Subgroups — C₃⋊D₃×#2171 #72255424

Order 2304.

1962 conjugacy classes of subgroups.

The subgroup lattice has 633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×#504	C₂	1	2	yes	maximal, complemented
2	C₃⋊D₃×#443	C₂	1	1	yes	maximal, characteristic
3	#11797595	C₂	1	1	yes	maximal, characteristic, complemented
4	#11797592	C₂	1	1	yes	maximal, characteristic, complemented
5	#11797589	C₂	1	1	yes	maximal, characteristic, complemented
6	#11797586	C₂	1	2	yes	maximal, complemented
7	#11797583	C₂	1	2	yes	maximal, complemented
8	C₃⋊D₃×#364	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃⋊D₃×#350	C₂	1	2	yes	maximal, complemented
10	C₃⋊D₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×#2171	C₂	1	1	yes	maximal, characteristic, complemented
12	D₃×#2171	—	3	4	no	maximal
13	C₃⋊D₃×#135	C₄	1	1	yes	characteristic
14	C₃⋊D₃×#131	C₂²	1	2	yes	—
15	C₃²×#504	C₂²	1	2	yes	complemented
16	C₃²×#443	C₂²	1	1	yes	characteristic
17	#10592895	C₄	1	1	yes	characteristic
18	#10592843	C₂²	1	2	yes	—
19	#10592839	C₂²	1	2	yes	complemented
20	#10592606	—	2	2	no	—
21	#10592606	C₂²	1	2	yes	complemented
22	C₃⋊D₃×M₃₂	—	2	2	no	—
23	C₃⋊D₃×M₃₂	C₂²	1	2	yes	—
24	#10592600	—	2	2	no	—
25	#10592600	C₂²	1	2	yes	complemented
26	C₂×C₁₆×C₃⋊D₃	—	2	2	no	—
27	C₂×C₁₆×C₃⋊D₃	C₂²	1	1	yes	characteristic
28	C₂×C₁₆×C₃⋊D₃	C₂²	1	1	yes	characteristic
29	#10592594	C₄	1	1	yes	characteristic
30	C₃⋊D₃×#108	C₄	1	1	yes	characteristic
31	#10592523	C₄	1	2	yes	—
32	C₃⋊D₃×#104	C₄	1	2	yes	—
33	#10592399	C₂²	1	1	yes	characteristic
34	C₄×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
35	C₃²×#364	C₂²	1	1	yes	characteristic, complemented
36	C₃²×#350	C₂²	1	2	yes	complemented
37	C₃²×#346	C₂²	1	1	yes	characteristic, complemented
38	#10589427	C₂²	1	2	yes	complemented
39	#10589381	C₂²	1	2	yes	complemented
40	#10589377	C₂²	1	2	yes	complemented
41	#10589374	C₂²	1	2	yes	complemented
42	#10589368	C₂²	1	1	yes	characteristic, complemented
43	#10589368	C₂²	1	1	yes	characteristic, complemented
44	#10589329	C₂²	1	1	yes	characteristic, complemented
45	#10589327	C₂²	1	1	yes	characteristic, complemented
46	D₃×#504	—	3	8	no	—
47	D₃×#443	—	3	4	no	—
48	C₃×#2171	D₃	1	4	yes	complemented
49	#71453	—	3	8	no	—
50	#70924	—	3	4	no	—
51	D₃×#364	—	3	4	no	—
52	#69301	—	3	4	no	—
53	D₃×#350	—	3	8	no	—
54	#69123	—	3	8	no	—
55	#69076	—	3	4	no	—
56	D₃×#346	—	3	4	no	—
57	#41×C₃⋊D₃	C₂×C₄	1	2	yes	—
58	C₃²×#135	C₂×C₄	1	1	yes	characteristic
59	C₃²×#131	C₂³	1	2	yes	—
