Subgroups — C₂×D₃×#819 #11858620

Order 1152.

1013 conjugacy classes of subgroups.

The subgroup lattice has 437 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×D₃×#208	C₂	1	2	yes	maximal
3	C₂×#63646	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#63577	C₂	1	2	yes	maximal, complemented
6	D₃×#819	C₂	1	8	yes	maximal, direct product factor
7	C₂²×#819	—	3	1	no	maximal
8	C₂×D₃×#108	—	3	1	no	maximal
9	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
10	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
11	C₂×#3748	C₂²	1	2	yes	—
12	C₂×C₃×#208	C₂²	1	2	yes	—
13	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₃×C₈	C₄	1	2	yes	—
15	C₂×C₃×D₃×C₈	C₄	1	4	yes	—
16	C₂×C₃×D₃×C₈	C₄	1	2	yes	—
17	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
18	C₂×#3711	—	2	2	no	—
19	D₃×#208	—	2	4	no	—
20	D₃×#208	C₂²	1	8	yes	—
21	C₂×D₃×C₃⋊C₈	—	2	2	no	—
22	#63646	C₂²	1	4	yes	complemented
23	C₃×#819	C₂²	1	4	yes	complemented
24	#63577	C₂²	1	8	yes	complemented
25	C₂³×C₃×C₈	—	3	1	no	—
26	C₂²×#208	—	3	2	no	—
27	C₂×D₃×M₁₆	—	3	2	no	—
28	C₂²×D₃×C₈	D₃	1	1	yes	characteristic
29	C₂×C₃×#108	—	3	1	no	—
30	C₂×#822	—	3	2	no	—
31	C₂×#819	—	3	1	no	—
32	C₂×#819	—	3	1	no	—
33	C₂×#819	—	3	2	no	—
34	C₂×#819	—	3	8	no	—
35	C₂×#819	—	6	1	no	—
36	C₂×#819	D₃	1	1	yes	characteristic, direct product factor
37	D₃×#108	—	3	8	no	—
38	C₂³×C₃×D₃	Q₈	1	1	yes	characteristic
39	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
40	C₂²×C₃×Dic₃	Q₈	1	1	yes	characteristic
41	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
45	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
46	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
47	C₂×C₃×C₄×D₃	Q₈	1	2	yes	—
48	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
49	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
50	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
51	C₂×C₃²×C₈	C₂³	1	2	yes	—
52	#3748	—	2	2	no	—
53	#3748	C₂³	1	4	yes	—
54	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
55	C₃×#208	—	2	2	no	—
56	C₃×#208	C₂³	1	4	yes	—
57	C₂×C₃×C₃⋊C₈	—	2	2	no	—
58	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
59	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
60	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
61	C₃×D₃×C₈	C₂×C₄	1	8	yes	—
62	C₃×D₃×C₈	C₂×C₄	1	8	yes	—
63	#3711	—	2	8	no	—
64	D₃×C₃⋊C₈	—	2	8	no	—
65	C₂²×#108	—	9	1	no	Sylow
66	C₂³×C₃×C₄	—	3	1	no	—
67	C₂²×C₄×D₃	C₂×D₃	1	1	yes	characteristic
68	C₂×C₃×M₁₆	—	3	2	no	—
69	C₂²×C₃×C₈	—	2	1	no	—
70	C₂²×C₃×C₈	—	3	1	no	—
71	C₂²×C₃×C₈	—	3	2	no	—
72	C₂²×C₃×C₈	—	3	4	no	—
73	C₂²×C₃×C₈	—	3	2	no	—
74	C₂²×C₃×C₈	—	3	4	no	—
75	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
76	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
77	C₂×#208	—	3	2	no	—
78	C₂×#208	—	3	2	no	—
79	C₂×#208	—	3	8	no	—
80	C₂×#208	—	6	2	no	—
81	C₂×#208	—	6	2	no	—
82	C₂×#208	—	6	4	no	—
83	C₂×#208	C₂×D₃	1	2	yes	—
