Subgroups — #26204128

Order 12032.

784 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20254532	C₂	1	1	yes	maximal, characteristic, complemented
2	#20254313	C₂	1	1	yes	maximal, characteristic
3	#20253947	C₂	1	1	yes	maximal, characteristic
4	#20253930	C₂	1	1	yes	maximal, characteristic, complemented
5	#20253845	C₂	1	1	yes	maximal, characteristic
6	#20243020	C₂	1	2	yes	maximal, complemented
7	#20243013	C₂	1	2	yes	maximal, complemented
8	#20242983	C₂	1	2	yes	maximal, complemented
9	#20242976	C₂	1	2	yes	maximal, complemented
10	C₈×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094055	—	2	2	no	—
13	#15689680	C₂²	1	1	yes	characteristic
14	#15689673	C₂²	1	1	yes	characteristic
15	#15689529	—	2	2	no	—
16	#15689526	C₂²	1	2	yes	—
17	#15689521	C₂²	1	1	yes	characteristic
18	#15689519	C₂²	1	2	yes	—
19	#15689519	C₂²	1	2	yes	—
20	#15689515	—	2	2	no	—
21	#15689502	C₂²	1	2	yes	—
22	#15689497	C₂²	1	2	yes	—
23	#15689497	C₂²	1	2	yes	—
24	#15689496	C₂²	1	1	yes	characteristic
25	#15689475	C₂²	1	2	yes	—
26	#15689474	C₂²	1	1	yes	characteristic
27	#15689473	C₂²	1	2	yes	—
28	#15689470	C₂²	1	1	yes	characteristic
29	#15689453	—	2	2	no	—
30	#15689405	—	2	2	no	—
31	#15689352	—	2	2	no	—
32	#15689325	—	2	2	no	—
33	#15689262	—	2	2	no	—
34	C₄×#10625325	—	2	2	no	—
35	#15689176	C₂²	1	1	yes	characteristic
36	#15689163	—	2	2	no	—
37	C₄×#10625329	C₂²	1	1	yes	characteristic
38	#15688845	C₂²	1	2	yes	—
39	C₈×C₄₇⋊C₈	C₂²	1	2	yes	—
40	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#498	—	2	2	no	—
43	C₄₇×#498	C₂²	1	2	yes	—
44	C₄₇×#498	C₂²	1	2	yes	—
45	C₂×#106×C₄₇	—	2	2	no	—
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#10625350	—	2	1	no	—
48	#13094055	—	4	8	no	—
49	C₂×#10625337	—	2	4	no	—
50	C₂×#10625325	—	2	2	no	—
51	C₂×#10625336	—	2	4	no	—
52	C₂×#10625336	—	2	4	no	—
53	C₂×#10625329	D₄	1	2	yes	—
54	#13094024	C₂³	1	1	yes	characteristic
55	#13094024	C₂³	1	1	yes	characteristic
56	#13094024	C₂³	1	1	yes	characteristic
57	#13094021	C₂³	1	1	yes	characteristic
58	#13094016	—	2	1	no	—
59	#13094012	—	2	1	no	—
60	#13094003	—	2	1	no	—
61	#13094003	—	2	1	no	—
62	#13093998	—	2	1	no	—
63	#13093998	—	2	1	no	—
64	C₄×Dic₉₄	—	2	1	no	—
65	C₄×Dic₉₄	—	2	1	no	—
66	C₄×D₁₈₈	—	2	1	no	—
67	C₄×D₁₈₈	—	2	1	no	—
68	#13093983	—	2	1	no	—
69	#13093957	—	2	4	no	—
70	#13093956	—	2	2	no	—
71	#13093955	—	2	4	no	—
72	#13093955	—	2	4	no	—
73	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
74	#13093949	—	2	2	no	—
75	#13093948	—	2	4	no	—
76	#13093947	—	2	4	no	—
77	#13093946	—	2	2	no	—
78	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
79	#13093935	D₄	1	2	yes	—
80	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
81	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
82	C₂²×Q₈×C₄₇	—	2	1	no	—
83	C₂²×Q₈×C₄₇	—	2	1	no	—
84	C₂²×C₈×C₄₇	D₄	1	2	yes	—
85	C₄⋊Q₈×C₄₇	—	2	1	no	—
86	C₄⋊Q₈×C₄₇	—	2	1	no	—
87	C₄⋊Q₈×C₄₇	—	2	1	no	—
88	C₄⋊Q₈×C₄₇	—	2	1	no	—
89	C₄⋊Q₈×C₄₇	—	2	1	no	—
90	C₄⋊Q₈×C₄₇	—	2	1	no	—
91	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
92	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
