Subgroups — #25118420

Order 11008.

822 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583185	C₂	1	1	yes	maximal, characteristic
2	#19137653	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic
4	#19135556	C₂	1	1	yes	maximal, characteristic
5	#19135359	C₂	1	1	yes	maximal, characteristic
6	#19135323	C₂	1	2	yes	maximal
7	#19135181	C₂	1	2	yes	maximal
8	#19134866	C₂	1	2	yes	maximal
9	C₄×#13063250	C₂	1	2	yes	maximal
10	C₄×#13063250	C₂	1	1	yes	maximal, characteristic
11	C₈×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063325	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₈₆	C₂²	1	2	yes	—
14	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
15	C₂×#13063290	—	2	1	no	—
16	#14583185	C₄	1	8	yes	complemented
17	C₂×#13063257	C₂²	1	2	yes	—
18	C₂×#13063257	C₂²	1	2	yes	—
19	C₂×#13063250	C₂²	1	1	yes	characteristic
20	C₂×#13063250	C₂²	1	2	yes	—
21	C₂×#13063250	C₂²	1	1	yes	characteristic
22	#14582804	—	2	1	no	—
23	#14582797	C₂²	1	2	yes	—
24	#14582797	C₂²	1	2	yes	—
25	#14582796	—	2	2	no	—
26	#14582784	—	2	2	no	—
27	#14582769	C₂²	1	1	yes	characteristic
28	#14582768	—	2	1	no	—
29	C₄⋊C₄×Dic₄₃	—	2	1	no	—
30	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
32	#14582662	C₂²	1	2	yes	—
33	#14582662	C₂²	1	2	yes	—
34	#14582662	C₂²	1	1	yes	characteristic
35	#14582662	C₂²	1	2	yes	—
36	#14582662	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
40	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#336	C₂²	1	2	yes	—
42	C₂²×Dic₈₆	—	2	1	no	—
43	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
44	#13063325	—	2	2	no	—
45	#13063325	C₂×C₄	1	4	yes	—
46	C₄×Dic₈₆	—	2	2	no	—
47	C₄×Dic₈₆	—	2	4	no	—
48	C₄×Dic₈₆	—	4	2	no	—
49	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
50	#13063290	—	4	4	no	—
51	C₂×C₄⋊Dic₄₃	—	2	1	no	—
52	C₂×C₄⋊Dic₄₃	—	2	1	no	—
53	C₂×C₄⋊Dic₄₃	—	2	1	no	—
54	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
56	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
58	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
59	C₂×Dic₄₃⋊C₄	—	2	1	no	—
60	C₂×Dic₄₃⋊C₄	—	2	2	no	—
61	C₂×Dic₄₃⋊C₄	—	2	2	no	—
62	C₂×Dic₄₃⋊C₄	—	2	2	no	—
63	C₂×C₄×Dic₄₃	—	2	1	no	—
64	C₂×C₄×Dic₄₃	—	2	2	no	—
65	C₂×C₄×Dic₄₃	—	2	2	no	—
66	C₂×C₄×Dic₄₃	—	2	1	no	—
67	#13063257	—	4	2	no	—
68	#13063257	C₂×C₄	1	8	yes	—
69	#13063250	—	2	2	no	—
70	#13063250	C₂×C₄	1	8	yes	—
71	#13063250	Q₈	1	4	yes	complemented
72	C₄₃⋊#95	—	2	1	no	—
73	C₄₃⋊#95	—	2	2	no	—
74	C₄₃⋊#95	—	2	2	no	—
75	C₄₃⋊#95	—	2	2	no	—
76	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
78	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
