Subgroups — #26376684

Order 12032.

4006 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689598	C₂	1	2	yes	maximal, complemented
2	#20246453	C₂	1	8	yes	maximal, complemented
3	D₄×C₂²⋊Dic₄₇	C₂	1	8	yes	maximal, complemented
4	#20246114	C₂	1	4	yes	maximal, complemented
5	#20245970	C₂	1	2	yes	maximal, complemented
6	#127×Dic₄₇	C₂	1	4	yes	maximal, complemented
7	#20245795	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#127×C₄₇	C₂	1	1	yes	maximal, characteristic
10	#15689598	—	2	16	no	—
11	C₂×D₄×Dic₄₇	C₂²	1	8	yes	complemented
12	C₂×D₄×Dic₄₇	C₂²	1	8	yes	complemented
13	C₂×D₄×Dic₄₇	C₂²	1	16	yes	complemented
14	C₂×#13093983	C₂²	1	2	yes	—
15	C₂×#13093983	C₂²	1	1	yes	characteristic
16	C₂×#13093983	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊Dic₄₇	C₂²	1	8	yes	—
18	#15689026	C₂²	1	8	yes	complemented
19	#15689026	C₂²	1	8	yes	complemented
20	#15689026	C₂²	1	16	yes	complemented
21	#15689003	C₂²	1	32	yes	complemented
22	#15688993	C₂²	1	2	yes	complemented
23	#15688989	C₂²	1	2	yes	complemented
24	#15688983	C₂²	1	4	yes	—
25	#15688979	C₂²	1	8	yes	—
26	C₄×C₄⋊Dic₄₇	C₂²	1	4	yes	complemented
27	C₄×C₄⋊Dic₄₇	C₂²	1	4	yes	complemented
28	C₄×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
29	#15688969	C₂²	1	2	yes	complemented
30	C₄²×Dic₄₇	C₂²	1	2	yes	complemented
31	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
32	C₂³×D₄×C₄₇	C₂²	1	4	yes	—
33	C₂×#127×C₄₇	C₄	1	16	yes	complemented
34	C₂×#127×C₄₇	C₂²	1	2	yes	—
35	C₂×#127×C₄₇	C₂²	1	4	yes	—
36	C₂×#127×C₄₇	C₂²	1	2	yes	—
37	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
38	C₂³×Dic₄₇	C₂³	1	16	yes	—
39	D₄×Dic₄₇	—	2	32	no	—
40	D₄×Dic₄₇	—	2	32	no	—
41	D₄×Dic₄₇	—	4	32	no	—
42	#13093983	—	2	8	no	—
43	#13093983	—	2	4	no	—
44	#13093983	D₄	1	8	yes	complemented
45	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
46	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
47	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
49	C₂×C₂²⋊Dic₄₇	—	2	32	no	—
50	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
51	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
52	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
53	C₂×C₂²⋊Dic₄₇	C₂³	1	32	yes	—
54	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
55	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
56	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
57	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
58	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
59	C₄₇⋊#95	C₂³	1	8	yes	—
60	C₄₇⋊#95	C₂³	1	8	yes	—
61	C₂⁵×C₄₇	C₂³	1	4	yes	—
62	C₂²×D₄×C₄₇	—	2	8	no	—
63	C₂²×D₄×C₄₇	—	2	8	no	—
64	C₂²×D₄×C₄₇	—	4	16	no	—
65	C₂²×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
66	C₂²×D₄×C₄₇	C₂×C₄	1	32	yes	complemented
67	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
68	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
69	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
