Subgroups — #30652286

Order 16256.

1132 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550595	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550590	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550582	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550571	C₂	1	2	yes	maximal, complemented
5	#22550564	C₂	1	1	yes	maximal, characteristic, complemented
6	#22550562	C₂	1	2	yes	maximal, complemented
7	#22550560	C₂	1	1	yes	maximal, characteristic, complemented
8	#22550554	C₂	1	2	yes	maximal, complemented
9	#22550551	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	#22550430	C₂	1	1	yes	maximal, characteristic, complemented
14	#22550408	C₂	1	2	yes	maximal, complemented
15	#22550408	C₂	1	1	yes	maximal, characteristic, complemented
16	#22550404	C₂	1	2	yes	maximal, complemented
17	#22550385	C₂	1	2	yes	maximal, complemented
18	C₄×#14523249	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#14523248	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#14523248	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₁₂₇	C₂	1	2	yes	maximal, complemented
23	#529×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×#14523248	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₁₂₇	C₂²	1	2	yes	—
29	#16861208	C₂²	1	1	yes	characteristic, complemented
30	#16861207	C₂²	1	1	yes	characteristic, complemented
31	#16861204	C₂²	1	2	yes	complemented
32	#16861202	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	#16861200	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	1	yes	characteristic
41	#16861196	C₂²	1	2	yes	complemented
42	#16861195	C₂²	1	2	yes	complemented
43	#16861194	C₂²	1	2	yes	—
44	#16861194	C₂²	1	2	yes	complemented
45	#16861191	C₂²	1	2	yes	—
46	#16861191	C₂²	1	2	yes	—
47	#16861191	C₂²	1	2	yes	—
48	#16861191	C₂²	1	2	yes	complemented
49	#16861191	C₂²	1	2	yes	complemented
50	#16861189	C₂²	1	1	yes	characteristic
51	#16861189	C₂²	1	1	yes	characteristic, complemented
52	#16861189	C₂²	1	2	yes	complemented
53	#16861187	C₂²	1	2	yes	—
54	#16861187	C₂²	1	2	yes	complemented
55	#16861187	C₂²	1	2	yes	complemented
56	#16861186	C₂²	1	2	yes	complemented
57	#16861185	C₂²	1	1	yes	characteristic
58	#16861182	C₂²	1	2	yes	—
59	#16861182	C₂²	1	2	yes	complemented
60	#16861181	C₂²	1	2	yes	complemented
61	#16861180	C₂²	1	2	yes	—
62	#16861180	C₂²	1	1	yes	characteristic
63	#16861179	C₂²	1	2	yes	—
64	#16861177	C₂²	1	2	yes	—
65	Q₈×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
66	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
67	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
68	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
69	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
70	C₄×Dic₂₅₄	C₂²	1	2	yes	complemented
71	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
72	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
73	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
74	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
75	C₄×D₅₀₈	C₂²	1	2	yes	complemented
