Subgroups — #10948756

Order 768.

552 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#235	C₂	1	1	yes	maximal, characteristic
2	C₃×#2163	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#4461	C₂	1	1	yes	maximal, characteristic, complemented
4	#69282	C₂	1	2	yes	maximal, complemented
5	#69278	C₂	1	2	yes	maximal, complemented
6	#69102	C₂	1	2	yes	maximal, complemented
7	#67⋊C₁₆	C₂	1	2	yes	maximal, complemented
8	#69073	C₂	1	1	yes	maximal, characteristic, complemented
9	#69073	C₂	1	1	yes	maximal, characteristic, complemented
10	#69071	C₂	1	1	yes	maximal, characteristic, complemented
11	D₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
12	#33484	—	3	1	no	maximal, Sylow
13	C₄×#235	C₄	1	1	yes	characteristic
14	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
15	C₈×#67	C₄	1	1	yes	characteristic
16	C₈×#67	C₄	1	1	yes	characteristic
17	C₈×#67	C₂²	1	1	yes	characteristic
18	C₈×#67	C₂²	1	1	yes	characteristic
19	C₂²×C₃⋊C₁₆	C₂²	1	2	yes	—
20	#4925	C₄	1	1	yes	characteristic
21	C₂×#798	C₂²	1	2	yes	—
22	C₂×D₃×C₁₆	C₂²	1	2	yes	—
23	C₈×D₁₂	C₄	1	1	yes	characteristic
24	C₈×D₁₂	C₂²	1	1	yes	characteristic
25	#4685	C₄	1	1	yes	characteristic
26	#4685	C₄	1	1	yes	characteristic
27	C₄×D₃×C₈	C₂²	1	1	yes	characteristic
28	C₄×D₃×C₈	C₂²	1	1	yes	characteristic
29	C₈×Dic₆	C₄	1	1	yes	characteristic
30	C₈×Dic₆	C₂²	1	1	yes	characteristic
31	C₃×C₄⋊C₁₆	C₂²	1	2	yes	—
32	C₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
33	C₃×#346	C₂²	1	1	yes	characteristic
34	C₃×#346	C₂²	1	1	yes	characteristic
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	#4461	C₂²	1	2	yes	—
42	#4461	C₂²	1	1	yes	characteristic
43	#4461	C₂²	1	1	yes	characteristic
44	C₈×#41	—	3	1	no	—
45	#2183	—	3	2	no	—
46	#2168	—	3	2	no	—
47	#2168	—	3	2	no	—
48	D₄×C₁₆	—	3	2	no	—
49	#2163	—	3	1	no	—
50	#2163	—	3	1	no	—
51	#2163	D₃	1	1	yes	characteristic, complemented
52	C₄×M₃₂	—	3	1	no	—
53	C₂×#346	—	3	1	no	—
54	C₂×#346	—	3	1	no	—
55	C₂×#235	C₈	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	C₂×C₄	1	1	yes	characteristic
62	C₄×#67	C₂×C₄	1	1	yes	characteristic
63	#926	C₈	1	1	yes	characteristic
64	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
65	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
66	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
67	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
68	C₄×D₁₂	C₈	1	1	yes	characteristic
69	C₄×D₁₂	C₂×C₄	1	1	yes	characteristic
70	#872	C₈	1	1	yes	characteristic
71	#872	C₈	1	1	yes	characteristic
72	C₄²×D₃	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₃	C₂×C₄	1	1	yes	characteristic
74	C₄×Dic₆	C₈	1	1	yes	characteristic
75	C₄×Dic₆	C₂×C₄	1	1	yes	characteristic
76	C₂×C₃×C₁₆	C₂³	1	2	yes	—
77	C₂×C₃×C₁₆	C₂³	1	2	yes	—
78	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
79	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
80	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
81	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
82	#830	C₂×C₄	1	1	yes	characteristic
83	#830	C₂×C₄	1	1	yes	characteristic
84	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
85	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
86	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
