Subgroups — #30647541

Order 16256.

548 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16861233	C₂	1	1	yes	maximal, characteristic
2	C₄×#14523247	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#22549986	C₂	1	1	yes	maximal, characteristic, complemented
5	#22549978	C₂	1	1	yes	maximal, characteristic, complemented
6	#22549976	C₂	1	1	yes	maximal, characteristic, complemented
7	#22549967	C₂	1	1	yes	maximal, characteristic, complemented
8	#22549963	C₂	1	1	yes	maximal, characteristic, complemented
9	D₈×Dic₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#22549956	C₂	1	1	yes	maximal, characteristic, complemented
11	#22549915	C₂	1	1	yes	maximal, characteristic, complemented
12	#22549879	C₂	1	1	yes	maximal, characteristic, complemented
13	#22549874	C₂	1	1	yes	maximal, characteristic, complemented
14	#22549828	C₂	1	1	yes	maximal, characteristic, complemented
15	#442×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14523247	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₂₇	—	2	1	no	—
19	#16861233	C₄	1	8	yes	complemented
20	C₂×#14523237	C₂²	1	1	yes	characteristic
21	C₂×#14523236	C₂²	1	1	yes	characteristic
22	C₂×#14523233	C₂²	1	1	yes	characteristic
23	C₂×#14523231	C₂²	1	1	yes	characteristic
24	C₂×#14523231	C₂²	1	1	yes	characteristic
25	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
26	#16861174	C₂²	1	1	yes	characteristic, complemented
27	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
28	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
29	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
30	#16861171	C₂²	1	1	yes	characteristic
31	C₄×C₂²⋊D₁₂₇	—	2	1	no	—
32	C₄×C₂²⋊D₁₂₇	—	2	1	no	—
33	(C₂²⋊D₁₂₇)⋊C₄	—	2	1	no	—
34	(C₂²⋊D₁₂₇)⋊C₄	—	2	1	no	—
35	#16861167	C₂²	1	1	yes	characteristic
36	#16861165	—	2	1	no	—
37	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
38	C₂²⋊C₄×D₁₂₇	—	2	1	no	—
39	C₂×C₄×Dic₁₂₇	—	2	1	no	—
40	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic
41	#16861143	C₂²	1	1	yes	characteristic, complemented
42	#16861142	C₂²	1	1	yes	characteristic, complemented
43	#16861140	C₂²	1	1	yes	characteristic, complemented
44	#16861134	C₂²	1	1	yes	characteristic, complemented
45	#16861132	C₂²	1	1	yes	characteristic, complemented
46	#16861131	C₂²	1	1	yes	characteristic
47	#16861130	C₂²	1	1	yes	characteristic
48	#16861130	C₂²	1	1	yes	characteristic, complemented
49	#16861129	C₂²	1	1	yes	characteristic
50	#16861120	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×D₈×C₁₂₇	C₂²	1	1	yes	characteristic
54	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
55	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
