Subgroups — C₃×#78980 #11861135

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5822	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	C₂×C₃²×#104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5124	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#805	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×#208	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×#2956	—	3	1	no	maximal
11	#78980	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	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
16	C₃×#951	C₄	1	2	yes	complemented
17	C₃×#950	C₂²	1	4	yes	—
18	C₃×#949	C₄	1	2	yes	complemented
19	C₃×#948	—	2	2	no	—
20	C₃×#948	C₂²	1	4	yes	complemented
21	C₃×#942	C₄	1	2	yes	complemented
22	C₃×#932	C₄	1	2	yes	complemented
23	C₂×C₃×#208	—	2	2	no	—
24	C₂×C₃×#208	C₂²	1	1	yes	characteristic
25	C₂×C₃×#208	C₂²	1	1	yes	characteristic
26	C₂×C₃×#208	C₂²	1	1	yes	characteristic
27	C₃×#907	C₂²	1	4	yes	complemented
28	C₃×D₃×M₁₆	—	2	2	no	—
29	C₃×#901	—	2	2	no	—
30	C₃²×#104	C₂²	1	2	yes	complemented
31	C₃²×#104	C₂²	1	2	yes	complemented
32	C₃×#822	C₂²	1	4	yes	complemented
33	C₃×#805	C₂²	1	2	yes	complemented
34	C₃×#805	C₂²	1	2	yes	complemented
35	C₃×#803	C₂²	1	2	yes	complemented
36	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	complemented
37	C₃×#575	—	3	1	no	—
38	C₃×#568	—	3	1	no	—
39	C₃×#568	—	3	1	no	—
40	#5822	C₂×C₃	1	1	yes	characteristic
41	#5819	C₂×C₃	1	1	yes	characteristic, complemented
42	#5745	C₂×C₃	1	1	yes	characteristic, complemented
43	C₃×#444	—	3	4	no	—
44	C₃×#443	—	3	4	no	—
45	C₃×#430	—	3	1	no	—
46	C₂×C₃×#104	—	2	1	no	—
47	C₂×C₃×#104	—	3	1	no	—
48	C₂×C₃×#104	D₃	1	1	yes	characteristic, complemented
49	C₂×C₃×#104	C₂×C₃	1	1	yes	characteristic, complemented
50	C₃×C₄×M₁₆	—	3	1	no	—
51	#5124	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×#805	C₂×C₃	1	1	yes	characteristic, complemented
53	C₄×#208	C₂×C₃	1	1	yes	characteristic, complemented
54	#4824	C₂×C₃	1	4	yes	complemented
55	#4823	C₂×C₃	1	4	yes	complemented
56	C₃²×#41	—	2	1	no	—
57	C₃²×#41	—	2	1	no	—
58	C₃²×#41	C₂×C₄	1	2	yes	—
59	C₃²×#41	C₂³	1	2	yes	—
60	C₂×C₃²×Q₈	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃²×D₄	—	2	1	no	—
62	C₂×C₃²×D₄	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₃²×C₄	—	2	1	no	—
64	C₂²×C₃²×C₄	—	2	1	no	—
65	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
66	C₂×C₃×#67	—	2	1	no	—
67	C₃×#235	—	2	1	no	—
68	C₃×#235	—	2	1	no	—
69	C₃×#235	C₂×C₄	1	2	yes	—
