Subgroups — C₃×#10596276 #13179556

Order 1728.

2948 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#3828	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64162	C₂	1	4	yes	maximal, complemented
4	C₃×#64149	C₂	1	2	yes	maximal, complemented
5	C₃×#64147	C₂	1	4	yes	maximal, complemented
6	C₃×#64145	C₂	1	2	yes	maximal, complemented
7	C₃×#64135	C₂	1	1	yes	maximal, characteristic, complemented
8	#10596276	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₃×#5805	—	3	4	no	maximal
10	C₂⁴×C₃³	C₂²	1	2	yes	—
11	C₂×C₃³×D₄	—	2	4	no	—
12	C₂×C₃³×D₄	C₂²	1	2	yes	—
13	C₂×C₃³×D₄	C₂²	1	2	yes	—
14	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×#638	C₂²	1	2	yes	—
16	C₂×C₃×#638	C₂²	1	8	yes	complemented
17	C₃×#3828	—	2	4	no	—
18	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	complemented
20	C₂×C₃×#634	C₂²	1	1	yes	characteristic, complemented
21	C₃×#3757	C₂²	1	2	yes	—
22	C₃×#3757	C₂²	1	8	yes	complemented
23	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	complemented
24	C₃×C₄×C₃⋊Dic₃	C₂²	1	2	yes	complemented
25	C₂²×C₃²×D₄	—	2	4	no	—
26	C₂²×C₃²×D₄	D₃	1	4	yes	complemented
27	C₂²×C₃²×D₄	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×#3828	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×C₃×#235	—	3	4	no	—
30	#64162	C₂×C₃	1	4	yes	complemented
31	#64149	C₂×C₃	1	2	yes	complemented
32	#64147	C₂×C₃	1	4	yes	complemented
33	#64145	C₂×C₃	1	2	yes	complemented
34	#64135	C₂×C₃	1	1	yes	characteristic, complemented
35	C₃×#953	—	3	16	no	—
36	C₃×#940	—	3	8	no	—
37	C₃×#938	—	3	16	no	—
38	C₃×#936	—	3	8	no	—
39	C₃×#926	—	3	4	no	—
40	C₂³×C₃³	—	2	4	no	—
41	C₂³×C₃³	—	4	4	no	—
42	C₂³×C₃³	C₂³	1	4	yes	—
43	C₂³×C₃³	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
45	C₃³×D₄	—	2	4	no	—
46	C₃³×D₄	—	2	4	no	—
47	C₂×C₃³×C₄	D₄	1	4	yes	complemented
48	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
49	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
50	C₃×#638	—	2	4	no	—
51	C₃×#638	—	4	8	no	—
52	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	—
53	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
54	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
55	C₃×C₄×C₃⋊D₃	—	2	4	no	—
56	C₃×#634	—	2	2	no	—
57	C₃×#535	—	9	1	no	—
58	#5805	—	3	4	no	—
59	C₂⁴×C₃²	—	2	8	no	—
60	C₂⁴×C₃²	C₂×D₃	1	8	yes	—
61	C₂⁴×C₃²	C₂²×C₃	1	2	yes	—
62	C₂×C₃²×D₄	—	2	32	no	—
63	C₂×C₃²×D₄	—	2	8	no	—
64	C₂×C₃²×D₄	—	2	8	no	—
65	C₂×C₃²×D₄	—	2	16	no	—
66	C₂×C₃²×D₄	—	2	4	no	—
67	C₂×C₃²×D₄	C₂×D₃	1	8	yes	—
68	C₂×C₃²×D₄	C₂×D₃	1	8	yes	—
69	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
70	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
71	C₂²×C₃²×C₄	—	2	4	no	—
72	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
73	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
74	C₂×#638	C₂²×C₃	1	2	yes	—
75	C₂×#638	C₂²×C₃	1	8	yes	complemented
76	#3828	—	2	4	no	—
