Subgroups — #19148409

Order 5504.

1060 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583629	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583626	C₂	1	2	yes	maximal, complemented
4	#14583607	C₂	1	2	yes	maximal, complemented
5	#14583606	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583604	C₂	1	2	yes	maximal, complemented
7	D₄×Dic₈₆	C₂	1	2	yes	maximal, complemented
8	#14583562	C₂	1	4	yes	maximal, complemented
9	#14583529	C₂	1	2	yes	maximal, complemented
10	#14583528	C₂	1	4	yes	maximal, complemented
11	#14583453	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583451	C₂	1	2	yes	maximal, complemented
13	C₂×#13063324	C₂	1	2	yes	maximal, complemented
14	C₄⋊Q₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#14583378	C₂	1	2	yes	maximal
16	C₄×#10621900	C₂	1	1	yes	maximal, characteristic
17	C₄₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10621900	C₂²	1	1	yes	characteristic
19	C₂²×Dic₈₆	C₂²	1	4	yes	—
20	C₂×Q₈×D₄₃	C₂²	1	2	yes	—
21	#13063325	C₂²	1	2	yes	—
22	#13063325	C₂²	1	1	yes	characteristic
23	#13063324	C₂²	1	4	yes	—
24	#13063324	C₂²	1	4	yes	—
25	#13063324	C₂²	1	2	yes	—
26	#13063324	C₂²	1	2	yes	—
27	#13063324	C₂²	1	2	yes	—
28	#13063324	C₂²	1	2	yes	—
29	#13063324	C₂²	1	2	yes	—
30	#13063324	C₂²	1	1	yes	characteristic
31	#13063324	C₂²	1	4	yes	—
32	#13063323	C₂²	1	4	yes	—
33	#13063323	C₂²	1	2	yes	—
34	#13063323	C₂²	1	1	yes	characteristic
35	#13063316	C₂²	1	2	yes	—
36	#13063315	C₂²	1	4	yes	—
37	#13063315	C₂²	1	4	yes	—
38	#13063315	C₂²	1	4	yes	—
39	#13063315	C₂²	1	2	yes	—
40	#13063305	C₂²	1	4	yes	—
41	#13063305	C₂²	1	1	yes	characteristic
42	#13063304	C₂²	1	4	yes	—
43	#13063304	C₂²	1	2	yes	—
44	#13063303	C₂²	1	2	yes	—
45	#13063303	C₂²	1	4	yes	—
46	#13063302	C₂²	1	4	yes	—
47	#13063302	C₂²	1	4	yes	—
48	#13063302	C₂²	1	4	yes	—
49	#13063301	C₂²	1	1	yes	characteristic
50	Q₈×Dic₄₃	C₂²	1	2	yes	—
51	C₄×Dic₈₆	C₂²	1	2	yes	—
52	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
53	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
54	C₄×Dic₈₆	C₂²	1	2	yes	—
55	#13063290	C₂²	1	4	yes	—
56	#13063290	C₂²	1	2	yes	—
57	#13063290	C₂²	1	1	yes	characteristic
58	#13063290	C₂²	1	2	yes	—
59	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
60	D₄×Dic₄₃	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₄₃	C₂²	1	4	yes	—
62	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
63	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	—
64	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	—
65	#13063283	C₂²	1	1	yes	characteristic
66	#13063282	C₂²	1	2	yes	—
67	#13063281	C₂²	1	2	yes	—
68	#13063281	C₂²	1	4	yes	—
69	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
70	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
71	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
72	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
73	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
