Subgroups — #10948772

Order 768.

618 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₈×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃×#2168	C₂	1	1	yes	maximal, characteristic, complemented
3	#71433	C₂	1	1	yes	maximal, characteristic, complemented
4	#71431	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×(C₂×D₃)⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#71407	C₂	1	1	yes	maximal, characteristic, complemented
7	#70857	C₂	1	1	yes	maximal, characteristic, complemented
8	#69278	C₂	1	1	yes	maximal, characteristic, complemented
9	#69275	C₂	1	1	yes	maximal, characteristic, complemented
10	#69106	C₂	1	1	yes	maximal, characteristic, complemented
11	D₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#69103	C₂	1	1	yes	maximal, characteristic, complemented
13	#69102	C₂	1	1	yes	maximal, characteristic, complemented
14	#69075	C₂	1	1	yes	maximal, characteristic, complemented
15	#69073	C₂	1	1	yes	maximal, characteristic, complemented
16	#33487	—	3	1	no	maximal, Sylow
17	C₂²×D₃×C₈	C₂²	1	1	yes	characteristic
18	C₂²×D₃×C₈	C₂²	1	1	yes	characteristic
19	C₄×D₃×D₄	C₄	1	1	yes	characteristic
20	C₂×C₃×M₃₂	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₈×D₄	C₂²	1	1	yes	characteristic
23	C₈×#67	C₂²	1	1	yes	characteristic
24	C₈×#67	C₂²	1	1	yes	characteristic
25	C₂×#812	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
27	D₄×C₃⋊C₈	C₄	1	1	yes	characteristic
28	C₂×#798	C₂²	1	1	yes	characteristic, complemented
29	C₂×#798	C₂²	1	1	yes	characteristic, complemented
30	C₂×D₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₂×D₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
32	#4834	C₄	1	1	yes	characteristic
33	D₃×C₄⋊C₈	C₄	1	1	yes	characteristic
34	#67⋊C₈	C₄	1	1	yes	characteristic
35	#67⋊C₈	C₄	1	1	yes	characteristic
36	D₃×C₂²⋊C₈	C₄	1	1	yes	characteristic
37	D₃×C₂²⋊C₈	C₄	1	1	yes	characteristic
38	C₈×D₁₂	C₂²	1	1	yes	characteristic
39	C₄×D₃×C₈	C₂²	1	1	yes	characteristic
40	C₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
43	C₃×#346	C₂²	1	1	yes	characteristic, complemented
44	#4549	C₂²	1	1	yes	characteristic, complemented
45	#4549	C₂²	1	1	yes	characteristic, complemented
46	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic
47	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic
48	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic
49	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic
50	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
52	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
53	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
54	#4502	C₂²	1	1	yes	characteristic, complemented
55	#4502	C₂²	1	1	yes	characteristic, complemented
56	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
57	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
58	C₄⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
