Subgroups — C₃×#69469 #11775047

Order 1152.

665 conjugacy classes of subgroups.

The subgroup lattice has 407 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5477	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#4925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4451	C₂	1	4	yes	maximal, complemented
5	C₃×#1502	—	3	1	no	maximal
6	#69469	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₃×#235	—	2	1	no	—
8	C₂×C₃²×C₄⋊C₄	—	2	1	no	—
9	C₂×C₃²×C₄²	—	2	1	no	—
10	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
11	C₃×#930	—	2	1	no	—
12	C₃×#930	C₂²	1	2	yes	—
13	C₃×#875	—	2	1	no	—
14	C₃×#874	C₄	1	1	yes	characteristic, complemented
15	C₃×C₄×D₁₂	—	2	1	no	—
16	C₃×C₄×D₁₂	C₄	1	2	yes	complemented
17	C₃×#869	C₄	1	1	yes	characteristic, complemented
18	C₃²×#95	C₂²	1	2	yes	—
19	C₃×#830	C₂²	1	2	yes	—
20	C₃×C₄⋊(C₃⋊C₈)	—	2	1	no	—
21	C₃×C₄×C₃⋊C₈	—	2	1	no	—
22	C₃×#532	—	3	1	no	—
23	#5477	C₂×C₃	1	1	yes	characteristic
24	C₃×#431	—	3	1	no	—
25	C₃×C₄×C₄⋊C₄	—	2	1	no	—
26	C₃×C₄×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
27	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
28	#4925	C₂×C₃	1	1	yes	characteristic, complemented
29	C₃×#327	—	3	4	no	—
30	#4451	C₂×C₃	1	4	yes	complemented
31	C₂²×C₃²×C₄	—	2	2	no	—
32	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
33	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
34	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
35	C₂×C₃×#67	—	2	2	no	—
36	C₃×#235	—	4	2	no	—
37	C₃×#235	—	4	2	no	—
38	C₂×C₃×D₁₂	—	2	1	no	—
39	C₂×C₃×D₁₂	—	2	1	no	—
40	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
41	C₂×C₃×C₄×D₃	—	2	2	no	—
42	C₂×C₃×Dic₆	—	2	1	no	—
43	C₃²×C₄⋊C₄	—	2	4	no	—
44	C₃²×C₄²	—	4	2	no	—
45	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
46	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
47	C₃²×C₄²	D₄	1	1	yes	characteristic
48	C₃²×C₄²	D₄	1	1	yes	characteristic
49	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
50	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
51	C₃×C₄⋊Dic₃	—	2	1	no	—
52	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
53	C₂×C₃×C₃⋊C₈	—	2	2	no	—
54	#1502	—	3	1	no	Sylow
55	C₂×C₃×#41	—	6	1	no	—
56	C₂×#235	—	2	1	no	—
57	C₃×C₄⋊Q₈	—	3	1	no	—
58	C₃×#127	—	3	1	no	—
59	C₃×#124	—	6	1	no	—
60	C₃×#121	—	3	2	no	—
61	C₃×#121	—	6	1	no	—
62	C₃×C₄×D₄	—	3	2	no	—
63	C₃×C₄×D₄	—	6	1	no	—
64	C₂×C₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₃×C₄²	—	2	2	no	—
68	C₂×C₃×C₄²	—	2	1	no	—
69	C₂×C₃×C₄²	—	2	1	no	—
70	C₂×C₃×C₄²	—	2	1	no	—
71	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