70	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
71	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
72	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
73	#127×C₄₇	C₂×C₄	1	16	yes	complemented
74	#127×C₄₇	C₂×C₄	1	32	yes	complemented
75	#127×C₄₇	C₂×C₄	1	16	yes	complemented
76	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
80	C₂⁴×C₄₇	—	2	8	no	—
81	C₂⁴×C₄₇	—	2	8	no	—
82	C₂⁴×C₄₇	—	4	16	no	—
83	C₂⁴×C₄₇	C₂²×C₄	1	16	yes	—
84	C₂⁴×C₄₇	C₂⁴	1	8	yes	—
85	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
86	C₂×D₄×C₄₇	—	2	64	no	—
87	C₂×D₄×C₄₇	—	2	8	no	—
88	C₂×D₄×C₄₇	—	2	8	no	—
89	C₂×D₄×C₄₇	—	2	8	no	—
90	C₂×D₄×C₄₇	—	2	8	no	—
91	C₂×D₄×C₄₇	—	2	32	no	—
92	C₂×D₄×C₄₇	—	4	64	no	—
93	C₂×D₄×C₄₇	—	4	16	no	—
94	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
95	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
96	C₂×D₄×C₄₇	C₂²×C₄	1	32	yes	—
97	C₂×D₄×C₄₇	C₂²×C₄	1	32	yes	—
98	C₂²×C₄×C₄₇	—	2	8	no	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₄₇	#41	1	4	yes	—
103	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
107	C₂²×Dic₄₇	—	2	32	no	—
108	C₂²×Dic₄₇	—	4	32	no	—
109	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
110	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
111	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
112	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
113	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
114	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
115	C₂²⋊Dic₄₇	—	2	8	no	—
116	C₂²⋊Dic₄₇	—	2	4	no	—
117	C₂²⋊Dic₄₇	—	2	32	no	—
118	C₂²⋊Dic₄₇	—	4	32	no	—
119	C₂²⋊Dic₄₇	C₂×D₄	1	8	yes	—
120	C₄⋊Dic₄₇	—	2	8	no	—
121	C₄⋊Dic₄₇	—	2	4	no	—
122	C₄⋊Dic₄₇	—	2	16	no	—
123	C₄⋊Dic₄₇	C₂×D₄	1	8	yes	complemented
124	C₄×Dic₄₇	—	2	8	no	—
125	C₄×Dic₄₇	—	2	4	no	—
126	C₄×Dic₄₇	—	2	16	no	—
127	C₄×Dic₄₇	C₂×D₄	1	8	yes	complemented
128	C₂³×C₄₇	—	2	4	no	—
129	C₂³×C₄₇	—	2	8	no	—
130	C₂³×C₄₇	—	2	8	no	—
131	C₂³×C₄₇	—	2	32	no	—
132	C₂³×C₄₇	—	2	32	no	—
133	C₂³×C₄₇	—	4	32	no	—
134	C₂³×C₄₇	—	8	16	no	—
135	C₂³×C₄₇	—	8	16	no	—
136	C₂³×C₄₇	C₂³×C₄	1	16	yes	—
137	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
138	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
139	C₂³×C₄₇	C₂×#41	1	2	yes	—
140	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
141	D₄×C₄₇	—	2	32	no	—
142	D₄×C₄₇	—	2	32	no	—
143	D₄×C₄₇	—	2	64	no	—
144	D₄×C₄₇	—	4	32	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	16	no	—
147	C₂×C₄×C₄₇	C₄×D₄	1	16	yes	complemented
148	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
149	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
150	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
152	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
153	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
154	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
155	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
156	C₂×C₄×C₄₇	H(5,𝔽₂)	1	8	yes	—