70	C₃×#235	C₂³	1	2	yes	—
71	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
72	C₂×C₃×C₄×D₃	—	2	1	no	—
73	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
74	C₃²×M₁₆	—	2	1	no	—
75	C₃²×M₁₆	C₂³	1	2	yes	—
76	C₂×C₃²×C₈	—	2	1	no	—
77	C₃²×C₄²	—	2	1	no	—
78	C₃²×C₄²	C₂³	1	1	yes	characteristic
79	C₃²×C₄²	C₂³	1	1	yes	characteristic
80	C₃×#216	C₂×C₄	1	4	yes	complemented
81	C₃×#215	C₂×C₄	1	4	yes	complemented
82	C₃×#214	C₂×C₄	1	4	yes	complemented
83	C₃×#213	C₂×C₄	1	4	yes	complemented
84	C₃×#208	—	2	1	no	—
85	C₃×#208	—	2	4	no	—
86	C₃×#208	C₂×C₄	1	2	yes	—
87	C₃×#208	C₂×C₄	1	2	yes	—
88	C₃×#208	D₄	1	2	yes	—
89	C₃×#208	D₄	1	2	yes	—
90	C₃×#208	C₂³	1	2	yes	—
91	C₂×C₃×C₃⋊C₈	—	2	1	no	—
92	C₂×C₃×C₃⋊C₈	—	2	4	no	—
93	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
94	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
95	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
96	C₃×D₃×C₈	—	2	4	no	—
97	#2956	—	3	1	no	Sylow
98	C₂×C₃×#41	—	2	1	no	—
99	C₂×C₃×#41	—	3	1	no	—
100	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
101	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
102	C₂×#235	C₂²×C₃	1	1	yes	characteristic
103	C₃×#137	—	3	2	no	—
104	C₃×#137	—	3	2	no	—
105	C₃×AGL(1,ℤ/8)	—	3	2	no	—
106	C₃×AGL(1,ℤ/8)	—	3	2	no	—
107	C₃×#135	—	3	4	no	—
108	C₃×#131	—	3	4	no	—
109	C₃×#131	—	3	4	no	—
110	C₃×#131	—	6	2	no	—
111	C₃×#131	—	6	2	no	—
112	C₂×C₃×M₁₆	—	2	1	no	—
113	C₂×C₃×M₁₆	—	3	1	no	—
114	C₂×C₃×M₁₆	—	3	1	no	—
115	C₂×C₃×M₁₆	—	3	1	no	—
116	C₂×C₃×M₁₆	—	6	2	no	—
117	C₂×C₃×M₁₆	—	6	2	no	—
118	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
119	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₃×C₄²	—	2	1	no	—
121	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
122	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
123	#951	C₃×C₄	1	2	yes	complemented
124	#950	C₂²×C₃	1	4	yes	—
125	#949	C₃×C₄	1	2	yes	complemented
126	#948	—	2	2	no	—
127	#948	C₂²×C₃	1	4	yes	complemented
128	#942	C₃×C₄	1	2	yes	complemented
129	#932	C₃×C₄	1	2	yes	complemented
130	C₂×#208	—	2	2	no	—
131	C₂×#208	C₂²×C₃	1	1	yes	characteristic
132	C₂×#208	C₂²×C₃	1	1	yes	characteristic
133	C₂×#208	C₂²×C₃	1	1	yes	characteristic
134	#907	C₂²×C₃	1	4	yes	complemented
135	D₃×M₁₆	—	2	2	no	—
136	#901	—	2	2	no	—
137	C₃×#108	—	3	4	no	—
138	C₃×#104	—	2	2	no	—
139	C₃×#104	—	2	2	no	—
140	C₃×#104	—	3	2	no	—
141	C₃×#104	—	3	2	no	—
142	C₃×#104	C₂×D₃	1	2	yes	complemented
143	C₃×#104	C₂×D₃	1	2	yes	complemented
