Subgroups — C₃×#10596228 #13179508

Order 1728.

1912 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#64361	C₂	1	2	yes	maximal, complemented
2	C₂×C₃³×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64141	C₂	1	2	yes	maximal, complemented
4	C₃×#64121	C₂	1	2	yes	maximal, complemented
5	C₃×#64120	C₂	1	4	yes	maximal, complemented
6	C₃×D₈×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
7	C₃×#64113	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64110	C₂	1	1	yes	maximal, characteristic, complemented
9	#10596228	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#5757	—	3	4	no	maximal
11	C₂×C₃³×D₄	C₂²	1	2	yes	complemented
12	C₂×C₃×#638	—	2	4	no	—
13	C₃×#3830	—	2	2	no	—
14	C₃×#3830	C₂²	1	4	yes	complemented
15	C₃×D₄×C₃⋊D₃	—	2	2	no	—
16	C₃×D₄×C₃⋊D₃	C₂²	1	4	yes	complemented
17	C₃×#3828	C₂²	1	1	yes	characteristic
18	C₃×#3828	C₂²	1	2	yes	complemented
19	C₃³×D₈	C₂²	1	2	yes	complemented
20	C₃³×D₈	C₂²	1	2	yes	complemented
21	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic, complemented
22	C₃×#3754	C₂²	1	4	yes	complemented
23	C₃×#3753	C₂²	1	4	yes	complemented
24	C₃×#3748	C₂²	1	1	yes	characteristic, complemented
25	C₃×#3746	C₂²	1	1	yes	characteristic, complemented
26	C₃×#3745	C₂²	1	1	yes	characteristic, complemented
27	C₃×#3744	C₂²	1	2	yes	complemented
28	C₃×#3743	C₂²	1	2	yes	complemented
29	C₃×C₈×C₃⋊D₃	C₂²	1	2	yes	complemented
30	#64361	C₂×C₃	1	2	yes	complemented
31	C₃×#1004	—	3	8	no	—
32	C₂×C₃²×D₈	—	2	4	no	—
33	C₂×C₃²×D₈	D₃	1	4	yes	complemented
34	C₂×C₃²×D₈	C₂×C₃	1	1	yes	characteristic, complemented
35	#64141	C₂×C₃	1	2	yes	complemented
36	#64121	C₂×C₃	1	2	yes	complemented
37	#64120	C₂×C₃	1	4	yes	complemented
38	D₈×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
39	#64113	C₂×C₃	1	1	yes	characteristic, complemented
40	#64110	C₂×C₃	1	1	yes	characteristic, complemented
41	C₃×#932	—	3	8	no	—
42	C₃×#912	—	3	8	no	—
43	C₃×#911	—	3	16	no	—
44	C₃×D₃×D₈	—	3	8	no	—
45	C₃×#904	—	3	4	no	—
46	C₃×#901	—	3	4	no	—
47	C₂³×C₃³	—	2	2	no	—
48	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
49	C₃³×D₄	—	2	2	no	—
50	C₃³×D₄	C₂³	1	4	yes	—
51	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
52	C₃×#638	—	2	2	no	—
53	C₃×#638	—	2	4	no	—
54	C₃×#638	—	2	4	no	—
55	C₃×#638	D₄	1	2	yes	—
56	C₂×C₃×C₃⋊Dic₃	—	2	4	no	—
57	C₃×C₄⋊(C₃⋊D₃)	D₄	1	1	yes	characteristic
58	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	2	yes	—
59	C₃×C₄×C₃⋊D₃	—	2	2	no	—
60	C₃×C₄×C₃⋊D₃	C₂³	1	2	yes	—
61	C₃×#634	D₄	1	1	yes	characteristic
62	C₃×#634	C₂³	1	2	yes	—
63	C₃³×C₈	C₂³	1	1	yes	characteristic
64	C₃³×C₈	C₂³	1	1	yes	characteristic
65	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	—
