Subgroups — C₃×#25451 #10644058

Order 768.

834 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#476	C₂	1	1	yes	maximal, characteristic
3	C₃×#2542	C₂	1	1	yes	maximal, characteristic
4	C₃×#2369	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2084	C₂	1	2	yes	maximal, complemented
6	C₃×#2065	C₂	1	2	yes	maximal
7	C₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1948	C₂	1	2	yes	maximal, complemented
9	C₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#1926	C₂	1	2	yes	maximal
11	C₃×C₄×#102	C₂	1	1	yes	maximal, characteristic
12	#25451	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
16	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
17	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
18	C₃×#498	—	2	4	no	—
19	C₃×#476	—	2	4	no	—
20	C₂×C₃×#106	C₂²	1	2	yes	—
21	C₂×C₃×#106	C₂²	1	2	yes	—
22	C₂×C₃×#106	C₂²	1	2	yes	—
23	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₃×#102	C₂²	1	2	yes	—
27	C₂×C₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
29	C₃×#399	—	2	2	no	—
30	C₃×#391	—	2	2	no	—
31	C₃×#390	C₂²	1	2	yes	—
32	C₃×#389	—	2	1	no	—
33	C₃×#389	C₂²	1	2	yes	—
34	C₃×#384	C₂²	1	2	yes	—
35	C₃×C₄×C₄⋊C₄	—	2	1	no	—
36	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
38	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×#340	C₂²	1	1	yes	characteristic
40	C₃×#340	C₂²	1	1	yes	characteristic
41	C₃×#340	C₂²	1	2	yes	—
42	C₃×#340	C₂²	1	2	yes	—
43	C₃×#336	C₂²	1	2	yes	—
44	C₂×#498	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×#476	C₂×C₃	1	1	yes	characteristic
46	#2542	C₂×C₃	1	1	yes	characteristic
47	#2369	C₂×C₃	1	1	yes	characteristic, complemented
48	#2084	C₂×C₃	1	2	yes	complemented
49	#2065	C₂×C₃	1	2	yes	—
50	#1988	C₂×C₃	1	1	yes	characteristic, complemented
51	#1948	C₂×C₃	1	2	yes	complemented
52	#1939	C₂×C₃	1	1	yes	characteristic, complemented
53	#1926	C₂×C₃	1	2	yes	—
54	C₄×#102	C₂×C₃	1	1	yes	characteristic
55	C₂²×C₃×Q₈	—	2	1	no	—
56	C₂²×C₃×Q₈	—	2	1	no	—
57	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
58	C₂³×C₃×C₄	—	2	1	no	—
59	C₂²×C₃×C₈	C₂³	1	2	yes	—
60	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
62	C₃×C₄⋊Q₈	—	2	2	no	—
63	C₃×C₄⋊Q₈	—	2	2	no	—
64	C₃×C₄⋊Q₈	—	2	2	no	—
65	C₃×C₄⋊Q₈	D₄	1	4	yes	—
66	C₃×C₂²⋊Q₈	—	4	4	no	—
67	C₃×C₂²⋊Q₈	—	4	4	no	—
68	C₃×C₄×D₄	—	2	2	no	—
69	C₃×C₄×D₄	—	2	2	no	—
70	C₂×C₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₃×C₄⋊C₄	—	2	2	no	—
72	C₂×C₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
76	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
77	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
83	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
