Subgroups — C₂×C₃×#4896 #11867968

Order 1152.

949 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#909	C₂	1	2	yes	maximal
2	C₂²×C₃×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃²×#108	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#824	C₂	1	2	yes	maximal, complemented
6	C₃×#4896	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#473	—	3	1	no	maximal
8	C₂×#4896	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃×#235	C₂²	1	1	yes	characteristic
10	C₂²×C₃×Dic₆	C₂²	1	2	yes	—
11	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×#208	C₂²	1	1	yes	characteristic
14	C₃×#909	—	2	4	no	—
15	C₃×#909	C₂²	1	8	yes	—
16	C₂×C₃×Dic₁₂	—	2	2	no	—
17	C₂×C₃×Dic₁₂	—	2	1	no	—
18	C₂×C₃×Dic₁₂	—	2	1	no	—
19	C₂×C₃×Dic₁₂	—	2	2	no	—
20	C₂×C₃×Dic₁₂	C₂²	1	4	yes	complemented
21	C₂×C₃×#204	—	2	2	no	—
22	C₃×#901	—	2	2	no	—
23	C₃×#901	C₂²	1	4	yes	—
24	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
25	C₂×C₃×D₃×C₈	—	2	1	no	—
26	C₃²×#108	C₂²	1	4	yes	complemented
27	C₃×#824	C₂²	1	8	yes	complemented
28	C₂×C₃×#137	—	3	2	no	—
29	C₂²×C₃×Q₁₆	—	3	1	no	—
30	C₂×C₃×#131	—	3	1	no	—
31	C₂×#909	C₂×C₃	1	2	yes	—
32	C₂²×Dic₁₂	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×#901	C₂×C₃	1	1	yes	characteristic
34	C₃×#473	—	3	8	no	—
35	C₂×C₃×#108	—	2	1	no	—
36	C₂×C₃×#108	D₃	1	1	yes	characteristic, complemented
37	C₂×C₃×#108	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×C₃×#101	—	3	2	no	—
39	C₂×#824	C₂×C₃	1	2	yes	complemented
40	#4896	C₂×C₃	1	8	yes	direct product factor
41	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
42	C₂×C₃×#67	—	2	1	no	—
43	C₂²×C₃×Dic₃	—	2	2	no	—
44	C₃×#235	—	2	1	no	—
45	C₃×#235	—	2	1	no	—
46	C₃×#235	D₄	1	2	yes	—
47	C₃×#235	C₂³	1	2	yes	—
48	C₂×C₃×D₁₂	D₄	1	1	yes	characteristic
49	C₂×C₃×C₄×D₃	—	2	1	no	—
50	C₂×C₃×Dic₆	—	2	2	no	—
51	C₂×C₃×Dic₆	—	2	2	no	—
52	C₂×C₃×Dic₆	—	2	2	no	—
53	C₂×C₃×Dic₆	—	2	2	no	—
54	C₂×C₃×Dic₆	—	2	2	no	—
55	C₂×C₃×Dic₆	D₄	1	1	yes	characteristic
56	C₂×C₃×Dic₆	C₂³	1	4	yes	—
57	C₃²×M₁₆	—	2	2	no	—
58	C₃²×M₁₆	C₂³	1	4	yes	—
59	C₂×C₃²×C₈	—	2	2	no	—
60	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
61	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
62	C₂×C₃²×C₈	D₄	1	2	yes	—
63	C₂×C₃²×C₈	C₂³	1	2	yes	—
64	C₃×#208	—	2	1	no	—
65	C₃×#208	C₂³	1	2	yes	—
66	C₂×C₃×C₃⋊C₈	—	2	1	no	—
67	C₃×Dic₁₂	—	2	8	no	—
68	C₃×Dic₁₂	—	2	4	no	—
69	C₃×Dic₁₂	—	2	4	no	—
70	C₃×#204	—	2	8	no	—
71	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
