Subgroups — C₂×C₃×#4883 #11866739

Order 1152.

1297 conjugacy classes of subgroups.

The subgroup lattice has 415 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#895	C₂	1	2	yes	maximal, complemented
4	C₂×C₃²×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#809	C₂	1	2	yes	maximal, complemented
6	C₃×#4883	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#466	—	3	1	no	maximal
8	C₂×#4883	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×D₁₂	—	2	2	no	—
10	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
11	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
15	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×D₂₄	—	2	4	no	—
17	C₂×C₃×D₂₄	C₂²	1	4	yes	complemented
18	C₂×C₃×D₃×C₈	—	2	4	no	—
19	C₂×C₃×D₃×C₈	C₂²	1	4	yes	complemented
20	C₃×#895	—	2	4	no	—
21	C₃×#895	C₂²	1	8	yes	complemented
22	C₃²×#107	C₂²	1	4	yes	complemented
23	C₃×#809	C₂²	1	8	yes	complemented
24	C₂²×C₃×D₈	—	3	1	no	—
25	C₂³×C₃×C₈	—	3	1	no	—
26	C₂×C₃×#121	—	3	2	no	—
27	C₂²×D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂²×D₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×#895	C₂×C₃	1	2	yes	complemented
30	C₃×#466	—	3	8	no	—
31	C₂×C₃×#107	—	2	1	no	—
32	C₂×C₃×#107	D₃	1	1	yes	characteristic, complemented
33	C₂×C₃×#107	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₃×#102	—	3	2	no	—
35	C₂×#809	C₂×C₃	1	2	yes	complemented
36	#4883	C₂×C₃	1	8	yes	direct product factor
37	C₂³×C₃×D₃	—	2	2	no	—
38	C₂³×C₃×D₃	D₄	1	1	yes	characteristic
39	C₂²×C₃²×C₄	—	2	2	no	—
40	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
41	C₂²×C₃×Dic₃	D₄	1	1	yes	characteristic
42	C₂×C₃×D₁₂	—	2	4	no	—
43	C₂×C₃×D₁₂	—	2	4	no	—
44	C₂×C₃×D₁₂	—	2	8	no	—
45	C₂×C₃×D₁₂	—	2	2	no	—
46	C₂×C₃×D₁₂	—	4	8	no	—
47	C₂×C₃×D₁₂	C₂³	1	4	yes	—
48	C₂×C₃×C₄×D₃	—	2	2	no	—
49	C₂×C₃×C₄×D₃	—	2	2	no	—
50	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
51	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
52	C₂×C₃²×C₈	D₄	1	4	yes	complemented
53	C₂×C₃²×C₈	C₂³	1	2	yes	—
54	C₃²×C₄⋊C₄	—	2	2	no	—
55	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
56	C₃×(C₂×D₃)⋊C₄	—	2	8	no	—
57	C₂×C₃×C₃⋊C₈	—	2	2	no	—
58	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
59	C₃×D₂₄	—	2	8	no	—
60	C₃×D₃×C₈	—	2	8	no	—
61	C₂×#466	—	3	1	no	Sylow
62	C₂²×C₃×D₄	—	3	2	no	—
63	C₂²×C₃×D₄	—	6	2	no	—
64	C₂³×C₃×C₄	—	3	1	no	—
65	C₂²×D₁₂	—	2	2	no	—
66	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
67	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₃×D₈	—	3	4	no	—
69	C₂×C₃×D₈	—	6	4	no	—
70	C₂²×C₃×C₈	—	2	1	no	—
71	C₂²×C₃×C₈	—	3	1	no	—
72	C₂²×C₃×C₈	—	3	4	no	—
73	C₂²×C₃×C₈	—	6	4	no	—
74	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
75	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
76	C₃×#121	—	3	8	no	—
77	C₃×#121	—	6	4	no	—
78	C₂×C₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
80	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
82	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