84	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₃×C₄²	—	2	1	no	—
86	C₂×C₃×C₄²	—	2	2	no	—
87	C₂×C₃×C₄²	C₂³	1	2	yes	—
88	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
89	C₃×#106	—	2	4	no	—
90	C₃×#106	—	2	4	no	—
91	C₃×#106	—	2	4	no	—
92	C₃×C₄⋊C₈	—	2	4	no	—
93	C₃×C₄⋊C₈	—	2	2	no	—
94	C₃×#102	—	2	2	no	—
95	C₃×#102	—	2	4	no	—
96	C₃×#102	Q₈	1	4	yes	complemented
97	C₃×C₄×C₈	—	2	2	no	—
98	C₃×#95	—	2	2	no	—
99	C₃×#95	—	2	2	no	—
100	C₃×#95	—	2	1	no	—
101	C₃×#95	D₄	1	2	yes	—
102	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₂²⋊Q₈	—	2	1	no	—
105	C₂×C₂²⋊Q₈	—	2	1	no	—
106	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
107	#498	—	2	4	no	—
108	#476	—	2	4	no	—
109	C₂×#106	C₂²×C₃	1	2	yes	—
110	C₂×#106	C₂²×C₃	1	2	yes	—
111	C₂×#106	C₂²×C₃	1	2	yes	—
112	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	—
113	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
114	C₂×#102	C₂²×C₃	1	1	yes	characteristic
115	C₂×#102	C₂²×C₃	1	2	yes	—
116	C₂×#102	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
118	#399	—	2	2	no	—
119	#391	—	2	2	no	—
120	#390	C₂²×C₃	1	2	yes	—
121	#389	—	2	1	no	—
122	#389	C₂²×C₃	1	2	yes	—
123	#384	C₂²×C₃	1	2	yes	—
124	C₄×C₄⋊C₄	—	2	1	no	—
125	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
126	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	#340	C₂²×C₃	1	2	yes	—
129	#340	C₂²×C₃	1	1	yes	characteristic
130	#340	C₂²×C₃	1	2	yes	—
131	#340	C₂²×C₃	1	1	yes	characteristic
132	#336	C₂²×C₃	1	2	yes	—
133	C₂⁴×C₃	—	2	1	no	—
134	C₂×C₃×Q₈	—	2	4	no	—
135	C₂×C₃×Q₈	—	4	2	no	—
136	C₂×C₃×Q₈	—	4	2	no	—
137	C₂×C₃×Q₈	—	4	2	no	—
138	C₂×C₃×Q₈	—	8	1	no	—
139	C₂×C₃×Q₈	—	8	1	no	—
140	C₂×C₃×D₄	—	2	1	no	—
141	C₂×C₃×D₄	—	2	1	no	—
142	C₂×C₃×D₄	—	2	1	no	—
143	C₂×C₃×D₄	—	2	1	no	—
144	C₂×C₃×D₄	—	2	1	no	—
145	C₂×C₃×D₄	C₂×Q₈	1	2	yes	—
146	C₂²×C₃×C₄	—	2	1	no	—
147	C₂²×C₃×C₄	—	2	2	no	—
148	C₂²×C₃×C₄	—	2	1	no	—
149	C₂²×C₃×C₄	—	2	2	no	—
150	C₂²×C₃×C₄	—	2	1	no	—
151	C₂²×C₃×C₄	—	4	2	no	—
152	C₂²×C₃×C₄	—	4	2	no	—
153	C₂²×C₃×C₄	—	4	2	no	—
154	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
155	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
157	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
159	C₂×C₃×C₈	—	2	1	no	—
160	C₂×C₃×C₈	—	2	1	no	—
161	C₂×C₃×C₈	—	2	1	no	—
162	C₂×C₃×C₈	—	2	1	no	—
163	C₂×C₃×C₈	—	2	2	no	—
164	C₂×C₃×C₈	—	2	2	no	—
165	C₂×C₃×C₈	—	2	2	no	—
166	C₂×C₃×C₈	C₂×Q₈	1	2	yes	—
167	C₂×C₃×C₈	#41	1	2	yes	—
168	C₃×C₄⋊C₄	—	2	4	no	—
169	C₃×C₄⋊C₄	—	2	2	no	—
170	C₃×C₄⋊C₄	—	2	2	no	—
171	C₃×C₄⋊C₄	—	2	1	no	—
172	C₃×C₄⋊C₄	—	2	1	no	—
173	C₃×C₄⋊C₄	—	2	2	no	—
174	C₃×C₄⋊C₄	—	2	1	no	—
175	C₃×C₄⋊C₄	—	2	1	no	—