56	#106×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
57	#102×C₁₂₇	C₂²	1	1	yes	characteristic
58	#102×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
59	#97×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₁₂₇	—	2	1	no	—
61	#14523247	—	2	2	no	—
62	#14523247	C₂×C₄	1	4	yes	complemented
63	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
64	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊D₁₂₇	—	2	1	no	—
66	C₂×C₂²⋊D₁₂₇	—	2	1	no	—
67	D₄×D₁₂₇	—	2	2	no	—
68	D₄×D₁₂₇	C₂×C₄	1	4	yes	complemented
69	C₂²×Dic₁₂₇	—	2	1	no	—
70	C₂²×Dic₁₂₇	—	2	1	no	—
71	C₂²×Dic₁₂₇	—	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	#14523233	C₂×C₄	1	4	yes	complemented
82	#14523231	—	2	2	no	—
83	#14523231	C₂×C₄	1	4	yes	complemented
84	C₂×C₁₂₇⋊C₈	C₂³	1	1	yes	characteristic
85	C₂×C₁₂₇⋊C₈	C₂³	1	1	yes	characteristic
86	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
87	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
88	Dic₁₂₇⋊C₄	—	2	1	no	—
89	Dic₁₂₇⋊C₄	—	2	1	no	—
90	Dic₁₂₇⋊C₄	—	2	1	no	—
91	C₂²⋊Dic₁₂₇	—	2	1	no	—
92	C₂²⋊Dic₁₂₇	—	2	1	no	—
93	(C₂×D₁₂₇)⋊C₄	—	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×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
103	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₁₂₇	—	2	1	no	—
105	C₂²×C₄×C₁₂₇	—	2	1	no	—
106	D₈×C₁₂₇	C₂×C₄	1	4	yes	complemented
107	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
108	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
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	C₂²⋊C₄×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	C₂²×C₄	1	2	yes	complemented
121	D₅₀₈	—	2	1	no	—
122	D₅₀₈	C₂²×C₄	1	2	yes	—
123	C₂²⋊D₁₂₇	—	2	4	no	—
124	C₂²⋊D₁₂₇	—	2	4	no	—
125	C₂×Dic₁₂₇	—	2	1	no	—
126	C₂×Dic₁₂₇	—	2	4	no	—
127	C₂×Dic₁₂₇	—	2	1	no	—
128	C₂×Dic₁₂₇	—	2	1	no	—
129	C₂×Dic₁₂₇	—	4	2	no	—
130	C₂×Dic₁₂₇	—	4	2	no	—
131	C₂×Dic₁₂₇	C₂×D₄	1	1	yes	characteristic
132	C₂×Dic₁₂₇	C₂×D₄	1	1	yes	characteristic
133	C₂×Dic₁₂₇	C₂×D₄	1	1	yes	characteristic
134	C₄×D₁₂₇	—	2	2	no	—
135	C₄×D₁₂₇	—	4	1	no	—
136	C₄×D₁₂₇	—	4	2	no	—
137	C₄×D₁₂₇	—	4	2	no	—
138	C₄×D₁₂₇	—	4	2	no	—
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	C₂³×C₁₂₇	—	2	1	no	—
145	D₄×C₁₂₇	—	2	1	no	—
146	D₄×C₁₂₇	—	2	1	no	—
147	D₄×C₁₂₇	C₂²×C₄	1	2	yes	—
148	D₄×C₁₂₇	C₂²×C₄	1	2	yes	complemented
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	—	4	2	no	—
153	C₂×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
156	C₈×C₁₂₇	—	2	1	no	—
157	C₈×C₁₂₇	C₂²×C₄	1	2	yes	complemented
158	C₂²×C₁₂₇	—	2	2	no	—
159	C₂²×C₁₂₇	—	2	2	no	—
160	C₂²×C₁₂₇	—	4	1	no	—
161	C₂²×C₁₂₇	—	4	1	no	—
162	C₂²×C₁₂₇	—	4	1	no	—
