Subgroups — #10948303

Order 768.

590 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#901	C₂	1	1	yes	maximal, characteristic
2	C₃×#2163	C₂	1	1	yes	maximal, characteristic, complemented
3	#69744	C₂	1	1	yes	maximal, characteristic, complemented
4	#69284	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#69275	C₂	1	1	yes	maximal, characteristic, complemented
7	#69274	C₂	1	1	yes	maximal, characteristic, complemented
8	#69107	C₂	1	2	yes	maximal
9	#69094	C₂	1	2	yes	maximal, complemented
10	#69074	C₂	1	2	yes	maximal, complemented
11	#69072	C₂	1	2	yes	maximal, complemented
12	#33423	—	3	1	no	maximal, Sylow
13	C₂×#901	C₄	1	1	yes	characteristic
14	C₂×#901	C₂²	1	1	yes	characteristic
15	C₄×#235	C₄	1	1	yes	characteristic
16	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
17	#5101	C₄	1	1	yes	characteristic
18	#5101	C₂²	1	1	yes	characteristic
19	C₄×#208	C₄	1	1	yes	characteristic
20	C₂×#798	C₂²	1	2	yes	—
21	C₂×D₃×C₁₆	C₂²	1	2	yes	—
22	#4689	C₄	1	1	yes	characteristic
23	#4689	C₄	1	1	yes	characteristic
24	#4689	C₂²	1	1	yes	characteristic
25	#4689	C₂²	1	1	yes	characteristic
26	C₄×ΓL(1,𝔽₂₅)	C₄	1	1	yes	characteristic
27	C₄×ΓL(1,𝔽₂₅)	C₄	1	1	yes	characteristic
28	C₄×D₃×C₈	C₂²	1	1	yes	characteristic
29	C₄×D₃×C₈	C₂²	1	1	yes	characteristic
30	C₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
31	C₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
32	C₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
33	C₃×#346	C₂²	1	2	yes	—
34	#4549	C₂²	1	2	yes	—
35	(C₂×D₃)⋊C₁₆	C₂²	1	2	yes	—
36	(C₂×D₃)⋊C₁₆	C₂²	1	2	yes	—
37	#4502	C₂²	1	2	yes	—
38	Dic₃⋊C₁₆	C₂²	1	2	yes	—
39	Dic₃⋊C₁₆	C₂²	1	2	yes	—
40	Dic₃×C₁₆	C₂²	1	2	yes	—
41	C₄⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic
42	C₄⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic
43	C₄×C₃⋊C₁₆	C₂²	1	2	yes	—
44	C₄×#131	—	3	1	no	—
45	#2164	—	3	2	no	—
46	#2164	—	3	2	no	—
47	#2163	—	3	1	no	—
48	#2163	D₃	1	1	yes	characteristic, complemented
49	#2162	—	3	1	no	—
50	#2162	—	3	1	no	—
51	#2150	—	3	1	no	—
52	C₂×C₄⋊C₁₆	—	3	1	no	—
53	#2113	—	3	2	no	—
54	#2108	—	3	2	no	—
55	C₂×#235	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₃×C₈	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
59	C₄×#67	C₈	1	1	yes	characteristic
60	C₄×#67	C₈	1	1	yes	characteristic
61	C₄×#67	C₈	1	1	yes	characteristic
62	C₄×#67	C₈	1	1	yes	characteristic
63	#926	C₂×C₄	1	1	yes	characteristic
64	C₂×#208	C₂×C₄	1	1	yes	characteristic
65	C₂×#208	C₂×C₄	1	1	yes	characteristic
66	#901	—	2	4	no	—
67	#901	—	2	2	no	—
68	#901	—	2	2	no	—
69	C₂×ΓL(1,𝔽₂₅)	C₂×C₄	1	1	yes	characteristic
70	C₂×ΓL(1,𝔽₂₅)	C₂×C₄	1	1	yes	characteristic
71	C₂×ΓL(1,𝔽₂₅)	C₂×C₄	1	1	yes	characteristic
72	C₂×ΓL(1,𝔽₂₅)	C₂×C₄	1	1	yes	characteristic
73	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
74	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
75	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
