Subgroups — #26122008

Order 12032.

854 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093934	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688886	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688885	C₂	1	2	yes	maximal
4	#20241617	C₂	1	2	yes	maximal
5	C₂×C₄₇×#340	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂×#13093934	—	2	4	no	—
10	C₂×#13093934	C₄	1	4	yes	complemented
11	C₂×C₄₇⋊#95	—	2	2	no	—
12	C₂×C₄₇⋊#95	—	2	2	no	—
13	#15688886	C₄	1	4	yes	complemented
14	#15688885	—	2	4	no	—
15	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
17	C₄₇×#340	C₄	1	4	yes	complemented
18	C₂³×Dic₄₇	—	2	2	no	—
19	C₂³×Dic₄₇	D₄	1	2	yes	—
20	C₂²×C₄₇⋊C₈	—	2	2	no	—
21	C₂²×C₄₇⋊C₈	—	2	1	no	—
22	C₂²×C₄₇⋊C₈	—	2	1	no	—
23	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
24	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
25	C₂×C₄⋊Dic₄₇	—	2	2	no	—
26	C₂×C₄⋊Dic₄₇	—	2	2	no	—
27	C₂×C₄⋊Dic₄₇	—	2	2	no	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
31	C₂×C₄×Dic₄₇	—	2	2	no	—
32	C₂×C₄×Dic₄₇	—	2	2	no	—
33	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
34	C₂×C₄×Dic₄₇	Q₈	1	2	yes	—
35	#13093934	—	2	8	no	—
36	C₄₇⋊#95	—	4	4	no	—
37	C₄₇⋊#95	—	4	4	no	—
38	C₂³×C₄×C₄₇	—	2	2	no	—
39	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₄₇	—	2	2	no	—
41	C₂²×C₈×C₄₇	—	2	2	no	—
42	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
43	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
51	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₄₇	—	2	4	no	—
53	C₂²×C₄×C₄₇	—	4	2	no	—
54	C₂²×C₄×C₄₇	—	4	2	no	—
55	C₂²×C₄×C₄₇	—	4	2	no	—
56	C₂²×C₄×C₄₇	—	4	2	no	—
57	C₂²×C₄×C₄₇	—	4	2	no	—
58	C₂²×C₄×C₄₇	—	4	2	no	—
59	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
63	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
64	C₂²×C₄×C₄₇	#41	1	2	yes	—
65	C₂²×C₄×C₄₇	#41	1	2	yes	—
66	C₂²×C₄×C₄₇	#41	1	2	yes	—
67	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
69	C₂²×Dic₄₇	—	2	2	no	—
70	C₂²×Dic₄₇	—	2	2	no	—
71	C₂²×Dic₄₇	—	2	2	no	—
72	C₂²×Dic₄₇	—	2	2	no	—
73	C₂²×Dic₄₇	—	2	2	no	—
74	C₂²×Dic₄₇	—	2	2	no	—
75	C₂²×Dic₄₇	—	2	4	no	—
76	C₂²×Dic₄₇	—	4	2	no	—
77	C₂²×Dic₄₇	—	4	2	no	—
78	C₂²×Dic₄₇	—	4	2	no	—
79	C₂²×Dic₄₇	—	4	2	no	—
80	C₂²×Dic₄₇	—	4	2	no	—
81	C₂²×Dic₄₇	—	4	2	no	—
82	C₂²×Dic₄₇	C₄⋊C₄	1	4	yes	—
83	C₂×C₈×C₄₇	—	2	2	no	—
84	C₂×C₈×C₄₇	—	2	2	no	—
85	C₂×C₈×C₄₇	—	2	4	no	—
86	C₂×C₈×C₄₇	—	2	4	no	—
87	C₂×C₈×C₄₇	C₄²	1	4	yes	—
88	C₄⋊C₄×C₄₇	—	2	4	no	—
89	C₄⋊C₄×C₄₇	—	2	4	no	—
90	C₄⋊C₄×C₄₇	—	4	2	no	—
91	C₄⋊C₄×C₄₇	—	4	2	no	—
92	C₄⋊Dic₄₇	—	2	4	no	—
93	C₄⋊Dic₄₇	—	2	4	no	—
94	C₄⋊Dic₄₇	—	4	2	no	—
95	C₄⋊Dic₄₇	—	4	2	no	—
96	C₄×Dic₄₇	—	2	2	no	—
97	C₄×Dic₄₇	—	2	2	no	—
98	C₄×Dic₄₇	—	2	4	no	—
99	C₂×C₄₇⋊C₈	—	2	2	no	—
100	C₂×C₄₇⋊C₈	—	2	2	no	—
101	C₂×C₄₇⋊C₈	—	2	4	no	—
102	C₂×C₄₇⋊C₈	—	2	4	no	—
103	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	—
104	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
105	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
106	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