144	C₃×#104	C₂²×C₃	1	2	yes	complemented
145	C₃×#104	C₂²×C₃	1	2	yes	complemented
146	C₃×#97	—	3	2	no	—
147	C₃×C₄×C₈	—	3	2	no	—
148	#822	C₂²×C₃	1	4	yes	complemented
149	#805	C₂²×C₃	1	2	yes	complemented
150	#805	C₂²×C₃	1	2	yes	complemented
151	#803	C₂²×C₃	1	2	yes	complemented
152	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	complemented
153	C₂³×C₃²	—	2	1	no	—
154	C₂³×C₃²	#41	1	1	yes	characteristic
155	C₂²×C₃×D₃	—	2	1	no	—
156	C₃²×Q₈	—	2	1	no	—
157	C₃²×Q₈	C₂²×C₄	1	2	yes	—
158	C₃²×D₄	—	2	2	no	—
159	C₃²×D₄	—	2	2	no	—
160	C₃²×D₄	—	2	1	no	—
161	C₃²×D₄	C₂²×C₄	1	2	yes	—
162	C₂×C₃²×C₄	—	2	1	no	—
163	C₂×C₃²×C₄	—	2	1	no	—
164	C₂×C₃²×C₄	—	2	2	no	—
165	C₂×C₃²×C₄	—	2	2	no	—
166	C₂×C₃²×C₄	—	2	1	no	—
167	C₂×C₃²×C₄	—	4	2	no	—
168	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
171	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
172	C₂×C₃²×C₄	#41	1	1	yes	characteristic
173	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
174	C₃×#67	—	2	2	no	—
175	C₃×#67	—	2	2	no	—
176	C₂×C₃×Dic₃	—	2	1	no	—
177	C₃×D₁₂	—	2	1	no	—
178	C₃×D₁₂	C₂²×C₄	1	2	yes	—
179	C₃×C₄×D₃	—	2	2	no	—
180	C₃×C₄×D₃	—	2	2	no	—
181	C₃×Dic₆	—	2	1	no	—
182	C₃×Dic₆	C₂²×C₄	1	2	yes	—
183	C₃²×C₈	—	2	2	no	—
184	C₃×C₃⋊C₈	—	2	2	no	—
185	C₃×C₃⋊C₈	C₂²×C₄	1	4	yes	—
186	C₃×C₃⋊C₈	C₂×D₄	1	4	yes	—
187	#575	—	3	1	no	—
188	#568	—	3	1	no	—
189	#568	—	3	1	no	—
190	#444	—	3	4	no	—
191	#443	—	3	4	no	—
192	#430	—	3	1	no	—
193	C₂×#104	—	3	1	no	—
194	C₂×#104	C₃×D₃	1	1	yes	characteristic, complemented
195	C₄×M₁₆	—	3	1	no	—
196	C₃×#41	—	2	1	no	—
197	C₃×#41	—	2	1	no	—
198	C₃×#41	—	2	1	no	—
199	C₃×#41	—	2	1	no	—
200	C₃×#41	—	2	2	no	—
201	C₃×#41	—	2	2	no	—
202	C₃×#41	—	3	2	no	—
203	C₃×#41	—	3	2	no	—
204	C₃×#41	—	4	1	no	—
205	C₃×#41	—	4	1	no	—
206	C₃×#41	—	6	1	no	—
207	C₃×#41	—	6	1	no	—
208	C₃×#41	C₄×D₃	1	2	yes	—
209	C₃×#41	C₂×C₃×C₄	1	2	yes	—
210	C₃×#41	C₂²×D₃	1	2	yes	—
211	C₃×#41	C₂³×C₃	1	2	yes	—
212	C₂×C₃×Q₈	—	2	1	no	—
213	C₂×C₃×Q₈	—	3	1	no	—
214	C₂×C₃×Q₈	C₄×D₃	1	1	yes	characteristic
215	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
216	C₂×C₃×D₄	—	2	1	no	—
217	C₂×C₃×D₄	—	2	1	no	—
218	C₂×C₃×D₄	—	2	1	no	—
219	C₂×C₃×D₄	—	3	1	no	—
220	C₂×C₃×D₄	—	4	1	no	—
221	C₂×C₃×D₄	—	6	1	no	—
222	C₂×C₃×D₄	C₄×D₃	1	1	yes	characteristic
223	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
224	C₂²×C₃×C₄	—	2	1	no	—
225	C₂²×C₃×C₄	—	2	1	no	—
226	C₂²×C₃×C₄	—	2	1	no	—
227	C₂²×C₃×C₄	—	2	1	no	—
228	C₂²×C₃×C₄	—	2	1	no	—
229	C₂²×C₃×C₄	—	4	1	no	—
