Subgroups — C₄×SD₁₆×D₁₂₇ #30647483

Order 16256.

552 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₁₂₇	C₂	1	1	yes	maximal, characteristic
4	#22549967	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#14523237	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₁₆×Dic₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#14523235	C₂	1	1	yes	maximal, characteristic, complemented
8	#22549963	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#14523236	C₂	1	1	yes	maximal, characteristic, complemented
10	#22549961	C₂	1	1	yes	maximal, characteristic, complemented
11	#106×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#103×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#102×D₁₂₇	C₂	1	1	yes	maximal, characteristic
14	C₄×C₈×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₁₂₇	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₂₇	—	2	1	no	—
19	C₂×#14523237	C₂²	1	1	yes	characteristic
20	C₂×#14523236	C₂²	1	1	yes	characteristic
21	C₂×#14523235	C₂²	1	1	yes	characteristic
22	SD₁₆×D₁₂₇	C₄	1	8	yes	direct product factor
23	C₂×C₈×D₁₂₇	C₂²	1	1	yes	characteristic
24	C₂×C₈×D₁₂₇	C₂²	1	1	yes	characteristic
25	Q₈×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
26	C₄×Dic₂₅₄	—	2	1	no	—
27	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
28	#16861174	—	2	1	no	—
29	#16861174	C₂²	1	1	yes	characteristic, complemented
30	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
31	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
32	#16861171	C₂²	1	1	yes	characteristic
33	C₄×C₂²⋊D₁₂₇	—	2	1	no	—
34	(C₂²⋊D₁₂₇)⋊C₄	—	2	1	no	—
35	C₄⋊C₄×D₁₂₇	—	2	1	no	—
36	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
37	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
38	C₂²⋊C₄×D₁₂₇	—	2	1	no	—
39	C₄²×D₁₂₇	—	2	1	no	—
40	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic
41	#16861141	C₂²	1	1	yes	characteristic, complemented
42	#16861140	C₂²	1	1	yes	characteristic, complemented
43	#16861140	C₂²	1	1	yes	characteristic, complemented
44	#16861134	C₂²	1	1	yes	characteristic, complemented
45	#16861133	C₂²	1	1	yes	characteristic, complemented
46	#16861132	C₂²	1	1	yes	characteristic, complemented
47	#16861131	C₂²	1	1	yes	characteristic
48	#16861130	C₂²	1	1	yes	characteristic
49	#16861129	C₂²	1	1	yes	characteristic
