Subgroups — #25095034

Order 11008.

1234 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582978	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582976	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#10621872	C₂	1	2	yes	maximal, complemented
4	C₄×#13063287	C₂	1	1	yes	maximal, characteristic
5	C₄⋊C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134450	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134378	C₂	1	2	yes	maximal, complemented
8	#19134375	C₂	1	2	yes	maximal, complemented
9	#19134356	C₂	1	2	yes	maximal, complemented
10	C₄×#13063235	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10621872	C₂²	1	2	yes	—
13	C₂²×#10621872	C₂²	1	2	yes	—
14	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
15	C₂×#13063287	C₄	1	2	yes	—
16	C₂×C₄²×D₄₃	C₂²	1	2	yes	—
17	#14582978	C₄	1	8	yes	complemented
18	#14582976	C₄	1	8	yes	complemented
19	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	2	yes	—
21	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	2	yes	—
22	C₄×#10621872	—	2	8	no	—
23	C₂×#13063235	C₂²	1	1	yes	characteristic
24	C₂×#13063235	C₂²	1	1	yes	characteristic
25	C₂×#13063235	C₂²	1	1	yes	characteristic
26	C₂×#13063235	C₂²	1	2	yes	—
27	C₂×#13063235	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
29	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₄⋊C₄×Dic₄₃	C₄	1	2	yes	—
31	C₄×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
32	#14582746	C₄	1	4	yes	—
33	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
34	#14582654	C₂²	1	2	yes	—
35	#14582653	C₂²	1	2	yes	—
36	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#336	C₂²	1	2	yes	—
41	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₄₃	C₂×C₄	1	4	yes	—
43	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
44	C₂×#10621872	—	2	4	no	—
45	C₂×#10621872	—	2	4	no	—
46	C₂×#10621872	—	2	4	no	—
47	C₂×#10621872	—	2	4	no	—
48	C₂×#10621872	C₂×C₄	1	8	yes	complemented
49	C₂×#10621872	C₂×C₄	1	8	yes	complemented
50	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
52	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
53	C₄×D₁₇₂	C₂×C₄	1	4	yes	—
54	C₄×D₁₇₂	C₂×C₄	1	4	yes	—
55	#13063287	—	2	8	no	—
56	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
57	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	4	yes	—
58	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₄₃	C₂×C₄	1	4	yes	—
60	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
61	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
62	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
63	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
64	C₄²×D₄₃	—	2	4	no	—
65	C₄²×D₄₃	—	2	4	no	—
66	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	complemented
67	(C₂×D₄₃)⋊C₈	C₂×C₄	1	8	yes	complemented
68	(C₂×D₄₃)⋊C₈	C₂×C₄	1	8	yes	complemented
69	#13063235	—	2	2	no	—
70	#13063235	—	2	4	no	—
71	#13063235	—	2	2	no	—
