Subgroups — C₃×#60489 #10679096

Order 768.

2002 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3428	C₂	1	1	yes	maximal, characteristic
3	C₃×#3084	C₂	1	4	yes	maximal, complemented
4	C₃×#3083	C₂	1	4	yes	maximal, complemented
5	C₃×#3082	C₂	1	4	yes	maximal, complemented
6	C₃×#3081	C₂	1	4	yes	maximal, complemented
7	C₃×#3076	C₂	1	8	yes	maximal, complemented
8	C₃×#2911	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2896	C₂	1	1	yes	maximal, characteristic
12	C₂×C₃×#416	C₂	1	1	yes	maximal, characteristic
13	#60489	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
15	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
16	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
17	C₃×#544	—	2	2	no	—
18	C₃×#544	C₂²	1	4	yes	—
19	C₃×#544	C₂²	1	4	yes	complemented
20	C₃×#543	—	2	2	no	—
21	C₃×#533	—	2	2	no	—
22	C₃×#533	—	2	2	no	—
23	C₃×#533	C₂²	1	4	yes	complemented
24	C₃×#520	—	2	2	no	—
25	C₃×#520	C₂²	1	4	yes	—
26	C₃×#519	C₂²	1	2	yes	—
27	C₃×#518	—	2	2	no	—
28	C₃×#518	C₂²	1	2	yes	—
29	C₃×C₄×#41	—	2	2	no	—
30	C₃×C₄×#41	C₂²	1	4	yes	—
31	C₂×C₃×#117	—	2	2	no	—
32	C₂×C₃×#117	C₂²	1	1	yes	characteristic
33	C₂×C₃×#117	C₂²	1	1	yes	characteristic
34	C₂×C₃×#117	C₂²	1	1	yes	characteristic
35	C₂×C₃×#117	C₂²	1	1	yes	characteristic
36	C₃×#479	C₂²	1	8	yes	complemented
37	C₃×#479	C₂²	1	8	yes	complemented
38	C₃×#478	C₂²	1	8	yes	complemented
39	C₃×#478	C₂²	1	8	yes	complemented
40	C₃×#477	C₂²	1	8	yes	complemented
41	C₃×#476	C₂²	1	8	yes	complemented
42	C₃×#475	C₂²	1	8	yes	complemented
43	C₃×#474	C₂²	1	8	yes	complemented
44	C₃×#428	C₂²	1	4	yes	—
45	C₃×#428	C₂²	1	4	yes	complemented
46	C₃×#427	C₂²	1	4	yes	—
47	C₃×#427	C₂²	1	4	yes	complemented
48	C₃×#427	C₂²	1	4	yes	complemented
49	C₂×C₃×#107	C₂²	1	2	yes	complemented
50	C₂×C₃×#106	C₂²	1	2	yes	complemented
51	C₃×#424	C₂²	1	4	yes	—
52	C₃×#424	C₂²	1	2	yes	complemented
53	C₃×#424	C₂²	1	2	yes	complemented
54	C₂×C₃×C₄⋊C₈	C₂²	1	4	yes	complemented
55	C₃×#419	C₂²	1	2	yes	—
56	C₃×#418	C₂²	1	2	yes	—
57	C₃×#417	C₂²	1	4	yes	—
58	C₃×#416	C₂²	1	4	yes	—
59	C₃×#416	C₂²	1	2	yes	—
60	C₃×#416	C₂²	1	2	yes	—
61	C₃×#416	C₂²	1	4	yes	—
62	C₂×C₃×#103	C₂²	1	2	yes	—
63	C₂×C₃×#102	C₂²	1	2	yes	—
64	#3458	C₂×C₃	1	1	yes	characteristic, complemented
65	#3428	C₂×C₃	1	1	yes	characteristic
66	#3084	C₂×C₃	1	4	yes	complemented
67	#3083	C₂×C₃	1	4	yes	complemented
68	#3082	C₂×C₃	1	4	yes	complemented
69	#3081	C₂×C₃	1	4	yes	complemented
70	#3076	C₂×C₃	1	8	yes	complemented
