Subgroups — C₃×#69867 #11791396

Order 1152.

743 conjugacy classes of subgroups.

The subgroup lattice has 416 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×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#825	C₂	1	4	yes	maximal, complemented
4	C₃×C₄×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#1980	—	3	1	no	maximal
6	#69867	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₃×#235	C₂²	1	2	yes	—
8	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
9	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
10	C₃×#930	—	2	1	no	—
11	C₃×#930	—	2	1	no	—
12	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
13	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	—
14	C₃×#875	C₄	1	2	yes	complemented
15	C₃×#874	C₄	1	1	yes	characteristic, complemented
16	C₃×C₄×D₁₂	—	2	1	no	—
17	C₃×C₄×D₁₂	—	2	1	no	—
18	C₃×#869	C₄	1	1	yes	characteristic, complemented
19	C₃²×#97	—	2	1	no	—
20	C₃²×C₄×C₈	—	2	1	no	—
21	C₃×C₃⋊#95	—	2	1	no	—
22	C₃×#825	—	2	8	no	—
23	C₃×#532	—	3	1	no	—
24	#5477	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×#104	—	3	4	no	—
26	C₃×C₄×M₁₆	—	2	1	no	—
27	C₃×C₄×M₁₆	D₃	1	1	yes	characteristic, complemented
28	C₃×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
29	C₃×C₄×C₄⋊C₄	—	3	1	no	—
30	C₂×#825	C₂×C₃	1	4	yes	complemented
31	C₄×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
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	C₂²×C₃×Dic₃	—	2	2	no	—
37	C₃×#235	—	2	4	no	—
38	C₃×#235	—	2	4	no	—
39	C₂×C₃×D₁₂	—	2	1	no	—
40	C₂×C₃×D₁₂	—	2	1	no	—
41	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₄×D₃	—	2	2	no	—
43	C₂×C₃×Dic₆	C₂×C₄	1	2	yes	—
44	C₃²×M₁₆	—	2	2	no	—
45	C₃²×M₁₆	D₄	1	4	yes	complemented
46	C₂×C₃²×C₈	—	2	2	no	—
47	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
48	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
49	C₃²×C₄²	D₄	1	1	yes	characteristic
50	C₃²×C₄²	D₄	1	1	yes	characteristic
51	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
52	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
53	C₃×C₄⋊Dic₃	—	2	4	no	—
54	C₃×C₄⋊Dic₃	—	2	1	no	—
55	C₃×C₄⋊Dic₃	—	2	1	no	—
56	C₃×C₄×Dic₃	—	2	4	no	—
57	#1980	—	3	1	no	Sylow
58	C₂×C₃×#41	—	3	2	no	—
59	C₂×#235	C₂²×C₃	1	2	yes	—
60	C₂×C₃×M₁₆	—	2	2	no	—
61	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
62	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
63	C₃×C₄⋊Q₈	—	3	1	no	—
64	C₃×#127	—	3	1	no	—
65	C₃×#124	—	3	2	no	—
66	C₃×#121	—	6	1	no	—
67	C₃×#121	—	6	1	no	—
68	C₃×C₄×D₄	—	6	1	no	—
69	C₃×C₄×D₄	—	6	1	no	—
70	C₂×C₃×C₄⋊C₄	—	6	1	no	—
71	C₂×C₃×C₄²	—	2	1	no	—
72	C₂×C₃×C₄²	—	3	2	no	—
73	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
74	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
75	#930	—	2	1	no	—
