Subgroups — C₁₂₇×#21659 #44585332

Order 32512.

722 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₂₇×#3131	C₂	1	1	yes	maximal, characteristic
2	C₁₂₇×#2961	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₂₇×#2932	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1995	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₂₇×#1963	C₂	1	1	yes	maximal, characteristic
6	C₁₂₇×#1938	C₂	1	2	yes	maximal, complemented
7	C₁₂₇×#1937	C₂	1	2	yes	maximal, complemented
8	C₁₂₇×#1837	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₂₇×#1765	C₂	1	2	yes	maximal, complemented
10	C₁₂₇×#1764	C₂	1	2	yes	maximal, complemented
11	C₁₂₇×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#131×C₁₂₇	C₂²	1	2	yes	—
13	#533×C₁₂₇	C₂²	1	1	yes	characteristic
14	#532×C₁₂₇	C₂²	1	1	yes	characteristic
15	#488×C₁₂₇	C₄	1	4	yes	complemented
16	#487×C₁₂₇	C₄	1	2	yes	complemented
17	#486×C₁₂₇	C₄	1	2	yes	complemented
18	#446×C₁₂₇	—	2	4	no	—
19	#435×C₁₂₇	—	2	4	no	—
20	#424×C₁₂₇	C₂²	1	2	yes	—
21	#423×C₁₂₇	C₂²	1	1	yes	characteristic
22	#423×C₁₂₇	C₂²	1	1	yes	characteristic
23	C₂×#104×C₁₂₇	C₂²	1	2	yes	—
24	C₂×#104×C₁₂₇	C₂²	1	2	yes	—
25	#416×C₁₂₇	C₂²	1	2	yes	—
26	#416×C₁₂₇	C₂²	1	2	yes	—
27	#408×C₁₂₇	C₂²	1	2	yes	—
28	#405×C₁₂₇	C₂²	1	2	yes	—
29	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
30	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
31	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
35	#376×C₁₂₇	C₂²	1	1	yes	characteristic
36	#341×C₁₂₇	C₂²	1	2	yes	—
37	#341×C₁₂₇	C₂²	1	2	yes	—
38	#339×C₁₂₇	C₂²	1	2	yes	—
39	#339×C₁₂₇	C₂²	1	2	yes	—
40	C₂×#41×C₁₂₇	C₂³	1	2	yes	—
41	#131×C₁₂₇	—	2	4	no	—
42	#131×C₁₂₇	—	2	4	no	—
43	C₂×M₁₆×C₁₂₇	—	2	2	no	—
44	C₂×M₁₆×C₁₂₇	C₂³	1	2	yes	—
45	C₂×M₁₆×C₁₂₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₂₇	—	2	2	no	—
47	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
51	C₄⋊Q₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
52	C₄⋊Q₈×C₁₂₇	C₂×C₄	1	2	yes	—
53	#127×C₁₂₇	C₂×C₄	1	1	yes	characteristic
54	#125×C₁₂₇	C₂×C₄	1	2	yes	—
55	#124×C₁₂₇	C₂×C₄	1	2	yes	—
56	C₂²⋊Q₈×C₁₂₇	—	2	2	no	—
57	#121×C₁₂₇	—	2	2	no	—
58	C₄×Q₈×C₁₂₇	—	2	2	no	—
59	C₄×D₄×C₁₂₇	—	2	2	no	—
60	#117×C₁₂₇	C₂³	1	2	yes	—
61	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
64	C₄⋊C₈×C₁₂₇	—	2	4	no	—
65	C₄⋊C₈×C₁₂₇	—	2	2	no	—
66	C₄⋊C₈×C₁₂₇	—	2	2	no	—
67	#104×C₁₂₇	—	2	4	no	—
68	#104×C₁₂₇	—	2	4	no	—
69	#103×C₁₂₇	C₂×C₄	1	4	yes	—
70	#103×C₁₂₇	C₂×C₄	1	4	yes	—