94	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
96	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	#106×C₄₇	—	2	4	no	—
99	#106×C₄₇	—	2	4	no	—
100	C₄×C₈×C₄₇	D₄	1	2	yes	—
101	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	2	2	no	—
105	C₂×Q₈×C₄₇	—	4	1	no	—
106	C₂×Q₈×C₄₇	—	4	1	no	—
107	C₂×Q₈×C₄₇	—	4	4	no	—
108	C₂×Q₈×C₄₇	—	8	2	no	—
109	C₂²×C₄×C₄₇	—	4	1	no	—
110	C₂²×C₄×C₄₇	—	4	1	no	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂×C₂²⋊D₄₇	—	4	1	no	—
115	#10625350	—	4	4	no	—
116	C₂×D₁₈₈	—	2	1	no	—
117	C₂×D₁₈₈	—	2	1	no	—
118	C₂×D₁₈₈	—	2	1	no	—
119	C₂×C₄×D₄₇	—	4	1	no	—
120	C₂×Dic₉₄	—	2	1	no	—
121	C₂×Dic₉₄	—	2	1	no	—
122	C₂×Dic₉₄	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	4	no	—
124	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	—	2	2	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	—	4	1	no	—
131	C₄⋊C₄×C₄₇	—	4	1	no	—
132	C₄⋊C₄×C₄₇	—	4	1	no	—
133	C₄⋊C₄×C₄₇	—	4	1	no	—
134	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
138	C₂²⋊Dic₄₇	—	4	1	no	—
139	#10625337	—	4	8	no	—
140	#10625336	—	4	8	no	—
141	#10625336	—	8	4	no	—
142	(C₂×D₄₇)⋊C₄	—	4	1	no	—
143	(C₂×D₄₇)⋊C₄	—	4	1	no	—
144	C₄⋊Dic₄₇	—	2	1	no	—
145	C₄⋊Dic₄₇	—	2	1	no	—
146	C₄⋊Dic₄₇	—	2	1	no	—
147	C₄⋊Dic₄₇	—	2	1	no	—
148	C₄⋊Dic₄₇	—	2	1	no	—
149	C₄⋊Dic₄₇	—	2	1	no	—
150	Dic₄₇⋊C₄	—	4	1	no	—
151	Dic₄₇⋊C₄	—	4	1	no	—
152	C₄×Dic₄₇	—	4	1	no	—
153	#10625329	SD₁₆	1	8	yes	complemented
154	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
155	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
156	#10625325	—	4	4	no	—
157	C₂³×C₄₇	#127	1	1	yes	characteristic
158	C₂²×D₄₇	—	4	1	no	—
159	Q₈×C₄₇	—	4	4	no	—
160	Q₈×C₄₇	—	4	4	no	—
161	Q₈×C₄₇	—	8	2	no	—
162	Q₈×C₄₇	—	8	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	8	2	no	—
168	C₂×C₄×C₄₇	—	8	2	no	—
169	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
170	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
171	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
173	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	C₂²⋊D₄₇	—	8	2	no	—
177	C₂×Dic₄₇	—	4	1	no	—
178	C₂×Dic₄₇	—	4	1	no	—
179	C₂×Dic₄₇	—	4	1	no	—
180	D₁₈₈	—	4	2	no	—
181	D₁₈₈	—	4	2	no	—
182	D₁₈₈	—	4	2	no	—
183	C₄×D₄₇	—	8	2	no	—
184	Dic₉₄	—	4	2	no	—
185	Dic₉₄	—	4	2	no	—
186	Dic₉₄	—	4	2	no	—
187	C₈×C₄₇	—	2	2	no	—
188	C₈×C₄₇	#137	1	4	yes	complemented
189	C₄₇⋊C₈	—	2	4	no	—
190	C₄₇⋊C₈	C₂×SD₁₆	1	8	yes	—
191	#19622	—	47	1	no	maximal, Sylow
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	#492	1	2	yes	—
195	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
196	C₂×D₄₇	—	8	1	no	—
197	C₂×D₄₇	—	8	1	no	—
198	C₂×D₄₇	—	8	1	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	2	1	no	—
201	C₄×C₄₇	—	8	2	no	—
202	C₄×C₄₇	—	8	2	no	—
203	C₄×C₄₇	#492	1	2	yes	—
204	C₄×C₄₇	C₂²×SD₁₆	1	2	yes	—
205	C₄×C₄₇	C₂×#137	1	2	yes	—
206	C₄×C₄₇	#577	1	2	yes	—
207	Dic₄₇	—	8	1	no	—
208	Dic₄₇	—	8	1	no	—
209	Dic₄₇	—	8	1	no	—
210	#3229	—	47	1	no	—
211	#3206	—	47	1	no	—
212	#3167	—	47	1	no	—
213	#3165	—	47	1	no	—
214	C₂×#498	D₄₇	1	1	yes	characteristic, complemented
