Subgroups — #25067534

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	#19144635	C₂	1	1	yes	maximal, characteristic
2	M₁₆×Dic₈₆	C₂	1	1	yes	maximal, characteristic
3	#19143542	C₂	1	1	yes	maximal, characteristic
4	#19133493	C₂	1	2	yes	maximal, complemented
5	#19133447	C₂	1	2	yes	maximal, complemented
6	#19133447	C₂	1	2	yes	maximal, complemented
7	C₈×Dic₁₇₂	C₂	1	2	yes	maximal, complemented
8	#19133370	C₂	1	1	yes	maximal, characteristic
9	#19133051	C₂	1	1	yes	maximal, characteristic
10	C₂×#14582631	C₂	1	1	yes	maximal, characteristic
11	C₈×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
12	#14583456	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
14	#14583235	C₄	1	2	yes	—
15	#14583195	C₄	1	1	yes	characteristic
16	#14583195	C₄	1	1	yes	characteristic
17	#14583110	C₄	1	1	yes	characteristic
18	#14583110	C₄	1	1	yes	characteristic
19	#14583057	C₄	1	2	yes	—
20	#14583029	C₂²	1	2	yes	—
21	#14583029	C₂²	1	2	yes	—
22	#14583027	—	2	2	no	—
23	#14583027	—	2	2	no	—
24	C₈×Dic₈₆	C₂²	1	2	yes	—
25	C₈×Dic₈₆	C₂²	1	2	yes	—
26	C₄×Dic₁₇₂	C₂²	1	2	yes	—
27	C₄×Dic₁₇₂	C₂²	1	2	yes	—
28	#14582927	—	2	1	no	—
29	#14582923	C₂²	1	1	yes	characteristic
30	#14582922	—	2	1	no	—
31	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
32	#14582857	—	2	1	no	—
33	M₁₆×Dic₄₃	—	2	1	no	—
34	#14582652	C₂²	1	2	yes	—
35	#14582652	C₂²	1	2	yes	—
36	#14582631	C₂²	1	1	yes	characteristic
37	#14582631	C₂²	1	1	yes	characteristic
38	#14582631	C₂²	1	2	yes	—
39	#14582631	C₂²	1	1	yes	characteristic
40	#14582631	C₂²	1	1	yes	characteristic
41	#14582631	C₂²	1	2	yes	—
42	C₄₃×#431	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#322	C₂²	1	2	yes	—
46	C₈²×C₄₃	C₂²	1	2	yes	—
47	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
48	C₂×Dic₁₇₂	C₂×C₄	1	2	yes	—
49	C₂×Dic₁₇₂	C₂×C₄	1	2	yes	—
50	C₂×#10621877	—	2	1	no	—
51	C₂²×C₄₃⋊C₈	—	2	1	no	—
52	#13063325	C₂×C₄	1	1	yes	characteristic
53	#13063325	C₂×C₄	1	1	yes	characteristic
54	#13063317	—	2	1	no	—
55	#13063304	—	2	1	no	—
56	#13063304	C₂×C₄	1	2	yes	—
57	C₄×Dic₈₆	—	2	1	no	—
58	C₄×Dic₈₆	—	2	1	no	—
59	C₄×Dic₈₆	—	2	1	no	—
60	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
63	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
64	C₄×Dic₈₆	C₂³	1	2	yes	—
65	#13063284	—	2	1	no	—
66	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
67	C₂×Dic₄₃⋊C₄	—	2	1	no	—
68	C₂×C₄×Dic₄₃	—	2	1	no	—
69	#13063259	C₂×C₄	1	2	yes	—
70	#13063259	C₂×C₄	1	2	yes	—
71	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
72	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
73	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
74	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
75	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
76	Dic₄₃⋊C₈	—	2	2	no	—
77	Dic₄₃⋊C₈	—	2	2	no	—
78	Dic₄₃⋊C₈	—	2	2	no	—
79	Dic₄₃⋊C₈	—	2	2	no	—
80	#13063250	C₂×C₄	1	2	yes	—
81	#13063250	C₂×C₄	1	2	yes	—
82	#13063250	C₂×C₄	1	2	yes	—
83	#13063250	C₂×C₄	1	2	yes	—
