Subgroups — #30652796

Order 16256.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550600	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550595	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550587	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550578	C₂	1	1	yes	maximal, characteristic, complemented
5	#22550571	C₂	1	2	yes	maximal, complemented
6	#22550568	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550560	C₂	1	2	yes	maximal, complemented
8	#22550553	C₂	1	2	yes	maximal, complemented
9	#22550549	C₂	1	2	yes	maximal, complemented
10	#22550528	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550523	C₂	1	1	yes	maximal, characteristic, complemented
12	#22550519	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550484	C₂	1	1	yes	maximal, characteristic, complemented
14	#22550467	C₂	1	2	yes	maximal, complemented
15	#22550460	C₂	1	2	yes	maximal, complemented
16	#22550408	C₂	1	1	yes	maximal, characteristic, complemented
17	#22550405	C₂	1	2	yes	maximal, complemented
18	#22550404	C₂	1	1	yes	maximal, characteristic, complemented
19	#126×D₁₂₇	C₂	1	2	yes	maximal, complemented
20	#22550356	C₂	1	1	yes	maximal, characteristic, complemented
21	#22550348	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#14523249	C₂	1	1	yes	maximal, characteristic, complemented
23	#542×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14523249	C₂²	1	1	yes	characteristic
25	C₂×#14523248	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
27	#16861207	C₂²	1	1	yes	characteristic, complemented
28	#16861204	C₂²	1	2	yes	—
29	#16861204	C₂²	1	2	yes	—
30	#16861204	C₂²	1	2	yes	—
31	#16861204	C₂²	1	1	yes	characteristic
32	#16861204	C₂²	1	2	yes	complemented
33	#16861203	C₂²	1	2	yes	—
34	#16861202	C₂²	1	2	yes	complemented
35	#16861202	C₂²	1	2	yes	complemented
36	#16861202	C₂²	1	2	yes	complemented
37	#16861202	C₂²	1	2	yes	complemented
38	#16861202	C₂²	1	1	yes	characteristic, complemented
39	#16861201	C₂²	1	2	yes	complemented
40	#16861200	C₂²	1	2	yes	complemented
41	#16861200	C₂²	1	1	yes	characteristic, complemented
42	#16861200	C₂²	1	1	yes	characteristic, complemented
43	#16861199	C₂²	1	1	yes	characteristic, complemented
44	#16861199	C₂²	1	2	yes	complemented
45	#16861198	C₂²	1	2	yes	—
46	#16861196	C₂²	1	1	yes	characteristic
47	#16861195	C₂²	1	1	yes	characteristic
48	#16861194	C₂²	1	1	yes	characteristic
49	#16861194	C₂²	1	2	yes	complemented
50	#16861193	C₂²	1	2	yes	—
51	#16861193	C₂²	1	2	yes	complemented
52	#16861191	C₂²	1	2	yes	—
53	#16861191	C₂²	1	2	yes	—
54	#16861191	C₂²	1	2	yes	complemented
55	#16861191	C₂²	1	1	yes	characteristic, complemented
56	#16861191	C₂²	1	2	yes	complemented
57	#16861189	C₂²	1	1	yes	characteristic
58	#16861189	C₂²	1	1	yes	characteristic, complemented
59	#16861189	C₂²	1	2	yes	complemented
60	#16861187	C₂²	1	1	yes	characteristic, complemented
61	#16861186	C₂²	1	2	yes	complemented
62	#16861185	C₂²	1	1	yes	characteristic
63	#16861185	C₂²	1	2	yes	complemented
64	#16861185	C₂²	1	2	yes	complemented
65	#16861182	C₂²	1	2	yes	—
66	#16861182	C₂²	1	1	yes	characteristic
67	#16861182	C₂²	1	2	yes	complemented
