Subgroups — C₂×C₃×#4515 #11796078

Order 1152.

493 conjugacy classes of subgroups.

The subgroup lattice has 369 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	1	yes	maximal, characteristic
2	C₂×C₃²×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4515	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃×#350	—	3	1	no	maximal
6	C₂×#4515	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₃×#235	C₄	1	1	yes	characteristic
8	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₃×#208	C₄	1	1	yes	characteristic
10	C₃×#901	—	2	1	no	—
11	C₃×#901	—	2	1	no	—
12	C₃×#901	C₄	1	2	yes	—
13	C₃×#901	C₂²	1	2	yes	—
14	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
15	C₂×C₃×D₃×C₈	—	2	1	no	—
16	C₃²×M₃₂	—	2	1	no	—
17	C₃²×M₃₂	C₂²	1	2	yes	complemented
18	C₂×C₃²×C₁₆	—	2	1	no	—
19	C₂×C₃×C₃⋊C₁₆	—	2	1	no	—
20	C₂×C₃×C₃⋊C₁₆	—	2	1	no	—
21	C₂×C₃×C₃⋊C₁₆	C₂²	1	2	yes	complemented
22	C₂×C₃×#131	—	3	1	no	—
23	C₂×#901	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×M₃₂	—	2	1	no	—
25	C₂×C₃×M₃₂	D₃	1	1	yes	characteristic, complemented
26	C₂×C₃×M₃₂	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂²×C₃×C₁₆	—	3	1	no	—
28	C₂²×C₃⋊C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
29	C₃×#350	—	3	4	no	—
30	#4515	C₂×C₃	1	4	yes	direct product factor
31	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
32	C₂×C₃×#67	—	2	1	no	—
33	C₃×#235	—	2	1	no	—
34	C₃×#235	—	2	1	no	—
35	C₃×#235	C₈	1	2	yes	—
36	C₃×#235	C₂×C₄	1	2	yes	—
37	C₂×C₃×D₁₂	C₈	1	1	yes	characteristic
38	C₂×C₃×C₄×D₃	—	2	1	no	—
39	C₂×C₃×Dic₆	C₈	1	1	yes	characteristic
40	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
42	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
43	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
44	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
45	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
46	C₃×#208	—	2	1	no	—
47	C₃×#208	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₃⋊C₈	—	2	1	no	—
49	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
50	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
51	C₃×D₃×C₈	—	2	2	no	—
52	C₃×D₃×C₈	—	2	2	no	—
53	C₃²×C₁₆	—	2	2	no	—
54	C₃×C₃⋊C₁₆	—	2	2	no	—
55	C₂×#350	—	3	1	no	Sylow
56	C₂×C₃×#41	—	3	1	no	—
57	C₂×#235	C₃×C₄	1	1	yes	characteristic
58	C₃×#131	—	3	2	no	—
59	C₃×#131	—	3	2	no	—
60	C₃×#131	—	6	1	no	—
61	C₃×#131	—	6	1	no	—
62	C₂×C₃×M₁₆	—	3	1	no	—
63	C₂×C₃×M₁₆	—	6	1	no	—
64	C₂²×C₃×C₈	—	2	1	no	—
65	C₂²×C₃×C₈	—	6	1	no	—
66	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
67	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
68	C₂×#208	C₃×C₄	1	1	yes	characteristic
69	#901	—	2	1	no	—
70	#901	—	2	1	no	—
71	#901	C₃×C₄	1	2	yes	—
72	#901	C₂²×C₃	1	2	yes	—
73	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
