Subgroups — C₃×#83843 #11860733

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×#5812	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5798	C₂	1	1	yes	maximal, characteristic
4	C₃×#5225	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5215	C₂	1	1	yes	maximal, characteristic
6	C₃×#5164	C₂	1	4	yes	maximal, complemented
7	C₃×Dic₃×SD₁₆	C₂	1	4	yes	maximal, complemented
8	C₃×#5106	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5101	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2949	—	3	1	no	maximal
11	#83843	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₃²×SD₁₆	C₄	1	8	yes	complemented
15	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
17	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₃×#217	—	2	2	no	—
19	C₃×Q₈×Dic₃	—	2	2	no	—
20	C₃×Q₈×Dic₃	C₂²	1	4	yes	complemented
21	C₃×D₄×Dic₃	—	2	2	no	—
22	C₃×D₄×Dic₃	C₂²	1	4	yes	—
23	C₃×#926	—	2	2	no	—
24	C₃×#926	C₂²	1	1	yes	characteristic
25	C₃×#926	C₂²	1	1	yes	characteristic
26	C₃×#926	C₂²	1	1	yes	characteristic
27	C₂×C₃×#208	C₂²	1	1	yes	characteristic
28	C₃×#835	C₂²	1	4	yes	complemented
29	C₃×#832	C₂²	1	4	yes	—
30	C₃×#818	C₂²	1	2	yes	complemented
31	C₃×#817	C₂²	1	2	yes	complemented
32	C₃×#815	C₂²	1	2	yes	complemented
33	C₃×C₈×Dic₃	C₂²	1	2	yes	complemented
34	C₂²×C₃×SD₁₆	—	2	1	no	—
35	C₂²×C₃×SD₁₆	D₃	1	1	yes	characteristic
36	C₂²×C₃×SD₁₆	C₂×C₃	1	1	yes	characteristic
37	C₃×#519	—	3	1	no	—
38	C₃×#518	—	3	1	no	—
39	#5812	C₂×C₃	1	1	yes	characteristic, complemented
40	#5798	C₂×C₃	1	1	yes	characteristic
41	C₃×#440	—	3	4	no	—
42	C₃×C₄×SD₁₆	—	3	4	no	—
43	C₃×#427	—	3	1	no	—
44	C₃×#419	—	3	1	no	—
45	C₃×#418	—	3	1	no	—
46	C₃×#405	—	3	1	no	—
47	#5225	C₂×C₃	1	1	yes	characteristic, complemented
48	#5215	C₂×C₃	1	1	yes	characteristic
49	#5164	C₂×C₃	1	4	yes	complemented
50	Dic₃×SD₁₆	C₂×C₃	1	4	yes	complemented
51	#5106	C₂×C₃	1	1	yes	characteristic, complemented
52	#5101	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂⁴×C₃²	—	2	1	no	—
54	C₂×C₃²×Q₈	—	2	1	no	—
55	C₂×C₃²×Q₈	—	2	2	no	—
56	C₂×C₃²×Q₈	C₂×C₄	1	4	yes	complemented
57	C₂×C₃²×Q₈	C₂³	1	2	yes	—
58	C₂×C₃²×D₄	—	2	1	no	—
59	C₂×C₃²×D₄	—	2	2	no	—
60	C₂×C₃²×D₄	C₂×C₄	1	4	yes	—
61	C₂×C₃²×D₄	C₂³	1	2	yes	—
62	C₂²×C₃²×C₄	—	2	1	no	—
63	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
64	C₂²×C₃×Dic₃	—	2	4	no	—
65	C₃²×SD₁₆	C₂×C₄	1	8	yes	complemented
66	C₃²×SD₁₆	C₂×C₄	1	8	yes	complemented
67	C₂×C₃²×C₈	C₂×C₄	1	4	yes	complemented
68	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
69	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
70	C₃×#217	—	2	1	no	—
71	C₃×#217	—	2	1	no	—
72	C₃×#217	—	2	4	no	—
73	C₃×#217	D₄	1	2	yes	—
74	C₃×C₄⋊Dic₃	—	2	4	no	—
75	C₃×C₄⋊Dic₃	D₄	1	2	yes	—
76	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
77	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
