Subgroups — C₂×C₃×#4894 #11861039

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#907	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×#904	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#825	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#815	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4894	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#444	—	3	1	no	maximal
8	C₂×#4894	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃×#235	C₂²	1	2	yes	—
10	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₃×#907	—	2	4	no	—
15	C₃×#907	C₂²	1	8	yes	complemented
16	C₂×C₃×Dic₁₂	C₄	1	1	yes	characteristic, complemented
17	C₃×#904	C₄	1	4	yes	complemented
18	C₃×#904	C₂²	1	4	yes	—
19	C₂×C₃×D₂₄	C₄	1	1	yes	characteristic, complemented
20	C₂×C₃×#204	C₄	1	2	yes	complemented
21	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
22	C₂×C₃×D₃×C₈	—	2	2	no	—
23	C₃²×#108	C₂²	1	4	yes	complemented
24	C₃×#825	C₂²	1	8	yes	complemented
25	C₃×#815	C₂²	1	4	yes	complemented
26	C₂×C₃×#135	—	3	1	no	—
27	C₂×C₃×#131	—	3	2	no	—
28	C₂×#907	C₂×C₃	1	2	yes	complemented
29	C₂×#904	C₂×C₃	1	1	yes	characteristic
30	C₃×#444	—	3	8	no	—
31	C₂×C₃×#108	—	2	1	no	—
32	C₂×C₃×#108	D₃	1	1	yes	characteristic, complemented
33	C₂×C₃×#108	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₃×#104	—	3	2	no	—
35	C₂×C₃×#97	—	3	1	no	—
36	C₂×#825	C₂×C₃	1	2	yes	complemented
37	C₂×#815	C₂×C₃	1	1	yes	characteristic, complemented
38	#4894	C₂×C₃	1	8	yes	direct product factor
39	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
40	C₂×C₃×#67	—	2	2	no	—
41	C₂²×C₃×Dic₃	—	2	1	no	—
42	C₃×#235	—	2	2	no	—
43	C₃×#235	—	2	2	no	—
44	C₃×#235	C₂×C₄	1	4	yes	—
45	C₃×#235	C₂³	1	4	yes	—
46	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
47	C₂×C₃×C₄×D₃	—	2	2	no	—
48	C₂×C₃×Dic₆	C₂×C₄	1	2	yes	—
49	C₃²×M₁₆	—	2	2	no	—
50	C₃²×M₁₆	C₂³	1	4	yes	—
51	C₂×C₃²×C₈	—	2	2	no	—
52	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
53	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
54	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
55	C₂×C₃²×C₈	C₂³	1	2	yes	—
56	C₃×C₄×Dic₃	—	2	1	no	—
57	C₃×C₄×Dic₃	C₂³	1	2	yes	—
58	C₂×C₃×C₃⋊C₈	D₄	1	2	yes	—
59	C₂×C₃×C₃⋊C₈	D₄	1	2	yes	—
60	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
61	C₃×Dic₁₂	C₂×C₄	1	4	yes	complemented
62	C₃×D₂₄	C₂×C₄	1	4	yes	complemented
63	C₃×#204	C₂×C₄	1	8	yes	complemented
64	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
65	C₃×D₃×C₈	—	2	8	no	—
66	C₂×#444	—	3	1	no	Sylow
67	C₂×C₃×#41	—	3	2	no	—
68	C₂×#235	C₂²×C₃	1	2	yes	—
69	C₃×#135	—	3	4	no	—
70	C₃×#135	—	3	4	no	—
71	C₂×C₃×Q₁₆	—	3	1	no	—
72	C₂×C₃×SD₁₆	—	3	2	no	—
73	C₂×C₃×D₈	—	3	1	no	—
74	C₃×#131	—	3	8	no	—
75	C₃×#131	—	6	4	no	—
76	C₂×C₃×M₁₆	—	2	2	no	—
77	C₂×C₃×M₁₆	—	6	2	no	—
78	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
79	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
80	C₂²×C₃×C₈	—	2	1	no	—
81	C₂²×C₃×C₈	—	3	1	no	—
