Subgroups — C₃×#78990 #11861189

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#950	C₂	1	1	yes	maximal, characteristic
2	C₃×#5819	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5745	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#421	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#822	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5005	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4824	C₂	1	4	yes	maximal, complemented
9	C₃×#4823	C₂	1	4	yes	maximal, complemented
10	C₃×#2957	—	3	1	no	maximal
11	#78990	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	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
15	C₃²×#117	C₂²	1	1	yes	characteristic
16	C₃×#950	C₄	1	2	yes	complemented
17	C₃×#950	C₄	1	2	yes	complemented
18	C₃×#950	C₂²	1	2	yes	—
19	C₃×#950	C₂²	1	2	yes	—
20	C₃×#948	—	2	2	no	—
21	C₃×#948	C₂²	1	4	yes	complemented
22	C₂×C₃×#216	C₄	1	1	yes	characteristic, complemented
23	C₂×C₃×#215	C₄	1	1	yes	characteristic, complemented
24	C₂×C₃×#214	C₄	1	1	yes	characteristic, complemented
25	C₂×C₃×#213	C₄	1	1	yes	characteristic, complemented
26	C₂×C₃×#208	—	2	2	no	—
27	C₂×C₃×#208	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	C₂²	1	4	yes	complemented
31	C₃×D₃×M₁₆	—	2	2	no	—
32	C₃×#901	—	2	2	no	—
33	C₃²×#104	C₂²	1	4	yes	complemented
34	C₃×#822	C₂²	1	2	yes	complemented
35	C₃×#822	C₂²	1	2	yes	complemented
36	C₃×#805	C₂²	1	4	yes	complemented
37	C₃×#803	C₂²	1	2	yes	complemented
38	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	complemented
39	C₂×C₃×#135	—	3	1	no	—
40	C₃×#568	—	3	1	no	—
41	C₃×#568	—	3	1	no	—
42	C₂×#950	C₂×C₃	1	1	yes	characteristic
43	#5819	C₂×C₃	1	1	yes	characteristic, complemented
44	#5745	C₂×C₃	1	1	yes	characteristic, complemented
45	C₃×#444	—	3	4	no	—
46	C₃×#443	—	3	4	no	—
47	C₂×C₃×#108	—	3	1	no	—
48	C₃×#421	—	2	1	no	—
49	C₃×#421	—	3	1	no	—
50	C₃×#421	D₃	1	1	yes	characteristic, complemented
51	C₃×#421	C₂×C₃	1	1	yes	characteristic, complemented
52	C₃×#405	—	3	1	no	—
53	C₂×#822	C₂×C₃	1	1	yes	characteristic, complemented
54	#5005	C₂×C₃	1	1	yes	characteristic, complemented
55	#4997	C₂×C₃	1	1	yes	characteristic, complemented
56	#4824	C₂×C₃	1	4	yes	complemented
57	#4823	C₂×C₃	1	4	yes	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	C₂³	1	2	yes	—
77	C₂×C₃²×C₈	—	2	1	no	—
78	C₃²×C₄⋊C₄	—	2	1	no	—
79	C₃²×C₂²⋊C₄	—	2	1	no	—
80	C₃²×C₄²	C₂³	1	2	yes	—
81	C₃×#216	C₂×C₄	1	2	yes	—
82	C₃×#216	C₂×C₄	1	2	yes	—