59	#4461	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₈×D₄	—	3	1	no	—
61	#2168	—	3	1	no	—
62	#2168	—	3	1	no	—
63	#2168	—	3	1	no	—
64	#2168	—	3	1	no	—
65	#2168	—	3	1	no	—
66	#2168	—	3	1	no	—
67	#2168	—	3	1	no	—
68	#2168	D₃	1	1	yes	characteristic, complemented
69	#2163	—	3	1	no	—
70	#2163	—	3	1	no	—
71	#2112	—	3	1	no	—
72	#2112	—	3	1	no	—
73	C₂×C₂²⋊C₁₆	—	3	1	no	—
74	C₂×C₂²⋊C₁₆	—	3	1	no	—
75	C₂×D₃×D₄	C₈	1	1	yes	characteristic
76	C₂²×C₄×D₃	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₄×D₃	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
80	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
81	D₄×Dic₃	C₈	1	1	yes	characteristic
82	C₄×#67	C₂×C₄	1	1	yes	characteristic
83	C₄×#67	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₂×D₃×C₈	—	4	1	no	—
87	C₂×D₃×C₈	—	4	1	no	—
88	C₂×D₃×C₈	—	4	1	no	—
89	C₂×D₃×C₈	—	4	1	no	—
90	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
91	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
92	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
93	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
94	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
95	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
96	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
97	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
98	#893	C₈	1	1	yes	characteristic
99	D₃×C₄⋊C₄	C₈	1	1	yes	characteristic
100	#67⋊C₄	C₈	1	1	yes	characteristic
101	#67⋊C₄	C₈	1	1	yes	characteristic
102	D₃×C₂²⋊C₄	C₈	1	1	yes	characteristic
103	D₃×C₂²⋊C₄	C₈	1	1	yes	characteristic
104	C₄×D₁₂	C₂×C₄	1	1	yes	characteristic
105	C₄²×D₃	C₂×C₄	1	1	yes	characteristic
106	C₃×M₃₂	—	4	1	no	—
107	C₂×C₃×C₁₆	—	4	1	no	—
108	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
109	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
110	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
111	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
112	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
113	C₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
114	C₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
115	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
116	#830	C₂×C₄	1	1	yes	characteristic
117	#830	C₂×C₄	1	1	yes	characteristic
118	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
119	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
120	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
121	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
122	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
123	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
124	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
125	C₈×Dic₃	C₂³	1	1	yes	characteristic
126	#812	—	4	1	no	—
127	C₂×C₃⋊C₁₆	—	4	1	no	—
128	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