78	C₃×C₄×Dic₃	—	2	1	no	—
79	C₃×C₄×Dic₃	—	2	1	no	—
80	C₃×C₄×Dic₃	—	2	4	no	—
81	C₃×C₄×Dic₃	C₂³	1	2	yes	—
82	C₃×#208	—	2	2	no	—
83	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
84	#2949	—	3	1	no	Sylow
85	C₂²×C₃×Q₈	—	2	1	no	—
86	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic
87	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₃×D₄	—	2	1	no	—
89	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
90	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃×SD₁₆	—	2	8	no	—
92	C₂×C₃×SD₁₆	—	2	2	no	—
93	C₂×C₃×SD₁₆	—	2	2	no	—
94	C₂×C₃×SD₁₆	Dic₃	1	8	yes	complemented
95	C₂×C₃×SD₁₆	C₃×C₄	1	8	yes	complemented
96	C₂×C₃×SD₁₆	C₂×D₃	1	2	yes	—
97	C₂×C₃×SD₁₆	C₂×D₃	1	2	yes	—
98	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
99	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
100	C₂×C₃×M₁₆	—	3	1	no	—
101	C₂²×C₃×C₈	—	2	1	no	—
102	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
103	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
104	C₃×C₄×Q₈	—	3	4	no	—
105	C₃×C₄×Q₈	—	6	2	no	—
106	C₃×C₄×D₄	—	3	4	no	—
107	C₃×C₄×D₄	—	6	2	no	—
108	C₃×#117	—	3	1	no	—
109	C₃×#117	—	3	1	no	—
110	C₃×#117	—	3	1	no	—
111	C₃×#117	—	6	2	no	—
112	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
113	C₂×#217	—	2	2	no	—
114	Q₈×Dic₃	—	2	2	no	—
115	Q₈×Dic₃	C₂²×C₃	1	4	yes	complemented
116	D₄×Dic₃	—	2	2	no	—
117	D₄×Dic₃	C₂²×C₃	1	4	yes	—
118	#926	—	2	2	no	—
119	#926	C₂²×C₃	1	1	yes	characteristic
120	#926	C₂²×C₃	1	1	yes	characteristic
121	#926	C₂²×C₃	1	1	yes	characteristic
122	C₂×#208	C₂²×C₃	1	1	yes	characteristic
123	C₃×#107	—	3	2	no	—
124	C₃×#106	—	3	2	no	—
125	C₃×#103	—	3	4	no	—
126	C₃×#102	—	3	4	no	—
127	C₃×#97	—	3	2	no	—
128	C₃×C₄×C₈	—	3	2	no	—
129	#835	C₂²×C₃	1	4	yes	complemented
130	#832	C₂²×C₃	1	4	yes	—
131	#818	C₂²×C₃	1	2	yes	complemented
132	#817	C₂²×C₃	1	2	yes	complemented
133	#815	C₂²×C₃	1	2	yes	complemented
134	C₈×Dic₃	C₂²×C₃	1	2	yes	complemented
135	C₂³×C₃²	—	2	2	no	—
136	C₂³×C₃²	—	2	4	no	—
137	C₂³×C₃²	—	8	2	no	—
138	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
139	C₃²×Q₈	—	2	4	no	—
140	C₃²×Q₈	—	2	2	no	—
141	C₃²×Q₈	C₂²×C₄	1	4	yes	—
142	C₃²×D₄	—	2	4	no	—
143	C₃²×D₄	—	2	2	no	—
144	C₃²×D₄	C₂²×C₄	1	4	yes	—
145	C₂×C₃²×C₄	—	2	4	no	—
146	C₂×C₃²×C₄	—	2	2	no	—
147	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
148	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
149	C₂×C₃²×C₄	#41	1	2	yes	—
150	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
151	C₂×C₃×Dic₃	—	2	2	no	—
152	C₂×C₃×Dic₃	—	2	2	no	—
153	C₂×C₃×Dic₃	—	8	4	no	—
154	C₂×C₃×Dic₃	C₂×D₄	1	4	yes	—
155	C₃²×C₈	C₂²×C₄	1	2	yes	—
156	C₃²×C₈	C₂²×C₄	1	2	yes	—
157	C₃×C₃⋊C₈	—	2	2	no	—
158	C₂²×SD₁₆	C₃×D₃	1	1	yes	characteristic
159	#519	—	3	1	no	—
160	#518	—	3	1	no	—
161	#440	—	3	4	no	—
162	C₄×SD₁₆	—	3	4	no	—