74	C₄²×D₄₃	C₂²	1	1	yes	characteristic
75	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
76	#125×C₄₃	C₂²	1	2	yes	—
77	C₂²⋊Q₈×C₄₃	C₂²	1	4	yes	—
78	C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
79	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
80	C₄×D₄×C₄₃	C₂²	1	2	yes	—
81	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
83	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
85	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
87	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
88	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
89	C₂²×Dic₄₃	C₂³	1	2	yes	—
90	C₂²×Dic₄₃	C₂³	1	4	yes	—
91	C₂²×Dic₄₃	C₂³	1	2	yes	—
92	Q₈×D₄₃	—	4	4	no	—
93	#10621900	Q₈	1	8	yes	complemented
94	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
95	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
96	C₂×C₄×D₄₃	C₂³	1	4	yes	—
97	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
98	C₂×Dic₈₆	—	4	8	no	—
99	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
100	C₂×Dic₈₆	C₂³	1	4	yes	—
101	C₂×Dic₈₆	C₂³	1	2	yes	—
102	C₂×Dic₈₆	C₂³	1	2	yes	—
103	C₂×Dic₈₆	C₂³	1	4	yes	—
104	C₂×Dic₈₆	C₂³	1	4	yes	—
105	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
106	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
107	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
108	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
109	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
111	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
112	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
113	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
114	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
115	C₄²×C₄₃	C₂³	1	2	yes	—
116	C₄²×C₄₃	C₂³	1	1	yes	characteristic
117	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
118	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
119	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
120	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
121	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
122	C₄⋊Dic₄₃	C₂³	1	2	yes	—
123	C₄⋊Dic₄₃	C₂³	1	2	yes	—
124	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
125	C₄⋊Dic₄₃	C₂³	1	4	yes	—
126	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
127	C₄⋊Dic₄₃	C₂³	1	2	yes	—
128	C₄⋊Dic₄₃	C₂³	1	4	yes	—
129	Dic₄₃⋊C₄	C₂³	1	4	yes	—
130	Dic₄₃⋊C₄	C₂³	1	4	yes	—
131	Dic₄₃⋊C₄	C₂³	1	2	yes	—
132	Dic₄₃⋊C₄	C₂³	1	4	yes	—
133	Dic₄₃⋊C₄	C₂³	1	4	yes	—
134	Dic₄₃⋊C₄	C₂³	1	2	yes	—
135	Dic₄₃⋊C₄	C₂³	1	2	yes	—
136	Dic₄₃⋊C₄	C₂³	1	2	yes	—
137	Dic₄₃⋊C₄	C₂³	1	2	yes	—
138	Dic₄₃⋊C₄	C₂³	1	4	yes	—
139	Dic₄₃⋊C₄	C₂³	1	4	yes	—
140	Dic₄₃⋊C₄	C₂³	1	2	yes	—
141	Dic₄₃⋊C₄	C₂³	1	2	yes	—
142	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
143	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
144	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
145	C₄×Dic₄₃	C₂³	1	2	yes	—
