Subgroups — #25116293

Order 11008.

722 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#135×Dic₄₃	C₂	1	1	yes	maximal, characteristic
2	#19143257	C₂	1	2	yes	maximal, complemented
3	#19135484	C₂	1	1	yes	maximal, characteristic
4	#19135246	C₂	1	2	yes	maximal, complemented
5	#19135240	C₂	1	2	yes	maximal, complemented
6	#19134765	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134613	C₂	1	2	yes	maximal, complemented
8	#19134477	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134474	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×Dic₄₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1974	C₂	1	1	yes	maximal, characteristic
12	#41×Dic₄₃	C₂²	1	2	yes	—
13	Q₁₆×Dic₄₃	C₄	1	1	yes	characteristic, complemented
14	Q₁₆×Dic₄₃	C₄	1	1	yes	characteristic, complemented
15	SD₁₆×Dic₄₃	C₄	1	2	yes	complemented
16	SD₁₆×Dic₄₃	C₄	1	2	yes	complemented
17	D₈×Dic₄₃	C₄	1	1	yes	characteristic, complemented
18	D₈×Dic₄₃	C₄	1	1	yes	characteristic, complemented
19	#14582957	—	2	2	no	—
20	#14582957	—	2	2	no	—
21	#14582953	—	2	2	no	—
22	#14582949	—	2	2	no	—
23	C₂×#13063261	C₂²	1	1	yes	characteristic
24	C₂×#13063260	C₂²	1	2	yes	—
25	#14582937	C₂²	1	1	yes	characteristic
26	#14582922	C₂²	1	2	yes	—
27	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×#13063252	C₂²	1	2	yes	—
29	#14582895	C₂²	1	2	yes	—
30	#14582866	C₂²	1	2	yes	—
31	#14582857	C₂²	1	2	yes	—
32	#14582854	C₂²	1	2	yes	—
33	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
35	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
36	#14582660	C₂²	1	2	yes	—
37	#14582659	C₂²	1	2	yes	—
38	#14582654	C₂²	1	1	yes	characteristic
39	#14582653	C₂²	1	1	yes	characteristic
40	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
42	C₂×#104×C₄₃	C₂²	1	2	yes	—
43	C₄₃×#408	C₂²	1	2	yes	—
44	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₂×#10621877	C₂³	1	2	yes	—
46	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
48	Q₈×Dic₄₃	C₂×C₄	1	2	yes	—
49	Q₈×Dic₄₃	C₂×C₄	1	2	yes	—
50	D₄×Dic₄₃	—	2	2	no	—
51	D₄×Dic₄₃	—	2	2	no	—
52	D₄×Dic₄₃	C₂×C₄	1	2	yes	—
53	D₄×Dic₄₃	C₂×C₄	1	2	yes	—
54	#13063284	—	2	2	no	—
55	#13063284	C₂³	1	2	yes	—
56	C₂×Dic₄₃⋊C₄	—	2	1	no	—
57	C₂×C₄×Dic₄₃	—	2	2	no	—
58	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
60	#13063261	—	2	2	no	—
61	#13063260	—	4	2	no	—
62	#13063259	C₂×C₄	1	1	yes	characteristic
63	#13063259	C₂×C₄	1	1	yes	characteristic
64	#13063257	C₂×C₄	1	2	yes	—
65	Dic₄₃⋊C₈	—	2	2	no	—
66	Dic₄₃⋊C₈	—	2	2	no	—
67	Dic₄₃⋊C₈	D₄	1	1	yes	characteristic
68	Dic₄₃⋊C₈	D₄	1	1	yes	characteristic
69	Dic₄₃⋊C₈	D₄	1	1	yes	characteristic
70	Dic₄₃⋊C₈	D₄	1	1	yes	characteristic
71	#13063252	—	4	2	no	—
72	#13063249	C₂×C₄	1	2	yes	—
73	#13063249	C₂×C₄	1	2	yes	—
74	#13063246	C₂×C₄	1	2	yes	—
