Subgroups — C₃×#25984 #10644591

Order 768.

876 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3083	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2897	C₂	1	1	yes	maximal, characteristic
4	C₃×#2897	C₂	1	1	yes	maximal, characteristic
5	C₃×#2092	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2027	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#1866	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#1866	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#1860	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#1860	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#1816	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#1815	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#1792	C₂	1	1	yes	maximal, characteristic
16	#25984	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×C₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
18	C₂×C₃×#131	C₂²	1	1	yes	characteristic
19	C₂×C₃×#131	C₂²	1	1	yes	characteristic
20	C₃×#544	C₂²	1	1	yes	characteristic, complemented
21	C₃×#520	C₂²	1	1	yes	characteristic
22	C₃×#520	C₂²	1	1	yes	characteristic
23	C₃×#479	—	2	1	no	—
24	C₃×#479	—	2	1	no	—
25	C₃×#478	—	2	1	no	—
26	C₃×#478	—	2	1	no	—
27	C₃×#477	—	2	1	no	—
28	C₃×#476	—	2	1	no	—
29	C₃×#475	—	2	1	no	—
30	C₃×#474	—	2	1	no	—
31	C₂×C₃×#108	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×#108	C₂²	1	1	yes	characteristic, complemented
33	C₃×#428	C₂²	1	1	yes	characteristic, complemented
34	C₃×#428	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×#107	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×#106	C₂²	1	1	yes	characteristic, complemented
37	C₃×#424	C₂²	1	1	yes	characteristic, complemented
38	C₃×#424	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×#104	C₂²	1	1	yes	characteristic
40	C₂×C₃×#104	C₂²	1	1	yes	characteristic
41	C₃×#418	—	2	1	no	—
42	C₃×#418	—	2	1	no	—
43	C₃×#418	C₂²	1	1	yes	characteristic
44	C₃×#418	C₂²	1	1	yes	characteristic
45	C₃×#417	—	2	1	no	—
46	C₃×#417	—	2	1	no	—
47	C₃×#417	C₂²	1	1	yes	characteristic
48	C₃×#417	C₂²	1	1	yes	characteristic
49	C₃×#417	C₂²	1	1	yes	characteristic
50	C₃×#417	C₂²	1	1	yes	characteristic
51	C₃×#416	—	2	1	no	—
52	C₃×#416	—	2	1	no	—
53	C₃×#416	C₂²	1	1	yes	characteristic
54	C₃×#416	C₂²	1	1	yes	characteristic
55	C₂×C₃×#102	—	2	1	no	—
56	C₂×C₃×#102	—	2	1	no	—
57	C₂×C₃×#102	C₂²	1	1	yes	characteristic
58	C₂×C₃×#102	C₂²	1	1	yes	characteristic
59	C₂×C₃×#100	C₂²	1	1	yes	characteristic
60	C₃×#390	C₂²	1	1	yes	characteristic
61	C₃×#382	C₂²	1	1	yes	characteristic, complemented
62	C₃×#343	C₂²	1	1	yes	characteristic, complemented
63	C₃×#343	C₂²	1	1	yes	characteristic, complemented
64	C₃×#343	C₂²	1	1	yes	characteristic, complemented
65	C₃×#339	C₂²	1	1	yes	characteristic, complemented