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	—
84	C₄×C₈×C₄₃	—	2	2	no	—
85	C₄×C₈×C₄₃	—	4	2	no	—
86	#95×C₄₃	D₄	1	2	yes	—
87	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
92	C₂²×Dic₄₃	—	2	1	no	—
93	C₂²×Dic₄₃	—	2	1	no	—
94	C₂²×Dic₄₃	—	2	1	no	—
95	C₂²×Dic₄₃	—	2	2	no	—
96	C₂²×Dic₄₃	—	2	1	no	—
97	C₂²×Dic₄₃	—	2	2	no	—
98	C₂×Dic₈₆	—	2	1	no	—
99	C₂×Dic₈₆	—	2	1	no	—
100	C₂×Dic₈₆	—	2	1	no	—
101	C₂×Dic₈₆	—	2	4	no	—
102	C₂×Dic₈₆	—	4	2	no	—
103	C₂×Dic₈₆	—	4	2	no	—
104	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
105	C₂×Dic₈₆	C₂×Q₈	1	2	yes	—
106	C₂×Dic₈₆	#41	1	2	yes	—
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	—	2	2	no	—
111	C₂×C₈×C₄₃	—	2	1	no	—
112	C₂×C₈×C₄₃	—	2	1	no	—
113	C₂×C₈×C₄₃	—	2	1	no	—
114	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
115	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
116	C₄⋊C₄×C₄₃	—	2	2	no	—
117	C₄⋊C₄×C₄₃	SD₁₆	1	4	yes	—
118	C₄²×C₄₃	—	2	2	no	—
119	C₄²×C₄₃	—	2	2	no	—
120	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
121	C₄²×C₄₃	#41	1	2	yes	—
122	C₄⋊Dic₄₃	—	2	4	no	—
123	C₄⋊Dic₄₃	—	2	1	no	—
124	C₄⋊Dic₄₃	—	2	2	no	—
125	C₄⋊Dic₄₃	—	2	1	no	—
126	C₄⋊Dic₄₃	—	2	1	no	—
127	C₄⋊Dic₄₃	—	2	2	no	—
128	C₄⋊Dic₄₃	—	2	1	no	—
129	C₄⋊Dic₄₃	—	2	2	no	—
130	C₄⋊Dic₄₃	—	4	2	no	—
131	C₄⋊Dic₄₃	—	8	1	no	—
132	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
133	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
134	C₄⋊Dic₄₃	C₂×Q₈	1	2	yes	—
135	Dic₄₃⋊C₄	—	2	4	no	—
136	Dic₄₃⋊C₄	—	4	4	no	—
137	Dic₄₃⋊C₄	—	4	4	no	—
138	Dic₄₃⋊C₄	—	8	2	no	—
139	C₄×Dic₄₃	—	2	4	no	—
140	C₄×Dic₄₃	—	4	4	no	—
141	C₄×Dic₄₃	—	4	4	no	—
142	C₄×Dic₄₃	—	4	2	no	—
143	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₄₃	—	2	2	no	—
145	C₂×C₄×C₄₃	—	2	1	no	—
146	C₂×C₄×C₄₃	—	2	1	no	—
147	C₂×C₄×C₄₃	—	2	2	no	—
148	C₂×C₄×C₄₃	—	2	2	no	—
149	C₂×C₄×C₄₃	—	2	2	no	—
150	C₂×C₄×C₄₃	—	2	2	no	—
151	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₄₃	C₂×SD₁₆	1	4	yes	—
154	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
155	C₂×C₄×C₄₃	#135	1	2	yes	—
156	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₂²×Q₈	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×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
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	4	no	—
167	C₂×Dic₄₃	—	2	2	no	—
168	C₂×Dic₄₃	—	4	1	no	—
169	C₂×Dic₄₃	—	4	2	no	—
170	C₂×Dic₄₃	—	4	2	no	—
171	C₂×Dic₄₃	—	4	1	no	—
172	C₂×Dic₄₃	—	4	1	no	—
173	C₂×Dic₄₃	—	4	1	no	—
174	C₂×Dic₄₃	—	4	2	no	—
175	C₂×Dic₄₃	—	4	1	no	—
176	C₂×Dic₄₃	—	4	1	no	—
177	C₂×Dic₄₃	—	4	2	no	—
178	C₂×Dic₄₃	—	4	2	no	—