76	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
77	C₄×D₁₂	C₈	1	1	yes	characteristic
78	C₄×D₁₂	C₈	1	1	yes	characteristic
79	#872	C₂×C₄	1	1	yes	characteristic
80	#872	C₂×C₄	1	1	yes	characteristic
81	C₄²×D₃	C₂×C₄	1	1	yes	characteristic
82	C₄²×D₃	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₆	C₈	1	1	yes	characteristic
84	C₄×Dic₆	C₈	1	1	yes	characteristic
85	C₂×C₃×C₁₆	C₂³	1	2	yes	—
86	C₂×C₃×C₁₆	C₂³	1	2	yes	—
87	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
88	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
89	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
90	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
91	#815	C₂×C₄	1	1	yes	characteristic
92	#815	C₂×C₄	1	1	yes	characteristic
93	#815	C₂×C₄	1	1	yes	characteristic
94	#815	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₃	C₂³	1	1	yes	characteristic
98	C₈×Dic₃	C₂³	1	1	yes	characteristic
99	C₂×C₃⋊C₁₆	C₂³	1	2	yes	—
100	C₂×C₃⋊C₁₆	C₂³	1	2	yes	—
101	#803	C₂×C₄	1	1	yes	characteristic
102	#803	C₂×C₄	1	1	yes	characteristic
103	C₄×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
104	C₄×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
105	#798	—	2	4	no	—
106	D₃×C₁₆	—	2	4	no	—
107	C₂×#131	—	3	1	no	—
108	C₂×#131	—	3	1	no	—
109	C₄×#41	—	3	1	no	—
110	C₂×M₃₂	—	3	2	no	—
111	C₂²×C₁₆	—	3	2	no	—
112	#405	—	3	1	no	—
113	#405	—	3	1	no	—
114	#405	—	3	1	no	—
115	#405	—	3	1	no	—
116	#405	—	3	1	no	—
117	#405	—	3	1	no	—
118	C₄×M₁₆	—	3	1	no	—
119	C₄×M₁₆	—	3	1	no	—
120	C₄×M₁₆	—	3	1	no	—
121	C₂×C₄×C₈	—	3	1	no	—
122	C₂×C₄×C₈	—	3	1	no	—
123	C₂×C₄×C₈	C₂×D₃	1	1	yes	characteristic
124	C₄⋊C₁₆	—	3	2	no	—
125	C₄⋊C₁₆	—	3	2	no	—
126	C₄⋊C₁₆	—	3	1	no	—
127	C₄⋊C₁₆	—	3	1	no	—
128	C₄⋊C₁₆	C₂×D₃	1	1	yes	characteristic
129	C₄⋊C₁₆	C₂×D₃	1	1	yes	characteristic
130	C₂²⋊C₁₆	—	3	2	no	—
131	C₂²⋊C₁₆	—	3	2	no	—
132	C₂²⋊C₁₆	—	3	2	no	—
133	C₂²⋊C₁₆	C₂×D₃	1	2	yes	—
134	#346	—	3	2	no	—
135	#346	C₂×D₃	1	2	yes	—
136	C₄×C₁₆	—	3	2	no	—
137	C₄×C₁₆	—	3	2	no	—
138	C₂²×C₃×C₄	C₂×C₈	1	1	yes	characteristic
139	C₂²×C₃×C₄	C₂×C₈	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
141	C₂×#67	C₂×C₈	1	1	yes	characteristic
142	C₂×#67	C₂×C₈	1	1	yes	characteristic
143	#235	—	2	2	no	—
144	#235	—	2	2	no	—
145	C₂×D₁₂	C₂×C₈	1	1	yes	characteristic
146	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
147	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
148	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
149	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
150	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×Dic₆	C₂×C₈	1	1	yes	characteristic
153	C₂×C₃×C₈	—	2	2	no	—
154	C₂×C₃×C₈	—	2	1	no	—
155	C₂×C₃×C₈	—	2	1	no	—
156	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
160	C₃×C₄²	C₂×C₈	1	1	yes	characteristic
161	C₃×C₄²	C₂×C₈	1	1	yes	characteristic
162	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
163	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
