Subgroups — C₄×#14583018 #25095166

Order 11008.

1022 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583018	C₂	1	2	yes	maximal
2	C₄×#13063345	C₂	1	1	yes	maximal, characteristic
3	C₄×#13063333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#13063332	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#13063260	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134478	C₂	1	2	yes	maximal, complemented
7	#19134440	C₂	1	2	yes	maximal, complemented
8	#19134436	C₂	1	2	yes	maximal, complemented
9	C₄×#13063253	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13063236	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#104×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063345	C₂²	1	1	yes	characteristic
13	C₂×#13063333	C₂²	1	2	yes	—
14	C₂×#13063332	C₂²	1	2	yes	—
15	C₄×#10621898	C₂²	1	1	yes	characteristic
16	#14583018	C₄	1	16	yes	direct product factor
17	C₄×#10621885	C₄	1	2	yes	complemented
18	C₄×#10621884	C₄	1	2	yes	complemented
19	C₄×#10621883	C₄	1	2	yes	complemented
20	C₄×#10621882	C₄	1	2	yes	complemented
21	C₂×#13063260	C₂²	1	2	yes	—
22	#14582935	C₂²	1	1	yes	characteristic
23	C₂×#13063253	C₂²	1	2	yes	—
24	#14582895	C₂²	1	1	yes	characteristic
25	#14582893	C₂²	1	1	yes	characteristic
26	#14582857	C₂²	1	2	yes	—
27	#14582856	—	2	2	no	—
28	#14582855	—	2	2	no	—
29	#14582855	C₂²	1	2	yes	—
30	C₄×#10621877	—	2	1	no	—
31	C₄×#10621877	C₂²	1	1	yes	characteristic
32	C₄×#10621872	—	2	1	no	—
33	C₂×#13063236	C₂²	1	2	yes	—
34	C₂×#13063236	C₂²	1	2	yes	—
35	C₂×C₄×C₄₃⋊C₈	—	2	1	no	—
36	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
38	C₄×C₈×D₄₃	—	2	1	no	—
39	#14582663	C₂²	1	2	yes	—
40	#14582659	C₂²	1	2	yes	—
41	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
42	C₂×#104×C₄₃	C₂²	1	2	yes	—
43	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
44	C₄³×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#339	C₂²	1	2	yes	—
46	C₂×#10621898	C₂³	1	1	yes	characteristic
47	#13063345	C₂×C₄	1	8	yes	—
48	C₂×#10621885	C₂×C₄	1	1	yes	characteristic
49	C₂×#10621883	C₂×C₄	1	1	yes	characteristic
50	C₂×#10621884	C₂×C₄	1	1	yes	characteristic
51	C₂×#10621882	C₂×C₄	1	1	yes	characteristic
52	#13063333	—	2	4	no	—
53	#13063333	C₂×C₄	1	8	yes	complemented
54	#13063332	—	2	4	no	—
55	#13063332	C₂×C₄	1	8	yes	complemented
56	C₂×#10621877	—	2	2	no	—
57	C₂×#10621877	C₂³	1	2	yes	—
58	C₂×#10621872	—	2	2	no	—
59	C₂²×C₄₃⋊C₈	—	2	2	no	—
60	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
63	C₂×C₈×D₄₃	—	2	2	no	—
64	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
65	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
66	C₄×C₂²⋊D₄₃	—	2	2	no	—
67	#13063284	C₂³	1	1	yes	characteristic
68	#13063282	—	2	1	no	—
69	C₄²×D₄₃	—	2	1	no	—
70	#13063260	C₂×C₄	1	8	yes	complemented
71	#13063258	C₂×C₄	1	2	yes	—
72	#13063256	C₂×C₄	1	2	yes	—
73	#13063253	C₂×C₄	1	8	yes	complemented
74	#13063249	C₂×C₄	1	2	yes	—
75	#13063248	C₂×C₄	1	2	yes	—
76	#13063246	C₂×C₄	1	2	yes	—
