Subgroups — #30652783

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	#22550596	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550595	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550583	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550578	C₂	1	2	yes	maximal, complemented
5	#22550573	C₂	1	1	yes	maximal, characteristic, complemented
6	#22550563	C₂	1	2	yes	maximal, complemented
7	#22550560	C₂	1	1	yes	maximal, characteristic, complemented
8	#22550557	C₂	1	2	yes	maximal, complemented
9	#22550552	C₂	1	2	yes	maximal, complemented
10	#22550525	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550520	C₂	1	1	yes	maximal, characteristic, complemented
12	#22550495	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550486	C₂	1	1	yes	maximal, characteristic, complemented
14	#22550471	C₂	1	2	yes	maximal, complemented
15	#22550461	C₂	1	2	yes	maximal, complemented
16	#22550407	C₂	1	1	yes	maximal, characteristic, complemented
17	#22550406	C₂	1	1	yes	maximal, characteristic, complemented
18	#22550403	C₂	1	2	yes	maximal, complemented
19	C₂×#16861202	C₂	1	2	yes	maximal, complemented
20	#22550355	C₂	1	1	yes	maximal, characteristic, complemented
21	#22550351	C₂	1	1	yes	maximal, characteristic, complemented
22	#41×Dic₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14523247	C₂²	1	1	yes	characteristic
25	#16861209	C₂²	1	1	yes	characteristic, complemented
26	#16861207	C₂²	1	1	yes	characteristic, complemented
27	#16861204	C₂²	1	1	yes	characteristic, complemented
28	#16861202	C₂²	1	2	yes	—
29	#16861202	C₂²	1	2	yes	—
30	#16861202	C₂²	1	2	yes	—
31	#16861202	C₂²	1	1	yes	characteristic
32	#16861202	C₂²	1	2	yes	—
33	#16861202	C₂²	1	2	yes	complemented
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	2	yes	complemented
39	#16861200	C₂²	1	1	yes	characteristic, complemented
40	#16861200	C₂²	1	2	yes	complemented
41	#16861200	C₂²	1	1	yes	characteristic, complemented
42	#16861199	C₂²	1	2	yes	complemented
43	#16861199	C₂²	1	1	yes	characteristic, complemented
44	#16861199	C₂²	1	2	yes	complemented
45	#16861196	C₂²	1	2	yes	—
46	#16861196	C₂²	1	1	yes	characteristic
47	#16861195	C₂²	1	1	yes	characteristic
48	#16861195	C₂²	1	2	yes	complemented
49	#16861193	C₂²	1	2	yes	complemented
50	#16861193	C₂²	1	1	yes	characteristic, complemented
51	#16861192	C₂²	1	2	yes	complemented
52	#16861191	C₂²	1	2	yes	—
53	#16861190	C₂²	1	1	yes	characteristic
54	#16861190	C₂²	1	2	yes	—
55	#16861190	C₂²	1	2	yes	complemented
56	#16861190	C₂²	1	2	yes	complemented
57	#16861190	C₂²	1	2	yes	complemented
58	#16861188	C₂²	1	1	yes	characteristic
59	#16861188	C₂²	1	2	yes	complemented
60	#16861188	C₂²	1	1	yes	characteristic, complemented
61	#16861186	C₂²	1	2	yes	complemented
62	#16861186	C₂²	1	2	yes	complemented
63	#16861186	C₂²	1	2	yes	complemented
64	#16861186	C₂²	1	2	yes	complemented
65	#16861186	C₂²	1	1	yes	characteristic, complemented
66	#16861185	C₂²	1	1	yes	characteristic, complemented
67	#16861181	C₂²	1	2	yes	—
68	#16861181	C₂²	1	1	yes	characteristic
69	#16861181	C₂²	1	2	yes	complemented
70	#16861180	C₂²	1	1	yes	characteristic
71	#16861180	C₂²	1	2	yes	complemented
72	#16861178	C₂²	1	2	yes	—
73	Q₈×Dic₁₂₇	C₂²	1	1	yes	characteristic, 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	#16861174	C₂²	1	2	yes	complemented
78	#16861174	C₂²	1	1	yes	characteristic, complemented
79	D₄×Dic₁₂₇	C₂²	1	2	yes	—
80	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