77	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic, complemented
78	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
79	C₂×#634	C₂²×C₃	1	1	yes	characteristic, complemented
80	C₂×C₃×#67	—	3	8	no	—
81	C₂×C₃×#67	—	3	32	no	—
82	C₃×#235	—	6	16	no	—
83	C₂×C₃×D₁₂	—	3	4	no	—
84	C₂×C₃×C₄×D₃	—	3	8	no	—
85	C₂×C₃×Dic₆	—	3	4	no	—
86	#3757	C₂²×C₃	1	2	yes	—
87	#3757	C₂²×C₃	1	8	yes	complemented
88	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	complemented
89	C₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	complemented
90	C₃×#217	—	3	8	no	—
91	C₃×#217	—	3	32	no	—
92	C₃×C₄⋊Dic₃	—	3	8	no	—
93	C₃×C₄×Dic₃	—	3	8	no	—
94	C₂²×C₃³	—	2	2	no	—
95	C₂²×C₃³	—	2	4	no	—
96	C₂²×C₃³	—	2	8	no	—
97	C₂²×C₃³	—	4	8	no	—
98	C₂²×C₃³	C₂×D₄	1	2	yes	—
99	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
100	C₂×C₃×C₃⋊D₃	—	2	2	no	—
101	C₂×C₃×C₃⋊D₃	—	2	4	no	—
102	C₃³×C₄	C₂×D₄	1	2	yes	—
103	C₃³×C₄	C₂×D₄	1	2	yes	—
104	C₃×C₃⋊Dic₃	—	2	2	no	—
105	C₃×C₃⋊Dic₃	—	2	4	no	—
106	C₂×C₃×#41	—	9	1	no	—
107	C₂²×C₃×D₄	—	2	4	no	—
108	C₂²×C₃×D₄	C₃×D₃	1	4	yes	complemented
109	C₂²×C₃×D₄	C₃⋊D₃	1	1	yes	characteristic, complemented
110	C₂×#235	—	3	4	no	—
111	C₃×#127	—	9	2	no	—
112	C₃×#124	—	9	2	no	—
113	C₃×#121	—	9	4	no	—
114	C₃×#120	—	9	4	no	—
115	C₃×#117	—	9	1	no	—
116	#953	—	3	16	no	—
117	#940	—	3	8	no	—
118	#938	—	3	16	no	—
119	#936	—	3	8	no	—
120	#926	—	3	4	no	—
121	C₂³×C₃²	—	2	32	no	—
122	C₂³×C₃²	—	2	16	no	—
123	C₂³×C₃²	—	2	4	no	—
124	C₂³×C₃²	—	2	4	no	—
125	C₂³×C₃²	—	2	16	no	—
126	C₂³×C₃²	—	4	16	no	—
127	C₂³×C₃²	—	4	4	no	—
128	C₂³×C₃²	—	4	32	no	—
129	C₂³×C₃²	C₂²×D₃	1	16	yes	—
130	C₂³×C₃²	C₂²×D₃	1	4	yes	—
131	C₂³×C₃²	C₂³×C₃	1	4	yes	—
132	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
133	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
134	C₂²×C₃×D₃	—	3	8	no	—
135	C₃²×D₄	—	2	32	no	—
136	C₃²×D₄	—	2	32	no	—
137	C₃²×D₄	—	2	16	no	—
138	C₃²×D₄	—	2	16	no	—
139	C₃²×D₄	—	2	4	no	—
140	C₃²×D₄	—	2	4	no	—
141	C₂×C₃²×C₄	—	2	16	no	—
142	C₂×C₃²×C₄	—	2	4	no	—
143	C₂×C₃²×C₄	—	2	4	no	—
144	C₂×C₃²×C₄	#67	1	16	yes	complemented
145	C₂×C₃²×C₄	C₃×D₄	1	4	yes	complemented
146	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
147	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
148	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
149	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
150	#638	—	2	4	no	—
151	#638	—	4	8	no	—
152	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	—
153	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
154	C₄⋊(C₃⋊D₃)	—	2	2	no	—
155	C₄×C₃⋊D₃	—	2	4	no	—
156	#634	—	2	2	no	—
157	C₃×#67	—	6	16	no	—
158	C₃×#67	—	12	32	no	—
159	C₂×C₃×Dic₃	—	3	16	no	—
160	C₂×C₃×Dic₃	—	3	8	no	—
161	C₃×D₁₂	—	6	8	no	—
162	C₃×C₄×D₃	—	6	16	no	—
163	C₃×Dic₆	—	6	8	no	—
164	#535	—	9	1	no	Sylow
165	C₂×C₃³	—	2	2	no	—
166	C₂×C₃³	—	4	4	no	—