77	#13063245	C₂×C₄	1	2	yes	—
78	#13063236	—	2	1	no	—
79	#13063236	—	2	2	no	—
80	#13063236	—	2	4	no	—
81	#13063236	C₂×C₄	1	8	yes	complemented
82	#13063235	—	2	2	no	—
83	C₄×C₄₃⋊C₈	—	2	1	no	—
84	C₄×C₄₃⋊C₈	—	2	2	no	—
85	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
86	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
87	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
88	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
89	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
90	C₈×Dic₄₃	—	2	2	no	—
91	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
93	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
94	C₄×D₄×C₄₃	—	2	2	no	—
95	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
96	#117×C₄₃	—	2	1	no	—
97	#117×C₄₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₄₃	—	2	1	no	—
99	C₂×C₄²×C₄₃	—	2	2	no	—
100	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
101	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
102	#104×C₄₃	C₂×C₄	1	8	yes	complemented
103	#97×C₄₃	—	2	1	no	—
104	C₄×C₈×C₄₃	—	2	1	no	—
105	#41×C₄₃	—	2	2	no	—
106	#41×C₄₃	C₂²×C₄	1	4	yes	—
107	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×D₄×C₄₃	—	2	1	no	—
109	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	#41	1	2	yes	—
114	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
115	C₂×C₂²⋊D₄₃	—	2	1	no	—
116	#10621898	—	2	2	no	—
117	#10621898	C₂²×C₄	1	4	yes	—
118	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₄₃	—	2	1	no	—
120	C₂×C₄×D₄₃	—	2	2	no	—
121	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
122	M₁₆×C₄₃	—	2	2	no	—
123	M₁₆×C₄₃	C₂²×C₄	1	4	yes	—
124	C₂×C₈×C₄₃	—	2	2	no	—
125	C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
127	C₂²⋊C₄×C₄₃	—	2	2	no	—
128	C₂²⋊C₄×C₄₃	—	2	1	no	—
129	C₄²×C₄₃	—	2	2	no	—
130	C₄²×C₄₃	—	2	1	no	—
131	C₄²×C₄₃	—	2	2	no	—
132	C₄²×C₄₃	—	4	4	no	—
133	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
134	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
135	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₂²⋊Dic₄₃	—	2	1	no	—
138	#10621885	C₄²	1	4	yes	complemented
139	#10621884	C₄²	1	4	yes	complemented
140	#10621883	C₄²	1	4	yes	complemented
141	#10621882	C₄²	1	4	yes	complemented
142	(C₂×D₄₃)⋊C₄	—	2	2	no	—
143	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
144	Dic₄₃⋊C₄	—	2	2	no	—
145	C₄×Dic₄₃	—	2	2	no	—
146	C₄×Dic₄₃	—	2	1	no	—
147	#10621877	—	2	2	no	—
148	#10621877	—	2	8	no	—
149	#10621877	C₂²×C₄	1	4	yes	—
150	C₂×C₄₃⋊C₈	—	2	2	no	—
151	C₂×C₄₃⋊C₈	—	2	2	no	—
152	C₂×C₄₃⋊C₈	—	2	8	no	—
153	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
154	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
157	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
158	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
159	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
160	C₂×C₄₃⋊C₈	#41	1	4	yes	—
161	#10621872	—	2	8	no	—
162	C₈×D₄₃	—	2	8	no	—
163	C₂³×C₄₃	—	2	1	no	—
