Subgroups — C₁₂₇×#19631 #44583304

Order 32512.

922 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₂₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₂₇×#3205	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₂₇×#3169	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₂₇×#3152	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₂₇×#3151	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#486×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₂₇×#1722	C₂	1	2	yes	maximal, complemented
8	C₁₂₇×#1721	C₂	1	2	yes	maximal, complemented
9	C₁₂₇×#1709	C₂	1	2	yes	maximal, complemented
10	C₁₂₇×#1706	C₂	1	2	yes	maximal, complemented
11	C₈×M₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₁₂₇	—	2	2	no	—
13	C₂×AGL(1,ℤ/8)×C₁₂₇	—	2	2	no	—
14	#532×C₁₂₇	C₂²	1	1	yes	characteristic
15	#532×C₁₂₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic
17	C₂×#127×C₁₂₇	C₂²	1	1	yes	characteristic
18	#500×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
19	#500×C₁₂₇	C₂²	1	2	yes	complemented
20	#497×C₁₂₇	—	2	2	no	—
21	#496×C₁₂₇	—	2	2	no	—
22	#494×C₁₂₇	C₂²	1	2	yes	complemented
23	#493×C₁₂₇	C₂²	1	2	yes	—
24	#493×C₁₂₇	C₂²	1	2	yes	—
25	#493×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
26	#492×C₁₂₇	C₂²	1	2	yes	—
27	#492×C₁₂₇	C₂²	1	2	yes	complemented
28	#486×C₁₂₇	—	2	2	no	—
29	#486×C₁₂₇	C₂²	1	2	yes	—
30	#486×C₁₂₇	C₂²	1	2	yes	—
31	#486×C₁₂₇	C₂²	1	2	yes	—
32	#486×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
33	#486×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
34	#486×C₁₂₇	C₂²	1	2	yes	complemented
35	#480×C₁₂₇	—	2	2	no	—
36	#474×C₁₂₇	—	2	2	no	—
37	#466×C₁₂₇	—	2	2	no	—
38	#459×C₁₂₇	—	2	2	no	—
39	#447×C₁₂₇	—	2	2	no	—
40	C₄×D₈×C₁₂₇	—	2	2	no	—
41	#431×C₁₂₇	C₂²	1	1	yes	characteristic
42	C₂×#102×C₁₂₇	—	2	2	no	—
43	C₄×M₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
45	#322×C₁₂₇	C₂²	1	2	yes	complemented
46	C₈²×C₁₂₇	C₂²	1	2	yes	complemented
47	C₂×#41×C₁₂₇	—	2	1	no	—
48	C₂×#41×C₁₂₇	—	2	1	no	—
49	C₂²×Q₈×C₁₂₇	—	2	1	no	—
50	C₂²×D₄×C₁₂₇	—	2	1	no	—
51	C₂²×D₄×C₁₂₇	—	2	1	no	—
52	C₂²×D₄×C₁₂₇	—	2	1	no	—
53	#137×C₁₂₇	—	4	8	no	—
54	AGL(1,ℤ/8)×C₁₂₇	—	4	8	no	—
55	C₂×Q₁₆×C₁₂₇	—	2	4	no	—
56	C₂×SD₁₆×C₁₂₇	—	2	4	no	—
57	C₂×SD₁₆×C₁₂₇	—	2	4	no	—
58	C₂×D₈×C₁₂₇	—	2	4	no	—
59	C₂×D₈×C₁₂₇	—	2	2	no	—
60	C₂×D₈×C₁₂₇	—	2	4	no	—
61	C₂×M₁₆×C₁₂₇	D₄	1	2	yes	—
62	C₂²×C₈×C₁₂₇	D₄	1	2	yes	—
63	C₄⋊Q₈×C₁₂₇	—	2	1	no	—
64	C₄⋊Q₈×C₁₂₇	—	2	1	no	—
65	C₄⋊Q₈×C₁₂₇	—	2	1	no	—
66	C₄⋊Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₁₂₇	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
