Subgroups — C₂×C₃×#4563 #11796879

Order 1152.

681 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×D₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#812	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4563	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃×#361	—	3	1	no	maximal
6	C₂×#4563	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂²×C₃²×D₄	—	2	1	no	—
8	C₂×C₃²×D₈	—	2	1	no	—
9	C₂×C₃²×D₈	—	2	1	no	—
10	C₂×C₃²×D₈	—	2	1	no	—
11	C₂×C₃²×D₈	C₄	1	2	yes	—
12	C₂×C₃²×D₈	C₄	1	2	yes	—
13	C₂×C₃²×D₈	C₂²	1	2	yes	—
14	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×#208	—	2	1	no	—
16	C₃×#819	—	2	1	no	—
17	C₃×#819	C₂²	1	2	yes	complemented
18	C₃×#812	—	2	1	no	—
19	C₃×#812	C₂²	1	2	yes	complemented
20	C₂×C₃×C₃⋊C₁₆	—	2	1	no	—
21	C₂²×C₃×D₈	—	2	1	no	—
22	C₂²×C₃×D₈	D₃	1	1	yes	characteristic
23	C₂²×C₃×D₈	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×M₃₂	—	3	1	no	—
25	C₂×C₃×#108	—	3	1	no	—
26	C₂×#819	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×#812	C₂×C₃	1	1	yes	characteristic, complemented
28	C₃×#361	—	3	4	no	—
29	#4563	C₂×C₃	1	4	yes	direct product factor
30	C₂⁴×C₃²	—	4	1	no	—
31	C₂×C₃²×D₄	—	2	2	no	—
32	C₂×C₃²×D₄	—	2	2	no	—
33	C₂×C₃²×D₄	—	2	2	no	—
34	C₂×C₃²×D₄	—	4	1	no	—
35	C₂×C₃²×D₄	—	4	1	no	—
36	C₂×C₃²×D₄	—	4	1	no	—
37	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
38	C₃²×D₈	—	2	2	no	—
39	C₃²×D₈	—	2	2	no	—
40	C₃²×D₈	—	2	2	no	—
41	C₃²×D₈	C₂×C₄	1	4	yes	—
42	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
45	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
46	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
47	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
48	C₃×#208	—	2	2	no	—
49	C₃×#208	—	4	1	no	—
50	C₂×C₃×C₃⋊C₈	—	4	1	no	—
51	C₃×C₃⋊C₁₆	—	2	2	no	—
52	C₂×#361	—	3	1	no	Sylow
53	C₂²×C₃×D₄	—	2	2	no	—
54	C₂²×C₃×D₄	—	2	1	no	—
55	C₂²×C₃×D₄	—	2	1	no	—
56	C₂×C₃×D₈	—	2	2	no	—
57	C₂×C₃×D₈	—	2	2	no	—
58	C₂×C₃×D₈	—	2	2	no	—
59	C₂×C₃×D₈	—	2	1	no	—
60	C₂×C₃×D₈	—	2	1	no	—
61	C₂×C₃×D₈	—	2	1	no	—
62	C₂×C₃×D₈	—	2	1	no	—
63	C₂×C₃×D₈	—	2	1	no	—
64	C₂×C₃×D₈	—	2	1	no	—
65	C₂×C₃×D₈	—	2	2	no	—
66	C₂×C₃×D₈	—	2	2	no	—
67	C₂×C₃×D₈	—	2	2	no	—
68	C₂×C₃×D₈	Dic₃	1	2	yes	—
69	C₂×C₃×D₈	Dic₃	1	2	yes	—
70	C₂×C₃×D₈	C₃×C₄	1	2	yes	—
71	C₂×C₃×D₈	C₃×C₄	1	2	yes	—
72	C₂×C₃×D₈	C₂×D₃	1	2	yes	—
73	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
74	C₂×C₃×M₁₆	—	6	1	no	—
75	C₂²×C₃×C₈	—	2	1	no	—
76	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
78	C₂×#208	—	2	1	no	—
79	C₃×M₃₂	—	3	2	no	—
80	C₃×M₃₂	—	6	1	no	—