81	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
82	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
83	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
84	D₄×Dic₁₂₇	C₂²	1	2	yes	—
85	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
86	D₄×Dic₁₂₇	C₂²	1	2	yes	complemented
87	D₄×Dic₁₂₇	C₂²	1	2	yes	complemented
88	D₄×Dic₁₂₇	C₂²	1	2	yes	complemented
89	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
92	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
93	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
94	#16861168	C₂²	1	1	yes	characteristic
95	#16861168	C₂²	1	1	yes	characteristic
96	#16861168	C₂²	1	2	yes	complemented
97	#16861168	C₂²	1	1	yes	characteristic, complemented
98	#16861167	C₂²	1	2	yes	complemented
99	#16861166	C₂²	1	1	yes	characteristic, complemented
100	#16861165	C₂²	1	2	yes	complemented
101	#16861165	C₂²	1	2	yes	complemented
102	#16861165	C₂²	1	2	yes	complemented
103	C₂×C₄⋊Dic₁₂₇	C₂²	1	2	yes	complemented
104	C₂×Dic₁₂₇⋊C₄	C₂²	1	2	yes	complemented
105	C₂×Dic₁₂₇⋊C₄	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₂²⋊Dic₁₂₇	C₂²	1	2	yes	—
108	C₂×C₂²⋊Dic₁₂₇	C₂²	1	2	yes	—
109	C₂×C₂²⋊Dic₁₂₇	C₂²	1	2	yes	—
110	C₂×C₄×Dic₁₂₇	C₂²	1	2	yes	complemented
111	C₂×C₄×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₁₂₇	C₂²	1	1	yes	characteristic
113	C₂²×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
114	#124×C₁₂₇	C₂²	1	1	yes	characteristic
115	#123×C₁₂₇	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic
117	#121×C₁₂₇	C₂²	1	1	yes	characteristic
118	#121×C₁₂₇	C₂²	1	2	yes	—
119	#120×C₁₂₇	C₂²	1	2	yes	—
120	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₁₂₇	C₂²	1	2	yes	—
123	#14523247	—	2	4	no	—
124	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
125	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
126	C₂×Dic₂₅₄	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
131	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
132	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
133	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
134	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
135	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
136	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
137	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
138	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
139	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
141	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
143	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
144	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
145	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
146	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
147	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
149	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
152	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
153	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
154	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
155	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
156	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
157	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
158	Dic₁₂₇⋊C₄	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	2	yes	—
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	2	yes	—
168	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
169	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