69	#127×C₁₂₇	—	2	1	no	—
70	#127×C₁₂₇	—	2	1	no	—
71	#127×C₁₂₇	—	2	1	no	—
72	#127×C₁₂₇	C₂³	1	2	yes	—
73	#127×C₁₂₇	C₂³	1	1	yes	characteristic
74	#127×C₁₂₇	C₂³	1	1	yes	characteristic
75	#124×C₁₂₇	—	2	1	no	—
76	#124×C₁₂₇	—	2	1	no	—
77	#121×C₁₂₇	—	2	1	no	—
78	#121×C₁₂₇	—	2	1	no	—
79	#121×C₁₂₇	—	2	1	no	—
80	#121×C₁₂₇	—	2	1	no	—
81	C₄×D₄×C₁₂₇	—	2	1	no	—
82	C₄×D₄×C₁₂₇	—	2	1	no	—
83	C₄×D₄×C₁₂₇	—	2	1	no	—
84	C₄×D₄×C₁₂₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₂₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₂₇	—	2	1	no	—
87	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
88	#107×C₁₂₇	—	2	2	no	—
89	#107×C₁₂₇	—	2	4	no	—
90	C₄⋊C₈×C₁₂₇	D₄	1	2	yes	—
91	#102×C₁₂₇	—	2	4	no	—
92	#102×C₁₂₇	—	2	4	no	—
93	#102×C₁₂₇	—	2	2	no	—
94	#102×C₁₂₇	—	2	2	no	—
95	#102×C₁₂₇	—	2	4	no	—
96	#102×C₁₂₇	—	2	4	no	—
97	C₂²⋊C₈×C₁₂₇	D₄	1	2	yes	—
98	#97×C₁₂₇	D₄	1	2	yes	—
99	C₄×C₈×C₁₂₇	D₄	1	2	yes	—
100	C₄×C₈×C₁₂₇	C₂³	1	2	yes	—
101	C₄×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₁₂₇	C₂³	1	2	yes	—
104	C₂⁴×C₁₂₇	—	4	1	no	—
105	#41×C₁₂₇	—	4	4	no	—
106	#41×C₁₂₇	—	4	4	no	—
107	C₂×Q₈×C₁₂₇	—	2	1	no	—
108	C₂×Q₈×C₁₂₇	—	2	1	no	—
109	C₂×Q₈×C₁₂₇	—	2	2	no	—
110	C₂×Q₈×C₁₂₇	—	4	1	no	—
111	C₂×Q₈×C₁₂₇	—	4	4	no	—
112	C₂×D₄×C₁₂₇	—	2	1	no	—
113	C₂×D₄×C₁₂₇	—	2	2	no	—
114	C₂×D₄×C₁₂₇	—	2	1	no	—
115	C₂×D₄×C₁₂₇	—	2	1	no	—
116	C₂×D₄×C₁₂₇	—	2	2	no	—
117	C₂×D₄×C₁₂₇	—	2	1	no	—
118	C₂×D₄×C₁₂₇	—	2	1	no	—
119	C₂×D₄×C₁₂₇	—	2	1	no	—
120	C₂×D₄×C₁₂₇	—	2	2	no	—
121	C₂×D₄×C₁₂₇	—	4	4	no	—
122	C₂×D₄×C₁₂₇	—	4	1	no	—
123	C₂×D₄×C₁₂₇	—	4	1	no	—
124	C₂×D₄×C₁₂₇	—	4	1	no	—
125	C₂×D₄×C₁₂₇	—	4	1	no	—
126	C₂×D₄×C₁₂₇	—	4	1	no	—
127	C₂×D₄×C₁₂₇	—	4	4	no	—
128	C₂×D₄×C₁₂₇	—	8	2	no	—
129	C₂²×C₄×C₁₂₇	—	4	1	no	—
130	C₂²×C₄×C₁₂₇	—	4	1	no	—
131	C₂²×C₄×C₁₂₇	—	4	1	no	—
132	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
135	Q₁₆×C₁₂₇	—	4	8	no	—
136	SD₁₆×C₁₂₇	—	4	8	no	—
137	SD₁₆×C₁₂₇	—	4	8	no	—
138	D₈×C₁₂₇	—	4	4	no	—
139	D₈×C₁₂₇	—	4	8	no	—
140	D₈×C₁₂₇	—	8	4	no	—
141	M₁₆×C₁₂₇	D₈	1	8	yes	complemented
142	C₂×C₈×C₁₂₇	—	4	2	no	—
143	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₁₂₇	C₂×D₄	1	4	yes	—
146	C₂×C₈×C₁₂₇	C₂×D₄	1	4	yes	—
147	C₄⋊C₄×C₁₂₇	—	2	2	no	—
148	C₄⋊C₄×C₁₂₇	—	2	1	no	—
149	C₄⋊C₄×C₁₂₇	—	2	2	no	—
150	C₄⋊C₄×C₁₂₇	—	2	1	no	—
151	C₄⋊C₄×C₁₂₇	—	2	1	no	—
152	C₄⋊C₄×C₁₂₇	—	2	1	no	—
153	C₄⋊C₄×C₁₂₇	—	4	1	no	—
154	C₄⋊C₄×C₁₂₇	—	4	1	no	—
155	C₂²⋊C₄×C₁₂₇	—	4	1	no	—
156	C₂²⋊C₄×C₁₂₇	—	4	1	no	—
157	C₂²⋊C₄×C₁₂₇	—	4	1	no	—
158	C₂²⋊C₄×C₁₂₇	—	4	1	no	—