82	C₂²×C₃×C₈	—	6	2	no	—
83	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
84	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃×C₄²	—	3	1	no	—
86	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
87	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
88	#907	—	2	4	no	—
89	#907	C₂²×C₃	1	8	yes	complemented
90	C₂×Dic₁₂	C₃×C₄	1	1	yes	characteristic, complemented
91	#904	C₃×C₄	1	4	yes	complemented
92	#904	C₂²×C₃	1	4	yes	—
93	C₂×D₂₄	C₃×C₄	1	1	yes	characteristic, complemented
94	C₂×#204	C₃×C₄	1	2	yes	complemented
95	C₂×ΓL(1,𝔽₂₅)	—	2	2	no	—
96	C₂×D₃×C₈	—	2	2	no	—
97	C₃×#108	—	2	4	no	—
98	C₃×#108	C₂×D₃	1	4	yes	complemented
99	C₃×#108	C₂²×C₃	1	4	yes	complemented
100	C₃×#104	—	3	8	no	—
101	C₃×#97	—	3	4	no	—
102	#825	C₂²×C₃	1	8	yes	complemented
103	#815	C₂²×C₃	1	4	yes	complemented
104	C₂³×C₃²	#41	1	1	yes	characteristic
105	C₂²×C₃×D₃	—	2	2	no	—
106	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃²×C₄	#41	1	1	yes	characteristic
111	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
112	C₃×#67	—	2	4	no	—
113	C₃×#67	—	2	4	no	—
114	C₂×C₃×Dic₃	—	2	2	no	—
115	C₂×C₃×Dic₃	—	2	2	no	—
116	C₂×C₃×Dic₃	—	4	2	no	—
117	C₃×D₁₂	—	2	2	no	—
118	C₃×D₁₂	C₂²×C₄	1	4	yes	—
119	C₃×C₄×D₃	—	2	4	no	—
120	C₃×C₄×D₃	—	2	4	no	—
121	C₃×Dic₆	—	2	2	no	—
122	C₃×Dic₆	C₂²×C₄	1	4	yes	—
123	C₃²×C₈	—	2	4	no	—
124	C₃²×C₈	C₂²×C₄	1	2	yes	—
125	C₃²×C₈	C₂²×C₄	1	2	yes	—
126	C₃×C₃⋊C₈	C₂×D₄	1	4	yes	—
127	C₂×#135	—	3	1	no	—
128	C₂×#131	—	3	2	no	—
129	#444	—	3	8	no	—
130	C₂×#108	C₃×D₃	1	1	yes	characteristic, complemented
131	C₂×#104	—	3	2	no	—
132	C₂×#97	—	3	1	no	—
133	C₃×#41	—	3	4	no	—
134	C₃×#41	—	3	4	no	—
135	C₃×#41	—	6	2	no	—
136	C₃×#41	—	6	2	no	—
137	C₂×C₃×Q₈	—	3	2	no	—
138	C₂×C₃×D₄	—	3	2	no	—
139	C₂×C₃×D₄	—	6	2	no	—
140	C₂²×C₃×C₄	—	2	1	no	—
141	C₂²×C₃×C₄	—	6	2	no	—
142	C₂²×C₃×C₄	—	6	1	no	—
143	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
145	C₂×#67	—	2	2	no	—
146	C₂²×Dic₃	—	2	1	no	—
147	#235	—	2	2	no	—
148	#235	—	2	2	no	—
149	#235	C₂×C₃×C₄	1	4	yes	—
150	#235	C₂³×C₃	1	4	yes	—
151	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
152	C₂×C₄×D₃	—	2	2	no	—
153	C₂×Dic₆	C₂×C₃×C₄	1	2	yes	—
154	C₃×Q₁₆	—	3	4	no	—
155	C₃×SD₁₆	—	3	8	no	—
156	C₃×D₈	—	3	4	no	—
157	C₃×M₁₆	—	2	2	no	—
158	C₃×M₁₆	—	2	2	no	—
159	C₃×M₁₆	—	2	4	no	—
160	C₃×M₁₆	—	4	2	no	—
161	C₃×M₁₆	—	6	8	no	—
162	C₃×M₁₆	C₂²×D₃	1	4	yes	—
163	C₃×M₁₆	C₂³×C₃	1	4	yes	—
164	C₂×C₃×C₈	—	2	2	no	—
165	C₂×C₃×C₈	—	2	2	no	—
166	C₂×C₃×C₈	—	2	1	no	—
167	C₂×C₃×C₈	—	2	1	no	—
168	C₂×C₃×C₈	—	2	2	no	—
169	C₂×C₃×C₈	—	2	2	no	—
170	C₂×C₃×C₈	—	3	2	no	—
171	C₂×C₃×C₈	—	3	2	no	—
172	C₂×C₃×C₈	—	3	2	no	—
173	C₂×C₃×C₈	—	4	2	no	—
174	C₂×C₃×C₈	—	6	8	no	—
175	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
176	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
177	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
178	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
