Subgroups — C₁₂₇×#3012 #30635964

Order 16256.

764 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×H(5,𝔽₂)×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×AGL(1,ℤ/8)×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#135×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#537×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#452×C₁₂₇	C₂	1	2	yes	maximal, complemented
6	#450×C₁₂₇	C₂	1	2	yes	maximal, complemented
7	#449×C₁₂₇	C₂	1	2	yes	maximal, complemented
8	#447×C₁₂₇	C₂	1	2	yes	maximal, complemented
9	#417×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#102×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#408×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
12	H(5,𝔽₂)×C₁₂₇	—	2	4	no	—
13	H(5,𝔽₂)×C₁₂₇	—	2	4	no	—
14	C₂×#41×C₁₂₇	—	2	1	no	—
15	C₂×#41×C₁₂₇	C₂²	1	2	yes	—
16	C₂×#41×C₁₂₇	C₂²	1	1	yes	characteristic
17	C₂×#41×C₁₂₇	C₂²	1	1	yes	characteristic
18	C₂×#41×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₄×C₁₂₇	—	2	2	no	—
20	C₂²×D₄×C₁₂₇	—	2	1	no	—
21	C₂²×D₄×C₁₂₇	C₂²	1	2	yes	—
22	C₂²×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
23	AGL(1,ℤ/8)×C₁₂₇	—	2	4	no	—
24	#135×C₁₂₇	—	2	4	no	—
25	C₂×Q₁₆×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×SD₁₆×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×SD₁₆×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×SD₁₆×C₁₂₇	C₂²	1	2	yes	complemented
29	C₂×D₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
30	C₂×D₈×C₁₂₇	C₂²	1	2	yes	complemented
31	C₂×M₁₆×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
33	C₂²⋊Q₈×C₁₂₇	—	2	1	no	—
34	C₂²⋊Q₈×C₁₂₇	C₂²	1	2	yes	complemented
35	#121×C₁₂₇	—	2	1	no	—
36	#121×C₁₂₇	—	2	2	no	—
37	#121×C₁₂₇	C₂²	1	2	yes	complemented
38	C₂×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
39	#103×C₁₂₇	C₂²	1	2	yes	complemented
40	#102×C₁₂₇	C₂²	1	2	yes	complemented
41	#102×C₁₂₇	C₂²	1	2	yes	complemented
42	#102×C₁₂₇	C₂²	1	2	yes	complemented
43	C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	complemented
44	C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	complemented
45	C₂⁴×C₁₂₇	—	2	2	no	—
46	C₂⁴×C₁₂₇	—	2	1	no	—
47	#41×C₁₂₇	—	2	8	no	—
48	#41×C₁₂₇	—	2	4	no	—
49	#41×C₁₂₇	—	2	4	no	—
50	#41×C₁₂₇	—	2	2	no	—
51	#41×C₁₂₇	—	2	2	no	—
52	#41×C₁₂₇	—	2	2	no	—
53	#41×C₁₂₇	—	2	2	no	—
54	#41×C₁₂₇	—	2	2	no	—
55	#41×C₁₂₇	D₄	1	4	yes	complemented
56	C₂×Q₈×C₁₂₇	D₄	1	1	yes	characteristic
57	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
58	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
59	C₂×D₄×C₁₂₇	—	2	16	no	—
60	C₂×D₄×C₁₂₇	—	2	8	no	—
61	C₂×D₄×C₁₂₇	—	2	2	no	—
62	C₂×D₄×C₁₂₇	—	2	1	no	—
63	C₂×D₄×C₁₂₇	—	2	4	no	—
64	C₂×D₄×C₁₂₇	—	2	4	no	—
65	C₂×D₄×C₁₂₇	—	2	1	no	—
66	C₂×D₄×C₁₂₇	—	2	2	no	—
67	C₂×D₄×C₁₂₇	—	2	2	no	—
68	C₂×D₄×C₁₂₇	—	2	1	no	—
69	C₂×D₄×C₁₂₇	—	2	2	no	—
