Subgroups — #25115461

Order 11008.

774 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583026	C₂	1	1	yes	maximal, characteristic
2	#19137554	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic
4	#19135366	C₂	1	2	yes	maximal
5	#19135355	C₂	1	2	yes	maximal
6	#19135354	C₂	1	1	yes	maximal, characteristic
7	#19134760	C₂	1	2	yes	maximal
8	#19134751	C₂	1	1	yes	maximal, characteristic
9	#19134491	C₂	1	2	yes	maximal
10	C₄×#13063258	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1948	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₈₆	—	2	1	no	—
13	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
14	#14583026	C₄	1	8	yes	complemented
15	C₂×#13063259	C₂²	1	2	yes	—
16	C₂×#13063258	C₂²	1	1	yes	characteristic
17	C₂×#13063258	C₂²	1	1	yes	characteristic
18	C₂×#13063256	C₂²	1	2	yes	—
19	C₂×#13063256	C₂²	1	2	yes	—
20	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
21	C₂×#13063235	C₂²	1	2	yes	—
22	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
23	#14582804	—	2	1	no	—
24	#14582797	—	2	1	no	—
25	#14582796	—	2	2	no	—
26	#14582780	—	2	2	no	—
27	#14582769	C₂²	1	1	yes	characteristic
28	#14582768	C₂²	1	2	yes	—
29	#14582764	C₂²	1	2	yes	—
30	C₄⋊C₄×Dic₄₃	—	2	1	no	—
31	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
32	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
33	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
34	#14582662	C₂²	1	2	yes	—
35	#14582661	C₂²	1	1	yes	characteristic
36	#14582661	C₂²	1	1	yes	characteristic
37	C₂×#106×C₄₃	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#384	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
43	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
45	C₄×Dic₈₆	—	4	4	no	—
46	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
47	C₄×Dic₈₆	Q₈	1	4	yes	—
48	C₂×C₄⋊Dic₄₃	—	2	1	no	—
49	C₂×C₄⋊Dic₄₃	—	2	1	no	—
50	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
51	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
52	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
53	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
54	C₂×Dic₄₃⋊C₄	—	2	2	no	—
55	C₂×Dic₄₃⋊C₄	—	2	2	no	—
56	C₂×Dic₄₃⋊C₄	D₄	1	2	yes	—
57	C₂×C₄×Dic₄₃	—	2	1	no	—
58	C₂×C₄×Dic₄₃	—	2	2	no	—
59	C₂×C₄×Dic₄₃	—	2	2	no	—
60	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
61	#13063259	—	4	2	no	—
62	#13063258	—	2	2	no	—
63	#13063258	Q₈	1	4	yes	complemented
64	#13063256	—	2	4	no	—
65	#13063256	—	4	2	no	—
66	Dic₄₃⋊C₈	C₂×C₄	1	8	yes	—
67	#13063235	C₂×C₄	1	8	yes	—
68	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
69	C₄₃⋊#95	—	2	1	no	—
70	C₄₃⋊#95	—	2	2	no	—
71	C₄₃⋊#95	—	2	2	no	—
72	C₄₃⋊#95	—	2	2	no	—
73	C₄₃⋊#95	—	2	2	no	—
74	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	—	2	1	no	—
81	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
82	#106×C₄₃	—	4	2	no	—
83	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
84	#95×C₄₃	—	2	1	no	—
85	C₂²×C₄×C₄₃	—	2	1	no	—
86	C₂²×C₄×C₄₃	—	2	1	no	—
87	C₂²×C₄×C₄₃	—	2	2	no	—
88	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
91	C₂²×Dic₄₃	—	2	1	no	—
92	C₂²×Dic₄₃	—	2	1	no	—
93	C₂²×Dic₄₃	—	2	2	no	—