179	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
180	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
181	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
182	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
183	C₃×C₄²	—	3	2	no	—
184	C₃×C₄²	—	6	1	no	—
185	C₄×Dic₃	—	2	1	no	—
186	C₄×Dic₃	C₂³×C₃	1	2	yes	—
187	C₂×C₃⋊C₈	C₃×D₄	1	2	yes	—
188	C₂×C₃⋊C₈	C₃×D₄	1	2	yes	—
189	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
190	Dic₁₂	C₂×C₃×C₄	1	4	yes	complemented
191	D₂₄	C₂×C₃×C₄	1	4	yes	complemented
192	#204	C₂×C₃×C₄	1	8	yes	complemented
193	ΓL(1,𝔽₂₅)	—	2	8	no	—
194	D₃×C₈	—	2	8	no	—
195	C₂²×C₃²	—	2	2	no	—
196	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
197	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
198	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
199	C₂×C₃×D₃	—	2	4	no	—
200	C₂×C₃×D₃	—	4	4	no	—
201	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
202	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
203	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
204	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
205	C₃×Dic₃	—	2	4	no	—
206	C₃×Dic₃	—	4	2	no	—
207	C₂×#41	—	3	2	no	—
208	#135	—	3	4	no	—
209	#135	—	3	4	no	—
210	C₂×Q₁₆	—	3	1	no	—
211	C₂×SD₁₆	—	3	2	no	—
212	C₂×D₈	—	3	1	no	—
213	#131	—	3	8	no	—
214	#131	—	6	4	no	—
215	C₂×M₁₆	—	6	2	no	—
216	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
217	C₂²×C₈	—	3	1	no	—
218	C₂²×C₈	—	6	2	no	—
219	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
220	C₂×C₄²	—	3	1	no	—
221	#108	C₂×C₃×D₃	1	4	yes	complemented
222	#104	—	3	8	no	—
223	#97	—	3	4	no	—
224	C₂³×C₃	—	2	1	no	—
225	C₂³×C₃	—	6	2	no	—
226	C₂³×C₃	#239	1	1	yes	characteristic
227	C₂³×C₃	C₃×#41	1	1	yes	characteristic
228	C₂²×D₃	—	2	2	no	—
229	C₃×Q₈	—	3	4	no	—
230	C₃×Q₈	—	6	2	no	—
231	C₃×D₄	—	3	4	no	—
232	C₃×D₄	—	6	4	no	—
233	C₃×D₄	—	6	4	no	—
234	C₃×D₄	—	6	2	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	6	2	no	—
242	C₂×C₃×C₄	—	6	4	no	—
243	C₂×C₃×C₄	—	6	4	no	—
244	C₂×C₃×C₄	—	6	2	no	—
245	C₂×C₃×C₄	—	12	2	no	—
246	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
248	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
249	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
250	C₂×C₃×C₄	#239	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
255	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
258	#67	—	2	4	no	—
259	#67	—	2	4	no	—
260	C₂×Dic₃	—	2	2	no	—
261	C₂×Dic₃	—	2	2	no	—
262	C₂×Dic₃	—	4	2	no	—
263	D₁₂	—	2	2	no	—
264	D₁₂	C₂²×C₃×C₄	1	4	yes	—
265	C₄×D₃	—	2	4	no	—
266	C₄×D₃	—	2	4	no	—
267	Dic₆	—	2	2	no	—
268	Dic₆	C₂²×C₃×C₄	1	4	yes	—
269	C₃×C₈	—	2	4	no	—
270	C₃×C₈	—	2	4	no	—
271	C₃×C₈	—	2	2	no	—
272	C₃×C₈	—	2	2	no	—
273	C₃×C₈	—	3	4	no	—
274	C₃×C₈	—	4	4	no	—
275	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
276	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
277	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