70	C₂×D₄×C₁₂₇	D₄	1	2	yes	—
71	C₂×D₄×C₁₂₇	D₄	1	1	yes	characteristic
72	C₂×D₄×C₁₂₇	D₄	1	4	yes	complemented
73	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
74	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
75	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
76	C₂²×C₄×C₁₂₇	—	2	2	no	—
77	C₂²×C₄×C₁₂₇	—	2	1	no	—
78	C₂²×C₄×C₁₂₇	—	2	1	no	—
79	C₂²×C₄×C₁₂₇	—	2	1	no	—
80	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
81	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
82	Q₁₆×C₁₂₇	—	2	2	no	—
83	SD₁₆×C₁₂₇	—	2	2	no	—
84	SD₁₆×C₁₂₇	—	2	2	no	—
85	SD₁₆×C₁₂₇	—	2	4	no	—
86	D₈×C₁₂₇	—	2	2	no	—
87	D₈×C₁₂₇	—	2	4	no	—
88	M₁₆×C₁₂₇	—	2	2	no	—
89	C₂×C₈×C₁₂₇	—	2	2	no	—
90	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
91	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
92	C₂×C₈×C₁₂₇	C₂³	1	2	yes	—
93	C₄⋊C₄×C₁₂₇	—	2	1	no	—
94	C₄⋊C₄×C₁₂₇	—	2	2	no	—
95	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
96	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
97	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
98	C₂³×C₁₂₇	—	2	8	no	—
99	C₂³×C₁₂₇	—	2	2	no	—
100	C₂³×C₁₂₇	—	2	1	no	—
101	C₂³×C₁₂₇	—	2	4	no	—
102	C₂³×C₁₂₇	—	2	1	no	—
103	C₂³×C₁₂₇	—	8	1	no	—
104	C₂³×C₁₂₇	—	8	1	no	—
105	C₂³×C₁₂₇	—	8	2	no	—
106	C₂³×C₁₂₇	—	8	2	no	—
107	C₂³×C₁₂₇	C₂×D₄	1	2	yes	—
108	C₂³×C₁₂₇	C₂×D₄	1	1	yes	characteristic
109	Q₈×C₁₂₇	—	2	2	no	—
110	Q₈×C₁₂₇	—	2	1	no	—
111	Q₈×C₁₂₇	—	2	1	no	—
112	Q₈×C₁₂₇	—	2	1	no	—
113	Q₈×C₁₂₇	C₂×D₄	1	2	yes	—
114	D₄×C₁₂₇	—	2	8	no	—
115	D₄×C₁₂₇	—	2	8	no	—
116	D₄×C₁₂₇	—	2	4	no	—
117	D₄×C₁₂₇	—	2	4	no	—
118	D₄×C₁₂₇	—	2	2	no	—
119	D₄×C₁₂₇	—	2	4	no	—
120	D₄×C₁₂₇	—	2	2	no	—
121	D₄×C₁₂₇	—	2	1	no	—
122	D₄×C₁₂₇	—	2	1	no	—
123	D₄×C₁₂₇	—	2	1	no	—
124	D₄×C₁₂₇	—	4	2	no	—
125	D₄×C₁₂₇	—	8	2	no	—
126	D₄×C₁₂₇	C₂×D₄	1	2	yes	—
127	D₄×C₁₂₇	C₂×D₄	1	4	yes	—
128	C₂×C₄×C₁₂₇	—	2	8	no	—
129	C₂×C₄×C₁₂₇	—	2	1	no	—
130	C₂×C₄×C₁₂₇	—	2	4	no	—
131	C₂×C₄×C₁₂₇	—	2	2	no	—
132	C₂×C₄×C₁₂₇	—	2	2	no	—
133	C₂×C₄×C₁₂₇	—	2	2	no	—
134	C₂×C₄×C₁₂₇	—	2	1	no	—
135	C₂×C₄×C₁₂₇	—	4	2	no	—
136	C₂×C₄×C₁₂₇	—	8	1	no	—
137	C₂×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
138	C₂×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
140	C₂×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
141	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
142	C₈×C₁₂₇	—	2	1	no	—
143	C₈×C₁₂₇	—	2	1	no	—
144	C₈×C₁₂₇	—	2	2	no	—
145	C₂²×C₁₂₇	—	2	1	no	—
146	C₂²×C₁₂₇	—	2	1	no	—
147	C₂²×C₁₂₇	—	2	2	no	—
148	C₂²×C₁₂₇	—	2	4	no	—
149	C₂²×C₁₂₇	—	2	2	no	—
150	C₂²×C₁₂₇	—	2	2	no	—
151	C₂²×C₁₂₇	—	2	2	no	—
152	C₂²×C₁₂₇	—	4	2	no	—
153	C₂²×C₁₂₇	—	4	1	no	—
154	C₂²×C₁₂₇	—	4	2	no	—
155	C₂²×C₁₂₇	—	4	1	no	—
156	C₂²×C₁₂₇	—	4	1	no	—
157	C₂²×C₁₂₇	—	4	1	no	—
158	C₂²×C₁₂₇	—	4	1	no	—
159	C₂²×C₁₂₇	—	8	4	no	—
160	C₂²×C₁₂₇	—	8	8	no	—
161	C₂²×C₁₂₇	#120	1	2	yes	—