83	C₃×#215	C₂×C₄	1	2	yes	—
84	C₃×#215	C₂×C₄	1	2	yes	—
85	C₃×#214	C₂×C₄	1	2	yes	—
86	C₃×#214	C₂×C₄	1	2	yes	—
87	C₃×#213	C₂×C₄	1	2	yes	—
88	C₃×#213	C₂×C₄	1	2	yes	—
89	C₃×#208	—	2	1	no	—
90	C₃×#208	—	2	4	no	—
91	C₃×#208	D₄	1	2	yes	—
92	C₃×#208	D₄	1	2	yes	—
93	C₃×#208	C₂³	1	2	yes	—
94	C₂×C₃×C₃⋊C₈	—	2	1	no	—
95	C₂×C₃×C₃⋊C₈	—	2	4	no	—
96	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
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	—	3	4	no	—
120	C₃×#131	—	3	4	no	—
121	C₃×#131	—	6	2	no	—
122	C₃×#131	—	6	2	no	—
123	C₂×C₃×M₁₆	—	2	1	no	—
124	C₂×C₃×M₁₆	—	3	1	no	—
125	C₂×C₃×M₁₆	—	3	1	no	—
126	C₂×C₃×M₁₆	—	6	2	no	—
127	C₂×C₃×M₁₆	—	6	2	no	—
128	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
129	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
130	C₂²×C₃×C₈	—	3	1	no	—
131	C₃×#117	—	2	1	no	—
132	C₃×#117	C₂×D₃	1	1	yes	characteristic
133	C₃×#117	C₂²×C₃	1	1	yes	characteristic
134	#950	C₃×C₄	1	2	yes	complemented
135	#950	C₃×C₄	1	2	yes	complemented
136	#950	C₂²×C₃	1	2	yes	—
137	#950	C₂²×C₃	1	2	yes	—
138	#948	—	2	2	no	—
139	#948	C₂²×C₃	1	4	yes	complemented
140	C₂×#216	C₃×C₄	1	1	yes	characteristic, complemented
141	C₂×#215	C₃×C₄	1	1	yes	characteristic, complemented
142	C₂×#214	C₃×C₄	1	1	yes	characteristic, complemented
143	C₂×#213	C₃×C₄	1	1	yes	characteristic, complemented
144	C₂×#208	—	2	2	no	—
145	C₂×#208	C₂²×C₃	1	1	yes	characteristic
146	C₂×#208	C₂²×C₃	1	1	yes	characteristic
147	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
148	#907	C₂²×C₃	1	4	yes	complemented
149	D₃×M₁₆	—	2	2	no	—
150	#901	—	2	2	no	—
151	C₃×#108	—	3	2	no	—
152	C₃×#108	—	3	2	no	—
153	C₃×#104	—	2	4	no	—
154	C₃×#104	—	3	4	no	—
155	C₃×#104	C₂×D₃	1	4	yes	complemented
156	C₃×#104	C₂²×C₃	1	4	yes	complemented
157	C₃×#97	—	3	2	no	—
158	C₃×C₄×C₈	—	3	2	no	—
159	#822	C₂²×C₃	1	2	yes	complemented
160	#822	C₂²×C₃	1	2	yes	complemented
161	#805	C₂²×C₃	1	4	yes	complemented
162	#803	C₂²×C₃	1	2	yes	complemented
163	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	complemented
164	C₂³×C₃²	—	2	1	no	—
165	C₂³×C₃²	#41	1	1	yes	characteristic
166	C₂²×C₃×D₃	—	2	1	no	—
167	C₃²×Q₈	—	2	1	no	—
168	C₃²×Q₈	C₂²×C₄	1	2	yes	—
169	C₃²×D₄	—	2	2	no	—
170	C₃²×D₄	—	2	2	no	—
171	C₃²×D₄	—	2	1	no	—
172	C₃²×D₄	C₂²×C₄	1	2	yes	—
173	C₂×C₃²×C₄	—	2	1	no	—
174	C₂×C₃²×C₄	—	2	2	no	—
175	C₂×C₃²×C₄	—	2	2	no	—
176	C₂×C₃²×C₄	—	2	2	no	—
177	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
180	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