83	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
84	C₂×D₂₄	—	2	4	no	—
85	C₂×D₂₄	C₂²×C₃	1	4	yes	complemented
86	C₂×D₃×C₈	—	2	4	no	—
87	C₂×D₃×C₈	C₂²×C₃	1	4	yes	complemented
88	#895	—	2	4	no	—
89	#895	C₂²×C₃	1	8	yes	complemented
90	C₃×#107	—	2	4	no	—
91	C₃×#107	C₂×D₃	1	4	yes	complemented
92	C₃×#107	C₂²×C₃	1	4	yes	complemented
93	C₃×#102	—	3	8	no	—
94	#809	C₂²×C₃	1	8	yes	complemented
95	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₃×D₃	—	2	2	no	—
97	C₂²×C₃×D₃	—	2	2	no	—
98	C₂²×C₃×D₃	—	2	4	no	—
99	C₂²×C₃×D₃	—	4	4	no	—
100	C₂²×C₃×D₃	—	4	4	no	—
101	C₂²×C₃×D₃	—	4	4	no	—
102	C₂²×C₃×D₃	D₈	1	4	yes	complemented
103	C₂²×C₃×D₃	C₂×D₄	1	2	yes	—
104	C₂×C₃²×C₄	—	2	4	no	—
105	C₂×C₃²×C₄	—	4	4	no	—
106	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
107	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃²×C₄	#41	1	2	yes	—
109	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
110	C₂×C₃×Dic₃	—	2	2	no	—
111	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
112	C₃×D₁₂	—	2	4	no	—
113	C₃×D₁₂	—	2	4	no	—
114	C₃×D₁₂	—	4	16	no	—
115	C₃×D₁₂	—	4	4	no	—
116	C₃×C₄×D₃	—	2	4	no	—
117	C₃×C₄×D₃	—	2	2	no	—
118	C₃×C₄×D₃	—	2	2	no	—
119	C₃²×C₈	C₂×D₄	1	4	yes	complemented
120	C₃×C₃⋊C₈	—	2	2	no	—
121	C₂²×D₈	—	3	1	no	—
122	C₂³×C₈	—	3	1	no	—
123	C₂×#121	—	3	2	no	—
124	#466	—	3	8	no	—
125	C₂×#107	C₃×D₃	1	1	yes	characteristic, complemented
126	C₂×#102	—	3	2	no	—
127	C₂⁴×C₃	—	3	1	no	—
128	C₂⁴×C₃	—	6	2	no	—
129	C₂³×D₃	—	2	2	no	—
130	C₂³×D₃	C₃×D₄	1	1	yes	characteristic
131	C₂×C₃×D₄	—	3	4	no	—
132	C₂×C₃×D₄	—	6	8	no	—
133	C₂×C₃×D₄	—	6	4	no	—
134	C₂×C₃×D₄	—	6	2	no	—
135	C₂×C₃×D₄	—	6	4	no	—
136	C₂×C₃×D₄	—	12	8	no	—
137	C₂²×C₃×C₄	—	2	2	no	—
138	C₂²×C₃×C₄	—	2	2	no	—
139	C₂²×C₃×C₄	—	2	1	no	—
140	C₂²×C₃×C₄	—	3	1	no	—
141	C₂²×C₃×C₄	—	3	2	no	—
142	C₂²×C₃×C₄	—	3	2	no	—
143	C₂²×C₃×C₄	—	4	2	no	—
144	C₂²×C₃×C₄	—	6	2	no	—
145	C₂²×C₃×C₄	—	6	2	no	—
146	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
147	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
148	C₂²×Dic₃	C₃×D₄	1	1	yes	characteristic
149	C₂×D₁₂	—	2	4	no	—
150	C₂×D₁₂	—	2	4	no	—
151	C₂×D₁₂	—	2	8	no	—
152	C₂×D₁₂	—	2	2	no	—
153	C₂×D₁₂	—	4	8	no	—
154	C₂×D₁₂	C₂³×C₃	1	4	yes	—
155	C₂×C₄×D₃	—	2	2	no	—
156	C₂×C₄×D₃	—	2	2	no	—
157	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
158	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
159	C₃×D₈	—	6	8	no	—
160	C₂×C₃×C₈	—	2	4	no	—
161	C₂×C₃×C₈	—	2	2	no	—
162	C₂×C₃×C₈	—	3	2	no	—
163	C₂×C₃×C₈	—	6	2	no	—
164	C₂×C₃×C₈	—	6	8	no	—
165	C₂×C₃×C₈	D₁₂	1	4	yes	complemented
166	C₂×C₃×C₈	C₃×D₄	1	4	yes	complemented
167	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
168	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
169	C₃×C₄⋊C₄	—	2	2	no	—
170	C₃×C₄⋊C₄	—	2	2	no	—
171	C₃×C₄⋊C₄	—	2	4	no	—
172	C₃×C₄⋊C₄	—	4	2	no	—
173	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
174	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
