Subgroups — C₂×#22550683 #30653486

Order 16256.

1460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16861256	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16861255	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550683	C₂	1	16	yes	maximal, direct product factor
4	C₂×#16861241	C₂	1	2	yes	maximal, complemented
5	C₂×#16861239	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16861234	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16861233	C₂	1	2	yes	maximal, complemented
8	C₂×#16861230	C₂	1	2	yes	maximal, complemented
9	C₂²×#14523237	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×SD₁₆×D₁₂₇	C₂	1	2	yes	maximal, complemented
11	C₂×#16861215	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#16861256	—	2	4	no	—
14	#16861256	C₂²	1	8	yes	complemented
15	#16861255	—	2	4	no	—
16	#16861255	C₂²	1	8	yes	complemented
17	C₂×#14523249	C₂²	1	2	yes	—
18	C₂×#14523248	—	2	1	no	—
19	C₂×#14523248	—	2	1	no	—
20	C₂×#14523248	C₂²	1	1	yes	characteristic
21	C₂×#14523247	—	2	2	no	—
22	C₂×#14523247	C₂²	1	2	yes	complemented
23	C₂²×Dic₂₅₄	—	2	1	no	—
24	C₂²×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
25	C₂×Q₈×D₁₂₇	C₂²	1	2	yes	complemented
26	C₂²×D₅₀₈	—	2	1	no	—
27	C₂²×D₅₀₈	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₁₂₇	—	2	2	no	—
29	C₂×D₄×D₁₂₇	C₂²	1	2	yes	—
30	#16861241	C₂²	1	16	yes	complemented
31	#16861239	C₂²	1	8	yes	complemented
32	#16861234	C₂²	1	8	yes	complemented
33	#16861233	C₂²	1	16	yes	complemented
34	#16861230	C₂²	1	16	yes	complemented
35	C₂×#14523238	C₂²	1	2	yes	complemented
36	C₂×#14523237	C₂²	1	2	yes	complemented
37	C₂×#14523237	C₂²	1	2	yes	complemented
38	C₂×#14523237	C₂²	1	8	yes	complemented
39	C₂×#14523236	C₂²	1	2	yes	complemented
40	C₂×#14523235	C₂²	1	2	yes	complemented
41	SD₁₆×D₁₂₇	C₂²	1	16	yes	complemented
42	C₂×#14523233	C₂²	1	2	yes	complemented
43	#16861215	C₂²	1	8	yes	complemented
44	C₂×#14523232	C₂²	1	1	yes	characteristic, complemented
45	C₂×#14523231	C₂²	1	2	yes	complemented
46	C₂×C₈×D₁₂₇	C₂²	1	2	yes	complemented
47	C₂×#41×C₁₂₇	C₂²	1	1	yes	characteristic
48	C₂×#41×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
49	#135×C₁₂₇	C₂²	1	8	yes	complemented
50	C₂×Q₁₆×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
51	C₂×SD₁₆×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
52	C₂×SD₁₆×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
53	C₂×D₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
55	C₂³×D₁₂₇	—	2	2	no	—
