Subgroups — C₃×#78458 #11859473

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#901	C₂	1	2	yes	maximal, complemented
2	C₃×#5477	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5110	C₂	1	2	yes	maximal, complemented
5	C₃×#4924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4688	C₂	1	4	yes	maximal, complemented
7	C₃×C₈×D₁₂	C₂	1	4	yes	maximal, complemented
8	C₃×#2931	—	3	1	no	maximal
9	#78458	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃×#235	C₂²	1	2	yes	—
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₃×#930	C₄	1	4	yes	—
15	C₂×C₃×#208	C₂²	1	2	yes	—
16	C₃×#901	—	2	8	no	—
17	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
18	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
19	C₃×#875	C₄	1	2	yes	—
20	C₃×#874	C₄	1	1	yes	characteristic
21	C₃×C₄×D₁₂	C₂²	1	4	yes	—
22	C₃×#869	C₄	1	1	yes	characteristic
23	C₃²×C₄×C₈	C₂²	1	2	yes	—
24	C₃²×C₄×C₈	C₂²	1	2	yes	—
25	C₃×(C₂×D₃)⋊C₈	C₂²	1	8	yes	—
26	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	—
27	C₂×C₃×#131	—	3	2	no	—
28	C₃×#532	—	3	1	no	—
29	C₂×#901	C₂×C₃	1	2	yes	complemented
30	#5477	C₂×C₃	1	1	yes	characteristic
31	C₃×#436	—	3	4	no	—
32	C₃×C₈×D₄	—	3	4	no	—
33	C₃×#423	—	3	1	no	—
34	C₃×#408	—	3	2	no	—
35	C₂×C₃×C₄×C₈	—	2	1	no	—
36	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic, complemented
37	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
38	#5110	C₂×C₃	1	2	yes	complemented
39	#4924	C₂×C₃	1	1	yes	characteristic, complemented
40	#4688	C₂×C₃	1	4	yes	complemented
41	C₈×D₁₂	C₂×C₃	1	4	yes	complemented
42	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
43	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
44	C₂×C₃×#67	C₂×C₄	1	4	yes	—
45	C₃×#235	—	2	4	no	—
46	C₃×#235	—	2	4	no	—
47	C₂×C₃×D₁₂	C₂×C₄	1	4	yes	—
48	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
49	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
50	C₂×C₃×Dic₆	C₂×C₄	1	2	yes	—
51	C₂×C₃²×C₈	—	2	2	no	—
52	C₂×C₃²×C₈	D₄	1	4	yes	complemented
53	C₂×C₃²×C₈	C₂³	1	2	yes	—
54	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
55	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
56	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
57	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
58	C₃²×C₄²	C₂³	1	2	yes	—
59	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
60	C₃×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
61	C₃×#208	—	2	4	no	—
62	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
63	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
64	C₃×D₃×C₈	—	2	8	no	—
65	#2931	—	3	1	no	Sylow
66	C₂×C₃×#41	—	3	2	no	—
67	C₂×#235	C₂²×C₃	1	2	yes	—
68	C₃×#131	—	6	8	no	—
69	C₂×C₃×M₁₆	—	3	2	no	—
70	C₂×C₃×M₁₆	—	3	4	no	—
71	C₂²×C₃×C₈	—	2	1	no	—
72	C₂²×C₃×C₈	—	2	1	no	—
73	C₂²×C₃×C₈	—	3	4	no	—
74	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
75	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
76	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
78	C₃×C₄⋊Q₈	—	3	1	no	—
79	C₃×#127	—	3	1	no	—
80	C₃×#124	—	3	2	no	—
81	C₃×#121	—	3	4	no	—
82	C₃×C₄×D₄	—	3	4	no	—
83	C₂×C₃×C₄²	—	2	1	no	—
84	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
85	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
86	#930	C₃×C₄	1	4	yes	—
87	C₂×#208	C₂²×C₃	1	2	yes	—
88	#901	—	2	8	no	—
89	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	4	yes	—
90	C₂×D₃×C₈	C₂²×C₃	1	4	yes	—
91	#875	C₃×C₄	1	2	yes	—
92	#874	C₃×C₄	1	1	yes	characteristic
93	C₄×D₁₂	C₂²×C₃	1	4	yes	—
94	#869	C₃×C₄	1	1	yes	characteristic
