Subgroups — C₂×C₃×#64151 #13179562

Order 1728.

2172 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#3828	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3756	C₂	1	2	yes	maximal, complemented
4	C₃×#64151	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3755	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#3748	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#64151	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#942	—	3	4	no	maximal
9	C₂×C₃³×Q₈	—	2	1	no	—
10	C₂×C₃³×Q₈	—	2	2	no	—
11	C₂×C₃³×Q₈	C₂²	1	2	yes	—
12	C₂×C₃³×Q₈	C₂²	1	4	yes	complemented
13	C₂²×C₃³×C₄	—	2	1	no	—
14	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×#638	—	2	1	no	—
16	C₃×#3828	—	2	2	no	—
17	C₃×#3828	C₂²	1	4	yes	—
18	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×C₃⋊D₃	—	2	1	no	—
20	C₂×C₃×#634	C₂²	1	1	yes	characteristic
21	C₃×#3756	C₂²	1	8	yes	complemented
22	C₃×#3755	C₂²	1	8	yes	complemented
23	C₃×#3748	C₂²	1	4	yes	complemented
24	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	—
25	C₂²×C₃²×Q₈	—	2	4	no	—
26	C₂²×C₃²×Q₈	D₃	1	4	yes	complemented
27	C₂²×C₃²×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×#3828	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃×#235	—	3	4	no	—
30	C₂×#3756	C₂×C₃	1	2	yes	complemented
31	#64151	C₂×C₃	1	8	yes	direct product factor
32	C₂×#3755	C₂×C₃	1	2	yes	complemented
33	C₂×#3748	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₃×#216	—	3	8	no	—
35	C₃×#942	—	3	32	no	—
36	C₂×C₃×#215	—	3	8	no	—
37	C₂×C₃×#208	—	3	4	no	—
38	C₂³×C₃³	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₃⋊D₃	—	2	1	no	—
40	C₃³×Q₈	—	2	2	no	—
41	C₃³×Q₈	—	2	4	no	—
42	C₃³×Q₈	C₂³	1	4	yes	—
43	C₂×C₃³×C₄	—	2	2	no	—
44	C₂×C₃³×C₄	—	2	4	no	—
45	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
46	C₂×C₃³×C₄	D₄	1	2	yes	—
47	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
48	C₂×C₃³×C₄	C₂³	1	2	yes	—
49	C₃×#638	—	2	4	no	—
50	C₂×C₃×C₃⋊Dic₃	—	2	1	no	—
51	C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
52	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	2	yes	—
53	C₃×C₄×C₃⋊D₃	—	2	4	no	—
54	C₃×#634	—	2	1	no	—
55	C₃×#634	C₂³	1	2	yes	—
56	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	4	yes	—
57	C₂×C₃×#137	—	9	1	no	—
58	C₂×#942	—	3	4	no	—
59	C₂×C₃²×Q₈	—	2	8	no	—
60	C₂×C₃²×Q₈	—	2	16	no	—
61	C₂×C₃²×Q₈	—	2	8	no	—
62	C₂×C₃²×Q₈	—	2	16	no	—
63	C₂×C₃²×Q₈	—	2	4	no	—
64	C₂×C₃²×Q₈	—	2	8	no	—
65	C₂×C₃²×Q₈	—	2	1	no	—
66	C₂×C₃²×Q₈	—	2	2	no	—
67	C₂×C₃²×Q₈	C₂×D₃	1	8	yes	—
68	C₂×C₃²×Q₈	C₂×D₃	1	16	yes	complemented
69	C₂×C₃²×Q₈	C₂²×C₃	1	2	yes	—
70	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	complemented
71	C₂²×C₃²×C₄	—	2	8	no	—
72	C₂²×C₃²×C₄	—	2	4	no	—
73	C₂²×C₃²×C₄	—	2	4	no	—
74	C₂²×C₃²×C₄	—	2	1	no	—
75	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
76	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂×#638	—	2	1	no	—
