Subgroups — C₃×#79090 #11868938

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5521	C₂	1	1	yes	maximal, characteristic
2	C₃×#5519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5131	C₂	1	1	yes	maximal, characteristic
5	C₃×#5121	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#821	C₂	1	1	yes	maximal, characteristic
7	C₃×#5106	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4847	C₂	1	2	yes	maximal, complemented
9	C₃×#4847	C₂	1	2	yes	maximal, complemented
10	C₃×#4846	C₂	1	2	yes	maximal, complemented
11	C₃×#4842	C₂	1	2	yes	maximal, complemented
12	C₃×#3081	—	3	1	no	maximal
13	#79090	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
15	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
17	C₃²×#117	C₂²	1	1	yes	characteristic
18	C₃×#926	C₂²	1	1	yes	characteristic
19	C₃×#926	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
21	C₃×#893	—	2	1	no	—
22	C₃×#893	—	2	1	no	—
23	C₃×#890	—	2	1	no	—
24	C₃×#888	—	2	1	no	—
25	C₃×D₃×C₂²⋊C₄	—	2	2	no	—
26	C₃×#878	—	2	2	no	—
27	C₃×C₄×D₁₂	C₂²	1	2	yes	—
28	C₃×C₄×D₁₂	C₂²	1	2	yes	—
29	C₃×#870	C₂²	1	2	yes	complemented
30	C₃×#869	C₂²	1	2	yes	complemented
31	C₃²×C₄⋊C₈	C₂²	1	2	yes	complemented
32	C₃²×C₄⋊C₈	C₂²	1	2	yes	complemented
33	C₃×#821	C₂²	1	2	yes	—
34	C₃×#821	C₂²	1	2	yes	—
35	C₃×#821	C₂²	1	2	yes	—
36	C₃×#821	C₂²	1	2	yes	—
37	C₃×#818	C₂²	1	1	yes	characteristic, complemented
38	C₃×#818	C₂²	1	2	yes	complemented
39	C₃×#818	C₂²	1	1	yes	characteristic, complemented
40	C₃×#817	C₂²	1	1	yes	characteristic, complemented
41	C₃×#817	C₂²	1	2	yes	complemented
42	C₃×#817	C₂²	1	1	yes	characteristic, complemented
43	C₃×#544	—	3	1	no	—
44	C₃×#518	—	3	1	no	—
45	#5521	C₂×C₃	1	1	yes	characteristic
46	#5519	C₂×C₃	1	1	yes	characteristic, complemented
47	C₃×#478	—	3	2	no	—
48	C₃×#478	—	3	2	no	—
49	C₃×#476	—	3	2	no	—
50	C₃×#474	—	3	2	no	—
51	C₃×#428	—	3	1	no	—
52	C₃×#427	—	3	1	no	—
53	C₃×#424	—	2	1	no	—
54	C₃×#424	D₃	1	1	yes	characteristic, complemented
55	C₃×#424	C₂×C₃	1	1	yes	characteristic, complemented
56	C₃×#418	—	3	1	no	—
57	C₂×C₃×#102	—	3	1	no	—
58	#5131	C₂×C₃	1	1	yes	characteristic
59	#5121	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×#821	C₂×C₃	1	1	yes	characteristic
61	#5106	C₂×C₃	1	1	yes	characteristic, complemented
62	#4847	C₂×C₃	1	2	yes	complemented
63	#4847	C₂×C₃	1	2	yes	complemented
64	#4846	C₂×C₃	1	2	yes	complemented
65	#4842	C₂×C₃	1	2	yes	complemented
66	C₂³×C₃×D₃	—	2	1	no	—
67	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
68	C₂²×C₃×Dic₃	—	2	1	no	—
69	C₂×C₃×D₁₂	—	2	1	no	—
70	C₂×C₃×D₁₂	—	2	2	no	—
71	C₂×C₃×D₁₂	Q₈	1	4	yes	complemented
72	C₂×C₃×D₁₂	C₂³	1	2	yes	—
73	C₂×C₃×C₄×D₃	—	2	2	no	—
74	C₂×C₃×C₄×D₃	—	2	2	no	—
