Subgroups — #19148555

Order 5504.

1142 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583622	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583614	C₂	1	2	yes	maximal, complemented
3	#14583572	C₂	1	4	yes	maximal, complemented
4	Q₈×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583557	C₂	1	2	yes	maximal, complemented
6	#14583544	C₂	1	2	yes	maximal, complemented
7	#14583542	C₂	1	2	yes	maximal, complemented
8	#14583534	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583518	C₂	1	2	yes	maximal, complemented
10	#14583485	C₂	1	4	yes	maximal, complemented
11	#14583447	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583436	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583431	C₂	1	2	yes	maximal, complemented
14	#124×D₄₃	C₂	1	2	yes	maximal, complemented
15	#14583371	C₂	1	2	yes	maximal, complemented
16	C₄×#10621902	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10621902	C₂²	1	1	yes	characteristic
19	C₂×#10621900	C₂²	1	2	yes	complemented
20	C₂×Q₈×D₄₃	C₂²	1	2	yes	complemented
21	C₂×D₄×D₄₃	C₂²	1	2	yes	—
22	C₂×D₄×D₄₃	C₂²	1	2	yes	—
23	#13063325	C₂²	1	2	yes	complemented
24	#13063325	C₂²	1	1	yes	characteristic, complemented
25	#13063320	C₂²	1	2	yes	complemented
26	#13063320	C₂²	1	4	yes	complemented
27	#13063318	C₂²	1	4	yes	complemented
28	#13063316	C₂²	1	1	yes	characteristic, complemented
29	#13063314	C₂²	1	1	yes	characteristic
30	#13063313	C₂²	1	2	yes	—
31	#13063312	C₂²	1	2	yes	complemented
32	#13063311	C₂²	1	4	yes	complemented
33	#13063311	C₂²	1	4	yes	complemented
34	#13063311	C₂²	1	4	yes	complemented
35	#13063310	C₂²	1	2	yes	complemented
36	#13063309	C₂²	1	4	yes	complemented
37	#13063307	C₂²	1	4	yes	complemented
38	#13063305	C₂²	1	4	yes	complemented
39	#13063305	C₂²	1	2	yes	complemented
40	#13063302	C₂²	1	4	yes	complemented
41	#13063301	C₂²	1	1	yes	characteristic, complemented
42	#13063301	C₂²	1	2	yes	complemented
43	#13063300	C₂²	1	1	yes	characteristic
44	#13063299	C₂²	1	4	yes	complemented
45	#13063298	C₂²	1	4	yes	complemented
46	#13063296	C₂²	1	2	yes	—
47	#13063296	C₂²	1	2	yes	—
48	#13063296	C₂²	1	2	yes	complemented
49	#13063296	C₂²	1	2	yes	complemented
50	#13063295	C₂²	1	4	yes	complemented
51	#13063293	C₂²	1	4	yes	—
52	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
53	C₄×Dic₈₆	C₂²	1	2	yes	complemented
54	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
55	C₄×D₁₇₂	C₂²	1	2	yes	—
56	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
57	C₄×D₁₇₂	C₂²	1	2	yes	complemented
58	C₄×D₁₇₂	C₂²	1	2	yes	complemented
59	D₄×Dic₄₃	C₂²	1	2	yes	complemented
60	D₄×Dic₄₃	C₂²	1	2	yes	complemented
61	#13063287	C₂²	1	1	yes	characteristic
62	#13063287	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
64	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	complemented
