Subgroups — C₃×#83355 #11878822

Order 1152.

1087 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#874	C₂	1	1	yes	maximal, characteristic
3	C₃×#5088	C₂	1	2	yes	maximal, complemented
4	C₃×#5085	C₂	1	2	yes	maximal, complemented
5	C₃×#5046	C₂	1	4	yes	maximal, complemented
6	C₃×#5027	C₂	1	4	yes	maximal, complemented
7	C₃×#4925	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#3208	—	3	1	no	maximal
9	#83355	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂²×C₃×D₁₂	—	2	1	no	—
11	C₂²×C₃×D₁₂	—	2	1	no	—
12	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
13	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₃²×#125	—	2	1	no	—
16	C₃²×C₂²⋊Q₈	—	2	1	no	—
17	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₃²×C₄×Q₈	—	2	1	no	—
19	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
20	C₃²×#117	—	2	1	no	—
21	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
22	C₂×C₃×#215	C₂²	1	8	yes	complemented
23	C₃×#874	—	2	1	no	—
24	C₃×#874	—	2	1	no	—
25	C₃×#874	C₂²	1	2	yes	—
26	C₃×#874	C₂²	1	2	yes	—
27	C₃×#830	C₂²	1	2	yes	—
28	C₃×#809	C₂²	1	8	yes	complemented
29	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
30	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	complemented
31	C₃×#533	—	2	1	no	—
32	C₃×#533	D₃	1	1	yes	characteristic, complemented
33	C₃×#533	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₃×#127	—	3	1	no	—
35	C₂×#874	C₂×C₃	1	1	yes	characteristic
36	C₃×#492	—	3	2	no	—
37	C₃×#486	—	3	2	no	—
38	C₃×#460	—	3	4	no	—
39	C₃×#450	—	3	4	no	—
40	C₃×#431	—	3	1	no	—
41	#5088	C₂×C₃	1	2	yes	complemented
42	#5085	C₂×C₃	1	2	yes	complemented
43	#5046	C₂×C₃	1	4	yes	complemented
44	#5027	C₂×C₃	1	4	yes	complemented
45	#4925	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂³×C₃×D₃	—	2	2	no	—
47	C₂×C₃²×Q₈	—	2	1	no	—
48	C₂×C₃²×Q₈	C₂³	1	2	yes	—
49	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
50	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
51	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
52	C₂×C₃×D₁₂	—	2	2	no	—
53	C₂×C₃×D₁₂	—	2	2	no	—
54	C₂×C₃×D₁₂	—	2	2	no	—
55	C₂×C₃×D₁₂	—	2	2	no	—
56	C₂×C₃×D₁₂	—	2	2	no	—
57	C₂×C₃×D₁₂	—	4	4	no	—
58	C₂×C₃×D₁₂	—	4	4	no	—
59	C₂×C₃×D₁₂	—	4	4	no	—
60	C₂×C₃×D₁₂	C₂³	1	4	yes	—
61	C₃²×C₄⋊C₄	—	2	1	no	—
62	C₃²×C₄⋊C₄	—	2	1	no	—
63	C₃²×C₄⋊C₄	—	2	1	no	—
64	C₃²×C₄⋊C₄	—	2	2	no	—
65	C₃²×C₄⋊C₄	—	2	2	no	—
66	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
67	C₃²×C₂²⋊C₄	—	2	2	no	—
68	C₃²×C₄²	—	2	2	no	—
69	C₃²×C₄²	D₄	1	1	yes	characteristic
70	C₃²×C₄²	D₄	1	1	yes	characteristic
71	C₃²×C₄²	C₂³	1	1	yes	characteristic
72	C₃²×C₄²	C₂³	1	1	yes	characteristic