181	C₂×C₃²×C₄	#41	1	1	yes	characteristic
182	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
183	C₃×#67	—	2	2	no	—
184	C₃×#67	—	2	2	no	—
185	C₂×C₃×Dic₃	—	2	1	no	—
186	C₃×D₁₂	—	2	1	no	—
187	C₃×D₁₂	C₂²×C₄	1	2	yes	—
188	C₃×C₄×D₃	—	2	2	no	—
189	C₃×C₄×D₃	—	2	2	no	—
190	C₃×Dic₆	—	2	1	no	—
191	C₃×Dic₆	C₂²×C₄	1	2	yes	—
192	C₃²×C₈	—	2	2	no	—
193	C₃×C₃⋊C₈	—	2	2	no	—
194	C₃×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
195	C₃×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
196	C₃×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
197	C₃×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
198	C₃×C₃⋊C₈	C₂×D₄	1	4	yes	—
199	C₂×#135	—	3	1	no	—
200	#568	—	3	1	no	—
201	#568	—	3	1	no	—
202	#444	—	3	4	no	—
203	#443	—	3	4	no	—
204	C₂×#108	—	3	1	no	—
205	#421	—	3	1	no	—
206	#421	C₃×D₃	1	1	yes	characteristic, complemented
207	#405	—	3	1	no	—
208	C₃×#41	—	2	1	no	—
209	C₃×#41	—	2	1	no	—
210	C₃×#41	—	2	1	no	—
211	C₃×#41	—	2	1	no	—
212	C₃×#41	—	2	2	no	—
213	C₃×#41	—	2	2	no	—
214	C₃×#41	—	3	2	no	—
215	C₃×#41	—	3	2	no	—
216	C₃×#41	—	4	1	no	—
217	C₃×#41	—	4	1	no	—
218	C₃×#41	—	6	1	no	—
219	C₃×#41	—	6	1	no	—
220	C₃×#41	C₄×D₃	1	2	yes	—
221	C₃×#41	C₂×C₃×C₄	1	2	yes	—
222	C₃×#41	C₂²×D₃	1	2	yes	—
223	C₃×#41	C₂³×C₃	1	2	yes	—
224	C₂×C₃×Q₈	—	2	1	no	—
225	C₂×C₃×Q₈	—	3	1	no	—
226	C₂×C₃×Q₈	C₄×D₃	1	1	yes	characteristic
227	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
228	C₂×C₃×D₄	—	2	1	no	—
229	C₂×C₃×D₄	—	2	1	no	—
230	C₂×C₃×D₄	—	2	1	no	—
231	C₂×C₃×D₄	—	3	1	no	—
232	C₂×C₃×D₄	—	4	1	no	—
233	C₂×C₃×D₄	—	6	1	no	—
234	C₂×C₃×D₄	C₄×D₃	1	1	yes	characteristic
235	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
236	C₂²×C₃×C₄	—	2	1	no	—
237	C₂²×C₃×C₄	—	2	1	no	—
238	C₂²×C₃×C₄	—	2	1	no	—
239	C₂²×C₃×C₄	—	4	1	no	—
240	C₂²×C₃×C₄	—	6	1	no	—
241	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
242	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
243	C₂×#67	—	2	1	no	—
244	#235	—	2	1	no	—
245	#235	—	2	1	no	—
246	#235	C₂×C₃×C₄	1	2	yes	—
247	#235	C₂³×C₃	1	2	yes	—
248	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
249	C₂×C₄×D₃	—	2	1	no	—
250	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
251	C₃×Q₁₆	—	3	2	no	—
252	C₃×Q₁₆	—	3	2	no	—
253	C₃×SD₁₆	—	3	2	no	—
254	C₃×SD₁₆	—	3	2	no	—
255	C₃×SD₁₆	—	3	2	no	—
256	C₃×SD₁₆	—	3	2	no	—
257	C₃×D₈	—	3	2	no	—
258	C₃×D₈	—	3	2	no	—
259	C₃×M₁₆	—	2	1	no	—
260	C₃×M₁₆	—	2	1	no	—
261	C₃×M₁₆	—	2	2	no	—
262	C₃×M₁₆	—	3	2	no	—
