Subgroups — C₃×#27792 #10646399

Order 768.

810 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#467	C₂	1	1	yes	maximal, characteristic
3	C₃×#2492	C₂	1	2	yes	maximal
4	C₃×#2036	C₂	1	2	yes	maximal
5	C₃×#2024	C₂	1	2	yes	maximal, complemented
6	C₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1928	C₂	1	2	yes	maximal, complemented
9	C₃×#1808	C₂	1	1	yes	maximal, characteristic
10	C₃×C₄×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	#27792	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₃×#500	—	2	4	no	—
18	C₃×#467	—	2	4	no	—
19	C₂×C₃×#107	C₂²	1	2	yes	—
20	C₂×C₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₃×#107	C₂²	1	1	yes	characteristic
23	C₂×C₃×#103	C₂²	1	2	yes	—
24	C₂×C₃×#103	C₂²	1	2	yes	—
25	C₂×C₃×#103	C₂²	1	2	yes	—
26	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
29	C₃×#400	—	2	2	no	—
30	C₃×#393	—	2	2	no	—
31	C₃×#391	—	2	2	no	—
32	C₃×#391	C₂²	1	2	yes	—
33	C₃×#391	C₂²	1	2	yes	—
34	C₃×#388	—	2	2	no	—
35	C₃×#380	C₂²	1	2	yes	—
36	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
37	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×#340	C₂²	1	2	yes	—
39	C₃×#340	C₂²	1	2	yes	—
40	C₃×#336	C₂²	1	1	yes	characteristic
41	C₃×#336	C₂²	1	1	yes	characteristic
42	C₂×#500	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×#467	C₂×C₃	1	1	yes	characteristic
44	#2492	C₂×C₃	1	2	yes	—
45	#2036	C₂×C₃	1	2	yes	—
46	#2024	C₂×C₃	1	2	yes	complemented
47	#1969	C₂×C₃	1	1	yes	characteristic, complemented
48	#1969	C₂×C₃	1	1	yes	characteristic, complemented
49	#1928	C₂×C₃	1	2	yes	complemented
50	#1808	C₂×C₃	1	1	yes	characteristic
51	C₄×#107	C₂×C₃	1	1	yes	characteristic, complemented
52	C₈×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
53	C₂²×C₃×Q₈	—	2	2	no	—
54	C₂²×C₃×Q₈	C₂³	1	2	yes	—
55	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
56	C₂×C₃×Q₁₆	—	2	2	no	—
57	C₂×C₃×Q₁₆	—	2	2	no	—
58	C₂×C₃×Q₁₆	—	2	2	no	—
59	C₂²×C₃×C₈	—	2	2	no	—
60	C₂²×C₃×C₈	—	2	2	no	—
61	C₂²×C₃×C₈	—	2	2	no	—
62	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
66	C₃×C₄⋊Q₈	—	2	4	no	—
67	C₃×C₄⋊Q₈	—	4	2	no	—
68	C₃×C₂²⋊Q₈	—	2	4	no	—
69	C₃×C₂²⋊Q₈	—	4	2	no	—
70	C₂×C₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₃×C₄⋊C₄	—	2	2	no	—
72	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
78	C₂×C₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
79	C₂×C₃×C₄²	—	2	2	no	—
80	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
82	C₃×#107	—	2	2	no	—
83	C₃×#107	—	2	2	no	—
84	C₃×#107	—	2	4	no	—
85	C₃×#107	D₄	1	4	yes	—
86	C₃×#103	—	2	4	no	—
87	C₃×#103	—	2	4	no	—
88	C₃×#103	—	4	2	no	—
89	C₃×C₂²⋊C₈	—	2	2	no	—
90	C₃×C₄×C₈	—	2	2	no	—
91	C₃×C₄×C₈	—	2	2	no	—
92	C₃×#95	—	2	2	no	—
93	C₃×#95	—	2	2	no	—
94	C₃×#95	—	2	2	no	—
95	C₃×#95	—	2	2	no	—
96	C₃×#95	—	2	2	no	—
97	C₃×#95	—	2	2	no	—
98	C₃×#95	D₄	1	1	yes	characteristic
99	C₃×#95	D₄	1	1	yes	characteristic
100	C₂²×Q₁₆	C₂²×C₃	1	1	yes	characteristic
101	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
103	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
