Subgroups — #24989287

Order 11008.

688 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	C₄²×D₁₇₂	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14582626	C₂	1	2	yes	maximal
4	#19132434	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1831	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₁₇₂	C₄	1	1	yes	characteristic
7	C₂×C₄×D₁₇₂	C₄	1	1	yes	characteristic
8	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×C₄²×D₄₃	—	2	1	no	—
10	C₂×C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
11	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
12	C₄×C₄⋊Dic₄₃	C₄	1	1	yes	characteristic
13	C₄×C₄⋊Dic₄₃	C₄	1	1	yes	characteristic
14	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	C₄×(C₂×D₄₃)⋊C₄	—	2	1	no	—
16	C₄×(C₂×D₄₃)⋊C₄	—	2	1	no	—
17	C₄×(C₂×D₄₃)⋊C₄	—	2	1	no	—
18	#14582654	—	2	1	no	—
19	#14582626	—	2	4	no	—
20	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
21	C₄³×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#336	—	2	1	no	—
23	C₄₃×#336	—	2	1	no	—
24	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×D₄₃	—	2	1	no	—
26	C₂²×C₄×D₄₃	—	2	1	no	—
27	C₂²×C₄×D₄₃	—	2	1	no	—
28	C₂²×C₄₃⋊C₈	—	2	2	no	—
29	C₄×D₁₇₂	—	2	2	no	—
30	C₄×D₁₇₂	—	2	2	no	—
31	C₄×D₁₇₂	—	2	1	no	—
32	C₄×D₁₇₂	—	2	1	no	—
33	C₄×D₁₇₂	—	2	2	no	—
34	C₄×D₁₇₂	C₈	1	4	yes	complemented
35	C₄×D₁₇₂	D₄	1	2	yes	—
36	C₄×D₁₇₂	Q₈	1	2	yes	—
37	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
40	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
41	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
42	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
43	C₂×C₄×Dic₄₃	—	2	1	no	—
44	C₂×C₄×Dic₄₃	—	2	1	no	—
45	C₂×C₄×Dic₄₃	—	2	1	no	—
46	C₄²×D₄₃	—	4	4	no	—
47	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
48	C₄×C₄₃⋊C₈	—	2	2	no	—
49	C₄×C₄₃⋊C₈	—	2	2	no	—
50	C₄₃⋊#95	—	2	1	no	—
51	C₄₃⋊#95	—	2	1	no	—
52	C₄₃⋊#95	—	2	1	no	—
53	C₂²×C₈×C₄₃	—	2	2	no	—
54	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₄₃	—	2	2	no	—
62	C₄⋊C₈×C₄₃	—	2	2	no	—
63	C₂³×D₄₃	—	2	1	no	—
64	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
71	C₂²×Dic₄₃	—	2	1	no	—
72	C₂²×Dic₄₃	—	2	1	no	—
73	C₂²×Dic₄₃	—	2	1	no	—
74	C₂×D₁₇₂	—	2	1	no	—
75	C₂×D₁₇₂	—	2	1	no	—
76	C₂×D₁₇₂	—	2	1	no	—
77	C₂×D₁₇₂	C₄⋊C₄	1	2	yes	—
78	C₂×D₁₇₂	C₂×C₈	1	2	yes	—
79	C₂×D₁₇₂	M₁₆	1	2	yes	—
80	C₂×C₄×D₄₃	—	2	4	no	—
81	C₂×C₄×D₄₃	—	2	4	no	—
82	C₂×C₄×D₄₃	—	2	2	no	—
83	C₂×C₄×D₄₃	—	2	2	no	—
84	C₂×C₄×D₄₃	—	4	2	no	—
85	C₂×C₄×D₄₃	—	4	2	no	—
86	C₂×C₄×D₄₃	—	4	2	no	—
87	C₂×C₄×D₄₃	—	4	2	no	—
88	C₂×C₄×D₄₃	—	4	2	no	—