164	#217	C₂×C₈	1	1	yes	characteristic
165	#217	C₂×C₈	1	1	yes	characteristic
166	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
167	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
168	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
169	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
170	C₄⋊Dic₃	C₂×C₈	1	1	yes	characteristic
171	C₄⋊Dic₃	C₂×C₈	1	1	yes	characteristic
172	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
173	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
174	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
175	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
176	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
177	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
178	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
179	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
180	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
181	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
182	#208	—	2	2	no	—
183	#208	—	2	2	no	—
184	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
188	ΓL(1,𝔽₂₅)	—	2	2	no	—
189	ΓL(1,𝔽₂₅)	—	2	2	no	—
190	ΓL(1,𝔽₂₅)	—	2	2	no	—
191	ΓL(1,𝔽₂₅)	M₁₆	1	4	yes	—
192	D₃×C₈	—	2	2	no	—
193	D₃×C₈	—	2	1	no	—
194	D₃×C₈	—	2	1	no	—
195	D₃×C₈	—	2	2	no	—
196	D₃×C₈	#41	1	2	yes	—
197	D₃×C₈	#41	1	2	yes	—
198	C₃×C₁₆	—	2	2	no	—
199	C₃×C₁₆	—	2	2	no	—
200	C₃⋊C₁₆	—	2	2	no	—
201	C₃⋊C₁₆	—	2	2	no	—
202	C₂×#41	—	3	1	no	—
203	#131	—	6	2	no	—
204	#131	—	6	2	no	—
205	#131	—	6	4	no	—
206	C₂×M₁₆	—	3	1	no	—
207	C₂×M₁₆	—	3	1	no	—
208	C₂×M₁₆	—	3	1	no	—
209	C₂×M₁₆	—	3	1	no	—
210	C₂×M₁₆	—	3	1	no	—
211	C₂×M₁₆	—	3	1	no	—
212	C₂²×C₈	—	3	1	no	—
213	C₂²×C₈	—	3	1	no	—
214	C₂²×C₈	—	3	1	no	—
215	C₂²×C₈	—	3	1	no	—
216	C₂²×C₈	C₄×D₃	1	1	yes	characteristic
217	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
218	C₄×Q₈	—	3	1	no	—
219	C₄×Q₈	—	3	1	no	—
220	C₄×D₄	—	3	1	no	—
221	C₄×D₄	—	3	1	no	—
222	C₄×D₄	—	3	1	no	—
223	C₄×D₄	—	3	1	no	—
224	C₄×D₄	—	3	1	no	—
225	C₄×D₄	—	3	1	no	—
226	#117	—	3	1	no	—
227	#117	—	3	1	no	—
228	#117	—	3	1	no	—
229	C₂×C₄²	—	3	1	no	—
230	C₂×C₄²	—	3	1	no	—
231	C₂×C₄²	C₄×D₃	1	1	yes	characteristic
232	M₃₂	—	6	4	no	—
233	C₂×C₁₆	—	3	2	no	—
234	C₂×C₁₆	—	3	2	no	—
235	C₂×C₁₆	—	6	4	no	—
236	C₂×C₁₆	C₂²×D₃	1	2	yes	—
237	C₂×C₁₆	C₂²×D₃	1	2	yes	—
238	#97	—	3	1	no	—
239	#97	—	3	1	no	—
240	#97	—	3	1	no	—
241	#97	—	3	1	no	—
242	#97	—	3	1	no	—
243	#97	—	3	1	no	—
244	C₄×C₈	—	3	1	no	—
245	C₄×C₈	—	3	1	no	—
246	C₄×C₈	—	3	1	no	—
247	C₄×C₈	—	3	1	no	—
248	C₄×C₈	—	3	1	no	—
249	C₄×C₈	—	3	1	no	—
250	C₄×C₈	C₄×D₃	1	1	yes	characteristic
251	C₄×C₈	C₄×D₃	1	1	yes	characteristic
252	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
253	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
254	C₂³×C₃	C₂²×C₈	1	1	yes	characteristic
255	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
256	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	4	1	no	—
