Subgroups — C₃×#24674 #10643281

Order 768.

796 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2052	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2051	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2019	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2018	C₂	1	1	yes	maximal, characteristic
9	C₃×#1978	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#1977	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#1967	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#1931	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#1800	C₂	1	1	yes	maximal, characteristic, complemented
16	#24674	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×C₃×#137	C₂²	1	1	yes	characteristic
18	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₃×D₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×#124	C₂²	1	1	yes	characteristic
23	C₃×C₄×#41	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
25	C₃×#464	—	2	1	no	—
26	C₃×#464	—	2	1	no	—
27	C₃×#463	—	2	1	no	—
28	C₃×#463	—	2	1	no	—
29	C₃×#463	—	2	1	no	—
30	C₃×#463	—	2	1	no	—
31	C₃×#463	—	2	1	no	—
32	C₃×#463	—	2	1	no	—
33	C₃×#442	—	2	1	no	—
34	C₃×#440	—	2	1	no	—
35	C₃×C₄×SD₁₆	—	2	1	no	—
36	C₃×C₄×D₈	—	2	1	no	—
37	C₃×#433	—	2	1	no	—
38	C₃×#433	—	2	1	no	—
39	C₃×#432	—	2	1	no	—
40	C₃×#431	—	2	1	no	—
41	C₂×C₃×#108	C₂²	1	1	yes	characteristic
42	C₂×C₃×#108	C₂²	1	1	yes	characteristic
43	C₃×#428	C₂²	1	1	yes	characteristic
44	C₃×#423	C₂²	1	1	yes	characteristic
45	C₃×#423	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₃×#419	C₂²	1	1	yes	characteristic
48	C₃×#418	C₂²	1	1	yes	characteristic
49	C₃×#418	C₂²	1	1	yes	characteristic
50	C₃×#417	C₂²	1	1	yes	characteristic
51	C₂×C₃×#103	C₂²	1	1	yes	characteristic
52	C₂×C₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₃×#101	C₂²	1	1	yes	characteristic
54	C₂×C₃×#101	C₂²	1	1	yes	characteristic
55	C₂×C₃×#100	C₂²	1	1	yes	characteristic
56	C₂×C₃×#100	C₂²	1	1	yes	characteristic
57	C₂×C₃×#100	C₂²	1	1	yes	characteristic
58	C₂×C₃×#100	C₂²	1	1	yes	characteristic
59	C₃×#408	C₂²	1	1	yes	characteristic
60	C₃×#408	C₂²	1	1	yes	characteristic
61	C₃×#405	C₂²	1	1	yes	characteristic
62	C₃×#405	C₂²	1	1	yes	characteristic
63	C₃×C₄×M₁₆	C₂²	1	1	yes	characteristic
64	C₃×#343	C₂²	1	1	yes	characteristic
65	C₃×#343	C₂²	1	1	yes	characteristic
66	C₃×#341	C₂²	1	1	yes	characteristic
67	C₃×#341	C₂²	1	1	yes	characteristic
68	#3040	C₂×C₃	1	1	yes	characteristic, complemented
69	C₂×#463	C₂×C₃	1	1	yes	characteristic, complemented
70	C₄×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
71	#2925	C₂×C₃	1	1	yes	characteristic, complemented
72	#2052	C₂×C₃	1	1	yes	characteristic, complemented