74	C₂×D₃×C₈	—	2	1	no	—
75	C₃×M₃₂	—	2	2	no	—
76	C₃×M₃₂	—	2	1	no	—
77	C₃×M₃₂	—	2	1	no	—
78	C₃×M₃₂	—	2	2	no	—
79	C₃×M₃₂	C₂×D₃	1	2	yes	complemented
80	C₃×M₃₂	C₂²×C₃	1	2	yes	complemented
81	C₂×C₃×C₁₆	—	2	2	no	—
82	C₂×C₃×C₁₆	—	2	1	no	—
83	C₂×C₃×C₁₆	—	2	1	no	—
84	C₂×C₃×C₁₆	—	3	2	no	—
85	C₂×C₃×C₁₆	—	6	1	no	—
86	C₂×C₃×C₁₆	—	6	1	no	—
87	C₂×C₃⋊C₁₆	—	2	1	no	—
88	C₂×C₃⋊C₁₆	—	2	1	no	—
89	C₂×C₃⋊C₁₆	C₂²×C₃	1	2	yes	complemented
90	C₂³×C₃²	M₁₆	1	1	yes	characteristic
91	C₂²×C₃×D₃	—	2	1	no	—
92	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
95	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
96	C₂×C₃²×C₄	M₁₆	1	1	yes	characteristic
97	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
98	C₃×#67	—	2	2	no	—
99	C₃×#67	—	2	2	no	—
100	C₂×C₃×Dic₃	—	2	1	no	—
101	C₃×D₁₂	—	2	1	no	—
102	C₃×D₁₂	C₂×C₈	1	2	yes	—
103	C₃×C₄×D₃	—	2	2	no	—
104	C₃×C₄×D₃	—	2	2	no	—
105	C₃×Dic₆	—	2	1	no	—
106	C₃×Dic₆	C₂×C₈	1	2	yes	—
107	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
108	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
109	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
110	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
111	C₃×C₃⋊C₈	—	2	2	no	—
112	C₂×#131	—	3	1	no	—
113	C₂×M₃₂	C₃×D₃	1	1	yes	characteristic, complemented
114	C₂²×C₁₆	—	3	1	no	—
115	#350	—	3	4	no	—
116	C₃×#41	—	3	2	no	—
117	C₃×#41	—	3	2	no	—
118	C₃×#41	—	6	1	no	—
119	C₃×#41	—	6	1	no	—
120	C₂×C₃×Q₈	—	3	1	no	—
121	C₂×C₃×D₄	—	3	1	no	—
122	C₂×C₃×D₄	—	6	1	no	—
123	C₂²×C₃×C₄	—	2	1	no	—
124	C₂²×C₃×C₄	—	6	1	no	—
125	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
126	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
127	C₂×#67	—	2	1	no	—
128	#235	—	2	1	no	—
129	#235	—	2	1	no	—
130	#235	C₃×C₈	1	2	yes	—
131	#235	C₂×C₃×C₄	1	2	yes	—
132	C₂×D₁₂	C₃×C₈	1	1	yes	characteristic
133	C₂×C₄×D₃	—	2	1	no	—
134	C₂×Dic₆	C₃×C₈	1	1	yes	characteristic
135	C₃×M₁₆	—	3	2	no	—
136	C₃×M₁₆	—	6	1	no	—
137	C₃×M₁₆	—	6	2	no	—
138	C₃×M₁₆	—	6	2	no	—
139	C₂×C₃×C₈	—	2	1	no	—
140	C₂×C₃×C₈	—	2	1	no	—
141	C₂×C₃×C₈	—	2	1	no	—
142	C₂×C₃×C₈	—	2	1	no	—
143	C₂×C₃×C₈	—	2	1	no	—
144	C₂×C₃×C₈	—	2	1	no	—
145	C₂×C₃×C₈	—	6	1	no	—
146	C₂×C₃×C₈	—	6	2	no	—
147	C₂×C₃×C₈	—	6	2	no	—
148	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
149	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
150	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
151	C₂×C₃×C₈	#67	1	1	yes	characteristic
152	C₂×C₃×C₈	#67	1	1	yes	characteristic
153	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
154	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
155	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
156	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
157	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