73	C₃×#215	—	4	8	no	—
74	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
75	#3208	—	3	1	no	Sylow
76	C₂²×C₃×D₄	—	3	2	no	—
77	C₂²×C₃×D₄	—	6	1	no	—
78	C₂²×C₃×D₄	—	6	1	no	—
79	C₂²×D₁₂	—	2	1	no	—
80	C₂²×D₁₂	—	2	1	no	—
81	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
82	C₂×C₃×SD₁₆	—	3	8	no	—
83	C₃×C₄⋊Q₈	—	2	1	no	—
84	C₃×C₄⋊Q₈	—	2	1	no	—
85	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
86	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
87	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
88	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
89	C₃×#127	—	3	2	no	—
90	C₃×#127	—	3	2	no	—
91	C₃×#127	—	6	1	no	—
92	C₃×#127	—	6	1	no	—
93	C₃×#125	—	2	2	no	—
94	C₃×#125	—	2	1	no	—
95	C₃×#125	—	2	1	no	—
96	C₃×C₂²⋊Q₈	—	2	2	no	—
97	C₃×C₂²⋊Q₈	—	2	1	no	—
98	C₃×C₂²⋊Q₈	—	2	1	no	—
99	C₃×C₂²⋊Q₈	—	2	2	no	—
100	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
101	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
102	C₃×C₄×Q₈	—	2	2	no	—
103	C₃×C₄×Q₈	—	2	1	no	—
104	C₃×C₄×Q₈	—	2	1	no	—
105	C₃×C₄×Q₈	—	2	2	no	—
106	C₃×C₄×Q₈	C₂×D₃	1	2	yes	complemented
107	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
108	C₃×#117	—	2	2	no	—
109	C₃×#117	—	2	1	no	—
110	C₃×#117	—	2	1	no	—
111	C₂×C₃×C₄²	—	2	1	no	—
112	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
113	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
114	C₂×#215	C₂²×C₃	1	8	yes	complemented
115	#874	—	2	1	no	—
116	#874	—	2	1	no	—
117	#874	C₂²×C₃	1	2	yes	—
118	#874	C₂²×C₃	1	2	yes	—
119	C₃×C₄⋊C₈	—	3	2	no	—
120	C₃×#102	—	3	8	no	—
121	C₃×C₂²⋊C₈	—	3	2	no	—
122	C₃×C₄×C₈	—	3	2	no	—
123	#830	C₂²×C₃	1	2	yes	—
124	#809	C₂²×C₃	1	8	yes	complemented
125	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	complemented
126	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	complemented
127	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₃×D₃	—	2	4	no	—
129	C₂²×C₃×D₃	—	4	4	no	—
130	C₂²×C₃×D₃	—	4	4	no	—
131	C₂²×C₃×D₃	—	4	4	no	—
132	C₃²×Q₈	—	2	4	no	—
133	C₃²×Q₈	—	4	2	no	—
134	C₂×C₃²×C₄	—	2	2	no	—
135	C₂×C₃²×C₄	—	2	2	no	—
136	C₂×C₃²×C₄	—	2	2	no	—
137	C₂×C₃²×C₄	—	2	2	no	—
138	C₂×C₃²×C₄	SD₁₆	1	4	yes	complemented
139	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
143	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
144	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
145	C₃×D₁₂	—	2	8	no	—
146	C₃×D₁₂	—	4	4	no	—
147	C₃×D₁₂	—	4	4	no	—
148	C₃×D₁₂	—	4	4	no	—
149	C₃×D₁₂	—	4	4	no	—
150	C₃×D₁₂	—	4	4	no	—
151	C₃×C₃⋊C₈	—	2	4	no	—
152	#533	C₃×D₃	1	1	yes	characteristic, complemented
153	C₂×#127	—	3	1	no	—
154	#492	—	3	2	no	—
155	#486	—	3	2	no	—