71	#2911	C₂×C₃	1	1	yes	characteristic, complemented
72	C₂×#427	C₂×C₃	1	1	yes	characteristic, complemented
73	C₂×#424	C₂×C₃	1	1	yes	characteristic, complemented
74	#2896	C₂×C₃	1	1	yes	characteristic
75	C₂×#416	C₂×C₃	1	1	yes	characteristic
76	C₂×C₃×#41	—	2	1	no	—
77	C₂×C₃×#41	—	2	1	no	—
78	C₂×C₃×#41	—	2	4	no	—
79	C₂×C₃×#41	Q₈	1	8	yes	complemented
80	C₂×C₃×#41	C₂³	1	2	yes	—
81	C₂×C₃×#41	C₂³	1	2	yes	—
82	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
83	C₂²×C₃×D₄	—	2	1	no	—
84	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
85	C₂³×C₃×C₄	—	2	1	no	—
86	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
87	C₂×C₃×M₁₆	—	2	4	no	—
88	C₂×C₃×M₁₆	C₂³	1	2	yes	—
89	C₂×C₃×M₁₆	C₂³	1	2	yes	—
90	C₂²×C₃×C₈	—	2	4	no	—
91	C₂²×C₃×C₈	C₂³	1	2	yes	—
92	C₂²×C₃×C₈	C₂³	1	2	yes	—
93	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
94	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
95	C₂²×C₃×C₈	C₂³	1	2	yes	—
96	C₃×C₄⋊Q₈	—	2	4	no	—
97	C₃×C₄⋊Q₈	—	2	4	no	—
98	C₃×C₄⋊Q₈	C₂³	1	8	yes	—
99	C₃×#125	—	2	4	no	—
100	C₃×#125	—	2	4	no	—
101	C₃×#125	C₂³	1	8	yes	—
102	C₃×C₂²⋊Q₈	—	2	8	no	—
103	C₃×C₂²⋊Q₈	—	2	8	no	—
104	C₃×C₂²⋊Q₈	—	2	8	no	—
105	C₃×C₄×Q₈	—	2	4	no	—
106	C₃×C₄×Q₈	—	2	8	no	—
107	C₃×C₄×Q₈	C₂³	1	8	yes	—
108	C₃×C₄×D₄	—	2	8	no	—
109	C₃×C₄×D₄	—	2	4	no	—
110	C₃×C₄×D₄	—	2	8	no	—
111	C₃×C₄×D₄	C₂³	1	8	yes	—
112	C₃×#117	—	2	1	no	—
113	C₃×#117	—	2	1	no	—
114	C₃×#117	—	2	1	no	—
115	C₃×#117	—	2	1	no	—
116	C₃×#117	—	2	1	no	—
117	C₃×#117	—	2	1	no	—
118	C₃×#117	—	2	4	no	—
119	C₃×#117	—	2	4	no	—
120	C₃×#117	—	2	4	no	—
121	C₃×#117	D₄	1	2	yes	—
122	C₃×#117	D₄	1	2	yes	—
123	C₃×#117	C₂³	1	2	yes	—
124	C₃×#117	C₂³	1	2	yes	—
125	C₃×#117	C₂³	1	2	yes	—
126	C₃×#117	C₂³	1	2	yes	—
127	C₃×#117	C₂³	1	2	yes	—
128	C₃×#117	C₂³	1	2	yes	—
129	C₃×#117	C₂³	1	2	yes	—
130	C₃×#117	C₂³	1	2	yes	—
131	C₂×C₃×C₄⋊C₄	—	2	4	no	—
132	C₂×C₃×C₄⋊C₄	D₄	1	2	yes	—
133	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
137	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
138	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
139	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
140	C₂×C₃×C₂²⋊C₄	D₄	1	2	yes	—
141	C₂×C₃×C₄²	—	2	1	no	—
142	C₂×C₃×C₄²	—	2	1	no	—
143	C₂×C₃×C₄²	—	2	1	no	—
144	C₂×C₃×C₄²	—	2	4	no	—
145	C₂×C₃×C₄²	C₂³	1	2	yes	—
146	C₃×#107	C₂³	1	4	yes	—
147	C₃×#107	C₂³	1	4	yes	—
148	C₃×#107	C₂³	1	8	yes	—
149	C₃×#106	C₂³	1	4	yes	—
150	C₃×#106	C₂³	1	4	yes	—
151	C₃×#106	C₂³	1	8	yes	—