129	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
130	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
131	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
132	C₄⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
133	C₄×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
134	#798	—	4	1	no	—
135	#798	—	4	1	no	—
136	D₃×C₁₆	—	4	1	no	—
137	D₃×C₁₆	—	4	1	no	—
138	C₂³×C₈	—	3	1	no	—
139	C₂³×C₈	—	3	1	no	—
140	C₂×C₄×D₄	—	3	1	no	—
141	C₂×M₃₂	—	3	1	no	—
142	C₂×M₃₂	—	3	1	no	—
143	C₂×M₃₂	—	3	1	no	—
144	C₂×M₃₂	C₂×D₃	1	1	yes	characteristic, complemented
145	C₂²×C₁₆	—	3	1	no	—
146	C₂²×C₁₆	—	3	1	no	—
147	C₂²×C₁₆	—	3	1	no	—
148	C₂²×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
149	C₈×D₄	—	3	1	no	—
150	C₈×D₄	—	3	1	no	—
151	C₈×D₄	—	3	1	no	—
152	C₈×D₄	—	3	1	no	—
153	C₈×D₄	—	3	1	no	—
154	C₈×D₄	—	3	1	no	—
155	C₈×D₄	—	3	1	no	—
156	C₈×D₄	C₂×D₃	1	1	yes	characteristic
157	C₂×C₄⋊C₈	—	3	1	no	—
158	C₂×C₂²⋊C₈	—	3	1	no	—
159	C₂×C₂²⋊C₈	—	3	1	no	—
160	C₂×C₄×C₈	—	3	1	no	—
161	C₄⋊C₁₆	—	3	1	no	—
162	C₄⋊C₁₆	—	3	1	no	—
163	C₄⋊C₁₆	—	3	1	no	—
164	C₄⋊C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
165	C₂²⋊C₁₆	—	3	1	no	—
166	C₂²⋊C₁₆	—	3	1	no	—
167	C₂²⋊C₁₆	—	3	1	no	—
168	C₂²⋊C₁₆	—	3	1	no	—
169	C₂²⋊C₁₆	—	3	1	no	—
170	C₂²⋊C₁₆	—	3	1	no	—
171	C₂²⋊C₁₆	—	3	1	no	—
172	C₂²⋊C₁₆	—	3	1	no	—
173	C₂²⋊C₁₆	—	3	1	no	—
174	C₂²⋊C₁₆	—	3	1	no	—
175	C₂²⋊C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
176	C₂²⋊C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
177	#346	—	3	1	no	—
178	#346	—	3	1	no	—
179	#346	—	3	1	no	—
180	#346	C₂×D₃	1	1	yes	characteristic, complemented
181	C₂³×D₃	C₂×C₈	1	1	yes	characteristic
182	C₂³×D₃	C₂×C₈	1	1	yes	characteristic
183	C₂×C₃×D₄	C₂×C₈	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
186	C₂×#67	C₂×C₈	1	1	yes	characteristic
187	C₂×#67	C₂×C₈	1	1	yes	characteristic
188	C₂²×Dic₃	C₂×C₈	1	1	yes	characteristic
189	C₂²×Dic₃	C₂×C₈	1	1	yes	characteristic
190	D₃×D₄	—	2	4	no	—
191	C₂×D₁₂	C₂×C₈	1	1	yes	characteristic
192	C₂×C₄×D₃	—	4	1	no	—
193	C₂×C₄×D₃	—	4	1	no	—
194	C₂×C₄×D₃	—	4	1	no	—
195	C₂×C₄×D₃	—	4	1	no	—
196	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
197	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
198	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
199	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
200	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
201	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
202	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₃×C₈	—	2	1	no	—
206	C₂×C₃×C₈	—	2	1	no	—
207	C₂×C₃×C₈	—	2	1	no	—
208	C₂×C₃×C₈	—	2	1	no	—
209	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
210	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
213	C₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
214	C₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
