Subgroups — #24988712

Order 11008.

848 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583609	C₂	1	1	yes	maximal, characteristic
2	#19135397	C₂	1	1	yes	maximal, characteristic, complemented
3	#19134600	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134596	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582647	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14582628	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583609	—	2	2	no	—
9	#14583609	—	2	2	no	—
10	#14583609	—	2	2	no	—
11	#14583609	C₄	1	4	yes	complemented
12	C₂×#13063325	C₂²	1	1	yes	characteristic
13	C₂×#13063317	—	2	1	no	—
14	C₂×#13063303	—	2	2	no	—
15	C₂×#13063301	—	2	1	no	—
16	C₂×C₄×D₁₇₂	—	2	1	no	—
17	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₄×D₄₃	—	2	1	no	—
19	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#13063250	—	2	2	no	—
21	C₂×#13063249	—	2	1	no	—
22	C₂×#13063247	—	2	1	no	—
23	#14582769	C₂²	1	1	yes	characteristic
24	#14582662	—	2	1	no	—
25	#14582661	—	2	1	no	—
26	#14582647	—	2	2	no	—
27	#14582628	—	2	2	no	—
28	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₄₃×Q₈⋊C₈	—	2	2	no	—
32	C₂²×Dic₈₆	D₄	1	2	yes	—
33	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
34	C₂²×C₄×D₄₃	—	2	1	no	—
35	C₂²×C₄×D₄₃	—	2	2	no	—
36	C₂²×C₄₃⋊C₈	—	2	1	no	—
37	#13063325	—	2	1	no	—
38	#13063325	—	2	1	no	—
39	#13063325	C₂×C₄	1	2	yes	—
40	#13063325	D₄	1	2	yes	—
41	#13063317	—	2	4	no	—
42	#13063317	—	2	4	no	—
43	#13063303	—	2	8	no	—
44	#13063303	—	2	8	no	—
45	#13063301	—	2	4	no	—
46	#13063301	—	2	4	no	—
47	C₄×D₁₇₂	—	2	4	no	—
48	C₄×D₁₇₂	—	2	4	no	—
49	C₄×D₁₇₂	—	2	1	no	—
50	C₄×D₁₇₂	—	2	1	no	—
51	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
52	C₄×D₁₇₂	D₄	1	2	yes	—
53	C₂×C₄⋊Dic₄₃	—	2	1	no	—
54	C₂×C₄⋊Dic₄₃	—	2	1	no	—
55	C₂×C₄⋊Dic₄₃	—	2	1	no	—
56	C₂×C₄⋊Dic₄₃	—	2	1	no	—
57	C₂×C₄⋊Dic₄₃	—	2	1	no	—
58	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
59	C₂×Dic₄₃⋊C₄	—	2	2	no	—
60	C₂×Dic₄₃⋊C₄	—	2	2	no	—
61	C₄⋊C₄×D₄₃	—	2	4	no	—
62	C₄⋊C₄×D₄₃	—	2	4	no	—
63	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
64	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
65	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
66	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
67	#13063250	—	4	4	no	—
68	#13063249	—	4	2	no	—
69	#13063247	—	4	2	no	—
70	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
