Subgroups — #19148272

Order 5504.

1522 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063373	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#10621902	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₂²⋊D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583561	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583560	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583552	C₂	1	3	yes	maximal, complemented
7	#14583551	C₂	1	3	yes	maximal, complemented
8	#14583545	C₂	1	3	yes	maximal, complemented
9	#14583540	C₂	1	3	yes	maximal, complemented
10	#14583479	C₂	1	3	yes	maximal, complemented
11	#14583474	C₂	1	3	yes	maximal, complemented
12	#14583408	C₂	1	3	yes	maximal, complemented
13	C₂²⋊Q₈×D₄₃	C₂	1	3	yes	maximal, complemented
14	#14583381	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#13063373	—	2	8	no	—
17	C₂×#10621902	—	2	8	no	—
18	C₂×#10621902	C₂²	1	3	yes	—
19	C₂×#10621902	C₂²	1	1	yes	characteristic
20	C₂×#10621902	C₂²	1	3	yes	—
21	C₂×#10621902	C₂²	1	1	yes	characteristic
22	C₂×#10621902	C₂²	1	3	yes	complemented
23	C₂×#10621898	C₂²	1	3	yes	complemented
24	C₂×#10621898	C₂²	1	3	yes	complemented
25	C₂×Q₈×D₄₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₄₃	C₂²	1	3	yes	complemented
27	C₂²×D₁₇₂	C₂²	1	3	yes	—
28	C₂²×C₄×D₄₃	C₂²	1	3	yes	—
29	#13063323	C₂²	1	3	yes	complemented
30	#13063314	C₂²	1	3	yes	complemented
31	#13063313	C₂²	1	3	yes	complemented
32	#13063310	C₂²	1	3	yes	complemented
33	#13063310	C₂²	1	6	yes	complemented
34	#13063310	C₂²	1	6	yes	complemented
35	#13063307	C₂²	1	3	yes	complemented
36	#13063305	C₂²	1	3	yes	complemented
37	#13063304	C₂²	1	3	yes	—
38	#13063303	C₂²	1	6	yes	complemented
39	#13063303	C₂²	1	3	yes	complemented
40	#13063302	C₂²	1	3	yes	—
41	#13063301	C₂²	1	3	yes	complemented
42	#13063301	C₂²	1	3	yes	complemented
43	#13063300	C₂²	1	6	yes	complemented
44	#13063300	C₂²	1	3	yes	complemented
45	#13063299	C₂²	1	3	yes	complemented
46	#13063298	C₂²	1	3	yes	complemented
47	#13063298	C₂²	1	6	yes	complemented
48	#13063297	C₂²	1	1	yes	characteristic
49	#13063295	C₂²	1	3	yes	—
50	#13063293	C₂²	1	3	yes	—
51	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
52	C₄×D₁₇₂	C₂²	1	3	yes	complemented
53	C₄×D₁₇₂	C₂²	1	3	yes	complemented
54	#13063287	C₂²	1	3	yes	complemented
55	C₄×C₂²⋊D₄₃	C₂²	1	3	yes	—
56	C₄×C₂²⋊D₄₃	C₂²	1	3	yes	complemented
