Subgroups — #25067536

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144630	C₂	1	1	yes	maximal, characteristic
2	#19143546	C₂	1	1	yes	maximal, characteristic
3	#19143544	C₂	1	1	yes	maximal, characteristic
4	#19133489	C₂	1	2	yes	maximal, complemented
5	#19133448	C₂	1	2	yes	maximal, complemented
6	#19133442	C₂	1	2	yes	maximal, complemented
7	#19133399	C₂	1	2	yes	maximal, complemented
8	#19133371	C₂	1	1	yes	maximal, characteristic
9	C₂×#14582631	C₂	1	1	yes	maximal, characteristic
10	C₈×#10621877	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1493	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
13	#14583232	C₄	1	2	yes	—
14	#14583191	C₄	1	1	yes	characteristic
15	#14583191	C₄	1	1	yes	characteristic
16	#14583106	C₄	1	1	yes	characteristic
17	#14583106	C₄	1	1	yes	characteristic
18	#14583054	C₄	1	2	yes	—
19	#14583030	—	2	2	no	—
20	#14583030	C₂²	1	2	yes	—
21	#14583028	—	2	2	no	—
22	#14583026	C₂²	1	2	yes	—
23	Q₈×C₄₃⋊C₈	C₂²	1	2	yes	—
24	#14583023	C₂²	1	2	yes	—
25	C₄×#10621885	C₂²	1	2	yes	—
26	C₄×#10621885	C₂²	1	2	yes	—
27	#14582952	C₂²	1	1	yes	characteristic
28	#14582926	—	2	1	no	—
29	#14582922	—	2	1	no	—
30	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
31	#14582855	—	2	1	no	—
32	C₄×#10621877	C₂²	1	1	yes	characteristic
33	M₁₆×Dic₄₃	—	2	1	no	—
34	#14582651	C₂²	1	2	yes	—
35	#14582651	C₂²	1	2	yes	—
36	#14582631	C₂²	1	1	yes	characteristic
37	#14582631	C₂²	1	1	yes	characteristic
38	#14582631	C₂²	1	1	yes	characteristic
39	#14582631	C₂²	1	1	yes	characteristic
40	#14582621	C₂²	1	2	yes	—
41	C₈×C₄₃⋊C₈	C₂²	1	2	yes	—
42	C₄₃×#533	C₂²	1	1	yes	characteristic
43	C₄₃×#423	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₄₃×Q₈⋊C₈	C₂²	1	2	yes	—
47	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
48	C₂×#10621885	C₂×C₄	1	2	yes	—
49	C₂×#10621885	C₂×C₄	1	2	yes	—
50	C₂×#10621877	D₄	1	1	yes	characteristic
51	C₂×#10621877	D₄	1	1	yes	characteristic
52	C₂²×C₄₃⋊C₈	—	2	1	no	—
53	C₄×Dic₈₆	—	2	1	no	—
54	C₄×Dic₈₆	—	2	1	no	—
55	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
56	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
57	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
58	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
60	C₂×Dic₄₃⋊C₄	—	2	1	no	—
61	C₂×C₄×Dic₄₃	—	2	1	no	—
62	#13063258	C₂×C₄	1	2	yes	—
63	#13063258	C₂×C₄	1	2	yes	—
64	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
65	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
66	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
67	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
68	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
69	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
70	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
71	Dic₄₃⋊C₈	—	2	2	no	—
72	Dic₄₃⋊C₈	—	2	2	no	—
73	#13063249	C₂×C₄	1	2	yes	—
74	#13063249	C₂×C₄	1	2	yes	—
75	#13063248	C₂×C₄	1	2	yes	—
76	#13063248	C₂×C₄	1	2	yes	—
77	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
78	#13063236	—	2	2	no	—
79	#13063236	D₄	1	2	yes	—
80	#13063235	—	2	2	no	—
81	C₄×C₄₃⋊C₈	—	2	2	no	—
82	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
83	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
84	C₈×Dic₄₃	—	2	2	no	—
85	C₂×M₁₆×C₄₃	—	2	1	no	—
86	C₂²×C₈×C₄₃	—	2	1	no	—