167	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₃³	H(5,𝔽₂)	1	2	yes	—
169	C₃×C₃⋊D₃	—	4	2	no	—
170	C₂⁴×C₃	—	2	8	no	—
171	C₂⁴×C₃	C₂×C₃×D₃	1	8	yes	—
172	C₂⁴×C₃	C₂×C₃⋊D₃	1	2	yes	—
173	C₃×#41	—	18	4	no	—
174	C₂×C₃×Q₈	—	9	1	no	—
175	C₂×C₃×D₄	—	2	32	no	—
176	C₂×C₃×D₄	—	2	16	no	—
177	C₂×C₃×D₄	—	2	4	no	—
178	C₂×C₃×D₄	—	2	8	no	—
179	C₂×C₃×D₄	—	2	8	no	—
180	C₂×C₃×D₄	—	9	2	no	—
181	C₂×C₃×D₄	—	9	8	no	—
182	C₂×C₃×D₄	—	9	1	no	—
183	C₂×C₃×D₄	C₂×C₃×D₃	1	8	yes	—
184	C₂×C₃×D₄	C₂×C₃×D₃	1	8	yes	—
185	C₂×C₃×D₄	C₂×C₃⋊D₃	1	2	yes	—
186	C₂×C₃×D₄	C₂×C₃⋊D₃	1	2	yes	—
187	C₂²×C₃×C₄	—	2	4	no	—
188	C₂²×C₃×C₄	—	9	2	no	—
189	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
190	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
191	C₂×#67	—	3	8	no	—
192	C₂×#67	—	3	32	no	—
193	#235	—	6	16	no	—
194	C₂×D₁₂	—	3	4	no	—
195	C₂×C₄×D₃	—	3	8	no	—
196	C₂×Dic₆	—	3	4	no	—
197	C₃×C₄⋊C₄	—	9	2	no	—
198	C₃×C₂²⋊C₄	—	9	2	no	—
199	C₃×C₂²⋊C₄	—	9	8	no	—
200	C₃×C₄²	—	9	2	no	—
201	#217	—	3	8	no	—
202	#217	—	3	32	no	—
203	C₄⋊Dic₃	—	3	8	no	—
204	C₄×Dic₃	—	3	8	no	—
205	C₂²×C₃²	—	2	16	no	—
206	C₂²×C₃²	—	2	8	no	—
207	C₂²×C₃²	—	2	2	no	—
208	C₂²×C₃²	—	2	32	no	—
209	C₂²×C₃²	—	2	16	no	—
210	C₂²×C₃²	—	2	4	no	—
211	C₂²×C₃²	—	2	8	no	—
212	C₂²×C₃²	—	2	4	no	—
213	C₂²×C₃²	—	2	8	no	—
214	C₂²×C₃²	—	2	32	no	—
215	C₂²×C₃²	—	4	32	no	—
216	C₂²×C₃²	—	4	64	no	—
217	C₂²×C₃²	—	4	32	no	—
218	C₂²×C₃²	—	4	8	no	—
219	C₂²×C₃²	C₂×#67	1	8	yes	—
220	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
221	C₂²×C₃²	C₂³×D₃	1	4	yes	—
222	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
223	C₂×C₃⋊D₃	—	2	2	no	—
224	C₂×C₃⋊D₃	—	2	4	no	—
225	C₂×C₃×D₃	—	6	16	no	—
226	C₂×C₃×D₃	—	6	8	no	—
227	C₃²×C₄	—	2	8	no	—
228	C₃²×C₄	—	2	8	no	—
229	C₃²×C₄	C₂×#67	1	8	yes	—
230	C₃²×C₄	C₂×#67	1	8	yes	—
231	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
232	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
233	C₃⋊Dic₃	—	2	2	no	—
234	C₃⋊Dic₃	—	2	4	no	—
235	C₃×Dic₃	—	6	16	no	—
236	C₃×Dic₃	—	6	8	no	—
237	C₂×#41	—	9	1	no	—
238	C₂²×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
239	#127	—	9	2	no	—
240	#124	—	9	2	no	—
241	#121	—	9	4	no	—
242	#120	—	9	4	no	—
243	#117	—	9	1	no	—
244	C₃³	#535	1	1	yes	characteristic, complemented, Sylow
245	C₂³×C₃	—	2	32	no	—
246	C₂³×C₃	—	2	16	no	—
247	C₂³×C₃	—	2	4	no	—
248	C₂³×C₃	—	2	4	no	—
249	C₂³×C₃	—	2	16	no	—
250	C₂³×C₃	—	4	16	no	—
251	C₂³×C₃	—	4	4	no	—
252	C₂³×C₃	—	4	32	no	—
253	C₂³×C₃	—	9	2	no	—
254	C₂³×C₃	C₂²×C₃×D₃	1	16	yes	—
255	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
256	C₂³×C₃	C₂²×C₃⋊D₃	1	4	yes	—
257	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
258	C₂²×D₃	—	3	8	no	—
259	C₃×Q₈	—	18	2	no	—
260	C₃×D₄	—	2	32	no	—
261	C₃×D₄	—	2	32	no	—
262	C₃×D₄	—	2	16	no	—
263	C₃×D₄	—	2	16	no	—
264	C₃×D₄	—	2	4	no	—
265	C₃×D₄	—	2	4	no	—
266	C₃×D₄	—	18	4	no	—
267	C₃×D₄	—	18	2	no	—
268	C₃×D₄	—	36	8	no	—