107	C₂³×C₄₇	#121	1	2	yes	—
108	C₂³×C₄₇	#124	1	2	yes	—
109	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
110	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
111	C₂³×C₄₇	#137	1	2	yes	—
112	C₂³×C₄₇	#137	1	2	yes	—
113	C₂×C₄×C₄₇	—	4	4	no	—
114	C₂×C₄×C₄₇	—	4	4	no	—
115	C₂×C₄×C₄₇	—	4	4	no	—
116	C₂×C₄×C₄₇	—	8	2	no	—
117	C₂×C₄×C₄₇	—	8	2	no	—
118	C₂×C₄×C₄₇	—	8	2	no	—
119	C₂×C₄×C₄₇	—	8	2	no	—
120	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
121	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
123	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
124	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
125	C₂×C₄×C₄₇	#117	1	2	yes	—
126	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
127	C₂×C₄×C₄₇	#117	1	2	yes	—
128	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
129	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
130	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
131	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
132	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
133	C₂×C₄×C₄₇	#123	1	2	yes	—
134	C₂×C₄×C₄₇	#123	1	2	yes	—
135	C₂×C₄×C₄₇	#125	1	2	yes	—
136	C₂×C₄×C₄₇	#126	1	2	yes	—
137	C₂×C₄×C₄₇	#126	1	2	yes	—
138	C₂×Dic₄₇	—	2	4	no	—
139	C₂×Dic₄₇	—	2	4	no	—
140	C₂×Dic₄₇	—	2	4	no	—
141	C₂×Dic₄₇	—	4	2	no	—
142	C₂×Dic₄₇	—	4	2	no	—
143	C₂×Dic₄₇	—	4	2	no	—
144	C₂×Dic₄₇	—	4	2	no	—
145	C₂×Dic₄₇	—	4	4	no	—
146	C₂×Dic₄₇	—	4	4	no	—
147	C₂×Dic₄₇	—	4	4	no	—
148	C₂×Dic₄₇	—	8	2	no	—
149	C₂×Dic₄₇	—	8	2	no	—
150	C₂×Dic₄₇	—	8	2	no	—
151	C₂×Dic₄₇	—	8	2	no	—
152	C₈×C₄₇	—	2	4	no	—
153	C₄₇⋊C₈	—	2	4	no	—
154	#10821	—	47	1	no	maximal, Sylow
155	C₂²×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
156	C₂²×C₄₇	#380	1	1	yes	characteristic
157	C₂²×C₄₇	#382	1	1	yes	characteristic
158	C₂²×C₄₇	#388	1	2	yes	—
159	C₂²×C₄₇	#388	1	2	yes	—
160	C₂²×C₄₇	#428	1	2	yes	—
161	C₂²×C₄₇	#428	1	2	yes	—
162	C₂²×C₄₇	#440	1	2	yes	—
163	C₂²×C₄₇	#440	1	2	yes	—
164	C₂²×C₄₇	#441	1	1	yes	characteristic
165	C₂²×C₄₇	#441	1	1	yes	characteristic
166	C₂²×C₄₇	#442	1	1	yes	characteristic
167	C₂²×C₄₇	#442	1	1	yes	characteristic
168	C₂²×C₄₇	#468	1	2	yes	—
169	C₂²×C₄₇	#468	1	2	yes	—
170	C₂²×C₄₇	#469	1	2	yes	—
171	C₂²×C₄₇	#470	1	2	yes	—
172	C₂²×C₄₇	#489	1	2	yes	—
173	C₂²×C₄₇	#489	1	2	yes	—
174	C₂²×C₄₇	#490	1	2	yes	—
175	C₂²×C₄₇	#491	1	2	yes	—
176	C₄×C₄₇	—	8	4	no	—
177	C₄×C₄₇	#376	1	1	yes	characteristic
178	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
179	C₄×C₄₇	#381	1	1	yes	characteristic
180	C₄×C₄₇	#383	1	1	yes	characteristic
181	C₄×C₄₇	#387	1	2	yes	—
182	C₄×C₄₇	#387	1	2	yes	—
183	Dic₄₇	—	4	4	no	—
184	Dic₄₇	—	8	4	no	—
185	C₂²×#97	—	47	1	no	—
186	C₂×#340	—	47	1	no	—
187	C₂×#340	—	47	2	no	—
188	C₂×#340	D₄₇	1	1	yes	characteristic
189	C₄⋊#95	—	47	2	no	—
190	C₂×C₄₇	#1434	1	1	yes	characteristic
191	C₂×C₄₇	#1776	1	1	yes	characteristic
192	C₂×C₄₇	#1776	1	1	yes	characteristic
193	C₂×C₄₇	#1809	1	2	yes	—
194	C₂×C₄₇	#1836	1	2	yes	—
195	C₂×C₄₇	#1935	1	2	yes	—
196	C₂×C₄₇	#1935	1	2	yes	—
