Subgroups — C₂×#22550673 #30653474

Order 16256.

1484 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₂₇	C₂	1	2	yes	maximal, complemented
2	#22550673	C₂	1	16	yes	maximal, direct product factor
3	C₂×#16861241	C₂	1	2	yes	maximal, complemented
4	C₂×#16861238	C₂	1	2	yes	maximal, complemented
5	C₂×#16861236	C₂	1	2	yes	maximal, complemented
6	C₂×#16861233	C₂	1	2	yes	maximal, complemented
7	C₂×#16861231	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16861229	C₂	1	2	yes	maximal, complemented
9	C₂²×#14523231	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#135×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#14523249	C₂²	1	2	yes	—
12	C₂×#14523248	—	2	2	no	—
13	C₂×#14523248	C₂²	1	2	yes	complemented
14	C₂×#14523247	—	2	2	no	—
15	C₂×#14523247	C₂²	1	2	yes	—
16	#41×D₁₂₇	—	2	8	no	—
17	#41×D₁₂₇	C₂²	1	16	yes	complemented
18	C₂×Q₈×D₁₂₇	C₂²	1	2	yes	complemented
19	C₂×D₄×D₁₂₇	—	2	2	no	—
20	C₂×D₄×D₁₂₇	C₂²	1	2	yes	complemented
21	C₂²×C₄×D₁₂₇	—	2	2	no	—
22	C₂²×C₄×D₁₂₇	C₂²	1	1	yes	characteristic
23	#16861241	C₂²	1	16	yes	complemented
24	#16861238	C₂²	1	16	yes	complemented
25	#16861236	C₂²	1	16	yes	complemented
26	#16861233	C₂²	1	16	yes	complemented
27	#16861231	C₂²	1	8	yes	complemented
28	#16861229	C₂²	1	16	yes	complemented
29	C₂×Dic₅₀₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×#14523238	C₂²	1	2	yes	complemented
31	C₂×#14523237	C₂²	1	2	yes	complemented
32	C₂×#14523236	C₂²	1	2	yes	complemented
33	C₂×#14523235	C₂²	1	2	yes	complemented
34	C₂×D₁₀₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₂×#14523233	C₂²	1	2	yes	complemented
36	C₂×#14523231	C₂²	1	2	yes	complemented
37	C₂×#14523231	C₂²	1	2	yes	complemented
38	C₂×#14523231	C₂²	1	8	yes	complemented
39	C₂²×C₁₂₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×#41×C₁₂₇	C₂²	1	2	yes	complemented
41	#135×C₁₂₇	C₂²	1	8	yes	complemented
42	C₂×Q₁₆×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×SD₁₆×C₁₂₇	C₂²	1	2	yes	complemented
44	C₂×D₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
46	C₂³×D₁₂₇	—	2	2	no	—
47	C₂³×D₁₂₇	D₄	1	1	yes	characteristic
48	#14523249	—	2	4	no	—
49	#14523249	C₂³	1	8	yes	—