230	C₂²×C₃×C₄	—	4	1	no	—
231	C₂²×C₃×C₄	—	6	1	no	—
232	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
234	C₂×#67	—	2	1	no	—
235	#235	—	2	1	no	—
236	#235	—	2	1	no	—
237	#235	C₂×C₃×C₄	1	2	yes	—
238	#235	C₂³×C₃	1	2	yes	—
239	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
240	C₂×C₄×D₃	—	2	1	no	—
241	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
242	C₃×Q₁₆	—	3	4	no	—
243	C₃×SD₁₆	—	3	4	no	—
244	C₃×SD₁₆	—	3	4	no	—
245	C₃×D₈	—	3	4	no	—
246	C₃×M₁₆	—	2	1	no	—
247	C₃×M₁₆	—	2	1	no	—
248	C₃×M₁₆	—	2	2	no	—
249	C₃×M₁₆	—	3	2	no	—
250	C₃×M₁₆	—	3	2	no	—
251	C₃×M₁₆	—	3	2	no	—
252	C₃×M₁₆	—	3	2	no	—
253	C₃×M₁₆	—	3	2	no	—
254	C₃×M₁₆	—	4	1	no	—
255	C₃×M₁₆	—	6	4	no	—
256	C₃×M₁₆	—	6	4	no	—
257	C₃×M₁₆	—	6	1	no	—
258	C₃×M₁₆	C₂²×D₃	1	2	yes	—
259	C₃×M₁₆	C₂³×C₃	1	2	yes	—
260	C₂×C₃×C₈	—	2	1	no	—
261	C₂×C₃×C₈	—	2	1	no	—
262	C₂×C₃×C₈	—	3	2	no	—
263	C₂×C₃×C₈	—	3	2	no	—
264	C₂×C₃×C₈	—	4	1	no	—
265	C₂×C₃×C₈	—	6	4	no	—
266	C₂×C₃×C₈	—	6	4	no	—
267	C₂×C₃×C₈	—	6	1	no	—
268	C₃×C₄²	—	2	1	no	—
269	C₃×C₄²	—	2	1	no	—
270	C₃×C₄²	—	2	1	no	—
271	C₃×C₄²	—	2	1	no	—
272	C₃×C₄²	—	4	1	no	—
273	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
274	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
275	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
276	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
277	#216	C₂×C₃×C₄	1	4	yes	complemented
278	#215	C₂×C₃×C₄	1	4	yes	complemented
279	#214	C₂×C₃×C₄	1	4	yes	complemented
280	#213	C₂×C₃×C₄	1	4	yes	complemented
281	#208	—	2	1	no	—
282	#208	—	2	4	no	—
283	#208	C₂×C₃×C₄	1	2	yes	—
284	#208	C₂×C₃×C₄	1	2	yes	—
285	#208	C₃×D₄	1	2	yes	—
286	#208	C₃×D₄	1	2	yes	—
287	#208	C₂³×C₃	1	2	yes	—
288	C₂×C₃⋊C₈	—	2	1	no	—
289	C₂×C₃⋊C₈	—	2	4	no	—
290	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
291	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
292	ΓL(1,𝔽₂₅)	—	2	4	no	—
293	D₃×C₈	—	2	4	no	—
294	C₂²×C₃²	—	2	2	no	—
295	C₂²×C₃²	—	4	1	no	—
296	C₂²×C₃²	—	8	1	no	—
297	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
298	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
299	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
300	C₂×C₃×D₃	—	2	2	no	—
301	C₂×C₃×D₃	—	8	1	no	—
302	C₃²×C₄	—	2	2	no	—
303	C₃²×C₄	—	2	2	no	—
304	C₃²×C₄	—	4	1	no	—
305	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
306	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
307	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
308	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