157	C₂×Dic₄₇	—	2	8	no	—
158	C₂×Dic₄₇	—	2	8	no	—
159	C₂×Dic₄₇	—	2	4	no	—
160	C₂×Dic₄₇	—	2	8	no	—
161	C₂×Dic₄₇	—	2	16	no	—
162	C₂×Dic₄₇	—	8	32	no	—
163	C₂×Dic₄₇	C₂²×D₄	1	8	yes	—
164	#34210	—	47	1	no	maximal, Sylow
165	C₂²×C₄₇	—	2	4	no	—
166	C₂²×C₄₇	—	2	4	no	—
167	C₂²×C₄₇	—	2	4	no	—
168	C₂²×C₄₇	—	2	16	no	—
169	C₂²×C₄₇	—	2	32	no	—
170	C₂²×C₄₇	—	4	16	no	—
171	C₂²×C₄₇	—	4	16	no	—
172	C₂²×C₄₇	—	8	32	no	—
173	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
174	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
175	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
176	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
177	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
178	C₄×C₄₇	—	2	4	no	—
179	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
180	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
181	C₄×C₄₇	#518	1	8	yes	complemented
182	Dic₄₇	—	2	8	no	—
183	Dic₄₇	—	4	8	no	—
184	Dic₄₇	—	4	4	no	—
185	C₂²×#127	D₄₇	1	1	yes	characteristic
186	C₂×#518	—	47	2	no	—
187	#2366	—	47	8	no	—
188	D₄×C₂²⋊C₄	—	47	8	no	—
189	#2328	—	47	4	no	—
190	#2309	—	47	2	no	—
191	C₄×#127	—	47	4	no	—
192	#2285	—	47	1	no	—
193	C₄×#117	—	47	1	no	—
194	C₂×C₄₇	—	2	4	no	—
195	C₂×C₄₇	—	4	16	no	—
196	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
197	C₂×C₄₇	C₂×#518	1	2	yes	—
198	C₂×C₄₇	#3498	1	2	yes	—
199	C₂×C₄₇	#3508	1	2	yes	—
200	C₂³×D₄	C₂×D₄₇	1	2	yes	—
201	C₂³×D₄	C₂×D₄₇	1	4	yes	—
202	C₂×#127	Dic₄₇	1	16	yes	complemented
203	C₂×#127	C₂×D₄₇	1	2	yes	—
204	C₂×#127	C₂×D₄₇	1	2	yes	—
205	C₂×#127	C₂×D₄₇	1	4	yes	—
206	#518	—	94	16	no	—
207	C₂×C₄×D₄	—	47	8	no	—
208	C₂×C₄×D₄	—	47	8	no	—
209	C₂×C₄×D₄	—	47	16	no	—
210	C₂×#117	—	47	1	no	—
211	C₂×#117	—	47	1	no	—
212	C₂×#117	—	47	2	no	—
213	C₂²×C₂²⋊C₄	—	47	8	no	—
214	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
215	#390	—	47	8	no	—
216	#390	—	47	16	no	—
217	#390	—	47	8	no	—
218	#386	—	47	32	no	—
219	#384	—	47	2	no	—
220	#382	—	47	2	no	—
221	#380	—	47	4	no	—
222	#379	—	47	8	no	—
223	C₄×C₄⋊C₄	—	47	4	no	—
224	C₄×C₄⋊C₄	—	47	4	no	—
225	C₄×C₂²⋊C₄	—	47	4	no	—
226	#376	—	47	2	no	—
227	C₄³	—	47	2	no	—
228	C₄₇	#34210	1	1	yes	characteristic, complemented, Sylow
229	C₂⁵	C₂²×D₄₇	1	4	yes	—
230	C₂²×D₄	—	2	8	no	—
231	C₂²×D₄	—	2	8	no	—
232	C₂²×D₄	—	4	16	no	—
233	C₂²×D₄	C₂×Dic₄₇	1	16	yes	complemented
234	C₂²×D₄	C₂×Dic₄₇	1	32	yes	complemented
235	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
236	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
237	C₂²×D₄	C₂²×D₄₇	1	8	yes	—
238	C₂²×D₄	C₂²×D₄₇	1	8	yes	—
239	C₂³×C₄	—	47	16	no	—
240	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
241	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
242	#127	C₂×Dic₄₇	1	16	yes	complemented
243	#127	C₂×Dic₄₇	1	32	yes	complemented
244	#127	C₂×Dic₄₇	1	16	yes	complemented
245	C₄×D₄	—	94	32	no	—
246	C₄×D₄	—	94	32	no	—
247	C₄×D₄	—	188	32	no	—
248	#117	—	47	8	no	—