263	C₃×M₁₆	—	3	2	no	—
264	C₃×M₁₆	—	3	2	no	—
265	C₃×M₁₆	—	4	1	no	—
266	C₃×M₁₆	—	6	4	no	—
267	C₃×M₁₆	—	6	4	no	—
268	C₃×M₁₆	—	6	1	no	—
269	C₃×M₁₆	C₂²×D₃	1	2	yes	—
270	C₃×M₁₆	C₂³×C₃	1	2	yes	—
271	C₂×C₃×C₈	—	2	1	no	—
272	C₂×C₃×C₈	—	2	1	no	—
273	C₂×C₃×C₈	—	3	1	no	—
274	C₂×C₃×C₈	—	3	1	no	—
275	C₂×C₃×C₈	—	3	1	no	—
276	C₂×C₃×C₈	—	3	1	no	—
277	C₂×C₃×C₈	—	3	1	no	—
278	C₂×C₃×C₈	—	3	2	no	—
279	C₂×C₃×C₈	—	3	1	no	—
280	C₂×C₃×C₈	—	4	1	no	—
281	C₂×C₃×C₈	—	6	4	no	—
282	C₂×C₃×C₈	—	6	4	no	—
283	C₂×C₃×C₈	—	6	1	no	—
284	C₃×C₄⋊C₄	—	2	1	no	—
285	C₃×C₄⋊C₄	—	2	1	no	—
286	C₃×C₄⋊C₄	—	4	1	no	—
287	C₃×C₂²⋊C₄	—	2	1	no	—
288	C₃×C₂²⋊C₄	—	2	1	no	—
289	C₃×C₂²⋊C₄	—	4	1	no	—
290	C₃×C₄²	—	2	2	no	—
291	C₃×C₄²	C₂²×D₃	1	2	yes	—
292	C₃×C₄²	C₂³×C₃	1	2	yes	—
293	#216	C₂×C₃×C₄	1	2	yes	—
294	#216	C₂×C₃×C₄	1	2	yes	—
295	#215	C₂×C₃×C₄	1	2	yes	—
296	#215	C₂×C₃×C₄	1	2	yes	—
297	#214	C₂×C₃×C₄	1	2	yes	—
298	#214	C₂×C₃×C₄	1	2	yes	—
299	#213	C₂×C₃×C₄	1	2	yes	—
300	#213	C₂×C₃×C₄	1	2	yes	—
301	#208	—	2	1	no	—
302	#208	—	2	4	no	—
303	#208	C₃×D₄	1	2	yes	—
304	#208	C₃×D₄	1	2	yes	—
305	#208	C₂³×C₃	1	2	yes	—
306	C₂×C₃⋊C₈	—	2	1	no	—
307	C₂×C₃⋊C₈	—	2	4	no	—
308	C₂×C₃⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
309	C₂×C₃⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
310	C₂×C₃⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
311	C₂×C₃⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
312	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
313	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
314	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
315	ΓL(1,𝔽₂₅)	—	2	4	no	—
316	D₃×C₈	—	2	4	no	—
317	C₂²×C₃²	—	2	2	no	—
318	C₂²×C₃²	—	4	1	no	—
319	C₂²×C₃²	—	8	1	no	—
320	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
321	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
322	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
323	C₂×C₃×D₃	—	2	2	no	—
324	C₂×C₃×D₃	—	8	1	no	—
325	C₃²×C₄	—	2	2	no	—
326	C₃²×C₄	—	4	2	no	—
327	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
328	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
329	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
330	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
331	C₃×Dic₃	—	2	2	no	—
332	C₂×#41	—	3	1	no	—
333	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
334	#135	—	3	2	no	—
335	#135	—	3	2	no	—
336	#135	—	3	2	no	—
337	#135	—	3	2	no	—
338	C₂×Q₁₆	—	3	1	no	—
339	C₂×SD₁₆	—	3	1	no	—
340	C₂×SD₁₆	—	3	1	no	—