163	#427	—	3	1	no	—
164	#419	—	3	1	no	—
165	#418	—	3	1	no	—
166	#405	—	3	1	no	—
167	C₂⁴×C₃	—	2	1	no	—
168	C₂⁴×C₃	—	2	1	no	—
169	C₂⁴×C₃	—	4	1	no	—
170	C₂×C₃×Q₈	—	2	1	no	—
171	C₂×C₃×Q₈	—	2	2	no	—
172	C₂×C₃×Q₈	—	2	1	no	—
173	C₂×C₃×Q₈	—	2	2	no	—
174	C₂×C₃×Q₈	—	2	4	no	—
175	C₂×C₃×Q₈	—	2	2	no	—
176	C₂×C₃×Q₈	—	4	1	no	—
177	C₂×C₃×Q₈	—	4	2	no	—
178	C₂×C₃×Q₈	C₂×Dic₃	1	4	yes	complemented
179	C₂×C₃×Q₈	C₂×C₃×C₄	1	4	yes	complemented
180	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
181	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
182	C₂×C₃×D₄	—	2	1	no	—
183	C₂×C₃×D₄	—	2	2	no	—
184	C₂×C₃×D₄	—	2	1	no	—
185	C₂×C₃×D₄	—	2	2	no	—
186	C₂×C₃×D₄	—	2	4	no	—
187	C₂×C₃×D₄	—	2	2	no	—
188	C₂×C₃×D₄	—	4	1	no	—
189	C₂×C₃×D₄	—	4	2	no	—
190	C₂×C₃×D₄	C₂×Dic₃	1	4	yes	—
191	C₂×C₃×D₄	C₂×C₃×C₄	1	4	yes	—
192	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
193	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
194	C₂²×C₃×C₄	—	2	1	no	—
195	C₂²×C₃×C₄	—	2	1	no	—
196	C₂²×C₃×C₄	—	2	1	no	—
197	C₂²×C₃×C₄	—	4	1	no	—
198	C₂²×C₃×C₄	—	6	4	no	—
199	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
201	C₂²×Dic₃	—	2	4	no	—
202	C₃×SD₁₆	—	2	8	no	—
203	C₃×SD₁₆	—	2	8	no	—
204	C₃×SD₁₆	C₂×Dic₃	1	8	yes	complemented
205	C₃×SD₁₆	C₂×Dic₃	1	8	yes	complemented
206	C₃×SD₁₆	C₂×C₃×C₄	1	8	yes	complemented
207	C₃×SD₁₆	C₂×C₃×C₄	1	8	yes	complemented
208	C₃×M₁₆	—	6	2	no	—
209	C₂×C₃×C₈	—	2	4	no	—
210	C₂×C₃×C₈	—	2	1	no	—
211	C₂×C₃×C₈	—	2	1	no	—
212	C₂×C₃×C₈	—	3	2	no	—
213	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	complemented
214	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
215	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
216	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
217	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
218	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
219	C₃×C₄⋊C₄	—	3	2	no	—
220	C₃×C₄⋊C₄	—	3	2	no	—
221	C₃×C₄⋊C₄	—	3	2	no	—
222	C₃×C₄⋊C₄	—	6	4	no	—
223	C₃×C₂²⋊C₄	—	3	2	no	—
224	C₃×C₂²⋊C₄	—	6	4	no	—
225	C₃×C₂²⋊C₄	—	6	1	no	—
226	C₃×C₂²⋊C₄	—	6	1	no	—
227	C₃×C₄²	—	3	2	no	—
228	C₃×C₄²	—	6	4	no	—
229	C₃×C₄²	—	6	1	no	—
230	C₃×C₄²	—	6	1	no	—
231	#217	—	2	1	no	—
232	#217	—	2	1	no	—
233	#217	—	2	4	no	—
234	#217	C₃×D₄	1	2	yes	—
235	C₄⋊Dic₃	—	2	4	no	—
236	C₄⋊Dic₃	C₃×D₄	1	2	yes	—
237	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
238	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
239	C₄×Dic₃	—	2	1	no	—
240	C₄×Dic₃	—	2	1	no	—
241	C₄×Dic₃	—	2	4	no	—
242	C₄×Dic₃	C₂³×C₃	1	2	yes	—
243	#208	—	2	2	no	—
244	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
245	C₂²×C₃²	—	2	2	no	—
246	C₂²×C₃²	—	2	4	no	—
247	C₂²×C₃²	—	4	4	no	—
248	C₂²×C₃²	—	8	4	no	—
249	C₂²×C₃²	C₄×D₄	1	2	yes	—
250	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
251	C₃²×C₄	—	2	4	no	—