278	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
279	C₃⋊C₈	C₂×C₃×D₄	1	4	yes	—
280	C₂×C₃²	—	2	1	no	—
281	C₂×C₃²	—	2	1	no	—
282	C₂×C₃²	#444	1	2	yes	complemented
283	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
284	C₃×D₃	—	4	4	no	—
285	#41	—	3	4	no	—
286	#41	—	3	4	no	—
287	#41	—	6	2	no	—
288	#41	—	6	2	no	—
289	C₂×Q₈	—	3	2	no	—
290	C₂×D₄	—	3	2	no	—
291	C₂×D₄	—	6	2	no	—
292	C₂²×C₄	—	6	2	no	—
293	C₂²×C₄	—	6	1	no	—
294	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
295	Q₁₆	—	3	4	no	—
296	SD₁₆	—	3	8	no	—
297	D₈	—	3	4	no	—
298	M₁₆	—	2	2	no	—
299	M₁₆	—	6	8	no	—
300	M₁₆	C₂²×C₃×D₃	1	4	yes	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	3	2	no	—
303	C₂×C₈	—	3	2	no	—
304	C₂×C₈	—	3	2	no	—
305	C₂×C₈	—	6	8	no	—
306	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
307	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
308	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
309	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
310	C₄²	—	3	2	no	—
311	C₄²	—	6	1	no	—
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	—	2	2	no	—
314	C₂²×C₃	—	2	1	no	—
315	C₂²×C₃	—	2	1	no	—
316	C₂²×C₃	—	2	1	no	—
317	C₂²×C₃	—	4	2	no	—
318	C₂²×C₃	—	6	4	no	—
319	C₂²×C₃	—	12	4	no	—
320	C₂²×C₃	#893	1	1	yes	characteristic
321	C₂²×C₃	#893	1	1	yes	characteristic
322	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
323	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
324	C₂²×C₃	C₂×#239	1	1	yes	characteristic
325	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
326	C₂×D₃	—	2	4	no	—
327	C₂×D₃	—	4	4	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	—	6	4	no	—
333	C₃×C₄	—	12	2	no	—
334	C₃×C₄	#893	1	1	yes	characteristic
335	C₃×C₄	#893	1	1	yes	characteristic
336	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
337	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
338	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
339	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
340	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
341	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
342	Dic₃	—	2	4	no	—
343	Dic₃	—	4	2	no	—
344	C₃²	C₂×#444	1	1	yes	characteristic, complemented, Sylow
345	C₂³	—	6	2	no	—
346	C₂³	C₃×#239	1	1	yes	characteristic
347	Q₈	—	3	4	no	—
348	Q₈	—	6	2	no	—
349	D₄	—	3	4	no	—
350	D₄	—	6	4	no	—
351	D₄	—	6	4	no	—
352	D₄	—	6	2	no	—
353	C₂×C₄	—	6	2	no	—
354	C₂×C₄	—	6	4	no	—
355	C₂×C₄	—	6	4	no	—
356	C₂×C₄	—	6	2	no	—
357	C₂×C₄	—	12	2	no	—
358	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
359	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
360	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
361	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
362	C₂×C₄	C₃×#239	1	1	yes	characteristic
363	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
364	C₈	—	2	4	no	—
365	C₈	—	3	4	no	—
366	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