50	C₄×C₁₂₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	C₈×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
53	C₂×SD₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
54	C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
55	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
56	#106×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
57	#103×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
58	#102×C₁₂₇	C₂²	1	1	yes	characteristic
59	C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₁₂₇	—	2	1	no	—
61	C₂×Dic₂₅₄	—	2	1	no	—
62	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
63	Q₈×D₁₂₇	—	2	2	no	—
64	Q₈×D₁₂₇	C₂×C₄	1	4	yes	complemented
65	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₁₂₇	—	2	1	no	—
67	D₄×D₁₂₇	—	2	2	no	—
68	D₄×D₁₂₇	C₂×C₄	1	4	yes	—
69	C₂²×Dic₁₂₇	—	2	1	no	—
70	C₂×C₄×D₁₂₇	—	2	1	no	—
71	C₂×C₄×D₁₂₇	—	2	1	no	—
72	C₂×C₄×D₁₂₇	—	2	1	no	—
73	C₂×C₄×D₁₂₇	—	2	1	no	—
74	C₂×C₄×D₁₂₇	—	2	1	no	—
75	C₂×C₄×D₁₂₇	—	4	4	no	—
76	C₂×C₄×D₁₂₇	D₄	1	1	yes	characteristic
77	C₂×C₄×D₁₂₇	D₄	1	1	yes	characteristic
78	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
79	#14523237	C₂×C₄	1	4	yes	complemented
80	#14523236	C₂×C₄	1	4	yes	complemented
81	#14523235	C₂×C₄	1	4	yes	complemented
82	C₂×C₁₂₇⋊C₈	C₂³	1	1	yes	characteristic
83	C₂×C₁₂₇⋊C₈	C₂³	1	1	yes	characteristic
84	C₈×D₁₂₇	—	2	2	no	—
85	C₈×D₁₂₇	C₂×C₄	1	4	yes	complemented
86	C₄⋊Dic₁₂₇	—	2	1	no	—
87	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
88	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
89	Dic₁₂₇⋊C₄	—	2	1	no	—
90	Dic₁₂₇⋊C₄	—	2	1	no	—
91	Dic₁₂₇⋊C₄	—	2	1	no	—
92	Dic₁₂₇⋊C₄	—	2	1	no	—
93	C₂²⋊Dic₁₂₇	—	2	1	no	—
94	(C₂×D₁₂₇)⋊C₄	—	2	1	no	—
95	(C₂×D₁₂₇)⋊C₄	—	2	1	no	—
96	C₄×Dic₁₂₇	—	2	1	no	—
97	C₄×Dic₁₂₇	—	2	1	no	—
98	C₄×Dic₁₂₇	—	2	1	no	—
99	C₄×Dic₁₂₇	D₄	1	1	yes	characteristic
100	C₄×Dic₁₂₇	D₄	1	1	yes	characteristic
101	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
103	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₁₂₇	—	2	1	no	—
105	SD₁₆×C₁₂₇	C₂×C₄	1	4	yes	complemented
106	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
108	C₄⋊C₄×C₁₂₇	—	2	1	no	—
109	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
111	C₂²⋊C₄×C₁₂₇	—	2	1	no	—
112	C₄²×C₁₂₇	—	2	1	no	—
113	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
114	C₂²×D₁₂₇	—	2	1	no	—
115	C₂²×D₁₂₇	—	2	4	no	—
116	C₂²×D₁₂₇	—	4	2	no	—
117	C₂²×D₁₂₇	—	4	2	no	—