146	C₄×Dic₄₃	C₂³	1	2	yes	—
147	C₄×Dic₄₃	C₂³	1	2	yes	—
148	C₄×Dic₄₃	C₂³	1	4	yes	—
149	C₄×Dic₄₃	C₂³	1	4	yes	—
150	C₄×Dic₄₃	C₂³	1	2	yes	—
151	C₂³×C₄₃	C₂⁴	1	2	yes	—
152	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
153	Q₈×C₄₃	—	2	2	no	—
154	Q₈×C₄₃	—	4	2	no	—
155	D₄×C₄₃	C₂×Q₈	1	4	yes	complemented
156	C₂×C₄×C₄₃	—	2	4	no	—
157	C₂×C₄×C₄₃	—	4	4	no	—
158	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
159	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
160	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂⁴	1	4	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	C₂²⋊D₄₃	C₂×Q₈	1	8	yes	complemented
166	C₂×Dic₄₃	—	2	4	no	—
167	C₂×Dic₄₃	—	4	4	no	—
168	C₂×Dic₄₃	C₂×Q₈	1	8	yes	complemented
169	C₂×Dic₄₃	C₂⁴	1	2	yes	—
170	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
171	C₂×Dic₄₃	C₂⁴	1	2	yes	—
172	C₂×Dic₄₃	C₂⁴	1	2	yes	—
173	C₂×Dic₄₃	C₂⁴	1	4	yes	—
174	C₂×Dic₄₃	C₂⁴	1	2	yes	—
175	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
176	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
177	C₄×D₄₃	—	2	2	no	—
178	C₄×D₄₃	—	2	2	no	—
179	C₄×D₄₃	—	4	4	no	—
180	C₄×D₄₃	C₂×Q₈	1	4	yes	complemented
181	Dic₈₆	—	2	2	no	—
182	Dic₈₆	—	2	4	no	—
183	Dic₈₆	—	2	8	no	—
184	Dic₈₆	—	4	4	no	—
185	Dic₈₆	—	4	4	no	—
186	Dic₈₆	—	4	2	no	—
187	Dic₈₆	C₂×Q₈	1	4	yes	complemented
188	C₂²×C₄₃	—	2	2	no	—
189	C₂²×C₄₃	—	2	2	no	—
190	C₂²×C₄₃	C₂²×Q₈	1	4	yes	—
191	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
192	C₂×D₄₃	—	2	1	no	—
193	C₂×D₄₃	—	2	1	no	—
194	C₂×D₄₃	C₂²×Q₈	1	2	yes	—
195	C₄×C₄₃	—	2	2	no	—
196	C₄×C₄₃	—	2	4	no	—
197	C₄×C₄₃	—	2	1	no	—
198	C₄×C₄₃	—	2	2	no	—
199	C₄×C₄₃	—	2	2	no	—
200	C₄×C₄₃	C₂²×Q₈	1	2	yes	—
201	C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
202	Dic₄₃	—	2	4	no	—
203	Dic₄₃	—	2	2	no	—
204	Dic₄₃	—	2	2	no	—
205	Dic₄₃	—	2	2	no	—
206	Dic₄₃	—	2	1	no	—
207	Dic₄₃	C₂²×Q₈	1	4	yes	—
208	Dic₄₃	C₂²×Q₈	1	2	yes	—
209	Dic₄₃	H(5,𝔽₂)	1	2	yes	—
210	#3503	—	43	1	no	maximal, Sylow
211	C₂×C₄₃	—	2	4	no	—
212	C₂×C₄₃	C₂³×Q₈	1	1	yes	characteristic
213	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
214	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
215	D₄₃	—	2	2	no	—
216	Q₈²	—	43	1	no	—
217	Q₈²	—	43	1	no	—
218	#557	—	43	2	no	—
219	#554	—	43	2	no	—
220	#554	—	43	1	no	—
221	#554	—	43	2	no	—
222	#554	D₄₃	1	1	yes	characteristic, complemented
223	D₄×Q₈	—	43	4	no	—
224	D₄×Q₈	—	43	2	no	—
225	#544	—	43	2	no	—
226	#544	—	43	4	no	—
227	#533	—	43	2	no	—
228	#533	—	43	1	no	—
229	C₂×C₄⋊Q₈	—	43	1	no	—
230	C₂×C₄⋊Q₈	—	43	2	no	—
231	#520	—	43	2	no	—
232	C₄×#41	—	43	1	no	—
233	C₄₃	#3503	1	1	yes	characteristic, complemented, Sylow
234	C₂×#41	—	43	1	no	—
235	C₂²×Q₈	—	43	2	no	—
236	C₂²×Q₈	—	43	4	no	—
237	C₄⋊Q₈	—	43	2	no	—
238	C₄⋊Q₈	—	43	1	no	—
239	C₄⋊Q₈	—	43	4	no	—
240	C₄⋊Q₈	—	43	2	no	—
241	C₄⋊Q₈	—	43	1	no	—
242	C₄⋊Q₈	—	43	4	no	—
243	C₄⋊Q₈	—	43	4	no	—
244	C₄⋊Q₈	—	43	2	no	—
245	C₄⋊Q₈	—	43	2	no	—
