Subgroups — #30649191

Order 16256.

572 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16861241	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16861238	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16861236	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16861233	C₂	1	1	yes	maximal, characteristic, complemented
5	#22550425	C₂	1	1	yes	maximal, characteristic, complemented
6	#124×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550269	C₂	1	1	yes	maximal, characteristic, complemented
8	#22550267	C₂	1	1	yes	maximal, characteristic, complemented
9	#22550264	C₂	1	1	yes	maximal, characteristic, complemented
10	#22550262	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550260	C₂	1	1	yes	maximal, characteristic, complemented
12	#22550258	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550258	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#14523231	C₂	1	1	yes	maximal, characteristic, complemented
15	#495×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14523249	C₂²	1	1	yes	characteristic
17	C₂×#14523247	C₂²	1	1	yes	characteristic
18	C₂×Q₈×D₁₂₇	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
20	#16861241	—	2	4	no	—
21	#16861238	—	2	4	no	—
22	#16861236	—	2	4	no	—
23	#16861233	—	2	4	no	—
24	C₂×Dic₅₀₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×#14523238	C₂²	1	1	yes	characteristic, complemented
26	C₂×#14523238	C₂²	1	1	yes	characteristic, complemented
27	C₂×#14523237	C₂²	1	1	yes	characteristic
28	C₂×#14523237	C₂²	1	1	yes	characteristic, complemented
29	C₂×#14523236	C₂²	1	1	yes	characteristic
30	C₂×#14523236	C₂²	1	1	yes	characteristic, complemented
31	C₂×#14523235	C₂²	1	1	yes	characteristic
32	C₂×#14523235	C₂²	1	1	yes	characteristic, complemented
33	C₂×D₁₀₁₆	C₂²	1	1	yes	characteristic
34	C₂×#14523233	C₂²	1	1	yes	characteristic
35	C₂×#14523233	C₂²	1	1	yes	characteristic
36	C₂×#14523231	C₂²	1	1	yes	characteristic
37	C₂×#14523231	C₂²	1	1	yes	characteristic
38	#16861207	C₂²	1	1	yes	characteristic, complemented
39	#16861205	C₂²	1	1	yes	characteristic, complemented
40	#16861198	C₂²	1	1	yes	characteristic
41	#16861197	C₂²	1	1	yes	characteristic
42	#16861197	C₂²	1	1	yes	characteristic, complemented
43	#16861196	C₂²	1	1	yes	characteristic
44	#16861195	—	2	2	no	—
45	#16861182	—	2	2	no	—
46	(C₂²⋊D₁₂₇)⋊C₄	—	2	2	no	—
47	C₂²⋊C₄×D₁₂₇	—	2	2	no	—
48	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic
49	#16861119	C₂²	1	1	yes	characteristic, complemented
50	#16861119	C₂²	1	1	yes	characteristic, complemented
51	C₄×C₁₂₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₂×Q₁₆×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
53	C₂×SD₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