162	C₂²×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
163	C₄×C₁₂₇	—	2	2	no	—
164	C₄×C₁₂₇	—	2	2	no	—
165	C₄×C₁₂₇	—	4	1	no	—
166	C₄×C₁₂₇	—	4	2	no	—
167	C₄×C₁₂₇	#120	1	2	yes	—
168	C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
169	C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₁₂₇	—	2	2	no	—
171	C₂×C₁₂₇	—	4	2	no	—
172	C₂×C₁₂₇	—	4	4	no	—
173	C₂×C₁₂₇	—	4	2	no	—
174	C₂×C₁₂₇	—	8	1	no	—
175	C₂×C₁₂₇	C₂×#120	1	1	yes	characteristic
176	C₂×C₁₂₇	#576	1	1	yes	characteristic
177	C₂×C₁₂₇	#577	1	1	yes	characteristic
178	#3012	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₁₂₇	#3012	1	1	yes	characteristic, direct product factor, Sylow
180	C₂×H(5,𝔽₂)	C₂×C₁₂₇	1	1	yes	characteristic, complemented
181	C₂×AGL(1,ℤ/8)	C₂×C₁₂₇	1	1	yes	characteristic, complemented
182	C₂×#135	C₂×C₁₂₇	1	1	yes	characteristic, complemented
183	#537	C₂×C₁₂₇	1	1	yes	characteristic, complemented
184	#452	C₂×C₁₂₇	1	2	yes	complemented
185	#450	C₂×C₁₂₇	1	2	yes	complemented
186	#449	C₂×C₁₂₇	1	2	yes	complemented
187	#447	C₂×C₁₂₇	1	2	yes	complemented
188	#417	C₂×C₁₂₇	1	1	yes	characteristic, complemented
189	C₂×#102	C₂×C₁₂₇	1	1	yes	characteristic, complemented
190	#408	C₂×C₁₂₇	1	1	yes	characteristic, complemented
191	H(5,𝔽₂)	—	2	4	no	—
192	H(5,𝔽₂)	—	2	4	no	—
193	C₂×#41	—	2	1	no	—
194	C₂×#41	C₂²×C₁₂₇	1	2	yes	—
195	C₂×#41	C₂²×C₁₂₇	1	1	yes	characteristic
196	C₂×#41	C₂²×C₁₂₇	1	1	yes	characteristic
197	C₂×#41	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
198	C₂²×D₄	—	2	2	no	—
199	C₂²×D₄	—	2	1	no	—
200	C₂²×D₄	C₂²×C₁₂₇	1	2	yes	—
201	C₂²×D₄	C₂²×C₁₂₇	1	1	yes	characteristic
202	AGL(1,ℤ/8)	—	2	4	no	—
203	#135	—	2	4	no	—
204	C₂×Q₁₆	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
205	C₂×SD₁₆	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
206	C₂×SD₁₆	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
207	C₂×SD₁₆	C₂²×C₁₂₇	1	2	yes	complemented
208	C₂×D₈	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
209	C₂×D₈	C₂²×C₁₂₇	1	2	yes	complemented
210	C₂×M₁₆	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
211	C₂²×C₈	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
212	C₂²⋊Q₈	—	2	1	no	—
213	C₂²⋊Q₈	C₂²×C₁₂₇	1	2	yes	complemented
214	#121	—	2	1	no	—
215	#121	—	2	2	no	—
216	#121	C₂²×C₁₂₇	1	2	yes	complemented
217	C₂×C₄⋊C₄	C₂²×C₁₂₇	1	1	yes	characteristic, complemented
218	#103	C₂²×C₁₂₇	1	2	yes	complemented
219	#102	C₂²×C₁₂₇	1	2	yes	complemented
220	#102	C₂²×C₁₂₇	1	2	yes	complemented
221	#102	C₂²×C₁₂₇	1	2	yes	complemented
222	C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	complemented
223	C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	complemented
224	C₂⁴	—	2	2	no	—
225	C₂⁴	—	2	1	no	—
226	#41	—	2	8	no	—
227	#41	—	2	4	no	—
228	#41	—	2	4	no	—
229	#41	—	2	2	no	—
230	#41	—	2	2	no	—
231	#41	—	2	2	no	—