71	#102×C₁₂₇	C₂×C₄	1	4	yes	—
72	#102×C₁₂₇	C₂×C₄	1	4	yes	—
73	C₂²⋊C₈×C₁₂₇	—	2	4	no	—
74	#97×C₁₂₇	—	2	2	no	—
75	#97×C₁₂₇	—	2	2	no	—
76	#97×C₁₂₇	—	2	2	no	—
77	#97×C₁₂₇	D₄	1	4	yes	—
78	C₄×C₈×C₁₂₇	—	2	2	no	—
79	C₄×C₈×C₁₂₇	—	2	2	no	—
80	C₄×C₈×C₁₂₇	—	2	2	no	—
81	C₄×C₈×C₁₂₇	C₂×C₄	1	2	yes	—
82	C₄×C₈×C₁₂₇	C₂×C₄	1	2	yes	—
83	#95×C₁₂₇	—	2	2	no	—
84	#41×C₁₂₇	—	2	2	no	—
85	#41×C₁₂₇	—	2	2	no	—
86	#41×C₁₂₇	—	2	2	no	—
87	#41×C₁₂₇	—	2	2	no	—
88	C₂×Q₈×C₁₂₇	—	2	2	no	—
89	C₂×Q₈×C₁₂₇	C₂²×C₄	1	2	yes	—
90	C₂×D₄×C₁₂₇	—	2	2	no	—
91	C₂×D₄×C₁₂₇	—	2	2	no	—
92	C₂×D₄×C₁₂₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₂₇	—	2	1	no	—
94	C₂²×C₄×C₁₂₇	—	2	1	no	—
95	C₂²×C₄×C₁₂₇	—	2	2	no	—
96	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
97	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
98	M₁₆×C₁₂₇	—	2	2	no	—
99	M₁₆×C₁₂₇	—	2	2	no	—
100	M₁₆×C₁₂₇	—	2	2	no	—
101	M₁₆×C₁₂₇	—	2	2	no	—
102	M₁₆×C₁₂₇	—	4	4	no	—
103	C₂×C₈×C₁₂₇	—	2	1	no	—
104	C₂×C₈×C₁₂₇	—	2	1	no	—
105	C₂×C₈×C₁₂₇	—	2	1	no	—
106	C₂×C₈×C₁₂₇	—	2	1	no	—
107	C₂×C₈×C₁₂₇	—	2	1	no	—
108	C₂×C₈×C₁₂₇	—	2	1	no	—
109	C₂×C₈×C₁₂₇	—	2	2	no	—
110	C₂×C₈×C₁₂₇	—	2	2	no	—
111	C₂×C₈×C₁₂₇	—	4	4	no	—
112	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₁₂₇	#41	1	2	yes	—
117	C₂×C₈×C₁₂₇	#41	1	2	yes	—
118	C₄⋊C₄×C₁₂₇	—	2	2	no	—
119	C₄⋊C₄×C₁₂₇	—	2	4	no	—
120	C₄⋊C₄×C₁₂₇	—	2	2	no	—
121	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
122	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
123	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
124	C₄²×C₁₂₇	—	2	2	no	—
125	C₄²×C₁₂₇	—	2	1	no	—
126	C₄²×C₁₂₇	—	2	1	no	—
127	C₄²×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
130	C₄²×C₁₂₇	#41	1	2	yes	—
131	C₄²×C₁₂₇	#41	1	2	yes	—
132	C₂³×C₁₂₇	—	2	2	no	—
133	C₂³×C₁₂₇	C₂×#41	1	1	yes	characteristic
134	Q₈×C₁₂₇	—	2	2	no	—
135	Q₈×C₁₂₇	—	2	2	no	—
136	Q₈×C₁₂₇	—	8	2	no	—
137	D₄×C₁₂₇	—	2	2	no	—
138	D₄×C₁₂₇	—	2	2	no	—
139	D₄×C₁₂₇	—	4	2	no	—
140	D₄×C₁₂₇	—	4	2	no	—
141	D₄×C₁₂₇	—	8	2	no	—
142	C₂×C₄×C₁₂₇	—	2	4	no	—
143	C₂×C₄×C₁₂₇	—	2	2	no	—
144	C₂×C₄×C₁₂₇	—	2	2	no	—
145	C₂×C₄×C₁₂₇	—	2	2	no	—
146	C₂×C₄×C₁₂₇	—	4	2	no	—
147	C₂×C₄×C₁₂₇	—	4	2	no	—
148	C₂×C₄×C₁₂₇	—	4	2	no	—
149	C₂×C₄×C₁₂₇	—	4	2	no	—
150	C₂×C₄×C₁₂₇	—	4	2	no	—
151	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
159	C₈×C₁₂₇	—	2	2	no	—
160	C₈×C₁₂₇	—	2	2	no	—
161	C₈×C₁₂₇	—	2	2	no	—
162	C₈×C₁₂₇	—	4	2	no	—
163	C₈×C₁₂₇	—	4	2	no	—