309	C₃×Dic₃	—	2	2	no	—
310	C₂×#41	—	3	1	no	—
311	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
312	#137	—	3	2	no	—
313	#137	—	3	2	no	—
314	AGL(1,ℤ/8)	—	3	2	no	—
315	AGL(1,ℤ/8)	—	3	2	no	—
316	#135	—	3	4	no	—
317	#131	—	3	4	no	—
318	#131	—	3	4	no	—
319	#131	—	6	2	no	—
320	#131	—	6	2	no	—
321	C₂×M₁₆	—	3	1	no	—
322	C₂×M₁₆	—	3	1	no	—
323	C₂×M₁₆	—	3	1	no	—
324	C₂×M₁₆	—	6	2	no	—
325	C₂×M₁₆	—	6	2	no	—
326	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
327	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
328	#108	—	3	4	no	—
329	#104	—	3	2	no	—
330	#104	—	3	2	no	—
331	#104	C₂×C₃×D₃	1	2	yes	complemented
332	#104	C₂×C₃×D₃	1	2	yes	complemented
333	#97	—	3	2	no	—
334	C₄×C₈	—	3	2	no	—
335	C₂³×C₃	—	2	1	no	—
336	C₂³×C₃	—	2	1	no	—
337	C₂³×C₃	—	2	1	no	—
338	C₂³×C₃	—	4	1	no	—
339	C₂³×C₃	—	6	1	no	—
340	C₂³×C₃	#237	1	1	yes	characteristic
341	C₂³×C₃	C₃×#41	1	1	yes	characteristic
342	C₂²×D₃	—	2	1	no	—
343	C₃×Q₈	—	2	1	no	—
344	C₃×Q₈	—	2	1	no	—
345	C₃×Q₈	—	2	2	no	—
346	C₃×Q₈	—	3	2	no	—
347	C₃×Q₈	—	4	1	no	—
348	C₃×Q₈	—	6	1	no	—
349	C₃×Q₈	C₂×C₄×D₃	1	2	yes	—
350	C₃×Q₈	C₂²×C₃×C₄	1	2	yes	—
351	C₃×D₄	—	2	2	no	—
352	C₃×D₄	—	2	2	no	—
353	C₃×D₄	—	2	2	no	—
354	C₃×D₄	—	2	2	no	—
355	C₃×D₄	—	2	1	no	—
356	C₃×D₄	—	2	1	no	—
357	C₃×D₄	—	2	2	no	—
358	C₃×D₄	—	3	2	no	—
359	C₃×D₄	—	4	1	no	—
360	C₃×D₄	—	4	2	no	—
361	C₃×D₄	—	4	2	no	—
362	C₃×D₄	—	6	2	no	—
363	C₃×D₄	—	6	2	no	—
364	C₃×D₄	—	6	1	no	—
365	C₃×D₄	C₂×C₄×D₃	1	2	yes	—
366	C₃×D₄	C₂²×C₃×C₄	1	2	yes	—
367	C₂×C₃×C₄	—	2	1	no	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	4	2	no	—
384	C₂×C₃×C₄	—	4	2	no	—
385	C₂×C₃×C₄	—	4	1	no	—
386	C₂×C₃×C₄	—	4	1	no	—
387	C₂×C₃×C₄	—	4	1	no	—
388	C₂×C₃×C₄	—	4	2	no	—
389	C₂×C₃×C₄	—	4	2	no	—
390	C₂×C₃×C₄	—	4	4	no	—
391	C₂×C₃×C₄	—	6	1	no	—
392	C₂×C₃×C₄	—	6	2	no	—
393	C₂×C₃×C₄	—	6	2	no	—
394	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
395	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
396	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
397	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
398	C₂×C₃×C₄	#237	1	1	yes	characteristic
399	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
400	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
401	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
402	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
403	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
405	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
