Subgroups — #30653499

Order 16256.

1424 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550712	C₂	1	2	yes	maximal, complemented
2	#22550690	C₂	1	2	yes	maximal, complemented
3	#22550689	C₂	1	2	yes	maximal, complemented
4	#22550683	C₂	1	4	yes	maximal, complemented
5	#22550682	C₂	1	4	yes	maximal, complemented
6	#22550678	C₂	1	2	yes	maximal, complemented
7	#22550677	C₂	1	2	yes	maximal, complemented
8	#22550674	C₂	1	2	yes	maximal, complemented
9	#22550673	C₂	1	4	yes	maximal, complemented
10	C₂×#16861231	C₂	1	1	yes	maximal, characteristic, complemented
11	#135×D₁₂₇	C₂	1	4	yes	maximal, complemented
12	C₂×#16861215	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#135×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#16861257	C₂²	1	4	yes	complemented
15	#16861256	—	2	2	no	—
16	#16861256	C₂²	1	4	yes	complemented
17	#16861255	—	2	2	no	—
18	#16861255	C₂²	1	4	yes	complemented
19	#16861254	—	2	4	no	—
20	#16861254	C₂²	1	4	yes	complemented
21	C₂×#14523248	—	2	4	no	—
22	C₂×#14523248	C₂²	1	1	yes	characteristic
23	C₂×#14523248	C₂²	1	2	yes	complemented
24	#41×D₁₂₇	—	2	4	no	—
25	#41×D₁₂₇	C₂²	1	8	yes	complemented
26	#16861241	C₂²	1	8	yes	complemented
27	#16861240	C₂²	1	4	yes	complemented
28	#16861239	C₂²	1	4	yes	complemented
29	#16861238	C₂²	1	8	yes	complemented
30	#16861236	C₂²	1	8	yes	complemented
31	#16861235	C₂²	1	4	yes	complemented
32	#16861234	C₂²	1	4	yes	complemented
33	#16861233	C₂²	1	8	yes	complemented
34	#16861232	C₂²	1	4	yes	complemented
35	#16861231	C₂²	1	2	yes	complemented
36	#16861231	C₂²	1	2	yes	complemented
37	#16861231	C₂²	1	2	yes	complemented
38	#16861231	C₂²	1	2	yes	complemented
39	#16861230	C₂²	1	8	yes	complemented
40	#16861229	C₂²	1	8	yes	complemented
41	#16861228	C₂²	1	4	yes	complemented
42	C₂×Dic₅₀₈	C₂²	1	1	yes	characteristic, complemented
43	Q₁₆×D₁₂₇	C₂²	1	4	yes	complemented
44	C₂×#14523237	C₂²	1	2	yes	complemented
45	SD₁₆×D₁₂₇	C₂²	1	8	yes	complemented
46	C₂×D₁₀₁₆	C₂²	1	1	yes	characteristic, complemented
47	D₈×D₁₂₇	C₂²	1	4	yes	complemented
48	#16861215	C₂²	1	2	yes	complemented
49	#16861215	C₂²	1	2	yes	complemented
50	#16861215	C₂²	1	2	yes	complemented
51	#16861215	C₂²	1	2	yes	complemented
52	C₂×#14523232	C₂²	1	1	yes	characteristic, complemented
53	C₂×#14523231	C₂²	1	2	yes	complemented
54	C₂×C₈×D₁₂₇	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₂₇	C₂²	1	2	yes	complemented
56	#135×C₁₂₇	C₂²	1	2	yes	complemented
57	#135×C₁₂₇	C₂²	1	2	yes	complemented
58	#135×C₁₂₇	C₂²	1	2	yes	complemented
59	#135×C₁₂₇	C₂²	1	2	yes	complemented
60	C₂×Q₁₆×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
