Subgroups — #26234591

Order 12032.

914 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689230	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	Q₈×Dic₄₇⋊C₄	C₂	1	2	yes	maximal
4	#20244126	C₂	1	1	yes	maximal, characteristic
5	#20244124	C₂	1	1	yes	maximal, characteristic
6	#20243656	C₂	1	2	yes	maximal
7	#20243654	C₂	1	2	yes	maximal
8	#20243543	C₂	1	1	yes	maximal, characteristic
9	#20243391	C₂	1	2	yes	maximal
10	#20243256	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄₇×#441	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
13	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
14	#15689230	—	2	4	no	—
15	Q₁₆×Dic₄₇	C₄	1	8	yes	complemented
16	C₂×#13093958	C₂²	1	1	yes	characteristic
17	C₂×#13093956	C₂²	1	1	yes	characteristic
18	C₂×#13093955	C₂²	1	2	yes	—
19	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×#13093948	C₂²	1	2	yes	—
21	C₂×#13093948	C₂²	1	2	yes	—
22	C₂×#13093934	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
24	#15689021	—	2	2	no	—
25	#15689021	C₂²	1	2	yes	—
26	#15689019	—	2	2	no	—
27	#15689019	C₂²	1	2	yes	—
28	#15688992	—	2	2	no	—
29	#15688992	C₂²	1	2	yes	—
30	C₄×Dic₄₇⋊C₄	—	2	2	no	—
31	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
32	#15688886	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	#15688878	C₂²	1	1	yes	characteristic
35	#15688877	C₂²	1	1	yes	characteristic
36	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
38	C₄₇×#441	—	2	4	no	—
39	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#103×C₄₇	C₂²	1	2	yes	—
41	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	Q₈×Dic₄₇	—	2	4	no	—
45	Q₈×Dic₄₇	—	2	4	no	—
46	Q₈×Dic₄₇	—	4	2	no	—
47	Q₈×Dic₄₇	C₂×C₄	1	8	yes	—
48	C₂×C₄⋊Dic₄₇	—	2	2	no	—
49	C₂×C₄⋊Dic₄₇	—	2	2	no	—
50	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
52	C₂×Dic₄₇⋊C₄	—	2	2	no	—
53	C₂×Dic₄₇⋊C₄	—	2	2	no	—
54	C₂×Dic₄₇⋊C₄	—	2	2	no	—
55	C₂×Dic₄₇⋊C₄	—	2	2	no	—
56	C₂×Dic₄₇⋊C₄	D₄	1	2	yes	—
57	C₂×C₄×Dic₄₇	—	2	2	no	—
58	C₂×C₄×Dic₄₇	—	2	2	no	—
59	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
61	#13093958	C₂×C₄	1	4	yes	—
62	#13093956	—	2	2	no	—
63	#13093955	—	4	2	no	—
64	Dic₄₇⋊C₈	—	2	2	no	—
65	#13093948	—	2	4	no	—
66	#13093948	C₂×C₄	1	8	yes	—
67	#13093934	—	2	2	no	—
68	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
69	C₄₇⋊#95	—	2	2	no	—
70	C₄₇⋊#95	—	2	2	no	—
71	C₄₇⋊#95	D₄	1	2	yes	—
72	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
73	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
74	C₂×Q₁₆×C₄₇	D₄	1	4	yes	—
75	C₂×Q₁₆×C₄₇	Q₈	1	4	yes	—
76	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
78	C₄×Q₈×C₄₇	—	2	4	no	—
79	C₄×Q₈×C₄₇	—	4	2	no	—
80	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
82	C₂×C₄²×C₄₇	—	2	2	no	—
83	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
84	#106×C₄₇	—	2	2	no	—
85	#103×C₄₇	—	2	4	no	—
86	#97×C₄₇	—	2	2	no	—
87	C₂×Q₈×C₄₇	—	2	2	no	—
88	C₂×Q₈×C₄₇	—	2	2	no	—