163	C₂²×C₁₂₇	—	4	1	no	—
164	C₂²×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
165	C₂×D₁₂₇	—	2	1	no	—
166	C₂×D₁₂₇	—	2	1	no	—
167	C₂×D₁₂₇	—	2	2	no	—
168	C₂×D₁₂₇	—	4	8	no	—
169	C₂×D₁₂₇	—	4	1	no	—
170	C₂×D₁₂₇	—	4	1	no	—
171	C₂×D₁₂₇	C₄×D₄	1	2	yes	—
172	C₄×C₁₂₇	—	2	1	no	—
173	C₄×C₁₂₇	—	2	1	no	—
174	C₄×C₁₂₇	—	4	1	no	—
175	C₄×C₁₂₇	—	4	1	no	—
176	C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
177	C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
178	Dic₁₂₇	—	2	2	no	—
179	Dic₁₂₇	—	2	1	no	—
180	Dic₁₂₇	—	4	1	no	—
181	Dic₁₂₇	—	4	1	no	—
182	Dic₁₂₇	C₄×D₄	1	2	yes	—
183	Dic₁₂₇	AGL(1,ℤ/8)	1	2	yes	complemented
184	C₂×C₁₂₇	—	4	2	no	—
185	C₂×C₁₂₇	—	4	2	no	—
186	C₂×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
187	C₂×C₁₂₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂×C₁₂₇	#575	1	1	yes	characteristic
189	D₁₂₇	—	2	2	no	—
190	D₁₂₇	—	4	2	no	—
191	C₄×AGL(1,ℤ/8)	—	127	1	no	maximal, Sylow
192	C₁₂₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
193	C₂×AGL(1,ℤ/8)	—	127	1	no	—
194	C₄×#41	—	127	1	no	—
195	C₂×C₄×D₄	—	127	1	no	—
196	#442	—	127	1	no	—
197	#442	D₁₂₇	1	1	yes	characteristic, complemented
198	#440	—	127	1	no	—
199	#440	—	127	1	no	—
200	C₄×SD₁₆	—	127	1	no	—
201	C₄×SD₁₆	—	127	1	no	—
202	C₄×D₈	—	127	1	no	—
203	C₄×D₈	—	127	1	no	—
204	#428	—	127	1	no	—
205	#418	—	127	1	no	—
206	#417	—	127	1	no	—
207	C₄×M₁₆	—	127	1	no	—
208	C₂×#41	—	127	1	no	—
209	C₂²×D₄	—	127	1	no	—
210	C₂³×C₄	—	254	1	no	—
211	AGL(1,ℤ/8)	—	127	8	no	—
212	C₂×SD₁₆	—	127	1	no	—
213	C₂×SD₁₆	—	127	1	no	—
214	C₂×D₈	—	127	1	no	—
215	C₂×D₈	C₂×D₁₂₇	1	1	yes	characteristic
216	C₂×M₁₆	—	127	1	no	—
217	C₂×M₁₆	—	127	1	no	—
218	C₄×Q₈	—	127	1	no	—
219	C₄×Q₈	—	127	1	no	—
220	C₄×D₄	—	127	1	no	—
221	C₄×D₄	—	127	1	no	—
222	C₄×D₄	—	127	1	no	—
223	C₄×D₄	—	127	1	no	—
224	C₄×D₄	—	254	1	no	—
225	C₄×D₄	—	254	1	no	—
226	C₄×D₄	—	254	1	no	—
227	C₄×D₄	—	254	1	no	—
228	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
229	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
230	#117	—	127	1	no	—
231	#117	—	254	1	no	—
232	C₂×C₄⋊C₄	—	127	1	no	—
233	C₂×C₂²⋊C₄	—	254	1	no	—
234	C₂×C₄²	—	127	1	no	—
235	C₂×C₄²	—	254	1	no	—
236	#107	—	127	1	no	—
237	#107	—	127	1	no	—
238	#106	—	127	1	no	—
239	#106	C₂×D₁₂₇	1	1	yes	characteristic, complemented
240	#103	—	127	1	no	—
241	#103	—	127	1	no	—
242	#102	—	127	1	no	—
243	#102	—	127	1	no	—
244	#102	—	127	1	no	—
245	#102	—	127	1	no	—
246	#102	C₂×D₁₂₇	1	1	yes	characteristic
247	#102	C₂×D₁₂₇	1	1	yes	characteristic, complemented
248	#97	—	127	1	no	—
249	#97	C₂×D₁₂₇	1	1	yes	characteristic, complemented
250	C₄×C₈	—	127	1	no	—
251	C₄×C₈	—	127	1	no	—