78	#3828	—	2	2	no	—
79	#3828	C₂²×C₃	1	4	yes	—
80	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₄×C₃⋊D₃	—	2	1	no	—
82	C₂×#634	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×#67	—	6	4	no	—
84	C₃×#235	—	3	16	no	—
85	C₃×#235	—	6	8	no	—
86	C₂×C₃×D₁₂	—	3	4	no	—
87	C₂×C₃×C₄×D₃	—	6	4	no	—
88	C₂×C₃×Dic₆	—	3	4	no	—
89	#3756	C₂²×C₃	1	8	yes	complemented
90	#3755	C₂²×C₃	1	8	yes	complemented
91	#3748	C₂²×C₃	1	4	yes	complemented
92	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
93	C₃×#216	—	3	32	no	—
94	C₃×#215	—	3	32	no	—
95	C₃×#208	—	3	16	no	—
96	C₂×C₃×C₃⋊C₈	—	3	8	no	—
97	C₂²×C₃³	—	2	2	no	—
98	C₂²×C₃³	C₂×D₄	1	2	yes	—
99	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₃⋊D₃	—	2	2	no	—
101	C₂×C₃×C₃⋊D₃	—	4	2	no	—
102	C₃³×C₄	—	2	4	no	—
103	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
104	C₃³×C₄	C₂×D₄	1	2	yes	—
105	C₃³×C₄	C₂⁴	1	1	yes	characteristic
106	C₃×C₃⋊Dic₃	—	2	2	no	—
107	C₂×C₃×#41	—	9	1	no	—
108	C₂²×C₃×Q₈	—	2	4	no	—
109	C₂²×C₃×Q₈	C₃×D₃	1	4	yes	complemented
110	C₂²×C₃×Q₈	C₃⋊D₃	1	1	yes	characteristic, complemented
111	C₂×#235	—	3	4	no	—
112	C₃×#137	—	9	8	no	—
113	C₂×C₃×Q₁₆	—	9	2	no	—
114	C₂×C₃×SD₁₆	—	9	2	no	—
115	C₂×C₃×M₁₆	—	9	1	no	—
116	C₂×#216	—	3	8	no	—
117	#942	—	3	32	no	—
118	C₂×#215	—	3	8	no	—
119	C₂×#208	—	3	4	no	—
120	C₂³×C₃²	—	2	4	no	—
121	C₂³×C₃²	#67	1	4	yes	—
122	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
123	C₂²×C₃⋊D₃	—	2	1	no	—
124	C₂²×C₃×D₃	—	6	4	no	—
125	C₃²×Q₈	—	2	16	no	—
126	C₃²×Q₈	—	2	32	no	—
127	C₃²×Q₈	—	2	8	no	—
128	C₃²×Q₈	—	2	16	no	—
129	C₃²×Q₈	—	2	2	no	—
130	C₃²×Q₈	—	2	4	no	—
131	C₃²×Q₈	—	2	16	no	—
132	C₃²×Q₈	C₂²×D₃	1	16	yes	—
133	C₃²×Q₈	C₂³×C₃	1	4	yes	—
134	C₂×C₃²×C₄	—	2	16	no	—
135	C₂×C₃²×C₄	—	2	32	no	—
136	C₂×C₃²×C₄	—	2	8	no	—
137	C₂×C₃²×C₄	—	2	16	no	—
138	C₂×C₃²×C₄	—	2	2	no	—
139	C₂×C₃²×C₄	—	2	4	no	—
140	C₂×C₃²×C₄	—	2	4	no	—
141	C₂×C₃²×C₄	—	2	8	no	—
142	C₂×C₃²×C₄	—	2	4	no	—
143	C₂×C₃²×C₄	—	2	8	no	—
144	C₂×C₃²×C₄	#67	1	4	yes	—
145	C₂×C₃²×C₄	#67	1	8	yes	—
146	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
147	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
148	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
149	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
150	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
151	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
152	#638	—	2	4	no	—
153	C₂×C₃⋊Dic₃	—	2	1	no	—
154	C₄⋊(C₃⋊D₃)	—	2	1	no	—
155	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	2	yes	—
156	C₄×C₃⋊D₃	—	2	4	no	—
157	#634	—	2	1	no	—
158	#634	C₂³×C₃	1	2	yes	—
159	C₃×#67	—	6	16	no	—
160	C₂×C₃×Dic₃	—	6	4	no	—
161	C₃×D₁₂	—	3	8	no	—
162	C₃×D₁₂	—	6	4	no	—
163	C₃×C₄×D₃	—	6	16	no	—
164	C₃×Dic₆	—	3	8	no	—
165	C₃×Dic₆	—	6	4	no	—
166	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	4	yes	—
167	C₃×C₃⋊C₈	—	3	16	no	—