87	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
88	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
89	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
90	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
91	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₃	C₂³	1	1	yes	characteristic
95	C₈×Dic₃	C₂³	1	1	yes	characteristic
96	C₂×C₃⋊C₁₆	—	2	4	no	—
97	C₂×C₃⋊C₁₆	C₂³	1	2	yes	—
98	C₂×C₃⋊C₁₆	C₂³	1	2	yes	—
99	C₄⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
100	C₄⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
101	C₄×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
102	C₄×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
103	#798	—	2	4	no	—
104	D₃×C₁₆	—	2	4	no	—
105	C₄×#41	—	3	1	no	—
106	C₂×M₃₂	—	3	2	no	—
107	C₂²×C₁₆	—	3	2	no	—
108	C₂²×C₁₆	—	3	2	no	—
109	C₈×Q₈	—	3	1	no	—
110	C₈×Q₈	—	3	1	no	—
111	C₈×D₄	—	3	1	no	—
112	C₈×D₄	—	3	1	no	—
113	C₈×D₄	—	3	1	no	—
114	C₈×D₄	—	3	1	no	—
115	C₈×D₄	—	3	1	no	—
116	C₈×D₄	—	3	1	no	—
117	#431	—	3	1	no	—
118	#431	—	3	1	no	—
119	#431	—	3	1	no	—
120	C₂×C₄×C₈	—	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	C₂×D₃	1	2	yes	—
126	C₂²⋊C₁₆	—	3	2	no	—
127	C₂²⋊C₁₆	—	3	2	no	—
128	C₂²⋊C₁₆	C₂×D₃	1	2	yes	—
129	#346	—	3	2	no	—
130	#346	—	3	1	no	—
131	#346	—	3	1	no	—
132	#346	—	3	2	no	—
133	#346	C₂×D₃	1	1	yes	characteristic
134	#346	C₂×D₃	1	1	yes	characteristic
135	C₄×C₁₆	—	3	2	no	—
136	C₂²×C₃×C₄	C₂×C₈	1	1	yes	characteristic
137	C₂²×C₃×C₄	C₂×C₈	1	1	yes	characteristic
138	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
139	C₂×#67	C₂×C₈	1	1	yes	characteristic
140	C₂×#67	C₂×C₈	1	1	yes	characteristic
141	#235	—	2	4	no	—
142	C₂×D₁₂	C₂×C₈	1	1	yes	characteristic
143	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
144	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
145	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
146	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
147	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₆	C₂×C₈	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	#217	C₂×C₈	1	1	yes	characteristic
161	#217	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	C₄⋊Dic₃	C₂×C₈	1	1	yes	characteristic
167	C₄⋊Dic₃	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	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
173	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
174	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
175	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
176	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
177	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
182	D₃×C₈	—	2	2	no	—
183	D₃×C₈	—	2	2	no	—
184	D₃×C₈	—	2	2	no	—
185	D₃×C₈	—	2	2	no	—
186	C₃×C₁₆	—	2	2	no	—
187	C₃×C₁₆	—	2	2	no	—
188	C₃⋊C₁₆	—	2	2	no	—
189	C₃⋊C₁₆	#41	1	4	yes	complemented
190	C₂×#41	—	3	1	no	—
191	C₂²×C₈	—	3	1	no	—
192	C₂²×C₈	—	3	1	no	—
193	C₂²×C₈	—	3	1	no	—
194	C₂²×C₈	—	3	1	no	—
195	C₂²×C₈	C₄×D₃	1	1	yes	characteristic
196	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
197	C₄×Q₈	—	3	1	no	—
198	C₄×Q₈	—	3	1	no	—
199	C₄×D₄	—	3	1	no	—
200	C₄×D₄	—	3	1	no	—
201	C₄×D₄	—	3	1	no	—
202	C₄×D₄	—	3	1	no	—
203	C₄×D₄	—	3	1	no	—
204	C₄×D₄	—	3	1	no	—
205	#117	—	3	1	no	—
206	#117	—	3	1	no	—