54	C₂×SD₁₆×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
55	C₂×D₈×C₁₂₇	C₂²	1	1	yes	characteristic
56	#124×C₁₂₇	C₂²	1	1	yes	characteristic
57	#124×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₁₂₇	—	2	1	no	—
60	#14523249	—	2	2	no	—
61	#14523249	—	2	2	no	—
62	#14523247	—	2	2	no	—
63	#14523247	—	2	2	no	—
64	C₂×Dic₂₅₄	—	2	1	no	—
65	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
66	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
67	Q₈×D₁₂₇	—	2	2	no	—
68	Q₈×D₁₂₇	—	2	2	no	—
69	C₂×D₅₀₈	—	2	1	no	—
70	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
71	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊D₁₂₇	—	2	1	no	—
73	C₂×C₂²⋊D₁₂₇	—	2	1	no	—
74	C₂×C₂²⋊D₁₂₇	—	2	2	no	—
75	D₄×D₁₂₇	—	2	2	no	—
76	D₄×D₁₂₇	—	2	2	no	—
77	C₂²×Dic₁₂₇	—	2	1	no	—
78	C₂×C₄×D₁₂₇	—	2	1	no	—
79	C₂×C₄×D₁₂₇	—	2	1	no	—
80	C₂×C₄×D₁₂₇	D₄	1	2	yes	—
81	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
82	Dic₅₀₈	—	2	2	no	—
83	#14523238	—	2	2	no	—
84	#14523238	—	2	2	no	—
85	#14523237	—	2	2	no	—
86	#14523237	—	2	2	no	—
87	#14523236	—	2	2	no	—
88	#14523236	—	2	2	no	—
89	#14523235	—	2	2	no	—
90	#14523235	—	2	2	no	—
91	D₁₀₁₆	—	2	2	no	—
92	#14523233	—	2	2	no	—
93	#14523233	—	2	2	no	—
94	#14523231	D₄	1	4	yes	complemented
95	#14523231	D₄	1	4	yes	complemented
96	C₂×C₁₂₇⋊C₈	C₂³	1	1	yes	characteristic
97	C₂×C₁₂₇⋊C₈	C₂³	1	1	yes	characteristic
98	Dic₁₂₇⋊C₄	—	2	2	no	—
99	C₂²⋊Dic₁₂₇	—	2	2	no	—
100	(C₂×D₁₂₇)⋊C₄	—	2	2	no	—
101	(C₂×D₁₂₇)⋊C₄	—	2	2	no	—
102	(C₂×D₁₂₇)⋊C₄	—	2	2	no	—
103	C₄×Dic₁₂₇	D₄	1	2	yes	—
104	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
105	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
106	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
107	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
109	Q₁₆×C₁₂₇	—	2	2	no	—
110	SD₁₆×C₁₂₇	—	2	2	no	—
111	SD₁₆×C₁₂₇	—	2	2	no	—
112	D₈×C₁₂₇	—	2	2	no	—
113	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
115	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
116	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
117	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
118	C₂²×D₁₂₇	—	2	1	no	—
119	C₂²×D₁₂₇	—	2	1	no	—
120	C₂²×D₁₂₇	—	4	4	no	—
121	C₂²×D₁₂₇	—	4	2	no	—
122	C₂²×D₁₂₇	C₂×D₄	1	1	yes	characteristic
123	Dic₂₅₄	—	2	1	no	—
124	Dic₂₅₄	—	2	1	no	—
125	Dic₂₅₄	—	2	1	no	—
126	Dic₂₅₄	—	2	1	no	—
127	Dic₂₅₄	—	4	2	no	—
128	D₅₀₈	—	2	1	no	—
129	D₅₀₈	—	2	1	no	—
130	D₅₀₈	—	2	1	no	—
131	D₅₀₈	—	2	1	no	—
132	D₅₀₈	—	4	2	no	—
133	C₂²⋊D₁₂₇	—	4	4	no	—
134	C₂²⋊D₁₂₇	—	4	2	no	—
135	C₂²⋊D₁₂₇	—	4	2	no	—
136	C₂×Dic₁₂₇	—	2	1	no	—
137	C₂×Dic₁₂₇	—	2	1	no	—
138	C₂×Dic₁₂₇	—	4	2	no	—
139	C₂×Dic₁₂₇	C₂×D₄	1	2	yes	—
140	C₂×Dic₁₂₇	C₂×D₄	1	1	yes	characteristic
141	C₄×D₁₂₇	—	4	2	no	—
