Subgroups — D₃×#4828 #11861315

Order 1152.

847 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₃×Dic₆	C₂	1	1	yes	maximal, characteristic
2	#10592527	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×#4828	C₂	1	1	yes	maximal, characteristic, complemented
5	#10590789	C₂	1	1	yes	maximal, characteristic, complemented
6	#10590788	C₂	1	1	yes	maximal, characteristic, complemented
7	#10590785	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×#815	C₂	1	1	yes	maximal, characteristic
9	D₃×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic
10	D₃×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic
11	D₃×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic
12	#10590646	C₂	1	1	yes	maximal, characteristic, complemented
13	D₃×#803	C₂	1	1	yes	maximal, characteristic
14	#10590255	C₂	1	1	yes	maximal, characteristic, complemented
15	#10590252	C₂	1	1	yes	maximal, characteristic, complemented
16	D₃×#446	—	3	1	no	maximal
17	C₂×#4828	—	3	1	no	maximal
18	C₂×D₃×Dic₆	C₄	1	1	yes	characteristic
19	C₄×#634	C₂²	1	1	yes	characteristic
20	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
22	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
23	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
24	C₄×#627	C₂²	1	1	yes	characteristic
25	C₄×#627	C₂²	1	1	yes	characteristic
26	D₃×C₄⋊Dic₃	C₄	1	1	yes	characteristic
27	D₃×Dic₃⋊C₄	C₄	1	1	yes	characteristic
28	D₃×Dic₃⋊C₄	C₄	1	1	yes	characteristic
29	C₄×D₃×Dic₃	C₂²	1	1	yes	characteristic
30	C₄×D₃×Dic₃	C₂²	1	1	yes	characteristic
31	#63844	C₄	1	1	yes	characteristic
32	Dic₃×Dic₆	C₄	1	1	yes	characteristic
33	#63837	C₄	1	1	yes	characteristic
34	#63837	C₄	1	1	yes	characteristic
35	C₂×D₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×D₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
37	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	#63642	C₂²	1	1	yes	characteristic
39	#63641	C₂²	1	1	yes	characteristic
40	#63641	C₂²	1	1	yes	characteristic
41	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
42	#63630	C₂²	1	1	yes	characteristic
43	C₃×#815	C₂²	1	1	yes	characteristic
44	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
45	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
46	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
47	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
48	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
49	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
50	C₃×#803	C₂²	1	1	yes	characteristic
51	#63572	C₂²	1	1	yes	characteristic
52	#63572	C₂²	1	1	yes	characteristic
53	Dic₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
54	Dic₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
55	#63555	C₂²	1	1	yes	characteristic
56	#63554	C₂²	1	1	yes	characteristic
57	#63554	C₂²	1	1	yes	characteristic