84	#13063235	—	2	2	no	—
85	#13063235	—	2	2	no	—
86	C₈×Dic₄₃	—	2	2	no	—
87	C₈×Dic₄₃	—	2	2	no	—
88	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
89	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
90	C₂²×C₈×C₄₃	—	2	1	no	—
91	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
93	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
95	#97×C₄₃	D₄	1	2	yes	—
96	C₄×C₈×C₄₃	—	2	1	no	—
97	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₄₃	C₂³	1	2	yes	—
100	C₄×C₈×C₄₃	C₂³	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
104	C₂²×Dic₄₃	—	2	1	no	—
105	C₂²×Dic₄₃	—	2	1	no	—
106	C₂×Dic₈₆	—	2	2	no	—
107	C₂×Dic₈₆	—	2	1	no	—
108	C₂×Dic₈₆	—	2	1	no	—
109	C₂×Dic₈₆	—	4	1	no	—
110	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
111	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
112	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
113	M₁₆×C₄₃	—	2	2	no	—
114	M₁₆×C₄₃	Q₁₆	1	4	yes	complemented
115	C₂×C₈×C₄₃	—	2	1	no	—
116	C₂×C₈×C₄₃	—	2	1	no	—
117	C₂×C₈×C₄₃	—	4	2	no	—
118	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
122	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₄₃	#41	1	1	yes	characteristic
125	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
126	C₂²⋊Dic₄₃	—	2	2	no	—
127	C₄⋊Dic₄₃	—	2	1	no	—
128	C₄⋊Dic₄₃	—	2	1	no	—
129	C₄⋊Dic₄₃	—	2	1	no	—
130	C₄⋊Dic₄₃	—	2	1	no	—
131	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
132	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
133	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
134	Dic₄₃⋊C₄	—	2	1	no	—
135	Dic₄₃⋊C₄	—	2	1	no	—
136	Dic₄₃⋊C₄	—	2	2	no	—
137	Dic₄₃⋊C₄	—	2	1	no	—
138	Dic₄₃⋊C₄	—	2	1	no	—
139	Dic₄₃⋊C₄	—	2	2	no	—
140	C₄×Dic₄₃	—	2	1	no	—
141	C₄×Dic₄₃	—	2	1	no	—
142	C₄×Dic₄₃	—	2	1	no	—
143	C₄×Dic₄₃	—	2	2	no	—
144	C₄×Dic₄₃	—	2	1	no	—
145	#10621877	—	4	2	no	—
146	C₂×C₄₃⋊C₈	—	2	1	no	—
147	C₂×C₄₃⋊C₈	—	2	2	no	—
148	C₂×C₄₃⋊C₈	—	2	1	no	—
149	C₂×C₄₃⋊C₈	—	4	2	no	—
150	Dic₁₇₂	—	2	4	no	—
151	Dic₁₇₂	—	4	2	no	—
152	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	2	1	no	—
155	C₂×C₄×C₄₃	—	4	1	no	—
156	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
160	C₂×C₄×C₄₃	#135	1	2	yes	—
161	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
164	C₂×Dic₄₃	—	2	1	no	—
165	C₂×Dic₄₃	—	2	1	no	—
166	C₂×Dic₄₃	—	2	1	no	—
167	C₂×Dic₄₃	—	2	1	no	—
168	C₂×Dic₄₃	—	2	2	no	—
169	C₂×Dic₄₃	—	2	2	no	—
170	C₂×Dic₄₃	—	4	2	no	—
171	C₂×Dic₄₃	—	8	1	no	—
172	Dic₈₆	—	2	1	no	—
173	Dic₈₆	—	2	2	no	—
174	Dic₈₆	—	2	1	no	—
175	Dic₈₆	—	2	1	no	—
176	Dic₈₆	—	2	2	no	—
177	Dic₈₆	—	4	2	no	—
178	Dic₈₆	—	8	1	no	—
179	Dic₈₆	#131	1	2	yes	—
180	C₈×C₄₃	—	2	2	no	—
181	C₈×C₄₃	—	2	2	no	—
182	C₈×C₄₃	—	2	2	no	—
183	C₈×C₄₃	—	2	2	no	—
184	C₈×C₄₃	—	4	1	no	—
185	C₈×C₄₃	C₂×Q₁₆	1	4	yes	—
186	C₄₃⋊C₈	—	4	1	no	—
187	C₄₃⋊C₈	—	4	1	no	—
188	C₄₃⋊C₈	—	4	2	no	—
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	C₄×Q₁₆	1	2	yes	—
198	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