179	C₂×Dic₄₃	—	4	1	no	—
180	Dic₈₆	—	2	2	no	—
181	Dic₈₆	—	2	2	no	—
182	Dic₈₆	—	2	2	no	—
183	Dic₈₆	—	4	8	no	—
184	Dic₈₆	C₄×Q₈	1	4	yes	complemented
185	C₈×C₄₃	—	2	4	no	—
186	C₈×C₄₃	—	2	2	no	—
187	C₈×C₄₃	—	4	1	no	—
188	#22964	—	43	1	no	maximal, Sylow
189	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
190	C₂²×C₄₃	#546	1	1	yes	characteristic
191	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
192	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
193	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
194	C₂²×C₄₃	#577	1	1	yes	characteristic
195	C₂²×C₄₃	#578	1	1	yes	characteristic
196	C₄×C₄₃	—	2	2	no	—
197	C₄×C₄₃	—	2	4	no	—
198	C₄×C₄₃	—	4	2	no	—
199	C₄×C₄₃	C₄×SD₁₆	1	4	yes	—
200	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
201	C₄×C₄₃	#520	1	1	yes	characteristic
202	C₄×C₄₃	#552	1	1	yes	characteristic
203	C₄×C₄₃	#554	1	1	yes	characteristic
204	Dic₄₃	—	2	4	no	—
205	Dic₄₃	—	4	2	no	—
206	Dic₄₃	—	4	4	no	—
207	Dic₄₃	—	4	2	no	—
208	Dic₄₃	—	8	1	no	—
209	Dic₄₃	—	8	2	no	—
210	C₂×#475	—	43	1	no	—
211	#2365	—	43	1	no	—
212	Q₈×C₄⋊C₄	—	43	1	no	—
213	#1990	—	43	1	no	—
214	#1948	—	43	1	no	—
215	#1941	—	43	2	no	—
216	#1920	—	43	2	no	—
217	#1865	—	43	2	no	—
218	C₈×C₄⋊C₄	D₄₃	1	1	yes	characteristic
219	C₄×#103	—	43	1	no	—
220	C₄×#103	—	43	2	no	—
221	C₂×C₄₃	#2360	1	1	yes	characteristic
222	C₂×C₄₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
223	C₂×C₄₃	#2947	1	1	yes	characteristic
224	C₂×C₄₃	#3298	1	1	yes	characteristic
225	C₂×C₄₃	#3304	1	1	yes	characteristic
226	C₂×C₄₃	Q₈×SD₁₆	1	1	yes	characteristic
227	C₂×C₄₃	#3383	1	1	yes	characteristic
228	C₂×C₄⋊Q₈	—	43	1	no	—
229	C₂×C₄×Q₈	—	43	1	no	—
230	C₂×C₄×Q₈	—	43	2	no	—
231	C₂×C₄×Q₈	—	86	1	no	—
232	#475	—	43	8	no	—
233	C₂×#106	—	43	2	no	—
234	C₂×#106	—	43	2	no	—
235	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
236	C₂×#103	—	43	2	no	—
237	C₂×#103	—	43	1	no	—
238	C₂×#103	—	43	1	no	—
239	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
240	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
241	#391	—	86	1	no	—
242	#389	—	43	2	no	—
243	#389	—	43	2	no	—
244	#389	—	86	2	no	—
245	#387	—	86	2	no	—
246	#384	—	43	1	no	—
247	#384	—	86	1	no	—
248	C₄×C₄⋊C₄	—	43	2	no	—
249	C₄×C₄⋊C₄	—	43	1	no	—
250	C₄×C₄⋊C₄	—	86	1	no	—
251	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
252	#340	—	43	2	no	—
253	#340	—	43	1	no	—
254	#340	—	43	2	no	—
255	#340	—	43	1	no	—
256	#340	—	43	2	no	—
257	#336	C₂×D₄₃	1	2	yes	—
258	C₄₃	#22964	1	1	yes	characteristic, complemented, Sylow
259	C₂²×Q₈	—	43	1	no	—
260	C₂²×Q₈	—	86	1	no	—