197	C₂×C₄₇	#1936	1	2	yes	—
198	C₂×C₄₇	#1936	1	2	yes	—
199	C₂³×C₈	—	47	1	no	—
200	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
201	C₂²×C₄⋊C₄	—	47	2	no	—
202	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
203	C₂²×C₄²	—	47	1	no	—
204	C₂×#97	—	47	4	no	—
205	C₂×#97	—	94	4	no	—
206	C₂×#95	—	94	2	no	—
207	C₂×#95	—	94	2	no	—
208	#340	—	47	4	no	—
209	#340	—	94	4	no	—
210	#340	Dic₄₇	1	4	yes	complemented
211	C₄₇	#10821	1	1	yes	characteristic, complemented, Sylow
212	C₂³×C₄	—	2	2	no	—
213	C₂³×C₄	—	47	2	no	—
214	C₂³×C₄	—	94	2	no	—
215	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
216	C₂²×C₈	—	2	2	no	—
217	C₂²×C₈	—	2	2	no	—
218	C₂²×C₈	—	47	2	no	—
219	C₂²×C₈	—	47	4	no	—
220	C₂²×C₈	—	94	2	no	—
221	C₂²×C₈	—	94	1	no	—
222	C₂²×C₈	—	94	1	no	—
223	C₂²×C₈	C₄×D₄₇	1	2	yes	—
224	C₂²×C₈	C₄×D₄₇	1	2	yes	—
225	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	47	4	no	—
232	C₂×C₄⋊C₄	—	94	2	no	—
233	C₂×C₄⋊C₄	—	94	2	no	—
234	C₂×C₄⋊C₄	—	94	2	no	—
235	C₂×C₄⋊C₄	—	94	2	no	—
236	C₂×C₄⋊C₄	—	94	2	no	—
237	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
238	C₂×C₄²	—	47	2	no	—
239	C₂×C₄²	—	47	2	no	—
240	C₂×C₄²	—	94	2	no	—
241	C₂×C₄²	—	94	2	no	—
242	#97	—	94	8	no	—
243	#95	—	188	4	no	—
244	#95	—	188	4	no	—
245	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	4	2	no	—
248	C₂²×C₄	—	4	2	no	—
249	C₂²×C₄	—	4	2	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	—	4	2	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	47	4	no	—
254	C₂²×C₄	—	94	2	no	—
255	C₂²×C₄	—	94	2	no	—
256	C₂²×C₄	—	94	2	no	—
257	C₂²×C₄	—	94	2	no	—
258	C₂²×C₄	—	94	2	no	—
259	C₂²×C₄	—	94	2	no	—
260	C₂²×C₄	—	94	4	no	—
261	C₂²×C₄	—	188	2	no	—
262	C₂²×C₄	—	188	2	no	—
263	C₂²×C₄	—	188	2	no	—
264	C₂²×C₄	—	188	2	no	—
265	C₂²×C₄	—	188	2	no	—
266	C₂²×C₄	—	188	2	no	—
267	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
269	C₂²×C₄	#10625350	1	2	yes	—
270	C₂²×C₄	#10625350	1	2	yes	—
271	C₂²×C₄	D₄×D₄₇	1	2	yes	—
272	C₂²×C₄	#10625352	1	2	yes	—
273	C₂²×C₄	#10625352	1	1	yes	characteristic
274	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
275	C₂²×C₄	#10625354	1	1	yes	characteristic
276	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	47	4	no	—
282	C₂×C₈	—	94	2	no	—
283	C₂×C₈	—	94	2	no	—
284	C₂×C₈	—	94	4	no	—
285	C₂×C₈	—	94	4	no	—
286	C₂×C₈	C₄×Dic₄₇	1	4	yes	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	4	2	no	—
290	C₄⋊C₄	—	4	2	no	—
291	C₄⋊C₄	—	94	4	no	—
292	C₄⋊C₄	—	94	4	no	—
293	C₄⋊C₄	—	188	2	no	—
294	C₄⋊C₄	—	188	2	no	—
295	C₄²	—	94	2	no	—
296	C₄²	—	94	2	no	—
297	C₄²	—	94	4	no	—
298	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
299	C₂³	#13093986	1	1	yes	characteristic
300	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
301	C₂³	#13093997	1	2	yes	—
302	C₂³	#13094010	1	2	yes	—
303	C₂³	#13094048	1	2	yes	—
304	C₂³	#13094051	1	2	yes	—
305	C₂³	#13094053	1	2	yes	—
306	C₂³	#13094056	1	2	yes	—
307	C₂×C₄	—	4	4	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	—	8	2	no	—
311	C₂×C₄	—	8	2	no	—
312	C₂×C₄	—	8	2	no	—