71	C₂²×C₈×C₄₃	—	2	1	no	—
72	C₂²×C₈×C₄₃	—	2	1	no	—
73	C₄×Q₈×C₄₃	—	2	1	no	—
74	C₄×Q₈×C₄₃	—	2	1	no	—
75	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
76	C₄×Q₈×C₄₃	D₄	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₃	—	2	1	no	—
80	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₄₃	—	2	1	no	—
82	C₄⋊C₈×C₄₃	—	2	1	no	—
83	C₄×C₈×C₄₃	—	2	1	no	—
84	C₄×C₈×C₄₃	—	2	1	no	—
85	C₂³×D₄₃	—	2	1	no	—
86	C₂×Q₈×C₄₃	—	2	1	no	—
87	C₂×Q₈×C₄₃	—	2	1	no	—
88	C₂×Q₈×C₄₃	—	2	1	no	—
89	C₂×Q₈×C₄₃	—	2	1	no	—
90	C₂×Q₈×C₄₃	—	2	1	no	—
91	C₂×Q₈×C₄₃	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₄₃	—	2	1	no	—
93	C₂²×C₄×C₄₃	—	2	1	no	—
94	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×Dic₄₃	—	2	1	no	—
98	C₂²×Dic₄₃	—	2	2	no	—
99	C₂²×Dic₄₃	—	4	1	no	—
100	C₂×D₁₇₂	—	2	1	no	—
101	C₂×D₁₇₂	—	2	1	no	—
102	C₂×D₁₇₂	—	2	1	no	—
103	C₂×D₁₇₂	C₂²⋊C₄	1	2	yes	—
104	C₂×D₁₇₂	SD₁₆	1	2	yes	—
105	C₂×D₁₇₂	Q₁₆	1	2	yes	—
106	C₂×C₄×D₄₃	—	2	2	no	—
107	C₂×C₄×D₄₃	—	2	2	no	—
108	C₂×C₄×D₄₃	—	2	8	no	—
109	C₂×C₄×D₄₃	—	4	1	no	—
110	C₂×C₄×D₄₃	—	4	1	no	—
111	C₂×C₄×D₄₃	—	4	1	no	—
112	C₂×C₄×D₄₃	—	4	1	no	—
113	C₂×C₄×D₄₃	—	8	2	no	—
114	C₂×C₄×D₄₃	—	8	2	no	—
115	C₂×Dic₈₆	—	2	2	no	—
116	C₂×Dic₈₆	—	4	2	no	—
117	C₂×Dic₈₆	—	4	2	no	—
118	C₂×Dic₈₆	C₂²⋊C₄	1	4	yes	—
119	C₂×C₈×C₄₃	—	2	2	no	—
120	C₂×C₈×C₄₃	—	4	1	no	—
121	C₂×C₈×C₄₃	—	4	1	no	—
122	C₂×C₈×C₄₃	—	4	1	no	—
123	C₂×C₈×C₄₃	—	4	1	no	—
124	C₂×C₈×C₄₃	—	4	1	no	—
125	C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	2	1	no	—
128	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₄₃	—	2	2	no	—
130	C₄²×C₄₃	—	2	2	no	—
131	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
135	(C₂×D₄₃)⋊C₄	—	2	8	no	—
136	(C₂×D₄₃)⋊C₄	—	2	2	no	—
137	(C₂×D₄₃)⋊C₄	—	2	2	no	—
138	C₄⋊Dic₄₃	—	2	2	no	—
139	C₄⋊Dic₄₃	—	2	2	no	—
140	C₄⋊Dic₄₃	—	2	2	no	—
141	C₄⋊Dic₄₃	—	2	2	no	—
142	C₄⋊Dic₄₃	—	2	1	no	—
143	C₄⋊Dic₄₃	—	4	2	no	—
144	C₄⋊Dic₄₃	—	4	1	no	—
145	C₄⋊Dic₄₃	—	4	1	no	—
146	C₄⋊Dic₄₃	—	4	1	no	—
147	C₄⋊Dic₄₃	—	4	1	no	—
148	C₄⋊Dic₄₃	C₂²⋊C₄	1	2	yes	—
149	Dic₄₃⋊C₄	—	2	8	no	—
150	Dic₄₃⋊C₄	—	2	8	no	—
151	C₂×C₄₃⋊C₈	—	4	1	no	—
152	C₂×C₄₃⋊C₈	—	4	1	no	—
153	C₂×C₄₃⋊C₈	—	4	1	no	—
154	C₂³×C₄₃	#120	1	1	yes	characteristic
155	C₂²×D₄₃	—	2	2	no	—
156	C₂²×D₄₃	—	2	2	no	—
157	C₂²×D₄₃	—	2	2	no	—
158	C₂²×D₄₃	—	4	1	no	—
159	C₂²×D₄₃	—	4	1	no	—
160	C₂²×D₄₃	—	4	1	no	—
161	C₂²×D₄₃	—	4	1	no	—
162	Q₈×C₄₃	—	2	2	no	—
163	Q₈×C₄₃	—	2	2	no	—