75	C₂×C₃×Dic₆	—	2	2	no	—
76	C₃²×M₁₆	—	2	2	no	—
77	C₂×C₃²×C₈	—	2	2	no	—
78	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
79	C₂×C₃²×C₈	C₂³	1	2	yes	—
80	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
81	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
82	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
83	C₃²×C₂²⋊C₄	D₄	1	2	yes	—
84	C₃²×C₄²	C₂³	1	2	yes	—
85	C₃×#217	—	2	1	no	—
86	C₃×#217	—	2	1	no	—
87	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
88	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
89	C₃×C₄⋊Dic₃	—	2	2	no	—
90	C₃×C₄⋊Dic₃	—	2	1	no	—
91	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
92	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
93	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
94	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
95	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
96	C₃×Dic₃⋊C₄	—	2	2	no	—
97	C₃×Dic₃⋊C₄	—	2	2	no	—
98	C₃×C₄×Dic₃	—	2	1	no	—
99	C₃×C₄×Dic₃	—	2	1	no	—
100	#3081	—	3	1	no	Sylow
101	C₂²×C₃×D₄	—	3	1	no	—
102	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₃×M₁₆	—	2	1	no	—
104	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
105	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
106	C₂²×C₃×C₈	—	2	1	no	—
107	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
108	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
109	C₃×C₄⋊Q₈	—	3	2	no	—
110	C₃×C₄⋊Q₈	—	6	1	no	—
111	C₃×#125	—	3	2	no	—
112	C₃×#125	—	6	1	no	—
113	C₃×C₂²⋊Q₈	—	6	2	no	—
114	C₃×C₄×D₄	—	3	2	no	—
115	C₃×C₄×D₄	—	3	2	no	—
116	C₃×C₄×D₄	—	6	1	no	—
117	C₃×C₄×D₄	—	6	1	no	—
118	C₃×#117	—	2	1	no	—
119	C₃×#117	—	3	1	no	—
120	C₃×#117	—	3	1	no	—
121	C₃×#117	C₂×D₃	1	1	yes	characteristic
122	C₃×#117	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₃×C₄⋊C₄	—	3	1	no	—
124	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
125	#926	C₂²×C₃	1	1	yes	characteristic
126	#926	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
128	#893	—	2	1	no	—
129	#893	—	2	1	no	—
130	#890	—	2	1	no	—
131	#888	—	2	1	no	—
132	D₃×C₂²⋊C₄	—	2	2	no	—
133	#878	—	2	2	no	—
134	C₄×D₁₂	C₂²×C₃	1	2	yes	—
135	C₄×D₁₂	C₂²×C₃	1	2	yes	—
136	#870	C₂²×C₃	1	2	yes	complemented
137	#869	C₂²×C₃	1	2	yes	complemented
138	C₃×#107	—	3	1	no	—
139	C₃×#107	—	3	1	no	—
140	C₃×#107	—	3	2	no	—
141	C₃×#106	—	3	1	no	—
142	C₃×#106	—	3	1	no	—
143	C₃×#106	—	3	2	no	—
144	C₃×C₄⋊C₈	—	2	2	no	—
145	C₃×C₄⋊C₈	—	2	2	no	—
146	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	complemented
147	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	complemented
148	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
149	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
