Subgroups — #30653512

Order 16256.

1412 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550711	C₂	1	1	yes	maximal, characteristic, complemented
2	2₋¹⁺⁴×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550693	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550692	C₂	1	3	yes	maximal, complemented
5	#22550691	C₂	1	1	yes	maximal, characteristic, complemented
6	#22550690	C₂	1	3	yes	maximal, complemented
7	#22550687	C₂	1	1	yes	maximal, characteristic, complemented
8	#22550686	C₂	1	3	yes	maximal, complemented
9	#22550682	C₂	1	3	yes	maximal, complemented
10	#22550673	C₂	1	3	yes	maximal, complemented
11	#22550672	C₂	1	3	yes	maximal, complemented
12	C₂×#16861238	C₂	1	3	yes	maximal, complemented
13	#137×D₁₂₇	C₂	1	3	yes	maximal, complemented
14	#22550641	C₂	1	1	yes	maximal, characteristic, complemented
15	#577×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
16	#16861257	—	2	1	no	—
17	#16861257	C₂²	1	3	yes	complemented
18	#16861256	—	2	3	no	—
19	#16861256	—	2	1	no	—
20	#16861256	C₂²	1	1	yes	characteristic, complemented
21	#16861256	C₂²	1	1	yes	characteristic, complemented
22	#16861256	C₂²	1	3	yes	complemented
23	#16861256	C₂²	1	3	yes	complemented
24	#16861254	—	2	3	no	—
25	#16861254	C₂²	1	3	yes	complemented
26	C₂×#14523247	—	2	3	no	—
27	C₂×#14523247	C₂²	1	3	yes	—
28	#41×D₁₂₇	—	2	1	no	—
29	#41×D₁₂₇	—	2	3	no	—
30	#41×D₁₂₇	C₂²	1	3	yes	—
31	#41×D₁₂₇	C₂²	1	1	yes	characteristic
32	#41×D₁₂₇	C₂²	1	3	yes	complemented
33	C₂×Q₈×D₁₂₇	—	2	1	no	—
34	C₂×Q₈×D₁₂₇	C₂²	1	3	yes	complemented
35	#16861242	C₂²	1	3	yes	complemented
36	#16861242	C₂²	1	3	yes	complemented
37	#16861241	C₂²	1	3	yes	complemented
38	#16861241	C₂²	1	3	yes	complemented
39	#16861240	C₂²	1	3	yes	complemented
40	#16861239	C₂²	1	3	yes	complemented
41	#16861239	C₂²	1	3	yes	complemented
42	#16861238	C₂²	1	6	yes	complemented
43	#16861238	C₂²	1	3	yes	complemented
44	#16861238	C₂²	1	6	yes	complemented
45	#16861238	C₂²	1	6	yes	complemented
46	#16861238	C₂²	1	3	yes	complemented
47	#16861236	C₂²	1	1	yes	characteristic, complemented
48	#16861236	C₂²	1	3	yes	complemented
