Subgroups — #10948295

Order 768.

600 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#4689	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	#69285	C₂	1	2	yes	maximal, complemented
5	#69276	C₂	1	2	yes	maximal, complemented
6	#69106	C₂	1	1	yes	maximal, characteristic
7	D₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
8	#69093	C₂	1	1	yes	maximal, characteristic, complemented
9	#69092	C₂	1	1	yes	maximal, characteristic, complemented
10	#69074	C₂	1	2	yes	maximal, complemented
11	#69072	C₂	1	2	yes	maximal, complemented
12	#33422	—	3	1	no	maximal, Sylow
13	C₂²×ΓL(1,𝔽₂₅)	C₄	1	1	yes	characteristic
14	C₂²×D₃×C₈	C₂²	1	1	yes	characteristic
15	C₂×#872	C₄	1	1	yes	characteristic
16	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
17	C₂×#815	C₄	1	1	yes	characteristic
18	C₂×C₈×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×#803	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	C₄	1	1	yes	characteristic
25	#4689	C₄	1	1	yes	characteristic
26	#4689	C₂²	1	1	yes	characteristic
27	#4689	C₂²	1	1	yes	characteristic
28	#4689	C₂²	1	1	yes	characteristic
29	#4689	C₂²	1	1	yes	characteristic
30	C₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
31	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
32	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
33	C₃×#346	C₂²	1	2	yes	complemented
34	#4549	C₂²	1	1	yes	characteristic
35	#4549	C₂²	1	1	yes	characteristic
36	(C₂×D₃)⋊C₁₆	C₂²	1	2	yes	—
37	(C₂×D₃)⋊C₁₆	C₂²	1	2	yes	—
38	#4502	C₂²	1	2	yes	complemented
39	Dic₃⋊C₁₆	C₂²	1	2	yes	complemented
40	Dic₃⋊C₁₆	C₂²	1	2	yes	complemented
41	Dic₃×C₁₆	C₂²	1	2	yes	complemented
42	C₄⋊(C₃⋊C₁₆)	C₂²	1	2	yes	complemented
43	C₄×C₃⋊C₁₆	C₂²	1	2	yes	complemented
44	C₂×#405	—	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	#2151	—	3	2	no	—
52	#2112	—	3	1	no	—
53	C₂×C₂²⋊C₁₆	—	3	1	no	—
54	#2108	—	3	2	no	—
55	C₂²×C₄×D₃	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	C₂×(C₂×D₃)⋊C₄	C₈	1	1	yes	characteristic
60	C₂×(C₂×D₃)⋊C₄	C₈	1	1	yes	characteristic
61	C₂×Dic₃⋊C₄	C₈	1	1	yes	characteristic
62	C₂×Dic₃⋊C₄	C₈	1	1	yes	characteristic
63	C₂×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
66	C₂×ΓL(1,𝔽₂₅)	—	2	4	no	—
67	C₂×ΓL(1,𝔽₂₅)	C₂×C₄	1	1	yes	characteristic
68	C₂×ΓL(1,𝔽₂₅)	C₂×C₄	1	1	yes	characteristic
69	C₂×ΓL(1,𝔽₂₅)	C₂×C₄	1	1	yes	characteristic
70	C₂×ΓL(1,𝔽₂₅)	C₂×C₄	1	1	yes	characteristic
71	C₂×D₃×C₈	—	2	4	no	—
72	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
73	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
74	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
75	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
76	#872	C₈	1	1	yes	characteristic