89	C₂×C₄×D₄₃	—	4	2	no	—
90	C₂×C₈×C₄₃	—	4	2	no	—
91	C₂×C₈×C₄₃	—	4	2	no	—
92	C₂×C₈×C₄₃	—	4	2	no	—
93	C₄²×C₄₃	—	2	2	no	—
94	C₄²×C₄₃	—	2	1	no	—
95	C₄²×C₄₃	—	2	1	no	—
96	C₄²×C₄₃	—	2	2	no	—
97	C₄²×C₄₃	—	2	2	no	—
98	C₄²×C₄₃	—	4	1	no	—
99	C₄²×C₄₃	C₂×C₈	1	2	yes	—
100	C₄²×C₄₃	M₁₆	1	2	yes	—
101	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
103	C₄²×C₄₃	#41	1	1	yes	characteristic
104	C₄²×C₄₃	#41	1	1	yes	characteristic
105	(C₂×D₄₃)⋊C₄	—	2	4	no	—
106	(C₂×D₄₃)⋊C₄	—	2	4	no	—
107	(C₂×D₄₃)⋊C₄	—	2	2	no	—
108	(C₂×D₄₃)⋊C₄	—	2	2	no	—
109	C₄⋊Dic₄₃	—	2	1	no	—
110	C₄⋊Dic₄₃	—	2	1	no	—
111	C₄⋊Dic₄₃	—	2	1	no	—
112	C₄⋊Dic₄₃	C₄⋊C₄	1	2	yes	—
113	C₄⋊Dic₄₃	C₂×C₈	1	2	yes	—
114	C₄⋊Dic₄₃	M₁₆	1	2	yes	—
115	C₄×Dic₄₃	—	4	2	no	—
116	C₄×Dic₄₃	—	4	2	no	—
117	C₄×Dic₄₃	—	4	2	no	—
118	C₂×C₄₃⋊C₈	—	2	4	no	—
119	C₂×C₄₃⋊C₈	—	4	2	no	—
120	C₂×C₄₃⋊C₈	—	4	2	no	—
121	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×D₄₃	—	2	2	no	—
123	C₂²×D₄₃	—	2	2	no	—
124	C₂²×D₄₃	—	2	2	no	—
125	C₂²×D₄₃	—	4	1	no	—
126	C₂²×D₄₃	—	4	1	no	—
127	C₂²×D₄₃	—	4	1	no	—
128	C₂²×D₄₃	—	4	1	no	—
129	C₂×C₄×C₄₃	—	2	1	no	—
130	C₂×C₄×C₄₃	—	2	1	no	—
131	C₂×C₄×C₄₃	—	2	1	no	—
132	C₂×C₄×C₄₃	—	2	1	no	—
133	C₂×C₄×C₄₃	—	2	1	no	—
134	C₂×C₄×C₄₃	—	2	1	no	—
135	C₂×C₄×C₄₃	—	2	1	no	—
136	C₂×C₄×C₄₃	—	2	1	no	—
137	C₂×C₄×C₄₃	—	2	1	no	—
138	C₂×C₄×C₄₃	—	2	1	no	—
139	C₂×C₄×C₄₃	—	2	1	no	—
140	C₂×C₄×C₄₃	C₂²⋊C₈	1	2	yes	—
141	C₂×C₄×C₄₃	C₂²⋊C₈	1	2	yes	—
142	C₂×C₄×C₄₃	#104	1	2	yes	—
143	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
145	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
146	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
147	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
148	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
149	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
151	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
152	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
153	C₂×C₄×C₄₃	#135	1	2	yes	—
154	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×Dic₄₃	—	2	2	no	—
156	C₂×Dic₄₃	—	2	2	no	—
157	C₂×Dic₄₃	—	2	2	no	—
158	C₂×Dic₄₃	—	4	1	no	—
159	C₂×Dic₄₃	—	4	1	no	—
160	C₂×Dic₄₃	—	4	1	no	—
161	C₂×Dic₄₃	—	4	1	no	—
162	C₂×Dic₄₃	—	4	1	no	—
163	C₂×Dic₄₃	—	4	1	no	—
164	D₁₇₂	—	2	2	no	—
165	D₁₇₂	—	2	2	no	—
166	D₁₇₂	—	2	2	no	—
167	D₁₇₂	C₄⋊C₈	1	4	yes	complemented
168	C₄×D₄₃	—	4	8	no	—
169	C₄×D₄₃	—	4	8	no	—
170	C₄×D₄₃	—	4	4	no	—
171	C₄×D₄₃	—	4	4	no	—
172	C₈×C₄₃	—	8	2	no	—
173	C₄₃⋊C₈	—	4	4	no	—
174	#8565	—	43	1	no	maximal, Sylow