164	C₈×C₁₂₇	#124	1	4	yes	—
165	C₂²×C₁₂₇	—	2	2	no	—
166	C₂²×C₁₂₇	—	4	4	no	—
167	C₂²×C₁₂₇	—	4	2	no	—
168	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
169	C₂²×C₁₂₇	#529	1	1	yes	characteristic
170	C₂²×C₁₂₇	#529	1	1	yes	characteristic
171	C₄×C₁₂₇	—	2	2	no	—
172	C₄×C₁₂₇	—	2	2	no	—
173	C₄×C₁₂₇	—	4	2	no	—
174	C₄×C₁₂₇	—	4	2	no	—
175	C₄×C₁₂₇	—	4	4	no	—
176	C₄×C₁₂₇	—	4	2	no	—
177	C₄×C₁₂₇	C₄×#41	1	1	yes	characteristic
178	C₄×C₁₂₇	C₄×#41	1	1	yes	characteristic
179	C₄×C₁₂₇	C₂×#124	1	1	yes	characteristic
180	C₄×C₁₂₇	#532	1	1	yes	characteristic
181	#21659	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	—	8	2	no	—
185	C₂×C₁₂₇	C₄×#124	1	1	yes	characteristic
186	C₂×C₁₂₇	#2957	1	2	yes	—
187	#3131	C₂×C₁₂₇	1	1	yes	characteristic
188	#2961	C₂×C₁₂₇	1	1	yes	characteristic, complemented
189	#2932	C₂×C₁₂₇	1	1	yes	characteristic
190	#1995	C₂×C₁₂₇	1	1	yes	characteristic, complemented
191	#1963	C₂×C₁₂₇	1	1	yes	characteristic
192	#1938	C₂×C₁₂₇	1	2	yes	complemented
193	#1937	C₂×C₁₂₇	1	2	yes	complemented
194	#1837	C₂×C₁₂₇	1	1	yes	characteristic, complemented
195	#1765	C₂×C₁₂₇	1	2	yes	complemented
196	#1764	C₂×C₁₂₇	1	2	yes	complemented
197	#1726	C₂×C₁₂₇	1	1	yes	characteristic, complemented
198	C₁₂₇	#21659	1	1	yes	characteristic, direct product factor, Sylow
199	C₂×#131	C₂²×C₁₂₇	1	2	yes	—
200	#533	C₂²×C₁₂₇	1	1	yes	characteristic
201	#532	C₂²×C₁₂₇	1	1	yes	characteristic
202	#488	C₄×C₁₂₇	1	4	yes	complemented
203	#487	C₄×C₁₂₇	1	2	yes	complemented
204	#486	C₄×C₁₂₇	1	2	yes	complemented
205	#446	—	2	4	no	—
206	#435	—	2	4	no	—
207	#424	C₂²×C₁₂₇	1	2	yes	—
208	#423	C₂²×C₁₂₇	1	1	yes	characteristic
209	#423	C₂²×C₁₂₇	1	1	yes	characteristic
210	C₂×#104	C₂²×C₁₂₇	1	2	yes	—
211	C₂×#104	C₂²×C₁₂₇	1	2	yes	—
212	#416	C₂²×C₁₂₇	1	2	yes	—
213	#416	C₂²×C₁₂₇	1	2	yes	—
214	#408	C₂²×C₁₂₇	1	2	yes	—
215	#405	C₂²×C₁₂₇	1	2	yes	—
216	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
217	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
218	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
219	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
220	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
222	#376	C₂²×C₁₂₇	1	1	yes	characteristic
223	#341	C₂²×C₁₂₇	1	2	yes	—
224	#341	C₂²×C₁₂₇	1	2	yes	—
225	#339	C₂²×C₁₂₇	1	2	yes	—
226	#339	C₂²×C₁₂₇	1	2	yes	—
227	C₂×#41	C₂³×C₁₂₇	1	2	yes	—
228	#131	—	2	4	no	—
229	#131	—	2	4	no	—
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	C₂³×C₁₂₇	1	2	yes	—