252	C₂⁴	—	254	1	no	—
253	#41	—	127	4	no	—
254	#41	—	254	2	no	—
255	C₂×Q₈	—	127	1	no	—
256	C₂×D₄	—	127	4	no	—
257	C₂×D₄	—	127	1	no	—
258	C₂×D₄	—	254	2	no	—
259	C₂×D₄	—	254	1	no	—
260	C₂×D₄	—	254	1	no	—
261	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
262	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	127	1	no	—
266	C₂²×C₄	—	127	1	no	—
267	C₂²×C₄	—	127	1	no	—
268	C₂²×C₄	—	508	4	no	—
269	C₂²×C₄	—	254	1	no	—
270	C₂²×C₄	—	254	1	no	—
271	C₂²×C₄	—	254	1	no	—
272	C₂²×C₄	—	254	1	no	—
273	C₂²×C₄	—	254	1	no	—
274	C₂²×C₄	—	254	1	no	—
275	SD₁₆	—	127	4	no	—
276	SD₁₆	—	127	4	no	—
277	D₈	—	127	4	no	—
278	D₈	C₄×D₁₂₇	1	4	yes	complemented
279	M₁₆	—	127	4	no	—
280	M₁₆	—	254	2	no	—
281	C₂×C₈	—	127	1	no	—
282	C₂×C₈	—	127	1	no	—
283	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
284	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
285	C₄⋊C₄	—	127	1	no	—
286	C₄⋊C₄	—	127	1	no	—
287	C₄⋊C₄	—	254	1	no	—
288	C₄⋊C₄	—	254	1	no	—
289	C₄⋊C₄	—	254	1	no	—
290	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
291	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₂²⋊C₄	—	254	1	no	—
295	C₂²⋊C₄	—	254	1	no	—
296	C₂²⋊C₄	—	254	1	no	—
297	C₂²⋊C₄	—	254	1	no	—
298	C₂²⋊C₄	—	254	1	no	—
299	C₄²	—	127	1	no	—
300	C₄²	—	127	1	no	—
301	C₄²	—	127	1	no	—
302	C₄²	—	254	1	no	—
303	C₄²	—	254	1	no	—
304	C₄²	—	254	1	no	—
305	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	127	1	no	—
309	C₂³	—	508	2	no	—
310	C₂³	—	508	2	no	—
311	C₂³	—	254	4	no	—
312	C₂³	—	254	1	no	—
313	Q₈	—	127	2	no	—
314	Q₈	—	254	1	no	—
315	D₄	—	2	1	no	—
316	D₄	—	2	1	no	—
317	D₄	—	127	2	no	—
318	D₄	—	254	4	no	—
319	D₄	—	254	4	no	—
320	D₄	—	254	1	no	—
321	D₄	C₂×C₄×D₁₂₇	1	2	yes	—
322	D₄	C₂×C₄×D₁₂₇	1	2	yes	complemented
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	127	1	no	—
328	C₂×C₄	—	127	1	no	—
329	C₂×C₄	—	127	2	no	—
330	C₂×C₄	—	127	2	no	—
331	C₂×C₄	—	127	1	no	—
332	C₂×C₄	—	508	2	no	—
333	C₂×C₄	—	508	1	no	—
334	C₂×C₄	—	508	2	no	—
335	C₂×C₄	—	508	2	no	—
336	C₂×C₄	—	508	2	no	—
337	C₂×C₄	—	508	2	no	—
338	C₂×C₄	—	254	2	no	—
339	C₂×C₄	—	254	4	no	—
340	C₂×C₄	—	254	1	no	—
341	C₂×C₄	—	254	1	no	—
342	C₂×C₄	—	254	1	no	—
343	C₂×C₄	D₄×D₁₂₇	1	1	yes	characteristic
344	C₂×C₄	D₄×D₁₂₇	1	1	yes	characteristic
345	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
346	C₈	—	2	1	no	—
347	C₈	—	127	2	no	—
348	C₈	—	254	1	no	—
349	C₈	C₂×C₄×D₁₂₇	1	2	yes	complemented
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	127	2	no	—
357	C₂²	—	508	8	no	—
358	C₂²	—	508	1	no	—
359	C₂²	—	508	1	no	—
360	C₂²	—	254	2	no	—
361	C₂²	—	254	1	no	—
362	C₂²	—	254	1	no	—