232	#41	—	2	2	no	—
233	#41	—	2	2	no	—
234	#41	D₄×C₁₂₇	1	4	yes	complemented
235	C₂×Q₈	D₄×C₁₂₇	1	1	yes	characteristic
236	C₂×Q₈	C₂³×C₁₂₇	1	1	yes	characteristic
237	C₂×Q₈	C₂³×C₁₂₇	1	1	yes	characteristic
238	C₂×D₄	—	2	16	no	—
239	C₂×D₄	—	2	8	no	—
240	C₂×D₄	—	2	2	no	—
241	C₂×D₄	—	2	1	no	—
242	C₂×D₄	—	2	4	no	—
243	C₂×D₄	—	2	4	no	—
244	C₂×D₄	—	2	1	no	—
245	C₂×D₄	—	2	2	no	—
246	C₂×D₄	—	2	2	no	—
247	C₂×D₄	—	2	1	no	—
248	C₂×D₄	—	2	2	no	—
249	C₂×D₄	D₄×C₁₂₇	1	2	yes	—
250	C₂×D₄	D₄×C₁₂₇	1	1	yes	characteristic
251	C₂×D₄	D₄×C₁₂₇	1	4	yes	complemented
252	C₂×D₄	C₂³×C₁₂₇	1	1	yes	characteristic
253	C₂×D₄	C₂³×C₁₂₇	1	1	yes	characteristic
254	C₂×D₄	C₂³×C₁₂₇	1	2	yes	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	C₂³×C₁₂₇	1	2	yes	—
260	C₂²×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
261	Q₁₆	—	2	2	no	—
262	SD₁₆	—	2	2	no	—
263	SD₁₆	—	2	2	no	—
264	SD₁₆	—	2	4	no	—
265	D₈	—	2	2	no	—
266	D₈	—	2	4	no	—
267	M₁₆	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
270	C₂×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
271	C₂×C₈	C₂³×C₁₂₇	1	2	yes	—
272	C₄⋊C₄	—	2	1	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	C₂³×C₁₂₇	1	2	yes	—
275	C₂²⋊C₄	—	2	2	no	—
276	C₂²⋊C₄	—	2	2	no	—
277	C₂³	—	2	8	no	—
278	C₂³	—	2	2	no	—
279	C₂³	—	2	1	no	—
280	C₂³	—	2	4	no	—
281	C₂³	—	2	1	no	—
282	C₂³	—	8	1	no	—
283	C₂³	—	8	1	no	—
284	C₂³	—	8	2	no	—
285	C₂³	—	8	2	no	—
286	C₂³	C₂×D₄×C₁₂₇	1	2	yes	—
287	C₂³	C₂×D₄×C₁₂₇	1	1	yes	characteristic
288	Q₈	—	2	2	no	—
289	Q₈	—	2	1	no	—
290	Q₈	—	2	1	no	—
291	Q₈	—	2	1	no	—
292	Q₈	C₂×D₄×C₁₂₇	1	2	yes	—
293	D₄	—	2	8	no	—
294	D₄	—	2	8	no	—
295	D₄	—	2	4	no	—
296	D₄	—	2	4	no	—
297	D₄	—	2	2	no	—
298	D₄	—	2	4	no	—
299	D₄	—	2	2	no	—
300	D₄	—	2	1	no	—
301	D₄	—	2	1	no	—
302	D₄	—	2	1	no	—
303	D₄	—	4	2	no	—
304	D₄	—	8	2	no	—
305	D₄	C₂×D₄×C₁₂₇	1	2	yes	—
306	D₄	C₂×D₄×C₁₂₇	1	4	yes	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	8	1	no	—
316	C₂×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
317	C₂×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
318	C₂×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
319	C₂×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
320	C₂×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
321	C₈	—	2	1	no	—
322	C₈	—	2	1	no	—
323	C₈	—	2	2	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	2	4	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	4	2	no	—
332	C₂²	—	4	1	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	4	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	8	4	no	—
339	C₂²	—	8	8	no	—
340	C₂²	#120×C₁₂₇	1	2	yes	—
341	C₂²	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
342	C₄	—	2	2	no	—
343	C₄	—	2	2	no	—
344	C₄	—	4	1	no	—
345	C₄	—	4	2	no	—
346	C₄	#120×C₁₂₇	1	2	yes	—
347	C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
