Subgroups — #30653507

Order 16256.

1464 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550712	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16861255	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550685	C₂	1	4	yes	maximal, complemented
4	#22550683	C₂	1	4	yes	maximal, complemented
5	#22550680	C₂	1	4	yes	maximal, complemented
6	#22550678	C₂	1	4	yes	maximal, complemented
7	#22550675	C₂	1	4	yes	maximal, complemented
8	#22550674	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16861237	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16861234	C₂	1	1	yes	maximal, characteristic, complemented
11	AGL(1,ℤ/8)×D₁₂₇	C₂	1	4	yes	maximal, complemented
12	#22550642	C₂	1	1	yes	maximal, characteristic, complemented
13	#575×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#16861257	C₂²	1	2	yes	complemented
15	#16861256	—	2	1	no	—
16	#16861256	C₂²	1	2	yes	complemented
17	#16861255	—	2	2	no	—
18	#16861255	—	2	2	no	—
19	#16861255	—	2	1	no	—
20	#16861255	C₂²	1	4	yes	complemented
21	#16861255	C₂²	1	4	yes	complemented
22	#16861255	C₂²	1	2	yes	complemented
23	#16861254	—	2	2	no	—
24	#16861254	C₂²	1	2	yes	complemented
25	C₂×#14523249	C₂²	1	2	yes	complemented
26	C₂×#14523248	—	2	2	no	—
27	C₂×#14523248	—	2	1	no	—
28	C₂×#14523248	C₂²	1	1	yes	characteristic
29	C₂×#14523248	C₂²	1	1	yes	characteristic, complemented
30	#41×D₁₂₇	—	2	2	no	—
31	#41×D₁₂₇	C₂²	1	4	yes	complemented
32	C₂²×D₅₀₈	—	2	1	no	—
33	C₂²×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×D₄×D₁₂₇	—	2	2	no	—
35	C₂×D₄×D₁₂₇	C₂²	1	2	yes	complemented
36	#16861241	C₂²	1	8	yes	complemented
37	#16861240	C₂²	1	2	yes	complemented
38	#16861239	C₂²	1	2	yes	complemented
39	#16861237	C₂²	1	4	yes	complemented
40	#16861237	C₂²	1	4	yes	complemented
41	#16861236	C₂²	1	8	yes	complemented
42	#16861236	C₂²	1	8	yes	complemented
43	#16861235	C₂²	1	2	yes	complemented
44	#16861234	C₂²	1	4	yes	complemented
45	#16861234	C₂²	1	2	yes	complemented
46	#16861234	C₂²	1	4	yes	complemented
47	#16861233	C₂²	1	8	yes	complemented
48	#16861232	C₂²	1	8	yes	complemented
49	#16861230	C₂²	1	8	yes	complemented
50	#16861229	C₂²	1	4	yes	complemented
51	C₂×#14523237	C₂²	1	2	yes	complemented
52	C₂×#14523235	C₂²	1	2	yes	complemented
53	SD₁₆×D₁₂₇	C₂²	1	8	yes	complemented
54	C₂×D₁₀₁₆	C₂²	1	2	yes	complemented
55	C₂×#14523233	C₂²	1	2	yes	complemented
56	D₈×D₁₂₇	C₂²	1	8	yes	complemented
57	#16861217	C₂²	1	4	yes	complemented
