Subgroups — C₃×#78580 #11861204

Order 1152.

969 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5745	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×#904	C₂	1	1	yes	maximal, characteristic
3	C₃²×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5005	C₂	1	2	yes	maximal, complemented
6	C₃×#4717	C₂	1	4	yes	maximal, complemented
7	C₃×#4700	C₂	1	4	yes	maximal, complemented
8	C₃×#2957	—	3	1	no	maximal
9	#78580	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃×#235	C₂²	1	2	yes	—
11	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₃²×#117	C₂²	1	1	yes	characteristic
14	C₂×C₃×#208	C₂²	1	2	yes	—
15	C₃×#907	—	2	4	no	—
16	C₃×D₃×M₁₆	—	2	4	no	—
17	C₂×C₃×Dic₁₂	C₄	1	1	yes	characteristic, complemented
18	C₃×#904	C₄	1	2	yes	complemented
19	C₃×#904	C₄	1	2	yes	complemented
20	C₃×#904	C₂²	1	2	yes	—
21	C₃×#904	C₂²	1	2	yes	—
22	C₂×C₃×D₂₄	C₄	1	1	yes	characteristic, complemented
23	C₂×C₃×#204	C₄	1	2	yes	complemented
24	C₃×#901	C₂²	1	8	yes	complemented
25	C₃²×#97	C₂²	1	2	yes	complemented
26	C₃²×C₄×C₈	C₂²	1	2	yes	complemented
27	C₃×#819	C₂²	1	2	yes	complemented
28	C₃×#819	C₂²	1	2	yes	complemented
29	C₃×#805	C₂²	1	8	yes	complemented
30	C₂×C₃×#135	—	3	1	no	—
31	C₃×#568	—	3	2	no	—
32	#5745	C₂×C₃	1	2	yes	complemented
33	C₂×#904	C₂×C₃	1	1	yes	characteristic
34	C₃×#444	—	3	4	no	—
35	C₃×#443	—	3	4	no	—
36	C₂×C₃×#108	—	3	1	no	—
37	C₃×#421	—	3	2	no	—
38	C₃×#405	—	2	1	no	—
39	C₃×#405	D₃	1	1	yes	characteristic, complemented
40	C₃×#405	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×#819	C₂×C₃	1	1	yes	characteristic, complemented
42	#5005	C₂×C₃	1	2	yes	complemented
43	#4717	C₂×C₃	1	4	yes	complemented
44	#4700	C₂×C₃	1	4	yes	complemented
45	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
46	C₂×C₃×#67	—	2	2	no	—
47	C₃×#235	—	2	2	no	—
48	C₃×#235	—	2	2	no	—
49	C₃×#235	C₂×C₄	1	4	yes	—
50	C₃×#235	C₂³	1	4	yes	—
51	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
52	C₂×C₃×C₄×D₃	—	2	2	no	—
53	C₂×C₃×Dic₆	C₂×C₄	1	2	yes	—
54	C₃²×M₁₆	D₄	1	2	yes	—
55	C₃²×M₁₆	D₄	1	2	yes	—
56	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
57	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
61	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
62	C₂×C₃²×C₈	C₂³	1	2	yes	—
63	C₃²×C₄⋊C₄	—	2	1	no	—
64	C₃²×C₂²⋊C₄	—	2	1	no	—
65	C₃²×C₄²	C₂³	1	2	yes	—
66	C₃×#208	—	2	2	no	—
67	C₃×#208	C₂³	1	4	yes	—
68	C₂×C₃×C₃⋊C₈	—	2	2	no	—
69	C₃×Dic₁₂	C₂×C₄	1	2	yes	—
70	C₃×Dic₁₂	C₂×C₄	1	2	yes	—
71	C₃×D₂₄	C₂×C₄	1	2	yes	—
72	C₃×D₂₄	C₂×C₄	1	2	yes	—
73	C₃×#204	C₂×C₄	1	4	yes	—
74	C₃×#204	C₂×C₄	1	4	yes	—
75	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
76	C₃×D₃×C₈	—	2	8	no	—
77	#2957	—	3	1	no	Sylow
78	C₂×C₃×#41	—	3	2	no	—