348	C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
349	C₂	—	2	2	no	—
350	C₂	—	4	2	no	—
351	C₂	—	4	4	no	—
352	C₂	—	4	2	no	—
353	C₂	—	8	1	no	—
354	C₂	C₂×#120×C₁₂₇	1	1	yes	characteristic
355	C₂	#576×C₁₂₇	1	1	yes	characteristic
356	C₂	#577×C₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₂₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₂₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₂₇ ◁ C₂×#41×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×H(5,𝔽₂)×C₁₂₇	C₂	semidirect
2. C₂×AGL(1,ℤ/8)×C₁₂₇	C₂	semidirect
3. C₂×#135×C₁₂₇	C₂	semidirect
4. #537×C₁₂₇	C₂	semidirect
5. #452×C₁₂₇	C₂	semidirect
6. #450×C₁₂₇	C₂	semidirect
7. #449×C₁₂₇	C₂	semidirect
8. #447×C₁₂₇	C₂	semidirect
9. #417×C₁₂₇	C₂	semidirect
10. C₂×#102×C₁₂₇	C₂	semidirect
11. #408×C₁₂₇	C₂	semidirect
18. C₂×#41×C₁₂₇	C₂²	semidirect
25. C₂×Q₁₆×C₁₂₇	C₂²	semidirect
26. C₂×SD₁₆×C₁₂₇	C₂²	semidirect
27. C₂×SD₁₆×C₁₂₇	C₂²	semidirect
28. C₂×SD₁₆×C₁₂₇	C₂²	semidirect
29. C₂×D₈×C₁₂₇	C₂²	semidirect
30. C₂×D₈×C₁₂₇	C₂²	semidirect
31. C₂×M₁₆×C₁₂₇	C₂²	semidirect
32. C₂²×C₈×C₁₂₇	C₂²	semidirect
34. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
37. #121×C₁₂₇	C₂²	semidirect
38. C₂×C₄⋊C₄×C₁₂₇	C₂²	semidirect
39. #103×C₁₂₇	C₂²	semidirect
40. #102×C₁₂₇	C₂²	semidirect
41. #102×C₁₂₇	C₂²	semidirect
42. #102×C₁₂₇	C₂²	semidirect
43. C₂²⋊C₈×C₁₂₇	C₂²	semidirect
44. C₂²⋊C₈×C₁₂₇	C₂²	semidirect
55. #41×C₁₂₇	D₄	semidirect
72. C₂×D₄×C₁₂₇	D₄	semidirect
178. #3012	C₁₂₇	direct (N × H)
179. C₁₂₇	#3012	direct (N × H)
180. C₂×H(5,𝔽₂)	C₂×C₁₂₇	semidirect
181. C₂×AGL(1,ℤ/8)	C₂×C₁₂₇	semidirect
182. C₂×#135	C₂×C₁₂₇	semidirect
183. #537	C₂×C₁₂₇	semidirect
184. #452	C₂×C₁₂₇	semidirect
185. #450	C₂×C₁₂₇	semidirect
186. #449	C₂×C₁₂₇	semidirect
187. #447	C₂×C₁₂₇	semidirect
188. #417	C₂×C₁₂₇	semidirect
189. C₂×#102	C₂×C₁₂₇	semidirect
190. #408	C₂×C₁₂₇	semidirect
197. C₂×#41	C₂²×C₁₂₇	semidirect
204. C₂×Q₁₆	C₂²×C₁₂₇	semidirect
205. C₂×SD₁₆	C₂²×C₁₂₇	semidirect
206. C₂×SD₁₆	C₂²×C₁₂₇	semidirect
207. C₂×SD₁₆	C₂²×C₁₂₇	semidirect
208. C₂×D₈	C₂²×C₁₂₇	semidirect
209. C₂×D₈	C₂²×C₁₂₇	semidirect
210. C₂×M₁₆	C₂²×C₁₂₇	semidirect
211. C₂²×C₈	C₂²×C₁₂₇	semidirect
213. C₂²⋊Q₈	C₂²×C₁₂₇	semidirect
216. #121	C₂²×C₁₂₇	semidirect
217. C₂×C₄⋊C₄	C₂²×C₁₂₇	semidirect
218. #103	C₂²×C₁₂₇	semidirect
219. #102	C₂²×C₁₂₇	semidirect
220. #102	C₂²×C₁₂₇	semidirect
221. #102	C₂²×C₁₂₇	semidirect
222. C₂²⋊C₈	C₂²×C₁₂₇	semidirect
223. C₂²⋊C₈	C₂²×C₁₂₇	semidirect
234. #41	D₄×C₁₂₇	semidirect
251. C₂×D₄	D₄×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×H(5,𝔽₂)×C₁₂₇	2
C₂×AGL(1,ℤ/8)×C₁₂₇	2
C₂×#135×C₁₂₇	2
#537×C₁₂₇	2
#452×C₁₂₇	2
#450×C₁₂₇	2
#449×C₁₂₇	2
#447×C₁₂₇	2
#417×C₁₂₇	2
C₂×#102×C₁₂₇	2
#408×C₁₂₇	2
#3012	127

Subgroups — C127×#3012 #30635964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#3012 #30635964