76	#930	—	2	1	no	—
77	C₂×C₄⋊Dic₃	—	2	1	no	—
78	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	—
79	#875	C₃×C₄	1	2	yes	complemented
80	#874	C₃×C₄	1	1	yes	characteristic, complemented
81	C₄×D₁₂	—	2	1	no	—
82	C₄×D₁₂	—	2	1	no	—
83	#869	C₃×C₄	1	1	yes	characteristic, complemented
84	C₃×#104	—	6	8	no	—
85	C₃×#97	—	2	2	no	—
86	C₃×#97	—	2	1	no	—
87	C₃×#97	—	2	1	no	—
88	C₃×C₄×C₈	—	2	2	no	—
89	C₃×C₄×C₈	—	2	1	no	—
90	C₃×C₄×C₈	—	2	1	no	—
91	C₃×#95	—	6	1	no	—
92	C₃⋊#95	—	2	1	no	—
93	#825	—	2	8	no	—
94	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₃×D₃	—	2	2	no	—
96	C₂×C₃²×C₄	—	2	2	no	—
97	C₂×C₃²×C₄	—	4	1	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	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
104	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃²×C₄	#41	1	2	yes	—
106	C₃×#67	—	4	2	no	—
107	C₃×#67	—	4	2	no	—
108	C₂×C₃×Dic₃	—	2	4	no	—
109	C₂×C₃×Dic₃	—	2	2	no	—
110	C₂×C₃×Dic₃	—	4	2	no	—
111	C₂×C₃×Dic₃	—	4	2	no	—
112	C₃×D₁₂	—	2	4	no	—
113	C₃×D₁₂	—	4	2	no	—
114	C₃×D₁₂	—	4	2	no	—
115	C₃×C₄×D₃	—	4	4	no	—
116	C₃×Dic₆	—	2	4	no	—
117	C₃²×C₈	—	2	4	no	—
118	#532	—	3	1	no	—
119	C₂×#104	—	3	4	no	—
120	C₄×M₁₆	C₃×D₃	1	1	yes	characteristic, complemented
121	C₄×C₄⋊C₄	—	3	1	no	—
122	C₃×#41	—	6	4	no	—
123	C₃×#41	—	6	4	no	—
124	C₂×C₃×Q₈	—	3	2	no	—
125	C₂×C₃×D₄	—	3	2	no	—
126	C₂×C₃×D₄	—	6	2	no	—
127	C₂×C₃×D₄	—	6	1	no	—
128	C₂×C₃×D₄	—	6	1	no	—
129	C₂²×C₃×C₄	—	2	1	no	—
130	C₂²×C₃×C₄	—	2	1	no	—
131	C₂²×C₃×C₄	—	2	1	no	—
132	C₂²×C₃×C₄	—	6	2	no	—
133	C₂²×C₃×C₄	—	6	2	no	—
134	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
135	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
137	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
138	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
139	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
140	C₂×#67	—	2	2	no	—
141	C₂²×Dic₃	—	2	2	no	—
142	#235	—	2	4	no	—
143	#235	—	2	4	no	—
144	C₂×D₁₂	—	2	1	no	—
145	C₂×D₁₂	—	2	1	no	—
146	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
147	C₂×C₄×D₃	—	2	2	no	—
148	C₂×Dic₆	C₂×C₃×C₄	1	2	yes	—
149	C₃×M₁₆	—	2	4	no	—
150	C₃×M₁₆	—	2	2	no	—
151	C₃×M₁₆	—	2	2	no	—
152	C₃×M₁₆	—	2	4	no	—
153	C₃×M₁₆	D₁₂	1	4	yes	complemented
154	C₃×M₁₆	C₃×D₄	1	4	yes	complemented
155	C₂×C₃×C₈	—	2	4	no	—
156	C₂×C₃×C₈	—	2	2	no	—
157	C₂×C₃×C₈	—	2	2	no	—
158	C₃×C₄⋊C₄	—	6	4	no	—
159	C₃×C₄⋊C₄	—	6	1	no	—
160	C₃×C₄⋊C₄	—	6	1	no	—
161	C₃×C₂²⋊C₄	—	6	2	no	—
162	C₃×C₂²⋊C₄	—	6	2	no	—
163	C₃×C₄²	—	2	1	no	—
164	C₃×C₄²	—	2	1	no	—
165	C₃×C₄²	—	2	1	no	—
166	C₃×C₄²	—	2	1	no	—
167	C₃×C₄²	—	6	4	no	—
168	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
169	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
170	C₃×C₄²	#67	1	1	yes	characteristic