50	#14523248	—	2	16	no	—
51	#14523248	—	2	4	no	—
52	#14523248	C₂³	1	8	yes	complemented
53	#14523247	—	2	16	no	—
54	#14523247	—	2	4	no	—
55	#14523247	C₂³	1	8	yes	—
56	C₂×Dic₂₅₄	—	2	2	no	—
57	C₂×Dic₂₅₄	C₂³	1	2	yes	—
58	Q₈×D₁₂₇	—	2	4	no	—
59	Q₈×D₁₂₇	C₂³	1	8	yes	complemented
60	C₂×D₅₀₈	—	2	2	no	—
61	C₂×D₅₀₈	C₂³	1	2	yes	—
62	C₂×C₂²⋊D₁₂₇	—	2	2	no	—
63	C₂×C₂²⋊D₁₂₇	—	2	2	no	—
64	C₂×C₂²⋊D₁₂₇	—	2	2	no	—
65	D₄×D₁₂₇	—	2	16	no	—
66	D₄×D₁₂₇	—	2	4	no	—
67	D₄×D₁₂₇	C₂³	1	8	yes	complemented
68	C₂²×Dic₁₂₇	—	2	2	no	—
69	C₂²×Dic₁₂₇	D₄	1	1	yes	characteristic
70	C₂×C₄×D₁₂₇	—	2	2	no	—
71	C₂×C₄×D₁₂₇	—	2	2	no	—
72	C₂×C₄×D₁₂₇	—	2	16	no	—
73	C₂×C₄×D₁₂₇	—	2	2	no	—
74	C₂×C₄×D₁₂₇	D₄	1	2	yes	—
75	C₂×C₄×D₁₂₇	D₄	1	4	yes	—
76	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
77	C₂×C₄×D₁₂₇	C₂³	1	4	yes	—
78	Dic₅₀₈	C₂³	1	4	yes	complemented
79	#14523238	C₂³	1	8	yes	complemented
80	#14523237	C₂³	1	8	yes	complemented
81	#14523236	C₂³	1	8	yes	complemented
82	#14523235	C₂³	1	8	yes	complemented
83	D₁₀₁₆	C₂³	1	4	yes	complemented
84	#14523233	C₂³	1	8	yes	complemented
85	#14523231	C₂³	1	8	yes	complemented
86	#14523231	C₂³	1	8	yes	complemented
87	C₂×C₁₂₇⋊C₈	C₂³	1	2	yes	—
88	C₂×C₁₂₇⋊C₈	C₂³	1	4	yes	complemented
89	#41×C₁₂₇	—	2	4	no	—
90	#41×C₁₂₇	C₂³	1	8	yes	complemented
91	C₂×Q₈×C₁₂₇	C₂³	1	2	yes	—
92	C₂×D₄×C₁₂₇	—	2	2	no	—
93	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
94	C₂²×C₄×C₁₂₇	—	2	2	no	—
95	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
96	Q₁₆×C₁₂₇	C₂³	1	4	yes	complemented
97	SD₁₆×C₁₂₇	C₂³	1	8	yes	complemented
98	D₈×C₁₂₇	C₂³	1	4	yes	complemented
99	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
100	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
101	C₂×C₈×C₁₂₇	C₂³	1	4	yes	complemented
102	C₂²×D₁₂₇	—	2	2	no	—
103	C₂²×D₁₂₇	—	2	8	no	—
104	C₂²×D₁₂₇	—	4	2	no	—
105	C₂²×D₁₂₇	—	4	8	no	—
106	C₂²×D₁₂₇	C₂×D₄	1	2	yes	—
107	C₂²×D₁₂₇	C₂×D₄	1	4	yes	—
108	Dic₂₅₄	—	2	2	no	—
109	Dic₂₅₄	—	2	8	no	—
110	Dic₂₅₄	C₂⁴	1	4	yes	—
111	D₅₀₈	—	2	8	no	—
112	D₅₀₈	—	2	2	no	—
113	D₅₀₈	C₂⁴	1	4	yes	—
114	C₂²⋊D₁₂₇	—	2	8	no	—
115	C₂²⋊D₁₂₇	—	2	8	no	—
116	C₂²⋊D₁₂₇	—	2	8	no	—
117	C₂×Dic₁₂₇	—	2	2	no	—
118	C₂×Dic₁₂₇	—	2	8	no	—