215	#3152	—	47	1	no	—
216	#1716	—	47	2	no	—
217	#1714	—	47	2	no	—
218	#1707	—	47	2	no	—
219	#1705	—	47	2	no	—
220	C₈×M₁₆	—	47	1	no	—
221	C₂×C₄₇	—	2	2	no	—
222	C₂×C₄₇	C₂×#492	1	1	yes	characteristic
223	C₂×C₄₇	#3152	1	1	yes	characteristic
224	C₂×C₄₇	#3154	1	1	yes	characteristic
225	D₄₇	—	16	1	no	—
226	C₂×#137	—	94	2	no	—
227	#533	—	47	1	no	—
228	#532	—	47	1	no	—
229	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
230	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
231	#501	—	94	2	no	—
232	#500	—	47	2	no	—
233	#498	—	2	2	no	—
234	#498	—	47	2	no	—
235	#498	—	47	2	no	—
236	#498	—	47	1	no	—
237	#498	C₂×D₄₇	1	2	yes	—
238	#498	C₂×D₄₇	1	2	yes	—
239	#497	—	94	2	no	—
240	#494	—	47	2	no	—
241	#492	—	47	2	no	—
242	#492	—	47	2	no	—
243	#492	—	47	1	no	—
244	#487	—	47	2	no	—
245	#487	—	47	2	no	—
246	#487	—	47	1	no	—
247	#486	—	47	1	no	—
248	#483	—	94	2	no	—
249	#475	—	94	2	no	—
250	#465	—	94	2	no	—
251	#461	—	94	2	no	—
252	#448	—	94	2	no	—
253	C₄×SD₁₆	—	94	2	no	—
254	#431	—	47	1	no	—
255	#428	—	94	2	no	—
256	C₂×#106	—	2	2	no	—
257	C₄×M₁₆	—	47	1	no	—
258	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
259	#322	—	47	2	no	—
260	C₈²	—	47	2	no	—
261	C₄₇	#19622	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	94	1	no	—
263	C₂²×Q₈	—	2	1	no	—
264	C₂²×Q₈	—	2	1	no	—
265	#137	—	188	8	no	—
266	C₂×Q₁₆	—	94	4	no	—
267	C₂×SD₁₆	—	94	4	no	—
268	C₂×SD₁₆	—	94	4	no	—
269	C₂×SD₁₆	—	94	2	no	—
270	C₂×M₁₆	—	47	2	no	—
271	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
272	C₄⋊Q₈	—	2	1	no	—
273	C₄⋊Q₈	—	2	1	no	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	—	2	1	no	—
278	C₄⋊Q₈	—	47	1	no	—
279	C₄⋊Q₈	—	47	1	no	—
280	C₄⋊Q₈	—	47	1	no	—
281	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
282	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
283	#127	—	47	1	no	—
284	#125	—	94	1	no	—
285	#124	—	94	1	no	—
286	C₂²⋊Q₈	—	94	1	no	—
287	C₂²⋊Q₈	—	94	1	no	—
288	#121	—	94	1	no	—
289	#121	—	94	1	no	—
290	C₄×Q₈	—	94	1	no	—
291	C₄×Q₈	—	94	1	no	—
292	C₄×D₄	—	94	1	no	—
293	C₄×D₄	—	94	1	no	—
294	#117	—	94	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
300	#107	—	94	4	no	—
301	#106	—	2	4	no	—
302	#106	—	2	4	no	—
303	#106	—	94	4	no	—
304	#106	—	94	4	no	—
305	#106	—	94	2	no	—
306	C₄⋊C₈	—	47	2	no	—
307	#103	—	94	4	no	—
308	#103	—	94	4	no	—
309	#103	—	94	2	no	—
310	#102	—	94	2	no	—
311	C₂²⋊C₈	—	47	2	no	—
312	#97	—	47	2	no	—
313	C₄×C₈	—	47	2	no	—
314	C₄×C₈	—	47	2	no	—
315	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
316	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
318	#41	—	188	4	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	4	1	no	—
322	C₂×Q₈	—	4	1	no	—
323	C₂×Q₈	—	4	4	no	—
324	C₂×Q₈	—	8	2	no	—
325	C₂×Q₈	—	94	1	no	—
326	C₂×Q₈	—	94	1	no	—
327	C₂×Q₈	—	94	1	no	—
328	C₂×D₄	—	94	1	no	—
329	C₂×D₄	—	94	1	no	—
330	C₂×D₄	—	94	1	no	—
331	C₂×D₄	—	188	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	188	1	no	—
335	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
336	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
338	Q₁₆	—	188	8	no	—