61	C₂×SD₁₆×C₁₂₇	C₂²	1	2	yes	complemented
62	C₂×D₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
63	C₂²×C₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
64	#14523249	—	2	4	no	—
65	#14523249	C₂³	1	8	yes	—
66	#14523248	—	2	4	no	—
67	#14523248	—	2	4	no	—
68	#14523248	—	2	8	no	—
69	#14523248	—	2	8	no	—
70	#14523248	—	2	2	no	—
71	#14523248	—	2	2	no	—
72	#14523248	D₄	1	2	yes	—
73	#14523248	D₄	1	2	yes	—
74	#14523248	C₂³	1	4	yes	—
75	#14523248	C₂³	1	4	yes	—
76	#14523248	C₂³	1	2	yes	—
77	#14523248	C₂³	1	2	yes	—
78	#14523247	—	2	4	no	—
79	#14523247	—	2	8	no	—
80	#14523247	—	2	8	no	—
81	#14523247	C₂³	1	8	yes	—
82	C₂×Dic₂₅₄	—	2	4	no	—
83	C₂×Dic₂₅₄	D₄	1	1	yes	characteristic
84	C₂×Dic₂₅₄	C₂³	1	2	yes	—
85	Q₈×D₁₂₇	—	2	4	no	—
86	Q₈×D₁₂₇	C₂³	1	8	yes	—
87	C₂×D₅₀₈	—	2	4	no	—
88	C₂×D₅₀₈	D₄	1	1	yes	characteristic
89	C₂×D₅₀₈	C₂³	1	2	yes	—
90	C₂×C₂²⋊D₁₂₇	—	2	8	no	—
91	C₂×C₂²⋊D₁₂₇	—	2	2	no	—
92	C₂×C₂²⋊D₁₂₇	D₄	1	2	yes	—
93	D₄×D₁₂₇	—	2	8	no	—
94	D₄×D₁₂₇	—	2	4	no	—
95	D₄×D₁₂₇	—	2	8	no	—
96	D₄×D₁₂₇	C₂³	1	8	yes	—
97	C₂×C₄×D₁₂₇	—	2	8	no	—
98	C₂×C₄×D₁₂₇	—	2	2	no	—
99	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
100	Dic₅₀₈	C₂³	1	2	yes	—
101	Dic₅₀₈	C₂³	1	2	yes	—
102	#14523238	C₂³	1	8	yes	—
103	#14523237	C₂³	1	4	yes	—
104	#14523237	C₂³	1	4	yes	—
105	#14523236	C₂³	1	8	yes	—
106	#14523235	C₂³	1	8	yes	—
107	D₁₀₁₆	C₂³	1	2	yes	—
108	D₁₀₁₆	C₂³	1	2	yes	—
109	#14523233	C₂³	1	8	yes	—
110	#14523232	C₂³	1	2	yes	—
111	#14523232	C₂³	1	2	yes	—
112	#14523231	C₂³	1	4	yes	—
113	#14523231	C₂³	1	4	yes	—
114	C₂×C₁₂₇⋊C₈	C₂³	1	2	yes	—
115	C₈×D₁₂₇	C₂³	1	4	yes	—
116	C₈×D₁₂₇	C₂³	1	4	yes	—
117	#41×C₁₂₇	—	2	2	no	—
118	#41×C₁₂₇	—	2	2	no	—
119	#41×C₁₂₇	C₂³	1	4	yes	—
120	#41×C₁₂₇	C₂³	1	4	yes	—
121	C₂×Q₈×C₁₂₇	C₂³	1	2	yes	—
122	C₂×D₄×C₁₂₇	—	2	2	no	—
123	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
124	C₂²×C₄×C₁₂₇	—	2	2	no	—
125	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
126	Q₁₆×C₁₂₇	C₂³	1	2	yes	—
127	Q₁₆×C₁₂₇	C₂³	1	2	yes	—
128	SD₁₆×C₁₂₇	C₂³	1	4	yes	—
129	SD₁₆×C₁₂₇	C₂³	1	4	yes	—
130	D₈×C₁₂₇	C₂³	1	2	yes	—
131	D₈×C₁₂₇	C₂³	1	2	yes	—
132	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
133	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
134	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
135	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
136	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
137	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
138	C₂²×D₁₂₇	—	2	2	no	—
139	C₂²×D₁₂₇	—	2	8	no	—
140	C₂²×D₁₂₇	C₂×D₄	1	2	yes	—
141	Dic₂₅₄	—	2	2	no	—
142	Dic₂₅₄	—	2	8	no	—