156	#460	—	3	4	no	—
157	#450	—	3	4	no	—
158	#431	—	3	1	no	—
159	C₂⁴×C₃	—	6	2	no	—
160	C₂³×D₃	—	2	2	no	—
161	C₂×C₃×Q₈	—	2	2	no	—
162	C₂×C₃×Q₈	—	2	1	no	—
163	C₂×C₃×Q₈	—	2	1	no	—
164	C₂×C₃×Q₈	—	2	2	no	—
165	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
166	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
167	C₂×C₃×D₄	—	3	4	no	—
168	C₂×C₃×D₄	—	6	2	no	—
169	C₂×C₃×D₄	—	6	2	no	—
170	C₂×C₃×D₄	—	6	2	no	—
171	C₂×C₃×D₄	—	6	2	no	—
172	C₂×C₃×D₄	—	6	2	no	—
173	C₂×C₃×D₄	—	12	4	no	—
174	C₂×C₃×D₄	—	12	4	no	—
175	C₂×C₃×D₄	—	12	4	no	—
176	C₂²×C₃×C₄	—	2	1	no	—
177	C₂²×C₃×C₄	—	2	1	no	—
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	#67	1	1	yes	characteristic
180	C₂²×C₃×C₄	#67	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
185	C₂×D₁₂	—	2	2	no	—
186	C₂×D₁₂	—	2	2	no	—
187	C₂×D₁₂	—	2	2	no	—
188	C₂×D₁₂	—	2	2	no	—
189	C₂×D₁₂	—	2	2	no	—
190	C₂×D₁₂	—	4	4	no	—
191	C₂×D₁₂	—	4	4	no	—
192	C₂×D₁₂	—	4	4	no	—
193	C₂×D₁₂	C₂³×C₃	1	4	yes	—
194	C₃×SD₁₆	—	12	8	no	—
195	C₂×C₃×C₈	—	3	4	no	—
196	C₃×C₄⋊C₄	—	2	2	no	—
197	C₃×C₄⋊C₄	—	2	2	no	—
198	C₃×C₄⋊C₄	—	2	4	no	—
199	C₃×C₄⋊C₄	—	2	4	no	—
200	C₃×C₄⋊C₄	—	2	2	no	—
201	C₃×C₄⋊C₄	—	2	1	no	—
202	C₃×C₄⋊C₄	—	2	1	no	—
203	C₃×C₄⋊C₄	—	2	1	no	—
204	C₃×C₄⋊C₄	—	2	2	no	—
205	C₃×C₄⋊C₄	—	2	2	no	—
206	C₃×C₄⋊C₄	—	2	1	no	—
207	C₃×C₄⋊C₄	—	2	1	no	—
208	C₃×C₄⋊C₄	—	2	1	no	—
209	C₃×C₄⋊C₄	—	2	2	no	—
210	C₃×C₄⋊C₄	—	2	2	no	—
211	C₃×C₄⋊C₄	—	2	2	no	—
212	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
213	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
214	C₃×C₂²⋊C₄	—	2	4	no	—
215	C₃×C₂²⋊C₄	—	2	2	no	—
216	C₃×C₂²⋊C₄	—	2	2	no	—
217	C₃×C₄²	—	2	4	no	—
218	C₃×C₄²	—	2	2	no	—
219	C₃×C₄²	—	2	2	no	—
220	C₃×C₄²	—	2	1	no	—
221	C₃×C₄²	—	2	1	no	—
222	C₃×C₄²	—	2	1	no	—
223	C₃×C₄²	—	2	1	no	—
224	C₃×C₄²	#67	1	1	yes	characteristic
225	C₃×C₄²	#67	1	1	yes	characteristic
226	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
227	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
228	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
229	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
230	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
231	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
232	#215	—	4	8	no	—
233	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
234	C₂²×C₃²	—	2	1	no	—
235	C₂²×C₃²	—	2	1	no	—
236	C₂²×C₃²	C₂×SD₁₆	1	2	yes	—
237	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₃×D₃	—	4	4	no	—
239	C₂×C₃×D₃	—	4	4	no	—
240	C₂×C₃×D₃	—	4	4	no	—
241	C₂×C₃×D₃	—	8	8	no	—
242	C₃²×C₄	—	2	1	no	—
243	C₃²×C₄	—	2	1	no	—
244	C₃²×C₄	—	4	2	no	—
245	C₃²×C₄	—	4	2	no	—
246	C₃²×C₄	C₂×SD₁₆	1	2	yes	—