89	C₂×Q₈×C₄₇	—	2	2	no	—
90	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
91	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
92	C₂×Q₈×C₄₇	C₂×Q₈	1	4	yes	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
97	C₂²×Dic₄₇	—	2	2	no	—
98	C₂²×Dic₄₇	—	2	2	no	—
99	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
100	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
102	Q₁₆×C₄₇	C₄⋊C₄	1	16	yes	complemented
103	C₂×C₈×C₄₇	—	2	1	no	—
104	C₂×C₈×C₄₇	—	2	1	no	—
105	C₂×C₈×C₄₇	—	2	1	no	—
106	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	4	4	no	—
112	C₄²×C₄₇	—	2	1	no	—
113	C₄²×C₄₇	—	2	1	no	—
114	C₄²×C₄₇	—	4	4	no	—
115	C₄⋊Dic₄₇	—	2	2	no	—
116	C₄⋊Dic₄₇	—	2	8	no	—
117	C₄⋊Dic₄₇	—	2	2	no	—
118	C₄⋊Dic₄₇	—	2	2	no	—
119	C₄⋊Dic₄₇	—	4	4	no	—
120	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
121	Dic₄₇⋊C₄	—	2	4	no	—
122	Dic₄₇⋊C₄	—	4	4	no	—
123	Dic₄₇⋊C₄	—	8	2	no	—
124	Dic₄₇⋊C₄	—	8	2	no	—
125	Dic₄₇⋊C₄	—	8	2	no	—
126	C₄×Dic₄₇	—	2	1	no	—
127	C₄×Dic₄₇	—	2	1	no	—
128	C₄×Dic₄₇	—	2	8	no	—
129	C₄×Dic₄₇	—	4	4	no	—
130	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
131	C₄×Dic₄₇	#41	1	2	yes	—
132	C₂×C₄₇⋊C₈	—	2	1	no	—
133	C₂×C₄₇⋊C₈	—	2	1	no	—
134	C₂×C₄₇⋊C₈	—	2	1	no	—
135	C₂×C₄₇⋊C₈	—	2	1	no	—
136	C₂×C₄₇⋊C₈	—	2	1	no	—
137	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
138	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₄₇	—	2	4	no	—
140	Q₈×C₄₇	—	2	4	no	—
141	Q₈×C₄₇	—	2	4	no	—
142	Q₈×C₄₇	C₂×C₄⋊C₄	1	8	yes	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
157	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
158	C₂×Dic₄₇	—	2	2	no	—
159	C₂×Dic₄₇	—	2	4	no	—
160	C₂×Dic₄₇	—	2	2	no	—
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	2	2	no	—
163	C₂×Dic₄₇	—	4	2	no	—
164	C₂×Dic₄₇	—	4	2	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
169	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
170	C₂×Dic₄₇	#137	1	4	yes	—
171	C₈×C₄₇	—	4	1	no	—
172	C₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
173	C₄₇⋊C₈	—	2	2	no	—
174	C₄₇⋊C₈	—	4	1	no	—
175	#22674	—	47	1	no	maximal, Sylow
176	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
177	C₂²×C₄₇	D₄²	1	1	yes	characteristic
178	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
179	C₂²×C₄₇	C₂×#137	1	2	yes	—
180	C₂²×C₄₇	#577	1	2	yes	—
181	C₄×C₄₇	—	2	8	no	—
182	C₄×C₄₇	—	4	2	no	—
183	C₄×C₄₇	—	8	2	no	—
184	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
185	C₄×C₄₇	#520	1	1	yes	characteristic
186	C₄×C₄₇	#547	1	1	yes	characteristic
187	C₄×C₄₇	#554	1	1	yes	characteristic
188	Dic₄₇	—	2	2	no	—
189	Dic₄₇	—	4	4	no	—
190	Dic₄₇	—	4	2	no	—
191	Dic₄₇	—	8	2	no	—
192	Dic₄₇	#441	1	4	yes	complemented
193	C₂×#441	—	47	1	no	—
194	C₂×#441	D₄₇	1	1	yes	characteristic
195	C₂×C₄×Q₁₆	—	47	1	no	—
196	Q₈×C₄⋊C₄	—	47	2	no	—
197	#1943	—	47	1	no	—
198	#1943	—	47	1	no	—
199	#1865	—	47	2	no	—
200	#1865	—	47	2	no	—
201	#1844	—	47	1	no	—
202	#1803	—	47	2	no	—
