Subgroups — #25148457

Order 11008.

750 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583195	C₂	1	1	yes	maximal, characteristic
2	#19139965	C₂	1	1	yes	maximal, characteristic
3	#19139800	C₂	1	1	yes	maximal, characteristic
4	#19136088	C₂	1	2	yes	maximal
5	#19135989	C₂	1	2	yes	maximal
6	#19135556	C₂	1	1	yes	maximal, characteristic
7	#19135354	C₂	1	1	yes	maximal, characteristic
8	#19135328	C₂	1	2	yes	maximal
9	#19135271	C₂	1	2	yes	maximal
10	C₄×#13063250	C₂	1	1	yes	maximal, characteristic
11	C₂×C₈×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063325	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
14	#14583195	—	2	4	no	—
15	C₂×#13063259	C₂²	1	2	yes	—
16	C₂×#13063259	C₂²	1	2	yes	—
17	C₂×#13063250	C₂²	1	2	yes	—
18	C₂×#13063250	C₂²	1	1	yes	characteristic
19	C₂×#13063250	C₂²	1	1	yes	characteristic
20	#14582832	—	2	2	no	—
21	#14582819	—	2	2	no	—
22	#14582806	—	2	1	no	—
23	#14582806	—	2	1	no	—
24	#14582805	C₂²	1	2	yes	—
25	#14582797	C₂²	1	2	yes	—
26	#14582797	C₂²	1	2	yes	—
27	#14582797	C₂²	1	2	yes	—
28	#14582795	—	2	1	no	—
29	#14582769	C₂²	1	1	yes	characteristic
30	#14582768	—	2	1	no	—
31	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
32	#14582662	C₂²	1	2	yes	—
33	#14582662	C₂²	1	2	yes	—
34	#14582662	C₂²	1	2	yes	—
35	#14582662	C₂²	1	1	yes	characteristic
36	#14582662	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₄₃	—	2	4	no	—
39	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
40	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
43	C₂²×Dic₈₆	—	2	1	no	—
44	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
45	#13063325	—	2	2	no	—
46	#13063325	—	2	2	no	—
47	C₄×Dic₈₆	—	2	2	no	—
48	C₄×Dic₈₆	—	2	2	no	—
49	C₂×C₄⋊Dic₄₃	—	2	1	no	—
50	C₂×C₄⋊Dic₄₃	—	2	1	no	—
51	C₂×C₄⋊Dic₄₃	—	2	1	no	—
52	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
54	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
56	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
57	C₂×Dic₄₃⋊C₄	—	2	1	no	—
58	C₂×Dic₄₃⋊C₄	—	2	2	no	—
59	C₂×Dic₄₃⋊C₄	—	2	2	no	—
60	C₂×Dic₄₃⋊C₄	—	2	2	no	—
61	C₂×C₄×Dic₄₃	—	2	1	no	—
62	C₂×C₄×Dic₄₃	—	2	1	no	—
63	#13063259	—	2	4	no	—
64	#13063259	—	2	4	no	—
65	#13063250	—	2	4	no	—
66	#13063250	—	2	2	no	—
67	#13063250	Q₈	1	4	yes	complemented
68	C₄₃⋊#95	—	2	2	no	—
69	C₄₃⋊#95	—	2	2	no	—
70	C₄₃⋊#95	—	2	2	no	—
71	C₄₃⋊#95	—	2	2	no	—
72	C₄₃⋊#95	—	2	2	no	—
73	C₄₃⋊#95	—	2	1	no	—
74	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
75	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
77	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