152	C₃×C₄⋊C₈	C₂³	1	8	yes	—
153	C₃×C₄⋊C₈	C₂³	1	8	yes	—
154	C₃×#103	C₂³	1	4	yes	—
155	C₃×#103	C₂³	1	4	yes	—
156	C₃×#103	C₂³	1	8	yes	—
157	C₃×#102	C₂³	1	4	yes	—
158	C₃×#102	C₂³	1	4	yes	—
159	C₃×#102	C₂³	1	8	yes	—
160	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
161	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
162	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
163	#544	—	2	2	no	—
164	#544	C₂²×C₃	1	4	yes	—
165	#544	C₂²×C₃	1	4	yes	complemented
166	#543	—	2	2	no	—
167	#533	—	2	2	no	—
168	#533	—	2	2	no	—
169	#533	C₂²×C₃	1	4	yes	complemented
170	#520	—	2	2	no	—
171	#520	C₂²×C₃	1	4	yes	—
172	#519	C₂²×C₃	1	2	yes	—
173	#518	—	2	2	no	—
174	#518	C₂²×C₃	1	2	yes	—
175	C₄×#41	—	2	2	no	—
176	C₄×#41	C₂²×C₃	1	4	yes	—
177	C₂×#117	—	2	2	no	—
178	C₂×#117	C₂²×C₃	1	1	yes	characteristic
179	C₂×#117	C₂²×C₃	1	1	yes	characteristic
180	C₂×#117	C₂²×C₃	1	1	yes	characteristic
181	C₂×#117	C₂²×C₃	1	1	yes	characteristic
182	#479	C₂²×C₃	1	8	yes	complemented
183	#479	C₂²×C₃	1	8	yes	complemented
184	#478	C₂²×C₃	1	8	yes	complemented
185	#478	C₂²×C₃	1	8	yes	complemented
186	#477	C₂²×C₃	1	8	yes	complemented
187	#476	C₂²×C₃	1	8	yes	complemented
188	#475	C₂²×C₃	1	8	yes	complemented
189	#474	C₂²×C₃	1	8	yes	complemented
190	#428	C₂²×C₃	1	4	yes	—
191	#428	C₂²×C₃	1	4	yes	complemented
192	#427	C₂²×C₃	1	4	yes	—
193	#427	C₂²×C₃	1	4	yes	complemented
194	#427	C₂²×C₃	1	4	yes	complemented
195	C₂×#107	C₂²×C₃	1	2	yes	complemented
196	C₂×#106	C₂²×C₃	1	2	yes	complemented
197	#424	C₂²×C₃	1	4	yes	—
198	#424	C₂²×C₃	1	2	yes	complemented
199	#424	C₂²×C₃	1	2	yes	complemented
200	C₂×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
201	#419	C₂²×C₃	1	2	yes	—
202	#418	C₂²×C₃	1	2	yes	—
203	#417	C₂²×C₃	1	4	yes	—
204	#416	C₂²×C₃	1	4	yes	—
205	#416	C₂²×C₃	1	4	yes	—
206	#416	C₂²×C₃	1	2	yes	—
207	#416	C₂²×C₃	1	2	yes	—
208	C₂×#103	C₂²×C₃	1	2	yes	—
209	C₂×#102	C₂²×C₃	1	2	yes	—
210	C₂⁴×C₃	—	2	1	no	—
211	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
212	C₃×#41	—	2	8	no	—
213	C₃×#41	—	2	8	no	—
214	C₃×#41	—	2	4	no	—
215	C₃×#41	—	2	4	no	—
216	C₃×#41	C₂×Q₈	1	8	yes	—
217	C₃×#41	C₂×Q₈	1	8	yes	—
218	C₂×C₃×Q₈	—	2	1	no	—
219	C₂×C₃×Q₈	—	2	8	no	—
220	C₂×C₃×Q₈	—	2	2	no	—
221	C₂×C₃×Q₈	C₂×Q₈	1	4	yes	—
222	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
223	C₂×C₃×D₄	—	2	8	no	—
224	C₂×C₃×D₄	—	2	2	no	—
225	C₂×C₃×D₄	—	2	2	no	—
226	C₂×C₃×D₄	—	2	1	no	—
227	C₂×C₃×D₄	—	2	2	no	—
228	C₂×C₃×D₄	C₂×Q₈	1	4	yes	—