159	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₁₂₇	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₁₂₇	C₂⁴	1	1	yes	characteristic
163	C₂³×C₁₂₇	—	4	1	no	—
164	C₂³×C₁₂₇	—	4	1	no	—
165	C₂³×C₁₂₇	—	4	2	no	—
166	C₂³×C₁₂₇	—	8	2	no	—
167	C₂³×C₁₂₇	—	8	2	no	—
168	C₂³×C₁₂₇	—	8	2	no	—
169	C₂³×C₁₂₇	#127	1	1	yes	characteristic
170	Q₈×C₁₂₇	—	4	2	no	—
171	Q₈×C₁₂₇	—	4	4	no	—
172	Q₈×C₁₂₇	—	4	2	no	—
173	Q₈×C₁₂₇	—	8	2	no	—
174	D₄×C₁₂₇	—	4	2	no	—
175	D₄×C₁₂₇	—	4	4	no	—
176	D₄×C₁₂₇	—	4	2	no	—
177	D₄×C₁₂₇	—	4	2	no	—
178	D₄×C₁₂₇	—	4	2	no	—
179	D₄×C₁₂₇	—	4	4	no	—
180	D₄×C₁₂₇	—	4	2	no	—
181	D₄×C₁₂₇	—	4	4	no	—
182	D₄×C₁₂₇	—	4	2	no	—
183	D₄×C₁₂₇	—	8	2	no	—
184	D₄×C₁₂₇	—	8	2	no	—
185	D₄×C₁₂₇	—	8	2	no	—
186	D₄×C₁₂₇	—	8	2	no	—
187	D₄×C₁₂₇	—	8	2	no	—
188	C₂×C₄×C₁₂₇	—	2	2	no	—
189	C₂×C₄×C₁₂₇	—	2	2	no	—
190	C₂×C₄×C₁₂₇	—	4	1	no	—
191	C₂×C₄×C₁₂₇	—	4	1	no	—
192	C₂×C₄×C₁₂₇	—	4	2	no	—
193	C₂×C₄×C₁₂₇	—	8	2	no	—
194	C₂×C₄×C₁₂₇	—	8	2	no	—
195	C₂×C₄×C₁₂₇	—	8	2	no	—
196	C₂×C₄×C₁₂₇	#127	1	1	yes	characteristic
197	C₂×C₄×C₁₂₇	#127	1	1	yes	characteristic
198	C₂×C₄×C₁₂₇	#127	1	1	yes	characteristic
199	C₂×C₄×C₁₂₇	C₂×D₈	1	4	yes	—
200	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
203	C₈×C₁₂₇	—	2	2	no	—
204	C₈×C₁₂₇	—	2	2	no	—
205	C₈×C₁₂₇	—	2	4	no	—
206	C₈×C₁₂₇	C₂×D₈	1	8	yes	—
207	C₂²×C₁₂₇	—	2	1	no	—
208	C₂²×C₁₂₇	—	2	1	no	—
209	C₂²×C₁₂₇	—	8	1	no	—
210	C₂²×C₁₂₇	—	8	1	no	—
211	C₂²×C₁₂₇	—	8	2	no	—
212	C₂²×C₁₂₇	—	8	2	no	—
213	C₂²×C₁₂₇	—	8	1	no	—
214	C₂²×C₁₂₇	—	8	1	no	—
215	C₂²×C₁₂₇	—	8	2	no	—
216	C₂²×C₁₂₇	—	8	1	no	—
217	C₂²×C₁₂₇	—	8	1	no	—
218	C₂²×C₁₂₇	—	16	4	no	—
219	C₂²×C₁₂₇	#493	1	2	yes	—
220	C₂²×C₁₂₇	C₂×#127	1	1	yes	characteristic
221	C₄×C₁₂₇	—	2	1	no	—
222	C₄×C₁₂₇	—	2	1	no	—
223	C₄×C₁₂₇	—	8	1	no	—
224	C₄×C₁₂₇	—	8	1	no	—
225	C₄×C₁₂₇	—	8	2	no	—
226	C₄×C₁₂₇	#493	1	2	yes	—
227	C₄×C₁₂₇	C₂²×D₈	1	2	yes	—
228	C₄×C₁₂₇	#575	1	2	yes	—
229	C₄×C₁₂₇	#577	1	2	yes	—
230	#19631	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂×C₁₂₇	—	2	2	no	—
232	C₂×C₁₂₇	—	16	1	no	—
233	C₂×C₁₂₇	—	16	1	no	—
234	C₂×C₁₂₇	—	16	2	no	—
235	C₂×C₁₂₇	C₂×#493	1	1	yes	characteristic
236	C₂×C₁₂₇	#3153	1	1	yes	characteristic
237	C₂×C₁₂₇	#3154	1	1	yes	characteristic
238	#3226	C₂×C₁₂₇	1	1	yes	characteristic, complemented
239	#3205	C₂×C₁₂₇	1	1	yes	characteristic, complemented
240	#3169	C₂×C₁₂₇	1	1	yes	characteristic, complemented
241	#3152	C₂×C₁₂₇	1	1	yes	characteristic, complemented
242	#3151	C₂×C₁₂₇	1	1	yes	characteristic, complemented
243	C₂×#486	C₂×C₁₂₇	1	1	yes	characteristic, complemented