203	#1770	—	47	1	no	—
204	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
205	C₂×C₄₇	C₂×#441	1	1	yes	characteristic
206	C₂×C₄₇	#2952	1	1	yes	characteristic
207	C₂×C₄₇	#3278	1	2	yes	—
208	C₂×C₄₇	#3387	1	2	yes	—
209	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
210	C₂×C₄×Q₈	—	47	2	no	—
211	C₂×C₄×Q₈	—	47	2	no	—
212	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
213	#441	—	2	4	no	—
214	#441	—	94	4	no	—
215	C₄×Q₁₆	—	47	8	no	—
216	C₂×#107	—	47	1	no	—
217	C₂×#106	—	47	1	no	—
218	C₂×#106	—	47	2	no	—
219	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
220	C₂×C₄⋊C₈	—	47	1	no	—
221	C₂×#103	—	47	2	no	—
222	C₂×#103	—	47	2	no	—
223	C₂×#103	C₂×D₄₇	1	2	yes	—
224	C₂×#97	—	47	1	no	—
225	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
226	C₂×C₄×C₈	—	47	1	no	—
227	#389	—	47	2	no	—
228	#389	—	47	2	no	—
229	#389	—	94	2	no	—
230	#389	—	94	2	no	—
231	#384	—	47	2	no	—
232	#384	—	94	2	no	—
233	C₄×C₄⋊C₄	—	47	1	no	—
234	C₄×C₄⋊C₄	—	94	2	no	—
235	#340	—	47	2	no	—
236	#340	—	47	2	no	—
237	#336	—	47	1	no	—
238	#336	—	47	1	no	—
239	C₄₇	#22674	1	1	yes	characteristic, complemented, Sylow
240	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
241	C₂×Q₁₆	Dic₉₄	1	4	yes	—
242	C₂×Q₁₆	C₄×D₄₇	1	4	yes	—
243	C₂×Q₁₆	C₂²⋊D₄₇	1	4	yes	—
244	C₂²×C₈	—	47	1	no	—
245	C₂²×C₈	—	47	1	no	—
246	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
247	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
248	C₄×Q₈	—	2	4	no	—
249	C₄×Q₈	—	4	2	no	—
250	C₄×Q₈	—	47	8	no	—
251	C₄×Q₈	—	94	4	no	—
252	C₄×Q₈	—	94	4	no	—
253	C₄×Q₈	—	188	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	47	2	no	—
256	C₂×C₄⋊C₄	—	47	2	no	—
257	C₂×C₄⋊C₄	—	47	2	no	—
258	C₂×C₄⋊C₄	—	94	2	no	—
259	C₂×C₄⋊C₄	—	94	2	no	—
260	C₂×C₄⋊C₄	—	94	2	no	—
261	C₂×C₄⋊C₄	—	94	2	no	—
262	C₂×C₄⋊C₄	—	94	2	no	—
263	C₂×C₄⋊C₄	—	94	2	no	—
264	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	47	1	no	—
267	C₂×C₄²	—	47	1	no	—
268	C₂×C₄²	—	94	2	no	—
269	C₂×C₄²	—	94	2	no	—
270	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
271	#107	—	47	4	no	—
272	#106	—	2	2	no	—
273	#106	—	94	2	no	—
274	#106	—	188	2	no	—
275	C₄⋊C₈	—	94	2	no	—
276	#103	—	2	4	no	—
277	#103	—	47	8	no	—
278	#103	—	94	4	no	—
279	#97	—	2	2	no	—
280	#97	—	94	2	no	—
281	C₄×C₈	—	47	4	no	—
282	#95	—	47	2	no	—
283	#95	—	94	2	no	—
284	#95	—	94	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	C₂×Dic₉₄	1	4	yes	—
289	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
290	C₂×Q₈	C₂×C₂²⋊D₄₇	1	4	yes	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	47	1	no	—
294	C₂²×C₄	—	47	1	no	—
295	C₂²×C₄	—	47	2	no	—
296	C₂²×C₄	—	94	2	no	—
297	C₂²×C₄	—	94	2	no	—
298	C₂²×C₄	D₄×D₄₇	1	2	yes	—
299	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
300	Q₁₆	Dic₄₇⋊C₄	1	16	yes	complemented
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	47	2	no	—
305	C₂×C₈	—	94	1	no	—
306	C₂×C₈	—	94	1	no	—
