Subgroups — C₃×#33590 #10652197

Order 768.

694 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#508	C₂	1	1	yes	maximal, characteristic
3	C₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2211	C₂	1	2	yes	maximal, complemented
6	C₃×#2210	C₂	1	2	yes	maximal, complemented
7	C₃×#2209	C₂	1	2	yes	maximal, complemented
8	C₃×#2208	C₂	1	2	yes	maximal, complemented
9	C₃×#2151	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2139	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#358	C₂	1	1	yes	maximal, characteristic, complemented
12	#33590	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×#137	—	2	1	no	—
14	C₂×C₃×#135	C₂²	1	1	yes	characteristic
15	C₂×C₃×#135	C₂²	1	1	yes	characteristic
16	C₂²×C₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₃×#536	—	2	1	no	—
18	C₃×#520	—	2	1	no	—
19	C₃×#510	—	2	4	no	—
20	C₃×#508	—	2	4	no	—
21	C₂×C₃×Q₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₃×Q₃₂	C₂²	1	2	yes	—
23	C₂×C₃×SD₃₂	C₂²	1	1	yes	characteristic
24	C₂×C₃×SD₃₂	C₂²	1	1	yes	characteristic
25	C₂×C₃×SD₃₂	C₂²	1	2	yes	—
26	C₂×C₃×D₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₃×M₃₂	C₂²	1	1	yes	characteristic
28	C₂²×C₃×C₁₆	C₂²	1	1	yes	characteristic
29	C₃×#497	—	2	2	no	—
30	C₃×#495	C₂²	1	2	yes	—
31	C₃×#494	C₂²	1	2	yes	—
32	C₃×#440	—	2	2	no	—
33	C₃×C₄×Q₁₆	C₂²	1	2	yes	—
34	C₃×C₄×D₈	C₂²	1	2	yes	—
35	C₂×C₃×#107	C₂²	1	1	yes	characteristic
36	C₃×#417	—	2	1	no	—
37	C₃×#405	C₂²	1	1	yes	characteristic
38	C₃×C₄⋊C₁₆	C₂²	1	2	yes	—
39	C₃×C₄⋊C₁₆	C₂²	1	2	yes	—
40	C₃×#358	C₂²	1	2	yes	—
41	C₃×#358	C₂²	1	2	yes	—
42	C₃×#358	C₂²	1	2	yes	—
43	C₃×#357	C₂²	1	2	yes	—
44	C₂×#510	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×#508	C₂×C₃	1	1	yes	characteristic
46	#3156	C₂×C₃	1	1	yes	characteristic, complemented
47	#2951	C₂×C₃	1	1	yes	characteristic, complemented
48	#2211	C₂×C₃	1	2	yes	complemented
49	#2210	C₂×C₃	1	2	yes	complemented
50	#2209	C₂×C₃	1	2	yes	complemented
51	#2208	C₂×C₃	1	2	yes	complemented
52	#2151	C₂×C₃	1	1	yes	characteristic, complemented
53	#2139	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×#358	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×C₃×#41	—	2	1	no	—
56	C₂×C₃×#41	—	2	1	no	—
57	C₂²×C₃×Q₈	—	2	1	no	—
58	C₃×#137	—	4	4	no	—
59	C₃×#135	—	2	2	no	—
60	C₃×#135	—	2	2	no	—
61	C₃×#135	—	2	2	no	—
62	C₃×#135	D₄	1	4	yes	—
63	C₂×C₃×Q₁₆	—	2	2	no	—
64	C₂×C₃×Q₁₆	—	2	1	no	—
65	C₂×C₃×Q₁₆	—	2	2	no	—
66	C₂×C₃×Q₁₆	—	2	2	no	—
67	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
68	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