363	C₂²	C₂×D₄×D₁₂₇	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	127	2	no	—
369	C₄	—	127	2	no	—
370	C₄	—	508	1	no	—
371	C₄	—	508	1	no	—
372	C₄	—	254	2	no	—
373	C₄	—	254	1	no	—
374	C₄	C₂²×C₄×D₁₂₇	1	1	yes	characteristic
375	C₄	#41×D₁₂₇	1	1	yes	characteristic
376	C₂	—	4	2	no	—
377	C₂	—	4	2	no	—
378	C₂	—	508	2	no	—
379	C₂	—	254	2	no	—
380	C₂	C₄×D₄×D₁₂₇	1	1	yes	characteristic
381	C₂	AGL(1,ℤ/8)×D₁₂₇	1	1	yes	characteristic
382	C₂	#22550672	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₂₇
commutator	C₄×C₁₂₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₂₇
Fitting	#442×C₁₂₇	C₂
socle	C₂²×C₁₂₇	C₂²×D₄
prime radical	C₂×#16861233	C₂
cosocle	C₂×C₄×C₁₂₇	C₂⁴
hypercenter	#442	D₁₂₇
hypocenter	C₁₂₇	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #442

Complements

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

N	H ≅ G/N	type
2. C₄×#14523247	C₂	semidirect
3. C₄×D₄×D₁₂₇	C₂	semidirect
4. #22549986	C₂	semidirect
5. #22549978	C₂	semidirect
6. #22549976	C₂	semidirect
7. #22549967	C₂	semidirect
8. #22549963	C₂	semidirect
9. D₈×Dic₁₂₇	C₂	semidirect
10. #22549956	C₂	semidirect
11. #22549915	C₂	semidirect
12. #22549879	C₂	semidirect
13. #22549874	C₂	semidirect
14. #22549828	C₂	semidirect
15. #442×C₁₂₇	C₂	semidirect
19. #16861233	C₄	semidirect
25. C₄×Dic₂₅₄	C₂²	semidirect
26. #16861174	C₂²	semidirect
29. D₄×Dic₁₂₇	C₂²	semidirect
41. #16861143	C₂²	semidirect
42. #16861142	C₂²	semidirect
43. #16861140	C₂²	semidirect
44. #16861134	C₂²	semidirect
45. #16861132	C₂²	semidirect
48. #16861130	C₂²	semidirect
50. #16861120	C₂²	semidirect
51. C₈×Dic₁₂₇	C₂²	semidirect
52. C₈×Dic₁₂₇	C₂²	semidirect
55. C₄×D₄×C₁₂₇	C₂²	semidirect
56. #106×C₁₂₇	C₂²	semidirect
58. #102×C₁₂₇	C₂²	semidirect
59. #97×C₁₂₇	C₂²	semidirect
62. #14523247	C₂×C₄	semidirect
68. D₄×D₁₂₇	C₂×C₄	semidirect
79. #14523237	C₂×C₄	semidirect
80. #14523236	C₂×C₄	semidirect
81. #14523233	C₂×C₄	semidirect
83. #14523231	C₂×C₄	semidirect
106. D₈×C₁₂₇	C₂×C₄	semidirect
120. Dic₂₅₄	C₂²×C₄	semidirect
142. C₁₂₇⋊C₈	C₂²×C₄	semidirect
148. D₄×C₁₂₇	C₂²×C₄	semidirect
157. C₈×C₁₂₇	C₂²×C₄	semidirect
183. Dic₁₂₇	AGL(1,ℤ/8)	semidirect
192. C₁₂₇	C₄×AGL(1,ℤ/8)	semidirect
197. #442	D₁₂₇	semidirect
229. C₄×D₄	C₂×D₁₂₇	semidirect
239. #106	C₂×D₁₂₇	semidirect
247. #102	C₂×D₁₂₇	semidirect
249. #97	C₂×D₁₂₇	semidirect
278. D₈	C₄×D₁₂₇	semidirect
322. D₄	C₂×C₄×D₁₂₇	semidirect
349. C₈	C₂×C₄×D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16861233	2
C₄×#14523247	2
C₄×D₄×D₁₂₇	2
#22549986	2
#22549978	2
#22549976	2
#22549967	2
#22549963	2
D₈×Dic₁₂₇	2
#22549956	2
#22549915	2
#22549879	2
#22549874	2
#22549828	2
#442×C₁₂₇	2
C₄×AGL(1,ℤ/8)	127