56	C₂³×D₁₂₇	—	2	1	no	—
57	#14523249	—	2	4	no	—
58	#14523249	C₂³	1	8	yes	—
59	#14523248	—	2	8	no	—
60	#14523248	—	2	8	no	—
61	#14523248	D₄	1	4	yes	—
62	#14523248	C₂³	1	4	yes	—
63	#14523247	—	2	16	no	—
64	#14523247	—	2	4	no	—
65	#14523247	C₂³	1	8	yes	complemented
66	C₂×Dic₂₅₄	—	2	8	no	—
67	C₂×Dic₂₅₄	—	2	2	no	—
68	C₂×Dic₂₅₄	—	2	1	no	—
69	C₂×Dic₂₅₄	—	2	2	no	—
70	C₂×Dic₂₅₄	D₄	1	1	yes	characteristic
71	C₂×Dic₂₅₄	C₂³	1	2	yes	—
72	C₂×Dic₂₅₄	C₂³	1	4	yes	complemented
73	Q₈×D₁₂₇	—	2	4	no	—
74	Q₈×D₁₂₇	C₂³	1	8	yes	complemented
75	C₂×D₅₀₈	—	2	2	no	—
76	C₂×D₅₀₈	—	2	8	no	—
77	C₂×D₅₀₈	—	2	1	no	—
78	C₂×D₅₀₈	—	2	2	no	—
79	C₂×D₅₀₈	D₄	1	1	yes	characteristic
80	C₂×D₅₀₈	C₂³	1	2	yes	—
81	C₂×D₅₀₈	C₂³	1	4	yes	—
82	C₂×C₂²⋊D₁₂₇	—	2	2	no	—
83	C₂×C₂²⋊D₁₂₇	—	2	2	no	—
84	C₂×C₂²⋊D₁₂₇	D₄	1	2	yes	—
85	D₄×D₁₂₇	—	2	16	no	—
86	D₄×D₁₂₇	—	2	4	no	—
87	D₄×D₁₂₇	C₂³	1	8	yes	—
88	C₂²×Dic₁₂₇	—	2	2	no	—
89	C₂²×Dic₁₂₇	—	2	1	no	—
90	C₂×C₄×D₁₂₇	—	2	2	no	—
91	C₂×C₄×D₁₂₇	—	2	2	no	—
92	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
93	#14523238	C₂³	1	8	yes	complemented
94	#14523237	C₂³	1	8	yes	complemented
95	#14523237	C₂³	1	8	yes	complemented
96	#14523236	C₂³	1	8	yes	complemented
97	#14523235	C₂³	1	8	yes	complemented
98	#14523233	C₂³	1	8	yes	complemented
99	#14523232	C₂³	1	4	yes	complemented
100	#14523231	C₂³	1	8	yes	complemented
101	C₂×C₁₂₇⋊C₈	C₂³	1	2	yes	—
102	C₈×D₁₂₇	C₂³	1	8	yes	complemented
103	#41×C₁₂₇	—	2	2	no	—
104	#41×C₁₂₇	—	2	2	no	—
105	#41×C₁₂₇	C₂³	1	4	yes	—
106	#41×C₁₂₇	C₂³	1	4	yes	complemented
107	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₁₂₇	—	2	1	no	—
110	C₂×D₄×C₁₂₇	—	2	1	no	—
111	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₁₂₇	—	2	1	no	—
114	C₂²×C₄×C₁₂₇	—	2	1	no	—
115	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
116	Q₁₆×C₁₂₇	C₂³	1	4	yes	complemented
117	SD₁₆×C₁₂₇	C₂³	1	4	yes	complemented
118	SD₁₆×C₁₂₇	C₂³	1	4	yes	complemented
119	D₈×C₁₂₇	C₂³	1	4	yes	complemented
120	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
121	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
122	C₂×C₈×C₁₂₇	C₂³	1	4	yes	complemented
123	C₂²×D₁₂₇	—	2	2	no	—
124	C₂²×D₁₂₇	—	2	4	no	—
125	C₂²×D₁₂₇	—	2	8	no	—
126	C₂²×D₁₂₇	—	8	4	no	—
127	C₂²×D₁₂₇	—	8	2	no	—
128	C₂²×D₁₂₇	C₂×D₄	1	2	yes	—
129	Dic₂₅₄	—	2	2	no	—
130	Dic₂₅₄	—	2	4	no	—
131	Dic₂₅₄	—	2	8	no	—
132	Dic₂₅₄	C₂×D₄	1	4	yes	—
133	Dic₂₅₄	C₂⁴	1	4	yes	—
134	D₅₀₈	—	2	8	no	—
135	D₅₀₈	—	2	2	no	—
136	D₅₀₈	—	2	4	no	—
137	D₅₀₈	C₂×D₄	1	4	yes	—
138	D₅₀₈	C₂⁴	1	4	yes	—