170	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
171	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
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	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
184	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
189	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
190	C₄×Dic₁₂₇	C₂³	1	2	yes	—
191	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
192	C₄×Dic₁₂₇	C₂³	1	2	yes	—
193	C₄×Dic₁₂₇	C₂³	1	2	yes	—
194	C₄×Dic₁₂₇	C₂³	1	2	yes	—
195	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₂₇	C₂³	1	2	yes	—
198	C₄×Dic₁₂₇	C₂³	1	2	yes	—
199	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
200	C₂⁴×C₁₂₇	C₂³	1	2	yes	—
201	#41×C₁₂₇	—	2	4	no	—
202	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
203	C₂×D₄×C₁₂₇	—	2	4	no	—
204	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
205	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
206	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
209	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
213	C₂²×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	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	2	yes	—
222	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
224	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
225	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
226	Dic₂₅₄	—	2	2	no	—
227	Dic₂₅₄	—	4	1	no	—
228	Dic₂₅₄	—	4	2	no	—
229	C₂²⋊D₁₂₇	—	2	4	no	—
230	C₂²⋊D₁₂₇	—	4	1	no	—
231	C₂²⋊D₁₂₇	—	4	1	no	—
232	C₂²⋊D₁₂₇	—	4	2	no	—
233	C₂×Dic₁₂₇	—	2	4	no	—
234	C₂×Dic₁₂₇	—	4	2	no	—
235	C₂×Dic₁₂₇	—	4	2	no	—
236	C₂×Dic₁₂₇	—	4	1	no	—
237	C₂×Dic₁₂₇	—	4	2	no	—
238	C₂×Dic₁₂₇	—	4	2	no	—
239	C₂×Dic₁₂₇	—	4	1	no	—
240	C₂×Dic₁₂₇	—	4	2	no	—
241	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
242	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
243	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
245	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
246	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
248	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
250	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
252	C₄×D₁₂₇	—	2	2	no	—
253	C₄×D₁₂₇	—	4	2	no	—
254	C₂³×C₁₂₇	—	2	4	no	—
255	C₂³×C₁₂₇	—	4	2	no	—
256	C₂³×C₁₂₇	—	4	2	no	—
257	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
258	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
259	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
260	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
261	Q₈×C₁₂₇	—	2	2	no	—
262	D₄×C₁₂₇	—	2	4	no	—
263	D₄×C₁₂₇	—	2	4	no	—
264	D₄×C₁₂₇	—	2	2	no	—
265	D₄×C₁₂₇	—	4	2	no	—
266	D₄×C₁₂₇	—	4	1	no	—
267	D₄×C₁₂₇	#41	1	4	yes	—
268	C₂×C₄×C₁₂₇	—	2	4	no	—
269	C₂×C₄×C₁₂₇	—	2	2	no	—
270	C₂×C₄×C₁₂₇	—	2	2	no	—
271	C₂×C₄×C₁₂₇	—	4	2	no	—
272	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
275	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
277	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₁₂₇	—	2	2	no	—
280	C₂²×C₁₂₇	—	2	2	no	—
281	C₂²×C₁₂₇	—	2	1	no	—
282	C₂²×C₁₂₇	—	2	1	no	—
283	C₂²×C₁₂₇	—	2	2	no	—
284	C₂²×C₁₂₇	—	2	1	no	—
285	C₂²×C₁₂₇	—	2	1	no	—
286	C₂²×C₁₂₇	—	2	2	no	—
287	C₂²×C₁₂₇	—	2	1	no	—
288	C₂²×C₁₂₇	—	2	1	no	—
289	C₂²×C₁₂₇	—	2	2	no	—
290	C₂²×C₁₂₇	—	8	4	no	—
291	C₂²×C₁₂₇	C₂×#41	1	4	yes	—
292	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
293	C₂×D₁₂₇	—	2	1	no	—
294	C₂×D₁₂₇	—	2	1	no	—
295	C₂×D₁₂₇	—	2	1	no	—
296	C₄×C₁₂₇	—	2	1	no	—
297	C₄×C₁₂₇	—	2	1	no	—
298	C₄×C₁₂₇	—	2	2	no	—