367	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
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	—	2	2	no	—
374	C₂×C₃	—	4	1	no	—
375	C₂×C₃	—	4	1	no	—
376	C₂×C₃	—	12	4	no	—
377	C₂×C₃	#4894	1	2	yes	direct product factor
378	C₂×C₃	C₃×#444	1	2	yes	complemented
379	C₂×C₃	C₂×#893	1	1	yes	characteristic
380	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
381	D₃	—	4	4	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	6	4	no	—
384	C₂²	—	12	4	no	—
385	C₂²	C₃×#893	1	1	yes	characteristic
386	C₂²	C₃×#893	1	1	yes	characteristic
387	C₂²	C₂×C₃×#239	1	1	yes	characteristic
388	C₄	—	6	4	no	—
389	C₄	—	12	2	no	—
390	C₄	C₃×#893	1	1	yes	characteristic
391	C₄	C₃×#893	1	1	yes	characteristic
392	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
393	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
394	C₃	—	2	1	no	—
395	C₃	C₂×#4894	1	1	yes	characteristic, direct product factor
396	C₃	C₂×C₃×#444	1	1	yes	characteristic, complemented
397	C₂	—	2	1	no	—
398	C₂	—	2	1	no	—
399	C₂	—	12	4	no	—
400	C₂	C₃×#4894	1	2	yes	direct product factor
401	C₂	C₂×C₃×#893	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#108	C₂
socle	C₂²×C₃²	C₄×D₄
prime radical	C₂×C₃×#904	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#108	D₃
hypocenter	C₃	C₂×C₃×#444
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#108

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#907	C₂	semidirect
3. C₂×C₃²×#108	C₂	semidirect
4. C₂×C₃×#825	C₂	semidirect
5. C₂×C₃×#815	C₂	semidirect
6. C₃×#4894	C₂	direct (N × H)
8. C₂×#4894	C₃	direct (N × H)
15. C₃×#907	C₂²	semidirect
16. C₂×C₃×Dic₁₂	C₄	semidirect
17. C₃×#904	C₄	semidirect
19. C₂×C₃×D₂₄	C₄	semidirect
20. C₂×C₃×#204	C₄	semidirect
23. C₃²×#108	C₂²	semidirect
24. C₃×#825	C₂²	semidirect
25. C₃×#815	C₂²	semidirect
28. C₂×#907	C₂×C₃	semidirect
32. C₂×C₃×#108	D₃	semidirect
33. C₂×C₃×#108	C₂×C₃	semidirect
36. C₂×#825	C₂×C₃	semidirect
37. C₂×#815	C₂×C₃	semidirect
38. #4894	C₂×C₃	direct (N × H)
61. C₃×Dic₁₂	C₂×C₄	semidirect
62. C₃×D₂₄	C₂×C₄	semidirect
63. C₃×#204	C₂×C₄	semidirect
89. #907	C₂²×C₃	semidirect
90. C₂×Dic₁₂	C₃×C₄	semidirect
91. #904	C₃×C₄	semidirect
93. C₂×D₂₄	C₃×C₄	semidirect
94. C₂×#204	C₃×C₄	semidirect
98. C₃×#108	C₂×D₃	semidirect
99. C₃×#108	C₂²×C₃	semidirect
102. #825	C₂²×C₃	semidirect
103. #815	C₂²×C₃	semidirect
130. C₂×#108	C₃×D₃	semidirect
190. Dic₁₂	C₂×C₃×C₄	semidirect
191. D₂₄	C₂×C₃×C₄	semidirect
192. #204	C₂×C₃×C₄	semidirect
221. #108	C₂×C₃×D₃	semidirect
282. C₂×C₃²	#444	semidirect
344. C₃²	C₂×#444	semidirect
377. C₂×C₃	#4894	direct (N × H)
378. C₂×C₃	C₃×#444	semidirect
395. C₃	C₂×#4894	direct (N × H)
396. C₃	C₂×C₃×#444	semidirect
400. C₂	C₃×#4894	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×#907	2
C₂×C₃×#904	2
C₂×C₃²×#108	2
C₂×C₃×#825	2
C₂×C₃×#815	2
C₃×#4894	2
C₂×C₃×#444	3
C₂×#4894	3

Subgroups — C2×C3×#4894 #11861039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4894 #11861039