Subgroups — #30652289

Order 16256.

1132 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550594	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550590	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550581	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550576	C₂	1	1	yes	maximal, characteristic, complemented
5	#22550566	C₂	1	1	yes	maximal, characteristic, complemented
6	#22550564	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550562	C₂	1	2	yes	maximal, complemented
8	#22550555	C₂	1	2	yes	maximal, complemented
9	#22550554	C₂	1	2	yes	maximal, complemented
10	#22550526	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550515	C₂	1	2	yes	maximal, complemented
12	#22550432	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550409	C₂	1	2	yes	maximal, complemented
14	#22550407	C₂	1	2	yes	maximal, complemented
15	#22550403	C₂	1	2	yes	maximal, complemented
16	#22550386	C₂	1	1	yes	maximal, characteristic, complemented
17	#22550386	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#14523247	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#14523247	C₂	1	2	yes	maximal, complemented
20	C₄×D₄×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#16861167	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#553×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14523247	C₂²	1	1	yes	characteristic
25	C₂×#14523247	C₂²	1	2	yes	—
26	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₁₂₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₁₂₇	C₂²	1	1	yes	characteristic
29	#16861208	C₂²	1	1	yes	characteristic, complemented
30	#16861208	C₂²	1	1	yes	characteristic, complemented
31	#16861204	C₂²	1	2	yes	complemented
32	#16861203	C₂²	1	2	yes	complemented
33	#16861202	C₂²	1	2	yes	complemented
34	#16861202	C₂²	1	2	yes	complemented
35	#16861202	C₂²	1	2	yes	complemented
36	#16861201	C₂²	1	1	yes	characteristic, complemented
37	#16861200	C₂²	1	2	yes	complemented
38	#16861199	C₂²	1	2	yes	complemented
39	#16861199	C₂²	1	2	yes	complemented
40	#16861196	C₂²	1	2	yes	complemented
41	#16861195	C₂²	1	2	yes	—
42	#16861195	C₂²	1	2	yes	complemented
43	#16861194	C₂²	1	2	yes	—
44	#16861192	C₂²	1	2	yes	complemented
45	#16861191	C₂²	1	2	yes	—
46	#16861191	C₂²	1	2	yes	—
47	#16861191	C₂²	1	2	yes	complemented
48	#16861190	C₂²	1	2	yes	—
49	#16861190	C₂²	1	2	yes	complemented
50	#16861189	C₂²	1	1	yes	characteristic, complemented
51	#16861189	C₂²	1	1	yes	characteristic, complemented
52	#16861188	C₂²	1	2	yes	complemented
53	#16861188	C₂²	1	1	yes	characteristic, complemented
54	#16861188	C₂²	1	1	yes	characteristic, complemented
55	#16861187	C₂²	1	2	yes	—
56	#16861187	C₂²	1	2	yes	—
57	#16861187	C₂²	1	2	yes	complemented
58	#16861186	C₂²	1	2	yes	complemented
59	#16861182	C₂²	1	2	yes	—
60	#16861181	C₂²	1	2	yes	—
61	#16861180	C₂²	1	1	yes	characteristic, complemented
62	#16861180	C₂²	1	1	yes	characteristic, complemented
63	#16861177	C₂²	1	2	yes	—
64	#16861177	C₂²	1	2	yes	—
65	C₄×Dic₂₅₄	C₂²	1	2	yes	complemented
66	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
67	#16861174	C₂²	1	1	yes	characteristic, complemented
68	#16861174	C₂²	1	2	yes	complemented
69	#16861174	C₂²	1	2	yes	complemented