58	#16861215	C₂²	1	4	yes	complemented
59	C₂×#14523232	C₂²	1	1	yes	characteristic, complemented
60	M₁₆×D₁₂₇	C₂²	1	4	yes	complemented
61	C₂×#41×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
62	C₂×#41×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
63	#137×C₁₂₇	C₂²	1	2	yes	complemented
64	#137×C₁₂₇	C₂²	1	2	yes	complemented
65	AGL(1,ℤ/8)×C₁₂₇	C₂²	1	2	yes	complemented
66	AGL(1,ℤ/8)×C₁₂₇	C₂²	1	2	yes	complemented
67	#135×C₁₂₇	C₂²	1	4	yes	complemented
68	C₂×M₁₆×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
69	C₂³×D₁₂₇	—	2	2	no	—
70	C₂³×D₁₂₇	—	2	1	no	—
71	#14523249	—	2	2	no	—
72	#14523249	—	2	4	no	—
73	#14523249	C₂³	1	8	yes	—
74	#14523249	C₂³	1	4	yes	complemented
75	#14523248	—	2	4	no	—
76	#14523248	—	2	4	no	—
77	#14523248	—	2	2	no	—
78	#14523248	—	2	2	no	—
79	#14523248	—	2	4	no	—
80	#14523248	—	2	4	no	—
81	#14523248	—	2	1	no	—
82	#14523248	—	2	1	no	—
83	#14523248	D₄	1	2	yes	—
84	#14523248	D₄	1	2	yes	—
85	#14523248	C₂³	1	2	yes	—
86	#14523248	C₂³	1	2	yes	—
87	#14523248	C₂³	1	2	yes	—
88	#14523248	C₂³	1	2	yes	complemented
89	#14523247	—	2	2	no	—
90	#14523247	—	2	4	no	—
91	#14523247	—	2	4	no	—
92	#14523247	C₂³	1	4	yes	complemented
93	C₂×Dic₂₅₄	—	2	2	no	—
94	C₂×Dic₂₅₄	D₄	1	1	yes	characteristic
95	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic, complemented
96	Q₈×D₁₂₇	—	2	2	no	—
97	Q₈×D₁₂₇	C₂³	1	4	yes	complemented
98	C₂×D₅₀₈	—	2	2	no	—
99	C₂×D₅₀₈	—	2	4	no	—
100	C₂×D₅₀₈	—	2	4	no	—
101	C₂×D₅₀₈	—	2	2	no	—
102	C₂×D₅₀₈	—	2	1	no	—
103	C₂×D₅₀₈	—	2	1	no	—
104	C₂×D₅₀₈	—	2	1	no	—
105	C₂×D₅₀₈	D₄	1	1	yes	characteristic
106	C₂×D₅₀₈	C₂³	1	2	yes	—
107	C₂×D₅₀₈	C₂³	1	2	yes	—
108	C₂×D₅₀₈	C₂³	1	2	yes	—
109	C₂×D₅₀₈	C₂³	1	1	yes	characteristic, complemented
110	C₂×C₂²⋊D₁₂₇	—	2	4	no	—
111	C₂×C₂²⋊D₁₂₇	—	2	2	no	—
112	C₂×C₂²⋊D₁₂₇	—	2	1	no	—
113	C₂×C₂²⋊D₁₂₇	D₄	1	2	yes	—
114	D₄×D₁₂₇	—	2	4	no	—
115	D₄×D₁₂₇	—	2	2	no	—
116	D₄×D₁₂₇	—	2	8	no	—
117	D₄×D₁₂₇	—	2	8	no	—
118	D₄×D₁₂₇	—	2	4	no	—
119	D₄×D₁₂₇	—	2	4	no	—
120	D₄×D₁₂₇	C₂³	1	8	yes	—
121	D₄×D₁₂₇	C₂³	1	4	yes	complemented
122	C₂×C₄×D₁₂₇	—	2	2	no	—
123	C₂×C₄×D₁₂₇	—	2	4	no	—
124	C₂×C₄×D₁₂₇	—	2	1	no	—
125	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
126	#14523238	C₂³	1	4	yes	complemented
127	#14523237	C₂³	1	8	yes	complemented
128	#14523236	C₂³	1	4	yes	complemented
129	#14523235	C₂³	1	8	yes	complemented
130	#14523235	C₂³	1	4	yes	complemented
131	D₁₀₁₆	C₂³	1	8	yes	complemented