171	C₃×C₄²	#67	1	1	yes	characteristic
172	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
173	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
174	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
175	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
176	(C₂×D₃)⋊C₄	—	2	2	no	—
177	(C₂×D₃)⋊C₄	—	2	2	no	—
178	C₄⋊Dic₃	—	2	4	no	—
179	C₄⋊Dic₃	—	2	1	no	—
180	C₄⋊Dic₃	—	2	1	no	—
181	C₄×Dic₃	—	2	4	no	—
182	C₂²×C₃²	—	2	1	no	—
183	C₂²×C₃²	—	2	1	no	—
184	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×C₃²	#124	1	1	yes	characteristic
186	C₂²×C₃²	#127	1	1	yes	characteristic
187	C₂×C₃×D₃	—	4	2	no	—
188	C₂×C₃×D₃	—	4	2	no	—
189	C₂×C₃×D₃	—	4	2	no	—
190	C₃²×C₄	—	2	1	no	—
191	C₃²×C₄	—	2	1	no	—
192	C₃²×C₄	—	2	1	no	—
193	C₃²×C₄	#104	1	2	yes	complemented
194	C₃²×C₄	C₄×D₄	1	2	yes	—
195	C₃²×C₄	#121	1	2	yes	—
196	C₃×Dic₃	—	4	4	no	—
197	C₃×Dic₃	—	4	2	no	—
198	C₂×#41	—	3	2	no	—
199	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
200	C₄⋊Q₈	—	3	1	no	—
201	#127	—	3	1	no	—
202	#124	—	3	2	no	—
203	#121	—	6	1	no	—
204	#121	—	6	1	no	—
205	C₄×D₄	—	6	1	no	—
206	C₄×D₄	—	6	1	no	—
207	C₂×C₄⋊C₄	—	6	1	no	—
208	C₂×C₄²	—	3	2	no	—
209	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
210	#104	—	6	8	no	—
211	#97	—	2	1	no	—
212	C₄×C₈	—	2	1	no	—
213	#95	—	6	1	no	—
214	C₂³×C₃	—	2	1	no	—
215	C₂³×C₃	—	6	2	no	—
216	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
217	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
218	C₂²×D₃	—	2	2	no	—
219	C₃×Q₈	—	6	4	no	—
220	C₃×D₄	—	6	4	no	—
221	C₃×D₄	—	12	2	no	—
222	C₃×D₄	—	12	2	no	—
223	C₃×D₄	—	12	2	no	—
224	C₃×D₄	—	12	2	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	—	2	1	no	—
230	C₂×C₃×C₄	—	2	1	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	—	2	1	no	—
235	C₂×C₃×C₄	—	4	2	no	—
236	C₂×C₃×C₄	—	4	1	no	—
237	C₂×C₃×C₄	—	4	1	no	—
238	C₂×C₃×C₄	—	4	2	no	—
239	C₂×C₃×C₄	—	6	4	no	—
240	C₂×C₃×C₄	—	6	2	no	—
241	C₂×C₃×C₄	—	12	2	no	—
242	C₂×C₃×C₄	—	12	2	no	—
243	C₂×C₃×C₄	—	12	4	no	—
244	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
245	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
246	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
247	C₂×C₃×C₄	(C₂×D₃)⋊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×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
254	C₂×C₃×C₄	#235	1	2	yes	—
255	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
258	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
259	C₂×C₃×C₄	C₃×#41	1	2	yes	—
260	#67	—	4	2	no	—
261	#67	—	4	2	no	—
262	C₂×Dic₃	—	2	4	no	—
263	C₂×Dic₃	—	2	2	no	—
264	C₂×Dic₃	—	4	2	no	—
265	C₂×Dic₃	—	4	2	no	—
266	D₁₂	—	2	4	no	—
267	D₁₂	—	4	2	no	—
268	D₁₂	—	4	2	no	—
269	C₄×D₃	—	4	4	no	—
270	Dic₆	—	2	4	no	—
271	C₃×C₈	—	2	8	no	—
