	1	1	yes	characteristic
250	#95	C₂×C₄×C₁₂₇	1	1	yes	characteristic
251	#95	C₂×C₄×C₁₂₇	1	2	yes	—
252	#95	C₂×C₄×C₁₂₇	1	2	yes	—
253	#95	C₂×C₄×C₁₂₇	1	2	yes	—
254	#95	C₂×C₄×C₁₂₇	1	2	yes	—
255	#95	C₂×C₄×C₁₂₇	1	1	yes	characteristic
256	#95	C₂×C₄×C₁₂₇	1	1	yes	characteristic
257	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
258	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
259	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
260	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
261	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
262	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
263	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
264	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
265	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
266	C₂×C₈	—	2	1	no	—
267	C₂×C₈	—	2	1	no	—
268	C₂×C₈	—	2	1	no	—
269	C₂×C₈	—	2	1	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	2	1	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	C₂×Q₈×C₁₂₇	1	2	yes	—
279	C₂×C₈	C₂×Q₈×C₁₂₇	1	2	yes	—
280	C₂×C₈	#41×C₁₂₇	1	2	yes	—
281	C₂×C₈	#41×C₁₂₇	1	2	yes	—
282	C₂×C₈	#41×C₁₂₇	1	2	yes	—
283	C₂×C₈	#41×C₁₂₇	1	2	yes	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	4	2	no	—
288	C₄⋊C₄	—	4	2	no	—
289	C₄⋊C₄	—	4	2	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	1	no	—
292	C₄²	—	2	1	no	—
293	C₄²	—	2	1	no	—
294	C₄²	—	2	1	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	C₂×Q₈×C₁₂₇	1	2	yes	—
299	C₄²	#41×C₁₂₇	1	2	yes	—
300	C₂³	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	C₄×Q₈×C₁₂₇	1	2	yes	—
321	C₂×C₄	C₄×Q₈×C₁₂₇	1	2	yes	—
322	C₂×C₄	#131×C₁₂₇	1	4	yes	—
323	C₂×C₄	C₂²×Q₈×C₁₂₇	1	1	yes	characteristic
324	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
325	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
326	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
327	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
328	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
329	C₈	—	2	2	no	—
330	C₈	—	2	2	no	—
331	C₈	—	2	2	no	—
332	C₈	—	4	2	no	—
333	C₈	—	4	2	no	—
334	C₈	#125×C₁₂₇	1	4	yes	—
335	C₂²	C₂×C₄×Q₈×C₁₂₇	1	1	yes	characteristic
336	C₂²	C₄×#41×C₁₂₇	1	1	yes	characteristic
337	C₂²	C₄×#41×C₁₂₇	1	1	yes	characteristic
338	C₂²	C₂×#131×C₁₂₇	1	2	yes	—
339	C₂²	#568×C₁₂₇	1	2	yes	—
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	4	no	—
343	C₄	—	4	2	no	—
344	C₄	—	4	2	no	—
345	C₄	—	4	2	no	—
346	C₄	—	4	2	no	—
347	C₄	—	4	2	no	—
348	C₄	C₂×#125×C₁₂₇	1	1	yes	characteristic
349	C₄	#529×C₁₂₇	1	1	yes	characteristic
350	C₄	#529×C₁₂₇	1	1	yes	characteristic
351	C₄	#533×C₁₂₇	1	1	yes	characteristic
352	C₂	C₄×#125×C₁₂₇	1	1	yes	characteristic
353	C₂	C₁₂₇×#2960	1	1	yes	characteristic
354	C₂	C₁₂₇×#2961	1	1	yes	characteristic
355	C₂	C₁₂₇×#2968	1	2	yes	—
356	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, prime radical	C₂³×C₁₂₇	C₂³×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
173. #21679	C₁₂₇	direct (N × H)
190. C₁₂₇	#21679	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₂₇×#2402	2
C₁₂₇×#1940	2
C₁₂₇×#1916	2
C₁₂₇×#1832	2
C₁₂₇×#1771	2
C₁₂₇×#1770	2
C₈×C₄⋊C₄×C₁₂₇	2
C₁₂₇×#1726	2
#21679	127

Subgroups — C127×#21679 #44585352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#21679 #44585352