66	C₃×#576	—	9	1	no	—
67	#5757	—	3	4	no	—
68	C₂×C₃²×D₄	—	2	8	no	—
69	C₂×C₃²×D₄	C₂×D₃	1	8	yes	complemented
70	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	complemented
71	C₂×#638	—	2	4	no	—
72	#3830	—	2	2	no	—
73	#3830	C₂²×C₃	1	4	yes	complemented
74	D₄×C₃⋊D₃	—	2	2	no	—
75	D₄×C₃⋊D₃	C₂²×C₃	1	4	yes	complemented
76	#3828	C₂²×C₃	1	1	yes	characteristic
77	#3828	C₂²×C₃	1	2	yes	complemented
78	C₂×C₃×#67	—	6	16	no	—
79	C₃×#237	—	3	16	no	—
80	C₃×#237	—	6	8	no	—
81	C₃×D₃×D₄	—	3	16	no	—
82	C₃×D₃×D₄	—	6	8	no	—
83	C₃×#235	—	3	4	no	—
84	C₃×#235	—	3	8	no	—
85	C₃²×D₈	—	2	8	no	—
86	C₃²×D₈	—	2	8	no	—
87	C₃²×D₈	C₂×D₃	1	8	yes	complemented
88	C₃²×D₈	C₂×D₃	1	8	yes	complemented
89	C₃²×D₈	C₂²×C₃	1	2	yes	complemented
90	C₃²×D₈	C₂²×C₃	1	2	yes	complemented
91	C₂×C₃²×C₈	—	2	4	no	—
92	C₂×C₃²×C₈	C₂×D₃	1	4	yes	complemented
93	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
94	#3754	C₂²×C₃	1	4	yes	complemented
95	#3753	C₂²×C₃	1	4	yes	complemented
96	#3748	C₂²×C₃	1	1	yes	characteristic, complemented
97	#3746	C₂²×C₃	1	1	yes	characteristic, complemented
98	#3745	C₂²×C₃	1	1	yes	characteristic, complemented
99	#3744	C₂²×C₃	1	2	yes	complemented
100	#3743	C₂²×C₃	1	2	yes	complemented
101	C₈×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
102	C₃×#214	—	3	16	no	—
103	C₃×#213	—	3	16	no	—
104	C₃×#208	—	3	4	no	—
105	C₃×Dic₁₂	—	3	4	no	—
106	C₃×D₂₄	—	3	4	no	—
107	C₃×#204	—	3	8	no	—
108	C₃×ΓL(1,𝔽₂₅)	—	3	8	no	—
109	C₃×D₃×C₈	—	3	8	no	—
110	C₂²×C₃³	—	2	4	no	—
111	C₂²×C₃³	—	8	2	no	—
112	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₃⋊D₃	—	2	2	no	—
114	C₂×C₃×C₃⋊D₃	—	8	4	no	—
115	C₂×C₃×C₃⋊D₃	C₂×D₄	1	2	yes	—
116	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
117	C₃³×C₄	C₂⁴	1	1	yes	characteristic
118	C₃×C₃⋊Dic₃	—	2	2	no	—
119	C₃×C₃⋊Dic₃	C₂×D₄	1	2	yes	—
120	C₃×H(5,𝔽₂)	—	9	2	no	—
121	#1004	—	3	8	no	—
122	C₃×AGL(1,ℤ/8)	—	9	2	no	—
123	C₃×AGL(1,ℤ/8)	—	9	4	no	—
124	C₃×#135	—	9	2	no	—
125	C₃×#135	—	9	1	no	—
126	C₂×C₃×D₈	—	2	4	no	—
127	C₂×C₃×D₈	—	9	2	no	—
128	C₂×C₃×D₈	C₃×D₃	1	4	yes	complemented
129	C₂×C₃×D₈	C₃⋊D₃	1	1	yes	characteristic, complemented
130	C₃×#131	—	9	1	no	—
131	#932	—	3	8	no	—
132	#912	—	3	8	no	—
133	#911	—	3	16	no	—
134	D₃×D₈	—	3	8	no	—
135	#904	—	3	4	no	—
136	#901	—	3	4	no	—
137	C₂³×C₃²	—	2	2	no	—
138	C₂³×C₃²	—	2	8	no	—
139	C₂³×C₃²	—	4	8	no	—
140	C₂²×C₃⋊D₃	—	2	4	no	—
141	C₂²×C₃×D₃	—	6	16	no	—
142	C₃²×D₄	—	2	2	no	—
143	C₃²×D₄	—	2	16	no	—
144	C₃²×D₄	—	2	8	no	—
145	C₃²×D₄	—	4	8	no	—
146	C₃²×D₄	C₂²×D₃	1	16	yes	—
147	C₃²×D₄	C₂³×C₃	1	4	yes	—
148	C₂×C₃²×C₄	—	2	4	no	—
149	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