272	C₃×C₈	—	2	4	no	—
273	C₃×C₈	—	2	4	no	—
274	C₂×C₃²	—	2	1	no	—
275	C₂×C₃²	—	2	1	no	—
276	C₂×C₃²	#390	1	1	yes	characteristic
277	C₂×C₃²	C₂×#104	1	1	yes	characteristic
278	C₂×C₃²	#421	1	1	yes	characteristic
279	C₃×D₃	—	8	2	no	—
280	#41	—	6	4	no	—
281	#41	—	6	4	no	—
282	C₂×Q₈	—	3	2	no	—
283	C₂×D₄	—	3	2	no	—
284	C₂×D₄	—	6	2	no	—
285	C₂×D₄	—	6	1	no	—
286	C₂×D₄	—	6	1	no	—
287	C₂²×C₄	—	6	2	no	—
288	C₂²×C₄	—	6	2	no	—
289	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
290	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
292	M₁₆	—	2	2	no	—
293	M₁₆	C₃×D₁₂	1	4	yes	complemented
294	C₂×C₈	—	2	2	no	—
295	C₄⋊C₄	—	6	4	no	—
296	C₄⋊C₄	—	6	1	no	—
297	C₄⋊C₄	—	6	1	no	—
298	C₂²⋊C₄	—	6	2	no	—
299	C₂²⋊C₄	—	6	2	no	—
300	C₄²	—	6	4	no	—
301	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
302	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
303	C₄²	C₃×#67	1	1	yes	characteristic
304	C₄²	C₃×#67	1	1	yes	characteristic
305	C₂²×C₃	—	2	1	no	—
306	C₂²×C₃	—	2	1	no	—
307	C₂²×C₃	—	2	1	no	—
308	C₂²×C₃	—	2	1	no	—
309	C₂²×C₃	—	2	1	no	—
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	2	1	no	—
312	C₂²×C₃	—	4	1	no	—
313	C₂²×C₃	—	4	1	no	—
314	C₂²×C₃	—	12	2	no	—
315	C₂²×C₃	—	12	2	no	—
316	C₂²×C₃	—	12	2	no	—
317	C₂²×C₃	#874	1	1	yes	characteristic
318	C₂²×C₃	#875	1	1	yes	characteristic
319	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
320	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
321	C₂²×C₃	C₃×#124	1	1	yes	characteristic
322	C₂²×C₃	C₃×#127	1	1	yes	characteristic
323	C₂×D₃	—	4	2	no	—
324	C₂×D₃	—	4	2	no	—
325	C₂×D₃	—	4	2	no	—
326	C₃×C₄	—	2	2	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	2	1	no	—
329	C₃×C₄	—	2	1	no	—
330	C₃×C₄	—	2	1	no	—
331	C₃×C₄	—	2	1	no	—
332	C₃×C₄	—	2	1	no	—
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	2	2	no	—
335	C₃×C₄	—	2	2	no	—
336	C₃×C₄	—	4	1	no	—
337	C₃×C₄	—	4	1	no	—
338	C₃×C₄	—	12	4	no	—
339	C₃×C₄	—	12	2	no	—
340	C₃×C₄	#825	1	2	yes	complemented
341	C₃×C₄	C₃×#104	1	2	yes	complemented
342	C₃×C₄	C₄×D₁₂	1	2	yes	—
343	C₃×C₄	#930	1	2	yes	—
344	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
345	C₃×C₄	C₃×#121	1	2	yes	—
346	Dic₃	—	4	4	no	—
347	Dic₃	—	4	2	no	—
348	C₃²	#1980	1	1	yes	characteristic, complemented, Sylow
349	C₂³	—	6	2	no	—
350	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
351	Q₈	—	6	4	no	—
352	D₄	—	6	4	no	—
353	D₄	—	12	2	no	—
354	D₄	—	12	2	no	—
355	D₄	—	12	2	no	—
356	D₄	—	12	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	6	4	no	—
360	C₂×C₄	—	6	2	no	—
361	C₂×C₄	—	12	2	no	—
362	C₂×C₄	—	12	2	no	—
363	C₂×C₄	—	12	4	no	—
364	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
365	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