175	C₂²×C₄₃	#380	1	1	yes	characteristic
176	C₂²×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
177	C₂²×C₄₃	#407	1	1	yes	characteristic
178	C₂²×C₄₃	#416	1	1	yes	characteristic
179	C₂²×C₄₃	#418	1	1	yes	characteristic
180	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
181	C₂²×C₄₃	#421	1	1	yes	characteristic
182	C₂×D₄₃	—	2	4	no	—
183	C₂×D₄₃	—	4	2	no	—
184	C₂×D₄₃	—	4	2	no	—
185	C₂×D₄₃	—	4	2	no	—
186	C₂×D₄₃	—	4	2	no	—
187	C₂×D₄₃	—	4	2	no	—
188	C₂×D₄₃	—	4	2	no	—
189	C₄×C₄₃	—	2	1	no	—
190	C₄×C₄₃	—	2	1	no	—
191	C₄×C₄₃	—	2	2	no	—
192	C₄×C₄₃	—	2	2	no	—
193	C₄×C₄₃	—	2	2	no	—
194	C₄×C₄₃	—	4	1	no	—
195	C₄×C₄₃	C₂×C₄⋊C₈	1	1	yes	characteristic
196	C₄×C₄₃	#423	1	1	yes	characteristic
197	C₄×C₄₃	#431	1	1	yes	characteristic
198	C₄×C₄₃	#432	1	1	yes	characteristic
199	C₄×C₄₃	#463	1	2	yes	—
200	C₄×C₄₃	#478	1	2	yes	—
201	Dic₄₃	—	4	2	no	—
202	Dic₄₃	—	4	2	no	—
203	Dic₄₃	—	4	2	no	—
204	C₄²×D₄	—	43	1	no	—
205	#1831	D₄₃	1	1	yes	characteristic, complemented
206	C₄×C₄⋊C₈	—	43	1	no	—
207	C₂×D₄⋊C₈	—	43	2	no	—
208	#1279	—	43	2	no	—
209	C₂×C₄₃	#1476	1	1	yes	characteristic
210	C₂×C₄₃	#1478	1	1	yes	characteristic
211	C₂×C₄₃	#1488	1	1	yes	characteristic
212	C₂×C₄₃	#1490	1	1	yes	characteristic
213	C₂×C₄₃	#1797	1	1	yes	characteristic
214	C₂×C₄₃	#1804	1	1	yes	characteristic
215	C₂×C₄₃	#1806	1	1	yes	characteristic
216	D₄₃	—	4	4	no	—
217	C₂×C₄×D₄	—	43	1	no	—
218	C₂×C₄×D₄	—	43	1	no	—
219	C₂×C₄×D₄	—	43	1	no	—
220	C₂²×C₄²	—	86	1	no	—
221	C₂×C₄⋊C₈	—	86	1	no	—
222	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
223	C₂×C₄×C₈	—	43	2	no	—
224	C₄×C₄⋊C₄	—	43	1	no	—
225	C₄×C₄⋊C₄	—	43	1	no	—
226	C₄×C₄⋊C₄	—	43	1	no	—
227	C₄×C₂²⋊C₄	—	86	1	no	—
228	C₄×C₂²⋊C₄	—	86	1	no	—
229	C₄×C₂²⋊C₄	—	86	1	no	—
230	C₄³	C₂×D₄₃	1	1	yes	characteristic
231	#336	—	2	1	no	—
232	#336	—	2	1	no	—
233	#336	—	86	1	no	—
234	D₄⋊C₈	—	86	4	no	—
235	C₄₃	#8565	1	1	yes	characteristic, complemented, Sylow
236	C₂²×D₄	—	43	1	no	—
237	C₂³×C₄	—	86	1	no	—
238	C₂³×C₄	—	86	1	no	—
239	C₂³×C₄	—	86	1	no	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	86	2	no	—
242	C₄×D₄	—	43	4	no	—
243	C₄×D₄	—	43	2	no	—
244	C₄×D₄	—	43	2	no	—
245	C₄×D₄	—	86	2	no	—
246	C₄×D₄	—	86	2	no	—
247	C₄×D₄	—	86	2	no	—
248	C₄×D₄	—	86	1	no	—
249	C₄×D₄	—	86	1	no	—
250	C₂×C₄⋊C₄	—	43	1	no	—
251	C₂×C₄⋊C₄	—	43	1	no	—
252	C₂×C₄⋊C₄	—	43	1	no	—
253	C₂×C₂²⋊C₄	—	86	1	no	—
254	C₂×C₂²⋊C₄	—	86	1	no	—
255	C₂×C₂²⋊C₄	—	86	1	no	—
256	C₂×C₄²	—	86	1	no	—
257	C₂×C₄²	—	86	1	no	—
258	C₂×C₄²	—	86	1	no	—
259	C₂×C₄²	—	172	4	no	—
260	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