57	#13063282	C₂²	1	3	yes	complemented
58	C₄⋊C₄×D₄₃	C₂²	1	6	yes	complemented
59	C₄⋊C₄×D₄₃	C₂²	1	3	yes	complemented
60	C₂²⋊C₄×D₄₃	C₂²	1	6	yes	—
61	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
63	C₄⋊Q₈×C₄₃	C₂²	1	3	yes	complemented
64	C₂²⋊Q₈×C₄₃	C₂²	1	3	yes	—
65	C₂²⋊Q₈×C₄₃	C₂²	1	3	yes	complemented
66	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
67	C₄×D₄×C₄₃	C₂²	1	3	yes	—
68	C₂³×D₄₃	C₂³	1	3	yes	—
69	C₂×Q₈×C₄₃	—	2	4	no	—
70	C₂×Q₈×C₄₃	—	2	4	no	—
71	C₂×Q₈×C₄₃	C₂³	1	3	yes	—
72	C₂×Q₈×C₄₃	C₂³	1	3	yes	—
73	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
74	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
76	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
77	C₂×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₂²⋊D₄₃	C₂³	1	3	yes	—
79	C₂×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₂²⋊D₄₃	C₂³	1	3	yes	—
81	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
82	#10621902	—	2	4	no	—
83	#10621902	—	2	12	no	—
84	#10621902	—	2	12	no	—
85	#10621902	—	2	12	no	—
86	#10621902	D₄	1	8	yes	complemented
87	Q₈×D₄₃	—	2	4	no	—
88	Q₈×D₄₃	—	2	12	no	—
89	#10621898	—	2	12	no	—
90	#10621898	—	2	12	no	—
91	C₂×D₁₇₂	—	2	12	no	—
92	C₂×D₁₇₂	C₂³	1	3	yes	—
93	C₂×D₁₇₂	C₂³	1	6	yes	—
94	C₂×D₁₇₂	C₂³	1	3	yes	—
95	C₂×D₁₇₂	C₂³	1	3	yes	—
96	C₂×D₁₇₂	C₂³	1	3	yes	—
97	C₂×C₄×D₄₃	—	2	12	no	—
98	C₂×C₄×D₄₃	C₂³	1	6	yes	—
99	C₂×C₄×D₄₃	C₂³	1	3	yes	—
100	C₂×C₄×D₄₃	C₂³	1	3	yes	—
101	C₂×C₄×D₄₃	C₂³	1	3	yes	—
102	C₂×C₄×D₄₃	C₂³	1	3	yes	—
103	C₂×C₄×D₄₃	C₂³	1	6	yes	—
104	C₂×C₄×D₄₃	C₂³	1	3	yes	—
105	C₂×Dic₈₆	C₂³	1	3	yes	—
106	C₂×Dic₈₆	C₂³	1	3	yes	—
107	C₄⋊C₄×C₄₃	C₂³	1	3	yes	—
108	C₄⋊C₄×C₄₃	C₂³	1	3	yes	—
109	C₄⋊C₄×C₄₃	C₂³	1	6	yes	—
110	C₂²⋊C₄×C₄₃	C₂³	1	3	yes	—
111	C₂²⋊C₄×C₄₃	C₂³	1	3	yes	—
112	C₄²×C₄₃	C₂³	1	3	yes	—
113	C₂²⋊Dic₄₃	C₂³	1	3	yes	—
114	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
115	(C₂×D₄₃)⋊C₄	C₂³	1	6	yes	—
116	(C₂×D₄₃)⋊C₄	C₂³	1	6	yes	—
117	(C₂×D₄₃)⋊C₄	C₂³	1	3	yes	—
118	(C₂×D₄₃)⋊C₄	C₂³	1	3	yes	—
119	(C₂×D₄₃)⋊C₄	C₂³	1	3	yes	—
120	(C₂×D₄₃)⋊C₄	C₂³	1	3	yes	—
121	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
122	(C₂×D₄₃)⋊C₄	C₂³	1	3	yes	—
123	C₄⋊Dic₄₃	C₂³	1	3	yes	—
124	C₄⋊Dic₄₃	C₂³	1	3	yes	—
125	Dic₄₃⋊C₄	C₂³	1	3	yes	—
126	Dic₄₃⋊C₄	C₂³	1	3	yes	—
127	Dic₄₃⋊C₄	C₂³	1	6	yes	—
128	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