366	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
367	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
368	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
369	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
370	C₂×C₄	C₃×#235	1	2	yes	—
371	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
372	C₈	—	2	4	no	—
373	C₂×C₃	—	2	1	no	—
374	C₂×C₃	—	2	1	no	—
375	C₂×C₃	—	2	1	no	—
376	C₂×C₃	—	2	1	no	—
377	C₂×C₃	—	2	1	no	—
378	C₂×C₃	—	2	1	no	—
379	C₂×C₃	—	2	1	no	—
380	C₂×C₃	—	4	1	no	—
381	C₂×C₃	—	4	1	no	—
382	C₂×C₃	—	24	2	no	—
383	C₂×C₃	#4939	1	1	yes	characteristic
384	C₂×C₃	C₂×#825	1	1	yes	characteristic
385	C₂×C₃	#5139	1	1	yes	characteristic
386	C₂×C₃	C₃×#390	1	1	yes	characteristic
387	C₂×C₃	C₂×C₃×#104	1	1	yes	characteristic
388	C₂×C₃	C₃×#421	1	1	yes	characteristic
389	D₃	—	8	2	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	12	2	no	—
393	C₂²	—	12	2	no	—
394	C₂²	—	12	2	no	—
395	C₂²	C₃×#874	1	1	yes	characteristic
396	C₂²	C₃×#875	1	1	yes	characteristic
397	C₂²	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	12	4	no	—
402	C₄	—	12	2	no	—
403	C₄	C₃×#825	1	2	yes	complemented
404	C₄	C₃×C₄×D₁₂	1	2	yes	—
405	C₄	C₃×#930	1	2	yes	—
406	C₃	—	2	1	no	—
407	C₃	#69867	1	1	yes	characteristic, direct product factor
408	C₃	C₃×#1980	1	1	yes	characteristic, complemented
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	24	2	no	—
412	C₂	C₃×#4939	1	1	yes	characteristic
413	C₂	C₂×C₃×#825	1	1	yes	characteristic
414	C₂	C₃×#5139	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×#67
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₃²×C₄×M₁₆	C₂
socle	C₂²×C₃²	C₂×C₂²⋊C₄
prime radical	C₃×#5477	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₃×C₄×M₁₆	D₃
hypocenter	C₃	C₃×#1980
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃²×C₄×M₁₆	C₂	semidirect
3. C₂×C₃×#825	C₂	semidirect
4. C₃×C₄×C₄⋊Dic₃	C₂	semidirect
6. #69867	C₃	direct (N × H)
14. C₃×#875	C₄	semidirect
15. C₃×#874	C₄	semidirect
18. C₃×#869	C₄	semidirect
27. C₃×C₄×M₁₆	D₃	semidirect
28. C₃×C₄×M₁₆	C₂×C₃	semidirect
30. C₂×#825	C₂×C₃	semidirect
31. C₄×C₄⋊Dic₃	C₂×C₃	semidirect
45. C₃²×M₁₆	D₄	semidirect
79. #875	C₃×C₄	semidirect
80. #874	C₃×C₄	semidirect
83. #869	C₃×C₄	semidirect
120. C₄×M₁₆	C₃×D₃	semidirect
153. C₃×M₁₆	D₁₂	semidirect
154. C₃×M₁₆	C₃×D₄	semidirect
193. C₃²×C₄	#104	semidirect
293. M₁₆	C₃×D₁₂	semidirect
340. C₃×C₄	#825	semidirect
341. C₃×C₄	C₃×#104	semidirect
348. C₃²	#1980	semidirect
403. C₄	C₃×#825	semidirect
407. C₃	#69867	direct (N × H)
408. C₃	C₃×#1980	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×M₁₆	2
C₂×C₃×#825	2
C₃×C₄×C₄⋊Dic₃	2
C₃×#1980	3
#69867	3

Subgroups — C3×#69867 #11791396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69867 #11791396