76	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
77	#16861171	C₂²	1	1	yes	characteristic
78	#16861171	C₂²	1	1	yes	characteristic
79	#16861171	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
82	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	—
83	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
87	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
88	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	—
89	#16861168	C₂²	1	1	yes	characteristic, complemented
90	#16861168	C₂²	1	2	yes	complemented
91	#16861168	C₂²	1	1	yes	characteristic, complemented
92	#16861167	C₂²	1	2	yes	—
93	#16861167	C₂²	1	2	yes	—
94	#16861167	C₂²	1	2	yes	complemented
95	#16861167	C₂²	1	1	yes	characteristic, complemented
96	#16861166	C₂²	1	1	yes	characteristic
97	#16861166	C₂²	1	2	yes	—
98	#16861166	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	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
103	C₄⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
104	C₄⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
106	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
108	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic
109	C₄²×D₁₂₇	C₂²	1	2	yes	complemented
110	C₄²×D₁₂₇	C₂²	1	2	yes	complemented
111	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
112	#126×C₁₂₇	C₂²	1	2	yes	complemented
113	#125×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
114	#124×C₁₂₇	C₂²	1	1	yes	characteristic
115	#123×C₁₂₇	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₂₇	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₁₂₇	C₂²	1	2	yes	complemented
121	#117×C₁₂₇	C₂²	1	2	yes	complemented
122	C₂×C₄²×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	#14523248	—	2	4	no	—
127	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
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×D₅₀₈	C₂³	1	2	yes	—
132	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
138	D₄×D₁₂₇	—	2	4	no	—
139	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
140	C₂×C₄×D₁₂₇	—	2	8	no	—
141	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
143	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
145	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
146	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
147	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
148	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
151	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
152	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₁₂₇	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	2	yes	—
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	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	2	yes	—
167	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
168	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
169	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
170	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
171	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
172	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