215	C₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
216	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
217	#217	C₂×C₈	1	1	yes	characteristic
218	#217	C₂×C₈	1	1	yes	characteristic
219	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
220	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
221	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
222	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
223	C₄⋊Dic₃	C₂×C₈	1	1	yes	characteristic
224	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
225	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
226	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
227	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
228	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
229	C₂×C₃⋊C₈	—	4	1	no	—
230	C₂×C₃⋊C₈	—	4	1	no	—
231	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
232	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
233	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
234	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
235	D₃×C₈	—	2	1	no	—
236	D₃×C₈	—	2	1	no	—
237	D₃×C₈	—	2	1	no	—
238	D₃×C₈	—	2	1	no	—
239	D₃×C₈	—	2	1	no	—
240	D₃×C₈	—	2	1	no	—
241	D₃×C₈	—	4	1	no	—
242	D₃×C₈	—	4	1	no	—
243	D₃×C₈	—	4	1	no	—
244	D₃×C₈	—	4	1	no	—
245	D₃×C₈	—	4	1	no	—
246	C₃×C₁₆	—	2	1	no	—
247	C₃×C₁₆	—	2	1	no	—
248	C₃×C₁₆	—	2	1	no	—
249	C₃×C₁₆	—	2	1	no	—
250	C₃⋊C₁₆	—	2	1	no	—
251	C₃⋊C₁₆	—	2	1	no	—
252	C₃⋊C₁₆	—	2	1	no	—
253	C₃⋊C₁₆	—	2	1	no	—
254	C₂²×D₄	—	3	1	no	—
255	C₂³×C₄	—	3	1	no	—
256	C₂³×C₄	—	3	1	no	—
257	C₂²×C₈	—	3	1	no	—
258	C₂²×C₈	—	3	1	no	—
259	C₂²×C₈	—	3	1	no	—
260	C₂²×C₈	—	3	1	no	—
261	C₂²×C₈	—	3	1	no	—
262	C₂²×C₈	—	3	1	no	—
263	C₂²×C₈	—	3	1	no	—
264	C₂²×C₈	—	3	1	no	—
265	C₂²×C₈	—	3	1	no	—
266	C₂²×C₈	—	3	1	no	—
267	C₂²×C₈	—	12	1	no	—
268	C₂²×C₈	—	12	1	no	—
269	C₂²×C₈	—	12	1	no	—
270	C₂²×C₈	—	12	1	no	—
271	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
272	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
273	C₄×D₄	—	3	1	no	—
274	C₄×D₄	—	3	1	no	—
275	C₄×D₄	—	3	1	no	—
276	C₄×D₄	—	3	1	no	—
277	C₄×D₄	—	3	1	no	—
278	C₄×D₄	—	3	1	no	—
279	C₄×D₄	—	3	1	no	—
280	C₄×D₄	C₄×D₃	1	1	yes	characteristic
281	C₂×C₄⋊C₄	—	3	1	no	—
282	C₂×C₂²⋊C₄	—	3	1	no	—
283	C₂×C₂²⋊C₄	—	3	1	no	—
284	C₂×C₄²	—	3	1	no	—
285	M₃₂	—	4	1	no	—
286	M₃₂	—	12	1	no	—
287	M₃₂	—	12	1	no	—
288	M₃₂	—	12	1	no	—
289	C₂×C₁₆	—	3	1	no	—
290	C₂×C₁₆	—	3	1	no	—
291	C₂×C₁₆	—	3	1	no	—
292	C₂×C₁₆	—	3	1	no	—
293	C₂×C₁₆	—	4	1	no	—
294	C₂×C₁₆	—	12	1	no	—
295	C₂×C₁₆	—	12	1	no	—
296	C₂×C₁₆	—	12	1	no	—
297	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
298	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
299	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
300	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
301	C₄⋊C₈	—	3	1	no	—
302	C₄⋊C₈	—	3	1	no	—
303	C₄⋊C₈	—	3	1	no	—