49	#16861235	C₂²	1	3	yes	complemented
50	#16861233	C₂²	1	3	yes	complemented
51	#16861233	C₂²	1	3	yes	complemented
52	#16861231	C₂²	1	3	yes	complemented
53	#16861230	C₂²	1	6	yes	complemented
54	#16861229	C₂²	1	3	yes	complemented
55	#16861229	C₂²	1	3	yes	complemented
56	#16861228	C₂²	1	6	yes	complemented
57	C₂×Dic₅₀₈	C₂²	1	3	yes	complemented
58	C₂×#14523238	C₂²	1	3	yes	complemented
59	Q₁₆×D₁₂₇	C₂²	1	6	yes	complemented
60	C₂×#14523236	C₂²	1	3	yes	complemented
61	SD₁₆×D₁₂₇	C₂²	1	6	yes	complemented
62	#16861217	C₂²	1	3	yes	complemented
63	#16861216	C₂²	1	1	yes	characteristic, complemented
64	#16861215	C₂²	1	3	yes	complemented
65	C₂×#14523231	C₂²	1	3	yes	complemented
66	M₁₆×D₁₂₇	C₂²	1	3	yes	complemented
67	2₋¹⁺⁴×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
68	H(5,𝔽₂)×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
69	#137×C₁₂₇	C₂²	1	3	yes	complemented
70	AGL(1,ℤ/8)×C₁₂₇	C₂²	1	3	yes	complemented
71	#135×C₁₂₇	C₂²	1	3	yes	complemented
72	C₂×SD₁₆×C₁₂₇	C₂²	1	3	yes	complemented
73	#131×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
74	#14523249	—	2	3	no	—
75	#14523249	D₄	1	1	yes	characteristic
76	#14523249	C₂³	1	3	yes	—
77	#14523249	C₂³	1	1	yes	characteristic
78	#14523248	—	2	3	no	—
79	#14523248	—	2	3	no	—
80	#14523248	—	2	6	no	—
81	#14523248	—	2	3	no	—
82	#14523248	—	2	3	no	—
83	#14523248	C₂³	1	3	yes	—
84	#14523248	C₂³	1	3	yes	—
85	#14523248	C₂³	1	3	yes	—
86	#14523247	—	2	3	no	—
87	#14523247	—	2	6	no	—
88	#14523247	—	2	6	no	—
89	#14523247	—	2	3	no	—
90	#14523247	—	2	3	no	—
91	#14523247	—	2	3	no	—
92	#14523247	—	2	3	no	—
93	#14523247	—	2	3	no	—
94	#14523247	—	2	3	no	—
95	#14523247	D₄	1	3	yes	—
96	#14523247	C₂³	1	3	yes	—
97	#14523247	C₂³	1	6	yes	—
98	#14523247	C₂³	1	3	yes	—
99	C₂×Dic₂₅₄	—	2	3	no	—
100	C₂×Dic₂₅₄	—	2	3	no	—
101	C₂×Dic₂₅₄	—	2	3	no	—
102	C₂×Dic₂₅₄	C₂³	1	3	yes	—
103	C₂×Dic₂₅₄	C₂³	1	3	yes	—
104	Q₈×D₁₂₇	—	2	3	no	—
105	Q₈×D₁₂₇	—	2	3	no	—
106	Q₈×D₁₂₇	—	2	3	no	—
107	Q₈×D₁₂₇	—	2	1	no	—
108	Q₈×D₁₂₇	—	2	1	no	—
109	Q₈×D₁₂₇	D₄	1	1	yes	characteristic
110	Q₈×D₁₂₇	C₂³	1	6	yes	—
111	Q₈×D₁₂₇	C₂³	1	3	yes	—
112	Q₈×D₁₂₇	C₂³	1	3	yes	—