78	C₄×Q₈×C₄₃	—	2	2	no	—
79	C₄×Q₈×C₄₃	—	2	2	no	—
80	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
82	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₄₃	—	2	4	no	—
85	C₄⋊C₈×C₄₃	D₄	1	4	yes	—
86	C₄×C₈×C₄₃	—	2	4	no	—
87	C₄×C₈×C₄₃	—	2	2	no	—
88	C₂×Q₈×C₄₃	—	2	2	no	—
89	C₂×Q₈×C₄₃	—	2	2	no	—
90	C₂×Q₈×C₄₃	Q₁₆	1	4	yes	—
91	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
96	C₂²×Dic₄₃	—	2	1	no	—
97	C₂²×Dic₄₃	—	2	1	no	—
98	C₂²×Dic₄₃	—	2	1	no	—
99	C₂²×Dic₄₃	—	2	2	no	—
100	C₂²×Dic₄₃	—	2	1	no	—
101	C₂²×Dic₄₃	—	2	2	no	—
102	C₂×Dic₈₆	—	2	1	no	—
103	C₂×Dic₈₆	—	2	1	no	—
104	C₂×Dic₈₆	—	2	1	no	—
105	C₂×Dic₈₆	—	2	1	no	—
106	C₂×Dic₈₆	—	2	1	no	—
107	C₂×Dic₈₆	—	4	2	no	—
108	C₂×Dic₈₆	—	8	1	no	—
109	C₂×Dic₈₆	—	8	1	no	—
110	C₂×Dic₈₆	C₂×Q₈	1	2	yes	—
111	C₂×C₈×C₄₃	—	2	1	no	—
112	C₂×C₈×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	—	2	1	no	—
115	C₂×C₈×C₄₃	—	2	1	no	—
116	C₂×C₈×C₄₃	—	2	1	no	—
117	C₂×C₈×C₄₃	—	2	1	no	—
118	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
119	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
120	C₄⋊C₄×C₄₃	—	2	4	no	—
121	C₄⋊C₄×C₄₃	—	2	2	no	—
122	C₄²×C₄₃	—	2	2	no	—
123	C₄²×C₄₃	—	2	2	no	—
124	C₄²×C₄₃	C₂×D₄	1	2	yes	—
125	C₄²×C₄₃	#41	1	2	yes	—
126	C₄⋊Dic₄₃	—	2	1	no	—
127	C₄⋊Dic₄₃	—	2	1	no	—
128	C₄⋊Dic₄₃	—	2	2	no	—
129	C₄⋊Dic₄₃	—	2	1	no	—
130	C₄⋊Dic₄₃	—	2	2	no	—
131	C₄⋊Dic₄₃	—	2	1	no	—
132	C₄⋊Dic₄₃	—	2	2	no	—
133	C₄⋊Dic₄₃	—	2	2	no	—
134	C₄⋊Dic₄₃	—	4	2	no	—
135	C₄⋊Dic₄₃	—	4	2	no	—
136	C₄⋊Dic₄₃	—	8	1	no	—
137	C₄⋊Dic₄₃	C₂×Q₈	1	2	yes	—
138	C₄⋊Dic₄₃	#41	1	2	yes	—
139	Dic₄₃⋊C₄	—	4	2	no	—
140	Dic₄₃⋊C₄	—	8	2	no	—
141	Dic₄₃⋊C₄	—	8	2	no	—
142	Dic₄₃⋊C₄	—	8	2	no	—
143	C₄×Dic₄₃	—	4	2	no	—
144	C₄×Dic₄₃	—	4	2	no	—
145	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₄₃	—	2	8	no	—
147	C₂×C₄×C₄₃	—	2	2	no	—
148	C₂×C₄×C₄₃	—	2	2	no	—
149	C₂×C₄×C₄₃	—	2	1	no	—
150	C₂×C₄×C₄₃	—	2	1	no	—
151	C₂×C₄×C₄₃	—	2	2	no	—
152	C₂×C₄×C₄₃	—	2	2	no	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	#121	1	2	yes	—
155	C₂×C₄×C₄₃	#121	1	2	yes	—
156	C₂×C₄×C₄₃	C₂×Q₁₆	1	4	yes	—
157	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
158	C₂×C₄×C₄₃	#135	1	2	yes	—
159	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
164	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
165	C₂×Dic₄₃	—	2	2	no	—
166	C₂×Dic₄₃	—	2	2	no	—
167	C₂×Dic₄₃	—	2	2	no	—
168	C₂×Dic₄₃	—	4	1	no	—
169	C₂×Dic₄₃	—	4	1	no	—
170	C₂×Dic₄₃	—	4	1	no	—
171	C₂×Dic₄₃	—	4	1	no	—
172	C₂×Dic₄₃	—	4	1	no	—
173	C₂×Dic₄₃	—	4	1	no	—
174	C₂×Dic₄₃	—	4	1	no	—
175	C₂×Dic₄₃	—	4	2	no	—
176	C₂×Dic₄₃	—	4	2	no	—
177	C₂×Dic₄₃	—	4	2	no	—