299	C₄×C₁₂₇	—	2	1	no	—
300	C₄×C₁₂₇	—	2	2	no	—
301	C₄×C₁₂₇	—	2	1	no	—
302	C₄×C₁₂₇	C₂×#41	1	2	yes	—
303	Dic₁₂₇	—	2	1	no	—
304	Dic₁₂₇	—	2	2	no	—
305	Dic₁₂₇	—	2	2	no	—
306	Dic₁₂₇	—	2	1	no	—
307	Dic₁₂₇	—	2	1	no	—
308	Dic₁₂₇	—	2	1	no	—
309	Dic₁₂₇	—	2	1	no	—
310	Dic₁₂₇	—	2	1	no	—
311	Dic₁₂₇	—	2	2	no	—
312	Dic₁₂₇	—	2	1	no	—
313	Dic₁₂₇	—	2	2	no	—
314	C₂×C₁₂₇	—	2	4	no	—
315	C₂×C₁₂₇	—	4	1	no	—
316	C₂×C₁₂₇	—	4	2	no	—
317	C₂×C₁₂₇	—	4	1	no	—
318	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
319	C₂×C₁₂₇	#585	1	1	yes	characteristic
320	C₂×C₁₂₇	#585	1	1	yes	characteristic
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	1	no	—
328	#553	—	127	2	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	D₁₂₇	1	1	yes	characteristic, complemented
336	#542	—	127	1	no	—
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	C₂×D₁₂₇	1	1	yes	characteristic
349	C₂²×D₄	C₂×D₁₂₇	1	1	yes	characteristic
350	C₄⋊Q₈	—	127	1	no	—
351	C₄⋊Q₈	—	127	1	no	—
352	#126	—	127	1	no	—
353	#126	—	127	1	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	2	no	—
361	#126	—	127	2	no	—
362	#126	—	127	2	no	—
363	#126	—	127	2	no	—
364	#125	—	127	2	no	—
365	#125	—	127	1	no	—
366	#125	—	127	2	no	—
367	#125	—	127	1	no	—
368	#125	—	127	2	no	—
369	#125	—	127	1	no	—
370	#124	—	127	1	no	—
371	#124	—	127	2	no	—
372	#124	—	127	1	no	—
373	#124	—	127	2	no	—
374	#124	C₂×D₁₂₇	1	1	yes	characteristic
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	2	no	—
382	#123	—	127	1	no	—
383	#123	—	127	2	no	—
384	#123	C₂×D₁₂₇	1	2	yes	—
385	C₂²⋊Q₈	—	127	1	no	—
386	C₂²⋊Q₈	—	127	1	no	—
387	C₂²⋊Q₈	—	127	1	no	—
388	C₂²⋊Q₈	—	127	2	no	—
389	C₂²⋊Q₈	—	127	1	no	—
390	C₂²⋊Q₈	—	127	2	no	—
391	C₂²⋊Q₈	—	127	2	no	—
392	C₂²⋊Q₈	—	127	2	no	—
393	C₂²⋊Q₈	—	127	2	no	—
394	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic
395	#121	—	127	1	no	—
396	#121	—	127	2	no	—
397	#121	—	127	2	no	—
398	#121	—	127	2	no	—
399	#121	—	127	1	no	—
400	#121	C₂×D₁₂₇	1	1	yes	characteristic
401	#121	C₂×D₁₂₇	1	2	yes	—
402	#120	—	127	2	no	—
403	#120	C₂×D₁₂₇	1	2	yes	—
404	C₄×Q₈	—	127	1	no	—
405	C₄×Q₈	—	127	1	no	—
406	C₄×Q₈	—	127	1	no	—
407	C₄×Q₈	—	127	2	no	—
408	C₄×Q₈	—	127	1	no	—
409	C₄×Q₈	—	127	1	no	—
410	C₄×D₄	—	127	1	no	—
411	C₄×D₄	—	127	2	no	—
412	C₄×D₄	—	127	1	no	—
413	C₄×D₄	—	127	2	no	—
414	C₄×D₄	—	127	2	no	—
415	C₄×D₄	—	127	1	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	1	no	—
422	C₄×D₄	—	127	1	no	—
423	C₄×D₄	—	127	2	no	—
424	C₄×D₄	—	127	2	no	—
425	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
426	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
427	#117	—	127	2	no	—
428	#117	—	127	1	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	2	no	—
435	#117	—	127	1	no	—
436	C₂×C₄⋊C₄	—	127	2	no	—
437	C₂×C₄⋊C₄	—	127	2	no	—
438	C₂×C₄⋊C₄	—	127	2	no	—
439	C₂×C₄⋊C₄	—	127	1	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	C₂×D₁₂₇	1	2	yes	—
444	C₂×C₄²	—	127	2	no	—
445	C₂×C₄²	—	127	1	no	—
446	C₂⁴	C₂²×D₁₂₇	1	2	yes	—
447	#41	—	2	4	no	—
448	#41	—	254	4	no	—
449	C₂×Q₈	—	127	1	no	—
450	C₂×Q₈	—	127	2	no	—
451	C₂×Q₈	—	127	1	no	—
452	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	127	1	no	—
455	C₂×D₄	—	127	2	no	—
456	C₂×D₄	—	127	1	no	—
457	C₂×D₄	—	127	2	no	—
458	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
459	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
460	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
461	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