113	C₂×C₂²⋊D₁₂₇	—	2	3	no	—
114	C₂×C₂²⋊D₁₂₇	—	2	6	no	—
115	D₄×D₁₂₇	—	2	3	no	—
116	D₄×D₁₂₇	—	2	3	no	—
117	D₄×D₁₂₇	—	2	3	no	—
118	D₄×D₁₂₇	D₄	1	3	yes	—
119	D₄×D₁₂₇	C₂³	1	3	yes	—
120	D₄×D₁₂₇	C₂³	1	1	yes	characteristic
121	C₂²×Dic₁₂₇	—	2	3	no	—
122	C₂×C₄×D₁₂₇	—	2	3	no	—
123	C₂×C₄×D₁₂₇	—	2	3	no	—
124	C₂×C₄×D₁₂₇	—	2	3	no	—
125	C₂×C₄×D₁₂₇	C₂³	1	3	yes	—
126	Dic₅₀₈	C₂³	1	6	yes	—
127	Dic₅₀₈	C₂³	1	3	yes	—
128	#14523238	C₂³	1	3	yes	—
129	#14523238	C₂³	1	6	yes	—
130	#14523238	C₂³	1	3	yes	—
131	#14523237	C₂³	1	3	yes	—
132	#14523237	C₂³	1	3	yes	—
133	#14523236	C₂³	1	6	yes	—
134	#14523236	C₂³	1	3	yes	—
135	#14523236	C₂³	1	3	yes	—
136	#14523235	C₂³	1	3	yes	—
137	#14523235	C₂³	1	1	yes	characteristic
138	D₁₀₁₆	C₂³	1	1	yes	characteristic
139	#14523233	C₂³	1	1	yes	characteristic
140	#14523233	C₂³	1	3	yes	—
141	#14523232	C₂³	1	3	yes	—
142	#14523231	C₂³	1	3	yes	—
143	#14523231	C₂³	1	1	yes	characteristic
144	#14523231	C₂³	1	3	yes	—
145	#14523231	C₂³	1	3	yes	—
146	C₂×C₁₂₇⋊C₈	C₂³	1	3	yes	—
147	C₈×D₁₂₇	C₂³	1	6	yes	—
148	#41×C₁₂₇	—	2	1	no	—
149	#41×C₁₂₇	—	2	3	no	—
150	#41×C₁₂₇	C₂³	1	3	yes	—
151	#41×C₁₂₇	C₂³	1	3	yes	—
152	#41×C₁₂₇	C₂³	1	1	yes	characteristic
153	C₂×Q₈×C₁₂₇	—	2	1	no	—
154	C₂×Q₈×C₁₂₇	C₂³	1	3	yes	—
155	C₂×D₄×C₁₂₇	—	2	3	no	—
156	C₂×D₄×C₁₂₇	C₂³	1	3	yes	—
157	Q₁₆×C₁₂₇	C₂³	1	3	yes	—
158	SD₁₆×C₁₂₇	C₂³	1	6	yes	—
159	SD₁₆×C₁₂₇	C₂³	1	3	yes	—
160	SD₁₆×C₁₂₇	C₂³	1	1	yes	characteristic
161	D₈×C₁₂₇	C₂³	1	3	yes	—
162	M₁₆×C₁₂₇	C₂³	1	3	yes	—
163	C₂×C₈×C₁₂₇	C₂³	1	3	yes	—
164	C₂²×D₁₂₇	—	2	1	no	—
165	C₂²×D₁₂₇	—	2	3	no	—
166	C₂²×D₁₂₇	C₂×D₄	1	3	yes	—
167	Dic₂₅₄	—	2	3	no	—
168	Dic₂₅₄	—	2	3	no	—
169	Dic₂₅₄	—	2	3	no	—
170	Dic₂₅₄	—	2	6	no	—
171	Dic₂₅₄	—	2	3	no	—
172	Dic₂₅₄	C₂×D₄	1	3	yes	—
173	Dic₂₅₄	C₂⁴	1	3	yes	—
174	Dic₂₅₄	C₂⁴	1	3	yes	—
175	D₅₀₈	—	2	1	no	—
176	D₅₀₈	—	2	3	no	—
177	D₅₀₈	C₂×D₄	1	3	yes	—
178	D₅₀₈	C₂⁴	1	1	yes	characteristic
179	D₅₀₈	C₂⁴	1	1	yes	characteristic
180	C₂²⋊D₁₂₇	—	2	3	no	—
181	C₂²⋊D₁₂₇	—	2	3	no	—
182	C₂²⋊D₁₂₇	—	2	3	no	—
183	C₂²⋊D₁₂₇	—	2	6	no	—
184	C₂²⋊D₁₂₇	—	2	3	no	—
185	C₂²⋊D₁₂₇	—	2	3	no	—
186	C₂²⋊D₁₂₇	—	2	1	no	—
187	C₂²⋊D₁₂₇	C₂×D₄	1	6	yes	—