60	#64159	C₂×C₄	1	2	yes	—
61	#64157	C₂×C₄	1	2	yes	—
62	#64128	C₈	1	1	yes	characteristic
63	Q₁₆×C₃⋊D₃	C₈	1	1	yes	characteristic
64	#64125	C₈	1	2	yes	—
65	SD₁₆×C₃⋊D₃	C₈	1	2	yes	—
66	#64121	C₈	1	1	yes	characteristic
67	D₈×C₃⋊D₃	C₈	1	1	yes	characteristic
68	#64116	—	2	2	no	—
69	#64116	C₂×C₄	1	2	yes	—
70	M₁₆×C₃⋊D₃	—	2	2	no	—
71	M₁₆×C₃⋊D₃	C₂×C₄	1	2	yes	—
72	#64113	C₂×C₄	1	1	yes	characteristic
73	#64110	—	2	2	no	—
74	#64110	C₂³	1	2	yes	—
75	C₂×C₈×C₃⋊D₃	—	2	2	no	—
76	C₂×C₈×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×C₃⋊D₃	C₂³	1	1	yes	characteristic
78	C₄²×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
79	C₃²×M₃₂	—	2	2	no	—
80	C₃²×M₃₂	C₂³	1	2	yes	—
81	C₂×C₃²×C₁₆	—	2	2	no	—
82	C₂×C₃²×C₁₆	C₂³	1	1	yes	characteristic
83	C₂×C₃²×C₁₆	C₂³	1	1	yes	characteristic
84	C₃²×#108	C₂×C₄	1	1	yes	characteristic
85	C₃²×#104	C₂×C₄	1	2	yes	—
86	C₃²×C₄×C₈	C₂³	1	1	yes	characteristic
87	#63664	C₂×C₄	1	2	yes	—
88	#63652	C₂×C₄	1	2	yes	—
89	#63649	C₂×C₄	1	2	yes	—
90	#63646	C₂×C₄	1	1	yes	characteristic
91	C₈×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
92	C₈×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
93	#63639	—	2	2	no	—
94	#63639	C₂³	1	2	yes	—
95	C₂×C₃⋊(C₃⋊C₁₆)	—	2	2	no	—
96	C₂×C₃⋊(C₃⋊C₁₆)	C₂³	1	1	yes	characteristic
97	C₂×C₃⋊(C₃⋊C₁₆)	C₂³	1	1	yes	characteristic
98	#63632	C₂×C₄	1	2	yes	—
99	C₄×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
100	#63625	—	2	2	no	—
101	#63625	—	2	2	no	—
102	#63625	—	2	2	no	—
103	C₁₆×C₃⋊D₃	—	2	2	no	—
104	C₁₆×C₃⋊D₃	—	2	1	no	—
105	C₁₆×C₃⋊D₃	—	2	1	no	—
106	C₁₆×C₃⋊D₃	—	2	2	no	—
107	C₁₆×C₃⋊D₃	—	2	2	no	—
108	C₁₆×C₃⋊D₃	D₄	1	2	yes	—
109	C₁₆×C₃⋊D₃	D₄	1	2	yes	—
110	C₂×#2171	—	9	1	no	Sylow
111	D₃×#135	—	3	4	no	—
112	D₃×#131	—	3	8	no	—
113	C₃×#504	C₂×D₃	1	8	yes	complemented
114	C₃×#443	C₂×D₃	1	4	yes	—
115	#5196	—	3	4	no	—
116	#5144	—	3	8	no	—
117	#5140	—	3	8	no	—
118	#4907	—	3	8	no	—
119	#4907	—	6	8	no	—
120	D₃×M₃₂	—	3	8	no	—
121	D₃×M₃₂	—	6	8	no	—
122	#4901	—	3	8	no	—
123	#4901	—	6	8	no	—
124	C₂×D₃×C₁₆	—	3	4	no	—
125	C₂×D₃×C₁₆	—	3	4	no	—
126	C₂×D₃×C₁₆	—	6	8	no	—
127	#4895	—	3	4	no	—
128	D₃×#108	—	3	4	no	—
129	#4824	—	3	8	no	—
130	D₃×#104	—	3	8	no	—
131	#4700	—	3	4	no	—
132	C₄×D₃×C₈	—	3	4	no	—
133	C₃×#364	C₂×D₃	1	4	yes	complemented
134	C₃×#350	C₂×D₃	1	8	yes	complemented
135	C₃×#346	C₂×D₃	1	4	yes	complemented
136	#4561	—	3	8	no	—
137	#4515	—	3	8	no	—
138	#4511	—	3	8	no	—
139	#4508	—	3	8	no	—
140	#4502	—	3	4	no	—
141	#4502	—	3	4	no	—
