Subgroups — #19148935

Order 5504.

1004 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583651	C₂	1	4	yes	maximal, complemented
2	Q₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583614	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583609	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583606	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583591	C₂	1	2	yes	maximal, complemented
7	#14583589	C₂	1	2	yes	maximal, complemented
8	#14583553	C₂	1	2	yes	maximal, complemented
9	#14583549	C₂	1	2	yes	maximal, complemented
10	#14583529	C₂	1	2	yes	maximal, complemented
11	#14583527	C₂	1	2	yes	maximal, complemented
12	#14583520	C₂	1	2	yes	maximal, complemented
13	#14583518	C₂	1	2	yes	maximal, complemented
14	#14583471	C₂	1	4	yes	maximal, complemented
15	C₂×#13063325	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10621900	C₂²	1	4	yes	—
19	C₂²×Dic₈₆	C₂²	1	2	yes	—
20	#13063325	C₂²	1	2	yes	—
21	#13063325	C₂²	1	1	yes	characteristic
22	#13063325	C₂²	1	1	yes	characteristic
23	#13063325	C₂²	1	2	yes	—
24	#13063325	C₂²	1	2	yes	—
25	#13063325	C₂²	1	2	yes	—
26	#13063324	C₂²	1	4	yes	—
27	#13063324	C₂²	1	2	yes	—
28	#13063324	C₂²	1	4	yes	—
29	#13063320	C₂²	1	4	yes	—
30	#13063319	C₂²	1	2	yes	—
31	#13063318	C₂²	1	4	yes	—
32	#13063317	C₂²	1	2	yes	—
33	#13063317	C₂²	1	1	yes	characteristic
34	#13063316	C₂²	1	2	yes	—
35	#13063316	C₂²	1	4	yes	—
36	#13063315	C₂²	1	4	yes	—
37	#13063313	C₂²	1	1	yes	characteristic
38	#13063311	C₂²	1	4	yes	—
39	#13063311	C₂²	1	4	yes	—
40	#13063309	C₂²	1	4	yes	—
41	#13063309	C₂²	1	4	yes	—
42	#13063308	C₂²	1	2	yes	—
43	#13063307	C₂²	1	4	yes	—
44	#13063306	C₂²	1	4	yes	—
45	#13063305	C₂²	1	4	yes	—
46	#13063304	C₂²	1	1	yes	characteristic
47	#13063304	C₂²	1	2	yes	—
48	#13063303	C₂²	1	4	yes	—
49	#13063303	C₂²	1	4	yes	—
50	#13063302	C₂²	1	4	yes	—
51	#13063302	C₂²	1	4	yes	—
52	#13063302	C₂²	1	4	yes	—
53	#13063301	C₂²	1	2	yes	—
54	#13063299	C₂²	1	1	yes	characteristic
55	#13063299	C₂²	1	2	yes	—
56	#13063296	C₂²	1	2	yes	—
57	Q₈×Dic₄₃	C₂²	1	2	yes	—
58	C₄×Dic₈₆	C₂²	1	2	yes	—
59	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
60	C₄×D₁₇₂	C₂²	1	2	yes	—
61	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
62	D₄×Dic₄₃	C₂²	1	2	yes	—
63	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
64	#13063284	C₂²	1	2	yes	—
65	#13063283	C₂²	1	2	yes	—
66	#13063282	C₂²	1	2	yes	—
67	#13063281	C₂²	1	4	yes	—
68	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
69	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
70	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
71	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
72	#126×C₄₃	C₂²	1	2	yes	—
73	#125×C₄₃	C₂²	1	1	yes	characteristic
74	#124×C₄₃	C₂²	1	1	yes	characteristic
75	#123×C₄₃	C₂²	1	2	yes	—
76	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
77	#121×C₄₃	C₂²	1	1	yes	characteristic
78	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
79	C₄×D₄×C₄₃	C₂²	1	2	yes	—
80	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
81	#117×C₄₃	C₂²	1	2	yes	—
82	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
83	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×D₄×C₄₃	C₂³	1	2	yes	—
85	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
90	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
92	C₂²×Dic₄₃	C₂³	1	4	yes	—
93	C₂²×Dic₄₃	C₂³	1	4	yes	—
94	#10621900	—	4	8	no	—
95	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