164	Q₈×C₄₃	—	4	1	no	—
165	Q₈×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	—	4	1	no	—
174	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
178	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
179	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
182	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
183	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
184	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
186	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
187	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
188	C₂×Dic₄₃	—	2	2	no	—
189	C₂×Dic₄₃	—	2	4	no	—
190	C₂×Dic₄₃	—	4	1	no	—
191	C₂×Dic₄₃	—	4	1	no	—
192	C₂×Dic₄₃	—	4	2	no	—
193	C₂×Dic₄₃	—	4	2	no	—
194	C₂×Dic₄₃	—	8	1	no	—
195	C₂×Dic₄₃	—	8	1	no	—
196	C₂×Dic₄₃	—	8	1	no	—
197	D₁₇₂	—	2	2	no	—
198	D₁₇₂	—	2	2	no	—
199	D₁₇₂	—	2	2	no	—
200	D₁₇₂	#103	1	4	yes	complemented
201	C₄×D₄₃	—	4	2	no	—
202	C₄×D₄₃	—	4	2	no	—
203	C₄×D₄₃	—	4	2	no	—
204	C₄×D₄₃	—	4	2	no	—
205	C₄×D₄₃	—	8	8	no	—
206	Dic₈₆	—	4	4	no	—
207	Dic₈₆	—	8	2	no	—
208	C₈×C₄₃	—	4	2	no	—
209	C₈×C₄₃	—	8	1	no	—
210	C₄₃⋊C₈	—	8	1	no	—
211	#8450	—	43	1	no	maximal, Sylow
212	C₂²×C₄₃	#379	1	1	yes	characteristic
213	C₂²×C₄₃	#448	1	1	yes	characteristic
214	C₂²×C₄₃	#449	1	1	yes	characteristic
215	C₂²×C₄₃	#451	1	1	yes	characteristic
216	C₂²×C₄₃	#452	1	1	yes	characteristic
217	C₂²×C₄₃	#453	1	1	yes	characteristic
218	C₂²×C₄₃	#455	1	1	yes	characteristic
219	C₂×D₄₃	—	2	4	no	—
220	C₂×D₄₃	—	4	2	no	—
221	C₂×D₄₃	—	4	2	no	—
222	C₂×D₄₃	—	4	2	no	—
223	C₂×D₄₃	—	4	2	no	—
224	C₂×D₄₃	—	4	2	no	—
225	C₂×D₄₃	—	4	2	no	—
226	C₄×C₄₃	—	2	1	no	—
227	C₄×C₄₃	—	2	1	no	—
228	C₄×C₄₃	—	4	2	no	—
229	C₄×C₄₃	—	4	2	no	—
230	C₄×C₄₃	C₂×#103	1	1	yes	characteristic
231	C₄×C₄₃	#416	1	1	yes	characteristic
232	C₄×C₄₃	#417	1	1	yes	characteristic
233	C₄×C₄₃	#419	1	1	yes	characteristic
234	C₄×C₄₃	#448	1	1	yes	characteristic
235	C₄×C₄₃	#449	1	1	yes	characteristic
236	C₄×C₄₃	#451	1	1	yes	characteristic
237	C₄×C₄₃	#452	1	1	yes	characteristic
238	Dic₄₃	—	4	4	no	—
239	Dic₄₃	—	4	2	no	—
240	Dic₄₃	—	16	1	no	—
241	C₂×#554	—	43	1	no	—
242	#1956	—	43	1	no	—
243	#1803	—	43	1	no	—
244	#1802	—	43	1	no	—
245	C₂×#333	—	43	1	no	—
246	C₂×Q₈⋊C₈	D₄₃	1	1	yes	characteristic, complemented
247	C₂×D₄⋊C₈	—	43	1	no	—
248	C₂×C₄₃	#1622	1	1	yes	characteristic
249	C₂×C₄₃	#1632	1	1	yes	characteristic
250	C₂×C₄₃	#1643	1	1	yes	characteristic