229	C₂×C₃×D₄	C₂⁴	1	2	yes	—
230	C₂²×C₃×C₄	—	2	1	no	—
231	C₂²×C₃×C₄	—	2	8	no	—
232	C₂²×C₃×C₄	—	2	2	no	—
233	C₂²×C₃×C₄	—	2	2	no	—
234	C₂²×C₃×C₄	—	2	2	no	—
235	C₂²×C₃×C₄	—	2	2	no	—
236	C₂²×C₃×C₄	—	2	2	no	—
237	C₂²×C₃×C₄	—	2	8	no	—
238	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
239	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
243	C₂²×C₃×C₄	#41	1	4	yes	—
244	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
246	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
247	C₃×M₁₆	—	2	4	no	—
248	C₃×M₁₆	—	2	4	no	—
249	C₂×C₃×C₈	—	2	4	no	—
250	C₂×C₃×C₈	—	2	4	no	—
251	C₂×C₃×C₈	—	2	2	no	—
252	C₂×C₃×C₈	—	2	2	no	—
253	C₂×C₃×C₈	—	2	4	no	—
254	C₂×C₃×C₈	C₂⁴	1	2	yes	—
255	C₂×C₃×C₈	C₂⁴	1	4	yes	—
256	C₂×C₃×C₈	C₂⁴	1	2	yes	—
257	C₃×C₄⋊C₄	—	2	2	no	—
258	C₃×C₄⋊C₄	—	2	8	no	—
259	C₃×C₄⋊C₄	—	2	2	no	—
260	C₃×C₄⋊C₄	—	2	2	no	—
261	C₃×C₄⋊C₄	—	2	8	no	—
262	C₃×C₄⋊C₄	—	2	8	no	—
263	C₃×C₄⋊C₄	—	2	8	no	—
264	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
265	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
266	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
267	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
268	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
269	C₃×C₂²⋊C₄	—	2	2	no	—
270	C₃×C₂²⋊C₄	—	2	2	no	—
271	C₃×C₂²⋊C₄	—	2	2	no	—
272	C₃×C₂²⋊C₄	—	2	2	no	—
273	C₃×C₂²⋊C₄	—	2	2	no	—
274	C₃×C₂²⋊C₄	—	2	2	no	—
275	C₃×C₂²⋊C₄	—	2	8	no	—
276	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
277	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
278	C₃×C₄²	—	2	8	no	—
279	C₃×C₄²	—	2	2	no	—
280	C₃×C₄²	—	2	2	no	—
281	C₃×C₄²	—	2	2	no	—
282	C₃×C₄²	—	2	2	no	—
283	C₃×C₄²	—	2	2	no	—
284	C₃×C₄²	—	2	2	no	—
285	C₃×C₄²	C₂×D₄	1	4	yes	—
286	C₃×C₄²	C₂⁴	1	4	yes	—
287	C₂×#41	—	2	1	no	—
288	C₂×#41	—	2	1	no	—
289	C₂×#41	—	2	4	no	—
290	C₂×#41	C₃×Q₈	1	8	yes	complemented
291	C₂×#41	C₂³×C₃	1	2	yes	—
292	C₂×#41	C₂³×C₃	1	2	yes	—
293	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
296	C₂³×C₄	—	2	1	no	—
297	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
298	C₂×M₁₆	—	2	4	no	—
299	C₂×M₁₆	C₂³×C₃	1	2	yes	—
300	C₂×M₁₆	C₂³×C₃	1	2	yes	—
301	C₂²×C₈	—	2	4	no	—
302	C₂²×C₈	C₂³×C₃	1	2	yes	—
303	C₂²×C₈	C₂³×C₃	1	2	yes	—
304	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₃	1	2	yes	—
307	C₄⋊Q₈	—	2	4	no	—
308	C₄⋊Q₈	—	2	4	no	—
309	C₄⋊Q₈	C₂³×C₃	1	8	yes	—
310	#125	—	2	4	no	—
311	#125	—	2	4	no	—
312	#125	C₂³×C₃	1	8	yes	—
313	C₂²⋊Q₈	—	2	8	no	—
314	C₂²⋊Q₈	—	2	8	no	—
