Subgroups — #25079345

Order 11008.

642 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145174	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144656	C₂	1	2	yes	maximal, complemented
3	#19143561	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134136	C₂	1	2	yes	maximal, complemented
5	#19134129	C₂	1	2	yes	maximal, complemented
6	#19134124	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134119	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134080	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134075	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133255	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583449	C₂²	1	2	yes	—
13	C₄×#10621898	C₂²	1	1	yes	characteristic
14	#14583304	C₂²	1	1	yes	characteristic
15	#14583276	C₂²	1	1	yes	characteristic
16	#14583246	C₂²	1	2	yes	—
17	#14583224	—	2	2	no	—
18	#14583195	C₂²	1	2	yes	—
19	#14583190	C₂²	1	2	yes	—
20	#14583135	—	2	1	no	—
21	#14583135	—	2	1	no	—
22	#14583100	C₂²	1	2	yes	—
23	#14583095	C₂²	1	2	yes	—
24	#14583046	—	2	2	no	—
25	#14583029	C₂²	1	1	yes	characteristic
26	#14583029	C₂²	1	1	yes	characteristic
27	C₄×#10621873	—	2	2	no	—
28	C₄×D₃₄₄	—	2	2	no	—
29	C₄×D₃₄₄	—	2	1	no	—
30	C₄×D₃₄₄	—	2	1	no	—
31	#14582978	C₂²	1	1	yes	characteristic
32	#14582978	C₂²	1	1	yes	characteristic
33	#14582970	—	2	1	no	—
34	#14582970	—	2	1	no	—
35	#14582952	C₂²	1	1	yes	characteristic
36	#14582950	—	2	1	no	—
37	C₄×#10621872	—	2	1	no	—
38	#14582647	C₂²	1	2	yes	—
39	#14582647	C₂²	1	2	yes	—
40	#14582642	C₂²	1	2	yes	—
41	#14582642	C₂²	1	2	yes	—
42	C₄₃×#431	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#335	C₂²	1	2	yes	—
45	C₄₃×#334	C₂²	1	1	yes	characteristic
46	C₄₃×#334	C₂²	1	1	yes	characteristic
47	C₂×#10621898	—	2	2	no	—
48	C₂×#10621898	D₄	1	1	yes	characteristic
49	C₂×#10621873	—	2	2	no	—
50	C₂×D₃₄₄	—	2	2	no	—
51	C₂×D₃₄₄	—	2	1	no	—
52	C₂×D₃₄₄	—	2	1	no	—
53	C₂×#10621872	—	2	1	no	—
54	C₂×#10621872	—	2	1	no	—
55	#13063325	C₂³	1	2	yes	—
56	#13063322	C₂³	1	2	yes	—
57	#13063313	—	2	2	no	—
58	#13063299	—	2	2	no	—
59	#13063299	—	2	2	no	—
60	C₄×Dic₈₆	D₄	1	1	yes	characteristic
61	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
62	C₄×D₁₇₂	—	2	2	no	—
63	C₄×D₁₇₂	—	2	2	no	—
64	C₄×D₁₇₂	D₄	1	1	yes	characteristic
65	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
66	C₄×C₂²⋊D₄₃	—	2	1	no	—
67	C₄×C₂²⋊D₄₃	—	2	1	no	—
68	#13063284	D₄	1	1	yes	characteristic
69	#13063282	—	2	1	no	—
70	C₄²×D₄₃	—	2	1	no	—
71	#13063259	—	2	1	no	—
72	#13063259	—	2	1	no	—
73	#13063259	—	2	2	no	—
74	#13063257	—	2	2	no	—
75	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