87	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
88	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
89	#125×C₄₃	—	2	1	no	—
90	C₂²⋊Q₈×C₄₃	—	2	1	no	—
91	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
92	C₄×Q₈×C₄₃	—	2	1	no	—
93	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
94	#117×C₄₃	—	2	1	no	—
95	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₄₃	—	2	1	no	—
97	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
98	C₄×C₈×C₄₃	—	2	1	no	—
99	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
101	C₂×Q₈×C₄₃	—	2	1	no	—
102	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
106	C₂²×Dic₄₃	—	2	1	no	—
107	C₂²×Dic₄₃	—	2	1	no	—
108	C₂×Dic₈₆	—	2	2	no	—
109	C₂×Dic₈₆	—	2	1	no	—
110	C₂×Dic₈₆	—	4	1	no	—
111	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
112	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
113	M₁₆×C₄₃	—	4	2	no	—
114	C₂×C₈×C₄₃	—	2	1	no	—
115	C₂×C₈×C₄₃	—	2	2	no	—
116	C₂×C₈×C₄₃	—	2	1	no	—
117	C₂×C₈×C₄₃	—	4	2	no	—
118	C₄⋊C₄×C₄₃	—	2	1	no	—
119	C₄⋊C₄×C₄₃	—	2	1	no	—
120	C₄⋊C₄×C₄₃	—	2	1	no	—
121	C₄⋊C₄×C₄₃	—	2	2	no	—
122	C₄⋊C₄×C₄₃	—	2	2	no	—
123	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
124	C₂²⋊C₄×C₄₃	—	2	2	no	—
125	C₄²×C₄₃	—	2	2	no	—
126	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₄₃	#41	1	1	yes	characteristic
129	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
130	#10621885	—	2	4	no	—
131	#10621885	—	4	2	no	—
132	C₄⋊Dic₄₃	—	2	1	no	—
133	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
134	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
135	Dic₄₃⋊C₄	—	2	1	no	—
136	Dic₄₃⋊C₄	—	2	1	no	—
137	Dic₄₃⋊C₄	—	2	1	no	—
138	Dic₄₃⋊C₄	—	2	1	no	—
139	C₄×Dic₄₃	—	2	1	no	—
140	C₄×Dic₄₃	—	2	1	no	—
141	C₄×Dic₄₃	—	2	1	no	—
142	C₄×Dic₄₃	—	2	1	no	—
143	#10621877	—	2	2	no	—
144	#10621877	Q₁₆	1	4	yes	complemented
145	C₂×C₄₃⋊C₈	—	2	1	no	—
146	C₂×C₄₃⋊C₈	—	2	1	no	—
147	C₂×C₄₃⋊C₈	—	4	2	no	—
148	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
149	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
150	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
151	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
152	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
153	Q₈×C₄₃	—	2	2	no	—
154	Q₈×C₄₃	—	2	2	no	—
155	Q₈×C₄₃	—	8	1	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	4	1	no	—
161	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
165	C₂×C₄×C₄₃	#135	1	2	yes	—
166	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
169	C₂×Dic₄₃	—	2	1	no	—
170	C₂×Dic₄₃	—	2	1	no	—
171	C₂×Dic₄₃	—	2	1	no	—
172	C₂×Dic₄₃	—	2	1	no	—
173	C₂×Dic₄₃	—	4	2	no	—
174	C₂×Dic₄₃	—	8	1	no	—
175	Dic₈₆	—	2	1	no	—
176	Dic₈₆	—	2	1	no	—
177	Dic₈₆	—	2	1	no	—
178	Dic₈₆	—	4	2	no	—
179	Dic₈₆	#131	1	2	yes	—
180	C₈×C₄₃	—	2	2	no	—
181	C₈×C₄₃	—	4	1	no	—
182	C₈×C₄₃	—	4	2	no	—
183	C₄₃⋊C₈	—	2	2	no	—
184	C₄₃⋊C₈	—	2	2	no	—
185	C₄₃⋊C₈	—	2	2	no	—
186	C₄₃⋊C₈	—	4	1	no	—
187	C₄₃⋊C₈	—	4	1	no	—
188	C₄₃⋊C₈	C₂×Q₁₆	1	4	yes	—
189	#17998	—	43	1	no	maximal, Sylow
190	C₂²×C₄₃	—	2	1	no	—
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	C₄×Q₁₆	1	2	yes	—
193	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
194	C₄×C₄₃	—	2	1	no	—
195	C₄×C₄₃	—	2	1	no	—
196	C₄×C₄₃	—	2	1	no	—
197	C₄×C₄₃	—	4	2	no	—
198	C₄×C₄₃	—	4	2	no	—
199	C₄×C₄₃	C₄×Q₁₆	1	2	yes	—