143	Dic₂₅₄	C₂×D₄	1	2	yes	—
144	Dic₂₅₄	C₂×D₄	1	2	yes	—
145	Dic₂₅₄	C₂⁴	1	4	yes	—
146	D₅₀₈	—	2	8	no	—
147	D₅₀₈	—	2	2	no	—
148	D₅₀₈	C₂×D₄	1	2	yes	—
149	D₅₀₈	C₂×D₄	1	2	yes	—
150	D₅₀₈	C₂⁴	1	4	yes	—
151	C₂²⋊D₁₂₇	—	2	4	no	—
152	C₂²⋊D₁₂₇	—	2	4	no	—
153	C₂²⋊D₁₂₇	—	2	8	no	—
154	C₂²⋊D₁₂₇	—	2	8	no	—
155	C₂²⋊D₁₂₇	C₂×D₄	1	4	yes	—
156	C₂²⋊D₁₂₇	C₂×D₄	1	4	yes	—
157	C₂×Dic₁₂₇	—	2	2	no	—
158	C₂×Dic₁₂₇	—	2	8	no	—
159	C₂×Dic₁₂₇	C₂×D₄	1	2	yes	—
160	C₄×D₁₂₇	—	2	8	no	—
161	C₄×D₁₂₇	—	2	4	no	—
162	C₄×D₁₂₇	—	2	4	no	—
163	C₄×D₁₂₇	—	2	8	no	—
164	C₄×D₁₂₇	C₂×D₄	1	4	yes	—
165	C₄×D₁₂₇	C₂⁴	1	4	yes	—
166	C₁₂₇⋊C₈	C₂⁴	1	4	yes	—
167	C₂³×C₁₂₇	—	2	2	no	—
168	C₂³×C₁₂₇	C₂×D₄	1	1	yes	characteristic
169	Q₈×C₁₂₇	—	2	2	no	—
170	Q₈×C₁₂₇	C₂⁴	1	4	yes	—
171	D₄×C₁₂₇	—	2	4	no	—
172	D₄×C₁₂₇	—	2	4	no	—
173	D₄×C₁₂₇	—	2	2	no	—
174	D₄×C₁₂₇	C₂⁴	1	4	yes	—
175	C₂×C₄×C₁₂₇	—	2	2	no	—
176	C₂×C₄×C₁₂₇	—	2	4	no	—
177	C₂×C₄×C₁₂₇	—	2	4	no	—
178	C₂×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
183	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
184	C₈×C₁₂₇	C₂⁴	1	1	yes	characteristic
185	C₈×C₁₂₇	C₂⁴	1	1	yes	characteristic
186	C₈×C₁₂₇	C₂⁴	1	1	yes	characteristic
187	C₈×C₁₂₇	C₂⁴	1	1	yes	characteristic
188	C₂²×C₁₂₇	—	2	4	no	—
189	C₂²×C₁₂₇	—	4	1	no	—
190	C₂²×C₁₂₇	—	8	2	no	—
191	C₂²×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
192	C₂²×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
193	C₂²×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
194	C₂×D₁₂₇	—	2	4	no	—
195	C₂×D₁₂₇	—	4	2	no	—
196	C₂×D₁₂₇	—	8	8	no	—
197	C₂×D₁₂₇	—	8	2	no	—
198	C₂×D₁₂₇	C₂²×D₄	1	4	yes	—
199	C₄×C₁₂₇	—	2	4	no	—
200	C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
201	C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
202	C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
203	C₄×C₁₂₇	C₂⁵	1	1	yes	characteristic
204	Dic₁₂₇	—	2	4	no	—
205	Dic₁₂₇	C₂²×D₄	1	4	yes	—
206	C₂×C₁₂₇	—	2	1	no	—
207	C₂×C₁₂₇	—	2	1	no	—
208	C₂×C₁₂₇	—	2	1	no	—
209	C₂×C₁₂₇	—	4	4	no	—
210	C₂×C₁₂₇	C₂³×D₄	1	1	yes	characteristic
211	D₁₂₇	—	2	4	no	—
212	D₁₂₇	—	4	4	no	—
213	#3584	—	127	1	no	maximal, Sylow
214	C₁₂₇	#3584	1	1	yes	characteristic, complemented, Sylow
215	#585	—	127	2	no	—
216	#578	—	127	2	no	—
217	#578	—	127	2	no	—
218	#577	—	127	4	no	—
219	#577	—	127	4	no	—
220	#576	—	127	2	no	—
221	#576	—	127	2	no	—
222	#575	—	127	2	no	—
223	#575	—	127	4	no	—
224	C₂×#135	—	127	4	no	—
225	C₂×#135	—	127	1	no	—
226	C₂×#135	D₁₂₇	1	1	yes	characteristic, complemented
227	C₂×#131	—	127	1	no	—
228	2₋¹⁺⁴	—	127	4	no	—
229	2₋¹⁺⁴	—	127	4	no	—
230	2₋¹⁺⁴	—	254	2	no	—
231	H(5,𝔽₂)	—	127	4	no	—
