Subgroups — #26245963

Order 12032.

752 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13094055	C₂	1	2	yes	maximal
2	#20252030	C₂	1	1	yes	maximal, characteristic
3	#20244894	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244829	C₂	1	1	yes	maximal, characteristic
5	#20244753	C₂	1	2	yes	maximal, complemented
6	#20244688	C₂	1	2	yes	maximal
7	#20244653	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244507	C₂	1	1	yes	maximal, characteristic
9	C₄×#13093960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13093943	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094055	C₂²	1	2	yes	—
13	C₄×#10625350	C₂²	1	1	yes	characteristic
14	#15689228	—	2	2	no	—
15	#15689221	—	2	2	no	—
16	C₄×#10625337	—	2	2	no	—
17	C₄×#10625336	—	2	2	no	—
18	#15689182	—	2	2	no	—
19	#15689174	—	2	2	no	—
20	C₂×#13093960	C₂²	1	2	yes	—
21	#15689163	C₂²	1	2	yes	—
22	#15689149	C₂²	1	1	yes	characteristic
23	#15689149	C₂²	1	1	yes	characteristic
24	#15689132	C₂²	1	2	yes	—
25	#15689122	C₂²	1	2	yes	—
26	C₂×#13093943	C₂²	1	2	yes	—
27	C₂×#13093943	C₂²	1	2	yes	—
28	#15689089	C₂²	1	1	yes	characteristic
29	#15689089	C₂²	1	1	yes	characteristic
30	C₄×#10625329	C₂²	1	2	yes	—
31	C₄×#10625329	C₂²	1	1	yes	characteristic
32	#15688892	C₂²	1	2	yes	—
33	#15688892	C₂²	1	2	yes	—
34	#15688888	C₂²	1	1	yes	characteristic
35	#15688888	C₂²	1	1	yes	characteristic
36	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
38	C₄×Q₁₆×C₄₇	—	2	2	no	—
39	C₄×Q₁₆×C₄₇	—	2	2	no	—
40	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#103×C₄₇	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×#10625350	C₂³	1	1	yes	characteristic
44	#13094055	—	2	4	no	—
45	#13094055	—	2	4	no	—
46	C₂×#10625337	—	2	2	no	—
47	C₂×#10625336	—	2	2	no	—
48	C₂×#10625329	C₂³	1	1	yes	characteristic
49	C₂×#10625329	C₂³	1	1	yes	characteristic
50	C₂×#10625329	C₂³	1	2	yes	—
51	C₂×#10625329	C₂³	1	2	yes	—
52	C₄×Dic₉₄	D₄	1	1	yes	characteristic
53	C₄×Dic₉₄	D₄	1	1	yes	characteristic
54	C₄×D₁₈₈	D₄	1	1	yes	characteristic
55	C₄×D₁₈₈	D₄	1	1	yes	characteristic
56	C₄×C₂²⋊D₄₇	—	2	1	no	—
57	C₄×C₂²⋊D₄₇	—	2	1	no	—
58	#13093983	C₂³	1	1	yes	characteristic
59	#13093981	—	2	1	no	—
60	C₄²×D₄₇	—	2	1	no	—
61	#13093960	—	2	4	no	—
62	#13093957	—	2	2	no	—
63	#13093955	—	2	2	no	—
64	Dic₄₇⋊C₈	—	2	2	no	—
65	Dic₄₇⋊C₈	—	2	2	no	—
66	#13093948	—	2	2	no	—
67	#13093948	—	2	2	no	—
68	#13093947	—	2	2	no	—
69	#13093944	—	2	2	no	—
70	#13093943	—	2	4	no	—
71	#13093943	—	2	4	no	—
72	(C₂×D₄₇)⋊C₈	—	2	2	no	—
73	(C₂×D₄₇)⋊C₈	—	2	2	no	—
74	#13093935	—	2	2	no	—
75	#13093935	—	2	1	no	—
76	C₄×C₄₇⋊C₈	—	2	2	no	—
77	C₄×C₄₇⋊C₈	—	2	1	no	—
78	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
79	C₂×Q₁₆×C₄₇	—	2	4	no	—
80	C₂×Q₁₆×C₄₇	—	2	2	no	—
81	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₄×Q₈×C₄₇	—	2	2	no	—
84	C₄×Q₈×C₄₇	—	2	2	no	—
85	C₄×Q₈×C₄₇	—	2	2	no	—
86	C₄×Q₈×C₄₇	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
89	C₂×C₄²×C₄₇	—	2	2	no	—