104	#500	—	2	4	no	—
105	#467	—	2	4	no	—
106	C₂×#107	C₂²×C₃	1	1	yes	characteristic
107	C₂×#107	C₂²×C₃	1	1	yes	characteristic
108	C₂×#107	C₂²×C₃	1	2	yes	—
109	C₂×#107	C₂²×C₃	1	1	yes	characteristic
110	C₂×#103	C₂²×C₃	1	2	yes	—
111	C₂×#103	C₂²×C₃	1	2	yes	—
112	C₂×#103	C₂²×C₃	1	2	yes	—
113	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
116	#400	—	2	2	no	—
117	#393	—	2	2	no	—
118	#391	—	2	2	no	—
119	#391	C₂²×C₃	1	2	yes	—
120	#391	C₂²×C₃	1	2	yes	—
121	#388	—	2	2	no	—
122	#380	C₂²×C₃	1	2	yes	—
123	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
124	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	#340	C₂²×C₃	1	2	yes	—
126	#340	C₂²×C₃	1	2	yes	—
127	#336	C₂²×C₃	1	1	yes	characteristic
128	#336	C₂²×C₃	1	1	yes	characteristic
129	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃×Q₈	—	2	2	no	—
131	C₂×C₃×Q₈	—	2	2	no	—
132	C₂×C₃×Q₈	—	2	2	no	—
133	C₂×C₃×Q₈	—	2	2	no	—
134	C₂×C₃×Q₈	—	2	2	no	—
135	C₂×C₃×Q₈	—	2	2	no	—
136	C₂×C₃×Q₈	—	4	4	no	—
137	C₂×C₃×Q₈	—	4	4	no	—
138	C₂×C₃×Q₈	—	8	2	no	—
139	C₂²×C₃×C₄	—	2	2	no	—
140	C₂²×C₃×C₄	—	2	1	no	—
141	C₂²×C₃×C₄	—	2	1	no	—
142	C₂²×C₃×C₄	—	2	1	no	—
143	C₂²×C₃×C₄	—	2	1	no	—
144	C₂²×C₃×C₄	—	2	1	no	—
145	C₂²×C₃×C₄	—	2	1	no	—
146	C₂²×C₃×C₄	—	2	2	no	—
147	C₂²×C₃×C₄	—	2	2	no	—
148	C₂²×C₃×C₄	—	2	2	no	—
149	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
155	C₃×Q₁₆	—	4	4	no	—
156	C₂×C₃×C₈	—	2	1	no	—
157	C₂×C₃×C₈	—	2	1	no	—
158	C₂×C₃×C₈	—	2	1	no	—
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	1	no	—
164	C₂×C₃×C₈	—	4	4	no	—
165	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
166	C₂×C₃×C₈	#41	1	2	yes	—
167	C₂×C₃×C₈	#41	1	2	yes	—
168	C₂×C₃×C₈	#41	1	2	yes	—
169	C₃×C₄⋊C₄	—	2	2	no	—
170	C₃×C₄⋊C₄	—	2	2	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄⋊C₄	—	2	2	no	—
173	C₃×C₄⋊C₄	—	2	2	no	—
174	C₃×C₄⋊C₄	—	4	4	no	—
175	C₃×C₄⋊C₄	—	4	4	no	—
176	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
177	C₃×C₂²⋊C₄	—	2	2	no	—
178	C₃×C₂²⋊C₄	—	4	4	no	—
179	C₃×C₂²⋊C₄	—	8	2	no	—
180	C₃×C₂²⋊C₄	Q₁₆	1	4	yes	complemented
181	C₃×C₄²	—	2	1	no	—
182	C₃×C₄²	—	2	1	no	—
183	C₃×C₄²	—	2	1	no	—
184	C₃×C₄²	—	2	1	no	—
185	C₃×C₄²	—	8	2	no	—
186	C₂²×Q₈	—	2	2	no	—
187	C₂²×Q₈	C₂³×C₃	1	2	yes	—
188	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
189	C₂×Q₁₆	—	2	2	no	—
190	C₂×Q₁₆	—	2	2	no	—
191	C₂×Q₁₆	—	2	2	no	—
192	C₂²×C₈	—	2	2	no	—
193	C₂²×C₈	—	2	2	no	—
194	C₂²×C₈	—	2	2	no	—
195	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
196	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
197	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
198	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
199	C₄⋊Q₈	—	2	4	no	—
200	C₄⋊Q₈	—	4	2	no	—
201	C₂²⋊Q₈	—	2	4	no	—
202	C₂²⋊Q₈	—	4	2	no	—
203	C₂×C₄⋊C₄	—	2	2	no	—
204	C₂×C₄⋊C₄	—	2	2	no	—
205	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
206	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
207	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
208	C₂×C₂²⋊C₄	—	2	2	no	—
209	C₂×C₂²⋊C₄	—	2	2	no	—
