Subgroups — C₃×#83812 #11861195

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#950	C₂	1	1	yes	maximal, characteristic
3	C₃×#5745	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5236	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5145	C₂	1	4	yes	maximal, complemented
6	C₃×#5144	C₂	1	4	yes	maximal, complemented
7	C₃×#5139	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#822	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5122	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2957	—	3	1	no	maximal
11	#83812	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
13	C₂×C₃×#235	C₂²	1	1	yes	characteristic
14	C₃²×#131	—	2	2	no	—
15	C₃²×#131	C₂²	1	4	yes	complemented
16	C₂×C₃²×M₁₆	—	2	2	no	—
17	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
19	C₃×#950	C₄	1	2	yes	complemented
20	C₃×#950	C₄	1	2	yes	complemented
21	C₃×#950	C₂²	1	2	yes	—
22	C₃×#950	C₂²	1	2	yes	—
23	C₂×C₃×#216	C₄	1	1	yes	characteristic, complemented
24	C₂×C₃×#215	C₄	1	1	yes	characteristic, complemented
25	C₂×C₃×#214	C₄	1	1	yes	characteristic, complemented
26	C₂×C₃×#213	C₄	1	1	yes	characteristic, complemented
27	C₃×#926	C₂²	1	1	yes	characteristic
28	C₂×C₃×#208	C₂²	1	1	yes	characteristic
29	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₃×#907	—	2	2	no	—
31	C₃×D₃×M₁₆	—	2	2	no	—
32	C₃×#901	C₂²	1	4	yes	complemented
33	C₃×#837	C₂²	1	4	yes	complemented
34	C₃×#825	C₂²	1	4	yes	complemented
35	C₃×#822	C₂²	1	2	yes	complemented
36	C₃×#822	C₂²	1	2	yes	complemented
37	C₃×#815	C₂²	1	2	yes	complemented
38	C₃×C₈×Dic₃	C₂²	1	2	yes	complemented
39	C₂×C₃×#135	—	3	1	no	—
40	C₃×#568	—	2	1	no	—
41	C₃×#568	—	3	1	no	—
42	C₃×#568	D₃	1	1	yes	characteristic, complemented
43	C₃×#568	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#950	C₂×C₃	1	1	yes	characteristic
45	#5745	C₂×C₃	1	1	yes	characteristic, complemented
46	C₃×#444	—	3	4	no	—
47	C₃×#443	—	3	4	no	—
48	C₂×C₃×#108	—	3	1	no	—
49	C₃×#421	—	3	1	no	—
50	C₃×#421	—	3	1	no	—
51	C₃×#405	—	3	1	no	—
52	#5236	C₂×C₃	1	1	yes	characteristic, complemented
53	#5145	C₂×C₃	1	4	yes	complemented
54	#5144	C₂×C₃	1	4	yes	complemented
55	#5139	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×#822	C₂×C₃	1	1	yes	characteristic, complemented
57	#5122	C₂×C₃	1	1	yes	characteristic, complemented
58	C₃²×#41	—	2	1	no	—
59	C₃²×#41	—	2	1	no	—
60	C₃²×#41	C₂×C₄	1	2	yes	—
61	C₃²×#41	C₂³	1	2	yes	—
62	C₂×C₃²×Q₈	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃²×D₄	—	2	1	no	—
64	C₂×C₃²×D₄	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₃²×C₄	—	2	1	no	—
66	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