68	#16861181	C₂²	1	2	yes	complemented
69	#16861180	C₂²	1	2	yes	—
70	#16861180	C₂²	1	1	yes	characteristic
71	#16861179	C₂²	1	2	yes	—
72	#16861177	C₂²	1	2	yes	—
73	Q₈×Dic₁₂₇	C₂²	1	2	yes	complemented
74	Q₈×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
75	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
76	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
78	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
79	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
80	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
81	C₄×D₅₀₈	C₂²	1	2	yes	complemented
82	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
83	D₄×Dic₁₂₇	C₂²	1	2	yes	complemented
84	#16861171	C₂²	1	1	yes	characteristic
85	#16861171	C₂²	1	1	yes	characteristic
86	#16861171	C₂²	1	2	yes	complemented
87	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	—
88	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
90	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
91	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	—
92	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
93	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
94	#16861168	C₂²	1	2	yes	complemented
95	#16861167	C₂²	1	1	yes	characteristic
96	#16861167	C₂²	1	2	yes	complemented
97	#16861167	C₂²	1	2	yes	complemented
98	#16861167	C₂²	1	1	yes	characteristic, complemented
99	#16861166	C₂²	1	1	yes	characteristic
100	#16861165	C₂²	1	2	yes	complemented
101	#16861165	C₂²	1	2	yes	complemented
102	C₂×C₄⋊Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
103	C₄⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
104	C₄⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
106	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
110	C₄²×D₁₂₇	C₂²	1	2	yes	complemented
111	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
112	C₄⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
113	#126×C₁₂₇	C₂²	1	2	yes	complemented
114	#124×C₁₂₇	C₂²	1	1	yes	characteristic
115	#124×C₁₂₇	C₂²	1	2	yes	complemented
116	#123×C₁₂₇	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
118	C₂²⋊Q₈×C₁₂₇	C₂²	1	2	yes	complemented
119	#121×C₁₂₇	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
122	#117×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₂₇	C₂³	1	2	yes	—
124	#14523249	—	2	4	no	—
125	#14523248	—	2	4	no	—
126	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
127	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
128	C₂×D₅₀₈	C₂³	1	2	yes	—
129	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
130	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
136	D₄×D₁₂₇	—	2	4	no	—
137	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
138	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
139	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
142	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
143	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
144	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
145	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
147	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
149	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