199	C₄×C₄₃	#568	1	1	yes	characteristic
200	C₄×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
201	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
202	Dic₄₃	—	2	2	no	—
203	Dic₄₃	—	4	1	no	—
204	Dic₄₃	—	4	2	no	—
205	Dic₄₃	—	4	2	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	—	43	1	no	—
217	C₂×Q₈⋊C₈	—	43	1	no	—
218	C₈×M₁₆	D₄₃	1	1	yes	characteristic
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	—	43	1	no	—
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	C₂×D₄₃	1	1	yes	characteristic
240	#424	—	86	1	no	—
241	#423	—	43	1	no	—
242	#423	—	86	1	no	—
243	C₂×C₄⋊C₈	—	43	1	no	—
244	#405	—	86	1	no	—
245	C₄×M₁₆	—	86	1	no	—
246	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
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	2	no	—
252	Q₈⋊C₈	—	43	1	no	—
253	Q₈⋊C₈	—	43	1	no	—
254	Q₈⋊C₈	—	43	2	no	—
255	Q₈⋊C₈	—	43	1	no	—
256	#322	C₂×D₄₃	1	2	yes	—
257	C₈²	C₂×D₄₃	1	2	yes	—
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	—	86	1	no	—
263	C₂×M₁₆	D₁₇₂	1	1	yes	characteristic
264	C₂×M₁₆	D₁₇₂	1	1	yes	characteristic
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	86	1	no	—
267	C₄⋊Q₈	—	43	1	no	—
268	C₄⋊Q₈	—	43	1	no	—
269	#125	—	86	1	no	—
270	C₂²⋊Q₈	—	43	2	no	—
271	C₂²⋊Q₈	—	86	1	no	—
272	C₄×Q₈	—	43	1	no	—
273	C₄×Q₈	—	43	1	no	—
274	C₄×Q₈	—	43	1	no	—
275	C₄×Q₈	—	43	1	no	—
276	C₄×Q₈	—	43	2	no	—
277	C₄×Q₈	—	86	1	no	—
278	C₄×Q₈	—	86	1	no	—
279	C₄×Q₈	—	86	1	no	—
280	#117	—	86	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	—	43	1	no	—
288	C₄⋊C₈	—	43	1	no	—
289	C₄⋊C₈	—	43	2	no	—
290	C₄⋊C₈	—	86	2	no	—
291	C₄⋊C₈	—	86	2	no	—
292	C₄⋊C₈	—	86	2	no	—
293	C₄⋊C₈	—	86	2	no	—
294	C₄⋊C₈	—	86	1	no	—
295	C₄⋊C₈	—	86	1	no	—
296	C₄⋊C₈	C₄×D₄₃	1	1	yes	characteristic
297	C₄⋊C₈	C₄×D₄₃	1	1	yes	characteristic
298	#103	—	43	2	no	—
299	#103	—	43	2	no	—
300	#103	—	43	2	no	—
301	#103	—	43	2	no	—
302	C₂²⋊C₈	C₄×D₄₃	1	2	yes	—
303	#97	—	86	2	no	—
304	#97	—	86	2	no	—
305	#97	D₁₇₂	1	2	yes	—
306	C₄×C₈	—	2	1	no	—
307	C₄×C₈	—	86	2	no	—
308	C₄×C₈	—	86	2	no	—
309	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
311	C₄×C₈	C₂²×D₄₃	1	2	yes	—
312	C₄×C₈	C₂²×D₄₃	1	2	yes	—
313	C₂×Q₈	—	43	1	no	—
314	C₂×Q₈	—	43	1	no	—
315	C₂×Q₈	—	43	2	no	—
316	C₂×Q₈	—	86	2	no	—
317	C₂×Q₈	—	86	1	no	—
318	C₂×Q₈	—	86	1	no	—
319	C₂×Q₈	—	172	1	no	—
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	C₂×D₁₇₂	1	1	yes	characteristic
324	C₂²×C₄	#10621898	1	1	yes	characteristic
325	Q₁₆	—	86	4	no	—
326	Q₁₆	—	172	2	no	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	172	2	no	—
329	M₁₆	Dic₁₇₂	1	4	yes	complemented
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	4	2	no	—
333	C₂×C₈	—	86	1	no	—
334	C₂×C₈	—	86	2	no	—
335	C₂×C₈	—	86	1	no	—
336	C₂×C₈	—	172	2	no	—
337	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
338	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
339	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