81	C₂×C₃×C₁₆	—	6	1	no	—
82	C₃×#108	—	3	2	no	—
83	C₃×#108	—	6	1	no	—
84	#819	—	2	1	no	—
85	#819	C₂²×C₃	1	2	yes	complemented
86	#812	—	2	1	no	—
87	#812	C₂²×C₃	1	2	yes	complemented
88	C₂×C₃⋊C₁₆	—	2	1	no	—
89	C₂³×C₃²	—	4	2	no	—
90	C₂³×C₃²	—	4	2	no	—
91	C₂³×C₃²	—	4	2	no	—
92	C₂³×C₃²	—	8	4	no	—
93	C₂³×C₃²	SD₁₆	1	1	yes	characteristic
94	C₃²×D₄	—	2	4	no	—
95	C₃²×D₄	—	4	2	no	—
96	C₃²×D₄	—	4	2	no	—
97	C₃²×D₄	—	4	2	no	—
98	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
101	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
102	C₂×C₃²×C₄	SD₁₆	1	1	yes	characteristic
103	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
104	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
105	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
106	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
107	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
108	C₃×C₃⋊C₈	—	4	2	no	—
109	C₂²×D₈	C₃×D₃	1	1	yes	characteristic
110	C₂×M₃₂	—	3	1	no	—
111	C₂×#108	—	3	1	no	—
112	#361	—	3	4	no	—
113	C₂⁴×C₃	—	4	2	no	—
114	C₂⁴×C₃	—	4	1	no	—
115	C₂⁴×C₃	—	4	1	no	—
116	C₂×C₃×D₄	—	2	4	no	—
117	C₂×C₃×D₄	—	2	4	no	—
118	C₂×C₃×D₄	—	2	4	no	—
119	C₂×C₃×D₄	—	2	2	no	—
120	C₂×C₃×D₄	—	2	2	no	—
121	C₂×C₃×D₄	—	2	2	no	—
122	C₂×C₃×D₄	—	2	2	no	—
123	C₂×C₃×D₄	—	2	2	no	—
124	C₂×C₃×D₄	—	2	2	no	—
125	C₂×C₃×D₄	—	4	2	no	—
126	C₂×C₃×D₄	—	4	2	no	—
127	C₂×C₃×D₄	—	4	2	no	—
128	C₂×C₃×D₄	—	4	1	no	—
129	C₂×C₃×D₄	—	4	1	no	—
130	C₂×C₃×D₄	—	4	1	no	—
131	C₂×C₃×D₄	—	4	1	no	—
132	C₂×C₃×D₄	—	4	1	no	—
133	C₂×C₃×D₄	—	4	1	no	—
134	C₂²×C₃×C₄	—	2	1	no	—
135	C₂²×C₃×C₄	#67	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
137	C₃×D₈	—	2	4	no	—
138	C₃×D₈	—	2	4	no	—
139	C₃×D₈	—	2	4	no	—
140	C₃×D₈	—	2	2	no	—
141	C₃×D₈	—	2	2	no	—
142	C₃×D₈	—	2	2	no	—
143	C₃×D₈	—	2	2	no	—
144	C₃×D₈	—	2	2	no	—
145	C₃×D₈	—	2	2	no	—
146	C₃×D₈	—	2	4	no	—
147	C₃×D₈	C₂×Dic₃	1	4	yes	—
148	C₃×D₈	C₂×C₃×C₄	1	4	yes	—
149	C₃×M₁₆	—	6	2	no	—
150	C₃×M₁₆	—	12	1	no	—
151	C₂×C₃×C₈	—	2	1	no	—
152	C₂×C₃×C₈	—	2	1	no	—
153	C₂×C₃×C₈	—	2	1	no	—
154	C₂×C₃×C₈	—	2	1	no	—
155	C₂×C₃×C₈	—	2	1	no	—
156	C₂×C₃×C₈	—	2	1	no	—
157	C₂×C₃×C₈	—	12	1	no	—
158	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
159	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
160	C₂×C₃×C₈	#67	1	1	yes	characteristic
161	C₂×C₃×C₈	#67	1	1	yes	characteristic
162	C₂×C₃×C₈	#67	1	1	yes	characteristic
163	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
164	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
165	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