246	C₄⋊Q₈	—	43	2	no	—
247	C₄⋊Q₈	—	43	4	no	—
248	C₄⋊Q₈	—	43	2	no	—
249	C₄⋊Q₈	—	43	1	no	—
250	C₄⋊Q₈	—	43	2	no	—
251	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
252	#125	—	43	2	no	—
253	#125	—	43	4	no	—
254	#125	—	43	4	no	—
255	#125	—	43	4	no	—
256	#125	—	43	2	no	—
257	#125	C₂×D₄₃	1	2	yes	—
258	C₂²⋊Q₈	—	43	1	no	—
259	C₂²⋊Q₈	—	43	2	no	—
260	C₂²⋊Q₈	—	43	4	no	—
261	C₂²⋊Q₈	—	43	2	no	—
262	C₂²⋊Q₈	—	43	1	no	—
263	C₂²⋊Q₈	—	43	4	no	—
264	C₂²⋊Q₈	—	43	4	no	—
265	C₂²⋊Q₈	—	43	4	no	—
266	C₂²⋊Q₈	—	43	4	no	—
267	C₂²⋊Q₈	—	43	4	no	—
268	C₂²⋊Q₈	C₂×D₄₃	1	2	yes	—
269	C₂²⋊Q₈	C₂×D₄₃	1	4	yes	—
270	C₄×Q₈	—	43	2	no	—
271	C₄×Q₈	—	43	1	no	—
272	C₄×Q₈	—	43	2	no	—
273	C₄×Q₈	—	43	4	no	—
274	C₄×Q₈	—	43	2	no	—
275	C₄×Q₈	—	43	1	no	—
276	C₄×Q₈	—	43	2	no	—
277	C₄×Q₈	—	43	2	no	—
278	C₄×Q₈	—	43	1	no	—
279	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
280	C₄×D₄	—	43	1	no	—
281	C₄×D₄	—	43	2	no	—
282	C₄×D₄	—	43	2	no	—
283	C₄×D₄	—	43	4	no	—
284	C₄×D₄	—	43	2	no	—
285	C₄×D₄	—	43	4	no	—
286	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
287	C₄×D₄	C₂×D₄₃	1	2	yes	—
288	#117	—	43	1	no	—
289	#117	—	43	2	no	—
290	#117	—	43	4	no	—
291	#117	—	43	2	no	—
292	C₂×C₄⋊C₄	—	43	4	no	—
293	C₂×C₄⋊C₄	—	43	2	no	—
294	C₂×C₄⋊C₄	—	43	2	no	—
295	C₂×C₄⋊C₄	—	43	2	no	—
296	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
297	C₂×C₄²	—	43	2	no	—
298	C₂×C₄²	—	43	1	no	—
299	#41	—	43	8	no	—
300	C₂×Q₈	—	43	1	no	—
301	C₂×Q₈	—	43	1	no	—
302	C₂×Q₈	—	43	4	no	—
303	C₂×Q₈	—	43	2	no	—
304	C₂×Q₈	—	43	4	no	—
305	C₂×Q₈	—	43	4	no	—
306	C₂×Q₈	—	43	2	no	—
307	C₂×Q₈	—	172	8	no	—
308	C₂×Q₈	—	172	4	no	—
309	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
310	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
311	C₂×D₄	—	43	2	no	—
312	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
313	C₂²×C₄	—	43	2	no	—
314	C₂²×C₄	—	43	1	no	—
315	C₂²×C₄	—	43	2	no	—
316	C₂²×C₄	—	43	4	no	—
317	C₂²×C₄	—	43	1	no	—
318	C₂²×C₄	—	43	1	no	—
319	C₂²×C₄	—	43	4	no	—
320	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
321	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
322	C₄⋊C₄	—	43	4	no	—
323	C₄⋊C₄	—	43	2	no	—
324	C₄⋊C₄	—	43	1	no	—
325	C₄⋊C₄	—	43	2	no	—
326	C₄⋊C₄	—	43	4	no	—
327	C₄⋊C₄	—	43	4	no	—
328	C₄⋊C₄	—	43	2	no	—
329	C₄⋊C₄	—	43	4	no	—
330	C₄⋊C₄	—	43	4	no	—
331	C₄⋊C₄	—	43	2	no	—
332	C₄⋊C₄	—	43	2	no	—
333	C₄⋊C₄	—	43	2	no	—
334	C₄⋊C₄	—	43	1	no	—
335	C₄⋊C₄	—	43	2	no	—
336	C₄⋊C₄	—	43	4	no	—
337	C₄⋊C₄	—	43	2	no	—
338	C₄⋊C₄	—	43	2	no	—
339	C₄⋊C₄	—	43	4	no	—
340	C₄⋊C₄	—	43	2	no	—
341	C₄⋊C₄	—	43	4	no	—
342	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
343	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
344	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
345	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
346	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
347	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