79	C₂×#235	C₂²×C₃	1	2	yes	—
80	C₃×#135	—	3	2	no	—
81	C₃×#135	—	3	2	no	—
82	C₃×#135	—	3	2	no	—
83	C₃×#135	—	3	2	no	—
84	C₂×C₃×Q₁₆	—	3	1	no	—
85	C₂×C₃×SD₁₆	—	3	2	no	—
86	C₂×C₃×D₈	—	3	1	no	—
87	C₃×#131	—	3	8	no	—
88	C₃×#131	—	6	4	no	—
89	C₂×C₃×M₁₆	—	2	1	no	—
90	C₂×C₃×M₁₆	—	3	2	no	—
91	C₂×C₃×M₁₆	—	6	4	no	—
92	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
93	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
94	C₂²×C₃×C₈	—	2	1	no	—
95	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
96	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
97	C₃×#117	—	2	1	no	—
98	C₃×#117	C₂×D₃	1	1	yes	characteristic
99	C₃×#117	C₂²×C₃	1	1	yes	characteristic
100	C₂×#208	C₂²×C₃	1	2	yes	—
101	#907	—	2	4	no	—
102	D₃×M₁₆	—	2	4	no	—
103	C₂×Dic₁₂	C₃×C₄	1	1	yes	characteristic, complemented
104	#904	C₃×C₄	1	2	yes	complemented
105	#904	C₃×C₄	1	2	yes	complemented
106	#904	C₂²×C₃	1	2	yes	—
107	#904	C₂²×C₃	1	2	yes	—
108	C₂×D₂₄	C₃×C₄	1	1	yes	characteristic, complemented
109	C₂×#204	C₃×C₄	1	2	yes	complemented
110	#901	C₂²×C₃	1	8	yes	complemented
111	C₃×#108	—	3	2	no	—
112	C₃×#108	—	3	2	no	—
113	C₃×#104	—	3	8	no	—
114	C₃×#97	—	2	2	no	—
115	C₃×#97	C₂×D₃	1	2	yes	complemented
116	C₃×#97	C₂²×C₃	1	2	yes	complemented
117	C₃×C₄×C₈	—	2	2	no	—
118	C₃×C₄×C₈	C₂×D₃	1	2	yes	complemented
119	C₃×C₄×C₈	C₂²×C₃	1	2	yes	complemented
120	#819	C₂²×C₃	1	2	yes	complemented
121	#819	C₂²×C₃	1	2	yes	complemented
122	#805	C₂²×C₃	1	8	yes	complemented
123	C₂³×C₃²	#41	1	1	yes	characteristic
124	C₂²×C₃×D₃	—	2	2	no	—
125	C₂×C₃²×C₄	—	2	2	no	—
126	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃²×C₄	#41	1	1	yes	characteristic
131	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
132	C₃×#67	—	2	4	no	—
133	C₃×#67	—	2	4	no	—
134	C₂×C₃×Dic₃	—	2	2	no	—
135	C₃×D₁₂	—	2	2	no	—
136	C₃×D₁₂	C₂²×C₄	1	4	yes	—
137	C₃×C₄×D₃	—	2	4	no	—
138	C₃×C₄×D₃	—	2	4	no	—
139	C₃×Dic₆	—	2	2	no	—
140	C₃×Dic₆	C₂²×C₄	1	4	yes	—
141	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
142	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
143	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
144	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
145	C₃²×C₈	C₂×D₄	1	4	yes	—
146	C₃×C₃⋊C₈	—	2	4	no	—
147	C₂×#135	—	3	1	no	—
148	#568	—	3	2	no	—
149	#444	—	3	4	no	—
150	#443	—	3	4	no	—
151	C₂×#108	—	3	1	no	—
152	#421	—	3	2	no	—
153	#405	C₃×D₃	1	1	yes	characteristic, complemented
154	C₃×#41	—	3	4	no	—
155	C₃×#41	—	3	4	no	—
156	C₃×#41	—	6	2	no	—
157	C₃×#41	—	6	2	no	—
158	C₂×C₃×Q₈	—	3	2	no	—
159	C₂×C₃×D₄	—	3	2	no	—
160	C₂×C₃×D₄	—	6	2	no	—
161	C₂²×C₃×C₄	—	2	1	no	—
162	C₂²×C₃×C₄	—	6	2	no	—
163	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
165	C₂×#67	—	2	2	no	—
166	#235	—	2	2	no	—