341	C₂×D₈	—	3	1	no	—
342	#131	—	3	4	no	—
343	#131	—	3	4	no	—
344	#131	—	6	2	no	—
345	#131	—	6	2	no	—
346	C₂×M₁₆	—	3	1	no	—
347	C₂×M₁₆	—	3	1	no	—
348	C₂×M₁₆	—	6	2	no	—
349	C₂×M₁₆	—	6	2	no	—
350	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
351	C₂²×C₈	—	3	1	no	—
352	#117	C₂×C₃×D₃	1	1	yes	characteristic
353	#108	—	3	2	no	—
354	#108	—	3	2	no	—
355	#104	—	3	4	no	—
356	#104	C₂×C₃×D₃	1	4	yes	complemented
357	#97	—	3	2	no	—
358	C₄×C₈	—	3	2	no	—
359	C₂³×C₃	—	2	1	no	—
360	C₂³×C₃	—	2	1	no	—
361	C₂³×C₃	—	2	1	no	—
362	C₂³×C₃	—	4	1	no	—
363	C₂³×C₃	—	6	1	no	—
364	C₂³×C₃	#237	1	1	yes	characteristic
365	C₂³×C₃	C₃×#41	1	1	yes	characteristic
366	C₂²×D₃	—	2	1	no	—
367	C₃×Q₈	—	2	1	no	—
368	C₃×Q₈	—	2	1	no	—
369	C₃×Q₈	—	2	2	no	—
370	C₃×Q₈	—	3	2	no	—
371	C₃×Q₈	—	4	1	no	—
372	C₃×Q₈	—	6	1	no	—
373	C₃×Q₈	C₂×C₄×D₃	1	2	yes	—
374	C₃×Q₈	C₂²×C₃×C₄	1	2	yes	—
375	C₃×D₄	—	2	2	no	—
376	C₃×D₄	—	2	2	no	—
377	C₃×D₄	—	2	2	no	—
378	C₃×D₄	—	2	2	no	—
379	C₃×D₄	—	2	1	no	—
380	C₃×D₄	—	2	1	no	—
381	C₃×D₄	—	2	2	no	—
382	C₃×D₄	—	3	2	no	—
383	C₃×D₄	—	4	1	no	—
384	C₃×D₄	—	4	2	no	—
385	C₃×D₄	—	4	2	no	—
386	C₃×D₄	—	6	2	no	—
387	C₃×D₄	—	6	2	no	—
388	C₃×D₄	—	6	1	no	—
389	C₃×D₄	C₂×C₄×D₃	1	2	yes	—
390	C₃×D₄	C₂²×C₃×C₄	1	2	yes	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	2	2	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	2	2	no	—
397	C₂×C₃×C₄	—	2	2	no	—
398	C₂×C₃×C₄	—	2	2	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	2	1	no	—
401	C₂×C₃×C₄	—	2	1	no	—
402	C₂×C₃×C₄	—	2	1	no	—
403	C₂×C₃×C₄	—	2	1	no	—
404	C₂×C₃×C₄	—	2	1	no	—
405	C₂×C₃×C₄	—	4	2	no	—
406	C₂×C₃×C₄	—	4	2	no	—
407	C₂×C₃×C₄	—	4	1	no	—
408	C₂×C₃×C₄	—	4	2	no	—
409	C₂×C₃×C₄	—	6	1	no	—
410	C₂×C₃×C₄	—	6	2	no	—
411	C₂×C₃×C₄	—	6	2	no	—
412	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
413	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
414	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
415	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
416	C₂×C₃×C₄	#237	1	1	yes	characteristic
417	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
419	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
420	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
421	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
422	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
423	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
424	#67	—	2	2	no	—
425	#67	—	2	2	no	—
426	C₂×Dic₃	—	2	1	no	—
427	D₁₂	—	2	1	no	—
