Subgroups — #25115036

Order 11008.

910 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582993	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582993	C₂	1	1	yes	maximal, characteristic
4	#19137514	C₂	1	2	yes	maximal
5	#19135329	C₂	1	1	yes	maximal, characteristic
6	#19134864	C₂	1	2	yes	maximal
7	#19134862	C₂	1	2	yes	maximal
8	#19134758	C₂	1	1	yes	maximal, characteristic
9	#19134609	C₂	1	2	yes	maximal
10	C₈×Dic₄₃⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1942	C₂	1	1	yes	maximal, characteristic
12	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₈₆	C₂²	1	2	yes	—
14	C₂×#13063290	C₂²	1	2	yes	—
15	C₂×#13063290	C₂²	1	2	yes	—
16	C₄×Dic₁₇₂	—	2	4	no	—
17	#14582993	—	2	4	no	—
18	#14582993	C₄	1	8	yes	complemented
19	C₂×#13063259	C₂²	1	1	yes	characteristic
20	C₂×#13063256	C₂²	1	2	yes	—
21	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×#13063250	C₂²	1	2	yes	—
23	C₂×#13063248	C₂²	1	2	yes	—
24	C₂×#13063248	C₂²	1	2	yes	—
25	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
27	#14582798	C₂²	1	2	yes	—
28	#14582796	—	2	2	no	—
29	#14582794	—	2	2	no	—
30	#14582764	C₂²	1	2	yes	—
31	#14582763	—	2	2	no	—
32	C₄⋊C₄×Dic₄₃	—	2	2	no	—
33	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
34	#14582661	C₂²	1	2	yes	—
35	#14582654	C₂²	1	1	yes	characteristic
36	#14582653	C₂²	1	1	yes	characteristic
37	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#389	C₂²	1	2	yes	—
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₂²×Dic₈₆	C₂³	1	2	yes	—
43	C₂×Dic₁₇₂	C₂×C₄	1	4	yes	—
44	C₂×Dic₁₇₂	D₄	1	4	yes	—
45	C₂×Dic₁₇₂	Q₈	1	4	yes	—
46	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
48	C₄×Dic₈₆	—	2	4	no	—
49	C₄×Dic₈₆	—	4	2	no	—
50	#13063290	—	2	4	no	—
51	#13063290	—	2	4	no	—
52	#13063290	—	4	2	no	—
53	#13063290	C₂×C₄	1	8	yes	—
54	C₂×C₄⋊Dic₄₃	—	2	2	no	—
55	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
56	C₂×Dic₄₃⋊C₄	—	2	2	no	—
57	C₂×Dic₄₃⋊C₄	—	2	2	no	—
58	C₂×Dic₄₃⋊C₄	—	2	2	no	—
59	C₂×Dic₄₃⋊C₄	D₄	1	1	yes	characteristic
60	C₂×Dic₄₃⋊C₄	D₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₃	—	2	2	no	—
62	C₂×C₄×Dic₄₃	—	2	2	no	—
63	C₂×C₄×Dic₄₃	—	2	2	no	—
64	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
66	#13063259	—	2	2	no	—
67	#13063256	—	4	2	no	—
68	Dic₄₃⋊C₈	—	2	2	no	—
69	#13063250	—	2	4	no	—
70	#13063248	—	2	4	no	—
71	#13063248	C₂×C₄	1	8	yes	—
72	C₈×Dic₄₃	—	2	2	no	—
73	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
74	C₄₃⋊#95	—	2	2	no	—
75	C₄₃⋊#95	—	2	2	no	—
76	C₄₃⋊#95	—	2	2	no	—
77	C₄₃⋊#95	D₄	1	1	yes	characteristic
78	C₄₃⋊#95	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
84	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
85	#107×C₄₃	—	2	2	no	—
86	#107×C₄₃	C₂×C₄	1	4	yes	—
87	C₄×C₈×C₄₃	—	2	2	no	—
88	#95×C₄₃	—	2	2	no	—
89	C₂²×C₄×C₄₃	—	2	2	no	—
90	C₂²×C₄×C₄₃	—	2	2	no	—
91	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₃	—	2	2	no	—
95	C₂²×Dic₄₃	—	2	2	no	—
96	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
100	C₂×Dic₈₆	—	2	2	no	—
101	C₂×Dic₈₆	—	2	2	no	—
102	C₂×Dic₈₆	—	2	2	no	—
103	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
104	C₂×Dic₈₆	C₂×D₄	1	4	yes	—