73	#2051	C₂×C₃	1	1	yes	characteristic, complemented
74	#2019	C₂×C₃	1	1	yes	characteristic, complemented
75	#2018	C₂×C₃	1	1	yes	characteristic
76	#1978	C₂×C₃	1	1	yes	characteristic, complemented
77	#1977	C₂×C₃	1	1	yes	characteristic, complemented
78	#1967	C₂×C₃	1	1	yes	characteristic, complemented
79	#1950	C₂×C₃	1	1	yes	characteristic, complemented
80	#1931	C₂×C₃	1	1	yes	characteristic, complemented
81	#1930	C₂×C₃	1	1	yes	characteristic, complemented
82	#1800	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂×C₃×#41	C₂³	1	1	yes	characteristic
84	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
85	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
86	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
87	C₂³×C₃×C₄	—	2	1	no	—
88	C₃×#137	—	4	1	no	—
89	C₃×#137	—	4	1	no	—
90	C₃×AGL(1,ℤ/8)	—	2	2	no	—
91	C₃×AGL(1,ℤ/8)	—	2	2	no	—
92	C₃×AGL(1,ℤ/8)	—	4	1	no	—
93	C₃×AGL(1,ℤ/8)	—	4	1	no	—
94	C₂×C₃×Q₁₆	—	2	1	no	—
95	C₂×C₃×SD₁₆	—	2	1	no	—
96	C₂×C₃×SD₁₆	—	2	1	no	—
97	C₂×C₃×SD₁₆	—	2	1	no	—
98	C₂×C₃×SD₁₆	—	2	2	no	—
99	C₂×C₃×SD₁₆	—	2	1	no	—
100	C₂×C₃×SD₁₆	—	2	1	no	—
101	C₂×C₃×SD₁₆	—	4	1	no	—
102	C₂×C₃×D₈	—	2	1	no	—
103	C₂×C₃×D₈	—	2	1	no	—
104	C₂×C₃×D₈	—	2	2	no	—
105	C₂×C₃×D₈	—	2	1	no	—
106	C₂×C₃×D₈	—	2	1	no	—
107	C₂×C₃×D₈	—	4	1	no	—
108	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
109	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
110	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
111	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
112	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
113	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
114	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
115	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
116	C₃×#124	—	2	1	no	—
117	C₃×#124	—	2	1	no	—
118	C₃×#124	—	2	1	no	—
119	C₃×#124	—	2	1	no	—
120	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
121	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
122	C₃×C₄×D₄	—	2	1	no	—
123	C₃×C₄×D₄	—	2	1	no	—
124	C₃×C₄×D₄	—	2	1	no	—
125	C₃×C₄×D₄	—	2	1	no	—
126	C₃×C₄×D₄	—	2	1	no	—
127	C₃×C₄×D₄	—	2	1	no	—
128	C₃×C₄×D₄	D₄	1	1	yes	characteristic
129	C₃×C₄×D₄	D₄	1	1	yes	characteristic
130	C₃×#117	—	2	1	no	—
131	C₃×#117	C₂³	1	1	yes	characteristic
132	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
134	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
135	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
136	C₂×C₃×C₄²	—	2	1	no	—
137	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
138	C₃×#108	—	4	1	no	—
139	C₃×#108	—	4	1	no	—
140	C₃×#107	—	2	1	no	—
141	C₃×#106	—	2	1	no	—
142	C₃×C₄⋊C₈	—	2	1	no	—
143	C₃×C₄⋊C₈	—	2	1	no	—