348	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
349	C₂²⋊C₄	—	43	4	no	—
350	C₂²⋊C₄	—	43	2	no	—
351	C₂²⋊C₄	—	43	2	no	—
352	C₂²⋊C₄	—	43	2	no	—
353	C₂²⋊C₄	—	43	2	no	—
354	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
355	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
356	C₄²	—	43	1	no	—
357	C₄²	—	43	1	no	—
358	C₄²	—	43	2	no	—
359	C₄²	—	43	2	no	—
360	C₄²	—	43	2	no	—
361	C₄²	—	43	1	no	—
362	C₄²	—	43	4	no	—
363	C₄²	—	43	4	no	—
364	C₄²	—	43	2	no	—
365	C₄²	C₂²×D₄₃	1	1	yes	characteristic
366	C₄²	C₂²×D₄₃	1	2	yes	—
367	C₂³	—	43	1	no	—
368	C₂³	C₂³×D₄₃	1	2	yes	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	43	4	no	—
372	Q₈	—	86	4	no	—
373	Q₈	—	86	8	no	—
374	Q₈	—	86	2	no	—
375	Q₈	—	172	4	no	—
376	Q₈	—	172	4	no	—
377	Q₈	—	172	2	no	—
378	D₄	—	43	8	no	—
379	D₄	Q₈×D₄₃	1	4	yes	complemented
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	43	8	no	—
383	C₂×C₄	—	43	2	no	—
384	C₂×C₄	—	43	1	no	—
385	C₂×C₄	—	43	1	no	—
386	C₂×C₄	—	43	4	no	—
387	C₂×C₄	—	43	2	no	—
388	C₂×C₄	—	43	1	no	—
389	C₂×C₄	—	43	2	no	—
390	C₂×C₄	—	43	4	no	—
391	C₂×C₄	—	43	2	no	—
392	C₂×C₄	—	86	2	no	—
393	C₂×C₄	—	86	4	no	—
394	C₂×C₄	—	86	2	no	—
395	C₂×C₄	—	172	4	no	—
396	C₂×C₄	—	172	4	no	—
397	C₂×C₄	C₂³×D₄₃	1	2	yes	—
398	C₂×C₄	C₂³×D₄₃	1	2	yes	—
399	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
400	C₂×C₄	C₂³×D₄₃	1	4	yes	—
401	C₂×C₄	C₂³×D₄₃	1	2	yes	—
402	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
403	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	43	2	no	—
407	C₂²	—	86	1	no	—
408	C₂²	—	86	1	no	—
409	C₂²	C₂×Q₈×D₄₃	1	4	yes	—
410	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	2	4	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	43	2	no	—
417	C₄	—	43	4	no	—
418	C₄	—	43	2	no	—
419	C₄	—	86	2	no	—
420	C₄	—	86	4	no	—
421	C₄	—	86	2	no	—
422	C₄	—	86	1	no	—
423	C₄	—	86	2	no	—
424	C₄	C₂×Q₈×D₄₃	1	2	yes	—
425	C₄	#13063372	1	2	yes	—
426	C₂	—	2	4	no	—
427	C₂	—	86	2	no	—
428	C₂	C₂²×Q₈×D₄₃	1	1	yes	characteristic
429	C₂	H(5,𝔽₂)×D₄₃	1	1	yes	characteristic
430	C₂	C₂×#13063372	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#554	C₂
hypercenter	#554	D₄₃
hypocenter	C₄₃	#3503
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. Q₈×Dic₈₆	C₂	semidirect
2. #14583629	C₂	semidirect
3. #14583626	C₂	semidirect
4. #14583607	C₂	semidirect
5. #14583606	C₂	semidirect
6. #14583604	C₂	semidirect
7. D₄×Dic₈₆	C₂	semidirect
8. #14583562	C₂	semidirect
9. #14583529	C₂	semidirect
10. #14583528	C₂	semidirect
11. #14583453	C₂	semidirect
12. #14583451	C₂	semidirect
13. C₂×#13063324	C₂	semidirect
14. C₄⋊Q₈×D₄₃	C₂	semidirect
17. C₄₃×#554	C₂	semidirect
93. #10621900	Q₈	semidirect
155. D₄×C₄₃	C₂×Q₈	semidirect
165. C₂²⋊D₄₃	C₂×Q₈	semidirect
168. C₂×Dic₄₃	C₂×Q₈	semidirect
180. C₄×D₄₃	C₂×Q₈	semidirect
187. Dic₈₆	C₂×Q₈	semidirect
222. #554	D₄₃	semidirect
233. C₄₃	#3503	semidirect
379. D₄	Q₈×D₄₃	semidirect