251	C₂×C₄₃	#1644	1	1	yes	characteristic
252	C₂×C₄₃	#1787	1	1	yes	characteristic
253	C₂×C₄₃	#1788	1	1	yes	characteristic
254	C₂×C₄₃	#1792	1	1	yes	characteristic
255	D₄₃	—	4	4	no	—
256	#554	—	43	4	no	—
257	#554	—	86	2	no	—
258	#554	—	86	2	no	—
259	#554	—	86	2	no	—
260	C₂×C₄⋊Q₈	—	43	1	no	—
261	C₂×#125	—	86	1	no	—
262	C₂×C₂²⋊Q₈	—	86	2	no	—
263	C₂×C₂²⋊Q₈	—	86	1	no	—
264	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
265	C₂×C₄×D₄	—	43	1	no	—
266	C₂×C₄×D₄	—	86	1	no	—
267	C₂²×C₄⋊C₄	—	86	1	no	—
268	C₂×C₄⋊C₈	—	43	1	no	—
269	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
270	C₂×#103	—	86	2	no	—
271	C₂×#103	—	86	1	no	—
272	C₂×#102	—	86	1	no	—
273	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
274	#384	—	43	1	no	—
275	#340	—	86	1	no	—
276	#340	—	86	1	no	—
277	#333	—	86	2	no	—
278	Q₈⋊C₈	—	2	2	no	—
279	D₄⋊C₈	—	86	2	no	—
280	C₄₃	#8450	1	1	yes	characteristic, complemented, Sylow
281	C₂²×Q₈	—	43	2	no	—
282	C₂²×Q₈	D₁₇₂	1	1	yes	characteristic
283	C₂²×D₄	—	43	1	no	—
284	C₂³×C₄	—	86	2	no	—
285	C₂³×C₄	—	86	1	no	—
286	C₂²×C₈	—	2	1	no	—
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	—	86	1	no	—
289	C₄⋊Q₈	—	43	2	no	—
290	C₄⋊Q₈	—	43	2	no	—
291	C₄⋊Q₈	—	86	1	no	—
292	C₄⋊Q₈	—	86	1	no	—
293	#125	—	86	4	no	—
294	#125	—	86	4	no	—
295	C₂²⋊Q₈	—	86	8	no	—
296	C₂²⋊Q₈	—	86	8	no	—
297	C₂²⋊Q₈	—	86	4	no	—
298	C₂²⋊Q₈	—	86	4	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×Q₈	C₄×D₄₃	1	2	yes	—
302	C₄×Q₈	C₂²⋊D₄₃	1	2	yes	—
303	C₄×D₄	—	43	2	no	—
304	C₄×D₄	—	43	2	no	—
305	C₄×D₄	—	86	4	no	—
306	C₄×D₄	—	86	4	no	—
307	C₄×D₄	—	86	1	no	—
308	C₄×D₄	—	86	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	43	1	no	—
311	C₂×C₄⋊C₄	—	86	4	no	—
312	C₂×C₄⋊C₄	—	86	2	no	—
313	C₂×C₄⋊C₄	—	86	2	no	—
314	C₂×C₄⋊C₄	—	86	1	no	—
315	C₂×C₄⋊C₄	—	86	1	no	—
316	C₂×C₄⋊C₄	—	86	4	no	—
317	C₂×C₄⋊C₄	—	86	1	no	—
318	C₂×C₄⋊C₄	—	86	1	no	—
319	C₂×C₄⋊C₄	—	86	1	no	—
320	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	—	86	2	no	—
322	C₂×C₂²⋊C₄	—	86	1	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	—	86	1	no	—
328	C₄⋊C₈	—	86	1	no	—
329	#103	—	172	4	no	—
330	#103	—	172	2	no	—
331	#102	—	172	2	no	—
332	C₄×C₈	—	2	1	no	—
333	C₄×C₈	—	2	1	no	—
334	C₂⁴	—	86	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	43	4	no	—
341	C₂×Q₈	—	86	2	no	—
342	C₂×Q₈	—	172	2	no	—
343	C₂×Q₈	—	172	2	no	—
344	C₂×Q₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