188	C₂×Dic₁₂₇	—	2	3	no	—
189	C₂×Dic₁₂₇	—	2	3	no	—
190	C₂×Dic₁₂₇	—	2	3	no	—
191	C₂×Dic₁₂₇	—	2	3	no	—
192	C₂×Dic₁₂₇	—	2	6	no	—
193	C₂×Dic₁₂₇	C₂×D₄	1	3	yes	—
194	C₄×D₁₂₇	—	2	3	no	—
195	C₄×D₁₂₇	—	2	3	no	—
196	C₄×D₁₂₇	—	2	6	no	—
197	C₄×D₁₂₇	—	2	3	no	—
198	C₄×D₁₂₇	—	2	3	no	—
199	C₄×D₁₂₇	—	2	1	no	—
200	C₄×D₁₂₇	—	2	3	no	—
201	C₄×D₁₂₇	C₂×D₄	1	3	yes	—
202	C₄×D₁₂₇	C₂×D₄	1	3	yes	—
203	C₄×D₁₂₇	C₂⁴	1	3	yes	—
204	C₄×D₁₂₇	C₂⁴	1	1	yes	characteristic
205	C₁₂₇⋊C₈	C₂⁴	1	3	yes	—
206	C₁₂₇⋊C₈	C₂⁴	1	1	yes	characteristic
207	C₂³×C₁₂₇	—	2	3	no	—
208	Q₈×C₁₂₇	—	2	3	no	—
209	Q₈×C₁₂₇	C₂×D₄	1	1	yes	characteristic
210	Q₈×C₁₂₇	C₂⁴	1	3	yes	—
211	Q₈×C₁₂₇	C₂⁴	1	1	yes	characteristic
212	D₄×C₁₂₇	—	2	3	no	—
213	D₄×C₁₂₇	—	2	3	no	—
214	D₄×C₁₂₇	—	2	3	no	—
215	D₄×C₁₂₇	C₂×D₄	1	3	yes	—
216	D₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
217	D₄×C₁₂₇	C₂⁴	1	3	yes	—
218	C₂×C₄×C₁₂₇	—	2	3	no	—
219	C₂×C₄×C₁₂₇	—	2	3	no	—
220	C₂×C₄×C₁₂₇	—	2	3	no	—
221	C₂×C₄×C₁₂₇	C₂⁴	1	3	yes	—
222	C₈×C₁₂₇	C₂⁴	1	1	yes	characteristic
223	C₈×C₁₂₇	C₂⁴	1	3	yes	—
224	C₂²×C₁₂₇	—	2	1	no	—
225	C₂²×C₁₂₇	—	2	3	no	—
226	C₂²×C₁₂₇	—	8	3	no	—
227	C₂²×C₁₂₇	C₂²×D₄	1	3	yes	—
228	C₂×D₁₂₇	—	2	1	no	—
229	C₂×D₁₂₇	—	2	1	no	—
230	C₂×D₁₂₇	—	4	3	no	—
231	C₂×D₁₂₇	—	4	2	no	—
232	C₂×D₁₂₇	—	8	3	no	—
233	C₂×D₁₂₇	C₂²×D₄	1	1	yes	characteristic
234	C₂×D₁₂₇	C₂²×D₄	1	3	yes	—
235	C₄×C₁₂₇	—	2	1	no	—
236	C₄×C₁₂₇	—	2	3	no	—
237	C₄×C₁₂₇	C₂²×D₄	1	3	yes	—
238	C₄×C₁₂₇	C₂⁵	1	1	yes	characteristic
239	Dic₁₂₇	—	2	3	no	—
240	Dic₁₂₇	—	2	3	no	—
241	Dic₁₂₇	C₂²×D₄	1	1	yes	characteristic
242	Dic₁₂₇	C₂²×D₄	1	3	yes	—
243	C₂×C₁₂₇	—	2	3	no	—
244	C₂×C₁₂₇	—	4	1	no	—
245	C₂×C₁₂₇	—	4	3	no	—
246	C₂×C₁₂₇	C₂³×D₄	1	1	yes	characteristic
247	D₁₂₇	—	2	1	no	—
248	D₁₂₇	—	2	3	no	—
249	D₁₂₇	—	4	1	no	—
250	D₁₂₇	—	4	1	no	—
251	#3586	—	127	1	no	maximal, Sylow
252	C₁₂₇	#3586	1	1	yes	characteristic, complemented, Sylow
253	#585	—	127	1	no	—
254	C₂×2₋¹⁺⁴	—	127	1	no	—
255	#578	—	127	1	no	—
256	#578	—	127	3	no	—
257	#578	—	127	3	no	—
258	#578	—	127	1	no	—
259	#577	—	127	1	no	—
260	#577	—	127	3	no	—
261	#577	—	127	3	no	—
262	#577	D₁₂₇	1	1	yes	characteristic, complemented