95	C₃×C₄⋊C₈	—	3	4	no	—
96	C₃×C₂²⋊C₈	—	3	8	no	—
97	C₃×C₄×C₈	—	2	2	no	—
98	C₃×C₄×C₈	—	2	2	no	—
99	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
100	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
101	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
102	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
103	(C₂×D₃)⋊C₈	C₂²×C₃	1	8	yes	—
104	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	4	yes	—
105	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₃×D₃	C₂²×C₄	1	4	yes	—
107	C₂×C₃²×C₄	—	2	4	no	—
108	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
109	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
111	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
112	C₂×C₃²×C₄	#41	1	2	yes	—
113	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
114	C₃×#67	—	2	8	no	—
115	C₂×C₃×Dic₃	C₂²×C₄	1	4	yes	—
116	C₃×D₁₂	—	2	4	no	—
117	C₃×D₁₂	—	2	8	no	—
118	C₃×C₄×D₃	—	2	4	no	—
119	C₃×C₄×D₃	—	2	4	no	—
120	C₃×Dic₆	—	2	4	no	—
121	C₃²×C₈	—	2	2	no	—
122	C₃²×C₈	C₂×D₄	1	2	yes	—
123	C₃²×C₈	C₂×D₄	1	2	yes	—
124	C₃×C₃⋊C₈	—	2	4	no	—
125	C₂×#131	—	3	2	no	—
126	#532	—	3	1	no	—
127	#436	—	3	4	no	—
128	C₈×D₄	—	3	4	no	—
129	#423	—	3	1	no	—
130	#408	—	3	2	no	—
131	C₂×C₄×C₈	C₃×D₃	1	1	yes	characteristic, complemented
132	C₃×#41	—	6	4	no	—
133	C₃×#41	—	6	4	no	—
134	C₂×C₃×Q₈	—	3	2	no	—
135	C₂×C₃×D₄	—	3	4	no	—
136	C₂×C₃×D₄	—	3	4	no	—
137	C₂×C₃×D₄	—	3	2	no	—
138	C₂²×C₃×C₄	—	2	2	no	—
139	C₂²×C₃×C₄	—	2	1	no	—
140	C₂²×C₃×C₄	—	3	4	no	—
141	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
142	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
143	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
145	C₂×#67	C₂×C₃×C₄	1	4	yes	—
146	#235	—	2	4	no	—
147	#235	—	2	4	no	—
148	C₂×D₁₂	C₂×C₃×C₄	1	4	yes	—
149	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
150	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
151	C₂×Dic₆	C₂×C₃×C₄	1	2	yes	—
152	C₃×M₁₆	—	6	4	no	—
153	C₃×M₁₆	—	6	8	no	—
154	C₂×C₃×C₈	—	2	4	no	—
155	C₂×C₃×C₈	—	2	2	no	—
156	C₂×C₃×C₈	—	2	2	no	—
157	C₂×C₃×C₈	—	2	4	no	—
158	C₂×C₃×C₈	—	2	2	no	—
159	C₂×C₃×C₈	—	2	1	no	—
160	C₂×C₃×C₈	—	2	1	no	—
161	C₂×C₃×C₈	—	3	4	no	—
162	C₂×C₃×C₈	—	6	8	no	—
163	C₂×C₃×C₈	D₁₂	1	4	yes	complemented
164	C₂×C₃×C₈	C₃×D₄	1	4	yes	complemented
165	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
166	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
167	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
168	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
169	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
170	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
171	C₃×C₄⋊C₄	—	3	4	no	—
172	C₃×C₂²⋊C₄	—	3	8	no	—
173	C₃×C₄²	—	2	1	no	—
174	C₃×C₄²	—	2	1	no	—
175	C₃×C₄²	—	2	2	no	—
176	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
177	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
178	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
179	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
180	C₃×C₄²	C₂²×D₃	1	2	yes	—
181	C₃×C₄²	C₂³×C₃	1	2	yes	—
182	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	8	yes	—
183	C₄⋊Dic₃	C₂×C₃×C₄	1	4	yes	—
184	#208	—	2	4	no	—
185	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
186	ΓL(1,𝔽₂₅)	—	2	8	no	—
187	D₃×C₈	—	2	8	no	—
188	C₂²×C₃²	—	2	2	no	—
189	C₂²×C₃²	C₄×D₄	1	2	yes	—
190	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₃×D₃	—	2	4	no	—
192	C₂×C₃×D₃	—	2	8	no	—
193	C₃²×C₄	—	2	2	no	—
194	C₃²×C₄	C₄×D₄	1	2	yes	—
195	C₃²×C₄	#131	1	4	yes	complemented