142	#4463	—	3	4	no	—
143	#4461	—	3	4	no	—
144	C₃²×#41	C₂²×C₄	1	2	yes	—
145	#3832	C₂×C₈	1	2	yes	—
146	Q₈×C₃⋊D₃	C₂×C₈	1	2	yes	—
147	#3830	—	2	2	no	—
148	#3830	C₂×C₈	1	2	yes	—
149	D₄×C₃⋊D₃	—	2	2	no	—
150	D₄×C₃⋊D₃	C₂×C₈	1	2	yes	—
151	#3828	—	2	2	no	—
152	#3828	C₂²×C₄	1	2	yes	—
153	C₂×C₄×C₃⋊D₃	—	2	2	no	—
154	C₂×C₄×C₃⋊D₃	—	2	1	no	—
155	C₂×C₄×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
156	C₃²×Q₁₆	C₂×C₈	1	1	yes	characteristic
157	C₃²×SD₁₆	C₂×C₈	1	2	yes	—
158	C₃²×D₈	C₂×C₈	1	1	yes	characteristic
159	C₃²×M₁₆	—	2	2	no	—
160	C₃²×M₁₆	C₂²×C₄	1	2	yes	—
161	C₂×C₃²×C₈	—	2	2	no	—
162	C₂×C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₃²×C₈	C₂⁴	1	1	yes	characteristic
164	C₃²×C₄²	C₂²×C₄	1	1	yes	characteristic
165	#3756	C₂×C₈	1	2	yes	—
166	#3755	C₂×C₈	1	2	yes	—
167	#3754	C₂×C₈	1	2	yes	—
168	#3753	C₂×C₈	1	2	yes	—
169	C₄×C₃⋊Dic₃	—	2	1	no	—
170	C₄×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
171	#3748	—	2	2	no	—
172	#3748	C₂²×C₄	1	2	yes	—
173	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
174	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₄	1	1	yes	characteristic
176	#3746	C₂×C₈	1	1	yes	characteristic
177	#3745	C₂×C₈	1	1	yes	characteristic
178	#3744	C₂×C₈	1	2	yes	—
179	#3743	—	2	2	no	—
180	#3743	—	2	2	no	—
181	#3743	—	2	2	no	—
182	C₈×C₃⋊D₃	—	2	2	no	—
183	C₈×C₃⋊D₃	—	2	2	no	—
184	C₈×C₃⋊D₃	—	2	2	no	—
185	C₈×C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
186	C₈×C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
187	C₈×C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
188	C₈×C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
189	C₈×C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
190	C₈×C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
191	C₈×C₃⋊D₃	#41	1	1	yes	characteristic
192	C₈×C₃⋊D₃	#41	1	1	yes	characteristic
193	C₃²×C₁₆	—	2	2	no	—
194	C₃²×C₁₆	—	2	1	no	—
195	C₃²×C₁₆	C₂×D₄	1	2	yes	—
196	C₃⋊(C₃⋊C₁₆)	—	2	2	no	—
197	C₃⋊(C₃⋊C₁₆)	—	2	1	no	—
198	C₃⋊(C₃⋊C₁₆)	C₂×D₄	1	2	yes	—
199	C₂×#504	—	9	2	no	—
200	C₂×#443	—	9	1	no	—
201	#2171	—	9	2	no	—
202	#2171	—	9	1	no	—
203	#2171	—	9	1	no	—
204	#2171	—	9	2	no	—
205	#2171	—	9	1	no	—
206	#2171	C₃⋊D₃	1	1	yes	characteristic, direct product factor
207	C₂×#364	—	9	1	no	—
208	C₂×#350	—	9	2	no	—
209	C₂×#346	—	9	1	no	—
210	D₃×#41	—	3	8	no	—
211	C₃×#135	C₄×D₃	1	4	yes	—
212	C₃×#131	C₂²×D₃	1	8	yes	—
213	#950	—	3	8	no	—
214	#948	—	3	8	no	—
215	#919	—	3	4	no	—
216	D₃×Q₁₆	—	3	4	no	—
