Subgroups — #25084447

Order 11008.

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	#19145739	C₂	1	1	yes	maximal, characteristic, complemented
2	#19145520	C₂	1	1	yes	maximal, characteristic
3	#19145154	C₂	1	1	yes	maximal, characteristic
4	#19145137	C₂	1	1	yes	maximal, characteristic, complemented
5	#19145052	C₂	1	1	yes	maximal, characteristic
6	#19134227	C₂	1	2	yes	maximal, complemented
7	#19134220	C₂	1	2	yes	maximal, complemented
8	#19134190	C₂	1	2	yes	maximal, complemented
9	#19134183	C₂	1	2	yes	maximal, complemented
10	C₈×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063356	—	2	2	no	—
13	#14583456	C₂²	1	1	yes	characteristic
14	#14583449	C₂²	1	1	yes	characteristic
15	#14583305	—	2	2	no	—
16	#14583302	C₂²	1	2	yes	—
17	#14583297	C₂²	1	1	yes	characteristic
18	#14583295	C₂²	1	2	yes	—
19	#14583295	C₂²	1	2	yes	—
20	#14583291	—	2	2	no	—
21	#14583278	C₂²	1	2	yes	—
22	#14583273	C₂²	1	2	yes	—
23	#14583273	C₂²	1	2	yes	—
24	#14583272	C₂²	1	1	yes	characteristic
25	#14583251	C₂²	1	2	yes	—
26	#14583250	C₂²	1	1	yes	characteristic
27	#14583249	C₂²	1	2	yes	—
28	#14583246	C₂²	1	1	yes	characteristic
29	#14583229	—	2	2	no	—
30	#14583181	—	2	2	no	—
31	#14583128	—	2	2	no	—
32	#14583101	—	2	2	no	—
33	#14583038	—	2	2	no	—
34	C₄×#10621873	—	2	2	no	—
35	#14582952	C₂²	1	1	yes	characteristic
36	#14582939	—	2	2	no	—
37	C₄×#10621877	C₂²	1	1	yes	characteristic
38	#14582621	C₂²	1	2	yes	—
39	C₈×C₄₃⋊C₈	C₂²	1	2	yes	—
40	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#498	—	2	2	no	—
43	C₄₃×#498	C₂²	1	2	yes	—
44	C₄₃×#498	C₂²	1	2	yes	—
45	C₂×#106×C₄₃	—	2	2	no	—
46	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#10621898	—	2	1	no	—
48	#13063356	—	4	8	no	—
49	C₂×#10621885	—	2	4	no	—
50	C₂×#10621873	—	2	2	no	—
51	C₂×#10621884	—	2	4	no	—
52	C₂×#10621884	—	2	4	no	—
53	C₂×#10621877	D₄	1	2	yes	—
54	#13063325	C₂³	1	1	yes	characteristic
55	#13063325	C₂³	1	1	yes	characteristic
56	#13063325	C₂³	1	1	yes	characteristic
57	#13063322	C₂³	1	1	yes	characteristic
58	#13063317	—	2	1	no	—
59	#13063313	—	2	1	no	—
60	#13063304	—	2	1	no	—
61	#13063304	—	2	1	no	—
62	#13063299	—	2	1	no	—
63	#13063299	—	2	1	no	—
64	C₄×Dic₈₆	—	2	1	no	—
65	C₄×Dic₈₆	—	2	1	no	—
66	C₄×D₁₇₂	—	2	1	no	—
67	C₄×D₁₇₂	—	2	1	no	—
68	#13063284	—	2	1	no	—
69	#13063258	—	2	4	no	—
70	#13063257	—	2	2	no	—
71	#13063256	—	2	4	no	—
72	#13063256	—	2	4	no	—
73	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
74	#13063250	—	2	2	no	—
75	#13063249	—	2	4	no	—
76	#13063248	—	2	4	no	—
77	#13063247	—	2	2	no	—
78	C₂²⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
79	#13063236	D₄	1	2	yes	—
80	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
81	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
82	C₂²×Q₈×C₄₃	—	2	1	no	—
83	C₂²×Q₈×C₄₃	—	2	1	no	—
84	C₂²×C₈×C₄₃	D₄	1	2	yes	—
85	C₄⋊Q₈×C₄₃	—	2	1	no	—
86	C₄⋊Q₈×C₄₃	—	2	1	no	—
87	C₄⋊Q₈×C₄₃	—	2	1	no	—
88	C₄⋊Q₈×C₄₃	—	2	1	no	—
89	C₄⋊Q₈×C₄₃	—	2	1	no	—
90	C₄⋊Q₈×C₄₃	—	2	1	no	—
91	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