72	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
73	#930	—	2	1	no	—
74	#930	C₂²×C₃	1	2	yes	—
75	#875	—	2	1	no	—
76	#874	C₃×C₄	1	1	yes	characteristic, complemented
77	C₄×D₁₂	—	2	1	no	—
78	C₄×D₁₂	C₃×C₄	1	2	yes	complemented
79	#869	C₃×C₄	1	1	yes	characteristic, complemented
80	C₃×C₄⋊C₈	—	6	1	no	—
81	C₃×C₂²⋊C₈	—	3	2	no	—
82	C₃×C₄×C₈	—	6	1	no	—
83	C₃×#95	—	2	2	no	—
84	C₃×#95	C₂×D₃	1	2	yes	—
85	C₃×#95	C₂²×C₃	1	2	yes	—
86	#830	C₂²×C₃	1	2	yes	—
87	C₄⋊(C₃⋊C₈)	—	2	1	no	—
88	C₄×C₃⋊C₈	—	2	1	no	—
89	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₃×D₃	—	2	2	no	—
91	C₂×C₃²×C₄	—	2	2	no	—
92	C₂×C₃²×C₄	—	2	4	no	—
93	C₂×C₃²×C₄	—	4	1	no	—
94	C₂×C₃²×C₄	—	4	2	no	—
95	C₂×C₃²×C₄	—	4	2	no	—
96	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
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	2	yes	—
101	C₂×C₃²×C₄	SD₁₆	1	2	yes	—
102	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
104	C₃×#67	—	4	2	no	—
105	C₃×#67	—	4	2	no	—
106	C₂×C₃×Dic₃	—	2	2	no	—
107	C₃×D₁₂	—	4	2	no	—
108	C₃×D₁₂	—	4	2	no	—
109	C₃×D₁₂	—	4	2	no	—
110	C₃×C₄×D₃	—	4	4	no	—
111	C₃×Dic₆	—	4	2	no	—
112	C₃×C₃⋊C₈	—	4	2	no	—
113	#532	—	3	1	no	—
114	#431	—	3	1	no	—
115	C₄×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic, complemented
116	#327	—	3	4	no	—
117	C₃×#41	—	12	2	no	—
118	C₃×#41	—	12	2	no	—
119	C₂×C₃×Q₈	—	6	1	no	—
120	C₂×C₃×D₄	—	3	2	no	—
121	C₂×C₃×D₄	—	6	2	no	—
122	C₂×C₃×D₄	—	6	1	no	—
123	C₂×C₃×D₄	—	6	1	no	—
124	C₂²×C₃×C₄	—	2	4	no	—
125	C₂²×C₃×C₄	—	2	2	no	—
126	C₂²×C₃×C₄	—	2	2	no	—
127	C₂²×C₃×C₄	—	2	1	no	—
128	C₂²×C₃×C₄	—	2	1	no	—
129	C₂²×C₃×C₄	—	2	1	no	—
130	C₂²×C₃×C₄	—	6	2	no	—
131	C₂²×C₃×C₄	#67	1	1	yes	characteristic
132	C₂²×C₃×C₄	#67	1	1	yes	characteristic
133	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
134	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
135	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
137	C₂×#67	—	2	2	no	—
138	#235	—	4	2	no	—
139	#235	—	4	2	no	—
140	C₂×D₁₂	—	2	1	no	—
141	C₂×D₁₂	—	2	1	no	—
142	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
143	C₂×C₄×D₃	—	2	2	no	—
144	C₂×Dic₆	—	2	1	no	—
145	C₂×C₃×C₈	—	6	2	no	—
146	C₃×C₄⋊C₄	—	2	8	no	—
147	C₃×C₄⋊C₄	—	2	4	no	—
148	C₃×C₄⋊C₄	—	2	4	no	—
149	C₃×C₄⋊C₄	—	3	2	no	—
150	C₃×C₄⋊C₄	—	6	1	no	—
151	C₃×C₂²⋊C₄	—	6	2	no	—
152	C₃×C₂²⋊C₄	—	6	2	no	—
153	C₃×C₄²	—	2	1	no	—
154	C₃×C₄²	—	2	1	no	—
155	C₃×C₄²	—	2	1	no	—
156	C₃×C₄²	—	2	1	no	—
157	C₃×C₄²	—	4	4	no	—
158	C₃×C₄²	—	4	2	no	—
159	C₃×C₄²	—	4	2	no	—
160	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
161	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
162	C₃×C₄²	D₁₂	1	1	yes	characteristic