151	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
152	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
153	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
154	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
155	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
158	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
159	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
160	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
161	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
162	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
163	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
164	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
165	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
166	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
168	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
169	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
170	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
171	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
178	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
183	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
193	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₂₇	C₂³	1	2	yes	—
196	C₄×Dic₁₂₇	C₂³	1	2	yes	—
197	C₄×Dic₁₂₇	C₂³	1	2	yes	—
198	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₂₇	C₂³	1	2	yes	—
201	C₄×Dic₁₂₇	C₂³	1	2	yes	—
202	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₁₂₇	C₂³	1	2	yes	—
204	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
206	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
208	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
222	C₄²×C₁₂₇	C₂³	1	2	yes	—
223	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
224	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
225	C₂²×D₁₂₇	—	2	4	no	—
226	C₂²×D₁₂₇	—	4	2	no	—
227	C₂²×D₁₂₇	—	4	2	no	—
228	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
229	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
230	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
231	Dic₂₅₄	—	2	2	no	—
232	Dic₂₅₄	—	4	1	no	—
233	D₅₀₈	—	2	4	no	—
234	D₅₀₈	—	4	1	no	—
235	D₅₀₈	#41	1	4	yes	—
236	C₂²⋊D₁₂₇	—	2	4	no	—
237	C₂²⋊D₁₂₇	—	2	4	no	—
238	C₂²⋊D₁₂₇	—	4	1	no	—
239	C₂²⋊D₁₂₇	—	4	2	no	—
240	C₂²⋊D₁₂₇	—	4	1	no	—
241	C₂×Dic₁₂₇	—	4	2	no	—
242	C₂×Dic₁₂₇	—	4	2	no	—
243	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
244	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
247	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
251	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
252	C₄×D₁₂₇	—	2	4	no	—
253	C₄×D₁₂₇	—	2	4	no	—
254	C₄×D₁₂₇	—	2	2	no	—
255	C₄×D₁₂₇	—	2	2	no	—
256	C₄×D₁₂₇	—	4	1	no	—
257	C₄×D₁₂₇	—	4	2	no	—
258	C₄×D₁₂₇	—	4	2	no	—
259	C₄×D₁₂₇	—	4	2	no	—
260	C₄×D₁₂₇	—	4	2	no	—
261	C₄×D₁₂₇	—	4	1	no	—
262	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
263	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
264	Q₈×C₁₂₇	—	2	2	no	—
265	Q₈×C₁₂₇	—	4	2	no	—
266	D₄×C₁₂₇	—	2	2	no	—
267	D₄×C₁₂₇	—	4	2	no	—
268	C₂×C₄×C₁₂₇	—	2	2	no	—
269	C₂×C₄×C₁₂₇	—	4	2	no	—
270	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