164	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
165	C₂²×D₄₃	—	2	1	no	—
166	Q₈×C₄₃	—	2	1	no	—
167	Q₈×C₄₃	C₂×C₄²	1	2	yes	—
168	D₄×C₄₃	—	2	4	no	—
169	D₄×C₄₃	—	2	1	no	—
170	D₄×C₄₃	C₂×C₄²	1	2	yes	—
171	C₂×C₄×C₄₃	—	2	1	no	—
172	C₂×C₄×C₄₃	—	2	4	no	—
173	C₂×C₄×C₄₃	—	2	4	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	2	4	no	—
176	C₂×C₄×C₄₃	—	4	4	no	—
177	C₂×C₄×C₄₃	—	4	4	no	—
178	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
181	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
184	C₂²⋊D₄₃	—	2	4	no	—
185	C₂×Dic₄₃	—	2	1	no	—
186	C₂×Dic₄₃	—	2	2	no	—
187	D₁₇₂	—	2	1	no	—
188	D₁₇₂	C₂×C₄²	1	2	yes	—
189	C₄×D₄₃	—	2	4	no	—
190	C₄×D₄₃	—	4	4	no	—
191	Dic₈₆	—	2	1	no	—
192	Dic₈₆	C₂×C₄²	1	2	yes	—
193	C₈×C₄₃	—	2	4	no	—
194	C₄₃⋊C₈	—	2	4	no	—
195	C₄₃⋊C₈	—	2	2	no	—
196	C₄₃⋊C₈	C₂×C₄²	1	2	yes	—
197	C₄₃⋊C₈	C₂×C₄²	1	2	yes	—
198	C₄₃⋊C₈	C₄×D₄	1	4	yes	—
199	C₄₃⋊C₈	C₄×D₄	1	4	yes	—
200	C₄×#444	—	43	1	no	maximal, Sylow
201	C₂²×C₄₃	—	2	2	no	—
202	C₂²×C₄₃	—	2	2	no	—
203	C₂²×C₄₃	—	4	2	no	—
204	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂²×C₄₃	C₄×#41	1	2	yes	—
206	C₂×D₄₃	—	2	2	no	—
207	C₂×D₄₃	—	4	2	no	—
208	C₄×C₄₃	—	2	2	no	—
209	C₄×C₄₃	—	2	2	no	—
210	C₄×C₄₃	—	4	4	no	—
211	C₄×C₄₃	—	4	2	no	—
212	C₄×C₄₃	#444	1	4	yes	complemented
213	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
214	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
215	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
216	Dic₄₃	—	2	2	no	—
217	Dic₄₃	—	4	2	no	—
218	C₂×#444	—	43	2	no	—
219	C₄×#135	—	43	1	no	—
220	C₄×#131	—	43	1	no	—
221	C₄×#131	—	43	1	no	—
222	C₄×#108	—	43	1	no	—
223	#1773	—	43	2	no	—
224	#1765	—	43	2	no	—
225	#1765	—	43	2	no	—
226	C₄×#104	—	43	1	no	—
227	C₄×#104	D₄₃	1	1	yes	characteristic, complemented
228	C₄×#97	—	43	1	no	—
229	C₂×C₄₃	—	2	2	no	—
230	C₂×C₄₃	—	4	2	no	—
231	C₂×C₄₃	C₄²×D₄	1	1	yes	characteristic
232	C₂×C₄₃	C₂×#444	1	2	yes	—
233	D₄₃	—	4	2	no	—
234	C₂×#135	—	43	1	no	—
235	C₂×#131	—	43	2	no	—
236	C₂×#131	—	43	2	no	—
237	C₄×#41	—	43	1	no	—
238	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
239	#444	—	43	16	no	—
240	C₄×Q₁₆	—	43	2	no	—
241	C₄×SD₁₆	—	43	2	no	—
242	C₄×SD₁₆	—	43	2	no	—
243	C₄×D₈	—	43	2	no	—
244	C₂×#108	—	43	2	no	—
245	#427	—	43	1	no	—
246	C₂×#104	—	43	2	no	—
247	C₂×#104	C₂×D₄₃	1	2	yes	—
248	#416	—	43	1	no	—
249	#416	—	43	1	no	—
250	#405	—	43	2	no	—
251	#405	—	43	2	no	—
252	#405	—	86	2	no	—
253	#405	—	86	2	no	—
254	C₄×M₁₆	—	43	1	no	—
255	C₄×M₁₆	—	86	1	no	—
256	C₄×M₁₆	—	86	1	no	—
257	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
258	C₂×#97	—	43	2	no	—
259	C₂×#97	—	43	2	no	—
260	C₂×C₄×C₈	—	43	1	no	—
261	C₂×C₄×C₈	—	43	1	no	—
262	C₂×C₄×C₈	—	86	1	no	—
263	C₂×C₄×C₈	—	86	1	no	—
264	C₄³	C₂×D₄₃	1	1	yes	characteristic
265	#341	—	43	2	no	—
266	#339	—	43	2	no	—
267	#339	C₂×D₄₃	1	2	yes	—
268	C₄₃	C₄×#444	1	1	yes	characteristic, complemented, Sylow
269	C₂×#41	—	43	1	no	—
270	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