139	C₂²⋊D₁₂₇	—	2	8	no	—
140	C₂²⋊D₁₂₇	—	2	8	no	—
141	C₂²⋊D₁₂₇	C₂×D₄	1	8	yes	—
142	C₂×Dic₁₂₇	—	2	2	no	—
143	C₂×Dic₁₂₇	—	2	4	no	—
144	C₂×Dic₁₂₇	—	2	8	no	—
145	C₂×Dic₁₂₇	C₂×D₄	1	2	yes	—
146	C₄×D₁₂₇	—	2	8	no	—
147	C₄×D₁₂₇	—	2	8	no	—
148	C₄×D₁₂₇	C₂×D₄	1	4	yes	—
149	C₄×D₁₂₇	C₂⁴	1	4	yes	—
150	C₁₂₇⋊C₈	C₂⁴	1	4	yes	—
151	C₂³×C₁₂₇	—	2	1	no	—
152	C₂³×C₁₂₇	—	2	1	no	—
153	C₂³×C₁₂₇	C₂×D₄	1	1	yes	characteristic
154	Q₈×C₁₂₇	—	2	1	no	—
155	Q₈×C₁₂₇	—	2	1	no	—
156	Q₈×C₁₂₇	C₂⁴	1	2	yes	—
157	Q₈×C₁₂₇	C₂⁴	1	2	yes	—
158	D₄×C₁₂₇	—	2	4	no	—
159	D₄×C₁₂₇	—	2	4	no	—
160	D₄×C₁₂₇	—	2	1	no	—
161	D₄×C₁₂₇	—	2	1	no	—
162	D₄×C₁₂₇	C₂⁴	1	2	yes	—
163	D₄×C₁₂₇	C₂⁴	1	2	yes	—
164	C₂×C₄×C₁₂₇	—	2	1	no	—
165	C₂×C₄×C₁₂₇	—	2	1	no	—
166	C₂×C₄×C₁₂₇	—	2	4	no	—
167	C₂×C₄×C₁₂₇	—	2	4	no	—
168	C₂×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
170	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
172	C₈×C₁₂₇	C₂⁴	1	2	yes	—
173	C₈×C₁₂₇	C₂⁴	1	2	yes	—
174	C₂²×C₁₂₇	—	2	2	no	—
175	C₂²×C₁₂₇	—	2	2	no	—
176	C₂²×C₁₂₇	—	2	2	no	—
177	C₂²×C₁₂₇	—	4	2	no	—
178	C₂²×C₁₂₇	—	4	2	no	—
179	C₂²×C₁₂₇	C₂²×D₄	1	2	yes	—
180	C₂²×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×D₁₂₇	—	2	4	no	—
182	C₂×D₁₂₇	—	2	4	no	—
183	C₂×D₁₂₇	—	4	4	no	—
184	C₂×D₁₂₇	—	8	8	no	—
185	C₂×D₁₂₇	—	8	4	no	—
186	C₂×D₁₂₇	C₂²×D₄	1	4	yes	—
187	C₄×C₁₂₇	—	2	2	no	—
188	C₄×C₁₂₇	—	2	2	no	—
189	C₄×C₁₂₇	C₂²×D₄	1	2	yes	—
190	C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
191	C₄×C₁₂₇	C₂⁵	1	1	yes	characteristic
192	Dic₁₂₇	—	2	4	no	—
193	Dic₁₂₇	C₂²×D₄	1	4	yes	—
194	C₂×C₁₂₇	—	2	2	no	—
195	C₂×C₁₂₇	—	4	2	no	—
196	C₂×C₁₂₇	—	4	2	no	—
197	C₂×C₁₂₇	#577	1	2	yes	complemented
198	C₂×C₁₂₇	C₂³×D₄	1	1	yes	characteristic
199	D₁₂₇	—	2	4	no	—
200	D₁₂₇	—	4	4	no	—
201	C₂×#577	—	127	1	no	maximal, Sylow
202	C₁₂₇	C₂×#577	1	1	yes	characteristic, complemented, Sylow
203	C₂×2₋¹⁺⁴	—	127	1	no	—
204	C₂×H(5,𝔽₂)	—	127	1	no	—
205	#577	—	127	16	no	—
206	C₂×#137	—	127	1	no	—
207	C₂×#137	—	127	2	no	—
208	C₂×AGL(1,ℤ/8)	—	127	1	no	—
209	C₂×AGL(1,ℤ/8)	—	127	2	no	—
210	C₂×#135	—	127	2	no	—
211	C₂×#135	D₁₂₇	1	1	yes	characteristic, complemented
212	C₂²×SD₁₆	—	127	2	no	—
213	C₂²×SD₁₆	—	127	1	no	—
214	C₂×#131	—	127	1	no	—
215	2₋¹⁺⁴	—	127	8	no	—
216	2₋¹⁺⁴	—	254	4	no	—
217	H(5,𝔽₂)	—	127	8	no	—
218	H(5,𝔽₂)	—	254	4	no	—
219	C₂×#41	—	127	1	no	—
220	C₂×#41	—	127	2	no	—
221	C₂×#41	—	127	2	no	—
222	C₂×#41	—	254	1	no	—
223	C₂×#41	—	254	1	no	—
224	C₂×#41	—	254	2	no	—
225	C₂×#41	C₂×D₁₂₇	1	1	yes	characteristic