345	C₂×D₄	—	43	2	no	—
346	C₂×D₄	—	43	2	no	—
347	C₂×D₄	—	43	2	no	—
348	C₂×D₄	—	86	1	no	—
349	C₂×D₄	—	86	1	no	—
350	C₂×D₄	—	86	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	86	8	no	—
354	C₂²×C₄	—	86	1	no	—
355	C₂²×C₄	—	86	2	no	—
356	C₂²×C₄	—	86	2	no	—
357	C₂²×C₄	—	86	2	no	—
358	C₂²×C₄	—	344	2	no	—
359	C₂²×C₄	—	344	2	no	—
360	C₂²×C₄	—	172	1	no	—
361	C₂²×C₄	—	172	1	no	—
362	C₂²×C₄	—	172	1	no	—
363	C₂²×C₄	—	172	1	no	—
364	C₂²×C₄	—	172	1	no	—
365	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
366	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
367	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	1	no	—
371	C₂×C₈	—	4	1	no	—
372	C₂×C₈	—	4	1	no	—
373	C₂×C₈	—	4	1	no	—
374	C₂×C₈	—	172	1	no	—
375	C₂×C₈	—	172	1	no	—
376	C₂×C₈	—	172	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	43	2	no	—
381	C₄⋊C₄	—	86	8	no	—
382	C₄⋊C₄	—	86	8	no	—
383	C₄⋊C₄	—	86	2	no	—
384	C₄⋊C₄	—	86	2	no	—
385	C₄⋊C₄	—	86	1	no	—
386	C₄⋊C₄	—	86	2	no	—
387	C₄⋊C₄	—	86	2	no	—
388	C₄⋊C₄	—	172	2	no	—
389	C₄⋊C₄	—	172	1	no	—
390	C₄⋊C₄	—	172	1	no	—
391	C₄⋊C₄	—	172	1	no	—
392	C₄⋊C₄	—	172	1	no	—
393	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
394	C₂²⋊C₄	—	86	8	no	—
395	C₂²⋊C₄	—	86	2	no	—
396	C₂²⋊C₄	—	86	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
400	C₄²	D₄×D₄₃	1	1	yes	characteristic
401	C₄²	D₄×D₄₃	1	1	yes	characteristic
402	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
403	C₂³	—	86	2	no	—
404	C₂³	—	86	2	no	—
405	C₂³	—	86	2	no	—
406	C₂³	—	172	1	no	—
407	C₂³	—	172	1	no	—
408	C₂³	—	172	1	no	—
409	C₂³	—	172	1	no	—
410	C₂³	#13063295	1	1	yes	characteristic
411	Q₈	—	2	2	no	—
412	Q₈	—	2	2	no	—
413	Q₈	—	4	1	no	—
414	Q₈	—	4	1	no	—
415	Q₈	—	344	2	no	—
416	Q₈	—	172	4	no	—
417	D₄	—	43	4	no	—
418	D₄	—	86	2	no	—
419	D₄	—	86	2	no	—
420	D₄	—	86	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	86	2	no	—
430	C₂×C₄	—	86	4	no	—
431	C₂×C₄	—	344	8	no	—
432	C₂×C₄	—	344	1	no	—
433	C₂×C₄	—	344	1	no	—
434	C₂×C₄	—	344	1	no	—
435	C₂×C₄	—	172	1	no	—
436	C₂×C₄	—	172	1	no	—
437	C₂×C₄	—	172	2	no	—
438	C₂×C₄	—	172	2	no	—
439	C₂×C₄	—	172	2	no	—
440	C₂×C₄	—	172	2	no	—
441	C₂×C₄	—	172	2	no	—
442	C₂×C₄	—	172	2	no	—
443	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
444	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
445	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