144	C₃×C₄⋊C₈	—	2	1	no	—
145	C₃×C₄⋊C₈	—	2	1	no	—
146	C₃×C₄⋊C₈	D₄	1	1	yes	characteristic
147	C₃×C₄⋊C₈	D₄	1	1	yes	characteristic
148	C₃×C₄⋊C₈	D₄	1	1	yes	characteristic
149	C₃×C₄⋊C₈	D₄	1	1	yes	characteristic
150	C₃×#103	—	2	1	no	—
151	C₃×#103	—	2	1	no	—
152	C₃×#103	—	2	1	no	—
153	C₃×#103	—	2	1	no	—
154	C₃×#103	—	2	1	no	—
155	C₃×#102	—	2	1	no	—
156	C₃×#102	—	2	1	no	—
157	C₃×#102	—	2	1	no	—
158	C₃×#102	—	2	1	no	—
159	C₃×#102	—	2	1	no	—
160	C₃×#102	—	2	1	no	—
161	C₃×#102	—	2	1	no	—
162	C₃×#101	—	2	2	no	—
163	C₃×#101	—	4	1	no	—
164	C₃×#100	—	2	2	no	—
165	C₃×#100	—	4	1	no	—
166	C₃×#100	—	4	1	no	—
167	C₃×#100	—	4	1	no	—
168	C₃×C₂²⋊C₈	—	2	1	no	—
169	C₃×C₂²⋊C₈	—	2	1	no	—
170	C₃×C₂²⋊C₈	—	2	1	no	—
171	C₃×C₂²⋊C₈	—	2	1	no	—
172	C₃×#97	—	2	1	no	—
173	C₃×#97	—	2	1	no	—
174	C₃×#97	—	2	1	no	—
175	C₃×C₄×C₈	—	2	1	no	—
176	C₃×C₄×C₈	—	2	1	no	—
177	C₃×C₄×C₈	—	2	1	no	—
178	C₂×#137	C₂²×C₃	1	1	yes	characteristic
179	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	1	yes	characteristic
180	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	1	yes	characteristic
181	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic
182	C₂²×D₈	C₂²×C₃	1	1	yes	characteristic
183	C₂×#124	C₂²×C₃	1	1	yes	characteristic
184	C₄×#41	C₂²×C₃	1	1	yes	characteristic
185	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
186	#464	—	2	1	no	—
187	#464	—	2	1	no	—
188	#463	—	2	1	no	—
189	#463	—	2	1	no	—
190	#463	—	2	1	no	—
191	#463	—	2	1	no	—
192	#463	—	2	1	no	—
193	#463	—	2	1	no	—
194	#442	—	2	1	no	—
195	#440	—	2	1	no	—
196	C₄×SD₁₆	—	2	1	no	—
197	C₄×D₈	—	2	1	no	—
198	#433	—	2	1	no	—
199	#433	—	2	1	no	—
200	#432	—	2	1	no	—
201	#431	—	2	1	no	—
202	C₂×#108	C₂²×C₃	1	1	yes	characteristic
203	C₂×#108	C₂²×C₃	1	1	yes	characteristic
204	#428	C₂²×C₃	1	1	yes	characteristic
205	#423	C₂²×C₃	1	1	yes	characteristic
206	#423	C₂²×C₃	1	1	yes	characteristic
207	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
208	#419	C₂²×C₃	1	1	yes	characteristic
209	#418	C₂²×C₃	1	1	yes	characteristic
210	#418	C₂²×C₃	1	1	yes	characteristic
211	#417	C₂²×C₃	1	1	yes	characteristic
212	C₂×#103	C₂²×C₃	1	1	yes	characteristic
213	C₂×#102	C₂²×C₃	1	1	yes	characteristic
214	C₂×#101	C₂²×C₃	1	1	yes	characteristic
215	C₂×#101	C₂²×C₃	1	1	yes	characteristic
216	C₂×#100	C₂²×C₃	1	1	yes	characteristic
217	C₂×#100	C₂²×C₃	1	1	yes	characteristic
218	C₂×#100	C₂²×C₃	1	1	yes	characteristic
219	C₂×#100	C₂²×C₃	1	1	yes	characteristic
220	#408	C₂²×C₃	1	1	yes	characteristic
221	#408	C₂²×C₃	1	1	yes	characteristic
222	#405	C₂²×C₃	1	1	yes	characteristic
223	#405	C₂²×C₃	1	1	yes	characteristic
224	C₄×M₁₆	C₂²×C₃	1	1	yes	characteristic