307	C₂×C₈	—	94	1	no	—
308	C₂×C₈	—	94	1	no	—
309	C₂×C₈	—	94	1	no	—
310	C₂×C₈	C₂×Dic₉₄	1	2	yes	—
311	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
312	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	4	4	no	—
316	C₄⋊C₄	—	47	4	no	—
317	C₄⋊C₄	—	94	4	no	—
318	C₄⋊C₄	—	94	8	no	—
319	C₄⋊C₄	—	94	2	no	—
320	C₄⋊C₄	—	94	2	no	—
321	C₄⋊C₄	—	94	2	no	—
322	C₄⋊C₄	—	376	2	no	—
323	C₄⋊C₄	—	376	2	no	—
324	C₄⋊C₄	—	376	2	no	—
325	C₄⋊C₄	—	188	4	no	—
326	C₄⋊C₄	—	188	4	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	4	4	no	—
330	C₄²	—	47	2	no	—
331	C₄²	—	47	2	no	—
332	C₄²	—	94	8	no	—
333	C₄²	—	94	1	no	—
334	C₄²	—	94	1	no	—
335	C₄²	—	188	4	no	—
336	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
337	Q₈	—	2	4	no	—
338	Q₈	—	2	4	no	—
339	Q₈	—	2	4	no	—
340	Q₈	C₂×Dic₄₇⋊C₄	1	8	yes	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	47	2	no	—
351	C₂×C₄	—	47	4	no	—
352	C₂×C₄	—	47	2	no	—
353	C₂×C₄	—	94	2	no	—
354	C₂×C₄	—	94	2	no	—
355	C₂×C₄	—	94	4	no	—
356	C₂×C₄	—	94	2	no	—
357	C₂×C₄	—	94	2	no	—
358	C₂×C₄	—	188	2	no	—
359	C₂×C₄	—	188	2	no	—
360	C₂×C₄	—	188	2	no	—
361	C₂×C₄	—	188	2	no	—
362	C₂×C₄	—	188	2	no	—
363	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
364	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
365	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
366	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
367	C₂×C₄	#13094069	1	1	yes	characteristic
368	C₂×C₄	#13094071	1	1	yes	characteristic
369	C₈	—	4	1	no	—
370	C₈	—	94	2	no	—
371	C₈	—	188	1	no	—
372	C₈	C₂×Dic₄₇⋊C₄	1	4	yes	—
373	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
374	C₂²	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
375	C₂²	D₄×Dic₉₄	1	1	yes	characteristic
376	C₂²	#137×D₄₇	1	2	yes	—
377	C₂²	#15689932	1	2	yes	—
378	C₄	—	2	8	no	—
379	C₄	—	4	2	no	—
380	C₄	—	8	2	no	—
381	C₄	—	47	4	no	—
382	C₄	—	94	2	no	—
383	C₄	—	376	2	no	—
384	C₄	—	188	2	no	—
385	C₄	—	188	4	no	—
386	C₄	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
387	C₄	#15689602	1	1	yes	characteristic
388	C₄	#15689772	1	1	yes	characteristic
389	C₄	#15689832	1	1	yes	characteristic
390	C₂	D₄×Dic₄₇⋊C₄	1	1	yes	characteristic
391	C₂	#441×D₄₇	1	1	yes	characteristic
392	C₂	#20252268	1	1	yes	characteristic
393	C₂	#20255048	1	2	yes	—
394	C₂	#20256321	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#441	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#441	D₄₇
hypocenter	C₄₇	#22674
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#441

Complements

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

N	H ≅ G/N	type
15. Q₁₆×Dic₄₇	C₄	semidirect
102. Q₁₆×C₄₇	C₄⋊C₄	semidirect
192. Dic₄₇	#441	semidirect
239. C₄₇	#22674	semidirect
300. Q₁₆	Dic₄₇⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689230	2
C₂×Q₁₆×Dic₄₇	2
Q₈×Dic₄₇⋊C₄	2
#20244126	2
#20244124	2
#20243656	2
#20243654	2
#20243543	2
#20243391	2
#20243256	2
C₂×C₄₇×#441	2
#22674	47