69	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
70	C₂×C₃×SD₁₆	—	2	1	no	—
71	C₂×C₃×SD₁₆	—	2	1	no	—
72	C₂×C₃×SD₁₆	—	2	2	no	—
73	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
74	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
75	C₂×C₃×M₁₆	D₄	1	1	yes	characteristic
76	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
77	C₃×C₄⋊Q₈	—	2	2	no	—
78	C₃×#124	—	2	2	no	—
79	C₃×#123	—	4	2	no	—
80	C₃×C₂²⋊Q₈	—	4	1	no	—
81	C₃×C₂²⋊Q₈	—	4	1	no	—
82	C₃×C₄×Q₈	—	2	2	no	—
83	C₃×C₄×D₄	—	2	2	no	—
84	C₃×C₄×D₄	—	4	2	no	—
85	C₃×#117	—	4	1	no	—
86	C₃×#117	D₄	1	1	yes	characteristic
87	C₂×C₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₃×C₄⋊C₄	—	4	1	no	—
89	C₃×Q₃₂	—	2	2	no	—
90	C₃×Q₃₂	—	2	4	no	—
91	C₃×SD₃₂	—	2	2	no	—
92	C₃×SD₃₂	—	2	2	no	—
93	C₃×SD₃₂	—	2	4	no	—
94	C₃×D₁₆	—	2	2	no	—
95	C₃×M₃₂	—	2	2	no	—
96	C₂×C₃×C₁₆	—	2	2	no	—
97	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₁₆	C₂³	1	2	yes	—
100	C₃×#107	—	2	1	no	—
101	C₃×#107	C₂³	1	2	yes	—
102	C₃×#103	—	2	2	no	—
103	C₃×#102	—	2	2	no	—
104	C₃×#97	D₄	1	2	yes	—
105	C₃×C₄×C₈	C₂³	1	2	yes	—
106	C₂×#137	—	2	1	no	—
107	C₂×#135	C₂²×C₃	1	1	yes	characteristic
108	C₂×#135	C₂²×C₃	1	1	yes	characteristic
109	C₂²×Q₁₆	C₂²×C₃	1	1	yes	characteristic
110	#536	—	2	1	no	—
111	#520	—	2	1	no	—
112	#510	—	2	4	no	—
113	#508	—	2	4	no	—
114	C₂×Q₃₂	C₂²×C₃	1	1	yes	characteristic
115	C₂×Q₃₂	C₂²×C₃	1	2	yes	—
116	C₂×SD₃₂	C₂²×C₃	1	1	yes	characteristic
117	C₂×SD₃₂	C₂²×C₃	1	1	yes	characteristic
118	C₂×SD₃₂	C₂²×C₃	1	2	yes	—
119	C₂×D₁₆	C₂²×C₃	1	1	yes	characteristic
120	C₂×M₃₂	C₂²×C₃	1	1	yes	characteristic
121	C₂²×C₁₆	C₂²×C₃	1	1	yes	characteristic
122	#497	—	2	2	no	—
123	#495	C₂²×C₃	1	2	yes	—
124	#494	C₂²×C₃	1	2	yes	—
125	#440	—	2	2	no	—
126	C₄×Q₁₆	C₂²×C₃	1	2	yes	—
127	C₄×D₈	C₂²×C₃	1	2	yes	—
128	C₂×#107	C₂²×C₃	1	1	yes	characteristic
129	#417	—	2	1	no	—
130	#405	C₂²×C₃	1	1	yes	characteristic
131	C₄⋊C₁₆	C₂²×C₃	1	2	yes	—
132	C₄⋊C₁₆	C₂²×C₃	1	2	yes	—
133	#358	C₂²×C₃	1	2	yes	—
134	#358	C₂²×C₃	1	2	yes	—
135	#358	C₂²×C₃	1	2	yes	—
136	#357	C₂²×C₃	1	2	yes	—
137	C₃×#41	—	2	4	no	—
138	C₃×#41	—	4	2	no	—
139	C₃×#41	—	4	2	no	—
140	C₃×#41	—	4	2	no	—
141	C₂×C₃×Q₈	—	2	1	no	—
142	C₂×C₃×Q₈	—	2	2	no	—
143	C₂×C₃×Q₈	—	2	1	no	—
144	C₂×C₃×Q₈	—	4	1	no	—
145	C₂×C₃×Q₈	—	4	2	no	—
146	C₂×C₃×Q₈	—	4	2	no	—
147	C₂×C₃×D₄	—	2	1	no	—
148	C₂×C₃×D₄	—	2	1	no	—
149	C₂×C₃×D₄	—	4	1	no	—
150	C₂×C₃×D₄	—	4	1	no	—
151	C₂²×C₃×C₄	—	4	1	no	—
152	C₂²×C₃×C₄	—	4	1	no	—
153	C₂²×C₃×C₄	—	4	1	no	—
154	C₂²×C₃×C₄	—	4	1	no	—
155	C₂²×C₃×C₄	—	4	2	no	—
156	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