158	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
159	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
160	#208	—	2	1	no	—
161	#208	C₂×C₃×C₄	1	2	yes	—
162	C₂×C₃⋊C₈	—	2	1	no	—
163	ΓL(1,𝔽₂₅)	—	2	2	no	—
164	ΓL(1,𝔽₂₅)	—	2	2	no	—
165	D₃×C₈	—	2	2	no	—
166	D₃×C₈	—	2	2	no	—
167	C₃×C₁₆	—	2	4	no	—
168	C₃×C₁₆	—	2	2	no	—
169	C₃×C₁₆	—	2	2	no	—
170	C₃×C₁₆	—	6	2	no	—
171	C₃⋊C₁₆	—	2	2	no	—
172	C₂²×C₃²	—	2	2	no	—
173	C₂²×C₃²	C₂²⋊C₈	1	1	yes	characteristic
174	C₂²×C₃²	C₂²⋊C₈	1	1	yes	characteristic
175	C₂²×C₃²	C₂×M₁₆	1	1	yes	characteristic
176	C₂×C₃×D₃	—	2	2	no	—
177	C₂×C₃×D₃	—	4	2	no	—
178	C₃²×C₄	C₂²⋊C₈	1	1	yes	characteristic
179	C₃²×C₄	C₂²⋊C₈	1	1	yes	characteristic
180	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
182	C₃×Dic₃	—	2	2	no	—
183	C₂×#41	—	3	1	no	—
184	#131	—	3	2	no	—
185	#131	—	3	2	no	—
186	#131	—	6	1	no	—
187	#131	—	6	1	no	—
188	C₂×M₁₆	—	3	1	no	—
189	C₂×M₁₆	—	6	1	no	—
190	C₂²×C₈	—	6	1	no	—
191	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
192	M₃₂	—	2	1	no	—
193	M₃₂	C₂×C₃×D₃	1	2	yes	complemented
194	C₂×C₁₆	—	2	1	no	—
195	C₂×C₁₆	—	3	2	no	—
196	C₂×C₁₆	—	6	1	no	—
197	C₂×C₁₆	—	6	1	no	—
198	C₂³×C₃	—	2	1	no	—
199	C₂³×C₃	—	6	1	no	—
200	C₂³×C₃	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
201	C₂³×C₃	C₃×M₁₆	1	1	yes	characteristic
202	C₂²×D₃	—	2	1	no	—
203	C₃×Q₈	—	3	2	no	—
204	C₃×Q₈	—	6	1	no	—
205	C₃×D₄	—	3	2	no	—
206	C₃×D₄	—	6	2	no	—
207	C₃×D₄	—	6	2	no	—
208	C₃×D₄	—	6	1	no	—
209	C₂×C₃×C₄	—	2	1	no	—
210	C₂×C₃×C₄	—	2	1	no	—
211	C₂×C₃×C₄	—	2	1	no	—
212	C₂×C₃×C₄	—	2	1	no	—
213	C₂×C₃×C₄	—	2	1	no	—
214	C₂×C₃×C₄	—	2	1	no	—
215	C₂×C₃×C₄	—	6	1	no	—
216	C₂×C₃×C₄	—	6	2	no	—
217	C₂×C₃×C₄	—	6	2	no	—
218	C₂×C₃×C₄	D₃×C₈	1	1	yes	characteristic
219	C₂×C₃×C₄	D₃×C₈	1	1	yes	characteristic
220	C₂×C₃×C₄	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
221	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
222	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
223	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₃×C₄	C₂×C₃×C₈	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂×C₃×C₈	1	1	yes	characteristic
227	C₂×C₃×C₄	C₃×M₁₆	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
229	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
230	#67	—	2	2	no	—
231	#67	—	2	2	no	—
232	C₂×Dic₃	—	2	1	no	—
233	D₁₂	—	2	1	no	—
234	D₁₂	C₂×C₃×C₈	1	2	yes	—
235	C₄×D₃	—	2	2	no	—
236	C₄×D₃	—	2	2	no	—
237	Dic₆	—	2	1	no	—
238	Dic₆	C₂×C₃×C₈	1	2	yes	—
239	C₃×C₈	—	2	1	no	—
240	C₃×C₈	—	2	1	no	—
241	C₃×C₈	—	2	1	no	—
242	C₃×C₈	—	2	1	no	—
243	C₃×C₈	—	6	2	no	—
244	C₃×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
245	C₃×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
246	C₃×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