175	C₃×C₂²⋊C₄	—	6	8	no	—
176	(C₂×D₃)⋊C₄	—	2	8	no	—
177	C₂×C₃⋊C₈	—	2	2	no	—
178	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
179	D₂₄	—	2	8	no	—
180	D₃×C₈	—	2	8	no	—
181	C₂²×C₃²	#121	1	2	yes	—
182	C₂²×C₃²	C₂×D₈	1	2	yes	—
183	C₂²×C₃²	#135	1	2	yes	—
184	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₃×D₃	—	2	2	no	—
186	C₂×C₃×D₃	—	2	2	no	—
187	C₂×C₃×D₃	—	2	8	no	—
188	C₂×C₃×D₃	—	4	4	no	—
189	C₂×C₃×D₃	—	4	4	no	—
190	C₂×C₃×D₃	—	4	4	no	—
191	C₂×C₃×D₃	—	8	8	no	—
192	C₂×C₃×D₃	C₂×D₈	1	4	yes	complemented
193	C₃²×C₄	—	4	4	no	—
194	C₃²×C₄	#121	1	2	yes	—
195	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
196	C₃²×C₄	C₂×#41	1	1	yes	characteristic
197	C₃×Dic₃	—	2	2	no	—
198	C₂²×D₄	—	3	2	no	—
199	C₂²×D₄	—	6	2	no	—
200	C₂³×C₄	—	3	1	no	—
201	C₂×D₈	—	3	4	no	—
202	C₂×D₈	—	6	4	no	—
203	C₂²×C₈	—	3	1	no	—
204	C₂²×C₈	—	3	4	no	—
205	C₂²×C₈	—	6	4	no	—
206	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
207	#121	—	3	8	no	—
208	#121	—	6	4	no	—
209	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
210	C₂×C₂²⋊C₄	—	6	2	no	—
211	#107	C₂×C₃×D₃	1	4	yes	complemented
212	#102	—	3	8	no	—
213	C₂³×C₃	—	2	1	no	—
214	C₂³×C₃	—	3	4	no	—
215	C₂³×C₃	—	3	2	no	—
216	C₂³×C₃	—	6	2	no	—
217	C₂³×C₃	—	6	2	no	—
218	C₂³×C₃	—	6	4	no	—
219	C₂³×C₃	—	12	4	no	—
220	C₂³×C₃	—	12	4	no	—
221	C₂³×C₃	—	12	4	no	—
222	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
223	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
224	C₂²×D₃	—	2	2	no	—
225	C₂²×D₃	—	2	2	no	—
226	C₂²×D₃	—	2	4	no	—
227	C₂²×D₃	—	4	4	no	—
228	C₂²×D₃	—	4	4	no	—
229	C₂²×D₃	—	4	4	no	—
230	C₂²×D₃	C₃×D₈	1	4	yes	complemented
231	C₂²×D₃	C₂×C₃×D₄	1	2	yes	—
232	C₃×D₄	—	6	4	no	—
233	C₃×D₄	—	6	4	no	—
234	C₃×D₄	—	12	16	no	—
235	C₃×D₄	—	12	4	no	—
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	2	4	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	3	2	no	—
243	C₂×C₃×C₄	—	4	4	no	—
244	C₂×C₃×C₄	—	4	4	no	—
245	C₂×C₃×C₄	—	4	4	no	—
246	C₂×C₃×C₄	—	6	2	no	—
247	C₂×C₃×C₄	—	6	4	no	—
248	C₂×C₃×C₄	—	6	2	no	—
249	C₂×C₃×C₄	—	6	2	no	—
250	C₂×C₃×C₄	—	8	4	no	—
251	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
252	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
253	C₂×C₃×C₄	#239	1	2	yes	—
254	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
255	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
256	C₂×C₃×C₄	C₃×#41	1	2	yes	—
257	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
259	C₂×Dic₃	—	2	2	no	—
260	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
261	D₁₂	—	2	4	no	—
262	D₁₂	—	2	4	no	—
263	D₁₂	—	4	16	no	—
264	D₁₂	—	4	4	no	—
265	C₄×D₃	—	2	4	no	—
266	C₄×D₃	—	2	2	no	—
267	C₄×D₃	—	2	2	no	—
268	C₃×C₈	—	2	4	no	—
269	C₃×C₈	—	6	2	no	—
270	C₃×C₈	C₂×D₁₂	1	4	yes	complemented
271	C₃×C₈	C₂×C₃×D₄	1	4	yes	complemented
272	C₃⋊C₈	—	2	2	no	—
273	C₂×C₃²	#466	1	4	yes	complemented
274	C₂×C₃²	C₂×#121	1	1	yes	characteristic
275	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