58	#63554	C₂²	1	1	yes	characteristic
59	#63553	C₂²	1	1	yes	characteristic
60	Dic₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
61	C₄×D₃×Q₈	—	3	1	no	—
62	C₂×C₄×Dic₆	—	3	1	no	—
63	C₃×#446	—	3	1	no	—
64	C₂×C₃×C₄⋊C₈	—	3	1	no	—
65	C₂×#815	—	3	1	no	—
66	C₂×Dic₃⋊C₈	—	3	1	no	—
67	C₂×Dic₃⋊C₈	—	3	1	no	—
68	C₂×C₈×Dic₃	—	3	1	no	—
69	#5024	—	3	1	no	—
70	C₂×#803	—	3	1	no	—
71	D₃×C₄⋊C₈	—	3	1	no	—
72	D₃×C₄⋊C₈	—	3	1	no	—
73	D₃×C₄⋊C₈	D₃	1	1	yes	characteristic
74	#4831	—	3	1	no	—
75	#4828	—	3	1	no	—
76	#4828	—	3	1	no	—
77	#4828	—	3	1	no	—
78	#4828	—	3	1	no	—
79	#4828	—	3	1	no	—
80	#4828	—	3	1	no	—
81	#4828	—	3	1	no	—
82	#4828	—	3	1	no	—
83	#4828	—	3	1	no	—
84	#4828	—	6	1	no	—
85	#4828	D₃	1	1	yes	characteristic, direct product factor
86	D₃×#97	—	3	1	no	—
87	D₃×#97	—	3	1	no	—
88	#4701	—	3	1	no	—
89	#4701	—	3	1	no	—
90	C₄×D₃×C₈	—	3	1	no	—
91	#4679	—	3	1	no	—
92	C₂×#634	C₂×C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
96	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
97	C₂×#627	C₂×C₄	1	1	yes	characteristic
98	C₂×#627	C₂×C₄	1	1	yes	characteristic
99	C₂×D₃×Dic₃	C₂×C₄	1	1	yes	characteristic
100	C₂×D₃×Dic₃	C₂×C₄	1	1	yes	characteristic
101	C₂×D₃×Dic₃	C₂×C₄	1	1	yes	characteristic
102	C₂×D₃×Dic₃	C₂×C₄	1	1	yes	characteristic
103	D₃×Dic₆	—	2	4	no	—
104	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
105	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
106	C₃²×C₄²	C₂³	1	1	yes	characteristic
107	C₄⋊(C₃⋊Dic₃)	C₂×C₄	1	1	yes	characteristic
108	#3750	C₂×C₄	1	1	yes	characteristic
109	#3750	C₂×C₄	1	1	yes	characteristic
110	C₄×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
111	C₄×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
112	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
113	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
114	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
115	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
118	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
119	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
120	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
121	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
122	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
123	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
125	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₃×D₃×C₈	—	2	2	no	—
127	C₃×D₃×C₈	—	2	2	no	—
128	#3724	C₂×C₄	1	1	yes	characteristic
129	#3724	C₂×C₄	1	1	yes	characteristic
130	Dic₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
131	Dic₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
132	Dic₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
133	Dic₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
134	Dic₃²	C₂×C₄	1	1	yes	characteristic
135	Dic₃²	C₂×C₄	1	1	yes	characteristic
136	Dic₃²	C₂×C₄	1	1	yes	characteristic