217	#916	—	3	8	no	—
218	D₃×SD₁₆	—	3	8	no	—
219	#912	—	3	4	no	—
220	D₃×D₈	—	3	4	no	—
221	#907	—	3	8	no	—
222	#907	—	6	8	no	—
223	D₃×M₁₆	—	3	8	no	—
224	D₃×M₁₆	—	6	8	no	—
225	#904	—	3	4	no	—
226	#901	—	3	8	no	—
227	#901	—	6	8	no	—
228	C₂×D₃×C₈	—	3	4	no	—
229	C₂×D₃×C₈	—	3	4	no	—
230	C₂×D₃×C₈	—	6	8	no	—
231	C₄²×D₃	—	3	4	no	—
232	C₃×M₃₂	—	2	8	no	—
233	C₃×M₃₂	C₂²×D₃	1	8	yes	—
234	C₂×C₃×C₁₆	—	2	8	no	—
235	C₂×C₃×C₁₆	C₂²×D₃	1	4	yes	—
236	C₂×C₃×C₁₆	C₂²×D₃	1	4	yes	—
237	C₃×#108	C₄×D₃	1	4	yes	—
238	C₃×#104	C₄×D₃	1	8	yes	—
239	C₃×C₄×C₈	C₂²×D₃	1	4	yes	—
240	#837	—	3	8	no	—
241	#825	—	3	8	no	—
242	#822	—	3	8	no	—
243	#819	—	3	4	no	—
244	C₈×Dic₃	—	3	4	no	—
245	C₈×Dic₃	—	3	4	no	—
246	#812	—	3	8	no	—
247	#812	—	6	8	no	—
248	C₂×C₃⋊C₁₆	—	3	4	no	—
249	C₂×C₃⋊C₁₆	—	3	4	no	—
250	C₂×C₃⋊C₁₆	—	6	8	no	—
251	#805	—	3	8	no	—
252	C₄×C₃⋊C₈	—	3	4	no	—
253	#798	—	6	8	no	—
254	#798	—	6	8	no	—
255	#798	—	6	8	no	—
256	D₃×C₁₆	—	3	8	no	—
257	D₃×C₁₆	—	3	8	no	—
258	D₃×C₁₆	—	6	8	no	—
259	D₃×C₁₆	—	6	4	no	—
260	D₃×C₁₆	—	6	4	no	—
261	D₃×C₁₆	—	6	8	no	—
262	D₃×C₁₆	—	6	8	no	—
263	C₂²×C₃⋊D₃	—	2	2	no	—
264	C₂²×C₃⋊D₃	#131	1	1	yes	characteristic
265	C₃²×Q₈	C₂²×C₈	1	2	yes	—
266	C₃²×D₄	—	2	2	no	—
267	C₃²×D₄	C₂²×C₈	1	2	yes	—
268	C₂×C₃²×C₄	—	2	2	no	—
269	C₂×C₃²×C₄	—	2	1	no	—
270	C₂×C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
271	#638	—	2	2	no	—
272	#638	—	2	2	no	—
273	#638	—	2	2	no	—
274	C₂×C₃⋊Dic₃	—	2	2	no	—
275	C₂×C₃⋊Dic₃	—	2	1	no	—
276	C₂×C₃⋊Dic₃	#131	1	1	yes	characteristic
277	C₄⋊(C₃⋊D₃)	—	2	2	no	—
278	C₄⋊(C₃⋊D₃)	C₂²×C₈	1	2	yes	—
279	C₄×C₃⋊D₃	—	2	2	no	—
280	C₄×C₃⋊D₃	—	2	2	no	—
281	C₄×C₃⋊D₃	—	2	2	no	—
282	C₄×C₃⋊D₃	—	4	2	no	—
283	C₄×C₃⋊D₃	C₄×D₄	1	1	yes	characteristic
284	C₄×C₃⋊D₃	C₄×D₄	1	1	yes	characteristic
285	C₄×C₃⋊D₃	C₂²×C₈	1	1	yes	characteristic
286	C₄×C₃⋊D₃	C₂²×C₈	1	1	yes	characteristic
287	#634	—	2	2	no	—
288	#634	C₂²×C₈	1	2	yes	—
289	C₃²×C₈	—	2	2	no	—
290	C₃²×C₈	C₂²×C₈	1	1	yes	characteristic
291	C₃²×C₈	C₂²×C₈	1	1	yes	characteristic
292	C₃²×C₈	C₂²×D₄	1	1	yes	characteristic
293	C₃²×C₈	C₂×#41	1	1	yes	characteristic
294	C₃⋊(C₃⋊C₈)	—	2	2	no	—
295	C₃⋊(C₃⋊C₈)	C₄×D₄	1	1	yes	characteristic
296	C₃⋊(C₃⋊C₈)	C₄×D₄	1	1	yes	characteristic
297	C₃⋊(C₃⋊C₈)	C₂²×C₈	1	1	yes	characteristic
298	C₃⋊(C₃⋊C₈)	C₂²×C₈	1	1	yes	characteristic
299	C₂×#135	—	9	1	no	—
300	C₂×#131	—	9	2	no	—
301	#504	—	9	2	no	—
302	#504	—	9	2	no	—
303	#504	—	9	2	no	—
304	#504	—	18	2	no	—
305	#504	—	18	2	no	—
306	#504	C₂×C₃⋊D₃	1	2	yes	complemented