72	#13063235	—	2	2	no	—
73	#13063235	D₄	1	4	yes	complemented
74	C₄×C₄₃⋊C₈	—	2	4	no	—
75	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	complemented
76	C₄₃⋊#95	C₂×C₄	1	4	yes	—
77	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
79	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
81	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
82	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	complemented
84	C₄×C₈×C₄₃	—	2	4	no	—
85	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
86	#95×C₄₃	C₂×C₄	1	2	yes	—
87	C₂³×D₄₃	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
92	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
93	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
94	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
95	C₂×D₁₇₂	—	2	4	no	—
96	C₂×D₁₇₂	C₄²	1	4	yes	—
97	C₂×C₄×D₄₃	—	2	2	no	—
98	C₂×C₄×D₄₃	—	2	2	no	—
99	C₂×C₄×D₄₃	—	2	2	no	—
100	C₂×C₄×D₄₃	—	2	2	no	—
101	C₂×C₄×D₄₃	—	2	8	no	—
102	C₂×C₄×D₄₃	—	2	8	no	—
103	C₂×C₄×D₄₃	—	4	4	no	—
104	C₂×C₄×D₄₃	C₂²×C₄	1	4	yes	—
105	C₂×C₄×D₄₃	C₂²×C₄	1	4	yes	—
106	C₂×C₈×C₄₃	—	2	2	no	—
107	C₂×C₈×C₄₃	—	2	1	no	—
108	C₂×C₈×C₄₃	—	2	1	no	—
109	C₂×C₈×C₄₃	—	2	2	no	—
110	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
111	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
112	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₄₃	#41	1	2	yes	—
115	C₄⋊C₄×C₄₃	M₁₆	1	8	yes	complemented
116	C₄²×C₄₃	—	2	2	no	—
117	C₄²×C₄₃	—	2	2	no	—
118	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
119	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
120	(C₂×D₄₃)⋊C₄	—	2	8	no	—
121	(C₂×D₄₃)⋊C₄	C₄²	1	8	yes	—
122	C₄⋊Dic₄₃	C₄²	1	4	yes	—
123	C₄×Dic₄₃	—	2	4	no	—
124	C₄×Dic₄₃	—	2	1	no	—
125	C₄×Dic₄₃	—	2	1	no	—
126	C₄×Dic₄₃	—	2	8	no	—
127	C₄×Dic₄₃	—	4	2	no	—
128	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
129	C₄×Dic₄₃	#41	1	2	yes	—
130	C₂×C₄₃⋊C₈	—	2	2	no	—
131	C₂×C₄₃⋊C₈	—	2	1	no	—
132	C₂×C₄₃⋊C₈	—	2	1	no	—
133	C₂×C₄₃⋊C₈	—	2	2	no	—
134	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
135	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
136	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
137	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
138	C₂×C₄₃⋊C₈	#41	1	2	yes	—
139	#10621872	—	2	16	no	—
140	#10621872	—	2	16	no	—
141	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
142	C₂²×D₄₃	—	2	2	no	—
143	C₂²×D₄₃	—	2	2	no	—
144	C₂²×D₄₃	—	2	4	no	—
145	C₂²×D₄₃	—	2	4	no	—
146	C₂²×D₄₃	C₂×C₄²	1	4	yes	—
147	C₂×C₄×C₄₃	—	2	4	no	—
148	C₂×C₄×C₄₃	—	2	2	no	—
149	C₂×C₄×C₄₃	—	2	4	no	—
150	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
151	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
152	C₂×C₄×C₄₃	C₂×M₁₆	1	8	yes	—
153	C₂×C₄×C₄₃	C₂×M₁₆	1	4	yes	—
154	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
160	C₂×Dic₄₃	—	2	2	no	—
161	C₂×Dic₄₃	—	2	2	no	—
162	C₂×Dic₄₃	—	2	2	no	—
163	C₂×Dic₄₃	—	2	2	no	—