276	C₂×C₃²	C₂×#135	1	1	yes	characteristic
277	C₃×D₃	—	2	4	no	—
278	C₃×D₃	—	8	4	no	—
279	C₂⁴	—	3	1	no	—
280	C₂⁴	—	6	2	no	—
281	C₂×D₄	—	3	4	no	—
282	C₂×D₄	—	6	8	no	—
283	C₂×D₄	—	6	4	no	—
284	C₂×D₄	—	6	2	no	—
285	C₂×D₄	—	6	4	no	—
286	C₂×D₄	—	12	8	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	3	1	no	—
289	C₂²×C₄	—	3	2	no	—
290	C₂²×C₄	—	3	2	no	—
291	C₂²×C₄	—	6	2	no	—
292	C₂²×C₄	—	6	2	no	—
293	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
294	D₈	—	6	8	no	—
295	C₂×C₈	—	3	2	no	—
296	C₂×C₈	—	6	2	no	—
297	C₂×C₈	—	6	8	no	—
298	C₂×C₈	C₃×D₁₂	1	4	yes	complemented
299	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
302	C₂²⋊C₄	—	6	8	no	—
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	2	1	no	—
307	C₂²×C₃	—	3	4	no	—
308	C₂²×C₃	—	6	8	no	—
309	C₂²×C₃	—	6	2	no	—
310	C₂²×C₃	—	6	2	no	—
311	C₂²×C₃	—	12	4	no	—
312	C₂²×C₃	—	12	4	no	—
313	C₂²×C₃	—	12	4	no	—
314	C₂²×C₃	—	24	8	no	—
315	C₂²×C₃	#895	1	2	yes	—
316	C₂²×C₃	D₃×D₈	1	2	yes	—
317	C₂²×C₃	#919	1	2	yes	—
318	C₂²×C₃	C₃×#121	1	2	yes	—
319	C₂²×C₃	C₂×C₃×D₈	1	2	yes	—
320	C₂²×C₃	C₃×#135	1	2	yes	—
321	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
322	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
323	C₂×D₃	—	2	2	no	—
324	C₂×D₃	—	2	8	no	—
325	C₂×D₃	—	2	2	no	—
326	C₂×D₃	—	4	4	no	—
327	C₂×D₃	—	4	4	no	—
328	C₂×D₃	—	4	4	no	—
329	C₂×D₃	—	8	8	no	—
330	C₂×D₃	C₂×C₃×D₈	1	4	yes	complemented
331	C₃×C₄	—	2	2	no	—
332	C₃×C₄	—	2	1	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	4	4	no	—
335	C₃×C₄	—	4	4	no	—
336	C₃×C₄	—	6	2	no	—
337	C₃×C₄	—	8	4	no	—
338	C₃×C₄	#895	1	2	yes	—
339	C₃×C₄	C₃×#121	1	2	yes	—
340	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
341	C₃×C₄	C₂×#239	1	1	yes	characteristic
342	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
343	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
344	Dic₃	—	2	2	no	—
345	C₃²	C₂×#466	1	1	yes	characteristic, complemented, Sylow
346	C₂³	—	3	4	no	—
347	C₂³	—	3	2	no	—
348	C₂³	—	6	2	no	—
349	C₂³	—	6	2	no	—
350	C₂³	—	6	4	no	—
351	C₂³	—	12	4	no	—
352	C₂³	—	12	4	no	—
353	C₂³	—	12	4	no	—
354	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
355	D₄	—	6	4	no	—
356	D₄	—	6	4	no	—
357	D₄	—	12	16	no	—
358	D₄	—	12	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	3	2	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	6	2	no	—
363	C₂×C₄	—	6	4	no	—
364	C₂×C₄	—	6	2	no	—
365	C₂×C₄	—	6	2	no	—
366	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
367	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
368	C₂×C₄	C₃×#239	1	2	yes	—
369	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
370	C₈	—	6	2	no	—
371	C₈	C₂×C₃×D₁₂	1	4	yes	complemented
372	C₂×C₃	—	2	1	no	—
373	C₂×C₃	—	2	1	no	—
374	C₂×C₃	—	2	1	no	—
375	C₂×C₃	—	2	4	no	—
376	C₂×C₃	—	6	4	no	—
377	C₂×C₃	—	24	4	no	—
378	C₂×C₃	#4883	1	4	yes	direct product factor
379	C₂×C₃	C₃×#466	1	4	yes	complemented
380	C₂×C₃	C₂×#895	1	1	yes	characteristic