75	#13063246	C₂×C₄	1	2	yes	—
76	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
77	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
78	#13063235	—	2	2	no	—
79	#13063235	—	2	2	no	—
80	C₈×Dic₄₃	—	2	2	no	—
81	C₈×Dic₄₃	—	2	2	no	—
82	C₈×Dic₄₃	—	2	2	no	—
83	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
87	C₄₃⋊#95	—	2	1	no	—
88	C₂×#41×C₄₃	C₂³	1	2	yes	—
89	#135×C₄₃	—	2	2	no	—
90	#135×C₄₃	—	2	2	no	—
91	C₂×Q₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
92	C₂×SD₁₆×C₄₃	C₂×C₄	1	2	yes	—
93	C₂×D₈×C₄₃	C₂×C₄	1	1	yes	characteristic
94	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
95	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
98	#108×C₄₃	—	2	2	no	—
99	#104×C₄₃	—	4	2	no	—
100	C₂²⋊C₈×C₄₃	—	2	2	no	—
101	C₂²⋊C₈×C₄₃	—	2	2	no	—
102	C₄×C₈×C₄₃	—	2	2	no	—
103	#41×C₄₃	—	2	2	no	—
104	#41×C₄₃	—	2	2	no	—
105	#41×C₄₃	—	2	2	no	—
106	#41×C₄₃	—	2	2	no	—
107	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
108	C₂×D₄×C₄₃	—	2	2	no	—
109	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	2	1	no	—
112	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
113	C₂²×Dic₄₃	—	2	2	no	—
114	C₂²×Dic₄₃	—	2	2	no	—
115	C₂²×Dic₄₃	—	2	1	no	—
116	C₂²×Dic₄₃	#41	1	1	yes	characteristic
117	C₂²×Dic₄₃	#41	1	1	yes	characteristic
118	Q₁₆×C₄₃	—	2	2	no	—
119	SD₁₆×C₄₃	—	2	4	no	—
120	D₈×C₄₃	—	2	2	no	—
121	M₁₆×C₄₃	—	2	2	no	—
122	M₁₆×C₄₃	—	2	2	no	—
123	C₂×C₈×C₄₃	—	2	1	no	—
124	C₂×C₈×C₄₃	—	2	1	no	—
125	C₂×C₈×C₄₃	—	2	2	no	—
126	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₄₃	#41	1	2	yes	—
131	C₂×C₈×C₄₃	#41	1	2	yes	—
132	C₄²×C₄₃	—	2	1	no	—
133	C₄²×C₄₃	—	2	1	no	—
134	C₂²⋊Dic₄₃	—	2	2	no	—
135	C₂²⋊Dic₄₃	—	2	2	no	—
136	C₂²⋊Dic₄₃	—	2	2	no	—
137	C₄⋊Dic₄₃	—	2	2	no	—
138	C₄⋊Dic₄₃	—	2	2	no	—
139	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
140	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
141	Dic₄₃⋊C₄	—	2	4	no	—
142	C₄×Dic₄₃	—	2	2	no	—
143	C₄×Dic₄₃	—	2	2	no	—
144	C₄×Dic₄₃	—	2	2	no	—
145	C₄×Dic₄₃	—	2	1	no	—
146	C₄×Dic₄₃	—	2	1	no	—
147	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
151	#10621877	—	2	2	no	—
152	#10621877	—	2	2	no	—
153	C₂×C₄₃⋊C₈	—	2	1	no	—
154	C₂×C₄₃⋊C₈	—	2	1	no	—
155	C₂×C₄₃⋊C₈	—	2	1	no	—
156	C₂×C₄₃⋊C₈	—	2	1	no	—
157	C₂×C₄₃⋊C₈	—	2	2	no	—
158	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
162	C₂³×C₄₃	—	2	2	no	—
163	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
164	Q₈×C₄₃	—	2	2	no	—
165	Q₈×C₄₃	—	2	2	no	—
166	D₄×C₄₃	—	2	2	no	—
167	D₄×C₄₃	—	2	2	no	—
168	D₄×C₄₃	—	4	2	no	—
169	D₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	—	4	1	no	—
174	C₂×C₄×C₄₃	—	4	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
181	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
182	C₂×Dic₄₃	—	2	2	no	—
183	C₂×Dic₄₃	—	2	2	no	—