226	C₂×#41	C₂×D₁₂₇	1	1	yes	characteristic, complemented
227	C₂²×Q₈	—	127	2	no	—
228	C₂²×Q₈	—	127	1	no	—
229	C₂²×Q₈	—	254	1	no	—
230	C₂²×D₄	—	127	2	no	—
231	C₂²×D₄	—	127	1	no	—
232	C₂²×D₄	—	254	1	no	—
233	C₂²×D₄	—	254	2	no	—
234	#137	—	127	8	no	—
235	#137	—	127	16	no	—
236	AGL(1,ℤ/8)	—	127	8	no	—
237	AGL(1,ℤ/8)	—	127	16	no	—
238	#135	—	127	16	no	—
239	#135	C₂×D₁₂₇	1	8	yes	complemented
240	C₂×Q₁₆	—	127	2	no	—
241	C₂×Q₁₆	C₂×D₁₂₇	1	1	yes	characteristic, complemented
242	C₂×SD₁₆	—	127	2	no	—
243	C₂×SD₁₆	—	127	2	no	—
244	C₂×SD₁₆	—	127	16	no	—
245	C₂×SD₁₆	—	127	2	no	—
246	C₂×SD₁₆	—	127	2	no	—
247	C₂×SD₁₆	—	127	8	no	—
248	C₂×SD₁₆	C₂×D₁₂₇	1	1	yes	characteristic, complemented
249	C₂×SD₁₆	C₂×D₁₂₇	1	1	yes	characteristic, complemented
250	C₂×D₈	—	127	2	no	—
251	C₂×D₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
252	#131	—	127	8	no	—
253	C₂×M₁₆	—	127	1	no	—
254	C₂×M₁₆	—	127	2	no	—
255	C₂²×C₈	—	127	2	no	—
256	C₂²×C₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
257	C₂⁴	—	254	2	no	—
258	C₂⁴	—	254	1	no	—
259	#41	—	2	2	no	—
260	#41	—	2	2	no	—
261	#41	—	127	4	no	—
262	#41	—	127	4	no	—
263	#41	—	127	8	no	—
264	#41	—	127	8	no	—
265	#41	—	254	8	no	—
266	#41	—	254	8	no	—
267	#41	—	254	4	no	—
268	#41	—	254	4	no	—
269	#41	—	254	16	no	—
270	#41	C₂²×D₁₂₇	1	4	yes	—
271	#41	C₂²×D₁₂₇	1	4	yes	complemented
272	C₂×Q₈	—	127	1	no	—
273	C₂×Q₈	—	127	8	no	—
274	C₂×Q₈	—	127	2	no	—
275	C₂×Q₈	—	127	4	no	—
276	C₂×Q₈	—	254	2	no	—
277	C₂×Q₈	—	254	8	no	—
278	C₂×Q₈	—	254	4	no	—
279	C₂×Q₈	—	254	1	no	—
280	C₂×Q₈	—	254	2	no	—
281	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
282	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	127	2	no	—
286	C₂×D₄	—	127	8	no	—
287	C₂×D₄	—	127	1	no	—
288	C₂×D₄	—	127	2	no	—
289	C₂×D₄	—	127	4	no	—
290	C₂×D₄	—	254	8	no	—
291	C₂×D₄	—	254	2	no	—
292	C₂×D₄	—	254	4	no	—
293	C₂×D₄	—	254	2	no	—
294	C₂×D₄	—	254	16	no	—
295	C₂×D₄	—	254	2	no	—
296	C₂×D₄	—	254	1	no	—
297	C₂×D₄	—	254	2	no	—
298	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
299	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	127	2	no	—
303	C₂²×C₄	—	254	2	no	—
304	C₂²×C₄	—	254	2	no	—
305	C₂²×C₄	—	254	2	no	—
306	C₂²×C₄	—	254	1	no	—
307	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
308	Q₁₆	—	127	8	no	—
309	Q₁₆	C₂²×D₁₂₇	1	4	yes	complemented
310	SD₁₆	—	127	8	no	—
311	SD₁₆	—	127	8	no	—
312	SD₁₆	—	127	8	no	—
313	SD₁₆	—	127	8	no	—
314	SD₁₆	C₂²×D₁₂₇	1	4	yes	complemented
315	SD₁₆	C₂²×D₁₂₇	1	4	yes	complemented