118	C₂²×D₁₂₇	C₂×D₄	1	1	yes	characteristic
119	Dic₂₅₄	—	2	1	no	—
120	Dic₂₅₄	—	2	4	no	—
121	Dic₂₅₄	C₂²×C₄	1	2	yes	complemented
122	D₅₀₈	—	2	1	no	—
123	D₅₀₈	C₂²×C₄	1	2	yes	—
124	C₂²⋊D₁₂₇	—	2	4	no	—
125	C₂×Dic₁₂₇	—	2	1	no	—
126	C₂×Dic₁₂₇	—	2	1	no	—
127	C₂×Dic₁₂₇	—	2	1	no	—
128	C₂×Dic₁₂₇	—	4	2	no	—
129	C₂×Dic₁₂₇	C₂×D₄	1	1	yes	characteristic
130	C₂×Dic₁₂₇	C₂×D₄	1	1	yes	characteristic
131	C₂×Dic₁₂₇	C₂×D₄	1	1	yes	characteristic
132	C₄×D₁₂₇	—	2	4	no	—
133	C₄×D₁₂₇	—	2	2	no	—
134	C₄×D₁₂₇	—	4	2	no	—
135	C₄×D₁₂₇	—	4	2	no	—
136	C₄×D₁₂₇	—	4	2	no	—
137	C₄×D₁₂₇	—	4	2	no	—
138	C₄×D₁₂₇	SD₁₆	1	4	yes	direct product factor
139	C₄×D₁₂₇	C₂²×C₄	1	2	yes	—
140	C₄×D₁₂₇	#41	1	2	yes	—
141	C₁₂₇⋊C₈	—	2	1	no	—
142	C₁₂₇⋊C₈	C₂²×C₄	1	2	yes	complemented
143	C₂³×C₁₂₇	—	2	1	no	—
144	Q₈×C₁₂₇	—	2	1	no	—
145	Q₈×C₁₂₇	C₂²×C₄	1	2	yes	complemented
146	D₄×C₁₂₇	—	2	1	no	—
147	D₄×C₁₂₇	C₂²×C₄	1	2	yes	—
148	C₂×C₄×C₁₂₇	—	2	1	no	—
149	C₂×C₄×C₁₂₇	—	2	1	no	—
150	C₂×C₄×C₁₂₇	—	2	1	no	—
151	C₂×C₄×C₁₂₇	—	4	2	no	—
152	C₂×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
155	C₈×C₁₂₇	—	2	1	no	—
156	C₈×C₁₂₇	C₂²×C₄	1	2	yes	complemented
157	C₂²×C₁₂₇	—	2	2	no	—
158	C₂²×C₁₂₇	—	4	1	no	—
159	C₂²×C₁₂₇	—	4	1	no	—
160	C₂²×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×D₁₂₇	—	2	2	no	—
162	C₂×D₁₂₇	—	4	1	no	—
163	C₂×D₁₂₇	—	4	1	no	—
164	C₂×D₁₂₇	—	4	8	no	—
165	C₂×D₁₂₇	C₄×D₄	1	2	yes	—
166	C₂×D₁₂₇	C₂×SD₁₆	1	2	yes	—
167	C₂×D₁₂₇	#135	1	2	yes	—
168	C₄×C₁₂₇	—	2	2	no	—
169	C₄×C₁₂₇	—	2	1	no	—
170	C₄×C₁₂₇	—	4	1	no	—
171	C₄×C₁₂₇	—	4	1	no	—
172	C₄×C₁₂₇	C₂×SD₁₆	1	2	yes	complemented
173	C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
174	C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
175	Dic₁₂₇	—	2	2	no	—
176	Dic₁₂₇	—	2	1	no	—
177	Dic₁₂₇	—	4	1	no	—
178	Dic₁₂₇	—	4	1	no	—
179	Dic₁₂₇	C₄×D₄	1	2	yes	—
180	Dic₁₂₇	C₂×SD₁₆	1	2	yes	complemented
181	C₂×C₁₂₇	—	4	2	no	—
182	C₂×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
183	C₂×C₁₂₇	C₂²×SD₁₆	1	1	yes	characteristic
184	C₂×C₁₂₇	C₂×#135	1	1	yes	characteristic
185	D₁₂₇	—	4	2	no	—
186	D₁₂₇	C₄×SD₁₆	1	4	yes	direct product factor
187	C₂×C₄×SD₁₆	—	127	1	no	maximal, Sylow
188	C₁₂₇	C₂×C₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
189	C₂²×SD₁₆	—	127	1	no	—
190	C₂×C₄×Q₈	—	127	1	no	—
191	C₂×C₄×D₄	—	127	1	no	—
192	C₄×SD₁₆	—	127	1	no	—
193	C₄×SD₁₆	—	127	1	no	—
194	C₄×SD₁₆	—	127	1	no	—