184	C₂×Dic₄₃	—	2	2	no	—
185	C₂×Dic₄₃	—	2	2	no	—
186	C₂×Dic₄₃	—	4	1	no	—
187	C₂×Dic₄₃	—	4	1	no	—
188	C₂×Dic₄₃	—	4	1	no	—
189	C₂×Dic₄₃	—	4	4	no	—
190	C₂×Dic₄₃	—	8	2	no	—
191	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
192	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
193	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
194	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
195	C₈×C₄₃	—	2	1	no	—
196	C₈×C₄₃	—	2	1	no	—
197	C₈×C₄₃	—	4	2	no	—
198	C₈×C₄₃	#117	1	2	yes	—
199	C₈×C₄₃	#117	1	2	yes	—
200	C₄₃⋊C₈	—	2	1	no	—
201	C₄₃⋊C₈	—	2	1	no	—
202	C₄₃⋊C₈	—	2	1	no	—
203	C₄₃⋊C₈	—	2	1	no	—
204	C₄₃⋊C₈	—	4	2	no	—
205	#22802	—	43	1	no	maximal, Sylow
206	C₂²×C₄₃	—	2	1	no	—
207	C₂²×C₄₃	—	2	1	no	—
208	C₂²×C₄₃	—	4	2	no	—
209	C₂²×C₄₃	—	4	2	no	—
210	C₂²×C₄₃	—	4	2	no	—
211	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
212	C₂²×C₄₃	#555	1	1	yes	characteristic
213	C₂²×C₄₃	#556	1	1	yes	characteristic
214	C₄×C₄₃	—	4	2	no	—
215	C₄×C₄₃	—	4	2	no	—
216	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
217	C₄×C₄₃	#520	1	1	yes	characteristic
218	C₄×C₄₃	#547	1	1	yes	characteristic
219	C₄×C₄₃	#550	1	1	yes	characteristic
220	Dic₄₃	—	2	1	no	—
221	Dic₄₃	—	2	1	no	—
222	Dic₄₃	—	2	1	no	—
223	Dic₄₃	—	4	2	no	—
224	Dic₄₃	—	4	2	no	—
225	Dic₄₃	—	4	2	no	—
226	Dic₄₃	#443	1	2	yes	—
227	C₄×#135	—	43	1	no	—
228	#2925	—	43	2	no	—
229	#1974	—	43	1	no	—
230	#1974	D₄₃	1	1	yes	characteristic
231	#1929	—	43	2	no	—
232	#1929	—	43	2	no	—
233	#1848	—	43	1	no	—
234	#1806	—	43	2	no	—
235	#1772	—	43	1	no	—
236	#1772	—	43	1	no	—
237	C₈×C₄⋊C₄	—	43	1	no	—
238	C₂×C₄₃	—	2	1	no	—
239	C₂×C₄₃	—	2	1	no	—
240	C₂×C₄₃	—	8	2	no	—
241	C₂×C₄₃	#2354	1	1	yes	characteristic
242	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
243	C₂×C₄₃	#2957	1	1	yes	characteristic
244	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
245	C₄×#41	—	43	2	no	—
246	C₄×Q₁₆	—	43	1	no	—
247	C₄×Q₁₆	—	43	1	no	—
248	C₄×SD₁₆	—	43	2	no	—
249	C₄×SD₁₆	—	43	2	no	—
250	C₄×D₈	—	43	1	no	—
251	C₄×D₈	—	43	1	no	—
252	#433	—	86	2	no	—
253	#433	—	86	2	no	—
254	#432	—	86	2	no	—
255	#431	—	86	2	no	—
256	C₂×#108	—	43	1	no	—
257	C₂×#108	—	43	2	no	—
258	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
259	#427	—	43	1	no	—
260	#423	—	43	2	no	—
261	C₂×C₄⋊C₈	—	43	1	no	—
262	C₂×#104	—	43	2	no	—
263	C₂×#104	C₂×D₄₃	1	2	yes	—
264	#416	—	43	2	no	—
265	#408	—	43	2	no	—
266	#408	C₂×D₄₃	1	2	yes	—
267	#405	—	43	2	no	—
268	#405	—	43	2	no	—
269	C₂×C₄×C₈	—	43	1	no	—
270	C₂×C₄×C₈	—	43	1	no	—
271	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
272	C₄×C₄⋊C₄	—	43	1	no	—
273	#339	—	43	2	no	—
274	#339	—	43	2	no	—
275	#336	—	43	1	no	—
276	#336	—	43	1	no	—
277	C₄₃	#22802	1	1	yes	characteristic, complemented, Sylow
278	C₂×#41	C₂²×D₄₃	1	2	yes	—