105	C₂×Dic₈₆	C₂×Q₈	1	4	yes	—
106	C₂×C₈×C₄₃	—	2	1	no	—
107	C₂×C₈×C₄₃	—	2	1	no	—
108	C₂×C₈×C₄₃	—	2	1	no	—
109	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
112	C₄⋊C₄×C₄₃	—	2	2	no	—
113	C₄⋊C₄×C₄₃	—	2	2	no	—
114	C₄⋊C₄×C₄₃	—	2	2	no	—
115	C₄⋊C₄×C₄₃	—	4	4	no	—
116	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
117	C₄²×C₄₃	—	2	1	no	—
118	C₄²×C₄₃	—	2	1	no	—
119	C₄⋊Dic₄₃	—	2	2	no	—
120	C₄⋊Dic₄₃	—	2	2	no	—
121	C₄⋊Dic₄₃	—	4	4	no	—
122	Dic₄₃⋊C₄	—	2	2	no	—
123	Dic₄₃⋊C₄	—	2	8	no	—
124	Dic₄₃⋊C₄	—	2	2	no	—
125	Dic₄₃⋊C₄	—	4	4	no	—
126	Dic₄₃⋊C₄	—	4	4	no	—
127	C₄×Dic₄₃	—	2	1	no	—
128	C₄×Dic₄₃	—	2	1	no	—
129	C₄×Dic₄₃	—	2	8	no	—
130	C₄×Dic₄₃	—	4	4	no	—
131	C₄×Dic₄₃	—	4	4	no	—
132	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
133	C₄×Dic₄₃	#41	1	2	yes	—
134	C₂×C₄₃⋊C₈	—	2	1	no	—
135	C₂×C₄₃⋊C₈	—	2	1	no	—
136	C₂×C₄₃⋊C₈	—	2	1	no	—
137	C₂×C₄₃⋊C₈	—	2	1	no	—
138	C₂×C₄₃⋊C₈	—	2	1	no	—
139	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
140	Dic₁₇₂	C₄⋊C₄	1	16	yes	complemented
141	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₄₃	—	2	1	no	—
143	C₂×C₄×C₄₃	—	2	1	no	—
144	C₂×C₄×C₄₃	—	2	4	no	—
145	C₂×C₄×C₄₃	—	2	1	no	—
146	C₂×C₄×C₄₃	—	2	1	no	—
147	C₂×C₄×C₄₃	—	2	1	no	—
148	C₂×C₄×C₄₃	—	4	2	no	—
149	C₂×C₄×C₄₃	—	4	2	no	—
150	C₂×C₄×C₄₃	—	4	2	no	—
151	C₂×C₄×C₄₃	—	4	2	no	—
152	C₂×C₄×C₄₃	—	4	2	no	—
153	C₂×C₄×C₄₃	#135	1	2	yes	—
154	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
159	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
160	C₂×Dic₄₃	—	2	4	no	—
161	C₂×Dic₄₃	—	2	1	no	—
162	C₂×Dic₄₃	—	2	4	no	—
163	C₂×Dic₄₃	—	2	4	no	—
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	1	no	—
169	C₂×Dic₄₃	—	2	1	no	—
170	C₂×Dic₄₃	—	2	1	no	—
171	C₂×Dic₄₃	—	2	1	no	—
172	C₂×Dic₄₃	—	4	2	no	—
173	C₂×Dic₄₃	—	4	2	no	—
174	C₂×Dic₄₃	—	4	2	no	—
175	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
176	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
177	C₂×Dic₄₃	#135	1	2	yes	—
178	Dic₈₆	—	2	4	no	—
179	Dic₈₆	—	2	4	no	—
180	Dic₈₆	—	2	4	no	—
181	Dic₈₆	C₂×C₄⋊C₄	1	8	yes	—
182	C₈×C₄₃	—	4	1	no	—
183	C₈×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
184	C₄₃⋊C₈	—	2	2	no	—
185	C₄₃⋊C₈	—	4	1	no	—
186	#22685	—	43	1	no	maximal, Sylow
187	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂²×C₄₃	D₄²	1	1	yes	characteristic
189	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
190	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
191	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
192	C₂²×C₄₃	#578	1	1	yes	characteristic
193	C₂²×C₄₃	#578	1	1	yes	characteristic
194	C₄×C₄₃	—	2	2	no	—
195	C₄×C₄₃	—	4	4	no	—
196	C₄×C₄₃	—	4	1	no	—
197	C₄×C₄₃	—	8	2	no	—
198	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
199	C₄×C₄₃	#520	1	1	yes	characteristic
200	C₄×C₄₃	#547	1	1	yes	characteristic
201	C₄×C₄₃	#554	1	1	yes	characteristic
202	Dic₄₃	—	2	8	no	—
203	Dic₄₃	—	2	2	no	—
204	Dic₄₃	—	2	2	no	—
205	Dic₄₃	—	2	2	no	—
206	Dic₄₃	—	4	1	no	—
207	Dic₄₃	—	8	2	no	—
208	C₂×C₄×Q₁₆	—	43	1	no	—
209	C₂×C₄×Q₁₆	—	43	1	no	—
210	C₂×C₄×Q₁₆	—	43	1	no	—
211	#2351	—	43	2	no	—
212	#1942	—	43	1	no	—
213	#1942	D₄₃	1	1	yes	characteristic