406	#67	—	2	2	no	—
407	#67	—	2	2	no	—
408	C₂×Dic₃	—	2	1	no	—
409	D₁₂	—	2	1	no	—
410	D₁₂	C₂²×C₃×C₄	1	2	yes	—
411	C₄×D₃	—	2	2	no	—
412	C₄×D₃	—	2	2	no	—
413	Dic₆	—	2	1	no	—
414	Dic₆	C₂²×C₃×C₄	1	2	yes	—
415	C₃×C₈	—	2	2	no	—
416	C₃×C₈	—	2	2	no	—
417	C₃×C₈	—	3	4	no	—
418	C₃×C₈	—	3	4	no	—
419	C₃×C₈	—	4	2	no	—
420	C₃×C₈	—	6	2	no	—
421	C₃⋊C₈	—	2	2	no	—
422	C₃⋊C₈	C₂²×C₃×C₄	1	4	yes	—
423	C₃⋊C₈	C₂×C₃×D₄	1	4	yes	—
424	C₂×C₃²	—	2	1	no	—
425	C₂×C₃²	—	2	1	no	—
426	C₂×C₃²	—	2	1	no	—
427	C₂×C₃²	—	4	2	no	—
428	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
429	C₃×D₃	—	4	2	no	—
430	#41	—	2	1	no	—
431	#41	—	2	1	no	—
432	#41	—	3	2	no	—
433	#41	—	3	2	no	—
434	#41	—	6	1	no	—
435	#41	—	6	1	no	—
436	#41	C₃×C₄×D₃	1	2	yes	—
437	#41	C₂²×C₃×D₃	1	2	yes	—
438	C₂×Q₈	—	3	1	no	—
439	C₂×Q₈	C₃×C₄×D₃	1	1	yes	characteristic
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	3	1	no	—
442	C₂×D₄	—	6	1	no	—
443	C₂×D₄	C₃×C₄×D₃	1	1	yes	characteristic
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	6	1	no	—
447	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
448	Q₁₆	—	3	4	no	—
449	SD₁₆	—	3	4	no	—
450	SD₁₆	—	3	4	no	—
451	D₈	—	3	4	no	—
452	M₁₆	—	2	1	no	—
453	M₁₆	—	3	2	no	—
454	M₁₆	—	3	2	no	—
455	M₁₆	—	3	2	no	—
456	M₁₆	—	3	2	no	—
457	M₁₆	—	3	2	no	—
458	M₁₆	—	6	4	no	—
459	M₁₆	—	6	4	no	—
460	M₁₆	—	6	1	no	—
461	M₁₆	C₂²×C₃×D₃	1	2	yes	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	3	2	no	—
464	C₂×C₈	—	3	2	no	—
465	C₂×C₈	—	6	4	no	—
466	C₂×C₈	—	6	4	no	—
467	C₂×C₈	—	6	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
470	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
471	C₂²×C₃	—	2	2	no	—
472	C₂²×C₃	—	2	2	no	—
473	C₂²×C₃	—	2	1	no	—
474	C₂²×C₃	—	2	1	no	—
475	C₂²×C₃	—	2	1	no	—
476	C₂²×C₃	—	4	2	no	—
477	C₂²×C₃	—	4	1	no	—
478	C₂²×C₃	—	4	1	no	—
479	C₂²×C₃	—	4	2	no	—
480	C₂²×C₃	—	6	2	no	—
481	C₂²×C₃	—	8	1	no	—
482	C₂²×C₃	—	8	1	no	—
483	C₂²×C₃	—	8	2	no	—
484	C₂²×C₃	—	24	1	no	—
485	C₂²×C₃	#67⋊C₄	1	1	yes	characteristic
486	C₂²×C₃	#67⋊C₄	1	1	yes	characteristic
487	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
488	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
489	C₂²×C₃	C₂×#237	1	1	yes	characteristic
490	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
491	C₂×D₃	—	2	2	no	—
492	C₂×D₃	—	8	1	no	—
493	C₃×C₄	—	2	2	no	—
494	C₃×C₄	—	2	2	no	—
495	C₃×C₄	—	2	2	no	—
496	C₃×C₄	—	2	2	no	—
497	C₃×C₄	—	2	1	no	—
498	C₃×C₄	—	2	1	no	—
499	C₃×C₄	—	2	1	no	—
500	C₃×C₄	—	2	1	no	—