195	C₄×SD₁₆	—	127	1	no	—
196	C₄×SD₁₆	—	127	1	no	—
197	C₄×SD₁₆	—	127	1	no	—
198	C₄×SD₁₆	—	127	1	no	—
199	C₄×SD₁₆	D₁₂₇	1	1	yes	characteristic, direct product factor
200	C₂×#106	—	127	1	no	—
201	C₂×#103	—	127	1	no	—
202	C₂×#102	—	127	1	no	—
203	C₂×C₄×C₈	—	127	1	no	—
204	C₂²×Q₈	—	127	1	no	—
205	C₂²×D₄	—	127	1	no	—
206	C₂³×C₄	—	254	1	no	—
207	C₂×SD₁₆	—	127	1	no	—
208	C₂×SD₁₆	—	127	1	no	—
209	C₂×SD₁₆	—	127	8	no	—
210	C₂×SD₁₆	—	127	1	no	—
211	C₂×SD₁₆	C₂×D₁₂₇	1	1	yes	characteristic
212	C₂²×C₈	—	127	1	no	—
213	C₂²×C₈	—	127	1	no	—
214	C₄×Q₈	—	127	1	no	—
215	C₄×Q₈	—	127	1	no	—
216	C₄×Q₈	—	127	1	no	—
217	C₄×Q₈	—	254	1	no	—
218	C₄×Q₈	—	254	1	no	—
219	C₄×Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
220	C₄×D₄	—	127	1	no	—
221	C₄×D₄	—	127	1	no	—
222	C₄×D₄	—	127	1	no	—
223	C₄×D₄	—	254	1	no	—
224	C₄×D₄	—	254	1	no	—
225	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
226	C₂×C₄⋊C₄	—	127	1	no	—
227	C₂×C₄⋊C₄	—	127	1	no	—
228	C₂×C₄⋊C₄	—	254	1	no	—
229	C₂×C₂²⋊C₄	—	254	1	no	—
230	C₂×C₄²	—	127	1	no	—
231	C₂×C₄²	—	254	1	no	—
232	#106	—	127	1	no	—
233	#106	—	127	1	no	—
234	#106	—	127	1	no	—
235	#106	C₂×D₁₂₇	1	1	yes	characteristic, complemented
236	#103	—	127	1	no	—
237	#103	—	127	1	no	—
238	#103	—	127	1	no	—
239	#103	C₂×D₁₂₇	1	1	yes	characteristic, complemented
240	#102	—	127	1	no	—
241	#102	—	127	1	no	—
242	#102	—	127	1	no	—
243	#102	C₂×D₁₂₇	1	1	yes	characteristic
244	C₄×C₈	—	127	1	no	—
245	C₄×C₈	—	127	1	no	—
246	C₄×C₈	—	127	1	no	—
247	C₄×C₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
248	C₂⁴	—	254	1	no	—
249	C₂×Q₈	—	127	4	no	—
250	C₂×Q₈	—	127	1	no	—
251	C₂×Q₈	—	254	1	no	—
252	C₂×Q₈	—	254	2	no	—
253	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
254	C₂×D₄	—	127	4	no	—
255	C₂×D₄	—	127	1	no	—
256	C₂×D₄	—	254	2	no	—
257	C₂×D₄	—	254	1	no	—
258	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	127	1	no	—
261	C₂²×C₄	—	127	1	no	—
262	C₂²×C₄	—	127	1	no	—
263	C₂²×C₄	—	508	4	no	—
264	C₂²×C₄	—	254	1	no	—
265	C₂²×C₄	—	254	1	no	—
266	C₂²×C₄	—	254	1	no	—
267	C₂²×C₄	—	254	1	no	—
268	C₂²×C₄	—	254	1	no	—
269	C₂²×C₄	—	254	1	no	—
270	SD₁₆	—	127	4	no	—
271	SD₁₆	—	127	4	no	—
272	SD₁₆	—	127	4	no	—
273	SD₁₆	C₄×D₁₂₇	1	4	yes	direct product factor
274	C₂×C₈	—	127	1	no	—
275	C₂×C₈	—	127	4	no	—
276	C₂×C₈	—	127	1	no	—
277	C₂×C₈	—	254	2	no	—
278	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