315	C₂²⋊Q₈	—	2	8	no	—
316	C₄×Q₈	—	2	4	no	—
317	C₄×Q₈	—	2	8	no	—
318	C₄×Q₈	C₂³×C₃	1	8	yes	—
319	C₄×D₄	—	2	8	no	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	—	2	8	no	—
322	C₄×D₄	C₂³×C₃	1	8	yes	—
323	#117	—	2	1	no	—
324	#117	—	2	1	no	—
325	#117	—	2	1	no	—
326	#117	—	2	1	no	—
327	#117	—	2	1	no	—
328	#117	—	2	1	no	—
329	#117	—	2	4	no	—
330	#117	—	2	4	no	—
331	#117	—	2	4	no	—
332	#117	C₃×D₄	1	2	yes	—
333	#117	C₃×D₄	1	2	yes	—
334	#117	C₂³×C₃	1	2	yes	—
335	#117	C₂³×C₃	1	2	yes	—
336	#117	C₂³×C₃	1	2	yes	—
337	#117	C₂³×C₃	1	2	yes	—
338	#117	C₂³×C₃	1	2	yes	—
339	#117	C₂³×C₃	1	2	yes	—
340	#117	C₂³×C₃	1	2	yes	—
341	#117	C₂³×C₃	1	2	yes	—
342	C₂×C₄⋊C₄	—	2	4	no	—
343	C₂×C₄⋊C₄	C₃×D₄	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	4	no	—
351	C₂×C₂²⋊C₄	C₃×D₄	1	2	yes	—
352	C₂×C₄²	—	2	1	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	—	2	1	no	—
355	C₂×C₄²	—	2	4	no	—
356	C₂×C₄²	C₂³×C₃	1	2	yes	—
357	#107	C₂³×C₃	1	4	yes	—
358	#107	C₂³×C₃	1	4	yes	—
359	#107	C₂³×C₃	1	8	yes	—
360	#106	C₂³×C₃	1	4	yes	—
361	#106	C₂³×C₃	1	4	yes	—
362	#106	C₂³×C₃	1	8	yes	—
363	C₄⋊C₈	C₂³×C₃	1	8	yes	—
364	C₄⋊C₈	C₂³×C₃	1	8	yes	—
365	#103	C₂³×C₃	1	4	yes	—
366	#103	C₂³×C₃	1	4	yes	—
367	#103	C₂³×C₃	1	8	yes	—
368	#102	C₂³×C₃	1	4	yes	—
369	#102	C₂³×C₃	1	4	yes	—
370	#102	C₂³×C₃	1	8	yes	—
371	C₂³×C₃	—	2	2	no	—
372	C₂³×C₃	—	2	4	no	—
373	C₂³×C₃	—	4	2	no	—
374	C₂³×C₃	—	8	2	no	—
375	C₂³×C₃	C₂²⋊Q₈	1	4	yes	—
376	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
377	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
378	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
379	C₃×Q₈	—	2	4	no	—
380	C₃×Q₈	—	2	2	no	—
381	C₃×Q₈	—	8	8	no	—
382	C₃×Q₈	C₂²×Q₈	1	4	yes	—
383	C₃×D₄	—	2	8	no	—
384	C₃×D₄	—	2	8	no	—
385	C₃×D₄	—	2	4	no	—
386	C₃×D₄	—	2	2	no	—
387	C₃×D₄	C₂²×Q₈	1	4	yes	—
388	C₂×C₃×C₄	—	2	4	no	—
389	C₂×C₃×C₄	—	2	2	no	—
390	C₂×C₃×C₄	—	2	8	no	—
391	C₂×C₃×C₄	—	2	8	no	—
392	C₂×C₃×C₄	—	2	4	no	—
393	C₂×C₃×C₄	—	2	4	no	—
394	C₂×C₃×C₄	—	2	4	no	—
395	C₂×C₃×C₄	—	4	4	no	—
396	C₂×C₃×C₄	—	8	8	no	—
397	C₂×C₃×C₄	—	8	2	no	—
398	C₂×C₃×C₄	—	8	2	no	—
399	C₂×C₃×C₄	—	8	2	no	—
400	C₂×C₃×C₄	C₂²⋊Q₈	1	4	yes	—
401	C₂×C₃×C₄	C₂²⋊Q₈	1	4	yes	—
402	C₂×C₃×C₄	C₂²⋊Q₈	1	4	yes	—
403	C₂×C₃×C₄	C₂²×D₄	1	8	yes	—
404	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
408	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
409	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
410	C₂×C₃×C₄	C₂×#41	1	2	yes	—