84	C₂²×C₃⋊C₈	—	6	2	no	—
85	C₂²×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
86	D₃×M₁₆	—	3	8	no	—
87	D₃×M₁₆	—	6	4	no	—
88	C₂×ΓL(1,𝔽₂₅)	—	6	2	no	—
89	C₂×D₃×C₈	—	6	2	no	—
90	C₂×D₃×C₈	Dic₃	1	2	yes	—
91	C₂×D₃×C₈	Dic₃	1	4	yes	—
92	C₂×D₃×C₈	Dic₃	1	2	yes	—
93	C₂×D₃×C₈	C₂×D₃	1	4	yes	—
94	C₃×#108	—	3	4	no	—
95	#822	—	3	8	no	—
96	#819	—	3	4	no	—
97	#819	—	3	4	no	—
98	#819	—	3	8	no	—
99	#819	—	6	4	no	—
100	#819	C₂×D₃	1	4	yes	direct product factor
101	C₂³×C₃²	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₃×D₃	—	2	4	no	—
103	C₂²×C₃×D₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×C₃×D₃	C₄⋊C₄	1	2	yes	—
105	C₂²×C₃×D₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂²×C₃×D₃	C₂×Q₈	1	2	yes	—
107	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
112	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
113	C₂×C₃×Dic₃	C₄⋊C₄	1	2	yes	—
114	C₂×C₃×Dic₃	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₃×Dic₃	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₃×Dic₃	C₂×Q₈	1	2	yes	—
117	C₃×C₄×D₃	C₄⋊C₄	1	2	yes	—
118	C₃×C₄×D₃	C₄⋊C₄	1	2	yes	—
119	C₃×C₄×D₃	C₄⋊C₄	1	2	yes	—
120	C₃×C₄×D₃	C₄⋊C₄	1	2	yes	—
121	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
122	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
123	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
124	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
125	C₃²×C₈	C₂²×C₄	1	4	yes	—
126	C₃⋊(C₃⋊C₈)	—	2	4	no	—
127	C₃×C₃⋊C₈	—	2	4	no	—
128	C₃×C₃⋊C₈	C₂²×C₄	1	4	yes	—
129	C₂²×M₁₆	—	9	2	no	—
130	C₂³×C₈	—	3	1	no	—
131	C₂×#108	—	3	1	no	—
132	C₂×#108	—	9	8	no	—
133	C₂×#108	—	9	2	no	—
134	C₂×#108	—	9	1	no	—
135	C₂⁴×C₃	—	3	1	no	—
136	C₂³×D₃	Dic₆	1	1	yes	characteristic
137	C₂²×C₃×C₄	—	2	1	no	—
138	C₂²×C₃×C₄	—	3	1	no	—
139	C₂²×C₃×C₄	—	3	1	no	—
140	C₂²×C₃×C₄	—	3	2	no	—
141	C₂²×C₃×C₄	—	3	1	no	—
142	C₂²×C₃×C₄	—	3	1	no	—
143	C₂²×C₃×C₄	—	3	2	no	—
144	C₂²×C₃×C₄	—	3	1	no	—
145	C₂²×C₃×C₄	—	3	2	no	—
146	C₂²×C₃×C₄	—	3	2	no	—
147	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
148	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
149	C₂²×Dic₃	Dic₆	1	1	yes	characteristic
150	C₂×C₄×D₃	Dic₆	1	2	yes	—
151	C₂×C₄×D₃	D₁₂	1	1	yes	characteristic
152	C₂×C₄×D₃	D₁₂	1	1	yes	characteristic
153	C₂×C₄×D₃	D₁₂	1	2	yes	—
154	C₂×C₄×D₃	C₂×Dic₃	1	2	yes	—
155	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
156	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
157	C₂×C₄×D₃	C₂²×D₃	1	2	yes	—
158	C₃×M₁₆	—	3	4	no	—
159	C₃×M₁₆	—	6	2	no	—
160	C₂×C₃×C₈	—	2	2	no	—
161	C₂×C₃×C₈	—	2	2	no	—
162	C₂×C₃×C₈	—	2	2	no	—
163	C₂×C₃×C₈	—	3	2	no	—
164	C₂×C₃×C₈	—	3	2	no	—
165	C₂×C₃×C₈	—	3	2	no	—
166	C₂×C₃×C₈	—	3	8	no	—
167	C₂×C₃×C₈	—	3	8	no	—
168	C₂×C₃×C₈	—	6	2	no	—
169	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
170	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
171	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