307	C₂×M₃₂	—	9	2	no	—
308	C₂×M₃₂	—	18	2	no	—
309	C₂²×C₁₆	—	9	1	no	—
310	C₂²×C₁₆	—	9	1	no	—
311	C₂²×C₁₆	—	18	2	no	—
312	#443	—	9	1	no	—
313	#443	—	9	2	no	—
314	#443	—	9	1	no	—
315	#443	—	9	2	no	—
316	#443	—	9	1	no	—
317	#443	C₂×C₃⋊D₃	1	1	yes	characteristic
318	C₂×#108	—	9	1	no	—
319	C₂×#104	—	9	2	no	—
320	C₂×C₄×C₈	—	9	1	no	—
321	#364	—	9	2	no	—
322	#364	—	9	1	no	—
323	#364	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
324	#350	—	9	2	no	—
325	#350	—	9	2	no	—
326	#350	—	9	2	no	—
327	#350	C₂×C₃⋊D₃	1	2	yes	complemented
328	#346	—	9	1	no	—
329	#346	—	9	1	no	—
330	#346	—	9	1	no	—
331	#346	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
332	C₃×#41	C₂×C₄×D₃	1	8	yes	—
333	#239	—	3	8	no	—
334	D₃×Q₈	—	3	8	no	—
335	#237	—	3	8	no	—
336	#237	—	6	8	no	—
337	D₃×D₄	—	3	8	no	—
338	D₃×D₄	—	6	8	no	—
339	#235	—	3	8	no	—
340	#235	—	6	8	no	—
341	C₂×C₄×D₃	—	3	4	no	—
342	C₂×C₄×D₃	—	6	8	no	—
343	C₂×C₄×D₃	—	6	4	no	—
344	C₃×Q₁₆	D₃×C₈	1	4	yes	—
345	C₃×SD₁₆	D₃×C₈	1	8	yes	—
346	C₃×D₈	D₃×C₈	1	4	yes	—
347	C₃×M₁₆	—	2	8	no	—
348	C₃×M₁₆	C₂×C₄×D₃	1	8	yes	—
349	C₂×C₃×C₈	—	2	8	no	—
350	C₂×C₃×C₈	C₂×C₄×D₃	1	4	yes	—
351	C₂×C₃×C₈	C₂³×D₃	1	4	yes	—
352	C₃×C₄²	C₂×C₄×D₃	1	4	yes	—
353	#216	—	3	8	no	—
354	#215	—	3	8	no	—
355	#214	—	3	8	no	—
356	#213	—	3	8	no	—
357	C₄×Dic₃	—	3	4	no	—
358	C₄×Dic₃	—	6	4	no	—
359	#208	—	3	8	no	—
360	#208	—	6	8	no	—
361	C₂×C₃⋊C₈	—	3	4	no	—
362	C₂×C₃⋊C₈	—	3	4	no	—
363	C₂×C₃⋊C₈	—	6	8	no	—
364	Dic₁₂	—	3	4	no	—
365	D₂₄	—	3	4	no	—
366	#204	—	3	8	no	—
367	ΓL(1,𝔽₂₅)	—	6	8	no	—
368	ΓL(1,𝔽₂₅)	—	6	8	no	—
369	ΓL(1,𝔽₂₅)	—	6	8	no	—
370	D₃×C₈	—	3	4	no	—
371	D₃×C₈	—	3	4	no	—
372	D₃×C₈	—	3	4	no	—
373	D₃×C₈	—	3	4	no	—
374	D₃×C₈	—	3	4	no	—
375	D₃×C₈	—	3	4	no	—
376	D₃×C₈	—	3	4	no	—
377	D₃×C₈	—	3	4	no	—
378	D₃×C₈	—	6	8	no	—
379	D₃×C₈	—	6	8	no	—
380	D₃×C₈	—	6	8	no	—
381	C₃×C₁₆	—	2	8	no	—
382	C₃×C₁₆	—	2	4	no	—
383	C₃×C₁₆	D₃×D₄	1	8	yes	—
384	C₃⋊C₁₆	—	3	8	no	—
385	C₃⋊C₁₆	—	6	8	no	—
386	C₃⋊C₁₆	—	6	4	no	—
387	C₂²×C₃²	—	2	2	no	—
388	C₂²×C₃²	C₂×#131	1	1	yes	characteristic
389	C₂×C₃⋊D₃	—	2	2	no	—
390	C₂×C₃⋊D₃	—	2	2	no	—
391	C₂×C₃⋊D₃	—	4	4	no	—
392	C₂×C₃⋊D₃	C₈×D₄	1	1	yes	characteristic
393	C₂×C₃⋊D₃	C₈×D₄	1	1	yes	characteristic
394	C₃²×C₄	—	2	2	no	—
395	C₃²×C₄	—	4	1	no	—
396	C₃²×C₄	C₂×C₄×D₄	1	1	yes	characteristic
397	C₃²×C₄	C₂³×C₈	1	1	yes	characteristic
398	C₃⋊Dic₃	—	2	2	no	—
399	C₃⋊Dic₃	—	4	1	no	—
400	C₃⋊Dic₃	C₈×D₄	1	1	yes	characteristic
401	C₃⋊Dic₃	C₈×D₄	1	1	yes	characteristic
402	C₂×#41	—	9	2	no	—