501	C₃×C₄	—	4	2	no	—
502	C₃×C₄	—	4	2	no	—
503	C₃×C₄	—	4	1	no	—
504	C₃×C₄	—	4	1	no	—
505	C₃×C₄	—	4	2	no	—
506	C₃×C₄	—	6	2	no	—
507	C₃×C₄	#67⋊C₄	1	1	yes	characteristic
508	C₃×C₄	#67⋊C₄	1	1	yes	characteristic
509	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
510	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
511	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
512	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
513	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
514	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
515	Dic₃	—	2	2	no	—
516	C₃²	#2956	1	1	yes	characteristic, complemented, Sylow
517	C₂³	—	2	1	no	—
518	C₂³	—	6	1	no	—
519	C₂³	C₃×#237	1	1	yes	characteristic
520	Q₈	—	2	1	no	—
521	Q₈	—	3	2	no	—
522	Q₈	—	6	1	no	—
523	Q₈	C₂×C₃×C₄×D₃	1	2	yes	—
524	D₄	—	2	2	no	—
525	D₄	—	2	2	no	—
526	D₄	—	2	1	no	—
527	D₄	—	3	2	no	—
528	D₄	—	6	2	no	—
529	D₄	—	6	2	no	—
530	D₄	—	6	1	no	—
531	D₄	C₂×C₃×C₄×D₃	1	2	yes	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	6	1	no	—
539	C₂×C₄	—	6	2	no	—
540	C₂×C₄	—	6	2	no	—
541	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
542	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
543	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
544	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
545	C₂×C₄	C₃×#237	1	1	yes	characteristic
546	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
547	C₈	—	2	2	no	—
548	C₈	—	3	4	no	—
549	C₈	—	3	4	no	—
550	C₈	—	6	2	no	—
551	C₂×C₃	—	2	2	no	—
552	C₂×C₃	—	2	1	no	—
553	C₂×C₃	—	2	1	no	—
554	C₂×C₃	—	2	1	no	—
555	C₂×C₃	—	2	1	no	—
556	C₂×C₃	—	2	1	no	—
557	C₂×C₃	—	2	1	no	—
558	C₂×C₃	—	2	1	no	—
559	C₂×C₃	—	4	1	no	—
560	C₂×C₃	—	4	1	no	—
561	C₂×C₃	—	4	2	no	—
562	C₂×C₃	—	4	2	no	—
563	C₂×C₃	—	8	2	no	—
564	C₂×C₃	—	12	2	no	—
565	C₂×C₃	C₂×#67⋊C₄	1	1	yes	characteristic
566	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
567	D₃	—	4	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	6	2	no	—
571	C₂²	—	8	1	no	—
572	C₂²	—	24	1	no	—
573	C₂²	C₃×#67⋊C₄	1	1	yes	characteristic
574	C₂²	C₃×#67⋊C₄	1	1	yes	characteristic
575	C₂²	C₂×C₃×#237	1	1	yes	characteristic
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	4	1	no	—
579	C₄	—	6	2	no	—
580	C₄	C₃×#67⋊C₄	1	1	yes	characteristic
581	C₄	C₃×#67⋊C₄	1	1	yes	characteristic
582	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
583	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
584	C₃	—	2	1	no	—
