Subgroups — C₁₂₇×#21032 #44584705

Order 32512.

926 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#427×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₁₂₇×#2296	C₂	1	1	yes	maximal, characteristic
3	C₄×#117×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1921	C₂	1	2	yes	maximal, complemented
5	C₁₂₇×#1920	C₂	1	2	yes	maximal, complemented
6	C₁₂₇×#1919	C₂	1	2	yes	maximal, complemented
7	C₁₂₇×#1918	C₂	1	2	yes	maximal, complemented
8	C₁₂₇×#1735	C₂	1	1	yes	maximal, characteristic
9	C₁₂₇×#1735	C₂	1	1	yes	maximal, characteristic
10	C₁₂₇×#1735	C₂	1	1	yes	maximal, characteristic
11	C₂×#336×C₁₂₇	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
14	C₂×#117×C₁₂₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₂₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₁₂₇	C₂²	1	1	yes	characteristic
17	C₂×#117×C₁₂₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
19	#427×C₁₂₇	C₄	1	8	yes	complemented
20	C₂×#107×C₁₂₇	C₂²	1	1	yes	characteristic
21	C₂×#107×C₁₂₇	C₂²	1	1	yes	characteristic
22	C₂×#106×C₁₂₇	C₂²	1	1	yes	characteristic
23	C₂×#106×C₁₂₇	C₂²	1	1	yes	characteristic
24	#389×C₁₂₇	C₂²	1	2	yes	—
25	#389×C₁₂₇	C₂²	1	2	yes	—
26	#385×C₁₂₇	—	2	2	no	—
27	C₄×C₄⋊C₄×C₁₂₇	—	2	1	no	—
28	C₄×C₄⋊C₄×C₁₂₇	—	2	1	no	—
29	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
31	C₄×C₂²⋊C₄×C₁₂₇	—	2	2	no	—
32	#376×C₁₂₇	—	2	1	no	—
33	C₄³×C₁₂₇	—	2	1	no	—
34	#340×C₁₂₇	C₂²	1	2	yes	—
35	#340×C₁₂₇	C₂²	1	2	yes	—
36	#340×C₁₂₇	C₂²	1	2	yes	—
37	#340×C₁₂₇	C₂²	1	2	yes	—
38	#340×C₁₂₇	C₂²	1	2	yes	—
39	#340×C₁₂₇	C₂²	1	2	yes	—
40	#336×C₁₂₇	C₂²	1	2	yes	—
41	#336×C₁₂₇	C₂²	1	2	yes	—
42	C₂³×C₄×C₁₂₇	D₄	1	2	yes	—
43	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₂₇	—	2	2	no	—
45	C₂²×C₈×C₁₂₇	—	2	2	no	—
46	C₂²×C₈×C₁₂₇	—	2	2	no	—
47	C₂²×C₈×C₁₂₇	—	2	2	no	—
48	C₂²×C₈×C₁₂₇	—	2	2	no	—
49	C₂²×C₈×C₁₂₇	C₂×C₄	1	4	yes	—
50	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
53	#117×C₁₂₇	—	2	2	no	—
54	#117×C₁₂₇	—	2	2	no	—
55	#117×C₁₂₇	—	2	2	no	—
56	#117×C₁₂₇	—	2	2	no	—
57	#117×C₁₂₇	—	2	2	no	—
58	#117×C₁₂₇	C₂×C₄	1	4	yes	—
59	#117×C₁₂₇	C₂×C₄	1	4	yes	—
60	#117×C₁₂₇	Q₈	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₂₇	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₂₇	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₁₂₇	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₂₇	—	2	1	no	—
73	C₂×C₄²×C₁₂₇	—	2	1	no	—
74	C₂×C₄²×C₁₂₇	—	2	1	no	—
75	C₂×C₄²×C₁₂₇	—	2	1	no	—
76	C₂×C₄²×C₁₂₇	—	2	2	no	—
77	C₂×C₄²×C₁₂₇	—	2	2	no	—
78	C₂×C₄²×C₁₂₇	—	2	2	no	—
79	C₂×C₄²×C₁₂₇	—	2	2	no	—
80	C₂×C₄²×C₁₂₇	—	2	1	no	—
81	C₂×C₄²×C₁₂₇	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₂₇	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