150	C₃×#102	—	3	2	no	—
151	C₃×#102	—	3	2	no	—
152	C₃×#102	—	3	2	no	—
153	C₃×#102	—	3	2	no	—
154	#821	C₂²×C₃	1	2	yes	—
155	#821	C₂²×C₃	1	2	yes	—
156	#821	C₂²×C₃	1	2	yes	—
157	#821	C₂²×C₃	1	2	yes	—
158	#818	C₂²×C₃	1	2	yes	complemented
159	#818	C₂²×C₃	1	1	yes	characteristic, complemented
160	#818	C₂²×C₃	1	1	yes	characteristic, complemented
161	#817	C₂²×C₃	1	2	yes	complemented
162	#817	C₂²×C₃	1	1	yes	characteristic, complemented
163	#817	C₂²×C₃	1	1	yes	characteristic, complemented
164	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₃×D₃	—	2	2	no	—
166	C₂²×C₃×D₃	—	2	4	no	—
167	C₂²×C₃×D₃	—	8	1	no	—
168	C₂²×C₃×D₃	—	8	1	no	—
169	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
170	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
171	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
172	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
173	C₂×C₃²×C₄	#41	1	2	yes	—
174	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
175	C₂×C₃×Dic₃	—	2	1	no	—
176	C₂×C₃×Dic₃	—	2	1	no	—
177	C₂×C₃×Dic₃	—	2	1	no	—
178	C₂×C₃×Dic₃	—	2	1	no	—
179	C₂×C₃×Dic₃	—	2	2	no	—
180	C₂×C₃×Dic₃	—	8	1	no	—
181	C₃×D₁₂	—	2	4	no	—
182	C₃×D₁₂	—	2	2	no	—
183	C₃×D₁₂	C₂×Q₈	1	4	yes	—
184	C₃×C₄×D₃	—	8	2	no	—
185	C₃×C₄×D₃	—	8	2	no	—
186	C₃×Dic₆	—	8	2	no	—
187	C₃²×C₈	—	2	1	no	—
188	C₃²×C₈	—	2	1	no	—
189	C₃²×C₈	—	2	2	no	—
190	#544	—	3	1	no	—
191	#518	—	3	1	no	—
192	#478	—	3	2	no	—
193	#478	—	3	2	no	—
194	#476	—	3	2	no	—
195	#474	—	3	2	no	—
196	#428	—	3	1	no	—
197	#427	—	3	1	no	—
198	#424	C₃×D₃	1	1	yes	characteristic, complemented
199	#418	—	3	1	no	—
200	C₂×#102	—	3	1	no	—
201	C₂⁴×C₃	—	6	1	no	—
202	C₂³×D₃	—	2	1	no	—
203	C₂×C₃×Q₈	—	6	2	no	—
204	C₂×C₃×D₄	—	3	4	no	—
205	C₂×C₃×D₄	—	3	2	no	—
206	C₂×C₃×D₄	—	6	1	no	—
207	C₂×C₃×D₄	—	6	2	no	—
208	C₂²×C₃×C₄	—	2	1	no	—
209	C₂²×C₃×C₄	—	6	1	no	—
210	C₂²×C₃×C₄	—	6	2	no	—
211	C₂²×C₃×C₄	—	6	2	no	—
212	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
213	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
214	C₂²×Dic₃	—	2	1	no	—
215	C₂×D₁₂	—	2	1	no	—
216	C₂×D₁₂	—	2	2	no	—
217	C₂×D₁₂	C₃×Q₈	1	4	yes	complemented
218	C₂×D₁₂	C₂³×C₃	1	2	yes	—
219	C₂×C₄×D₃	—	2	2	no	—
220	C₂×C₄×D₃	—	2	2	no	—
221	C₂×Dic₆	—	2	2	no	—
222	C₃×M₁₆	—	2	2	no	—
223	C₃×M₁₆	—	2	2	no	—
224	C₃×M₁₆	—	4	2	no	—
225	C₂×C₃×C₈	—	2	2	no	—
226	C₂×C₃×C₈	—	2	2	no	—
227	C₂×C₃×C₈	—	2	1	no	—
228	C₂×C₃×C₈	—	2	1	no	—
229	C₂×C₃×C₈	—	2	2	no	—
230	C₂×C₃×C₈	—	4	2	no	—
231	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
232	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
233	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
234	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
235	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