168	C₂×#137	—	9	1	no	Sylow
169	C₂×C₃³	—	2	2	no	—
170	C₂×C₃³	#137	1	2	yes	complemented
171	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
172	C₃×C₃⋊D₃	—	4	2	no	—
173	C₃×#41	—	9	4	no	—
174	C₃×#41	—	18	2	no	—
175	C₂×C₃×Q₈	—	2	8	no	—
176	C₂×C₃×Q₈	—	2	16	no	—
177	C₂×C₃×Q₈	—	2	4	no	—
178	C₂×C₃×Q₈	—	2	8	no	—
179	C₂×C₃×Q₈	—	2	2	no	—
180	C₂×C₃×Q₈	—	2	1	no	—
181	C₂×C₃×Q₈	—	2	8	no	—
182	C₂×C₃×Q₈	—	2	16	no	—
183	C₂×C₃×Q₈	—	9	1	no	—
184	C₂×C₃×Q₈	C₂×C₃×D₃	1	8	yes	—
185	C₂×C₃×Q₈	C₂×C₃×D₃	1	16	yes	complemented
186	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	2	yes	—
187	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	4	yes	complemented
188	C₂×C₃×D₄	—	9	1	no	—
189	C₂×C₃×D₄	—	18	1	no	—
190	C₂²×C₃×C₄	—	2	8	no	—
191	C₂²×C₃×C₄	—	2	4	no	—
192	C₂²×C₃×C₄	—	2	1	no	—
193	C₂²×C₃×C₄	—	2	4	no	—
194	C₂²×C₃×C₄	—	18	1	no	—
195	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
196	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
197	C₂×#67	—	6	4	no	—
198	#235	—	3	16	no	—
199	#235	—	6	8	no	—
200	C₂×D₁₂	—	3	4	no	—
201	C₂×C₄×D₃	—	6	4	no	—
202	C₂×Dic₆	—	3	4	no	—
203	C₃×Q₁₆	—	9	8	no	—
204	C₃×SD₁₆	—	9	8	no	—
205	C₃×M₁₆	—	9	4	no	—
206	C₂×C₃×C₈	—	9	2	no	—
207	#216	—	3	32	no	—
208	#215	—	3	32	no	—
209	#208	—	3	16	no	—
210	C₂×C₃⋊C₈	—	3	8	no	—
211	C₂²×C₃²	—	2	16	no	—
212	C₂²×C₃²	—	2	8	no	—
213	C₂²×C₃²	—	2	2	no	—
214	C₂²×C₃²	—	2	8	no	—
215	C₂²×C₃²	—	2	4	no	—
216	C₂²×C₃²	C₂×#67	1	8	yes	—
217	C₂²×C₃²	C₂×#67	1	4	yes	—
218	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
219	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
220	C₂×C₃⋊D₃	—	2	2	no	—
221	C₂×C₃⋊D₃	—	4	2	no	—
222	C₂×C₃×D₃	—	6	8	no	—
223	C₂×C₃×D₃	—	12	8	no	—
224	C₃²×C₄	—	2	32	no	—
225	C₃²×C₄	—	2	16	no	—
226	C₃²×C₄	—	2	4	no	—
227	C₃²×C₄	—	2	4	no	—
228	C₃²×C₄	—	2	4	no	—
229	C₃²×C₄	—	2	8	no	—
230	C₃²×C₄	C₂×#67	1	4	yes	—
231	C₃²×C₄	C₂×#67	1	8	yes	—
232	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
233	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
234	C₃²×C₄	C₂³×D₃	1	4	yes	—
235	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
236	C₃⋊Dic₃	—	2	2	no	—
237	C₃×Dic₃	—	6	8	no	—
238	C₂×#41	—	9	1	no	—
239	C₂²×Q₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
240	#137	—	9	8	no	—
241	C₂×Q₁₆	—	9	2	no	—
242	C₂×SD₁₆	—	9	2	no	—
243	C₂×M₁₆	—	9	1	no	—
244	C₃³	C₂×#137	1	1	yes	characteristic, complemented, Sylow
245	C₂³×C₃	—	2	4	no	—
246	C₂³×C₃	—	18	1	no	—
247	C₂³×C₃	C₃×#67	1	4	yes	—
248	C₂³×C₃	#638	1	1	yes	characteristic
249	C₂²×D₃	—	6	4	no	—
250	C₃×Q₈	—	2	16	no	—
251	C₃×Q₈	—	2	32	no	—
252	C₃×Q₈	—	2	8	no	—
253	C₃×Q₈	—	2	16	no	—
254	C₃×Q₈	—	2	2	no	—
255	C₃×Q₈	—	2	4	no	—
256	C₃×Q₈	—	2	16	no	—
257	C₃×Q₈	—	9	2	no	—
258	C₃×Q₈	—	18	1	no	—
259	C₃×Q₈	C₂²×C₃×D₃	1	16	yes	—
260	C₃×Q₈	C₂²×C₃⋊D₃	1	4	yes	—
261	C₃×D₄	—	9	2	no	—
262	C₃×D₄	—	18	4	no	—
263	C₃×D₄	—	18	1	no	—
264	C₂×C₃×C₄	—	2	16	no	—