77	#872	C₈	1	1	yes	characteristic
78	#872	C₈	1	1	yes	characteristic
79	#872	C₈	1	1	yes	characteristic
80	#872	C₂×C₄	1	1	yes	characteristic
81	#872	C₂×C₄	1	1	yes	characteristic
82	#872	C₂×C₄	1	1	yes	characteristic
83	#872	C₂×C₄	1	1	yes	characteristic
84	C₂×C₃×C₁₆	C₂³	1	2	yes	—
85	C₂×C₃×C₁₆	C₂³	1	2	yes	—
86	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
87	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
88	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
89	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
90	#815	C₂×C₄	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	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₃	C₂³	1	1	yes	characteristic
97	C₈×Dic₃	C₂³	1	1	yes	characteristic
98	C₂×C₃⋊C₁₆	C₂³	1	2	yes	—
99	C₂×C₃⋊C₁₆	C₂³	1	2	yes	—
100	#803	C₂×C₄	1	1	yes	characteristic
101	#803	C₂×C₄	1	1	yes	characteristic
102	#803	C₂×C₄	1	1	yes	characteristic
103	#803	C₂×C₄	1	1	yes	characteristic
104	#798	—	2	4	no	—
105	D₃×C₁₆	—	2	4	no	—
106	C₂²×M₁₆	—	3	1	no	—
107	C₂³×C₈	—	3	1	no	—
108	C₂×#117	—	3	1	no	—
109	C₂×M₃₂	—	3	2	no	—
110	C₂²×C₁₆	—	3	2	no	—
111	#405	—	3	1	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	#405	—	3	1	no	—
119	C₂×#97	—	3	1	no	—
120	C₂×#97	—	3	1	no	—
121	C₂×C₄×C₈	—	3	1	no	—
122	C₂×C₄×C₈	C₂×D₃	1	1	yes	characteristic
123	C₄⋊C₁₆	—	3	2	no	—
124	C₄⋊C₁₆	—	3	2	no	—
125	C₄⋊C₁₆	—	3	2	no	—
126	C₄⋊C₁₆	C₂×D₃	1	2	yes	complemented
127	C₂²⋊C₁₆	—	3	1	no	—
128	C₂²⋊C₁₆	—	3	1	no	—
129	C₂²⋊C₁₆	—	3	2	no	—
130	C₂²⋊C₁₆	—	3	2	no	—
131	C₂²⋊C₁₆	C₂×D₃	1	1	yes	characteristic
132	C₂²⋊C₁₆	C₂×D₃	1	1	yes	characteristic
133	#346	—	3	2	no	—
134	#346	C₂×D₃	1	2	yes	complemented
135	C₄×C₁₆	—	3	2	no	—
136	C₄×C₁₆	—	3	2	no	—
137	C₂³×D₃	C₂×C₈	1	1	yes	characteristic
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	C₂²×Dic₃	C₂×C₈	1	1	yes	characteristic
142	C₂²×Dic₃	C₂×C₈	1	1	yes	characteristic
143	C₂²×Dic₃	C₂×C₈	1	1	yes	characteristic
144	C₂×C₄×D₃	—	2	2	no	—
145	C₂×C₄×D₃	—	2	2	no	—
146	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
147	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
148	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×C₈	—	2	2	no	—
151	C₂×C₃×C₈	—	2	2	no	—
152	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
156	C₃×C₄²	C₂×C₈	1	1	yes	characteristic
157	C₃×C₄²	C₂×C₈	1	1	yes	characteristic
158	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
159	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
160	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
161	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
162	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