142	C₄×D₁₂₇	—	4	2	no	—
143	C₄×D₁₂₇	—	4	2	no	—
144	C₄×D₁₂₇	C₂×D₄	1	2	yes	—
145	C₄×D₁₂₇	C₂×D₄	1	2	yes	—
146	C₁₂₇⋊C₈	C₂×D₄	1	2	yes	—
147	C₁₂₇⋊C₈	C₂×D₄	1	2	yes	—
148	C₂³×C₁₂₇	—	2	1	no	—
149	C₂³×C₁₂₇	—	2	1	no	—
150	Q₈×C₁₂₇	—	2	1	no	—
151	Q₈×C₁₂₇	—	2	1	no	—
152	Q₈×C₁₂₇	—	2	1	no	—
153	Q₈×C₁₂₇	—	2	1	no	—
154	D₄×C₁₂₇	—	2	1	no	—
155	D₄×C₁₂₇	—	2	1	no	—
156	D₄×C₁₂₇	—	2	1	no	—
157	D₄×C₁₂₇	—	2	1	no	—
158	C₂×C₄×C₁₂₇	—	2	1	no	—
159	C₂×C₄×C₁₂₇	—	2	1	no	—
160	C₂×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
161	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
162	C₈×C₁₂₇	C₂×D₄	1	2	yes	—
163	C₈×C₁₂₇	C₂×D₄	1	2	yes	—
164	C₂²×C₁₂₇	—	4	1	no	—
165	C₂²×C₁₂₇	—	4	1	no	—
166	C₂²×C₁₂₇	—	4	2	no	—
167	C₂²×C₁₂₇	—	4	2	no	—
168	C₂²×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×D₁₂₇	—	2	2	no	—
170	C₂×D₁₂₇	—	4	1	no	—
171	C₂×D₁₂₇	—	4	1	no	—
172	C₂×D₁₂₇	—	4	2	no	—
173	C₂×D₁₂₇	—	4	2	no	—
174	C₂×D₁₂₇	—	8	4	no	—
175	C₂×D₁₂₇	#127	1	2	yes	—
176	C₄×C₁₂₇	—	2	2	no	—
177	C₄×C₁₂₇	—	4	1	no	—
178	C₄×C₁₂₇	—	4	1	no	—
179	C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
180	C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
181	Dic₁₂₇	—	2	2	no	—
182	Dic₁₂₇	—	4	1	no	—
183	Dic₁₂₇	—	4	1	no	—
184	Dic₁₂₇	#127	1	2	yes	—
185	C₂×C₁₂₇	—	8	1	no	—
186	C₂×C₁₂₇	—	8	1	no	—
187	C₂×C₁₂₇	C₂×#127	1	1	yes	characteristic
188	C₂×C₁₂₇	#575	1	2	yes	—
189	D₁₂₇	—	2	2	no	—
190	D₁₂₇	—	8	1	no	—
191	D₁₂₇	—	8	1	no	—
192	#3153	—	127	1	no	maximal, Sylow
193	C₁₂₇	#3153	1	1	yes	characteristic, complemented, Sylow
194	C₂×#137	—	127	1	no	—
195	C₂×#137	—	127	1	no	—
196	C₂×AGL(1,ℤ/8)	—	127	1	no	—
197	C₂×AGL(1,ℤ/8)	—	127	1	no	—
198	#532	—	127	1	no	—
199	C₂×#124	—	127	1	no	—
200	#497	—	127	1	no	—
201	#497	—	127	1	no	—
202	#496	—	127	1	no	—
203	#496	—	127	1	no	—
204	#495	—	127	1	no	—
205	#495	—	127	1	no	—
206	#495	—	127	1	no	—
207	#495	D₁₂₇	1	1	yes	characteristic, complemented
208	C₄×M₁₆	—	127	1	no	—
209	C₂×#41	—	127	1	no	—
210	C₂×#41	—	127	1	no	—
211	C₂²×Q₈	—	127	1	no	—
212	C₂²×D₄	—	127	1	no	—
213	#137	—	254	4	no	—
214	#137	—	254	4	no	—
215	AGL(1,ℤ/8)	—	254	4	no	—
216	AGL(1,ℤ/8)	—	254	4	no	—
217	C₂×Q₁₆	—	127	1	no	—
218	C₂×Q₁₆	—	127	1	no	—
219	C₂×Q₁₆	—	127	1	no	—
220	C₂×Q₁₆	C₂×D₁₂₇	1	1	yes	characteristic, complemented
221	C₂×SD₁₆	—	127	1	no	—
222	C₂×SD₁₆	—	127	1	no	—
223	C₂×SD₁₆	—	127	1	no	—
224	C₂×SD₁₆	—	127	1	no	—
225	C₂×SD₁₆	—	127	1	no	—
226	C₂×SD₁₆	—	127	1	no	—
227	C₂×SD₁₆	C₂×D₁₂₇	1	1	yes	characteristic
228	C₂×SD₁₆	C₂×D₁₂₇	1	1	yes	characteristic, complemented
229	C₂×D₈	—	127	1	no	—
230	C₂×D₈	—	127	1	no	—
231	C₂×D₈	—	127	1	no	—
232	C₂×D₈	C₂×D₁₂₇	1	1	yes	characteristic
233	C₂×M₁₆	—	127	1	no	—
234	C₂×M₁₆	—	127	1	no	—
235	C₄⋊Q₈	—	127	1	no	—
236	#127	—	127	1	no	—
237	#124	—	127	1	no	—