119	C₂×Dic₁₂₇	C₂×D₄	1	2	yes	—
120	C₂×Dic₁₂₇	C₂×D₄	1	4	yes	—
121	C₄×D₁₂₇	—	2	8	no	—
122	C₄×D₁₂₇	—	2	8	no	—
123	C₄×D₁₂₇	—	2	8	no	—
124	C₄×D₁₂₇	C₂×D₄	1	8	yes	—
125	C₄×D₁₂₇	C₂×D₄	1	4	yes	—
126	C₄×D₁₂₇	C₂⁴	1	4	yes	—
127	C₁₂₇⋊C₈	C₂⁴	1	4	yes	—
128	C₂³×C₁₂₇	—	2	2	no	—
129	C₂³×C₁₂₇	C₂×D₄	1	1	yes	characteristic
130	Q₈×C₁₂₇	—	2	2	no	—
131	Q₈×C₁₂₇	C₂⁴	1	4	yes	—
132	D₄×C₁₂₇	—	2	8	no	—
133	D₄×C₁₂₇	—	2	2	no	—
134	D₄×C₁₂₇	C₂⁴	1	4	yes	—
135	C₂×C₄×C₁₂₇	—	2	2	no	—
136	C₂×C₄×C₁₂₇	—	2	8	no	—
137	C₂×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
138	C₂×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
140	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
141	C₈×C₁₂₇	C₂⁴	1	2	yes	—
142	C₈×C₁₂₇	C₂⁴	1	2	yes	—
143	C₂²×C₁₂₇	—	2	2	no	—
144	C₂²×C₁₂₇	—	2	4	no	—
145	C₂²×C₁₂₇	—	4	4	no	—
146	C₂²×C₁₂₇	C₂²×D₄	1	2	yes	—
147	C₂²×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×D₁₂₇	—	2	4	no	—
149	C₂×D₁₂₇	—	2	4	no	—
150	C₂×D₁₂₇	—	4	4	no	—
151	C₂×D₁₂₇	—	4	16	no	—
152	C₂×D₁₂₇	—	4	4	no	—
153	C₂×D₁₂₇	C₂²×D₄	1	4	yes	—
154	C₄×C₁₂₇	—	2	4	no	—
155	C₄×C₁₂₇	C₂²×D₄	1	2	yes	—
156	C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
157	C₄×C₁₂₇	C₂⁵	1	1	yes	characteristic
158	Dic₁₂₇	—	2	4	no	—
159	Dic₁₂₇	C₂²×D₄	1	4	yes	—
160	C₂×C₁₂₇	—	2	2	no	—
161	C₂×C₁₂₇	—	4	4	no	—
162	C₂×C₁₂₇	#575	1	2	yes	complemented
163	C₂×C₁₂₇	C₂³×D₄	1	1	yes	characteristic
164	D₁₂₇	—	2	4	no	—
165	D₁₂₇	—	4	4	no	—
166	C₂×#575	—	127	1	no	maximal, Sylow
167	C₁₂₇	C₂×#575	1	1	yes	characteristic, complemented, Sylow
168	C₂²×#41	—	127	2	no	—
169	#575	—	127	16	no	—
170	C₂×#137	—	127	2	no	—
171	C₂×#137	—	127	2	no	—
172	C₂×AGL(1,ℤ/8)	—	127	2	no	—
173	C₂×AGL(1,ℤ/8)	—	127	2	no	—
174	C₂×#135	—	127	2	no	—
175	C₂×#135	—	127	1	no	—
176	C₂×#135	D₁₂₇	1	1	yes	characteristic, complemented
177	C₂²×M₁₆	—	127	1	no	—
178	C₂×#41	—	127	16	no	—
179	C₂×#41	—	127	2	no	—
180	C₂×#41	—	127	2	no	—
181	C₂×#41	—	127	2	no	—
182	C₂×#41	—	254	2	no	—
183	C₂×#41	—	254	2	no	—
184	C₂×#41	—	254	8	no	—
185	C₂×#41	C₂×D₁₂₇	1	2	yes	complemented
186	C₂²×Q₈	—	127	2	no	—
187	C₂²×D₄	—	127	2	no	—
188	C₂²×D₄	—	254	2	no	—
189	C₂³×C₄	—	127	1	no	—
190	C₂³×C₄	—	254	2	no	—
191	#137	—	127	16	no	—