214	#1865	—	43	2	no	—
215	#1865	—	43	2	no	—
216	#1846	—	43	1	no	—
217	#1805	—	43	2	no	—
218	C₈×C₄⋊C₄	—	43	1	no	—
219	C₂×C₄₃	D₄×C₄⋊C₄	1	1	yes	characteristic
220	C₂×C₄₃	C₄×#135	1	1	yes	characteristic
221	C₂×C₄₃	#2950	1	1	yes	characteristic
222	C₂×C₄₃	#3285	1	1	yes	characteristic
223	C₂×C₄₃	#3285	1	1	yes	characteristic
224	C₂×C₄₃	#3383	1	1	yes	characteristic
225	C₂×C₄₃	#3383	1	1	yes	characteristic
226	C₂²×Q₁₆	—	43	1	no	—
227	C₂×C₄×Q₈	—	43	2	no	—
228	C₂×C₄×Q₈	—	43	2	no	—
229	C₂×C₄×Q₈	—	43	2	no	—
230	C₄×Q₁₆	—	43	8	no	—
231	C₄×Q₁₆	—	86	4	no	—
232	C₄×Q₁₆	—	86	4	no	—
233	C₂×#107	—	43	1	no	—
234	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
235	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
236	C₂×#106	—	43	2	no	—
237	C₂×C₄⋊C₈	—	43	1	no	—
238	C₂×#103	—	43	2	no	—
239	C₂×#103	—	43	2	no	—
240	C₂×#103	—	43	2	no	—
241	C₂×C₄×C₈	—	43	1	no	—
242	C₂×C₄×C₈	—	43	1	no	—
243	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
244	#389	—	43	2	no	—
245	#389	—	86	2	no	—
246	#389	—	86	2	no	—
247	#389	C₂×D₄₃	1	2	yes	—
248	#382	—	43	2	no	—
249	#382	—	86	2	no	—
250	C₄×C₄⋊C₄	—	43	1	no	—
251	C₄×C₄⋊C₄	—	86	2	no	—
252	#340	—	43	2	no	—
253	#340	C₂×D₄₃	1	2	yes	—
254	#336	—	43	1	no	—
255	#336	—	43	1	no	—
256	C₄₃	#22685	1	1	yes	characteristic, complemented, Sylow
257	C₂²×Q₈	—	43	2	no	—
258	C₂×Q₁₆	—	43	4	no	—
259	C₂×Q₁₆	—	43	4	no	—
260	C₂×Q₁₆	—	43	4	no	—
261	C₂²×C₈	—	43	1	no	—
262	C₂²×C₈	—	43	1	no	—
263	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
264	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
265	C₄×Q₈	—	43	8	no	—
266	C₄×Q₈	—	86	4	no	—
267	C₄×Q₈	—	86	4	no	—
268	C₄×Q₈	—	86	4	no	—
269	C₄×Q₈	—	172	2	no	—
270	C₄×Q₈	—	172	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	43	1	no	—
273	C₂×C₄⋊C₄	—	43	1	no	—
274	C₂×C₄⋊C₄	—	43	2	no	—
275	C₂×C₄⋊C₄	—	86	2	no	—
276	C₂×C₄⋊C₄	—	86	2	no	—
277	C₂×C₄⋊C₄	—	86	2	no	—
278	C₂×C₄⋊C₄	—	86	2	no	—
279	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
280	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
281	C₂×C₄²	—	43	1	no	—
282	C₂×C₄²	—	43	1	no	—
283	C₂×C₄²	—	86	2	no	—
284	C₂×C₄²	—	86	2	no	—
285	C₂×C₄²	—	86	2	no	—
286	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
287	#107	—	2	2	no	—
288	#107	—	86	2	no	—
289	#107	C₄×D₄₃	1	4	yes	—
290	#106	—	172	2	no	—
291	C₄⋊C₈	—	86	2	no	—
292	#103	—	43	8	no	—
293	#103	—	86	4	no	—
294	#103	—	86	4	no	—
295	C₄×C₈	—	2	2	no	—
296	C₄×C₈	—	43	4	no	—
297	C₄×C₈	—	86	2	no	—
298	#95	—	2	2	no	—
299	#95	—	43	1	no	—
300	#95	—	43	1	no	—
301	#95	—	86	2	no	—
302	#95	—	86	2	no	—
303	#95	—	86	2	no	—
304	C₂×Q₈	—	43	4	no	—
305	C₂×Q₈	—	43	4	no	—
306	C₂×Q₈	—	43	4	no	—
307	C₂×Q₈	—	86	2	no	—
308	C₂×Q₈	—	86	2	no	—
309	C₂×Q₈	—	86	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	43	1	no	—
313	C₂²×C₄	—	43	1	no	—
314	C₂²×C₄	—	43	1	no	—
315	C₂²×C₄	—	43	1	no	—
316	C₂²×C₄	—	86	2	no	—
317	C₂²×C₄	—	86	2	no	—
318	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
319	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
320	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
321	Q₁₆	—	43	16	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	43	2	no	—