132	#14523233	C₂³	1	4	yes	complemented
133	#14523233	C₂³	1	8	yes	complemented
134	#14523232	C₂³	1	2	yes	—
135	#14523232	C₂³	1	2	yes	complemented
136	#14523231	C₂³	1	8	yes	complemented
137	C₂×C₁₂₇⋊C₈	C₂³	1	2	yes	complemented
138	C₈×D₁₂₇	C₂³	1	8	yes	complemented
139	#41×C₁₂₇	—	2	1	no	—
140	#41×C₁₂₇	—	2	1	no	—
141	#41×C₁₂₇	—	2	1	no	—
142	#41×C₁₂₇	—	2	1	no	—
143	#41×C₁₂₇	C₂³	1	2	yes	—
144	#41×C₁₂₇	C₂³	1	2	yes	—
145	#41×C₁₂₇	C₂³	1	2	yes	—
146	#41×C₁₂₇	C₂³	1	2	yes	complemented
147	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
148	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
149	C₂×D₄×C₁₂₇	—	2	1	no	—
150	C₂×D₄×C₁₂₇	—	2	1	no	—
151	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
152	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
153	C₂²×C₄×C₁₂₇	—	2	1	no	—
154	C₂²×C₄×C₁₂₇	—	2	1	no	—
155	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
156	Q₁₆×C₁₂₇	C₂³	1	4	yes	complemented
157	SD₁₆×C₁₂₇	C₂³	1	4	yes	complemented
158	SD₁₆×C₁₂₇	C₂³	1	4	yes	complemented
159	D₈×C₁₂₇	C₂³	1	4	yes	complemented
160	M₁₆×C₁₂₇	C₂³	1	2	yes	—
161	M₁₆×C₁₂₇	C₂³	1	2	yes	complemented
162	C₂×C₈×C₁₂₇	C₂³	1	2	yes	complemented
163	C₂²×D₁₂₇	—	2	2	no	—
164	C₂²×D₁₂₇	—	2	1	no	—
165	C₂²×D₁₂₇	—	2	2	no	—
166	C₂²×D₁₂₇	—	2	2	no	—
167	C₂²×D₁₂₇	—	2	4	no	—
168	C₂²×D₁₂₇	—	2	8	no	—
169	C₂²×D₁₂₇	—	8	4	no	—
170	C₂²×D₁₂₇	—	8	2	no	—
171	C₂²×D₁₂₇	C₂×D₄	1	2	yes	—
172	Dic₂₅₄	—	2	1	no	—
173	Dic₂₅₄	—	2	4	no	—
174	Dic₂₅₄	C₂×D₄	1	2	yes	—
175	Dic₂₅₄	C₂×D₄	1	2	yes	—
176	Dic₂₅₄	C₂⁴	1	2	yes	—
177	D₅₀₈	—	2	8	no	—
178	D₅₀₈	—	2	4	no	—
179	D₅₀₈	—	2	2	no	—
180	D₅₀₈	—	2	2	no	—
181	D₅₀₈	—	2	2	no	—
182	D₅₀₈	—	2	1	no	—
183	D₅₀₈	C₂×D₄	1	2	yes	—
184	D₅₀₈	C₂×D₄	1	2	yes	—
185	D₅₀₈	C₂⁴	1	2	yes	—
186	D₅₀₈	C₂⁴	1	4	yes	—
187	C₂²⋊D₁₂₇	—	2	2	no	—
188	C₂²⋊D₁₂₇	—	2	2	no	—
189	C₂²⋊D₁₂₇	—	2	4	no	—
190	C₂²⋊D₁₂₇	—	2	8	no	—
191	C₂²⋊D₁₂₇	—	2	4	no	—
192	C₂²⋊D₁₂₇	C₂×D₄	1	4	yes	—
193	C₂²⋊D₁₂₇	C₂×D₄	1	4	yes	—
194	C₂×Dic₁₂₇	—	2	1	no	—
195	C₂×Dic₁₂₇	—	2	4	no	—
196	C₂×Dic₁₂₇	C₂×D₄	1	2	yes	—
197	C₄×D₁₂₇	—	2	4	no	—
198	C₄×D₁₂₇	—	2	2	no	—
199	C₄×D₁₂₇	—	2	2	no	—
200	C₄×D₁₂₇	—	2	8	no	—
201	C₄×D₁₂₇	—	2	4	no	—
202	C₄×D₁₂₇	C₂×D₄	1	4	yes	—
203	C₄×D₁₂₇	C₂⁴	1	4	yes	—
204	C₁₂₇⋊C₈	C₂⁴	1	4	yes	—
205	C₂³×C₁₂₇	—	2	1	no	—
206	C₂³×C₁₂₇	—	2	1	no	—
207	C₂³×C₁₂₇	C₂×D₄	1	1	yes	characteristic
208	Q₈×C₁₂₇	—	2	1	no	—
209	Q₈×C₁₂₇	—	2	1	no	—
210	Q₈×C₁₂₇	C₂⁴	1	2	yes	—
211	Q₈×C₁₂₇	C₂⁴	1	2	yes	—
212	D₄×C₁₂₇	—	2	2	no	—