84	#107×C₁₂₇	C₂×C₄	1	4	yes	complemented
85	#107×C₁₂₇	C₂×C₄	1	4	yes	complemented
86	#106×C₁₂₇	C₂×C₄	1	4	yes	complemented
87	#106×C₁₂₇	C₂×C₄	1	4	yes	complemented
88	#95×C₁₂₇	—	2	2	no	—
89	#95×C₁₂₇	—	2	2	no	—
90	#95×C₁₂₇	—	2	2	no	—
91	#95×C₁₂₇	—	2	2	no	—
92	C₂⁴×C₁₂₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₂₇	—	2	4	no	—
94	C₂²×C₄×C₁₂₇	—	2	1	no	—
95	C₂²×C₄×C₁₂₇	—	2	1	no	—
96	C₂²×C₄×C₁₂₇	—	2	2	no	—
97	C₂²×C₄×C₁₂₇	—	2	1	no	—
98	C₂²×C₄×C₁₂₇	—	2	1	no	—
99	C₂²×C₄×C₁₂₇	—	2	4	no	—
100	C₂²×C₄×C₁₂₇	—	2	2	no	—
101	C₂²×C₄×C₁₂₇	—	4	2	no	—
102	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₂₇	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
108	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
109	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
110	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
111	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₁₂₇	—	2	8	no	—
113	C₂×C₈×C₁₂₇	—	2	1	no	—
114	C₂×C₈×C₁₂₇	—	2	1	no	—
115	C₂×C₈×C₁₂₇	—	2	1	no	—
116	C₂×C₈×C₁₂₇	—	2	1	no	—
117	C₂×C₈×C₁₂₇	—	2	2	no	—
118	C₂×C₈×C₁₂₇	—	2	2	no	—
119	C₂×C₈×C₁₂₇	—	2	2	no	—
120	C₂×C₈×C₁₂₇	—	4	4	no	—
121	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
123	C₄⋊C₄×C₁₂₇	—	2	1	no	—
124	C₄⋊C₄×C₁₂₇	—	2	1	no	—
125	C₄⋊C₄×C₁₂₇	—	2	1	no	—
126	C₄⋊C₄×C₁₂₇	—	2	1	no	—
127	C₄⋊C₄×C₁₂₇	—	2	2	no	—
128	C₄⋊C₄×C₁₂₇	—	2	2	no	—
129	C₄⋊C₄×C₁₂₇	—	2	2	no	—
130	C₄⋊C₄×C₁₂₇	—	4	4	no	—
131	C₄⋊C₄×C₁₂₇	—	4	4	no	—
132	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
133	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
134	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
135	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
136	C₄⋊C₄×C₁₂₇	C₂×Q₈	1	4	yes	—
137	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
138	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
139	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
140	C₂²⋊C₄×C₁₂₇	—	4	2	no	—
141	C₄²×C₁₂₇	—	2	4	no	—
142	C₄²×C₁₂₇	—	2	4	no	—
143	C₄²×C₁₂₇	—	2	4	no	—
144	C₄²×C₁₂₇	—	2	2	no	—
145	C₄²×C₁₂₇	—	2	2	no	—
146	C₄²×C₁₂₇	—	2	2	no	—
147	C₄²×C₁₂₇	—	2	2	no	—
148	C₄²×C₁₂₇	—	4	4	no	—
149	C₄²×C₁₂₇	—	4	2	no	—
150	C₄²×C₁₂₇	—	4	4	no	—
151	C₂³×C₁₂₇	—	2	2	no	—
152	C₂³×C₁₂₇	—	2	2	no	—
153	C₂³×C₁₂₇	C₄×D₄	1	2	yes	—
154	C₂³×C₁₂₇	C₂²⋊Q₈	1	2	yes	—
155	C₂³×C₁₂₇	#123	1	2	yes	—
156	C₂³×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₂₇	—	2	2	no	—
158	C₂×C₄×C₁₂₇	—	2	2	no	—
159	C₂×C₄×C₁₂₇	—	2	2	no	—
160	C₂×C₄×C₁₂₇	—	2	2	no	—
161	C₂×C₄×C₁₂₇	—	2	2	no	—
162	C₂×C₄×C₁₂₇	—	2	2	no	—
163	C₂×C₄×C₁₂₇	—	2	4	no	—
164	C₂×C₄×C₁₂₇	—	2	2	no	—
165	C₂×C₄×C₁₂₇	—	2	2	no	—
166	C₂×C₄×C₁₂₇	—	2	2	no	—
167	C₂×C₄×C₁₂₇	—	4	8	no	—
168	C₂×C₄×C₁₂₇	—	4	2	no	—