77	Dic₄₃⋊C₈	—	2	1	no	—
78	Dic₄₃⋊C₈	—	2	1	no	—
79	#13063250	—	2	2	no	—
80	#13063247	—	2	2	no	—
81	#13063247	—	2	2	no	—
82	#13063247	—	2	2	no	—
83	#13063247	—	2	2	no	—
84	#13063247	—	2	2	no	—
85	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
86	(C₂×D₄₃)⋊C₈	—	2	1	no	—
87	(C₂×D₄₃)⋊C₈	—	2	1	no	—
88	#13063235	—	2	1	no	—
89	#13063235	—	2	1	no	—
90	C₄×C₄₃⋊C₈	—	2	1	no	—
91	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
92	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
95	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
96	C₂²⋊C₈×C₄₃	—	2	2	no	—
97	C₄×C₈×C₄₃	—	2	2	no	—
98	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
99	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
105	C₂×C₂²⋊D₄₃	—	2	1	no	—
106	C₂×C₂²⋊D₄₃	—	4	2	no	—
107	#10621898	—	4	2	no	—
108	#10621898	—	8	4	no	—
109	C₂×D₁₇₂	—	2	2	no	—
110	C₂×D₁₇₂	—	2	2	no	—
111	C₂×D₁₇₂	—	2	2	no	—
112	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
113	C₂×C₄×D₄₃	—	2	1	no	—
114	C₂×C₄×D₄₃	—	2	1	no	—
115	C₂×C₄×D₄₃	—	2	1	no	—
116	C₂×C₄×D₄₃	—	4	2	no	—
117	C₂×Dic₈₆	—	2	2	no	—
118	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₄₃	—	2	2	no	—
120	C₂×C₈×C₄₃	—	2	2	no	—
121	C₂×C₈×C₄₃	—	2	2	no	—
122	C₂×C₈×C₄₃	—	4	1	no	—
123	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₃	#41	1	1	yes	characteristic
130	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
131	C₂²⋊Dic₄₃	—	2	1	no	—
132	(C₂×D₄₃)⋊C₄	—	2	1	no	—
133	(C₂×D₄₃)⋊C₄	—	2	1	no	—
134	(C₂×D₄₃)⋊C₄	—	4	2	no	—
135	(C₂×D₄₃)⋊C₄	—	4	2	no	—
136	C₄⋊Dic₄₃	—	2	2	no	—
137	C₄⋊Dic₄₃	—	2	2	no	—
138	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
139	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
140	Dic₄₃⋊C₄	—	2	1	no	—
141	Dic₄₃⋊C₄	—	2	1	no	—
142	C₄×Dic₄₃	—	2	1	no	—
143	C₄×Dic₄₃	—	2	1	no	—
144	C₄×Dic₄₃	—	2	1	no	—
145	C₂×C₄₃⋊C₈	—	2	1	no	—
146	C₂×C₄₃⋊C₈	—	2	1	no	—
147	D₃₄₄	—	4	2	no	—
148	D₃₄₄	—	4	4	no	—
149	D₃₄₄	—	4	2	no	—
150	#10621873	—	4	4	no	—
151	#10621872	—	4	2	no	—
152	#10621872	—	4	2	no	—
153	C₂³×C₄₃	#121	1	1	yes	characteristic
154	C₂²×D₄₃	—	2	1	no	—
155	C₂²×D₄₃	—	4	2	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
161	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
162	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
166	C₂²⋊D₄₃	—	4	2	no	—
167	C₂²⋊D₄₃	—	8	4	no	—
168	C₂×Dic₄₃	—	2	1	no	—
169	C₂×Dic₄₃	—	2	1	no	—
170	C₂×Dic₄₃	—	2	1	no	—
171	C₂×Dic₄₃	—	4	2	no	—
172	D₁₇₂	—	2	2	no	—
173	D₁₇₂	—	4	2	no	—
174	D₁₇₂	—	4	2	no	—
175	D₁₇₂	—	4	2	no	—
176	D₁₇₂	—	4	2	no	—
177	D₁₇₂	—	8	2	no	—
178	C₄×D₄₃	—	4	2	no	—