585	C₃	#78980	1	1	yes	characteristic, direct product factor
586	C₃	C₃×#2956	1	1	yes	characteristic, complemented
587	C₂	—	2	1	no	—
588	C₂	—	2	1	no	—
589	C₂	—	2	1	no	—
590	C₂	—	4	2	no	—
591	C₂	—	12	2	no	—
592	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	C₂×C₃²×#104	C₂
socle	C₂×C₃²	C₂×C₄×D₄
prime radical	C₃×#5822	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#104	D₃
hypocenter	C₃	C₃×#2956
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#104

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. C₂×C₃²×#104	C₂	semidirect
5. C₃×#5124	C₂	semidirect
6. C₂×C₃×#805	C₂	semidirect
7. C₃×C₄×#208	C₂	semidirect
8. C₃×#4824	C₂	semidirect
9. C₃×#4823	C₂	semidirect
11. #78980	C₃	direct (N × H)
16. C₃×#951	C₄	semidirect
18. C₃×#949	C₄	semidirect
20. C₃×#948	C₂²	semidirect
21. C₃×#942	C₄	semidirect
22. C₃×#932	C₄	semidirect
27. C₃×#907	C₂²	semidirect
30. C₃²×#104	C₂²	semidirect
31. C₃²×#104	C₂²	semidirect
32. C₃×#822	C₂²	semidirect
33. C₃×#805	C₂²	semidirect
34. C₃×#805	C₂²	semidirect
35. C₃×#803	C₂²	semidirect
36. C₃×C₄×C₃⋊C₈	C₂²	semidirect
41. #5819	C₂×C₃	semidirect
42. #5745	C₂×C₃	semidirect
48. C₂×C₃×#104	D₃	semidirect
49. C₂×C₃×#104	C₂×C₃	semidirect
51. #5124	C₂×C₃	semidirect
52. C₂×#805	C₂×C₃	semidirect
53. C₄×#208	C₂×C₃	semidirect
54. #4824	C₂×C₃	semidirect
55. #4823	C₂×C₃	semidirect
80. C₃×#216	C₂×C₄	semidirect
81. C₃×#215	C₂×C₄	semidirect
82. C₃×#214	C₂×C₄	semidirect
83. C₃×#213	C₂×C₄	semidirect
123. #951	C₃×C₄	semidirect
125. #949	C₃×C₄	semidirect
127. #948	C₂²×C₃	semidirect
128. #942	C₃×C₄	semidirect
129. #932	C₃×C₄	semidirect
134. #907	C₂²×C₃	semidirect
142. C₃×#104	C₂×D₃	semidirect
143. C₃×#104	C₂×D₃	semidirect
144. C₃×#104	C₂²×C₃	semidirect
145. C₃×#104	C₂²×C₃	semidirect
148. #822	C₂²×C₃	semidirect
149. #805	C₂²×C₃	semidirect
150. #805	C₂²×C₃	semidirect
151. #803	C₂²×C₃	semidirect
152. C₄×C₃⋊C₈	C₂²×C₃	semidirect
194. C₂×#104	C₃×D₃	semidirect
277. #216	C₂×C₃×C₄	semidirect
278. #215	C₂×C₃×C₄	semidirect
279. #214	C₂×C₃×C₄	semidirect
280. #213	C₂×C₃×C₄	semidirect
331. #104	C₂×C₃×D₃	semidirect
332. #104	C₂×C₃×D₃	semidirect
516. C₃²	#2956	semidirect
585. C₃	#78980	direct (N × H)
586. C₃	C₃×#2956	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5822	2
C₃×#5819	2
C₃×#5745	2
C₂×C₃²×#104	2
C₃×#5124	2
C₂×C₃×#805	2
C₃×C₄×#208	2
C₃×#4824	2
C₃×#4823	2
C₃×#2956	3
#78980	3

Subgroups — C3×#78980 #11861135

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#78980 #11861135