249	#117	—	94	8	no	—
250	#117	—	94	4	no	—
251	C₂×C₄⋊C₄	—	47	2	no	—
252	C₂×C₄⋊C₄	—	47	4	no	—
253	C₂×C₄⋊C₄	—	47	2	no	—
254	C₂×C₄⋊C₄	—	47	8	no	—
255	C₂×C₂²⋊C₄	—	47	2	no	—
256	C₂×C₂²⋊C₄	—	47	4	no	—
257	C₂×C₂²⋊C₄	—	47	16	no	—
258	C₂×C₂²⋊C₄	—	47	2	no	—
259	C₂×C₂²⋊C₄	—	47	32	no	—
260	C₂×C₂²⋊C₄	—	94	32	no	—
261	C₂×C₄²	—	47	2	no	—
262	C₂×C₄²	—	47	4	no	—
263	C₂×C₄²	—	47	2	no	—
264	C₂×C₄²	—	47	8	no	—
265	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
266	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
267	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
268	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
269	#95	—	47	8	no	—
270	#95	—	47	8	no	—
271	C₂⁴	—	2	8	no	—
272	C₂⁴	—	2	8	no	—
273	C₂⁴	—	4	16	no	—
274	C₂⁴	C₂²×Dic₄₇	1	16	yes	—
275	C₂⁴	C₂³×D₄₇	1	8	yes	—
276	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
277	C₂×D₄	—	2	64	no	—
278	C₂×D₄	—	2	8	no	—
279	C₂×D₄	—	2	8	no	—
280	C₂×D₄	—	2	8	no	—
281	C₂×D₄	—	2	8	no	—
282	C₂×D₄	—	2	32	no	—
283	C₂×D₄	—	4	64	no	—
284	C₂×D₄	—	4	16	no	—
285	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
286	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
287	C₂×D₄	C₂²×Dic₄₇	1	32	yes	—
288	C₂×D₄	C₂²×Dic₄₇	1	32	yes	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	47	4	no	—
291	C₂²×C₄	—	47	4	no	—
292	C₂²×C₄	—	47	8	no	—
293	C₂²×C₄	—	94	32	no	—
294	C₂²×C₄	—	188	32	no	—
295	C₂²×C₄	D₄×D₄₇	1	4	yes	—
296	C₂²×C₄	#10625352	1	4	yes	—
297	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
298	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
299	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
300	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
301	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
302	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
303	C₄⋊C₄	—	47	8	no	—
304	C₄⋊C₄	—	94	8	no	—
305	C₄⋊C₄	—	94	4	no	—
306	C₄⋊C₄	—	94	16	no	—
307	C₂²⋊C₄	—	47	8	no	—
308	C₂²⋊C₄	—	94	32	no	—
309	C₂²⋊C₄	—	94	8	no	—
310	C₂²⋊C₄	—	94	4	no	—
311	C₂²⋊C₄	—	188	32	no	—
312	C₄²	—	47	8	no	—
313	C₄²	—	94	8	no	—
314	C₄²	—	94	4	no	—
315	C₄²	—	94	16	no	—
316	C₄²	C₂²×Dic₄₇	1	4	yes	—
317	C₄²	C₂²×Dic₄₇	1	8	yes	—
318	C₄²	C₂²×Dic₄₇	1	4	yes	—
319	C₂³	—	2	4	no	—
320	C₂³	—	2	8	no	—
321	C₂³	—	2	8	no	—
322	C₂³	—	2	32	no	—
323	C₂³	—	2	32	no	—
324	C₂³	—	4	32	no	—
325	C₂³	—	8	16	no	—
326	C₂³	—	8	16	no	—
327	C₂³	C₂³×Dic₄₇	1	16	yes	—
328	C₂³	C₂³×Dic₄₇	1	2	yes	—
329	C₂³	C₂×D₄×D₄₇	1	2	yes	—
330	C₂³	C₂×#10625352	1	2	yes	—
331	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
332	D₄	—	2	32	no	—
333	D₄	—	2	32	no	—
334	D₄	—	2	64	no	—
335	D₄	—	4	32	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	16	no	—
338	C₂×C₄	—	47	8	no	—
339	C₂×C₄	—	94	8	no	—
340	C₂×C₄	—	94	8	no	—
341	C₂×C₄	—	94	4	no	—
342	C₂×C₄	—	94	8	no	—
343	C₂×C₄	—	94	16	no	—
344	C₂×C₄	—	376	32	no	—
345	C₂×C₄	D₄×Dic₄₇	1	16	yes	complemented
346	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