92	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
96	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
97	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
98	#106×C₄₃	—	2	4	no	—
99	#106×C₄₃	—	2	4	no	—
100	C₄×C₈×C₄₃	D₄	1	2	yes	—
101	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
103	C₂×Q₈×C₄₃	—	2	2	no	—
104	C₂×Q₈×C₄₃	—	2	2	no	—
105	C₂×Q₈×C₄₃	—	4	1	no	—
106	C₂×Q₈×C₄₃	—	4	1	no	—
107	C₂×Q₈×C₄₃	—	4	4	no	—
108	C₂×Q₈×C₄₃	—	8	2	no	—
109	C₂²×C₄×C₄₃	—	4	1	no	—
110	C₂²×C₄×C₄₃	—	4	1	no	—
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₂²⋊D₄₃	—	4	1	no	—
115	#10621898	—	4	4	no	—
116	C₂×D₁₇₂	—	2	1	no	—
117	C₂×D₁₇₂	—	2	1	no	—
118	C₂×D₁₇₂	—	2	1	no	—
119	C₂×C₄×D₄₃	—	4	1	no	—
120	C₂×Dic₈₆	—	2	1	no	—
121	C₂×Dic₈₆	—	2	1	no	—
122	C₂×Dic₈₆	—	2	1	no	—
123	C₂×C₈×C₄₃	—	2	4	no	—
124	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	2	2	no	—
128	C₄⋊C₄×C₄₃	—	2	2	no	—
129	C₄⋊C₄×C₄₃	—	2	2	no	—
130	C₄⋊C₄×C₄₃	—	4	1	no	—
131	C₄⋊C₄×C₄₃	—	4	1	no	—
132	C₄⋊C₄×C₄₃	—	4	1	no	—
133	C₄⋊C₄×C₄₃	—	4	1	no	—
134	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
138	C₂²⋊Dic₄₃	—	4	1	no	—
139	#10621885	—	4	8	no	—
140	#10621884	—	4	8	no	—
141	#10621884	—	8	4	no	—
142	(C₂×D₄₃)⋊C₄	—	4	1	no	—
143	(C₂×D₄₃)⋊C₄	—	4	1	no	—
144	C₄⋊Dic₄₃	—	2	1	no	—
145	C₄⋊Dic₄₃	—	2	1	no	—
146	C₄⋊Dic₄₃	—	2	1	no	—
147	C₄⋊Dic₄₃	—	2	1	no	—
148	C₄⋊Dic₄₃	—	2	1	no	—
149	C₄⋊Dic₄₃	—	2	1	no	—
150	Dic₄₃⋊C₄	—	4	1	no	—
151	Dic₄₃⋊C₄	—	4	1	no	—
152	C₄×Dic₄₃	—	4	1	no	—
153	#10621877	SD₁₆	1	8	yes	complemented
154	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
155	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
156	#10621873	—	4	4	no	—
157	C₂³×C₄₃	#127	1	1	yes	characteristic
158	C₂²×D₄₃	—	4	1	no	—
159	Q₈×C₄₃	—	4	4	no	—
160	Q₈×C₄₃	—	4	4	no	—
161	Q₈×C₄₃	—	8	2	no	—
162	Q₈×C₄₃	—	8	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	4	2	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	8	2	no	—
168	C₂×C₄×C₄₃	—	8	2	no	—
169	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
170	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
171	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂×SD₁₆	1	4	yes	—
173	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
176	C₂²⋊D₄₃	—	8	2	no	—
177	C₂×Dic₄₃	—	4	1	no	—
178	C₂×Dic₄₃	—	4	1	no	—
179	C₂×Dic₄₃	—	4	1	no	—
180	D₁₇₂	—	4	2	no	—
181	D₁₇₂	—	4	2	no	—
182	D₁₇₂	—	4	2	no	—
183	C₄×D₄₃	—	8	2	no	—
184	Dic₈₆	—	4	2	no	—
185	Dic₈₆	—	4	2	no	—
186	Dic₈₆	—	4	2	no	—
187	C₈×C₄₃	—	2	2	no	—
188	C₈×C₄₃	#137	1	4	yes	complemented
189	C₄₃⋊C₈	—	2	4	no	—
190	C₄₃⋊C₈	C₂×SD₁₆	1	8	yes	—
191	#19622	—	43	1	no	maximal, Sylow
192	C₂²×C₄₃	—	2	1	no	—
193	C₂²×C₄₃	—	2	1	no	—
194	C₂²×C₄₃	#492	1	2	yes	—
195	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
196	C₂×D₄₃	—	8	1	no	—
197	C₂×D₄₃	—	8	1	no	—
198	C₂×D₄₃	—	8	1	no	—
199	C₄×C₄₃	—	2	1	no	—
200	C₄×C₄₃	—	2	1	no	—
201	C₄×C₄₃	—	8	2	no	—
202	C₄×C₄₃	—	8	2	no	—
203	C₄×C₄₃	#492	1	2	yes	—
204	C₄×C₄₃	C₂²×SD₁₆	1	2	yes	—
205	C₄×C₄₃	C₂×#137	1	2	yes	—
206	C₄×C₄₃	#577	1	2	yes	—
207	Dic₄₃	—	8	1	no	—
208	Dic₄₃	—	8	1	no	—
