Subgroups — #25115056

Order 11008.

858 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583022	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583017	C₂	1	1	yes	maximal, characteristic
3	#19143397	C₂	1	1	yes	maximal, characteristic
4	#19143160	C₂	1	2	yes	maximal, complemented
5	#19135348	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135343	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134873	C₂	1	2	yes	maximal, complemented
8	#19134873	C₂	1	2	yes	maximal, complemented
9	#19134770	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134616	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	C₂²	1	1	yes	characteristic
13	C₂×#13063331	C₂²	1	2	yes	—
14	C₂×#13063331	C₂²	1	2	yes	—
15	C₄×#10621898	C₂²	1	2	yes	—
16	#14583022	—	2	4	no	—
17	#14583017	—	2	4	no	—
18	#14583012	C₄	1	2	yes	complemented
19	#14583007	C₄	1	2	yes	complemented
20	#14583001	C₄	1	2	yes	complemented
21	#14583001	C₄	1	2	yes	complemented
22	C₂×#13063261	C₂²	1	1	yes	characteristic
23	C₂×#13063261	C₂²	1	1	yes	characteristic
24	C₂×#13063261	C₂²	1	2	yes	—
25	#14582937	C₂²	1	1	yes	characteristic
26	#14582925	C₂²	1	2	yes	—
27	#14582925	C₂²	1	2	yes	—
28	#14582924	—	2	2	no	—
29	#14582924	—	2	2	no	—
30	#14582923	C₂²	1	2	yes	—
31	#14582921	—	2	2	no	—
32	C₄⋊C₈×D₄₃	—	2	2	no	—
33	C₂×#13063253	C₂²	1	2	yes	—
34	C₂×#13063253	C₂²	1	2	yes	—
35	#14582896	C₂²	1	2	yes	—
36	#14582659	C₂²	1	2	yes	—
37	#14582659	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#336	C₂²	1	1	yes	characteristic
44	C₄₃×#336	C₂²	1	1	yes	characteristic
45	C₂×#10621898	C₂³	1	2	yes	—
46	#13063347	D₄	1	4	yes	—
47	#13063347	Q₈	1	4	yes	—
48	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic
49	C₂×#10621873	C₂×C₄	1	2	yes	—
50	C₂×D₃₄₄	C₂×C₄	1	1	yes	characteristic
51	#13063331	—	2	4	no	—
52	#13063331	—	2	4	no	—
53	#13063331	—	4	2	no	—
54	#13063331	—	4	2	no	—
55	C₂×#10621877	C₂³	1	2	yes	—
56	C₂×#10621877	C₂³	1	2	yes	—
57	C₂×#10621872	—	2	2	no	—
58	C₂×#10621872	—	2	2	no	—
59	C₂×C₈×D₄₃	—	2	2	no	—
60	C₂×C₈×D₄₃	—	2	2	no	—
61	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
62	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
63	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
64	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
65	C₄×C₂²⋊D₄₃	—	2	2	no	—
66	C₄×C₂²⋊D₄₃	—	2	2	no	—
67	#13063284	C₂³	1	2	yes	—
68	#13063282	—	2	2	no	—
69	C₄²×D₄₃	—	2	2	no	—
70	#13063261	—	2	2	no	—
71	#13063261	—	2	2	no	—
72	#13063261	—	4	2	no	—
73	#13063259	C₂×C₄	1	1	yes	characteristic
74	#13063259	C₂×C₄	1	1	yes	characteristic
75	#13063257	C₂×C₄	1	2	yes	—
76	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
77	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
78	Dic₄₃⋊C₈	—	2	2	no	—
79	Dic₄₃⋊C₈	—	2	2	no	—
80	Dic₄₃⋊C₈	—	2	2	no	—
81	Dic₄₃⋊C₈	—	2	2	no	—
82	#13063253	—	2	4	no	—
83	#13063253	—	2	4	no	—
84	#13063250	C₂×C₄	1	2	yes	—
85	#13063250	C₂×C₄	1	2	yes	—
86	#13063247	C₂×C₄	1	2	yes	—
87	#13063247	C₂×C₄	1	2	yes	—
88	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
93	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
97	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
98	#97×C₄₃	—	2	2	no	—
99	#97×C₄₃	C₂×C₄	1	2	yes	—
100	#97×C₄₃	C₂×C₄	1	2	yes	—
101	C₄×C₈×C₄₃	—	2	2	no	—
102	#95×C₄₃	—	2	1	no	—
103	C₂²×C₄×C₄₃	—	2	1	no	—
104	C₂²×C₄×C₄₃	—	2	1	no	—