66	C₃×#339	C₂²	1	1	yes	characteristic, complemented
67	C₃×#336	C₂²	1	1	yes	characteristic, complemented
68	#3084	C₂×C₃	1	1	yes	characteristic, complemented
69	#3083	C₂×C₃	1	1	yes	characteristic, complemented
70	#2897	C₂×C₃	1	1	yes	characteristic
71	#2897	C₂×C₃	1	1	yes	characteristic
72	#2092	C₂×C₃	1	1	yes	characteristic, complemented
73	#2063	C₂×C₃	1	1	yes	characteristic, complemented
74	#2063	C₂×C₃	1	1	yes	characteristic, complemented
75	#2027	C₂×C₃	1	1	yes	characteristic, complemented
76	#1866	C₂×C₃	1	1	yes	characteristic, complemented
77	#1866	C₂×C₃	1	1	yes	characteristic, complemented
78	#1860	C₂×C₃	1	1	yes	characteristic, complemented
79	#1860	C₂×C₃	1	1	yes	characteristic, complemented
80	#1816	C₂×C₃	1	1	yes	characteristic, complemented
81	#1815	C₂×C₃	1	1	yes	characteristic, complemented
82	#1792	C₂×C₃	1	1	yes	characteristic
83	C₃×H(5,𝔽₂)	—	2	2	no	—
84	C₃×H(5,𝔽₂)	—	2	2	no	—
85	C₃×H(5,𝔽₂)	—	4	1	no	—
86	C₃×H(5,𝔽₂)	Q₈	1	4	yes	complemented
87	C₂×C₃×#41	—	2	1	no	—
88	C₂×C₃×#41	—	2	1	no	—
89	C₂×C₃×#41	C₂³	1	1	yes	characteristic
90	C₂×C₃×#41	C₂³	1	1	yes	characteristic
91	C₂²×C₃×D₄	—	2	1	no	—
92	C₂²×C₃×D₄	—	2	1	no	—
93	C₂²×C₃×D₄	—	4	1	no	—
94	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
95	C₃×#131	—	2	2	no	—
96	C₃×#131	—	2	2	no	—
97	C₃×#131	—	4	1	no	—
98	C₃×#131	—	4	1	no	—
99	C₂×C₃×M₁₆	—	2	1	no	—
100	C₂×C₃×M₁₆	—	2	1	no	—
101	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
102	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
103	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
104	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
105	C₂²×C₃×C₈	—	2	1	no	—
106	C₂²×C₃×C₈	—	2	1	no	—
107	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
108	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
109	C₃×C₄⋊Q₈	—	2	1	no	—
110	C₃×C₄⋊Q₈	—	2	1	no	—
111	C₃×#125	—	2	1	no	—
112	C₃×#125	—	2	1	no	—
113	C₃×C₂²⋊Q₈	—	4	1	no	—
114	C₃×C₄×Q₈	—	2	1	no	—
115	C₃×C₄×Q₈	—	2	1	no	—
116	C₃×C₄×D₄	—	2	1	no	—
117	C₃×C₄×D₄	—	2	1	no	—
118	C₃×C₄×D₄	—	4	1	no	—
119	C₃×C₄×D₄	—	4	1	no	—
120	C₃×#117	—	2	1	no	—
121	C₃×#117	—	2	1	no	—
122	C₃×#117	C₂³	1	1	yes	characteristic
123	C₃×#117	C₂³	1	1	yes	characteristic
124	C₂×C₃×C₄⋊C₄	—	2	1	no	—
125	C₂×C₃×C₄⋊C₄	—	2	1	no	—
126	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₃×C₂²⋊C₄	—	4	1	no	—
130	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
131	C₃×#108	—	4	1	no	—
132	C₃×#108	—	4	1	no	—
133	C₃×#107	—	2	1	no	—
134	C₃×#107	—	2	1	no	—
135	C₃×#107	—	2	1	no	—
136	C₃×#107	—	2	1	no	—
137	C₃×#106	—	2	1	no	—
138	C₃×#106	—	2	1	no	—
139	C₃×#106	—	2	1	no	—
140	C₃×#106	—	2	1	no	—
141	C₃×C₄⋊C₈	—	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×#104	—	2	2	no	—
146	C₃×#104	—	2	2	no	—
147	C₃×#103	—	2	1	no	—