279	#135	—	2	2	no	—
280	#135	—	2	2	no	—
281	C₂×Q₁₆	C₄×D₄₃	1	1	yes	characteristic
282	C₂×SD₁₆	C₄×D₄₃	1	2	yes	—
283	C₂×D₈	C₄×D₄₃	1	1	yes	characteristic
284	C₂×M₁₆	—	43	2	no	—
285	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
286	C₂²×C₈	—	43	1	no	—
287	C₂²×C₈	—	43	1	no	—
288	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
289	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
290	C₄×Q₈	—	43	2	no	—
291	C₄×Q₈	—	43	2	no	—
292	C₄×D₄	—	43	2	no	—
293	C₄×D₄	—	43	2	no	—
294	C₄×D₄	—	86	2	no	—
295	C₄×D₄	—	86	2	no	—
296	#117	—	43	2	no	—
297	#117	—	86	2	no	—
298	C₂×C₄⋊C₄	—	86	1	no	—
299	C₂×C₄²	—	43	1	no	—
300	C₂×C₄²	—	43	1	no	—
301	C₂×C₄²	—	86	2	no	—
302	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
303	#108	—	2	2	no	—
304	#108	—	86	2	no	—
305	#108	—	172	2	no	—
306	#107	—	43	1	no	—
307	#107	—	43	1	no	—
308	#106	—	43	2	no	—
309	C₄⋊C₈	—	43	1	no	—
310	C₄⋊C₈	—	43	1	no	—
311	C₄⋊C₈	—	43	1	no	—
312	C₄⋊C₈	—	43	1	no	—
313	C₄⋊C₈	—	86	2	no	—
314	C₄⋊C₈	—	86	2	no	—
315	#104	—	4	2	no	—
316	#104	—	172	2	no	—
317	#103	—	43	2	no	—
318	#103	—	43	2	no	—
319	#102	—	43	2	no	—
320	#102	—	43	2	no	—
321	C₂²⋊C₈	—	2	2	no	—
322	C₂²⋊C₈	—	2	2	no	—
323	C₂²⋊C₈	—	86	2	no	—
324	C₂²⋊C₈	—	86	2	no	—
325	#97	—	86	2	no	—
326	#97	—	86	2	no	—
327	C₄×C₈	—	2	2	no	—
328	C₄×C₈	—	43	1	no	—
329	C₄×C₈	—	43	1	no	—
330	C₄×C₈	—	43	1	no	—
331	C₄×C₈	—	43	1	no	—
332	C₄×C₈	—	86	2	no	—
333	C₄×C₈	—	86	2	no	—
334	C₄×C₈	—	86	2	no	—
335	#95	—	86	1	no	—
336	#41	—	2	2	no	—
337	#41	—	2	2	no	—
338	#41	—	2	2	no	—
339	#41	—	2	2	no	—
340	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	43	1	no	—
346	C₂²×C₄	—	43	1	no	—
347	C₂²×C₄	—	86	2	no	—
348	C₂²×C₄	—	86	2	no	—
349	C₂²×C₄	—	86	1	no	—
350	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
351	Q₁₆	—	2	2	no	—
352	SD₁₆	—	2	4	no	—
353	D₈	—	2	2	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	86	2	no	—
357	M₁₆	—	86	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	43	1	no	—
362	C₂×C₈	—	43	1	no	—
363	C₂×C₈	—	43	1	no	—
364	C₂×C₈	—	43	1	no	—
365	C₂×C₈	—	86	1	no	—
366	C₂×C₈	—	86	1	no	—
367	C₂×C₈	—	86	1	no	—
368	C₂×C₈	—	86	1	no	—
369	C₂×C₈	—	86	2	no	—
370	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
371	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
372	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
373	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
374	C₂×C₈	#10621900	1	2	yes	—
375	C₂×C₈	#10621900	1	2	yes	—
376	C₄⋊C₄	—	43	2	no	—
377	C₄⋊C₄	—	43	2	no	—
378	C₄⋊C₄	—	86	2	no	—
379	C₄⋊C₄	—	86	2	no	—
380	C₄⋊C₄	—	86	4	no	—
381	C₂²⋊C₄	—	86	2	no	—
382	C₂²⋊C₄	—	86	2	no	—
383	C₂²⋊C₄	—	86	2	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	43	1	no	—
387	C₄²	—	43	1	no	—
388	C₄²	—	43	1	no	—
389	C₄²	—	43	1	no	—