137	Dic₃²	C₂×C₄	1	1	yes	characteristic
138	D₃×C₃⋊C₈	—	2	2	no	—
139	D₃×C₃⋊C₈	Q₈	1	4	yes	complemented
140	C₂×#446	—	9	1	no	Sylow
141	C₂×D₃×Q₈	—	3	1	no	—
142	C₂²×Dic₆	—	3	1	no	—
143	C₂²×C₃×C₈	—	3	1	no	—
144	C₂²×C₃×C₈	—	3	1	no	—
145	C₃×C₄×Q₈	—	3	1	no	—
146	C₂×C₃×C₄²	—	3	1	no	—
147	Q₈×Dic₃	—	3	1	no	—
148	C₂×C₄⋊Dic₃	—	3	1	no	—
149	C₂×Dic₃⋊C₄	—	3	1	no	—
150	C₂×Dic₃⋊C₄	—	3	1	no	—
151	C₂×C₄×Dic₃	—	3	1	no	—
152	C₂×C₄×Dic₃	—	3	1	no	—
153	C₂²×C₃⋊C₈	—	3	1	no	—
154	C₂²×C₃⋊C₈	—	3	1	no	—
155	C₂×D₃×C₈	—	3	1	no	—
156	C₂×D₃×C₈	—	3	1	no	—
157	C₂×D₃×C₈	C₂×D₃	1	1	yes	characteristic
158	C₂×D₃×C₈	C₂×D₃	1	1	yes	characteristic
159	D₃×C₄⋊C₄	—	3	1	no	—
160	D₃×C₄⋊C₄	—	3	1	no	—
161	D₃×C₄⋊C₄	—	3	1	no	—
162	#887	—	3	1	no	—
163	#887	—	3	1	no	—
164	#887	—	3	1	no	—
165	C₄²×D₃	—	3	1	no	—
166	C₄²×D₃	—	3	1	no	—
167	C₄²×D₃	C₂×D₃	1	1	yes	characteristic
168	C₄×Dic₆	—	3	1	no	—
169	C₄×Dic₆	—	3	1	no	—
170	C₄×Dic₆	—	3	1	no	—
171	C₄×Dic₆	—	3	1	no	—
172	C₄×Dic₆	—	3	1	no	—
173	C₄×Dic₆	—	3	1	no	—
174	C₄×Dic₆	—	3	1	no	—
175	C₄×Dic₆	—	3	1	no	—
176	C₄×Dic₆	—	3	1	no	—
177	C₄×Dic₆	—	3	1	no	—
178	C₄×Dic₆	—	6	1	no	—
179	C₄×Dic₆	C₂×D₃	1	1	yes	characteristic
180	C₃×C₄⋊C₈	—	2	1	no	—
181	C₃×C₄⋊C₈	—	3	1	no	—
182	C₃×C₄⋊C₈	—	3	1	no	—
183	C₃×C₄⋊C₈	—	3	1	no	—
184	C₃×C₄⋊C₈	—	3	1	no	—
185	C₃×C₄⋊C₈	—	3	1	no	—
186	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
187	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
188	C₃×#97	—	3	1	no	—
189	C₃×#97	—	3	1	no	—
190	C₃×C₄×C₈	—	3	1	no	—
191	#815	—	3	1	no	—
192	#815	—	3	1	no	—
193	#815	—	3	1	no	—
194	#815	—	3	1	no	—
195	#815	—	3	1	no	—
196	#815	—	3	1	no	—
197	#815	—	3	1	no	—
198	#815	—	6	1	no	—
199	#815	C₂×D₃	1	1	yes	characteristic
200	Dic₃⋊C₈	—	3	1	no	—
201	Dic₃⋊C₈	—	3	1	no	—
202	Dic₃⋊C₈	—	3	1	no	—
203	Dic₃⋊C₈	—	3	1	no	—
204	Dic₃⋊C₈	—	3	1	no	—
205	Dic₃⋊C₈	—	3	1	no	—
206	Dic₃⋊C₈	—	3	1	no	—
207	Dic₃⋊C₈	—	3	1	no	—
208	Dic₃⋊C₈	—	3	1	no	—
209	Dic₃⋊C₈	—	3	1	no	—
210	Dic₃⋊C₈	—	6	1	no	—
211	Dic₃⋊C₈	—	6	1	no	—
212	Dic₃⋊C₈	C₂×D₃	1	1	yes	characteristic
213	Dic₃⋊C₈	C₂×D₃	1	1	yes	characteristic
214	Dic₃⋊C₈	C₂×D₃	1	1	yes	characteristic
215	Dic₃⋊C₈	C₂×D₃	1	1	yes	characteristic
216	C₈×Dic₃	—	3	1	no	—
217	C₈×Dic₃	—	3	1	no	—
218	C₈×Dic₃	—	3	1	no	—
219	C₈×Dic₃	—	3	1	no	—
220	C₈×Dic₃	—	3	1	no	—
221	C₈×Dic₃	—	6	1	no	—
222	C₈×Dic₃	C₂×D₃	1	1	yes	characteristic
223	C₄⋊(C₃⋊C₈)	—	3	1	no	—
224	C₄⋊(C₃⋊C₈)	—	3	1	no	—
225	C₄⋊(C₃⋊C₈)	C₂×D₃	1	1	yes	characteristic
226	#803	—	3	1	no	—
227	#803	—	3	1	no	—
228	#803	—	3	1	no	—
229	#803	—	3	1	no	—
230	#803	—	3	1	no	—
231	#803	—	6	1	no	—
232	#803	C₂×D₃	1	1	yes	characteristic
233	C₄×C₃⋊C₈	—	3	1	no	—
234	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
235	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
236	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
237	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