403	#135	—	9	2	no	—
404	#135	—	9	1	no	—
405	#135	—	9	2	no	—
406	#135	—	9	1	no	—
407	#135	—	9	1	no	—
408	#135	C₄×C₃⋊D₃	1	1	yes	characteristic
409	C₂×Q₁₆	—	9	1	no	—
410	C₂×SD₁₆	—	9	2	no	—
411	C₂×D₈	—	9	1	no	—
412	#131	—	9	2	no	—
413	#131	—	9	2	no	—
414	#131	—	9	2	no	—
415	#131	—	18	2	no	—
416	#131	—	18	2	no	—
417	#131	C₂²×C₃⋊D₃	1	2	yes	—
418	C₂×M₁₆	—	9	2	no	—
419	C₂×M₁₆	—	18	2	no	—
420	C₂²×C₈	—	9	1	no	—
421	C₂²×C₈	—	9	1	no	—
422	C₂²×C₈	—	18	2	no	—
423	C₂×C₄²	—	9	1	no	—
424	M₃₂	—	2	2	no	—
425	M₃₂	—	9	2	no	—
426	M₃₂	—	18	2	no	—
427	M₃₂	—	18	2	no	—
428	M₃₂	—	18	2	no	—
429	M₃₂	—	18	2	no	—
430	M₃₂	C₂²×C₃⋊D₃	1	2	yes	—
431	C₂×C₁₆	—	2	2	no	—
432	C₂×C₁₆	—	9	1	no	—
433	C₂×C₁₆	—	9	2	no	—
434	C₂×C₁₆	—	9	2	no	—
435	C₂×C₁₆	—	9	1	no	—
436	C₂×C₁₆	—	18	2	no	—
437	C₂×C₁₆	—	18	1	no	—
438	C₂×C₁₆	—	18	1	no	—
439	C₂×C₁₆	—	18	2	no	—
440	C₂×C₁₆	—	18	2	no	—
441	C₂×C₁₆	—	18	2	no	—
442	C₂×C₁₆	C₂²×C₃⋊D₃	1	1	yes	characteristic
443	C₂×C₁₆	C₂²×C₃⋊D₃	1	1	yes	characteristic
444	#108	—	9	2	no	—
445	#108	—	9	1	no	—
446	#108	C₄×C₃⋊D₃	1	1	yes	characteristic
447	#104	—	9	2	no	—
448	#104	—	9	2	no	—
449	#104	—	9	2	no	—
450	#104	C₄×C₃⋊D₃	1	2	yes	—
451	C₄×C₈	—	9	1	no	—
452	C₄×C₈	—	9	1	no	—
453	C₄×C₈	—	9	1	no	—
454	C₄×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
455	C₂²×D₃	—	3	4	no	—
456	C₂²×D₃	—	6	8	no	—
457	C₃×Q₈	C₂×D₃×C₈	1	8	yes	—
458	C₃×D₄	—	2	8	no	—
459	C₃×D₄	C₂×D₃×C₈	1	8	yes	—
460	C₂×C₃×C₄	—	2	8	no	—
461	C₂×C₃×C₄	—	2	4	no	—
462	C₂×C₃×C₄	C₂²×C₄×D₃	1	4	yes	—
463	#67	—	6	8	no	—
464	#67	—	6	8	no	—
465	#67	—	6	8	no	—
466	C₂×Dic₃	—	3	4	no	—
467	C₂×Dic₃	—	6	8	no	—
468	C₂×Dic₃	—	6	4	no	—
469	D₁₂	—	3	8	no	—
470	D₁₂	—	6	8	no	—
471	C₄×D₃	—	3	4	no	—
472	C₄×D₃	—	3	4	no	—
473	C₄×D₃	—	3	4	no	—
474	C₄×D₃	—	3	4	no	—
475	C₄×D₃	—	6	8	no	—
476	C₄×D₃	—	6	8	no	—
477	C₄×D₃	—	6	8	no	—
478	C₄×D₃	—	12	8	no	—
479	Dic₆	—	3	8	no	—
480	Dic₆	—	6	8	no	—
481	C₃×C₈	—	2	8	no	—
482	C₃×C₈	C₂×D₃×C₈	1	4	yes	—
483	C₃×C₈	C₂×D₃×C₈	1	4	yes	—
484	C₃×C₈	C₂×D₃×D₄	1	4	yes	—
485	C₃×C₈	D₃×#41	1	4	yes	—
486	C₃⋊C₈	—	3	4	no	—
487	C₃⋊C₈	—	3	4	no	—
488	C₃⋊C₈	—	3	4	no	—
489	C₃⋊C₈	—	3	4	no	—
490	C₃⋊C₈	—	6	8	no	—
491	C₂×C₃²	—	2	1	no	—
492	C₂×C₃²	—	4	2	no	—
493	C₂×C₃²	C₂×C₈×D₄	1	1	yes	characteristic
494	C₃⋊D₃	—	2	1	no	—
495	C₃⋊D₃	—	4	2	no	—
496	C₃⋊D₃	#2171	1	2	yes	direct product factor
497	#41	—	9	2	no	—
498	#41	—	9	2	no	—
499	#41	—	9	2	no	—
500	#41	—	18	2	no	—
501	#41	—	18	2	no	—
502	#41	C₂×C₄×C₃⋊D₃	1	2	yes	—
503	C₂×Q₈	—	9	2	no	—
504	C₂×D₄	—	9	2	no	—