269	C₂×C₃×C₄	—	2	16	no	—
270	C₂×C₃×C₄	—	2	4	no	—
271	C₂×C₃×C₄	—	2	4	no	—
272	C₂×C₃×C₄	—	9	4	no	—
273	C₂×C₃×C₄	—	9	2	no	—
274	C₂×C₃×C₄	—	18	4	no	—
275	C₂×C₃×C₄	C₃×#67	1	16	yes	complemented
276	C₂×C₃×C₄	#638	1	4	yes	complemented
277	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
278	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
279	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
281	#67	—	6	16	no	—
282	#67	—	12	32	no	—
283	C₂×Dic₃	—	3	16	no	—
284	C₂×Dic₃	—	3	8	no	—
285	D₁₂	—	6	8	no	—
286	C₄×D₃	—	6	16	no	—
287	Dic₆	—	6	8	no	—
288	C₂×C₃²	—	2	16	no	—
289	C₂×C₃²	—	2	8	no	—
290	C₂×C₃²	—	2	2	no	—
291	C₂×C₃²	—	2	8	no	—
292	C₂×C₃²	—	2	4	no	—
293	C₂×C₃²	—	4	32	no	—
294	C₂×C₃²	—	4	16	no	—
295	C₂×C₃²	—	4	4	no	—
296	C₂×C₃²	#1004	1	8	yes	—
297	C₂×C₃²	C₂²×#67	1	4	yes	—
298	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
299	C₂×C₃²	C₃×H(5,𝔽₂)	1	2	yes	—
300	C₃⋊D₃	—	4	2	no	—
301	C₃×D₃	—	12	8	no	—
302	C₂⁴	C₂×C₃×C₃⋊D₃	1	2	yes	—
303	#41	—	18	4	no	—
304	C₂×Q₈	—	9	1	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	9	2	no	—
307	C₂×D₄	—	9	8	no	—
308	C₂×D₄	—	9	1	no	—
309	C₂×D₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
310	C₂×D₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
311	C₂²×C₄	—	9	2	no	—
312	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
313	C₄⋊C₄	—	9	2	no	—
314	C₂²⋊C₄	—	9	2	no	—
315	C₂²⋊C₄	—	9	8	no	—
316	C₄²	—	9	2	no	—
317	C₂²×C₃	—	2	16	no	—
318	C₂²×C₃	—	2	8	no	—
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	2	32	no	—
321	C₂²×C₃	—	2	32	no	—
322	C₂²×C₃	—	2	16	no	—
323	C₂²×C₃	—	2	8	no	—
324	C₂²×C₃	—	2	4	no	—
325	C₂²×C₃	—	2	4	no	—
326	C₂²×C₃	—	2	8	no	—
327	C₂²×C₃	—	4	32	no	—
328	C₂²×C₃	—	4	64	no	—
329	C₂²×C₃	—	4	32	no	—
330	C₂²×C₃	—	4	8	no	—
331	C₂²×C₃	—	18	4	no	—
332	C₂²×C₃	—	18	2	no	—
333	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
334	C₂²×C₃	C₂×#638	1	2	yes	—
335	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
336	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
337	C₂×D₃	—	6	16	no	—
338	C₂×D₃	—	6	8	no	—
339	C₃×C₄	—	2	8	no	—
340	C₃×C₄	—	2	8	no	—
341	C₃×C₄	—	18	4	no	—
342	C₃×C₄	—	18	2	no	—
343	C₃×C₄	C₂×C₃×#67	1	8	yes	—
344	C₃×C₄	C₂×C₃×#67	1	8	yes	—
345	C₃×C₄	C₂×#638	1	2	yes	—
346	C₃×C₄	C₂×#638	1	2	yes	—
347	Dic₃	—	6	16	no	—
348	Dic₃	—	6	8	no	—
349	C₃²	—	2	4	no	—
350	C₃²	#5805	1	4	yes	complemented
351	C₃²	C₃×#535	1	1	yes	characteristic, complemented
352	C₂³	—	2	4	no	—
353	C₂³	—	4	4	no	—
354	C₂³	—	9	2	no	—
355	C₂³	C₂²×C₃×C₃⋊D₃	1	4	yes	—
356	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
357	Q₈	—	18	2	no	—
358	D₄	—	2	4	no	—
359	D₄	—	2	4	no	—
360	D₄	—	18	4	no	—
361	D₄	—	18	2	no	—
362	D₄	—	36	8	no	—
363	C₂×C₄	—	9	4	no	—
364	C₂×C₄	—	9	2	no	—
365	C₂×C₄	—	18	4	no	—
366	C₂×C₄	C₃×#638	1	4	yes	complemented
367	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