244	#1722	C₂×C₁₂₇	1	2	yes	complemented
245	#1721	C₂×C₁₂₇	1	2	yes	complemented
246	#1709	C₂×C₁₂₇	1	2	yes	complemented
247	#1706	C₂×C₁₂₇	1	2	yes	complemented
248	C₈×M₁₆	C₂×C₁₂₇	1	1	yes	characteristic, complemented
249	C₁₂₇	#19631	1	1	yes	characteristic, direct product factor, Sylow
250	C₂×#137	—	2	2	no	—
251	C₂×AGL(1,ℤ/8)	—	2	2	no	—
252	#532	C₂²×C₁₂₇	1	1	yes	characteristic
253	#532	C₂²×C₁₂₇	1	1	yes	characteristic
254	C₂×C₄⋊Q₈	C₂²×C₁₂₇	1	1	yes	characteristic
255	C₂×#127	C₂²×C₁₂₇	1	1	yes	characteristic
256	#500	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
257	#500	C₂²×C₁₂₇	1	2	yes	complemented
258	#497	—	2	2	no	—
259	#496	—	2	2	no	—
260	#494	C₂²×C₁₂₇	1	2	yes	complemented
261	#493	C₂²×C₁₂₇	1	2	yes	—
262	#493	C₂²×C₁₂₇	1	2	yes	—
263	#493	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
264	#492	C₂²×C₁₂₇	1	2	yes	—
265	#492	C₂²×C₁₂₇	1	2	yes	complemented
266	#486	—	2	2	no	—
267	#486	C₂²×C₁₂₇	1	2	yes	—
268	#486	C₂²×C₁₂₇	1	2	yes	—
269	#486	C₂²×C₁₂₇	1	2	yes	—
270	#486	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
271	#486	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
272	#486	C₂²×C₁₂₇	1	2	yes	complemented
273	#480	—	2	2	no	—
274	#474	—	2	2	no	—
275	#466	—	2	2	no	—
276	#459	—	2	2	no	—
277	#447	—	2	2	no	—
278	C₄×D₈	—	2	2	no	—
279	#431	C₂²×C₁₂₇	1	1	yes	characteristic
280	C₂×#102	—	2	2	no	—
281	C₄×M₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
282	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
283	#322	C₂²×C₁₂₇	1	2	yes	complemented
284	C₈²	C₂²×C₁₂₇	1	2	yes	complemented
285	C₂×#41	—	2	1	no	—
286	C₂×#41	—	2	1	no	—
287	C₂²×Q₈	—	2	1	no	—
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	—	2	1	no	—
290	C₂²×D₄	—	2	1	no	—
291	#137	—	4	8	no	—
292	AGL(1,ℤ/8)	—	4	8	no	—
293	C₂×Q₁₆	—	2	4	no	—
294	C₂×SD₁₆	—	2	4	no	—
295	C₂×SD₁₆	—	2	4	no	—
296	C₂×D₈	—	2	4	no	—
297	C₂×D₈	—	2	2	no	—
298	C₂×D₈	—	2	4	no	—
299	C₂×M₁₆	D₄×C₁₂₇	1	2	yes	—
300	C₂²×C₈	D₄×C₁₂₇	1	2	yes	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	C₂³×C₁₂₇	1	2	yes	—
305	C₄⋊Q₈	C₂³×C₁₂₇	1	1	yes	characteristic
306	C₄⋊Q₈	C₂³×C₁₂₇	1	1	yes	characteristic
307	#127	—	2	1	no	—
308	#127	—	2	1	no	—
309	#127	—	2	1	no	—
310	#127	C₂³×C₁₂₇	1	2	yes	—
311	#127	C₂³×C₁₂₇	1	1	yes	characteristic
312	#127	C₂³×C₁₂₇	1	1	yes	characteristic
313	#124	—	2	1	no	—
314	#124	—	2	1	no	—
315	#121	—	2	1	no	—
316	#121	—	2	1	no	—
317	#121	—	2	1	no	—
318	#121	—	2	1	no	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
326	#107	—	2	2	no	—