163	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
164	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
165	(C₂×D₃)⋊C₄	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	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
169	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
170	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
171	Dic₃⋊C₄	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	C₂²×C₄	1	1	yes	characteristic
179	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₃⋊C₈	—	2	2	no	—
181	C₂×C₃⋊C₈	—	2	2	no	—
182	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
186	ΓL(1,𝔽₂₅)	—	2	2	no	—
187	ΓL(1,𝔽₂₅)	—	2	2	no	—
188	ΓL(1,𝔽₂₅)	—	2	2	no	—
189	ΓL(1,𝔽₂₅)	M₁₆	1	4	yes	—
190	D₃×C₈	—	2	2	no	—
191	D₃×C₈	—	2	2	no	—
192	D₃×C₈	—	2	2	no	—
193	D₃×C₈	#41	1	4	yes	—
194	C₃×C₁₆	—	2	2	no	—
195	C₃×C₁₆	—	2	2	no	—
196	C₃⋊C₁₆	—	2	2	no	—
197	C₃⋊C₁₆	—	2	2	no	—
198	C₂³×C₄	—	3	1	no	—
199	C₂×M₁₆	—	3	1	no	—
200	C₂×M₁₆	—	3	1	no	—
201	C₂×M₁₆	—	3	1	no	—
202	C₂×M₁₆	—	3	1	no	—
203	C₂×M₁₆	—	6	4	no	—
204	C₂²×C₈	—	3	1	no	—
205	C₂²×C₈	—	3	1	no	—
206	C₂²×C₈	—	3	1	no	—
207	C₂²×C₈	—	3	1	no	—
208	C₂²×C₈	—	3	1	no	—
209	C₂²×C₈	—	3	1	no	—
210	C₂²×C₈	—	6	4	no	—
211	C₂²×C₈	C₄×D₃	1	1	yes	characteristic
212	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
213	#117	—	3	1	no	—
214	#117	—	3	1	no	—
215	#117	—	3	1	no	—
216	#117	—	3	1	no	—
217	#117	—	3	1	no	—
218	#117	—	3	1	no	—
219	#117	—	3	1	no	—
220	#117	—	3	1	no	—
221	C₂×C₄⋊C₄	—	3	1	no	—
222	C₂×C₄⋊C₄	—	3	1	no	—
223	C₂×C₂²⋊C₄	—	3	1	no	—
224	C₂×C₂²⋊C₄	—	3	1	no	—
225	C₂×C₄²	—	3	1	no	—
226	C₂×C₄²	C₄×D₃	1	1	yes	characteristic
227	M₃₂	—	6	4	no	—
228	C₂×C₁₆	—	3	2	no	—
229	C₂×C₁₆	—	3	2	no	—
230	C₂×C₁₆	—	6	4	no	—
231	C₂×C₁₆	C₂²×D₃	1	2	yes	—
232	C₂×C₁₆	C₂²×D₃	1	2	yes	—
233	#97	—	3	1	no	—
234	#97	—	3	1	no	—
235	#97	—	3	1	no	—
236	#97	—	3	1	no	—
237	#97	—	3	1	no	—
238	#97	—	3	1	no	—
239	#97	—	3	1	no	—
240	#97	—	3	1	no	—
241	C₄×C₈	—	3	1	no	—
242	C₄×C₈	—	3	1	no	—
243	C₄×C₈	—	3	1	no	—
244	C₄×C₈	—	3	1	no	—
245	C₄×C₈	C₄×D₃	1	1	yes	characteristic
246	C₄×C₈	C₄×D₃	1	1	yes	characteristic
247	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
248	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
249	C₂³×C₃	C₂²×C₈	1	1	yes	characteristic
250	C₂²×D₃	—	2	2	no	—
251	C₂²×D₃	—	2	2	no	—
252	C₂²×D₃	—	4	1	no	—
253	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
254	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	4	1	no	—
259	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
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	C₂³×C₄	1	1	yes	characteristic
265	C₂×Dic₃	—	2	2	no	—
266	C₂×Dic₃	—	2	2	no	—
267	C₂×Dic₃	—	4	1	no	—