67	C₂×C₃×#67	—	2	1	no	—
68	C₃×#235	—	2	1	no	—
69	C₃×#235	—	2	1	no	—
70	C₃×#235	C₂×C₄	1	2	yes	—
71	C₃×#235	C₂³	1	2	yes	—
72	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
73	C₂×C₃×C₄×D₃	—	2	1	no	—
74	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
75	C₃²×M₁₆	—	2	1	no	—
76	C₃²×M₁₆	—	2	4	no	—
77	C₃²×M₁₆	D₄	1	2	yes	—
78	C₃²×M₁₆	D₄	1	2	yes	—
79	C₃²×M₁₆	C₂³	1	2	yes	—
80	C₂×C₃²×C₈	—	2	1	no	—
81	C₂×C₃²×C₈	—	2	4	no	—
82	C₂×C₃²×C₈	C₂³	1	2	yes	—
83	C₃×#217	—	2	1	no	—
84	C₃×#216	C₂×C₄	1	2	yes	—
85	C₃×#216	C₂×C₄	1	2	yes	—
86	C₃×#215	C₂×C₄	1	2	yes	—
87	C₃×#215	C₂×C₄	1	2	yes	—
88	C₃×#214	C₂×C₄	1	2	yes	—
89	C₃×#214	C₂×C₄	1	2	yes	—
90	C₃×#213	C₂×C₄	1	2	yes	—
91	C₃×#213	C₂×C₄	1	2	yes	—
92	C₃×C₄⋊Dic₃	—	2	1	no	—
93	C₃×C₄×Dic₃	C₂³	1	2	yes	—
94	C₃×#208	—	2	1	no	—
95	C₃×#208	C₂³	1	2	yes	—
96	C₂×C₃×C₃⋊C₈	—	2	1	no	—
97	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
103	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
104	C₃×D₃×C₈	—	2	4	no	—
105	#2957	—	3	1	no	Sylow
106	C₂×C₃×#41	—	2	1	no	—
107	C₂×C₃×#41	—	3	1	no	—
108	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
109	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
110	C₂×#235	C₂²×C₃	1	1	yes	characteristic
111	C₃×#135	—	3	2	no	—
112	C₃×#135	—	3	2	no	—
113	C₃×#135	—	3	2	no	—
114	C₃×#135	—	3	2	no	—
115	C₂×C₃×Q₁₆	—	3	1	no	—
116	C₂×C₃×SD₁₆	—	3	1	no	—
117	C₂×C₃×SD₁₆	—	3	1	no	—
118	C₂×C₃×D₈	—	3	1	no	—
119	C₃×#131	—	2	4	no	—
120	C₃×#131	—	2	2	no	—
121	C₃×#131	—	2	2	no	—
122	C₃×#131	—	2	4	no	—
123	C₃×#131	—	3	4	no	—
124	C₃×#131	—	6	2	no	—
125	C₃×#131	C₂×D₃	1	4	yes	complemented
126	C₃×#131	C₂²×C₃	1	4	yes	complemented
127	C₂×C₃×M₁₆	—	2	4	no	—
128	C₂×C₃×M₁₆	—	2	2	no	—
129	C₂×C₃×M₁₆	—	2	2	no	—
130	C₂×C₃×M₁₆	—	2	1	no	—
131	C₂×C₃×M₁₆	—	2	1	no	—
132	C₂×C₃×M₁₆	—	3	1	no	—
133	C₂×C₃×M₁₆	—	6	2	no	—
134	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
135	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
136	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
138	C₂²×C₃×C₈	—	3	1	no	—
139	C₃×#117	—	3	1	no	—
140	#950	C₃×C₄	1	2	yes	complemented
141	#950	C₃×C₄	1	2	yes	complemented
142	#950	C₂²×C₃	1	2	yes	—
143	#950	C₂²×C₃	1	2	yes	—
144	C₂×#216	C₃×C₄	1	1	yes	characteristic, complemented
145	C₂×#215	C₃×C₄	1	1	yes	characteristic, complemented
146	C₂×#214	C₃×C₄	1	1	yes	characteristic, complemented
147	C₂×#213	C₃×C₄	1	1	yes	characteristic, complemented
148	#926	C₂²×C₃	1	1	yes	characteristic
149	C₂×#208	C₂²×C₃	1	1	yes	characteristic
150	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
151	#907	—	2	2	no	—
152	D₃×M₁₆	—	2	2	no	—
153	#901	C₂²×C₃	1	4	yes	complemented
154	C₃×#108	—	3	2	no	—