179	C₄×D₄₃	—	4	1	no	—
180	C₄×D₄₃	—	4	1	no	—
181	C₄×D₄₃	—	4	2	no	—
182	C₄×D₄₃	—	8	4	no	—
183	Dic₈₆	—	2	2	no	—
184	Dic₈₆	—	8	2	no	—
185	C₈×C₄₃	—	2	1	no	—
186	C₈×C₄₃	—	2	1	no	—
187	C₈×C₄₃	—	2	1	no	—
188	C₈×C₄₃	—	4	2	no	—
189	C₈×C₄₃	—	4	2	no	—
190	C₈×C₄₃	#135	1	2	yes	—
191	C₄₃⋊C₈	—	4	1	no	—
192	C₄₃⋊C₈	—	4	1	no	—
193	#19160	—	43	1	no	maximal, Sylow
194	C₂²×C₄₃	—	2	1	no	—
195	C₂²×C₄₃	—	2	1	no	—
196	C₂²×C₄₃	—	2	1	no	—
197	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
198	C₂×D₄₃	—	4	1	no	—
199	C₂×D₄₃	—	4	1	no	—
200	C₂×D₄₃	—	4	1	no	—
201	C₂×D₄₃	—	8	2	no	—
202	C₂×D₄₃	—	8	2	no	—
203	C₂×D₄₃	—	8	2	no	—
204	C₄×C₄₃	—	2	1	no	—
205	C₄×C₄₃	—	2	1	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	#472	1	2	yes	—
208	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
209	C₄×C₄₃	#575	1	2	yes	—
210	C₄×C₄₃	#575	1	1	yes	characteristic
211	Dic₄₃	—	4	1	no	—
212	Dic₄₃	—	4	1	no	—
213	Dic₄₃	—	4	1	no	—
214	Dic₄₃	—	8	2	no	—
215	#3169	—	43	1	no	—
216	#3106	—	43	2	no	—
217	#2965	—	43	1	no	—
218	#1698	—	43	2	no	—
219	#1697	—	43	2	no	—
220	#1696	—	43	1	no	—
221	#1695	—	43	1	no	—
222	#1688	—	43	1	no	—
223	#1687	—	43	1	no	—
224	#1564	D₄₃	1	1	yes	characteristic, complemented
225	#1543	—	43	2	no	—
226	C₂×C₄₃	—	4	1	no	—
227	C₂×C₄₃	#3035	1	1	yes	characteristic
228	C₂×C₄₃	#3054	1	1	yes	characteristic
229	C₂×C₄₃	C₂×#472	1	1	yes	characteristic
230	D₄₃	—	8	1	no	—
231	D₄₃	—	16	2	no	—
232	#532	—	43	2	no	—
233	C₄×#41	—	43	1	no	—
234	#500	—	43	1	no	—
235	#493	—	43	1	no	—
236	#486	—	43	2	no	—
237	#482	—	86	2	no	—
238	#477	—	43	2	no	—
239	#476	—	43	2	no	—
240	#466	—	86	1	no	—
241	#466	—	86	1	no	—
242	#460	—	43	2	no	—
243	#459	—	43	2	no	—
244	#449	—	86	2	no	—
245	#446	—	43	1	no	—
246	#446	—	43	1	no	—
247	C₄×SD₁₆	—	86	2	no	—
248	C₄×D₈	—	86	2	no	—
249	C₄×D₈	—	86	1	no	—
250	C₄×D₈	—	86	1	no	—
251	#436	—	43	1	no	—
252	#436	—	43	1	no	—
253	#435	—	86	1	no	—
254	#435	—	86	1	no	—
255	#431	—	43	1	no	—
256	#431	—	86	1	no	—
257	#431	C₂×D₄₃	1	2	yes	—
258	C₄×M₁₆	—	86	1	no	—
259	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
260	#335	C₂×D₄₃	1	2	yes	—
261	#334	C₂×D₄₃	1	1	yes	characteristic
262	#334	C₂×D₄₃	1	1	yes	characteristic
263	#333	—	43	2	no	—
264	#333	—	43	2	no	—
265	#331	—	43	2	no	—
266	#331	—	43	2	no	—
267	C₄₃	#19160	1	1	yes	characteristic, complemented, Sylow
268	C₂×#41	—	43	1	no	—
269	C₂×#41	—	86	2	no	—
270	C₂×SD₁₆	—	86	2	no	—
271	C₂×D₈	—	86	2	no	—
272	C₂×D₈	—	86	1	no	—
273	C₂×D₈	—	86	1	no	—
274	C₂×M₁₆	—	86	1	no	—
275	C₂×M₁₆	—	86	1	no	—
276	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