261	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
267	#67	—	2	2	no	—
268	#67	—	2	2	no	—
269	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
270	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
271	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
272	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
273	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
274	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
275	D₁₂	—	2	2	no	—
276	C₄×D₃	—	2	1	no	—
277	C₄×D₃	—	2	1	no	—
278	C₄×D₃	—	2	2	no	—
279	C₄×D₃	—	2	2	no	—
280	C₄×D₃	—	4	1	no	—
281	C₄×D₃	—	4	1	no	—
282	C₄×D₃	#117	1	2	yes	—
283	C₄×D₃	C₂×M₁₆	1	2	yes	—
284	Dic₆	—	2	2	no	—
285	C₃×C₈	—	2	1	no	—
286	C₃×C₈	—	2	1	no	—
287	C₃×C₈	C₂×M₁₆	1	2	yes	—
288	C₃×C₈	C₂×#41	1	1	yes	characteristic
289	C₃×C₈	C₂×#41	1	1	yes	characteristic
290	C₃⋊C₈	—	2	1	no	—
291	C₃⋊C₈	—	2	1	no	—
292	C₃⋊C₈	#117	1	2	yes	—
293	C₃⋊C₈	C₂×M₁₆	1	2	yes	—
294	#41	—	6	2	no	—
295	#41	—	6	2	no	—
296	C₂×Q₈	—	3	1	no	—
297	C₂×D₄	—	3	1	no	—
298	C₂×D₄	—	3	1	no	—
299	C₂×D₄	—	3	1	no	—
300	C₂²×C₄	—	3	1	no	—
301	C₂²×C₄	—	3	1	no	—
302	C₂²×C₄	—	3	1	no	—
303	C₂²×C₄	—	3	1	no	—
304	C₂²×C₄	—	3	1	no	—
305	C₂²×C₄	—	3	1	no	—
306	C₂²×C₄	D₃×C₈	1	1	yes	characteristic
307	C₂²×C₄	D₃×C₈	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
309	M₁₆	—	3	4	no	—
310	M₁₆	—	6	2	no	—
311	M₁₆	—	6	2	no	—
312	M₁₆	—	6	2	no	—
313	M₁₆	—	6	2	no	—
314	M₁₆	—	6	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	3	1	no	—
319	C₂×C₈	—	3	1	no	—
320	C₂×C₈	—	3	2	no	—
321	C₂×C₈	—	3	2	no	—
322	C₂×C₈	—	3	1	no	—
323	C₂×C₈	—	3	1	no	—
324	C₂×C₈	—	6	2	no	—
325	C₂×C₈	—	6	2	no	—
326	C₂×C₈	—	6	1	no	—
327	C₂×C₈	—	6	1	no	—
328	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
329	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
330	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
331	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
332	C₄⋊C₄	—	3	1	no	—
333	C₄⋊C₄	—	3	1	no	—
334	C₄⋊C₄	—	3	1	no	—
335	C₄⋊C₄	—	3	1	no	—
336	C₄⋊C₄	—	3	1	no	—
337	C₄⋊C₄	—	3	1	no	—
338	C₂²⋊C₄	—	3	1	no	—
339	C₂²⋊C₄	—	3	1	no	—
340	C₂²⋊C₄	—	3	1	no	—
341	C₂²⋊C₄	—	3	1	no	—
342	C₂²⋊C₄	—	3	1	no	—
343	C₂²⋊C₄	—	3	1	no	—
344	C₄²	—	3	1	no	—
345	C₄²	—	3	1	no	—
346	C₄²	—	3	1	no	—
347	C₄²	—	3	1	no	—
348	C₄²	—	3	1	no	—
349	C₄²	—	3	1	no	—
350	C₄²	D₃×C₈	1	1	yes	characteristic
351	C₄²	D₃×C₈	1	1	yes	characteristic
352	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
353	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
354	C₁₆	—	2	2	no	—
355	C₁₆	—	2	2	no	—
356	C₁₆	—	6	2	no	—
357	C₁₆	—	6	2	no	—
358	C₂²×C₃	—	2	1	no	—
359	C₂²×C₃	—	2	1	no	—
360	C₂²×C₃	—	2	1	no	—
361	C₂²×C₃	C₂³×C₈	1	1	yes	characteristic
362	C₂×D₃	—	2	1	no	—
363	C₂×D₃	—	2	1	no	—
364	C₂×D₃	—	2	1	no	—
365	C₂×D₃	—	2	1	no	—
366	C₂×D₃	—	2	1	no	—
367	C₂×D₃	#431	1	2	yes	—
368	C₃×C₄	—	2	1	no	—
369	C₃×C₄	—	2	1	no	—
370	C₃×C₄	—	2	1	no	—
371	C₃×C₄	—	2	1	no	—
372	C₃×C₄	#504	1	2	yes	—