163	C₃×C₄²	D₁₂	1	1	yes	characteristic
164	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
165	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
166	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
167	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
168	(C₂×D₃)⋊C₄	—	2	2	no	—
169	(C₂×D₃)⋊C₄	—	2	2	no	—
170	C₄⋊Dic₃	—	2	1	no	—
171	C₄⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
172	C₂×C₃⋊C₈	—	2	2	no	—
173	C₂²×C₃²	—	2	1	no	—
174	C₂²×C₃²	—	2	1	no	—
175	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
177	C₂²×C₃²	C₂×SD₁₆	1	1	yes	characteristic
178	C₂×C₃×D₃	—	4	2	no	—
179	C₂×C₃×D₃	—	4	2	no	—
180	C₂×C₃×D₃	—	4	2	no	—
181	C₃²×C₄	—	2	1	no	—
182	C₃²×C₄	—	2	1	no	—
183	C₃²×C₄	—	2	1	no	—
184	C₃²×C₄	—	4	4	no	—
185	C₃²×C₄	#102	1	2	yes	—
186	C₃²×C₄	#102	1	2	yes	—
187	C₃²×C₄	#104	1	2	yes	—
188	C₃×Dic₃	—	4	2	no	—
189	C₂×#41	—	6	1	no	—
190	C₄⋊Q₈	—	3	1	no	—
191	#127	—	3	1	no	—
192	#124	—	6	1	no	—
193	#121	—	3	2	no	—
194	#121	—	6	1	no	—
195	C₄×D₄	—	3	2	no	—
196	C₄×D₄	—	6	1	no	—
197	C₂×C₄⋊C₄	—	2	1	no	—
198	C₂×C₄²	—	2	1	no	—
199	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
200	C₄⋊C₈	—	6	1	no	—
201	C₂²⋊C₈	—	3	2	no	—
202	C₄×C₈	—	6	1	no	—
203	#95	C₂×C₃×D₃	1	2	yes	—
204	C₂³×C₃	—	2	1	no	—
205	C₂³×C₃	—	6	2	no	—
206	C₂³×C₃	C₂×#67	1	1	yes	characteristic
207	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
208	C₂²×D₃	—	2	2	no	—
209	C₃×Q₈	—	12	2	no	—
210	C₃×D₄	—	12	2	no	—
211	C₃×D₄	—	12	2	no	—
212	C₃×D₄	—	12	2	no	—
213	C₃×D₄	—	12	2	no	—
214	C₃×D₄	—	12	2	no	—
215	C₂×C₃×C₄	—	2	4	no	—
216	C₂×C₃×C₄	—	2	2	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	2	8	no	—
219	C₂×C₃×C₄	—	2	4	no	—
220	C₂×C₃×C₄	—	2	4	no	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	2	1	no	—
224	C₂×C₃×C₄	—	2	1	no	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	2	1	no	—
228	C₂×C₃×C₄	—	2	1	no	—
229	C₂×C₃×C₄	—	4	1	no	—
230	C₂×C₃×C₄	—	4	1	no	—
231	C₂×C₃×C₄	—	4	4	no	—
232	C₂×C₃×C₄	—	4	2	no	—
233	C₂×C₃×C₄	—	4	4	no	—
234	C₂×C₃×C₄	—	4	2	no	—
235	C₂×C₃×C₄	—	4	2	no	—
236	C₂×C₃×C₄	—	4	2	no	—
237	C₂×C₃×C₄	—	4	2	no	—
238	C₂×C₃×C₄	—	6	2	no	—
239	C₂×C₃×C₄	—	12	4	no	—
240	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
241	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
242	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
243	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
244	C₂×C₃×C₄	#213	1	2	yes	—
245	C₂×C₃×C₄	#215	1	2	yes	—
246	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₃×C₄	C₃×D₈	1	2	yes	—
251	C₂×C₃×C₄	C₃×SD₁₆	1	2	yes	—
252	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