369	C₂×C₃	—	2	16	no	—
370	C₂×C₃	—	2	8	no	—
371	C₂×C₃	—	2	2	no	—
372	C₂×C₃	—	2	8	no	—
373	C₂×C₃	—	2	4	no	—
374	C₂×C₃	—	4	32	no	—
375	C₂×C₃	—	4	16	no	—
376	C₂×C₃	—	4	4	no	—
377	C₂×C₃	—	36	2	no	—
378	C₂×C₃	C₃×#1004	1	8	yes	—
379	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
380	C₂×C₃	#64361	1	2	yes	—
381	C₂×C₃	C₂²×#638	1	1	yes	characteristic
382	D₃	—	12	8	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	8	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	18	4	no	—
388	C₂²	—	18	2	no	—
389	C₂²	C₂×C₃×#638	1	2	yes	—
390	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
391	C₄	—	18	4	no	—
392	C₄	—	18	2	no	—
393	C₄	C₂×C₃×#638	1	2	yes	—
394	C₄	C₂×C₃×#638	1	2	yes	—
395	C₃	—	2	4	no	—
396	C₃	C₃×#5805	1	4	yes	complemented
397	C₃	#10596276	1	1	yes	characteristic, direct product factor
398	C₂	—	2	2	no	—
399	C₂	—	4	4	no	—
400	C₂	—	36	2	no	—
401	C₂	C₃×#64361	1	2	yes	—
402	C₂	C₂²×C₃×#638	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₂²×C₃³×D₄	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₂²×C₃×D₄	C₃⋊D₃
hypocenter	C₃²	C₃×#535
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃³×D₄	C₂	semidirect
2. C₂×C₃×#3828	C₂	semidirect
3. C₃×#64162	C₂	semidirect
4. C₃×#64149	C₂	semidirect
5. C₃×#64147	C₂	semidirect
6. C₃×#64145	C₂	semidirect
7. C₃×#64135	C₂	semidirect
8. #10596276	C₃	direct (N × H)
16. C₂×C₃×#638	C₂²	semidirect
18. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
19. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
20. C₂×C₃×#634	C₂²	semidirect
22. C₃×#3757	C₂²	semidirect
23. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
24. C₃×C₄×C₃⋊Dic₃	C₂²	semidirect
26. C₂²×C₃²×D₄	D₃	semidirect
27. C₂²×C₃²×D₄	C₂×C₃	semidirect
28. C₂×#3828	C₂×C₃	semidirect
30. #64162	C₂×C₃	semidirect
31. #64149	C₂×C₃	semidirect
32. #64147	C₂×C₃	semidirect
33. #64145	C₂×C₃	semidirect
34. #64135	C₂×C₃	semidirect
47. C₂×C₃³×C₄	D₄	semidirect
75. C₂×#638	C₂²×C₃	semidirect
77. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
78. C₂×C₄×C₃⋊D₃	C₂²×C₃	semidirect
79. C₂×#634	C₂²×C₃	semidirect
87. #3757	C₂²×C₃	semidirect
88. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
89. C₄×C₃⋊Dic₃	C₂²×C₃	semidirect
108. C₂²×C₃×D₄	C₃×D₃	semidirect
109. C₂²×C₃×D₄	C₃⋊D₃	semidirect
144. C₂×C₃²×C₄	#67	semidirect
145. C₂×C₃²×C₄	C₃×D₄	semidirect
238. C₂²×D₄	C₃×C₃⋊D₃	semidirect
244. C₃³	#535	semidirect
275. C₂×C₃×C₄	C₃×#67	semidirect
276. C₂×C₃×C₄	#638	semidirect
350. C₃²	#5805	semidirect
351. C₃²	C₃×#535	semidirect
366. C₂×C₄	C₃×#638	semidirect
396. C₃	C₃×#5805	semidirect
397. C₃	#10596276	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃³×D₄	2
C₂×C₃×#3828	2
C₃×#64162	2
C₃×#64149	2
C₃×#64147	2
C₃×#64145	2
C₃×#64135	2
#10596276	3
C₃×#5805	3

Subgroups — C3×#10596276 #13179556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596276 #13179556