Subgroups — #25002324

Order 11008.

894 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582661	C₂	1	2	yes	maximal
3	C₂×#14582661	C₂	1	2	yes	maximal
4	#19132825	C₂	1	1	yes	maximal, characteristic
5	C₄₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
7	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₄₃	C₂²	1	2	yes	—
9	C₂×C₄×C₄₃⋊C₈	—	2	4	no	—
10	C₂×C₄×C₄₃⋊C₈	C₄	1	4	yes	complemented
11	C₂×C₄₃⋊#95	—	2	1	no	—
12	C₂×C₄₃⋊#95	—	2	1	no	—
13	#14582661	—	2	4	no	—
14	#14582661	C₄	1	8	yes	complemented
15	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#95×C₄₃	—	2	1	no	—
18	C₂×#95×C₄₃	—	2	1	no	—
19	C₂³×Dic₄₃	—	2	2	no	—
20	C₂²×C₄₃⋊C₈	—	2	2	no	—
21	C₂²×C₄₃⋊C₈	—	2	2	no	—
22	C₂²×C₄₃⋊C₈	—	2	1	no	—
23	C₂²×C₄₃⋊C₈	—	2	1	no	—
24	C₂²×C₄₃⋊C₈	—	2	1	no	—
25	C₂²×C₄₃⋊C₈	—	2	1	no	—
26	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
27	C₂²×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
28	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
29	C₂²×C₄₃⋊C₈	D₄	1	4	yes	—
30	C₂×C₄⋊Dic₄₃	—	2	2	no	—
31	C₂×C₄⋊Dic₄₃	—	2	2	no	—
32	C₂×C₄⋊Dic₄₃	—	2	2	no	—
33	C₂×C₄⋊Dic₄₃	—	2	2	no	—
34	C₂×C₄⋊Dic₄₃	—	2	2	no	—
35	C₂×C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
36	C₄×C₄₃⋊C₈	—	2	8	no	—
37	C₄₃⋊#95	—	4	2	no	—
38	C₄₃⋊#95	—	4	2	no	—
39	C₂³×C₄×C₄₃	—	2	2	no	—
40	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
49	C₂×C₄²×C₄₃	—	2	2	no	—
50	C₂×C₄²×C₄₃	—	2	2	no	—
51	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₄₃	Q₈	1	2	yes	—
53	#95×C₄₃	—	4	2	no	—
54	#95×C₄₃	—	4	2	no	—
55	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₃	—	2	4	no	—
57	C₂²×C₄×C₄₃	—	2	2	no	—
58	C₂²×C₄×C₄₃	—	2	2	no	—
59	C₂²×C₄×C₄₃	—	2	2	no	—
60	C₂²×C₄×C₄₃	—	2	2	no	—
61	C₂²×C₄×C₄₃	—	4	2	no	—
62	C₂²×C₄×C₄₃	—	4	2	no	—
63	C₂²×C₄×C₄₃	—	4	2	no	—
64	C₂²×C₄×C₄₃	—	4	2	no	—
65	C₂²×C₄×C₄₃	—	4	2	no	—
66	C₂²×C₄×C₄₃	—	4	2	no	—
67	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
68	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
69	C₂²×C₄×C₄₃	D₈	1	2	yes	—
70	C₂²×C₄×C₄₃	SD₁₆	1	2	yes	—
71	C₂²×C₄×C₄₃	SD₁₆	1	2	yes	—
72	C₂²×C₄×C₄₃	Q₁₆	1	2	yes	—
73	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₄₃	#41	1	2	yes	—
78	C₂²×C₄×C₄₃	#41	1	2	yes	—
79	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
80	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
81	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
82	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
83	C₂²×Dic₄₃	—	2	4	no	—
84	C₂²×Dic₄₃	—	4	2	no	—
85	C₂²×Dic₄₃	—	4	2	no	—
86	C₂²×Dic₄₃	—	4	2	no	—
87	C₂²×Dic₄₃	—	4	2	no	—
88	C₂²×Dic₄₃	—	4	2	no	—