155	C₃×#108	—	3	2	no	—
156	C₃×#104	—	3	4	no	—
157	C₃×#104	—	3	4	no	—
158	C₃×#97	—	3	2	no	—
159	C₃×C₄×C₈	—	3	2	no	—
160	#837	C₂²×C₃	1	4	yes	complemented
161	#825	C₂²×C₃	1	4	yes	complemented
162	#822	C₂²×C₃	1	2	yes	complemented
163	#822	C₂²×C₃	1	2	yes	complemented
164	#815	C₂²×C₃	1	2	yes	complemented
165	C₈×Dic₃	C₂²×C₃	1	2	yes	complemented
166	C₂³×C₃²	—	2	1	no	—
167	C₂³×C₃²	#41	1	1	yes	characteristic
168	C₂²×C₃×D₃	—	2	1	no	—
169	C₃²×Q₈	—	2	1	no	—
170	C₃²×Q₈	C₂²×C₄	1	2	yes	—
171	C₃²×D₄	—	2	2	no	—
172	C₃²×D₄	—	2	2	no	—
173	C₃²×D₄	—	2	1	no	—
174	C₃²×D₄	C₂²×C₄	1	2	yes	—
175	C₂×C₃²×C₄	—	2	1	no	—
176	C₂×C₃²×C₄	—	2	2	no	—
177	C₂×C₃²×C₄	—	2	2	no	—
178	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
181	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
182	C₂×C₃²×C₄	#41	1	1	yes	characteristic
183	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
184	C₃×#67	—	2	2	no	—
185	C₃×#67	—	2	2	no	—
186	C₂×C₃×Dic₃	—	2	1	no	—
187	C₂×C₃×Dic₃	—	2	2	no	—
188	C₃×D₁₂	—	2	1	no	—
189	C₃×D₁₂	C₂²×C₄	1	2	yes	—
190	C₃×C₄×D₃	—	2	2	no	—
191	C₃×C₄×D₃	—	2	2	no	—
192	C₃×Dic₆	—	2	1	no	—
193	C₃×Dic₆	C₂²×C₄	1	2	yes	—
194	C₃²×C₈	—	2	2	no	—
195	C₃²×C₈	C₂×D₄	1	4	yes	—
196	C₃×C₃⋊C₈	—	2	2	no	—
197	C₃×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
198	C₃×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
199	C₃×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
200	C₃×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
201	C₂×#135	—	3	1	no	—
202	#568	—	3	1	no	—
203	#568	C₃×D₃	1	1	yes	characteristic, complemented
204	#444	—	3	4	no	—
205	#443	—	3	4	no	—
206	C₂×#108	—	3	1	no	—
207	#421	—	3	1	no	—
208	#421	—	3	1	no	—
209	#405	—	3	1	no	—
210	C₃×#41	—	2	2	no	—
211	C₃×#41	—	2	2	no	—
212	C₃×#41	—	2	1	no	—
213	C₃×#41	—	2	1	no	—
214	C₃×#41	—	2	1	no	—
215	C₃×#41	—	2	1	no	—
216	C₃×#41	—	2	2	no	—
217	C₃×#41	—	2	2	no	—
218	C₃×#41	—	3	2	no	—
219	C₃×#41	—	3	2	no	—
220	C₃×#41	—	6	1	no	—
221	C₃×#41	—	6	1	no	—
222	C₃×#41	C₄×D₃	1	2	yes	—
223	C₃×#41	C₂×C₃×C₄	1	2	yes	—
224	C₃×#41	C₂²×D₃	1	2	yes	—
225	C₃×#41	C₂³×C₃	1	2	yes	—
226	C₂×C₃×Q₈	—	2	1	no	—
227	C₂×C₃×Q₈	—	3	1	no	—
228	C₂×C₃×Q₈	C₄×D₃	1	1	yes	characteristic
229	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
230	C₂×C₃×D₄	—	2	2	no	—
231	C₂×C₃×D₄	—	2	1	no	—
232	C₂×C₃×D₄	—	2	1	no	—
233	C₂×C₃×D₄	—	2	1	no	—
234	C₂×C₃×D₄	—	3	1	no	—
235	C₂×C₃×D₄	—	6	1	no	—
236	C₂×C₃×D₄	C₄×D₃	1	1	yes	characteristic
237	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
238	C₂²×C₃×C₄	—	2	2	no	—
239	C₂²×C₃×C₄	—	2	1	no	—
240	C₂²×C₃×C₄	—	2	1	no	—
241	C₂²×C₃×C₄	—	2	1	no	—
242	C₂²×C₃×C₄	—	6	1	no	—