326	C₂×C₈	—	86	1	no	—
327	C₂×C₈	—	86	1	no	—
328	C₂×C₈	—	86	1	no	—
329	C₂×C₈	—	86	1	no	—
330	C₂×C₈	—	86	1	no	—
331	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
332	C₂×C₈	D₄×D₄₃	1	2	yes	—
333	C₂×C₈	Q₈×D₄₃	1	2	yes	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	86	2	no	—
339	C₄⋊C₄	—	86	8	no	—
340	C₄⋊C₄	—	86	2	no	—
341	C₄⋊C₄	—	86	2	no	—
342	C₄⋊C₄	—	86	2	no	—
343	C₄⋊C₄	—	172	4	no	—
344	C₄⋊C₄	—	172	4	no	—
345	C₄⋊C₄	—	172	4	no	—
346	C₄⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	43	2	no	—
350	C₄²	—	43	2	no	—
351	C₄²	—	86	8	no	—
352	C₄²	—	86	1	no	—
353	C₄²	—	86	1	no	—
354	C₄²	—	172	4	no	—
355	C₄²	—	172	4	no	—
356	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
357	Q₈	—	43	8	no	—
358	Q₈	—	86	4	no	—
359	Q₈	—	86	4	no	—
360	Q₈	—	86	4	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	43	2	no	—
373	C₂×C₄	—	43	2	no	—
374	C₂×C₄	—	43	2	no	—
375	C₂×C₄	—	86	4	no	—
376	C₂×C₄	—	86	4	no	—
377	C₂×C₄	—	86	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	—	86	1	no	—
383	C₂×C₄	—	86	4	no	—
384	C₂×C₄	—	86	1	no	—
385	C₂×C₄	—	86	1	no	—
386	C₂×C₄	—	86	1	no	—
387	C₂×C₄	—	172	2	no	—
388	C₂×C₄	—	172	2	no	—
389	C₂×C₄	—	172	2	no	—
390	C₂×C₄	#13063344	1	2	yes	—
391	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
392	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
393	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
394	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
395	C₂×C₄	#13063371	1	1	yes	characteristic
396	C₂×C₄	#13063373	1	1	yes	characteristic
397	C₈	—	4	1	no	—
398	C₈	—	86	2	no	—
399	C₈	—	172	1	no	—
400	C₈	C₄⋊C₄×D₄₃	1	4	yes	—
401	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
402	C₂²	#14583533	1	1	yes	characteristic
403	C₂²	#14583564	1	1	yes	characteristic
404	C₂²	#135×D₄₃	1	1	yes	characteristic
405	C₂²	C₂×#13063344	1	1	yes	characteristic
406	C₂²	#14583712	1	1	yes	characteristic
407	C₂²	#14583713	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	4	no	—
411	C₄	—	8	2	no	—
412	C₄	—	86	2	no	—
413	C₄	—	86	2	no	—
414	C₄	—	86	2	no	—
415	C₄	—	86	8	no	—
416	C₄	—	344	2	no	—
417	C₄	—	172	1	no	—
418	C₄	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
419	C₄	#14583381	1	1	yes	characteristic
420	C₄	#14583551	1	1	yes	characteristic
421	C₄	#14583605	1	1	yes	characteristic
422	C₂	#19137496	1	1	yes	characteristic
423	C₂	C₄×#13063344	1	1	yes	characteristic
424	C₂	#19143458	1	1	yes	characteristic
425	C₂	#19146333	1	1	yes	characteristic
426	C₂	#19146339	1	1	yes	characteristic
427	C₂	#19147483	1	1	yes	characteristic
428	C₂	#19147488	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1942	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1942	D₄₃
hypocenter	C₄₃	#22685
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1942

Complements

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

N	H ≅ G/N	type
18. #14582993	C₄	semidirect
140. Dic₁₇₂	C₄⋊C₄	semidirect
256. C₄₃	#22685	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Dic₁₇₂	2
C₂×#14582993	2
#19137514	2
#19135329	2
#19134864	2
#19134862	2
#19134758	2
#19134609	2
C₈×Dic₄₃⋊C₄	2
C₄₃×#1942	2
#22685	43