390	C₄²	—	86	2	no	—
391	C₄²	—	86	2	no	—
392	C₄²	—	86	2	no	—
393	C₄²	—	86	1	no	—
394	C₄²	—	86	1	no	—
395	C₂³	—	2	2	no	—
396	C₂³	#41×D₄₃	1	1	yes	characteristic
397	Q₈	—	2	2	no	—
398	Q₈	—	2	2	no	—
399	D₄	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	43	1	no	—
410	C₂×C₄	—	43	1	no	—
411	C₂×C₄	—	43	1	no	—
412	C₂×C₄	—	43	1	no	—
413	C₂×C₄	—	86	2	no	—
414	C₂×C₄	—	86	2	no	—
415	C₂×C₄	—	86	2	no	—
416	C₂×C₄	—	86	2	no	—
417	C₂×C₄	—	344	2	no	—
418	C₂×C₄	—	172	4	no	—
419	C₂×C₄	—	172	1	no	—
420	C₂×C₄	—	172	1	no	—
421	C₂×C₄	—	172	1	no	—
422	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
423	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
424	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
425	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
426	C₂×C₄	#13063370	1	1	yes	characteristic
427	C₂×C₄	#13063372	1	1	yes	characteristic
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	4	2	no	—
431	C₈	—	86	1	no	—
432	C₈	—	86	1	no	—
433	C₈	—	86	1	no	—
434	C₈	—	86	1	no	—
435	C₈	—	172	2	no	—
436	C₈	#13063281	1	2	yes	—
437	C₈	#13063281	1	2	yes	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
444	C₂²	#14583613	1	1	yes	characteristic
445	C₂²	#14583618	1	1	yes	characteristic
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	43	2	no	—
449	C₄	—	86	1	no	—
450	C₄	—	86	1	no	—
451	C₄	—	86	1	no	—
452	C₄	—	172	2	no	—
453	C₄	—	172	2	no	—
454	C₄	—	172	2	no	—
455	C₄	C₂×#13063281	1	1	yes	characteristic
456	C₄	#14583378	1	1	yes	characteristic
457	C₄	#14583549	1	1	yes	characteristic
458	C₄	#14583569	1	1	yes	characteristic
459	C₂	—	2	1	no	—
460	C₂	—	2	1	no	—
461	C₂	—	8	2	no	—
462	C₂	#19137543	1	1	yes	characteristic
463	C₂	#443×D₄₃	1	1	yes	characteristic
464	C₂	#19143507	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1974	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#135×C₄₃	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1974	D₄₃
hypocenter	C₄₃	#22802
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1974

Complements

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

N	H ≅ G/N	type
2. #19143257	C₂	semidirect
4. #19135246	C₂	semidirect
5. #19135240	C₂	semidirect
6. #19134765	C₂	semidirect
7. #19134613	C₂	semidirect
8. #19134477	C₂	semidirect
9. #19134474	C₂	semidirect
10. C₈×Dic₄₃⋊C₄	C₂	semidirect
13. Q₁₆×Dic₄₃	C₄	semidirect
14. Q₁₆×Dic₄₃	C₄	semidirect
15. SD₁₆×Dic₄₃	C₄	semidirect
16. SD₁₆×Dic₄₃	C₄	semidirect
17. D₈×Dic₄₃	C₄	semidirect
18. D₈×Dic₄₃	C₄	semidirect
277. C₄₃	#22802	semidirect

Maximal subgroups

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

subgroup	index
#135×Dic₄₃	2
#19143257	2
#19135484	2
#19135246	2
#19135240	2
#19134765	2
#19134613	2
#19134477	2
#19134474	2
C₈×Dic₄₃⋊C₄	2
C₄₃×#1974	2
#22802	43