72	C₃×D₃×C₈	—	2	4	no	—
73	C₂×#473	—	3	1	no	Sylow
74	C₂×C₃×#41	—	3	1	no	—
75	C₂²×C₃×Q₈	—	3	2	no	—
76	C₂×#235	C₂²×C₃	1	1	yes	characteristic
77	C₂²×Dic₆	C₂²×C₃	1	2	yes	—
78	C₃×#137	—	3	8	no	—
79	C₃×#137	—	6	4	no	—
80	C₂×C₃×Q₁₆	—	3	4	no	—
81	C₂×C₃×Q₁₆	—	6	2	no	—
82	C₂×C₃×Q₁₆	—	6	1	no	—
83	C₂×C₃×Q₁₆	—	6	1	no	—
84	C₂×C₃×Q₁₆	—	6	2	no	—
85	C₂×C₃×SD₁₆	—	6	2	no	—
86	C₃×#131	—	3	4	no	—
87	C₃×#131	—	6	2	no	—
88	C₂×C₃×M₁₆	—	2	2	no	—
89	C₂×C₃×M₁₆	—	3	1	no	—
90	C₂×C₃×M₁₆	—	6	1	no	—
91	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
92	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
93	C₂²×C₃×C₈	—	2	1	no	—
94	C₂²×C₃×C₈	—	6	1	no	—
95	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
96	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
97	C₂×#208	C₂²×C₃	1	1	yes	characteristic
98	#909	—	2	4	no	—
99	#909	C₂²×C₃	1	8	yes	—
100	C₂×Dic₁₂	—	2	2	no	—
101	C₂×Dic₁₂	—	2	1	no	—
102	C₂×Dic₁₂	—	2	1	no	—
103	C₂×Dic₁₂	—	2	2	no	—
104	C₂×Dic₁₂	C₂²×C₃	1	4	yes	complemented
105	C₂×#204	—	2	2	no	—
106	#901	—	2	2	no	—
107	#901	C₂²×C₃	1	4	yes	—
108	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
109	C₂×D₃×C₈	—	2	1	no	—
110	C₃×#108	—	2	4	no	—
111	C₃×#108	C₂×D₃	1	4	yes	complemented
112	C₃×#108	C₂²×C₃	1	4	yes	complemented
113	C₃×#101	—	3	8	no	—
114	#824	C₂²×C₃	1	8	yes	complemented
115	C₂³×C₃²	#41	1	1	yes	characteristic
116	C₂²×C₃×D₃	—	2	1	no	—
117	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
118	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
120	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃²×C₄	#41	1	1	yes	characteristic
122	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
123	C₃×#67	—	2	2	no	—
124	C₃×#67	—	2	2	no	—
125	C₂×C₃×Dic₃	—	2	1	no	—
126	C₂×C₃×Dic₃	—	2	4	no	—
127	C₂×C₃×Dic₃	—	4	2	no	—
128	C₂×C₃×Dic₃	—	4	2	no	—
129	C₃×D₁₂	—	2	1	no	—
130	C₃×D₁₂	C₂×D₄	1	2	yes	—
131	C₃×C₄×D₃	—	2	2	no	—
132	C₃×C₄×D₃	—	2	2	no	—
133	C₃×Dic₆	—	2	1	no	—
134	C₃×Dic₆	—	2	4	no	—
135	C₃×Dic₆	—	2	4	no	—
136	C₃×Dic₆	—	4	2	no	—
137	C₃×Dic₆	—	4	2	no	—
138	C₃×Dic₆	C₂×D₄	1	2	yes	—
139	C₃²×C₈	—	2	4	no	—
140	C₃²×C₈	C₂×D₄	1	2	yes	—
141	C₃²×C₈	C₂×D₄	1	2	yes	—
142	C₃×C₃⋊C₈	—	2	2	no	—
143	C₂×#137	—	3	2	no	—
144	C₂²×Q₁₆	—	3	1	no	—
145	C₂×#131	—	3	1	no	—
146	#473	—	3	8	no	—
147	C₂×#108	C₃×D₃	1	1	yes	characteristic, complemented
148	C₂×#101	—	3	2	no	—
149	C₃×#41	—	3	2	no	—
150	C₃×#41	—	3	2	no	—
151	C₃×#41	—	6	1	no	—
152	C₃×#41	—	6	1	no	—
153	C₂×C₃×Q₈	—	3	1	no	—