271	#135	—	43	8	no	—
272	C₂×Q₁₆	—	43	1	no	—
273	C₂×SD₁₆	—	43	1	no	—
274	C₂×SD₁₆	—	43	1	no	—
275	C₂×D₈	—	43	1	no	—
276	#131	—	43	8	no	—
277	#131	—	43	8	no	—
278	#131	—	86	4	no	—
279	#131	—	86	4	no	—
280	C₂×M₁₆	—	43	2	no	—
281	C₂×M₁₆	—	86	2	no	—
282	C₂×M₁₆	—	86	2	no	—
283	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
284	C₂²×C₈	—	43	2	no	—
285	C₂²×C₈	—	43	1	no	—
286	C₂²×C₈	—	43	1	no	—
287	C₂²×C₈	—	86	2	no	—
288	C₂²×C₈	—	86	2	no	—
289	C₄×Q₈	—	43	2	no	—
290	C₄×Q₈	C₄×D₄₃	1	2	yes	—
291	C₄×D₄	—	2	2	no	—
292	C₄×D₄	—	43	2	no	—
293	C₄×D₄	—	86	2	no	—
294	C₄×D₄	C₄×D₄₃	1	2	yes	—
295	#117	—	2	1	no	—
296	#117	—	43	1	no	—
297	#117	—	86	1	no	—
298	#117	C₂²×D₄₃	1	1	yes	characteristic
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	—	86	1	no	—
302	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
303	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
304	#108	—	43	8	no	—
305	#107	—	43	2	no	—
306	#106	—	43	2	no	—
307	#104	—	43	8	no	—
308	#104	C₄×D₄₃	1	8	yes	complemented
309	#103	—	43	2	no	—
310	#103	—	43	2	no	—
311	#102	—	43	2	no	—
312	#102	—	43	2	no	—
313	#97	—	2	1	no	—
314	#97	—	43	8	no	—
315	#97	—	86	4	no	—
316	#97	—	86	2	no	—
317	#97	—	86	2	no	—
318	#97	—	86	1	no	—
319	C₄×C₈	—	2	1	no	—
320	C₄×C₈	—	43	2	no	—
321	C₄×C₈	—	43	2	no	—
322	C₄×C₈	—	43	2	no	—
323	C₄×C₈	—	43	1	no	—
324	C₄×C₈	—	43	1	no	—
325	C₄×C₈	—	86	2	no	—
326	C₄×C₈	—	86	2	no	—
327	C₄×C₈	—	86	1	no	—
328	#41	—	2	2	no	—
329	#41	—	43	4	no	—
330	#41	—	86	2	no	—
331	#41	C₂×C₄×D₄₃	1	4	yes	—
332	C₂×Q₈	—	43	1	no	—
333	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	43	1	no	—
336	C₂×D₄	—	86	1	no	—
337	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	86	1	no	—
342	C₂²×C₄	—	86	2	no	—
343	C₂²×C₄	#10621900	1	2	yes	—
344	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
345	Q₁₆	—	43	4	no	—
346	SD₁₆	—	43	4	no	—
347	SD₁₆	—	43	4	no	—
348	D₈	—	43	4	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	43	4	no	—
351	M₁₆	—	86	8	no	—
352	M₁₆	—	86	8	no	—
353	M₁₆	—	86	2	no	—
354	M₁₆	C₂×C₄×D₄₃	1	4	yes	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	43	1	no	—
357	C₂×C₈	—	43	1	no	—
358	C₂×C₈	—	43	4	no	—
359	C₂×C₈	—	43	4	no	—
360	C₂×C₈	—	43	2	no	—
361	C₂×C₈	—	43	2	no	—
362	C₂×C₈	—	43	4	no	—
363	C₂×C₈	—	43	2	no	—
364	C₂×C₈	—	86	8	no	—
365	C₂×C₈	—	86	8	no	—
366	C₂×C₈	—	86	2	no	—
367	C₂×C₈	—	86	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	43	2	no	—
370	C₄⋊C₄	—	86	2	no	—
371	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	86	1	no	—
375	C₂²⋊C₄	—	86	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	4	4	no	—
380	C₄²	—	86	2	no	—
381	C₄²	—	86	1	no	—
382	C₄²	C₂×C₄×D₄₃	1	4	yes	—
383	C₄²	C₂×C₄×D₄₃	1	2	yes	—
384	C₄²	D₄×D₄₃	1	1	yes	characteristic
385	C₄²	D₄×D₄₃	1	1	yes	characteristic
386	C₂³	—	2	1	no	—
387	C₂³	—	86	1	no	—
388	C₂³	C₂×#10621900	1	1	yes	characteristic
389	Q₈	—	2	1	no	—
390	Q₈	—	43	2	no	—
391	Q₈	—	86	1	no	—
392	Q₈	C₄²×D₄₃	1	2	yes	—