94	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
95	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
96	C₂×Dic₈₆	—	2	2	no	—
97	C₂×Dic₈₆	—	2	2	no	—
98	C₂×Dic₈₆	C₄⋊C₄	1	4	yes	—
99	C₂×C₈×C₄₃	—	2	2	no	—
100	C₂×C₈×C₄₃	—	2	2	no	—
101	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
102	C₄⋊C₄×C₄₃	—	2	1	no	—
103	C₄⋊C₄×C₄₃	—	2	2	no	—
104	C₄⋊C₄×C₄₃	—	2	1	no	—
105	C₄⋊C₄×C₄₃	—	2	1	no	—
106	C₄⋊C₄×C₄₃	—	2	2	no	—
107	C₄⋊C₄×C₄₃	—	4	2	no	—
108	C₄⋊C₄×C₄₃	—	8	1	no	—
109	C₄⋊C₄×C₄₃	C₂×Q₈	1	2	yes	—
110	C₄²×C₄₃	—	4	2	no	—
111	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
112	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
113	C₄⋊Dic₄₃	—	2	1	no	—
114	C₄⋊Dic₄₃	—	2	2	no	—
115	C₄⋊Dic₄₃	—	2	1	no	—
116	C₄⋊Dic₄₃	—	2	2	no	—
117	C₄⋊Dic₄₃	—	2	1	no	—
118	C₄⋊Dic₄₃	—	4	2	no	—
119	C₄⋊Dic₄₃	—	8	1	no	—
120	C₄⋊Dic₄₃	C₄⋊C₄	1	4	yes	—
121	C₄⋊Dic₄₃	C₂×Q₈	1	2	yes	—
122	Dic₄₃⋊C₄	—	4	4	no	—
123	Dic₄₃⋊C₄	—	8	2	no	—
124	Dic₄₃⋊C₄	C₄⋊C₄	1	8	yes	—
125	C₄×Dic₄₃	—	4	4	no	—
126	C₄×Dic₄₃	—	4	2	no	—
127	C₄×Dic₄₃	—	8	2	no	—
128	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
129	C₄×Dic₄₃	C₂×Q₈	1	4	yes	—
130	C₂×C₄₃⋊C₈	—	2	1	no	—
131	C₂×C₄₃⋊C₈	—	2	1	no	—
132	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
133	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
134	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
135	C₂×C₄₃⋊C₈	#41	1	2	yes	—
136	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₄₃	—	2	1	no	—
138	C₂×C₄×C₄₃	—	2	1	no	—
139	C₂×C₄×C₄₃	—	2	2	no	—
140	C₂×C₄×C₄₃	—	4	1	no	—
141	C₂×C₄×C₄₃	—	4	1	no	—
142	C₂×C₄×C₄₃	—	4	1	no	—
143	C₂×C₄×C₄₃	—	4	2	no	—
144	C₂×C₄×C₄₃	—	4	1	no	—
145	C₂×C₄×C₄₃	—	4	2	no	—
146	C₂×C₄×C₄₃	—	4	2	no	—
147	C₂×C₄×C₄₃	—	4	1	no	—
148	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
149	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
150	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
151	C₂×C₄×C₄₃	#137	1	2	yes	—
152	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
157	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
158	C₂×Dic₄₃	—	2	2	no	—
159	C₂×Dic₄₃	—	2	2	no	—
160	C₂×Dic₄₃	—	2	2	no	—
161	C₂×Dic₄₃	—	2	2	no	—
162	C₂×Dic₄₃	—	2	2	no	—
163	C₂×Dic₄₃	—	4	1	no	—
164	C₂×Dic₄₃	—	4	1	no	—
165	C₂×Dic₄₃	—	4	2	no	—
166	C₂×Dic₄₃	—	4	1	no	—
167	C₂×Dic₄₃	—	4	2	no	—
168	C₂×Dic₄₃	—	4	1	no	—
169	C₂×Dic₄₃	—	4	2	no	—
170	C₂×Dic₄₃	—	4	1	no	—
171	C₂×Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
172	C₂×Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
173	Dic₈₆	—	2	8	no	—
174	C₈×C₄₃	—	2	4	no	—
175	C₄₃⋊C₈	—	2	2	no	—
176	C₄₃⋊C₈	C₄×Q₈	1	4	yes	complemented
177	#22729	—	43	1	no	maximal, Sylow
178	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
179	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
180	C₂²×C₄₃	#550	1	1	yes	characteristic
181	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
183	C₂²×C₄₃	#577	1	1	yes	characteristic
184	C₂²×C₄₃	#577	1	1	yes	characteristic
185	C₄×C₄₃	—	2	2	no	—
186	C₄×C₄₃	—	4	2	no	—
187	C₄×C₄₃	—	8	1	no	—
188	C₄×C₄₃	—	8	2	no	—
189	C₄×C₄₃	#428	1	4	yes	—
190	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
191	C₄×C₄₃	#520	1	1	yes	characteristic
192	C₄×C₄₃	#557	1	1	yes	characteristic