243	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
244	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
245	C₂×#67	—	2	1	no	—
246	#235	—	2	1	no	—
247	#235	—	2	1	no	—
248	#235	C₂×C₃×C₄	1	2	yes	—
249	#235	C₂³×C₃	1	2	yes	—
250	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
251	C₂×C₄×D₃	—	2	1	no	—
252	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
253	C₃×Q₁₆	—	3	2	no	—
254	C₃×Q₁₆	—	3	2	no	—
255	C₃×SD₁₆	—	3	2	no	—
256	C₃×SD₁₆	—	3	2	no	—
257	C₃×SD₁₆	—	3	2	no	—
258	C₃×SD₁₆	—	3	2	no	—
259	C₃×D₈	—	3	2	no	—
260	C₃×D₈	—	3	2	no	—
261	C₃×M₁₆	—	2	2	no	—
262	C₃×M₁₆	—	2	8	no	—
263	C₃×M₁₆	—	2	1	no	—
264	C₃×M₁₆	—	2	1	no	—
265	C₃×M₁₆	—	2	4	no	—
266	C₃×M₁₆	—	2	4	no	—
267	C₃×M₁₆	—	2	2	no	—
268	C₃×M₁₆	—	2	2	no	—
269	C₃×M₁₆	—	2	2	no	—
270	C₃×M₁₆	—	3	2	no	—
271	C₃×M₁₆	—	6	1	no	—
272	C₃×M₁₆	—	6	4	no	—
273	C₃×M₁₆	#67	1	2	yes	—
274	C₃×M₁₆	#67	1	2	yes	—
275	C₃×M₁₆	C₃×D₄	1	2	yes	—
276	C₃×M₁₆	C₃×D₄	1	2	yes	—
277	C₃×M₁₆	C₂²×D₃	1	2	yes	—
278	C₃×M₁₆	C₂³×C₃	1	2	yes	—
279	C₂×C₃×C₈	—	2	2	no	—
280	C₂×C₃×C₈	—	2	8	no	—
281	C₂×C₃×C₈	—	2	1	no	—
282	C₂×C₃×C₈	—	2	1	no	—
283	C₂×C₃×C₈	—	2	4	no	—
284	C₂×C₃×C₈	—	2	4	no	—
285	C₂×C₃×C₈	—	2	2	no	—
286	C₂×C₃×C₈	—	3	1	no	—
287	C₂×C₃×C₈	—	3	1	no	—
288	C₂×C₃×C₈	—	3	1	no	—
289	C₂×C₃×C₈	—	3	1	no	—
290	C₂×C₃×C₈	—	3	1	no	—
291	C₂×C₃×C₈	—	3	1	no	—
292	C₂×C₃×C₈	—	6	1	no	—
293	C₂×C₃×C₈	—	6	4	no	—
294	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
295	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
296	C₃×C₄⋊C₄	—	6	1	no	—
297	C₃×C₂²⋊C₄	—	6	1	no	—
298	C₃×C₄²	—	3	2	no	—
299	#217	—	2	1	no	—
300	#216	C₂×C₃×C₄	1	2	yes	—
301	#216	C₂×C₃×C₄	1	2	yes	—
302	#215	C₂×C₃×C₄	1	2	yes	—
303	#215	C₂×C₃×C₄	1	2	yes	—
304	#214	C₂×C₃×C₄	1	2	yes	—
305	#214	C₂×C₃×C₄	1	2	yes	—
306	#213	C₂×C₃×C₄	1	2	yes	—
307	#213	C₂×C₃×C₄	1	2	yes	—
308	C₄⋊Dic₃	—	2	1	no	—
309	C₄×Dic₃	C₂³×C₃	1	2	yes	—
310	#208	—	2	1	no	—
311	#208	C₂³×C₃	1	2	yes	—
312	C₂×C₃⋊C₈	—	2	1	no	—
313	C₂×C₃⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
314	C₂×C₃⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
315	C₂×C₃⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
316	C₂×C₃⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
317	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
318	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
319	ΓL(1,𝔽₂₅)	—	2	4	no	—
320	D₃×C₈	—	2	4	no	—
321	C₂²×C₃²	—	2	2	no	—
322	C₂²×C₃²	—	4	1	no	—
323	C₂²×C₃²	—	8	1	no	—
324	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
325	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
326	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
327	C₂×C₃×D₃	—	2	2	no	—
328	C₂×C₃×D₃	—	8	1	no	—