263	#575	—	127	3	no	—
264	#575	—	127	3	no	—
265	C₂×#137	—	127	3	no	—
266	C₂×#137	—	127	3	no	—
267	#568	—	127	1	no	—
268	2₋¹⁺⁴	—	127	3	no	—
269	2₋¹⁺⁴	—	127	3	no	—
270	2₋¹⁺⁴	—	127	1	no	—
271	2₋¹⁺⁴	—	127	1	no	—
272	2₋¹⁺⁴	—	127	3	no	—
273	2₋¹⁺⁴	—	254	1	no	—
274	2₋¹⁺⁴	—	254	1	no	—
275	2₋¹⁺⁴	—	254	3	no	—
276	2₋¹⁺⁴	C₂×D₁₂₇	1	1	yes	characteristic, complemented
277	H(5,𝔽₂)	—	127	3	no	—
278	H(5,𝔽₂)	—	254	3	no	—
279	H(5,𝔽₂)	C₂×D₁₂₇	1	1	yes	characteristic, complemented
280	C₂×#41	—	127	1	no	—
281	C₂×#41	—	127	3	no	—
282	C₂×#41	—	127	3	no	—
283	C₂×#41	—	127	3	no	—
284	C₂×#41	—	254	3	no	—
285	C₂×#41	—	254	3	no	—
286	C₂×#41	—	254	1	no	—
287	C₂²×Q₈	—	127	3	no	—
288	C₂²×Q₈	—	254	1	no	—
289	#137	—	127	3	no	—
290	#137	—	127	3	no	—
291	#137	—	127	3	no	—
292	#137	—	127	3	no	—
293	#137	—	127	3	no	—
294	#137	—	127	6	no	—
295	#137	—	127	3	no	—
296	#137	—	127	6	no	—
297	#137	—	127	6	no	—
298	#137	—	127	3	no	—
299	#137	—	127	3	no	—
300	#137	—	127	3	no	—
301	#137	C₂×D₁₂₇	1	3	yes	complemented
302	AGL(1,ℤ/8)	—	127	3	no	—
303	AGL(1,ℤ/8)	—	127	1	no	—
304	AGL(1,ℤ/8)	—	127	3	no	—
305	AGL(1,ℤ/8)	—	127	3	no	—
306	AGL(1,ℤ/8)	—	127	3	no	—
307	AGL(1,ℤ/8)	C₂×D₁₂₇	1	3	yes	complemented
308	#135	—	127	3	no	—
309	#135	—	127	3	no	—
310	#135	—	127	6	no	—
311	#135	—	127	6	no	—
312	#135	—	127	3	no	—
313	#135	C₂×D₁₂₇	1	3	yes	complemented
314	C₂×Q₁₆	—	127	3	no	—
315	C₂×Q₁₆	—	127	6	no	—
316	C₂×Q₁₆	—	127	3	no	—
317	C₂×SD₁₆	—	127	3	no	—
318	C₂×SD₁₆	—	127	6	no	—
319	C₂×SD₁₆	C₂×D₁₂₇	1	3	yes	complemented
320	#131	—	127	1	no	—
321	#131	—	127	3	no	—
322	#131	—	127	3	no	—
323	#131	C₂×D₁₂₇	1	1	yes	characteristic, complemented
324	C₂×M₁₆	—	127	3	no	—
325	C₂×M₁₆	—	127	3	no	—
326	#41	—	2	1	no	—
327	#41	—	2	3	no	—
328	#41	—	127	1	no	—
329	#41	—	127	3	no	—
330	#41	—	127	3	no	—
331	#41	—	127	3	no	—
332	#41	—	127	1	no	—
333	#41	—	127	3	no	—
334	#41	—	127	6	no	—
335	#41	—	127	3	no	—
336	#41	—	127	3	no	—
337	#41	—	127	3	no	—
338	#41	—	254	3	no	—
339	#41	—	254	3	no	—
340	#41	—	254	3	no	—
341	#41	—	254	6	no	—
342	#41	—	254	3	no	—
343	#41	—	254	3	no	—
344	#41	—	254	3	no	—