247	C₃²×C₄	C₂×SD₁₆	1	2	yes	—
248	C₃²×C₄	AGL(1,ℤ/8)	1	2	yes	—
249	C₃²×C₄	H(5,𝔽₂)	1	2	yes	—
250	C₂²×D₄	—	3	2	no	—
251	C₂²×D₄	—	6	1	no	—
252	C₂²×D₄	—	6	1	no	—
253	C₂×SD₁₆	—	3	8	no	—
254	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
255	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
256	#127	—	3	2	no	—
257	#127	—	3	2	no	—
258	#127	—	6	1	no	—
259	#127	—	6	1	no	—
260	#125	—	2	1	no	—
261	C₂²⋊Q₈	—	2	1	no	—
262	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×Q₈	C₂×C₃×D₃	1	2	yes	complemented
265	#117	—	2	1	no	—
266	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
267	C₄⋊C₈	—	3	2	no	—
268	#102	—	3	8	no	—
269	C₂²⋊C₈	—	3	2	no	—
270	C₄×C₈	—	3	2	no	—
271	C₂³×C₃	—	2	1	no	—
272	C₂³×C₃	—	6	4	no	—
273	C₂³×C₃	—	12	4	no	—
274	C₂³×C₃	—	12	4	no	—
275	C₂³×C₃	—	12	4	no	—
276	C₂³×C₃	C₂×#67	1	1	yes	characteristic
277	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
278	C₂²×D₃	—	2	4	no	—
279	C₂²×D₃	—	4	4	no	—
280	C₂²×D₃	—	4	4	no	—
281	C₂²×D₃	—	4	4	no	—
282	C₃×Q₈	—	2	4	no	—
283	C₃×Q₈	—	2	4	no	—
284	C₃×Q₈	—	4	4	no	—
285	C₃×Q₈	—	4	4	no	—
286	C₃×Q₈	—	4	2	no	—
287	C₃×Q₈	—	4	2	no	—
288	C₃×D₄	—	6	8	no	—
289	C₃×D₄	—	12	4	no	—
290	C₃×D₄	—	12	4	no	—
291	C₃×D₄	—	12	4	no	—
292	C₃×D₄	—	12	4	no	—
293	C₃×D₄	—	12	4	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	4	no	—
299	C₂×C₃×C₄	—	2	4	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	1	no	—
305	C₂×C₃×C₄	—	2	4	no	—
306	C₂×C₃×C₄	—	2	1	no	—
307	C₂×C₃×C₄	—	2	1	no	—
308	C₂×C₃×C₄	—	2	1	no	—
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	2	1	no	—
311	C₂×C₃×C₄	—	4	2	no	—
312	C₂×C₃×C₄	—	4	2	no	—
313	C₂×C₃×C₄	#215	1	4	yes	complemented
314	C₂×C₃×C₄	C₃×SD₁₆	1	4	yes	complemented
315	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
317	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
319	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
321	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
327	D₁₂	—	2	8	no	—
328	D₁₂	—	4	4	no	—
329	D₁₂	—	4	4	no	—
330	D₁₂	—	4	4	no	—
331	D₁₂	—	4	4	no	—
332	D₁₂	—	4	4	no	—
333	C₃×C₈	—	6	4	no	—
334	C₃⋊C₈	—	2	4	no	—
335	C₂×C₃²	—	2	2	no	—
336	C₂×C₃²	#535	1	1	yes	characteristic
337	C₂×C₃²	C₂²×SD₁₆	1	1	yes	characteristic
338	C₂×C₃²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
339	C₃×D₃	—	8	4	no	—
340	C₂⁴	—	6	2	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
343	C₂×D₄	—	3	4	no	—
344	C₂×D₄	—	6	2	no	—
345	C₂×D₄	—	6	2	no	—
346	C₂×D₄	—	6	2	no	—
347	C₂×D₄	—	6	2	no	—
348	C₂×D₄	—	6	2	no	—
349	C₂×D₄	—	12	4	no	—
350	C₂×D₄	—	12	4	no	—
351	C₂×D₄	—	12	4	no	—
352	C₂²×C₄	C₃×#67	1	1	yes	characteristic