329	C₃²×C₄	—	2	2	no	—
330	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
331	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
332	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
333	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
334	C₃×Dic₃	—	2	2	no	—
335	C₃×Dic₃	—	4	2	no	—
336	C₂×#41	—	3	1	no	—
337	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
338	#135	—	3	2	no	—
339	#135	—	3	2	no	—
340	#135	—	3	2	no	—
341	#135	—	3	2	no	—
342	C₂×Q₁₆	—	3	1	no	—
343	C₂×SD₁₆	—	3	1	no	—
344	C₂×SD₁₆	—	3	1	no	—
345	C₂×D₈	—	3	1	no	—
346	#131	—	2	2	no	—
347	#131	—	3	4	no	—
348	#131	—	6	2	no	—
349	#131	C₂×C₃×D₃	1	4	yes	complemented
350	C₂×M₁₆	—	2	2	no	—
351	C₂×M₁₆	—	3	1	no	—
352	C₂×M₁₆	—	6	2	no	—
353	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
354	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
355	C₂²×C₈	—	3	1	no	—
356	#117	—	3	1	no	—
357	#108	—	3	2	no	—
358	#108	—	3	2	no	—
359	#104	—	3	4	no	—
360	#104	—	3	4	no	—
361	#97	—	3	2	no	—
362	C₄×C₈	—	3	2	no	—
363	C₂³×C₃	—	2	2	no	—
364	C₂³×C₃	—	2	1	no	—
365	C₂³×C₃	—	2	1	no	—
366	C₂³×C₃	—	2	1	no	—
367	C₂³×C₃	—	6	1	no	—
368	C₂³×C₃	#235	1	1	yes	characteristic
369	C₂³×C₃	C₃×#41	1	1	yes	characteristic
370	C₂²×D₃	—	2	1	no	—
371	C₃×Q₈	—	2	2	no	—
372	C₃×Q₈	—	2	1	no	—
373	C₃×Q₈	—	2	1	no	—
374	C₃×Q₈	—	2	2	no	—
375	C₃×Q₈	—	3	2	no	—
376	C₃×Q₈	—	6	1	no	—
377	C₃×Q₈	C₂×C₄×D₃	1	2	yes	—
378	C₃×Q₈	C₂²×C₃×C₄	1	2	yes	—
379	C₃×D₄	—	2	4	no	—
380	C₃×D₄	—	2	4	no	—
381	C₃×D₄	—	2	2	no	—
382	C₃×D₄	—	2	2	no	—
383	C₃×D₄	—	2	2	no	—
384	C₃×D₄	—	2	2	no	—
385	C₃×D₄	—	2	2	no	—
386	C₃×D₄	—	2	1	no	—
387	C₃×D₄	—	2	1	no	—
388	C₃×D₄	—	2	2	no	—
389	C₃×D₄	—	3	2	no	—
390	C₃×D₄	—	6	2	no	—
391	C₃×D₄	—	6	2	no	—
392	C₃×D₄	—	6	1	no	—
393	C₃×D₄	C₂×C₄×D₃	1	2	yes	—
394	C₃×D₄	C₂²×C₃×C₄	1	2	yes	—
395	C₂×C₃×C₄	—	2	4	no	—
396	C₂×C₃×C₄	—	2	2	no	—
397	C₂×C₃×C₄	—	2	4	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	2	2	no	—
402	C₂×C₃×C₄	—	2	2	no	—
403	C₂×C₃×C₄	—	2	2	no	—
404	C₂×C₃×C₄	—	2	1	no	—
405	C₂×C₃×C₄	—	2	1	no	—
406	C₂×C₃×C₄	—	2	1	no	—
407	C₂×C₃×C₄	—	2	1	no	—
408	C₂×C₃×C₄	—	2	1	no	—
409	C₂×C₃×C₄	—	2	1	no	—
410	C₂×C₃×C₄	—	6	1	no	—
411	C₂×C₃×C₄	—	6	2	no	—
412	C₂×C₃×C₄	—	6	2	no	—
413	C₂×C₃×C₄	—	6	2	no	—
414	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
415	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
416	C₂×C₃×C₄	#235	1	1	yes	characteristic
417	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
419	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
420	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
421	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