209	Dic₄₃	—	8	1	no	—
210	#3229	—	43	1	no	—
211	#3206	—	43	1	no	—
212	#3167	—	43	1	no	—
213	#3165	—	43	1	no	—
214	C₂×#498	D₄₃	1	1	yes	characteristic, complemented
215	#3152	—	43	1	no	—
216	#1716	—	43	2	no	—
217	#1714	—	43	2	no	—
218	#1707	—	43	2	no	—
219	#1705	—	43	2	no	—
220	C₈×M₁₆	—	43	1	no	—
221	C₂×C₄₃	—	2	2	no	—
222	C₂×C₄₃	C₂×#492	1	1	yes	characteristic
223	C₂×C₄₃	#3152	1	1	yes	characteristic
224	C₂×C₄₃	#3154	1	1	yes	characteristic
225	D₄₃	—	16	1	no	—
226	C₂×#137	—	86	2	no	—
227	#533	—	43	1	no	—
228	#532	—	43	1	no	—
229	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
230	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
231	#501	—	86	2	no	—
232	#500	—	43	2	no	—
233	#498	—	2	2	no	—
234	#498	—	43	2	no	—
235	#498	—	43	2	no	—
236	#498	—	43	1	no	—
237	#498	C₂×D₄₃	1	2	yes	—
238	#498	C₂×D₄₃	1	2	yes	—
239	#497	—	86	2	no	—
240	#494	—	43	2	no	—
241	#492	—	43	2	no	—
242	#492	—	43	2	no	—
243	#492	—	43	1	no	—
244	#487	—	43	2	no	—
245	#487	—	43	2	no	—
246	#487	—	43	1	no	—
247	#486	—	43	1	no	—
248	#483	—	86	2	no	—
249	#475	—	86	2	no	—
250	#465	—	86	2	no	—
251	#461	—	86	2	no	—
252	#448	—	86	2	no	—
253	C₄×SD₁₆	—	86	2	no	—
254	#431	—	43	1	no	—
255	#428	—	86	2	no	—
256	C₂×#106	—	2	2	no	—
257	C₄×M₁₆	—	43	1	no	—
258	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
259	#322	—	43	2	no	—
260	C₈²	—	43	2	no	—
261	C₄₃	#19622	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	86	1	no	—
263	C₂²×Q₈	—	2	1	no	—
264	C₂²×Q₈	—	2	1	no	—
265	#137	—	172	8	no	—
266	C₂×Q₁₆	—	86	4	no	—
267	C₂×SD₁₆	—	86	4	no	—
268	C₂×SD₁₆	—	86	4	no	—
269	C₂×SD₁₆	—	86	2	no	—
270	C₂×M₁₆	—	43	2	no	—
271	C₂²×C₈	C₂²⋊D₄₃	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	—	43	1	no	—
279	C₄⋊Q₈	—	43	1	no	—
280	C₄⋊Q₈	—	43	1	no	—
281	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
282	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
283	#127	—	43	1	no	—
284	#125	—	86	1	no	—
285	#124	—	86	1	no	—
286	C₂²⋊Q₈	—	86	1	no	—
287	C₂²⋊Q₈	—	86	1	no	—
288	#121	—	86	1	no	—
289	#121	—	86	1	no	—
290	C₄×Q₈	—	86	1	no	—
291	C₄×Q₈	—	86	1	no	—
292	C₄×D₄	—	86	1	no	—
293	C₄×D₄	—	86	1	no	—
294	#117	—	86	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×D₄₃	1	1	yes	characteristic
300	#107	—	86	4	no	—
301	#106	—	2	4	no	—
302	#106	—	2	4	no	—
303	#106	—	86	4	no	—
304	#106	—	86	4	no	—
305	#106	—	86	2	no	—
306	C₄⋊C₈	—	43	2	no	—
307	#103	—	86	4	no	—
308	#103	—	86	4	no	—
309	#103	—	86	2	no	—
310	#102	—	86	2	no	—
311	C₂²⋊C₈	—	43	2	no	—
312	#97	—	43	2	no	—
313	C₄×C₈	—	43	2	no	—
314	C₄×C₈	—	43	2	no	—
315	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
316	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
318	#41	—	172	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	—	86	1	no	—
326	C₂×Q₈	—	86	1	no	—
327	C₂×Q₈	—	86	1	no	—
328	C₂×D₄	—	86	1	no	—
329	C₂×D₄	—	86	1	no	—
330	C₂×D₄	—	86	1	no	—
331	C₂×D₄	—	172	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	172	1	no	—
335	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
336	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