167	#235	—	2	2	no	—
168	#235	C₂×C₃×C₄	1	4	yes	—
169	#235	C₂³×C₃	1	4	yes	—
170	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
171	C₂×C₄×D₃	—	2	2	no	—
172	C₂×Dic₆	C₂×C₃×C₄	1	2	yes	—
173	C₃×Q₁₆	—	3	2	no	—
174	C₃×Q₁₆	—	3	2	no	—
175	C₃×SD₁₆	—	3	4	no	—
176	C₃×SD₁₆	—	3	4	no	—
177	C₃×D₈	—	3	2	no	—
178	C₃×D₈	—	3	2	no	—
179	C₃×M₁₆	—	2	2	no	—
180	C₃×M₁₆	—	2	2	no	—
181	C₃×M₁₆	—	3	4	no	—
182	C₃×M₁₆	—	6	2	no	—
183	C₃×M₁₆	—	6	8	no	—
184	C₃×M₁₆	D₁₂	1	2	yes	—
185	C₃×M₁₆	D₁₂	1	2	yes	—
186	C₃×M₁₆	C₃×D₄	1	2	yes	—
187	C₃×M₁₆	C₃×D₄	1	2	yes	—
188	C₂×C₃×C₈	—	2	1	no	—
189	C₂×C₃×C₈	—	2	1	no	—
190	C₂×C₃×C₈	—	2	1	no	—
191	C₂×C₃×C₈	—	2	1	no	—
192	C₂×C₃×C₈	—	2	1	no	—
193	C₂×C₃×C₈	—	2	2	no	—
194	C₂×C₃×C₈	—	2	1	no	—
195	C₂×C₃×C₈	—	6	2	no	—
196	C₂×C₃×C₈	—	6	8	no	—
197	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
198	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
199	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
200	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
201	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
202	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
203	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
204	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
205	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
206	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
207	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
208	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
211	C₃×C₄⋊C₄	—	2	2	no	—
212	C₃×C₄⋊C₄	—	2	1	no	—
213	C₃×C₄⋊C₄	—	2	1	no	—
214	C₃×C₂²⋊C₄	—	2	2	no	—
215	C₃×C₂²⋊C₄	—	2	1	no	—
216	C₃×C₂²⋊C₄	—	2	1	no	—
217	C₃×C₄²	—	2	2	no	—
218	C₃×C₄²	C₂²×D₃	1	2	yes	—
219	C₃×C₄²	C₂³×C₃	1	2	yes	—
220	#208	—	2	2	no	—
221	#208	C₂³×C₃	1	4	yes	—
222	C₂×C₃⋊C₈	—	2	2	no	—
223	Dic₁₂	C₂×C₃×C₄	1	2	yes	—
224	Dic₁₂	C₂×C₃×C₄	1	2	yes	—
225	D₂₄	C₂×C₃×C₄	1	2	yes	—
226	D₂₄	C₂×C₃×C₄	1	2	yes	—
227	#204	C₂×C₃×C₄	1	4	yes	—
228	#204	C₂×C₃×C₄	1	4	yes	—
229	ΓL(1,𝔽₂₅)	—	2	8	no	—
230	D₃×C₈	—	2	8	no	—
231	C₂²×C₃²	—	4	1	no	—
232	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
233	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
234	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
235	C₂×C₃×D₃	—	2	4	no	—
236	C₂×C₃×D₃	—	8	2	no	—
237	C₃²×C₄	—	4	2	no	—
238	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
239	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
240	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
241	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
242	C₃×Dic₃	—	2	4	no	—
243	C₂×#41	—	3	2	no	—
244	#135	—	3	2	no	—
245	#135	—	3	2	no	—
246	#135	—	3	2	no	—
247	#135	—	3	2	no	—
248	C₂×Q₁₆	—	3	1	no	—
249	C₂×SD₁₆	—	3	2	no	—