177	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
181	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
194	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₂₇	C₂³	1	2	yes	—
196	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₂₇	C₂³	1	2	yes	—
198	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₂₇	C₂³	1	2	yes	—
200	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₂₇	C₂³	1	2	yes	—
204	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
207	C₂²×C₄×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	1	yes	characteristic
211	C₄⋊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	1	yes	characteristic
215	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
216	C₄⋊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	2	yes	—
220	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
222	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
223	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
224	C₄²×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	4	no	—
228	C₂²×D₁₂₇	—	2	4	no	—
229	C₂²×D₁₂₇	—	4	2	no	—
230	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
233	Dic₂₅₄	—	2	2	no	—
234	Dic₂₅₄	—	2	2	no	—
235	Dic₂₅₄	—	4	2	no	—
236	D₅₀₈	—	2	2	no	—
237	D₅₀₈	—	2	4	no	—
238	D₅₀₈	#41	1	4	yes	complemented
239	C₂²⋊D₁₂₇	—	2	4	no	—
240	C₂²⋊D₁₂₇	—	2	2	no	—
241	C₂²⋊D₁₂₇	—	2	4	no	—
242	C₂²⋊D₁₂₇	—	2	2	no	—
243	C₂²⋊D₁₂₇	—	4	2	no	—
244	C₂×Dic₁₂₇	—	2	4	no	—
245	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
246	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
252	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
254	C₄×D₁₂₇	—	2	4	no	—
255	C₄×D₁₂₇	—	2	4	no	—
256	C₄×D₁₂₇	—	2	4	no	—
257	C₄×D₁₂₇	—	2	4	no	—
258	C₄×D₁₂₇	—	2	2	no	—
259	C₄×D₁₂₇	—	2	2	no	—
260	C₄×D₁₂₇	—	2	2	no	—
261	C₄×D₁₂₇	—	2	4	no	—
262	C₄×D₁₂₇	—	4	1	no	—
263	C₄×D₁₂₇	—	4	2	no	—
264	C₄×D₁₂₇	—	4	2	no	—
265	C₄×D₁₂₇	—	4	1	no	—
266	C₄×D₁₂₇	#41	1	4	yes	complemented
267	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
268	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
269	Q₈×C₁₂₇	—	2	2	no	—
270	D₄×C₁₂₇	—	2	2	no	—
271	D₄×C₁₂₇	—	4	2	no	—
272	C₂×C₄×C₁₂₇	—	2	4	no	—
273	C₂×C₄×C₁₂₇	—	2	2	no	—
274	C₂×C₄×C₁₂₇	—	2	2	no	—
275	C₂×C₄×C₁₂₇	—	4	1	no	—
276	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
281	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
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	C₂²×C₁₂₇	—	2	2	no	—
286	C₂²×C₁₂₇	—	2	1	no	—
287	C₂²×C₁₂₇	—	2	1	no	—
288	C₂²×C₁₂₇	—	2	2	no	—
289	C₂²×C₁₂₇	—	2	1	no	—
290	C₂²×C₁₂₇	—	2	2	no	—
291	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
292	C₂×D₁₂₇	—	2	2	no	—
293	C₂×D₁₂₇	—	2	1	no	—
294	C₂×D₁₂₇	—	2	2	no	—
295	C₂×D₁₂₇	—	2	1	no	—
296	C₂×D₁₂₇	—	2	1	no	—
297	C₂×D₁₂₇	—	2	1	no	—
298	C₂×D₁₂₇	—	2	1	no	—
299	C₂×D₁₂₇	—	4	8	no	—
300	C₂×D₁₂₇	C₂×#41	1	2	yes	—
301	C₂×D₁₂₇	C₂×#41	1	4	yes	—
302	C₄×C₁₂₇	—	2	1	no	—
303	C₄×C₁₂₇	—	2	2	no	—
304	C₄×C₁₂₇	—	2	1	no	—
305	C₄×C₁₂₇	—	2	2	no	—
306	C₄×C₁₂₇	—	2	1	no	—
307	C₄×C₁₂₇	—	2	1	no	—
308	C₄×C₁₂₇	—	2	2	no	—