193	C₄×C₄₃	Q₈²	1	1	yes	characteristic
194	Dic₄₃	—	2	4	no	—
195	Dic₄₃	—	2	4	no	—
196	Dic₄₃	—	4	2	no	—
197	Dic₄₃	—	8	2	no	—
198	Dic₄₃	—	8	1	no	—
199	C₂×#446	—	43	1	no	—
200	#2355	—	43	1	no	—
201	Q₈×C₄⋊C₄	—	43	1	no	—
202	#1949	—	43	2	no	—
203	#1948	—	43	2	no	—
204	#1948	D₄₃	1	1	yes	characteristic
205	#1947	—	43	1	no	—
206	#1847	—	43	2	no	—
207	#1844	—	43	1	no	—
208	#1776	—	43	2	no	—
209	C₄×#107	—	43	1	no	—
210	C₂×C₄₃	Q₈×C₄⋊C₄	1	1	yes	characteristic
211	C₂×C₄₃	C₂×#428	1	1	yes	characteristic
212	C₂×C₄₃	#2912	1	1	yes	characteristic
213	C₂×C₄₃	#3384	1	1	yes	characteristic
214	C₂×C₄₃	#3387	1	1	yes	characteristic
215	C₂×C₄₃	#3397	1	1	yes	characteristic
216	C₂×C₄₃	#3400	1	1	yes	characteristic
217	C₂×C₄×Q₈	—	43	1	no	—
218	C₂×C₄×Q₈	—	86	1	no	—
219	#446	—	43	8	no	—
220	C₂×#107	—	43	1	no	—
221	C₂×#107	—	43	1	no	—
222	C₂×#107	—	43	2	no	—
223	C₂×#106	—	43	2	no	—
224	C₂×#106	—	43	2	no	—
225	C₂×#106	C₂×D₄₃	1	2	yes	—
226	C₂×C₄⋊C₈	—	43	2	no	—
227	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
228	C₂×#97	—	43	2	no	—
229	C₂×C₄×C₈	—	43	1	no	—
230	#391	—	86	1	no	—
231	#389	—	86	2	no	—
232	#389	—	86	1	no	—
233	#387	—	86	2	no	—
234	#384	—	43	2	no	—
235	#384	—	43	1	no	—
236	#384	C₂×D₄₃	1	1	yes	characteristic
237	#382	—	43	2	no	—
238	C₄×C₄⋊C₄	—	43	2	no	—
239	C₄×C₄⋊C₄	—	43	2	no	—
240	C₄×C₄⋊C₄	—	43	1	no	—
241	C₄×C₄⋊C₄	—	86	1	no	—
242	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
243	#340	—	43	2	no	—
244	#340	—	43	1	no	—
245	#340	—	43	1	no	—
246	#340	C₂×D₄₃	1	2	yes	—
247	C₄₃	#22729	1	1	yes	characteristic, complemented, Sylow
248	C₂²×Q₈	—	43	1	no	—
249	C₂²×C₈	—	43	1	no	—
250	C₂²×C₈	—	43	1	no	—
251	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
252	C₄×Q₈	—	43	4	no	—
253	C₄×Q₈	—	43	4	no	—
254	C₄×Q₈	—	172	4	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	43	2	no	—
258	C₂×C₄⋊C₄	—	43	1	no	—
259	C₂×C₄⋊C₄	—	43	1	no	—
260	C₂×C₄⋊C₄	—	43	1	no	—
261	C₂×C₄⋊C₄	—	43	2	no	—
262	C₂×C₄⋊C₄	—	86	2	no	—
263	C₂×C₄⋊C₄	—	86	1	no	—
264	C₂×C₄⋊C₄	—	86	2	no	—
265	C₂×C₄⋊C₄	—	86	1	no	—
266	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
268	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	—	43	2	no	—
271	C₂×C₄²	—	86	2	no	—
272	C₂×C₄²	—	86	2	no	—
273	C₂×C₄²	—	86	1	no	—
274	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
275	#107	—	43	4	no	—
276	#107	—	86	2	no	—
277	#107	—	172	2	no	—
278	#106	—	4	2	no	—
279	#106	—	86	4	no	—
280	#106	—	172	2	no	—
281	C₄⋊C₈	—	43	8	no	—
282	C₄⋊C₈	C₄×D₄₃	1	4	yes	—
283	#97	—	43	8	no	—
284	C₄×C₈	—	43	4	no	—
285	#95	—	2	1	no	—
286	#95	—	86	2	no	—
287	#95	—	86	2	no	—
288	#95	—	86	2	no	—
289	#95	—	86	2	no	—
290	#95	—	86	1	no	—
291	C₂×Q₈	—	43	4	no	—
292	C₂×Q₈	—	86	2	no	—
293	C₂×Q₈	—	86	2	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	43	2	no	—
298	C₂²×C₄	—	43	2	no	—
299	C₂²×C₄	—	86	1	no	—
300	C₂²×C₄	—	86	1	no	—
301	C₂²×C₄	—	86	2	no	—
302	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
303	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
304	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	43	2	no	—
308	C₂×C₈	—	43	2	no	—
309	C₂×C₈	—	43	2	no	—
310	C₂×C₈	—	43	2	no	—