250	C₂×D₈	—	3	1	no	—
251	#131	—	3	8	no	—
252	#131	—	6	4	no	—
253	C₂×M₁₆	—	3	2	no	—
254	C₂×M₁₆	—	6	4	no	—
255	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
256	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
257	#117	C₂×C₃×D₃	1	1	yes	characteristic
258	#108	—	3	2	no	—
259	#108	—	3	2	no	—
260	#104	—	3	8	no	—
261	#97	C₂×C₃×D₃	1	2	yes	complemented
262	C₄×C₈	C₂×C₃×D₃	1	2	yes	complemented
263	C₂³×C₃	—	2	1	no	—
264	C₂³×C₃	—	6	2	no	—
265	C₂³×C₃	#235	1	1	yes	characteristic
266	C₂³×C₃	C₃×#41	1	1	yes	characteristic
267	C₂²×D₃	—	2	2	no	—
268	C₃×Q₈	—	3	4	no	—
269	C₃×Q₈	—	6	2	no	—
270	C₃×D₄	—	3	4	no	—
271	C₃×D₄	—	6	4	no	—
272	C₃×D₄	—	6	4	no	—
273	C₃×D₄	—	6	2	no	—
274	C₂×C₃×C₄	—	2	4	no	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	2	1	no	—
281	C₂×C₃×C₄	—	2	1	no	—
282	C₂×C₃×C₄	—	2	1	no	—
283	C₂×C₃×C₄	—	6	2	no	—
284	C₂×C₃×C₄	—	6	4	no	—
285	C₂×C₃×C₄	—	6	4	no	—
286	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
290	C₂×C₃×C₄	#235	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
298	#67	—	2	4	no	—
299	#67	—	2	4	no	—
300	C₂×Dic₃	—	2	2	no	—
301	D₁₂	—	2	2	no	—
302	D₁₂	C₂²×C₃×C₄	1	4	yes	—
303	C₄×D₃	—	2	4	no	—
304	C₄×D₃	—	2	4	no	—
305	Dic₆	—	2	2	no	—
306	Dic₆	C₂²×C₃×C₄	1	4	yes	—
307	C₃×C₈	—	2	1	no	—
308	C₃×C₈	—	2	1	no	—
309	C₃×C₈	—	2	1	no	—
310	C₃×C₈	—	2	1	no	—
311	C₃×C₈	—	2	4	no	—
312	C₃×C₈	—	6	4	no	—
313	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
314	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
315	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
316	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
317	C₃×C₈	C₂×D₁₂	1	4	yes	—
318	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
319	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
320	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
321	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
322	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
323	C₃⋊C₈	—	2	4	no	—
324	C₂×C₃²	—	2	1	no	—
325	C₂×C₃²	—	2	1	no	—
326	C₂×C₃²	—	2	1	no	—
327	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
328	C₃×D₃	—	4	4	no	—
329	#41	—	3	4	no	—
330	#41	—	3	4	no	—
331	#41	—	6	2	no	—
332	#41	—	6	2	no	—
333	C₂×Q₈	—	3	2	no	—
334	C₂×D₄	—	3	2	no	—
335	C₂×D₄	—	6	2	no	—
336	C₂²×C₄	—	6	2	no	—
337	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
338	Q₁₆	—	3	2	no	—
339	Q₁₆	—	3	2	no	—
340	SD₁₆	—	3	4	no	—
341	SD₁₆	—	3	4	no	—
342	D₈	—	3	2	no	—
343	D₈	—	3	2	no	—
344	M₁₆	—	3	4	no	—
345	M₁₆	—	6	2	no	—
346	M₁₆	—	6	8	no	—
347	M₁₆	C₃×D₁₂	1	2	yes	—
348	M₁₆	C₃×D₁₂	1	2	yes	—
349	C₂×C₈	—	6	2	no	—
350	C₂×C₈	—	6	8	no	—
351	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
352	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