273	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
276	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
278	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₁₂₇	—	2	1	no	—
280	C₂²×C₁₂₇	—	2	2	no	—
281	C₂²×C₁₂₇	—	2	2	no	—
282	C₂²×C₁₂₇	—	2	1	no	—
283	C₂²×C₁₂₇	—	2	1	no	—
284	C₂²×C₁₂₇	—	2	2	no	—
285	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
286	C₂×D₁₂₇	—	2	2	no	—
287	C₂×D₁₂₇	—	2	2	no	—
288	C₂×D₁₂₇	—	2	1	no	—
289	C₂×D₁₂₇	—	2	1	no	—
290	C₂×D₁₂₇	—	2	1	no	—
291	C₂×D₁₂₇	—	2	1	no	—
292	C₂×D₁₂₇	—	2	1	no	—
293	C₂×D₁₂₇	—	2	1	no	—
294	C₂×D₁₂₇	—	8	4	no	—
295	C₂×D₁₂₇	C₂×#41	1	4	yes	—
296	C₄×C₁₂₇	—	2	1	no	—
297	C₄×C₁₂₇	—	2	2	no	—
298	C₄×C₁₂₇	—	2	1	no	—
299	C₄×C₁₂₇	—	2	2	no	—
300	C₄×C₁₂₇	—	2	2	no	—
301	C₄×C₁₂₇	—	2	1	no	—
302	C₄×C₁₂₇	—	2	1	no	—
303	C₄×C₁₂₇	—	2	1	no	—
304	C₄×C₁₂₇	C₂×#41	1	2	yes	—
305	Dic₁₂₇	—	2	1	no	—
306	Dic₁₂₇	—	2	1	no	—
307	Dic₁₂₇	—	2	2	no	—
308	Dic₁₂₇	—	2	1	no	—
309	Dic₁₂₇	—	2	1	no	—
310	Dic₁₂₇	—	2	2	no	—
311	Dic₁₂₇	—	2	2	no	—
312	Dic₁₂₇	—	2	1	no	—
313	Dic₁₂₇	—	2	1	no	—
314	C₂×C₁₂₇	—	4	2	no	—
315	C₂×C₁₂₇	—	4	1	no	—
316	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
317	C₂×C₁₂₇	#585	1	1	yes	characteristic
318	C₂×C₁₂₇	#585	1	1	yes	characteristic
319	D₁₂₇	—	2	4	no	—
320	D₁₂₇	—	4	1	no	—
321	D₁₂₇	—	4	1	no	—
322	#3521	—	127	1	no	maximal, Sylow
323	C₁₂₇	#3521	1	1	yes	characteristic, complemented, Sylow
324	#556	—	127	1	no	—
325	#556	—	127	1	no	—
326	#554	—	127	1	no	—
327	#553	—	127	2	no	—
328	#553	—	127	1	no	—
329	#552	—	127	2	no	—
330	#552	—	127	1	no	—
331	#551	—	127	2	no	—
332	#551	—	127	2	no	—
333	#547	—	127	1	no	—
334	#546	—	127	1	no	—
335	#546	—	127	1	no	—
336	#542	D₁₂₇	1	1	yes	characteristic, complemented
337	#541	—	127	1	no	—
338	#539	—	127	2	no	—
339	#538	—	127	2	no	—
340	#529	—	127	2	no	—
341	#529	—	127	1	no	—
342	#529	—	127	1	no	—
343	C₂×#126	—	127	2	no	—
344	#520	—	127	1	no	—
345	#518	—	127	1	no	—
346	C₄×#41	—	127	1	no	—
347	C₂×#41	—	127	1	no	—
348	C₂×#41	—	127	1	no	—
349	C₂²×D₄	—	127	1	no	—
350	C₄⋊Q₈	—	127	1	no	—
351	C₄⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
352	#126	—	127	1	no	—
353	#126	—	127	2	no	—
354	#126	—	127	2	no	—
355	#126	—	127	2	no	—
356	#126	—	127	2	no	—
357	#126	—	127	2	no	—
358	#126	—	127	2	no	—
359	#126	—	127	2	no	—
360	#126	—	127	1	no	—
361	#126	—	127	2	no	—
362	#126	—	127	2	no	—
363	#126	C₂×D₁₂₇	1	2	yes	complemented
364	#125	—	127	1	no	—
365	#125	—	127	2	no	—
366	#125	—	127	1	no	—
367	#125	—	127	2	no	—
368	#125	—	127	1	no	—
369	#125	—	127	2	no	—
370	#124	—	127	2	no	—
371	#124	—	127	1	no	—
372	#124	—	127	1	no	—
373	#124	C₂×D₁₂₇	1	1	yes	characteristic
374	#124	C₂×D₁₂₇	1	2	yes	complemented
375	#123	—	127	1	no	—
376	#123	—	127	2	no	—
377	#123	—	127	2	no	—
378	#123	—	127	2	no	—
379	#123	—	127	2	no	—
380	#123	—	127	2	no	—
381	#123	—	127	1	no	—
382	#123	—	127	2	no	—
383	#123	—	127	2	no	—
384	#123	C₂×D₁₂₇	1	2	yes	complemented
385	C₂²⋊Q₈	—	127	1	no	—
386	C₂²⋊Q₈	—	127	2	no	—
387	C₂²⋊Q₈	—	127	2	no	—
388	C₂²⋊Q₈	—	127	1	no	—
389	C₂²⋊Q₈	—	127	1	no	—
390	C₂²⋊Q₈	—	127	1	no	—
391	C₂²⋊Q₈	—	127	2	no	—
392	C₂²⋊Q₈	—	127	2	no	—
393	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