304	C₄⋊C₈	C₄×D₃	1	1	yes	characteristic
305	C₂²⋊C₈	—	3	1	no	—
306	C₂²⋊C₈	—	3	1	no	—
307	C₂²⋊C₈	—	3	1	no	—
308	C₂²⋊C₈	—	3	1	no	—
309	C₂²⋊C₈	—	3	1	no	—
310	C₂²⋊C₈	—	3	1	no	—
311	C₂²⋊C₈	C₄×D₃	1	1	yes	characteristic
312	C₂²⋊C₈	C₄×D₃	1	1	yes	characteristic
313	C₄×C₈	—	3	1	no	—
314	C₄×C₈	—	3	1	no	—
315	C₄×C₈	—	3	1	no	—
316	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
317	C₂³×C₃	C₂²×C₈	1	1	yes	characteristic
318	C₂³×C₃	C₂²×C₈	1	1	yes	characteristic
319	C₂²×D₃	—	2	2	no	—
320	C₂²×D₃	—	4	1	no	—
321	C₂²×D₃	—	4	1	no	—
322	C₂²×D₃	—	4	1	no	—
323	C₂²×D₃	—	4	1	no	—
324	C₂²×D₃	M₃₂	1	4	yes	complemented
325	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
326	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
327	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
328	C₃×D₄	—	2	2	no	—
329	C₂×C₃×C₄	—	2	1	no	—
330	C₂×C₃×C₄	—	2	1	no	—
331	C₂×C₃×C₄	—	2	1	no	—
332	C₂×C₃×C₄	—	2	1	no	—
333	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
337	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
338	#67	—	2	2	no	—
339	#67	—	2	2	no	—
340	C₂×Dic₃	—	4	1	no	—
341	C₂×Dic₃	—	4	1	no	—
342	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
343	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
344	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
345	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
346	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
347	D₁₂	—	2	2	no	—
348	C₄×D₃	—	2	2	no	—
349	C₄×D₃	—	2	1	no	—
350	C₄×D₃	—	2	1	no	—
351	C₄×D₃	—	2	1	no	—
352	C₄×D₃	—	2	1	no	—
353	C₄×D₃	—	2	1	no	—
354	C₄×D₃	—	2	1	no	—
355	C₄×D₃	—	4	1	no	—
356	C₄×D₃	—	4	1	no	—
357	C₄×D₃	—	4	1	no	—
358	C₄×D₃	—	4	1	no	—
359	C₄×D₃	—	4	1	no	—
360	C₃×C₈	—	2	1	no	—
361	C₃×C₈	—	2	1	no	—
362	C₃×C₈	—	2	1	no	—
363	C₃×C₈	H(5,𝔽₂)	1	1	yes	characteristic
364	C₃×C₈	H(5,𝔽₂)	1	1	yes	characteristic
365	C₃⋊C₈	—	2	1	no	—
366	C₃⋊C₈	—	2	1	no	—
367	C₃⋊C₈	—	2	1	no	—
368	C₃⋊C₈	—	2	1	no	—
369	C₂⁴	—	3	1	no	—
370	C₂⁴	—	3	1	no	—
371	C₂×D₄	—	3	1	no	—
372	C₂×D₄	—	3	1	no	—
373	C₂×D₄	—	3	1	no	—
374	C₂×D₄	—	6	4	no	—
375	C₂×D₄	D₃×C₈	1	1	yes	characteristic
376	C₂²×C₄	—	3	1	no	—
377	C₂²×C₄	—	3	1	no	—
378	C₂²×C₄	—	3	1	no	—
379	C₂²×C₄	—	3	1	no	—
380	C₂²×C₄	—	3	1	no	—
381	C₂²×C₄	—	3	1	no	—
382	C₂²×C₄	—	3	1	no	—
383	C₂²×C₄	—	3	1	no	—
384	C₂²×C₄	—	3	1	no	—
385	C₂²×C₄	—	3	1	no	—
386	C₂²×C₄	—	3	1	no	—
387	C₂²×C₄	—	12	1	no	—
388	C₂²×C₄	—	12	1	no	—
389	C₂²×C₄	—	12	1	no	—
390	C₂²×C₄	—	12	1	no	—
391	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
392	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	3	1	no	—
398	C₂×C₈	—	3	1	no	—
399	C₂×C₈	—	3	1	no	—
400	C₂×C₈	—	3	1	no	—
401	C₂×C₈	—	6	1	no	—
402	C₂×C₈	—	6	1	no	—
403	C₂×C₈	—	6	1	no	—
404	C₂×C₈	—	6	1	no	—
405	C₂×C₈	—	6	1	no	—
406	C₂×C₈	—	6	1	no	—
407	C₂×C₈	—	12	1	no	—
408	C₂×C₈	—	12	1	no	—
409	C₂×C₈	—	12	1	no	—
410	C₂×C₈	—	12	1	no	—
411	C₂×C₈	—	12	1	no	—