169	C₂×C₄×C₁₂₇	—	4	2	no	—
170	C₂×C₄×C₁₂₇	—	4	2	no	—
171	C₂×C₄×C₁₂₇	—	4	2	no	—
172	C₂×C₄×C₁₂₇	—	4	2	no	—
173	C₂×C₄×C₁₂₇	—	4	2	no	—
174	C₂×C₄×C₁₂₇	—	4	2	no	—
175	C₂×C₄×C₁₂₇	—	4	2	no	—
176	C₂×C₄×C₁₂₇	—	4	2	no	—
177	C₂×C₄×C₁₂₇	#117	1	4	yes	—
178	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₁₂₇	C₄×Q₈	1	4	yes	—
180	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	2	yes	—
181	C₂×C₄×C₁₂₇	#123	1	2	yes	—
182	C₂×C₄×C₁₂₇	#125	1	4	yes	—
183	C₂×C₄×C₁₂₇	#126	1	4	yes	—
184	C₂×C₄×C₁₂₇	#135	1	4	yes	—
185	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₂₇	C₂²×Q₈	1	1	yes	characteristic
187	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
191	C₈×C₁₂₇	—	2	2	no	—
192	C₈×C₁₂₇	—	2	2	no	—
193	C₈×C₁₂₇	—	4	2	no	—
194	C₂²×C₁₂₇	—	2	4	no	—
195	C₂²×C₁₂₇	—	2	4	no	—
196	C₂²×C₁₂₇	—	2	2	no	—
197	C₂²×C₁₂₇	—	2	2	no	—
198	C₂²×C₁₂₇	#387	1	4	yes	—
199	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
200	C₂²×C₁₂₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
201	C₂²×C₁₂₇	C₂×#123	1	1	yes	characteristic
202	C₂²×C₁₂₇	C₂×#135	1	2	yes	—
203	C₂²×C₁₂₇	#575	1	2	yes	—
204	C₄×C₁₂₇	—	2	4	no	—
205	C₄×C₁₂₇	—	4	4	no	—
206	C₄×C₁₂₇	—	4	2	no	—
207	C₄×C₁₂₇	—	4	2	no	—
208	C₄×C₁₂₇	—	4	2	no	—
209	C₄×C₁₂₇	—	4	2	no	—
210	C₄×C₁₂₇	—	4	2	no	—
211	C₄×C₁₂₇	—	8	2	no	—
212	C₄×C₁₂₇	#387	1	4	yes	—
213	C₄×C₁₂₇	C₂×#117	1	1	yes	characteristic
214	C₄×C₁₂₇	C₂×C₄×Q₈	1	1	yes	characteristic
215	C₄×C₁₂₇	C₂×#125	1	1	yes	characteristic
216	C₄×C₁₂₇	C₂×#126	1	1	yes	characteristic
217	#21032	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂×C₁₂₇	—	2	4	no	—
219	C₂×C₁₂₇	C₂×#387	1	1	yes	characteristic
220	C₂×C₁₂₇	C₄×#135	1	1	yes	characteristic
221	C₂×C₁₂₇	#2943	1	1	yes	characteristic
222	C₂×C₁₂₇	#3076	1	2	yes	—
223	C₂×C₁₂₇	#3091	1	2	yes	—
224	C₂×#427	C₂×C₁₂₇	1	1	yes	characteristic
225	#2296	C₂×C₁₂₇	1	1	yes	characteristic
226	C₄×#117	C₂×C₁₂₇	1	1	yes	characteristic
227	#1921	C₂×C₁₂₇	1	2	yes	complemented
228	#1920	C₂×C₁₂₇	1	2	yes	complemented
229	#1919	C₂×C₁₂₇	1	2	yes	complemented
230	#1918	C₂×C₁₂₇	1	2	yes	complemented
231	#1735	C₂×C₁₂₇	1	1	yes	characteristic
232	#1735	C₂×C₁₂₇	1	1	yes	characteristic
233	#1735	C₂×C₁₂₇	1	1	yes	characteristic
234	C₂×#336	C₂×C₁₂₇	1	1	yes	characteristic
235	C₁₂₇	#21032	1	1	yes	characteristic, direct product factor, Sylow
236	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
237	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
238	C₂×#117	C₂²×C₁₂₇	1	1	yes	characteristic
239	C₂×#117	C₂²×C₁₂₇	1	1	yes	characteristic
240	C₂×#117	C₂²×C₁₂₇	1	1	yes	characteristic
241	C₂×#117	C₂²×C₁₂₇	1	1	yes	characteristic
242	C₂²×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
243	#427	C₄×C₁₂₇	1	8	yes	complemented