157	C₃×Q₁₆	—	2	2	no	—
158	C₃×Q₁₆	—	2	1	no	—
159	C₃×Q₁₆	—	2	1	no	—
160	C₃×Q₁₆	—	2	2	no	—
161	C₃×Q₁₆	—	2	1	no	—
162	C₃×Q₁₆	—	4	4	no	—
163	C₃×Q₁₆	—	4	2	no	—
164	C₃×Q₁₆	C₂×D₄	1	2	yes	—
165	C₃×SD₁₆	—	2	4	no	—
166	C₃×SD₁₆	—	4	4	no	—
167	C₃×SD₁₆	—	4	2	no	—
168	C₃×D₈	—	2	1	no	—
169	C₃×D₈	—	2	1	no	—
170	C₃×D₈	—	2	1	no	—
171	C₃×D₈	C₂×D₄	1	2	yes	—
172	C₃×M₁₆	—	2	2	no	—
173	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
174	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
175	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
176	C₂×C₃×C₈	#41	1	2	yes	—
177	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
178	C₃×C₄⋊C₄	—	2	2	no	—
179	C₃×C₄⋊C₄	—	4	1	no	—
180	C₃×C₄⋊C₄	—	4	2	no	—
181	C₃×C₄⋊C₄	—	4	2	no	—
182	C₃×C₄⋊C₄	—	4	2	no	—
183	C₃×C₄⋊C₄	D₈	1	1	yes	characteristic
184	C₃×C₄⋊C₄	D₈	1	1	yes	characteristic
185	C₃×C₂²⋊C₄	—	4	2	no	—
186	C₃×C₂²⋊C₄	—	4	2	no	—
187	C₃×C₂²⋊C₄	—	4	2	no	—
188	C₃×C₂²⋊C₄	D₈	1	2	yes	—
189	C₃×C₄²	—	4	2	no	—
190	C₃×C₄²	C₂×D₄	1	2	yes	—
191	C₃×C₁₆	—	2	1	no	—
192	C₃×C₁₆	—	2	1	no	—
193	C₃×C₁₆	—	2	2	no	—
194	C₂×#41	—	2	1	no	—
195	C₂×#41	—	2	1	no	—
196	C₂²×Q₈	—	2	1	no	—
197	#137	—	4	4	no	—
198	#135	—	2	2	no	—
199	#135	—	2	2	no	—
200	#135	—	2	2	no	—
201	#135	C₃×D₄	1	4	yes	—
202	C₂×Q₁₆	—	2	2	no	—
203	C₂×Q₁₆	—	2	1	no	—
204	C₂×Q₁₆	—	2	2	no	—
205	C₂×Q₁₆	—	2	2	no	—
206	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
207	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
208	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
209	C₂×SD₁₆	—	2	1	no	—
210	C₂×SD₁₆	—	2	1	no	—
211	C₂×SD₁₆	—	2	2	no	—
212	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
213	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
214	C₂×M₁₆	C₃×D₄	1	1	yes	characteristic
215	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
216	C₄⋊Q₈	—	2	2	no	—
217	#124	—	2	2	no	—
218	#123	—	4	2	no	—
219	C₂²⋊Q₈	—	4	1	no	—
220	C₂²⋊Q₈	—	4	1	no	—
221	C₄×Q₈	—	2	2	no	—
222	C₄×D₄	—	2	2	no	—
223	C₄×D₄	—	4	2	no	—
224	#117	—	4	1	no	—
225	#117	C₃×D₄	1	1	yes	characteristic
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₄⋊C₄	—	4	1	no	—
228	Q₃₂	—	2	2	no	—
229	Q₃₂	—	2	4	no	—
230	SD₃₂	—	2	2	no	—
231	SD₃₂	—	2	2	no	—
232	SD₃₂	—	2	4	no	—
233	D₁₆	—	2	2	no	—
234	M₃₂	—	2	2	no	—
235	C₂×C₁₆	—	2	2	no	—
236	C₂×C₁₆	C₂³×C₃	1	2	yes	—
237	C₂×C₁₆	C₂³×C₃	1	1	yes	characteristic
238	C₂×C₁₆	C₂³×C₃	1	1	yes	characteristic
239	#107	—	2	1	no	—
240	#107	C₂³×C₃	1	2	yes	—
241	#103	—	2	2	no	—
242	#102	—	2	2	no	—
243	#97	C₃×D₄	1	2	yes	—
244	C₄×C₈	C₂³×C₃	1	2	yes	—
245	C₂³×C₃	—	4	1	no	—