265	C₂×C₃×C₄	—	2	32	no	—
266	C₂×C₃×C₄	—	2	8	no	—
267	C₂×C₃×C₄	—	2	16	no	—
268	C₂×C₃×C₄	—	2	4	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	4	no	—
271	C₂×C₃×C₄	—	2	8	no	—
272	C₂×C₃×C₄	—	2	4	no	—
273	C₂×C₃×C₄	—	2	8	no	—
274	C₂×C₃×C₄	—	18	1	no	—
275	C₂×C₃×C₄	—	18	4	no	—
276	C₂×C₃×C₄	C₃×#67	1	4	yes	—
277	C₂×C₃×C₄	C₃×#67	1	8	yes	—
278	C₂×C₃×C₄	#638	1	2	yes	—
279	C₂×C₃×C₄	#638	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
281	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
282	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
283	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
284	#67	—	6	16	no	—
285	C₂×Dic₃	—	6	4	no	—
286	D₁₂	—	3	8	no	—
287	D₁₂	—	6	4	no	—
288	C₄×D₃	—	6	16	no	—
289	Dic₆	—	3	8	no	—
290	Dic₆	—	6	4	no	—
291	C₃×C₈	—	9	4	no	—
292	C₃⋊C₈	—	3	16	no	—
293	C₂×C₃²	—	2	16	no	—
294	C₂×C₃²	—	2	2	no	—
295	C₂×C₃²	—	2	8	no	—
296	C₂×C₃²	—	2	8	no	—
297	C₂×C₃²	—	2	4	no	—
298	C₂×C₃²	#942	1	8	yes	complemented
299	C₂×C₃²	C₃×#137	1	2	yes	complemented
300	C₂×C₃²	C₂²×#67	1	4	yes	—
301	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
302	C₃⋊D₃	—	4	2	no	—
303	C₃×D₃	—	12	8	no	—
304	#41	—	9	4	no	—
305	#41	—	18	2	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	9	1	no	—
309	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	2	yes	—
310	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	4	yes	complemented
311	C₂×D₄	—	9	1	no	—
312	C₂×D₄	—	18	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	18	1	no	—
315	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
316	Q₁₆	—	9	8	no	—
317	SD₁₆	—	9	8	no	—
318	M₁₆	—	9	4	no	—
319	C₂×C₈	—	9	2	no	—
320	C₂²×C₃	—	2	16	no	—
321	C₂²×C₃	—	2	8	no	—
322	C₂²×C₃	—	2	2	no	—
323	C₂²×C₃	—	2	8	no	—
324	C₂²×C₃	—	2	4	no	—
325	C₂²×C₃	—	18	2	no	—
326	C₂²×C₃	—	36	2	no	—
327	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
328	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
329	C₂²×C₃	C₂×#638	1	2	yes	—
330	C₂²×C₃	C₂×#638	1	1	yes	characteristic
331	C₂×D₃	—	6	8	no	—
332	C₂×D₃	—	12	8	no	—
333	C₃×C₄	—	2	32	no	—
334	C₃×C₄	—	2	16	no	—
335	C₃×C₄	—	2	4	no	—
336	C₃×C₄	—	2	4	no	—
337	C₃×C₄	—	2	8	no	—
338	C₃×C₄	—	2	4	no	—
339	C₃×C₄	—	18	2	no	—
340	C₃×C₄	C₂×C₃×#67	1	4	yes	—
341	C₃×C₄	C₂×C₃×#67	1	8	yes	—
342	C₃×C₄	C₂×#638	1	2	yes	—
343	C₃×C₄	C₂×#638	1	1	yes	characteristic
344	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
345	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
346	Dic₃	—	6	8	no	—
347	C₃²	—	2	4	no	—
348	C₃²	C₂×#942	1	4	yes	complemented
349	C₃²	C₂×C₃×#137	1	1	yes	characteristic, complemented
350	C₂³	—	18	1	no	—
351	C₂³	C₃×#638	1	1	yes	characteristic
352	Q₈	—	2	2	no	—
353	Q₈	—	2	4	no	—
354	Q₈	—	9	2	no	—
355	Q₈	—	18	1	no	—
356	Q₈	C₂²×C₃×C₃⋊D₃	1	4	yes	—
357	D₄	—	9	2	no	—
358	D₄	—	18	4	no	—
359	D₄	—	18	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	18	1	no	—