210	C₂×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
211	C₂×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
212	C₂×C₄²	—	2	2	no	—
213	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
214	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
215	#107	—	2	2	no	—
216	#107	—	2	2	no	—
217	#107	—	2	4	no	—
218	#107	C₃×D₄	1	4	yes	—
219	#103	—	2	4	no	—
220	#103	—	2	4	no	—
221	#103	—	4	2	no	—
222	C₂²⋊C₈	—	2	2	no	—
223	C₄×C₈	—	2	2	no	—
224	C₄×C₈	—	2	2	no	—
225	#95	—	2	2	no	—
226	#95	—	2	2	no	—
227	#95	—	2	2	no	—
228	#95	—	2	2	no	—
229	#95	—	2	2	no	—
230	#95	—	2	2	no	—
231	#95	C₃×D₄	1	1	yes	characteristic
232	#95	C₃×D₄	1	1	yes	characteristic
233	C₂³×C₃	—	2	1	no	—
234	C₂³×C₃	—	2	1	no	—
235	C₂³×C₃	—	2	1	no	—
236	C₂³×C₃	—	2	1	no	—
237	C₂³×C₃	—	2	1	no	—
238	C₂³×C₃	—	2	1	no	—
239	C₂³×C₃	C₂×Q₁₆	1	2	yes	—
240	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
241	C₃×Q₈	—	4	2	no	—
242	C₃×Q₈	—	4	2	no	—
243	C₃×Q₈	—	4	2	no	—
244	C₃×Q₈	—	4	2	no	—
245	C₃×Q₈	—	8	8	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	4	2	no	—
260	C₂×C₃×C₄	—	4	2	no	—
261	C₂×C₃×C₄	—	4	1	no	—
262	C₂×C₃×C₄	—	4	1	no	—
263	C₂×C₃×C₄	—	4	1	no	—
264	C₂×C₃×C₄	—	4	1	no	—
265	C₂×C₃×C₄	—	4	2	no	—
266	C₂×C₃×C₄	—	4	2	no	—
267	C₂×C₃×C₄	—	4	2	no	—
268	C₂×C₃×C₄	—	4	2	no	—
269	C₂×C₃×C₄	—	4	2	no	—
270	C₂×C₃×C₄	—	4	2	no	—
271	C₂×C₃×C₄	—	4	2	no	—
272	C₂×C₃×C₄	—	4	2	no	—
273	C₂×C₃×C₄	—	4	2	no	—
274	C₂×C₃×C₄	C₂×Q₁₆	1	2	yes	—
275	C₂×C₃×C₄	C₂×Q₁₆	1	2	yes	—
276	C₂×C₃×C₄	#135	1	2	yes	—
277	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
281	C₂×C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
282	C₂×C₃×C₄	2₋¹⁺⁴	1	1	yes	characteristic
283	C₃×C₈	—	2	2	no	—
284	C₃×C₈	—	4	1	no	—
285	C₃×C₈	—	4	1	no	—
286	C₃×C₈	#124	1	4	yes	—
287	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	4	4	no	—
295	C₂×Q₈	—	4	4	no	—
296	C₂×Q₈	—	8	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
312	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
313	Q₁₆	—	4	4	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
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	—	4	4	no	—
323	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
324	C₂×C₈	C₃×#41	1	2	yes	—
325	C₂×C₈	C₃×#41	1	2	yes	—
326	C₂×C₈	C₃×#41	1	2	yes	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	4	no	—
333	C₄⋊C₄	—	4	4	no	—
334	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	4	4	no	—
337	C₂²⋊C₄	—	8	2	no	—
338	C₂²⋊C₄	C₃×Q₁₆	1	4	yes	complemented
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	8	2	no	—
344	C₂²×C₃	—	2	2	no	—
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	4	1	no	—
348	C₂²×C₃	—	4	1	no	—
349	C₂²×C₃	—	4	1	no	—
350	C₂²×C₃	—	4	1	no	—
351	C₂²×C₃	#532	1	1	yes	characteristic
352	C₂²×C₃	D₄²	1	1	yes	characteristic
353	C₂²×C₃	#547	1	1	yes	characteristic
354	C₂²×C₃	C₂²×Q₁₆	1	1	yes	characteristic
355	C₂²×C₃	C₂×#135	1	1	yes	characteristic
356	C₂²×C₃	#576	1	1	yes	characteristic
357	C₂²×C₃	#578	1	1	yes	characteristic
358	C₃×C₄	—	2	2	no	—
359	C₃×C₄	—	2	2	no	—