277	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
278	C₄⋊Q₈	—	43	2	no	—
279	#127	—	43	2	no	—
280	#124	—	86	2	no	—
281	#121	—	86	2	no	—
282	#121	—	86	2	no	—
283	C₄×Q₈	—	43	1	no	—
284	C₄×Q₈	—	43	1	no	—
285	C₄×D₄	—	43	1	no	—
286	C₄×D₄	—	43	1	no	—
287	C₄×D₄	—	86	1	no	—
288	C₄×D₄	—	86	1	no	—
289	C₄×D₄	—	86	2	no	—
290	C₄×D₄	—	86	2	no	—
291	#117	—	43	1	no	—
292	#117	—	86	1	no	—
293	C₂×C₄²	—	86	1	no	—
294	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
295	#107	—	86	2	no	—
296	#107	—	86	1	no	—
297	#107	—	86	1	no	—
298	#106	—	86	2	no	—
299	C₄⋊C₈	—	43	1	no	—
300	C₄⋊C₈	—	43	1	no	—
301	C₄⋊C₈	—	86	1	no	—
302	C₄⋊C₈	—	86	1	no	—
303	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
304	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
305	#103	—	86	2	no	—
306	#102	—	86	2	no	—
307	#102	—	86	2	no	—
308	#102	—	86	2	no	—
309	#102	—	86	2	no	—
310	#102	—	86	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	C₂²⋊C₈	—	86	1	no	—
313	C₂²⋊C₈	—	86	1	no	—
314	C₂²⋊C₈	—	86	1	no	—
315	#97	—	86	1	no	—
316	#97	—	86	1	no	—
317	C₄×C₈	—	2	2	no	—
318	C₄×C₈	—	86	1	no	—
319	C₄×C₈	D₁₇₂	1	1	yes	characteristic
320	C₄×C₈	D₁₇₂	1	1	yes	characteristic
321	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
322	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
323	#41	—	344	4	no	—
324	#41	—	172	2	no	—
325	C₂×Q₈	—	43	1	no	—
326	C₂×Q₈	—	86	2	no	—
327	C₂×D₄	—	43	1	no	—
328	C₂×D₄	—	86	1	no	—
329	C₂×D₄	—	86	2	no	—
330	C₂×D₄	—	86	2	no	—
331	C₂×D₄	—	86	2	no	—
332	C₂×D₄	—	172	2	no	—
333	C₂²×C₄	—	86	1	no	—
334	C₂²×C₄	—	86	1	no	—
335	C₂²×C₄	—	86	1	no	—
336	C₂²×C₄	—	172	2	no	—
337	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
338	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
339	C₂²×C₄	#10621902	1	1	yes	characteristic
340	SD₁₆	—	172	4	no	—
341	D₈	—	172	2	no	—
342	D₈	—	172	4	no	—
343	D₈	—	172	2	no	—
344	M₁₆	—	172	2	no	—
345	M₁₆	—	172	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	86	1	no	—
351	C₂×C₈	—	86	1	no	—
352	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
353	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
354	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
355	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
356	C₄⋊C₄	—	43	1	no	—
357	C₄⋊C₄	—	43	1	no	—
358	C₄⋊C₄	—	86	1	no	—
359	C₄⋊C₄	—	86	1	no	—
360	C₄⋊C₄	—	86	2	no	—
361	C₄⋊C₄	—	86	2	no	—
362	C₂²⋊C₄	—	86	1	no	—
363	C₂²⋊C₄	—	86	1	no	—
364	C₂²⋊C₄	—	86	1	no	—
365	C₂²⋊C₄	—	172	2	no	—
366	C₂²⋊C₄	—	172	2	no	—
367	C₄²	—	86	1	no	—
368	C₄²	—	86	1	no	—
369	C₄²	—	86	1	no	—
370	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