261	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
262	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
263	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
264	C₄⋊Q₈	—	43	4	no	—
265	C₄⋊Q₈	—	86	2	no	—
266	C₄×Q₈	—	43	4	no	—
267	C₄×Q₈	—	86	4	no	—
268	C₄×Q₈	—	86	2	no	—
269	C₄×Q₈	—	172	2	no	—
270	C₄×Q₈	—	172	4	no	—
271	C₂×C₄⋊C₄	—	43	1	no	—
272	C₂×C₄⋊C₄	—	43	2	no	—
273	C₂×C₄⋊C₄	—	43	1	no	—
274	C₂×C₄⋊C₄	—	43	2	no	—
275	C₂×C₄⋊C₄	—	43	1	no	—
276	C₂×C₄⋊C₄	—	86	1	no	—
277	C₂×C₄⋊C₄	—	86	1	no	—
278	C₂×C₄⋊C₄	—	86	2	no	—
279	C₂×C₄⋊C₄	—	86	1	no	—
280	C₂×C₄⋊C₄	—	86	2	no	—
281	C₂×C₄⋊C₄	—	86	2	no	—
282	C₂×C₄⋊C₄	—	86	1	no	—
283	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
284	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
285	C₂×C₄²	—	86	1	no	—
286	C₂×C₄²	—	86	2	no	—
287	C₂×C₄²	—	86	2	no	—
288	C₂×C₄²	—	86	1	no	—
289	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
290	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
291	#106	—	43	8	no	—
292	#106	—	172	2	no	—
293	C₄⋊C₈	C₄×D₄₃	1	4	yes	—
294	#103	—	43	8	no	—
295	#103	—	43	4	no	—
296	#103	—	86	2	no	—
297	C₄×C₈	—	2	2	no	—
298	C₄×C₈	—	4	2	no	—
299	#95	—	86	1	no	—
300	#95	—	86	2	no	—
301	#95	—	86	2	no	—
302	#95	—	86	2	no	—
303	#95	D₁₇₂	1	2	yes	—
304	C₂×Q₈	—	43	2	no	—
305	C₂×Q₈	—	43	2	no	—
306	C₂×Q₈	—	43	2	no	—
307	C₂×Q₈	—	86	4	no	—
308	C₂×Q₈	—	86	1	no	—
309	C₂×Q₈	—	86	1	no	—
310	C₂×Q₈	—	86	1	no	—
311	C₂×Q₈	—	172	2	no	—
312	C₂×Q₈	—	172	2	no	—
313	C₂²×C₄	—	86	1	no	—
314	C₂²×C₄	—	86	1	no	—
315	C₂²×C₄	—	86	1	no	—
316	C₂²×C₄	—	86	2	no	—
317	C₂²×C₄	—	86	1	no	—
318	C₂²×C₄	—	86	2	no	—
319	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
320	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
322	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
323	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
332	C₂×C₈	Q₈×D₄₃	1	2	yes	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	43	4	no	—
335	C₄⋊C₄	—	43	2	no	—
336	C₄⋊C₄	—	43	2	no	—
337	C₄⋊C₄	—	86	4	no	—
338	C₄⋊C₄	—	86	4	no	—
339	C₄⋊C₄	—	86	1	no	—
340	C₄⋊C₄	—	86	2	no	—
341	C₄⋊C₄	—	86	1	no	—
342	C₄⋊C₄	—	86	1	no	—
343	C₄⋊C₄	—	86	2	no	—
344	C₄⋊C₄	—	86	1	no	—
345	C₄⋊C₄	—	86	2	no	—
346	C₄⋊C₄	—	344	2	no	—
347	C₄⋊C₄	—	344	1	no	—
348	C₄⋊C₄	—	172	4	no	—
349	C₄⋊C₄	—	172	4	no	—
350	C₄⋊C₄	—	172	2	no	—
351	C₄⋊C₄	#10621873	1	4	yes	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	86	4	no	—
355	C₄²	—	172	4	no	—
356	C₄²	—	172	2	no	—
357	C₄²	—	172	4	no	—
358	C₄²	C₂×C₄×D₄₃	1	2	yes	—
359	C₄²	#10621898	1	2	yes	—
360	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
361	Q₈	—	43	4	no	—
