Subgroups — C₃×#69492 #11791393

Order 1152.

769 conjugacy classes of subgroups.

The subgroup lattice has 419 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	C₂×C₃×#805	C₂	1	4	yes	maximal, complemented
4	C₃×C₄×#208	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#1980	—	3	1	no	maximal
6	#69492	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₃×#235	C₂²	1	2	yes	—
8	C₂×C₃²×C₄⋊C₄	—	2	1	no	—
9	C₂×C₃²×C₄²	C₂²	1	2	yes	—
10	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
11	C₃×#930	—	2	1	no	—
12	C₃×#930	—	2	1	no	—
13	C₂×C₃×#208	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×#95	—	2	1	no	—
20	C₃×#805	—	2	8	no	—
21	C₃×#803	—	2	1	no	—
22	C₃×C₄×C₃⋊C₈	—	2	1	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	—	3	1	no	—
27	C₃×C₄×C₄⋊C₄	—	2	1	no	—
28	C₃×C₄×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
29	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×#805	C₂×C₃	1	4	yes	complemented
31	C₄×#208	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂²×C₃²×C₄	—	2	2	no	—
33	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
34	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
35	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
36	C₂×C₃×#67	—	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×C₄⋊C₄	—	2	4	no	—
45	C₃²×C₄²	—	2	4	no	—
46	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
47	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
48	C₃²×C₄²	D₄	1	1	yes	characteristic
49	C₃²×C₄²	D₄	1	1	yes	characteristic
50	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
51	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
52	C₃×C₄⋊Dic₃	—	2	1	no	—
53	C₃×C₄⋊Dic₃	—	2	1	no	—
54	C₃×#208	—	2	2	no	—
55	C₃×#208	D₄	1	4	yes	complemented
56	C₂×C₃×C₃⋊C₈	—	2	2	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	—	3	2	no	—
61	C₃×C₄⋊Q₈	—	3	1	no	—
62	C₃×#127	—	3	1	no	—
63	C₃×#124	—	3	2	no	—
64	C₃×#121	—	6	1	no	—
65	C₃×#121	—	6	1	no	—
66	C₃×C₄×D₄	—	6	1	no	—
67	C₃×C₄×D₄	—	6	1	no	—
68	C₂×C₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₃×C₄²	—	2	1	no	—
72	C₂×C₃×C₄²	—	2	2	no	—
73	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
74	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
75	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
76	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
77	#930	—	2	1	no	—
78	#930	—	2	1	no	—
79	C₂×#208	C₂²×C₃	1	2	yes	—
80	#875	C₃×C₄	1	2	yes	complemented
81	#874	C₃×C₄	1	1	yes	characteristic, complemented
82	C₄×D₁₂	—	2	1	no	—
83	C₄×D₁₂	—	2	1	no	—
84	#869	C₃×C₄	1	1	yes	characteristic, complemented
85	C₃×#104	—	6	8	no	—
86	C₃×#97	—	6	1	no	—
87	C₃×C₄×C₈	—	6	1	no	—
88	C₃×#95	—	2	2	no	—
89	C₃×#95	—	2	1	no	—
90	C₃×#95	—	2	1	no	—
91	#805	—	2	8	no	—
92	#803	—	2	1	no	—
93	C₄×C₃⋊C₈	—	2	1	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	—	2	4	no	—
98	C₂×C₃²×C₄	—	4	1	no	—
99	C₂×C₃²×C₄	—	4	2	no	—
100	C₂×C₃²×C₄	—	4	2	no	—
101	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