411	C₂×C₃×C₄	C₂×#41	1	2	yes	—
412	C₂×C₃×C₄	C₂×#41	1	2	yes	—
413	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
414	C₃×C₈	—	2	2	no	—
415	C₃×C₈	—	2	2	no	—
416	C₃×C₈	—	2	4	no	—
417	C₂⁴	—	2	1	no	—
418	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
419	#41	—	2	8	no	—
420	#41	—	2	8	no	—
421	#41	—	2	4	no	—
422	#41	—	2	4	no	—
423	#41	C₂×C₃×Q₈	1	8	yes	—
424	#41	C₂×C₃×Q₈	1	8	yes	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	8	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	C₂×C₃×Q₈	1	4	yes	—
429	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
430	C₂×D₄	—	2	8	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	C₂×C₃×Q₈	1	4	yes	—
436	C₂×D₄	C₂⁴×C₃	1	2	yes	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	8	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	8	no	—
445	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
446	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
447	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
448	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
449	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
450	C₂²×C₄	C₃×#41	1	4	yes	—
451	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
452	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
453	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
454	M₁₆	—	2	4	no	—
455	M₁₆	—	2	4	no	—
456	C₂×C₈	—	2	4	no	—
457	C₂×C₈	—	2	4	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	4	no	—
461	C₂×C₈	C₂⁴×C₃	1	2	yes	—
462	C₂×C₈	C₂⁴×C₃	1	4	yes	—
463	C₂×C₈	C₂⁴×C₃	1	2	yes	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	8	no	—
469	C₄⋊C₄	—	2	8	no	—
470	C₄⋊C₄	—	2	8	no	—
471	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
472	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
473	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
474	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
475	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
476	C₂²⋊C₄	—	2	2	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
484	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	8	no	—
487	C₄²	—	2	2	no	—
488	C₄²	—	2	2	no	—
489	C₄²	—	2	2	no	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	2	no	—
492	C₄²	C₂×C₃×D₄	1	4	yes	—
493	C₄²	C₂⁴×C₃	1	4	yes	—
494	C₂²×C₃	—	2	2	no	—
495	C₂²×C₃	—	2	2	no	—
496	C₂²×C₃	—	2	2	no	—
497	C₂²×C₃	—	2	4	no	—
498	C₂²×C₃	—	4	4	no	—
499	C₂²×C₃	—	4	4	no	—
500	C₂²×C₃	—	8	4	no	—
501	C₂²×C₃	C₂×C₂²⋊Q₈	1	2	yes	—