422	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
423	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
424	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
425	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
426	#67	—	2	2	no	—
427	#67	—	2	2	no	—
428	C₂×Dic₃	—	2	1	no	—
429	C₂×Dic₃	—	2	2	no	—
430	D₁₂	—	2	1	no	—
431	D₁₂	C₂²×C₃×C₄	1	2	yes	—
432	C₄×D₃	—	2	2	no	—
433	C₄×D₃	—	2	2	no	—
434	Dic₆	—	2	1	no	—
435	Dic₆	C₂²×C₃×C₄	1	2	yes	—
436	C₃×C₈	—	2	4	no	—
437	C₃×C₈	—	2	2	no	—
438	C₃×C₈	—	2	2	no	—
439	C₃×C₈	—	2	4	no	—
440	C₃×C₈	—	3	1	no	—
441	C₃×C₈	—	3	1	no	—
442	C₃×C₈	—	3	1	no	—
443	C₃×C₈	—	3	1	no	—
444	C₃×C₈	—	6	2	no	—
445	C₃×C₈	C₂×#67	1	4	yes	—
446	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
447	C₃⋊C₈	—	2	2	no	—
448	C₃⋊C₈	C₂²×C₃×C₄	1	1	yes	characteristic
449	C₃⋊C₈	C₂²×C₃×C₄	1	1	yes	characteristic
450	C₃⋊C₈	C₂²×C₃×C₄	1	1	yes	characteristic
451	C₃⋊C₈	C₂²×C₃×C₄	1	1	yes	characteristic
452	C₂×C₃²	—	2	1	no	—
453	C₂×C₃²	—	2	1	no	—
454	C₂×C₃²	—	2	1	no	—
455	C₂×C₃²	—	4	2	no	—
456	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
457	C₃×D₃	—	4	2	no	—
458	#41	—	2	1	no	—
459	#41	—	2	1	no	—
460	#41	—	3	2	no	—
461	#41	—	3	2	no	—
462	#41	—	6	1	no	—
463	#41	—	6	1	no	—
464	#41	C₃×C₄×D₃	1	2	yes	—
465	#41	C₂²×C₃×D₃	1	2	yes	—
466	C₂×Q₈	—	3	1	no	—
467	C₂×Q₈	C₃×C₄×D₃	1	1	yes	characteristic
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	3	1	no	—
470	C₂×D₄	—	6	1	no	—
471	C₂×D₄	C₃×C₄×D₃	1	1	yes	characteristic
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	6	1	no	—
474	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
475	Q₁₆	—	3	2	no	—
476	Q₁₆	—	3	2	no	—
477	SD₁₆	—	3	2	no	—
478	SD₁₆	—	3	2	no	—
479	SD₁₆	—	3	2	no	—
480	SD₁₆	—	3	2	no	—
481	D₈	—	3	2	no	—
482	D₈	—	3	2	no	—
483	M₁₆	—	2	1	no	—
484	M₁₆	—	2	4	no	—
485	M₁₆	—	3	2	no	—
486	M₁₆	—	6	1	no	—
487	M₁₆	—	6	4	no	—
488	M₁₆	C₃×#67	1	2	yes	—
489	M₁₆	C₃×#67	1	2	yes	—
490	M₁₆	C₂²×C₃×D₃	1	2	yes	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	4	no	—
493	C₂×C₈	—	3	1	no	—
494	C₂×C₈	—	3	1	no	—
495	C₂×C₈	—	3	1	no	—
496	C₂×C₈	—	3	1	no	—
497	C₂×C₈	—	3	1	no	—
498	C₂×C₈	—	3	1	no	—
499	C₂×C₈	—	6	1	no	—
500	C₂×C₈	—	6	4	no	—
501	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
502	C₄⋊C₄	—	6	1	no	—
503	C₂²⋊C₄	—	6	1	no	—
504	C₄²	—	3	2	no	—
505	C₂²×C₃	—	2	4	no	—
506	C₂²×C₃	—	2	2	no	—
507	C₂²×C₃	—	2	2	no	—
508	C₂²×C₃	—	2	1	no	—
509	C₂²×C₃	—	2	1	no	—
510	C₂²×C₃	—	2	1	no	—
511	C₂²×C₃	—	4	1	no	—
512	C₂²×C₃	—	4	1	no	—
513	C₂²×C₃	—	6	2	no	—
514	C₂²×C₃	—	8	1	no	—
515	C₂²×C₃	—	8	1	no	—
516	C₂²×C₃	—	8	1	no	—
517	C₂²×C₃	—	8	2	no	—
518	C₂²×C₃	—	24	1	no	—
519	C₂²×C₃	C₄×#67	1	1	yes	characteristic