362	Q₈	—	86	2	no	—
363	Q₈	—	86	2	no	—
364	Q₈	—	86	2	no	—
365	Q₈	—	172	8	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	86	2	no	—
374	C₂×C₄	—	86	2	no	—
375	C₂×C₄	—	86	2	no	—
376	C₂×C₄	—	86	2	no	—
377	C₂×C₄	—	86	2	no	—
378	C₂×C₄	—	86	4	no	—
379	C₂×C₄	—	172	1	no	—
380	C₂×C₄	—	172	2	no	—
381	C₂×C₄	—	172	2	no	—
382	C₂×C₄	—	172	1	no	—
383	C₂×C₄	—	172	2	no	—
384	C₂×C₄	—	172	1	no	—
385	C₂×C₄	—	172	1	no	—
386	C₂×C₄	—	172	2	no	—
387	C₂×C₄	—	172	2	no	—
388	C₂×C₄	—	172	1	no	—
389	C₂×C₄	—	172	1	no	—
390	C₂×C₄	—	172	1	no	—
391	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
392	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
393	C₂×C₄	C₂×#10621873	1	4	yes	—
394	C₂×C₄	C₂×#10621873	1	2	yes	—
395	C₂×C₄	#13063347	1	2	yes	—
396	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
397	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
398	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
399	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
400	C₂×C₄	#13063370	1	1	yes	characteristic
401	C₂×C₄	#13063372	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	2	4	no	—
404	C₈	—	4	1	no	—
405	C₂²	C₂×C₄×D₁₇₂	1	1	yes	characteristic
406	C₂²	#14583544	1	1	yes	characteristic
407	C₂²	Q₈×D₁₇₂	1	1	yes	characteristic
408	C₂²	C₂²×#10621873	1	1	yes	characteristic
409	C₂²	C₂×#13063347	1	1	yes	characteristic
410	C₂²	#14583711	1	1	yes	characteristic
411	C₂²	#14583716	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	2	4	no	—
414	C₄	—	4	2	no	—
415	C₄	—	86	4	no	—
416	C₄	—	344	2	no	—
417	C₄	—	344	1	no	—
418	C₄	—	172	2	no	—
419	C₄	—	172	4	no	—
420	C₄	—	172	2	no	—
421	C₄	C₄×#10621873	1	4	yes	—
422	C₄	C₄×Q₈×D₄₃	1	1	yes	characteristic
423	C₄	#14583378	1	1	yes	characteristic
424	C₄	#14583588	1	1	yes	characteristic
425	C₄	#14583604	1	1	yes	characteristic
426	C₂	#19137602	1	1	yes	characteristic
427	C₂	C₂×C₄×#10621873	1	1	yes	characteristic
428	C₂	#19143440	1	1	yes	characteristic
429	C₂	#19146461	1	1	yes	characteristic
430	C₂	#19146535	1	1	yes	characteristic
431	C₂	Q₈×#10621873	1	1	yes	characteristic
432	C₂	#19147487	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₈×C₄⋊C₄×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₄₃
hypocenter	C₄₃	#22964
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
16. #14583185	C₄	semidirect
71. #13063250	Q₈	semidirect
184. Dic₈₆	C₄×Q₈	semidirect
258. C₄₃	#22964	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583185	2
#19137653	2
C₄⋊C₄×Dic₈₆	2
#19135556	2
#19135359	2
#19135323	2
#19135181	2
#19134866	2
C₄×#13063250	2
C₈×C₄⋊C₄×C₄₃	2
#22964	43