150	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
151	#638	—	2	2	no	—
152	#638	—	2	4	no	—
153	#638	—	2	4	no	—
154	#638	C₃×D₄	1	2	yes	—
155	C₂×C₃⋊Dic₃	—	2	4	no	—
156	C₄⋊(C₃⋊D₃)	C₃×D₄	1	1	yes	characteristic
157	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	2	yes	—
158	C₄×C₃⋊D₃	—	2	2	no	—
159	C₄×C₃⋊D₃	C₂³×C₃	1	2	yes	—
160	#634	C₃×D₄	1	1	yes	characteristic
161	#634	C₂³×C₃	1	2	yes	—
162	C₃×#67	—	3	8	no	—
163	C₃×#67	—	6	16	no	—
164	C₃×#67	—	6	16	no	—
165	C₃×#67	—	6	8	no	—
166	C₂×C₃×Dic₃	—	6	16	no	—
167	C₃×D₁₂	—	3	4	no	—
168	C₃×D₁₂	—	3	8	no	—
169	C₃×C₄×D₃	—	3	8	no	—
170	C₃×C₄×D₃	—	6	8	no	—
171	C₃×Dic₆	—	3	4	no	—
172	C₃×Dic₆	—	3	8	no	—
173	C₃²×C₈	—	2	4	no	—
174	C₃²×C₈	—	2	4	no	—
175	C₃²×C₈	C₂²×D₃	1	4	yes	—
176	C₃²×C₈	C₂²×D₃	1	4	yes	—
177	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
178	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
179	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	2	yes	—
180	C₃×C₃⋊C₈	—	3	8	no	—
181	#576	—	9	1	no	Sylow
182	C₂×C₃³	—	2	1	no	—
183	C₂×C₃³	—	4	4	no	—
184	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
185	C₃×C₃⋊D₃	—	2	2	no	—
186	C₃×C₃⋊D₃	—	4	2	no	—
187	C₃×#41	—	9	1	no	—
188	C₃×#41	—	9	4	no	—
189	C₃×#41	—	9	2	no	—
190	C₃×#41	—	18	2	no	—
191	C₂×C₃×D₄	—	2	8	no	—
192	C₂×C₃×D₄	—	9	4	no	—
193	C₂×C₃×D₄	—	18	2	no	—
194	C₂×C₃×D₄	—	18	4	no	—
195	C₂×C₃×D₄	C₂×C₃×D₃	1	8	yes	complemented
196	C₂×C₃×D₄	C₂×C₃⋊D₃	1	2	yes	complemented
197	C₂×#67	—	6	16	no	—
198	#237	—	3	16	no	—
199	#237	—	6	8	no	—
200	D₃×D₄	—	3	16	no	—
201	D₃×D₄	—	6	8	no	—
202	#235	—	3	4	no	—
203	#235	—	3	8	no	—
204	C₃×Q₁₆	—	9	1	no	—
205	C₃×SD₁₆	—	9	4	no	—
206	C₃×SD₁₆	—	9	2	no	—
207	C₃×D₈	—	2	8	no	—
208	C₃×D₈	—	2	8	no	—
209	C₃×D₈	—	9	4	no	—
210	C₃×D₈	—	9	1	no	—
211	C₃×D₈	C₂×C₃×D₃	1	8	yes	complemented
212	C₃×D₈	C₂×C₃×D₃	1	8	yes	complemented
213	C₃×D₈	C₂×C₃⋊D₃	1	2	yes	complemented
214	C₃×D₈	C₂×C₃⋊D₃	1	2	yes	complemented
215	C₃×M₁₆	—	9	1	no	—
216	C₃×M₁₆	—	9	2	no	—
217	C₂×C₃×C₈	—	2	4	no	—
218	C₂×C₃×C₈	—	9	2	no	—
219	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	complemented
220	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
221	#214	—	3	16	no	—
222	#213	—	3	16	no	—
223	#208	—	3	4	no	—
224	Dic₁₂	—	3	4	no	—
225	D₂₄	—	3	4	no	—
226	#204	—	3	8	no	—
227	ΓL(1,𝔽₂₅)	—	3	8	no	—
228	D₃×C₈	—	3	8	no	—
229	C₂²×C₃²	—	2	4	no	—
230	C₂²×C₃²	—	2	4	no	—
231	C₂²×C₃²	—	2	16	no	—
232	C₂²×C₃²	—	4	16	no	—
233	C₂²×C₃²	—	8	2	no	—
234	C₂²×C₃²	—	8	8	no	—
235	C₂²×C₃²	—	8	16	no	—
236	C₂²×C₃²	D₃×D₄	1	4	yes	—
237	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
238	C₂×C₃⋊D₃	—	2	2	no	—
239	C₂×C₃⋊D₃	—	8	4	no	—
240	C₂×C₃⋊D₃	C₂×C₃×D₄	1	2	yes	—