70	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
71	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
72	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
73	D₄×Dic₁₂₇	C₂²	1	2	yes	complemented
74	D₄×Dic₁₂₇	C₂²	1	2	yes	complemented
75	#16861171	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	—
77	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
78	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	—
79	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
80	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
81	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	—
82	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
83	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
84	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
85	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
86	#16861168	C₂²	1	1	yes	characteristic, complemented
87	#16861167	C₂²	1	2	yes	—
88	#16861167	C₂²	1	1	yes	characteristic
89	#16861167	C₂²	1	1	yes	characteristic
90	#16861167	C₂²	1	1	yes	characteristic
91	#16861167	C₂²	1	2	yes	complemented
92	#16861167	C₂²	1	1	yes	characteristic, complemented
93	#16861167	C₂²	1	1	yes	characteristic, complemented
94	#16861167	C₂²	1	2	yes	complemented
95	#16861166	C₂²	1	2	yes	—
96	#16861165	C₂²	1	2	yes	complemented
97	#16861165	C₂²	1	2	yes	complemented
98	#16861165	C₂²	1	2	yes	complemented
99	#16861165	C₂²	1	2	yes	complemented
100	C₂×C₄⋊Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
101	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
102	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
103	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
104	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	2	yes	—
105	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
106	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
108	C₂×C₄×Dic₁₂₇	C₂²	1	2	yes	complemented
109	C₂×C₄×Dic₁₂₇	C₂²	1	2	yes	complemented
110	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic
111	C₄²×D₁₂₇	C₂²	1	2	yes	complemented
112	#126×C₁₂₇	C₂²	1	2	yes	complemented
113	#125×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
114	#123×C₁₂₇	C₂²	1	2	yes	complemented
115	#121×C₁₂₇	C₂²	1	2	yes	—
116	#121×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₁₂₇	C₂²	1	2	yes	complemented
120	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
121	#117×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
124	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
125	#14523247	—	2	8	no	—
126	#14523247	—	2	4	no	—
127	C₂×Dic₂₅₄	C₂³	1	2	yes	—
128	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₅₄	C₂³	1	2	yes	—
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	1	yes	characteristic
134	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
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	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
141	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
142	C₂×C₄×D₁₂₇	—	2	4	no	—
143	C₂×C₄×D₁₂₇	—	2	4	no	—
144	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
150	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
154	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
