Subgroups — C₂×C₃×#4924 #11858242

Order 1152.

1401 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×#208	C₂	1	2	yes	maximal
3	C₃×#4924	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	4	yes	maximal, complemented
5	C₂×C₃×#423	—	3	1	no	maximal
6	C₂×#4924	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂³×C₃²×C₄	C₄	1	2	yes	—
8	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
9	C₂×C₃²×C₄²	C₄	1	1	yes	characteristic
10	C₂×C₃²×C₄²	C₄	1	4	yes	—
11	C₂×C₃²×C₄²	C₄	1	1	yes	characteristic
12	C₂×C₃²×C₄²	C₂²	1	2	yes	—
13	C₂×C₃²×C₄²	C₂²	1	4	yes	—
14	C₂×C₃×#208	—	2	8	no	—
15	C₂×C₃×#208	C₂²	1	8	yes	—
16	C₂²×C₃×C₃⋊C₈	C₂²	1	4	yes	—
17	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	16	yes	complemented
18	C₂²×C₃×M₁₆	—	3	2	no	—
19	C₂²×C₃×C₄²	—	2	1	no	—
20	C₂²×C₃×C₄²	D₃	1	1	yes	characteristic
21	C₂²×C₃×C₄²	C₂×C₃	1	1	yes	characteristic
22	C₂²×#208	C₂×C₃	1	2	yes	—
23	C₃×#423	—	3	8	no	—
24	C₂×C₃×C₄⋊C₈	—	3	4	no	—
25	#4924	C₂×C₃	1	8	yes	direct product factor
26	C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	1	4	yes	complemented
27	C₂⁴×C₃²	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃²×C₄	—	2	8	no	—
29	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
30	C₂²×C₃²×C₄	C₂×C₄	1	8	yes	—
31	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
32	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
34	C₂²×C₃²×C₄	D₄	1	4	yes	—
35	C₂²×C₃²×C₄	Q₈	1	4	yes	—
36	C₂²×C₃²×C₄	C₂³	1	2	yes	—
37	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
38	C₃²×C₄²	C₂×C₄	1	4	yes	—
39	C₃²×C₄²	C₂×C₄	1	4	yes	—
40	C₃²×C₄²	C₂×C₄	1	4	yes	—
41	C₃²×C₄²	C₂³	1	4	yes	—
42	C₃×#208	—	2	16	no	—
43	C₂×C₃×C₃⋊C₈	—	2	8	no	—
44	C₂×C₃×C₃⋊C₈	C₂³	1	8	yes	—
45	C₂×#423	—	3	1	no	Sylow
46	C₂³×C₃×C₄	—	2	2	no	—
47	C₂³×C₃×C₄	—	2	1	no	—
48	C₂³×C₃×C₄	Dic₃	1	2	yes	—
49	C₂³×C₃×C₄	C₃×C₄	1	2	yes	—
50	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
51	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
52	C₂×C₃×M₁₆	—	3	8	no	—
53	C₂×C₃×M₁₆	—	6	8	no	—
54	C₂²×C₃×C₈	—	3	4	no	—
55	C₂×C₃×C₄²	—	2	1	no	—
56	C₂×C₃×C₄²	—	2	4	no	—
57	C₂×C₃×C₄²	—	2	1	no	—
58	C₂×C₃×C₄²	—	2	2	no	—
59	C₂×C₃×C₄²	—	2	4	no	—
60	C₂×C₃×C₄²	Dic₃	1	1	yes	characteristic
61	C₂×C₃×C₄²	Dic₃	1	4	yes	—
62	C₂×C₃×C₄²	Dic₃	1	1	yes	characteristic
63	C₂×C₃×C₄²	C₃×C₄	1	1	yes	characteristic
64	C₂×C₃×C₄²	C₃×C₄	1	4	yes	—
65	C₂×C₃×C₄²	C₃×C₄	1	1	yes	characteristic
66	C₂×C₃×C₄²	C₂×D₃	1	4	yes	—
67	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
68	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
69	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
70	C₂×#208	—	2	8	no	—
71	C₂×#208	C₂²×C₃	1	8	yes	—
72	C₂²×C₃⋊C₈	C₂²×C₃	1	4	yes	—
73	C₃×C₄⋊C₈	—	3	16	no	—
74	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	16	yes	complemented