313	C₂×C₄	—	8	2	no	—
314	C₂×C₄	—	94	4	no	—
315	C₂×C₄	—	94	4	no	—
316	C₂×C₄	—	94	4	no	—
317	C₂×C₄	—	376	2	no	—
318	C₂×C₄	—	376	2	no	—
319	C₂×C₄	—	376	2	no	—
320	C₂×C₄	—	376	2	no	—
321	C₂×C₄	—	188	4	no	—
322	C₂×C₄	—	188	4	no	—
323	C₂×C₄	—	188	4	no	—
324	C₂×C₄	—	188	2	no	—
325	C₂×C₄	—	188	2	no	—
326	C₂×C₄	—	188	2	no	—
327	C₂×C₄	—	188	2	no	—
328	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
329	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
330	C₂×C₄	#13093980	1	1	yes	characteristic
331	C₂×C₄	#13093981	1	1	yes	characteristic
332	C₂×C₄	#13093981	1	1	yes	characteristic
333	C₂×C₄	#13093981	1	2	yes	—
334	C₂×C₄	#13093982	1	1	yes	characteristic
335	C₂×C₄	#13093983	1	2	yes	—
336	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
337	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
338	C₂×C₄	#13093989	1	1	yes	characteristic
339	C₂×C₄	Q₈×Dic₄₇	1	1	yes	characteristic
340	C₂×C₄	#13094002	1	2	yes	—
341	C₂×C₄	#13094006	1	2	yes	—
342	C₂×C₄	#13094009	1	2	yes	—
343	C₂×C₄	#13094014	1	2	yes	—
344	C₂×C₄	#13094017	1	2	yes	—
345	C₂×C₄	#13094019	1	2	yes	—
346	C₈	—	2	4	no	—
347	C₈	—	94	4	no	—
348	C₂²	C₄⋊C₄×Dic₄₇	1	1	yes	characteristic
349	C₂²	#15688982	1	1	yes	characteristic
350	C₂²	#15688987	1	1	yes	characteristic
351	C₂²	#15689012	1	2	yes	—
352	C₂²	#15689016	1	2	yes	—
353	C₂²	#15689162	1	2	yes	—
354	C₂²	#15689164	1	2	yes	—
355	C₂²	#15689222	1	2	yes	—
356	C₂²	#15689224	1	2	yes	—
357	C₂²	#15689229	1	1	yes	characteristic
358	C₂²	#15689230	1	1	yes	characteristic
359	C₂²	#15689234	1	1	yes	characteristic
360	C₂²	#15689235	1	1	yes	characteristic
361	C₂²	#15689368	1	2	yes	—
362	C₂²	#15689372	1	2	yes	—
363	C₂²	#15689375	1	2	yes	—
364	C₂²	#15689380	1	2	yes	—
365	C₂²	#15689481	1	2	yes	—
366	C₂²	#15689484	1	2	yes	—
367	C₂²	#15689486	1	2	yes	—
368	C₂²	#15689490	1	2	yes	—
369	C₄	—	8	4	no	—
370	C₄	—	376	4	no	—
371	C₄	—	188	4	no	—
372	C₄	#15688969	1	1	yes	characteristic
373	C₄	C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
374	C₄	#15688985	1	1	yes	characteristic
375	C₄	#15688990	1	1	yes	characteristic
376	C₄	#15689005	1	2	yes	—
377	C₄	#15689009	1	2	yes	—
378	C₂	#20241613	1	1	yes	characteristic
379	C₂	#20243287	1	1	yes	characteristic
380	C₂	#20243288	1	1	yes	characteristic
381	C₂	#20243420	1	2	yes	—
382	C₂	#20243520	1	2	yes	—
383	C₂	#20244076	1	2	yes	—
384	C₂	#20244080	1	2	yes	—
385	C₂	#20244083	1	2	yes	—
386	C₂	#20244087	1	2	yes	—

	subgroup	G/H
center	C₂⁴	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#340	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#340	D₄₇
hypocenter	C₄₇	#10821
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂×#340

Complements

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

N	H ≅ G/N	type
10. C₂×#13093934	C₄	semidirect
13. #15688886	C₄	semidirect
17. C₄₇×#340	C₄	semidirect
210. #340	Dic₄₇	semidirect
211. C₄₇	#10821	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13093934	2
C₂×#15688886	2
C₂×#15688885	2
#20241617	2
C₂×C₄₇×#340	2
#10821	47