311	C₂×C₈	—	86	1	no	—
312	C₂×C₈	—	86	1	no	—
313	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	8	1	no	—
321	C₄⋊C₄	—	43	8	no	—
322	C₄⋊C₄	—	43	4	no	—
323	C₄⋊C₄	—	43	2	no	—
324	C₄⋊C₄	—	86	1	no	—
325	C₄⋊C₄	—	86	2	no	—
326	C₄⋊C₄	—	86	1	no	—
327	C₄⋊C₄	—	86	2	no	—
328	C₄⋊C₄	—	86	1	no	—
329	C₄⋊C₄	—	344	1	no	—
330	C₄⋊C₄	—	344	2	no	—
331	C₄⋊C₄	—	172	4	no	—
332	C₄⋊C₄	—	172	2	no	—
333	C₄⋊C₄	Q₈×D₄₃	1	2	yes	—
334	C₄²	—	4	2	no	—
335	C₄²	—	43	4	no	—
336	C₄²	—	43	4	no	—
337	C₄²	—	344	2	no	—
338	C₄²	—	172	4	no	—
339	C₄²	—	172	2	no	—
340	C₄²	C₂×C₄×D₄₃	1	2	yes	—
341	C₄²	Q₈×D₄₃	1	2	yes	—
342	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
343	Q₈	—	86	8	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	43	4	no	—
356	C₂×C₄	—	43	4	no	—
357	C₂×C₄	—	86	2	no	—
358	C₂×C₄	—	86	2	no	—
359	C₂×C₄	—	86	2	no	—
360	C₂×C₄	—	86	2	no	—
361	C₂×C₄	—	86	2	no	—
362	C₂×C₄	—	172	2	no	—
363	C₂×C₄	—	172	1	no	—
364	C₂×C₄	—	172	2	no	—
365	C₂×C₄	—	172	1	no	—
366	C₂×C₄	—	172	2	no	—
367	C₂×C₄	—	172	1	no	—
368	C₂×C₄	—	172	1	no	—
369	C₂×C₄	—	172	1	no	—
370	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
371	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
372	C₂×C₄	#13063352	1	2	yes	—
373	C₂×C₄	#13063354	1	2	yes	—
374	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
375	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
376	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
377	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
378	C₂×C₄	#13063370	1	1	yes	characteristic
379	C₂×C₄	#13063372	1	1	yes	characteristic
380	C₈	—	2	4	no	—
381	C₈	—	43	4	no	—
382	C₈	—	86	2	no	—
383	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
384	C₂²	#14583562	1	1	yes	characteristic
385	C₂²	#14583567	1	1	yes	characteristic
386	C₂²	C₂×#13063352	1	1	yes	characteristic
387	C₂²	C₂×#13063354	1	1	yes	characteristic
388	C₂²	#14583708	1	1	yes	characteristic
389	C₂²	#14583709	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	8	1	no	—
393	C₄	—	8	2	no	—
394	C₄	—	86	4	no	—
395	C₄	—	86	4	no	—
396	C₄	—	344	2	no	—
397	C₄	—	344	1	no	—
398	C₄	—	172	2	no	—
399	C₄	#14582938	1	4	yes	—
400	C₄	C₄×Q₈×D₄₃	1	1	yes	characteristic
401	C₄	#14583378	1	1	yes	characteristic
402	C₄	#14583626	1	1	yes	characteristic
403	C₄	#14583629	1	1	yes	characteristic
404	C₂	#19137509	1	1	yes	characteristic
405	C₂	C₂×#14582938	1	1	yes	characteristic
406	C₂	#19143189	1	1	yes	characteristic
407	C₂	#19147493	1	1	yes	characteristic
408	C₂	#19147526	1	1	yes	characteristic
409	C₂	#19147614	1	1	yes	characteristic
410	C₂	#19147647	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1948	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1948	D₄₃
hypocenter	C₄₃	#22729
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1948

Complements

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

N	H ≅ G/N	type
14. #14583026	C₄	semidirect
63. #13063258	Q₈	semidirect
176. C₄₃⋊C₈	C₄×Q₈	semidirect
247. C₄₃	#22729	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583026	2
#19137554	2
C₄⋊C₄×Dic₈₆	2
#19135366	2
#19135355	2
#19135354	2
#19134760	2
#19134751	2
#19134491	2
C₄×#13063258	2
C₄₃×#1948	2
#22729	43