75	C₂³×C₃²	—	2	4	no	—
76	C₂³×C₃²	C₄⋊C₄	1	4	yes	—
77	C₂³×C₃²	C₂²×C₄	1	2	yes	—
78	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₃²×C₄	—	2	4	no	—
80	C₂×C₃²×C₄	—	2	16	no	—
81	C₂×C₃²×C₄	C₄⋊C₄	1	8	yes	—
82	C₂×C₃²×C₄	C₄⋊C₄	1	4	yes	—
83	C₂×C₃²×C₄	M₁₆	1	8	yes	complemented
84	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
85	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
86	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
88	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
89	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
90	C₂×C₃²×C₄	C₂×Q₈	1	4	yes	—
91	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
92	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
93	C₃×C₃⋊C₈	—	2	8	no	—
94	C₂²×M₁₆	—	3	2	no	—
95	C₂²×C₄²	C₃×D₃	1	1	yes	characteristic
96	#423	—	3	8	no	—
97	C₂×C₄⋊C₈	—	3	4	no	—
98	C₂⁴×C₃	—	2	1	no	—
99	C₂⁴×C₃	C₂×Dic₃	1	1	yes	characteristic
100	C₂⁴×C₃	C₂×C₃×C₄	1	1	yes	characteristic
101	C₂²×C₃×C₄	—	2	16	no	—
102	C₂²×C₃×C₄	—	2	8	no	—
103	C₂²×C₃×C₄	—	2	8	no	—
104	C₂²×C₃×C₄	—	2	4	no	—
105	C₂²×C₃×C₄	—	2	4	no	—
106	C₂²×C₃×C₄	—	2	2	no	—
107	C₂²×C₃×C₄	—	2	8	no	—
108	C₂²×C₃×C₄	—	2	2	no	—
109	C₂²×C₃×C₄	—	2	2	no	—
110	C₂²×C₃×C₄	—	2	1	no	—
111	C₂²×C₃×C₄	—	2	1	no	—
112	C₂²×C₃×C₄	—	2	2	no	—
113	C₂²×C₃×C₄	Dic₆	1	4	yes	—
114	C₂²×C₃×C₄	D₁₂	1	4	yes	—
115	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
116	C₂²×C₃×C₄	C₂×Dic₃	1	8	yes	—
117	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
118	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
119	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
120	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
121	C₂²×C₃×C₄	C₂×C₃×C₄	1	8	yes	—
122	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
123	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
124	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
125	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
126	C₂²×C₃×C₄	C₃×Q₈	1	4	yes	—
127	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
128	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
129	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
130	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
131	C₃×M₁₆	—	6	16	no	—
132	C₂×C₃×C₈	—	3	8	no	—
133	C₂×C₃×C₈	—	6	8	no	—
134	C₃×C₄²	—	2	4	no	—
135	C₃×C₄²	—	2	4	no	—
136	C₃×C₄²	—	2	4	no	—
137	C₃×C₄²	—	2	4	no	—
138	C₃×C₄²	C₂×Dic₃	1	4	yes	—
139	C₃×C₄²	C₂×Dic₃	1	4	yes	—
140	C₃×C₄²	C₂×Dic₃	1	4	yes	—
141	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
142	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
143	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
144	C₃×C₄²	C₂²×D₃	1	4	yes	—
145	C₃×C₄²	C₂³×C₃	1	4	yes	—
146	#208	—	2	16	no	—
147	C₂×C₃⋊C₈	—	2	8	no	—