89	C₂²×Dic₄₃	—	4	2	no	—
90	C₄⋊C₄×C₄₃	—	2	4	no	—
91	C₄⋊C₄×C₄₃	—	2	4	no	—
92	C₄⋊C₄×C₄₃	—	4	2	no	—
93	C₄⋊C₄×C₄₃	—	4	2	no	—
94	C₄²×C₄₃	—	2	2	no	—
95	C₄²×C₄₃	—	2	2	no	—
96	C₄²×C₄₃	—	2	4	no	—
97	C₄⋊Dic₄₃	—	2	4	no	—
98	C₄⋊Dic₄₃	—	2	4	no	—
99	C₄⋊Dic₄₃	—	4	2	no	—
100	C₄⋊Dic₄₃	—	4	2	no	—
101	C₂×C₄₃⋊C₈	—	2	2	no	—
102	C₂×C₄₃⋊C₈	—	2	2	no	—
103	C₂×C₄₃⋊C₈	—	2	2	no	—
104	C₂×C₄₃⋊C₈	—	2	2	no	—
105	C₂×C₄₃⋊C₈	—	2	4	no	—
106	C₂×C₄₃⋊C₈	—	2	4	no	—
107	C₂×C₄₃⋊C₈	—	2	4	no	—
108	C₂×C₄₃⋊C₈	—	2	4	no	—
109	C₂×C₄₃⋊C₈	C₄²	1	4	yes	—
110	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	4	yes	—
111	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
112	C₂³×C₄₃	C₄×D₄	1	2	yes	—
113	C₂³×C₄₃	#121	1	2	yes	—
114	C₂³×C₄₃	#124	1	1	yes	characteristic
115	C₂³×C₄₃	#124	1	1	yes	characteristic
116	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
117	C₂³×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
118	C₂³×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
119	C₂³×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
120	C₂³×C₄₃	#135	1	2	yes	—
121	C₂³×C₄₃	#135	1	2	yes	—
122	C₂×C₄×C₄₃	—	2	2	no	—
123	C₂×C₄×C₄₃	—	2	2	no	—
124	C₂×C₄×C₄₃	—	2	2	no	—
125	C₂×C₄×C₄₃	—	2	2	no	—
126	C₂×C₄×C₄₃	—	2	4	no	—
127	C₂×C₄×C₄₃	—	2	4	no	—
128	C₂×C₄×C₄₃	—	2	4	no	—
129	C₂×C₄×C₄₃	—	2	4	no	—
130	C₂×C₄×C₄₃	—	4	4	no	—
131	C₂×C₄×C₄₃	—	4	4	no	—
132	C₂×C₄×C₄₃	—	4	4	no	—
133	C₂×C₄×C₄₃	—	8	2	no	—
134	C₂×C₄×C₄₃	—	8	2	no	—
135	C₂×C₄×C₄₃	—	8	2	no	—
136	C₂×C₄×C₄₃	—	8	2	no	—
137	C₂×C₄×C₄₃	#106	1	4	yes	—
138	C₂×C₄×C₄₃	#107	1	4	yes	—
139	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
140	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
142	C₂×C₄×C₄₃	#117	1	2	yes	—
143	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
144	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
145	C₂×C₄×C₄₃	#117	1	2	yes	—
146	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
147	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
148	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₄₃	C₄×Q₈	1	2	yes	—
150	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
151	C₂×C₄×C₄₃	#123	1	2	yes	—
152	C₂×C₄×C₄₃	#123	1	2	yes	—
153	C₂×C₄×C₄₃	#125	1	1	yes	characteristic
154	C₂×C₄×C₄₃	#125	1	1	yes	characteristic
155	C₂×C₄×C₄₃	#126	1	2	yes	—
156	C₂×C₄×C₄₃	#126	1	2	yes	—
157	C₂×Dic₄₃	—	4	4	no	—
158	C₂×Dic₄₃	—	4	4	no	—
159	C₂×Dic₄₃	—	4	4	no	—
160	C₂×Dic₄₃	—	8	2	no	—
161	C₂×Dic₄₃	—	8	2	no	—
162	C₂×Dic₄₃	—	8	2	no	—
163	C₂×Dic₄₃	—	8	2	no	—
164	C₄₃⋊C₈	—	2	4	no	—
165	C₄₃⋊C₈	—	2	4	no	—
166	#10820	—	43	1	no	maximal, Sylow