65	#13063284	C₂²	1	4	yes	complemented
66	#13063283	C₂²	1	2	yes	complemented
67	#13063283	C₂²	1	1	yes	characteristic, complemented
68	#13063283	C₂²	1	2	yes	complemented
69	#13063282	C₂²	1	2	yes	complemented
70	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	complemented
71	C₂²⋊C₄×D₄₃	C₂²	1	4	yes	complemented
72	C₂²⋊C₄×D₄₃	C₂²	1	4	yes	complemented
73	C₄²×D₄₃	C₂²	1	2	yes	complemented
74	C₄²×D₄₃	C₂²	1	1	yes	characteristic, complemented
75	#127×C₄₃	C₂²	1	1	yes	characteristic
76	#124×C₄₃	C₂²	1	2	yes	complemented
77	#124×C₄₃	C₂²	1	2	yes	complemented
78	#123×C₄₃	C₂²	1	4	yes	complemented
79	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
80	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
82	C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
83	C₂³×D₄₃	C₂³	1	4	yes	—
84	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₄₃	C₂³	1	2	yes	—
87	C₂×D₄×C₄₃	C₂³	1	2	yes	—
88	C₂×D₄×C₄₃	C₂³	1	2	yes	—
89	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
92	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
93	C₂²×Dic₄₃	C₂³	1	4	yes	—
94	#10621902	—	2	4	no	—
95	Q₈×D₄₃	—	4	4	no	—
96	#10621900	—	4	4	no	—
97	D₄×D₄₃	—	2	8	no	—
98	D₄×D₄₃	—	4	4	no	—
99	C₂×D₁₇₂	C₂³	1	2	yes	—
100	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
101	C₂×D₁₇₂	C₂³	1	2	yes	—
102	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₄₃	C₂³	1	2	yes	—
104	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₄₃	C₂³	1	2	yes	—
106	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₄₃	C₂³	1	2	yes	—
108	C₂×C₄×D₄₃	C₂³	1	2	yes	—
109	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
110	C₂×C₄×D₄₃	C₂³	1	4	yes	—
111	C₂×Dic₈₆	C₂³	1	2	yes	—
112	C₂×Dic₈₆	C₂³	1	4	yes	—
113	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
114	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
116	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
118	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
119	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
120	C₄²×C₄₃	C₂³	1	2	yes	—
121	C₄²×C₄₃	C₂³	1	2	yes	—
122	C₄²×C₄₃	C₂³	1	1	yes	characteristic
123	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
124	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
125	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
126	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
128	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
132	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
133	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
134	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
135	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
136	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
137	C₄⋊Dic₄₃	C₂³	1	2	yes	—
138	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₄₃	C₂³	1	2	yes	—