108	C₂×C₃²×C₄	#41	1	2	yes	—
109	C₃×#67	—	4	2	no	—
110	C₃×#67	—	4	2	no	—
111	C₂×C₃×Dic₃	—	2	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	C₃×C₃⋊C₈	—	2	4	no	—
118	#532	—	3	1	no	—
119	C₂×#104	—	3	4	no	—
120	C₄×M₁₆	—	3	1	no	—
121	C₄×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic, complemented
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	4	no	—
130	C₂²×C₃×C₄	—	2	2	no	—
131	C₂²×C₃×C₄	—	2	2	no	—
132	C₂²×C₃×C₄	—	2	1	no	—
133	C₂²×C₃×C₄	—	2	1	no	—
134	C₂²×C₃×C₄	—	2	1	no	—
135	C₂²×C₃×C₄	—	6	2	no	—
136	C₂²×C₃×C₄	#67	1	1	yes	characteristic
137	C₂²×C₃×C₄	#67	1	1	yes	characteristic
138	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
139	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
141	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
142	C₂×#67	—	2	2	no	—
143	#235	—	2	4	no	—
144	#235	—	2	4	no	—
145	C₂×D₁₂	—	2	1	no	—
146	C₂×D₁₂	—	2	1	no	—
147	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
148	C₂×C₄×D₃	—	2	2	no	—
149	C₂×Dic₆	C₂×C₃×C₄	1	2	yes	—
150	C₃×M₁₆	—	3	4	no	—
151	C₃×M₁₆	—	6	2	no	—
152	C₂×C₃×C₈	—	6	2	no	—
153	C₃×C₄⋊C₄	—	2	8	no	—
154	C₃×C₄⋊C₄	—	2	4	no	—
155	C₃×C₄⋊C₄	—	2	4	no	—
156	C₃×C₄⋊C₄	—	6	1	no	—
157	C₃×C₄⋊C₄	—	6	1	no	—
158	C₃×C₂²⋊C₄	—	6	2	no	—
159	C₃×C₂²⋊C₄	—	6	2	no	—
160	C₃×C₄²	—	2	4	no	—
161	C₃×C₄²	—	2	4	no	—
162	C₃×C₄²	—	2	1	no	—
163	C₃×C₄²	—	2	1	no	—
164	C₃×C₄²	—	2	1	no	—
165	C₃×C₄²	—	2	1	no	—
166	C₃×C₄²	—	4	4	no	—
167	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
168	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
169	C₃×C₄²	D₁₂	1	1	yes	characteristic
170	C₃×C₄²	D₁₂	1	1	yes	characteristic
171	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
172	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
173	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
174	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
175	(C₂×D₃)⋊C₄	—	2	2	no	—
176	(C₂×D₃)⋊C₄	—	2	2	no	—
177	C₄⋊Dic₃	—	2	1	no	—
178	C₄⋊Dic₃	—	2	1	no	—
179	#208	—	2	2	no	—
180	#208	C₃×D₄	1	4	yes	complemented
181	C₂×C₃⋊C₈	—	2	2	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	—	4	4	no	—
194	C₃²×C₄	#104	1	2	yes	complemented
195	C₃²×C₄	C₄×D₄	1	2	yes	—
196	C₃²×C₄	#121	1	2	yes	—
197	C₃×Dic₃	—	4	2	no	—
198	C₂×#41	—	3	2	no	—
199	C₂×M₁₆	—	3	2	no	—
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	—	2	1	no	—
208	C₂×C₄²	C₂×C₃×D₃	1	2	yes	—
209	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
210	#104	—	6	8	no	—
211	#97	—	6	1	no	—
212	C₄×C₈	—	6	1	no	—
213	#95	—	2	1	no	—
214	C₂³×C₃	—	2	1	no	—
215	C₂³×C₃	—	6	2	no	—
216	C₂³×C₃	C₂×#67	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	4	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	8	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	4	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	—	2	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	4	1	no	—
240	C₂×C₃×C₄	—	4	1	no	—
241	C₂×C₃×C₄	—	4	4	no	—
242	C₂×C₃×C₄	—	4	2	no	—
243	C₂×C₃×C₄	—	4	4	no	—
244	C₂×C₃×C₄	—	4	2	no	—