154	C₂×C₃×Q₈	—	3	4	no	—
155	C₂×C₃×Q₈	—	6	2	no	—
156	C₂×C₃×Q₈	—	6	2	no	—
157	C₂×C₃×Q₈	—	6	2	no	—
158	C₂×C₃×Q₈	—	6	2	no	—
159	C₂×C₃×Q₈	—	6	2	no	—
160	C₂×C₃×D₄	—	3	1	no	—
161	C₂×C₃×D₄	—	6	1	no	—
162	C₂²×C₃×C₄	—	2	1	no	—
163	C₂²×C₃×C₄	—	6	1	no	—
164	C₂²×C₃×C₄	—	6	2	no	—
165	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
167	C₂×#67	—	2	1	no	—
168	C₂²×Dic₃	—	2	2	no	—
169	#235	—	2	1	no	—
170	#235	—	2	1	no	—
171	#235	C₃×D₄	1	2	yes	—
172	#235	C₂³×C₃	1	2	yes	—
173	C₂×D₁₂	C₃×D₄	1	1	yes	characteristic
174	C₂×C₄×D₃	—	2	1	no	—
175	C₂×Dic₆	—	2	2	no	—
176	C₂×Dic₆	—	2	2	no	—
177	C₂×Dic₆	—	2	2	no	—
178	C₂×Dic₆	—	2	2	no	—
179	C₂×Dic₆	—	2	2	no	—
180	C₂×Dic₆	C₃×D₄	1	1	yes	characteristic
181	C₂×Dic₆	C₂³×C₃	1	4	yes	—
182	C₃×Q₁₆	—	6	8	no	—
183	C₃×Q₁₆	—	6	4	no	—
184	C₃×Q₁₆	—	6	4	no	—
185	C₃×SD₁₆	—	6	8	no	—
186	C₃×M₁₆	—	2	2	no	—
187	C₃×M₁₆	—	2	2	no	—
188	C₃×M₁₆	—	2	4	no	—
189	C₃×M₁₆	—	3	2	no	—
190	C₃×M₁₆	—	4	2	no	—
191	C₃×M₁₆	—	6	1	no	—
192	C₃×M₁₆	—	6	4	no	—
193	C₃×M₁₆	C₂²×D₃	1	4	yes	—
194	C₃×M₁₆	C₂³×C₃	1	4	yes	—
195	C₂×C₃×C₈	—	2	2	no	—
196	C₂×C₃×C₈	—	2	2	no	—
197	C₂×C₃×C₈	—	2	1	no	—
198	C₂×C₃×C₈	—	2	1	no	—
199	C₂×C₃×C₈	—	2	2	no	—
200	C₂×C₃×C₈	—	2	2	no	—
201	C₂×C₃×C₈	—	4	2	no	—
202	C₂×C₃×C₈	—	6	1	no	—
203	C₂×C₃×C₈	—	6	4	no	—
204	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
205	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
206	C₂×C₃×C₈	D₁₂	1	2	yes	—
207	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
208	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
209	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
210	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
211	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
212	#208	—	2	1	no	—
213	#208	C₂³×C₃	1	2	yes	—
214	C₂×C₃⋊C₈	—	2	1	no	—
215	Dic₁₂	—	2	8	no	—
216	Dic₁₂	—	2	4	no	—
217	Dic₁₂	—	2	4	no	—
218	#204	—	2	8	no	—
219	ΓL(1,𝔽₂₅)	—	2	4	no	—
220	D₃×C₈	—	2	4	no	—
221	C₂²×C₃²	—	2	2	no	—
222	C₂²×C₃²	#121	1	1	yes	characteristic
223	C₂²×C₃²	#121	1	1	yes	characteristic
224	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
225	C₂×C₃×D₃	—	2	2	no	—
226	C₂×C₃×D₃	—	4	2	no	—
227	C₃²×C₄	#121	1	1	yes	characteristic
228	C₃²×C₄	#121	1	1	yes	characteristic
229	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
230	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
231	C₃×Dic₃	—	2	2	no	—
232	C₃×Dic₃	—	4	4	no	—
233	C₂×#41	—	3	1	no	—
234	C₂²×Q₈	—	3	2	no	—
235	#137	—	3	8	no	—
236	#137	—	6	4	no	—