241	C₂×C₃×D₃	—	3	8	no	—
242	C₂×C₃×D₃	—	6	8	no	—
243	C₂×C₃×D₃	—	24	16	no	—
244	C₃²×C₄	—	2	4	no	—
245	C₃²×C₄	—	2	4	no	—
246	C₃²×C₄	D₃×D₄	1	4	yes	—
247	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
248	C₃²×C₄	C₂³×D₃	1	4	yes	—
249	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
250	C₃⋊Dic₃	—	2	2	no	—
251	C₃⋊Dic₃	C₂×C₃×D₄	1	2	yes	—
252	C₃×Dic₃	—	3	8	no	—
253	C₃×Dic₃	—	6	8	no	—
254	H(5,𝔽₂)	—	9	2	no	—
255	AGL(1,ℤ/8)	—	9	2	no	—
256	AGL(1,ℤ/8)	—	9	4	no	—
257	#135	—	9	2	no	—
258	#135	—	9	1	no	—
259	C₂×D₈	—	9	2	no	—
260	C₂×D₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
261	#131	—	9	1	no	—
262	C₃³	#576	1	1	yes	characteristic, complemented, Sylow
263	C₂³×C₃	—	2	8	no	—
264	C₂³×C₃	—	2	2	no	—
265	C₂³×C₃	—	4	8	no	—
266	C₂³×C₃	—	18	4	no	—
267	C₂²×D₃	—	6	16	no	—
268	C₃×Q₈	—	9	1	no	—
269	C₃×Q₈	—	9	2	no	—
270	C₃×D₄	—	2	8	no	—
271	C₃×D₄	—	2	2	no	—
272	C₃×D₄	—	2	16	no	—
273	C₃×D₄	—	4	8	no	—
274	C₃×D₄	—	9	2	no	—
275	C₃×D₄	—	9	2	no	—
276	C₃×D₄	—	9	1	no	—
277	C₃×D₄	—	18	4	no	—
278	C₃×D₄	—	18	4	no	—
279	C₃×D₄	—	18	2	no	—
280	C₃×D₄	C₂²×C₃×D₃	1	16	yes	—
281	C₃×D₄	C₂²×C₃⋊D₃	1	4	yes	—
282	C₂×C₃×C₄	—	2	4	no	—
283	C₂×C₃×C₄	—	9	2	no	—
284	C₂×C₃×C₄	—	18	4	no	—
285	C₂×C₃×C₄	—	18	2	no	—
286	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
287	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
288	#67	—	3	8	no	—
289	#67	—	6	16	no	—
290	#67	—	6	16	no	—
291	#67	—	6	8	no	—
292	C₂×Dic₃	—	6	16	no	—
293	D₁₂	—	3	8	no	—
294	D₁₂	—	3	4	no	—
295	C₄×D₃	—	3	8	no	—
296	C₄×D₃	—	6	8	no	—
297	Dic₆	—	3	4	no	—
298	Dic₆	—	3	8	no	—
299	C₃×C₈	—	2	4	no	—
300	C₃×C₈	—	2	4	no	—
301	C₃×C₈	—	9	2	no	—
302	C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
303	C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
304	C₃×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
305	C₃×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
306	C₃⋊C₈	—	3	8	no	—
307	C₂×C₃²	—	2	8	no	—
308	C₂×C₃²	—	2	1	no	—
309	C₂×C₃²	—	2	4	no	—
310	C₂×C₃²	—	2	4	no	—
311	C₂×C₃²	—	4	4	no	—
312	C₂×C₃²	—	4	16	no	—
313	C₂×C₃²	—	8	16	no	—
314	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
315	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
316	C₃⋊D₃	—	2	2	no	—
317	C₃⋊D₃	—	4	2	no	—
318	C₃×D₃	—	6	8	no	—
319	C₃×D₃	—	12	8	no	—
320	#41	—	9	1	no	—
321	#41	—	9	4	no	—
322	#41	—	9	2	no	—
323	#41	—	18	2	no	—
324	C₂×D₄	—	9	4	no	—
325	C₂×D₄	—	18	2	no	—
326	C₂×D₄	—	18	4	no	—
327	C₂×D₄	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
328	Q₁₆	—	9	1	no	—
329	SD₁₆	—	9	4	no	—
330	SD₁₆	—	9	2	no	—
331	D₈	—	9	4	no	—
332	D₈	—	9	1	no	—
333	D₈	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