252	C₃²×C₄	C₄×D₄	1	2	yes	—
253	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
254	C₃²×C₄	C₂×#41	1	1	yes	characteristic
255	C₃×Dic₃	—	2	4	no	—
256	C₃×Dic₃	—	4	2	no	—
257	C₃×Dic₃	—	4	2	no	—
258	C₂²×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
259	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
260	C₂×SD₁₆	C₃×Dic₃	1	8	yes	complemented
261	C₂×SD₁₆	C₂×C₃×D₃	1	2	yes	—
262	C₂×SD₁₆	C₂×C₃×D₃	1	2	yes	—
263	C₂×M₁₆	—	3	1	no	—
264	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
265	C₄×Q₈	—	3	4	no	—
266	C₄×Q₈	—	6	2	no	—
267	C₄×D₄	—	3	4	no	—
268	C₄×D₄	—	6	2	no	—
269	#117	—	3	1	no	—
270	#117	—	3	1	no	—
271	#117	—	3	1	no	—
272	#117	—	6	2	no	—
273	C₂×C₂²⋊C₄	—	6	2	no	—
274	#107	—	3	2	no	—
275	#106	—	3	2	no	—
276	#103	—	3	4	no	—
277	#102	—	3	4	no	—
278	#97	—	3	2	no	—
279	C₄×C₈	—	3	2	no	—
280	C₂³×C₃	—	2	2	no	—
281	C₂³×C₃	—	2	2	no	—
282	C₂³×C₃	—	2	4	no	—
283	C₂³×C₃	—	2	4	no	—
284	C₂³×C₃	—	2	1	no	—
285	C₂³×C₃	—	4	2	no	—
286	C₂³×C₃	—	4	4	no	—
287	C₂³×C₃	—	8	2	no	—
288	C₂³×C₃	—	8	2	no	—
289	C₂³×C₃	—	8	4	no	—
290	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
291	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
292	C₃×Q₈	—	2	4	no	—
293	C₃×Q₈	—	2	4	no	—
294	C₃×Q₈	—	2	2	no	—
295	C₃×Q₈	—	2	2	no	—
296	C₃×Q₈	—	2	4	no	—
297	C₃×Q₈	—	4	4	no	—
298	C₃×Q₈	—	4	2	no	—
299	C₃×Q₈	C₂²×Dic₃	1	4	yes	—
300	C₃×Q₈	C₂²×C₃×C₄	1	4	yes	—
301	C₃×D₄	—	2	4	no	—
302	C₃×D₄	—	2	4	no	—
303	C₃×D₄	—	2	2	no	—
304	C₃×D₄	—	2	2	no	—
305	C₃×D₄	—	2	4	no	—
306	C₃×D₄	—	4	4	no	—
307	C₃×D₄	—	4	2	no	—
308	C₃×D₄	C₂²×Dic₃	1	4	yes	—
309	C₃×D₄	C₂²×C₃×C₄	1	4	yes	—
310	C₂×C₃×C₄	—	2	4	no	—
311	C₂×C₃×C₄	—	2	4	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	1	no	—
315	C₂×C₃×C₄	—	2	1	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	3	4	no	—
319	C₂×C₃×C₄	—	4	4	no	—
320	C₂×C₃×C₄	—	4	2	no	—
321	C₂×C₃×C₄	—	6	2	no	—
322	C₂×C₃×C₄	—	6	2	no	—
323	C₂×C₃×C₄	—	24	4	no	—
324	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
325	C₂×C₃×C₄	#237	1	2	yes	—
326	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
327	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
328	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
329	C₂×C₃×C₄	C₃×#41	1	2	yes	—
330	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
332	C₂×Dic₃	—	2	2	no	—
333	C₂×Dic₃	—	2	2	no	—
334	C₂×Dic₃	—	8	4	no	—
335	C₂×Dic₃	C₂×C₃×D₄	1	4	yes	—
336	C₃×C₈	—	2	2	no	—
337	C₃×C₈	—	2	2	no	—
338	C₃×C₈	—	6	2	no	—
339	C₃×C₈	C₂²×Dic₃	1	2	yes	—
340	C₃×C₈	C₂²×Dic₃	1	2	yes	—
341	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
342	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
343	C₃⋊C₈	—	2	2	no	—
344	C₂×C₃²	—	2	2	no	—
345	C₂×C₃²	—	4	4	no	—
346	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
347	C₂×C₃²	#577	1	2	yes	—
348	C₂⁴	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	C₂×C₃×Dic₃	1	4	yes	complemented