178	C₂×Dic₄₃	—	4	1	no	—
179	C₂×Dic₄₃	—	4	2	no	—
180	C₂×Dic₄₃	—	4	2	no	—
181	C₂×Dic₄₃	—	4	2	no	—
182	C₂×Dic₄₃	—	4	1	no	—
183	Dic₈₆	—	2	2	no	—
184	Dic₈₆	—	2	2	no	—
185	Dic₈₆	—	4	1	no	—
186	Dic₈₆	—	4	1	no	—
187	Dic₈₆	—	8	4	no	—
188	C₈×C₄₃	—	2	4	no	—
189	C₈×C₄₃	—	2	2	no	—
190	C₈×C₄₃	—	4	1	no	—
191	#25471	—	43	1	no	maximal, Sylow
192	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
193	C₂²×C₄₃	#548	1	1	yes	characteristic
194	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
195	C₂²×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
196	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
197	C₂²×C₄₃	#576	1	1	yes	characteristic
198	C₂²×C₄₃	#577	1	1	yes	characteristic
199	C₄×C₄₃	—	2	4	no	—
200	C₄×C₄₃	—	2	2	no	—
201	C₄×C₄₃	—	4	2	no	—
202	C₄×C₄₃	#467	1	4	yes	—
203	C₄×C₄₃	#533	1	1	yes	characteristic
204	C₄×C₄₃	#541	1	1	yes	characteristic
205	C₄×C₄₃	#547	1	1	yes	characteristic
206	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
207	Dic₄₃	—	4	2	no	—
208	Dic₄₃	—	4	2	no	—
209	Dic₄₃	—	4	2	no	—
210	Dic₄₃	—	8	2	no	—
211	Dic₄₃	—	8	2	no	—
212	Dic₄₃	—	8	1	no	—
213	C₂×#477	—	43	1	no	—
214	C₂×C₈×Q₈	D₄₃	1	1	yes	characteristic
215	#2582	—	43	1	no	—
216	#2567	—	43	1	no	—
217	#2087	—	43	2	no	—
218	#2068	—	43	2	no	—
219	#1990	—	43	1	no	—
220	#1947	—	43	1	no	—
221	#1942	—	43	2	no	—
222	#1933	—	43	2	no	—
223	C₄×#103	—	43	1	no	—
224	C₂×C₄₃	#2429	1	1	yes	characteristic
225	C₂×C₄₃	C₂×#467	1	1	yes	characteristic
226	C₂×C₄₃	#3062	1	1	yes	characteristic
227	C₂×C₄₃	#3361	1	1	yes	characteristic
228	C₂×C₄₃	#3363	1	1	yes	characteristic
229	C₂×C₄₃	#3381	1	1	yes	characteristic
230	C₂×C₄₃	Q₈×Q₁₆	1	1	yes	characteristic
231	C₂×C₄⋊Q₈	—	43	1	no	—
232	C₂×C₄×Q₈	—	43	1	no	—
233	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
234	#477	—	86	4	no	—
235	C₈×Q₈	—	2	4	no	—
236	C₂×#107	—	43	2	no	—
237	C₂×#107	—	43	2	no	—
238	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
239	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
240	C₂×#103	—	43	1	no	—
241	C₂×#103	—	43	2	no	—
242	C₂×#103	—	43	1	no	—
243	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
244	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
245	#398	—	86	2	no	—
246	#395	—	86	2	no	—
247	#391	—	43	2	no	—
248	#391	—	86	1	no	—
249	#391	—	86	1	no	—
250	#389	—	43	2	no	—
251	#389	—	43	2	no	—
252	#389	—	43	2	no	—
253	#389	—	86	1	no	—
254	#384	—	43	1	no	—
255	#384	—	86	1	no	—
256	C₄×C₄⋊C₄	—	43	1	no	—
257	#340	—	43	2	no	—
258	#340	—	43	1	no	—
259	#340	—	43	2	no	—
260	#340	—	43	2	no	—
261	#340	—	43	1	no	—