237	C₂×Q₁₆	—	3	4	no	—
238	C₂×Q₁₆	—	6	2	no	—
239	C₂×Q₁₆	—	6	1	no	—
240	C₂×Q₁₆	—	6	1	no	—
241	C₂×Q₁₆	—	6	2	no	—
242	C₂×SD₁₆	—	6	2	no	—
243	#131	—	3	4	no	—
244	#131	—	6	2	no	—
245	C₂×M₁₆	—	3	1	no	—
246	C₂×M₁₆	—	6	1	no	—
247	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
248	C₂²×C₈	—	6	1	no	—
249	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
250	#108	C₂×C₃×D₃	1	4	yes	complemented
251	#101	—	3	8	no	—
252	C₂³×C₃	—	2	1	no	—
253	C₂³×C₃	—	6	1	no	—
254	C₂³×C₃	#239	1	1	yes	characteristic
255	C₂³×C₃	C₃×#41	1	1	yes	characteristic
256	C₂²×D₃	—	2	1	no	—
257	C₃×Q₈	—	3	2	no	—
258	C₃×Q₈	—	6	1	no	—
259	C₃×Q₈	—	6	4	no	—
260	C₃×Q₈	—	6	4	no	—
261	C₃×Q₈	—	12	2	no	—
262	C₃×Q₈	—	12	2	no	—
263	C₃×D₄	—	3	2	no	—
264	C₃×D₄	—	6	2	no	—
265	C₃×D₄	—	6	2	no	—
266	C₃×D₄	—	6	1	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	6	1	no	—
274	C₂×C₃×C₄	—	6	2	no	—
275	C₂×C₃×C₄	—	6	2	no	—
276	C₂×C₃×C₄	—	6	4	no	—
277	C₂×C₃×C₄	—	12	2	no	—
278	C₂×C₃×C₄	—	12	2	no	—
279	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
281	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
282	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
283	C₂×C₃×C₄	#239	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
291	#67	—	2	2	no	—
292	#67	—	2	2	no	—
293	C₂×Dic₃	—	2	1	no	—
294	C₂×Dic₃	—	2	4	no	—
295	C₂×Dic₃	—	4	2	no	—
296	C₂×Dic₃	—	4	2	no	—
297	D₁₂	—	2	1	no	—
298	D₁₂	C₂×C₃×D₄	1	2	yes	—
299	C₄×D₃	—	2	2	no	—
300	C₄×D₃	—	2	2	no	—
301	Dic₆	—	2	1	no	—
302	Dic₆	—	2	4	no	—
303	Dic₆	—	2	4	no	—
304	Dic₆	—	4	2	no	—
305	Dic₆	—	4	2	no	—
306	Dic₆	C₂×C₃×D₄	1	2	yes	—
307	C₃×C₈	—	2	4	no	—
308	C₃×C₈	—	2	4	no	—
309	C₃×C₈	—	2	2	no	—
310	C₃×C₈	—	2	2	no	—
311	C₃×C₈	—	4	4	no	—
312	C₃×C₈	—	6	2	no	—
313	C₃×C₈	C₂×D₁₂	1	2	yes	—
314	C₃×C₈	C₂×D₁₂	1	2	yes	—
315	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
316	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
317	C₃⋊C₈	—	2	2	no	—
318	C₂×C₃²	—	2	1	no	—
319	C₂×C₃²	—	2	1	no	—
320	C₂×C₃²	#473	1	2	yes	complemented
321	C₂×C₃²	C₂×#121	1	1	yes	characteristic
322	C₃×D₃	—	4	2	no	—
323	#41	—	3	2	no	—
324	#41	—	3	2	no	—
325	#41	—	6	1	no	—
326	#41	—	6	1	no	—
327	C₂×Q₈	—	3	4	no	—
328	C₂×Q₈	—	3	1	no	—
329	C₂×Q₈	—	6	2	no	—
330	C₂×Q₈	—	6	2	no	—
331	C₂×Q₈	—	6	2	no	—
332	C₂×Q₈	—	6	2	no	—
333	C₂×Q₈	—	6	2	no	—
334	C₂×D₄	—	3	1	no	—
335	C₂×D₄	—	6	1	no	—
336	C₂²×C₄	—	6	1	no	—
337	C₂²×C₄	—	6	2	no	—
338	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
339	Q₁₆	—	6	8	no	—