129	Dic₄₃⋊C₄	C₂³	1	3	yes	—
130	C₄×Dic₄₃	C₂³	1	3	yes	—
131	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
132	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
133	C₂²×D₄₃	—	2	6	no	—
134	C₂²×D₄₃	—	2	6	no	—
135	C₂²×D₄₃	—	4	3	no	—
136	C₂²×D₄₃	C₂⁴	1	3	yes	—
137	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
138	C₂²×D₄₃	C₂⁴	1	3	yes	—
139	Q₈×C₄₃	—	2	6	no	—
140	Q₈×C₄₃	—	2	6	no	—
141	Q₈×C₄₃	C₂×D₄	1	4	yes	—
142	D₄×C₄₃	—	2	2	no	—
143	C₂×C₄×C₄₃	—	2	6	no	—
144	C₂×C₄×C₄₃	—	2	6	no	—
145	C₂×C₄×C₄₃	C₂⁴	1	3	yes	—
146	C₂×C₄×C₄₃	C₂⁴	1	3	yes	—
147	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
148	C₂×C₄×C₄₃	C₂⁴	1	3	yes	—
149	C₂×C₄×C₄₃	C₂⁴	1	3	yes	—
150	C₂²⋊D₄₃	—	2	2	no	—
151	C₂²⋊D₄₃	—	2	6	no	—
152	C₂²⋊D₄₃	—	2	2	no	—
153	C₂²⋊D₄₃	—	4	3	no	—
154	C₂×Dic₄₃	—	2	2	no	—
155	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
156	C₂×Dic₄₃	C₂⁴	1	3	yes	—
157	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
158	C₂×Dic₄₃	C₂⁴	1	3	yes	—
159	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
160	D₁₇₂	—	2	12	no	—
161	D₁₇₂	—	2	6	no	—
162	D₁₇₂	—	2	6	no	—
163	D₁₇₂	—	4	3	no	—
164	D₁₇₂	C₂×D₄	1	12	yes	—
165	C₄×D₄₃	—	2	6	no	—
166	C₄×D₄₃	—	2	12	no	—
167	C₄×D₄₃	—	2	6	no	—
168	C₄×D₄₃	—	2	6	no	—
169	C₄×D₄₃	—	2	6	no	—
170	C₄×D₄₃	—	4	6	no	—
171	C₄×D₄₃	C₂×D₄	1	12	yes	—
172	Dic₈₆	—	2	6	no	—
173	Dic₈₆	—	2	6	no	—
174	C₂²×C₄₃	—	2	1	no	—
175	C₂²×C₄₃	—	2	1	no	—
176	C₂²×C₄₃	—	2	1	no	—
177	C₂²×C₄₃	—	2	1	no	—
178	C₂²×C₄₃	—	2	1	no	—
179	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	complemented
180	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
181	C₂×D₄₃	—	2	3	no	—
182	C₂×D₄₃	—	2	3	no	—
183	C₂×D₄₃	—	2	3	no	—
184	C₂×D₄₃	—	2	1	no	—
185	C₂×D₄₃	—	2	3	no	—
186	C₂×D₄₃	—	2	1	no	—
187	C₂×D₄₃	—	2	3	no	—
188	C₂×D₄₃	—	2	1	no	—
189	C₂×D₄₃	—	4	12	no	—
190	C₂×D₄₃	C₂²×D₄	1	6	yes	—
191	C₄×C₄₃	—	2	3	no	—
192	C₄×C₄₃	—	2	3	no	—
193	C₄×C₄₃	—	2	1	no	—
194	C₄×C₄₃	—	2	3	no	—
195	C₄×C₄₃	C₂²×D₄	1	6	yes	—
196	Dic₄₃	—	2	3	no	—
197	Dic₄₃	—	2	1	no	—
198	Dic₄₃	—	2	1	no	—
199	Dic₄₃	—	2	3	no	—
200	Dic₄₃	C₂²×D₄	1	2	yes	—
201	#3489	—	43	1	no	maximal, Sylow
202	C₂×C₄₃	—	2	2	no	—
203	C₂×C₄₃	—	4	1	no	—
204	C₂×C₄₃	C₂³×D₄	1	1	yes	characteristic
205	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
206	C₂×C₄₃	#585	1	1	yes	characteristic
207	D₄₃	—	2	6	no	—
208	D₄₃	—	4	1	no	—
209	D₄₃	—	4	3	no	—
210	C₂×2₋¹⁺⁴	—	43	1	no	—