502	C₂²×C₃	C₂×C₂²⋊Q₈	1	2	yes	—
503	C₂²×C₃	C₂×C₂²⋊Q₈	1	2	yes	—
504	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
505	C₃×C₄	—	2	8	no	—
506	C₃×C₄	—	2	4	no	—
507	C₃×C₄	—	4	4	no	—
508	C₃×C₄	—	4	4	no	—
509	C₃×C₄	—	4	4	no	—
510	C₃×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
511	C₃×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
512	C₃×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
513	C₃×C₄	C₂³×Q₈	1	1	yes	characteristic
514	C₃×C₄	C₂²×#41	1	1	yes	characteristic
515	C₂³	—	2	2	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	8	2	no	—
519	C₂³	C₃×C₂²⋊Q₈	1	4	yes	—
520	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
521	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
522	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
523	Q₈	—	2	2	no	—
524	Q₈	—	2	4	no	—
525	Q₈	—	8	8	no	—
526	Q₈	C₂²×C₃×Q₈	1	4	yes	—
527	D₄	—	2	8	no	—
528	D₄	—	2	8	no	—
529	D₄	—	2	2	no	—
530	D₄	—	2	4	no	—
531	D₄	C₂²×C₃×Q₈	1	4	yes	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	8	no	—
535	C₂×C₄	—	2	8	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	4	4	no	—
540	C₂×C₄	—	8	8	no	—
541	C₂×C₄	—	8	2	no	—
542	C₂×C₄	—	8	2	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	C₃×C₂²⋊Q₈	1	4	yes	—
545	C₂×C₄	C₃×C₂²⋊Q₈	1	4	yes	—
546	C₂×C₄	C₃×C₂²⋊Q₈	1	4	yes	—
547	C₂×C₄	C₂²×C₃×D₄	1	8	yes	—
548	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
549	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
550	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
551	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
552	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
553	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
554	C₂×C₄	C₂×C₃×#41	1	2	yes	—
555	C₂×C₄	C₂×C₃×#41	1	2	yes	—
556	C₂×C₄	C₂×C₃×#41	1	2	yes	—
557	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
558	C₈	—	2	2	no	—
559	C₈	—	2	2	no	—
560	C₈	—	2	4	no	—
561	C₂×C₃	—	2	2	no	—
562	C₂×C₃	—	2	2	no	—
563	C₂×C₃	—	2	2	no	—
564	C₂×C₃	—	4	4	no	—
565	C₂×C₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
566	C₂×C₃	#3584	1	2	yes	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	4	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	8	4	no	—
574	C₂²	C₂×C₃×C₂²⋊Q₈	1	2	yes	—
575	C₂²	C₂×C₃×C₂²⋊Q₈	1	2	yes	—
576	C₂²	C₂×C₃×C₂²⋊Q₈	1	2	yes	—
577	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
578	C₄	—	2	4	no	—
579	C₄	—	2	8	no	—
580	C₄	—	4	4	no	—
581	C₄	—	4	4	no	—
582	C₄	—	4	4	no	—