166	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
167	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
168	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
169	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
170	#208	—	2	2	no	—
171	#208	—	4	1	no	—
172	C₂×C₃⋊C₈	—	4	1	no	—
173	C₃×C₁₆	—	6	2	no	—
174	C₃⋊C₁₆	—	2	2	no	—
175	C₂²×C₃²	—	2	2	no	—
176	C₂²×C₃²	—	4	4	no	—
177	C₂²×C₃²	—	8	4	no	—
178	C₂²×C₃²	—	8	4	no	—
179	C₂²×C₃²	—	8	4	no	—
180	C₂²×C₃²	#102	1	1	yes	characteristic
181	C₂²×C₃²	#102	1	1	yes	characteristic
182	C₂²×C₃²	C₂×SD₁₆	1	1	yes	characteristic
183	C₃²×C₄	#102	1	1	yes	characteristic
184	C₃²×C₄	#102	1	1	yes	characteristic
185	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
187	C₂²×D₄	—	2	1	no	—
188	C₂×D₈	—	2	1	no	—
189	C₂×D₈	—	2	1	no	—
190	C₂×D₈	—	2	1	no	—
191	C₂×D₈	C₃×Dic₃	1	2	yes	—
192	C₂×D₈	C₃×Dic₃	1	2	yes	—
193	C₂×D₈	C₂×C₃×D₃	1	2	yes	—
194	C₂×M₁₆	—	6	1	no	—
195	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
196	M₃₂	—	3	2	no	—
197	M₃₂	—	6	1	no	—
198	C₂×C₁₆	—	6	1	no	—
199	#108	—	3	2	no	—
200	#108	—	6	1	no	—
201	C₂³×C₃	—	2	1	no	—
202	C₂³×C₃	—	4	4	no	—
203	C₂³×C₃	—	4	4	no	—
204	C₂³×C₃	—	4	4	no	—
205	C₂³×C₃	—	4	2	no	—
206	C₂³×C₃	—	4	2	no	—
207	C₂³×C₃	—	4	2	no	—
208	C₂³×C₃	—	4	2	no	—
209	C₂³×C₃	—	4	2	no	—
210	C₂³×C₃	—	4	2	no	—
211	C₂³×C₃	—	8	8	no	—
212	C₂³×C₃	—	8	4	no	—
213	C₂³×C₃	—	8	4	no	—
214	C₂³×C₃	#214	1	1	yes	characteristic
215	C₂³×C₃	C₃×SD₁₆	1	1	yes	characteristic
216	C₃×D₄	—	2	8	no	—
217	C₃×D₄	—	2	4	no	—
218	C₃×D₄	—	2	4	no	—
219	C₃×D₄	—	4	4	no	—
220	C₃×D₄	—	4	4	no	—
221	C₃×D₄	—	4	4	no	—
222	C₃×D₄	—	4	2	no	—
223	C₃×D₄	—	4	2	no	—
224	C₃×D₄	—	4	2	no	—
225	C₃×D₄	—	4	2	no	—
226	C₃×D₄	—	4	2	no	—
227	C₃×D₄	—	4	2	no	—
228	C₂×C₃×C₄	—	2	1	no	—
229	C₂×C₃×C₄	—	2	1	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	2	1	no	—
233	C₂×C₃×C₄	—	2	1	no	—
234	C₂×C₃×C₄	#213	1	1	yes	characteristic
235	C₂×C₃×C₄	#213	1	1	yes	characteristic
236	C₂×C₃×C₄	#214	1	1	yes	characteristic
237	C₂×C₃×C₄	#217	1	1	yes	characteristic
238	C₂×C₃×C₄	#217	1	1	yes	characteristic
239	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₃×C₄	C₃×D₈	1	1	yes	characteristic
242	C₂×C₃×C₄	C₃×D₈	1	1	yes	characteristic
243	C₂×C₃×C₄	C₃×SD₁₆	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
246	C₃×C₈	—	2	1	no	—
247	C₃×C₈	—	2	1	no	—
248	C₃×C₈	—	2	1	no	—
249	C₃×C₈	—	2	1	no	—
250	C₃×C₈	—	12	2	no	—
251	C₃×C₈	#217	1	1	yes	characteristic
252	C₃×C₈	#217	1	1	yes	characteristic
253	C₃×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