238	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
239	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
240	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
241	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
242	#634	—	2	2	no	—
243	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
244	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
245	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
246	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
247	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
248	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
249	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
250	C₃×C₄×D₃	—	2	2	no	—
251	C₃×C₄×D₃	—	2	2	no	—
252	C₃×C₄×D₃	C₂×Q₈	1	2	yes	—
253	C₃×C₄×D₃	#41	1	2	yes	—
254	C₃×Dic₆	—	2	2	no	—
255	#627	—	2	2	no	—
256	#627	—	2	2	no	—
257	D₃×Dic₃	—	2	2	no	—
258	D₃×Dic₃	—	2	2	no	—
259	D₃×Dic₃	—	2	2	no	—
260	D₃×Dic₃	M₁₆	1	4	yes	—
261	C₃²×C₈	—	2	1	no	—
262	C₃²×C₈	—	2	1	no	—
263	C₃⋊(C₃⋊C₈)	—	2	1	no	—
264	C₃⋊(C₃⋊C₈)	C₂×Q₈	1	2	yes	complemented
265	C₃×C₃⋊C₈	—	2	1	no	—
266	C₃×C₃⋊C₈	—	2	1	no	—
267	C₃×C₃⋊C₈	—	2	1	no	—
268	C₃×C₃⋊C₈	C₂×Q₈	1	2	yes	complemented
269	C₂×C₄×Q₈	—	9	1	no	—
270	#446	—	3	1	no	—
271	#446	—	9	1	no	—
272	#446	—	9	1	no	—
273	#446	—	9	1	no	—
274	#446	—	9	1	no	—
275	#446	—	9	1	no	—
276	#446	—	9	1	no	—
277	#446	—	9	1	no	—
278	C₂×C₄⋊C₈	—	3	1	no	—
279	C₂×C₄⋊C₈	—	9	1	no	—
280	C₂×C₄⋊C₈	—	9	1	no	—
281	C₂×#97	—	9	1	no	—
282	C₂×#97	—	9	1	no	—
283	C₂×C₄×C₈	—	9	1	no	—
284	C₂×C₃×Q₈	—	3	1	no	—
285	C₂²×C₃×C₄	—	3	1	no	—
286	C₂²×C₃×C₄	—	3	1	no	—
287	C₂²×C₃×C₄	—	3	1	no	—
288	C₂²×Dic₃	—	3	1	no	—
289	C₂²×Dic₃	—	3	1	no	—
290	C₂²×Dic₃	—	3	1	no	—
291	C₂²×Dic₃	—	3	1	no	—
292	D₃×Q₈	—	6	4	no	—
293	C₂×C₄×D₃	—	3	1	no	—
294	C₂×C₄×D₃	—	3	1	no	—
295	C₂×C₄×D₃	—	3	1	no	—
296	C₂×C₄×D₃	—	3	1	no	—
297	C₂×C₄×D₃	C₄×D₃	1	1	yes	characteristic
298	C₂×C₄×D₃	C₄×D₃	1	1	yes	characteristic
299	C₂×C₄×D₃	C₂²×D₃	1	1	yes	characteristic
300	C₂×Dic₆	—	3	1	no	—
301	C₂×Dic₆	—	3	1	no	—
302	C₂×Dic₆	—	3	1	no	—
303	C₂×Dic₆	—	3	1	no	—
304	C₂×Dic₆	—	3	1	no	—
305	C₂×Dic₆	—	3	1	no	—
306	C₂×Dic₆	—	6	1	no	—
307	C₂×Dic₆	—	6	4	no	—
308	C₂×Dic₆	C₄×D₃	1	1	yes	characteristic
309	C₂×C₃×C₈	—	2	1	no	—
310	C₂×C₃×C₈	—	2	1	no	—
311	C₂×C₃×C₈	—	3	1	no	—
312	C₂×C₃×C₈	—	3	1	no	—
313	C₂×C₃×C₈	—	3	1	no	—
314	C₂×C₃×C₈	—	3	1	no	—
315	C₂×C₃×C₈	—	6	2	no	—
316	C₂×C₃×C₈	—	6	2	no	—
317	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
318	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
319	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
320	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
321	C₃×C₄⋊C₄	—	3	1	no	—
322	C₃×C₄⋊C₄	—	3	1	no	—
323	C₃×C₄⋊C₄	—	3	1	no	—
324	C₃×C₄²	—	2	1	no	—
325	C₃×C₄²	—	3	1	no	—
326	C₃×C₄²	—	3	1	no	—
327	C₃×C₄²	—	3	1	no	—
328	C₃×C₄²	—	3	1	no	—