238	#124	—	127	1	no	—
239	#124	—	127	1	no	—
240	#124	—	127	1	no	—
241	#124	—	254	2	no	—
242	#124	C₂×D₁₂₇	1	1	yes	characteristic
243	#124	C₂×D₁₂₇	1	1	yes	characteristic, complemented
244	#121	—	254	2	no	—
245	C₄×D₄	—	254	2	no	—
246	C₂×C₂²⋊C₄	—	254	2	no	—
247	C₂×C₄²	—	127	1	no	—
248	#97	—	127	1	no	—
249	#97	—	127	1	no	—
250	C₄×C₈	—	127	1	no	—
251	C₄×C₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
252	C₂⁴	—	254	1	no	—
253	#41	—	254	2	no	—
254	#41	—	254	2	no	—
255	#41	—	254	2	no	—
256	#41	—	254	2	no	—
257	C₂×Q₈	—	127	1	no	—
258	C₂×Q₈	—	127	1	no	—
259	C₂×Q₈	—	254	1	no	—
260	C₂×Q₈	—	254	2	no	—
261	C₂×Q₈	—	254	2	no	—
262	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
263	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
264	C₂×D₄	—	127	1	no	—
265	C₂×D₄	—	127	1	no	—
266	C₂×D₄	—	254	1	no	—
267	C₂×D₄	—	254	2	no	—
268	C₂×D₄	—	254	2	no	—
269	C₂×D₄	—	254	2	no	—
270	C₂×D₄	—	254	1	no	—
271	C₂×D₄	—	254	1	no	—
272	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
273	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
274	C₂²×C₄	—	127	1	no	—
275	C₂²×C₄	—	127	2	no	—
276	C₂²×C₄	—	254	1	no	—
277	C₂²×C₄	—	254	1	no	—
278	C₂²×C₄	—	254	1	no	—
279	Q₁₆	—	2	2	no	—
280	Q₁₆	—	254	2	no	—
281	Q₁₆	—	254	2	no	—
282	Q₁₆	—	254	2	no	—
283	SD₁₆	—	2	2	no	—
284	SD₁₆	—	2	2	no	—
285	SD₁₆	—	254	2	no	—
286	SD₁₆	—	254	2	no	—
287	SD₁₆	—	254	2	no	—
288	SD₁₆	—	254	2	no	—
289	SD₁₆	—	254	2	no	—
290	SD₁₆	—	254	2	no	—
291	D₈	—	2	2	no	—
292	D₈	—	254	2	no	—
293	D₈	—	254	2	no	—
294	D₈	—	254	2	no	—
295	M₁₆	—	127	4	no	—
296	M₁₆	—	127	4	no	—
297	C₂×C₈	—	127	1	no	—
298	C₂×C₈	—	127	1	no	—
299	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
300	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
301	C₄⋊C₄	—	254	2	no	—
302	C₂²⋊C₄	—	2	2	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	254	2	no	—
305	C₂²⋊C₄	—	254	2	no	—
306	C₂²⋊C₄	—	254	2	no	—
307	C₂²⋊C₄	—	254	2	no	—
308	C₄²	—	127	2	no	—
309	C₄²	—	127	1	no	—
310	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	127	1	no	—
314	C₂³	—	508	2	no	—
315	C₂³	—	508	4	no	—
316	C₂³	—	254	1	no	—
317	C₂³	—	254	1	no	—
318	Q₈	—	2	1	no	—
319	Q₈	—	2	1	no	—
320	Q₈	—	2	1	no	—
321	Q₈	—	2	1	no	—
322	Q₈	—	508	2	no	—
323	Q₈	—	254	1	no	—
324	Q₈	—	254	1	no	—
325	Q₈	—	254	1	no	—
326	Q₈	—	254	1	no	—
327	D₄	—	2	1	no	—
328	D₄	—	2	1	no	—
329	D₄	—	2	1	no	—
330	D₄	—	2	1	no	—
331	D₄	—	508	2	no	—
332	D₄	—	508	2	no	—
333	D₄	—	508	2	no	—
334	D₄	—	508	4	no	—
335	D₄	—	254	1	no	—
336	D₄	—	254	1	no	—
337	D₄	—	254	1	no	—
338	D₄	—	254	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	127	1	no	—
342	C₂×C₄	—	127	2	no	—
343	C₂×C₄	—	127	2	no	—
344	C₂×C₄	—	127	2	no	—
345	C₂×C₄	—	508	2	no	—
346	C₂×C₄	—	508	2	no	—
347	C₂×C₄	—	508	2	no	—