412	C₂×C₈	—	12	1	no	—
413	C₂×C₈	—	12	1	no	—
414	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
415	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
416	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
417	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
418	C₄⋊C₄	—	3	1	no	—
419	C₄⋊C₄	—	3	1	no	—
420	C₄⋊C₄	—	3	1	no	—
421	C₄⋊C₄	D₃×C₈	1	1	yes	characteristic
422	C₂²⋊C₄	—	3	1	no	—
423	C₂²⋊C₄	—	3	1	no	—
424	C₂²⋊C₄	—	3	1	no	—
425	C₂²⋊C₄	—	3	1	no	—
426	C₂²⋊C₄	—	3	1	no	—
427	C₂²⋊C₄	—	3	1	no	—
428	C₂²⋊C₄	D₃×C₈	1	1	yes	characteristic
429	C₂²⋊C₄	D₃×C₈	1	1	yes	characteristic
430	C₄²	—	3	1	no	—
431	C₄²	—	3	1	no	—
432	C₄²	—	3	1	no	—
433	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
434	C₁₆	—	2	1	no	—
435	C₁₆	—	2	1	no	—
436	C₁₆	—	2	1	no	—
437	C₁₆	—	2	1	no	—
438	C₁₆	—	6	1	no	—
439	C₁₆	—	6	1	no	—
440	C₁₆	—	6	1	no	—
441	C₁₆	—	6	1	no	—
442	C₂²×C₃	—	2	1	no	—
443	C₂²×C₃	—	2	1	no	—
444	C₂²×C₃	—	2	1	no	—
445	C₂²×C₃	—	2	1	no	—
446	C₂²×C₃	—	2	1	no	—
447	C₂²×C₃	C₂×M₃₂	1	2	yes	—
448	C₂²×C₃	C₂³×C₈	1	1	yes	characteristic
449	C₂×D₃	—	2	1	no	—
450	C₂×D₃	—	2	1	no	—
451	C₂×D₃	—	2	1	no	—
452	C₂×D₃	—	2	1	no	—
453	C₂×D₃	—	2	1	no	—
454	C₂×D₃	—	2	1	no	—
455	C₂×D₃	—	2	1	no	—
456	C₂×D₃	—	4	4	no	—
457	C₂×D₃	—	4	4	no	—
458	C₂×D₃	C₂×M₃₂	1	2	yes	—
459	C₂×D₃	C₂×M₃₂	1	2	yes	—
460	C₃×C₄	—	2	1	no	—
461	C₃×C₄	—	2	1	no	—
462	C₃×C₄	—	2	1	no	—
463	C₃×C₄	—	2	1	no	—
464	C₃×C₄	#518	1	1	yes	characteristic
465	C₃×C₄	#568	1	1	yes	characteristic
466	Dic₃	—	2	1	no	—
467	Dic₃	—	2	1	no	—
468	Dic₃	—	2	1	no	—
469	Dic₃	—	2	1	no	—
470	Dic₃	—	2	1	no	—
471	C₂³	—	3	1	no	—
472	C₂³	—	3	1	no	—
473	C₂³	—	3	4	no	—
474	C₂³	—	3	1	no	—
475	C₂³	—	6	2	no	—
476	C₂³	—	12	1	no	—
477	C₂³	—	12	1	no	—
478	C₂³	—	12	1	no	—
479	C₂³	—	12	1	no	—
480	C₂³	C₂×D₃×C₈	1	1	yes	characteristic
481	C₂³	C₂×D₃×C₈	1	1	yes	characteristic
482	D₄	—	2	2	no	—
483	D₄	—	6	2	no	—
484	D₄	—	6	2	no	—
485	D₄	—	6	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	3	1	no	—
491	C₂×C₄	—	3	1	no	—
492	C₂×C₄	—	3	1	no	—
493	C₂×C₄	—	3	1	no	—
494	C₂×C₄	—	3	1	no	—
495	C₂×C₄	—	6	2	no	—
496	C₂×C₄	—	6	1	no	—
497	C₂×C₄	—	6	1	no	—
498	C₂×C₄	—	6	1	no	—
499	C₂×C₄	—	6	1	no	—
500	C₂×C₄	—	6	1	no	—
501	C₂×C₄	—	6	1	no	—
502	C₂×C₄	—	12	1	no	—
503	C₂×C₄	—	12	1	no	—
504	C₂×C₄	—	12	1	no	—
505	C₂×C₄	—	12	1	no	—
506	C₂×C₄	—	12	1	no	—
507	C₂×C₄	—	12	1	no	—
508	C₂×C₄	—	12	1	no	—
509	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
510	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
511	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
512	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
513	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
514	C₈	—	2	1	no	—
515	C₈	—	2	1	no	—
516	C₈	—	2	1	no	—
517	C₈	—	6	1	no	—
518	C₈	—	6	1	no	—
519	C₈	—	6	1	no	—
520	C₈	—	6	1	no	—
521	C₈	#1004	1	1	yes	characteristic
522	C₈	#1009	1	1	yes	characteristic