394	C₂²⋊Q₈	C₂×D₁₂₇	1	2	yes	complemented
395	#121	—	127	1	no	—
396	#121	—	127	2	no	—
397	#121	—	127	2	no	—
398	#121	—	127	1	no	—
399	#121	—	127	2	no	—
400	#121	—	127	2	no	—
401	#121	C₂×D₁₂₇	1	1	yes	characteristic
402	#120	—	127	2	no	—
403	#120	—	127	2	no	—
404	C₄×Q₈	—	127	1	no	—
405	C₄×Q₈	—	127	2	no	—
406	C₄×Q₈	—	127	1	no	—
407	C₄×Q₈	—	127	1	no	—
408	C₄×Q₈	—	127	1	no	—
409	C₄×Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
410	C₄×D₄	—	127	1	no	—
411	C₄×D₄	—	127	2	no	—
412	C₄×D₄	—	127	2	no	—
413	C₄×D₄	—	127	1	no	—
414	C₄×D₄	—	127	1	no	—
415	C₄×D₄	—	127	2	no	—
416	C₄×D₄	—	127	1	no	—
417	C₄×D₄	—	127	2	no	—
418	C₄×D₄	—	127	1	no	—
419	C₄×D₄	—	127	2	no	—
420	C₄×D₄	—	127	2	no	—
421	C₄×D₄	—	127	2	no	—
422	C₄×D₄	—	127	1	no	—
423	C₄×D₄	—	127	2	no	—
424	C₄×D₄	—	127	1	no	—
425	C₄×D₄	—	127	1	no	—
426	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
427	#117	—	127	2	no	—
428	#117	—	127	2	no	—
429	#117	—	127	1	no	—
430	#117	—	127	1	no	—
431	#117	—	127	2	no	—
432	#117	—	127	2	no	—
433	#117	—	127	2	no	—
434	#117	—	127	1	no	—
435	#117	C₂×D₁₂₇	1	1	yes	characteristic, complemented
436	C₂×C₄⋊C₄	—	127	1	no	—
437	C₂×C₄⋊C₄	—	127	2	no	—
438	C₂×C₄⋊C₄	—	127	2	no	—
439	C₂×C₄⋊C₄	—	127	2	no	—
440	C₂×C₂²⋊C₄	—	127	2	no	—
441	C₂×C₂²⋊C₄	—	127	2	no	—
442	C₂×C₂²⋊C₄	—	127	2	no	—
443	C₂×C₂²⋊C₄	—	127	2	no	—
444	C₂×C₄²	—	127	2	no	—
445	C₂×C₄²	—	127	1	no	—
446	C₂⁴	—	127	2	no	—
447	#41	—	254	4	no	—
448	#41	—	254	4	no	—
449	C₂×Q₈	—	127	1	no	—
450	C₂×Q₈	—	127	1	no	—
451	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
452	C₂×Q₈	C₂²×D₁₂₇	1	2	yes	—
453	C₂×D₄	—	127	1	no	—
454	C₂×D₄	—	127	2	no	—
455	C₂×D₄	—	127	1	no	—
456	C₂×D₄	—	127	2	no	—
457	C₂×D₄	—	127	2	no	—
458	C₂×D₄	—	127	1	no	—
459	C₂×D₄	—	127	1	no	—
460	C₂×D₄	—	127	2	no	—
461	C₂×D₄	—	254	4	no	—
462	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
463	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
464	C₂²×C₄	—	127	2	no	—
465	C₂²×C₄	—	127	2	no	—
466	C₂²×C₄	—	127	2	no	—
467	C₂²×C₄	—	127	2	no	—
468	C₂²×C₄	—	127	1	no	—
469	C₂²×C₄	—	127	1	no	—
470	C₂²×C₄	—	127	2	no	—
471	C₂²×C₄	—	127	2	no	—
472	C₂²×C₄	—	127	2	no	—
473	C₂²×C₄	—	127	1	no	—
474	C₂²×C₄	—	127	2	no	—
475	C₂²×C₄	—	127	1	no	—
476	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
477	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
478	C₄⋊C₄	—	127	1	no	—
479	C₄⋊C₄	—	127	2	no	—
480	C₄⋊C₄	—	127	2	no	—
481	C₄⋊C₄	—	127	2	no	—
482	C₄⋊C₄	—	127	2	no	—
483	C₄⋊C₄	—	127	2	no	—
484	C₄⋊C₄	—	127	1	no	—
485	C₄⋊C₄	—	127	1	no	—
486	C₄⋊C₄	—	127	1	no	—
487	C₄⋊C₄	—	127	2	no	—
488	C₄⋊C₄	—	127	2	no	—
489	C₄⋊C₄	—	127	1	no	—
490	C₄⋊C₄	—	127	1	no	—
491	C₄⋊C₄	—	127	2	no	—
492	C₄⋊C₄	—	127	1	no	—
493	C₄⋊C₄	—	127	1	no	—
494	C₄⋊C₄	—	127	2	no	—
495	C₄⋊C₄	—	127	1	no	—
496	C₄⋊C₄	—	127	2	no	—
497	C₄⋊C₄	—	127	2	no	—
498	C₄⋊C₄	—	127	1	no	—
499	C₄⋊C₄	—	127	2	no	—
500	C₄⋊C₄	—	127	2	no	—
501	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
503	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
504	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
508	C₂²⋊C₄	—	127	2	no	—
509	C₂²⋊C₄	—	127	2	no	—
510	C₂²⋊C₄	—	127	2	no	—
511	C₂²⋊C₄	—	127	1	no	—
512	C₂²⋊C₄	—	127	2	no	—