428	D₁₂	C₂²×C₃×C₄	1	2	yes	—
429	C₄×D₃	—	2	2	no	—
430	C₄×D₃	—	2	2	no	—
431	Dic₆	—	2	1	no	—
432	Dic₆	C₂²×C₃×C₄	1	2	yes	—
433	C₃×C₈	—	2	2	no	—
434	C₃×C₈	—	2	2	no	—
435	C₃×C₈	—	3	1	no	—
436	C₃×C₈	—	3	1	no	—
437	C₃×C₈	—	3	1	no	—
438	C₃×C₈	—	3	1	no	—
439	C₃×C₈	—	3	4	no	—
440	C₃×C₈	—	4	2	no	—
441	C₃×C₈	—	6	2	no	—
442	C₃⋊C₈	—	2	2	no	—
443	C₃⋊C₈	C₂²×C₃×C₄	1	1	yes	characteristic
444	C₃⋊C₈	C₂²×C₃×C₄	1	1	yes	characteristic
445	C₃⋊C₈	C₂²×C₃×C₄	1	1	yes	characteristic
446	C₃⋊C₈	C₂²×C₃×C₄	1	1	yes	characteristic
447	C₃⋊C₈	C₂×C₃×D₄	1	4	yes	—
448	C₂×C₃²	—	2	1	no	—
449	C₂×C₃²	—	2	1	no	—
450	C₂×C₃²	—	2	1	no	—
451	C₂×C₃²	—	4	2	no	—
452	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
453	C₃×D₃	—	4	2	no	—
454	#41	—	2	1	no	—
455	#41	—	2	1	no	—
456	#41	—	3	2	no	—
457	#41	—	3	2	no	—
458	#41	—	6	1	no	—
459	#41	—	6	1	no	—
460	#41	C₃×C₄×D₃	1	2	yes	—
461	#41	C₂²×C₃×D₃	1	2	yes	—
462	C₂×Q₈	—	3	1	no	—
463	C₂×Q₈	C₃×C₄×D₃	1	1	yes	characteristic
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	3	1	no	—
466	C₂×D₄	—	6	1	no	—
467	C₂×D₄	C₃×C₄×D₃	1	1	yes	characteristic
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	6	1	no	—
470	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
471	Q₁₆	—	3	2	no	—
472	Q₁₆	—	3	2	no	—
473	SD₁₆	—	3	2	no	—
474	SD₁₆	—	3	2	no	—
475	SD₁₆	—	3	2	no	—
476	SD₁₆	—	3	2	no	—
477	D₈	—	3	2	no	—
478	D₈	—	3	2	no	—
479	M₁₆	—	2	1	no	—
480	M₁₆	—	3	2	no	—
481	M₁₆	—	3	2	no	—
482	M₁₆	—	3	2	no	—
483	M₁₆	—	6	4	no	—
484	M₁₆	—	6	4	no	—
485	M₁₆	—	6	1	no	—
486	M₁₆	C₂²×C₃×D₃	1	2	yes	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	3	1	no	—
489	C₂×C₈	—	3	2	no	—
490	C₂×C₈	—	3	1	no	—
491	C₂×C₈	—	3	1	no	—
492	C₂×C₈	—	3	1	no	—
493	C₂×C₈	—	3	1	no	—
494	C₂×C₈	—	3	1	no	—
495	C₂×C₈	—	6	4	no	—
496	C₂×C₈	—	6	4	no	—
497	C₂×C₈	—	6	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₄²	C₂²×C₃×D₃	1	2	yes	—
501	C₂²×C₃	—	2	2	no	—
502	C₂²×C₃	—	2	2	no	—
503	C₂²×C₃	—	2	1	no	—
504	C₂²×C₃	—	2	1	no	—
505	C₂²×C₃	—	2	1	no	—
506	C₂²×C₃	—	4	2	no	—
507	C₂²×C₃	—	4	1	no	—
508	C₂²×C₃	—	4	1	no	—
509	C₂²×C₃	—	6	2	no	—
510	C₂²×C₃	—	8	1	no	—
511	C₂²×C₃	—	8	1	no	—
512	C₂²×C₃	—	8	1	no	—
513	C₂²×C₃	—	8	2	no	—
514	C₂²×C₃	—	24	1	no	—
515	C₂²×C₃	#67⋊C₄	1	1	yes	characteristic
516	C₂²×C₃	#67⋊C₄	1	1	yes	characteristic
517	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
518	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
519	C₂²×C₃	C₂×#237	1	1	yes	characteristic
520	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