348	C₂×C₄	—	508	2	no	—
349	C₂×C₄	—	254	1	no	—
350	C₂×C₄	—	254	1	no	—
351	C₂×C₄	D₄×D₁₂₇	1	2	yes	—
352	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
353	C₈	—	127	2	no	—
354	C₈	—	127	2	no	—
355	C₈	D₄×D₁₂₇	1	2	yes	—
356	C₈	D₄×D₁₂₇	1	2	yes	—
357	C₂²	—	4	1	no	—
358	C₂²	—	4	1	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	127	2	no	—
362	C₂²	—	1016	4	no	—
363	C₂²	—	508	1	no	—
364	C₂²	—	508	1	no	—
365	C₂²	—	508	2	no	—
366	C₂²	—	508	2	no	—
367	C₂²	—	254	2	no	—
368	C₂²	C₂×D₄×D₁₂₇	1	1	yes	characteristic
369	C₄	—	2	2	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	1	no	—
372	C₄	—	127	2	no	—
373	C₄	—	508	1	no	—
374	C₄	—	508	1	no	—
375	C₄	—	254	2	no	—
376	C₄	C₂×D₄×D₁₂₇	1	1	yes	characteristic
377	C₄	C₂×D₄×D₁₂₇	1	1	yes	characteristic
378	C₂	—	8	1	no	—
379	C₂	—	8	1	no	—
380	C₂	—	1016	1	no	—
381	C₂	—	1016	1	no	—
382	C₂	—	254	2	no	—
383	C₂	#127×D₁₂₇	1	1	yes	characteristic
384	C₂	#22550673	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₂₇
commutator, cosocle	C₂×C₄×C₁₂₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₂₇
Fitting	#495×C₁₂₇	C₂
socle	C₂²×C₁₂₇	C₂²×D₄
hypercenter	#495	D₁₂₇
hypocenter	C₁₂₇	#3153
LCS	G ▷ C₂×C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #495

Complements

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

N	H ≅ G/N	type
1. C₂×#16861241	C₂	semidirect
2. C₂×#16861238	C₂	semidirect
3. C₂×#16861236	C₂	semidirect
4. C₂×#16861233	C₂	semidirect
5. #22550425	C₂	semidirect
6. #124×D₁₂₇	C₂	semidirect
7. #22550269	C₂	semidirect
8. #22550267	C₂	semidirect
9. #22550264	C₂	semidirect
10. #22550262	C₂	semidirect
11. #22550260	C₂	semidirect
12. #22550258	C₂	semidirect
13. #22550258	C₂	semidirect
14. C₄×#14523231	C₂	semidirect
15. #495×C₁₂₇	C₂	semidirect
24. C₂×Dic₅₀₈	C₂²	semidirect
25. C₂×#14523238	C₂²	semidirect
26. C₂×#14523238	C₂²	semidirect
28. C₂×#14523237	C₂²	semidirect
30. C₂×#14523236	C₂²	semidirect
32. C₂×#14523235	C₂²	semidirect
38. #16861207	C₂²	semidirect
39. #16861205	C₂²	semidirect
42. #16861197	C₂²	semidirect
49. #16861119	C₂²	semidirect
50. #16861119	C₂²	semidirect
51. C₄×C₁₂₇⋊C₈	C₂²	semidirect
52. C₂×Q₁₆×C₁₂₇	C₂²	semidirect
54. C₂×SD₁₆×C₁₂₇	C₂²	semidirect
57. #124×C₁₂₇	C₂²	semidirect
58. C₄×C₈×C₁₂₇	C₂²	semidirect
94. #14523231	D₄	semidirect
95. #14523231	D₄	semidirect
193. C₁₂₇	#3153	semidirect
207. #495	D₁₂₇	semidirect
220. C₂×Q₁₆	C₂×D₁₂₇	semidirect
228. C₂×SD₁₆	C₂×D₁₂₇	semidirect
243. #124	C₂×D₁₂₇	semidirect
251. C₄×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
C₂×#16861241	2
C₂×#16861238	2
C₂×#16861236	2
C₂×#16861233	2
#22550425	2
#124×D₁₂₇	2
#22550269	2
#22550267	2
#22550264	2
#22550262	2
#22550260	2
#22550258	2
C₄×#14523231	2
#495×C₁₂₇	2
#3153	127