245	C₂×C₃×C₄	—	4	2	no	—
246	C₂×C₃×C₄	—	4	2	no	—
247	C₂×C₃×C₄	—	4	2	no	—
248	C₂×C₃×C₄	—	6	2	no	—
249	C₂×C₃×C₄	—	12	4	no	—
250	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
251	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
252	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
253	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
254	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
260	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
261	C₂×C₃×C₄	#239	1	2	yes	—
262	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
265	C₂×C₃×C₄	C₃×#41	1	2	yes	—
266	#67	—	4	2	no	—
267	#67	—	4	2	no	—
268	C₂×Dic₃	—	2	2	no	—
269	D₁₂	—	2	4	no	—
270	D₁₂	—	4	2	no	—
271	D₁₂	—	4	2	no	—
272	C₄×D₃	—	4	4	no	—
273	Dic₆	—	2	4	no	—
274	C₃×C₈	—	6	4	no	—
275	C₃⋊C₈	—	2	4	no	—
276	C₂×C₃²	—	2	1	no	—
277	C₂×C₃²	—	2	1	no	—
278	C₂×C₃²	#390	1	1	yes	characteristic
279	C₂×C₃²	C₂×#104	1	1	yes	characteristic
280	C₂×C₃²	#421	1	1	yes	characteristic
281	C₃×D₃	—	8	2	no	—
282	#41	—	6	4	no	—
283	#41	—	6	4	no	—
284	C₂×Q₈	—	3	2	no	—
285	C₂×D₄	—	3	2	no	—
286	C₂×D₄	—	6	2	no	—
287	C₂×D₄	—	6	1	no	—
288	C₂×D₄	—	6	1	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	6	2	no	—
291	C₂²×C₄	C₃×#67	1	1	yes	characteristic
292	C₂²×C₄	C₃×#67	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
294	M₁₆	—	3	4	no	—
295	M₁₆	—	6	2	no	—
296	C₂×C₈	—	6	2	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	6	1	no	—
299	C₄⋊C₄	—	6	1	no	—
300	C₂²⋊C₄	—	6	2	no	—
301	C₂²⋊C₄	—	6	2	no	—
302	C₄²	—	2	4	no	—
303	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
304	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
305	C₄²	C₃×D₁₂	1	1	yes	characteristic
306	C₄²	C₃×D₁₂	1	1	yes	characteristic
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	2	2	no	—
309	C₂²×C₃	—	2	1	no	—
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	2	1	no	—
312	C₂²×C₃	—	2	1	no	—
313	C₂²×C₃	—	2	1	no	—
314	C₂²×C₃	—	2	1	no	—
315	C₂²×C₃	—	2	1	no	—
316	C₂²×C₃	—	12	2	no	—
317	C₂²×C₃	—	12	2	no	—
318	C₂²×C₃	—	12	2	no	—
319	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
320	C₂²×C₃	#940	1	1	yes	characteristic
321	C₂²×C₃	#947	1	1	yes	characteristic
322	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
323	C₂²×C₃	C₃×#124	1	1	yes	characteristic
324	C₂²×C₃	C₃×#127	1	1	yes	characteristic
325	C₂×D₃	—	4	2	no	—
326	C₂×D₃	—	4	2	no	—
327	C₂×D₃	—	4	2	no	—
328	C₃×C₄	—	2	2	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	1	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	2	2	no	—
336	C₃×C₄	—	2	2	no	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	4	1	no	—
339	C₃×C₄	—	4	1	no	—
340	C₃×C₄	—	4	8	no	—
341	C₃×C₄	—	4	4	no	—
342	C₃×C₄	—	4	4	no	—
343	C₃×C₄	—	12	2	no	—
344	C₃×C₄	#805	1	2	yes	complemented
345	C₃×C₄	C₃×#104	1	2	yes	complemented
346	C₃×C₄	#893	1	2	yes	—
347	C₃×C₄	#895	1	2	yes	—
348	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
349	C₃×C₄	C₃×#121	1	2	yes	—
350	Dic₃	—	4	2	no	—
351	C₃²	#1980	1	1	yes	characteristic, complemented, Sylow