236	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
237	C₃×C₄⋊C₄	—	2	1	no	—
238	C₃×C₄⋊C₄	—	2	1	no	—
239	C₃×C₄⋊C₄	—	3	2	no	—
240	C₃×C₄⋊C₄	—	3	1	no	—
241	C₃×C₄⋊C₄	—	3	1	no	—
242	C₃×C₄⋊C₄	—	3	1	no	—
243	C₃×C₄⋊C₄	—	3	1	no	—
244	C₃×C₄⋊C₄	—	6	2	no	—
245	C₃×C₄⋊C₄	—	6	2	no	—
246	C₃×C₄⋊C₄	—	6	1	no	—
247	C₃×C₄⋊C₄	—	6	2	no	—
248	C₃×C₄⋊C₄	D₁₂	1	1	yes	characteristic
249	C₃×C₄⋊C₄	D₁₂	1	1	yes	characteristic
250	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
251	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
252	C₃×C₂²⋊C₄	—	2	2	no	—
253	C₃×C₂²⋊C₄	—	6	1	no	—
254	C₃×C₂²⋊C₄	—	6	1	no	—
255	C₃×C₂²⋊C₄	—	6	2	no	—
256	C₃×C₂²⋊C₄	—	6	2	no	—
257	C₃×C₂²⋊C₄	D₁₂	1	2	yes	—
258	C₃×C₂²⋊C₄	C₃×D₄	1	2	yes	—
259	C₃×C₄²	—	2	2	no	—
260	C₃×C₄²	—	6	1	no	—
261	C₃×C₄²	—	6	1	no	—
262	C₃×C₄²	C₂²×D₃	1	2	yes	—
263	C₃×C₄²	C₂³×C₃	1	2	yes	—
264	#217	—	2	1	no	—
265	#217	—	2	1	no	—
266	(C₂×D₃)⋊C₄	—	2	2	no	—
267	(C₂×D₃)⋊C₄	—	2	2	no	—
268	C₄⋊Dic₃	—	2	2	no	—
269	C₄⋊Dic₃	—	2	1	no	—
270	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
271	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
272	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
273	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
274	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
275	Dic₃⋊C₄	—	2	2	no	—
276	Dic₃⋊C₄	—	2	2	no	—
277	C₄×Dic₃	—	2	1	no	—
278	C₄×Dic₃	—	2	1	no	—
279	C₂²×C₃²	—	2	1	no	—
280	C₂²×C₃²	—	2	1	no	—
281	C₂²×C₃²	C₂²⋊Q₈	1	2	yes	—
282	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₃×D₃	—	2	4	no	—
284	C₂×C₃×D₃	—	4	2	no	—
285	C₂×C₃×D₃	—	4	2	no	—
286	C₂×C₃×D₃	—	8	4	no	—
287	C₃²×C₄	—	2	2	no	—
288	C₃²×C₄	—	2	2	no	—
289	C₃²×C₄	C₂²⋊Q₈	1	2	yes	—
290	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
291	C₃²×C₄	C₂×#41	1	1	yes	characteristic
292	C₃×Dic₃	—	4	1	no	—
293	C₃×Dic₃	—	4	2	no	—
294	C₃×Dic₃	—	4	1	no	—
295	C₃×Dic₃	—	4	1	no	—
296	C₃×Dic₃	—	4	1	no	—
297	C₂²×D₄	—	3	1	no	—
298	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
299	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
300	C₄⋊Q₈	—	3	2	no	—
301	C₄⋊Q₈	—	6	1	no	—
302	#125	—	3	2	no	—
303	#125	—	6	1	no	—
304	C₂²⋊Q₈	—	6	2	no	—
305	C₄×D₄	—	3	2	no	—
306	C₄×D₄	—	3	2	no	—
307	C₄×D₄	—	6	1	no	—
308	C₄×D₄	—	6	1	no	—
309	#117	—	3	1	no	—
310	#117	—	3	1	no	—
311	#117	C₂×C₃×D₃	1	1	yes	characteristic
312	C₂×C₄⋊C₄	—	3	1	no	—
313	C₂×C₂²⋊C₄	—	6	2	no	—
314	#107	—	3	1	no	—
315	#107	—	3	1	no	—
316	#107	—	3	2	no	—
317	#106	—	3	1	no	—
318	#106	—	3	1	no	—
319	#106	—	3	2	no	—
320	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	complemented
321	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	complemented
322	#102	—	3	2	no	—
323	#102	—	3	2	no	—