200	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
201	C₄×C₄₃	#568	1	1	yes	characteristic
202	C₄×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
203	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
204	Dic₄₃	—	2	2	no	—
205	Dic₄₃	—	4	1	no	—
206	Dic₄₃	—	4	1	no	—
207	Dic₄₃	—	4	1	no	—
208	#3104	—	43	1	no	—
209	Q₈×M₁₆	—	43	1	no	—
210	#2962	—	43	1	no	—
211	#1591	—	43	2	no	—
212	#1584	—	43	2	no	—
213	#1584	—	43	2	no	—
214	C₈×Q₁₆	—	43	2	no	—
215	#1571	—	43	1	no	—
216	#1493	D₄₃	1	1	yes	characteristic
217	C₂×Q₈⋊C₈	—	43	1	no	—
218	C₈×M₁₆	—	43	1	no	—
219	C₂×C₄₃	—	2	2	no	—
220	C₂×C₄₃	#2933	1	1	yes	characteristic
221	C₂×C₄₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
222	C₂×C₄₃	#2956	1	1	yes	characteristic
223	#533	C₂×D₄₃	1	1	yes	characteristic
224	C₂×C₄×Q₈	—	43	1	no	—
225	#484	—	43	2	no	—
226	#477	—	43	1	no	—
227	#477	—	43	1	no	—
228	#462	—	43	1	no	—
229	#462	—	43	1	no	—
230	#451	—	43	2	no	—
231	#446	—	43	2	no	—
232	#446	—	43	2	no	—
233	#446	—	86	2	no	—
234	#446	—	86	2	no	—
235	C₈×Q₈	—	43	2	no	—
236	C₈×Q₈	—	43	2	no	—
237	C₄×Q₁₆	—	43	2	no	—
238	C₄×Q₁₆	—	43	2	no	—
239	#431	—	43	1	no	—
240	#424	—	86	1	no	—
241	#423	—	86	1	no	—
242	#423	C₂×D₄₃	1	1	yes	characteristic
243	C₂×C₄⋊C₈	—	43	1	no	—
244	#405	—	86	1	no	—
245	C₄×M₁₆	—	43	1	no	—
246	C₄×M₁₆	—	86	1	no	—
247	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
248	#335	—	43	2	no	—
249	#335	—	43	2	no	—
250	Q₈⋊C₈	—	43	1	no	—
251	Q₈⋊C₈	—	43	1	no	—
252	Q₈⋊C₈	—	43	1	no	—
253	Q₈⋊C₈	—	43	1	no	—
254	Q₈⋊C₈	C₂×D₄₃	1	2	yes	—
255	Q₈⋊C₈	C₂×D₄₃	1	2	yes	—
256	#322	—	43	2	no	—
257	C₈²	—	43	2	no	—
258	C₄₃	#17998	1	1	yes	characteristic, complemented, Sylow
259	C₂²×Q₈	—	43	1	no	—
260	C₂×Q₁₆	—	43	2	no	—
261	C₂×Q₁₆	—	43	2	no	—
262	C₂×M₁₆	—	2	1	no	—
263	C₂×M₁₆	—	43	1	no	—
264	C₂×M₁₆	—	43	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	86	1	no	—
267	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
268	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
269	#125	—	2	1	no	—
270	C₂²⋊Q₈	—	2	1	no	—
271	C₂²⋊Q₈	C₄×D₄₃	1	2	yes	—
272	C₄×Q₈	—	2	1	no	—
273	C₄×Q₈	—	43	1	no	—
274	C₄×Q₈	—	43	1	no	—
275	C₄×Q₈	—	43	1	no	—
276	C₄×Q₈	—	43	1	no	—
277	C₄×Q₈	—	86	1	no	—
278	C₄×Q₈	—	86	1	no	—
279	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
280	#117	—	2	1	no	—
281	C₂×C₄⋊C₄	—	43	1	no	—
282	C₂×C₄⋊C₄	—	86	1	no	—
283	C₂×C₄²	—	86	1	no	—
284	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
285	#107	—	43	2	no	—
286	#107	—	43	2	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	43	1	no	—
289	C₄⋊C₈	—	43	1	no	—
290	C₄⋊C₈	—	43	1	no	—
291	C₄⋊C₈	—	43	1	no	—
292	C₄⋊C₈	—	86	2	no	—
293	C₄⋊C₈	—	86	2	no	—
294	C₄⋊C₈	—	86	2	no	—
295	C₄⋊C₈	—	86	2	no	—
296	C₄⋊C₈	—	86	1	no	—
297	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
298	#103	—	43	2	no	—
299	#103	—	43	2	no	—
300	#103	—	43	2	no	—
301	#103	—	43	2	no	—
302	C₂²⋊C₈	—	43	2	no	—
303	#97	—	43	2	no	—
304	#97	—	86	2	no	—
305	#97	—	86	2	no	—
306	C₄×C₈	—	2	1	no	—
307	C₄×C₈	—	43	2	no	—
308	C₄×C₈	—	43	2	no	—
309	C₄×C₈	—	86	2	no	—
310	C₄×C₈	—	86	2	no	—
311	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	43	1	no	—
315	C₂×Q₈	—	43	1	no	—
316	C₂×Q₈	—	86	2	no	—
317	C₂×Q₈	—	86	1	no	—
318	C₂×Q₈	—	172	1	no	—
319	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
320	C₂²×C₄	—	86	1	no	—