520	C₂²×C₃	C₄×#67	1	1	yes	characteristic
521	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
522	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
523	C₂²×C₃	C₂×#235	1	1	yes	characteristic
524	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
525	C₂×D₃	—	2	2	no	—
526	C₂×D₃	—	8	1	no	—
527	C₃×C₄	—	2	4	no	—
528	C₃×C₄	—	2	2	no	—
529	C₃×C₄	—	2	2	no	—
530	C₃×C₄	—	2	1	no	—
531	C₃×C₄	—	2	1	no	—
532	C₃×C₄	—	2	1	no	—
533	C₃×C₄	—	2	1	no	—
534	C₃×C₄	—	6	2	no	—
535	C₃×C₄	—	12	2	no	—
536	C₃×C₄	C₄×#67	1	1	yes	characteristic
537	C₃×C₄	C₄×#67	1	1	yes	characteristic
538	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
539	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
540	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
541	C₃×C₄	C₂²×#67	1	1	yes	characteristic
542	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
543	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
544	Dic₃	—	2	2	no	—
545	Dic₃	—	4	2	no	—
546	C₃²	#2957	1	1	yes	characteristic, complemented, Sylow
547	C₂³	—	2	1	no	—
548	C₂³	—	6	1	no	—
549	C₂³	C₃×#235	1	1	yes	characteristic
550	Q₈	—	2	1	no	—
551	Q₈	—	3	2	no	—
552	Q₈	—	6	1	no	—
553	Q₈	C₂×C₃×C₄×D₃	1	2	yes	—
554	D₄	—	2	2	no	—
555	D₄	—	2	2	no	—
556	D₄	—	2	1	no	—
557	D₄	—	3	2	no	—
558	D₄	—	6	2	no	—
559	D₄	—	6	2	no	—
560	D₄	—	6	1	no	—
561	D₄	C₂×C₃×C₄×D₃	1	2	yes	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	6	1	no	—
566	C₂×C₄	—	6	2	no	—
567	C₂×C₄	—	6	2	no	—
568	C₂×C₄	—	6	2	no	—
569	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
570	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
571	C₂×C₄	C₃×#235	1	1	yes	characteristic
572	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
573	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
574	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
575	C₈	—	2	2	no	—
576	C₈	—	3	1	no	—
577	C₈	—	3	1	no	—
578	C₈	—	3	1	no	—
579	C₈	—	3	1	no	—
580	C₈	—	6	2	no	—
581	C₈	C₂×C₃×#67	1	4	yes	—
582	C₂×C₃	—	2	1	no	—
583	C₂×C₃	—	2	1	no	—
584	C₂×C₃	—	2	1	no	—
585	C₂×C₃	—	2	1	no	—
586	C₂×C₃	—	2	1	no	—
587	C₂×C₃	—	2	1	no	—
588	C₂×C₃	—	2	1	no	—
589	C₂×C₃	—	4	1	no	—
590	C₂×C₃	—	4	1	no	—
591	C₂×C₃	—	4	1	no	—
592	C₂×C₃	—	4	4	no	—
593	C₂×C₃	—	4	2	no	—
594	C₂×C₃	—	4	2	no	—
595	C₂×C₃	—	12	2	no	—
596	C₂×C₃	C₂×C₄×#67	1	1	yes	characteristic
597	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
598	D₃	—	4	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	6	2	no	—
602	C₂²	—	8	1	no	—
603	C₂²	—	24	1	no	—
604	C₂²	C₃×C₄×#67	1	1	yes	characteristic
605	C₂²	C₃×C₄×#67	1	1	yes	characteristic
606	C₂²	C₂×C₃×#235	1	1	yes	characteristic
607	C₄	—	2	2	no	—