262	C₄₃	#25471	1	1	yes	characteristic, complemented, Sylow
263	C₂²×Q₈	—	43	1	no	—
264	C₂²×Q₈	—	86	1	no	—
265	C₂²×Q₈	D₁₇₂	1	1	yes	characteristic
266	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
269	C₄⋊Q₈	—	86	2	no	—
270	C₄⋊Q₈	—	86	2	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	—	86	2	no	—
274	C₄×Q₈	—	86	2	no	—
275	C₂×C₄⋊C₄	—	43	1	no	—
276	C₂×C₄⋊C₄	—	43	1	no	—
277	C₂×C₄⋊C₄	—	43	1	no	—
278	C₂×C₄⋊C₄	—	43	2	no	—
279	C₂×C₄⋊C₄	—	43	2	no	—
280	C₂×C₄⋊C₄	—	86	2	no	—
281	C₂×C₄⋊C₄	—	86	2	no	—
282	C₂×C₄⋊C₄	—	86	2	no	—
283	C₂×C₄⋊C₄	—	86	1	no	—
284	C₂×C₄⋊C₄	—	86	1	no	—
285	C₂×C₄⋊C₄	—	86	1	no	—
286	C₂×C₄⋊C₄	—	86	1	no	—
287	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
288	C₂×C₄⋊C₄	D₁₇₂	1	2	yes	—
289	C₂×C₄²	—	86	1	no	—
290	C₂×C₄²	—	86	1	no	—
291	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
292	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
293	#107	—	86	4	no	—
294	#107	—	86	4	no	—
295	C₄⋊C₈	—	2	4	no	—
296	C₄⋊C₈	C₂²⋊D₄₃	1	4	yes	—
297	#103	—	43	4	no	—
298	#103	—	86	2	no	—
299	#103	—	86	4	no	—
300	C₄×C₈	—	2	4	no	—
301	C₄×C₈	—	2	2	no	—
302	#95	—	86	1	no	—
303	#95	—	86	2	no	—
304	#95	—	86	2	no	—
305	#95	—	86	2	no	—
306	#95	—	86	2	no	—
307	#95	—	86	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	43	2	no	—
311	C₂×Q₈	—	86	1	no	—
312	C₂×Q₈	—	86	1	no	—
313	C₂×Q₈	—	86	1	no	—
314	C₂×Q₈	—	86	1	no	—
315	C₂×Q₈	—	86	1	no	—
316	C₂×Q₈	—	344	1	no	—
317	C₂×Q₈	—	344	1	no	—
318	C₂×Q₈	—	172	2	no	—
319	C₂×Q₈	Dic₁₇₂	1	4	yes	—
320	C₂²×C₄	—	86	1	no	—
321	C₂²×C₄	—	86	1	no	—
322	C₂²×C₄	—	86	1	no	—
323	C₂²×C₄	—	86	2	no	—
324	C₂²×C₄	—	86	1	no	—
325	C₂²×C₄	—	86	2	no	—
326	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
327	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
329	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
330	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	Q₈×D₄₃	1	2	yes	—
339	C₂×C₈	C₂×C₂²⋊D₄₃	1	4	yes	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	43	2	no	—
343	C₄⋊C₄	—	43	2	no	—
344	C₄⋊C₄	—	86	1	no	—
345	C₄⋊C₄	—	86	1	no	—
346	C₄⋊C₄	—	86	2	no	—
347	C₄⋊C₄	—	86	1	no	—
348	C₄⋊C₄	—	86	2	no	—
349	C₄⋊C₄	—	86	1	no	—
350	C₄⋊C₄	—	86	2	no	—
351	C₄⋊C₄	—	86	2	no	—
352	C₄⋊C₄	—	344	2	no	—
353	C₄⋊C₄	—	344	2	no	—
354	C₄⋊C₄	—	344	2	no	—
355	C₄⋊C₄	—	344	1	no	—
356	C₄⋊C₄	—	172	2	no	—
357	C₄⋊C₄	—	172	2	no	—
358	C₄⋊C₄	—	172	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	172	2	no	—
362	C₄²	—	172	2	no	—
363	C₄²	#10621898	1	2	yes	—
364	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
365	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