213	D₄×C₁₂₇	—	2	2	no	—
214	D₄×C₁₂₇	—	2	2	no	—
215	D₄×C₁₂₇	—	2	2	no	—
216	D₄×C₁₂₇	—	2	1	no	—
217	D₄×C₁₂₇	—	2	1	no	—
218	D₄×C₁₂₇	C₂⁴	1	2	yes	—
219	D₄×C₁₂₇	C₂⁴	1	2	yes	—
220	C₂×C₄×C₁₂₇	—	2	1	no	—
221	C₂×C₄×C₁₂₇	—	2	1	no	—
222	C₂×C₄×C₁₂₇	—	2	2	no	—
223	C₂×C₄×C₁₂₇	—	2	2	no	—
224	C₂×C₄×C₁₂₇	—	2	2	no	—
225	C₂×C₄×C₁₂₇	—	2	2	no	—
226	C₂×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
230	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
231	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
232	C₈×C₁₂₇	C₂⁴	1	4	yes	—
233	C₂²×C₁₂₇	—	2	2	no	—
234	C₂²×C₁₂₇	—	2	2	no	—
235	C₂²×C₁₂₇	—	4	1	no	—
236	C₂²×C₁₂₇	—	4	2	no	—
237	C₂²×C₁₂₇	—	8	1	no	—
238	C₂²×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
239	C₂²×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
240	C₂²×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
241	C₂×D₁₂₇	—	2	2	no	—
242	C₂×D₁₂₇	—	2	4	no	—
243	C₂×D₁₂₇	—	4	2	no	—
244	C₂×D₁₂₇	—	4	4	no	—
245	C₂×D₁₂₇	—	8	4	no	—
246	C₂×D₁₂₇	—	8	8	no	—
247	C₂×D₁₂₇	—	8	1	no	—
248	C₂×D₁₂₇	—	8	2	no	—
249	C₂×D₁₂₇	—	8	2	no	—
250	C₂×D₁₂₇	C₂²×D₄	1	4	yes	—
251	C₄×C₁₂₇	—	2	2	no	—
252	C₄×C₁₂₇	—	2	2	no	—
253	C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
254	C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
255	C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
256	C₄×C₁₂₇	C₂⁵	1	1	yes	characteristic
257	Dic₁₂₇	—	2	2	no	—
258	Dic₁₂₇	C₂²×D₄	1	4	yes	—
259	C₂×C₁₂₇	—	2	1	no	—
260	C₂×C₁₂₇	—	2	1	no	—
261	C₂×C₁₂₇	—	2	1	no	—
262	C₂×C₁₂₇	—	4	2	no	—
263	C₂×C₁₂₇	—	4	2	no	—
264	C₂×C₁₂₇	C₂³×D₄	1	1	yes	characteristic
265	D₁₂₇	—	2	4	no	—
266	D₁₂₇	—	4	4	no	—
267	D₁₂₇	—	4	2	no	—
268	#3585	—	127	1	no	maximal, Sylow
269	C₁₂₇	#3585	1	1	yes	characteristic, complemented, Sylow
270	#585	—	127	1	no	—
271	C₂×H(5,𝔽₂)	—	127	1	no	—
272	#577	—	127	4	no	—
273	#577	—	127	4	no	—
274	#576	—	127	4	no	—
275	#576	—	127	4	no	—
276	#575	—	127	1	no	—
277	#575	—	127	4	no	—
278	#575	D₁₂₇	1	1	yes	characteristic, complemented
279	C₂×AGL(1,ℤ/8)	—	127	1	no	—
280	C₂×AGL(1,ℤ/8)	—	127	4	no	—
281	C₂×AGL(1,ℤ/8)	—	127	1	no	—
282	#568	—	127	1	no	—
283	2₋¹⁺⁴	—	127	2	no	—
284	2₋¹⁺⁴	—	127	2	no	—
285	2₋¹⁺⁴	—	254	1	no	—
286	H(5,𝔽₂)	—	127	4	no	—
287	H(5,𝔽₂)	—	127	4	no	—
288	H(5,𝔽₂)	—	127	2	no	—
289	H(5,𝔽₂)	—	127	2	no	—
290	H(5,𝔽₂)	—	254	2	no	—
291	H(5,𝔽₂)	—	254	1	no	—
292	H(5,𝔽₂)	—	254	2	no	—
293	H(5,𝔽₂)	—	254	2	no	—
294	C₂×#41	—	127	1	no	—
295	C₂×#41	—	127	4	no	—
296	C₂×#41	—	127	2	no	—