172	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
173	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
174	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
175	#208	—	2	2	no	—
176	#208	—	3	4	no	—
177	#208	—	3	4	no	—
178	#208	—	6	4	no	—
179	#208	—	6	8	no	—
180	#208	—	6	2	no	—
181	#208	—	6	2	no	—
182	#208	—	12	2	no	—
183	#208	C₂²×D₃	1	4	yes	—
184	C₂×C₃⋊C₈	—	2	2	no	—
185	C₂×C₃⋊C₈	—	6	8	no	—
186	C₂×C₃⋊C₈	—	6	2	no	—
187	C₂×C₃⋊C₈	—	6	2	no	—
188	C₂×C₃⋊C₈	—	12	2	no	—
189	C₂×C₃⋊C₈	C₂×Dic₃	1	2	yes	—
190	C₂×C₃⋊C₈	C₂×Dic₃	1	2	yes	—
191	C₂×C₃⋊C₈	C₂²×D₃	1	2	yes	—
192	ΓL(1,𝔽₂₅)	—	6	8	no	—
193	D₃×C₈	—	6	8	no	—
194	D₃×C₈	C₂×Dic₃	1	8	yes	—
195	D₃×C₈	C₂×Dic₃	1	8	yes	—
196	C₂²×C₃²	—	2	2	no	—
197	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂²×C₃²	C₂²×Q₈	1	1	yes	characteristic
200	C₂×C₃×D₃	—	2	2	no	—
201	C₂×C₃×D₃	—	2	4	no	—
202	C₂×C₃×D₃	—	2	4	no	—
203	C₂×C₃×D₃	#108	1	4	yes	complemented
204	C₂×C₃×D₃	C₂×C₄⋊C₄	1	2	yes	—
205	C₂×C₃×D₃	C₂×C₄⋊C₄	1	2	yes	—
206	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
209	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
210	C₃×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
211	C₃×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
212	C₂³×C₄	—	3	1	no	—
213	C₂×M₁₆	—	3	2	no	—
214	C₂×M₁₆	—	9	8	no	—
215	C₂×M₁₆	—	9	2	no	—
216	C₂×M₁₆	—	18	2	no	—
217	C₂×M₁₆	—	18	4	no	—
218	C₂²×C₈	—	3	1	no	—
219	C₂²×C₈	—	3	2	no	—
220	C₂²×C₈	—	3	2	no	—
221	C₂²×C₈	—	3	4	no	—
222	C₂²×C₈	—	3	4	no	—
223	C₂²×C₈	—	18	2	no	—
224	C₂²×C₈	D₃²	1	1	yes	characteristic
225	#108	—	3	4	no	—
226	#108	—	9	8	no	—
227	#108	—	9	4	no	—
228	C₂³×C₃	—	2	1	no	—
229	C₂³×C₃	—	3	1	no	—
230	C₂³×C₃	—	3	2	no	—
231	C₂³×C₃	—	3	1	no	—
232	C₂³×C₃	—	3	2	no	—
233	C₂³×C₃	—	6	4	no	—
234	C₂³×C₃	C₂×Dic₆	1	1	yes	characteristic
235	C₂³×C₃	D₃×Q₈	1	1	yes	characteristic
236	C₂²×D₃	—	2	4	no	—
237	C₂²×D₃	C₄⋊Dic₃	1	1	yes	characteristic
238	C₂²×D₃	C₄⋊Dic₃	1	2	yes	—
239	C₂²×D₃	C₄⋊Dic₃	1	1	yes	characteristic
240	C₂²×D₃	C₂×Dic₆	1	2	yes	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	3	2	no	—
248	C₂×C₃×C₄	—	3	1	no	—
249	C₂×C₃×C₄	—	3	1	no	—
250	C₂×C₃×C₄	—	3	2	no	—
251	C₂×C₃×C₄	—	3	2	no	—
252	C₂×C₃×C₄	—	3	2	no	—
253	C₂×C₃×C₄	—	3	2	no	—
254	C₂×C₃×C₄	—	3	2	no	—
255	C₂×C₃×C₄	—	3	2	no	—
256	C₂×C₃×C₄	—	3	2	no	—
257	C₂×C₃×C₄	—	3	2	no	—
258	C₂×C₃×C₄	—	3	2	no	—
259	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
264	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
265	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
266	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
271	C₂×Dic₃	C₄⋊Dic₃	1	2	yes	—
272	C₂×Dic₃	C₄⋊Dic₃	1	1	yes	characteristic
273	C₂×Dic₃	C₄⋊Dic₃	1	1	yes	characteristic
274	C₂×Dic₃	C₂×Dic₆	1	2	yes	—
275	C₄×D₃	C₄⋊Dic₃	1	2	yes	—
276	C₄×D₃	C₄⋊Dic₃	1	2	yes	—
277	C₄×D₃	C₄⋊Dic₃	1	2	yes	—
278	C₄×D₃	C₄⋊Dic₃	1	2	yes	—
279	C₄×D₃	C₂×D₁₂	1	2	yes	—
280	C₄×D₃	C₂×D₁₂	1	2	yes	—
281	C₄×D₃	C₂²×Dic₃	1	2	yes	—