608	C₄	—	6	2	no	—
609	C₄	—	12	2	no	—
610	C₄	C₃×C₄×#67	1	1	yes	characteristic
611	C₄	C₃×C₄×#67	1	1	yes	characteristic
612	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
613	C₄	C₂²×C₃×#67	1	1	yes	characteristic
614	C₃	—	2	1	no	—
615	C₃	#83812	1	1	yes	characteristic, direct product factor
616	C₃	C₃×#2957	1	1	yes	characteristic, complemented
617	C₂	—	2	1	no	—
618	C₂	—	2	1	no	—
619	C₂	—	2	1	no	—
620	C₂	—	4	2	no	—
621	C₂	—	12	2	no	—
622	C₂	C₂×C₃×C₄×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂²×#67
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#568	C₂
socle	C₂×C₃²	C₂×C₄×D₄
prime radical	C₂×C₃×#950	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#568	D₃
hypocenter	C₃	C₃×#2957
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×M₁₆ ◁ C₃×#568

Complements

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

N	H ≅ G/N	type
1. C₃²×#568	C₂	semidirect
3. C₃×#5745	C₂	semidirect
4. C₃×#5236	C₂	semidirect
5. C₃×#5145	C₂	semidirect
6. C₃×#5144	C₂	semidirect
7. C₃×#5139	C₂	semidirect
8. C₂×C₃×#822	C₂	semidirect
9. C₃×#5122	C₂	semidirect
11. #83812	C₃	direct (N × H)
15. C₃²×#131	C₂²	semidirect
19. C₃×#950	C₄	semidirect
20. C₃×#950	C₄	semidirect
23. C₂×C₃×#216	C₄	semidirect
24. C₂×C₃×#215	C₄	semidirect
25. C₂×C₃×#214	C₄	semidirect
26. C₂×C₃×#213	C₄	semidirect
32. C₃×#901	C₂²	semidirect
33. C₃×#837	C₂²	semidirect
34. C₃×#825	C₂²	semidirect
35. C₃×#822	C₂²	semidirect
36. C₃×#822	C₂²	semidirect
37. C₃×#815	C₂²	semidirect
38. C₃×C₈×Dic₃	C₂²	semidirect
42. C₃×#568	D₃	semidirect
43. C₃×#568	C₂×C₃	semidirect
45. #5745	C₂×C₃	semidirect
52. #5236	C₂×C₃	semidirect
53. #5145	C₂×C₃	semidirect
54. #5144	C₂×C₃	semidirect
55. #5139	C₂×C₃	semidirect
56. C₂×#822	C₂×C₃	semidirect
57. #5122	C₂×C₃	semidirect
125. C₃×#131	C₂×D₃	semidirect
126. C₃×#131	C₂²×C₃	semidirect
140. #950	C₃×C₄	semidirect
141. #950	C₃×C₄	semidirect
144. C₂×#216	C₃×C₄	semidirect
145. C₂×#215	C₃×C₄	semidirect
146. C₂×#214	C₃×C₄	semidirect
147. C₂×#213	C₃×C₄	semidirect
153. #901	C₂²×C₃	semidirect
160. #837	C₂²×C₃	semidirect
161. #825	C₂²×C₃	semidirect
162. #822	C₂²×C₃	semidirect
163. #822	C₂²×C₃	semidirect
164. #815	C₂²×C₃	semidirect
165. C₈×Dic₃	C₂²×C₃	semidirect
203. #568	C₃×D₃	semidirect
349. #131	C₂×C₃×D₃	semidirect
546. C₃²	#2957	semidirect
615. C₃	#83812	direct (N × H)
616. C₃	C₃×#2957	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#568	2
C₂×C₃×#950	2
C₃×#5745	2
C₃×#5236	2
C₃×#5145	2
C₃×#5144	2
C₃×#5139	2
C₂×C₃×#822	2
C₃×#5122	2
C₃×#2957	3
#83812	3

Subgroups — C3×#83812 #11861195

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#83812 #11861195