373	C₃×C₄	C₂×#117	1	1	yes	characteristic
374	C₃×C₄	C₂²×M₁₆	1	1	yes	characteristic
375	Dic₃	—	2	1	no	—
376	Dic₃	—	2	1	no	—
377	Dic₃	—	2	1	no	—
378	Dic₃	—	2	1	no	—
379	Dic₃	—	2	1	no	—
380	Dic₃	#431	1	2	yes	—
381	C₂³	—	3	1	no	—
382	C₂³	—	3	1	no	—
383	C₂³	C₂×D₃×C₈	1	1	yes	characteristic
384	Q₈	—	6	2	no	—
385	D₄	—	6	2	no	—
386	D₄	—	6	2	no	—
387	D₄	—	6	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	3	1	no	—
392	C₂×C₄	—	3	2	no	—
393	C₂×C₄	—	3	2	no	—
394	C₂×C₄	—	3	1	no	—
395	C₂×C₄	—	3	1	no	—
396	C₂×C₄	—	3	1	no	—
397	C₂×C₄	—	3	1	no	—
398	C₂×C₄	—	3	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	6	2	no	—
401	C₂×C₄	—	6	2	no	—
402	C₂×C₄	—	6	1	no	—
403	C₂×C₄	—	6	1	no	—
404	C₂×C₄	—	12	1	no	—
405	C₂×C₄	—	12	1	no	—
406	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
407	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
408	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
409	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
410	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
412	C₈	—	2	1	no	—
413	C₈	—	2	1	no	—
414	C₈	—	3	2	no	—
415	C₈	—	3	2	no	—
416	C₈	—	6	1	no	—
417	C₈	—	6	1	no	—
418	C₈	D₃×M₁₆	1	2	yes	—
419	C₈	D₃×#41	1	1	yes	characteristic
420	C₈	D₃×#41	1	1	yes	characteristic
421	C₂×C₃	—	4	1	no	—
422	C₂×C₃	C₂×#431	1	1	yes	characteristic
423	C₂×C₃	C₂×#504	1	1	yes	characteristic
424	C₂×C₃	#3407	1	1	yes	characteristic
425	D₃	—	2	2	no	—
426	D₃	—	4	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	3	2	no	—
431	C₂²	—	6	1	no	—
432	C₂²	—	6	1	no	—
433	C₂²	—	6	1	no	—
434	C₂²	—	6	1	no	—
435	C₂²	—	6	1	no	—
436	C₂²	C₂²×D₃×C₈	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	3	2	no	—
442	C₄	—	6	1	no	—
443	C₄	—	6	1	no	—
444	C₄	—	6	1	no	—
445	C₄	—	6	1	no	—
446	C₄	—	6	1	no	—
447	C₄	#4907	1	2	yes	—
448	C₄	D₃×#117	1	1	yes	characteristic
449	C₄	C₂×D₃×M₁₆	1	1	yes	characteristic
450	C₃	#33423	1	1	yes	characteristic, complemented, Sylow
451	C₂	—	4	1	no	—
452	C₂	—	6	2	no	—
453	C₂	—	12	1	no	—
454	C₂	D₃×#431	1	1	yes	characteristic
455	C₂	C₂×#4907	1	1	yes	characteristic
456	C₂	#82007	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₃
commutator, socle	C₂²×C₃	C₂³×C₈
Fitting	C₃×#2163	C₂
prime radical	C₂×#235	C₂×C₄
cosocle	C₂×C₃×C₈	C₂⁴
hypercenter	#2163	D₃
hypocenter	C₃	#33423
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₈ ◁ #2163

Complements

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

N	H ≅ G/N	type
2. C₃×#2163	C₂	semidirect
3. #69744	C₂	semidirect
4. #69284	C₂	semidirect
5. D₃×C₄⋊C₁₆	C₂	semidirect
6. #69275	C₂	semidirect
7. #69274	C₂	semidirect
9. #69094	C₂	semidirect
10. #69074	C₂	semidirect
11. #69072	C₂	semidirect
48. #2163	D₃	semidirect
450. C₃	#33423	semidirect

Maximal subgroups

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

subgroup	index
C₄×#901	2
C₃×#2163	2
#69744	2
#69284	2
D₃×C₄⋊C₁₆	2
#69275	2
#69274	2
#69107	2
#69094	2
#69074	2
#69072	2
#33423	3