244	C₂×#107	C₂²×C₁₂₇	1	1	yes	characteristic
245	C₂×#107	C₂²×C₁₂₇	1	1	yes	characteristic
246	C₂×#106	C₂²×C₁₂₇	1	1	yes	characteristic
247	C₂×#106	C₂²×C₁₂₇	1	1	yes	characteristic
248	#389	C₂²×C₁₂₇	1	2	yes	—
249	#389	C₂²×C₁₂₇	1	2	yes	—
250	#385	—	2	2	no	—
251	C₄×C₄⋊C₄	—	2	1	no	—
252	C₄×C₄⋊C₄	—	2	1	no	—
253	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
254	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
255	C₄×C₂²⋊C₄	—	2	2	no	—
256	#376	—	2	1	no	—
257	C₄³	—	2	1	no	—
258	#340	C₂²×C₁₂₇	1	2	yes	—
259	#340	C₂²×C₁₂₇	1	2	yes	—
260	#340	C₂²×C₁₂₇	1	2	yes	—
261	#340	C₂²×C₁₂₇	1	2	yes	—
262	#340	C₂²×C₁₂₇	1	2	yes	—
263	#340	C₂²×C₁₂₇	1	2	yes	—
264	#336	C₂²×C₁₂₇	1	2	yes	—
265	#336	C₂²×C₁₂₇	1	2	yes	—
266	C₂³×C₄	D₄×C₁₂₇	1	2	yes	—
267	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	C₂×C₄×C₁₂₇	1	4	yes	—
274	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
275	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
277	#117	—	2	2	no	—
278	#117	—	2	2	no	—
279	#117	—	2	2	no	—
280	#117	—	2	2	no	—
281	#117	—	2	2	no	—
282	#117	C₂×C₄×C₁₂₇	1	4	yes	—
283	#117	C₂×C₄×C₁₂₇	1	4	yes	—
284	#117	Q₈×C₁₂₇	1	4	yes	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	2	yes	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	D₄×C₁₂₇	1	1	yes	characteristic
306	C₂×C₄²	D₄×C₁₂₇	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
308	#107	C₂×C₄×C₁₂₇	1	4	yes	complemented
309	#107	C₂×C₄×C₁₂₇	1	4	yes	complemented
310	#106	C₂×C₄×C₁₂₇	1	4	yes	complemented
311	#106	C₂×C₄×C₁₂₇	1	4	yes	complemented
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	#95	—	2	2	no	—
316	C₂⁴	C₂×D₄×C₁₂₇	1	1	yes	characteristic
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
330	C₂²×C₄	C₂×Q₈×C₁₂₇	1	2	yes	—
331	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
332	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
333	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
334	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
335	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
336	C₂×C₈	—	2	8	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	4	4	no	—
345	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
346	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
357	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
358	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
359	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
360	C₄⋊C₄	C₂×Q₈×C₁₂₇	1	4	yes	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	4	no	—
367	C₄²	—	2	4	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	4	4	no	—
373	C₄²	—	4	2	no	—
374	C₄²	—	4	4	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	C₄×D₄×C₁₂₇	1	2	yes	—