345	#41	—	254	3	no	—
346	#41	—	254	3	no	—
347	#41	—	254	6	no	—
348	#41	—	254	6	no	—
349	#41	—	254	3	no	—
350	#41	—	254	3	no	—
351	#41	—	254	3	no	—
352	#41	—	254	3	no	—
353	#41	C₂²×D₁₂₇	1	3	yes	—
354	#41	C₂²×D₁₂₇	1	3	yes	—
355	#41	C₂²×D₁₂₇	1	1	yes	characteristic
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	127	1	no	—
358	C₂×Q₈	—	127	6	no	—
359	C₂×Q₈	—	127	3	no	—
360	C₂×Q₈	—	127	3	no	—
361	C₂×Q₈	—	127	3	no	—
362	C₂×Q₈	—	127	3	no	—
363	C₂×Q₈	—	254	3	no	—
364	C₂×Q₈	—	254	3	no	—
365	C₂×Q₈	—	254	3	no	—
366	C₂×Q₈	—	254	3	no	—
367	C₂×Q₈	—	254	3	no	—
368	C₂×Q₈	—	254	3	no	—
369	C₂×Q₈	—	254	1	no	—
370	C₂×Q₈	—	254	1	no	—
371	C₂×Q₈	C₂²×D₁₂₇	1	3	yes	—
372	C₂×D₄	—	2	3	no	—
373	C₂×D₄	—	127	3	no	—
374	C₂×D₄	—	127	3	no	—
375	C₂×D₄	—	127	1	no	—
376	C₂×D₄	—	254	3	no	—
377	C₂×D₄	—	254	3	no	—
378	C₂×D₄	—	254	3	no	—
379	C₂×D₄	—	254	6	no	—
380	C₂×D₄	—	254	3	no	—
381	C₂×D₄	C₂²×D₁₂₇	1	3	yes	—
382	C₂²×C₄	—	127	3	no	—
383	C₂²×C₄	—	254	3	no	—
384	C₂²×C₄	—	254	3	no	—
385	C₂²×C₄	—	254	3	no	—
386	C₂²×C₄	—	254	3	no	—
387	Q₁₆	—	127	3	no	—
388	Q₁₆	—	127	6	no	—
389	Q₁₆	—	127	3	no	—
390	Q₁₆	—	127	6	no	—
391	Q₁₆	—	127	3	no	—
392	Q₁₆	C₂²×D₁₂₇	1	3	yes	—
393	SD₁₆	—	127	3	no	—
394	SD₁₆	—	127	1	no	—
395	SD₁₆	—	127	6	no	—
396	SD₁₆	—	127	3	no	—
397	SD₁₆	—	127	3	no	—
398	SD₁₆	—	127	3	no	—
399	SD₁₆	—	127	3	no	—
400	SD₁₆	C₂²×D₁₂₇	1	6	yes	—
401	SD₁₆	C₂²×D₁₂₇	1	3	yes	—
402	SD₁₆	C₂²×D₁₂₇	1	1	yes	characteristic
403	D₈	—	127	3	no	—
404	D₈	—	127	1	no	—
405	D₈	—	127	1	no	—
406	D₈	C₂²×D₁₂₇	1	3	yes	—
407	M₁₆	—	127	3	no	—
408	M₁₆	—	127	3	no	—
409	M₁₆	—	127	1	no	—
410	M₁₆	—	127	3	no	—
411	M₁₆	—	127	3	no	—
412	M₁₆	C₂²×D₁₂₇	1	3	yes	—
413	C₂×C₈	—	127	3	no	—
414	C₂×C₈	—	127	6	no	—
415	C₂×C₈	C₂²×D₁₂₇	1	3	yes	—
416	C₂³	—	2	3	no	—
417	C₂³	—	127	3	no	—
418	C₂³	—	254	3	no	—
419	C₂³	—	254	1	no	—
420	Q₈	—	2	3	no	—
421	Q₈	—	127	3	no	—
422	Q₈	—	127	3	no	—
423	Q₈	—	127	3	no	—
424	Q₈	—	254	3	no	—
425	Q₈	—	254	6	no	—
426	Q₈	—	254	3	no	—
427	Q₈	—	254	3	no	—
428	Q₈	—	254	3	no	—
429	Q₈	D₄×D₁₂₇	1	1	yes	characteristic
430	Q₈	C₂³×D₁₂₇	1	3	yes	—
431	Q₈	C₂³×D₁₂₇	1	1	yes	characteristic
432	D₄	—	2	3	no	—