196	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
197	C₃²×C₄	C₂×#41	1	1	yes	characteristic
198	C₃×Dic₃	—	2	4	no	—
199	C₂×#41	—	3	2	no	—
200	#131	—	6	8	no	—
201	C₂×M₁₆	—	3	2	no	—
202	C₂×M₁₆	—	3	4	no	—
203	C₂²×C₈	—	3	4	no	—
204	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
205	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
206	C₄⋊Q₈	—	3	1	no	—
207	#127	—	3	1	no	—
208	#124	—	3	2	no	—
209	#121	—	3	4	no	—
210	C₄×D₄	—	3	4	no	—
211	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
212	C₄⋊C₈	—	3	4	no	—
213	C₂²⋊C₈	—	3	8	no	—
214	C₄×C₈	C₂×C₃×D₃	1	2	yes	—
215	C₄×C₈	C₂×C₃×D₃	1	2	yes	—
216	C₂³×C₃	—	2	1	no	—
217	C₂³×C₃	—	3	4	no	—
218	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
219	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
220	C₂²×D₃	C₂²×C₃×C₄	1	4	yes	—
221	C₃×Q₈	—	6	4	no	—
222	C₃×D₄	—	6	8	no	—
223	C₃×D₄	—	6	4	no	—
224	C₃×D₄	—	6	8	no	—
225	C₂×C₃×C₄	—	2	8	no	—
226	C₂×C₃×C₄	—	2	4	no	—
227	C₂×C₃×C₄	—	2	4	no	—
228	C₂×C₃×C₄	—	2	1	no	—
229	C₂×C₃×C₄	—	2	2	no	—
230	C₂×C₃×C₄	—	2	2	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	3	4	no	—
235	C₂×C₃×C₄	—	6	4	no	—
236	C₂×C₃×C₄	—	6	4	no	—
237	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
238	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
240	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
241	C₂×C₃×C₄	#235	1	2	yes	—
242	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
243	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
245	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
246	C₂×C₃×C₄	C₃×#41	1	2	yes	—
247	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
249	#67	—	2	8	no	—
250	C₂×Dic₃	C₂²×C₃×C₄	1	4	yes	—
251	D₁₂	—	2	4	no	—
252	D₁₂	—	2	8	no	—
253	C₄×D₃	—	2	4	no	—
254	C₄×D₃	—	2	4	no	—
255	Dic₆	—	2	4	no	—
256	C₃×C₈	—	2	4	no	—
257	C₃×C₈	—	2	2	no	—
258	C₃×C₈	—	2	2	no	—
259	C₃×C₈	—	2	2	no	—
260	C₃×C₈	—	2	2	no	—
261	C₃×C₈	—	6	4	no	—
262	C₃×C₈	C₂×D₁₂	1	2	yes	—
263	C₃×C₈	C₂×D₁₂	1	2	yes	—
264	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
265	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
266	C₃⋊C₈	—	2	4	no	—
267	C₂×C₃²	—	2	2	no	—
268	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
269	C₂×C₃²	C₂×#131	1	2	yes	—
270	C₃×D₃	—	4	4	no	—
271	#41	—	6	4	no	—
272	#41	—	6	4	no	—
273	C₂×Q₈	—	3	2	no	—
274	C₂×D₄	—	3	4	no	—
275	C₂×D₄	—	3	4	no	—
276	C₂×D₄	—	3	2	no	—
277	C₂²×C₄	—	3	4	no	—
278	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
279	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
280	M₁₆	—	6	4	no	—
281	M₁₆	—	6	8	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	3	4	no	—
284	C₂×C₈	—	6	8	no	—
285	C₂×C₈	C₃×D₁₂	1	4	yes	complemented
286	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
287	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
288	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
289	C₄⋊C₄	—	3	4	no	—
290	C₂²⋊C₄	—	3	8	no	—
291	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
292	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
293	C₄²	C₂²×C₃×D₃	1	2	yes	—
294	C₂²×C₃	—	2	4	no	—
295	C₂²×C₃	—	2	2	no	—
296	C₂²×C₃	—	2	2	no	—
297	C₂²×C₃	—	2	1	no	—
298	C₂²×C₃	—	2	2	no	—
299	C₂²×C₃	—	6	4	no	—
300	C₂²×C₃	—	6	8	no	—
301	C₂²×C₃	C₄×D₁₂	1	2	yes	—
302	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
303	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
304	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
305	C₂×D₃	—	2	8	no	—
306	C₂×D₃	—	2	4	no	—
307	C₃×C₄	—	2	4	no	—