340	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
341	C₄⋊C₄	—	43	1	no	—
342	C₄⋊C₄	—	43	1	no	—
343	C₄⋊C₄	—	43	2	no	—
344	C₄⋊C₄	—	86	1	no	—
345	C₄⋊C₄	—	86	1	no	—
346	C₄⋊C₄	—	86	1	no	—
347	C₄⋊C₄	—	86	1	no	—
348	C₄⋊C₄	—	86	1	no	—
349	C₄⋊C₄	—	86	2	no	—
350	C₄⋊C₄	—	86	1	no	—
351	C₄⋊C₄	—	86	1	no	—
352	C₄⋊C₄	—	86	1	no	—
353	C₄⋊C₄	—	86	2	no	—
354	C₂²⋊C₄	—	86	2	no	—
355	C₄²	—	86	1	no	—
356	C₄²	—	86	1	no	—
357	C₄²	—	86	1	no	—
358	C₄²	—	86	2	no	—
359	C₄²	—	86	1	no	—
360	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
361	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
362	C₄²	#10621898	1	1	yes	characteristic
363	C₄²	C₂³×D₄₃	1	1	yes	characteristic
364	C₂³	C₄×D₁₇₂	1	1	yes	characteristic
365	Q₈	—	43	2	no	—
366	Q₈	—	86	1	no	—
367	Q₈	—	86	2	no	—
368	Q₈	—	86	1	no	—
369	Q₈	—	86	1	no	—
370	Q₈	—	86	2	no	—
371	Q₈	—	344	1	no	—
372	Q₈	—	172	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	86	1	no	—
377	C₂×C₄	—	86	1	no	—
378	C₂×C₄	—	86	1	no	—
379	C₂×C₄	—	86	1	no	—
380	C₂×C₄	—	86	2	no	—
381	C₂×C₄	—	86	2	no	—
382	C₂×C₄	—	344	1	no	—
383	C₂×C₄	—	172	2	no	—
384	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
385	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
386	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
387	C₂×C₄	C₂×Dic₁₇₂	1	2	yes	—
388	C₂×C₄	#13063347	1	2	yes	—
389	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
390	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
391	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
392	C₈	—	2	2	no	—
393	C₈	—	2	2	no	—
394	C₈	—	2	2	no	—
395	C₈	—	2	2	no	—
396	C₈	—	4	1	no	—
397	C₈	—	172	1	no	—
398	C₈	—	172	1	no	—
399	C₈	—	172	2	no	—
400	C₈	C₂×Dic₁₇₂	1	4	yes	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	C₄×Dic₁₇₂	1	2	yes	—
404	C₂²	C₂×C₄×D₁₇₂	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	86	2	no	—
409	C₄	—	172	1	no	—
410	C₄	—	172	1	no	—
411	C₄	—	172	2	no	—
412	C₄	—	172	1	no	—
413	C₄	—	172	2	no	—
414	C₄	C₄×Dic₁₇₂	1	2	yes	—
415	C₄	#131×D₄₃	1	1	yes	characteristic
416	C₄	#14583664	1	1	yes	characteristic
417	C₄	C₂²×Dic₁₇₂	1	1	yes	characteristic
418	C₄	C₂×#13063347	1	1	yes	characteristic
419	C₂	—	2	2	no	—
420	C₂	#19143323	1	1	yes	characteristic
421	C₂	C₂×C₄×Dic₁₇₂	1	1	yes	characteristic
422	C₂	#19143506	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₈×M₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂³×C₄₃	C₄×D₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	C₈×M₁₆	D₄₃
hypocenter	C₄₃	#17998
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
4. #19133493	C₂	semidirect
5. #19133447	C₂	semidirect
6. #19133447	C₂	semidirect
7. C₈×Dic₁₇₂	C₂	semidirect
114. M₁₆×C₄₃	Q₁₆	semidirect
258. C₄₃	#17998	semidirect
329. M₁₆	Dic₁₇₂	semidirect

Maximal subgroups

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

subgroup	index
#19144635	2
M₁₆×Dic₈₆	2
#19143542	2
#19133493	2
#19133447	2
C₈×Dic₁₇₂	2
#19133370	2
#19133051	2
C₂×#14582631	2
C₈×M₁₆×C₄₃	2
#17998	43