105	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
108	C₂×C₂²⋊D₄₃	—	2	2	no	—
109	#10621898	—	2	2	no	—
110	#10621898	—	2	2	no	—
111	#10621898	C₂×D₄	1	4	yes	—
112	#10621898	C₂×Q₈	1	4	yes	—
113	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
114	C₂×C₄×D₄₃	—	2	2	no	—
115	C₂×C₄×D₄₃	—	2	2	no	—
116	C₂×C₄×D₄₃	—	2	2	no	—
117	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₃	—	2	1	no	—
119	C₂×C₈×C₄₃	—	2	1	no	—
120	C₂×C₈×C₄₃	—	2	1	no	—
121	C₂×C₈×C₄₃	—	2	1	no	—
122	C₂×C₈×C₄₃	—	2	1	no	—
123	C₂×C₈×C₄₃	—	2	1	no	—
124	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
132	C₄⋊C₄×C₄₃	—	4	2	no	—
133	C₄²×C₄₃	—	2	1	no	—
134	C₄²×C₄₃	—	2	1	no	—
135	C₄²×C₄₃	—	2	1	no	—
136	C₄²×C₄₃	—	2	1	no	—
137	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
138	C₄²×C₄₃	C₂×D₄	1	2	yes	—
139	C₂²⋊Dic₄₃	—	2	2	no	—
140	(C₂×D₄₃)⋊C₄	—	2	2	no	—
141	(C₂×D₄₃)⋊C₄	—	2	2	no	—
142	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
143	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
144	Dic₄₃⋊C₄	—	2	2	no	—
145	Dic₄₃⋊C₄	—	2	2	no	—
146	C₄×Dic₄₃	—	2	2	no	—
147	C₄×Dic₄₃	—	2	2	no	—
148	C₄×Dic₄₃	—	2	2	no	—
149	#10621877	—	2	2	no	—
150	#10621877	—	2	2	no	—
151	#10621877	—	2	2	no	—
152	#10621877	—	2	2	no	—
153	C₂×C₄₃⋊C₈	—	2	2	no	—
154	C₂×C₄₃⋊C₈	—	2	2	no	—
155	Dic₁₇₂	C₄⋊C₄	1	4	yes	complemented
156	D₃₄₄	C₄⋊C₄	1	4	yes	complemented
157	#10621873	C₄⋊C₄	1	8	yes	complemented
158	#10621872	—	4	4	no	—
159	#10621872	—	4	4	no	—
160	C₈×D₄₃	—	4	4	no	—
161	C₈×D₄₃	—	4	4	no	—
162	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
163	C₂²×D₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	4	1	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	—	4	1	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
180	C₂²⋊D₄₃	—	2	4	no	—
181	C₂²⋊D₄₃	—	2	4	no	—
182	C₂×Dic₄₃	—	2	2	no	—
183	C₂×Dic₄₃	—	2	2	no	—
184	C₂×Dic₄₃	—	2	2	no	—
185	D₁₇₂	—	2	2	no	—
186	D₁₇₂	C₂×C₄⋊C₄	1	4	yes	—
187	C₄×D₄₃	—	2	4	no	—
188	C₄×D₄₃	—	2	4	no	—
189	C₄×D₄₃	—	4	4	no	—
190	C₄×D₄₃	—	8	2	no	—
191	Dic₈₆	—	2	2	no	—
192	Dic₈₆	C₂×C₄⋊C₄	1	4	yes	—
193	C₈×C₄₃	—	2	2	no	—
194	C₈×C₄₃	—	2	1	no	—
195	C₈×C₄₃	—	2	2	no	—
196	C₈×C₄₃	—	2	1	no	—
197	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
198	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
199	C₄₃⋊C₈	—	4	2	no	—
200	C₄₃⋊C₈	—	4	2	no	—
201	#22687	—	43	1	no	maximal, Sylow
202	C₂²×C₄₃	—	2	1	no	—
203	C₂²×C₄₃	—	2	1	no	—
204	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂²×C₄₃	#547	1	1	yes	characteristic
206	C₂²×C₄₃	#554	1	1	yes	characteristic
207	C₂×D₄₃	—	2	4	no	—
208	C₂×D₄₃	—	4	2	no	—
209	C₂×D₄₃	—	4	2	no	—
210	C₄×C₄₃	—	2	2	no	—
211	C₄×C₄₃	—	2	2	no	—
212	C₄×C₄₃	—	4	2	no	—
213	C₄×C₄₃	—	8	1	no	—
214	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
215	C₄×C₄₃	#520	1	1	yes	characteristic
216	C₄×C₄₃	D₄²	1	1	yes	characteristic
217	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
218	Dic₄₃	—	2	4	no	—
219	Dic₄₃	—	4	2	no	—
220	Dic₄₃	—	4	2	no	—
221	C₂×#444	—	43	1	no	—
222	C₂×#443	—	43	1	no	—
223	#2943	—	43	1	no	—
224	#2906	—	43	2	no	—
225	#1946	—	43	1	no	—
226	#1945	—	43	1	no	—
227	#1866	—	43	2	no	—
228	#1866	—	43	2	no	—
229	#1849	—	43	1	no	—
230	#1806	—	43	2	no	—
231	#1771	D₄₃	1	1	yes	characteristic, complemented
232	C₂×C₄₃	—	2	1	no	—
233	C₂×C₄₃	—	2	1	no	—
234	C₂×C₄₃	D₄×C₄⋊C₄	1	1	yes	characteristic