232	C₂×M₁₆	C₂³×C₁₂₇	1	2	yes	—
233	C₂²×C₈	—	2	2	no	—
234	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
238	C₄⋊Q₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
239	C₄⋊Q₈	C₂×C₄×C₁₂₇	1	2	yes	—
240	#127	C₂×C₄×C₁₂₇	1	1	yes	characteristic
241	#125	C₂×C₄×C₁₂₇	1	2	yes	—
242	#124	C₂×C₄×C₁₂₇	1	2	yes	—
243	C₂²⋊Q₈	—	2	2	no	—
244	#121	—	2	2	no	—
245	C₄×Q₈	—	2	2	no	—
246	C₄×D₄	—	2	2	no	—
247	#117	C₂³×C₁₂₇	1	2	yes	—
248	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
251	C₄⋊C₈	—	2	4	no	—
252	C₄⋊C₈	—	2	2	no	—
253	C₄⋊C₈	—	2	2	no	—
254	#104	—	2	4	no	—
255	#104	—	2	4	no	—
256	#103	C₂×C₄×C₁₂₇	1	4	yes	—
257	#103	C₂×C₄×C₁₂₇	1	4	yes	—
258	#102	C₂×C₄×C₁₂₇	1	4	yes	—
259	#102	C₂×C₄×C₁₂₇	1	4	yes	—
260	C₂²⋊C₈	—	2	4	no	—
261	#97	—	2	2	no	—
262	#97	—	2	2	no	—
263	#97	—	2	2	no	—
264	#97	D₄×C₁₂₇	1	4	yes	—
265	C₄×C₈	—	2	2	no	—
266	C₄×C₈	—	2	2	no	—
267	C₄×C₈	—	2	2	no	—
268	C₄×C₈	C₂×C₄×C₁₂₇	1	2	yes	—
269	C₄×C₈	C₂×C₄×C₁₂₇	1	2	yes	—
270	#95	—	2	2	no	—
271	#41	—	2	2	no	—
272	#41	—	2	2	no	—
273	#41	—	2	2	no	—
274	#41	—	2	2	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	C₂²×C₄×C₁₂₇	1	2	yes	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	C₂²×C₄×C₁₂₇	1	2	yes	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
284	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
285	M₁₆	—	2	2	no	—
286	M₁₆	—	2	2	no	—
287	M₁₆	—	2	2	no	—
288	M₁₆	—	2	2	no	—
289	M₁₆	—	4	4	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	4	4	no	—
299	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
300	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
301	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
302	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
303	C₂×C₈	#41×C₁₂₇	1	2	yes	—
304	C₂×C₈	#41×C₁₂₇	1	2	yes	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	4	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	1	no	—
313	C₄²	—	2	1	no	—
314	C₄²	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
315	C₄²	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
316	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
317	C₄²	#41×C₁₂₇	1	2	yes	—
318	C₄²	#41×C₁₂₇	1	2	yes	—
319	C₂³	—	2	2	no	—
320	C₂³	C₂×#41×C₁₂₇	1	1	yes	characteristic
321	Q₈	—	2	2	no	—
322	Q₈	—	2	2	no	—
323	Q₈	—	8	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	8	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