282	C₄×D₃	C₂²×Dic₃	1	2	yes	—
283	C₃×C₈	—	2	4	no	—
284	C₃×C₈	—	3	4	no	—
285	C₃×C₈	—	6	4	no	—
286	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
287	C₃×C₈	C₂²×Dic₃	1	4	yes	—
288	C₃⋊C₈	—	2	4	no	—
289	C₃⋊C₈	—	6	4	no	—
290	C₃⋊C₈	—	6	4	no	—
291	C₃⋊C₈	—	12	4	no	—
292	C₃⋊C₈	C₂²×Dic₃	1	4	yes	—
293	C₂×C₃²	—	2	1	no	—
294	C₂×C₃²	—	2	1	no	—
295	C₂×C₃²	C₂×#108	1	2	yes	complemented
296	C₂×C₃²	C₂²×C₄⋊C₄	1	1	yes	characteristic
297	C₃×D₃	—	2	2	no	—
298	C₃×D₃	C₂×#108	1	4	yes	complemented
299	C₂⁴	—	3	1	no	—
300	C₂²×C₄	—	3	1	no	—
301	C₂²×C₄	—	3	2	no	—
302	C₂²×C₄	—	3	2	no	—
303	C₂²×C₄	—	3	2	no	—
304	C₂²×C₄	—	3	1	no	—
305	C₂²×C₄	—	3	1	no	—
306	C₂²×C₄	—	3	1	no	—
307	C₂²×C₄	—	3	2	no	—
308	C₂²×C₄	—	3	1	no	—
309	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
310	M₁₆	—	3	4	no	—
311	M₁₆	—	6	2	no	—
312	M₁₆	—	9	4	no	—
313	M₁₆	—	18	8	no	—
314	M₁₆	—	18	2	no	—
315	C₂×C₈	—	3	2	no	—
316	C₂×C₈	—	3	2	no	—
317	C₂×C₈	—	3	2	no	—
318	C₂×C₈	—	3	8	no	—
319	C₂×C₈	—	3	8	no	—
320	C₂×C₈	—	6	2	no	—
321	C₂×C₈	—	18	8	no	—
322	C₂×C₈	—	18	2	no	—
323	C₂×C₈	D₃×Dic₃	1	2	yes	—
324	C₂×C₈	D₃×Dic₃	1	2	yes	—
325	C₂×C₈	C₂×D₃²	1	2	yes	—
326	C₂²×C₃	—	2	2	no	—
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	—	2	1	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	3	4	no	—
332	C₂²×C₃	—	3	2	no	—
333	C₂²×C₃	—	3	2	no	—
334	C₂²×C₃	—	4	2	no	—
335	C₂²×C₃	—	6	4	no	—
336	C₂²×C₃	—	6	4	no	—
337	C₂²×C₃	—	6	2	no	—
338	C₂²×C₃	D₃×C₄⋊C₄	1	1	yes	characteristic
339	C₂²×C₃	D₃×C₄⋊C₄	1	1	yes	characteristic
340	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
341	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
342	C₂²×C₃	C₂²×Dic₆	1	1	yes	characteristic
343	C₂²×C₃	C₂×D₃×Q₈	1	1	yes	characteristic
344	C₂×D₃	—	2	2	no	—
345	C₂×D₃	—	2	4	no	—
346	C₂×D₃	—	2	4	no	—
347	C₂×D₃	#819	1	4	yes	direct product factor
348	C₂×D₃	C₂×C₄⋊Dic₃	1	2	yes	—
349	C₂×D₃	C₂×C₄⋊Dic₃	1	2	yes	—
350	C₃×C₄	—	2	1	no	—
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	3	2	no	—
355	C₃×C₄	—	3	2	no	—
356	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
357	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
358	C₃×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
359	C₃×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
360	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
361	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
362	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
363	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
364	Dic₃	C₂×C₄⋊Dic₃	1	2	yes	—
365	Dic₃	C₂×C₄⋊Dic₃	1	2	yes	—
366	C₃²	C₂²×#108	1	1	yes	characteristic, complemented, Sylow
367	C₂³	—	3	1	no	—
368	C₂³	—	3	2	no	—
369	C₂³	—	3	2	no	—
370	C₂³	—	3	1	no	—
371	C₂³	—	6	4	no	—
372	C₂³	D₃×Dic₆	1	1	yes	characteristic
373	C₂×C₄	—	3	2	no	—
374	C₂×C₄	—	3	2	no	—
375	C₂×C₄	—	3	1	no	—
376	C₂×C₄	—	3	1	no	—
377	C₂×C₄	—	3	2	no	—
378	C₂×C₄	—	3	2	no	—
379	C₂×C₄	—	3	2	no	—