164	C₂×Dic₄₃	—	2	2	no	—
165	C₂×Dic₄₃	—	2	2	no	—
166	C₂×Dic₄₃	—	2	2	no	—
167	C₂×Dic₄₃	C₂×C₄²	1	4	yes	—
168	C₂×Dic₄₃	C₄×D₄	1	4	yes	—
169	D₁₇₂	—	2	8	no	—
170	C₄×D₄₃	—	2	4	no	—
171	C₄×D₄₃	—	2	4	no	—
172	C₄×D₄₃	—	2	4	no	—
173	C₄×D₄₃	—	2	4	no	—
174	C₄×D₄₃	—	4	16	no	—
175	C₈×C₄₃	—	2	4	no	—
176	C₈×C₄₃	—	2	2	no	—
177	C₈×C₄₃	C₄×D₄	1	4	yes	complemented
178	C₄₃⋊C₈	—	2	4	no	—
179	C₄₃⋊C₈	—	2	2	no	—
180	C₄₃⋊C₈	C₄×D₄	1	4	yes	complemented
181	#20494	—	43	1	no	maximal, Sylow
182	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
183	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
184	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
185	C₂²×C₄₃	C₂²×M₁₆	1	2	yes	—
186	C₂²×C₄₃	#568	1	2	yes	—
187	C₂×D₄₃	—	2	4	no	—
188	C₂×D₄₃	—	2	4	no	—
189	C₂×D₄₃	—	2	4	no	—
190	C₂×D₄₃	—	4	4	no	—
191	C₂×D₄₃	—	4	4	no	—
192	C₄×C₄₃	—	2	2	no	—
193	C₄×C₄₃	—	2	8	no	—
194	C₄×C₄₃	C₄×M₁₆	1	4	yes	complemented
195	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
196	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
197	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
198	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
199	Dic₄₃	—	2	4	no	—
200	Dic₄₃	—	2	4	no	—
201	Dic₄₃	—	4	2	no	—
202	C₂×#436	—	43	1	no	—
203	C₂×#436	—	43	1	no	—
204	C₂×C₄×M₁₆	—	43	2	no	—
205	C₄²×D₄	—	43	1	no	—
206	C₈×C₄⋊C₄	—	43	1	no	—
207	C₈×C₄⋊C₄	D₄₃	1	1	yes	characteristic, complemented
208	#1767	—	43	1	no	—
209	#1753	—	43	2	no	—
210	#1753	—	43	2	no	—
211	#1749	—	43	2	no	—
212	C₄×#97	—	43	1	no	—
213	C₂×C₄₃	C₄²×D₄	1	1	yes	characteristic
214	C₂×C₄₃	C₂×C₄×M₁₆	1	1	yes	characteristic
215	C₂×C₄₃	#2875	1	1	yes	characteristic
216	C₂×C₄₃	D₄×M₁₆	1	2	yes	—
217	C₂×C₄₃	#2971	1	2	yes	—
218	D₄₃	—	4	4	no	—
219	C₂²×M₁₆	—	43	2	no	—
220	C₂²×M₁₆	—	43	2	no	—
221	C₂×C₄×D₄	—	43	2	no	—
222	C₂×C₄×D₄	—	43	1	no	—
223	C₂²×C₄²	—	43	2	no	—
224	#436	—	43	8	no	—
225	#436	—	43	8	no	—
226	C₂×C₄⋊C₈	—	43	1	no	—
227	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
228	C₂×C₂²⋊C₈	—	43	2	no	—
229	C₂×C₂²⋊C₈	—	43	2	no	—
230	C₄×M₁₆	—	86	8	no	—
231	C₂×#97	—	43	1	no	—
232	C₂×#97	—	43	2	no	—
233	C₂×#97	—	43	1	no	—
234	C₂×#97	—	43	1	no	—
235	C₂×#97	—	43	1	no	—
236	C₂×C₄×C₈	—	43	1	no	—
237	C₂×C₄×C₈	—	43	2	no	—
238	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
239	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
240	C₄×C₄⋊C₄	—	43	2	no	—
241	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
242	C₄×C₂²⋊C₄	—	43	2	no	—
243	C₄×C₂²⋊C₄	—	43	4	no	—
244	C₄³	—	43	1	no	—
245	#336	—	43	2	no	—
246	#336	—	43	2	no	—
247	#336	C₂×D₄₃	1	2	yes	—
248	C₄₃	#20494	1	1	yes	characteristic, complemented, Sylow
249	C₂²×D₄	—	43	1	no	—
250	C₂³×C₄	—	43	2	no	—
251	C₂³×C₄	—	43	4	no	—
252	C₂×M₁₆	—	43	8	no	—
253	C₂×M₁₆	—	43	8	no	—
254	C₂×M₁₆	—	86	4	no	—
255	C₂×M₁₆	—	86	4	no	—
256	C₂×M₁₆	—	86	4	no	—
257	C₂×M₁₆	—	86	4	no	—
258	C₂²×C₈	—	43	1	no	—
259	C₂²×C₈	—	43	2	no	—
260	C₂²×C₈	—	43	1	no	—