433	D₄	—	2	3	no	—
434	D₄	—	2	3	no	—
435	D₄	—	127	6	no	—
436	D₄	—	127	3	no	—
437	D₄	—	127	1	no	—
438	D₄	—	127	1	no	—
439	D₄	—	254	1	no	—
440	D₄	—	254	3	no	—
441	D₄	—	254	3	no	—
442	D₄	—	254	1	no	—
443	D₄	—	254	3	no	—
444	D₄	—	254	6	no	—
445	D₄	—	254	3	no	—
446	D₄	—	254	3	no	—
447	D₄	—	254	3	no	—
448	D₄	D₄×D₁₂₇	1	3	yes	—
449	D₄	C₂³×D₁₂₇	1	1	yes	characteristic
450	D₄	C₂³×D₁₂₇	1	3	yes	—
451	C₂×C₄	—	2	3	no	—
452	C₂×C₄	—	2	3	no	—
453	C₂×C₄	—	2	3	no	—
454	C₂×C₄	—	127	3	no	—
455	C₂×C₄	—	127	3	no	—
456	C₂×C₄	—	127	3	no	—
457	C₂×C₄	—	127	3	no	—
458	C₂×C₄	—	127	1	no	—
459	C₂×C₄	—	254	1	no	—
460	C₂×C₄	—	254	3	no	—
461	C₂×C₄	—	254	3	no	—
462	C₂×C₄	—	254	3	no	—
463	C₂×C₄	—	254	6	no	—
464	C₂×C₄	—	254	3	no	—
465	C₂×C₄	—	254	6	no	—
466	C₂×C₄	—	254	3	no	—
467	C₂×C₄	—	254	3	no	—
468	C₂×C₄	—	254	3	no	—
469	C₂×C₄	—	254	3	no	—
470	C₂×C₄	—	254	3	no	—
471	C₂×C₄	C₂³×D₁₂₇	1	3	yes	—
472	C₈	—	127	1	no	—
473	C₈	—	127	3	no	—
474	C₈	C₂³×D₁₂₇	1	3	yes	—
475	C₈	C₂³×D₁₂₇	1	1	yes	characteristic
476	C₂²	—	2	1	no	—
477	C₂²	—	2	3	no	—
478	C₂²	—	8	3	no	—
479	C₂²	—	127	1	no	—
480	C₂²	—	127	3	no	—
481	C₂²	—	1016	3	no	—
482	C₂²	—	508	3	no	—
483	C₂²	—	508	2	no	—
484	C₂²	—	254	1	no	—
485	C₂²	—	254	1	no	—
486	C₂²	C₂×D₄×D₁₂₇	1	3	yes	—
487	C₄	—	2	1	no	—
488	C₄	—	2	3	no	—
489	C₄	—	127	1	no	—
490	C₄	—	127	3	no	—
491	C₄	—	254	3	no	—
492	C₄	—	254	3	no	—
493	C₄	C₂×D₄×D₁₂₇	1	3	yes	—
494	C₄	C₂⁴×D₁₂₇	1	1	yes	characteristic
495	C₂	—	2	3	no	—
496	C₂	—	4	3	no	—
497	C₂	—	4	1	no	—
498	C₂	—	508	1	no	—
499	C₂	—	508	1	no	—
500	C₂	—	254	3	no	—
501	C₂	—	254	1	no	—
502	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	#577×C₁₂₇	C₂
socle	C₂×C₁₂₇	C₂³×D₄
hypercenter	#577	D₁₂₇
hypocenter	C₁₂₇	#3586
LCS	G ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂ ◁ #41 ◁ #577

Complements

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

N	H ≅ G/N	type
1. #22550711	C₂	semidirect
2. 2₋¹⁺⁴×D₁₂₇	C₂	semidirect
3. #22550693	C₂	semidirect
4. #22550692	C₂	semidirect
5. #22550691	C₂	semidirect
6. #22550690	C₂	semidirect
7. #22550687	C₂	semidirect
8. #22550686	C₂	semidirect
9. #22550682	C₂	semidirect