339	SD₁₆	—	376	4	no	—
340	SD₁₆	—	188	8	no	—
341	SD₁₆	—	188	4	no	—
342	M₁₆	—	47	8	no	—
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	—	47	4	no	—
345	C₂×C₈	—	47	4	no	—
346	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
347	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	94	1	no	—
357	C₄⋊C₄	—	94	1	no	—
358	C₄⋊C₄	—	94	1	no	—
359	C₄⋊C₄	—	94	1	no	—
360	C₄⋊C₄	—	94	1	no	—
361	C₄⋊C₄	—	94	1	no	—
362	C₄⋊C₄	—	188	1	no	—
363	C₄⋊C₄	—	188	1	no	—
364	C₂²⋊C₄	—	188	1	no	—
365	C₂²⋊C₄	—	188	1	no	—
366	C₂²⋊C₄	—	188	1	no	—
367	C₄²	—	188	1	no	—
368	C₄²	D₄×D₄₇	1	1	yes	characteristic
369	C₄²	D₄×D₄₇	1	1	yes	characteristic
370	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
371	C₄²	C₂³×D₄₇	1	1	yes	characteristic
372	C₂³	—	188	1	no	—
373	C₂³	#13094020	1	1	yes	characteristic
374	Q₈	—	4	4	no	—
375	Q₈	—	4	4	no	—
376	Q₈	—	8	2	no	—
377	Q₈	—	8	2	no	—
378	Q₈	—	188	2	no	—
379	Q₈	—	188	2	no	—
380	Q₈	—	188	2	no	—
381	D₄	—	376	2	no	—
382	D₄	—	188	2	no	—
383	D₄	—	188	2	no	—
384	D₄	—	188	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	—	8	2	no	—
391	C₂×C₄	—	376	2	no	—
392	C₂×C₄	—	188	1	no	—
393	C₂×C₄	—	188	1	no	—
394	C₂×C₄	—	188	1	no	—
395	C₂×C₄	#13094020	1	1	yes	characteristic
396	C₂×C₄	#13094020	1	1	yes	characteristic
397	C₂×C₄	#13094020	1	1	yes	characteristic
398	C₂×C₄	SD₁₆×D₄₇	1	4	yes	—
399	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
400	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	47	8	no	—
404	C₈	—	94	4	no	—
405	C₈	#13094055	1	4	yes	complemented
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	376	1	no	—
409	C₂²	—	376	1	no	—
410	C₂²	—	376	1	no	—
411	C₂²	#15689494	1	2	yes	—
412	C₂²	C₂×#13094020	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	8	2	no	—
416	C₄	—	8	2	no	—
417	C₄	—	376	1	no	—
418	C₄	—	376	1	no	—
419	C₄	—	376	1	no	—
420	C₄	#15689494	1	2	yes	—
421	C₄	C₂×SD₁₆×D₄₇	1	2	yes	—
422	C₄	C₂×#13094055	1	2	yes	—
423	C₄	#15689929	1	2	yes	—
424	C₂	—	2	2	no	—
425	C₂	—	752	1	no	—
426	C₂	C₂×#15689494	1	1	yes	characteristic
427	C₂	#20253845	1	1	yes	characteristic
428	C₂	#20253858	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13094020
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#498	C₂
socle	C₂²×C₄₇	C₂×#127
prime radical	#15689673	C₂²
hypercenter	C₂×#498	D₄₇
hypocenter	C₄₇	#19622
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#498

Complements

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

N	H ≅ G/N	type
1. #20254532	C₂	semidirect
4. #20253930	C₂	semidirect
6. #20243020	C₂	semidirect
7. #20243013	C₂	semidirect
8. #20242983	C₂	semidirect
9. #20242976	C₂	semidirect
10. C₈×#10625329	C₂	semidirect
11. C₂×C₄₇×#498	C₂	semidirect
153. #10625329	SD₁₆	semidirect
188. C₈×C₄₇	#137	semidirect
214. C₂×#498	D₄₇	semidirect
261. C₄₇	#19622	semidirect
405. C₈	#13094055	semidirect

Maximal subgroups

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

subgroup	index
#20254532	2
#20254313	2
#20253947	2
#20253930	2
#20253845	2
#20243020	2
#20243013	2
#20242983	2
#20242976	2
C₈×#10625329	2
C₂×C₄₇×#498	2
#19622	47