324	#102	—	3	2	no	—
325	#102	—	3	2	no	—
326	C₂³×C₃	—	2	1	no	—
327	C₂³×C₃	—	6	2	no	—
328	C₂³×C₃	—	6	4	no	—
329	C₂³×C₃	—	24	1	no	—
330	C₂³×C₃	—	24	1	no	—
331	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
332	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
333	C₂²×D₃	—	2	2	no	—
334	C₂²×D₃	—	2	4	no	—
335	C₂²×D₃	—	8	1	no	—
336	C₂²×D₃	—	8	1	no	—
337	C₃×Q₈	—	24	2	no	—
338	C₃×D₄	—	3	4	no	—
339	C₃×D₄	—	6	4	no	—
340	C₃×D₄	—	6	2	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	—	2	2	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	2	2	no	—
347	C₂×C₃×C₄	—	6	1	no	—
348	C₂×C₃×C₄	—	6	1	no	—
349	C₂×C₃×C₄	—	6	1	no	—
350	C₂×C₃×C₄	—	6	1	no	—
351	C₂×C₃×C₄	—	6	2	no	—
352	C₂×C₃×C₄	—	24	2	no	—
353	C₂×C₃×C₄	—	24	2	no	—
354	C₂×C₃×C₄	—	24	1	no	—
355	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
356	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
357	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
358	C₂×C₃×C₄	#237	1	2	yes	—
359	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
360	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
361	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
362	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
364	C₂×C₃×C₄	C₃×#41	1	2	yes	—
365	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
366	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
367	C₂×Dic₃	—	2	1	no	—
368	C₂×Dic₃	—	2	1	no	—
369	C₂×Dic₃	—	2	1	no	—
370	C₂×Dic₃	—	2	1	no	—
371	C₂×Dic₃	—	2	2	no	—
372	C₂×Dic₃	—	8	1	no	—
373	D₁₂	—	2	4	no	—
374	D₁₂	—	2	2	no	—
375	D₁₂	C₂×C₃×Q₈	1	4	yes	—
376	C₄×D₃	—	8	2	no	—
377	C₄×D₃	—	8	2	no	—
378	Dic₆	—	8	2	no	—
379	C₃×C₈	—	2	1	no	—
380	C₃×C₈	—	2	1	no	—
381	C₃×C₈	—	2	2	no	—
382	C₃×C₈	—	2	1	no	—
383	C₃×C₈	—	2	1	no	—
384	C₃×C₈	—	2	2	no	—
385	C₃×C₈	—	4	1	no	—
386	C₃×C₈	—	4	1	no	—
387	C₃×C₈	—	4	2	no	—
388	C₂×C₃²	—	2	2	no	—
389	C₂×C₃²	C₂×C₂²⋊Q₈	1	1	yes	characteristic
390	C₂×C₃²	#576	1	1	yes	characteristic
391	C₂×C₃²	#577	1	1	yes	characteristic
392	C₃×D₃	—	4	4	no	—
393	C₂⁴	—	6	1	no	—
394	C₂×Q₈	—	6	2	no	—
395	C₂×D₄	—	3	2	no	—
396	C₂×D₄	—	3	4	no	—
397	C₂×D₄	—	6	1	no	—
398	C₂×D₄	—	6	2	no	—
399	C₂²×C₄	—	6	1	no	—
400	C₂²×C₄	—	6	2	no	—
401	C₂²×C₄	—	6	2	no	—
402	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
403	M₁₆	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
406	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
407	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
408	C₄⋊C₄	—	3	2	no	—
409	C₄⋊C₄	—	3	1	no	—
410	C₄⋊C₄	—	3	1	no	—
411	C₄⋊C₄	—	3	1	no	—
412	C₄⋊C₄	—	3	1	no	—
413	C₄⋊C₄	—	6	1	no	—
414	C₄⋊C₄	—	6	2	no	—
415	C₄⋊C₄	—	6	2	no	—
416	C₄⋊C₄	—	6	2	no	—
417	C₄⋊C₄	C₃×D₁₂	1	1	yes	characteristic