211	C₂²×#41	—	43	1	no	—
212	D₄×Q₈	—	43	1	no	—
213	D₄×Q₈	D₄₃	1	1	yes	characteristic, complemented
214	#548	—	43	1	no	—
215	#548	—	43	1	no	—
216	#547	—	43	3	no	—
217	#547	—	43	3	no	—
218	#546	—	43	3	no	—
219	#546	—	43	3	no	—
220	#537	—	43	3	no	—
221	#536	—	43	3	no	—
222	#525	—	43	3	no	—
223	C₂×C₂²⋊Q₈	—	43	3	no	—
224	#520	—	43	1	no	—
225	C₄₃	#3489	1	1	yes	characteristic, complemented, Sylow
226	2₋¹⁺⁴	—	86	8	no	—
227	C₂×#41	—	43	1	no	—
228	C₂×#41	—	43	3	no	—
229	C₂×#41	—	43	3	no	—
230	C₂×#41	—	43	3	no	—
231	C₂×#41	—	43	1	no	—
232	C₂×#41	—	43	3	no	—
233	C₂×#41	—	43	3	no	—
234	C₂×#41	—	86	8	no	—
235	C₂²×Q₈	—	43	3	no	—
236	C₂²×Q₈	—	43	1	no	—
237	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
238	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
239	C₂²×D₄	—	43	3	no	—
240	C₂³×C₄	—	43	3	no	—
241	C₄⋊Q₈	—	43	3	no	—
242	C₄⋊Q₈	C₂×D₄₃	1	3	yes	complemented
243	#124	—	43	3	no	—
244	#124	—	43	3	no	—
245	#123	—	43	3	no	—
246	#123	—	43	6	no	—
247	#123	—	43	6	no	—
248	#123	—	43	3	no	—
249	C₂²⋊Q₈	—	43	3	no	—
250	C₂²⋊Q₈	—	43	3	no	—
251	C₂²⋊Q₈	—	43	3	no	—
252	C₂²⋊Q₈	—	43	6	no	—
253	C₂²⋊Q₈	—	43	3	no	—
254	C₂²⋊Q₈	—	43	3	no	—
255	C₂²⋊Q₈	—	43	3	no	—
256	C₂²⋊Q₈	C₂×D₄₃	1	3	yes	—
257	C₂²⋊Q₈	C₂×D₄₃	1	3	yes	complemented
258	#121	—	43	1	no	—
259	#121	—	43	3	no	—
260	#121	—	43	6	no	—
261	#121	—	43	3	no	—
262	#121	—	43	3	no	—
263	#121	—	43	6	no	—
264	#120	—	43	3	no	—
265	#120	—	43	3	no	—
266	C₄×Q₈	—	43	1	no	—
267	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
268	C₄×D₄	—	43	3	no	—
269	C₄×D₄	—	43	3	no	—
270	C₄×D₄	—	43	3	no	—
271	C₄×D₄	—	43	3	no	—
272	C₄×D₄	—	43	3	no	—
273	C₄×D₄	C₂×D₄₃	1	3	yes	—
274	#117	—	43	3	no	—
275	C₂×C₄⋊C₄	—	43	3	no	—
276	C₂×C₄⋊C₄	—	43	6	no	—
277	C₂×C₂²⋊C₄	—	43	6	no	—
278	C₂⁴	—	43	3	no	—
279	#41	—	43	8	no	—
280	#41	—	86	12	no	—
281	#41	—	86	12	no	—
282	#41	—	86	12	no	—
283	#41	—	86	12	no	—
284	#41	—	86	12	no	—
285	#41	—	86	4	no	—
286	C₂×Q₈	—	2	4	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	43	3	no	—
289	C₂×Q₈	—	43	3	no	—
290	C₂×Q₈	—	86	12	no	—
291	C₂×Q₈	—	86	4	no	—
292	C₂×Q₈	C₂²×D₄₃	1	3	yes	—
293	C₂×Q₈	C₂²×D₄₃	1	3	yes	—
294	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
295	C₂×D₄	—	43	1	no	—
296	C₂×D₄	—	43	3	no	—
297	C₂×D₄	—	43	1	no	—
298	C₂×D₄	—	43	3	no	—
299	C₂×D₄	—	43	3	no	—
300	C₂×D₄	—	43	3	no	—
301	C₂×D₄	—	43	6	no	—