247	C₃×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
248	C₃×C₈	C₂×D₁₂	1	1	yes	characteristic
249	C₃×C₈	C₂×#67	1	1	yes	characteristic
250	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
251	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
252	C₃⋊C₈	—	2	2	no	—
253	C₂×C₃²	—	2	1	no	—
254	C₂×C₃²	—	2	1	no	—
255	C₂×C₃²	#350	1	2	yes	complemented
256	C₂×C₃²	C₂×C₂²⋊C₈	1	1	yes	characteristic
257	C₃×D₃	—	4	2	no	—
258	#41	—	3	2	no	—
259	#41	—	3	2	no	—
260	#41	—	6	1	no	—
261	#41	—	6	1	no	—
262	C₂×Q₈	—	3	1	no	—
263	C₂×D₄	—	3	1	no	—
264	C₂×D₄	—	6	1	no	—
265	C₂²×C₄	—	6	1	no	—
266	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
267	M₁₆	—	3	2	no	—
268	M₁₆	—	6	1	no	—
269	M₁₆	—	6	2	no	—
270	M₁₆	—	6	2	no	—
271	C₂×C₈	—	6	1	no	—
272	C₂×C₈	—	6	2	no	—
273	C₂×C₈	—	6	2	no	—
274	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
275	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
276	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
277	C₂×C₈	C₃×#67	1	1	yes	characteristic
278	C₂×C₈	C₃×#67	1	1	yes	characteristic
279	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
280	C₁₆	—	2	2	no	—
281	C₁₆	—	6	2	no	—
282	C₂²×C₃	—	2	2	no	—
283	C₂²×C₃	—	2	2	no	—
284	C₂²×C₃	—	2	1	no	—
285	C₂²×C₃	—	2	1	no	—
286	C₂²×C₃	—	2	1	no	—
287	C₂²×C₃	—	4	2	no	—
288	C₂²×C₃	—	6	2	no	—
289	C₂²×C₃	—	12	2	no	—
290	C₂²×C₃	(C₂×D₃)⋊C₈	1	1	yes	characteristic
291	C₂²×C₃	(C₂×D₃)⋊C₈	1	1	yes	characteristic
292	C₂²×C₃	C₃×C₂²⋊C₈	1	1	yes	characteristic
293	C₂²×C₃	C₃×C₂²⋊C₈	1	1	yes	characteristic
294	C₂²×C₃	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
295	C₂²×C₃	C₂×C₃×M₁₆	1	1	yes	characteristic
296	C₂×D₃	—	2	2	no	—
297	C₂×D₃	—	4	2	no	—
298	C₃×C₄	—	2	1	no	—
299	C₃×C₄	—	2	1	no	—
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	2	1	no	—
302	C₃×C₄	—	6	2	no	—
303	C₃×C₄	(C₂×D₃)⋊C₈	1	1	yes	characteristic
304	C₃×C₄	(C₂×D₃)⋊C₈	1	1	yes	characteristic
305	C₃×C₄	C₃×C₂²⋊C₈	1	1	yes	characteristic
306	C₃×C₄	C₃×C₂²⋊C₈	1	1	yes	characteristic
307	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
308	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
309	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
310	C₃×C₄	C₂²×C₃×C₈	1	1	yes	characteristic
311	Dic₃	—	2	2	no	—
312	C₃²	C₂×#350	1	1	yes	characteristic, complemented, Sylow
313	C₂³	—	6	1	no	—
314	C₂³	C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
315	Q₈	—	3	2	no	—
316	Q₈	—	6	1	no	—
317	D₄	—	3	2	no	—
318	D₄	—	6	2	no	—
319	D₄	—	6	2	no	—
320	D₄	—	6	1	no	—
321	C₂×C₄	—	6	1	no	—
322	C₂×C₄	—	6	2	no	—
323	C₂×C₄	—	6	2	no	—
324	C₂×C₄	C₃×D₃×C₈	1	1	yes	characteristic
325	C₂×C₄	C₃×D₃×C₈	1	1	yes	characteristic
326	C₂×C₄	C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
327	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