308	C₃×C₄	—	2	2	no	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	2	4	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	2	no	—
314	C₃×C₄	—	6	4	no	—
315	C₃×C₄	C₄×D₁₂	1	2	yes	—
316	C₃×C₄	#901	1	4	yes	complemented
317	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
318	C₃×C₄	C₃×#131	1	4	yes	complemented
319	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
320	C₃×C₄	C₂×#235	1	1	yes	characteristic
321	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
322	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
323	Dic₃	—	2	4	no	—
324	C₃²	#2931	1	1	yes	characteristic, complemented, Sylow
325	C₂³	—	3	4	no	—
326	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
327	Q₈	—	6	4	no	—
328	D₄	—	6	8	no	—
329	D₄	—	6	8	no	—
330	D₄	—	6	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	3	4	no	—
333	C₂×C₄	—	6	4	no	—
334	C₂×C₄	—	6	4	no	—
335	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
336	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
337	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
338	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
339	C₂×C₄	C₃×#235	1	2	yes	—
340	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
341	C₈	—	2	2	no	—
342	C₈	—	6	4	no	—
343	C₈	C₂×C₃×D₁₂	1	2	yes	—
344	C₈	C₂×C₃×D₁₂	1	2	yes	—
345	C₂×C₃	—	2	4	no	—
346	C₂×C₃	—	2	2	no	—
347	C₂×C₃	—	2	2	no	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	2	2	no	—
350	C₂×C₃	—	12	4	no	—
351	C₂×C₃	C₂×C₄×D₁₂	1	1	yes	characteristic
352	C₂×C₃	C₂×#901	1	2	yes	—
353	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
354	C₂×C₃	C₂×C₃×#131	1	2	yes	—
355	D₃	—	4	4	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	6	4	no	—
358	C₂²	—	6	8	no	—
359	C₂²	C₃×C₄×D₁₂	1	2	yes	—
360	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
361	C₄	—	2	2	no	—
362	C₄	—	6	4	no	—
363	C₄	C₃×C₄×D₁₂	1	2	yes	—
364	C₄	C₃×#901	1	4	yes	complemented
365	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
366	C₄	C₂×C₃×#235	1	1	yes	characteristic
367	C₃	—	2	1	no	—
368	C₃	#78458	1	1	yes	characteristic, direct product factor
369	C₃	C₃×#2931	1	1	yes	characteristic, complemented
370	C₂	—	2	2	no	—
371	C₂	—	12	4	no	—
372	C₂	C₂×C₃×C₄×D₁₂	1	1	yes	characteristic
373	C₂	C₂×C₃×#901	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₈	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×C₄×C₈	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₃×#5477	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×C₈	D₃
hypocenter	C₃	C₃×#2931
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#901	C₂	semidirect
3. C₂×C₃²×C₄×C₈	C₂	semidirect
4. C₃×#5110	C₂	semidirect
5. C₃×#4924	C₂	semidirect
6. C₃×#4688	C₂	semidirect
7. C₃×C₈×D₁₂	C₂	semidirect
9. #78458	C₃	direct (N × H)
29. C₂×#901	C₂×C₃	semidirect
36. C₂×C₃×C₄×C₈	D₃	semidirect
37. C₂×C₃×C₄×C₈	C₂×C₃	semidirect
38. #5110	C₂×C₃	semidirect
39. #4924	C₂×C₃	semidirect
40. #4688	C₂×C₃	semidirect
41. C₈×D₁₂	C₂×C₃	semidirect
52. C₂×C₃²×C₈	D₄	semidirect
131. C₂×C₄×C₈	C₃×D₃	semidirect
163. C₂×C₃×C₈	D₁₂	semidirect
164. C₂×C₃×C₈	C₃×D₄	semidirect
195. C₃²×C₄	#131	semidirect
285. C₂×C₈	C₃×D₁₂	semidirect
316. C₃×C₄	#901	semidirect
318. C₃×C₄	C₃×#131	semidirect
324. C₃²	#2931	semidirect
364. C₄	C₃×#901	semidirect
368. C₃	#78458	direct (N × H)
369. C₃	C₃×#2931	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#901	2
C₃×#5477	2
C₂×C₃²×C₄×C₈	2
C₃×#5110	2
C₃×#4924	2
C₃×#4688	2
C₃×C₈×D₁₂	2
C₃×#2931	3
#78458	3

Subgroups — C3×#78458 #11859473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#78458 #11859473