338	Q₁₆	—	172	8	no	—
339	SD₁₆	—	344	4	no	—
340	SD₁₆	—	172	8	no	—
341	SD₁₆	—	172	4	no	—
342	M₁₆	—	43	8	no	—
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	—	43	4	no	—
345	C₂×C₈	—	43	4	no	—
346	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
347	C₂×C₈	C₂×C₂²⋊D₄₃	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	—	86	1	no	—
357	C₄⋊C₄	—	86	1	no	—
358	C₄⋊C₄	—	86	1	no	—
359	C₄⋊C₄	—	86	1	no	—
360	C₄⋊C₄	—	86	1	no	—
361	C₄⋊C₄	—	86	1	no	—
362	C₄⋊C₄	—	172	1	no	—
363	C₄⋊C₄	—	172	1	no	—
364	C₂²⋊C₄	—	172	1	no	—
365	C₂²⋊C₄	—	172	1	no	—
366	C₂²⋊C₄	—	172	1	no	—
367	C₄²	—	172	1	no	—
368	C₄²	D₄×D₄₃	1	1	yes	characteristic
369	C₄²	D₄×D₄₃	1	1	yes	characteristic
370	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
371	C₄²	C₂³×D₄₃	1	1	yes	characteristic
372	C₂³	—	172	1	no	—
373	C₂³	#13063321	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	—	172	2	no	—
379	Q₈	—	172	2	no	—
380	Q₈	—	172	2	no	—
381	D₄	—	344	2	no	—
382	D₄	—	172	2	no	—
383	D₄	—	172	2	no	—
384	D₄	—	172	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	—	344	2	no	—
392	C₂×C₄	—	172	1	no	—
393	C₂×C₄	—	172	1	no	—
394	C₂×C₄	—	172	1	no	—
395	C₂×C₄	#13063321	1	1	yes	characteristic
396	C₂×C₄	#13063321	1	1	yes	characteristic
397	C₂×C₄	#13063321	1	1	yes	characteristic
398	C₂×C₄	SD₁₆×D₄₃	1	4	yes	—
399	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
400	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	43	8	no	—
404	C₈	—	86	4	no	—
405	C₈	#13063356	1	4	yes	complemented
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	344	1	no	—
409	C₂²	—	344	1	no	—
410	C₂²	—	344	1	no	—
411	C₂²	#14583270	1	2	yes	—
412	C₂²	C₂×#13063321	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	—	344	1	no	—
418	C₄	—	344	1	no	—
419	C₄	—	344	1	no	—
420	C₄	#14583270	1	2	yes	—
421	C₄	C₂×SD₁₆×D₄₃	1	2	yes	—
422	C₄	C₂×#13063356	1	2	yes	—
423	C₄	#14583705	1	2	yes	—
424	C₂	—	2	2	no	—
425	C₂	—	688	1	no	—
426	C₂	C₂×#14583270	1	1	yes	characteristic
427	C₂	#19145052	1	1	yes	characteristic
428	C₂	#19145065	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063321
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₄₃×#498	C₂
socle	C₂²×C₄₃	C₂×#127
prime radical	#14583449	C₂²
hypercenter	C₂×#498	D₄₃
hypocenter	C₄₃	#19622
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#498

Complements

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

N	H ≅ G/N	type
1. #19145739	C₂	semidirect
4. #19145137	C₂	semidirect
6. #19134227	C₂	semidirect
7. #19134220	C₂	semidirect
8. #19134190	C₂	semidirect
9. #19134183	C₂	semidirect
10. C₈×#10621877	C₂	semidirect
11. C₂×C₄₃×#498	C₂	semidirect
153. #10621877	SD₁₆	semidirect
188. C₈×C₄₃	#137	semidirect
214. C₂×#498	D₄₃	semidirect
261. C₄₃	#19622	semidirect
405. C₈	#13063356	semidirect

Maximal subgroups

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

subgroup	index
#19145739	2
#19145520	2
#19145154	2
#19145137	2
#19145052	2
#19134227	2
#19134220	2
#19134190	2
#19134183	2
C₈×#10621877	2
C₂×C₄₃×#498	2
#19622	43