140	C₄⋊Dic₄₃	C₂³	1	2	yes	—
141	C₄⋊Dic₄₃	C₂³	1	4	yes	—
142	C₄⋊Dic₄₃	C₂³	1	2	yes	—
143	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
144	Dic₄₃⋊C₄	C₂³	1	2	yes	—
145	Dic₄₃⋊C₄	C₂³	1	2	yes	—
146	Dic₄₃⋊C₄	C₂³	1	4	yes	—
147	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
148	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
149	C₄×Dic₄₃	C₂³	1	2	yes	—
150	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
151	C₄×Dic₄₃	C₂³	1	2	yes	—
152	C₄×Dic₄₃	C₂³	1	4	yes	—
153	C₂³×C₄₃	C₂⁴	1	4	yes	—
154	C₂²×D₄₃	—	2	8	no	—
155	C₂²×D₄₃	—	4	4	no	—
156	C₂²×D₄₃	—	4	4	no	—
157	C₂²×D₄₃	C₂⁴	1	2	yes	—
158	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
159	C₂²×D₄₃	C₂⁴	1	2	yes	—
160	Q₈×C₄₃	—	2	2	no	—
161	Q₈×C₄₃	—	2	2	no	—
162	D₄×C₄₃	—	2	4	no	—
163	D₄×C₄₃	—	2	4	no	—
164	D₄×C₄₃	—	4	2	no	—
165	C₂×C₄×C₄₃	—	4	4	no	—
166	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
171	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₄₃	—	2	8	no	—
174	C₂²⋊D₄₃	—	4	4	no	—
175	C₂²⋊D₄₃	—	4	4	no	—
176	C₂×Dic₄₃	—	4	4	no	—
177	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
178	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
179	C₂×Dic₄₃	C₂⁴	1	2	yes	—
180	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
181	C₂×Dic₄₃	C₂⁴	1	2	yes	—
182	C₂×Dic₄₃	C₂⁴	1	4	yes	—
183	D₁₇₂	—	2	4	no	—
184	D₁₇₂	—	2	2	no	—
185	D₁₇₂	—	4	2	no	—
186	D₁₇₂	#41	1	4	yes	complemented
187	C₄×D₄₃	—	2	4	no	—
188	C₄×D₄₃	—	2	4	no	—
189	C₄×D₄₃	—	2	2	no	—
190	C₄×D₄₃	—	2	4	no	—
191	C₄×D₄₃	—	2	2	no	—
192	C₄×D₄₃	—	4	2	no	—
193	C₄×D₄₃	—	4	1	no	—
194	C₄×D₄₃	—	4	4	no	—
195	Dic₈₆	—	2	4	no	—
196	Dic₈₆	—	4	4	no	—
197	C₂²×C₄₃	—	2	4	no	—
198	C₂²×C₄₃	—	2	4	no	—
199	C₂²×C₄₃	—	2	4	no	—
200	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
201	C₂×D₄₃	—	2	2	no	—
202	C₂×D₄₃	—	2	2	no	—
203	C₂×D₄₃	—	2	2	no	—
204	C₂×D₄₃	—	2	1	no	—
205	C₂×D₄₃	—	2	2	no	—
206	C₂×D₄₃	—	2	1	no	—
207	C₂×D₄₃	—	2	2	no	—
208	C₂×D₄₃	—	2	1	no	—
209	C₂×D₄₃	—	8	8	no	—
210	C₂×D₄₃	C₂×#41	1	4	yes	—
211	C₄×C₄₃	—	2	2	no	—
212	C₄×C₄₃	—	2	2	no	—
213	C₄×C₄₃	—	2	2	no	—
214	C₄×C₄₃	—	2	1	no	—
215	C₄×C₄₃	—	2	2	no	—
216	C₄×C₄₃	C₂×#41	1	2	yes	—
217	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
218	Dic₄₃	—	2	1	no	—
219	Dic₄₃	—	2	2	no	—
220	Dic₄₃	—	2	4	no	—
221	Dic₄₃	—	2	2	no	—
222	Dic₄₃	—	2	1	no	—
223	Dic₄₃	—	2	1	no	—
224	#3514	—	43	1	no	maximal, Sylow
225	C₂×C₄₃	—	4	4	no	—
226	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
227	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₄₃	#585	1	1	yes	characteristic
229	D₄₃	—	2	4	no	—
230	D₄₃	—	4	1	no	—
231	D₄₃	—	4	2	no	—
232	#559	D₄₃	1	1	yes	characteristic, complemented
233	#556	—	43	1	no	—
234	#555	—	43	2	no	—
235	#551	—	43	4	no	—
236	D₄×Q₈	—	43	1	no	—
237	#548	—	43	2	no	—
238	#546	—	43	2	no	—