148	C₃×#103	—	2	1	no	—
149	C₃×#103	—	2	1	no	—
150	C₃×#103	—	2	1	no	—
151	C₃×#103	D₄	1	1	yes	characteristic
152	C₃×#103	D₄	1	1	yes	characteristic
153	C₃×#103	D₄	1	1	yes	characteristic
154	C₃×#103	D₄	1	1	yes	characteristic
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×#102	—	2	1	no	—
163	C₃×#102	—	2	1	no	—
164	C₃×#102	—	2	1	no	—
165	C₃×#102	—	2	1	no	—
166	C₃×#102	—	2	1	no	—
167	C₃×#102	D₄	1	1	yes	characteristic
168	C₃×#102	D₄	1	1	yes	characteristic
169	C₃×#102	D₄	1	1	yes	characteristic
170	C₃×#102	D₄	1	1	yes	characteristic
171	C₃×#100	—	4	1	no	—
172	C₃×#95	—	4	1	no	—
173	C₂×H(5,𝔽₂)	C₂²×C₃	1	1	yes	characteristic
174	C₂×#131	C₂²×C₃	1	1	yes	characteristic
175	C₂×#131	C₂²×C₃	1	1	yes	characteristic
176	#544	C₂²×C₃	1	1	yes	characteristic, complemented
177	#520	C₂²×C₃	1	1	yes	characteristic
178	#520	C₂²×C₃	1	1	yes	characteristic
179	#479	—	2	1	no	—
180	#479	—	2	1	no	—
181	#478	—	2	1	no	—
182	#478	—	2	1	no	—
183	#477	—	2	1	no	—
184	#476	—	2	1	no	—
185	#475	—	2	1	no	—
186	#474	—	2	1	no	—
187	C₂×#108	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₂×#108	C₂²×C₃	1	1	yes	characteristic, complemented
189	#428	C₂²×C₃	1	1	yes	characteristic, complemented
190	#428	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₂×#107	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₂×#106	C₂²×C₃	1	1	yes	characteristic, complemented
193	#424	C₂²×C₃	1	1	yes	characteristic, complemented
194	#424	C₂²×C₃	1	1	yes	characteristic, complemented
195	C₂×#104	C₂²×C₃	1	1	yes	characteristic
196	C₂×#104	C₂²×C₃	1	1	yes	characteristic
197	#418	—	2	1	no	—
198	#418	—	2	1	no	—
199	#418	C₂²×C₃	1	1	yes	characteristic
200	#418	C₂²×C₃	1	1	yes	characteristic
201	#417	—	2	1	no	—
202	#417	—	2	1	no	—
203	#417	C₂²×C₃	1	1	yes	characteristic
204	#417	C₂²×C₃	1	1	yes	characteristic
205	#417	C₂²×C₃	1	1	yes	characteristic
206	#417	C₂²×C₃	1	1	yes	characteristic
207	#416	—	2	1	no	—
208	#416	—	2	1	no	—
209	#416	C₂²×C₃	1	1	yes	characteristic
210	#416	C₂²×C₃	1	1	yes	characteristic
211	C₂×#102	—	2	1	no	—
212	C₂×#102	—	2	1	no	—
213	C₂×#102	C₂²×C₃	1	1	yes	characteristic
214	C₂×#102	C₂²×C₃	1	1	yes	characteristic
215	C₂×#100	C₂²×C₃	1	1	yes	characteristic
216	#390	C₂²×C₃	1	1	yes	characteristic
217	#382	C₂²×C₃	1	1	yes	characteristic, complemented
218	#343	C₂²×C₃	1	1	yes	characteristic, complemented
219	#343	C₂²×C₃	1	1	yes	characteristic, complemented
220	#343	C₂²×C₃	1	1	yes	characteristic, complemented
221	#339	C₂²×C₃	1	1	yes	characteristic, complemented
222	#339	C₂²×C₃	1	1	yes	characteristic, complemented
223	#336	C₂²×C₃	1	1	yes	characteristic, complemented
224	C₂⁴×C₃	—	2	1	no	—
225	C₂⁴×C₃	—	4	1	no	—
226	C₃×#41	—	2	1	no	—
227	C₃×#41	—	2	1	no	—
228	C₃×#41	—	2	1	no	—
229	C₃×#41	—	2	1	no	—
230	C₃×#41	—	2	4	no	—