148	C₂×C₃⋊C₈	C₂³×C₃	1	8	yes	—
149	C₂²×C₃²	—	2	4	no	—
150	C₂²×C₃²	—	2	8	no	—
151	C₂²×C₃²	C₂×C₄⋊C₄	1	4	yes	—
152	C₂²×C₃²	C₂×C₄⋊C₄	1	2	yes	—
153	C₂²×C₃²	C₂×M₁₆	1	4	yes	—
154	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
155	C₃²×C₄	—	2	4	no	—
156	C₃²×C₄	C₂×C₄⋊C₄	1	2	yes	—
157	C₃²×C₄	C₂×C₄⋊C₄	1	4	yes	—
158	C₃²×C₄	C₂×M₁₆	1	8	yes	complemented
159	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
160	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
161	C₂³×C₄	C₃×Dic₃	1	2	yes	—
162	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
163	C₂×M₁₆	—	3	8	no	—
164	C₂×M₁₆	—	6	8	no	—
165	C₂²×C₈	—	3	4	no	—
166	C₂×C₄²	C₃×Dic₃	1	1	yes	characteristic
167	C₂×C₄²	C₃×Dic₃	1	4	yes	—
168	C₂×C₄²	C₃×Dic₃	1	1	yes	characteristic
169	C₂×C₄²	C₂×C₃×D₃	1	2	yes	—
170	C₂×C₄²	C₂×C₃×D₃	1	4	yes	—
171	C₄⋊C₈	—	3	16	no	—
172	C₂³×C₃	—	2	8	no	—
173	C₂³×C₃	—	2	4	no	—
174	C₂³×C₃	—	2	4	no	—
175	C₂³×C₃	—	2	4	no	—
176	C₂³×C₃	—	2	2	no	—
177	C₂³×C₃	—	2	1	no	—
178	C₂³×C₃	C₄⋊Dic₃	1	4	yes	—
179	C₂³×C₃	C₃×C₄⋊C₄	1	4	yes	—
180	C₂³×C₃	C₂²×Dic₃	1	2	yes	—
181	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
182	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
183	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
184	C₂×C₃×C₄	—	2	8	no	—
185	C₂×C₃×C₄	—	2	32	no	—
186	C₂×C₃×C₄	—	2	4	no	—
187	C₂×C₃×C₄	—	2	4	no	—
188	C₂×C₃×C₄	—	2	16	no	—
189	C₂×C₃×C₄	—	2	16	no	—
190	C₂×C₃×C₄	—	2	1	no	—
191	C₂×C₃×C₄	—	2	8	no	—
192	C₂×C₃×C₄	—	2	8	no	—
193	C₂×C₃×C₄	—	2	4	no	—
194	C₂×C₃×C₄	—	2	4	no	—
195	C₂×C₃×C₄	—	2	2	no	—
196	C₂×C₃×C₄	—	2	2	no	—
197	C₂×C₃×C₄	—	2	4	no	—
198	C₂×C₃×C₄	—	2	4	no	—
199	C₂×C₃×C₄	—	2	4	no	—
200	C₂×C₃×C₄	—	2	1	no	—
201	C₂×C₃×C₄	—	2	2	no	—
202	C₂×C₃×C₄	#208	1	8	yes	complemented
203	C₂×C₃×C₄	C₄⋊Dic₃	1	8	yes	—
204	C₂×C₃×C₄	C₄⋊Dic₃	1	4	yes	—
205	C₂×C₃×C₄	C₃×C₄⋊C₄	1	8	yes	—
206	C₂×C₃×C₄	C₃×C₄⋊C₄	1	4	yes	—
207	C₂×C₃×C₄	C₃×M₁₆	1	8	yes	complemented
208	C₂×C₃×C₄	C₂×Dic₆	1	4	yes	—
209	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
210	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
211	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
212	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
213	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
214	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
215	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
216	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
217	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
218	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
219	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
220	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
221	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
222	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	—