462	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
463	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
464	C₂²×C₄	—	127	2	no	—
465	C₂²×C₄	—	127	2	no	—
466	C₂²×C₄	—	127	1	no	—
467	C₂²×C₄	—	127	1	no	—
468	C₂²×C₄	—	127	2	no	—
469	C₂²×C₄	—	127	2	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	C₂²×D₁₂₇	1	2	yes	—
475	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
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	1	no	—
481	C₄⋊C₄	—	127	2	no	—
482	C₄⋊C₄	—	127	2	no	—
483	C₄⋊C₄	—	127	2	no	—
484	C₄⋊C₄	—	127	2	no	—
485	C₄⋊C₄	—	127	2	no	—
486	C₄⋊C₄	—	127	1	no	—
487	C₄⋊C₄	—	127	1	no	—
488	C₄⋊C₄	—	127	2	no	—
489	C₄⋊C₄	—	127	2	no	—
490	C₄⋊C₄	—	127	2	no	—
491	C₄⋊C₄	—	127	1	no	—
492	C₄⋊C₄	—	127	1	no	—
493	C₄⋊C₄	—	127	2	no	—
494	C₄⋊C₄	—	127	1	no	—
495	C₄⋊C₄	—	127	1	no	—
496	C₄⋊C₄	—	127	2	no	—
497	C₄⋊C₄	—	127	2	no	—
498	C₄⋊C₄	—	127	2	no	—
499	C₄⋊C₄	—	127	1	no	—
500	C₄⋊C₄	—	127	1	no	—
501	C₄⋊C₄	—	127	1	no	—
502	C₄⋊C₄	—	127	1	no	—
503	C₄⋊C₄	—	127	2	no	—
504	C₄⋊C₄	—	127	2	no	—
505	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
507	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
508	C₂²⋊C₄	—	127	1	no	—
509	C₂²⋊C₄	—	127	1	no	—
510	C₂²⋊C₄	—	127	2	no	—
511	C₂²⋊C₄	—	127	1	no	—
512	C₂²⋊C₄	—	127	2	no	—
513	C₂²⋊C₄	—	127	2	no	—
514	C₂²⋊C₄	—	127	2	no	—
515	C₂²⋊C₄	—	127	2	no	—
516	C₂²⋊C₄	—	127	2	no	—
517	C₂²⋊C₄	—	127	2	no	—
518	C₂²⋊C₄	—	127	2	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	1	no	—
524	C₂²⋊C₄	—	127	1	no	—
525	C₂²⋊C₄	—	127	1	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	1	yes	characteristic
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	2	yes	—
535	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
536	C₄²	—	127	1	no	—
537	C₄²	—	127	1	no	—
538	C₄²	—	127	1	no	—
539	C₄²	—	127	2	no	—
540	C₄²	—	127	2	no	—
541	C₄²	—	127	1	no	—
542	C₄²	—	127	2	no	—
543	C₄²	—	127	2	no	—
544	C₄²	—	127	2	no	—
545	C₄²	—	127	2	no	—
546	C₄²	—	127	1	no	—
547	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
548	C₂³	—	2	4	no	—
549	C₂³	—	4	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	127	1	no	—
552	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
553	C₂³	C₂³×D₁₂₇	1	2	yes	—
554	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
555	C₂³	C₂³×D₁₂₇	1	2	yes	—
556	Q₈	—	2	2	no	—
557	Q₈	—	508	1	no	—
558	Q₈	—	508	2	no	—
559	Q₈	—	254	2	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	2	no	—
563	D₄	—	4	2	no	—
564	D₄	—	4	1	no	—
565	D₄	—	508	1	no	—
566	D₄	—	508	1	no	—
567	D₄	—	508	2	no	—
568	D₄	—	254	4	no	—
569	D₄	#14523247	1	4	yes	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	127	1	no	—
575	C₂×C₄	—	127	2	no	—
576	C₂×C₄	—	127	1	no	—
577	C₂×C₄	—	127	1	no	—
578	C₂×C₄	—	127	2	no	—
579	C₂×C₄	—	127	1	no	—
580	C₂×C₄	—	127	2	no	—
581	C₂×C₄	—	127	1	no	—
582	C₂×C₄	—	127	2	no	—
583	C₂×C₄	—	127	1	no	—
584	C₂×C₄	—	127	1	no	—
585	C₂×C₄	—	508	2	no	—
586	C₂×C₄	—	508	2	no	—
587	C₂×C₄	—	508	2	no	—
588	C₂×C₄	—	508	1	no	—
589	C₂×C₄	—	508	1	no	—
590	C₂×C₄	—	508	2	no	—
591	C₂×C₄	—	508	2	no	—
592	C₂×C₄	—	508	2	no	—
593	C₂×C₄	—	254	4	no	—
594	C₂×C₄	—	254	2	no	—
595	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
598	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
600	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	8	4	no	—
614	C₂²	—	254	1	no	—
615	C₂²	—	254	1	no	—
616	C₂²	—	254	1	no	—
617	C₂²	C₂×#14523247	1	4	yes	—
618	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	254	1	no	—
626	C₄	—	254	2	no	—
627	C₄	—	254	2	no	—