309	C₄×C₁₂₇	C₂×#41	1	2	yes	—
310	C₄×C₁₂₇	C₂×#41	1	2	yes	—
311	Dic₁₂₇	—	2	1	no	—
312	Dic₁₂₇	—	2	2	no	—
313	Dic₁₂₇	—	2	1	no	—
314	Dic₁₂₇	—	2	2	no	—
315	Dic₁₂₇	—	2	1	no	—
316	Dic₁₂₇	—	2	1	no	—
317	Dic₁₂₇	—	2	2	no	—
318	Dic₁₂₇	—	2	1	no	—
319	Dic₁₂₇	C₂×#41	1	2	yes	—
320	C₂×C₁₂₇	—	4	2	no	—
321	C₂×C₁₂₇	—	4	1	no	—
322	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
323	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
324	C₂×C₁₂₇	#585	1	1	yes	characteristic
325	D₁₂₇	—	2	2	no	—
326	D₁₂₇	—	2	4	no	—
327	D₁₂₇	—	4	1	no	—
328	#3475	—	127	1	no	maximal, Sylow
329	C₁₂₇	#3475	1	1	yes	characteristic, complemented, Sylow
330	#556	—	127	1	no	—
331	#555	—	127	1	no	—
332	#554	—	127	1	no	—
333	#553	—	127	2	no	—
334	#552	—	127	2	no	—
335	#552	—	127	1	no	—
336	#552	—	127	1	no	—
337	#551	—	127	2	no	—
338	#551	—	127	2	no	—
339	#547	—	127	1	no	—
340	#546	—	127	1	no	—
341	#546	—	127	1	no	—
342	#533	—	127	1	no	—
343	#529	—	127	1	no	—
344	#529	—	127	2	no	—
345	#529	—	127	2	no	—
346	#529	D₁₂₇	1	1	yes	characteristic, complemented
347	#525	—	127	2	no	—
348	C₄×#41	—	127	1	no	—
349	C₄×#41	—	127	1	no	—
350	C₄×#41	—	127	1	no	—
351	C₂×C₄×D₄	—	127	1	no	—
352	C₂×#117	—	127	2	no	—
353	C₂×#41	—	127	1	no	—
354	C₂×#41	—	127	1	no	—
355	C₂×#41	—	127	1	no	—
356	C₂²×D₄	—	127	1	no	—
357	C₂³×C₄	—	127	2	no	—
358	C₄⋊Q₈	—	127	1	no	—
359	C₄⋊Q₈	—	127	1	no	—
360	#126	—	127	2	no	—
361	#126	—	127	2	no	—
362	#126	—	127	2	no	—
363	#126	—	127	2	no	—
364	#126	—	127	2	no	—
365	#126	C₂×D₁₂₇	1	2	yes	complemented
366	#125	—	127	2	no	—
367	#125	—	127	2	no	—
368	#125	—	127	2	no	—
369	#125	—	127	1	no	—
370	#125	C₂×D₁₂₇	1	1	yes	characteristic, complemented
371	#124	—	127	1	no	—
372	#124	—	127	2	no	—
373	#124	—	127	2	no	—
374	#124	C₂×D₁₂₇	1	1	yes	characteristic
375	#123	—	127	2	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	C₂×D₁₂₇	1	2	yes	complemented
383	C₂²⋊Q₈	—	127	1	no	—
384	C₂²⋊Q₈	—	127	2	no	—
385	C₂²⋊Q₈	—	127	2	no	—
386	C₂²⋊Q₈	—	127	2	no	—
387	C₂²⋊Q₈	—	127	1	no	—
388	C₂²⋊Q₈	—	127	1	no	—
389	C₂²⋊Q₈	—	127	2	no	—
390	C₂²⋊Q₈	—	127	2	no	—
391	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
392	#121	—	127	2	no	—
393	#121	—	127	2	no	—
394	#121	—	127	1	no	—
395	#121	—	127	2	no	—
396	#121	—	127	2	no	—
397	#121	C₂×D₁₂₇	1	1	yes	characteristic
398	#120	—	127	2	no	—
399	#120	—	127	2	no	—
400	C₄×Q₈	—	127	1	no	—
401	C₄×Q₈	—	127	1	no	—
402	C₄×Q₈	—	127	1	no	—
403	C₄×Q₈	—	127	1	no	—
404	C₄×Q₈	—	127	1	no	—
405	C₄×Q₈	—	127	2	no	—
406	C₄×Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
407	C₄×D₄	—	127	1	no	—
408	C₄×D₄	—	127	2	no	—
409	C₄×D₄	—	127	2	no	—
410	C₄×D₄	—	127	1	no	—
411	C₄×D₄	—	127	1	no	—
412	C₄×D₄	—	127	1	no	—
413	C₄×D₄	—	127	2	no	—
414	C₄×D₄	—	127	1	no	—
415	C₄×D₄	—	127	2	no	—
416	C₄×D₄	—	127	1	no	—
417	C₄×D₄	—	127	1	no	—
418	C₄×D₄	—	127	2	no	—
419	C₄×D₄	—	127	2	no	—
420	C₄×D₄	—	127	1	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	C₂×D₁₂₇	1	1	yes	characteristic
426	C₄×D₄	C₂×D₁₂₇	1	2	yes	complemented
427	#117	—	127	2	no	—
428	#117	—	127	1	no	—