223	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
224	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
225	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
226	C₃×C₈	—	6	8	no	—
227	C₃⋊C₈	—	2	8	no	—
228	C₂×C₃²	—	2	4	no	—
229	C₂×C₃²	#423	1	4	yes	complemented
230	C₂×C₃²	C₂²×C₄⋊C₄	1	1	yes	characteristic
231	C₂×C₃²	C₂²×M₁₆	1	2	yes	—
232	C₂⁴	C₂×C₃×Dic₃	1	1	yes	characteristic
233	C₂²×C₄	—	2	8	no	—
234	C₂²×C₄	C₃×Dic₆	1	4	yes	—
235	C₂²×C₄	C₃×D₁₂	1	4	yes	—
236	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
237	C₂²×C₄	C₂×C₃×Dic₃	1	8	yes	—
238	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
239	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
240	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
241	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
242	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
243	M₁₆	—	6	16	no	—
244	C₂×C₈	—	3	8	no	—
245	C₂×C₈	—	6	8	no	—
246	C₄²	C₂×C₃×Dic₃	1	4	yes	—
247	C₄²	C₂×C₃×Dic₃	1	4	yes	—
248	C₄²	C₂×C₃×Dic₃	1	4	yes	—
249	C₄²	C₂²×C₃×D₃	1	4	yes	—
250	C₂²×C₃	—	2	8	no	—
251	C₂²×C₃	—	2	16	no	—
252	C₂²×C₃	—	2	4	no	—
253	C₂²×C₃	—	2	8	no	—
254	C₂²×C₃	—	2	4	no	—
255	C₂²×C₃	—	2	8	no	—
256	C₂²×C₃	—	2	4	no	—
257	C₂²×C₃	—	2	4	no	—
258	C₂²×C₃	—	2	2	no	—
259	C₂²×C₃	—	2	1	no	—
260	C₂²×C₃	C₂×#208	1	4	yes	—
261	C₂²×C₃	C₂×C₄⋊Dic₃	1	4	yes	—
262	C₂²×C₃	C₂×C₄⋊Dic₃	1	2	yes	—
263	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
264	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
265	C₂²×C₃	C₂×C₃×M₁₆	1	4	yes	—
266	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
267	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
268	C₃×C₄	—	2	8	no	—
269	C₃×C₄	—	2	4	no	—
270	C₃×C₄	—	2	4	no	—
271	C₃×C₄	—	2	8	no	—
272	C₃×C₄	—	2	2	no	—
273	C₃×C₄	—	2	4	no	—
274	C₃×C₄	—	2	1	no	—
275	C₃×C₄	—	2	1	no	—
276	C₃×C₄	C₂×#208	1	8	yes	complemented
277	C₃×C₄	C₂×C₄⋊Dic₃	1	4	yes	—
278	C₃×C₄	C₂×C₄⋊Dic₃	1	2	yes	—
279	C₃×C₄	C₂×C₃×C₄⋊C₄	1	2	yes	—
280	C₃×C₄	C₂×C₃×C₄⋊C₄	1	4	yes	—
281	C₃×C₄	C₂×C₃×M₁₆	1	8	yes	complemented
282	C₃×C₄	C₂²×Dic₆	1	1	yes	characteristic
283	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
284	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
285	C₃×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
286	C₃²	C₂×#423	1	1	yes	characteristic, complemented, Sylow
287	C₂³	—	2	4	no	—
288	C₂³	C₃×C₄⋊Dic₃	1	4	yes	—
289	C₂³	C₂²×C₃×Dic₃	1	2	yes	—
290	C₂³	C₂²×C₃×Dic₃	1	1	yes	characteristic
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	16	no	—
293	C₂×C₄	C₃×#208	1	8	yes	complemented
294	C₂×C₄	C₃×C₄⋊Dic₃	1	8	yes	—
295	C₂×C₄	C₃×C₄⋊Dic₃	1	4	yes	—
296	C₂×C₄	C₂×C₃×Dic₆	1	4	yes	—
297	C₂×C₄	C₂×C₃×Dic₆	1	2	yes	—
298	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