329	C₃×C₄²	—	3	1	no	—
330	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
331	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
332	C₄⋊Dic₃	—	3	1	no	—
333	C₄⋊Dic₃	—	3	1	no	—
334	C₄⋊Dic₃	—	3	1	no	—
335	C₄⋊Dic₃	—	3	1	no	—
336	C₄⋊Dic₃	—	3	1	no	—
337	C₄⋊Dic₃	—	3	1	no	—
338	C₄⋊Dic₃	—	6	1	no	—
339	C₄⋊Dic₃	C₄×D₃	1	1	yes	characteristic
340	Dic₃⋊C₄	—	3	1	no	—
341	Dic₃⋊C₄	—	3	1	no	—
342	Dic₃⋊C₄	—	3	1	no	—
343	Dic₃⋊C₄	—	3	1	no	—
344	Dic₃⋊C₄	—	3	1	no	—
345	Dic₃⋊C₄	—	3	1	no	—
346	Dic₃⋊C₄	—	3	1	no	—
347	Dic₃⋊C₄	—	3	1	no	—
348	Dic₃⋊C₄	—	3	1	no	—
349	Dic₃⋊C₄	—	3	1	no	—
350	Dic₃⋊C₄	—	3	1	no	—
351	Dic₃⋊C₄	—	3	1	no	—
352	Dic₃⋊C₄	—	6	1	no	—
353	Dic₃⋊C₄	—	6	1	no	—
354	Dic₃⋊C₄	C₄×D₃	1	1	yes	characteristic
355	Dic₃⋊C₄	C₄×D₃	1	1	yes	characteristic
356	C₄×Dic₃	—	3	1	no	—
357	C₄×Dic₃	—	3	1	no	—
358	C₄×Dic₃	—	3	1	no	—
359	C₄×Dic₃	—	3	1	no	—
360	C₄×Dic₃	—	3	1	no	—
361	C₄×Dic₃	—	3	1	no	—
362	C₄×Dic₃	—	3	1	no	—
363	C₄×Dic₃	—	3	1	no	—
364	C₄×Dic₃	—	3	1	no	—
365	C₄×Dic₃	—	3	1	no	—
366	C₄×Dic₃	—	3	1	no	—
367	C₄×Dic₃	—	3	1	no	—
368	C₄×Dic₃	—	6	1	no	—
369	C₄×Dic₃	—	6	1	no	—
370	C₄×Dic₃	C₄×D₃	1	1	yes	characteristic
371	C₄×Dic₃	C₄×D₃	1	1	yes	characteristic
372	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
373	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
374	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
375	C₂×C₃⋊C₈	—	3	1	no	—
376	C₂×C₃⋊C₈	—	3	1	no	—
377	C₂×C₃⋊C₈	—	3	4	no	—
378	C₂×C₃⋊C₈	—	3	1	no	—
379	C₂×C₃⋊C₈	—	3	1	no	—
380	C₂×C₃⋊C₈	—	6	1	no	—
381	C₂×C₃⋊C₈	—	6	1	no	—
382	C₂×C₃⋊C₈	—	6	2	no	—
383	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
384	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
385	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
386	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
387	D₃×C₈	—	2	2	no	—
388	D₃×C₈	—	2	2	no	—
389	D₃×C₈	—	3	4	no	—
390	D₃×C₈	—	6	2	no	—
391	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
392	C₂×C₃×D₃	C₄×Q₈	1	2	yes	—
393	C₂×C₃×D₃	C₂×M₁₆	1	2	yes	—
394	C₂×C₃×D₃	#131	1	2	yes	—
395	C₃²×C₄	—	2	1	no	—
396	C₃²×C₄	—	2	1	no	—
397	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
398	C₃²×C₄	C₂×#41	1	1	yes	characteristic
399	C₃⋊Dic₃	—	2	1	no	—
400	C₃⋊Dic₃	—	2	1	no	—
401	C₃⋊Dic₃	—	2	1	no	—
402	C₃⋊Dic₃	C₂×M₁₆	1	2	yes	—
403	C₃×Dic₃	—	2	1	no	—
404	C₃×Dic₃	—	2	1	no	—
405	C₃×Dic₃	—	2	1	no	—
406	C₃×Dic₃	—	2	1	no	—
407	C₃×Dic₃	—	2	1	no	—
408	C₃×Dic₃	C₄×Q₈	1	2	yes	—
409	C₃×Dic₃	C₂×M₁₆	1	2	yes	—
410	C₂²×Q₈	—	9	1	no	—
411	C₂²×C₈	—	3	1	no	—
412	C₂²×C₈	—	3	1	no	—
413	C₂²×C₈	—	9	1	no	—
414	C₂²×C₈	—	9	1	no	—
415	C₄×Q₈	—	3	1	no	—
416	C₄×Q₈	—	9	1	no	—
417	C₄×Q₈	—	9	1	no	—
418	C₄×Q₈	—	9	1	no	—
419	C₄×Q₈	—	9	1	no	—
420	C₄×Q₈	—	9	1	no	—
421	C₄×Q₈	—	9	1	no	—
422	C₄×Q₈	—	9	1	no	—
423	C₂×C₄⋊C₄	—	9	1	no	—
424	C₂×C₄⋊C₄	—	9	1	no	—
425	C₂×C₄⋊C₄	—	9	1	no	—
426	C₂×C₄²	—	3	1	no	—