352	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	C₂×C₃×Dic₃	1	4	yes	—
356	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	6	4	no	—
359	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
360	SD₁₆	C₂×C₃×Dic₃	1	8	yes	complemented
361	SD₁₆	C₂×C₃×Dic₃	1	8	yes	complemented
362	M₁₆	—	6	2	no	—
363	C₂×C₈	—	3	2	no	—
364	C₂×C₈	C₂×C₃×Dic₃	1	4	yes	complemented
365	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
366	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
367	C₄⋊C₄	—	3	2	no	—
368	C₄⋊C₄	—	3	2	no	—
369	C₄⋊C₄	—	3	2	no	—
370	C₄⋊C₄	—	6	4	no	—
371	C₂²⋊C₄	—	3	2	no	—
372	C₂²⋊C₄	—	6	4	no	—
373	C₂²⋊C₄	—	6	1	no	—
374	C₂²⋊C₄	—	6	1	no	—
375	C₄²	—	3	2	no	—
376	C₄²	—	6	4	no	—
377	C₄²	—	6	1	no	—
378	C₄²	—	6	1	no	—
379	C₂²×C₃	—	2	4	no	—
380	C₂²×C₃	—	2	2	no	—
381	C₂²×C₃	—	2	2	no	—
382	C₂²×C₃	—	2	4	no	—
383	C₂²×C₃	—	2	4	no	—
384	C₂²×C₃	—	2	2	no	—
385	C₂²×C₃	—	2	1	no	—
386	C₂²×C₃	—	4	4	no	—
387	C₂²×C₃	—	4	4	no	—
388	C₂²×C₃	—	4	4	no	—
389	C₂²×C₃	—	8	4	no	—
390	C₂²×C₃	—	8	4	no	—
391	C₂²×C₃	—	8	4	no	—
392	C₂²×C₃	—	8	8	no	—
393	C₂²×C₃	D₄×Dic₃	1	2	yes	—
394	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
395	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
396	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
397	C₃×C₄	—	2	4	no	—
398	C₃×C₄	—	2	4	no	—
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	—	2	1	no	—
401	C₃×C₄	—	2	1	no	—
402	C₃×C₄	—	4	4	no	—
403	C₃×C₄	—	6	4	no	—
404	C₃×C₄	—	12	2	no	—
405	C₃×C₄	—	12	2	no	—
406	C₃×C₄	D₄×Dic₃	1	2	yes	—
407	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
408	C₃×C₄	C₂×#237	1	1	yes	characteristic
409	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
410	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
411	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
412	Dic₃	—	2	4	no	—
413	Dic₃	—	4	2	no	—
414	Dic₃	—	4	2	no	—
415	C₃²	#2949	1	1	yes	characteristic, complemented, Sylow
416	C₂³	—	2	2	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	8	2	no	—
419	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
420	Q₈	—	2	4	no	—
421	Q₈	—	2	2	no	—
422	Q₈	C₂²×C₃×Dic₃	1	4	yes	—
423	D₄	—	2	4	no	—
424	D₄	—	2	2	no	—
425	D₄	C₂²×C₃×Dic₃	1	4	yes	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	3	4	no	—
429	C₂×C₄	—	6	2	no	—
430	C₂×C₄	—	6	2	no	—
431	C₂×C₄	—	24	4	no	—
432	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
433	C₂×C₄	C₃×#237	1	2	yes	—
434	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
435	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
436	C₈	—	6	2	no	—
437	C₈	C₂²×C₃×Dic₃	1	2	yes	—
438	C₈	C₂²×C₃×Dic₃	1	2	yes	—
439	C₂×C₃	—	2	4	no	—
440	C₂×C₃	—	2	2	no	—
441	C₂×C₃	—	2	2	no	—
442	C₂×C₃	—	2	2	no	—
443	C₂×C₃	—	2	1	no	—
444	C₂×C₃	—	4	4	no	—
445	C₂×C₃	—	4	4	no	—