261	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
262	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
263	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
264	C₄×D₄	—	43	4	no	—
265	C₄×D₄	—	43	4	no	—
266	C₄×D₄	—	86	8	no	—
267	C₂×C₄⋊C₄	—	43	1	no	—
268	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
269	C₂×C₂²⋊C₄	—	43	2	no	—
270	C₂×C₂²⋊C₄	—	43	4	no	—
271	C₂×C₄²	—	43	1	no	—
272	C₂×C₄²	—	43	2	no	—
273	C₂×C₄²	—	43	4	no	—
274	C₂×C₄²	—	43	1	no	—
275	C₂×C₄²	—	43	2	no	—
276	C₂×C₄²	—	86	4	no	—
277	C₂×C₄²	—	86	4	no	—
278	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
279	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
280	C₄⋊C₈	—	43	4	no	—
281	C₄⋊C₈	C₄×D₄₃	1	4	yes	complemented
282	C₂²⋊C₈	—	43	8	no	—
283	C₂²⋊C₈	—	43	8	no	—
284	#97	—	43	4	no	—
285	#97	—	86	2	no	—
286	#97	—	86	4	no	—
287	#97	—	86	2	no	—
288	#97	—	86	2	no	—
289	C₄×C₈	—	2	4	no	—
290	C₄×C₈	—	43	4	no	—
291	C₄×C₈	—	86	4	no	—
292	C₄×C₈	C₄×D₄₃	1	4	yes	complemented
293	#95	—	43	4	no	—
294	#95	C₄×D₄₃	1	2	yes	—
295	C₂⁴	—	43	2	no	—
296	C₂×D₄	—	43	4	no	—
297	C₂×D₄	—	86	4	no	—
298	C₂²×C₄	—	43	2	no	—
299	C₂²×C₄	—	43	2	no	—
300	C₂²×C₄	—	43	4	no	—
301	C₂²×C₄	—	43	4	no	—
302	C₂²×C₄	—	43	2	no	—
303	C₂²×C₄	—	86	8	no	—
304	C₂²×C₄	—	86	2	no	—
305	C₂²×C₄	—	86	2	no	—
306	C₂²×C₄	—	86	2	no	—
307	C₂²×C₄	—	86	2	no	—
308	C₂²×C₄	—	86	8	no	—
309	C₂²×C₄	—	172	4	no	—
310	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
312	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
313	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
314	M₁₆	—	86	16	no	—
315	M₁₆	—	86	16	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	43	2	no	—
321	C₂×C₈	—	43	2	no	—
322	C₂×C₈	—	43	2	no	—
323	C₂×C₈	—	43	2	no	—
324	C₂×C₈	—	43	4	no	—
325	C₂×C₈	—	86	2	no	—
326	C₂×C₈	—	86	1	no	—
327	C₂×C₈	—	86	1	no	—
328	C₂×C₈	—	86	2	no	—
329	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
330	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
331	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
332	C₂×C₈	D₄×D₄₃	1	2	yes	—
333	C₂×C₈	#10621902	1	2	yes	—
334	C₄⋊C₄	—	43	4	no	—
335	C₄⋊C₄	#10621872	1	8	yes	complemented
336	C₂²⋊C₄	—	43	8	no	—
337	C₂²⋊C₄	—	86	8	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	43	2	no	—
341	C₄²	—	43	2	no	—
342	C₄²	—	86	8	no	—
343	C₄²	—	86	4	no	—
344	C₄²	—	86	1	no	—
345	C₄²	—	86	1	no	—
346	C₄²	—	172	2	no	—
347	C₄²	C₂×C₄×D₄₃	1	2	yes	—
348	C₄²	C₂×C₄×D₄₃	1	2	yes	—
349	C₂³	—	43	4	no	—
350	C₂³	—	86	2	no	—
351	C₂³	—	86	2	no	—
352	C₂³	—	86	4	no	—
353	C₂³	—	86	4	no	—
354	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
355	D₄	—	86	8	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	43	4	no	—
360	C₂×C₄	—	43	4	no	—
361	C₂×C₄	—	86	2	no	—
362	C₂×C₄	—	86	2	no	—
363	C₂×C₄	—	86	2	no	—
364	C₂×C₄	—	86	2	no	—
365	C₂×C₄	—	86	4	no	—
366	C₂×C₄	—	86	4	no	—
367	C₂×C₄	—	86	4	no	—
368	C₂×C₄	—	86	4	no	—