334	D₈	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
335	M₁₆	—	9	1	no	—
336	M₁₆	—	9	2	no	—
337	C₂×C₈	—	9	2	no	—
338	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
339	C₂²×C₃	—	2	16	no	—
340	C₂²×C₃	—	2	4	no	—
341	C₂²×C₃	—	2	4	no	—
342	C₂²×C₃	—	4	16	no	—
343	C₂²×C₃	—	8	8	no	—
344	C₂²×C₃	—	8	2	no	—
345	C₂²×C₃	—	8	16	no	—
346	C₂²×C₃	—	9	2	no	—
347	C₂²×C₃	—	18	2	no	—
348	C₂²×C₃	—	72	4	no	—
349	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
350	C₂²×C₃	D₄×C₃⋊D₃	1	1	yes	characteristic
351	C₂×D₃	—	3	8	no	—
352	C₂×D₃	—	6	8	no	—
353	C₂×D₃	—	24	16	no	—
354	C₃×C₄	—	2	4	no	—
355	C₃×C₄	—	2	4	no	—
356	C₃×C₄	—	9	2	no	—
357	C₃×C₄	—	18	2	no	—
358	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
359	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
360	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
361	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
362	Dic₃	—	3	8	no	—
363	Dic₃	—	6	8	no	—
364	C₃²	—	2	4	no	—
365	C₃²	#5757	1	4	yes	complemented
366	C₃²	C₃×#576	1	1	yes	characteristic, complemented
367	C₂³	—	2	2	no	—
368	C₂³	—	18	4	no	—
369	Q₈	—	9	1	no	—
370	Q₈	—	9	2	no	—
371	D₄	—	2	2	no	—
372	D₄	—	9	2	no	—
373	D₄	—	9	2	no	—
374	D₄	—	9	1	no	—
375	D₄	—	18	4	no	—
376	D₄	—	18	4	no	—
377	D₄	—	18	2	no	—
378	D₄	C₂²×C₃×C₃⋊D₃	1	4	yes	—
379	C₂×C₄	—	9	2	no	—
380	C₂×C₄	—	18	4	no	—
381	C₂×C₄	—	18	2	no	—
382	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
383	C₈	—	9	2	no	—
384	C₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
385	C₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
386	C₂×C₃	—	2	8	no	—
387	C₂×C₃	—	2	4	no	—
388	C₂×C₃	—	2	1	no	—
389	C₂×C₃	—	2	4	no	—
390	C₂×C₃	—	4	16	no	—
391	C₂×C₃	—	4	4	no	—
392	C₂×C₃	—	8	16	no	—
393	C₂×C₃	—	18	2	no	—
394	C₂×C₃	—	36	2	no	—
395	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
396	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
397	D₃	—	6	8	no	—
398	D₃	—	12	8	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	9	2	no	—
402	C₂²	—	18	2	no	—
403	C₂²	—	72	4	no	—
404	C₂²	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
405	C₄	—	9	2	no	—
406	C₄	—	18	2	no	—
407	C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
408	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
409	C₃	—	2	4	no	—
410	C₃	C₃×#5757	1	4	yes	complemented
411	C₃	#10596228	1	1	yes	characteristic, direct product factor
412	C₂	—	2	1	no	—
413	C₂	—	4	4	no	—
414	C₂	—	18	2	no	—
415	C₂	—	36	2	no	—
416	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄×C₃⋊D₃
commutator, cosocle	C₃²×C₄	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₂×C₃³×D₈	C₂
socle	C₂×C₃³	C₂²×D₄
hypercenter	C₂×C₃×D₈	C₃⋊D₃
hypocenter	C₃²	C₃×#576