231	C₃×#41	—	2	4	no	—
232	C₃×#41	—	4	2	no	—
233	C₃×#41	—	4	2	no	—
234	C₃×#41	C₂×Q₈	1	2	yes	—
235	C₃×#41	C₂×Q₈	1	2	yes	—
236	C₃×#41	#41	1	2	yes	—
237	C₃×#41	#41	1	2	yes	—
238	C₂×C₃×Q₈	—	4	1	no	—
239	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
240	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
241	C₂×C₃×D₄	—	2	1	no	—
242	C₂×C₃×D₄	—	2	1	no	—
243	C₂×C₃×D₄	—	2	4	no	—
244	C₂×C₃×D₄	—	2	4	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	—	4	2	no	—
251	C₂×C₃×D₄	—	4	2	no	—
252	C₂×C₃×D₄	—	4	1	no	—
253	C₂×C₃×D₄	—	4	1	no	—
254	C₂×C₃×D₄	—	4	4	no	—
255	C₂×C₃×D₄	—	4	4	no	—
256	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
257	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
258	C₂×C₃×D₄	C₂×Q₈	1	2	yes	—
259	C₂²×C₃×C₄	—	2	1	no	—
260	C₂²×C₃×C₄	—	2	1	no	—
261	C₂²×C₃×C₄	—	2	1	no	—
262	C₂²×C₃×C₄	—	2	1	no	—
263	C₂²×C₃×C₄	—	2	1	no	—
264	C₂²×C₃×C₄	—	2	1	no	—
265	C₂²×C₃×C₄	—	4	1	no	—
266	C₂²×C₃×C₄	—	4	1	no	—
267	C₂²×C₃×C₄	—	4	1	no	—
268	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
269	C₃×M₁₆	—	2	1	no	—
270	C₃×M₁₆	—	2	1	no	—
271	C₃×M₁₆	—	2	1	no	—
272	C₃×M₁₆	—	2	1	no	—
273	C₃×M₁₆	—	2	1	no	—
274	C₃×M₁₆	—	2	1	no	—
275	C₃×M₁₆	—	2	1	no	—
276	C₃×M₁₆	—	2	1	no	—
277	C₃×M₁₆	—	4	2	no	—
278	C₃×M₁₆	—	4	2	no	—
279	C₂×C₃×C₈	—	2	1	no	—
280	C₂×C₃×C₈	—	2	1	no	—
281	C₂×C₃×C₈	—	2	1	no	—
282	C₂×C₃×C₈	—	2	1	no	—
283	C₂×C₃×C₈	—	2	1	no	—
284	C₂×C₃×C₈	—	2	1	no	—
285	C₂×C₃×C₈	—	2	1	no	—
286	C₂×C₃×C₈	—	2	1	no	—
287	C₂×C₃×C₈	—	4	2	no	—
288	C₂×C₃×C₈	—	4	2	no	—
289	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
290	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
291	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
292	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
293	C₃×C₄⋊C₄	—	2	1	no	—
294	C₃×C₄⋊C₄	—	2	1	no	—
295	C₃×C₄⋊C₄	—	2	1	no	—
296	C₃×C₄⋊C₄	—	2	1	no	—
297	C₃×C₄⋊C₄	—	2	1	no	—
298	C₃×C₄⋊C₄	—	2	1	no	—
299	C₃×C₄⋊C₄	—	4	1	no	—
300	C₃×C₄⋊C₄	—	4	1	no	—
301	C₃×C₄⋊C₄	—	4	1	no	—
302	C₃×C₄⋊C₄	—	4	1	no	—
303	C₃×C₄⋊C₄	—	4	1	no	—
304	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
305	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
306	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
307	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
308	C₃×C₂²⋊C₄	—	2	1	no	—
309	C₃×C₂²⋊C₄	—	2	1	no	—
310	C₃×C₂²⋊C₄	—	4	1	no	—
311	C₃×C₂²⋊C₄	—	4	1	no	—
312	C₃×C₂²⋊C₄	—	8	2	no	—
313	C₃×C₄²	—	2	1	no	—
314	C₃×C₄²	—	2	1	no	—
315	C₃×C₄²	—	2	1	no	—
316	C₃×C₄²	—	2	1	no	—
317	C₃×C₄²	—	4	1	no	—
318	C₃×C₄²	—	4	1	no	—
319	H(5,𝔽₂)	—	2	2	no	—
320	H(5,𝔽₂)	—	2	2	no	—
321	H(5,𝔽₂)	—	4	1	no	—
322	H(5,𝔽₂)	C₃×Q₈	1	4	yes	complemented
323	C₂×#41	—	2	1	no	—
324	C₂×#41	—	2	1	no	—
325	C₂×#41	C₂³×C₃	1	1	yes	characteristic
326	C₂×#41	C₂³×C₃	1	1	yes	characteristic