352	C₂³	—	6	2	no	—
353	C₂³	C₂×C₃×#67	1	1	yes	characteristic
354	Q₈	—	6	4	no	—
355	D₄	—	6	4	no	—
356	D₄	—	12	2	no	—
357	D₄	—	12	2	no	—
358	D₄	—	12	2	no	—
359	D₄	—	12	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	6	2	no	—
366	C₂×C₄	—	12	4	no	—
367	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
368	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
369	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
370	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
371	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
372	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
373	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
374	C₂×C₄	C₃×#239	1	2	yes	—
375	C₈	—	6	4	no	—
376	C₂×C₃	—	2	2	no	—
377	C₂×C₃	—	2	2	no	—
378	C₂×C₃	—	2	1	no	—
379	C₂×C₃	—	2	1	no	—
380	C₂×C₃	—	2	1	no	—
381	C₂×C₃	—	2	1	no	—
382	C₂×C₃	—	2	1	no	—
383	C₂×C₃	—	2	1	no	—
384	C₂×C₃	—	2	1	no	—
385	C₂×C₃	—	24	2	no	—
386	C₂×C₃	C₂×#805	1	1	yes	characteristic
387	C₂×C₃	#4988	1	1	yes	characteristic
388	C₂×C₃	#5005	1	1	yes	characteristic
389	C₂×C₃	C₃×#390	1	1	yes	characteristic
390	C₂×C₃	C₂×C₃×#104	1	1	yes	characteristic
391	C₂×C₃	C₃×#421	1	1	yes	characteristic
392	D₃	—	8	2	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	12	2	no	—
396	C₂²	—	12	2	no	—
397	C₂²	—	12	2	no	—
398	C₂²	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
399	C₂²	C₃×#940	1	1	yes	characteristic
400	C₂²	C₃×#947	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	4	4	no	—
405	C₄	—	12	2	no	—
406	C₄	C₃×#805	1	2	yes	complemented
407	C₄	C₃×#893	1	2	yes	—
408	C₄	C₃×#895	1	2	yes	—
409	C₃	—	2	1	no	—
410	C₃	#69492	1	1	yes	characteristic, direct product factor
411	C₃	C₃×#1980	1	1	yes	characteristic, complemented
412	C₂	—	2	1	no	—
413	C₂	—	2	1	no	—
414	C₂	—	24	2	no	—
415	C₂	C₂×C₃×#805	1	1	yes	characteristic
416	C₂	C₃×#4988	1	1	yes	characteristic
417	C₂	C₃×#5005	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₁₂
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×#1980
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×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. C₂×C₃×#805	C₂	semidirect
4. C₃×C₄×#208	C₂	semidirect
6. #69492	C₃	direct (N × H)
14. C₃×#875	C₄	semidirect
15. C₃×#874	C₄	semidirect
18. C₃×#869	C₄	semidirect
28. C₃×C₄×C₄⋊C₄	D₃	semidirect
29. C₃×C₄×C₄⋊C₄	C₂×C₃	semidirect
30. C₂×#805	C₂×C₃	semidirect
31. C₄×#208	C₂×C₃	semidirect
55. C₃×#208	D₄	semidirect
80. #875	C₃×C₄	semidirect
81. #874	C₃×C₄	semidirect
84. #869	C₃×C₄	semidirect
121. C₄×C₄⋊C₄	C₃×D₃	semidirect
180. #208	C₃×D₄	semidirect
194. C₃²×C₄	#104	semidirect
344. C₃×C₄	#805	semidirect
345. C₃×C₄	C₃×#104	semidirect
351. C₃²	#1980	semidirect
406. C₄	C₃×#805	semidirect
410. C₃	#69492	direct (N × H)
411. 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×C₄⋊C₄	2
C₂×C₃×#805	2
C₃×C₄×#208	2
C₃×#1980	3
#69492	3

Subgroups — C3×#69492 #11791393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69492 #11791393