254	C₃×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
255	C₃×C₈	C₂²×Dic₃	1	1	yes	characteristic
256	C₃×C₈	C₂×#67	1	1	yes	characteristic
257	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
258	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
259	C₃⋊C₈	—	4	2	no	—
260	C₂×C₃²	—	2	1	no	—
261	C₂×C₃²	—	2	1	no	—
262	C₂×C₃²	—	8	4	no	—
263	C₂×C₃²	#361	1	2	yes	complemented
264	C₂×C₃²	C₂×#102	1	1	yes	characteristic
265	C₂⁴	—	4	1	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	4	1	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂×D₄	—	4	1	no	—
272	C₂²×C₄	C₃×#67	1	1	yes	characteristic
273	D₈	—	2	2	no	—
274	D₈	—	2	2	no	—
275	D₈	—	2	2	no	—
276	D₈	C₂×C₃×Dic₃	1	4	yes	—
277	M₁₆	—	6	2	no	—
278	M₁₆	—	12	1	no	—
279	C₂×C₈	—	12	1	no	—
280	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
281	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
282	C₂×C₈	C₃×#67	1	1	yes	characteristic
283	C₂×C₈	C₃×#67	1	1	yes	characteristic
284	C₂×C₈	C₃×#67	1	1	yes	characteristic
285	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
286	C₁₆	—	6	2	no	—
287	C₂²×C₃	—	2	4	no	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	2	2	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	2	1	no	—
293	C₂²×C₃	—	4	8	no	—
294	C₂²×C₃	—	4	4	no	—
295	C₂²×C₃	—	4	4	no	—
296	C₂²×C₃	—	8	8	no	—
297	C₂²×C₃	—	8	8	no	—
298	C₂²×C₃	—	8	4	no	—
299	C₂²×C₃	—	8	4	no	—
300	C₂²×C₃	—	8	4	no	—
301	C₂²×C₃	—	8	4	no	—
302	C₂²×C₃	—	8	8	no	—
303	C₂²×C₃	—	8	4	no	—
304	C₂²×C₃	—	8	4	no	—
305	C₂²×C₃	#832	1	1	yes	characteristic
306	C₂²×C₃	#832	1	1	yes	characteristic
307	C₂²×C₃	C₃×#102	1	1	yes	characteristic
308	C₂²×C₃	C₃×#102	1	1	yes	characteristic
309	C₂²×C₃	C₂×#214	1	1	yes	characteristic
310	C₂²×C₃	C₂×C₃×SD₁₆	1	1	yes	characteristic
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	#832	1	1	yes	characteristic
316	C₃×C₄	#832	1	1	yes	characteristic
317	C₃×C₄	C₃×#102	1	1	yes	characteristic
318	C₃×C₄	C₃×#102	1	1	yes	characteristic
319	C₃×C₄	C₂×#213	1	1	yes	characteristic
320	C₃×C₄	C₂×#217	1	1	yes	characteristic
321	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
322	C₃×C₄	C₂×C₃×D₈	1	1	yes	characteristic
323	C₃²	C₂×#361	1	1	yes	characteristic, complemented, Sylow
324	C₂³	—	4	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	8	4	no	—
328	C₂³	C₃×#214	1	1	yes	characteristic
329	D₄	—	2	4	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	2	no	—
333	C₂×C₄	C₃×#213	1	1	yes	characteristic
334	C₂×C₄	C₃×#213	1	1	yes	characteristic
335	C₂×C₄	C₃×#214	1	1	yes	characteristic