232	H(5,𝔽₂)	—	127	4	no	—
233	H(5,𝔽₂)	—	254	4	no	—
234	H(5,𝔽₂)	—	254	2	no	—
235	C₂×#41	—	127	1	no	—
236	C₂×#41	—	127	8	no	—
237	C₂×#41	—	127	2	no	—
238	C₂×#41	—	254	4	no	—
239	C₂×#41	—	254	4	no	—
240	C₂×#41	C₂×D₁₂₇	1	2	yes	complemented
241	#137	—	127	4	no	—
242	#137	—	127	4	no	—
243	#137	—	127	8	no	—
244	#137	—	127	8	no	—
245	AGL(1,ℤ/8)	—	127	4	no	—
246	AGL(1,ℤ/8)	—	127	4	no	—
247	AGL(1,ℤ/8)	—	127	8	no	—
248	AGL(1,ℤ/8)	—	127	8	no	—
249	#135	—	127	8	no	—
250	#135	—	127	4	no	—
251	#135	—	127	8	no	—
252	#135	—	127	4	no	—
253	#135	—	127	2	no	—
254	#135	—	127	2	no	—
255	#135	—	127	2	no	—
256	#135	—	127	2	no	—
257	#135	C₂×D₁₂₇	1	2	yes	complemented
258	#135	C₂×D₁₂₇	1	2	yes	complemented
259	#135	C₂×D₁₂₇	1	2	yes	complemented
260	#135	C₂×D₁₂₇	1	2	yes	complemented
261	C₂×Q₁₆	—	127	4	no	—
262	C₂×Q₁₆	—	127	1	no	—
263	C₂×Q₁₆	C₂×D₁₂₇	1	1	yes	characteristic, complemented
264	C₂×SD₁₆	—	127	8	no	—
265	C₂×SD₁₆	—	127	2	no	—
266	C₂×SD₁₆	C₂×D₁₂₇	1	2	yes	complemented
267	C₂×D₈	—	127	4	no	—
268	C₂×D₈	—	127	1	no	—
269	C₂×D₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
270	#131	—	127	2	no	—
271	#131	—	127	2	no	—
272	#131	—	127	2	no	—
273	#131	—	127	2	no	—
274	C₂×M₁₆	—	127	1	no	—
275	C₂×M₁₆	—	127	2	no	—
276	C₂²×C₈	—	127	2	no	—
277	C₂²×C₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
278	#41	—	2	2	no	—
279	#41	—	2	2	no	—
280	#41	—	127	2	no	—
281	#41	—	127	2	no	—
282	#41	—	127	2	no	—
283	#41	—	127	2	no	—
284	#41	—	127	8	no	—
285	#41	—	127	8	no	—
286	#41	—	127	4	no	—
287	#41	—	127	4	no	—
288	#41	—	254	8	no	—
289	#41	—	254	8	no	—
290	#41	—	254	4	no	—
291	#41	—	254	4	no	—
292	#41	—	254	8	no	—
293	#41	—	254	8	no	—
294	#41	—	254	4	no	—
295	#41	—	254	4	no	—
296	#41	—	254	2	no	—
297	#41	—	254	2	no	—
298	#41	C₂²×D₁₂₇	1	4	yes	—
299	#41	C₂²×D₁₂₇	1	4	yes	—
300	C₂×Q₈	—	127	1	no	—
301	C₂×Q₈	—	127	8	no	—
302	C₂×Q₈	—	127	2	no	—
303	C₂×Q₈	—	254	4	no	—
304	C₂×Q₈	—	254	4	no	—
305	C₂×Q₈	C₂²×D₁₂₇	1	2	yes	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	127	2	no	—
308	C₂×D₄	—	127	8	no	—
309	C₂×D₄	—	127	1	no	—
310	C₂×D₄	—	127	2	no	—
311	C₂×D₄	—	254	4	no	—
312	C₂×D₄	—	254	8	no	—
313	C₂×D₄	—	254	4	no	—
314	C₂×D₄	—	254	8	no	—
315	C₂×D₄	—	254	8	no	—
316	C₂×D₄	—	254	2	no	—
317	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	127	2	no	—
320	C₂²×C₄	—	254	8	no	—
321	C₂²×C₄	—	254	2	no	—
322	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
323	Q₁₆	—	127	8	no	—
324	Q₁₆	—	127	2	no	—
325	Q₁₆	—	127	2	no	—
326	Q₁₆	C₂²×D₁₂₇	1	2	yes	—
327	Q₁₆	C₂²×D₁₂₇	1	2	yes	—
328	SD₁₆	—	127	8	no	—
329	SD₁₆	—	127	8	no	—
330	SD₁₆	—	127	4	no	—