176	C₃×C₄⋊C₄	—	2	2	no	—
177	C₃×C₄⋊C₄	—	2	1	no	—
178	C₃×C₄⋊C₄	—	4	4	no	—
179	C₃×C₄⋊C₄	—	4	2	no	—
180	C₃×C₄⋊C₄	—	4	4	no	—
181	C₃×C₄⋊C₄	—	8	2	no	—
182	C₃×C₄⋊C₄	SD₁₆	1	4	yes	—
183	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
184	C₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
185	C₃×C₂²⋊C₄	—	4	4	no	—
186	C₃×C₂²⋊C₄	—	4	2	no	—
187	C₃×C₂²⋊C₄	—	4	4	no	—
188	C₃×C₄²	—	2	2	no	—
189	C₃×C₄²	—	2	2	no	—
190	C₃×C₄²	—	4	2	no	—
191	C₃×C₄²	—	8	2	no	—
192	C₃×C₄²	C₂×D₄	1	2	yes	—
193	C₃×C₄²	#41	1	2	yes	—
194	C₂²×Q₈	—	2	1	no	—
195	C₂²×Q₈	—	2	1	no	—
196	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
197	C₂³×C₄	—	2	1	no	—
198	C₂²×C₈	C₂³×C₃	1	2	yes	—
199	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
200	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
201	C₄⋊Q₈	—	2	2	no	—
202	C₄⋊Q₈	—	2	2	no	—
203	C₄⋊Q₈	—	2	2	no	—
204	C₄⋊Q₈	C₃×D₄	1	4	yes	—
205	C₂²⋊Q₈	—	4	4	no	—
206	C₂²⋊Q₈	—	4	4	no	—
207	C₄×D₄	—	2	2	no	—
208	C₄×D₄	—	2	2	no	—
209	C₂×C₄⋊C₄	—	2	1	no	—
210	C₂×C₄⋊C₄	—	2	2	no	—
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	—	2	1	no	—
213	C₂×C₄⋊C₄	—	2	2	no	—
214	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
218	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
220	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
221	C₂×C₂²⋊C₄	—	2	1	no	—
222	C₂×C₂²⋊C₄	—	2	2	no	—
223	C₂×C₂²⋊C₄	—	2	2	no	—
224	C₂×C₄²	—	2	1	no	—
225	C₂×C₄²	—	2	2	no	—
226	C₂×C₄²	C₂³×C₃	1	2	yes	—
227	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
228	#106	—	2	4	no	—
229	#106	—	2	4	no	—
230	#106	—	2	4	no	—
231	C₄⋊C₈	—	2	4	no	—
232	C₄⋊C₈	—	2	2	no	—
233	#102	—	2	2	no	—
234	#102	—	2	4	no	—
235	#102	C₃×Q₈	1	4	yes	complemented
236	C₄×C₈	—	2	2	no	—
237	#95	—	2	2	no	—
238	#95	—	2	2	no	—
239	#95	—	2	1	no	—
240	#95	C₃×D₄	1	2	yes	—
241	C₂³×C₃	—	2	2	no	—
242	C₂³×C₃	—	4	1	no	—
243	C₂³×C₃	—	4	1	no	—
244	C₂³×C₃	—	4	1	no	—
245	C₂³×C₃	—	4	1	no	—
246	C₂³×C₃	—	4	1	no	—
247	C₂³×C₃	—	4	1	no	—
248	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
249	C₃×Q₈	—	8	4	no	—
250	C₃×Q₈	—	8	4	no	—
251	C₃×D₄	—	2	2	no	—
252	C₃×D₄	—	2	2	no	—
253	C₃×D₄	—	4	1	no	—
254	C₃×D₄	—	4	1	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	4	1	no	—
265	C₂×C₃×C₄	—	4	1	no	—
266	C₂×C₃×C₄	—	4	2	no	—
267	C₂×C₃×C₄	—	4	2	no	—
268	C₂×C₃×C₄	—	4	1	no	—
269	C₂×C₃×C₄	—	4	2	no	—
270	C₂×C₃×C₄	—	4	1	no	—
271	C₂×C₃×C₄	—	4	2	no	—
272	C₂×C₃×C₄	—	4	1	no	—
273	C₂×C₃×C₄	—	4	1	no	—
274	C₂×C₃×C₄	—	4	2	no	—
275	C₂×C₃×C₄	—	4	1	no	—
276	C₂×C₃×C₄	—	4	1	no	—
277	C₂×C₃×C₄	—	8	4	no	—
278	C₂×C₃×C₄	#121	1	2	yes	—
279	C₂×C₃×C₄	#121	1	2	yes	—
280	C₂×C₃×C₄	C₂×SD₁₆	1	4	yes	—
281	C₂×C₃×C₄	C₂×SD₁₆	1	2	yes	—
282	C₂×C₃×C₄	AGL(1,ℤ/8)	1	2	yes	—