299	C₂×C₄	C₂×C₃×D₁₂	1	4	yes	—
300	C₂×C₄	C₂²×C₃×Dic₃	1	4	yes	—
301	C₂×C₄	C₂²×C₃×Dic₃	1	4	yes	—
302	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
303	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
304	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
305	C₈	—	6	8	no	—
306	C₂×C₃	—	2	8	no	—
307	C₂×C₃	—	2	4	no	—
308	C₂×C₃	—	2	4	no	—
309	C₂×C₃	—	2	4	no	—
310	C₂×C₃	—	2	2	no	—
311	C₂×C₃	—	2	1	no	—
312	C₂×C₃	#4924	1	4	yes	direct product factor
313	C₂×C₃	C₃×#423	1	4	yes	complemented
314	C₂×C₃	C₂²×#208	1	2	yes	—
315	C₂×C₃	C₂²×C₄⋊Dic₃	1	1	yes	characteristic
316	C₂×C₃	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
317	C₂×C₃	C₂²×C₃×M₁₆	1	2	yes	—
318	C₂²	—	2	8	no	—
319	C₂²	—	2	4	no	—
320	C₂²	C₂×C₃×#208	1	4	yes	—
321	C₂²	C₂×C₃×C₄⋊Dic₃	1	4	yes	—
322	C₂²	C₂×C₃×C₄⋊Dic₃	1	2	yes	—
323	C₂²	C₂³×C₃×Dic₃	1	1	yes	characteristic
324	C₄	—	2	4	no	—
325	C₄	C₂×C₃×#208	1	8	yes	complemented
326	C₄	C₂×C₃×C₄⋊Dic₃	1	2	yes	—
327	C₄	C₂×C₃×C₄⋊Dic₃	1	4	yes	—
328	C₄	C₂²×C₃×Dic₆	1	1	yes	characteristic
329	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
330	C₃	—	2	1	no	—
331	C₃	C₂×#4924	1	1	yes	characteristic, direct product factor
332	C₃	C₂×C₃×#423	1	1	yes	characteristic, complemented
333	C₂	—	2	4	no	—
334	C₂	C₃×#4924	1	4	yes	direct product factor
335	C₂	C₂²×C₃×#208	1	2	yes	—
336	C₂	C₂²×C₃×C₄⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂²×C₃²×C₄²	C₂
socle	C₂³×C₃²	C₂²×C₄
prime radical	C₂⁴×C₃²	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂²×C₃×C₄²	D₃
hypocenter	C₃	C₂×C₃×#423
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₄²

Complements

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

N	H ≅ G/N	type
3. C₃×#4924	C₂	direct (N × H)
4. C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	semidirect
6. C₂×#4924	C₃	direct (N × H)
17. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
25. #4924	C₂×C₃	direct (N × H)
26. C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	semidirect
74. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
83. C₂×C₃²×C₄	M₁₆	semidirect
158. C₃²×C₄	C₂×M₁₆	semidirect
202. C₂×C₃×C₄	#208	semidirect
207. C₂×C₃×C₄	C₃×M₁₆	semidirect
229. C₂×C₃²	#423	semidirect
276. C₃×C₄	C₂×#208	semidirect
281. C₃×C₄	C₂×C₃×M₁₆	semidirect
286. C₃²	C₂×#423	semidirect
293. C₂×C₄	C₃×#208	semidirect
312. C₂×C₃	#4924	direct (N × H)
313. C₂×C₃	C₃×#423	semidirect
325. C₄	C₂×C₃×#208	semidirect
331. C₃	C₂×#4924	direct (N × H)
332. C₃	C₂×C₃×#423	semidirect
334. C₂	C₃×#4924	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×C₃²×C₄²	2
C₂²×C₃×#208	2
C₃×#4924	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₂×C₃×#423	3
C₂×#4924	3

Subgroups — C2×C3×#4924 #11858242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4924 #11858242