261	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
262	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
263	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
264	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
265	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
266	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	86	4	no	—
270	C₄×C₈	—	86	2	no	—
271	C₄×C₈	—	86	2	no	—
272	#95	—	86	1	no	—
273	#95	—	86	1	no	—
274	#95	—	86	1	no	—
275	C₂⁴	—	86	1	no	—
276	C₂×D₄	—	43	2	no	—
277	C₂×D₄	—	43	2	no	—
278	C₂×D₄	—	43	2	no	—
279	C₂×D₄	—	86	1	no	—
280	C₂×D₄	—	86	1	no	—
281	C₂×D₄	—	86	1	no	—
282	C₂²×C₄	—	86	4	no	—
283	C₂²×C₄	—	86	1	no	—
284	C₂²×C₄	—	86	1	no	—
285	C₂²×C₄	—	86	1	no	—
286	C₂²×C₄	—	86	4	no	—
287	C₂²×C₄	—	86	2	no	—
288	C₂²×C₄	—	86	2	no	—
289	C₂²×C₄	—	172	2	no	—
290	C₂²×C₄	—	172	2	no	—
291	C₂²×C₄	—	172	2	no	—
292	C₂²×C₄	—	172	2	no	—
293	C₂²×C₄	—	172	2	no	—
294	C₂²×C₄	—	172	2	no	—
295	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
296	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
297	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
298	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
302	C₂×C₈	—	4	2	no	—
303	C₂×C₈	—	4	2	no	—
304	C₂×C₈	—	4	2	no	—
305	C₂×C₈	—	86	4	no	—
306	C₂×C₈	—	172	2	no	—
307	C₂×C₈	—	172	2	no	—
308	C₄⋊C₄	—	43	2	no	—
309	C₄⋊C₄	—	43	2	no	—
310	C₄⋊C₄	—	43	2	no	—
311	C₄⋊C₄	—	86	1	no	—
312	C₄⋊C₄	—	86	1	no	—
313	C₄⋊C₄	—	86	1	no	—
314	C₂²⋊C₄	—	86	4	no	—
315	C₂²⋊C₄	—	86	4	no	—
316	C₂²⋊C₄	—	86	2	no	—
317	C₂²⋊C₄	—	86	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	4	1	no	—
324	C₄²	—	172	2	no	—
325	C₄²	—	172	2	no	—
326	C₄²	—	172	2	no	—
327	C₄²	C₈×D₄₃	1	2	yes	—
328	C₄²	#10621872	1	2	yes	—
329	C₄²	D₄×D₄₃	1	1	yes	characteristic
330	C₄²	#10621900	1	1	yes	characteristic
331	C₄²	Q₈×D₄₃	1	1	yes	characteristic
332	C₄²	#10621902	1	1	yes	characteristic
333	C₂³	—	86	2	no	—
334	C₂³	—	86	2	no	—
335	C₂³	—	86	2	no	—
336	C₂³	—	172	1	no	—
337	C₂³	—	172	1	no	—
338	C₂³	—	172	1	no	—
339	C₂³	—	172	1	no	—
340	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
341	D₄	—	43	4	no	—
342	D₄	—	86	2	no	—
343	D₄	—	86	2	no	—
344	D₄	—	86	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	86	2	no	—
357	C₂×C₄	—	86	2	no	—
358	C₂×C₄	—	86	2	no	—
359	C₂×C₄	—	172	8	no	—
360	C₂×C₄	—	172	8	no	—
361	C₂×C₄	—	172	1	no	—
362	C₂×C₄	—	172	1	no	—
363	C₂×C₄	—	172	1	no	—
364	C₂×C₄	—	172	1	no	—
365	C₂×C₄	—	172	1	no	—
366	C₂×C₄	—	172	1	no	—
367	C₂×C₄	—	172	4	no	—