246	C₂³×C₃	—	4	1	no	—
247	C₂³×C₃	C₂×D₈	1	1	yes	characteristic
248	C₃×Q₈	—	2	2	no	—
249	C₃×Q₈	—	4	1	no	—
250	C₃×Q₈	—	4	1	no	—
251	C₃×Q₈	—	4	2	no	—
252	C₃×Q₈	—	4	2	no	—
253	C₃×Q₈	—	4	1	no	—
254	C₃×Q₈	—	8	2	no	—
255	C₃×D₄	—	2	2	no	—
256	C₃×D₄	—	4	4	no	—
257	C₃×D₄	—	4	1	no	—
258	C₃×D₄	—	4	1	no	—
259	C₃×D₄	—	4	1	no	—
260	C₃×D₄	—	8	2	no	—
261	C₂×C₃×C₄	—	4	1	no	—
262	C₂×C₃×C₄	—	4	4	no	—
263	C₂×C₃×C₄	—	4	2	no	—
264	C₂×C₃×C₄	—	4	2	no	—
265	C₂×C₃×C₄	—	4	1	no	—
266	C₂×C₃×C₄	—	8	2	no	—
267	C₂×C₃×C₄	—	8	2	no	—
268	C₂×C₃×C₄	—	16	2	no	—
269	C₂×C₃×C₄	—	16	1	no	—
270	C₂×C₃×C₄	#121	1	2	yes	—
271	C₂×C₃×C₄	C₂×D₈	1	2	yes	—
272	C₂×C₃×C₄	C₂×D₈	1	2	yes	—
273	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
274	C₂×C₃×C₄	AGL(1,ℤ/8)	1	2	yes	—
275	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
276	C₃×C₈	—	2	2	no	—
277	C₃×C₈	#121	1	2	yes	—
278	C₃×C₈	C₂²×D₄	1	1	yes	characteristic
279	C₃×C₈	C₂×#41	1	1	yes	characteristic
280	#41	—	2	4	no	—
281	#41	—	4	2	no	—
282	#41	—	4	2	no	—
283	#41	—	4	2	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
300	Q₁₆	—	2	2	no	—
301	Q₁₆	—	2	1	no	—
302	Q₁₆	—	2	1	no	—
303	Q₁₆	—	2	2	no	—
304	Q₁₆	—	2	1	no	—
305	Q₁₆	—	4	4	no	—
306	Q₁₆	—	4	2	no	—
307	Q₁₆	C₂×C₃×D₄	1	2	yes	—
308	SD₁₆	—	2	4	no	—
309	SD₁₆	—	4	4	no	—
310	SD₁₆	—	4	2	no	—
311	D₈	—	2	1	no	—
312	D₈	—	2	1	no	—
313	D₈	—	2	1	no	—
314	D₈	C₂×C₃×D₄	1	2	yes	—
315	M₁₆	—	2	2	no	—
316	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
317	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
318	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
319	C₂×C₈	C₃×#41	1	2	yes	—
320	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	C₃×D₈	1	1	yes	characteristic
327	C₄⋊C₄	C₃×D₈	1	1	yes	characteristic
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	C₃×D₈	1	2	yes	—
332	C₄²	—	4	2	no	—
333	C₄²	C₂×C₃×D₄	1	2	yes	—
334	C₁₆	—	2	1	no	—
335	C₁₆	—	2	1	no	—
336	C₁₆	—	2	2	no	—
337	C₂²×C₃	—	2	1	no	—
338	C₂²×C₃	—	2	1	no	—
339	C₂²×C₃	—	4	2	no	—
340	C₂²×C₃	—	8	1	no	—
341	C₂²×C₃	—	8	1	no	—
342	C₂²×C₃	—	8	1	no	—
343	C₂²×C₃	—	8	1	no	—
344	C₂²×C₃	—	8	1	no	—
345	C₂²×C₃	#459	1	2	yes	—
346	C₂²×C₃	C₂²×D₈	1	1	yes	characteristic
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	—	4	2	no	—
350	C₃×C₄	—	8	2	no	—
351	C₃×C₄	—	8	1	no	—
352	C₃×C₄	—	8	2	no	—
353	C₃×C₄	#459	1	2	yes	—
354	C₃×C₄	C₂×#121	1	1	yes	characteristic
355	C₃×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
356	C₂³	—	4	1	no	—
357	C₂³	—	4	1	no	—
358	C₂³	C₂×C₃×D₈	1	1	yes	characteristic
359	Q₈	—	2	2	no	—
360	Q₈	—	4	1	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	1	no	—