521	C₂×D₃	—	2	2	no	—
522	C₂×D₃	—	8	1	no	—
523	C₃×C₄	—	2	2	no	—
524	C₃×C₄	—	2	2	no	—
525	C₃×C₄	—	2	1	no	—
526	C₃×C₄	—	2	1	no	—
527	C₃×C₄	—	2	1	no	—
528	C₃×C₄	—	2	1	no	—
529	C₃×C₄	—	4	2	no	—
530	C₃×C₄	—	4	2	no	—
531	C₃×C₄	—	4	2	no	—
532	C₃×C₄	—	6	2	no	—
533	C₃×C₄	—	8	2	no	—
534	C₃×C₄	#67⋊C₄	1	1	yes	characteristic
535	C₃×C₄	#67⋊C₄	1	1	yes	characteristic
536	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
537	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
538	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
539	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
540	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
541	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
542	Dic₃	—	2	2	no	—
543	C₃²	#2957	1	1	yes	characteristic, complemented, Sylow
544	C₂³	—	2	1	no	—
545	C₂³	—	6	1	no	—
546	C₂³	C₃×#237	1	1	yes	characteristic
547	Q₈	—	2	1	no	—
548	Q₈	—	3	2	no	—
549	Q₈	—	6	1	no	—
550	Q₈	C₂×C₃×C₄×D₃	1	2	yes	—
551	D₄	—	2	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	2	1	no	—
554	D₄	—	3	2	no	—
555	D₄	—	6	2	no	—
556	D₄	—	6	2	no	—
557	D₄	—	6	1	no	—
558	D₄	C₂×C₃×C₄×D₃	1	2	yes	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	6	1	no	—
564	C₂×C₄	—	6	2	no	—
565	C₂×C₄	—	6	2	no	—
566	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
567	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
568	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
569	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
570	C₂×C₄	C₃×#237	1	1	yes	characteristic
571	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
572	C₈	—	2	2	no	—
573	C₈	—	3	1	no	—
574	C₈	—	3	1	no	—
575	C₈	—	3	1	no	—
576	C₈	—	3	1	no	—
577	C₈	—	3	4	no	—
578	C₈	—	6	2	no	—
579	C₂×C₃	—	2	1	no	—
580	C₂×C₃	—	2	1	no	—
581	C₂×C₃	—	2	1	no	—
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	—	4	1	no	—
587	C₂×C₃	—	4	1	no	—
588	C₂×C₃	—	4	1	no	—
589	C₂×C₃	—	4	2	no	—
590	C₂×C₃	—	4	2	no	—
591	C₂×C₃	—	8	2	no	—
592	C₂×C₃	—	12	2	no	—
593	C₂×C₃	C₂×#67⋊C₄	1	1	yes	characteristic
594	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
595	D₃	—	4	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	6	2	no	—
599	C₂²	—	8	1	no	—
600	C₂²	—	24	1	no	—
601	C₂²	C₃×#67⋊C₄	1	1	yes	characteristic
602	C₂²	C₃×#67⋊C₄	1	1	yes	characteristic
603	C₂²	C₂×C₃×#237	1	1	yes	characteristic
604	C₄	—	2	2	no	—
605	C₄	—	4	2	no	—
606	C₄	—	6	2	no	—
607	C₄	C₃×#67⋊C₄	1	1	yes	characteristic
608	C₄	C₃×#67⋊C₄	1	1	yes	characteristic