192	#137	—	127	16	no	—
193	AGL(1,ℤ/8)	—	127	16	no	—
194	AGL(1,ℤ/8)	—	127	16	no	—
195	#135	—	127	16	no	—
196	#135	—	127	8	no	—
197	#135	C₂×D₁₂₇	1	8	yes	complemented
198	C₂×Q₁₆	—	127	2	no	—
199	C₂×Q₁₆	—	127	1	no	—
200	C₂×Q₁₆	C₂×D₁₂₇	1	1	yes	characteristic, complemented
201	C₂×SD₁₆	—	127	2	no	—
202	C₂×SD₁₆	—	127	2	no	—
203	C₂×SD₁₆	—	127	2	no	—
204	C₂×SD₁₆	C₂×D₁₂₇	1	2	yes	complemented
205	C₂×D₈	—	127	2	no	—
206	C₂×D₈	—	127	1	no	—
207	C₂×D₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
208	C₂×M₁₆	—	127	2	no	—
209	C₂×M₁₆	—	127	2	no	—
210	C₂×M₁₆	—	127	8	no	—
211	C₂²×C₈	—	127	1	no	—
212	C₂²×C₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
213	C₂⁴	—	127	1	no	—
214	C₂⁴	—	254	2	no	—
215	#41	—	2	4	no	—
216	#41	—	127	8	no	—
217	#41	—	127	8	no	—
218	#41	—	127	8	no	—
219	#41	—	254	16	no	—
220	#41	—	254	16	no	—
221	#41	—	254	4	no	—
222	#41	—	254	4	no	—
223	#41	—	254	4	no	—
224	#41	C₂²×D₁₂₇	1	8	yes	complemented
225	C₂×Q₈	—	127	8	no	—
226	C₂×Q₈	—	127	2	no	—
227	C₂×Q₈	—	254	2	no	—
228	C₂×Q₈	—	254	4	no	—
229	C₂×Q₈	C₂²×D₁₂₇	1	2	yes	—
230	C₂×D₄	—	2	2	no	—
231	C₂×D₄	—	127	8	no	—
232	C₂×D₄	—	127	2	no	—
233	C₂×D₄	—	254	2	no	—
234	C₂×D₄	—	254	4	no	—
235	C₂×D₄	—	254	2	no	—
236	C₂×D₄	—	254	16	no	—
237	C₂×D₄	—	254	2	no	—
238	C₂×D₄	—	254	2	no	—
239	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	127	1	no	—
242	C₂²×C₄	—	127	4	no	—
243	C₂²×C₄	—	127	2	no	—
244	C₂²×C₄	—	127	2	no	—
245	C₂²×C₄	—	127	4	no	—
246	C₂²×C₄	—	254	2	no	—
247	C₂²×C₄	—	254	16	no	—
248	C₂²×C₄	—	254	2	no	—
249	C₂²×C₄	—	254	2	no	—
250	C₂²×C₄	—	254	2	no	—
251	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
252	Q₁₆	—	127	8	no	—
253	Q₁₆	—	127	4	no	—
254	Q₁₆	C₂²×D₁₂₇	1	4	yes	complemented
255	SD₁₆	—	127	8	no	—
256	SD₁₆	—	127	8	no	—
257	SD₁₆	—	127	8	no	—
258	SD₁₆	C₂²×D₁₂₇	1	8	yes	complemented
259	D₈	—	127	8	no	—
260	D₈	—	127	4	no	—
261	D₈	C₂²×D₁₂₇	1	4	yes	complemented
262	M₁₆	—	127	8	no	—
263	M₁₆	—	127	8	no	—
264	C₂×C₈	—	127	2	no	—
265	C₂×C₈	—	127	4	no	—
266	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
267	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
268	C₂×C₈	C₂²×D₁₂₇	1	4	yes	complemented