321	C₂²×C₄	—	86	1	no	—
322	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
323	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
324	C₂²×C₄	#10621900	1	1	yes	characteristic
325	Q₁₆	—	86	4	no	—
326	Q₁₆	—	172	2	no	—
327	M₁₆	—	4	2	no	—
328	M₁₆	—	43	4	no	—
329	M₁₆	—	86	2	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	4	2	no	—
334	C₂×C₈	—	43	2	no	—
335	C₂×C₈	—	43	2	no	—
336	C₂×C₈	—	43	2	no	—
337	C₂×C₈	—	43	2	no	—
338	C₂×C₈	—	86	1	no	—
339	C₂×C₈	—	86	1	no	—
340	C₂×C₈	—	172	2	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	43	1	no	—
347	C₄⋊C₄	—	43	1	no	—
348	C₄⋊C₄	—	86	1	no	—
349	C₄⋊C₄	—	86	1	no	—
350	C₄⋊C₄	—	86	1	no	—
351	C₄⋊C₄	—	86	1	no	—
352	C₄⋊C₄	—	86	1	no	—
353	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	86	1	no	—
357	C₄²	—	86	1	no	—
358	C₄²	—	86	1	no	—
359	C₄²	—	86	1	no	—
360	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
361	C₄²	D₄×D₄₃	1	1	yes	characteristic
362	C₄²	#10621900	1	1	yes	characteristic
363	C₄²	C₂³×D₄₃	1	1	yes	characteristic
364	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
365	Q₈	—	2	2	no	—
366	Q₈	—	2	2	no	—
367	Q₈	—	8	1	no	—
368	Q₈	—	43	2	no	—
369	Q₈	—	86	1	no	—
370	Q₈	—	86	1	no	—
371	Q₈	—	86	1	no	—
372	Q₈	—	172	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	86	1	no	—
379	C₂×C₄	—	86	1	no	—
380	C₂×C₄	—	86	1	no	—
381	C₂×C₄	—	86	1	no	—
382	C₂×C₄	—	344	1	no	—
383	C₂×C₄	—	172	2	no	—
384	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
385	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
386	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
387	C₂×C₄	Q₁₆×D₄₃	1	2	yes	—
388	C₂×C₄	#13063346	1	2	yes	—
389	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
390	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
391	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
392	C₈	—	2	2	no	—
393	C₈	—	4	1	no	—
394	C₈	—	4	2	no	—
395	C₈	—	43	4	no	—
396	C₈	—	86	2	no	—
397	C₈	—	86	2	no	—
398	C₈	—	86	2	no	—
399	C₈	—	172	1	no	—
400	C₈	—	172	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	#14582991	1	2	yes	—
404	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	86	2	no	—
411	C₄	—	172	1	no	—
412	C₄	—	172	1	no	—
413	C₄	—	172	1	no	—
414	C₄	#14582991	1	2	yes	—
415	C₄	#131×D₄₃	1	1	yes	characteristic
416	C₄	#14583664	1	1	yes	characteristic
417	C₄	C₂×Q₁₆×D₄₃	1	1	yes	characteristic
418	C₄	C₂×#13063346	1	1	yes	characteristic
419	C₂	—	2	2	no	—
420	C₂	#19143325	1	1	yes	characteristic
421	C₂	C₂×#14582991	1	1	yes	characteristic
422	C₂	#19143501	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1493	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂³×C₄₃	C₄×D₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1493	D₄₃
hypocenter	C₄₃	#17998
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1493

Complements

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

N	H ≅ G/N	type
4. #19133489	C₂	semidirect
5. #19133448	C₂	semidirect
6. #19133442	C₂	semidirect
7. #19133399	C₂	semidirect
144. #10621877	Q₁₆	semidirect
258. C₄₃	#17998	semidirect

Maximal subgroups

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

subgroup	index
#19144630	2
#19143546	2
#19143544	2
#19133489	2
#19133448	2
#19133442	2
#19133399	2
#19133371	2
C₂×#14582631	2
C₈×#10621877	2
C₄₃×#1493	2
#17998	43