505	C₂×D₄	—	18	2	no	—
506	C₂²×C₄	—	9	1	no	—
507	C₂²×C₄	—	18	2	no	—
508	C₂²×C₄	—	18	1	no	—
509	Q₁₆	—	9	2	no	—
510	Q₁₆	—	9	1	no	—
511	Q₁₆	C₈×C₃⋊D₃	1	1	yes	characteristic
512	SD₁₆	—	9	2	no	—
513	SD₁₆	—	9	2	no	—
514	SD₁₆	—	9	2	no	—
515	SD₁₆	C₈×C₃⋊D₃	1	2	yes	—
516	D₈	—	9	2	no	—
517	D₈	—	9	1	no	—
518	D₈	C₈×C₃⋊D₃	1	1	yes	characteristic
519	M₁₆	—	2	2	no	—
520	M₁₆	—	9	2	no	—
521	M₁₆	—	18	2	no	—
522	M₁₆	—	18	2	no	—
523	M₁₆	—	18	2	no	—
524	M₁₆	—	18	2	no	—
525	M₁₆	C₂×C₄×C₃⋊D₃	1	2	yes	—
526	C₂×C₈	—	2	2	no	—
527	C₂×C₈	—	9	1	no	—
528	C₂×C₈	—	9	1	no	—
529	C₂×C₈	—	9	1	no	—
530	C₂×C₈	—	9	1	no	—
531	C₂×C₈	—	9	1	no	—
532	C₂×C₈	—	9	1	no	—
533	C₂×C₈	—	9	1	no	—
534	C₂×C₈	—	9	1	no	—
535	C₂×C₈	—	9	1	no	—
536	C₂×C₈	—	9	1	no	—
537	C₂×C₈	—	18	2	no	—
538	C₂×C₈	—	18	2	no	—
539	C₂×C₈	—	18	2	no	—
540	C₂×C₈	—	18	2	no	—
541	C₂×C₈	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
542	C₂×C₈	C₂³×C₃⋊D₃	1	1	yes	characteristic
543	C₄²	—	9	1	no	—
544	C₄²	—	18	1	no	—
545	C₄²	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
546	C₁₆	—	2	2	no	—
547	C₁₆	—	2	1	no	—
548	C₁₆	—	9	2	no	—
549	C₁₆	—	18	2	no	—
550	C₁₆	—	18	1	no	—
551	C₁₆	D₄×C₃⋊D₃	1	2	yes	—
552	C₂²×C₃	—	2	8	no	—
553	C₂²×C₃	D₃×#131	1	4	yes	—
554	C₂×D₃	—	3	4	no	—
555	C₂×D₃	—	3	4	no	—
556	C₂×D₃	—	6	8	no	—
557	C₂×D₃	—	6	8	no	—
558	C₂×D₃	—	12	16	no	—
559	C₃×C₄	—	2	8	no	—
560	C₃×C₄	—	4	4	no	—
561	C₃×C₄	C₄×D₃×D₄	1	4	yes	—
562	C₃×C₄	C₂²×D₃×C₈	1	4	yes	—
563	Dic₃	—	3	4	no	—
564	Dic₃	—	3	4	no	—
565	Dic₃	—	6	8	no	—
566	Dic₃	—	12	4	no	—
567	C₃²	C₂×#2171	1	1	yes	characteristic, complemented, Sylow
568	C₂³	—	9	1	no	—
569	C₂³	—	18	2	no	—
570	Q₈	—	9	2	no	—
571	Q₈	—	18	2	no	—
572	Q₈	C₂×C₈×C₃⋊D₃	1	2	yes	—
573	D₄	—	2	2	no	—
574	D₄	—	9	2	no	—
575	D₄	—	18	2	no	—
576	D₄	—	18	2	no	—
577	D₄	—	18	2	no	—
578	D₄	—	18	2	no	—
579	D₄	C₂×C₈×C₃⋊D₃	1	2	yes	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	9	1	no	—
583	C₂×C₄	—	9	1	no	—
584	C₂×C₄	—	9	1	no	—
585	C₂×C₄	—	9	1	no	—
586	C₂×C₄	—	9	1	no	—
587	C₂×C₄	—	18	2	no	—
588	C₂×C₄	—	18	2	no	—
589	C₂×C₄	—	18	2	no	—
590	C₂×C₄	—	18	2	no	—
591	C₂×C₄	—	18	1	no	—
592	C₂×C₄	—	36	2	no	—
593	C₂×C₄	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
594	C₈	—	2	2	no	—
595	C₈	—	9	1	no	—
596	C₈	—	9	1	no	—
597	C₈	—	9	1	no	—
598	C₈	—	9	1	no	—
599	C₈	—	18	2	no	—
600	C₈	C₂×C₈×C₃⋊D₃	1	1	yes	characteristic
601	C₈	C₂×C₈×C₃⋊D₃	1	1	yes	characteristic
602	C₈	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
603	C₈	#41×C₃⋊D₃	1	1	yes	characteristic