256	#67	—	4	2	no	—
257	#67	—	4	2	no	—
258	C₂×Dic₃	—	2	2	no	—
259	D₁₂	—	4	2	no	—
260	D₁₂	—	4	2	no	—
261	D₁₂	—	4	2	no	—
262	C₄×D₃	—	4	4	no	—
263	Dic₆	—	4	2	no	—
264	C₃×C₈	—	12	2	no	—
265	C₃⋊C₈	—	4	2	no	—
266	C₂×C₃²	—	2	1	no	—
267	C₂×C₃²	—	2	1	no	—
268	C₂×C₃²	#410	1	1	yes	characteristic
269	C₂×C₃²	C₂×#102	1	1	yes	characteristic
270	C₂×C₃²	C₂×#104	1	1	yes	characteristic
271	C₃×D₃	—	8	2	no	—
272	#41	—	12	2	no	—
273	#41	—	12	2	no	—
274	C₂×Q₈	—	6	1	no	—
275	C₂×D₄	—	3	2	no	—
276	C₂×D₄	—	6	2	no	—
277	C₂×D₄	—	6	1	no	—
278	C₂×D₄	—	6	1	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	6	2	no	—
281	C₂²×C₄	C₃×#67	1	1	yes	characteristic
282	C₂²×C₄	C₃×#67	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
284	C₂×C₈	—	6	2	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	3	2	no	—
287	C₄⋊C₄	—	6	1	no	—
288	C₂²⋊C₄	—	6	2	no	—
289	C₂²⋊C₄	—	6	2	no	—
290	C₄²	—	4	2	no	—
291	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
292	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
293	C₄²	C₃×D₁₂	1	1	yes	characteristic
294	C₄²	C₃×D₁₂	1	1	yes	characteristic
295	C₂²×C₃	—	2	2	no	—
296	C₂²×C₃	—	2	2	no	—
297	C₂²×C₃	—	2	1	no	—
298	C₂²×C₃	—	2	1	no	—
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	2	1	no	—
302	C₂²×C₃	—	2	1	no	—
303	C₂²×C₃	—	2	1	no	—
304	C₂²×C₃	—	12	2	no	—
305	C₂²×C₃	—	12	2	no	—
306	C₂²×C₃	—	12	2	no	—
307	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
308	C₂²×C₃	C₂×#213	1	1	yes	characteristic
309	C₂²×C₃	C₂×#215	1	1	yes	characteristic
310	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
311	C₂²×C₃	C₂×C₃×D₈	1	1	yes	characteristic
312	C₂²×C₃	C₂×C₃×SD₁₆	1	1	yes	characteristic
313	C₂×D₃	—	4	2	no	—
314	C₂×D₃	—	4	2	no	—
315	C₂×D₃	—	4	2	no	—
316	C₃×C₄	—	2	2	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	2	1	no	—
319	C₃×C₄	—	2	1	no	—
320	C₃×C₄	—	2	1	no	—
321	C₃×C₄	—	2	1	no	—
322	C₃×C₄	—	2	1	no	—
323	C₃×C₄	—	2	2	no	—
324	C₃×C₄	—	2	2	no	—
325	C₃×C₄	—	2	2	no	—
326	C₃×C₄	—	4	1	no	—
327	C₃×C₄	—	4	1	no	—
328	C₃×C₄	—	4	8	no	—
329	C₃×C₄	—	4	4	no	—
330	C₃×C₄	—	4	4	no	—
331	C₃×C₄	—	12	2	no	—
332	C₃×C₄	#805	1	2	yes	—
333	C₃×C₄	#809	1	2	yes	—
334	C₃×C₄	#809	1	2	yes	—
335	C₃×C₄	C₃×#102	1	2	yes	—
336	C₃×C₄	C₃×#102	1	2	yes	—
337	C₃×C₄	C₃×#104	1	2	yes	—
338	Dic₃	—	4	2	no	—
339	C₃²	#1502	1	1	yes	characteristic, complemented, Sylow
340	C₂³	—	6	2	no	—
341	C₂³	C₂×C₃×#67	1	1	yes	characteristic
342	Q₈	—	12	2	no	—
343	D₄	—	12	2	no	—
344	D₄	—	12	2	no	—
345	D₄	—	12	2	no	—
346	D₄	—	12	2	no	—
347	D₄	—	12	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	6	2	no	—
354	C₂×C₄	—	12	4	no	—