353	C₂²×C₄	C₃×#67	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
355	SD₁₆	—	12	8	no	—
356	C₂×C₈	—	3	4	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	C₃×#67	1	1	yes	characteristic
366	C₄²	C₃×#67	1	1	yes	characteristic
367	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
368	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
369	C₂²×C₃	—	2	1	no	—
370	C₂²×C₃	—	2	1	no	—
371	C₂²×C₃	—	2	1	no	—
372	C₂²×C₃	—	2	1	no	—
373	C₂²×C₃	—	2	2	no	—
374	C₂²×C₃	—	2	1	no	—
375	C₂²×C₃	—	4	1	no	—
376	C₂²×C₃	—	4	1	no	—
377	C₂²×C₃	—	12	4	no	—
378	C₂²×C₃	—	12	4	no	—
379	C₂²×C₃	—	12	4	no	—
380	C₂²×C₃	—	24	8	no	—
381	C₂²×C₃	C₂×#215	1	2	yes	—
382	C₂²×C₃	C₂×C₃×SD₁₆	1	2	yes	—
383	C₂²×C₃	C₂²×#67	1	1	yes	characteristic
384	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
385	C₂×D₃	—	4	4	no	—
386	C₂×D₃	—	4	4	no	—
387	C₂×D₃	—	4	4	no	—
388	C₂×D₃	—	8	8	no	—
389	C₃×C₄	—	2	1	no	—
390	C₃×C₄	—	2	1	no	—
391	C₃×C₄	—	2	1	no	—
392	C₃×C₄	—	2	1	no	—
393	C₃×C₄	—	2	2	no	—
394	C₃×C₄	—	2	2	no	—
395	C₃×C₄	—	2	2	no	—
396	C₃×C₄	—	2	2	no	—
397	C₃×C₄	—	4	1	no	—
398	C₃×C₄	—	4	1	no	—
399	C₃×C₄	—	4	4	no	—
400	C₃×C₄	—	4	4	no	—
401	C₃×C₄	—	4	2	no	—
402	C₃×C₄	—	4	2	no	—
403	C₃×C₄	—	4	2	no	—
404	C₃×C₄	—	4	2	no	—
405	C₃×C₄	C₂×#215	1	2	yes	—
406	C₃×C₄	C₂×#215	1	2	yes	—
407	C₃×C₄	#949	1	2	yes	—
408	C₃×C₄	C₂×C₃×SD₁₆	1	2	yes	—
409	C₃×C₄	C₂×C₃×SD₁₆	1	2	yes	—
410	C₃×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
411	C₃×C₄	#1009	1	2	yes	—
412	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
413	C₃²	#3208	1	1	yes	characteristic, complemented, Sylow
414	C₂³	—	6	4	no	—
415	C₂³	—	12	4	no	—
416	C₂³	—	12	4	no	—
417	C₂³	—	12	4	no	—
418	C₂³	C₂×C₃×#67	1	1	yes	characteristic
419	Q₈	—	2	4	no	—
420	Q₈	—	4	2	no	—
421	D₄	—	6	8	no	—
422	D₄	—	12	4	no	—
423	D₄	—	12	4	no	—
424	D₄	—	12	4	no	—
425	D₄	—	12	4	no	—
426	D₄	—	12	4	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	C₃×#215	1	4	yes	complemented
432	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
433	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
434	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
435	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
436	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
437	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
438	C₈	—	6	4	no	—
439	C₂×C₃	—	2	2	no	—
440	C₂×C₃	—	2	2	no	—
441	C₂×C₃	—	2	1	no	—
442	C₂×C₃	—	2	1	no	—
443	C₂×C₃	—	2	1	no	—
444	C₂×C₃	—	4	2	no	—
445	C₂×C₃	—	24	4	no	—
446	C₂×C₃	C₂²×#215	1	1	yes	characteristic
447	C₂×C₃	C₂×#949	1	1	yes	characteristic
448	C₂×C₃	#5830	1	1	yes	characteristic
449	C₂×C₃	C₃×#535	1	1	yes	characteristic
450	C₂×C₃	C₂²×C₃×SD₁₆	1	1	yes	characteristic