336	C₂×C₄	C₃×#217	1	1	yes	characteristic
337	C₂×C₄	C₃×#217	1	1	yes	characteristic
338	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
339	C₈	—	12	2	no	—
340	C₈	C₃×#217	1	1	yes	characteristic
341	C₈	C₃×#217	1	1	yes	characteristic
342	C₈	C₂²×C₃×Dic₃	1	1	yes	characteristic
343	C₈	C₂×C₃×#67	1	1	yes	characteristic
344	C₂×C₃	—	2	2	no	—
345	C₂×C₃	—	2	2	no	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	2	1	no	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	2	1	no	—
350	C₂×C₃	—	2	1	no	—
351	C₂×C₃	—	2	2	no	—
352	C₂×C₃	—	8	8	no	—
353	C₂×C₃	—	8	4	no	—
354	C₂×C₃	—	8	4	no	—
355	C₂×C₃	#4563	1	2	yes	direct product factor
356	C₂×C₃	C₃×#361	1	2	yes	complemented
357	C₂×C₃	C₂×#832	1	1	yes	characteristic
358	C₂×C₃	C₂×C₃×#102	1	1	yes	characteristic
359	C₂²	—	2	2	no	—
360	C₂²	—	4	4	no	—
361	C₂²	—	8	4	no	—
362	C₂²	—	8	4	no	—
363	C₂²	—	8	4	no	—
364	C₂²	C₃×#832	1	1	yes	characteristic
365	C₂²	C₃×#832	1	1	yes	characteristic
366	C₂²	C₂×C₃×#214	1	1	yes	characteristic
367	C₄	C₃×#832	1	1	yes	characteristic
368	C₄	C₃×#832	1	1	yes	characteristic
369	C₄	C₂×C₃×#213	1	1	yes	characteristic
370	C₄	C₂×C₃×#217	1	1	yes	characteristic
371	C₃	—	2	1	no	—
372	C₃	C₂×#4563	1	1	yes	characteristic, direct product factor
373	C₃	C₂×C₃×#361	1	1	yes	characteristic, complemented
374	C₂	—	2	1	no	—
375	C₂	—	2	1	no	—
376	C₂	—	8	4	no	—
377	C₂	C₃×#4563	1	2	yes	direct product factor
378	C₂	C₂×C₃×#832	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#832
commutator	C₃×C₈	C₂²×C₃×C₄
Frattini	C₂×C₈	C₂²×C₃×D₃
Fitting, prime radical	C₂²×C₃²×D₈	C₂
socle	C₂²×C₃²	#102
cosocle	C₂×C₃×C₈	C₂³×C₃
hypercenter	C₂²×C₃×D₈	D₃
hypocenter	C₃	C₂×C₃×#361
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ C₂²×C₃×D₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#819	C₂	semidirect
3. C₂×C₃×#812	C₂	semidirect
4. C₃×#4563	C₂	direct (N × H)
6. C₂×#4563	C₃	direct (N × H)
17. C₃×#819	C₂²	semidirect
19. C₃×#812	C₂²	semidirect
26. C₂×#819	C₂×C₃	semidirect
27. C₂×#812	C₂×C₃	semidirect
29. #4563	C₂×C₃	direct (N × H)
85. #819	C₂²×C₃	semidirect
87. #812	C₂²×C₃	semidirect
263. C₂×C₃²	#361	semidirect
323. C₃²	C₂×#361	semidirect
355. C₂×C₃	#4563	direct (N × H)
356. C₂×C₃	C₃×#361	semidirect
372. C₃	C₂×#4563	direct (N × H)
373. C₃	C₂×C₃×#361	semidirect
377. C₂	C₃×#4563	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×D₈	2
C₂×C₃×#819	2
C₂×C₃×#812	2
C₃×#4563	2
C₂×C₃×#361	3
C₂×#4563	3

Subgroups — C2×C3×#4563 #11796879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4563 #11796879