355	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
357	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
358	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
359	C₂×C₄	C₃×#213	1	2	yes	—
360	C₂×C₄	C₃×#215	1	2	yes	—
361	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
362	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
363	C₈	—	12	2	no	—
364	C₂×C₃	—	2	2	no	—
365	C₂×C₃	—	2	2	no	—
366	C₂×C₃	—	2	1	no	—
367	C₂×C₃	—	2	1	no	—
368	C₂×C₃	—	2	1	no	—
369	C₂×C₃	—	2	1	no	—
370	C₂×C₃	—	2	1	no	—
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	—	2	1	no	—
373	C₂×C₃	—	24	2	no	—
374	C₂×C₃	C₂×#805	1	1	yes	characteristic
375	C₂×C₃	C₂×#809	1	1	yes	characteristic
376	C₂×C₃	#5006	1	1	yes	characteristic
377	C₂×C₃	C₃×#410	1	1	yes	characteristic
378	C₂×C₃	C₂×C₃×#102	1	1	yes	characteristic
379	C₂×C₃	C₂×C₃×#104	1	1	yes	characteristic
380	D₃	—	8	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	12	2	no	—
384	C₂²	—	12	2	no	—
385	C₂²	—	12	2	no	—
386	C₂²	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
387	C₂²	C₂×C₃×#213	1	1	yes	characteristic
388	C₂²	C₂×C₃×#215	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	4	4	no	—
393	C₄	—	12	2	no	—
394	C₄	C₃×#805	1	2	yes	—
395	C₄	C₃×#809	1	2	yes	—
396	C₄	C₃×#809	1	2	yes	—
397	C₃	—	2	1	no	—
398	C₃	#69469	1	1	yes	characteristic, direct product factor
399	C₃	C₃×#1502	1	1	yes	characteristic, complemented
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	24	2	no	—
403	C₂	C₂×C₃×#805	1	1	yes	characteristic
404	C₂	C₂×C₃×#809	1	1	yes	characteristic
405	C₂	C₃×#5006	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	(C₂×D₃)⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₃²×C₄×C₄⋊C₄	C₂
socle	C₂²×C₃²	C₂×C₂²⋊C₄
prime radical	C₃×#5477	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₃×C₄×C₄⋊C₄	D₃
hypocenter	C₃	C₃×#1502
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₃²×C₄×C₄⋊C₄	C₂	semidirect
3. C₃×#4925	C₂	semidirect
4. C₃×#4451	C₂	semidirect
6. #69469	C₃	direct (N × H)
14. C₃×#874	C₄	semidirect
16. C₃×C₄×D₁₂	C₄	semidirect
17. C₃×#869	C₄	semidirect
26. C₃×C₄×C₄⋊C₄	D₃	semidirect
27. C₃×C₄×C₄⋊C₄	C₂×C₃	semidirect
28. #4925	C₂×C₃	semidirect
30. #4451	C₂×C₃	semidirect
76. #874	C₃×C₄	semidirect
78. C₄×D₁₂	C₃×C₄	semidirect
79. #869	C₃×C₄	semidirect
115. C₄×C₄⋊C₄	C₃×D₃	semidirect
339. C₃²	#1502	semidirect
398. C₃	#69469	direct (N × H)
399. C₃	C₃×#1502	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5477	2
C₃²×C₄×C₄⋊C₄	2
C₃×#4925	2
C₃×#4451	2
C₃×#1502	3
#69469	3

Subgroups — C3×#69469 #11775047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69469 #11775047