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	#107×C₄₇	—	2	2	no	—
92	#103×C₄₇	—	2	4	no	—
93	C₄×C₈×C₄₇	D₄	1	2	yes	—
94	C₄×C₈×C₄₇	D₄	1	2	yes	—
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	—	2	2	no	—
99	C₂×Q₈×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	#41	1	4	yes	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₂×C₂²⋊D₄₇	—	2	1	no	—
107	#10625350	—	2	2	no	—
108	#10625350	—	2	2	no	—
109	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×D₄₇	—	2	1	no	—
111	C₂×C₄×D₄₇	—	2	1	no	—
112	C₂×C₄×D₄₇	—	2	1	no	—
113	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
114	Q₁₆×C₄₇	—	2	8	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	4	2	no	—
122	C₄⋊C₄×C₄₇	—	4	2	no	—
123	C₄²×C₄₇	—	4	2	no	—
124	C₄²×C₄₇	—	4	2	no	—
125	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²⋊Dic₄₇	—	2	1	no	—
130	#10625337	—	2	8	no	—
131	#10625336	—	2	8	no	—
132	(C₂×D₄₇)⋊C₄	—	2	1	no	—
133	(C₂×D₄₇)⋊C₄	—	2	1	no	—
134	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
136	Dic₄₇⋊C₄	—	2	1	no	—
137	Dic₄₇⋊C₄	—	2	1	no	—
138	C₄×Dic₄₇	—	2	1	no	—
139	C₄×Dic₄₇	—	2	1	no	—
140	C₄×Dic₄₇	—	2	1	no	—
141	#10625329	—	2	2	no	—
142	#10625329	—	2	2	no	—
143	#10625329	—	2	2	no	—
144	#10625329	—	2	2	no	—
145	#10625329	—	2	2	no	—
146	#10625329	#41	1	4	yes	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
152	C₂²×D₄₇	—	2	1	no	—
153	Q₈×C₄₇	—	2	4	no	—
154	Q₈×C₄₇	—	2	4	no	—
155	Q₈×C₄₇	—	4	2	no	—
156	Q₈×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	4	1	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	8	2	no	—
164	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
165	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
171	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
172	C₂²⋊D₄₇	—	4	2	no	—
173	C₂×Dic₄₇	—	2	1	no	—
174	C₂×Dic₄₇	—	2	1	no	—
175	C₂×Dic₄₇	—	2	1	no	—
176	D₁₈₈	—	2	2	no	—
177	C₄×D₄₇	—	4	2	no	—
178	C₄×D₄₇	—	4	1	no	—
179	C₄×D₄₇	—	4	1	no	—
180	C₄×D₄₇	—	4	2	no	—
181	Dic₉₄	—	2	2	no	—
182	C₈×C₄₇	—	2	2	no	—
183	C₈×C₄₇	—	2	2	no	—
184	C₄₇⋊C₈	—	2	4	no	—
185	C₄₇⋊C₈	—	4	2	no	—
186	C₄₇⋊C₈	—	4	1	no	—
187	C₄₇⋊C₈	—	4	1	no	—
188	#23717	—	47	1	no	maximal, Sylow
189	C₂²×C₄₇	—	2	1	no	—
190	C₂²×C₄₇	—	2	1	no	—
191	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
192	C₂²×C₄₇	#529	1	2	yes	—
193	C₂×D₄₇	—	4	1	no	—
194	C₂×D₄₇	—	4	1	no	—
195	C₂×D₄₇	—	4	1	no	—
196	C₄×C₄₇	—	2	1	no	—
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	4	4	no	—
200	C₄×C₄₇	—	8	2	no	—
201	C₄×C₄₇	#473	1	2	yes	—
202	C₄×C₄₇	#525	1	2	yes	—
203	C₄×C₄₇	#525	1	1	yes	characteristic
204	C₄×C₄₇	#532	1	1	yes	characteristic
205	Dic₄₇	—	4	1	no	—
206	Dic₄₇	—	4	1	no	—
207	Dic₄₇	—	4	1	no	—
208	C₄×#137	—	47	2	no	—
209	C₂×C₄×Q₁₆	D₄₇	1	1	yes	characteristic, complemented
210	#2922	—	47	1	no	—
211	#2089	—	47	1	no	—
212	#2078	—	47	1	no	—
213	#2064	—	47	2	no	—
214	#2052	—	47	2	no	—
215	#2047	—	47	1	no	—
216	#2020	—	47	1	no	—
217	C₄×#108	—	47	1	no	—
218	C₄×#101	—	47	2	no	—