363	C₂×C₄	—	18	4	no	—
364	C₂×C₄	C₃×#638	1	1	yes	characteristic
365	C₂×C₄	C₃×#638	1	2	yes	—
366	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
367	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
368	C₈	—	9	4	no	—
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	—	36	2	no	—
375	C₂×C₃	C₃×#942	1	8	yes	complemented
376	C₂×C₃	#64151	1	2	yes	direct product factor
377	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
378	C₂×C₃	C₂²×#638	1	1	yes	characteristic
379	D₃	—	12	8	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	18	2	no	—
382	C₂²	—	36	2	no	—
383	C₂²	C₂×C₃×#638	1	2	yes	—
384	C₂²	C₂×C₃×#638	1	1	yes	characteristic
385	C₄	—	2	4	no	—
386	C₄	—	18	2	no	—
387	C₄	C₂×C₃×#638	1	2	yes	—
388	C₄	C₂×C₃×#638	1	1	yes	characteristic
389	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
390	C₃	—	2	4	no	—
391	C₃	C₂×C₃×#942	1	4	yes	complemented
392	C₃	C₂×#64151	1	1	yes	characteristic, direct product factor
393	C₂	—	2	2	no	—
394	C₂	—	36	2	no	—
395	C₂	C₃×#64151	1	2	yes	direct product factor
396	C₂	C₂²×C₃×#638	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×#638
commutator, cosocle	C₃²×C₄	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₂²×C₃³×Q₈	C₂
socle	C₂²×C₃³	C₂×D₄
prime radical	C₂×C₃×#3828	C₂
hypercenter	C₂²×C₃×Q₈	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×#137
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃³×Q₈	C₂	semidirect
3. C₂×C₃×#3756	C₂	semidirect
4. C₃×#64151	C₂	direct (N × H)
5. C₂×C₃×#3755	C₂	semidirect
6. C₂×C₃×#3748	C₂	semidirect
7. C₂×#64151	C₃	direct (N × H)
12. C₂×C₃³×Q₈	C₂²	semidirect
21. C₃×#3756	C₂²	semidirect
22. C₃×#3755	C₂²	semidirect
23. C₃×#3748	C₂²	semidirect
26. C₂²×C₃²×Q₈	D₃	semidirect
27. C₂²×C₃²×Q₈	C₂×C₃	semidirect
30. C₂×#3756	C₂×C₃	semidirect
31. #64151	C₂×C₃	direct (N × H)
32. C₂×#3755	C₂×C₃	semidirect
33. C₂×#3748	C₂×C₃	semidirect
68. C₂×C₃²×Q₈	C₂×D₃	semidirect
70. C₂×C₃²×Q₈	C₂²×C₃	semidirect
89. #3756	C₂²×C₃	semidirect
90. #3755	C₂²×C₃	semidirect
91. #3748	C₂²×C₃	semidirect
109. C₂²×C₃×Q₈	C₃×D₃	semidirect
110. C₂²×C₃×Q₈	C₃⋊D₃	semidirect
170. C₂×C₃³	#137	semidirect
185. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
187. C₂×C₃×Q₈	C₂×C₃⋊D₃	semidirect
239. C₂²×Q₈	C₃×C₃⋊D₃	semidirect
244. C₃³	C₂×#137	semidirect
298. C₂×C₃²	#942	semidirect
299. C₂×C₃²	C₃×#137	semidirect
310. C₂×Q₈	C₂×C₃×C₃⋊D₃	semidirect
348. C₃²	C₂×#942	semidirect
349. C₃²	C₂×C₃×#137	semidirect
375. C₂×C₃	C₃×#942	semidirect
376. C₂×C₃	#64151	direct (N × H)
391. C₃	C₂×C₃×#942	semidirect
392. C₃	C₂×#64151	direct (N × H)
395. C₂	C₃×#64151	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×Q₈	2
C₂×C₃×#3828	2
C₂×C₃×#3756	2
C₃×#64151	2
C₂×C₃×#3755	2
C₂×C₃×#3748	2
C₂×#64151	3
C₂×C₃×#942	3

Subgroups — C2×C3×#64151 #13179562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64151 #13179562