225	#343	C₂²×C₃	1	1	yes	characteristic
226	#343	C₂²×C₃	1	1	yes	characteristic
227	#341	C₂²×C₃	1	1	yes	characteristic
228	#341	C₂²×C₃	1	1	yes	characteristic
229	C₂⁴×C₃	—	2	1	no	—
230	C₂⁴×C₃	—	2	1	no	—
231	C₃×#41	—	2	1	no	—
232	C₃×#41	—	2	1	no	—
233	C₃×#41	—	2	1	no	—
234	C₃×#41	—	2	1	no	—
235	C₂×C₃×Q₈	—	2	1	no	—
236	C₂×C₃×Q₈	—	2	1	no	—
237	C₂×C₃×Q₈	—	2	1	no	—
238	C₂×C₃×Q₈	—	2	1	no	—
239	C₂×C₃×Q₈	—	2	1	no	—
240	C₂×C₃×Q₈	—	2	1	no	—
241	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
242	C₂×C₃×D₄	—	2	1	no	—
243	C₂×C₃×D₄	—	2	1	no	—
244	C₂×C₃×D₄	—	2	1	no	—
245	C₂×C₃×D₄	—	2	1	no	—
246	C₂×C₃×D₄	—	2	1	no	—
247	C₂×C₃×D₄	—	2	1	no	—
248	C₂×C₃×D₄	—	2	1	no	—
249	C₂×C₃×D₄	—	2	1	no	—
250	C₂×C₃×D₄	—	2	1	no	—
251	C₂×C₃×D₄	—	2	1	no	—
252	C₂×C₃×D₄	—	2	1	no	—
253	C₂×C₃×D₄	—	2	1	no	—
254	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
255	C₂×C₃×D₄	#41	1	2	yes	—
256	C₂²×C₃×C₄	—	2	1	no	—
257	C₂²×C₃×C₄	—	2	1	no	—
258	C₂²×C₃×C₄	—	2	1	no	—
259	C₂²×C₃×C₄	—	2	1	no	—
260	C₂²×C₃×C₄	—	2	1	no	—
261	C₂²×C₃×C₄	—	4	1	no	—
262	C₂²×C₃×C₄	—	4	1	no	—
263	C₂²×C₃×C₄	—	8	2	no	—
264	C₂²×C₃×C₄	#41	1	1	yes	characteristic
265	C₂²×C₃×C₄	#41	1	1	yes	characteristic
266	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
267	C₃×Q₁₆	—	4	2	no	—
268	C₃×SD₁₆	—	2	4	no	—
269	C₃×SD₁₆	—	4	2	no	—
270	C₃×SD₁₆	—	4	2	no	—
271	C₃×SD₁₆	—	4	2	no	—
272	C₃×SD₁₆	—	4	2	no	—
273	C₃×D₈	—	2	4	no	—
274	C₃×D₈	—	4	2	no	—
275	C₃×D₈	—	4	2	no	—
276	C₃×D₈	—	4	2	no	—
277	C₃×M₁₆	—	2	1	no	—
278	C₃×M₁₆	—	2	1	no	—
279	C₃×M₁₆	—	2	1	no	—
280	C₃×M₁₆	—	2	1	no	—
281	C₃×M₁₆	—	2	1	no	—
282	C₃×M₁₆	—	2	1	no	—
283	C₃×M₁₆	—	2	1	no	—
284	C₃×M₁₆	—	2	1	no	—
285	C₃×M₁₆	—	2	1	no	—
286	C₃×M₁₆	—	2	1	no	—
287	C₃×M₁₆	—	2	1	no	—
288	C₃×M₁₆	#41	1	2	yes	—
289	C₂×C₃×C₈	—	2	1	no	—
290	C₂×C₃×C₈	—	2	1	no	—
291	C₂×C₃×C₈	—	2	1	no	—
292	C₂×C₃×C₈	—	2	1	no	—
293	C₂×C₃×C₈	—	2	1	no	—
294	C₂×C₃×C₈	—	2	1	no	—
295	C₂×C₃×C₈	—	2	1	no	—
296	C₂×C₃×C₈	—	2	1	no	—
297	C₂×C₃×C₈	—	2	1	no	—
298	C₂×C₃×C₈	—	2	1	no	—
299	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
300	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
301	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
302	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
303	C₃×C₄⋊C₄	—	2	1	no	—
304	C₃×C₄⋊C₄	—	2	1	no	—
305	C₃×C₄⋊C₄	—	2	1	no	—
306	C₃×C₄⋊C₄	—	2	1	no	—
307	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
308	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
309	C₃×C₂²⋊C₄	—	2	1	no	—
310	C₃×C₂²⋊C₄	—	2	1	no	—
311	C₃×C₂²⋊C₄	—	2	1	no	—
312	C₃×C₂²⋊C₄	—	4	1	no	—
313	C₃×C₂²⋊C₄	—	4	1	no	—
314	C₃×C₂²⋊C₄	—	4	1	no	—
315	C₃×C₂²⋊C₄	—	4	1	no	—
316	C₃×C₂²⋊C₄	—	4	1	no	—
317	C₃×C₂²⋊C₄	—	4	1	no	—
318	C₃×C₄²	—	2	1	no	—