167	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
168	C₂²×C₄₃	#380	1	1	yes	characteristic
169	C₂²×C₄₃	#382	1	1	yes	characteristic
170	C₂²×C₄₃	#388	1	2	yes	—
171	C₂²×C₄₃	#388	1	2	yes	—
172	C₂²×C₄₃	C₂×#106	1	1	yes	characteristic
173	C₂²×C₄₃	C₂×#107	1	1	yes	characteristic
174	C₂²×C₄₃	#427	1	1	yes	characteristic
175	C₂²×C₄₃	#427	1	1	yes	characteristic
176	C₂²×C₄₃	C₄×D₈	1	2	yes	—
177	C₂²×C₄₃	C₄×SD₁₆	1	2	yes	—
178	C₂²×C₄₃	C₄×SD₁₆	1	2	yes	—
179	C₂²×C₄₃	C₄×Q₁₆	1	2	yes	—
180	C₂²×C₄₃	#465	1	2	yes	—
181	C₂²×C₄₃	#465	1	2	yes	—
182	C₂²×C₄₃	#466	1	2	yes	—
183	C₂²×C₄₃	#467	1	2	yes	—
184	C₂²×C₄₃	#486	1	1	yes	characteristic
185	C₂²×C₄₃	#486	1	1	yes	characteristic
186	C₂²×C₄₃	#487	1	1	yes	characteristic
187	C₂²×C₄₃	#487	1	1	yes	characteristic
188	C₂²×C₄₃	#488	1	2	yes	—
189	C₂²×C₄₃	#488	1	2	yes	—
190	C₄×C₄₃	—	2	4	no	—
191	C₄×C₄₃	—	2	4	no	—
192	C₄×C₄₃	—	8	4	no	—
193	C₄×C₄₃	#376	1	1	yes	characteristic
194	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
195	C₄×C₄₃	#381	1	1	yes	characteristic
196	C₄×C₄₃	#383	1	1	yes	characteristic
197	C₄×C₄₃	#387	1	2	yes	—
198	C₄×C₄₃	#387	1	2	yes	—
199	Dic₄₃	—	8	4	no	—
200	C₂²×C₄×C₈	—	43	1	no	—
201	C₂×#340	—	43	2	no	—
202	C₂×#340	—	43	2	no	—
203	C₄⋊#95	—	43	1	no	—
204	C₄⋊#95	D₄₃	1	1	yes	characteristic
205	C₂×C₄₃	#1434	1	1	yes	characteristic
206	C₂×C₄₃	C₄×#106	1	1	yes	characteristic
207	C₂×C₄₃	C₄×#107	1	1	yes	characteristic
208	C₂×C₄₃	#1807	1	1	yes	characteristic
209	C₂×C₄₃	#1808	1	1	yes	characteristic
210	C₂×C₄₃	#1834	1	1	yes	characteristic
211	C₂×C₄₃	#1835	1	1	yes	characteristic
212	C₂×C₄₃	#1933	1	2	yes	—
213	C₂×C₄₃	#1933	1	2	yes	—
214	C₂×C₄₃	#1934	1	2	yes	—
215	C₂×C₄₃	#1934	1	2	yes	—
216	C₂³×C₈	—	43	1	no	—
217	C₂³×C₈	—	43	1	no	—
218	C₂²×C₄⋊C₄	—	43	2	no	—
219	C₂²×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
220	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
221	C₂×C₄×C₈	—	43	4	no	—
222	C₂×C₄×C₈	—	86	4	no	—
223	C₂×#95	—	2	1	no	—
224	C₂×#95	—	2	1	no	—
225	C₂×#95	—	86	1	no	—
226	C₂×#95	—	86	1	no	—
227	#340	—	43	8	no	—
228	#340	—	86	4	no	—
229	C₄₃	#10820	1	1	yes	characteristic, complemented, Sylow
230	C₂³×C₄	—	2	2	no	—
231	C₂³×C₄	—	86	2	no	—
232	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
233	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
234	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
235	C₂²×C₈	—	43	4	no	—
236	C₂²×C₈	—	43	2	no	—
237	C₂²×C₈	—	43	2	no	—
238	C₂²×C₈	—	43	4	no	—
239	C₂²×C₈	—	86	2	no	—
240	C₂²×C₈	—	86	2	no	—
241	C₂²×C₈	—	86	1	no	—
242	C₂²×C₈	—	86	1	no	—
243	C₂²×C₈	—	86	1	no	—