297	C₂×#41	—	127	1	no	—
298	C₂×#41	—	254	1	no	—
299	C₂×#41	—	254	2	no	—
300	C₂×#41	—	254	2	no	—
301	C₂×#41	C₂×D₁₂₇	1	1	yes	characteristic, complemented
302	C₂×#41	C₂×D₁₂₇	1	1	yes	characteristic, complemented
303	C₂²×D₄	—	127	2	no	—
304	C₂²×D₄	—	127	1	no	—
305	C₂²×D₄	—	254	1	no	—
306	C₂²×D₄	—	254	2	no	—
307	#137	—	127	2	no	—
308	#137	—	127	2	no	—
309	#137	—	127	8	no	—
310	#137	C₂×D₁₂₇	1	2	yes	complemented
311	#137	C₂×D₁₂₇	1	2	yes	complemented
312	AGL(1,ℤ/8)	—	127	4	no	—
313	AGL(1,ℤ/8)	—	127	2	no	—
314	AGL(1,ℤ/8)	—	127	4	no	—
315	AGL(1,ℤ/8)	—	127	2	no	—
316	AGL(1,ℤ/8)	—	127	8	no	—
317	AGL(1,ℤ/8)	—	127	8	no	—
318	AGL(1,ℤ/8)	—	127	8	no	—
319	AGL(1,ℤ/8)	—	127	4	no	—
320	AGL(1,ℤ/8)	—	127	4	no	—
321	AGL(1,ℤ/8)	C₂×D₁₂₇	1	2	yes	complemented
322	AGL(1,ℤ/8)	C₂×D₁₂₇	1	2	yes	complemented
323	#135	—	127	4	no	—
324	#135	—	127	8	no	—
325	#135	—	127	8	no	—
326	#135	C₂×D₁₂₇	1	4	yes	complemented
327	C₂×SD₁₆	—	127	2	no	—
328	C₂×SD₁₆	—	127	8	no	—
329	C₂×SD₁₆	—	127	2	no	—
330	C₂×D₈	—	127	2	no	—
331	C₂×D₈	—	127	8	no	—
332	C₂×D₈	—	127	2	no	—
333	#131	—	127	4	no	—
334	#131	—	127	4	no	—
335	C₂×M₁₆	—	127	1	no	—
336	C₂×M₁₆	—	127	4	no	—
337	C₂×M₁₆	C₂×D₁₂₇	1	1	yes	characteristic, complemented
338	C₂⁴	—	254	2	no	—
339	C₂⁴	—	254	1	no	—
340	#41	—	2	1	no	—
341	#41	—	2	1	no	—
342	#41	—	2	1	no	—
343	#41	—	2	1	no	—
344	#41	—	127	2	no	—
345	#41	—	127	2	no	—
346	#41	—	127	2	no	—
347	#41	—	127	2	no	—
348	#41	—	127	8	no	—
349	#41	—	127	4	no	—
350	#41	—	127	4	no	—
351	#41	—	127	2	no	—
352	#41	—	127	2	no	—
353	#41	—	254	4	no	—
354	#41	—	254	4	no	—
355	#41	—	254	2	no	—
356	#41	—	254	4	no	—
357	#41	—	254	4	no	—
358	#41	—	254	2	no	—
359	#41	—	254	4	no	—
360	#41	—	254	4	no	—
361	#41	—	254	4	no	—
362	#41	—	254	2	no	—
363	#41	—	254	2	no	—
364	#41	—	254	1	no	—
365	#41	—	254	1	no	—
366	#41	C₂²×D₁₂₇	1	2	yes	—
367	#41	C₂²×D₁₂₇	1	2	yes	—
368	#41	C₂²×D₁₂₇	1	2	yes	—
369	#41	C₂²×D₁₂₇	1	2	yes	complemented
370	C₂×Q₈	—	127	1	no	—
371	C₂×Q₈	—	127	4	no	—
372	C₂×Q₈	—	127	1	no	—
373	C₂×Q₈	—	254	2	no	—
374	C₂×Q₈	—	254	2	no	—
375	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
376	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	127	2	no	—
380	C₂×D₄	—	127	8	no	—
381	C₂×D₄	—	127	4	no	—
382	C₂×D₄	—	127	1	no	—
383	C₂×D₄	—	127	2	no	—
384	C₂×D₄	—	127	2	no	—
385	C₂×D₄	—	127	2	no	—
386	C₂×D₄	—	127	1	no	—
387	C₂×D₄	—	254	4	no	—
388	C₂×D₄	—	254	4	no	—
389	C₂×D₄	—	254	2	no	—