219	C₂×C₄₇	—	2	2	no	—
220	C₂×C₄₇	#2392	1	1	yes	characteristic
221	C₂×C₄₇	C₂×#473	1	1	yes	characteristic
222	C₂×C₄₇	#3067	1	1	yes	characteristic
223	D₄₇	—	8	1	no	—
224	C₂×#137	—	47	2	no	—
225	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
226	C₄×#41	—	47	1	no	—
227	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
228	#441	—	94	2	no	—
229	#440	—	94	2	no	—
230	C₄×Q₁₆	—	2	2	no	—
231	C₄×Q₁₆	—	2	2	no	—
232	C₄×Q₁₆	—	94	2	no	—
233	C₄×SD₁₆	—	94	2	no	—
234	#433	—	94	2	no	—
235	#431	—	94	2	no	—
236	C₂×#108	—	47	2	no	—
237	#428	—	47	2	no	—
238	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
239	#424	—	47	1	no	—
240	#424	—	47	1	no	—
241	#419	—	47	2	no	—
242	#417	—	47	2	no	—
243	C₂×#103	C₂×D₄₇	1	2	yes	—
244	C₂×#101	—	47	2	no	—
245	C₂×#101	—	47	2	no	—
246	#408	—	47	1	no	—
247	#408	—	47	1	no	—
248	C₄×M₁₆	—	47	1	no	—
249	C₄×M₁₆	—	47	2	no	—
250	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
251	#343	—	47	2	no	—
252	#343	—	47	2	no	—
253	#341	—	47	1	no	—
254	#341	—	47	1	no	—
255	C₄₇	#23717	1	1	yes	characteristic, complemented, Sylow
256	C₂×#41	—	47	1	no	—
257	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
258	#137	—	94	4	no	—
259	#137	—	94	4	no	—
260	C₂×Q₁₆	—	2	4	no	—
261	C₂×Q₁₆	—	2	2	no	—
262	C₂×Q₁₆	—	94	2	no	—
263	C₂×SD₁₆	—	94	2	no	—
264	C₂×M₁₆	—	47	2	no	—
265	C₂×M₁₆	—	47	2	no	—
266	C₂×M₁₆	—	47	1	no	—
267	C₂×M₁₆	—	47	1	no	—
268	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
269	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
270	C₄×Q₈	—	2	2	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	—	2	2	no	—
274	C₄×Q₈	—	47	1	no	—
275	C₄×Q₈	—	47	1	no	—
276	C₄×D₄	—	47	1	no	—
277	C₄×D₄	—	47	1	no	—
278	C₄×D₄	—	94	1	no	—
279	C₄×D₄	—	94	1	no	—
280	#117	—	47	1	no	—
281	#117	—	94	1	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	94	1	no	—
286	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
287	#108	—	94	4	no	—
288	#107	—	2	2	no	—
289	#107	—	94	2	no	—
290	#106	—	94	2	no	—
291	C₄⋊C₈	—	94	2	no	—
292	C₄⋊C₈	—	94	2	no	—
293	#103	—	2	4	no	—
294	#103	—	94	2	no	—
295	#103	—	94	2	no	—
296	#103	—	94	2	no	—
297	#102	—	94	2	no	—
298	#101	—	94	4	no	—
299	#101	—	94	4	no	—
300	C₂²⋊C₈	—	94	2	no	—
301	C₂²⋊C₈	—	94	2	no	—
302	#97	—	94	2	no	—
303	#97	—	94	1	no	—
304	C₄×C₈	—	94	2	no	—
305	C₄×C₈	—	94	1	no	—
306	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
307	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
308	#41	—	94	2	no	—
309	#41	—	94	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	47	1	no	—
316	C₂×Q₈	#10625350	1	4	yes	—
317	C₂×D₄	—	47	1	no	—
318	C₂×D₄	—	94	1	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	94	1	no	—
322	C₂²×C₄	—	94	1	no	—
323	C₂²×C₄	—	94	1	no	—
324	C₂²×C₄	#10625352	1	1	yes	characteristic
325	C₂²×C₄	#10625352	1	1	yes	characteristic
326	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
327	Q₁₆	—	2	8	no	—
328	Q₁₆	—	94	8	no	—
329	SD₁₆	—	94	8	no	—
330	M₁₆	—	47	4	no	—