235	C₂×C₄₃	#2955	1	1	yes	characteristic
236	C₂×C₄₃	#2956	1	1	yes	characteristic
237	D₄₃	—	4	4	no	—
238	C₂×#135	—	43	1	no	—
239	C₂×#131	—	43	2	no	—
240	C₂×#131	—	43	2	no	—
241	C₄×#41	—	43	2	no	—
242	#444	—	86	4	no	—
243	#443	—	86	4	no	—
244	#442	—	43	2	no	—
245	#441	—	43	2	no	—
246	#440	—	43	2	no	—
247	#440	—	43	2	no	—
248	C₂×#108	—	43	1	no	—
249	C₂×#108	—	43	1	no	—
250	C₂×#108	—	43	2	no	—
251	#427	—	43	1	no	—
252	#424	—	43	2	no	—
253	#424	—	43	2	no	—
254	#424	—	86	2	no	—
255	#424	—	86	2	no	—
256	#423	—	43	2	no	—
257	#423	—	86	2	no	—
258	C₂×C₄⋊C₈	—	86	2	no	—
259	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
260	C₂×#104	—	43	2	no	—
261	C₂×#104	—	43	2	no	—
262	#416	—	43	2	no	—
263	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
264	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
266	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
267	#339	—	43	2	no	—
268	#339	—	43	2	no	—
269	#336	C₂×D₄₃	1	1	yes	characteristic
270	#336	C₂×D₄₃	1	1	yes	characteristic
271	C₄₃	#22687	1	1	yes	characteristic, complemented, Sylow
272	C₂×#41	—	43	2	no	—
273	#135	—	43	4	no	—
274	#135	—	43	4	no	—
275	C₂×Q₁₆	—	43	1	no	—
276	C₂×SD₁₆	—	43	2	no	—
277	C₂×D₈	—	43	1	no	—
278	#131	—	86	4	no	—
279	#131	—	86	4	no	—
280	#131	—	172	2	no	—
281	#131	—	172	2	no	—
282	C₂×M₁₆	—	43	2	no	—
283	C₂×M₁₆	—	43	2	no	—
284	C₂×M₁₆	—	86	2	no	—
285	C₂×M₁₆	—	86	2	no	—
286	C₂²×C₈	—	86	2	no	—
287	C₂²×C₈	—	86	2	no	—
288	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
289	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
290	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
291	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
292	C₄×Q₈	—	43	2	no	—
293	C₄×Q₈	—	43	2	no	—
294	C₄×D₄	—	43	2	no	—
295	C₄×D₄	—	43	2	no	—
296	C₄×D₄	—	86	2	no	—
297	C₄×D₄	—	86	2	no	—
298	#117	—	43	2	no	—
299	#117	—	86	2	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄²	—	86	2	no	—
302	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
303	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
304	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
305	#108	—	86	2	no	—
306	#108	—	86	2	no	—
307	#108	—	172	2	no	—
308	#107	—	43	1	no	—
309	#107	—	43	1	no	—
310	#106	—	43	2	no	—
311	C₄⋊C₈	—	86	2	no	—
312	C₄⋊C₈	—	86	2	no	—
313	C₄⋊C₈	—	86	2	no	—
314	C₄⋊C₈	—	86	2	no	—
315	C₄⋊C₈	—	86	2	no	—
316	C₄⋊C₈	—	86	2	no	—
317	C₄⋊C₈	D₁₇₂	1	2	yes	—
318	C₄⋊C₈	D₁₇₂	1	2	yes	—
319	#104	—	86	4	no	—
320	#104	—	86	4	no	—
321	#103	—	43	2	no	—
322	#103	—	43	2	no	—
323	#102	—	43	2	no	—
324	#102	—	43	2	no	—
325	#97	—	2	2	no	—
326	#97	C₄×D₄₃	1	2	yes	—
327	#97	C₄×D₄₃	1	2	yes	—
328	C₄×C₈	—	2	2	no	—
329	#95	—	2	1	no	—
330	#41	—	43	4	no	—
331	#41	—	43	4	no	—
332	#41	—	86	2	no	—
333	#41	—	86	2	no	—
334	C₂×Q₈	—	43	2	no	—
335	C₂×D₄	—	43	2	no	—
336	C₂×D₄	—	86	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	86	2	no	—
340	C₂²×C₄	—	86	2	no	—
341	C₂²×C₄	—	86	2	no	—
342	C₂²×C₄	#10621898	1	1	yes	characteristic
343	C₂²×C₄	#10621898	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
345	Q₁₆	—	43	4	no	—
346	SD₁₆	—	43	8	no	—
347	D₈	—	43	4	no	—
348	M₁₆	—	86	2	no	—
349	M₁₆	—	86	2	no	—
350	M₁₆	—	86	2	no	—
351	M₁₆	—	86	2	no	—
352	M₁₆	—	172	4	no	—
353	M₁₆	—	172	4	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	86	2	no	—
361	C₂×C₈	—	86	2	no	—
362	C₂×C₈	—	172	4	no	—