269	C₂³	—	2	2	no	—
270	C₂³	—	127	4	no	—
271	C₂³	—	127	2	no	—
272	C₂³	—	508	2	no	—
273	C₂³	—	508	8	no	—
274	C₂³	—	254	8	no	—
275	C₂³	—	254	2	no	—
276	C₂³	D₄×D₁₂₇	1	1	yes	characteristic
277	Q₈	—	2	2	no	—
278	Q₈	—	127	4	no	—
279	Q₈	—	254	8	no	—
280	Q₈	—	254	2	no	—
281	Q₈	C₂³×D₁₂₇	1	4	yes	—
282	D₄	—	2	8	no	—
283	D₄	—	2	2	no	—
284	D₄	—	127	4	no	—
285	D₄	—	254	8	no	—
286	D₄	—	254	8	no	—
287	D₄	—	254	8	no	—
288	D₄	—	254	8	no	—
289	D₄	—	254	2	no	—
290	D₄	C₂³×D₁₂₇	1	4	yes	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	8	no	—
293	C₂×C₄	—	127	2	no	—
294	C₂×C₄	—	127	4	no	—
295	C₂×C₄	—	127	8	no	—
296	C₂×C₄	—	127	4	no	—
297	C₂×C₄	—	127	4	no	—
298	C₂×C₄	—	254	8	no	—
299	C₂×C₄	—	254	8	no	—
300	C₂×C₄	—	254	8	no	—
301	C₂×C₄	—	254	2	no	—
302	C₂×C₄	—	254	8	no	—
303	C₂×C₄	D₄×D₁₂₇	1	2	yes	—
304	C₂×C₄	D₄×D₁₂₇	1	1	yes	characteristic
305	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
306	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
307	C₈	—	127	4	no	—
308	C₈	C₂³×D₁₂₇	1	2	yes	—
309	C₈	C₂³×D₁₂₇	1	2	yes	—
310	C₂²	—	2	2	no	—
311	C₂²	—	2	4	no	—
312	C₂²	—	4	4	no	—
313	C₂²	—	127	4	no	—
314	C₂²	—	508	4	no	—
315	C₂²	—	508	16	no	—
316	C₂²	—	508	4	no	—
317	C₂²	—	254	4	no	—
318	C₂²	—	254	4	no	—
319	C₂²	C₂×D₄×D₁₂₇	1	2	yes	—
320	C₂²	C₂×D₄×D₁₂₇	1	1	yes	characteristic
321	C₄	—	2	4	no	—
322	C₄	—	127	4	no	—
323	C₄	—	254	4	no	—
324	C₄	C₂×D₄×D₁₂₇	1	2	yes	—
325	C₄	C₂×D₄×D₁₂₇	1	1	yes	characteristic
326	C₄	C₂⁴×D₁₂₇	1	1	yes	characteristic
327	C₂	—	2	2	no	—
328	C₂	—	4	4	no	—
329	C₂	—	508	4	no	—
330	C₂	—	254	4	no	—
331	C₂	#22550673	1	2	yes	direct product factor
332	C₂	C₂²×D₄×D₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₂₇
commutator, cosocle	C₄×C₁₂₇	C₂⁵
Frattini	C₄	C₂⁴×D₁₂₇
Fitting	C₂×#135×C₁₂₇	C₂
socle	C₂²×C₁₂₇	C₂²×D₄
hypercenter	C₂×#135	D₁₂₇
hypocenter	C₁₂₇	C₂×#575
LCS	G ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₂₇	C₂	semidirect
2. #22550673	C₂	direct (N × H)
3. C₂×#16861241	C₂	semidirect
4. C₂×#16861238	C₂	semidirect
5. C₂×#16861236	C₂	semidirect
6. C₂×#16861233	C₂	semidirect
7. C₂×#16861231	C₂	semidirect
8. C₂×#16861229	C₂	semidirect
9. C₂²×#14523231	C₂	semidirect