319	C₃×C₄²	—	2	1	no	—
320	C₃×C₄²	—	2	1	no	—
321	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
322	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
323	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
324	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
325	C₂×#41	C₂³×C₃	1	1	yes	characteristic
326	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
327	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
328	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
329	C₂³×C₄	—	2	1	no	—
330	#137	—	4	1	no	—
331	#137	—	4	1	no	—
332	AGL(1,ℤ/8)	—	2	2	no	—
333	AGL(1,ℤ/8)	—	2	2	no	—
334	AGL(1,ℤ/8)	—	4	1	no	—
335	AGL(1,ℤ/8)	—	4	1	no	—
336	C₂×Q₁₆	—	2	1	no	—
337	C₂×SD₁₆	—	2	1	no	—
338	C₂×SD₁₆	—	2	1	no	—
339	C₂×SD₁₆	—	2	1	no	—
340	C₂×SD₁₆	—	2	2	no	—
341	C₂×SD₁₆	—	2	1	no	—
342	C₂×SD₁₆	—	2	1	no	—
343	C₂×SD₁₆	—	4	1	no	—
344	C₂×D₈	—	2	1	no	—
345	C₂×D₈	—	2	1	no	—
346	C₂×D₈	—	2	2	no	—
347	C₂×D₈	—	2	1	no	—
348	C₂×D₈	—	2	1	no	—
349	C₂×D₈	—	4	1	no	—
350	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
351	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
352	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
353	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
354	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
355	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
356	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
357	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
358	#124	—	2	1	no	—
359	#124	—	2	1	no	—
360	#124	—	2	1	no	—
361	#124	—	2	1	no	—
362	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
363	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	C₃×D₄	1	1	yes	characteristic
371	C₄×D₄	C₃×D₄	1	1	yes	characteristic
372	#117	—	2	1	no	—
373	#117	C₂³×C₃	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
380	#108	—	4	1	no	—
381	#108	—	4	1	no	—
382	#107	—	2	1	no	—
383	#106	—	2	1	no	—
384	C₄⋊C₈	—	2	1	no	—
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	C₃×D₄	1	1	yes	characteristic
389	C₄⋊C₈	C₃×D₄	1	1	yes	characteristic
390	C₄⋊C₈	C₃×D₄	1	1	yes	characteristic
391	C₄⋊C₈	C₃×D₄	1	1	yes	characteristic
392	#103	—	2	1	no	—
393	#103	—	2	1	no	—
394	#103	—	2	1	no	—
395	#103	—	2	1	no	—
396	#103	—	2	1	no	—
397	#102	—	2	1	no	—
398	#102	—	2	1	no	—
399	#102	—	2	1	no	—
400	#102	—	2	1	no	—
401	#102	—	2	1	no	—
402	#102	—	2	1	no	—
403	#102	—	2	1	no	—
404	#101	—	2	2	no	—
405	#101	—	4	1	no	—
406	#100	—	2	2	no	—
407	#100	—	4	1	no	—
408	#100	—	4	1	no	—
409	#100	—	4	1	no	—
410	C₂²⋊C₈	—	2	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	2	1	no	—
414	#97	—	2	1	no	—
415	#97	—	2	1	no	—
416	#97	—	2	1	no	—