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	4	1	no	—
362	C₃×C₄	—	4	1	no	—
363	C₃×C₄	—	4	4	no	—
364	C₃×C₄	—	8	2	no	—
365	C₃×C₄	—	8	2	no	—
366	C₃×C₄	—	8	2	no	—
367	C₃×C₄	C₂×#124	1	1	yes	characteristic
368	C₃×C₄	#542	1	1	yes	characteristic
369	C₃×C₄	#548	1	1	yes	characteristic
370	C₃×C₄	#555	1	1	yes	characteristic
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	C₂×C₃×Q₁₆	1	2	yes	—
378	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	8	8	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	C₂×C₃×Q₁₆	1	2	yes	—
413	C₂×C₄	C₂×C₃×Q₁₆	1	2	yes	—
414	C₂×C₄	C₃×#135	1	2	yes	—
415	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
416	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
417	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
418	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
419	C₂×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
421	C₈	—	2	2	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	1	no	—
424	C₈	C₃×#124	1	4	yes	—
425	C₂×C₃	—	4	2	no	—
426	C₂×C₃	#2491	1	1	yes	characteristic
427	C₂×C₃	#3170	1	1	yes	characteristic
428	C₂×C₃	#3175	1	1	yes	characteristic
429	C₂×C₃	#3280	1	1	yes	characteristic
430	C₂×C₃	D₄×Q₁₆	1	1	yes	characteristic
431	C₂×C₃	#3338	1	1	yes	characteristic
432	C₂×C₃	#3342	1	1	yes	characteristic
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	C₃×#532	1	1	yes	characteristic
441	C₂²	C₃×D₄²	1	1	yes	characteristic
442	C₂²	C₃×#547	1	1	yes	characteristic
443	C₂²	C₂²×C₃×Q₁₆	1	1	yes	characteristic
444	C₂²	C₂×C₃×#135	1	1	yes	characteristic
445	C₂²	C₃×#576	1	1	yes	characteristic
446	C₂²	C₃×#578	1	1	yes	characteristic
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	4	no	—
452	C₄	—	4	1	no	—
453	C₄	—	8	2	no	—
454	C₄	—	8	2	no	—
455	C₄	—	8	2	no	—
456	C₄	C₂×C₃×#124	1	1	yes	characteristic
457	C₄	C₃×#542	1	1	yes	characteristic
458	C₄	C₃×#548	1	1	yes	characteristic
459	C₄	C₃×#555	1	1	yes	characteristic
460	C₃	#27792	1	1	yes	characteristic, direct product factor, Sylow
461	C₂	—	4	2	no	—
462	C₂	C₃×#2491	1	1	yes	characteristic
463	C₂	C₃×#3170	1	1	yes	characteristic
464	C₂	C₃×#3175	1	1	yes	characteristic
465	C₂	C₃×#3280	1	1	yes	characteristic
466	C₂	C₃×D₄×Q₁₆	1	1	yes	characteristic
467	C₂	C₃×#3338	1	1	yes	characteristic
468	C₂	C₃×#3342	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#500	C₂	semidirect
5. C₃×#2024	C₂	semidirect
6. C₃×#1969	C₂	semidirect
7. C₃×#1969	C₂	semidirect
8. C₃×#1928	C₂	semidirect
10. C₃×C₄×#107	C₂	semidirect
12. #27792	C₃	direct (N × H)
42. C₂×#500	C₂×C₃	semidirect
46. #2024	C₂×C₃	semidirect
47. #1969	C₂×C₃	semidirect
48. #1969	C₂×C₃	semidirect
49. #1928	C₂×C₃	semidirect
51. C₄×#107	C₂×C₃	semidirect
180. C₃×C₂²⋊C₄	Q₁₆	semidirect
338. C₂²⋊C₄	C₃×Q₁₆	semidirect
460. C₃	#27792	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×#500	2
C₂×C₃×#467	2
C₃×#2492	2
C₃×#2036	2
C₃×#2024	2
C₃×#1969	2
C₃×#1928	2
C₃×#1808	2
C₃×C₄×#107	2
C₃×C₈×C₂²⋊C₄	2
#27792	3

Subgroups — C3×#27792 #10646399

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#27792 #10646399