429	#117	—	127	1	no	—
430	#117	—	127	2	no	—
431	#117	—	127	2	no	—
432	#117	—	127	2	no	—
433	#117	—	127	1	no	—
434	#117	—	127	2	no	—
435	#117	—	127	2	no	—
436	#117	—	127	1	no	—
437	#117	—	127	2	no	—
438	#117	—	127	1	no	—
439	#117	—	127	2	no	—
440	#117	C₂×D₁₂₇	1	2	yes	complemented
441	C₂×C₄⋊C₄	—	127	2	no	—
442	C₂×C₄⋊C₄	—	127	2	no	—
443	C₂×C₄⋊C₄	—	127	1	no	—
444	C₂×C₂²⋊C₄	—	127	2	no	—
445	C₂×C₂²⋊C₄	—	127	2	no	—
446	C₂×C₂²⋊C₄	—	127	2	no	—
447	C₂×C₄²	—	127	2	no	—
448	C₂×C₄²	—	127	2	no	—
449	C₂×C₄²	—	127	1	no	—
450	C₂×C₄²	—	127	1	no	—
451	C₂×C₄²	C₂×D₁₂₇	1	1	yes	characteristic, complemented
452	C₂⁴	—	127	2	no	—
453	#41	—	254	4	no	—
454	#41	—	254	4	no	—
455	#41	—	254	4	no	—
456	C₂×Q₈	—	127	2	no	—
457	C₂×Q₈	—	127	1	no	—
458	C₂×Q₈	—	127	1	no	—
459	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
460	C₂×D₄	—	127	2	no	—
461	C₂×D₄	—	127	1	no	—
462	C₂×D₄	—	127	2	no	—
463	C₂×D₄	—	127	1	no	—
464	C₂×D₄	—	127	2	no	—
465	C₂×D₄	—	127	1	no	—
466	C₂×D₄	—	127	1	no	—
467	C₂×D₄	—	127	2	no	—
468	C₂×D₄	—	254	4	no	—
469	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
470	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
471	C₂²×C₄	—	127	1	no	—
472	C₂²×C₄	—	127	2	no	—
473	C₂²×C₄	—	127	1	no	—
474	C₂²×C₄	—	127	2	no	—
475	C₂²×C₄	—	127	2	no	—
476	C₂²×C₄	—	127	1	no	—
477	C₂²×C₄	—	127	2	no	—
478	C₂²×C₄	—	127	2	no	—
479	C₂²×C₄	—	127	1	no	—
480	C₂²×C₄	—	127	1	no	—
481	C₂²×C₄	—	127	2	no	—
482	C₂²×C₄	—	127	2	no	—
483	C₂²×C₄	—	127	2	no	—
484	C₂²×C₄	—	127	1	no	—
485	C₂²×C₄	—	254	8	no	—
486	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
489	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
490	C₄⋊C₄	—	127	1	no	—
491	C₄⋊C₄	—	127	1	no	—
492	C₄⋊C₄	—	127	2	no	—
493	C₄⋊C₄	—	127	2	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	—	127	2	no	—
502	C₄⋊C₄	—	127	1	no	—
503	C₄⋊C₄	—	127	2	no	—
504	C₄⋊C₄	—	127	2	no	—
505	C₄⋊C₄	—	127	1	no	—
506	C₄⋊C₄	—	127	1	no	—
507	C₄⋊C₄	—	127	2	no	—
508	C₄⋊C₄	—	127	1	no	—
509	C₄⋊C₄	—	127	2	no	—
510	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
511	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
512	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
515	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
516	C₂²⋊C₄	—	127	2	no	—
517	C₂²⋊C₄	—	127	2	no	—
518	C₂²⋊C₄	—	127	2	no	—
519	C₂²⋊C₄	—	127	1	no	—
520	C₂²⋊C₄	—	127	2	no	—
521	C₂²⋊C₄	—	127	1	no	—
522	C₂²⋊C₄	—	127	2	no	—
523	C₂²⋊C₄	—	127	1	no	—
524	C₂²⋊C₄	—	127	1	no	—
525	C₂²⋊C₄	—	127	2	no	—
526	C₂²⋊C₄	—	127	2	no	—
527	C₂²⋊C₄	—	127	2	no	—
528	C₂²⋊C₄	—	127	2	no	—
529	C₂²⋊C₄	—	127	2	no	—
530	C₂²⋊C₄	—	127	2	no	—
531	C₂²⋊C₄	—	127	1	no	—
532	C₂²⋊C₄	—	127	2	no	—
533	C₂²⋊C₄	—	127	1	no	—
534	C₂²⋊C₄	—	127	2	no	—
535	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
536	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
537	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
538	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
539	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
540	C₄²	—	127	2	no	—
541	C₄²	—	127	2	no	—