96	C₂×C₄×D₄₃	C₂³	1	2	yes	—
97	C₂×C₄×D₄₃	C₂³	1	4	yes	—
98	C₂×Dic₈₆	—	4	4	no	—
99	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
100	C₂×Dic₈₆	C₂³	1	2	yes	—
101	C₂×Dic₈₆	C₂³	1	4	yes	—
102	C₂×Dic₈₆	C₂³	1	4	yes	—
103	C₂×Dic₈₆	C₂³	1	2	yes	—
104	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
105	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
106	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
107	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
108	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
109	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
110	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
111	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
112	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
113	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
114	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
115	C₄²×C₄₃	C₂³	1	1	yes	characteristic
116	C₄²×C₄₃	C₂³	1	1	yes	characteristic
117	C₄²×C₄₃	C₂³	1	1	yes	characteristic
118	C₄²×C₄₃	C₂³	1	1	yes	characteristic
119	C₄²×C₄₃	C₂³	1	2	yes	—
120	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
121	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
122	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
123	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
124	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
125	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
126	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
129	C₄⋊Dic₄₃	C₂³	1	2	yes	—
130	C₄⋊Dic₄₃	C₂³	1	2	yes	—
131	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
132	C₄⋊Dic₄₃	C₂³	1	2	yes	—
133	C₄⋊Dic₄₃	C₂³	1	2	yes	—
134	C₄⋊Dic₄₃	C₂³	1	4	yes	—
135	C₄⋊Dic₄₃	C₂³	1	4	yes	—
136	C₄⋊Dic₄₃	C₂³	1	4	yes	—
137	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₄₃	C₂³	1	4	yes	—
139	Dic₄₃⋊C₄	C₂³	1	4	yes	—
140	Dic₄₃⋊C₄	C₂³	1	4	yes	—
141	Dic₄₃⋊C₄	C₂³	1	4	yes	—
142	Dic₄₃⋊C₄	C₂³	1	2	yes	—
143	Dic₄₃⋊C₄	C₂³	1	2	yes	—
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	4	yes	—
148	C₄×Dic₄₃	C₂³	1	4	yes	—
149	C₄×Dic₄₃	C₂³	1	2	yes	—
150	C₂³×C₄₃	C₂⁴	1	2	yes	—
151	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
152	C₂²×D₄₃	C₂⁴	1	2	yes	—
153	Q₈×C₄₃	—	2	2	no	—
154	D₄×C₄₃	—	2	4	no	—
155	D₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	4	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
161	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
162	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
163	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
169	C₂²⋊D₄₃	—	2	4	no	—
170	C₂²⋊D₄₃	—	4	4	no	—
171	C₂×Dic₄₃	—	2	8	no	—
172	C₂×Dic₄₃	—	4	4	no	—
173	C₂×Dic₄₃	C₂⁴	1	2	yes	—
174	C₂×Dic₄₃	C₂⁴	1	2	yes	—
175	C₂×Dic₄₃	C₂⁴	1	4	yes	—
176	C₂×Dic₄₃	C₂⁴	1	2	yes	—
177	C₂×Dic₄₃	C₂⁴	1	4	yes	—
178	D₁₇₂	—	2	2	no	—
179	C₄×D₄₃	—	2	4	no	—
180	C₄×D₄₃	—	4	4	no	—
181	Dic₈₆	—	2	2	no	—
182	Dic₈₆	—	4	2	no	—
183	Dic₈₆	—	4	4	no	—
184	Dic₈₆	—	4	2	no	—
185	Dic₈₆	—	4	4	no	—
186	C₂²×C₄₃	—	2	1	no	—
187	C₂²×C₄₃	—	2	1	no	—
188	C₂²×C₄₃	—	2	2	no	—
189	C₂²×C₄₃	—	2	2	no	—
190	C₂²×C₄₃	—	2	2	no	—
191	C₂²×C₄₃	H(5,𝔽₂)	1	2	yes	—
192	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
193	C₂×D₄₃	—	2	2	no	—
194	C₂×D₄₃	—	2	2	no	—
195	C₂×D₄₃	—	2	2	no	—
196	C₄×C₄₃	—	2	1	no	—
197	C₄×C₄₃	—	2	1	no	—
198	C₄×C₄₃	—	2	2	no	—
199	C₄×C₄₃	—	2	2	no	—
200	C₄×C₄₃	—	2	1	no	—
201	C₄×C₄₃	—	2	1	no	—
202	C₄×C₄₃	—	2	2	no	—