366	Q₈	—	2	8	no	—
367	Q₈	—	86	2	no	—
368	Q₈	—	86	2	no	—
369	Q₈	—	344	4	no	—
370	Q₈	—	172	1	no	—
371	Q₈	—	172	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	86	2	no	—
380	C₂×C₄	—	86	2	no	—
381	C₂×C₄	—	86	2	no	—
382	C₂×C₄	—	172	2	no	—
383	C₂×C₄	—	172	1	no	—
384	C₂×C₄	—	172	2	no	—
385	C₂×C₄	—	172	2	no	—
386	C₂×C₄	—	172	1	no	—
387	C₂×C₄	—	172	2	no	—
388	C₂×C₄	—	172	2	no	—
389	C₂×C₄	—	172	2	no	—
390	C₂×C₄	—	172	1	no	—
391	C₂×C₄	—	172	1	no	—
392	C₂×C₄	—	172	1	no	—
393	C₂×C₄	—	172	1	no	—
394	C₂×C₄	—	172	1	no	—
395	C₂×C₄	—	172	1	no	—
396	C₂×C₄	—	172	1	no	—
397	C₂×C₄	#13063299	1	2	yes	—
398	C₂×C₄	#13063299	1	2	yes	—
399	C₂×C₄	C₂×Dic₁₇₂	1	4	yes	—
400	C₂×C₄	C₂×Dic₁₇₂	1	2	yes	—
401	C₂×C₄	#13063347	1	2	yes	—
402	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
403	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
404	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
405	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
406	C₂×C₄	#13063372	1	1	yes	characteristic
407	C₂×C₄	#13063373	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	2	4	no	—
410	C₈	—	4	1	no	—
411	C₂²	C₂×#13063299	1	1	yes	characteristic
412	C₂²	#14583561	1	1	yes	characteristic
413	C₂²	Q₈×D₁₇₂	1	1	yes	characteristic
414	C₂²	C₂²×Dic₁₇₂	1	1	yes	characteristic
415	C₂²	C₂×#13063347	1	1	yes	characteristic
416	C₂²	#14583704	1	1	yes	characteristic
417	C₂²	#14583711	1	1	yes	characteristic
418	C₄	—	2	2	no	—
419	C₄	—	2	4	no	—
420	C₄	—	4	2	no	—
421	C₄	—	344	2	no	—
422	C₄	—	344	1	no	—
423	C₄	—	344	2	no	—
424	C₄	—	172	2	no	—
425	C₄	—	172	2	no	—
426	C₄	—	172	2	no	—
427	C₄	#14583140	1	4	yes	—
428	C₄	#14583453	1	1	yes	characteristic
429	C₄	#14583507	1	1	yes	characteristic
430	C₄	#14583548	1	1	yes	characteristic
431	C₄	Q₈×C₂²⋊D₄₃	1	1	yes	characteristic
432	C₂	#19138188	1	1	yes	characteristic
433	C₂	C₂×#14583140	1	1	yes	characteristic
434	C₂	#19144275	1	1	yes	characteristic
435	C₂	#19147257	1	1	yes	characteristic
436	C₂	#19147274	1	1	yes	characteristic
437	C₂	#19147472	1	1	yes	characteristic
438	C₂	Q₈×Dic₁₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₈×Q₈×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
hypercenter	C₂×C₈×Q₈	D₄₃
hypocenter	C₄₃	#25471
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈ ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
67. #13063250	Q₈	semidirect
262. C₄₃	#25471	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583195	2
#19139965	2
#19139800	2
#19136088	2
#19135989	2
#19135556	2
#19135354	2
#19135328	2
#19135271	2
C₄×#13063250	2
C₂×C₈×Q₈×C₄₃	2
#25471	43