417	C₄×C₈	—	2	1	no	—
418	C₄×C₈	—	2	1	no	—
419	C₄×C₈	—	2	1	no	—
420	C₂³×C₃	—	2	1	no	—
421	C₂³×C₃	—	2	2	no	—
422	C₂³×C₃	—	4	1	no	—
423	C₂³×C₃	—	4	1	no	—
424	C₂³×C₃	—	4	1	no	—
425	C₂³×C₃	—	4	1	no	—
426	C₂³×C₃	—	4	1	no	—
427	C₂³×C₃	—	8	1	no	—
428	C₂³×C₃	—	8	1	no	—
429	C₂³×C₃	—	8	1	no	—
430	C₂³×C₃	—	8	1	no	—
431	C₂³×C₃	C₂×#41	1	1	yes	characteristic
432	C₃×Q₈	—	2	1	no	—
433	C₃×Q₈	—	2	1	no	—
434	C₃×Q₈	—	4	1	no	—
435	C₃×Q₈	—	4	1	no	—
436	C₃×Q₈	—	4	1	no	—
437	C₃×Q₈	—	4	1	no	—
438	C₃×D₄	—	2	1	no	—
439	C₃×D₄	—	2	2	no	—
440	C₃×D₄	—	2	1	no	—
441	C₃×D₄	—	2	2	no	—
442	C₃×D₄	—	4	1	no	—
443	C₃×D₄	—	4	1	no	—
444	C₃×D₄	—	4	1	no	—
445	C₃×D₄	—	4	1	no	—
446	C₃×D₄	—	4	1	no	—
447	C₃×D₄	—	4	1	no	—
448	C₃×D₄	—	4	1	no	—
449	C₃×D₄	—	4	1	no	—
450	C₂×C₃×C₄	—	2	1	no	—
451	C₂×C₃×C₄	—	2	1	no	—
452	C₂×C₃×C₄	—	2	1	no	—
453	C₂×C₃×C₄	—	4	1	no	—
454	C₂×C₃×C₄	—	4	1	no	—
455	C₂×C₃×C₄	—	4	2	no	—
456	C₂×C₃×C₄	—	4	1	no	—
457	C₂×C₃×C₄	—	4	1	no	—
458	C₂×C₃×C₄	—	4	1	no	—
459	C₂×C₃×C₄	—	4	1	no	—
460	C₂×C₃×C₄	—	4	1	no	—
461	C₂×C₃×C₄	—	4	1	no	—
462	C₂×C₃×C₄	—	8	1	no	—
463	C₂×C₃×C₄	—	8	2	no	—
464	C₂×C₃×C₄	—	8	2	no	—
465	C₂×C₃×C₄	—	8	1	no	—
466	C₂×C₃×C₄	#121	1	1	yes	characteristic
467	C₂×C₃×C₄	#121	1	1	yes	characteristic
468	C₂×C₃×C₄	#121	1	1	yes	characteristic
469	C₂×C₃×C₄	#121	1	1	yes	characteristic
470	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
473	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
474	C₂×C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
475	C₂×C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
476	C₃×C₈	—	2	2	no	—
477	C₃×C₈	—	2	1	no	—
478	C₃×C₈	—	2	1	no	—
479	C₃×C₈	—	2	1	no	—
480	C₃×C₈	—	2	1	no	—
481	C₃×C₈	—	4	1	no	—
482	C₃×C₈	—	4	1	no	—
483	C₃×C₈	—	4	1	no	—
484	C₃×C₈	—	4	1	no	—
485	C₃×C₈	—	4	1	no	—
486	C₂⁴	—	2	1	no	—
487	C₂⁴	—	2	1	no	—
488	#41	—	2	1	no	—
489	#41	—	2	1	no	—
490	#41	—	2	1	no	—
491	#41	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
512	C₂×D₄	C₃×#41	1	2	yes	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	4	1	no	—
519	C₂²×C₄	—	4	1	no	—
520	C₂²×C₄	—	8	2	no	—
521	C₂²×C₄	C₃×#41	1	1	yes	characteristic
522	C₂²×C₄	C₃×#41	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
524	Q₁₆	—	4	2	no	—
525	SD₁₆	—	2	4	no	—
526	SD₁₆	—	4	2	no	—
527	SD₁₆	—	4	2	no	—
528	SD₁₆	—	4	2	no	—
529	SD₁₆	—	4	2	no	—
530	D₈	—	2	4	no	—
531	D₈	—	4	2	no	—
532	D₈	—	4	2	no	—
533	D₈	—	4	2	no	—
534	M₁₆	—	2	1	no	—
535	M₁₆	—	2	1	no	—
536	M₁₆	—	2	1	no	—
537	M₁₆	—	2	1	no	—
538	M₁₆	—	2	1	no	—
539	M₁₆	—	2	1	no	—
540	M₁₆	—	2	1	no	—
541	M₁₆	—	2	1	no	—
542	M₁₆	—	2	1	no	—
543	M₁₆	—	2	1	no	—
544	M₁₆	—	2	1	no	—
545	M₁₆	C₃×#41	1	2	yes	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