327	#107	—	2	4	no	—
328	C₄⋊C₈	D₄×C₁₂₇	1	2	yes	—
329	#102	—	2	4	no	—
330	#102	—	2	4	no	—
331	#102	—	2	2	no	—
332	#102	—	2	2	no	—
333	#102	—	2	4	no	—
334	#102	—	2	4	no	—
335	C₂²⋊C₈	D₄×C₁₂₇	1	2	yes	—
336	#97	D₄×C₁₂₇	1	2	yes	—
337	C₄×C₈	D₄×C₁₂₇	1	2	yes	—
338	C₄×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
339	C₄×C₈	C₂³×C₁₂₇	1	2	yes	—
340	C₄×C₈	C₂³×C₁₂₇	1	2	yes	—
341	C₄×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
342	C₂⁴	—	4	1	no	—
343	#41	—	4	4	no	—
344	#41	—	4	4	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	4	1	no	—
349	C₂×Q₈	—	4	4	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	—	4	1	no	—
361	C₂×D₄	—	4	1	no	—
362	C₂×D₄	—	4	1	no	—
363	C₂×D₄	—	4	1	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂×D₄	—	4	4	no	—
366	C₂×D₄	—	8	2	no	—
367	C₂²×C₄	—	4	1	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	—	4	1	no	—
370	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
373	Q₁₆	—	4	8	no	—
374	SD₁₆	—	4	8	no	—
375	SD₁₆	—	4	8	no	—
376	D₈	—	4	4	no	—
377	D₈	—	4	8	no	—
378	D₈	—	8	4	no	—
379	M₁₆	D₈×C₁₂₇	1	8	yes	complemented
380	C₂×C₈	—	4	2	no	—
381	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
382	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
383	C₂×C₈	C₂×D₄×C₁₂₇	1	4	yes	—
384	C₂×C₈	C₂×D₄×C₁₂₇	1	4	yes	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	4	1	no	—
392	C₄⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₂²⋊C₄	—	4	1	no	—
396	C₂²⋊C₄	—	4	1	no	—
397	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
398	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
399	C₄²	C₂×D₄×C₁₂₇	1	1	yes	characteristic
400	C₄²	C₂⁴×C₁₂₇	1	1	yes	characteristic
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	8	2	no	—
405	C₂³	—	8	2	no	—
406	C₂³	—	8	2	no	—
407	C₂³	#127×C₁₂₇	1	1	yes	characteristic
408	Q₈	—	4	2	no	—
409	Q₈	—	4	4	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	8	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	4	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	4	no	—
420	D₄	—	4	2	no	—
421	D₄	—	8	2	no	—
422	D₄	—	8	2	no	—
423	D₄	—	8	2	no	—
424	D₄	—	8	2	no	—
425	D₄	—	8	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	8	2	no	—
432	C₂×C₄	—	8	2	no	—
433	C₂×C₄	—	8	2	no	—
434	C₂×C₄	#127×C₁₂₇	1	1	yes	characteristic
435	C₂×C₄	#127×C₁₂₇	1	1	yes	characteristic
436	C₂×C₄	#127×C₁₂₇	1	1	yes	characteristic
437	C₂×C₄	C₂×D₈×C₁₂₇	1	4	yes	—
438	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
441	C₈	—	2	2	no	—
442	C₈	—	2	2	no	—
443	C₈	—	2	4	no	—