427	C₂×C₄²	—	9	1	no	—
428	C₂×C₄²	—	9	1	no	—
429	C₄⋊C₈	—	3	1	no	—
430	C₄⋊C₈	—	3	1	no	—
431	C₄⋊C₈	—	3	1	no	—
432	C₄⋊C₈	—	3	1	no	—
433	C₄⋊C₈	—	3	1	no	—
434	C₄⋊C₈	—	9	1	no	—
435	C₄⋊C₈	—	9	1	no	—
436	C₄⋊C₈	—	9	1	no	—
437	C₄⋊C₈	—	9	1	no	—
438	C₄⋊C₈	—	9	1	no	—
439	C₄⋊C₈	—	9	1	no	—
440	C₄⋊C₈	D₃²	1	1	yes	characteristic
441	#97	—	3	1	no	—
442	#97	—	3	1	no	—
443	#97	—	9	1	no	—
444	#97	—	9	1	no	—
445	#97	—	9	1	no	—
446	#97	—	9	1	no	—
447	#97	—	9	1	no	—
448	#97	—	9	1	no	—
449	C₄×C₈	—	3	1	no	—
450	C₄×C₈	—	9	1	no	—
451	C₄×C₈	—	9	1	no	—
452	C₄×C₈	—	9	1	no	—
453	C₂³×C₃	—	3	1	no	—
454	C₂²×D₃	C₂×C₄×D₃	1	1	yes	characteristic
455	C₃×Q₈	—	6	2	no	—
456	C₂×C₃×C₄	—	2	1	no	—
457	C₂×C₃×C₄	—	2	1	no	—
458	C₂×C₃×C₄	—	2	1	no	—
459	C₂×C₃×C₄	—	3	1	no	—
460	C₂×C₃×C₄	—	3	1	no	—
461	C₂×C₃×C₄	—	3	2	no	—
462	C₂×C₃×C₄	—	3	2	no	—
463	C₂×C₃×C₄	—	3	1	no	—
464	C₂×C₃×C₄	—	3	1	no	—
465	C₂×C₃×C₄	—	3	1	no	—
466	C₂×C₃×C₄	—	3	1	no	—
467	C₂×C₃×C₄	—	3	1	no	—
468	C₂×C₃×C₄	—	6	2	no	—
469	C₂×C₃×C₄	—	6	2	no	—
470	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
471	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
472	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
473	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
474	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
475	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
476	C₂×Dic₃	—	3	1	no	—
477	C₂×Dic₃	—	3	1	no	—
478	C₂×Dic₃	—	3	4	no	—
479	C₂×Dic₃	—	3	1	no	—
480	C₂×Dic₃	—	3	1	no	—
481	C₂×Dic₃	—	3	1	no	—
482	C₂×Dic₃	—	3	1	no	—
483	C₂×Dic₃	—	3	1	no	—
484	C₂×Dic₃	—	3	1	no	—
485	C₂×Dic₃	—	6	1	no	—
486	C₂×Dic₃	—	6	1	no	—
487	C₂×Dic₃	—	6	1	no	—
488	C₂×Dic₃	—	6	1	no	—
489	C₂×Dic₃	—	6	2	no	—
490	C₂×Dic₃	—	6	2	no	—
491	C₂×Dic₃	—	6	2	no	—
492	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
493	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
494	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
495	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
496	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
497	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
498	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
499	C₄×D₃	—	2	2	no	—
500	C₄×D₃	—	2	2	no	—
501	C₄×D₃	—	3	4	no	—
502	C₄×D₃	—	6	2	no	—
503	C₄×D₃	—	6	2	no	—
504	C₄×D₃	—	6	2	no	—
505	C₄×D₃	#237	1	2	yes	—
506	C₄×D₃	D₃×Q₈	1	2	yes	—
507	Dic₆	—	2	2	no	—
508	Dic₆	—	6	2	no	—
509	Dic₆	—	6	2	no	—
510	Dic₆	—	6	2	no	—
511	Dic₆	—	6	2	no	—
512	Dic₆	—	6	2	no	—
513	Dic₆	—	6	2	no	—
514	Dic₆	—	12	2	no	—
515	C₃×C₈	—	2	1	no	—
516	C₃×C₈	—	2	1	no	—
517	C₃×C₈	—	2	1	no	—
518	C₃×C₈	—	2	1	no	—
519	C₃×C₈	—	3	2	no	—
520	C₃×C₈	—	4	1	no	—
521	C₃×C₈	—	4	1	no	—
522	C₃×C₈	—	6	1	no	—
523	C₃×C₈	—	6	1	no	—
524	C₃×C₈	—	6	1	no	—
525	C₃⋊C₈	—	2	1	no	—
526	C₃⋊C₈	—	2	1	no	—
527	C₃⋊C₈	—	2	1	no	—
528	C₃⋊C₈	—	3	2	no	—
529	C₃⋊C₈	—	3	2	no	—
530	C₃⋊C₈	—	6	2	no	—