557	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
558	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
559	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
565	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
566	C₂²⋊C₄	—	2	1	no	—
567	C₂²⋊C₄	—	2	1	no	—
568	C₂²⋊C₄	—	2	1	no	—
569	C₂²⋊C₄	—	4	1	no	—
570	C₂²⋊C₄	—	4	1	no	—
571	C₂²⋊C₄	—	4	1	no	—
572	C₂²⋊C₄	—	4	1	no	—
573	C₂²⋊C₄	—	4	1	no	—
574	C₂²⋊C₄	—	4	1	no	—
575	C₄²	—	2	1	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
579	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
580	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
581	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
582	C₂²×C₃	—	2	1	no	—
583	C₂²×C₃	—	2	1	no	—
584	C₂²×C₃	—	4	1	no	—
585	C₂²×C₃	—	4	2	no	—
586	C₂²×C₃	—	4	1	no	—
587	C₂²×C₃	—	4	1	no	—
588	C₂²×C₃	—	8	2	no	—
589	C₂²×C₃	—	8	2	no	—
590	C₂²×C₃	—	8	1	no	—
591	C₂²×C₃	—	8	1	no	—
592	C₂²×C₃	—	8	1	no	—
593	C₂²×C₃	—	8	1	no	—
594	C₂²×C₃	—	8	1	no	—
595	C₂²×C₃	—	16	1	no	—
596	C₂²×C₃	—	16	1	no	—
597	C₂²×C₃	C₂×#121	1	1	yes	characteristic
598	C₂²×C₃	#553	1	1	yes	characteristic
599	C₂²×C₃	#555	1	1	yes	characteristic
600	C₃×C₄	—	2	1	no	—
601	C₃×C₄	—	2	1	no	—
602	C₃×C₄	—	2	1	no	—
603	C₃×C₄	—	2	1	no	—
604	C₃×C₄	—	4	1	no	—
605	C₃×C₄	—	4	1	no	—
606	C₃×C₄	—	4	1	no	—
607	C₃×C₄	—	8	1	no	—
608	C₃×C₄	—	8	1	no	—
609	C₃×C₄	#525	1	1	yes	characteristic
610	C₃×C₄	#535	1	1	yes	characteristic
611	C₃×C₄	#546	1	1	yes	characteristic
612	C₃×C₄	#550	1	1	yes	characteristic
613	C₂³	—	2	1	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	no	—
620	C₂³	—	8	1	no	—
621	C₂³	—	8	1	no	—
622	C₂³	—	8	1	no	—
623	C₂³	—	8	1	no	—
624	C₂³	C₂×C₃×#41	1	1	yes	characteristic
625	Q₈	—	2	1	no	—
626	Q₈	—	2	1	no	—
627	Q₈	—	4	1	no	—
628	Q₈	—	4	1	no	—
629	Q₈	—	4	1	no	—
630	Q₈	—	4	1	no	—
631	D₄	—	2	1	no	—
632	D₄	—	2	2	no	—
633	D₄	—	2	1	no	—
634	D₄	—	2	2	no	—
635	D₄	—	4	1	no	—
636	D₄	—	4	1	no	—
637	D₄	—	4	1	no	—
638	D₄	—	4	1	no	—
639	D₄	—	4	1	no	—
640	D₄	—	4	1	no	—
641	D₄	—	4	1	no	—
642	D₄	—	4	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	2	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	8	1	no	—
656	C₂×C₄	—	8	2	no	—
657	C₂×C₄	—	8	2	no	—
658	C₂×C₄	—	8	1	no	—
659	C₂×C₄	C₃×#121	1	1	yes	characteristic
660	C₂×C₄	C₃×#121	1	1	yes	characteristic
661	C₂×C₄	C₃×#121	1	1	yes	characteristic
662	C₂×C₄	C₃×#121	1	1	yes	characteristic
663	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
664	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
665	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
666	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
667	C₂×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