268	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
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	C₄×D₃	—	2	2	no	—
275	C₄×D₃	—	2	1	no	—
276	C₄×D₃	—	2	1	no	—
277	C₄×D₃	—	2	2	no	—
278	C₄×D₃	#117	1	2	yes	—
279	C₄×D₃	C₂×M₁₆	1	2	yes	—
280	C₃×C₈	—	2	1	no	—
281	C₃×C₈	—	2	1	no	—
282	C₃×C₈	C₂×M₁₆	1	2	yes	—
283	C₃×C₈	C₂×#41	1	2	yes	—
284	C₃⋊C₈	—	2	1	no	—
285	C₃⋊C₈	—	2	1	no	—
286	C₃⋊C₈	#117	1	2	yes	—
287	C₃⋊C₈	C₂×M₁₆	1	2	yes	—
288	C₂⁴	—	3	1	no	—
289	C₂²×C₄	—	3	1	no	—
290	C₂²×C₄	—	3	1	no	—
291	C₂²×C₄	—	3	1	no	—
292	C₂²×C₄	—	3	1	no	—
293	C₂²×C₄	—	3	1	no	—
294	C₂²×C₄	—	3	1	no	—
295	C₂²×C₄	—	3	1	no	—
296	C₂²×C₄	—	6	2	no	—
297	C₂²×C₄	—	6	2	no	—
298	C₂²×C₄	D₃×C₈	1	1	yes	characteristic
299	C₂²×C₄	D₃×C₈	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
301	M₁₆	—	3	4	no	—
302	M₁₆	—	6	2	no	—
303	M₁₆	—	6	2	no	—
304	M₁₆	—	6	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	3	1	no	—
308	C₂×C₈	—	3	1	no	—
309	C₂×C₈	—	3	4	no	—
310	C₂×C₈	—	3	1	no	—
311	C₂×C₈	—	3	1	no	—
312	C₂×C₈	—	6	2	no	—
313	C₂×C₈	—	6	2	no	—
314	C₂×C₈	—	6	2	no	—
315	C₂×C₈	—	6	2	no	—
316	C₂×C₈	—	6	2	no	—
317	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
318	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
319	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
320	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
321	C₄⋊C₄	—	3	1	no	—
322	C₄⋊C₄	—	3	1	no	—
323	C₄⋊C₄	—	3	1	no	—
324	C₄⋊C₄	—	3	1	no	—
325	C₄⋊C₄	—	3	1	no	—
326	C₄⋊C₄	—	3	1	no	—
327	C₄⋊C₄	—	3	1	no	—
328	C₄⋊C₄	—	3	1	no	—
329	C₂²⋊C₄	—	3	1	no	—
330	C₂²⋊C₄	—	3	1	no	—
331	C₂²⋊C₄	—	3	1	no	—
332	C₂²⋊C₄	—	3	1	no	—
333	C₂²⋊C₄	—	3	1	no	—
334	C₂²⋊C₄	—	3	1	no	—
335	C₂²⋊C₄	—	3	1	no	—
336	C₂²⋊C₄	—	3	1	no	—
337	C₄²	—	3	1	no	—
338	C₄²	—	3	1	no	—
339	C₄²	—	3	1	no	—
340	C₄²	—	3	1	no	—
341	C₄²	D₃×C₈	1	1	yes	characteristic
342	C₄²	D₃×C₈	1	1	yes	characteristic
343	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
344	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
345	C₁₆	—	2	2	no	—
346	C₁₆	—	2	2	no	—
347	C₁₆	—	6	2	no	—
348	C₁₆	—	6	2	no	—
349	C₂²×C₃	—	2	1	no	—
350	C₂²×C₃	—	2	1	no	—
351	C₂²×C₃	#504	1	2	yes	—
352	C₂²×C₃	C₂³×C₈	1	1	yes	characteristic
353	C₂×D₃	—	2	1	no	—
354	C₂×D₃	—	2	1	no	—
355	C₂×D₃	—	2	1	no	—
356	C₂×D₃	—	2	1	no	—
357	C₂×D₃	—	2	1	no	—
358	C₂×D₃	—	4	4	no	—
359	C₂×D₃	#431	1	2	yes	—
360	C₃×C₄	—	2	1	no	—
361	C₃×C₄	—	2	1	no	—
362	C₃×C₄	—	2	1	no	—
363	C₃×C₄	—	2	1	no	—
364	C₃×C₄	—	2	1	no	—
365	C₃×C₄	C₂×#117	1	1	yes	characteristic
366	C₃×C₄	C₂²×M₁₆	1	1	yes	characteristic
367	Dic₃	—	2	1	no	—
368	Dic₃	—	2	1	no	—
369	Dic₃	—	2	1	no	—
370	Dic₃	—	2	1	no	—
371	Dic₃	—	2	1	no	—
372	Dic₃	#431	1	2	yes	—
373	C₂³	—	3	1	no	—
374	C₂³	—	3	1	no	—