628	C₄	—	254	1	no	—
629	C₄	—	254	1	no	—
630	C₄	—	254	1	no	—
631	C₄	—	254	1	no	—
632	C₄	—	254	1	no	—
633	C₄	—	254	1	no	—
634	C₄	—	254	2	no	—
635	C₄	—	254	2	no	—
636	C₄	C₂×#14523247	1	2	yes	—
637	C₂	—	2	4	no	—
638	C₂	—	4	1	no	—
639	C₂	—	4	2	no	—
640	C₂	—	4	1	no	—
641	C₂	—	508	1	no	—
642	C₂	C₂²×#14523247	1	1	yes	characteristic
643	C₂	#22550711	1	1	yes	characteristic
644	C₂	#22550712	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Fitting	#546×C₁₂₇	C₂
hypercenter	#546	D₁₂₇
hypocenter	C₁₂₇	#3521
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #22550596	C₂	semidirect
2. #22550595	C₂	semidirect
3. #22550583	C₂	semidirect
4. #22550578	C₂	semidirect
5. #22550573	C₂	semidirect
6. #22550563	C₂	semidirect
7. #22550560	C₂	semidirect
8. #22550557	C₂	semidirect
9. #22550552	C₂	semidirect
10. #22550525	C₂	semidirect
11. #22550520	C₂	semidirect
12. #22550495	C₂	semidirect
13. #22550486	C₂	semidirect
14. #22550471	C₂	semidirect
15. #22550461	C₂	semidirect
16. #22550407	C₂	semidirect
17. #22550406	C₂	semidirect
18. #22550403	C₂	semidirect
19. C₂×#16861202	C₂	semidirect
20. #22550355	C₂	semidirect
21. #22550351	C₂	semidirect
22. #41×Dic₁₂₇	C₂	semidirect
23. #546×C₁₂₇	C₂	semidirect
25. #16861209	C₂²	semidirect
26. #16861207	C₂²	semidirect
27. #16861204	C₂²	semidirect
33. #16861202	C₂²	semidirect
34. #16861202	C₂²	semidirect
35. #16861202	C₂²	semidirect
36. #16861202	C₂²	semidirect
37. #16861202	C₂²	semidirect
38. #16861202	C₂²	semidirect
39. #16861200	C₂²	semidirect
40. #16861200	C₂²	semidirect
41. #16861200	C₂²	semidirect
42. #16861199	C₂²	semidirect
43. #16861199	C₂²	semidirect
44. #16861199	C₂²	semidirect
48. #16861195	C₂²	semidirect
49. #16861193	C₂²	semidirect
50. #16861193	C₂²	semidirect
51. #16861192	C₂²	semidirect
55. #16861190	C₂²	semidirect
56. #16861190	C₂²	semidirect
57. #16861190	C₂²	semidirect
59. #16861188	C₂²	semidirect
60. #16861188	C₂²	semidirect
61. #16861186	C₂²	semidirect
62. #16861186	C₂²	semidirect
63. #16861186	C₂²	semidirect
64. #16861186	C₂²	semidirect
65. #16861186	C₂²	semidirect
66. #16861185	C₂²	semidirect
69. #16861181	C₂²	semidirect
71. #16861180	C₂²	semidirect
73. Q₈×Dic₁₂₇	C₂²	semidirect
74. Q₈×Dic₁₂₇	C₂²	semidirect
75. C₄×Dic₂₅₄	C₂²	semidirect
76. C₄×Dic₂₅₄	C₂²	semidirect
77. #16861174	C₂²	semidirect
78. #16861174	C₂²	semidirect
86. D₄×Dic₁₂₇	C₂²	semidirect
87. D₄×Dic₁₂₇	C₂²	semidirect
88. D₄×Dic₁₂₇	C₂²	semidirect
90. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
91. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
92. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
93. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
96. #16861168	C₂²	semidirect
97. #16861168	C₂²	semidirect
98. #16861167	C₂²	semidirect
99. #16861166	C₂²	semidirect
100. #16861165	C₂²	semidirect
101. #16861165	C₂²	semidirect
102. #16861165	C₂²	semidirect
103. C₂×C₄⋊Dic₁₂₇	C₂²	semidirect
104. C₂×Dic₁₂₇⋊C₄	C₂²	semidirect
105. C₂×Dic₁₂₇⋊C₄	C₂²	semidirect
106. C₄⋊C₄×D₁₂₇	C₂²	semidirect
110. C₂×C₄×Dic₁₂₇	C₂²	semidirect
111. C₂×C₄×Dic₁₂₇	C₂²	semidirect
323. C₁₂₇	#3521	semidirect
335. #546	D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
#22550596	2
#22550595	2
#22550583	2
#22550578	2
#22550573	2
#22550563	2
#22550560	2
#22550557	2
#22550552	2
#22550525	2
#22550520	2
#22550495	2
#22550486	2
#22550471	2
#22550461	2
#22550407	2
#22550406	2
#22550403	2
C₂×#16861202	2
#22550355	2
#22550351	2
#41×Dic₁₂₇	2
#546×C₁₂₇	2
#3521	127