340	Q₁₆	—	6	4	no	—
341	Q₁₆	—	6	4	no	—
342	SD₁₆	—	6	8	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	3	2	no	—
345	M₁₆	—	6	1	no	—
346	M₁₆	—	6	4	no	—
347	M₁₆	C₂²×C₃×D₃	1	4	yes	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	6	1	no	—
350	C₂×C₈	—	6	4	no	—
351	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
352	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
353	C₂×C₈	C₃×D₁₂	1	2	yes	—
354	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
355	C₂²×C₃	—	2	2	no	—
356	C₂²×C₃	—	2	2	no	—
357	C₂²×C₃	—	2	1	no	—
358	C₂²×C₃	—	2	1	no	—
359	C₂²×C₃	—	2	1	no	—
360	C₂²×C₃	—	4	2	no	—
361	C₂²×C₃	—	6	2	no	—
362	C₂²×C₃	—	12	2	no	—
363	C₂²×C₃	#895	1	1	yes	characteristic
364	C₂²×C₃	#895	1	1	yes	characteristic
365	C₂²×C₃	C₃×#121	1	1	yes	characteristic
366	C₂²×C₃	C₃×#121	1	1	yes	characteristic
367	C₂²×C₃	C₂×#239	1	1	yes	characteristic
368	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
369	C₂×D₃	—	2	2	no	—
370	C₂×D₃	—	4	2	no	—
371	C₃×C₄	—	2	1	no	—
372	C₃×C₄	—	2	1	no	—
373	C₃×C₄	—	2	1	no	—
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	—	6	2	no	—
376	C₃×C₄	—	12	4	no	—
377	C₃×C₄	#895	1	1	yes	characteristic
378	C₃×C₄	#895	1	1	yes	characteristic
379	C₃×C₄	C₃×#121	1	1	yes	characteristic
380	C₃×C₄	C₃×#121	1	1	yes	characteristic
381	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
382	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
383	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
384	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
385	Dic₃	—	2	2	no	—
386	Dic₃	—	4	4	no	—
387	C₃²	C₂×#473	1	1	yes	characteristic, complemented, Sylow
388	C₂³	—	6	1	no	—
389	C₂³	C₃×#239	1	1	yes	characteristic
390	Q₈	—	3	2	no	—
391	Q₈	—	6	1	no	—
392	Q₈	—	6	4	no	—
393	Q₈	—	6	4	no	—
394	Q₈	—	12	2	no	—
395	Q₈	—	12	2	no	—
396	D₄	—	3	2	no	—
397	D₄	—	6	2	no	—
398	D₄	—	6	2	no	—
399	D₄	—	6	1	no	—
400	C₂×C₄	—	6	1	no	—
401	C₂×C₄	—	6	2	no	—
402	C₂×C₄	—	6	2	no	—
403	C₂×C₄	—	6	4	no	—
404	C₂×C₄	—	12	2	no	—
405	C₂×C₄	—	12	2	no	—
406	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
407	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
408	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
409	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
410	C₂×C₄	C₃×#239	1	1	yes	characteristic
411	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
412	C₈	—	2	4	no	—
413	C₈	—	6	2	no	—
414	C₈	C₂×C₃×D₁₂	1	2	yes	—
415	C₈	C₂×C₃×D₁₂	1	2	yes	—
416	C₂×C₃	—	2	1	no	—