369	C₂×C₄	—	86	2	no	—
370	C₂×C₄	—	86	2	no	—
371	C₂×C₄	—	86	2	no	—
372	C₂×C₄	—	172	16	no	—
373	C₂×C₄	C₄²×D₄₃	1	2	yes	—
374	C₂×C₄	C₄²×D₄₃	1	2	yes	—
375	C₂×C₄	C₂×#10621872	1	8	yes	—
376	C₂×C₄	C₂×#10621872	1	4	yes	—
377	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
379	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
380	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
381	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
382	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
383	C₈	—	2	4	no	—
384	C₈	—	2	2	no	—
385	C₈	—	43	4	no	—
386	C₈	—	86	4	no	—
387	C₈	—	86	2	no	—
388	C₈	#13063287	1	4	yes	complemented
389	C₂²	—	86	4	no	—
390	C₂²	—	86	4	no	—
391	C₂²	—	86	4	no	—
392	C₂²	—	172	4	no	—
393	C₂²	—	172	4	no	—
394	C₂²	C₂×C₄²×D₄₃	1	1	yes	characteristic
395	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
396	C₂²	C₄×#10621902	1	1	yes	characteristic
397	C₂²	C₂²×#10621872	1	2	yes	—
398	C₂²	#14583664	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	2	8	no	—
401	C₄	—	86	4	no	—
402	C₄	—	86	4	no	—
403	C₄	—	172	2	no	—
404	C₄	C₄×#10621872	1	4	yes	complemented
405	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
406	C₄	C₂×#13063287	1	1	yes	characteristic
407	C₄	#14583367	1	1	yes	characteristic
408	C₄	C₄×#10621902	1	1	yes	characteristic
409	C₂	—	172	4	no	—
410	C₂	C₄×#13063287	1	1	yes	characteristic
411	C₂	C₂×C₄×#10621872	1	1	yes	characteristic
412	C₂	#19143022	1	1	yes	characteristic
413	C₂	D₄×#10621872	1	2	yes	—
414	C₂	#19143614	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂²×C₄²
Fitting	C₈×C₄⋊C₄×C₄₃	C₂
socle	C₂³×C₄₃	C₂³×C₄
prime radical	C₂²×D₁₇₂	C₂×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₄₃
hypocenter	C₄₃	#20494
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×#10621872	C₂	semidirect
5. C₄⋊C₄×C₄₃⋊C₈	C₂	semidirect
6. #19134450	C₂	semidirect
7. #19134378	C₂	semidirect
8. #19134375	C₂	semidirect
9. #19134356	C₂	semidirect
10. C₄×#13063235	C₂	semidirect
11. C₈×C₄⋊C₄×C₄₃	C₂	semidirect
17. #14582978	C₄	semidirect
18. #14582976	C₄	semidirect
48. C₂×#10621872	C₂×C₄	semidirect
49. C₂×#10621872	C₂×C₄	semidirect
66. C₄⋊(C₄₃⋊C₈)	C₂×C₄	semidirect
67. (C₂×D₄₃)⋊C₈	C₂×C₄	semidirect
68. (C₂×D₄₃)⋊C₈	C₂×C₄	semidirect
73. #13063235	D₄	semidirect
75. C₄×C₄₃⋊C₈	C₂×C₄	semidirect
83. C₄⋊C₈×C₄₃	C₂×C₄	semidirect
85. C₄×C₈×C₄₃	C₂×C₄	semidirect
115. C₄⋊C₄×C₄₃	M₁₆	semidirect
177. C₈×C₄₃	C₄×D₄	semidirect
180. C₄₃⋊C₈	C₄×D₄	semidirect
194. C₄×C₄₃	C₄×M₁₆	semidirect
207. C₈×C₄⋊C₄	D₄₃	semidirect
248. C₄₃	#20494	semidirect
281. C₄⋊C₈	C₄×D₄₃	semidirect
292. C₄×C₈	C₄×D₄₃	semidirect
335. C₄⋊C₄	#10621872	semidirect
388. C₈	#13063287	semidirect
404. C₄	C₄×#10621872	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582978	2
C₂×#14582976	2
C₂×C₄×#10621872	2
C₄×#13063287	2
C₄⋊C₄×C₄₃⋊C₈	2
#19134450	2
#19134378	2
#19134375	2
#19134356	2
C₄×#13063235	2
C₈×C₄⋊C₄×C₄₃	2
#20494	43