371	C₄²	D₄×D₄₃	1	1	yes	characteristic
372	C₄²	#10621902	1	1	yes	characteristic
373	C₄²	C₂³×D₄₃	1	1	yes	characteristic
374	C₂³	—	86	1	no	—
375	C₂³	—	172	2	no	—
376	C₂³	#13063300	1	1	yes	characteristic
377	Q₈	—	86	2	no	—
378	Q₈	—	344	2	no	—
379	D₄	—	86	2	no	—
380	D₄	—	344	2	no	—
381	D₄	—	344	4	no	—
382	D₄	—	172	2	no	—
383	D₄	—	172	2	no	—
384	D₄	—	172	2	no	—
385	D₄	—	172	2	no	—
386	D₄	—	172	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	86	1	no	—
392	C₂×C₄	—	86	1	no	—
393	C₂×C₄	—	86	1	no	—
394	C₂×C₄	—	344	4	no	—
395	C₂×C₄	—	172	2	no	—
396	C₂×C₄	—	172	2	no	—
397	C₂×C₄	—	172	1	no	—
398	C₂×C₄	—	172	2	no	—
399	C₂×C₄	—	172	1	no	—
400	C₂×C₄	#13063300	1	1	yes	characteristic
401	C₂×C₄	#13063300	1	1	yes	characteristic
402	C₂×C₄	#13063300	1	1	yes	characteristic
403	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
404	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
405	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
406	C₈	—	2	1	no	—
407	C₈	—	2	1	no	—
408	C₈	—	2	1	no	—
409	C₈	—	4	2	no	—
410	C₈	—	4	2	no	—
411	C₈	—	172	1	no	—
412	C₈	—	172	1	no	—
413	C₈	#13063347	1	2	yes	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	344	2	no	—
418	C₂²	—	344	2	no	—
419	C₂²	—	344	2	no	—
420	C₂²	—	172	1	no	—
421	C₂²	—	172	1	no	—
422	C₂²	—	172	1	no	—
423	C₂²	C₂×#13063300	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	344	2	no	—
428	C₄	—	172	1	no	—
429	C₄	—	172	1	no	—
430	C₄	—	172	1	no	—
431	C₄	#14583170	1	2	yes	—
432	C₄	C₂×#13063347	1	1	yes	characteristic
433	C₄	#14583696	1	2	yes	—
434	C₄	#14583699	1	1	yes	characteristic
435	C₂	—	4	1	no	—
436	C₂	—	344	1	no	—
437	C₂	—	688	2	no	—
438	C₂	#19144052	1	1	yes	characteristic
439	C₂	#19144205	1	1	yes	characteristic
440	C₂	C₂×#14583170	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13063300
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1564	C₂
socle	C₂²×C₄₃	C₂×#121
hypercenter	#1564	D₄₃
hypocenter	C₄₃	#19160
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
1. #19145174	C₂	semidirect
2. #19144656	C₂	semidirect
3. #19143561	C₂	semidirect
4. #19134136	C₂	semidirect
5. #19134129	C₂	semidirect
6. #19134124	C₂	semidirect
7. #19134119	C₂	semidirect
8. #19134080	C₂	semidirect
9. #19134075	C₂	semidirect
10. #19133255	C₂	semidirect
11. C₄₃×#1564	C₂	semidirect
224. #1564	D₄₃	semidirect
267. C₄₃	#19160	semidirect

Maximal subgroups

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

subgroup	index
#19145174	2
#19144656	2
#19143561	2
#19134136	2
#19134129	2
#19134124	2
#19134119	2
#19134080	2
#19134075	2
#19133255	2
C₄₃×#1564	2
#19160	43