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	4	1	no	—
330	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
331	#131	—	2	2	no	—
332	#131	—	2	2	no	—
333	#131	—	4	1	no	—
334	#131	—	4	1	no	—
335	C₂×M₁₆	—	2	1	no	—
336	C₂×M₁₆	—	2	1	no	—
337	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
338	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
339	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
340	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
341	C₂²×C₈	—	2	1	no	—
342	C₂²×C₈	—	2	1	no	—
343	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
345	C₄⋊Q₈	—	2	1	no	—
346	C₄⋊Q₈	—	2	1	no	—
347	#125	—	2	1	no	—
348	#125	—	2	1	no	—
349	C₂²⋊Q₈	—	4	1	no	—
350	C₄×Q₈	—	2	1	no	—
351	C₄×Q₈	—	2	1	no	—
352	C₄×D₄	—	2	1	no	—
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	—	4	1	no	—
355	C₄×D₄	—	4	1	no	—
356	#117	—	2	1	no	—
357	#117	—	2	1	no	—
358	#117	C₂³×C₃	1	1	yes	characteristic
359	#117	C₂³×C₃	1	1	yes	characteristic
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	4	1	no	—
366	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
367	#108	—	4	1	no	—
368	#108	—	4	1	no	—
369	#107	—	2	1	no	—
370	#107	—	2	1	no	—
371	#107	—	2	1	no	—
372	#107	—	2	1	no	—
373	#106	—	2	1	no	—
374	#106	—	2	1	no	—
375	#106	—	2	1	no	—
376	#106	—	2	1	no	—
377	C₄⋊C₈	—	2	1	no	—
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	2	1	no	—
381	#104	—	2	2	no	—
382	#104	—	2	2	no	—
383	#103	—	2	1	no	—
384	#103	—	2	1	no	—
385	#103	—	2	1	no	—
386	#103	—	2	1	no	—
387	#103	C₃×D₄	1	1	yes	characteristic
388	#103	C₃×D₄	1	1	yes	characteristic
389	#103	C₃×D₄	1	1	yes	characteristic
390	#103	C₃×D₄	1	1	yes	characteristic
391	#102	—	2	1	no	—
392	#102	—	2	1	no	—
393	#102	—	2	1	no	—
394	#102	—	2	1	no	—
395	#102	—	2	1	no	—
396	#102	—	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	C₃×D₄	1	1	yes	characteristic
404	#102	C₃×D₄	1	1	yes	characteristic
405	#102	C₃×D₄	1	1	yes	characteristic
406	#102	C₃×D₄	1	1	yes	characteristic
407	#100	—	4	1	no	—
408	#95	—	4	1	no	—
409	C₂³×C₃	—	2	1	no	—
410	C₂³×C₃	—	2	1	no	—
411	C₂³×C₃	—	2	2	no	—
412	C₂³×C₃	—	4	4	no	—
413	C₂³×C₃	—	4	1	no	—
414	C₂³×C₃	—	4	1	no	—
415	C₂³×C₃	—	8	1	no	—
416	C₂³×C₃	—	8	1	no	—
417	C₂³×C₃	—	16	1	no	—
418	C₂³×C₃	—	16	1	no	—
419	C₂³×C₃	H(5,𝔽₂)	1	1	yes	characteristic
420	C₃×Q₈	—	2	1	no	—
421	C₃×Q₈	—	2	1	no	—
422	C₃×Q₈	—	16	1	no	—
423	C₃×Q₈	C₂²⋊Q₈	1	2	yes	—
424	C₃×Q₈	C₂²⋊Q₈	1	2	yes	—
425	C₃×D₄	—	2	2	no	—
426	C₃×D₄	—	2	2	no	—
427	C₃×D₄	—	2	2	no	—
428	C₃×D₄	—	2	2	no	—
429	C₃×D₄	—	2	2	no	—
430	C₃×D₄	—	2	2	no	—
431	C₃×D₄	—	2	1	no	—
432	C₃×D₄	—	2	1	no	—
433	C₃×D₄	—	4	4	no	—
434	C₃×D₄	—	4	4	no	—
435	C₃×D₄	—	4	1	no	—
436	C₃×D₄	—	4	1	no	—
437	C₃×D₄	C₂²⋊Q₈	1	2	yes	—
438	C₃×D₄	C₂²⋊Q₈	1	2	yes	—
439	C₂×C₃×C₄	—	2	1	no	—
440	C₂×C₃×C₄	—	2	1	no	—