604	C₂×C₃	—	2	4	no	—
605	C₂×C₃	—	4	8	no	—
606	C₂×C₃	D₃×C₈×D₄	1	4	yes	—
607	D₃	—	3	8	no	—
608	D₃	—	6	4	no	—
609	D₃	—	12	8	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	9	1	no	—
612	C₂²	—	9	1	no	—
613	C₂²	—	18	2	no	—
614	C₂²	—	18	2	no	—
615	C₂²	—	36	4	no	—
616	C₂²	C₃⋊D₃×#131	1	1	yes	characteristic
617	C₄	—	2	2	no	—
618	C₄	—	4	1	no	—
619	C₄	—	9	1	no	—
620	C₄	—	9	1	no	—
621	C₄	—	18	2	no	—
622	C₄	—	36	1	no	—
623	C₄	C₄×D₄×C₃⋊D₃	1	1	yes	characteristic
624	C₄	C₂²×C₈×C₃⋊D₃	1	1	yes	characteristic
625	C₃	D₃×#2171	1	4	yes	complemented
626	C₂	—	2	1	no	—
627	C₂	—	4	2	no	—
628	C₂	—	9	2	no	—
629	C₂	—	18	1	no	—
630	C₂	—	36	2	no	—
631	C₂	C₈×D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄×C₃⋊D₃
commutator	C₃²×C₄	C₂³×C₈
Frattini	C₂×C₈	C₂³×C₃⋊D₃
Fitting	C₃²×#2171	C₂
socle	C₂×C₃²	C₂×C₈×D₄
prime radical	C₃⋊D₃×#135	C₄
cosocle	C₂×C₃²×C₈	C₂⁴
hypercenter	#2171	C₃⋊D₃
hypocenter	C₃²	C₂×#2171
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #2171

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₃×#504	C₂	semidirect
3. #11797595	C₂	semidirect
4. #11797592	C₂	semidirect
5. #11797589	C₂	semidirect
6. #11797586	C₂	semidirect
7. #11797583	C₂	semidirect
8. C₃⋊D₃×#364	C₂	semidirect
9. C₃⋊D₃×#350	C₂	semidirect
10. C₃⋊D₃×#346	C₂	semidirect
11. C₃²×#2171	C₂	semidirect
15. C₃²×#504	C₂²	semidirect
19. #10592839	C₂²	semidirect
21. #10592606	C₂²	semidirect
25. #10592600	C₂²	semidirect
35. C₃²×#364	C₂²	semidirect
36. C₃²×#350	C₂²	semidirect
37. C₃²×#346	C₂²	semidirect
38. #10589427	C₂²	semidirect
39. #10589381	C₂²	semidirect
40. #10589377	C₂²	semidirect
41. #10589374	C₂²	semidirect
42. #10589368	C₂²	semidirect
43. #10589368	C₂²	semidirect
44. #10589329	C₂²	semidirect
45. #10589327	C₂²	semidirect
48. C₃×#2171	D₃	semidirect
113. C₃×#504	C₂×D₃	semidirect
133. C₃×#364	C₂×D₃	semidirect
134. C₃×#350	C₂×D₃	semidirect
135. C₃×#346	C₂×D₃	semidirect
206. #2171	C₃⋊D₃	direct (N × H)
306. #504	C₂×C₃⋊D₃	semidirect
323. #364	C₂×C₃⋊D₃	semidirect
327. #350	C₂×C₃⋊D₃	semidirect
331. #346	C₂×C₃⋊D₃	semidirect
496. C₃⋊D₃	#2171	direct (N × H)
567. C₃²	C₂×#2171	semidirect
625. C₃	D₃×#2171	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₃×#504	2
C₃⋊D₃×#443	2
#11797595	2
#11797592	2
#11797589	2
#11797586	2
#11797583	2
C₃⋊D₃×#364	2
C₃⋊D₃×#350	2
C₃⋊D₃×#346	2
C₃²×#2171	2
D₃×#2171	3

Subgroups — C3⋊D3×#2171 #72255424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×#2171 #72255424