378	C₂³	C₂²⋊Q₈×C₁₂₇	1	2	yes	—
379	C₂³	#123×C₁₂₇	1	2	yes	—
380	C₂³	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	#117×C₁₂₇	1	4	yes	—
402	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
403	C₂×C₄	C₄×Q₈×C₁₂₇	1	4	yes	—
404	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	2	yes	—
405	C₂×C₄	#123×C₁₂₇	1	2	yes	—
406	C₂×C₄	#125×C₁₂₇	1	4	yes	—
407	C₂×C₄	#126×C₁₂₇	1	4	yes	—
408	C₂×C₄	#135×C₁₂₇	1	4	yes	—
409	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
410	C₂×C₄	C₂²×Q₈×C₁₂₇	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
412	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
414	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	4	2	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	4	no	—
422	C₂²	#387×C₁₂₇	1	4	yes	—
423	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
424	C₂²	C₂×C₂²⋊Q₈×C₁₂₇	1	1	yes	characteristic
425	C₂²	C₂×#123×C₁₂₇	1	1	yes	characteristic
426	C₂²	C₂×#135×C₁₂₇	1	2	yes	—
427	C₂²	#575×C₁₂₇	1	2	yes	—
428	C₄	—	2	4	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	4	no	—
435	C₄	—	8	2	no	—
436	C₄	#387×C₁₂₇	1	4	yes	—
437	C₄	C₂×#117×C₁₂₇	1	1	yes	characteristic
438	C₄	C₂×C₄×Q₈×C₁₂₇	1	1	yes	characteristic
439	C₄	C₂×#125×C₁₂₇	1	1	yes	characteristic
440	C₄	C₂×#126×C₁₂₇	1	1	yes	characteristic
441	C₂	—	2	4	no	—
442	C₂	C₂×#387×C₁₂₇	1	1	yes	characteristic
443	C₂	C₄×#135×C₁₂₇	1	1	yes	characteristic
444	C₂	C₁₂₇×#2943	1	1	yes	characteristic
445	C₂	C₁₂₇×#3076	1	2	yes	—
446	C₂	C₁₂₇×#3091	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₂₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₂₇
socle	C₂³×C₁₂₇	C₂²×D₄
prime radical	C₂⁴×C₁₂₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₂₇ ◁ C₂²×C₄²×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₂₇×#1921	C₂	semidirect
5. C₁₂₇×#1920	C₂	semidirect
6. C₁₂₇×#1919	C₂	semidirect
7. C₁₂₇×#1918	C₂	semidirect
19. #427×C₁₂₇	C₄	semidirect
84. #107×C₁₂₇	C₂×C₄	semidirect
85. #107×C₁₂₇	C₂×C₄	semidirect
86. #106×C₁₂₇	C₂×C₄	semidirect
87. #106×C₁₂₇	C₂×C₄	semidirect
217. #21032	C₁₂₇	direct (N × H)
227. #1921	C₂×C₁₂₇	semidirect
228. #1920	C₂×C₁₂₇	semidirect
229. #1919	C₂×C₁₂₇	semidirect
230. #1918	C₂×C₁₂₇	semidirect
235. C₁₂₇	#21032	direct (N × H)
243. #427	C₄×C₁₂₇	semidirect
308. #107	C₂×C₄×C₁₂₇	semidirect
309. #107	C₂×C₄×C₁₂₇	semidirect
310. #106	C₂×C₄×C₁₂₇	semidirect
311. #106	C₂×C₄×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#427×C₁₂₇	2
C₁₂₇×#2296	2
C₄×#117×C₁₂₇	2
C₁₂₇×#1921	2
C₁₂₇×#1920	2
C₁₂₇×#1919	2
C₁₂₇×#1918	2
C₁₂₇×#1735	2
C₂×#336×C₁₂₇	2
#21032	127

Subgroups — C127×#21032 #44584705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#21032 #44584705