542	C₄²	—	127	2	no	—
543	C₄²	—	127	1	no	—
544	C₄²	—	127	2	no	—
545	C₄²	—	127	1	no	—
546	C₄²	—	127	1	no	—
547	C₄²	—	127	1	no	—
548	C₄²	—	127	1	no	—
549	C₄²	—	127	1	no	—
550	C₄²	—	127	2	no	—
551	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
552	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
553	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
554	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
555	C₄²	C₂²×D₁₂₇	1	2	yes	—
556	C₂³	—	127	1	no	—
557	C₂³	—	127	2	no	—
558	C₂³	—	127	1	no	—
559	C₂³	—	508	2	no	—
560	C₂³	—	254	4	no	—
561	C₂³	—	254	4	no	—
562	C₂³	C₂³×D₁₂₇	1	2	yes	—
563	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	508	2	no	—
566	Q₈	—	254	2	no	—
567	Q₈	—	254	2	no	—
568	D₄	—	2	2	no	—
569	D₄	—	4	2	no	—
570	D₄	—	127	4	no	—
571	D₄	—	508	2	no	—
572	D₄	—	254	2	no	—
573	D₄	—	254	4	no	—
574	D₄	—	254	2	no	—
575	D₄	—	254	4	no	—
576	D₄	—	254	2	no	—
577	D₄	—	254	4	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	127	1	no	—
583	C₂×C₄	—	127	4	no	—
584	C₂×C₄	—	127	2	no	—
585	C₂×C₄	—	127	1	no	—
586	C₂×C₄	—	127	1	no	—
587	C₂×C₄	—	127	1	no	—
588	C₂×C₄	—	127	1	no	—
589	C₂×C₄	—	127	2	no	—
590	C₂×C₄	—	127	2	no	—
591	C₂×C₄	—	127	1	no	—
592	C₂×C₄	—	508	1	no	—
593	C₂×C₄	—	508	2	no	—
594	C₂×C₄	—	508	1	no	—
595	C₂×C₄	—	508	2	no	—
596	C₂×C₄	—	254	4	no	—
597	C₂×C₄	—	254	4	no	—
598	C₂×C₄	—	254	4	no	—
599	C₂×C₄	—	254	4	no	—
600	C₂×C₄	—	254	4	no	—
601	C₂×C₄	—	254	4	no	—
602	C₂×C₄	—	254	2	no	—
603	C₂×C₄	—	254	2	no	—
604	C₂×C₄	—	254	2	no	—
605	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
609	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
610	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
612	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
614	C₂²	—	2	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	127	2	no	—
621	C₂²	—	127	4	no	—
622	C₂²	—	508	8	no	—
623	C₂²	—	254	1	no	—
624	C₂²	—	254	1	no	—
625	C₂²	—	254	1	no	—
626	C₂²	—	254	2	no	—
627	C₂²	—	254	1	no	—
628	C₂²	—	254	2	no	—
629	C₂²	—	254	1	no	—
630	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
631	C₄	—	2	2	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	2	no	—
638	C₄	—	127	2	no	—
639	C₄	—	254	2	no	—
640	C₄	—	254	1	no	—
641	C₄	—	254	1	no	—
642	C₄	—	254	1	no	—
643	C₄	—	254	2	no	—
644	C₄	—	254	1	no	—
645	C₄	—	254	2	no	—
646	C₄	—	254	1	no	—
647	C₄	#41×D₁₂₇	1	2	yes	—
648	C₄	#41×D₁₂₇	1	2	yes	—
649	C₂	—	4	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	508	1	no	—
652	C₂	—	254	2	no	—
653	C₂	—	254	4	no	—
654	C₂	C₂×#41×D₁₂₇	1	1	yes	characteristic
655	C₂	C₂×#41×D₁₂₇	1	1	yes	characteristic
656	C₂	#22550712	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Frattini	C₂²	C₂⁴×D₁₂₇
Fitting	#529×C₁₂₇	C₂
hypercenter	#529	D₁₂₇
hypocenter	C₁₂₇	#3475
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #22550595	C₂	semidirect
2. #22550590	C₂	semidirect
3. #22550582	C₂	semidirect
4. #22550571	C₂	semidirect
5. #22550564	C₂	semidirect
6. #22550562	C₂	semidirect
7. #22550560	C₂	semidirect
8. #22550554	C₂	semidirect