375	C₂³	—	6	2	no	—
376	C₂³	—	6	2	no	—
377	C₂³	—	12	1	no	—
378	C₂³	C₂×D₃×C₈	1	1	yes	characteristic
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	3	1	no	—
383	C₂×C₄	—	3	2	no	—
384	C₂×C₄	—	3	2	no	—
385	C₂×C₄	—	3	1	no	—
386	C₂×C₄	—	3	1	no	—
387	C₂×C₄	—	3	1	no	—
388	C₂×C₄	—	3	1	no	—
389	C₂×C₄	—	3	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	6	2	no	—
392	C₂×C₄	—	6	2	no	—
393	C₂×C₄	—	6	2	no	—
394	C₂×C₄	—	6	2	no	—
395	C₂×C₄	—	6	1	no	—
396	C₂×C₄	—	6	1	no	—
397	C₂×C₄	—	12	1	no	—
398	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
399	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
400	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
401	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
402	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	3	2	no	—
407	C₈	—	3	2	no	—
408	C₈	—	6	1	no	—
409	C₈	—	6	1	no	—
410	C₈	D₃×M₁₆	1	2	yes	—
411	C₈	D₃×#41	1	2	yes	—
412	C₂×C₃	—	2	2	no	—
413	C₂×C₃	C₂×#431	1	1	yes	characteristic
414	C₂×C₃	C₂×#504	1	1	yes	characteristic
415	C₂×C₃	#3407	1	1	yes	characteristic
416	D₃	—	2	2	no	—
417	D₃	—	4	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	3	2	no	—
421	C₂²	—	6	1	no	—
422	C₂²	—	6	1	no	—
423	C₂²	—	6	1	no	—
424	C₂²	—	6	1	no	—
425	C₂²	—	6	1	no	—
426	C₂²	—	12	4	no	—
427	C₂²	#4907	1	2	yes	—
428	C₂²	C₂²×D₃×C₈	1	1	yes	characteristic
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	3	2	no	—
435	C₄	—	6	1	no	—
436	C₄	—	6	1	no	—
437	C₄	—	6	1	no	—
438	C₄	—	6	1	no	—
439	C₄	—	6	1	no	—
440	C₄	D₃×#117	1	1	yes	characteristic
441	C₄	C₂×D₃×M₁₆	1	1	yes	characteristic
442	C₃	#33422	1	1	yes	characteristic, complemented, Sylow
443	C₂	—	2	2	no	—
444	C₂	—	6	2	no	—
445	C₂	—	12	1	no	—
446	C₂	D₃×#431	1	1	yes	characteristic
447	C₂	C₂×#4907	1	1	yes	characteristic
448	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	C₂³×D₃	C₂×C₈
cosocle	C₂×C₃×C₈	C₂⁴
hypercenter	#2163	D₃
hypocenter	C₃	#33422
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. #69285	C₂	semidirect
5. #69276	C₂	semidirect
8. #69093	C₂	semidirect
9. #69092	C₂	semidirect
10. #69074	C₂	semidirect
11. #69072	C₂	semidirect
30. C₃×C₄⋊C₁₆	C₂²	semidirect
33. C₃×#346	C₂²	semidirect
38. #4502	C₂²	semidirect
39. Dic₃⋊C₁₆	C₂²	semidirect
40. Dic₃⋊C₁₆	C₂²	semidirect
41. Dic₃×C₁₆	C₂²	semidirect
42. C₄⋊(C₃⋊C₁₆)	C₂²	semidirect
43. C₄×C₃⋊C₁₆	C₂²	semidirect
48. #2163	D₃	semidirect
126. C₄⋊C₁₆	C₂×D₃	semidirect
134. #346	C₂×D₃	semidirect
442. C₃	#33422	semidirect

Maximal subgroups

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

subgroup	index
C₂×#4689	2
C₃×#2163	2
#69744	2
#69285	2
#69276	2
#69106	2
D₃×C₂²⋊C₁₆	2
#69093	2
#69092	2
#69074	2
#69072	2
#33422	3