347	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
348	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
349	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
350	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
351	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
352	C₂×C₄	C₂×#10625352	1	2	yes	—
353	C₂×C₄	C₂×#10625352	1	2	yes	—
354	C₂×C₄	#13094069	1	8	yes	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	16	no	—
359	C₂²	—	2	32	no	—
360	C₂²	—	4	16	no	—
361	C₂²	—	4	16	no	—
362	C₂²	—	8	32	no	—
363	C₂²	C₂×D₄×Dic₄₇	1	4	yes	—
364	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
365	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
366	C₂²	C₂²×#10625352	1	1	yes	characteristic
367	C₂²	C₂×#13094069	1	4	yes	—
368	C₄	—	2	4	no	—
369	C₄	—	94	8	no	—
370	C₄	—	188	8	no	—
371	C₄	—	188	4	no	—
372	C₄	C₂×D₄×Dic₄₇	1	4	yes	—
373	C₄	C₂×D₄×Dic₄₇	1	4	yes	—
374	C₄	#15689598	1	8	yes	complemented
375	C₂	—	2	4	no	—
376	C₂	—	4	16	no	—
377	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
378	C₂	C₂×#15689598	1	2	yes	—
379	C₂	#20257164	1	2	yes	—
380	C₂	#20257262	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting, prime radical	C₂²×#127×C₄₇	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×#127	D₄₇
hypocenter	C₄₇	#34210
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×#127

Complements

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

N	H ≅ G/N	type
1. C₂×#15689598	C₂	semidirect
2. #20246453	C₂	semidirect
3. D₄×C₂²⋊Dic₄₇	C₂	semidirect
4. #20246114	C₂	semidirect
5. #20245970	C₂	semidirect
6. #127×Dic₄₇	C₂	semidirect
7. #20245795	C₂	semidirect
8. C₄×#13093983	C₂	semidirect
11. C₂×D₄×Dic₄₇	C₂²	semidirect
12. C₂×D₄×Dic₄₇	C₂²	semidirect
13. C₂×D₄×Dic₄₇	C₂²	semidirect
18. #15689026	C₂²	semidirect
19. #15689026	C₂²	semidirect
20. #15689026	C₂²	semidirect
21. #15689003	C₂²	semidirect
22. #15688993	C₂²	semidirect
23. #15688989	C₂²	semidirect
26. C₄×C₄⋊Dic₄₇	C₂²	semidirect
27. C₄×C₄⋊Dic₄₇	C₂²	semidirect
29. #15688969	C₂²	semidirect
30. C₄²×Dic₄₇	C₂²	semidirect
33. C₂×#127×C₄₇	C₄	semidirect
44. #13093983	D₄	semidirect
65. C₂²×D₄×C₄₇	C₂×C₄	semidirect
66. C₂²×D₄×C₄₇	C₂×C₄	semidirect
73. #127×C₄₇	C₂×C₄	semidirect
74. #127×C₄₇	C₂×C₄	semidirect
75. #127×C₄₇	C₂×C₄	semidirect
76. C₂×C₄²×C₄₇	C₂×C₄	semidirect
123. C₄⋊Dic₄₇	C₂×D₄	semidirect
127. C₄×Dic₄₇	C₂×D₄	semidirect
147. C₂×C₄×C₄₇	C₄×D₄	semidirect
181. C₄×C₄₇	#518	semidirect
202. C₂×#127	Dic₄₇	semidirect
228. C₄₇	#34210	semidirect
233. C₂²×D₄	C₂×Dic₄₇	semidirect
234. C₂²×D₄	C₂×Dic₄₇	semidirect
242. #127	C₂×Dic₄₇	semidirect
243. #127	C₂×Dic₄₇	semidirect
244. #127	C₂×Dic₄₇	semidirect
265. C₂×C₄²	C₂×Dic₄₇	semidirect
345. C₂×C₄	D₄×Dic₄₇	semidirect
374. C₄	#15689598	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689598	2
#20246453	2
D₄×C₂²⋊Dic₄₇	2
#20246114	2
#20245970	2
#127×Dic₄₇	2
#20245795	2
C₄×#13093983	2
C₂²×#127×C₄₇	2
#34210	47