446	C₂×C₄	#13063293	1	1	yes	characteristic
447	C₂×C₄	#13063293	1	1	yes	characteristic
448	C₂×C₄	#13063295	1	1	yes	characteristic
449	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
450	C₂×C₄	Q₁₆×D₄₃	1	1	yes	characteristic
451	C₂×C₄	#13063347	1	1	yes	characteristic
452	C₂×C₄	#13063347	1	1	yes	characteristic
453	C₂×C₄	#13063353	1	1	yes	characteristic
454	C₂×C₄	#13063354	1	1	yes	characteristic
455	C₂×C₄	#13063357	1	1	yes	characteristic
456	C₂×C₄	#13063358	1	1	yes	characteristic
457	C₈	—	4	2	no	—
458	C₈	—	8	1	no	—
459	C₈	—	344	1	no	—
460	C₂²	—	86	4	no	—
461	C₂²	—	172	2	no	—
462	C₂²	—	172	2	no	—
463	C₂²	—	172	2	no	—
464	C₂²	—	172	2	no	—
465	C₂²	—	172	2	no	—
466	C₂²	—	172	2	no	—
467	C₂²	#14582754	1	1	yes	characteristic
468	C₂²	#14583039	1	1	yes	characteristic
469	C₂²	#14583046	1	1	yes	characteristic
470	C₂²	#14583056	1	1	yes	characteristic
471	C₂²	#14583063	1	1	yes	characteristic
472	C₂²	#14583068	1	1	yes	characteristic
473	C₂²	#14583078	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	172	2	no	—
479	C₄	—	172	4	no	—
480	C₄	—	688	1	no	—
481	C₄	#103×D₄₃	1	1	yes	characteristic
482	C₄	#14582896	1	1	yes	characteristic
483	C₄	#14582901	1	1	yes	characteristic
484	C₄	#14582906	1	1	yes	characteristic
485	C₄	#14583036	1	1	yes	characteristic
486	C₄	#14583046	1	1	yes	characteristic
487	C₄	#14583053	1	1	yes	characteristic
488	C₄	#14583063	1	1	yes	characteristic
489	C₂	—	172	4	no	—
490	C₂	#19133670	1	1	yes	characteristic
491	C₂	#19133732	1	1	yes	characteristic
492	C₂	#19133805	1	1	yes	characteristic
493	C₂	#19133811	1	1	yes	characteristic
494	C₂	#19134528	1	1	yes	characteristic
495	C₂	#19134536	1	1	yes	characteristic
496	C₂	#19134550	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063295
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×Q₈⋊C₈	C₂
socle	C₂³×C₄₃	#120
prime radical	C₂²×D₁₇₂	D₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₂×Q₈⋊C₈	D₄₃
hypocenter	C₄₃	#8450
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. #19135397	C₂	semidirect
3. #19134600	C₂	semidirect
5. C₂×#14582647	C₂	semidirect
7. C₂×C₄₃×Q₈⋊C₈	C₂	semidirect
11. #14583609	C₄	semidirect
200. D₁₇₂	#103	semidirect
246. C₂×Q₈⋊C₈	D₄₃	semidirect
280. C₄₃	#8450	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583609	2
#19135397	2
#19134600	2
#19134596	2
C₂×#14582647	2
C₂×#14582628	2
C₂×C₄₃×Q₈⋊C₈	2
#8450	43