446	C₂×C₃	—	8	4	no	—
447	C₂×C₃	#5762	1	2	yes	—
448	C₂×C₃	C₂×D₄×Dic₃	1	1	yes	characteristic
449	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
450	C₂×C₃	C₃×#577	1	2	yes	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	4	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	8	4	no	—
455	C₂²	C₃×D₄×Dic₃	1	2	yes	—
456	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
457	C₄	—	2	4	no	—
458	C₄	—	6	4	no	—
459	C₄	—	12	2	no	—
460	C₄	—	12	2	no	—
461	C₄	C₃×D₄×Dic₃	1	2	yes	—
462	C₄	C₂×C₃×#237	1	1	yes	characteristic
463	C₄	C₂³×C₃×Dic₃	1	1	yes	characteristic
464	C₃	—	2	1	no	—
465	C₃	#83843	1	1	yes	characteristic, direct product factor
466	C₃	C₃×#2949	1	1	yes	characteristic, complemented
467	C₂	—	2	2	no	—
468	C₂	—	4	4	no	—
469	C₂	C₃×#5762	1	2	yes	—
470	C₂	C₂×C₃×D₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂²×C₃²×SD₁₆	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂²×C₃²×D₄	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂²×C₃×SD₁₆	D₃
hypocenter	C₃	C₃×#2949
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×#5812	C₂	semidirect
4. C₃×#5225	C₂	semidirect
6. C₃×#5164	C₂	semidirect
7. C₃×Dic₃×SD₁₆	C₂	semidirect
8. C₃×#5106	C₂	semidirect
9. C₃×#5101	C₂	semidirect
11. #83843	C₃	direct (N × H)
14. C₂×C₃²×SD₁₆	C₄	semidirect
20. C₃×Q₈×Dic₃	C₂²	semidirect
28. C₃×#835	C₂²	semidirect
30. C₃×#818	C₂²	semidirect
31. C₃×#817	C₂²	semidirect
32. C₃×#815	C₂²	semidirect
33. C₃×C₈×Dic₃	C₂²	semidirect
39. #5812	C₂×C₃	semidirect
47. #5225	C₂×C₃	semidirect
49. #5164	C₂×C₃	semidirect
50. Dic₃×SD₁₆	C₂×C₃	semidirect
51. #5106	C₂×C₃	semidirect
52. #5101	C₂×C₃	semidirect
56. C₂×C₃²×Q₈	C₂×C₄	semidirect
65. C₃²×SD₁₆	C₂×C₄	semidirect
66. C₃²×SD₁₆	C₂×C₄	semidirect
67. C₂×C₃²×C₈	C₂×C₄	semidirect
94. C₂×C₃×SD₁₆	Dic₃	semidirect
95. C₂×C₃×SD₁₆	C₃×C₄	semidirect
115. Q₈×Dic₃	C₂²×C₃	semidirect
129. #835	C₂²×C₃	semidirect
131. #818	C₂²×C₃	semidirect
132. #817	C₂²×C₃	semidirect
133. #815	C₂²×C₃	semidirect
134. C₈×Dic₃	C₂²×C₃	semidirect
178. C₂×C₃×Q₈	C₂×Dic₃	semidirect
179. C₂×C₃×Q₈	C₂×C₃×C₄	semidirect
204. C₃×SD₁₆	C₂×Dic₃	semidirect
205. C₃×SD₁₆	C₂×Dic₃	semidirect
206. C₃×SD₁₆	C₂×C₃×C₄	semidirect
207. C₃×SD₁₆	C₂×C₃×C₄	semidirect
213. C₂×C₃×C₈	C₂×Dic₃	semidirect
214. C₂×C₃×C₈	C₂×C₃×C₄	semidirect
260. C₂×SD₁₆	C₃×Dic₃	semidirect
351. C₂×Q₈	C₂×C₃×Dic₃	semidirect
360. SD₁₆	C₂×C₃×Dic₃	semidirect
361. SD₁₆	C₂×C₃×Dic₃	semidirect
364. C₂×C₈	C₂×C₃×Dic₃	semidirect
415. C₃²	#2949	semidirect
465. C₃	#83843	direct (N × H)
466. C₃	C₃×#2949	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃²×SD₁₆	2
C₃×#5812	2
C₃×#5798	2
C₃×#5225	2
C₃×#5215	2
C₃×#5164	2
C₃×Dic₃×SD₁₆	2
C₃×#5106	2
C₃×#5101	2
C₃×#2949	3
#83843	3

Subgroups — C3×#83843 #11860733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#83843 #11860733