331	M₁₆	—	94	2	no	—
332	M₁₆	—	94	2	no	—
333	M₁₆	—	94	2	no	—
334	M₁₆	—	94	2	no	—
335	M₁₆	—	94	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	94	2	no	—
339	C₂×C₈	—	94	2	no	—
340	C₂×C₈	—	94	1	no	—
341	C₂×C₈	—	94	1	no	—
342	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
343	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	47	1	no	—
349	C₄⋊C₄	—	47	1	no	—
350	C₄⋊C₄	—	94	1	no	—
351	C₄⋊C₄	—	94	1	no	—
352	C₂²⋊C₄	—	94	1	no	—
353	C₂²⋊C₄	—	94	1	no	—
354	C₂²⋊C₄	—	94	1	no	—
355	C₄²	—	4	2	no	—
356	C₄²	—	4	2	no	—
357	C₄²	—	94	1	no	—
358	C₄²	—	94	1	no	—
359	C₄²	—	94	1	no	—
360	C₄²	D₄×D₄₇	1	1	yes	characteristic
361	C₄²	D₄×D₄₇	1	1	yes	characteristic
362	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
363	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
364	C₂³	—	94	1	no	—
365	C₂³	C₂×#10625352	1	1	yes	characteristic
366	Q₈	—	2	4	no	—
367	Q₈	—	2	4	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	94	2	no	—
371	D₄	—	94	2	no	—
372	D₄	—	188	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	—	94	1	no	—
381	C₂×C₄	—	94	1	no	—
382	C₂×C₄	—	94	1	no	—
383	C₂×C₄	—	188	2	no	—
384	C₂×C₄	—	188	1	no	—
385	C₂×C₄	—	188	2	no	—
386	C₂×C₄	—	188	1	no	—
387	C₂×C₄	#13093995	1	1	yes	characteristic
388	C₂×C₄	#13093995	1	1	yes	characteristic
389	C₂×C₄	#13093995	1	1	yes	characteristic
390	C₂×C₄	#13093995	1	1	yes	characteristic
391	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
393	C₂×C₄	#41×D₄₇	1	2	yes	—
394	C₂×C₄	C₂×#10625350	1	2	yes	—
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	94	4	no	—
398	C₈	—	188	2	no	—
399	C₈	—	188	1	no	—
400	C₈	—	188	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	188	1	no	—
404	C₂²	—	188	1	no	—
405	C₂²	—	188	1	no	—
406	C₂²	C₂×#13093995	1	1	yes	characteristic
407	C₂²	#15689653	1	2	yes	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	4	4	no	—
412	C₄	—	8	2	no	—
413	C₄	—	188	1	no	—
414	C₄	—	188	1	no	—
415	C₄	—	188	1	no	—
416	C₄	#15689395	1	2	yes	—
417	C₄	#15689632	1	2	yes	—
418	C₄	#15689634	1	1	yes	characteristic
419	C₄	#15689669	1	1	yes	characteristic
420	C₂	—	2	2	no	—
421	C₂	—	376	1	no	—
422	C₂	#20246626	1	1	yes	characteristic
423	C₂	C₂×#15689395	1	1	yes	characteristic
424	C₂	#20253104	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093995
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×Q₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	C₂×#10625350	C₂³
hypercenter	C₂×C₄×Q₁₆	D₄₇
hypocenter	C₄₇	#23717
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
3. #20244894	C₂	semidirect
5. #20244753	C₂	semidirect
7. #20244653	C₂	semidirect
9. C₄×#13093960	C₂	semidirect
10. C₄×#13093943	C₂	semidirect
11. C₂×C₄×Q₁₆×C₄₇	C₂	semidirect
209. C₂×C₄×Q₁₆	D₄₇	semidirect
255. C₄₇	#23717	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13094055	2
#20252030	2
#20244894	2
#20244829	2
#20244753	2
#20244688	2
#20244653	2
#20244507	2
C₄×#13093960	2
C₄×#13093943	2
C₂×C₄×Q₁₆×C₄₇	2
#23717	47