207	#117	—	3	1	no	—
208	C₂×C₄²	—	3	1	no	—
209	C₂×C₄²	—	3	1	no	—
210	C₂×C₄²	C₄×D₃	1	1	yes	characteristic
211	M₃₂	—	6	4	no	—
212	C₂×C₁₆	—	3	2	no	—
213	C₂×C₁₆	—	3	2	no	—
214	C₂×C₁₆	—	6	4	no	—
215	C₂×C₁₆	—	6	4	no	—
216	C₂×C₁₆	C₂²×D₃	1	2	yes	—
217	C₂×C₁₆	C₂²×D₃	1	2	yes	—
218	C₄⋊C₈	—	3	1	no	—
219	C₄⋊C₈	—	3	1	no	—
220	C₄⋊C₈	—	3	1	no	—
221	C₄⋊C₈	—	3	1	no	—
222	C₄⋊C₈	—	3	1	no	—
223	C₄⋊C₈	—	3	1	no	—
224	C₂²⋊C₈	—	3	1	no	—
225	C₂²⋊C₈	—	3	1	no	—
226	C₂²⋊C₈	—	3	1	no	—
227	C₂²⋊C₈	—	3	1	no	—
228	C₂²⋊C₈	—	3	1	no	—
229	C₂²⋊C₈	—	3	1	no	—
230	C₄×C₈	—	3	1	no	—
231	C₄×C₈	—	3	1	no	—
232	C₄×C₈	—	3	1	no	—
233	C₄×C₈	—	3	1	no	—
234	C₄×C₈	—	3	1	no	—
235	C₄×C₈	—	3	1	no	—
236	C₄×C₈	C₄×D₃	1	1	yes	characteristic
237	C₄×C₈	C₄×D₃	1	1	yes	characteristic
238	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
239	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
240	C₂³×C₃	C₂²×C₈	1	1	yes	characteristic
241	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
242	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	4	1	no	—
247	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
253	#67	—	2	2	no	—
254	#67	M₃₂	1	4	yes	complemented
255	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
256	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
257	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
258	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
259	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
260	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
261	D₁₂	—	2	2	no	—
262	C₄×D₃	—	2	2	no	—
263	C₄×D₃	—	2	1	no	—
264	C₄×D₃	—	2	1	no	—
265	C₄×D₃	—	2	1	no	—
266	C₄×D₃	—	2	1	no	—
267	C₄×D₃	—	2	2	no	—
268	C₄×D₃	—	4	1	no	—
269	C₄×D₃	—	4	1	no	—
270	Dic₆	—	2	2	no	—
271	C₃×C₈	—	2	1	no	—
272	C₃×C₈	—	2	1	no	—
273	C₃×C₈	#131	1	2	yes	—
274	C₃×C₈	C₂×#41	1	2	yes	—
275	C₃⋊C₈	—	2	1	no	—
276	C₃⋊C₈	—	2	1	no	—
277	C₃⋊C₈	—	2	1	no	—
278	C₃⋊C₈	—	2	1	no	—
279	#41	—	6	4	no	—
280	C₂×Q₈	—	3	1	no	—
281	C₂×D₄	—	3	1	no	—
282	C₂×D₄	—	3	1	no	—
283	C₂×D₄	—	3	1	no	—
284	C₂²×C₄	—	3	1	no	—
285	C₂²×C₄	—	3	1	no	—
286	C₂²×C₄	—	3	1	no	—
287	C₂²×C₄	—	3	1	no	—
288	C₂²×C₄	—	3	1	no	—
289	C₂²×C₄	—	3	1	no	—
290	C₂²×C₄	D₃×C₈	1	1	yes	characteristic
291	C₂²×C₄	D₃×C₈	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	3	1	no	—
296	C₂×C₈	—	3	1	no	—
297	C₂×C₈	—	3	1	no	—
298	C₂×C₈	—	3	1	no	—
299	C₂×C₈	—	6	2	no	—
300	C₂×C₈	—	6	2	no	—
301	C₂×C₈	—	6	2	no	—
302	C₂×C₈	—	6	2	no	—
303	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
304	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
305	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
306	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
307	C₄⋊C₄	—	3	1	no	—
308	C₄⋊C₄	—	3	1	no	—
309	C₄⋊C₄	—	3	1	no	—
310	C₄⋊C₄	—	3	1	no	—
311	C₄⋊C₄	—	3	1	no	—
312	C₄⋊C₄	—	3	1	no	—
313	C₂²⋊C₄	—	3	1	no	—
314	C₂²⋊C₄	—	3	1	no	—
315	C₂²⋊C₄	—	3	1	no	—
316	C₂²⋊C₄	—	3	1	no	—
317	C₂²⋊C₄	—	3	1	no	—
318	C₂²⋊C₄	—	3	1	no	—
319	C₄²	—	3	1	no	—
320	C₄²	—	3	1	no	—
321	C₄²	—	3	1	no	—
322	C₄²	—	3	1	no	—
323	C₄²	—	3	1	no	—
324	C₄²	—	3	1	no	—
325	C₄²	D₃×C₈	1	1	yes	characteristic
326	C₄²	D₃×C₈	1	1	yes	characteristic
327	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
328	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