368	C₂×C₄	—	172	4	no	—
369	C₂×C₄	(C₂×D₄₃)⋊C₈	1	2	yes	—
370	C₂×C₄	(C₂×D₄₃)⋊C₈	1	2	yes	—
371	C₂×C₄	#13063251	1	2	yes	—
372	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
373	C₂×C₄	#13063283	1	1	yes	characteristic
374	C₂×C₄	#13063296	1	1	yes	characteristic
375	C₂×C₄	#13063300	1	1	yes	characteristic
376	C₂×C₄	#13063301	1	1	yes	characteristic
377	C₂×C₄	#13063305	1	1	yes	characteristic
378	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
379	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
380	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
381	C₂×C₄	C₂×#10621872	1	1	yes	characteristic
382	C₂×C₄	#13063345	1	2	yes	—
383	C₂×C₄	#13063350	1	2	yes	—
384	C₈	—	8	2	no	—
385	C₈	—	172	4	no	—
386	C₂²	—	86	4	no	—
387	C₂²	—	172	2	no	—
388	C₂²	—	172	2	no	—
389	C₂²	—	172	2	no	—
390	C₂²	—	172	2	no	—
391	C₂²	—	172	2	no	—
392	C₂²	—	172	2	no	—
393	C₂²	#14582756	1	1	yes	characteristic
394	C₂²	C₂×(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
395	C₂²	#14582862	1	1	yes	characteristic
396	C₂²	#14582893	1	1	yes	characteristic
397	C₂²	#14582903	1	1	yes	characteristic
398	C₂²	C₂×#13063251	1	1	yes	characteristic
399	C₂²	#14582915	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	4	1	no	—
406	C₄	—	172	2	no	—
407	C₄	—	172	2	no	—
408	C₄	—	172	2	no	—
409	C₄	C₄⋊C₈×D₄₃	1	1	yes	characteristic
410	C₄	#14582921	1	1	yes	characteristic
411	C₄	#14582951	1	1	yes	characteristic
412	C₄	#14582955	1	1	yes	characteristic
413	C₄	#14583111	1	2	yes	—
414	C₄	#14583196	1	2	yes	—
415	C₂	—	172	4	no	—
416	C₂	#19132975	1	1	yes	characteristic
417	C₂	#19132985	1	1	yes	characteristic
418	C₂	#19133027	1	1	yes	characteristic
419	C₂	#19133037	1	1	yes	characteristic
420	C₂	#19134572	1	1	yes	characteristic
421	C₂	#19134602	1	1	yes	characteristic
422	C₂	#19134612	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1831	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂²×D₁₇₂	C₂×C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1831	D₄₃
hypocenter	C₄₃	#8565
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1831

Complements

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

N	H ≅ G/N	type
2. C₄×C₄⋊(C₄₃⋊C₈)	C₂	semidirect
4. #19132434	C₂	semidirect
5. C₄₃×#1831	C₂	semidirect
34. C₄×D₁₇₂	C₈	semidirect
167. D₁₇₂	C₄⋊C₈	semidirect
205. #1831	D₄₃	semidirect
235. C₄₃	#8565	semidirect

Maximal subgroups

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

subgroup	index
C₄²×D₁₇₂	2
C₄×C₄⋊(C₄₃⋊C₈)	2
C₂×#14582626	2
#19132434	2
C₄₃×#1831	2
#8565	43