441	C₂×C₃×C₄	—	2	2	no	—
442	C₂×C₃×C₄	—	2	2	no	—
443	C₂×C₃×C₄	—	2	2	no	—
444	C₂×C₃×C₄	—	2	2	no	—
445	C₂×C₃×C₄	—	2	1	no	—
446	C₂×C₃×C₄	—	2	1	no	—
447	C₂×C₃×C₄	—	2	1	no	—
448	C₂×C₃×C₄	—	2	1	no	—
449	C₂×C₃×C₄	—	4	4	no	—
450	C₂×C₃×C₄	—	4	1	no	—
451	C₂×C₃×C₄	—	4	1	no	—
452	C₂×C₃×C₄	—	4	1	no	—
453	C₂×C₃×C₄	—	4	1	no	—
454	C₂×C₃×C₄	—	4	1	no	—
455	C₂×C₃×C₄	—	4	1	no	—
456	C₂×C₃×C₄	—	8	1	no	—
457	C₂×C₃×C₄	—	8	1	no	—
458	C₂×C₃×C₄	—	8	1	no	—
459	C₂×C₃×C₄	—	16	1	no	—
460	C₂×C₃×C₄	—	16	1	no	—
461	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₃×C₄	C₂²×Q₈	1	1	yes	characteristic
464	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
465	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
466	C₂×C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
467	C₃×C₈	—	2	1	no	—
468	C₃×C₈	—	2	1	no	—
469	C₃×C₈	—	2	1	no	—
470	C₃×C₈	—	2	1	no	—
471	C₃×C₈	—	4	1	no	—
472	C₃×C₈	—	4	1	no	—
473	C₃×C₈	—	4	1	no	—
474	C₃×C₈	—	4	1	no	—
475	C₂⁴	—	2	1	no	—
476	C₂⁴	—	4	1	no	—
477	#41	—	2	1	no	—
478	#41	—	2	1	no	—
479	#41	—	2	1	no	—
480	#41	—	2	1	no	—
481	#41	—	2	4	no	—
482	#41	—	2	4	no	—
483	#41	—	4	2	no	—
484	#41	—	4	2	no	—
485	#41	C₂×C₃×Q₈	1	2	yes	—
486	#41	C₂×C₃×Q₈	1	2	yes	—
487	#41	C₃×#41	1	2	yes	—
488	#41	C₃×#41	1	2	yes	—
489	C₂×Q₈	—	4	1	no	—
490	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
491	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	4	no	—
495	C₂×D₄	—	2	4	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	4	2	no	—
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	—	4	1	no	—
504	C₂×D₄	—	4	1	no	—
505	C₂×D₄	—	4	4	no	—
506	C₂×D₄	—	4	4	no	—
507	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
508	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
509	C₂×D₄	C₂×C₃×Q₈	1	2	yes	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	4	1	no	—
517	C₂²×C₄	—	4	1	no	—
518	C₂²×C₄	—	4	1	no	—
519	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
520	M₁₆	—	2	1	no	—
521	M₁₆	—	2	1	no	—
522	M₁₆	—	2	1	no	—
523	M₁₆	—	2	1	no	—
524	M₁₆	—	2	1	no	—
525	M₁₆	—	2	1	no	—
526	M₁₆	—	2	1	no	—
527	M₁₆	—	2	1	no	—
528	M₁₆	—	4	2	no	—
529	M₁₆	—	4	2	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	4	2	no	—
539	C₂×C₈	—	4	2	no	—
540	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
541	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
542	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
543	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	4	1	no	—
551	C₄⋊C₄	—	4	1	no	—
552	C₄⋊C₄	—	4	1	no	—
553	C₄⋊C₄	—	4	1	no	—
554	C₄⋊C₄	—	4	1	no	—
555	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
556	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
557	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
558	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