10. C₂×#135×C₁₂₇	C₂	semidirect
13. C₂×#14523248	C₂²	semidirect
17. #41×D₁₂₇	C₂²	semidirect
18. C₂×Q₈×D₁₂₇	C₂²	semidirect
20. C₂×D₄×D₁₂₇	C₂²	semidirect
23. #16861241	C₂²	semidirect
24. #16861238	C₂²	semidirect
25. #16861236	C₂²	semidirect
26. #16861233	C₂²	semidirect
27. #16861231	C₂²	semidirect
28. #16861229	C₂²	semidirect
29. C₂×Dic₅₀₈	C₂²	semidirect
30. C₂×#14523238	C₂²	semidirect
31. C₂×#14523237	C₂²	semidirect
32. C₂×#14523236	C₂²	semidirect
33. C₂×#14523235	C₂²	semidirect
34. C₂×D₁₀₁₆	C₂²	semidirect
35. C₂×#14523233	C₂²	semidirect
36. C₂×#14523231	C₂²	semidirect
37. C₂×#14523231	C₂²	semidirect
38. C₂×#14523231	C₂²	semidirect
39. C₂²×C₁₂₇⋊C₈	C₂²	semidirect
40. C₂×#41×C₁₂₇	C₂²	semidirect
41. #135×C₁₂₇	C₂²	semidirect
42. C₂×Q₁₆×C₁₂₇	C₂²	semidirect
43. C₂×SD₁₆×C₁₂₇	C₂²	semidirect
44. C₂×D₈×C₁₂₇	C₂²	semidirect
45. C₂²×C₈×C₁₂₇	C₂²	semidirect
52. #14523248	C₂³	semidirect
59. Q₈×D₁₂₇	C₂³	semidirect
67. D₄×D₁₂₇	C₂³	semidirect
78. Dic₅₀₈	C₂³	semidirect
79. #14523238	C₂³	semidirect
80. #14523237	C₂³	semidirect
81. #14523236	C₂³	semidirect
82. #14523235	C₂³	semidirect
83. D₁₀₁₆	C₂³	semidirect
84. #14523233	C₂³	semidirect
85. #14523231	C₂³	semidirect
86. #14523231	C₂³	semidirect
88. C₂×C₁₂₇⋊C₈	C₂³	semidirect
90. #41×C₁₂₇	C₂³	semidirect
96. Q₁₆×C₁₂₇	C₂³	semidirect
97. SD₁₆×C₁₂₇	C₂³	semidirect
98. D₈×C₁₂₇	C₂³	semidirect
101. C₂×C₈×C₁₂₇	C₂³	semidirect
162. C₂×C₁₂₇	#575	semidirect
167. C₁₂₇	C₂×#575	semidirect
176. C₂×#135	D₁₂₇	semidirect
185. C₂×#41	C₂×D₁₂₇	semidirect
197. #135	C₂×D₁₂₇	semidirect
200. C₂×Q₁₆	C₂×D₁₂₇	semidirect
204. C₂×SD₁₆	C₂×D₁₂₇	semidirect
207. C₂×D₈	C₂×D₁₂₇	semidirect
212. C₂²×C₈	C₂×D₁₂₇	semidirect
224. #41	C₂²×D₁₂₇	semidirect
254. Q₁₆	C₂²×D₁₂₇	semidirect
258. SD₁₆	C₂²×D₁₂₇	semidirect
261. D₈	C₂²×D₁₂₇	semidirect
268. C₂×C₈	C₂²×D₁₂₇	semidirect
331. C₂	#22550673	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×#41×D₁₂₇	2
#22550673	2
C₂×#16861241	2
C₂×#16861238	2
C₂×#16861236	2
C₂×#16861233	2
C₂×#16861231	2
C₂×#16861229	2
C₂²×#14523231	2
C₂×#135×C₁₂₇	2
C₂×#575	127

Subgroups — C2×#22550673 #30653474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22550673 #30653474