363	Q₈	—	4	1	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	8	2	no	—
366	D₄	—	2	2	no	—
367	D₄	—	4	4	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	1	no	—
370	D₄	—	4	1	no	—
371	D₄	—	8	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	8	2	no	—
378	C₂×C₄	—	8	2	no	—
379	C₂×C₄	—	16	2	no	—
380	C₂×C₄	—	16	1	no	—
381	C₂×C₄	C₃×#121	1	2	yes	—
382	C₂×C₄	C₂×C₃×D₈	1	2	yes	—
383	C₂×C₄	C₂×C₃×D₈	1	2	yes	—
384	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
385	C₂×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
386	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	C₃×#121	1	2	yes	—
389	C₈	C₂²×C₃×D₄	1	1	yes	characteristic
390	C₈	C₂×C₃×#41	1	1	yes	characteristic
391	C₂×C₃	—	2	2	no	—
392	C₂×C₃	—	8	2	no	—
393	C₂×C₃	—	16	1	no	—
394	C₂×C₃	C₂×#459	1	1	yes	characteristic
395	C₂×C₃	#3416	1	1	yes	characteristic
396	C₂×C₃	#3417	1	1	yes	characteristic
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	8	1	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	C₃×#459	1	2	yes	—
406	C₂²	C₂²×C₃×D₈	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	2	no	—
413	C₄	C₃×#459	1	2	yes	—
414	C₄	C₂×C₃×#121	1	1	yes	characteristic
415	C₄	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
416	C₃	#33590	1	1	yes	characteristic, direct product factor, Sylow
417	C₂	—	2	2	no	—
418	C₂	—	8	2	no	—
419	C₂	—	16	1	no	—
420	C₂	C₂×C₃×#459	1	1	yes	characteristic
421	C₂	C₃×#3416	1	1	yes	characteristic
422	C₂	C₃×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃
prime radical	C₂×C₃×#508	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ C₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#510	C₂	semidirect
3. C₃×#3156	C₂	semidirect
4. C₃×#2951	C₂	semidirect
5. C₃×#2211	C₂	semidirect
6. C₃×#2210	C₂	semidirect
7. C₃×#2209	C₂	semidirect
8. C₃×#2208	C₂	semidirect
9. C₃×#2151	C₂	semidirect
10. C₃×#2139	C₂	semidirect
11. C₂×C₃×#358	C₂	semidirect
12. #33590	C₃	direct (N × H)
44. C₂×#510	C₂×C₃	semidirect
46. #3156	C₂×C₃	semidirect
47. #2951	C₂×C₃	semidirect
48. #2211	C₂×C₃	semidirect
49. #2210	C₂×C₃	semidirect
50. #2209	C₂×C₃	semidirect
51. #2208	C₂×C₃	semidirect
52. #2151	C₂×C₃	semidirect
53. #2139	C₂×C₃	semidirect
54. C₂×#358	C₂×C₃	semidirect
416. C₃	#33590	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×#510	2
C₂×C₃×#508	2
C₃×#3156	2
C₃×#2951	2
C₃×#2211	2
C₃×#2210	2
C₃×#2209	2
C₃×#2208	2
C₃×#2151	2
C₃×#2139	2
C₂×C₃×#358	2
#33590	3

Subgroups — C3×#33590 #10652197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#33590 #10652197