390	C₂×D₄	—	254	2	no	—
391	C₂×D₄	—	254	4	no	—
392	C₂×D₄	—	254	2	no	—
393	C₂×D₄	—	254	8	no	—
394	C₂×D₄	—	254	8	no	—
395	C₂×D₄	—	254	4	no	—
396	C₂×D₄	—	254	2	no	—
397	C₂×D₄	—	254	4	no	—
398	C₂×D₄	—	254	4	no	—
399	C₂×D₄	—	254	1	no	—
400	C₂×D₄	—	254	1	no	—
401	C₂×D₄	—	254	1	no	—
402	C₂×D₄	—	254	1	no	—
403	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
404	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	127	2	no	—
408	C₂²×C₄	—	254	2	no	—
409	C₂²×C₄	—	254	4	no	—
410	C₂²×C₄	—	254	1	no	—
411	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
412	Q₁₆	—	127	4	no	—
413	Q₁₆	C₂²×D₁₂₇	1	4	yes	complemented
414	SD₁₆	—	127	8	no	—
415	SD₁₆	—	127	4	no	—
416	SD₁₆	—	127	4	no	—
417	SD₁₆	—	127	8	no	—
418	SD₁₆	C₂²×D₁₂₇	1	4	yes	complemented
419	SD₁₆	C₂²×D₁₂₇	1	4	yes	complemented
420	D₈	—	127	4	no	—
421	D₈	—	127	8	no	—
422	D₈	—	127	8	no	—
423	D₈	C₂²×D₁₂₇	1	4	yes	complemented
424	M₁₆	—	127	2	no	—
425	M₁₆	—	127	2	no	—
426	M₁₆	—	127	8	no	—
427	M₁₆	C₂²×D₁₂₇	1	2	yes	—
428	M₁₆	C₂²×D₁₂₇	1	2	yes	complemented
429	C₂×C₈	—	127	2	no	—
430	C₂×C₈	—	127	8	no	—
431	C₂×C₈	C₂²×D₁₂₇	1	2	yes	complemented
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	127	2	no	—
435	C₂³	—	1016	2	no	—
436	C₂³	—	1016	4	no	—
437	C₂³	—	254	4	no	—
438	C₂³	—	254	8	no	—
439	C₂³	—	254	1	no	—
440	C₂³	—	254	2	no	—
441	C₂³	—	254	2	no	—
442	C₂³	—	254	2	no	—
443	C₂³	D₄×D₁₂₇	1	1	yes	characteristic
444	Q₈	—	2	1	no	—
445	Q₈	—	2	1	no	—
446	Q₈	—	127	2	no	—
447	Q₈	—	127	2	no	—
448	Q₈	—	127	2	no	—
449	Q₈	—	254	4	no	—
450	Q₈	—	254	1	no	—
451	Q₈	C₂³×D₁₂₇	1	2	yes	—
452	Q₈	C₂³×D₁₂₇	1	2	yes	—
453	D₄	—	2	2	no	—
454	D₄	—	2	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	2	1	no	—
458	D₄	—	2	1	no	—
459	D₄	—	127	4	no	—
460	D₄	—	127	4	no	—
461	D₄	—	127	2	no	—
462	D₄	—	127	2	no	—
463	D₄	—	127	2	no	—
464	D₄	—	127	4	no	—
465	D₄	—	254	8	no	—
466	D₄	—	254	4	no	—
467	D₄	—	254	8	no	—
468	D₄	—	254	4	no	—
469	D₄	—	254	4	no	—
470	D₄	—	254	2	no	—
471	D₄	—	254	2	no	—
472	D₄	—	254	2	no	—
473	D₄	—	254	2	no	—
474	D₄	—	254	2	no	—
475	D₄	—	254	1	no	—
476	D₄	C₂³×D₁₂₇	1	2	yes	—
477	D₄	C₂³×D₁₂₇	1	2	yes	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	127	2	no	—
485	C₂×C₄	—	127	4	no	—
486	C₂×C₄	—	127	4	no	—
487	C₂×C₄	—	254	8	no	—
488	C₂×C₄	—	254	4	no	—
489	C₂×C₄	—	254	4	no	—
490	C₂×C₄	—	254	4	no	—
491	C₂×C₄	—	254	1	no	—
492	C₂×C₄	—	254	2	no	—
493	C₂×C₄	—	254	2	no	—
494	C₂×C₄	D₄×D₁₂₇	1	1	yes	characteristic