244	C₂²×C₈	—	86	1	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	43	4	no	—
251	C₂×C₄⋊C₄	—	86	2	no	—
252	C₂×C₄⋊C₄	—	86	2	no	—
253	C₂×C₄⋊C₄	—	86	2	no	—
254	C₂×C₄⋊C₄	—	86	2	no	—
255	C₂×C₄⋊C₄	—	86	2	no	—
256	C₂×C₄⋊C₄	C₄×D₄₃	1	4	yes	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	Dic₈₆	1	2	yes	—
260	C₂×C₄²	C₄×D₄₃	1	2	yes	—
261	C₄×C₈	—	86	8	no	—
262	#95	—	4	2	no	—
263	#95	—	4	2	no	—
264	#95	—	172	2	no	—
265	#95	—	172	2	no	—
266	C₂⁴	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	86	4	no	—
279	C₂²×C₄	—	172	2	no	—
280	C₂²×C₄	—	172	2	no	—
281	C₂²×C₄	—	172	2	no	—
282	C₂²×C₄	—	172	2	no	—
283	C₂²×C₄	—	172	2	no	—
284	C₂²×C₄	—	172	2	no	—
285	C₂²×C₄	Dic₄₃⋊C₄	1	2	yes	—
286	C₂²×C₄	Dic₄₃⋊C₄	1	2	yes	—
287	C₂²×C₄	#10621882	1	2	yes	—
288	C₂²×C₄	#10621883	1	2	yes	—
289	C₂²×C₄	#10621884	1	2	yes	—
290	C₂²×C₄	#10621885	1	2	yes	—
291	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
294	C₂²×C₄	#10621898	1	2	yes	—
295	C₂²×C₄	D₄×D₄₃	1	2	yes	—
296	C₂²×C₄	#10621900	1	2	yes	—
297	C₂²×C₄	#10621900	1	1	yes	characteristic
298	C₂²×C₄	#10621900	1	1	yes	characteristic
299	C₂²×C₄	#10621902	1	1	yes	characteristic
300	C₂²×C₄	#10621902	1	1	yes	characteristic
301	C₂×C₈	—	43	4	no	—
302	C₂×C₈	—	43	4	no	—
303	C₂×C₈	—	86	2	no	—
304	C₂×C₈	—	86	2	no	—
305	C₂×C₈	—	86	2	no	—
306	C₂×C₈	—	86	2	no	—
307	C₂×C₈	—	86	4	no	—
308	C₂×C₈	—	86	4	no	—
309	C₂×C₈	—	86	4	no	—
310	C₂×C₈	—	86	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	86	4	no	—
316	C₄⋊C₄	—	86	4	no	—
317	C₄⋊C₄	—	172	2	no	—
318	C₄⋊C₄	—	172	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	4	no	—
322	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
323	C₂³	C₄×C₂²⋊D₄₃	1	2	yes	—
324	C₂³	#13063297	1	2	yes	—
325	C₂³	#13063312	1	1	yes	characteristic
326	C₂³	#13063314	1	1	yes	characteristic
327	C₂³	C₂×#10621882	1	1	yes	characteristic
328	C₂³	C₂×#10621884	1	1	yes	characteristic
329	C₂³	C₂×#10621883	1	1	yes	characteristic
330	C₂³	C₂×#10621885	1	1	yes	characteristic
331	C₂³	#13063345	1	2	yes	—
332	C₂³	#13063345	1	2	yes	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	8	2	no	—
345	C₂×C₄	—	8	2	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	—	344	2	no	—
349	C₂×C₄	—	344	2	no	—
350	C₂×C₄	—	344	2	no	—
351	C₂×C₄	—	344	2	no	—
352	C₂×C₄	—	172	4	no	—
353	C₂×C₄	—	172	4	no	—
354	C₂×C₄	—	172	4	no	—
355	C₂×C₄	#13063256	1	4	yes	—
356	C₂×C₄	#13063258	1	4	yes	—
357	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
358	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
359	C₂×C₄	#13063281	1	1	yes	characteristic
360	C₂×C₄	#13063281	1	2	yes	—
361	C₂×C₄	#13063282	1	1	yes	characteristic