444	C₈	C₂×D₈×C₁₂₇	1	8	yes	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	2	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	16	4	no	—
457	C₂²	#493×C₁₂₇	1	2	yes	—
458	C₂²	C₂×#127×C₁₂₇	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	8	1	no	—
462	C₄	—	8	1	no	—
463	C₄	—	8	2	no	—
464	C₄	#493×C₁₂₇	1	2	yes	—
465	C₄	C₂²×D₈×C₁₂₇	1	2	yes	—
466	C₄	#575×C₁₂₇	1	2	yes	—
467	C₄	#577×C₁₂₇	1	2	yes	—
468	C₂	—	2	2	no	—
469	C₂	—	16	2	no	—
470	C₂	—	16	1	no	—
471	C₂	—	16	1	no	—
472	C₂	C₂×#493×C₁₂₇	1	1	yes	characteristic
473	C₂	C₁₂₇×#3153	1	1	yes	characteristic
474	C₂	C₁₂₇×#3154	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₂₇	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₂₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₂₇ ◁ C₂×C₄²×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₂₇×#3226	C₂	semidirect
2. C₁₂₇×#3205	C₂	semidirect
3. C₁₂₇×#3169	C₂	semidirect
4. C₁₂₇×#3152	C₂	semidirect
5. C₁₂₇×#3151	C₂	semidirect
6. C₂×#486×C₁₂₇	C₂	semidirect
7. C₁₂₇×#1722	C₂	semidirect
8. C₁₂₇×#1721	C₂	semidirect
9. C₁₂₇×#1709	C₂	semidirect
10. C₁₂₇×#1706	C₂	semidirect
11. C₈×M₁₆×C₁₂₇	C₂	semidirect
18. #500×C₁₂₇	C₂²	semidirect
19. #500×C₁₂₇	C₂²	semidirect
22. #494×C₁₂₇	C₂²	semidirect
25. #493×C₁₂₇	C₂²	semidirect
27. #492×C₁₂₇	C₂²	semidirect
32. #486×C₁₂₇	C₂²	semidirect
33. #486×C₁₂₇	C₂²	semidirect
34. #486×C₁₂₇	C₂²	semidirect
45. #322×C₁₂₇	C₂²	semidirect
46. C₈²×C₁₂₇	C₂²	semidirect
141. M₁₆×C₁₂₇	D₈	semidirect
230. #19631	C₁₂₇	direct (N × H)
238. #3226	C₂×C₁₂₇	semidirect
239. #3205	C₂×C₁₂₇	semidirect
240. #3169	C₂×C₁₂₇	semidirect
241. #3152	C₂×C₁₂₇	semidirect
242. #3151	C₂×C₁₂₇	semidirect
243. C₂×#486	C₂×C₁₂₇	semidirect
244. #1722	C₂×C₁₂₇	semidirect
245. #1721	C₂×C₁₂₇	semidirect
246. #1709	C₂×C₁₂₇	semidirect
247. #1706	C₂×C₁₂₇	semidirect
248. C₈×M₁₆	C₂×C₁₂₇	semidirect
249. C₁₂₇	#19631	direct (N × H)
256. #500	C₂²×C₁₂₇	semidirect
257. #500	C₂²×C₁₂₇	semidirect
260. #494	C₂²×C₁₂₇	semidirect
263. #493	C₂²×C₁₂₇	semidirect
265. #492	C₂²×C₁₂₇	semidirect
270. #486	C₂²×C₁₂₇	semidirect
271. #486	C₂²×C₁₂₇	semidirect
272. #486	C₂²×C₁₂₇	semidirect
283. #322	C₂²×C₁₂₇	semidirect
284. C₈²	C₂²×C₁₂₇	semidirect
379. M₁₆	D₈×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₂₇×#3226	2
C₁₂₇×#3205	2
C₁₂₇×#3169	2
C₁₂₇×#3152	2
C₁₂₇×#3151	2
C₂×#486×C₁₂₇	2
C₁₂₇×#1722	2
C₁₂₇×#1721	2
C₁₂₇×#1709	2
C₁₂₇×#1706	2
C₈×M₁₆×C₁₂₇	2
#19631	127

Subgroups — C127×#19631 #44583304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#19631 #44583304