531	C₃⋊C₈	—	6	1	no	—
532	C₃⋊C₈	—	6	1	no	—
533	C₃⋊C₈	—	12	1	no	—
534	C₃⋊C₈	D₃×Q₈	1	2	yes	complemented
535	C₂×C₃²	C₂×C₄×Q₈	1	1	yes	characteristic
536	C₂×C₃²	C₂²×M₁₆	1	1	yes	characteristic
537	C₂×C₃²	C₂×#131	1	1	yes	characteristic
538	C₃×D₃	#446	1	4	yes	complemented
539	C₂×Q₈	—	3	1	no	—
540	C₂×Q₈	—	9	1	no	—
541	C₂×Q₈	—	9	1	no	—
542	C₂×Q₈	—	9	1	no	—
543	C₂×Q₈	—	18	4	no	—
544	C₂²×C₄	—	3	1	no	—
545	C₂²×C₄	—	3	1	no	—
546	C₂²×C₄	—	3	1	no	—
547	C₂²×C₄	—	9	1	no	—
548	C₂²×C₄	—	9	1	no	—
549	C₂²×C₄	—	9	1	no	—
550	C₂²×C₄	—	9	1	no	—
551	C₂×C₈	—	3	1	no	—
552	C₂×C₈	—	3	1	no	—
553	C₂×C₈	—	3	1	no	—
554	C₂×C₈	—	3	1	no	—
555	C₂×C₈	—	6	2	no	—
556	C₂×C₈	—	6	2	no	—
557	C₂×C₈	—	9	4	no	—
558	C₂×C₈	—	9	1	no	—
559	C₂×C₈	—	9	1	no	—
560	C₂×C₈	—	18	2	no	—
561	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
562	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
563	C₄⋊C₄	—	3	1	no	—
564	C₄⋊C₄	—	3	1	no	—
565	C₄⋊C₄	—	3	1	no	—
566	C₄⋊C₄	—	9	1	no	—
567	C₄⋊C₄	—	9	1	no	—
568	C₄⋊C₄	—	9	1	no	—
569	C₄⋊C₄	—	9	1	no	—
570	C₄⋊C₄	—	9	1	no	—
571	C₄⋊C₄	—	9	1	no	—
572	C₄⋊C₄	—	9	1	no	—
573	C₄⋊C₄	—	9	1	no	—
574	C₄⋊C₄	—	9	1	no	—
575	C₄²	—	3	1	no	—
576	C₄²	—	3	1	no	—
577	C₄²	—	3	1	no	—
578	C₄²	—	3	1	no	—
579	C₄²	—	3	1	no	—
580	C₄²	—	9	1	no	—
581	C₄²	—	9	1	no	—
582	C₄²	—	9	1	no	—
583	C₄²	—	9	1	no	—
584	C₄²	—	9	1	no	—
585	C₄²	—	9	1	no	—
586	C₄²	C₂×D₃²	1	1	yes	characteristic
587	C₂²×C₃	—	2	1	no	—
588	C₂²×C₃	—	3	2	no	—
589	C₂²×C₃	—	3	2	no	—
590	C₂²×C₃	—	3	2	no	—
591	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
592	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
593	C₂×D₃	#887	1	2	yes	—
594	C₂×D₃	#901	1	2	yes	—
595	C₂×D₃	D₃×M₁₆	1	2	yes	—
596	C₃×C₄	—	2	1	no	—
597	C₃×C₄	—	2	1	no	—
598	C₃×C₄	—	2	1	no	—
599	C₃×C₄	—	2	1	no	—
600	C₃×C₄	—	2	1	no	—
601	C₃×C₄	—	2	1	no	—
602	C₃×C₄	—	3	2	no	—
603	C₃×C₄	—	3	2	no	—
604	C₃×C₄	—	4	1	no	—
605	C₃×C₄	—	4	1	no	—
606	C₃×C₄	—	6	1	no	—
607	C₃×C₄	—	6	1	no	—
608	C₃×C₄	—	6	1	no	—
609	C₃×C₄	—	6	1	no	—
610	C₃×C₄	—	6	1	no	—
611	C₃×C₄	C₂×#237	1	1	yes	characteristic
612	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
613	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
614	C₃×C₄	D₃×#41	1	1	yes	characteristic
615	Dic₃	—	2	1	no	—
616	Dic₃	—	2	1	no	—
617	Dic₃	—	2	1	no	—
618	Dic₃	—	2	1	no	—
619	Dic₃	—	2	1	no	—
620	Dic₃	—	3	2	no	—
621	Dic₃	—	3	2	no	—
622	Dic₃	—	6	2	no	—
623	Dic₃	—	6	1	no	—
624	Dic₃	—	6	1	no	—
625	Dic₃	—	6	1	no	—
626	Dic₃	—	6	1	no	—
627	Dic₃	—	6	1	no	—
628	Dic₃	—	6	1	no	—
629	Dic₃	—	12	1	no	—
630	Dic₃	—	12	1	no	—
631	Dic₃	—	12	1	no	—
632	Dic₃	#887	1	2	yes	—
633	Dic₃	D₃×M₁₆	1	2	yes	—
634	C₃²	C₂×#446	1	1	yes	characteristic, complemented, Sylow
635	C₂³	—	3	1	no	—
636	Q₈	—	6	2	no	—
637	Q₈	—	18	2	no	—
638	Q₈	—	18	2	no	—
639	Q₈	—	18	2	no	—
640	C₂×C₄	—	3	1	no	—
641	C₂×C₄	—	3	1	no	—
642	C₂×C₄	—	3	2	no	—