331	SD₁₆	—	127	4	no	—
332	SD₁₆	C₂²×D₁₂₇	1	4	yes	—
333	SD₁₆	C₂²×D₁₂₇	1	4	yes	—
334	D₈	—	127	8	no	—
335	D₈	—	127	2	no	—
336	D₈	—	127	2	no	—
337	D₈	C₂²×D₁₂₇	1	2	yes	—
338	D₈	C₂²×D₁₂₇	1	2	yes	—
339	M₁₆	—	127	2	no	—
340	M₁₆	—	127	2	no	—
341	M₁₆	—	127	4	no	—
342	M₁₆	—	127	4	no	—
343	C₂×C₈	—	127	2	no	—
344	C₂×C₈	—	127	4	no	—
345	C₂×C₈	—	127	4	no	—
346	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
347	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
348	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
349	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
350	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
351	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
352	C₂³	—	2	2	no	—
353	C₂³	—	127	2	no	—
354	C₂³	—	254	8	no	—
355	C₂³	—	254	2	no	—
356	C₂³	D₄×D₁₂₇	1	1	yes	characteristic
357	Q₈	—	2	2	no	—
358	Q₈	—	127	2	no	—
359	Q₈	—	127	2	no	—
360	Q₈	—	127	4	no	—
361	Q₈	—	254	8	no	—
362	Q₈	—	254	2	no	—
363	Q₈	C₂³×D₁₂₇	1	4	yes	—
364	D₄	—	2	4	no	—
365	D₄	—	2	4	no	—
366	D₄	—	2	2	no	—
367	D₄	—	127	4	no	—
368	D₄	—	127	4	no	—
369	D₄	—	127	2	no	—
370	D₄	—	127	2	no	—
371	D₄	—	127	4	no	—
372	D₄	—	254	8	no	—
373	D₄	—	254	8	no	—
374	D₄	—	254	8	no	—
375	D₄	—	254	4	no	—
376	D₄	—	254	4	no	—
377	D₄	—	254	2	no	—
378	D₄	C₂³×D₁₂₇	1	4	yes	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	127	2	no	—
383	C₂×C₄	—	127	4	no	—
384	C₂×C₄	—	127	4	no	—
385	C₂×C₄	—	254	8	no	—
386	C₂×C₄	—	254	8	no	—
387	C₂×C₄	—	254	8	no	—
388	C₂×C₄	—	254	2	no	—
389	C₂×C₄	—	254	4	no	—
390	C₂×C₄	—	254	4	no	—
391	C₂×C₄	D₄×D₁₂₇	1	1	yes	characteristic
392	C₂×C₄	D₄×D₁₂₇	1	1	yes	characteristic
393	C₂×C₄	D₄×D₁₂₇	1	1	yes	characteristic
394	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
395	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
396	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
397	C₈	—	127	4	no	—
398	C₈	C₂³×D₁₂₇	1	1	yes	characteristic
399	C₈	C₂³×D₁₂₇	1	1	yes	characteristic
400	C₈	C₂³×D₁₂₇	1	1	yes	characteristic
401	C₈	C₂³×D₁₂₇	1	1	yes	characteristic
402	C₂²	—	2	4	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	127	4	no	—
406	C₂²	—	1016	2	no	—
407	C₂²	—	1016	8	no	—
408	C₂²	—	508	2	no	—
409	C₂²	—	254	4	no	—
410	C₂²	C₂×D₄×D₁₂₇	1	1	yes	characteristic
411	C₂²	C₂×D₄×D₁₂₇	1	1	yes	characteristic
412	C₂²	C₂×D₄×D₁₂₇	1	1	yes	characteristic
413	C₄	—	2	4	no	—
414	C₄	—	127	4	no	—
415	C₄	—	254	4	no	—
416	C₄	C₂×D₄×D₁₂₇	1	1	yes	characteristic
417	C₄	C₂×D₄×D₁₂₇	1	1	yes	characteristic
418	C₄	C₂×D₄×D₁₂₇	1	1	yes	characteristic
419	C₄	C₂⁴×D₁₂₇	1	1	yes	characteristic
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	4	4	no	—