156	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
157	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
160	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
162	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
167	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
168	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
169	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
170	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
171	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
172	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
173	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
182	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
193	C₄×Dic₁₂₇	C₂³	1	2	yes	—
194	C₄×Dic₁₂₇	C₂³	1	2	yes	—
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	1	yes	characteristic
201	C₄×Dic₁₂₇	C₂³	1	2	yes	—
202	C₄×Dic₁₂₇	C₂³	1	2	yes	—
203	C₄×Dic₁₂₇	C₂³	1	2	yes	—
204	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
206	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
208	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
211	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
225	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
226	C₄²×C₁₂₇	C₂³	1	2	yes	—
227	C₂²×D₁₂₇	—	2	2	no	—
228	C₂²×D₁₂₇	—	2	2	no	—
229	C₂²×D₁₂₇	—	2	2	no	—
230	C₂²×D₁₂₇	—	2	2	no	—
231	C₂²×D₁₂₇	—	4	1	no	—
232	C₂²×D₁₂₇	—	4	1	no	—
233	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
236	Dic₂₅₄	—	2	2	no	—
237	Dic₂₅₄	—	2	4	no	—
238	Dic₂₅₄	—	4	2	no	—
239	D₅₀₈	—	2	2	no	—
240	C₂²⋊D₁₂₇	—	2	4	no	—
241	C₂²⋊D₁₂₇	—	2	4	no	—
242	C₂²⋊D₁₂₇	—	2	2	no	—
243	C₂²⋊D₁₂₇	—	4	2	no	—
244	C₂²⋊D₁₂₇	#41	1	4	yes	complemented
245	C₂×Dic₁₂₇	—	2	4	no	—
246	C₂×Dic₁₂₇	—	2	2	no	—
247	C₂×Dic₁₂₇	—	2	2	no	—
248	C₂×Dic₁₂₇	—	2	4	no	—
249	C₂×Dic₁₂₇	—	2	4	no	—
250	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
251	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
254	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
255	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
256	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
259	C₄×D₁₂₇	—	2	2	no	—
260	C₄×D₁₂₇	—	2	2	no	—
261	C₄×D₁₂₇	—	2	4	no	—
262	C₄×D₁₂₇	—	2	2	no	—
263	C₄×D₁₂₇	—	2	2	no	—
264	C₄×D₁₂₇	—	2	2	no	—
265	C₄×D₁₂₇	—	2	2	no	—
266	C₄×D₁₂₇	—	2	2	no	—
267	C₄×D₁₂₇	—	4	2	no	—
268	C₄×D₁₂₇	—	4	1	no	—
269	C₄×D₁₂₇	#41	1	4	yes	complemented
270	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
271	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
272	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
273	D₄×C₁₂₇	—	2	2	no	—
274	D₄×C₁₂₇	—	2	4	no	—
275	D₄×C₁₂₇	—	2	2	no	—
276	D₄×C₁₂₇	—	4	2	no	—
277	C₂×C₄×C₁₂₇	—	2	2	no	—
278	C₂×C₄×C₁₂₇	—	2	2	no	—
279	C₂×C₄×C₁₂₇	—	4	2	no	—
280	C₂×C₄×C₁₂₇	—	4	2	no	—
281	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
283	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
286	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
288	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₁₂₇	—	2	1	no	—
290	C₂²×C₁₂₇	—	2	1	no	—
291	C₂²×C₁₂₇	—	2	1	no	—
292	C₂²×C₁₂₇	—	2	2	no	—
293	C₂²×C₁₂₇	—	2	2	no	—
294	C₂²×C₁₂₇	—	2	1	no	—
295	C₂²×C₁₂₇	—	2	2	no	—
296	C₂²×C₁₂₇	—	2	1	no	—
297	C₂²×C₁₂₇	C₂×#41	1	2	yes	—