363	C₂×C₈	—	172	4	no	—
364	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
365	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
367	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
368	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
369	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
370	C₂×C₈	D₄×D₄₃	1	2	yes	—
371	C₂×C₈	Q₈×D₄₃	1	2	yes	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	43	2	no	—
374	C₄⋊C₄	—	43	2	no	—
375	C₄⋊C₄	—	86	2	no	—
376	C₄⋊C₄	—	86	2	no	—
377	C₂²⋊C₄	—	86	2	no	—
378	C₂²⋊C₄	—	86	2	no	—
379	C₂²⋊C₄	—	86	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	86	2	no	—
385	C₄²	—	86	2	no	—
386	C₄²	—	86	2	no	—
387	C₄²	C₂×C₄×D₄₃	1	2	yes	—
388	C₄²	C₂×D₁₇₂	1	2	yes	—
389	C₂³	—	86	2	no	—
390	C₂³	C₂×#10621898	1	1	yes	characteristic
391	Q₈	—	43	4	no	—
392	Q₈	—	86	2	no	—
393	D₄	—	43	4	no	—
394	D₄	—	86	4	no	—
395	D₄	—	86	4	no	—
396	D₄	—	86	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	86	2	no	—
406	C₂×C₄	—	86	4	no	—
407	C₂×C₄	—	86	4	no	—
408	C₂×C₄	—	86	2	no	—
409	C₂×C₄	—	86	2	no	—
410	C₂×C₄	—	344	2	no	—
411	C₂×C₄	—	172	4	no	—
412	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
413	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
414	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
415	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
417	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
418	C₂×C₄	#13063371	1	1	yes	characteristic
419	C₂×C₄	#13063372	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	2	1	no	—
422	C₈	—	2	2	no	—
423	C₈	—	2	1	no	—
424	C₈	—	172	2	no	—
425	C₈	—	172	2	no	—
426	C₈	C₄⋊C₄×D₄₃	1	2	yes	—
427	C₈	C₄⋊C₄×D₄₃	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	86	4	no	—
431	C₂²	—	172	2	no	—
432	C₂²	—	172	2	no	—
433	C₂²	C₂×C₄×D₁₇₂	1	1	yes	characteristic
434	C₂²	#14583554	1	1	yes	characteristic
435	C₂²	#14583609	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	8	1	no	—
440	C₄	—	86	4	no	—
441	C₄	—	172	2	no	—
442	C₄	—	172	2	no	—
443	C₄	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
444	C₄	#14583379	1	1	yes	characteristic
445	C₄	D₄×D₁₇₂	1	1	yes	characteristic
446	C₄	Q₈×D₁₇₂	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	172	4	no	—
450	C₂	C₄⋊C₄×D₁₇₂	1	1	yes	characteristic
451	C₂	#19143499	1	1	yes	characteristic
452	C₂	#19143506	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1771	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#13063347	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1771	D₄₃
hypocenter	C₄₃	#22687
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #1771

Complements

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

N	H ≅ G/N	type
4. #19143160	C₂	semidirect
5. #19135348	C₂	semidirect
6. #19135343	C₂	semidirect
7. #19134873	C₂	semidirect
8. #19134873	C₂	semidirect
9. #19134770	C₂	semidirect
10. #19134616	C₂	semidirect
11. C₄₃×#1771	C₂	semidirect
18. #14583012	C₄	semidirect
19. #14583007	C₄	semidirect
20. #14583001	C₄	semidirect
21. #14583001	C₄	semidirect
155. Dic₁₇₂	C₄⋊C₄	semidirect
156. D₃₄₄	C₄⋊C₄	semidirect
157. #10621873	C₄⋊C₄	semidirect
231. #1771	D₄₃	semidirect
271. C₄₃	#22687	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583022	2
C₂×#14583017	2
#19143397	2
#19143160	2
#19135348	2
#19135343	2
#19134873	2
#19134770	2
#19134616	2
C₄₃×#1771	2
#22687	43