393	D₄	—	2	4	no	—
394	D₄	—	2	1	no	—
395	D₄	—	43	2	no	—
396	D₄	—	86	4	no	—
397	D₄	—	86	1	no	—
398	D₄	C₄²×D₄₃	1	2	yes	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	86	1	no	—
407	C₂×C₄	—	86	4	no	—
408	C₂×C₄	—	86	2	no	—
409	C₂×C₄	—	172	4	no	—
410	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
411	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
412	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
413	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
414	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
415	C₂×C₄	#41×D₄₃	1	2	yes	—
416	C₈	—	2	4	no	—
417	C₈	—	43	2	no	—
418	C₈	—	43	2	no	—
419	C₈	—	43	4	no	—
420	C₈	—	43	4	no	—
421	C₈	—	86	4	no	—
422	C₈	—	86	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	86	2	no	—
427	C₂²	—	172	2	no	—
428	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
429	C₂²	C₄×#10621900	1	2	yes	—
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	—	4	4	no	—
433	C₄	—	4	2	no	—
434	C₄	—	86	2	no	—
435	C₄	—	172	2	no	—
436	C₄	#14583018	1	4	yes	direct product factor
437	C₄	C₂×C₄²×D₄₃	1	1	yes	characteristic
438	C₄	C₄×D₄×D₄₃	1	2	yes	—
439	C₄	#14583367	1	1	yes	characteristic
440	C₂	—	2	2	no	—
441	C₂	—	4	2	no	—
442	C₂	—	172	2	no	—
443	C₂	C₄×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
444	C₂	C₂×#14583018	1	2	yes	—

	subgroup	G/H
center	C₄²	D₄×D₄₃
commutator	C₄×C₄₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄×#104×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#13063345	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₄×#104	D₄₃
hypocenter	C₄₃	C₄×#444
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₄×#104

Complements

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

N	H ≅ G/N	type
3. C₄×#13063333	C₂	semidirect
4. C₄×#13063332	C₂	semidirect
5. C₄×#13063260	C₂	semidirect
6. #19134478	C₂	semidirect
7. #19134440	C₂	semidirect
8. #19134436	C₂	semidirect
9. C₄×#13063253	C₂	semidirect
10. C₄×#13063236	C₂	semidirect
11. C₄×#104×C₄₃	C₂	semidirect
16. #14583018	C₄	direct (N × H)
17. C₄×#10621885	C₄	semidirect
18. C₄×#10621884	C₄	semidirect
19. C₄×#10621883	C₄	semidirect
20. C₄×#10621882	C₄	semidirect
53. #13063333	C₂×C₄	semidirect
55. #13063332	C₂×C₄	semidirect
70. #13063260	C₂×C₄	semidirect
73. #13063253	C₂×C₄	semidirect
81. #13063236	C₂×C₄	semidirect
102. #104×C₄₃	C₂×C₄	semidirect
138. #10621885	C₄²	semidirect
139. #10621884	C₄²	semidirect
140. #10621883	C₄²	semidirect
141. #10621882	C₄²	semidirect
212. C₄×C₄₃	#444	semidirect
227. C₄×#104	D₄₃	semidirect
268. C₄₃	C₄×#444	semidirect
308. #104	C₄×D₄₃	semidirect
436. C₄	#14583018	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#14583018	2
C₄×#13063345	2
C₄×#13063333	2
C₄×#13063332	2
C₄×#13063260	2
#19134478	2
#19134440	2
#19134436	2
C₄×#13063253	2
C₄×#13063236	2
C₄×#104×C₄₃	2
C₄×#444	43

Subgroups — C4×#14583018 #25095166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#14583018 #25095166