668	C₂×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
669	C₈	—	2	2	no	—
670	C₈	—	2	1	no	—
671	C₈	—	2	1	no	—
672	C₈	—	2	1	no	—
673	C₈	—	2	1	no	—
674	C₈	—	4	1	no	—
675	C₈	—	4	1	no	—
676	C₈	—	4	1	no	—
677	C₈	—	4	1	no	—
678	C₈	—	4	1	no	—
679	C₂×C₃	—	2	1	no	—
680	C₂×C₃	—	2	1	no	—
681	C₂×C₃	—	8	1	no	—
682	C₂×C₃	—	8	2	no	—
683	C₂×C₃	—	16	1	no	—
684	C₂×C₃	#2414	1	1	yes	characteristic
685	C₂×C₃	#3067	1	1	yes	characteristic
686	C₂×C₃	#3068	1	1	yes	characteristic
687	C₂²	—	2	1	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	8	2	no	—
694	C₂²	—	8	2	no	—
695	C₂²	—	8	1	no	—
696	C₂²	—	8	1	no	—
697	C₂²	—	8	1	no	—
698	C₂²	—	8	1	no	—
699	C₂²	—	8	1	no	—
700	C₂²	—	16	1	no	—
701	C₂²	—	16	1	no	—
702	C₂²	C₂×C₃×#121	1	1	yes	characteristic
703	C₂²	C₃×#553	1	1	yes	characteristic
704	C₂²	C₃×#555	1	1	yes	characteristic
705	C₄	—	2	1	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	1	no	—
712	C₄	—	8	1	no	—
713	C₄	—	8	1	no	—
714	C₄	C₃×#525	1	1	yes	characteristic
715	C₄	C₃×#535	1	1	yes	characteristic
716	C₄	C₃×#546	1	1	yes	characteristic
717	C₄	C₃×#550	1	1	yes	characteristic
718	C₃	#24674	1	1	yes	characteristic, direct product factor, Sylow
719	C₂	—	2	1	no	—
720	C₂	—	2	1	no	—
721	C₂	—	8	1	no	—
722	C₂	—	8	2	no	—
723	C₂	—	16	1	no	—
724	C₂	C₃×#2414	1	1	yes	characteristic
725	C₂	C₃×#3067	1	1	yes	characteristic
726	C₂	C₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
prime radical	C₃×#2018	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3040	C₂	semidirect
2. C₂×C₃×#463	C₂	semidirect
3. C₃×C₄×AGL(1,ℤ/8)	C₂	semidirect
4. C₃×#2925	C₂	semidirect
5. C₃×#2052	C₂	semidirect
6. C₃×#2051	C₂	semidirect
7. C₃×#2019	C₂	semidirect
9. C₃×#1978	C₂	semidirect
10. C₃×#1977	C₂	semidirect
11. C₃×#1967	C₂	semidirect
12. C₃×#1950	C₂	semidirect
13. C₃×#1931	C₂	semidirect
14. C₃×#1930	C₂	semidirect
15. C₃×#1800	C₂	semidirect
16. #24674	C₃	direct (N × H)
68. #3040	C₂×C₃	semidirect
69. C₂×#463	C₂×C₃	semidirect
70. C₄×AGL(1,ℤ/8)	C₂×C₃	semidirect
71. #2925	C₂×C₃	semidirect
72. #2052	C₂×C₃	semidirect
73. #2051	C₂×C₃	semidirect
74. #2019	C₂×C₃	semidirect
76. #1978	C₂×C₃	semidirect
77. #1977	C₂×C₃	semidirect
78. #1967	C₂×C₃	semidirect
79. #1950	C₂×C₃	semidirect
80. #1931	C₂×C₃	semidirect
81. #1930	C₂×C₃	semidirect
82. #1800	C₂×C₃	semidirect
718. C₃	#24674	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3040	2
C₂×C₃×#463	2
C₃×C₄×AGL(1,ℤ/8)	2
C₃×#2925	2
C₃×#2052	2
C₃×#2051	2
C₃×#2019	2
C₃×#2018	2
C₃×#1978	2
C₃×#1977	2
C₃×#1967	2
C₃×#1950	2
C₃×#1931	2
C₃×#1930	2
C₃×#1800	2
#24674	3

Subgroups — C3×#24674 #10643281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#24674 #10643281