9. #22550551	C₂	semidirect
10. #22550528	C₂	semidirect
11. #22550523	C₂	semidirect
12. #22550519	C₂	semidirect
13. #22550430	C₂	semidirect
14. #22550408	C₂	semidirect
15. #22550408	C₂	semidirect
16. #22550404	C₂	semidirect
17. #22550385	C₂	semidirect
18. C₄×#14523249	C₂	semidirect
19. C₄×#14523248	C₂	semidirect
20. C₄×#14523248	C₂	semidirect
21. C₄×D₄×D₁₂₇	C₂	semidirect
22. #117×D₁₂₇	C₂	semidirect
23. #529×C₁₂₇	C₂	semidirect
29. #16861208	C₂²	semidirect
30. #16861207	C₂²	semidirect
31. #16861204	C₂²	semidirect
32. #16861202	C₂²	semidirect
33. #16861202	C₂²	semidirect
34. #16861202	C₂²	semidirect
35. #16861202	C₂²	semidirect
36. #16861200	C₂²	semidirect
37. #16861200	C₂²	semidirect
38. #16861199	C₂²	semidirect
39. #16861199	C₂²	semidirect
41. #16861196	C₂²	semidirect
42. #16861195	C₂²	semidirect
44. #16861194	C₂²	semidirect
48. #16861191	C₂²	semidirect
49. #16861191	C₂²	semidirect
51. #16861189	C₂²	semidirect
52. #16861189	C₂²	semidirect
54. #16861187	C₂²	semidirect
55. #16861187	C₂²	semidirect
56. #16861186	C₂²	semidirect
59. #16861182	C₂²	semidirect
60. #16861181	C₂²	semidirect
65. Q₈×Dic₁₂₇	C₂²	semidirect
66. C₄×Dic₂₅₄	C₂²	semidirect
67. C₄×Dic₂₅₄	C₂²	semidirect
68. C₄×Dic₂₅₄	C₂²	semidirect
69. C₄×Dic₂₅₄	C₂²	semidirect
70. C₄×Dic₂₅₄	C₂²	semidirect
75. C₄×D₅₀₈	C₂²	semidirect
79. #16861171	C₂²	semidirect
83. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
84. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
85. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
86. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
87. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
89. #16861168	C₂²	semidirect
90. #16861168	C₂²	semidirect
91. #16861168	C₂²	semidirect
94. #16861167	C₂²	semidirect
95. #16861167	C₂²	semidirect
98. #16861166	C₂²	semidirect
99. #16861166	C₂²	semidirect
100. #16861165	C₂²	semidirect
101. #16861165	C₂²	semidirect
103. C₄⋊C₄×D₁₂₇	C₂²	semidirect
104. C₄⋊C₄×D₁₂₇	C₂²	semidirect
109. C₄²×D₁₂₇	C₂²	semidirect
110. C₄²×D₁₂₇	C₂²	semidirect
111. C₄²×D₁₂₇	C₂²	semidirect
112. #126×C₁₂₇	C₂²	semidirect
113. #125×C₁₂₇	C₂²	semidirect
115. #123×C₁₂₇	C₂²	semidirect
116. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
118. C₄×Q₈×C₁₂₇	C₂²	semidirect
120. C₄×D₄×C₁₂₇	C₂²	semidirect
121. #117×C₁₂₇	C₂²	semidirect
122. C₂×C₄²×C₁₂₇	C₂²	semidirect
238. D₅₀₈	#41	semidirect
266. C₄×D₁₂₇	#41	semidirect
329. C₁₂₇	#3475	semidirect
346. #529	D₁₂₇	semidirect
365. #126	C₂×D₁₂₇	semidirect
370. #125	C₂×D₁₂₇	semidirect
382. #123	C₂×D₁₂₇	semidirect
391. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
406. C₄×Q₈	C₂×D₁₂₇	semidirect
426. C₄×D₄	C₂×D₁₂₇	semidirect
440. #117	C₂×D₁₂₇	semidirect
451. C₂×C₄²	C₂×D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
#22550595	2
#22550590	2
#22550582	2
#22550571	2
#22550564	2
#22550562	2
#22550560	2
#22550554	2
#22550551	2
#22550528	2
#22550523	2
#22550519	2
#22550430	2
#22550408	2
#22550404	2
#22550385	2
C₄×#14523249	2
C₄×#14523248	2
C₄×D₄×D₁₂₇	2
#117×D₁₂₇	2
#529×C₁₂₇	2
#3475	127