316	D₈	—	127	8	no	—
317	D₈	C₂²×D₁₂₇	1	4	yes	complemented
318	M₁₆	—	127	4	no	—
319	M₁₆	—	127	8	no	—
320	C₂×C₈	—	127	2	no	—
321	C₂×C₈	—	127	8	no	—
322	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
323	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
324	C₂×C₈	C₂²×D₁₂₇	1	4	yes	complemented
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	127	2	no	—
328	C₂³	—	1016	2	no	—
329	C₂³	—	1016	4	no	—
330	C₂³	—	254	8	no	—
331	C₂³	—	254	4	no	—
332	C₂³	—	254	2	no	—
333	C₂³	D₄×D₁₂₇	1	1	yes	characteristic
334	Q₈	—	2	1	no	—
335	Q₈	—	2	1	no	—
336	Q₈	—	127	4	no	—
337	Q₈	—	127	4	no	—
338	Q₈	—	254	8	no	—
339	Q₈	—	254	4	no	—
340	Q₈	—	254	2	no	—
341	Q₈	C₂³×D₁₂₇	1	2	yes	—
342	Q₈	C₂³×D₁₂₇	1	2	yes	—
343	D₄	—	2	4	no	—
344	D₄	—	2	4	no	—
345	D₄	—	2	1	no	—
346	D₄	—	2	1	no	—
347	D₄	—	127	8	no	—
348	D₄	—	127	4	no	—
349	D₄	—	127	4	no	—
350	D₄	—	254	8	no	—
351	D₄	—	254	8	no	—
352	D₄	—	254	8	no	—
353	D₄	—	254	4	no	—
354	D₄	—	254	2	no	—
355	D₄	C₂³×D₁₂₇	1	2	yes	—
356	D₄	C₂³×D₁₂₇	1	2	yes	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	127	2	no	—
362	C₂×C₄	—	127	4	no	—
363	C₂×C₄	—	127	4	no	—
364	C₂×C₄	—	254	8	no	—
365	C₂×C₄	—	254	8	no	—
366	C₂×C₄	—	254	8	no	—
367	C₂×C₄	—	254	4	no	—
368	C₂×C₄	—	254	2	no	—
369	C₂×C₄	D₄×D₁₂₇	1	2	yes	—
370	C₂×C₄	D₄×D₁₂₇	1	1	yes	characteristic
371	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
372	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
373	C₈	—	127	4	no	—
374	C₈	C₂³×D₁₂₇	1	2	yes	—
375	C₈	C₂³×D₁₂₇	1	2	yes	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	127	4	no	—
382	C₂²	—	1016	4	no	—
383	C₂²	—	1016	8	no	—
384	C₂²	—	508	4	no	—
385	C₂²	—	254	4	no	—
386	C₂²	—	254	4	no	—
387	C₂²	C₂×D₄×D₁₂₇	1	2	yes	—
388	C₂²	C₂×D₄×D₁₂₇	1	1	yes	characteristic
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	127	4	no	—
392	C₄	—	254	4	no	—
393	C₄	C₂×D₄×D₁₂₇	1	2	yes	—
394	C₄	C₂×D₄×D₁₂₇	1	1	yes	characteristic
395	C₄	C₂⁴×D₁₂₇	1	1	yes	characteristic
396	C₂	—	2	2	no	—
397	C₂	—	4	2	no	—
398	C₂	—	4	2	no	—
399	C₂	—	508	4	no	—
400	C₂	—	254	4	no	—
401	C₂	#22550683	1	2	yes	direct product factor
402	C₂	C₂²×D₄×D₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×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×#577
LCS	G ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#16861256	C₂	semidirect
2. C₂×#16861255	C₂	semidirect
3. #22550683	C₂	direct (N × H)
4. C₂×#16861241	C₂	semidirect
5. C₂×#16861239	C₂	semidirect
6. C₂×#16861234	C₂	semidirect
7. C₂×#16861233	C₂	semidirect