380	C₂×C₄	—	3	2	no	—
381	C₂×C₄	—	3	2	no	—
382	C₂×C₄	—	3	2	no	—
383	C₂×C₄	—	3	2	no	—
384	C₂×C₄	—	3	2	no	—
385	C₂×C₄	D₃×Dic₆	1	1	yes	characteristic
386	C₂×C₄	D₃×D₁₂	1	1	yes	characteristic
387	C₂×C₄	D₃×D₁₂	1	1	yes	characteristic
388	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
389	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
390	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
391	C₈	—	3	4	no	—
392	C₈	—	6	4	no	—
393	C₈	—	18	4	no	—
394	C₈	C₂×D₃×Dic₃	1	4	yes	—
395	C₂×C₃	—	2	1	no	—
396	C₂×C₃	—	2	1	no	—
397	C₂×C₃	—	2	1	no	—
398	C₂×C₃	—	2	1	no	—
399	C₂×C₃	—	2	1	no	—
400	C₂×C₃	—	2	2	no	—
401	C₂×C₃	—	3	4	no	—
402	C₂×C₃	—	4	1	no	—
403	C₂×C₃	—	4	1	no	—
404	C₂×C₃	—	6	2	no	—
405	C₂×C₃	D₃×#108	1	2	yes	complemented
406	C₂×C₃	C₂×#819	1	2	yes	complemented
407	C₂×C₃	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
408	C₂×C₃	C₂²×C₄⋊Dic₃	1	1	yes	characteristic
409	D₃	—	2	2	no	—
410	D₃	C₂×#819	1	4	yes	direct product factor
411	C₂²	—	2	2	no	—
412	C₂²	—	3	2	no	—
413	C₂²	—	3	4	no	—
414	C₂²	—	3	2	no	—
415	C₂²	—	6	4	no	—
416	C₂²	—	6	4	no	—
417	C₂²	—	6	2	no	—
418	C₂²	D₃×C₄⋊Dic₃	1	1	yes	characteristic
419	C₂²	D₃×C₄⋊Dic₃	1	1	yes	characteristic
420	C₂²	C₂×D₃×Dic₆	1	1	yes	characteristic
421	C₄	—	3	2	no	—
422	C₄	—	3	2	no	—
423	C₄	D₃×C₄⋊Dic₃	1	1	yes	characteristic
424	C₄	D₃×C₄⋊Dic₃	1	1	yes	characteristic
425	C₄	C₂×D₃×D₁₂	1	1	yes	characteristic
426	C₄	C₂²×D₃×Dic₃	1	1	yes	characteristic
427	C₃	—	2	1	no	—
428	C₃	C₂×D₃×#108	1	1	yes	characteristic, complemented
429	C₃	C₂²×#819	1	1	yes	characteristic, complemented
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	3	4	no	—
433	C₂	—	6	2	no	—
434	C₂	D₃×#819	1	2	yes	direct product factor
435	C₂	C₂×D₃×C₄⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃×D₁₂
commutator	C₃²×C₄	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃²
Fitting	C₂²×C₃²×C₈	C₂²
socle	C₂²×C₃²	C₂×C₄⋊C₄
prime radical	C₂³×C₃×D₃	Q₈
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	C₂²×C₈	D₃²
hypocenter	C₃²	C₂²×#108
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×#63646	C₂	semidirect
4. C₂×C₃×#819	C₂	semidirect
5. C₂×#63577	C₂	semidirect
6. D₃×#819	C₂	direct (N × H)
22. #63646	C₂²	semidirect
23. C₃×#819	C₂²	semidirect
24. #63577	C₂²	semidirect
36. C₂×#819	D₃	direct (N × H)
100. #819	C₂×D₃	direct (N × H)
203. C₂×C₃×D₃	#108	semidirect
295. C₂×C₃²	C₂×#108	semidirect
298. C₃×D₃	C₂×#108	semidirect
347. C₂×D₃	#819	direct (N × H)
366. C₃²	C₂²×#108	semidirect
405. C₂×C₃	D₃×#108	semidirect
406. C₂×C₃	C₂×#819	semidirect
410. D₃	C₂×#819	direct (N × H)
428. C₃	C₂×D₃×#108	semidirect
429. C₃	C₂²×#819	semidirect
434. C₂	D₃×#819	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×D₃×C₈	2
C₂×D₃×#208	2
C₂×#63646	2
C₂×C₃×#819	2
C₂×#63577	2
D₃×#819	2
C₂²×#819	3
C₂×D₃×#108	3

Subgroups — C2×D3×#819 #11858620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×#819 #11858620