279	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	127	1	no	—
282	C₄⋊C₄	—	127	1	no	—
283	C₄⋊C₄	—	254	1	no	—
284	C₄⋊C₄	—	254	1	no	—
285	C₄⋊C₄	—	254	1	no	—
286	C₄⋊C₄	—	254	1	no	—
287	C₄⋊C₄	—	254	1	no	—
288	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
289	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	254	1	no	—
292	C₂²⋊C₄	—	254	1	no	—
293	C₂²⋊C₄	—	254	1	no	—
294	C₄²	—	2	1	no	—
295	C₄²	—	127	1	no	—
296	C₄²	—	127	1	no	—
297	C₄²	—	127	1	no	—
298	C₄²	—	254	1	no	—
299	C₄²	—	254	1	no	—
300	C₄²	—	254	1	no	—
301	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
302	C₂³	—	2	1	no	—
303	C₂³	—	127	1	no	—
304	C₂³	—	508	2	no	—
305	C₂³	—	508	2	no	—
306	C₂³	—	254	4	no	—
307	C₂³	—	254	1	no	—
308	Q₈	—	2	1	no	—
309	Q₈	—	127	2	no	—
310	Q₈	—	254	4	no	—
311	Q₈	—	254	1	no	—
312	Q₈	C₂×C₄×D₁₂₇	1	2	yes	complemented
313	D₄	—	2	1	no	—
314	D₄	—	127	2	no	—
315	D₄	—	254	4	no	—
316	D₄	—	254	1	no	—
317	D₄	C₂×C₄×D₁₂₇	1	2	yes	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	127	1	no	—
323	C₂×C₄	—	127	1	no	—
324	C₂×C₄	—	127	4	no	—
325	C₂×C₄	—	127	2	no	—
326	C₂×C₄	—	127	2	no	—
327	C₂×C₄	—	127	1	no	—
328	C₂×C₄	—	508	2	no	—
329	C₂×C₄	—	508	2	no	—
330	C₂×C₄	—	508	2	no	—
331	C₂×C₄	—	508	2	no	—
332	C₂×C₄	—	508	2	no	—
333	C₂×C₄	—	254	2	no	—
334	C₂×C₄	—	254	4	no	—
335	C₂×C₄	—	254	1	no	—
336	C₂×C₄	—	254	1	no	—
337	C₂×C₄	—	254	1	no	—
338	C₂×C₄	D₄×D₁₂₇	1	1	yes	characteristic
339	C₂×C₄	D₄×D₁₂₇	1	1	yes	characteristic
340	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
341	C₈	—	2	1	no	—
342	C₈	—	127	2	no	—
343	C₈	—	254	1	no	—
344	C₈	C₂×C₄×D₁₂₇	1	2	yes	complemented
345	C₂²	—	2	2	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	127	2	no	—
349	C₂²	—	127	2	no	—
350	C₂²	—	127	2	no	—
351	C₂²	—	508	8	no	—
352	C₂²	—	508	1	no	—
353	C₂²	—	508	1	no	—
354	C₂²	—	254	2	no	—
355	C₂²	C₂×D₄×D₁₂₇	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	1	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	127	2	no	—
361	C₄	—	127	2	no	—
362	C₄	—	508	1	no	—
363	C₄	—	508	1	no	—
364	C₄	—	254	2	no	—
365	C₄	—	254	1	no	—
366	C₄	SD₁₆×D₁₂₇	1	2	yes	direct product factor
367	C₄	C₂²×C₄×D₁₂₇	1	1	yes	characteristic
368	C₄	#41×D₁₂₇	1	1	yes	characteristic
369	C₂	—	4	2	no	—
370	C₂	—	127	4	no	—
371	C₂	—	508	2	no	—
372	C₂	C₄×D₄×D₁₂₇	1	1	yes	characteristic
373	C₂	C₂×SD₁₆×D₁₂₇	1	1	yes	characteristic