353	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
354	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
355	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
356	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
357	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
358	C₄⋊C₄	—	2	1	no	—
359	C₂²⋊C₄	—	2	1	no	—
360	C₄²	C₂²×C₃×D₃	1	2	yes	—
361	C₂²×C₃	—	2	1	no	—
362	C₂²×C₃	—	2	1	no	—
363	C₂²×C₃	—	2	1	no	—
364	C₂²×C₃	—	4	1	no	—
365	C₂²×C₃	—	4	1	no	—
366	C₂²×C₃	—	4	2	no	—
367	C₂²×C₃	—	6	4	no	—
368	C₂²×C₃	—	24	2	no	—
369	C₂²×C₃	C₄×D₁₂	1	1	yes	characteristic
370	C₂²×C₃	C₄×D₁₂	1	1	yes	characteristic
371	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
372	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
373	C₂²×C₃	C₂×#235	1	1	yes	characteristic
374	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
375	C₂×D₃	—	2	4	no	—
376	C₂×D₃	—	8	2	no	—
377	C₃×C₄	—	2	1	no	—
378	C₃×C₄	—	2	1	no	—
379	C₃×C₄	—	2	1	no	—
380	C₃×C₄	—	2	1	no	—
381	C₃×C₄	—	4	4	no	—
382	C₃×C₄	—	4	2	no	—
383	C₃×C₄	—	4	2	no	—
384	C₃×C₄	—	6	4	no	—
385	C₃×C₄	C₄×D₁₂	1	1	yes	characteristic
386	C₃×C₄	C₄×D₁₂	1	1	yes	characteristic
387	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
388	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
389	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
390	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
391	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
392	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
393	Dic₃	—	2	4	no	—
394	C₃²	#2957	1	1	yes	characteristic, complemented, Sylow
395	C₂³	—	6	2	no	—
396	C₂³	C₃×#235	1	1	yes	characteristic
397	Q₈	—	3	4	no	—
398	Q₈	—	6	2	no	—
399	D₄	—	3	4	no	—
400	D₄	—	6	4	no	—
401	D₄	—	6	4	no	—
402	D₄	—	6	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	6	2	no	—
405	C₂×C₄	—	6	4	no	—
406	C₂×C₄	—	6	4	no	—
407	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
408	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
409	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
410	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
411	C₂×C₄	C₃×#235	1	1	yes	characteristic
412	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
413	C₈	—	6	4	no	—
414	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
415	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
416	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
417	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
418	C₈	C₂×C₃×D₁₂	1	4	yes	—
419	C₂×C₃	—	2	2	no	—
420	C₂×C₃	—	2	1	no	—
421	C₂×C₃	—	2	1	no	—
422	C₂×C₃	—	2	1	no	—
423	C₂×C₃	—	2	1	no	—
424	C₂×C₃	—	2	1	no	—
425	C₂×C₃	—	2	1	no	—
426	C₂×C₃	—	2	1	no	—
427	C₂×C₃	—	4	1	no	—
428	C₂×C₃	—	4	1	no	—