283	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂²×Q₈	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
287	C₂×C₃×C₄	2₋¹⁺⁴	1	1	yes	characteristic
288	C₂×C₃×C₄	2₋¹⁺⁴	1	1	yes	characteristic
289	C₃×C₈	—	2	2	no	—
290	C₃×C₈	—	2	2	no	—
291	C₃×C₈	—	4	2	no	—
292	C₂⁴	—	2	1	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	4	2	no	—
296	C₂×Q₈	—	4	2	no	—
297	C₂×Q₈	—	8	1	no	—
298	C₂×Q₈	—	8	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	C₂×C₃×Q₈	1	2	yes	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
314	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
316	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
317	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	C₂×C₃×Q₈	1	2	yes	—
326	C₂×C₈	C₃×#41	1	2	yes	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	4	no	—
340	C₄⋊C₄	—	8	2	no	—
341	C₄⋊C₄	C₃×SD₁₆	1	4	yes	—
342	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
343	C₄⋊C₄	C₂×C₃×Q₈	1	2	yes	—
344	C₂²⋊C₄	—	4	4	no	—
345	C₂²⋊C₄	—	4	2	no	—
346	C₂²⋊C₄	—	4	4	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	4	2	no	—
350	C₄²	—	8	2	no	—
351	C₄²	C₂×C₃×D₄	1	2	yes	—
352	C₄²	C₃×#41	1	2	yes	—
353	C₂²×C₃	—	4	2	no	—
354	C₂²×C₃	—	4	2	no	—
355	C₂²×C₃	—	4	2	no	—
356	C₂²×C₃	—	8	1	no	—
357	C₂²×C₃	—	8	1	no	—
358	C₂²×C₃	—	8	1	no	—
359	C₂²×C₃	—	8	1	no	—
360	C₂²×C₃	C₂×#121	1	1	yes	characteristic
361	C₂²×C₃	#547	1	1	yes	characteristic
362	C₂²×C₃	D₄×Q₈	1	1	yes	characteristic
363	C₂²×C₃	C₂²×SD₁₆	1	1	yes	characteristic
364	C₂²×C₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
365	C₂²×C₃	#577	1	1	yes	characteristic
366	C₂²×C₃	#577	1	1	yes	characteristic
367	C₃×C₄	—	2	4	no	—
368	C₃×C₄	—	2	2	no	—
369	C₃×C₄	—	4	2	no	—
370	C₃×C₄	—	4	2	no	—
371	C₃×C₄	—	4	4	no	—
372	C₃×C₄	—	8	1	no	—
373	C₃×C₄	—	8	1	no	—
374	C₃×C₄	—	8	2	no	—
375	C₃×C₄	#460	1	4	yes	—
376	C₃×C₄	#533	1	1	yes	characteristic
377	C₃×C₄	#541	1	1	yes	characteristic
378	C₃×C₄	#548	1	1	yes	characteristic
379	C₃×C₄	D₄×Q₈	1	1	yes	characteristic
380	C₂³	—	2	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	1	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	1	no	—
387	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
388	Q₈	—	8	4	no	—
389	Q₈	—	8	4	no	—
390	D₄	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	4	1	no	—
393	D₄	—	4	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	8	4	no	—
417	C₂×C₄	C₃×#121	1	2	yes	—
418	C₂×C₄	C₃×#121	1	2	yes	—
419	C₂×C₄	C₂×C₃×SD₁₆	1	4	yes	—
420	C₂×C₄	C₂×C₃×SD₁₆	1	2	yes	—
421	C₂×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
422	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