239	#546	—	43	2	no	—
240	D₄²	—	43	1	no	—
241	#542	—	43	2	no	—
242	#538	—	43	4	no	—
243	#532	—	43	1	no	—
244	#529	—	43	1	no	—
245	#529	—	43	2	no	—
246	C₂×#124	—	43	2	no	—
247	#518	—	43	2	no	—
248	C₄×#41	—	43	1	no	—
249	C₄₃	#3514	1	1	yes	characteristic, complemented, Sylow
250	C₂×#41	—	43	1	no	—
251	C₂×#41	—	43	2	no	—
252	C₂²×Q₈	—	43	2	no	—
253	C₂²×D₄	—	43	2	no	—
254	C₂²×D₄	—	43	2	no	—
255	C₄⋊Q₈	—	43	1	no	—
256	C₄⋊Q₈	—	43	2	no	—
257	#127	C₂×D₄₃	1	1	yes	characteristic
258	#126	—	43	2	no	—
259	#126	—	43	4	no	—
260	#126	—	43	4	no	—
261	#125	—	43	1	no	—
262	#124	—	43	1	no	—
263	#124	—	43	2	no	—
264	#124	—	43	4	no	—
265	#124	—	43	4	no	—
266	#124	—	43	4	no	—
267	#124	—	43	2	no	—
268	#124	C₂×D₄₃	1	2	yes	complemented
269	#124	C₂×D₄₃	1	2	yes	complemented
270	#123	—	43	2	no	—
271	#123	—	43	4	no	—
272	#123	—	43	4	no	—
273	#123	C₂×D₄₃	1	4	yes	complemented
274	C₂²⋊Q₈	—	43	1	no	—
275	C₂²⋊Q₈	—	43	2	no	—
276	C₂²⋊Q₈	—	43	2	no	—
277	C₂²⋊Q₈	—	43	4	no	—
278	C₂²⋊Q₈	—	43	4	no	—
279	#121	—	43	2	no	—
280	#121	—	43	2	no	—
281	#121	—	43	2	no	—
282	#121	—	43	2	no	—
283	#121	—	43	4	no	—
284	#121	—	43	1	no	—
285	#121	—	43	4	no	—
286	#120	—	43	4	no	—
287	#120	—	43	4	no	—
288	C₄×Q₈	—	43	1	no	—
289	C₄×Q₈	—	43	2	no	—
290	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
291	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
292	C₄×D₄	—	43	2	no	—
293	C₄×D₄	—	43	2	no	—
294	C₄×D₄	—	43	4	no	—
295	C₄×D₄	—	43	1	no	—
296	C₄×D₄	—	43	2	no	—
297	C₄×D₄	—	43	4	no	—
298	C₄×D₄	—	43	1	no	—
299	C₄×D₄	—	43	2	no	—
300	C₄×D₄	—	43	2	no	—
301	C₄×D₄	—	43	1	no	—
302	C₄×D₄	—	43	2	no	—
303	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
304	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
305	#117	—	43	4	no	—
306	#117	—	43	2	no	—
307	#117	—	43	1	no	—
308	#117	—	43	2	no	—
309	#117	—	43	2	no	—
310	C₂×C₂²⋊C₄	—	43	4	no	—
311	C₂×C₂²⋊C₄	—	43	4	no	—
312	C₂×C₂²⋊C₄	—	43	4	no	—
313	C₂×C₄²	—	43	2	no	—
314	C₂×C₄²	—	43	1	no	—
315	C₂⁴	—	43	4	no	—
316	#41	—	86	4	no	—
317	#41	—	172	4	no	—
318	C₂×Q₈	—	43	2	no	—
319	C₂×Q₈	—	43	4	no	—
320	C₂×Q₈	—	172	4	no	—
321	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
322	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
323	C₂×D₄	—	43	4	no	—
324	C₂×D₄	—	43	4	no	—
325	C₂×D₄	—	43	4	no	—
326	C₂×D₄	—	43	1	no	—
327	C₂×D₄	—	43	2	no	—
328	C₂×D₄	—	43	1	no	—
329	C₂×D₄	—	43	2	no	—
330	C₂×D₄	—	86	8	no	—
331	C₂×D₄	—	172	4	no	—
332	C₂×D₄	C₂²×D₄₃	1	2	yes	—
333	C₂×D₄	C₂²×D₄₃	1	2	yes	—
334	C₂×D₄	C₂²×D₄₃	1	2	yes	—
335	C₂²×C₄	—	43	4	no	—
336	C₂²×C₄	—	43	2	no	—
337	C₂²×C₄	—	43	1	no	—
338	C₂²×C₄	—	43	2	no	—
339	C₂²×C₄	—	43	1	no	—
340	C₂²×C₄	—	43	2	no	—
341	C₂²×C₄	—	43	2	no	—
342	C₂²×C₄	—	43	1	no	—
343	C₂²×C₄	—	43	4	no	—
344	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
345	C₄⋊C₄	—	43	2	no	—