203	C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
204	C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
205	Dic₄₃	—	2	4	no	—
206	Dic₄₃	—	2	4	no	—
207	Dic₄₃	—	2	2	no	—
208	Dic₄₃	—	2	2	no	—
209	Dic₄₃	—	2	2	no	—
210	#3544	—	43	1	no	maximal, Sylow
211	C₂×C₄₃	—	2	2	no	—
212	C₂×C₄₃	—	4	2	no	—
213	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
214	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
215	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
216	D₄₃	—	4	2	no	—
217	#563	—	43	4	no	—
218	Q₈²	—	43	1	no	—
219	#555	—	43	1	no	—
220	#554	—	43	1	no	—
221	#554	—	43	1	no	—
222	#552	—	43	2	no	—
223	#552	—	43	2	no	—
224	#547	—	43	2	no	—
225	#547	—	43	2	no	—
226	#544	—	43	2	no	—
227	#544	—	43	2	no	—
228	#542	—	43	2	no	—
229	#542	—	43	2	no	—
230	#536	—	43	4	no	—
231	C₂×C₄⋊Q₈	—	43	1	no	—
232	#529	—	43	1	no	—
233	#529	D₄₃	1	1	yes	characteristic, complemented
234	C₄₃	#3544	1	1	yes	characteristic, complemented, Sylow
235	C₂×#41	—	43	4	no	—
236	C₂²×Q₈	—	43	2	no	—
237	C₄⋊Q₈	—	43	4	no	—
238	C₄⋊Q₈	—	43	4	no	—
239	C₄⋊Q₈	—	43	2	no	—
240	C₄⋊Q₈	—	43	2	no	—
241	C₄⋊Q₈	—	43	2	no	—
242	C₄⋊Q₈	—	43	1	no	—
243	C₄⋊Q₈	—	43	1	no	—
244	C₄⋊Q₈	—	43	2	no	—
245	C₄⋊Q₈	—	43	2	no	—
246	#126	—	43	4	no	—
247	#126	—	43	4	no	—
248	#126	—	43	2	no	—
249	#126	C₂×D₄₃	1	2	yes	—
250	#125	—	43	2	no	—
251	#125	—	43	4	no	—
252	#125	—	43	4	no	—
253	#125	—	43	1	no	—
254	#125	—	43	2	no	—
255	#125	C₂×D₄₃	1	1	yes	characteristic
256	#124	—	43	4	no	—
257	#124	—	43	4	no	—
258	#124	—	43	1	no	—
259	#124	C₂×D₄₃	1	1	yes	characteristic
260	#123	—	43	4	no	—
261	#123	—	43	2	no	—
262	#123	—	43	4	no	—
263	#123	—	43	4	no	—
264	#123	—	43	4	no	—
265	#123	C₂×D₄₃	1	2	yes	—
266	C₂²⋊Q₈	—	43	2	no	—
267	C₂²⋊Q₈	—	43	1	no	—
268	C₂²⋊Q₈	—	43	2	no	—
269	C₂²⋊Q₈	—	43	4	no	—
270	C₂²⋊Q₈	—	43	4	no	—
271	C₂²⋊Q₈	—	43	4	no	—
272	C₂²⋊Q₈	—	43	4	no	—
273	C₂²⋊Q₈	—	43	4	no	—
274	C₂²⋊Q₈	—	43	4	no	—
275	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
276	#121	—	43	2	no	—
277	#121	—	43	1	no	—
278	#121	—	43	2	no	—
279	#121	C₂×D₄₃	1	1	yes	characteristic
280	C₄×Q₈	—	43	2	no	—
281	C₄×Q₈	—	43	1	no	—
282	C₄×Q₈	—	43	2	no	—
283	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
284	C₄×D₄	—	43	2	no	—
285	C₄×D₄	—	43	2	no	—
286	C₄×D₄	—	43	1	no	—
287	C₄×D₄	—	43	2	no	—
288	C₄×D₄	C₂×D₄₃	1	2	yes	—
289	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
290	#117	—	43	2	no	—
291	#117	—	43	2	no	—
292	#117	—	43	4	no	—
293	#117	—	43	2	no	—
294	#117	C₂×D₄₃	1	2	yes	—
295	C₂×C₄⋊C₄	—	43	2	no	—
296	C₂×C₄⋊C₄	—	43	2	no	—
297	C₂×C₄⋊C₄	—	43	2	no	—
298	C₂×C₄⋊C₄	—	43	2	no	—
299	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
300	#41	—	172	8	no	—
301	C₂×Q₈	—	43	1	no	—
302	C₂×Q₈	—	43	2	no	—
303	C₂×Q₈	—	43	4	no	—
304	C₂×Q₈	—	43	4	no	—
305	C₂×Q₈	—	43	2	no	—
306	C₂×Q₈	—	172	4	no	—
307	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
308	C₂×D₄	—	43	2	no	—
309	C₂×D₄	—	43	4	no	—
310	C₂×D₄	—	43	1	no	—
311	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
312	C₂×D₄	C₂²×D₄₃	1	2	yes	—
313	C₂²×C₄	—	43	4	no	—
314	C₂²×C₄	—	43	4	no	—
315	C₂²×C₄	—	43	2	no	—
316	C₂²×C₄	—	43	4	no	—
317	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
318	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
321	C₄⋊C₄	—	43	2	no	—
322	C₄⋊C₄	—	43	2	no	—
323	C₄⋊C₄	—	43	1	no	—
324	C₄⋊C₄	—	43	2	no	—
325	C₄⋊C₄	—	43	2	no	—
326	C₄⋊C₄	—	43	4	no	—
327	C₄⋊C₄	—	43	4	no	—
328	C₄⋊C₄	—	43	4	no	—