10. #22550673	C₂	semidirect
11. #22550672	C₂	semidirect
12. C₂×#16861238	C₂	semidirect
13. #137×D₁₂₇	C₂	semidirect
14. #22550641	C₂	semidirect
15. #577×C₁₂₇	C₂	semidirect
17. #16861257	C₂²	semidirect
20. #16861256	C₂²	semidirect
21. #16861256	C₂²	semidirect
22. #16861256	C₂²	semidirect
23. #16861256	C₂²	semidirect
25. #16861254	C₂²	semidirect
32. #41×D₁₂₇	C₂²	semidirect
34. C₂×Q₈×D₁₂₇	C₂²	semidirect
35. #16861242	C₂²	semidirect
36. #16861242	C₂²	semidirect
37. #16861241	C₂²	semidirect
38. #16861241	C₂²	semidirect
39. #16861240	C₂²	semidirect
40. #16861239	C₂²	semidirect
41. #16861239	C₂²	semidirect
42. #16861238	C₂²	semidirect
43. #16861238	C₂²	semidirect
44. #16861238	C₂²	semidirect
45. #16861238	C₂²	semidirect
46. #16861238	C₂²	semidirect
47. #16861236	C₂²	semidirect
48. #16861236	C₂²	semidirect
49. #16861235	C₂²	semidirect
50. #16861233	C₂²	semidirect
51. #16861233	C₂²	semidirect
52. #16861231	C₂²	semidirect
53. #16861230	C₂²	semidirect
54. #16861229	C₂²	semidirect
55. #16861229	C₂²	semidirect
56. #16861228	C₂²	semidirect
57. C₂×Dic₅₀₈	C₂²	semidirect
58. C₂×#14523238	C₂²	semidirect
59. Q₁₆×D₁₂₇	C₂²	semidirect
60. C₂×#14523236	C₂²	semidirect
61. SD₁₆×D₁₂₇	C₂²	semidirect
62. #16861217	C₂²	semidirect
63. #16861216	C₂²	semidirect
64. #16861215	C₂²	semidirect
65. C₂×#14523231	C₂²	semidirect
66. M₁₆×D₁₂₇	C₂²	semidirect
67. 2₋¹⁺⁴×C₁₂₇	C₂²	semidirect
68. H(5,𝔽₂)×C₁₂₇	C₂²	semidirect
69. #137×C₁₂₇	C₂²	semidirect
70. AGL(1,ℤ/8)×C₁₂₇	C₂²	semidirect
71. #135×C₁₂₇	C₂²	semidirect
72. C₂×SD₁₆×C₁₂₇	C₂²	semidirect
73. #131×C₁₂₇	C₂²	semidirect
252. C₁₂₇	#3586	semidirect
262. #577	D₁₂₇	semidirect
276. 2₋¹⁺⁴	C₂×D₁₂₇	semidirect
279. H(5,𝔽₂)	C₂×D₁₂₇	semidirect
301. #137	C₂×D₁₂₇	semidirect
307. AGL(1,ℤ/8)	C₂×D₁₂₇	semidirect
313. #135	C₂×D₁₂₇	semidirect
319. C₂×SD₁₆	C₂×D₁₂₇	semidirect
323. #131	C₂×D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
#22550711	2
2₋¹⁺⁴×D₁₂₇	2
#22550693	2
#22550692	2
#22550691	2
#22550690	2
#22550687	2
#22550686	2
#22550682	2
#22550673	2
#22550672	2
C₂×#16861238	2
#137×D₁₂₇	2
#22550641	2
#577×C₁₂₇	2
#3586	127