609	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
610	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
611	C₃	—	2	1	no	—
612	C₃	#78990	1	1	yes	characteristic, direct product factor
613	C₃	C₃×#2957	1	1	yes	characteristic, complemented
614	C₂	—	2	1	no	—
615	C₂	—	2	1	no	—
616	C₂	—	2	1	no	—
617	C₂	—	4	2	no	—
618	C₂	—	12	2	no	—
619	C₂	C₂×C₃×#67⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#421	C₂
socle	C₂×C₃²	C₂×C₄×D₄
prime radical	C₂×C₃×#950	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#421	D₃
hypocenter	C₃	C₃×#2957
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#421

Complements

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

N	H ≅ G/N	type
2. C₃×#5819	C₂	semidirect
3. C₃×#5745	C₂	semidirect
4. C₃²×#421	C₂	semidirect
5. C₂×C₃×#822	C₂	semidirect
6. C₃×#5005	C₂	semidirect
7. C₃×#4997	C₂	semidirect
8. C₃×#4824	C₂	semidirect
9. C₃×#4823	C₂	semidirect
11. #78990	C₃	direct (N × H)
16. C₃×#950	C₄	semidirect
17. C₃×#950	C₄	semidirect
21. C₃×#948	C₂²	semidirect
22. C₂×C₃×#216	C₄	semidirect
23. C₂×C₃×#215	C₄	semidirect
24. C₂×C₃×#214	C₄	semidirect
25. C₂×C₃×#213	C₄	semidirect
30. C₃×#907	C₂²	semidirect
33. C₃²×#104	C₂²	semidirect
34. C₃×#822	C₂²	semidirect
35. C₃×#822	C₂²	semidirect
36. C₃×#805	C₂²	semidirect
37. C₃×#803	C₂²	semidirect
38. C₃×C₄×C₃⋊C₈	C₂²	semidirect
43. #5819	C₂×C₃	semidirect
44. #5745	C₂×C₃	semidirect
50. C₃×#421	D₃	semidirect
51. C₃×#421	C₂×C₃	semidirect
53. C₂×#822	C₂×C₃	semidirect
54. #5005	C₂×C₃	semidirect
55. #4997	C₂×C₃	semidirect
56. #4824	C₂×C₃	semidirect
57. #4823	C₂×C₃	semidirect
134. #950	C₃×C₄	semidirect
135. #950	C₃×C₄	semidirect
139. #948	C₂²×C₃	semidirect
140. C₂×#216	C₃×C₄	semidirect
141. C₂×#215	C₃×C₄	semidirect
142. C₂×#214	C₃×C₄	semidirect
143. C₂×#213	C₃×C₄	semidirect
148. #907	C₂²×C₃	semidirect
155. C₃×#104	C₂×D₃	semidirect
156. C₃×#104	C₂²×C₃	semidirect
159. #822	C₂²×C₃	semidirect
160. #822	C₂²×C₃	semidirect
161. #805	C₂²×C₃	semidirect
162. #803	C₂²×C₃	semidirect
163. C₄×C₃⋊C₈	C₂²×C₃	semidirect
206. #421	C₃×D₃	semidirect
356. #104	C₂×C₃×D₃	semidirect
543. C₃²	#2957	semidirect
612. C₃	#78990	direct (N × H)
613. 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
C₂×C₃×#950	2
C₃×#5819	2
C₃×#5745	2
C₃²×#421	2
C₂×C₃×#822	2
C₃×#5005	2
C₃×#4997	2
C₃×#4824	2
C₃×#4823	2
C₃×#2957	3
#78990	3

Subgroups — C3×#78990 #11861189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#78990 #11861189