418	C₄⋊C₄	C₃×D₁₂	1	1	yes	characteristic
419	C₂²⋊C₄	—	6	1	no	—
420	C₂²⋊C₄	—	6	1	no	—
421	C₂²⋊C₄	—	6	2	no	—
422	C₂²⋊C₄	—	6	2	no	—
423	C₂²⋊C₄	C₃×D₁₂	1	2	yes	—
424	C₄²	—	6	1	no	—
425	C₄²	—	6	1	no	—
426	C₄²	C₂²×C₃×D₃	1	2	yes	—
427	C₂²×C₃	—	2	1	no	—
428	C₂²×C₃	—	2	1	no	—
429	C₂²×C₃	—	2	1	no	—
430	C₂²×C₃	—	2	1	no	—
431	C₂²×C₃	—	2	2	no	—
432	C₂²×C₃	—	2	1	no	—
433	C₂²×C₃	—	4	1	no	—
434	C₂²×C₃	—	4	1	no	—
435	C₂²×C₃	—	6	4	no	—
436	C₂²×C₃	—	12	2	no	—
437	C₂²×C₃	—	12	2	no	—
438	C₂²×C₃	—	24	4	no	—
439	C₂²×C₃	#897	1	2	yes	—
440	C₂²×C₃	C₃×C₂²⋊Q₈	1	2	yes	—
441	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
442	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
443	C₂×D₃	—	2	4	no	—
444	C₂×D₃	—	4	2	no	—
445	C₂×D₃	—	4	2	no	—
446	C₂×D₃	—	8	4	no	—
447	C₃×C₄	—	2	2	no	—
448	C₃×C₄	—	2	2	no	—
449	C₃×C₄	—	2	2	no	—
450	C₃×C₄	—	2	2	no	—
451	C₃×C₄	—	2	2	no	—
452	C₃×C₄	—	2	1	no	—
453	C₃×C₄	—	2	1	no	—
454	C₃×C₄	—	4	2	no	—
455	C₃×C₄	—	4	2	no	—
456	C₃×C₄	—	12	1	no	—
457	C₃×C₄	—	12	1	no	—
458	C₃×C₄	—	12	1	no	—
459	C₃×C₄	—	12	2	no	—
460	C₃×C₄	—	12	1	no	—
461	C₃×C₄	#897	1	2	yes	—
462	C₃×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
463	C₃×C₄	C₂×#237	1	1	yes	characteristic
464	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
465	C₃×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
466	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
467	Dic₃	—	4	1	no	—
468	Dic₃	—	4	2	no	—
469	Dic₃	—	4	1	no	—
470	Dic₃	—	4	1	no	—
471	Dic₃	—	4	1	no	—
472	C₃²	#3081	1	1	yes	characteristic, complemented, Sylow
473	C₂³	—	6	2	no	—
474	C₂³	—	6	4	no	—
475	C₂³	—	24	1	no	—
476	C₂³	—	24	1	no	—
477	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
478	Q₈	—	24	2	no	—
479	D₄	—	3	4	no	—
480	D₄	—	6	4	no	—
481	D₄	—	6	2	no	—
482	C₂×C₄	—	6	1	no	—
483	C₂×C₄	—	6	1	no	—
484	C₂×C₄	—	6	1	no	—
485	C₂×C₄	—	6	1	no	—
486	C₂×C₄	—	6	2	no	—
487	C₂×C₄	—	24	2	no	—
488	C₂×C₄	—	24	2	no	—
489	C₂×C₄	—	24	1	no	—
490	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
491	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
492	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
493	C₂×C₄	C₃×#237	1	2	yes	—
494	C₂×C₄	C₃×D₃×Q₈	1	2	yes	—
495	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
496	C₈	—	2	1	no	—
497	C₈	—	2	1	no	—
498	C₈	—	2	2	no	—
499	C₂×C₃	—	2	2	no	—
500	C₂×C₃	—	2	2	no	—
501	C₂×C₃	—	2	1	no	—
502	C₂×C₃	—	2	1	no	—
503	C₂×C₃	—	2	1	no	—
504	C₂×C₃	—	4	2	no	—
505	C₂×C₃	—	12	4	no	—
506	C₂×C₃	C₂×#897	1	1	yes	characteristic
507	C₂×C₃	#5751	1	1	yes	characteristic
508	C₂×C₃	#5752	1	1	yes	characteristic
509	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
510	C₂×C₃	C₃×#576	1	1	yes	characteristic
511	C₂×C₃	C₃×#577	1	1	yes	characteristic