559	C₂²⋊C₄	—	2	1	no	—
560	C₂²⋊C₄	—	2	1	no	—
561	C₂²⋊C₄	—	4	1	no	—
562	C₂²⋊C₄	—	4	1	no	—
563	C₂²⋊C₄	—	8	2	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	4	1	no	—
569	C₄²	—	4	1	no	—
570	C₂²×C₃	—	2	1	no	—
571	C₂²×C₃	—	2	1	no	—
572	C₂²×C₃	—	2	2	no	—
573	C₂²×C₃	—	2	2	no	—
574	C₂²×C₃	—	4	1	no	—
575	C₂²×C₃	—	4	1	no	—
576	C₂²×C₃	—	4	1	no	—
577	C₂²×C₃	—	4	1	no	—
578	C₂²×C₃	—	4	2	no	—
579	C₂²×C₃	—	8	2	no	—
580	C₂²×C₃	—	8	1	no	—
581	C₂²×C₃	—	8	1	no	—
582	C₂²×C₃	—	16	1	no	—
583	C₂²×C₃	—	16	4	no	—
584	C₂²×C₃	#543	1	1	yes	characteristic
585	C₂²×C₃	D₄²	1	1	yes	characteristic
586	C₂²×C₃	#551	1	1	yes	characteristic
587	C₃×C₄	—	2	2	no	—
588	C₃×C₄	—	2	2	no	—
589	C₃×C₄	—	4	1	no	—
590	C₃×C₄	—	4	1	no	—
591	C₃×C₄	—	4	1	no	—
592	C₃×C₄	—	4	1	no	—
593	C₃×C₄	—	8	1	no	—
594	C₃×C₄	—	8	1	no	—
595	C₃×C₄	—	8	1	no	—
596	C₃×C₄	—	8	1	no	—
597	C₃×C₄	C₂×C₂²⋊Q₈	1	1	yes	characteristic
598	C₃×C₄	C₂×C₂²⋊Q₈	1	1	yes	characteristic
599	C₃×C₄	#546	1	1	yes	characteristic
600	C₃×C₄	#546	1	1	yes	characteristic
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	4	4	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	8	1	no	—
608	C₂³	—	8	1	no	—
609	C₂³	—	16	1	no	—
610	C₂³	—	16	1	no	—
611	C₂³	C₃×H(5,𝔽₂)	1	1	yes	characteristic
612	Q₈	—	2	1	no	—
613	Q₈	—	2	1	no	—
614	Q₈	—	16	1	no	—
615	Q₈	C₃×C₂²⋊Q₈	1	2	yes	—
616	Q₈	C₃×C₂²⋊Q₈	1	2	yes	—
617	D₄	—	2	2	no	—
618	D₄	—	2	2	no	—
619	D₄	—	2	2	no	—
620	D₄	—	2	2	no	—
621	D₄	—	2	2	no	—
622	D₄	—	2	2	no	—
623	D₄	—	2	1	no	—
624	D₄	—	2	1	no	—
625	D₄	—	4	4	no	—
626	D₄	—	4	4	no	—
627	D₄	—	4	1	no	—
628	D₄	—	4	1	no	—
629	D₄	C₃×C₂²⋊Q₈	1	2	yes	—
630	D₄	C₃×C₂²⋊Q₈	1	2	yes	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	8	1	no	—
649	C₂×C₄	—	8	1	no	—
650	C₂×C₄	—	8	1	no	—
651	C₂×C₄	—	16	1	no	—
652	C₂×C₄	—	16	1	no	—
653	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
654	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
655	C₂×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
656	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
657	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
658	C₂×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
659	C₈	—	2	1	no	—
660	C₈	—	2	1	no	—
661	C₈	—	2	1	no	—
662	C₈	—	2	1	no	—
663	C₈	—	4	1	no	—
664	C₈	—	4	1	no	—
665	C₈	—	4	1	no	—
666	C₈	—	4	1	no	—
667	C₂×C₃	—	2	1	no	—
668	C₂×C₃	—	2	1	no	—
669	C₂×C₃	—	4	2	no	—
670	C₂×C₃	—	4	2	no	—
671	C₂×C₃	—	8	2	no	—
672	C₂×C₃	#2437	1	1	yes	characteristic
673	C₂×C₃	#3288	1	1	yes	characteristic
674	C₂×C₃	#3290	1	1	yes	characteristic
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	8	2	no	—
685	C₂²	—	8	1	no	—
686	C₂²	—	8	1	no	—
687	C₂²	—	16	1	no	—
688	C₂²	—	16	4	no	—
689	C₂²	C₃×#543	1	1	yes	characteristic
690	C₂²	C₃×D₄²	1	1	yes	characteristic
691	C₂²	C₃×#551	1	1	yes	characteristic