302	C₂×D₄	—	43	3	no	—
303	C₂×D₄	—	43	3	no	—
304	C₂×D₄	—	86	12	no	—
305	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
306	C₂²×C₄	—	43	3	no	—
307	C₂²×C₄	—	43	1	no	—
308	C₂²×C₄	—	43	6	no	—
309	C₂²×C₄	—	43	3	no	—
310	C₂²×C₄	—	43	3	no	—
311	C₂²×C₄	—	43	3	no	—
312	C₂²×C₄	—	43	3	no	—
313	C₂²×C₄	—	43	6	no	—
314	C₂²×C₄	—	86	12	no	—
315	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
316	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
317	C₄⋊C₄	—	43	3	no	—
318	C₄⋊C₄	—	43	3	no	—
319	C₄⋊C₄	—	43	3	no	—
320	C₄⋊C₄	—	43	3	no	—
321	C₄⋊C₄	—	43	6	no	—
322	C₄⋊C₄	—	43	1	no	—
323	C₄⋊C₄	—	43	3	no	—
324	C₄⋊C₄	C₂²×D₄₃	1	3	yes	—
325	C₄⋊C₄	C₂²×D₄₃	1	6	yes	—
326	C₄⋊C₄	C₂²×D₄₃	1	3	yes	—
327	C₂²⋊C₄	—	43	3	no	—
328	C₂²⋊C₄	—	43	1	no	—
329	C₂²⋊C₄	—	43	6	no	—
330	C₂²⋊C₄	—	43	6	no	—
331	C₂²⋊C₄	—	43	3	no	—
332	C₂²⋊C₄	—	43	3	no	—
333	C₂²⋊C₄	—	43	1	no	—
334	C₂²⋊C₄	—	43	3	no	—
335	C₂²⋊C₄	—	43	3	no	—
336	C₂²⋊C₄	—	43	3	no	—
337	C₂²⋊C₄	C₂²×D₄₃	1	3	yes	—
338	C₂²⋊C₄	C₂²×D₄₃	1	3	yes	—
339	C₄²	—	43	3	no	—
340	C₄²	C₂²×D₄₃	1	3	yes	—
341	C₂³	—	43	3	no	—
342	C₂³	—	43	3	no	—
343	C₂³	—	43	1	no	—
344	C₂³	—	86	6	no	—
345	C₂³	—	86	6	no	—
346	C₂³	—	172	3	no	—
347	C₂³	C₂³×D₄₃	1	1	yes	characteristic
348	C₂³	C₂³×D₄₃	1	1	yes	characteristic
349	Q₈	—	2	6	no	—
350	Q₈	—	2	6	no	—
351	Q₈	—	86	6	no	—
352	Q₈	—	86	6	no	—
353	Q₈	D₄×D₄₃	1	4	yes	—
354	D₄	—	2	2	no	—
355	D₄	—	43	12	no	—
356	D₄	—	86	12	no	—
357	D₄	—	86	6	no	—
358	D₄	—	86	2	no	—
359	D₄	—	86	6	no	—
360	D₄	—	86	2	no	—
361	D₄	—	86	6	no	—
362	D₄	—	172	3	no	—
363	D₄	—	172	3	no	—
364	C₂×C₄	—	2	6	no	—
365	C₂×C₄	—	2	6	no	—
366	C₂×C₄	—	43	1	no	—
367	C₂×C₄	—	43	12	no	—
368	C₂×C₄	—	43	1	no	—
369	C₂×C₄	—	43	3	no	—
370	C₂×C₄	—	43	3	no	—
371	C₂×C₄	—	43	1	no	—
372	C₂×C₄	—	86	6	no	—
373	C₂×C₄	—	86	6	no	—
374	C₂×C₄	—	86	12	no	—
375	C₂×C₄	—	86	2	no	—
376	C₂×C₄	—	86	6	no	—
377	C₂×C₄	—	86	6	no	—
378	C₂×C₄	—	172	6	no	—
379	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
380	C₂×C₄	C₂³×D₄₃	1	3	yes	—
381	C₂×C₄	C₂³×D₄₃	1	3	yes	—
382	C₂×C₄	C₂³×D₄₃	1	3	yes	—
383	C₂×C₄	C₂³×D₄₃	1	3	yes	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	43	6	no	—
390	C₂²	—	86	3	no	—
391	C₂²	—	86	3	no	—
392	C₂²	—	86	1	no	—
393	C₂²	—	86	3	no	—
394	C₂²	—	86	1	no	—
395	C₂²	—	86	3	no	—
396	C₂²	—	86	1	no	—
397	C₂²	—	86	3	no	—
398	C₂²	—	172	12	no	—
399	C₂²	#13063373	1	2	yes	complemented