424	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
425	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
426	C₂×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
427	C₂×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
428	C₈	—	2	2	no	—
429	C₈	—	2	2	no	—
430	C₈	—	4	2	no	—
431	C₂×C₃	—	8	2	no	—
432	C₂×C₃	#2429	1	1	yes	characteristic
433	C₂×C₃	C₂×#460	1	1	yes	characteristic
434	C₂×C₃	#3042	1	1	yes	characteristic
435	C₂×C₃	#3335	1	1	yes	characteristic
436	C₂×C₃	#3354	1	1	yes	characteristic
437	C₂×C₃	Q₈×SD₁₆	1	1	yes	characteristic
438	C₂×C₃	#3384	1	1	yes	characteristic
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	8	1	no	—
443	C₂²	—	8	1	no	—
444	C₂²	—	8	1	no	—
445	C₂²	—	8	1	no	—
446	C₂²	C₂×C₃×#121	1	1	yes	characteristic
447	C₂²	C₃×#547	1	1	yes	characteristic
448	C₂²	C₃×D₄×Q₈	1	1	yes	characteristic
449	C₂²	C₂²×C₃×SD₁₆	1	1	yes	characteristic
450	C₂²	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
451	C₂²	C₃×#577	1	1	yes	characteristic
452	C₂²	C₃×#577	1	1	yes	characteristic
453	C₄	—	2	2	no	—
454	C₄	—	2	4	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	4	no	—
457	C₄	—	4	2	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	2	no	—
460	C₄	—	8	1	no	—
461	C₄	C₃×#460	1	4	yes	—
462	C₄	C₃×#533	1	1	yes	characteristic
463	C₄	C₃×#541	1	1	yes	characteristic
464	C₄	C₃×#548	1	1	yes	characteristic
465	C₄	C₃×D₄×Q₈	1	1	yes	characteristic
466	C₃	#25451	1	1	yes	characteristic, direct product factor, Sylow
467	C₂	—	8	2	no	—
468	C₂	C₃×#2429	1	1	yes	characteristic
469	C₂	C₂×C₃×#460	1	1	yes	characteristic
470	C₂	C₃×#3042	1	1	yes	characteristic
471	C₂	C₃×#3335	1	1	yes	characteristic
472	C₂	C₃×#3354	1	1	yes	characteristic
473	C₂	C₃×Q₈×SD₁₆	1	1	yes	characteristic
474	C₂	C₃×#3384	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
prime radical	C₂²×C₃×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×C₄×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#498	C₂	semidirect
4. C₃×#2369	C₂	semidirect
5. C₃×#2084	C₂	semidirect
7. C₃×#1988	C₂	semidirect
8. C₃×#1948	C₂	semidirect
9. C₃×#1939	C₂	semidirect
12. #25451	C₃	direct (N × H)
44. C₂×#498	C₂×C₃	semidirect
47. #2369	C₂×C₃	semidirect
48. #2084	C₂×C₃	semidirect
50. #1988	C₂×C₃	semidirect
51. #1948	C₂×C₃	semidirect
52. #1939	C₂×C₃	semidirect
96. C₃×#102	Q₈	semidirect
235. #102	C₃×Q₈	semidirect
466. C₃	#25451	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#498	2
C₂×C₃×#476	2
C₃×#2542	2
C₃×#2369	2
C₃×#2084	2
C₃×#2065	2
C₃×#1988	2
C₃×#1948	2
C₃×#1939	2
C₃×#1926	2
C₃×C₄×#102	2
#25451	3

Subgroups — C3×#25451 #10644058

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#25451 #10644058