692	C₄	—	2	2	no	—
693	C₄	—	2	2	no	—
694	C₄	—	4	1	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	1	no	—
698	C₄	—	8	1	no	—
699	C₄	—	8	1	no	—
700	C₄	—	8	1	no	—
701	C₄	—	8	1	no	—
702	C₄	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
703	C₄	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
704	C₄	C₃×#546	1	1	yes	characteristic
705	C₄	C₃×#546	1	1	yes	characteristic
706	C₃	#25984	1	1	yes	characteristic, direct product factor, Sylow
707	C₂	—	2	1	no	—
708	C₂	—	2	1	no	—
709	C₂	—	4	2	no	—
710	C₂	—	4	2	no	—
711	C₂	—	8	2	no	—
712	C₂	C₃×#2437	1	1	yes	characteristic
713	C₂	C₃×#3288	1	1	yes	characteristic
714	C₂	C₃×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
prime radical	C₂×C₃×H(5,𝔽₂)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3084	C₂	semidirect
2. C₃×#3083	C₂	semidirect
5. C₃×#2092	C₂	semidirect
6. C₃×#2063	C₂	semidirect
7. C₃×#2063	C₂	semidirect
8. C₃×#2027	C₂	semidirect
9. C₃×#1866	C₂	semidirect
10. C₃×#1866	C₂	semidirect
11. C₃×#1860	C₂	semidirect
12. C₃×#1860	C₂	semidirect
13. C₃×#1816	C₂	semidirect
14. C₃×#1815	C₂	semidirect
16. #25984	C₃	direct (N × H)
20. C₃×#544	C₂²	semidirect
31. C₂×C₃×#108	C₂²	semidirect
32. C₂×C₃×#108	C₂²	semidirect
33. C₃×#428	C₂²	semidirect
34. C₃×#428	C₂²	semidirect
35. C₂×C₃×#107	C₂²	semidirect
36. C₂×C₃×#106	C₂²	semidirect
37. C₃×#424	C₂²	semidirect
38. C₃×#424	C₂²	semidirect
61. C₃×#382	C₂²	semidirect
62. C₃×#343	C₂²	semidirect
63. C₃×#343	C₂²	semidirect
64. C₃×#343	C₂²	semidirect
65. C₃×#339	C₂²	semidirect
66. C₃×#339	C₂²	semidirect
67. C₃×#336	C₂²	semidirect
68. #3084	C₂×C₃	semidirect
69. #3083	C₂×C₃	semidirect
72. #2092	C₂×C₃	semidirect
73. #2063	C₂×C₃	semidirect
74. #2063	C₂×C₃	semidirect
75. #2027	C₂×C₃	semidirect
76. #1866	C₂×C₃	semidirect
77. #1866	C₂×C₃	semidirect
78. #1860	C₂×C₃	semidirect
79. #1860	C₂×C₃	semidirect
80. #1816	C₂×C₃	semidirect
81. #1815	C₂×C₃	semidirect
86. C₃×H(5,𝔽₂)	Q₈	semidirect
176. #544	C₂²×C₃	semidirect
187. C₂×#108	C₂²×C₃	semidirect
188. C₂×#108	C₂²×C₃	semidirect
189. #428	C₂²×C₃	semidirect
190. #428	C₂²×C₃	semidirect
191. C₂×#107	C₂²×C₃	semidirect
192. C₂×#106	C₂²×C₃	semidirect
193. #424	C₂²×C₃	semidirect
194. #424	C₂²×C₃	semidirect
217. #382	C₂²×C₃	semidirect
218. #343	C₂²×C₃	semidirect
219. #343	C₂²×C₃	semidirect
220. #343	C₂²×C₃	semidirect
221. #339	C₂²×C₃	semidirect
222. #339	C₂²×C₃	semidirect
223. #336	C₂²×C₃	semidirect
322. H(5,𝔽₂)	C₃×Q₈	semidirect
706. C₃	#25984	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×#3084	2
C₃×#3083	2
C₃×#2897	2
C₃×#2092	2
C₃×#2063	2
C₃×#2027	2
C₃×#1866	2
C₃×#1860	2
C₃×#1816	2
C₃×#1815	2
C₃×#1792	2
#25984	3

Subgroups — C3×#25984 #10644591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#25984 #10644591