362	C₂×C₄	#13063283	1	2	yes	—
363	C₂×C₄	#13063283	1	1	yes	characteristic
364	C₂×C₄	#13063283	1	1	yes	characteristic
365	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
366	C₂×C₄	#13063287	1	2	yes	—
367	C₂×C₄	C₄×Dic₈₆	1	2	yes	—
368	C₂×C₄	#13063302	1	2	yes	—
369	C₂×C₄	#13063307	1	2	yes	—
370	C₂×C₄	#13063310	1	2	yes	—
371	C₂×C₄	#13063316	1	1	yes	characteristic
372	C₂×C₄	#13063316	1	1	yes	characteristic
373	C₂×C₄	#13063318	1	2	yes	—
374	C₂×C₄	#13063320	1	2	yes	—
375	C₈	—	86	4	no	—
376	C₈	—	86	4	no	—
377	C₂²	C₄×Dic₄₃⋊C₄	1	1	yes	characteristic
378	C₂²	#14582757	1	1	yes	characteristic
379	C₂²	#14582764	1	1	yes	characteristic
380	C₂²	#14582789	1	2	yes	—
381	C₂²	#14582793	1	2	yes	—
382	C₂²	C₂×#13063256	1	1	yes	characteristic
383	C₂²	C₂×#13063258	1	1	yes	characteristic
384	C₂²	#14582935	1	1	yes	characteristic
385	C₂²	#14582935	1	1	yes	characteristic
386	C₂²	C₄×#10621882	1	2	yes	—
387	C₂²	C₄×#10621883	1	2	yes	—
388	C₂²	C₄×#10621884	1	2	yes	—
389	C₂²	C₄×#10621885	1	2	yes	—
390	C₂²	#14583126	1	2	yes	—
391	C₂²	#14583130	1	2	yes	—
392	C₂²	#14583133	1	2	yes	—
393	C₂²	#14583138	1	2	yes	—
394	C₂²	#14583245	1	1	yes	characteristic
395	C₂²	#14583247	1	1	yes	characteristic
396	C₂²	#14583249	1	1	yes	characteristic
397	C₂²	#14583251	1	1	yes	characteristic
398	C₂²	#14583253	1	2	yes	—
399	C₂²	#14583256	1	2	yes	—
400	C₄	—	2	4	no	—
401	C₄	—	2	4	no	—
402	C₄	—	8	4	no	—
403	C₄	—	344	4	no	—
404	C₄	#14582744	1	1	yes	characteristic
405	C₄	#14582746	1	1	yes	characteristic
406	C₄	#14582761	1	1	yes	characteristic
407	C₄	#14582766	1	1	yes	characteristic
408	C₄	#14582782	1	2	yes	—
409	C₄	#14582786	1	2	yes	—
410	C₂	#19132821	1	1	yes	characteristic
411	C₂	C₄×#13063256	1	1	yes	characteristic
412	C₂	C₄×#13063258	1	1	yes	characteristic
413	C₂	#19134618	1	1	yes	characteristic
414	C₂	#19134622	1	1	yes	characteristic
415	C₂	#19134722	1	1	yes	characteristic
416	C₂	#19134725	1	1	yes	characteristic
417	C₂	#19135270	1	2	yes	—
418	C₂	#19135274	1	2	yes	—
419	C₂	#19135277	1	2	yes	—
420	C₂	#19135281	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₄₃×C₄⋊#95	C₂
socle, prime radical	C₂⁴×C₄₃	C₂×D₄
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₄⋊#95	D₄₃
hypocenter	C₄₃	#10820
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₄⋊#95

Complements

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

N	H ≅ G/N	type
10. C₂×C₄×C₄₃⋊C₈	C₄	semidirect
14. #14582661	C₄	semidirect
229. C₄₃	#10820	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₄₃⋊C₈	2
C₂×#14582661	2
#19132825	2
C₄₃×C₄⋊#95	2
#10820	43