346	C₄⋊C₄	—	43	2	no	—
347	C₄⋊C₄	—	43	2	no	—
348	C₄⋊C₄	—	43	2	no	—
349	C₄⋊C₄	—	43	1	no	—
350	C₄⋊C₄	—	43	2	no	—
351	C₄⋊C₄	—	43	4	no	—
352	C₄⋊C₄	—	43	1	no	—
353	C₄⋊C₄	—	43	2	no	—
354	C₄⋊C₄	—	43	4	no	—
355	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
356	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
357	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
358	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
359	C₂²⋊C₄	—	43	4	no	—
360	C₂²⋊C₄	—	43	4	no	—
361	C₂²⋊C₄	—	43	4	no	—
362	C₂²⋊C₄	—	43	2	no	—
363	C₂²⋊C₄	—	43	2	no	—
364	C₂²⋊C₄	—	43	4	no	—
365	C₂²⋊C₄	—	43	2	no	—
366	C₂²⋊C₄	—	43	2	no	—
367	C₂²⋊C₄	—	43	4	no	—
368	C₂²⋊C₄	—	43	4	no	—
369	C₂²⋊C₄	—	43	2	no	—
370	C₂²⋊C₄	—	43	2	no	—
371	C₂²⋊C₄	—	43	2	no	—
372	C₂²⋊C₄	—	43	2	no	—
373	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
374	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
375	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
376	C₄²	—	43	1	no	—
377	C₄²	—	43	2	no	—
378	C₄²	—	43	1	no	—
379	C₄²	—	43	1	no	—
380	C₄²	—	43	2	no	—
381	C₄²	—	43	4	no	—
382	C₄²	C₂²×D₄₃	1	1	yes	characteristic
383	C₄²	C₂²×D₄₃	1	2	yes	—
384	C₄²	C₂²×D₄₃	1	2	yes	—
385	C₂³	—	43	2	no	—
386	C₂³	—	43	2	no	—
387	C₂³	—	43	1	no	—
388	C₂³	—	86	8	no	—
389	C₂³	—	172	4	no	—
390	C₂³	—	172	4	no	—
391	C₂³	C₂³×D₄₃	1	4	yes	—
392	Q₈	—	2	2	no	—
393	Q₈	—	2	2	no	—
394	Q₈	—	86	4	no	—
395	Q₈	—	172	4	no	—
396	D₄	—	2	4	no	—
397	D₄	—	2	4	no	—
398	D₄	—	4	2	no	—
399	D₄	—	43	4	no	—
400	D₄	—	86	4	no	—
401	D₄	—	86	8	no	—
402	D₄	—	86	2	no	—
403	D₄	—	172	2	no	—
404	D₄	—	172	4	no	—
405	D₄	—	172	4	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	43	1	no	—
408	C₂×C₄	—	43	1	no	—
409	C₂×C₄	—	43	2	no	—
410	C₂×C₄	—	43	1	no	—
411	C₂×C₄	—	43	2	no	—
412	C₂×C₄	—	43	4	no	—
413	C₂×C₄	—	86	4	no	—
414	C₂×C₄	—	86	4	no	—
415	C₂×C₄	—	86	2	no	—
416	C₂×C₄	—	86	4	no	—
417	C₂×C₄	—	86	2	no	—
418	C₂×C₄	—	172	4	no	—
419	C₂×C₄	—	172	2	no	—
420	C₂×C₄	—	172	1	no	—
421	C₂×C₄	—	172	4	no	—
422	C₂×C₄	C₂³×D₄₃	1	2	yes	—
423	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₄₃	1	2	yes	—
425	C₂×C₄	C₂³×D₄₃	1	2	yes	—
426	C₂×C₄	C₂³×D₄₃	1	2	yes	—
427	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
428	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
429	C₂²	—	2	4	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	43	4	no	—
433	C₂²	—	86	2	no	—
434	C₂²	—	86	2	no	—
435	C₂²	—	86	1	no	—
436	C₂²	—	86	2	no	—
437	C₂²	—	86	1	no	—
438	C₂²	—	86	2	no	—
439	C₂²	—	86	1	no	—
440	C₂²	—	86	2	no	—
441	C₂²	—	344	8	no	—
442	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	2	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	1	no	—
448	C₄	—	86	1	no	—
449	C₄	—	86	2	no	—
450	C₄	—	86	1	no	—
451	C₄	—	86	2	no	—
452	C₄	—	86	4	no	—
453	C₄	—	86	1	no	—
454	C₄	#41×D₄₃	1	2	yes	—