374	C₂	#135×D₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₂₇
commutator	C₄×C₁₂₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₂₇
Fitting	C₄×SD₁₆×C₁₂₇	C₂
socle	C₂²×C₁₂₇	C₂²×D₄
prime radical	C₂×D₄×D₁₂₇	C₂²
cosocle	C₂×C₄×C₁₂₇	C₂⁴
hypercenter	C₄×SD₁₆	D₁₂₇
hypocenter	C₁₂₇	C₂×C₄×SD₁₆
LCS	G ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×Q₈×D₁₂₇	C₂	semidirect
4. #22549967	C₂	semidirect
5. C₄×#14523237	C₂	semidirect
6. SD₁₆×Dic₁₂₇	C₂	semidirect
7. C₄×#14523235	C₂	semidirect
8. #22549963	C₂	semidirect
9. C₄×#14523236	C₂	semidirect
10. #22549961	C₂	semidirect
11. #106×D₁₂₇	C₂	semidirect
12. #103×D₁₂₇	C₂	semidirect
14. C₄×C₈×D₁₂₇	C₂	semidirect
15. C₄×SD₁₆×C₁₂₇	C₂	semidirect
22. SD₁₆×D₁₂₇	C₄	direct (N × H)
25. Q₈×Dic₁₂₇	C₂²	semidirect
27. C₄×Dic₂₅₄	C₂²	semidirect
29. #16861174	C₂²	semidirect
41. #16861141	C₂²	semidirect
42. #16861140	C₂²	semidirect
43. #16861140	C₂²	semidirect
44. #16861134	C₂²	semidirect
45. #16861133	C₂²	semidirect
46. #16861132	C₂²	semidirect
50. C₄×C₁₂₇⋊C₈	C₂²	semidirect
51. C₈×Dic₁₂₇	C₂²	semidirect
52. C₈×Dic₁₂₇	C₂²	semidirect
54. C₄×Q₈×C₁₂₇	C₂²	semidirect
56. #106×C₁₂₇	C₂²	semidirect
57. #103×C₁₂₇	C₂²	semidirect
59. C₄×C₈×C₁₂₇	C₂²	semidirect
64. Q₈×D₁₂₇	C₂×C₄	semidirect
79. #14523237	C₂×C₄	semidirect
80. #14523236	C₂×C₄	semidirect
81. #14523235	C₂×C₄	semidirect
85. C₈×D₁₂₇	C₂×C₄	semidirect
105. SD₁₆×C₁₂₇	C₂×C₄	semidirect
121. Dic₂₅₄	C₂²×C₄	semidirect
138. C₄×D₁₂₇	SD₁₆	direct (N × H)
142. C₁₂₇⋊C₈	C₂²×C₄	semidirect
145. Q₈×C₁₂₇	C₂²×C₄	semidirect
156. C₈×C₁₂₇	C₂²×C₄	semidirect
172. C₄×C₁₂₇	C₂×SD₁₆	semidirect
180. Dic₁₂₇	C₂×SD₁₆	semidirect
186. D₁₂₇	C₄×SD₁₆	direct (N × H)
188. C₁₂₇	C₂×C₄×SD₁₆	semidirect
199. C₄×SD₁₆	D₁₂₇	direct (N × H)
219. C₄×Q₈	C₂×D₁₂₇	semidirect
235. #106	C₂×D₁₂₇	semidirect
239. #103	C₂×D₁₂₇	semidirect
247. C₄×C₈	C₂×D₁₂₇	semidirect
273. SD₁₆	C₄×D₁₂₇	direct (N × H)
312. Q₈	C₂×C₄×D₁₂₇	semidirect
344. C₈	C₂×C₄×D₁₂₇	semidirect
366. C₄	SD₁₆×D₁₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×D₁₂₇	2
C₄×Q₈×D₁₂₇	2
C₄×D₄×D₁₂₇	2
#22549967	2
C₄×#14523237	2
SD₁₆×Dic₁₂₇	2
C₄×#14523235	2
#22549963	2
C₄×#14523236	2
#22549961	2
#106×D₁₂₇	2
#103×D₁₂₇	2
#102×D₁₂₇	2
C₄×C₈×D₁₂₇	2
C₄×SD₁₆×C₁₂₇	2
C₂×C₄×SD₁₆	127

Subgroups — C4×SD16×D127 #30647483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×SD₁₆×D₁₂₇ #30647483