513	C₂²⋊C₄	—	127	1	no	—
514	C₂²⋊C₄	—	127	1	no	—
515	C₂²⋊C₄	—	127	2	no	—
516	C₂²⋊C₄	—	127	1	no	—
517	C₂²⋊C₄	—	127	1	no	—
518	C₂²⋊C₄	—	127	1	no	—
519	C₂²⋊C₄	—	127	2	no	—
520	C₂²⋊C₄	—	127	2	no	—
521	C₂²⋊C₄	—	127	2	no	—
522	C₂²⋊C₄	—	127	2	no	—
523	C₂²⋊C₄	—	127	2	no	—
524	C₂²⋊C₄	—	127	2	no	—
525	C₂²⋊C₄	—	127	2	no	—
526	C₂²⋊C₄	—	127	1	no	—
527	C₂²⋊C₄	—	127	2	no	—
528	C₂²⋊C₄	—	127	1	no	—
529	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
530	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
535	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
536	C₄²	—	127	1	no	—
537	C₄²	—	127	1	no	—
538	C₄²	—	127	2	no	—
539	C₄²	—	127	2	no	—
540	C₄²	—	127	1	no	—
541	C₄²	—	127	2	no	—
542	C₄²	—	127	2	no	—
543	C₄²	—	127	2	no	—
544	C₄²	—	127	1	no	—
545	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
546	C₄²	C₂²×D₁₂₇	1	2	yes	—
547	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
548	C₂³	—	127	2	no	—
549	C₂³	—	127	1	no	—
550	C₂³	—	127	1	no	—
551	C₂³	—	508	2	no	—
552	C₂³	—	508	2	no	—
553	C₂³	—	254	4	no	—
554	C₂³	C₂³×D₁₂₇	1	2	yes	—
555	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
556	Q₈	—	2	2	no	—
557	Q₈	—	4	2	no	—
558	Q₈	—	508	1	no	—
559	Q₈	—	254	2	no	—
560	D₄	—	2	2	no	—
561	D₄	—	4	2	no	—
562	D₄	—	127	4	no	—
563	D₄	—	508	1	no	—
564	D₄	—	508	1	no	—
565	D₄	—	508	2	no	—
566	D₄	—	508	1	no	—
567	D₄	—	254	4	no	—
568	D₄	—	254	4	no	—
569	D₄	—	254	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	127	1	no	—
573	C₂×C₄	—	127	1	no	—
574	C₂×C₄	—	127	2	no	—
575	C₂×C₄	—	127	2	no	—
576	C₂×C₄	—	127	1	no	—
577	C₂×C₄	—	127	1	no	—
578	C₂×C₄	—	127	1	no	—
579	C₂×C₄	—	127	1	no	—
580	C₂×C₄	—	127	2	no	—
581	C₂×C₄	—	508	1	no	—
582	C₂×C₄	—	508	2	no	—
583	C₂×C₄	—	508	2	no	—
584	C₂×C₄	—	508	2	no	—
585	C₂×C₄	—	508	1	no	—
586	C₂×C₄	—	508	2	no	—
587	C₂×C₄	—	508	2	no	—
588	C₂×C₄	—	508	2	no	—
589	C₂×C₄	—	254	4	no	—
590	C₂×C₄	—	254	4	no	—
591	C₂×C₄	—	254	2	no	—
592	C₂×C₄	—	254	2	no	—
593	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
597	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
598	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
599	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
602	C₂²	—	2	1	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	127	4	no	—
609	C₂²	—	1016	4	no	—
610	C₂²	—	254	1	no	—
611	C₂²	—	254	1	no	—
612	C₂²	—	254	1	no	—
613	C₂²	—	254	1	no	—
614	C₂²	—	254	1	no	—
615	C₂²	—	254	1	no	—
616	C₂²	—	254	2	no	—
617	C₂²	—	254	2	no	—
618	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	254	1	no	—
628	C₄	—	254	1	no	—
629	C₄	—	254	2	no	—
630	C₄	—	254	1	no	—
631	C₄	—	254	1	no	—
632	C₄	—	254	2	no	—
633	C₄	—	254	2	no	—
634	C₄	—	254	1	no	—
635	C₄	—	254	1	no	—
636	C₄	#41×D₁₂₇	1	2	yes	—
637	C₂	—	4	2	no	—
638	C₂	—	4	1	no	—
639	C₂	—	508	1	no	—
640	C₂	—	508	1	no	—
641	C₂	—	254	4	no	—
642	C₂	C₂×#41×D₁₂₇	1	1	yes	characteristic
643	C₂	#22550711	1	1	yes	characteristic
644	C₂	#22550713	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Fitting	#542×C₁₂₇	C₂
hypercenter	#542	D₁₂₇
hypocenter	C₁₂₇	#3521
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #22550600	C₂	semidirect
2. #22550595	C₂	semidirect
3. #22550587	C₂	semidirect