455	C₄	#13063371	1	2	yes	—
456	C₂	—	4	4	no	—
457	C₂	—	86	4	no	—
458	C₂	—	172	2	no	—
459	C₂	—	172	1	no	—
460	C₂	C₂×#41×D₄₃	1	1	yes	characteristic
461	C₂	C₂×#13063371	1	1	yes	characteristic
462	C₂	#14583734	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#559	C₂
hypercenter	#559	D₄₃
hypocenter	C₄₃	#3514
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #559

Complements

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

N	H ≅ G/N	type
1. #14583622	C₂	semidirect
2. #14583614	C₂	semidirect
3. #14583572	C₂	semidirect
4. Q₈×D₁₇₂	C₂	semidirect
5. #14583557	C₂	semidirect
6. #14583544	C₂	semidirect
7. #14583542	C₂	semidirect
8. #14583534	C₂	semidirect
9. #14583518	C₂	semidirect
10. #14583485	C₂	semidirect
11. #14583447	C₂	semidirect
12. #14583436	C₂	semidirect
13. #14583431	C₂	semidirect
14. #124×D₄₃	C₂	semidirect
15. #14583371	C₂	semidirect
16. C₄×#10621902	C₂	semidirect
17. C₄₃×#559	C₂	semidirect
19. C₂×#10621900	C₂²	semidirect
20. C₂×Q₈×D₄₃	C₂²	semidirect
23. #13063325	C₂²	semidirect
24. #13063325	C₂²	semidirect
25. #13063320	C₂²	semidirect
26. #13063320	C₂²	semidirect
27. #13063318	C₂²	semidirect
28. #13063316	C₂²	semidirect
31. #13063312	C₂²	semidirect
32. #13063311	C₂²	semidirect
33. #13063311	C₂²	semidirect
34. #13063311	C₂²	semidirect
35. #13063310	C₂²	semidirect
36. #13063309	C₂²	semidirect
37. #13063307	C₂²	semidirect
38. #13063305	C₂²	semidirect
39. #13063305	C₂²	semidirect
40. #13063302	C₂²	semidirect
41. #13063301	C₂²	semidirect
42. #13063301	C₂²	semidirect
44. #13063299	C₂²	semidirect
45. #13063298	C₂²	semidirect
48. #13063296	C₂²	semidirect
49. #13063296	C₂²	semidirect
50. #13063295	C₂²	semidirect
52. Q₈×Dic₄₃	C₂²	semidirect
53. C₄×Dic₈₆	C₂²	semidirect
57. C₄×D₁₇₂	C₂²	semidirect
58. C₄×D₁₇₂	C₂²	semidirect
59. D₄×Dic₄₃	C₂²	semidirect
60. D₄×Dic₄₃	C₂²	semidirect
62. #13063287	C₂²	semidirect
63. C₄×C₂²⋊D₄₃	C₂²	semidirect
64. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
65. #13063284	C₂²	semidirect
66. #13063283	C₂²	semidirect
67. #13063283	C₂²	semidirect
68. #13063283	C₂²	semidirect
69. #13063282	C₂²	semidirect
70. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
71. C₂²⋊C₄×D₄₃	C₂²	semidirect
72. C₂²⋊C₄×D₄₃	C₂²	semidirect
73. C₄²×D₄₃	C₂²	semidirect
74. C₄²×D₄₃	C₂²	semidirect
76. #124×C₄₃	C₂²	semidirect
77. #124×C₄₃	C₂²	semidirect
78. #123×C₄₃	C₂²	semidirect
79. C₄×Q₈×C₄₃	C₂²	semidirect
80. C₄×Q₈×C₄₃	C₂²	semidirect
81. C₄×D₄×C₄₃	C₂²	semidirect
82. C₄×D₄×C₄₃	C₂²	semidirect
186. D₁₇₂	#41	semidirect
232. #559	D₄₃	semidirect
249. C₄₃	#3514	semidirect
268. #124	C₂×D₄₃	semidirect
269. #124	C₂×D₄₃	semidirect
273. #123	C₂×D₄₃	semidirect
290. C₄×Q₈	C₂×D₄₃	semidirect
291. C₄×Q₈	C₂×D₄₃	semidirect
303. C₄×D₄	C₂×D₄₃	semidirect
304. C₄×D₄	C₂×D₄₃	semidirect