429	C₂×C₃	—	12	4	no	—
430	C₂×C₃	C₂×C₄×D₁₂	1	1	yes	characteristic
431	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
432	D₃	—	4	4	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	6	4	no	—
435	C₂²	—	24	2	no	—
436	C₂²	C₃×C₄×D₁₂	1	1	yes	characteristic
437	C₂²	C₃×C₄×D₁₂	1	1	yes	characteristic
438	C₂²	C₂×C₃×#235	1	1	yes	characteristic
439	C₄	—	4	2	no	—
440	C₄	—	6	4	no	—
441	C₄	C₃×C₄×D₁₂	1	1	yes	characteristic
442	C₄	C₃×C₄×D₁₂	1	1	yes	characteristic
443	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
444	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
445	C₃	—	2	1	no	—
446	C₃	#78580	1	1	yes	characteristic, direct product factor
447	C₃	C₃×#2957	1	1	yes	characteristic, complemented
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	2	1	no	—
451	C₂	—	12	4	no	—
452	C₂	C₂×C₃×C₄×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂²×D₁₂
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#405	C₂
socle	C₂×C₃²	C₂×C₄×D₄
prime radical	C₂×C₃×#904	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#405	D₃
hypocenter	C₃	C₃×#2957
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×M₁₆ ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
1. C₃×#5745	C₂	semidirect
3. C₃²×#405	C₂	semidirect
4. C₂×C₃×#819	C₂	semidirect
5. C₃×#5005	C₂	semidirect
6. C₃×#4717	C₂	semidirect
7. C₃×#4700	C₂	semidirect
9. #78580	C₃	direct (N × H)
17. C₂×C₃×Dic₁₂	C₄	semidirect
18. C₃×#904	C₄	semidirect
19. C₃×#904	C₄	semidirect
22. C₂×C₃×D₂₄	C₄	semidirect
23. C₂×C₃×#204	C₄	semidirect
24. C₃×#901	C₂²	semidirect
25. C₃²×#97	C₂²	semidirect
26. C₃²×C₄×C₈	C₂²	semidirect
27. C₃×#819	C₂²	semidirect
28. C₃×#819	C₂²	semidirect
29. C₃×#805	C₂²	semidirect
32. #5745	C₂×C₃	semidirect
39. C₃×#405	D₃	semidirect
40. C₃×#405	C₂×C₃	semidirect
41. C₂×#819	C₂×C₃	semidirect
42. #5005	C₂×C₃	semidirect
43. #4717	C₂×C₃	semidirect
44. #4700	C₂×C₃	semidirect
103. C₂×Dic₁₂	C₃×C₄	semidirect
104. #904	C₃×C₄	semidirect
105. #904	C₃×C₄	semidirect
108. C₂×D₂₄	C₃×C₄	semidirect
109. C₂×#204	C₃×C₄	semidirect
110. #901	C₂²×C₃	semidirect
115. C₃×#97	C₂×D₃	semidirect
116. C₃×#97	C₂²×C₃	semidirect
118. C₃×C₄×C₈	C₂×D₃	semidirect
119. C₃×C₄×C₈	C₂²×C₃	semidirect
120. #819	C₂²×C₃	semidirect
121. #819	C₂²×C₃	semidirect
122. #805	C₂²×C₃	semidirect
153. #405	C₃×D₃	semidirect
261. #97	C₂×C₃×D₃	semidirect
262. C₄×C₈	C₂×C₃×D₃	semidirect
394. C₃²	#2957	semidirect
446. C₃	#78580	direct (N × H)
447. C₃	C₃×#2957	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5745	2
C₂×C₃×#904	2
C₃²×#405	2
C₂×C₃×#819	2
C₃×#5005	2
C₃×#4717	2
C₃×#4700	2
C₃×#2957	3
#78580	3

Subgroups — C3×#78580 #11861204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#78580 #11861204