400	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
401	C₄	—	2	3	no	—
402	C₄	—	2	3	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	3	no	—
405	C₄	—	43	2	no	—
406	C₄	—	86	1	no	—
407	C₄	—	86	3	no	—
408	C₄	—	86	1	no	—
409	C₄	—	86	3	no	—
410	C₄	C₂×D₄×D₄₃	1	6	yes	—
411	C₂	—	2	2	no	—
412	C₂	—	4	1	no	—
413	C₂	—	86	6	no	—
414	C₂	—	172	3	no	—
415	C₂	—	172	1	no	—
416	C₂	C₂²×D₄×D₄₃	1	1	yes	characteristic
417	C₂	C₂×#13063373	1	1	yes	characteristic
418	C₂	#14583736	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	D₄×Q₈×C₄₃	C₂
hypercenter	D₄×Q₈	D₄₃
hypocenter	C₄₃	#3489
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#13063373	C₂	semidirect
2. C₂²×#10621902	C₂	semidirect
3. Q₈×C₂²⋊D₄₃	C₂	semidirect
4. #14583561	C₂	semidirect
5. #14583560	C₂	semidirect
6. #14583552	C₂	semidirect
7. #14583551	C₂	semidirect
8. #14583545	C₂	semidirect
9. #14583540	C₂	semidirect
10. #14583479	C₂	semidirect
11. #14583474	C₂	semidirect
12. #14583408	C₂	semidirect
13. C₂²⋊Q₈×D₄₃	C₂	semidirect
14. #14583381	C₂	semidirect
15. D₄×Q₈×C₄₃	C₂	semidirect
22. C₂×#10621902	C₂²	semidirect
23. C₂×#10621898	C₂²	semidirect
24. C₂×#10621898	C₂²	semidirect
25. C₂×Q₈×D₄₃	C₂²	semidirect
26. C₂×Q₈×D₄₃	C₂²	semidirect
29. #13063323	C₂²	semidirect
30. #13063314	C₂²	semidirect
31. #13063313	C₂²	semidirect
32. #13063310	C₂²	semidirect
33. #13063310	C₂²	semidirect
34. #13063310	C₂²	semidirect
35. #13063307	C₂²	semidirect
36. #13063305	C₂²	semidirect
38. #13063303	C₂²	semidirect
39. #13063303	C₂²	semidirect
41. #13063301	C₂²	semidirect
42. #13063301	C₂²	semidirect
43. #13063300	C₂²	semidirect
44. #13063300	C₂²	semidirect
45. #13063299	C₂²	semidirect
46. #13063298	C₂²	semidirect
47. #13063298	C₂²	semidirect
51. Q₈×Dic₄₃	C₂²	semidirect
52. C₄×D₁₇₂	C₂²	semidirect
53. C₄×D₁₇₂	C₂²	semidirect
54. #13063287	C₂²	semidirect
56. C₄×C₂²⋊D₄₃	C₂²	semidirect
57. #13063282	C₂²	semidirect
58. C₄⋊C₄×D₄₃	C₂²	semidirect
59. C₄⋊C₄×D₄₃	C₂²	semidirect
62. C₂²×Q₈×C₄₃	C₂²	semidirect
63. C₄⋊Q₈×C₄₃	C₂²	semidirect
65. C₂²⋊Q₈×C₄₃	C₂²	semidirect
66. C₄×Q₈×C₄₃	C₂²	semidirect
86. #10621902	D₄	semidirect
179. C₂²×C₄₃	2₋¹⁺⁴	semidirect
213. D₄×Q₈	D₄₃	semidirect
225. C₄₃	#3489	semidirect
238. C₂²×Q₈	C₂×D₄₃	semidirect
242. C₄⋊Q₈	C₂×D₄₃	semidirect
257. C₂²⋊Q₈	C₂×D₄₃	semidirect
267. C₄×Q₈	C₂×D₄₃	semidirect
399. C₂²	#13063373	semidirect