424	C₂	—	508	4	no	—
425	C₂	—	254	4	no	—
426	C₂	C₂²×D₄×D₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×D₁₂₇
commutator, cosocle	C₄×C₁₂₇	C₂⁵
Frattini	C₄	C₂⁴×D₁₂₇
Fitting	C₂×#135×C₁₂₇	C₂
socle	C₂×C₁₂₇	C₂³×D₄
hypercenter	C₂×#135	D₁₂₇
hypocenter	C₁₂₇	#3584
LCS	G ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. #22550712	C₂	semidirect
2. #22550690	C₂	semidirect
3. #22550689	C₂	semidirect
4. #22550683	C₂	semidirect
5. #22550682	C₂	semidirect
6. #22550678	C₂	semidirect
7. #22550677	C₂	semidirect
8. #22550674	C₂	semidirect
9. #22550673	C₂	semidirect
10. C₂×#16861231	C₂	semidirect
11. #135×D₁₂₇	C₂	semidirect
12. C₂×#16861215	C₂	semidirect
13. C₂×#135×C₁₂₇	C₂	semidirect
14. #16861257	C₂²	semidirect
16. #16861256	C₂²	semidirect
18. #16861255	C₂²	semidirect
20. #16861254	C₂²	semidirect
23. C₂×#14523248	C₂²	semidirect
25. #41×D₁₂₇	C₂²	semidirect
26. #16861241	C₂²	semidirect
27. #16861240	C₂²	semidirect
28. #16861239	C₂²	semidirect
29. #16861238	C₂²	semidirect
30. #16861236	C₂²	semidirect
31. #16861235	C₂²	semidirect
32. #16861234	C₂²	semidirect
33. #16861233	C₂²	semidirect
34. #16861232	C₂²	semidirect
35. #16861231	C₂²	semidirect
36. #16861231	C₂²	semidirect
37. #16861231	C₂²	semidirect
38. #16861231	C₂²	semidirect
39. #16861230	C₂²	semidirect
40. #16861229	C₂²	semidirect
41. #16861228	C₂²	semidirect
42. C₂×Dic₅₀₈	C₂²	semidirect
43. Q₁₆×D₁₂₇	C₂²	semidirect
44. C₂×#14523237	C₂²	semidirect
45. SD₁₆×D₁₂₇	C₂²	semidirect
46. C₂×D₁₀₁₆	C₂²	semidirect
47. D₈×D₁₂₇	C₂²	semidirect
48. #16861215	C₂²	semidirect
49. #16861215	C₂²	semidirect
50. #16861215	C₂²	semidirect
51. #16861215	C₂²	semidirect
52. C₂×#14523232	C₂²	semidirect
53. C₂×#14523231	C₂²	semidirect
54. C₂×C₈×D₁₂₇	C₂²	semidirect
55. C₂×#41×C₁₂₇	C₂²	semidirect
56. #135×C₁₂₇	C₂²	semidirect
57. #135×C₁₂₇	C₂²	semidirect
58. #135×C₁₂₇	C₂²	semidirect
59. #135×C₁₂₇	C₂²	semidirect
60. C₂×Q₁₆×C₁₂₇	C₂²	semidirect
61. C₂×SD₁₆×C₁₂₇	C₂²	semidirect
62. C₂×D₈×C₁₂₇	C₂²	semidirect
63. C₂²×C₈×C₁₂₇	C₂²	semidirect
214. C₁₂₇	#3584	semidirect
226. C₂×#135	D₁₂₇	semidirect
240. C₂×#41	C₂×D₁₂₇	semidirect
257. #135	C₂×D₁₂₇	semidirect
258. #135	C₂×D₁₂₇	semidirect
259. #135	C₂×D₁₂₇	semidirect
260. #135	C₂×D₁₂₇	semidirect
263. C₂×Q₁₆	C₂×D₁₂₇	semidirect
266. C₂×SD₁₆	C₂×D₁₂₇	semidirect
269. C₂×D₈	C₂×D₁₂₇	semidirect
277. C₂²×C₈	C₂×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
#22550690	2
#22550689	2
#22550683	2
#22550682	2
#22550678	2
#22550677	2
#22550674	2
#22550673	2
C₂×#16861231	2
#135×D₁₂₇	2
C₂×#16861215	2
C₂×#135×C₁₂₇	2
#3584	127