298	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
299	C₂×D₁₂₇	—	2	1	no	—
300	C₂×D₁₂₇	—	2	1	no	—
301	C₂×D₁₂₇	—	2	1	no	—
302	C₂×D₁₂₇	—	2	1	no	—
303	C₂×D₁₂₇	—	2	1	no	—
304	C₂×D₁₂₇	—	2	1	no	—
305	C₂×D₁₂₇	—	2	1	no	—
306	C₂×D₁₂₇	—	4	4	no	—
307	C₂×D₁₂₇	—	4	4	no	—
308	C₂×D₁₂₇	C₂×#41	1	2	yes	—
309	C₂×D₁₂₇	C₂×#41	1	2	yes	—
310	C₄×C₁₂₇	—	2	1	no	—
311	C₄×C₁₂₇	—	2	1	no	—
312	C₄×C₁₂₇	—	2	1	no	—
313	C₄×C₁₂₇	—	2	2	no	—
314	C₄×C₁₂₇	—	2	1	no	—
315	C₄×C₁₂₇	—	2	2	no	—
316	C₄×C₁₂₇	—	2	2	no	—
317	C₄×C₁₂₇	C₂×#41	1	2	yes	—
318	Dic₁₂₇	—	2	1	no	—
319	Dic₁₂₇	—	2	1	no	—
320	Dic₁₂₇	—	2	2	no	—
321	Dic₁₂₇	—	2	2	no	—
322	Dic₁₂₇	—	2	2	no	—
323	Dic₁₂₇	—	2	2	no	—
324	Dic₁₂₇	—	2	1	no	—
325	Dic₁₂₇	C₂×#41	1	2	yes	—
326	Dic₁₂₇	C₂×#41	1	2	yes	—
327	C₂×C₁₂₇	—	2	2	no	—
328	C₂×C₁₂₇	—	4	1	no	—
329	C₂×C₁₂₇	—	4	2	no	—
330	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
331	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
332	C₂×C₁₂₇	#585	1	1	yes	characteristic
333	D₁₂₇	—	2	2	no	—
334	D₁₂₇	—	2	2	no	—
335	D₁₂₇	—	4	1	no	—
336	#3475	—	127	1	no	maximal, Sylow
337	C₁₂₇	#3475	1	1	yes	characteristic, complemented, Sylow
338	#556	—	127	1	no	—
339	#555	—	127	1	no	—
340	#554	—	127	1	no	—
341	#553	—	127	1	no	—
342	#553	D₁₂₇	1	1	yes	characteristic, complemented
343	#552	—	127	2	no	—
344	#552	—	127	1	no	—
345	#552	—	127	1	no	—
346	#551	—	127	2	no	—
347	#551	—	127	2	no	—
348	#547	—	127	1	no	—
349	#546	—	127	2	no	—
350	#533	—	127	1	no	—
351	#529	—	127	2	no	—
352	#529	—	127	2	no	—
353	#529	—	127	2	no	—
354	#525	—	127	1	no	—
355	#525	—	127	1	no	—
356	C₄×#41	—	127	2	no	—
357	C₄×#41	—	127	1	no	—
358	C₂×C₄×D₄	—	127	1	no	—
359	C₂×#117	—	127	1	no	—
360	C₂×#117	—	127	1	no	—
361	C₂×#41	—	127	1	no	—
362	C₂×#41	—	127	2	no	—
363	C₂²×D₄	—	127	1	no	—
364	C₂³×C₄	—	127	1	no	—
365	C₂³×C₄	—	127	1	no	—
366	C₄⋊Q₈	—	127	1	no	—
367	C₄⋊Q₈	—	127	1	no	—
368	#126	—	127	2	no	—
369	#126	—	127	2	no	—
370	#126	—	127	2	no	—
371	#126	—	127	2	no	—
372	#126	—	127	2	no	—
373	#126	C₂×D₁₂₇	1	2	yes	complemented
374	#125	—	127	2	no	—
375	#125	—	127	2	no	—
376	#125	—	127	2	no	—
377	#125	—	127	1	no	—
378	#125	C₂×D₁₂₇	1	1	yes	characteristic, complemented
379	#124	—	127	2	no	—
380	#124	—	127	2	no	—
381	#124	—	127	2	no	—
382	#123	—	127	2	no	—
383	#123	—	127	2	no	—
384	#123	—	127	2	no	—
385	#123	—	127	2	no	—
386	#123	—	127	2	no	—
387	#123	—	127	2	no	—
388	#123	—	127	2	no	—
389	#123	C₂×D₁₂₇	1	2	yes	complemented
390	C₂²⋊Q₈	—	127	1	no	—
391	C₂²⋊Q₈	—	127	1	no	—
392	C₂²⋊Q₈	—	127	2	no	—
393	C₂²⋊Q₈	—	127	2	no	—
394	C₂²⋊Q₈	—	127	2	no	—
395	C₂²⋊Q₈	—	127	2	no	—
396	C₂²⋊Q₈	—	127	1	no	—
397	C₂²⋊Q₈	—	127	1	no	—
398	C₂²⋊Q₈	—	127	2	no	—
399	#121	—	127	1	no	—
400	#121	—	127	1	no	—
401	#121	—	127	2	no	—
402	#121	—	127	2	no	—
403	#121	C₂×D₁₂₇	1	2	yes	—
404	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
405	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
406	#120	—	127	2	no	—
407	#120	—	127	2	no	—
408	C₄×Q₈	—	127	2	no	—
409	C₄×Q₈	—	127	1	no	—
410	C₄×Q₈	—	127	2	no	—
411	C₄×Q₈	—	127	1	no	—
412	C₄×Q₈	—	127	2	no	—
413	C₄×D₄	—	127	1	no	—
414	C₄×D₄	—	127	2	no	—
415	C₄×D₄	—	127	1	no	—
416	C₄×D₄	—	127	2	no	—
417	C₄×D₄	—	127	1	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	1	no	—