512	D₃	—	4	4	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	6	4	no	—
516	C₂²	—	12	2	no	—
517	C₂²	—	12	2	no	—
518	C₂²	—	24	4	no	—
519	C₂²	C₃×#897	1	2	yes	—
520	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	12	1	no	—
524	C₄	—	12	1	no	—
525	C₄	—	12	1	no	—
526	C₄	—	12	2	no	—
527	C₄	—	12	1	no	—
528	C₄	C₃×#897	1	2	yes	—
529	C₄	C₂×C₃×#237	1	1	yes	characteristic
530	C₄	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
531	C₃	—	2	1	no	—
532	C₃	#79090	1	1	yes	characteristic, direct product factor
533	C₃	C₃×#3081	1	1	yes	characteristic, complemented
534	C₂	—	2	2	no	—
535	C₂	—	12	4	no	—
536	C₂	C₂×C₃×#897	1	1	yes	characteristic
537	C₂	C₃×#5751	1	1	yes	characteristic
538	C₂	C₃×#5752	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#424	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂²×C₃×D₁₂	C₂²
hypercenter	C₃×#424	D₃
hypocenter	C₃	C₃×#3081
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ C₃×#424

Complements

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

N	H ≅ G/N	type
2. C₃×#5519	C₂	semidirect
3. C₃²×#424	C₂	semidirect
5. C₃×#5121	C₂	semidirect
7. C₃×#5106	C₂	semidirect
8. C₃×#4847	C₂	semidirect
9. C₃×#4847	C₂	semidirect
10. C₃×#4846	C₂	semidirect
11. C₃×#4842	C₂	semidirect
13. #79090	C₃	direct (N × H)
29. C₃×#870	C₂²	semidirect
30. C₃×#869	C₂²	semidirect
31. C₃²×C₄⋊C₈	C₂²	semidirect
32. C₃²×C₄⋊C₈	C₂²	semidirect
37. C₃×#818	C₂²	semidirect
38. C₃×#818	C₂²	semidirect
39. C₃×#818	C₂²	semidirect
40. C₃×#817	C₂²	semidirect
41. C₃×#817	C₂²	semidirect
42. C₃×#817	C₂²	semidirect
46. #5519	C₂×C₃	semidirect
54. C₃×#424	D₃	semidirect
55. C₃×#424	C₂×C₃	semidirect
59. #5121	C₂×C₃	semidirect
61. #5106	C₂×C₃	semidirect
62. #4847	C₂×C₃	semidirect
63. #4847	C₂×C₃	semidirect
64. #4846	C₂×C₃	semidirect
65. #4842	C₂×C₃	semidirect
71. C₂×C₃×D₁₂	Q₈	semidirect
136. #870	C₂²×C₃	semidirect
137. #869	C₂²×C₃	semidirect
146. C₃×C₄⋊C₈	C₂×D₃	semidirect
147. C₃×C₄⋊C₈	C₂×D₃	semidirect
148. C₃×C₄⋊C₈	C₂²×C₃	semidirect
149. C₃×C₄⋊C₈	C₂²×C₃	semidirect
158. #818	C₂²×C₃	semidirect
159. #818	C₂²×C₃	semidirect
160. #818	C₂²×C₃	semidirect
161. #817	C₂²×C₃	semidirect
162. #817	C₂²×C₃	semidirect
163. #817	C₂²×C₃	semidirect
198. #424	C₃×D₃	semidirect
217. C₂×D₁₂	C₃×Q₈	semidirect
320. C₄⋊C₈	C₂×C₃×D₃	semidirect
321. C₄⋊C₈	C₂×C₃×D₃	semidirect
472. C₃²	#3081	semidirect
532. C₃	#79090	direct (N × H)
533. C₃	C₃×#3081	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5521	2
C₃×#5519	2
C₃²×#424	2
C₃×#5131	2
C₃×#5121	2
C₂×C₃×#821	2
C₃×#5106	2
C₃×#4847	2
C₃×#4846	2
C₃×#4842	2
C₃×#3081	3
#79090	3

Subgroups — C3×#79090 #11868938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79090 #11868938