8. C₂×#16861230	C₂	semidirect
9. C₂²×#14523237	C₂	semidirect
10. C₂×SD₁₆×D₁₂₇	C₂	semidirect
11. C₂×#16861215	C₂	semidirect
12. C₂×#135×C₁₂₇	C₂	semidirect
14. #16861256	C₂²	semidirect
16. #16861255	C₂²	semidirect
22. C₂×#14523247	C₂²	semidirect
24. C₂²×Dic₂₅₄	C₂²	semidirect
25. C₂×Q₈×D₁₂₇	C₂²	semidirect
30. #16861241	C₂²	semidirect
31. #16861239	C₂²	semidirect
32. #16861234	C₂²	semidirect
33. #16861233	C₂²	semidirect
34. #16861230	C₂²	semidirect
35. C₂×#14523238	C₂²	semidirect
36. C₂×#14523237	C₂²	semidirect
37. C₂×#14523237	C₂²	semidirect
38. C₂×#14523237	C₂²	semidirect
39. C₂×#14523236	C₂²	semidirect
40. C₂×#14523235	C₂²	semidirect
41. SD₁₆×D₁₂₇	C₂²	semidirect
42. C₂×#14523233	C₂²	semidirect
43. #16861215	C₂²	semidirect
44. C₂×#14523232	C₂²	semidirect
45. C₂×#14523231	C₂²	semidirect
46. C₂×C₈×D₁₂₇	C₂²	semidirect
48. C₂×#41×C₁₂₇	C₂²	semidirect
49. #135×C₁₂₇	C₂²	semidirect
50. C₂×Q₁₆×C₁₂₇	C₂²	semidirect
51. C₂×SD₁₆×C₁₂₇	C₂²	semidirect
52. C₂×SD₁₆×C₁₂₇	C₂²	semidirect
53. C₂×D₈×C₁₂₇	C₂²	semidirect
54. C₂²×C₈×C₁₂₇	C₂²	semidirect
65. #14523247	C₂³	semidirect
72. C₂×Dic₂₅₄	C₂³	semidirect
74. Q₈×D₁₂₇	C₂³	semidirect
93. #14523238	C₂³	semidirect
94. #14523237	C₂³	semidirect
95. #14523237	C₂³	semidirect
96. #14523236	C₂³	semidirect
97. #14523235	C₂³	semidirect
98. #14523233	C₂³	semidirect
99. #14523232	C₂³	semidirect
100. #14523231	C₂³	semidirect
102. C₈×D₁₂₇	C₂³	semidirect
106. #41×C₁₂₇	C₂³	semidirect
116. Q₁₆×C₁₂₇	C₂³	semidirect
117. SD₁₆×C₁₂₇	C₂³	semidirect
118. SD₁₆×C₁₂₇	C₂³	semidirect
119. D₈×C₁₂₇	C₂³	semidirect
122. C₂×C₈×C₁₂₇	C₂³	semidirect
197. C₂×C₁₂₇	#577	semidirect
202. C₁₂₇	C₂×#577	semidirect
211. C₂×#135	D₁₂₇	semidirect
226. C₂×#41	C₂×D₁₂₇	semidirect
239. #135	C₂×D₁₂₇	semidirect
241. C₂×Q₁₆	C₂×D₁₂₇	semidirect
248. C₂×SD₁₆	C₂×D₁₂₇	semidirect
249. C₂×SD₁₆	C₂×D₁₂₇	semidirect
251. C₂×D₈	C₂×D₁₂₇	semidirect
256. C₂²×C₈	C₂×D₁₂₇	semidirect
271. #41	C₂²×D₁₂₇	semidirect
309. Q₁₆	C₂²×D₁₂₇	semidirect
314. SD₁₆	C₂²×D₁₂₇	semidirect
315. SD₁₆	C₂²×D₁₂₇	semidirect
317. D₈	C₂²×D₁₂₇	semidirect
324. C₂×C₈	C₂²×D₁₂₇	semidirect
401. C₂	#22550683	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×#16861256	2
C₂×#16861255	2
#22550683	2
C₂×#16861241	2
C₂×#16861239	2
C₂×#16861234	2
C₂×#16861233	2
C₂×#16861230	2
C₂²×#14523237	2
C₂×SD₁₆×D₁₂₇	2
C₂×#16861215	2
C₂×#135×C₁₂₇	2
C₂×#577	127

Subgroups — C2×#22550683 #30653486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22550683 #30653486