424	C₄×D₄	—	127	1	no	—
425	C₄×D₄	—	127	2	no	—
426	C₄×D₄	—	127	2	no	—
427	C₄×D₄	—	127	2	no	—
428	C₄×D₄	—	127	1	no	—
429	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
430	C₄×D₄	C₂×D₁₂₇	1	2	yes	complemented
431	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
432	#117	—	127	1	no	—
433	#117	—	127	1	no	—
434	#117	—	127	1	no	—
435	#117	—	127	1	no	—
436	#117	—	127	2	no	—
437	#117	—	127	2	no	—
438	#117	—	127	1	no	—
439	#117	—	127	1	no	—
440	#117	—	127	2	no	—
441	#117	—	127	2	no	—
442	#117	—	127	2	no	—
443	#117	—	127	2	no	—
444	#117	—	127	2	no	—
445	#117	—	127	2	no	—
446	#117	C₂×D₁₂₇	1	1	yes	characteristic, complemented
447	C₂×C₄⋊C₄	—	127	1	no	—
448	C₂×C₄⋊C₄	—	127	1	no	—
449	C₂×C₄⋊C₄	—	127	1	no	—
450	C₂×C₄⋊C₄	—	127	1	no	—
451	C₂×C₄⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
452	C₂×C₂²⋊C₄	—	127	2	no	—
453	C₂×C₂²⋊C₄	—	127	2	no	—
454	C₂×C₂²⋊C₄	—	127	1	no	—
455	C₂×C₂²⋊C₄	—	127	1	no	—
456	C₂×C₄²	—	127	2	no	—
457	C₂×C₄²	—	127	2	no	—
458	C₂×C₄²	—	127	2	no	—
459	C₂×C₄²	—	127	1	no	—
460	C₂⁴	—	127	1	no	—
461	C₂⁴	—	127	1	no	—
462	#41	—	254	4	no	—
463	#41	—	254	8	no	—
464	C₂×Q₈	—	127	2	no	—
465	C₂×Q₈	—	127	1	no	—
466	C₂×Q₈	—	127	2	no	—
467	C₂×D₄	—	127	1	no	—
468	C₂×D₄	—	127	2	no	—
469	C₂×D₄	—	127	2	no	—
470	C₂×D₄	—	127	2	no	—
471	C₂×D₄	—	127	1	no	—
472	C₂×D₄	—	127	1	no	—
473	C₂×D₄	—	254	4	no	—
474	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
475	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
476	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
477	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
478	C₂²×C₄	—	127	1	no	—
479	C₂²×C₄	—	127	1	no	—
480	C₂²×C₄	—	127	2	no	—
481	C₂²×C₄	—	127	2	no	—
482	C₂²×C₄	—	127	2	no	—
483	C₂²×C₄	—	127	1	no	—
484	C₂²×C₄	—	127	1	no	—
485	C₂²×C₄	—	127	2	no	—
486	C₂²×C₄	—	127	1	no	—
487	C₂²×C₄	—	127	2	no	—
488	C₂²×C₄	—	127	1	no	—
489	C₂²×C₄	—	127	1	no	—
490	C₂²×C₄	—	127	1	no	—
491	C₂²×C₄	—	127	1	no	—
492	C₂²×C₄	—	127	1	no	—
493	C₂²×C₄	—	127	1	no	—
494	C₂²×C₄	—	254	4	no	—
495	C₂²×C₄	—	254	4	no	—
496	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
497	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
498	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
499	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
500	C₄⋊C₄	—	127	1	no	—
501	C₄⋊C₄	—	127	2	no	—
502	C₄⋊C₄	—	127	2	no	—
503	C₄⋊C₄	—	127	1	no	—
504	C₄⋊C₄	—	127	2	no	—
505	C₄⋊C₄	—	127	2	no	—
506	C₄⋊C₄	—	127	2	no	—
507	C₄⋊C₄	—	127	2	no	—
508	C₄⋊C₄	—	127	2	no	—
509	C₄⋊C₄	—	127	2	no	—
510	C₄⋊C₄	—	127	2	no	—
511	C₄⋊C₄	—	127	2	no	—
512	C₄⋊C₄	—	127	1	no	—
513	C₄⋊C₄	—	127	1	no	—
514	C₄⋊C₄	—	127	1	no	—
515	C₄⋊C₄	—	127	2	no	—
516	C₄⋊C₄	—	127	1	no	—
517	C₄⋊C₄	—	127	2	no	—
518	C₄⋊C₄	—	127	2	no	—
519	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
524	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
525	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
526	C₂²⋊C₄	—	127	2	no	—
527	C₂²⋊C₄	—	127	1	no	—
528	C₂²⋊C₄	—	127	1	no	—
529	C₂²⋊C₄	—	127	2	no	—
530	C₂²⋊C₄	—	127	2	no	—
531	C₂²⋊C₄	—	127	2	no	—
532	C₂²⋊C₄	—	127	2	no	—
533	C₂²⋊C₄	—	127	2	no	—
534	C₂²⋊C₄	—	127	2	no	—
535	C₂²⋊C₄	—	127	1	no	—
536	C₂²⋊C₄	—	127	2	no	—
537	C₂²⋊C₄	—	127	2	no	—