328	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
329	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
330	C₈	—	6	2	no	—
331	C₈	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
332	C₈	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
333	C₈	C₂×C₃×D₁₂	1	1	yes	characteristic
334	C₈	C₂×C₃×#67	1	1	yes	characteristic
335	C₂×C₃	—	2	1	no	—
336	C₂×C₃	—	2	1	no	—
337	C₂×C₃	—	2	1	no	—
338	C₂×C₃	—	2	1	no	—
339	C₂×C₃	—	2	2	no	—
340	C₂×C₃	—	2	1	no	—
341	C₂×C₃	—	4	1	no	—
342	C₂×C₃	—	4	1	no	—
343	C₂×C₃	—	12	2	no	—
344	C₂×C₃	#4515	1	2	yes	direct product factor
345	C₂×C₃	C₃×#350	1	2	yes	complemented
346	C₂×C₃	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic
347	C₂×C₃	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic
348	D₃	—	4	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	6	2	no	—
351	C₂²	—	12	2	no	—
352	C₂²	C₃×(C₂×D₃)⋊C₈	1	1	yes	characteristic
353	C₂²	C₃×(C₂×D₃)⋊C₈	1	1	yes	characteristic
354	C₂²	C₂×C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
355	C₄	—	6	2	no	—
356	C₄	C₃×(C₂×D₃)⋊C₈	1	1	yes	characteristic
357	C₄	C₃×(C₂×D₃)⋊C₈	1	1	yes	characteristic
358	C₄	C₂×C₃×D₃×C₈	1	1	yes	characteristic
359	C₄	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
360	C₃	—	2	1	no	—
361	C₃	C₂×#4515	1	1	yes	characteristic, direct product factor
362	C₃	C₂×C₃×#350	1	1	yes	characteristic, complemented
363	C₂	—	2	1	no	—
364	C₂	—	2	1	no	—
365	C₂	—	12	2	no	—
366	C₂	C₃×#4515	1	2	yes	direct product factor
367	C₂	C₂×C₃×(C₂×D₃)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₈	#67
commutator	C₃×C₄	C₂²×C₃×C₈
Frattini	C₂×C₈	C₂²×C₃×D₃
Fitting	C₂×C₃²×M₃₂	C₂
socle	C₂²×C₃²	C₂²⋊C₈
prime radical	C₂×C₃×#235	C₄
cosocle	C₂×C₃×C₈	C₂³×C₃
hypercenter	C₂×C₃×M₃₂	D₃
hypocenter	C₃	C₂×C₃×#350
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₂²×C₃×C₈ ◁ C₂×C₃×M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×M₃₂	C₂	semidirect
3. C₂²×C₃×C₃⋊C₁₆	C₂	semidirect
4. C₃×#4515	C₂	direct (N × H)
6. C₂×#4515	C₃	direct (N × H)
17. C₃²×M₃₂	C₂²	semidirect
21. C₂×C₃×C₃⋊C₁₆	C₂²	semidirect
25. C₂×C₃×M₃₂	D₃	semidirect
26. C₂×C₃×M₃₂	C₂×C₃	semidirect
28. C₂²×C₃⋊C₁₆	C₂×C₃	semidirect
30. #4515	C₂×C₃	direct (N × H)
79. C₃×M₃₂	C₂×D₃	semidirect
80. C₃×M₃₂	C₂²×C₃	semidirect
89. C₂×C₃⋊C₁₆	C₂²×C₃	semidirect
113. C₂×M₃₂	C₃×D₃	semidirect
193. M₃₂	C₂×C₃×D₃	semidirect
255. C₂×C₃²	#350	semidirect
312. C₃²	C₂×#350	semidirect
344. C₂×C₃	#4515	direct (N × H)
345. C₂×C₃	C₃×#350	semidirect
361. C₃	C₂×#4515	direct (N × H)
362. C₃	C₂×C₃×#350	semidirect
366. C₂	C₃×#4515	direct (N × H)

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
C₂×C₃²×M₃₂	2
C₂²×C₃×C₃⋊C₁₆	2
C₃×#4515	2
C₂×C₃×#350	3
C₂×#4515	3

Subgroups — C2×C3×#4515 #11796078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4515 #11796078