495	C₂×C₄	D₄×D₁₂₇	1	1	yes	characteristic
496	C₂×C₄	D₄×D₁₂₇	1	1	yes	characteristic
497	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
498	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
499	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
500	C₈	—	127	4	no	—
501	C₈	C₂³×D₁₂₇	1	4	yes	—
502	C₂²	—	2	2	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	127	4	no	—
508	C₂²	—	1016	2	no	—
509	C₂²	—	1016	2	no	—
510	C₂²	—	1016	1	no	—
511	C₂²	—	1016	8	no	—
512	C₂²	—	1016	4	no	—
513	C₂²	—	508	4	no	—
514	C₂²	—	508	2	no	—
515	C₂²	—	254	2	no	—
516	C₂²	—	254	4	no	—
517	C₂²	C₂×D₄×D₁₂₇	1	1	yes	characteristic
518	C₂²	C₂×D₄×D₁₂₇	1	1	yes	characteristic
519	C₂²	C₂×D₄×D₁₂₇	1	1	yes	characteristic
520	C₄	—	2	2	no	—
521	C₄	—	2	2	no	—
522	C₄	—	127	4	no	—
523	C₄	—	254	2	no	—
524	C₄	C₂×D₄×D₁₂₇	1	1	yes	characteristic
525	C₄	C₂×D₄×D₁₂₇	1	1	yes	characteristic
526	C₄	C₂×D₄×D₁₂₇	1	1	yes	characteristic
527	C₄	C₂⁴×D₁₂₇	1	1	yes	characteristic
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	2	1	no	—
531	C₂	—	4	2	no	—
532	C₂	—	4	2	no	—
533	C₂	—	508	4	no	—
534	C₂	—	508	2	no	—
535	C₂	—	254	4	no	—
536	C₂	C₂²×D₄×D₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₁₂₇
commutator, cosocle	C₄×C₁₂₇	C₂⁵
Frattini	C₄	C₂⁴×D₁₂₇
Fitting	#575×C₁₂₇	C₂
socle	C₂×C₁₂₇	C₂³×D₄
hypercenter	#575	D₁₂₇
hypocenter	C₁₂₇	#3585
LCS	G ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #575

Complements

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

N	H ≅ G/N	type
1. #22550712	C₂	semidirect
2. C₂×#16861255	C₂	semidirect
3. #22550685	C₂	semidirect
4. #22550683	C₂	semidirect
5. #22550680	C₂	semidirect
6. #22550678	C₂	semidirect
7. #22550675	C₂	semidirect
8. #22550674	C₂	semidirect
9. C₂×#16861237	C₂	semidirect
10. C₂×#16861234	C₂	semidirect
11. AGL(1,ℤ/8)×D₁₂₇	C₂	semidirect
12. #22550642	C₂	semidirect
13. #575×C₁₂₇	C₂	semidirect
14. #16861257	C₂²	semidirect
16. #16861256	C₂²	semidirect
20. #16861255	C₂²	semidirect
21. #16861255	C₂²	semidirect
22. #16861255	C₂²	semidirect
24. #16861254	C₂²	semidirect
25. C₂×#14523249	C₂²	semidirect
29. C₂×#14523248	C₂²	semidirect
31. #41×D₁₂₇	C₂²	semidirect
33. C₂²×D₅₀₈	C₂²	semidirect
35. C₂×D₄×D₁₂₇	C₂²	semidirect
36. #16861241	C₂²	semidirect
37. #16861240	C₂²	semidirect
38. #16861239	C₂²	semidirect
39. #16861237	C₂²	semidirect
40. #16861237	C₂²	semidirect
41. #16861236	C₂²	semidirect
42. #16861236	C₂²	semidirect
43. #16861235	C₂²	semidirect