329	C₁₆	—	2	2	no	—
330	C₁₆	—	2	2	no	—
331	C₁₆	—	3	4	no	—
332	C₁₆	—	6	2	no	—
333	C₂²×C₃	—	2	1	no	—
334	C₂²×C₃	—	2	1	no	—
335	C₂²×C₃	C₂×M₃₂	1	2	yes	—
336	C₂²×C₃	C₂³×C₈	1	1	yes	characteristic
337	C₂×D₃	—	2	1	no	—
338	C₂×D₃	—	2	1	no	—
339	C₂×D₃	—	2	1	no	—
340	C₂×D₃	—	2	1	no	—
341	C₂×D₃	—	2	1	no	—
342	C₂×D₃	C₂×M₃₂	1	2	yes	—
343	C₃×C₄	—	2	1	no	—
344	C₃×C₄	—	2	1	no	—
345	C₃×C₄	—	2	1	no	—
346	C₃×C₄	—	2	1	no	—
347	C₃×C₄	—	2	1	no	—
348	C₃×C₄	C₄×#41	1	1	yes	characteristic
349	C₃×C₄	C₂×#131	1	1	yes	characteristic
350	Dic₃	—	2	1	no	—
351	Dic₃	—	2	1	no	—
352	Dic₃	—	2	1	no	—
353	Dic₃	—	2	1	no	—
354	Dic₃	—	2	1	no	—
355	Dic₃	C₂×M₃₂	1	2	yes	—
356	C₂³	—	3	1	no	—
357	C₂³	—	3	1	no	—
358	C₂³	C₂×D₃×C₈	1	1	yes	characteristic
359	Q₈	—	6	2	no	—
360	D₄	—	3	4	no	—
361	D₄	—	6	2	no	—
362	D₄	—	6	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	3	1	no	—
367	C₂×C₄	—	3	1	no	—
368	C₂×C₄	—	3	1	no	—
369	C₂×C₄	—	3	1	no	—
370	C₂×C₄	—	3	1	no	—
371	C₂×C₄	—	3	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	6	2	no	—
374	C₂×C₄	—	6	2	no	—
375	C₂×C₄	—	6	1	no	—
376	C₂×C₄	—	6	1	no	—
377	C₂×C₄	—	6	1	no	—
378	C₂×C₄	—	6	1	no	—
379	C₂×C₄	—	12	1	no	—
380	C₂×C₄	—	12	1	no	—
381	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
382	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
383	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
384	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
385	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
386	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
387	C₈	—	2	1	no	—
388	C₈	—	2	1	no	—
389	C₈	—	6	1	no	—
390	C₈	—	6	1	no	—
391	C₈	—	6	1	no	—
392	C₈	—	6	1	no	—
393	C₈	#907	1	2	yes	—
394	C₈	D₃×#41	1	2	yes	—
395	C₂×C₃	—	2	2	no	—
396	C₂×C₃	C₈×#41	1	1	yes	characteristic
397	C₂×C₃	C₂²×M₃₂	1	1	yes	characteristic
398	C₂×C₃	#3407	1	1	yes	characteristic
399	D₃	—	2	2	no	—
400	D₃	—	4	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	3	2	no	—
404	C₂²	—	6	1	no	—
405	C₂²	—	6	1	no	—
406	C₂²	—	6	1	no	—
407	C₂²	—	6	1	no	—
408	C₂²	—	6	1	no	—
409	C₂²	D₃×M₃₂	1	2	yes	—
410	C₂²	C₂²×D₃×C₈	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	3	2	no	—
417	C₄	—	6	1	no	—
418	C₄	—	6	1	no	—
419	C₄	—	6	1	no	—
420	C₄	—	6	1	no	—
421	C₄	—	6	1	no	—
422	C₄	#5522	1	1	yes	characteristic
423	C₄	C₂×#907	1	1	yes	characteristic
424	C₃	#33484	1	1	yes	characteristic, complemented, Sylow
425	C₂	—	2	2	no	—
426	C₂	—	6	2	no	—
427	C₂	—	12	1	no	—
428	C₂	#79276	1	1	yes	characteristic
429	C₂	C₂×D₃×M₃₂	1	1	yes	characteristic
430	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	C₈
cosocle	C₂×C₃×C₈	C₂⁴
hypercenter	#2163	D₃
hypocenter	C₃	#33484
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. C₂×#4461	C₂	semidirect
4. #69282	C₂	semidirect
5. #69278	C₂	semidirect
6. #69102	C₂	semidirect
7. #67⋊C₁₆	C₂	semidirect
8. #69073	C₂	semidirect
9. #69073	C₂	semidirect
10. #69071	C₂	semidirect
11. D₃×#346	C₂	semidirect
51. #2163	D₃	semidirect
189. C₃⋊C₁₆	#41	semidirect
254. #67	M₃₂	semidirect
424. C₃	#33484	semidirect

Maximal subgroups

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

subgroup	index
C₈×#235	2
C₃×#2163	2
C₂×#4461	2
#69282	2
#69278	2
#69102	2
#67⋊C₁₆	2
#69073	2
#69071	2
D₃×#346	2
#33484	3