643	C₂×C₄	—	3	2	no	—
644	C₂×C₄	—	3	1	no	—
645	C₂×C₄	—	3	1	no	—
646	C₂×C₄	—	3	1	no	—
647	C₂×C₄	—	3	1	no	—
648	C₂×C₄	—	3	1	no	—
649	C₂×C₄	—	6	2	no	—
650	C₂×C₄	—	6	2	no	—
651	C₂×C₄	—	9	4	no	—
652	C₂×C₄	—	9	1	no	—
653	C₂×C₄	—	9	1	no	—
654	C₂×C₄	—	9	1	no	—
655	C₂×C₄	—	9	1	no	—
656	C₂×C₄	—	18	2	no	—
657	C₂×C₄	—	18	2	no	—
658	C₂×C₄	—	18	2	no	—
659	C₂×C₄	C₄×D₃²	1	1	yes	characteristic
660	C₂×C₄	C₄×D₃²	1	1	yes	characteristic
661	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
662	C₈	—	2	1	no	—
663	C₈	—	2	1	no	—
664	C₈	—	3	2	no	—
665	C₈	—	6	1	no	—
666	C₈	—	6	1	no	—
667	C₈	—	6	1	no	—
668	C₈	—	9	2	no	—
669	C₈	—	18	1	no	—
670	C₂×C₃	—	2	1	no	—
671	C₂×C₃	—	2	1	no	—
672	C₂×C₃	—	2	1	no	—
673	C₂×C₃	—	3	4	no	—
674	C₂×C₃	C₂×#887	1	1	yes	characteristic
675	C₂×C₃	C₄×D₃×Q₈	1	1	yes	characteristic
676	C₂×C₃	C₂×#901	1	1	yes	characteristic
677	C₂×C₃	C₂×D₃×M₁₆	1	1	yes	characteristic
678	C₂×C₃	C₂×D₃×M₁₆	1	1	yes	characteristic
679	C₂×C₃	D₃×#131	1	1	yes	characteristic
680	D₃	#4828	1	4	yes	direct product factor
681	C₂²	—	3	2	no	—
682	C₂²	—	3	2	no	—
683	C₂²	—	3	2	no	—
684	C₂²	C₂×C₄×D₃²	1	1	yes	characteristic
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	3	2	no	—
688	C₄	—	3	2	no	—
689	C₄	—	6	1	no	—
690	C₄	—	6	1	no	—
691	C₄	—	6	1	no	—
692	C₄	—	6	1	no	—
693	C₄	—	6	1	no	—
694	C₄	—	9	2	no	—
695	C₄	—	18	1	no	—
696	C₄	—	18	1	no	—
697	C₄	—	18	1	no	—
698	C₄	D₃×#237	1	1	yes	characteristic
699	C₄	D₃²×Q₈	1	1	yes	characteristic
700	C₃	—	2	1	no	—
701	C₃	C₂×#4828	1	1	yes	characteristic, complemented
702	C₃	D₃×#446	1	1	yes	characteristic, complemented
703	C₂	—	3	4	no	—
704	C₂	D₃×#887	1	1	yes	characteristic
705	C₂	D₃×#901	1	1	yes	characteristic
706	C₂	D₃²×M₁₆	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃²
commutator, socle	C₂²×C₃²	C₂³×C₄
Fitting	C₃²×C₄⋊C₈	C₂²
prime radical	C₂²×C₃×D₃	C₂²×C₄
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	C₄⋊C₈	D₃²
hypocenter	C₃²	C₂×#446
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. #10592527	C₂	semidirect
4. C₃×#4828	C₂	semidirect
5. #10590789	C₂	semidirect
6. #10590788	C₂	semidirect
7. #10590785	C₂	semidirect
12. #10590646	C₂	semidirect
14. #10590255	C₂	semidirect
15. #10590252	C₂	semidirect
85. #4828	D₃	direct (N × H)
139. D₃×C₃⋊C₈	Q₈	semidirect
264. C₃⋊(C₃⋊C₈)	C₂×Q₈	semidirect
268. C₃×C₃⋊C₈	C₂×Q₈	semidirect
534. C₃⋊C₈	D₃×Q₈	semidirect
538. C₃×D₃	#446	semidirect
634. C₃²	C₂×#446	semidirect
680. D₃	#4828	direct (N × H)
701. C₃	C₂×#4828	semidirect
702. C₃	D₃×#446	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₃×Dic₆	2
#10592527	2
C₃×D₃×C₄⋊C₈	2
C₃×#4828	2
#10590789	2
#10590788	2
#10590785	2
D₃×#815	2
D₃×Dic₃⋊C₈	2
D₃×C₈×Dic₃	2
#10590646	2
D₃×#803	2
#10590255	2
#10590252	2
D₃×#446	3
C₂×#4828	3

Subgroups — D3×#4828 #11861315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#4828 #11861315