583	C₄	C₂×C₃×C₂²⋊Q₈	1	2	yes	—
584	C₄	C₂×C₃×C₂²⋊Q₈	1	2	yes	—
585	C₄	C₂×C₃×C₂²⋊Q₈	1	2	yes	—
586	C₄	C₂³×C₃×Q₈	1	1	yes	characteristic
587	C₄	C₂²×C₃×#41	1	1	yes	characteristic
588	C₃	#60489	1	1	yes	characteristic, direct product factor, Sylow
589	C₂	—	2	2	no	—
590	C₂	—	2	2	no	—
591	C₂	—	2	2	no	—
592	C₂	—	4	4	no	—
593	C₂	C₂²×C₃×C₂²⋊Q₈	1	1	yes	characteristic
594	C₂	C₃×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂²×C₃	C₂³×D₄
prime radical	C₂²×C₃×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3458	C₂	semidirect
3. C₃×#3084	C₂	semidirect
4. C₃×#3083	C₂	semidirect
5. C₃×#3082	C₂	semidirect
6. C₃×#3081	C₂	semidirect
7. C₃×#3076	C₂	semidirect
8. C₃×#2911	C₂	semidirect
9. C₂×C₃×#427	C₂	semidirect
10. C₂×C₃×#424	C₂	semidirect
13. #60489	C₃	direct (N × H)
19. C₃×#544	C₂²	semidirect
23. C₃×#533	C₂²	semidirect
36. C₃×#479	C₂²	semidirect
37. C₃×#479	C₂²	semidirect
38. C₃×#478	C₂²	semidirect
39. C₃×#478	C₂²	semidirect
40. C₃×#477	C₂²	semidirect
41. C₃×#476	C₂²	semidirect
42. C₃×#475	C₂²	semidirect
43. C₃×#474	C₂²	semidirect
45. C₃×#428	C₂²	semidirect
47. C₃×#427	C₂²	semidirect
48. C₃×#427	C₂²	semidirect
49. C₂×C₃×#107	C₂²	semidirect
50. C₂×C₃×#106	C₂²	semidirect
52. C₃×#424	C₂²	semidirect
53. C₃×#424	C₂²	semidirect
54. C₂×C₃×C₄⋊C₈	C₂²	semidirect
64. #3458	C₂×C₃	semidirect
66. #3084	C₂×C₃	semidirect
67. #3083	C₂×C₃	semidirect
68. #3082	C₂×C₃	semidirect
69. #3081	C₂×C₃	semidirect
70. #3076	C₂×C₃	semidirect
71. #2911	C₂×C₃	semidirect
72. C₂×#427	C₂×C₃	semidirect
73. C₂×#424	C₂×C₃	semidirect
79. C₂×C₃×#41	Q₈	semidirect
165. #544	C₂²×C₃	semidirect
169. #533	C₂²×C₃	semidirect
182. #479	C₂²×C₃	semidirect
183. #479	C₂²×C₃	semidirect
184. #478	C₂²×C₃	semidirect
185. #478	C₂²×C₃	semidirect
186. #477	C₂²×C₃	semidirect
187. #476	C₂²×C₃	semidirect
188. #475	C₂²×C₃	semidirect
189. #474	C₂²×C₃	semidirect
191. #428	C₂²×C₃	semidirect
193. #427	C₂²×C₃	semidirect
194. #427	C₂²×C₃	semidirect
195. C₂×#107	C₂²×C₃	semidirect
196. C₂×#106	C₂²×C₃	semidirect
198. #424	C₂²×C₃	semidirect
199. #424	C₂²×C₃	semidirect
200. C₂×C₄⋊C₈	C₂²×C₃	semidirect
290. C₂×#41	C₃×Q₈	semidirect
588. C₃	#60489	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×#3458	2
C₃×#3428	2
C₃×#3084	2
C₃×#3083	2
C₃×#3082	2
C₃×#3081	2
C₃×#3076	2
C₃×#2911	2
C₂×C₃×#427	2
C₂×C₃×#424	2
C₃×#2896	2
C₂×C₃×#416	2
#60489	3

Subgroups — C3×#60489 #10679096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60489 #10679096