417	C₂×C₃	—	2	1	no	—
418	C₂×C₃	—	2	1	no	—
419	C₂×C₃	—	2	1	no	—
420	C₂×C₃	—	2	1	no	—
421	C₂×C₃	—	2	2	no	—
422	C₂×C₃	—	4	1	no	—
423	C₂×C₃	—	4	1	no	—
424	C₂×C₃	—	12	2	no	—
425	C₂×C₃	#4896	1	2	yes	direct product factor
426	C₂×C₃	C₃×#473	1	2	yes	complemented
427	C₂×C₃	C₂×#895	1	1	yes	characteristic
428	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
429	D₃	—	4	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	6	2	no	—
432	C₂²	—	12	2	no	—
433	C₂²	C₃×#895	1	1	yes	characteristic
434	C₂²	C₃×#895	1	1	yes	characteristic
435	C₂²	C₂×C₃×#239	1	1	yes	characteristic
436	C₄	—	6	2	no	—
437	C₄	—	12	4	no	—
438	C₄	C₃×#895	1	1	yes	characteristic
439	C₄	C₃×#895	1	1	yes	characteristic
440	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
441	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
442	C₃	—	2	1	no	—
443	C₃	C₂×#4896	1	1	yes	characteristic, direct product factor
444	C₃	C₂×C₃×#473	1	1	yes	characteristic, complemented
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	12	2	no	—
448	C₂	C₃×#4896	1	2	yes	direct product factor
449	C₂	C₂×C₃×#895	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#895
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#108	C₂
socle	C₂²×C₃²	#121
prime radical	C₂×C₃×#235	C₂²
hypercenter	C₂×C₃×#108	D₃
hypocenter	C₃	C₂×C₃×#473
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#108

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×Dic₁₂	C₂	semidirect
4. C₂×C₃²×#108	C₂	semidirect
5. C₂×C₃×#824	C₂	semidirect
6. C₃×#4896	C₂	direct (N × H)
8. C₂×#4896	C₃	direct (N × H)
20. C₂×C₃×Dic₁₂	C₂²	semidirect
26. C₃²×#108	C₂²	semidirect
27. C₃×#824	C₂²	semidirect
32. C₂²×Dic₁₂	C₂×C₃	semidirect
36. C₂×C₃×#108	D₃	semidirect
37. C₂×C₃×#108	C₂×C₃	semidirect
39. C₂×#824	C₂×C₃	semidirect
40. #4896	C₂×C₃	direct (N × H)
104. C₂×Dic₁₂	C₂²×C₃	semidirect
111. C₃×#108	C₂×D₃	semidirect
112. C₃×#108	C₂²×C₃	semidirect
114. #824	C₂²×C₃	semidirect
147. C₂×#108	C₃×D₃	semidirect
250. #108	C₂×C₃×D₃	semidirect
320. C₂×C₃²	#473	semidirect
387. C₃²	C₂×#473	semidirect
425. C₂×C₃	#4896	direct (N × H)
426. C₂×C₃	C₃×#473	semidirect
443. C₃	C₂×#4896	direct (N × H)
444. C₃	C₂×C₃×#473	semidirect
448. C₂	C₃×#4896	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#909	2
C₂²×C₃×Dic₁₂	2
C₂×C₃×#901	2
C₂×C₃²×#108	2
C₂×C₃×#824	2
C₃×#4896	2
C₂×C₃×#473	3
C₂×#4896	3

Subgroups — C2×C3×#4896 #11867968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4896 #11867968