339	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
340	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
341	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
342	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
343	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
344	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
345	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
346	C₈	—	2	2	no	—
347	C₈	—	2	2	no	—
348	C₈	—	2	2	no	—
349	C₈	—	4	2	no	—
350	C₈	—	4	2	no	—
351	C₈	#124×C₁₂₇	1	4	yes	—
352	C₂²	—	2	2	no	—
353	C₂²	—	4	4	no	—
354	C₂²	—	4	2	no	—
355	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
356	C₂²	#529×C₁₂₇	1	1	yes	characteristic
357	C₂²	#529×C₁₂₇	1	1	yes	characteristic
358	C₄	—	2	2	no	—
359	C₄	—	2	2	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	4	no	—
363	C₄	—	4	2	no	—
364	C₄	C₄×#41×C₁₂₇	1	1	yes	characteristic
365	C₄	C₄×#41×C₁₂₇	1	1	yes	characteristic
366	C₄	C₂×#124×C₁₂₇	1	1	yes	characteristic
367	C₄	#532×C₁₂₇	1	1	yes	characteristic
368	C₂	—	2	1	no	—
369	C₂	—	2	1	no	—
370	C₂	—	8	2	no	—
371	C₂	C₄×#124×C₁₂₇	1	1	yes	characteristic
372	C₂	C₁₂₇×#2957	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₂₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₂₇
socle	C₂²×C₁₂₇	C₂×C₄×D₄
prime radical	#532×C₁₂₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₂₇ ◁ C₂×#97×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₂₇×#2961	C₂	semidirect
4. C₁₂₇×#1995	C₂	semidirect
6. C₁₂₇×#1938	C₂	semidirect
7. C₁₂₇×#1937	C₂	semidirect
8. C₁₂₇×#1837	C₂	semidirect
9. C₁₂₇×#1765	C₂	semidirect
10. C₁₂₇×#1764	C₂	semidirect
11. C₁₂₇×#1726	C₂	semidirect
15. #488×C₁₂₇	C₄	semidirect
16. #487×C₁₂₇	C₄	semidirect
17. #486×C₁₂₇	C₄	semidirect
181. #21659	C₁₂₇	direct (N × H)
188. #2961	C₂×C₁₂₇	semidirect
190. #1995	C₂×C₁₂₇	semidirect
192. #1938	C₂×C₁₂₇	semidirect
193. #1937	C₂×C₁₂₇	semidirect
194. #1837	C₂×C₁₂₇	semidirect
195. #1765	C₂×C₁₂₇	semidirect
196. #1764	C₂×C₁₂₇	semidirect
197. #1726	C₂×C₁₂₇	semidirect
198. C₁₂₇	#21659	direct (N × H)
202. #488	C₄×C₁₂₇	semidirect
203. #487	C₄×C₁₂₇	semidirect
204. #486	C₄×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₂₇×#3131	2
C₁₂₇×#2961	2
C₁₂₇×#2932	2
C₁₂₇×#1995	2
C₁₂₇×#1963	2
C₁₂₇×#1938	2
C₁₂₇×#1937	2
C₁₂₇×#1837	2
C₁₂₇×#1765	2
C₁₂₇×#1764	2
C₁₂₇×#1726	2
#21659	127

Subgroups — C127×#21659 #44585332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#21659 #44585332