538	C₂²⋊C₄	—	127	2	no	—
539	C₂²⋊C₄	—	127	2	no	—
540	C₂²⋊C₄	—	127	1	no	—
541	C₂²⋊C₄	—	127	1	no	—
542	C₂²⋊C₄	—	127	1	no	—
543	C₂²⋊C₄	—	127	2	no	—
544	C₂²⋊C₄	—	127	2	no	—
545	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
546	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
548	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
549	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
551	C₄²	—	127	2	no	—
552	C₄²	—	127	1	no	—
553	C₄²	—	127	2	no	—
554	C₄²	—	127	2	no	—
555	C₄²	—	127	1	no	—
556	C₄²	—	127	2	no	—
557	C₄²	—	127	2	no	—
558	C₄²	—	127	2	no	—
559	C₄²	—	127	2	no	—
560	C₄²	—	127	1	no	—
561	C₄²	—	127	2	no	—
562	C₄²	C₂²×D₁₂₇	1	2	yes	—
563	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
564	C₂³	—	127	1	no	—
565	C₂³	—	127	1	no	—
566	C₂³	—	127	1	no	—
567	C₂³	—	508	1	no	—
568	C₂³	—	508	1	no	—
569	C₂³	—	254	2	no	—
570	C₂³	—	254	2	no	—
571	C₂³	—	254	2	no	—
572	C₂³	—	254	2	no	—
573	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
574	C₂³	C₂³×D₁₂₇	1	2	yes	—
575	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
576	Q₈	—	508	2	no	—
577	Q₈	—	254	4	no	—
578	Q₈	—	254	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	4	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	127	4	no	—
584	D₄	—	508	2	no	—
585	D₄	—	254	2	no	—
586	D₄	—	254	2	no	—
587	D₄	—	254	4	no	—
588	D₄	—	254	4	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	127	1	no	—
594	C₂×C₄	—	127	1	no	—
595	C₂×C₄	—	127	4	no	—
596	C₂×C₄	—	127	2	no	—
597	C₂×C₄	—	127	1	no	—
598	C₂×C₄	—	127	1	no	—
599	C₂×C₄	—	127	2	no	—
600	C₂×C₄	—	127	2	no	—
601	C₂×C₄	—	127	2	no	—
602	C₂×C₄	—	127	1	no	—
603	C₂×C₄	—	508	2	no	—
604	C₂×C₄	—	508	1	no	—
605	C₂×C₄	—	254	2	no	—
606	C₂×C₄	—	254	2	no	—
607	C₂×C₄	—	254	2	no	—
608	C₂×C₄	—	254	2	no	—
609	C₂×C₄	—	254	2	no	—
610	C₂×C₄	—	254	4	no	—
611	C₂×C₄	—	254	2	no	—
612	C₂×C₄	—	254	2	no	—
613	C₂×C₄	—	254	4	no	—
614	C₂×C₄	—	254	4	no	—
615	C₂×C₄	—	254	4	no	—
616	C₂×C₄	—	254	2	no	—
617	C₂×C₄	—	254	2	no	—
618	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
619	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
622	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
623	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	127	2	no	—
635	C₂²	—	127	2	no	—
636	C₂²	—	508	4	no	—
637	C₂²	—	508	4	no	—
638	C₂²	—	254	1	no	—
639	C₂²	—	254	1	no	—
640	C₂²	—	254	1	no	—
641	C₂²	—	254	1	no	—
642	C₂²	—	254	1	no	—
643	C₂²	—	254	1	no	—
644	C₂²	—	254	1	no	—
645	C₂²	#41×D₁₂₇	1	2	yes	—
646	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	127	2	no	—
655	C₄	—	127	2	no	—
656	C₄	—	254	2	no	—
657	C₄	—	254	1	no	—
658	C₄	—	254	1	no	—
659	C₄	—	254	2	no	—
660	C₄	—	254	2	no	—
661	C₄	—	254	2	no	—
662	C₄	—	254	1	no	—
663	C₄	#41×D₁₂₇	1	2	yes	—
664	C₂	—	2	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	2	no	—
667	C₂	—	508	1	no	—
668	C₂	—	254	2	no	—
669	C₂	—	254	2	no	—
670	C₂	C₂×#41×D₁₂₇	1	1	yes	characteristic
671	C₂	C₂×#41×D₁₂₇	1	1	yes	characteristic
672	C₂	#22550711	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Fitting	#553×C₁₂₇	C₂
hypercenter	#553	D₁₂₇
hypocenter	C₁₂₇	#3475
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #22550594	C₂	semidirect
2. #22550590	C₂	semidirect
3. #22550581	C₂	semidirect