523	C₂×C₃	—	2	2	no	—
524	C₂×C₃	—	4	1	no	—
525	C₂×C₃	#2972	1	1	yes	characteristic
526	C₂×C₃	C₂²×M₃₂	1	1	yes	characteristic
527	C₂×C₃	#3407	1	1	yes	characteristic
528	D₃	—	2	2	no	—
529	D₃	—	2	2	no	—
530	D₃	—	4	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	3	2	no	—
537	C₂²	—	3	2	no	—
538	C₂²	—	6	1	no	—
539	C₂²	—	6	1	no	—
540	C₂²	—	6	1	no	—
541	C₂²	—	6	1	no	—
542	C₂²	—	6	1	no	—
543	C₂²	—	6	1	no	—
544	C₂²	—	6	1	no	—
545	C₂²	—	12	4	no	—
546	C₂²	—	12	4	no	—
547	C₂²	D₃×M₃₂	1	2	yes	—
548	C₂²	C₂²×D₃×C₈	1	1	yes	characteristic
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	6	1	no	—
554	C₄	—	6	1	no	—
555	C₄	—	6	1	no	—
556	C₄	—	6	1	no	—
557	C₄	—	6	1	no	—
558	C₄	#5545	1	1	yes	characteristic
559	C₄	#5750	1	1	yes	characteristic
560	C₃	#33487	1	1	yes	characteristic, complemented, Sylow
561	C₂	—	2	2	no	—
562	C₂	—	4	1	no	—
563	C₂	—	6	2	no	—
564	C₂	—	6	2	no	—
565	C₂	—	12	1	no	—
566	C₂	#79426	1	1	yes	characteristic
567	C₂	C₂×D₃×M₃₂	1	1	yes	characteristic
568	C₂	#82012	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₃
commutator, socle	C₂²×C₃	C₂³×C₈
Fitting	C₃×#2168	C₂
prime radical	C₂×D₃×D₄	C₈
cosocle	C₂×C₃×C₈	C₂⁴
hypercenter	#2168	D₃
hypocenter	C₃	#33487
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
2. C₃×#2168	C₂	semidirect
3. #71433	C₂	semidirect
4. #71431	C₂	semidirect
5. C₂×(C₂×D₃)⋊C₁₆	C₂	semidirect
6. #71407	C₂	semidirect
7. #70857	C₂	semidirect
8. #69278	C₂	semidirect
9. #69275	C₂	semidirect
10. #69106	C₂	semidirect
11. D₃×C₂²⋊C₁₆	C₂	semidirect
12. #69103	C₂	semidirect
13. #69102	C₂	semidirect
14. #69075	C₂	semidirect
15. #69073	C₂	semidirect
20. C₂×C₃×M₃₂	C₂²	semidirect
21. C₂²×C₃×C₁₆	C₂²	semidirect
25. C₂×#812	C₂²	semidirect
26. C₂²×C₃⋊C₁₆	C₂²	semidirect
28. C₂×#798	C₂²	semidirect
29. C₂×#798	C₂²	semidirect
30. C₂×D₃×C₁₆	C₂²	semidirect
31. C₂×D₃×C₁₆	C₂²	semidirect
40. C₃×C₄⋊C₁₆	C₂²	semidirect
41. C₃×C₂²⋊C₁₆	C₂²	semidirect
42. C₃×C₂²⋊C₁₆	C₂²	semidirect
43. C₃×#346	C₂²	semidirect
44. #4549	C₂²	semidirect
45. #4549	C₂²	semidirect
50. (C₂×D₃)⋊C₁₆	C₂²	semidirect
51. (C₂×D₃)⋊C₁₆	C₂²	semidirect
52. (C₂×D₃)⋊C₁₆	C₂²	semidirect
53. (C₂×D₃)⋊C₁₆	C₂²	semidirect
54. #4502	C₂²	semidirect
55. #4502	C₂²	semidirect
56. Dic₃⋊C₁₆	C₂²	semidirect
57. Dic₃⋊C₁₆	C₂²	semidirect
58. C₄⋊(C₃⋊C₁₆)	C₂²	semidirect
59. #4461	C₂²	semidirect
68. #2168	D₃	semidirect
144. C₂×M₃₂	C₂×D₃	semidirect
148. C₂²×C₁₆	C₂×D₃	semidirect
164. C₄⋊C₁₆	C₂×D₃	semidirect
175. C₂²⋊C₁₆	C₂×D₃	semidirect
176. C₂²⋊C₁₆	C₂×D₃	semidirect
180. #346	C₂×D₃	semidirect
324. C₂²×D₃	M₃₂	semidirect
560. C₃	#33487	semidirect

Maximal subgroups

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

subgroup	index
D₃×C₈×D₄	2
C₃×#2168	2
#71433	2
#71431	2
C₂×(C₂×D₃)⋊C₁₆	2
#71407	2
#70857	2
#69278	2
#69275	2
#69106	2
D₃×C₂²⋊C₁₆	2
#69103	2
#69102	2
#69075	2
#69073	2
#33487	3