329	C₄⋊C₄	—	43	4	no	—
330	C₄⋊C₄	—	43	1	no	—
331	C₄⋊C₄	—	43	4	no	—
332	C₄⋊C₄	—	43	4	no	—
333	C₄⋊C₄	—	43	2	no	—
334	C₄⋊C₄	—	43	2	no	—
335	C₄⋊C₄	—	43	2	no	—
336	C₄⋊C₄	—	43	2	no	—
337	C₄⋊C₄	—	43	4	no	—
338	C₄⋊C₄	—	43	4	no	—
339	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
340	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
341	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
342	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
343	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
344	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
345	C₂²⋊C₄	—	43	2	no	—
346	C₂²⋊C₄	—	43	4	no	—
347	C₂²⋊C₄	—	43	4	no	—
348	C₂²⋊C₄	—	43	2	no	—
349	C₂²⋊C₄	—	43	4	no	—
350	C₂²⋊C₄	—	43	2	no	—
351	C₂²⋊C₄	—	43	4	no	—
352	C₂²⋊C₄	—	43	2	no	—
353	C₂²⋊C₄	—	43	2	no	—
354	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
355	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
356	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
357	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
358	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
359	C₄²	—	43	4	no	—
360	C₄²	—	43	2	no	—
361	C₄²	—	43	4	no	—
362	C₄²	C₂²×D₄₃	1	1	yes	characteristic
363	C₄²	C₂²×D₄₃	1	1	yes	characteristic
364	C₄²	C₂²×D₄₃	1	1	yes	characteristic
365	C₄²	C₂²×D₄₃	1	1	yes	characteristic
366	C₄²	C₂²×D₄₃	1	2	yes	—
367	C₂³	—	43	2	no	—
368	C₂³	C₂³×D₄₃	1	2	yes	—
369	C₂³	C₂³×D₄₃	1	1	yes	characteristic
370	Q₈	—	2	2	no	—
371	Q₈	—	86	2	no	—
372	Q₈	—	172	2	no	—
373	Q₈	—	172	4	no	—
374	Q₈	—	172	2	no	—
375	Q₈	—	172	4	no	—
376	D₄	—	2	4	no	—
377	D₄	—	2	2	no	—
378	D₄	—	86	4	no	—
379	D₄	—	86	2	no	—
380	D₄	—	172	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	43	2	no	—
386	C₂×C₄	—	43	2	no	—
387	C₂×C₄	—	43	4	no	—
388	C₂×C₄	—	43	2	no	—
389	C₂×C₄	—	43	4	no	—
390	C₂×C₄	—	86	8	no	—
391	C₂×C₄	—	86	4	no	—
392	C₂×C₄	—	172	4	no	—
393	C₂×C₄	—	172	4	no	—
394	C₂×C₄	C₂³×D₄₃	1	2	yes	—
395	C₂×C₄	C₂³×D₄₃	1	2	yes	—
396	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
397	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
398	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
399	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
400	C₂×C₄	C₂³×D₄₃	1	2	yes	—
401	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	86	2	no	—
409	C₂²	—	86	2	no	—
410	C₂²	—	86	2	no	—
411	C₂²	#13063371	1	2	yes	—
412	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	2	no	—
420	C₄	—	86	4	no	—
421	C₄	—	86	4	no	—
422	C₄	—	86	2	no	—
423	C₄	—	86	2	no	—
424	C₄	—	86	2	no	—
425	C₄	#13063372	1	2	yes	—
426	C₄	#13063372	1	2	yes	—
427	C₂	—	2	2	no	—
428	C₂	—	4	2	no	—
429	C₂	—	172	2	no	—
430	C₂	C₂×#13063371	1	1	yes	characteristic
431	C₂	C₂×#13063372	1	1	yes	characteristic
432	C₂	C₂×#13063372	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#529	C₂
hypercenter	#529	D₄₃
hypocenter	C₄₃	#3544
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #14583651	C₂	semidirect
2. Q₈×Dic₈₆	C₂	semidirect
3. #14583614	C₂	semidirect
4. #14583609	C₂	semidirect
5. #14583606	C₂	semidirect
6. #14583591	C₂	semidirect
7. #14583589	C₂	semidirect
8. #14583553	C₂	semidirect
9. #14583549	C₂	semidirect
10. #14583529	C₂	semidirect
11. #14583527	C₂	semidirect
12. #14583520	C₂	semidirect
13. #14583518	C₂	semidirect
14. #14583471	C₂	semidirect
15. C₂×#13063325	C₂	semidirect
16. #14583433	C₂	semidirect
17. C₄₃×#529	C₂	semidirect
233. #529	D₄₃	semidirect
234. C₄₃	#3544	semidirect