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×D₈

Complements

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

N	H ≅ G/N	type
1. C₃×#64361	C₂	semidirect
2. C₂×C₃³×D₈	C₂	semidirect
3. C₃×#64141	C₂	semidirect
4. C₃×#64121	C₂	semidirect
5. C₃×#64120	C₂	semidirect
6. C₃×D₈×C₃⋊D₃	C₂	semidirect
7. C₃×#64113	C₂	semidirect
8. C₃×#64110	C₂	semidirect
9. #10596228	C₃	direct (N × H)
11. C₂×C₃³×D₄	C₂²	semidirect
14. C₃×#3830	C₂²	semidirect
16. C₃×D₄×C₃⋊D₃	C₂²	semidirect
18. C₃×#3828	C₂²	semidirect
19. C₃³×D₈	C₂²	semidirect
20. C₃³×D₈	C₂²	semidirect
21. C₂×C₃³×C₈	C₂²	semidirect
22. C₃×#3754	C₂²	semidirect
23. C₃×#3753	C₂²	semidirect
24. C₃×#3748	C₂²	semidirect
25. C₃×#3746	C₂²	semidirect
26. C₃×#3745	C₂²	semidirect
27. C₃×#3744	C₂²	semidirect
28. C₃×#3743	C₂²	semidirect
29. C₃×C₈×C₃⋊D₃	C₂²	semidirect
30. #64361	C₂×C₃	semidirect
33. C₂×C₃²×D₈	D₃	semidirect
34. C₂×C₃²×D₈	C₂×C₃	semidirect
35. #64141	C₂×C₃	semidirect
36. #64121	C₂×C₃	semidirect
37. #64120	C₂×C₃	semidirect
38. D₈×C₃⋊D₃	C₂×C₃	semidirect
39. #64113	C₂×C₃	semidirect
40. #64110	C₂×C₃	semidirect
69. C₂×C₃²×D₄	C₂×D₃	semidirect
70. C₂×C₃²×D₄	C₂²×C₃	semidirect
73. #3830	C₂²×C₃	semidirect
75. D₄×C₃⋊D₃	C₂²×C₃	semidirect
77. #3828	C₂²×C₃	semidirect
87. C₃²×D₈	C₂×D₃	semidirect
88. C₃²×D₈	C₂×D₃	semidirect
89. C₃²×D₈	C₂²×C₃	semidirect
90. C₃²×D₈	C₂²×C₃	semidirect
92. C₂×C₃²×C₈	C₂×D₃	semidirect
93. C₂×C₃²×C₈	C₂²×C₃	semidirect
94. #3754	C₂²×C₃	semidirect
95. #3753	C₂²×C₃	semidirect
96. #3748	C₂²×C₃	semidirect
97. #3746	C₂²×C₃	semidirect
98. #3745	C₂²×C₃	semidirect
99. #3744	C₂²×C₃	semidirect
100. #3743	C₂²×C₃	semidirect
101. C₈×C₃⋊D₃	C₂²×C₃	semidirect
128. C₂×C₃×D₈	C₃×D₃	semidirect
129. C₂×C₃×D₈	C₃⋊D₃	semidirect
195. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
196. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
211. C₃×D₈	C₂×C₃×D₃	semidirect
212. C₃×D₈	C₂×C₃×D₃	semidirect
213. C₃×D₈	C₂×C₃⋊D₃	semidirect
214. C₃×D₈	C₂×C₃⋊D₃	semidirect
219. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
220. C₂×C₃×C₈	C₂×C₃⋊D₃	semidirect
260. C₂×D₈	C₃×C₃⋊D₃	semidirect
262. C₃³	#576	semidirect
327. C₂×D₄	C₂×C₃×C₃⋊D₃	semidirect
333. D₈	C₂×C₃×C₃⋊D₃	semidirect
334. D₈	C₂×C₃×C₃⋊D₃	semidirect
338. C₂×C₈	C₂×C₃×C₃⋊D₃	semidirect
365. C₃²	#5757	semidirect
366. C₃²	C₃×#576	semidirect
410. C₃	C₃×#5757	semidirect
411. C₃	#10596228	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×#64361	2
C₂×C₃³×D₈	2
C₃×#64141	2
C₃×#64121	2
C₃×#64120	2
C₃×D₈×C₃⋊D₃	2
C₃×#64113	2
C₃×#64110	2
#10596228	3
C₃×#5757	3

Subgroups — C3×#10596228 #13179508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596228 #13179508