44. #16861234	C₂²	semidirect
45. #16861234	C₂²	semidirect
46. #16861234	C₂²	semidirect
47. #16861233	C₂²	semidirect
48. #16861232	C₂²	semidirect
49. #16861230	C₂²	semidirect
50. #16861229	C₂²	semidirect
51. C₂×#14523237	C₂²	semidirect
52. C₂×#14523235	C₂²	semidirect
53. SD₁₆×D₁₂₇	C₂²	semidirect
54. C₂×D₁₀₁₆	C₂²	semidirect
55. C₂×#14523233	C₂²	semidirect
56. D₈×D₁₂₇	C₂²	semidirect
57. #16861217	C₂²	semidirect
58. #16861215	C₂²	semidirect
59. C₂×#14523232	C₂²	semidirect
60. M₁₆×D₁₂₇	C₂²	semidirect
61. C₂×#41×C₁₂₇	C₂²	semidirect
62. C₂×#41×C₁₂₇	C₂²	semidirect
63. #137×C₁₂₇	C₂²	semidirect
64. #137×C₁₂₇	C₂²	semidirect
65. AGL(1,ℤ/8)×C₁₂₇	C₂²	semidirect
66. AGL(1,ℤ/8)×C₁₂₇	C₂²	semidirect
67. #135×C₁₂₇	C₂²	semidirect
68. C₂×M₁₆×C₁₂₇	C₂²	semidirect
74. #14523249	C₂³	semidirect
88. #14523248	C₂³	semidirect
92. #14523247	C₂³	semidirect
95. C₂×Dic₂₅₄	C₂³	semidirect
97. Q₈×D₁₂₇	C₂³	semidirect
109. C₂×D₅₀₈	C₂³	semidirect
121. D₄×D₁₂₇	C₂³	semidirect
126. #14523238	C₂³	semidirect
127. #14523237	C₂³	semidirect
128. #14523236	C₂³	semidirect
129. #14523235	C₂³	semidirect
130. #14523235	C₂³	semidirect
131. D₁₀₁₆	C₂³	semidirect
132. #14523233	C₂³	semidirect
133. #14523233	C₂³	semidirect
135. #14523232	C₂³	semidirect
136. #14523231	C₂³	semidirect
137. C₂×C₁₂₇⋊C₈	C₂³	semidirect
138. C₈×D₁₂₇	C₂³	semidirect
146. #41×C₁₂₇	C₂³	semidirect
148. C₂×Q₈×C₁₂₇	C₂³	semidirect
152. C₂×D₄×C₁₂₇	C₂³	semidirect
156. Q₁₆×C₁₂₇	C₂³	semidirect
157. SD₁₆×C₁₂₇	C₂³	semidirect
158. SD₁₆×C₁₂₇	C₂³	semidirect
159. D₈×C₁₂₇	C₂³	semidirect
161. M₁₆×C₁₂₇	C₂³	semidirect
162. C₂×C₈×C₁₂₇	C₂³	semidirect
269. C₁₂₇	#3585	semidirect
278. #575	D₁₂₇	semidirect
301. C₂×#41	C₂×D₁₂₇	semidirect
302. C₂×#41	C₂×D₁₂₇	semidirect
310. #137	C₂×D₁₂₇	semidirect
311. #137	C₂×D₁₂₇	semidirect
321. AGL(1,ℤ/8)	C₂×D₁₂₇	semidirect
322. AGL(1,ℤ/8)	C₂×D₁₂₇	semidirect
326. #135	C₂×D₁₂₇	semidirect
337. C₂×M₁₆	C₂×D₁₂₇	semidirect
369. #41	C₂²×D₁₂₇	semidirect
376. C₂×Q₈	C₂²×D₁₂₇	semidirect
404. C₂×D₄	C₂²×D₁₂₇	semidirect
413. Q₁₆	C₂²×D₁₂₇	semidirect
418. SD₁₆	C₂²×D₁₂₇	semidirect
419. SD₁₆	C₂²×D₁₂₇	semidirect
423. D₈	C₂²×D₁₂₇	semidirect
428. M₁₆	C₂²×D₁₂₇	semidirect
431. C₂×C₈	C₂²×D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
#22550712	2
C₂×#16861255	2
#22550685	2
#22550683	2
#22550680	2
#22550678	2
#22550675	2
#22550674	2
C₂×#16861237	2
C₂×#16861234	2
AGL(1,ℤ/8)×D₁₂₇	2
#22550642	2
#575×C₁₂₇	2
#3585	127