451	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
452	D₃	—	8	4	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	12	4	no	—
456	C₂²	—	12	4	no	—
457	C₂²	—	12	4	no	—
458	C₂²	—	24	8	no	—
459	C₂²	C₂×C₃×#215	1	2	yes	—
460	C₂²	C₂²×C₃×#67	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	C₂×C₃×#215	1	2	yes	—
466	C₄	C₂×C₃×#215	1	2	yes	—
467	C₄	C₃×#949	1	2	yes	—
468	C₄	C₃×#1009	1	2	yes	—
469	C₃	—	2	1	no	—
470	C₃	#83355	1	1	yes	characteristic, direct product factor
471	C₃	C₃×#3208	1	1	yes	characteristic, complemented
472	C₂	—	2	2	no	—
473	C₂	—	24	4	no	—
474	C₂	C₂²×C₃×#215	1	1	yes	characteristic
475	C₂	C₂×C₃×#949	1	1	yes	characteristic
476	C₂	C₃×#5830	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#533	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃×#874	C₂
hypercenter	C₃×#533	D₃
hypocenter	C₃	C₃×#3208
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ C₃×#533

Complements

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

N	H ≅ G/N	type
1. C₃²×#533	C₂	semidirect
3. C₃×#5088	C₂	semidirect
4. C₃×#5085	C₂	semidirect
5. C₃×#5046	C₂	semidirect
6. C₃×#5027	C₂	semidirect
7. C₃×#4925	C₂	semidirect
9. #83355	C₃	direct (N × H)
13. C₃²×C₄⋊Q₈	C₂²	semidirect
14. C₃²×C₄⋊Q₈	C₂²	semidirect
19. C₃²×C₄×Q₈	C₂²	semidirect
22. C₂×C₃×#215	C₂²	semidirect
28. C₃×#809	C₂²	semidirect
29. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
30. C₃×C₄×C₃⋊C₈	C₂²	semidirect
32. C₃×#533	D₃	semidirect
33. C₃×#533	C₂×C₃	semidirect
41. #5088	C₂×C₃	semidirect
42. #5085	C₂×C₃	semidirect
43. #5046	C₂×C₃	semidirect
44. #5027	C₂×C₃	semidirect
45. #4925	C₂×C₃	semidirect
85. C₃×C₄⋊Q₈	C₂×D₃	semidirect
86. C₃×C₄⋊Q₈	C₂×D₃	semidirect
87. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
88. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
106. C₃×C₄×Q₈	C₂×D₃	semidirect
107. C₃×C₄×Q₈	C₂²×C₃	semidirect
114. C₂×#215	C₂²×C₃	semidirect
124. #809	C₂²×C₃	semidirect
125. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
126. C₄×C₃⋊C₈	C₂²×C₃	semidirect
138. C₂×C₃²×C₄	SD₁₆	semidirect
152. #533	C₃×D₃	semidirect
254. C₄⋊Q₈	C₂×C₃×D₃	semidirect
255. C₄⋊Q₈	C₂×C₃×D₃	semidirect
264. C₄×Q₈	C₂×C₃×D₃	semidirect
313. C₂×C₃×C₄	#215	semidirect
314. C₂×C₃×C₄	C₃×SD₁₆	semidirect
413. C₃²	#3208	semidirect
431. C₂×C₄	C₃×#215	semidirect
470. C₃	#83355	direct (N × H)
471. C₃	C₃×#3208	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#533	2
C₂×C₃×#874	2
C₃×#5088	2
C₃×#5085	2
C₃×#5046	2
C₃×#5027	2
C₃×#4925	2
C₃×#3208	3
#83355	3

Subgroups — C3×#83355 #11878822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#83355 #11878822