4. #22550578	C₂	semidirect
5. #22550571	C₂	semidirect
6. #22550568	C₂	semidirect
7. #22550560	C₂	semidirect
8. #22550553	C₂	semidirect
9. #22550549	C₂	semidirect
10. #22550528	C₂	semidirect
11. #22550523	C₂	semidirect
12. #22550519	C₂	semidirect
13. #22550484	C₂	semidirect
14. #22550467	C₂	semidirect
15. #22550460	C₂	semidirect
16. #22550408	C₂	semidirect
17. #22550405	C₂	semidirect
18. #22550404	C₂	semidirect
19. #126×D₁₂₇	C₂	semidirect
20. #22550356	C₂	semidirect
21. #22550348	C₂	semidirect
22. C₄×#14523249	C₂	semidirect
23. #542×C₁₂₇	C₂	semidirect
27. #16861207	C₂²	semidirect
32. #16861204	C₂²	semidirect
34. #16861202	C₂²	semidirect
35. #16861202	C₂²	semidirect
36. #16861202	C₂²	semidirect
37. #16861202	C₂²	semidirect
38. #16861202	C₂²	semidirect
39. #16861201	C₂²	semidirect
40. #16861200	C₂²	semidirect
41. #16861200	C₂²	semidirect
42. #16861200	C₂²	semidirect
43. #16861199	C₂²	semidirect
44. #16861199	C₂²	semidirect
49. #16861194	C₂²	semidirect
51. #16861193	C₂²	semidirect
54. #16861191	C₂²	semidirect
55. #16861191	C₂²	semidirect
56. #16861191	C₂²	semidirect
58. #16861189	C₂²	semidirect
59. #16861189	C₂²	semidirect
60. #16861187	C₂²	semidirect
61. #16861186	C₂²	semidirect
63. #16861185	C₂²	semidirect
64. #16861185	C₂²	semidirect
67. #16861182	C₂²	semidirect
68. #16861181	C₂²	semidirect
73. Q₈×Dic₁₂₇	C₂²	semidirect
74. Q₈×Dic₁₂₇	C₂²	semidirect
75. C₄×Dic₂₅₄	C₂²	semidirect
76. C₄×Dic₂₅₄	C₂²	semidirect
77. C₄×Dic₂₅₄	C₂²	semidirect
81. C₄×D₅₀₈	C₂²	semidirect
83. D₄×Dic₁₂₇	C₂²	semidirect
86. #16861171	C₂²	semidirect
89. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
90. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
92. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
93. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
94. #16861168	C₂²	semidirect
96. #16861167	C₂²	semidirect
97. #16861167	C₂²	semidirect
98. #16861167	C₂²	semidirect
100. #16861165	C₂²	semidirect
101. #16861165	C₂²	semidirect
102. C₂×C₄⋊Dic₁₂₇	C₂²	semidirect
103. C₄⋊C₄×D₁₂₇	C₂²	semidirect
104. C₄⋊C₄×D₁₂₇	C₂²	semidirect
105. C₄⋊C₄×D₁₂₇	C₂²	semidirect
110. C₄²×D₁₂₇	C₂²	semidirect
111. C₄²×D₁₂₇	C₂²	semidirect
112. C₄⋊Q₈×C₁₂₇	C₂²	semidirect
113. #126×C₁₂₇	C₂²	semidirect
115. #124×C₁₂₇	C₂²	semidirect
116. #123×C₁₂₇	C₂²	semidirect
117. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
118. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
120. C₄×Q₈×C₁₂₇	C₂²	semidirect
122. #117×C₁₂₇	C₂²	semidirect
323. C₁₂₇	#3521	semidirect
336. #542	D₁₂₇	semidirect
351. C₄⋊Q₈	C₂×D₁₂₇	semidirect
363. #126	C₂×D₁₂₇	semidirect
374. #124	C₂×D₁₂₇	semidirect
384. #123	C₂×D₁₂₇	semidirect
393. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
394. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
409. C₄×Q₈	C₂×D₁₂₇	semidirect
435. #117	C₂×D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
#22550600	2
#22550595	2
#22550587	2
#22550578	2
#22550571	2
#22550568	2
#22550560	2
#22550553	2
#22550549	2
#22550528	2
#22550523	2
#22550519	2
#22550484	2
#22550467	2
#22550460	2
#22550408	2
#22550405	2
#22550404	2
#126×D₁₂₇	2
#22550356	2
#22550348	2
C₄×#14523249	2
#542×C₁₂₇	2
#3521	127