4. #22550576	C₂	semidirect
5. #22550566	C₂	semidirect
6. #22550564	C₂	semidirect
7. #22550562	C₂	semidirect
8. #22550555	C₂	semidirect
9. #22550554	C₂	semidirect
10. #22550526	C₂	semidirect
11. #22550515	C₂	semidirect
12. #22550432	C₂	semidirect
13. #22550409	C₂	semidirect
14. #22550407	C₂	semidirect
15. #22550403	C₂	semidirect
16. #22550386	C₂	semidirect
17. #22550386	C₂	semidirect
18. C₄×#14523247	C₂	semidirect
19. C₄×#14523247	C₂	semidirect
20. C₄×D₄×D₁₂₇	C₂	semidirect
21. C₂×#16861167	C₂	semidirect
22. #117×D₁₂₇	C₂	semidirect
23. #553×C₁₂₇	C₂	semidirect
29. #16861208	C₂²	semidirect
30. #16861208	C₂²	semidirect
31. #16861204	C₂²	semidirect
32. #16861203	C₂²	semidirect
33. #16861202	C₂²	semidirect
34. #16861202	C₂²	semidirect
35. #16861202	C₂²	semidirect
36. #16861201	C₂²	semidirect
37. #16861200	C₂²	semidirect
38. #16861199	C₂²	semidirect
39. #16861199	C₂²	semidirect
40. #16861196	C₂²	semidirect
42. #16861195	C₂²	semidirect
44. #16861192	C₂²	semidirect
47. #16861191	C₂²	semidirect
49. #16861190	C₂²	semidirect
50. #16861189	C₂²	semidirect
51. #16861189	C₂²	semidirect
52. #16861188	C₂²	semidirect
53. #16861188	C₂²	semidirect
54. #16861188	C₂²	semidirect
57. #16861187	C₂²	semidirect
58. #16861186	C₂²	semidirect
61. #16861180	C₂²	semidirect
62. #16861180	C₂²	semidirect
65. C₄×Dic₂₅₄	C₂²	semidirect
66. C₄×Dic₂₅₄	C₂²	semidirect
67. #16861174	C₂²	semidirect
68. #16861174	C₂²	semidirect
69. #16861174	C₂²	semidirect
72. D₄×Dic₁₂₇	C₂²	semidirect
73. D₄×Dic₁₂₇	C₂²	semidirect
74. D₄×Dic₁₂₇	C₂²	semidirect
80. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
84. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
85. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
86. #16861168	C₂²	semidirect
91. #16861167	C₂²	semidirect
92. #16861167	C₂²	semidirect
93. #16861167	C₂²	semidirect
94. #16861167	C₂²	semidirect
96. #16861165	C₂²	semidirect
97. #16861165	C₂²	semidirect
98. #16861165	C₂²	semidirect
99. #16861165	C₂²	semidirect
100. C₂×C₄⋊Dic₁₂₇	C₂²	semidirect
102. C₄⋊C₄×D₁₂₇	C₂²	semidirect
103. C₄⋊C₄×D₁₂₇	C₂²	semidirect
108. C₂×C₄×Dic₁₂₇	C₂²	semidirect
109. C₂×C₄×Dic₁₂₇	C₂²	semidirect
111. C₄²×D₁₂₇	C₂²	semidirect
112. #126×C₁₂₇	C₂²	semidirect
113. #125×C₁₂₇	C₂²	semidirect
114. #123×C₁₂₇	C₂²	semidirect
116. #121×C₁₂₇	C₂²	semidirect
117. #121×C₁₂₇	C₂²	semidirect
119. C₄×D₄×C₁₂₇	C₂²	semidirect
120. C₄×D₄×C₁₂₇	C₂²	semidirect
121. #117×C₁₂₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₂₇	C₂²	semidirect
244. C₂²⋊D₁₂₇	#41	semidirect
269. C₄×D₁₂₇	#41	semidirect
337. C₁₂₇	#3475	semidirect
342. #553	D₁₂₇	semidirect
373. #126	C₂×D₁₂₇	semidirect
378. #125	C₂×D₁₂₇	semidirect
389. #123	C₂×D₁₂₇	semidirect
404. #121	C₂×D₁₂₇	semidirect
405. #121	C₂×D₁₂₇	semidirect
430. C₄×D₄	C₂×D₁₂₇	semidirect
431. C₄×D₄	C₂×D₁₂₇	semidirect
446. #117	C₂×D₁₂₇	semidirect
451. C₂×C₄⋊C₄	C₂×D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
#22550594	2
#22550590	2
#22550581	2
#22550576	2
#22550566	2
#22550564	2
#22550562	2
#22550555	2
#22550554	2
#22550526	2
#22550515	2
#22550432	2
#22550409	2
#22550407	2
#22550403	2
#22550386	2
C₄×#14523247	2
C₄×D₄×D₁₂₇	2
C₂×#16861167	2
#117×D₁₂₇	2
#553×C₁₂₇	2
#3475	127