381	C₂×C₃	C₂×D₃×D₈	1	1	yes	characteristic
382	C₂×C₃	C₂×#919	1	1	yes	characteristic
383	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
384	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
385	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
386	D₃	—	2	4	no	—
387	D₃	—	8	4	no	—
388	C₂²	—	3	4	no	—
389	C₂²	—	6	2	no	—
390	C₂²	—	6	2	no	—
391	C₂²	—	6	8	no	—
392	C₂²	—	12	4	no	—
393	C₂²	—	12	4	no	—
394	C₂²	—	12	4	no	—
395	C₂²	—	24	8	no	—
396	C₂²	C₃×#895	1	2	yes	—
397	C₂²	C₃×D₃×D₈	1	2	yes	—
398	C₂²	C₃×#919	1	2	yes	—
399	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
400	C₄	—	4	4	no	—
401	C₄	—	6	2	no	—
402	C₄	C₃×#895	1	2	yes	—
403	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
404	C₄	C₂×C₃×#239	1	1	yes	characteristic
405	C₃	—	2	1	no	—
406	C₃	C₂×#4883	1	1	yes	characteristic, direct product factor
407	C₃	C₂×C₃×#466	1	1	yes	characteristic, complemented
408	C₂	—	6	4	no	—
409	C₂	—	24	4	no	—
410	C₂	C₃×#4883	1	4	yes	direct product factor
411	C₂	C₂×C₃×#895	1	1	yes	characteristic
412	C₂	C₂×C₃×D₃×D₈	1	1	yes	characteristic
413	C₂	C₂×C₃×#919	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#107	C₂
socle	C₂³×C₃²	C₂×D₄
hypercenter	C₂×C₃×#107	D₃
hypocenter	C₃	C₂×C₃×#466
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#107

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₂₄	C₂	semidirect
2. C₂²×C₃×D₃×C₈	C₂	semidirect
3. C₂×C₃×#895	C₂	semidirect
4. C₂×C₃²×#107	C₂	semidirect
5. C₂×C₃×#809	C₂	semidirect
6. C₃×#4883	C₂	direct (N × H)
8. C₂×#4883	C₃	direct (N × H)
17. C₂×C₃×D₂₄	C₂²	semidirect
19. C₂×C₃×D₃×C₈	C₂²	semidirect
21. C₃×#895	C₂²	semidirect
22. C₃²×#107	C₂²	semidirect
23. C₃×#809	C₂²	semidirect
27. C₂²×D₂₄	C₂×C₃	semidirect
28. C₂²×D₃×C₈	C₂×C₃	semidirect
29. C₂×#895	C₂×C₃	semidirect
32. C₂×C₃×#107	D₃	semidirect
33. C₂×C₃×#107	C₂×C₃	semidirect
35. C₂×#809	C₂×C₃	semidirect
36. #4883	C₂×C₃	direct (N × H)
52. C₂×C₃²×C₈	D₄	semidirect
85. C₂×D₂₄	C₂²×C₃	semidirect
87. C₂×D₃×C₈	C₂²×C₃	semidirect
89. #895	C₂²×C₃	semidirect
91. C₃×#107	C₂×D₃	semidirect
92. C₃×#107	C₂²×C₃	semidirect
94. #809	C₂²×C₃	semidirect
102. C₂²×C₃×D₃	D₈	semidirect
119. C₃²×C₈	C₂×D₄	semidirect
125. C₂×#107	C₃×D₃	semidirect
165. C₂×C₃×C₈	D₁₂	semidirect
166. C₂×C₃×C₈	C₃×D₄	semidirect
192. C₂×C₃×D₃	C₂×D₈	semidirect
211. #107	C₂×C₃×D₃	semidirect
230. C₂²×D₃	C₃×D₈	semidirect
270. C₃×C₈	C₂×D₁₂	semidirect
271. C₃×C₈	C₂×C₃×D₄	semidirect
273. C₂×C₃²	#466	semidirect
298. C₂×C₈	C₃×D₁₂	semidirect
330. C₂×D₃	C₂×C₃×D₈	semidirect
345. C₃²	C₂×#466	semidirect
371. C₈	C₂×C₃×D₁₂	semidirect
378. C₂×C₃	#4883	direct (N × H)
379. C₂×C₃	C₃×#466	semidirect
406. C₃	C₂×#4883	direct (N × H)
407. C₃	C₂×C₃×#466	semidirect
410. C₂	C₃×#4883	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₂₄	2
C₂²×C₃×D₃×C₈	2
C₂×C₃×#895	2
C₂×C₃²×#107	2
C₂×C₃×#809	2
C₃×#4883	2
C₂×C₃×#466	3
C₂×#4883	3

Subgroups — C2×C3×#4883 #11866739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4883 #11866739