Subgroups — C₃×#3565 #87449

Order 384.

930 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#563	C₂	1	2	yes	maximal, complemented
2	C₃×#562	C₂	1	2	yes	maximal, complemented
3	C₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#556	C₂	1	2	yes	maximal, complemented
5	C₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#552	C₂	1	2	yes	maximal, complemented
11	C₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#542	C₂	1	2	yes	maximal, complemented
18	C₃×#542	C₂	1	2	yes	maximal, complemented
19	C₃×#541	C₂	1	2	yes	maximal, complemented
20	C₃×#539	C₂	1	2	yes	maximal, complemented
21	C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	#3565	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
26	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
27	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
30	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₃×#126	C₂²	1	2	yes	—
33	C₃×#126	C₂²	1	2	yes	—
34	C₃×#126	C₂²	1	2	yes	—
35	C₃×#126	C₂²	1	2	yes	—
36	C₃×#126	C₂²	1	2	yes	—
37	C₃×#126	C₂²	1	1	yes	characteristic
38	C₃×#126	C₂²	1	1	yes	characteristic
39	C₃×#126	C₂²	1	2	yes	—
40	C₃×#126	C₂²	1	2	yes	—
41	C₃×#126	C₂²	1	2	yes	—
42	C₃×#126	C₂²	1	2	yes	—
43	C₃×#125	C₂²	1	2	yes	—
44	C₃×#125	C₂²	1	2	yes	—
45	C₃×#125	C₂²	1	2	yes	—
46	C₃×#125	C₂²	1	1	yes	characteristic
47	C₃×#125	C₂²	1	1	yes	characteristic
48	C₃×#125	C₂²	1	1	yes	characteristic
49	C₃×#125	C₂²	1	1	yes	characteristic
50	C₃×#125	C₂²	1	2	yes	—
51	C₃×#125	C₂²	1	2	yes	—
52	C₃×#125	C₂²	1	2	yes	—
53	C₃×#125	C₂²	1	1	yes	characteristic
54	C₃×#125	C₂²	1	1	yes	characteristic
55	C₃×#124	C₂²	1	2	yes	—
56	C₃×#124	C₂²	1	2	yes	—
57	C₃×#124	C₂²	1	2	yes	—
58	C₃×#124	C₂²	1	1	yes	characteristic
59	C₃×#124	C₂²	1	1	yes	characteristic
60	C₃×#124	C₂²	1	2	yes	—
61	C₃×#124	C₂²	1	2	yes	—
62	C₃×#123	C₂²	1	2	yes	—
63	C₃×#123	C₂²	1	2	yes	—
64	C₃×#123	C₂²	1	2	yes	—
65	C₃×#123	C₂²	1	2	yes	—
66	C₃×#123	C₂²	1	2	yes	—
67	C₃×#123	C₂²	1	1	yes	characteristic
68	C₃×#123	C₂²	1	1	yes	characteristic
69	C₃×#123	C₂²	1	2	yes	—
70	C₃×#123	C₂²	1	2	yes	—
71	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
72	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
73	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
74	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
75	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
76	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
77	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
78	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
79	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
80	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
81	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
82	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
83	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
84	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
85	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
86	C₃×#121	C₂²	1	1	yes	characteristic
87	C₃×#121	C₂²	1	2	yes	—
88	C₃×#121	C₂²	1	2	yes	—
89	C₃×#121	C₂²	1	2	yes	—
90	C₃×#121	C₂²	1	1	yes	characteristic
91	C₃×#121	C₂²	1	1	yes	characteristic
92	C₃×#121	C₂²	1	1	yes	characteristic
93	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
94	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
95	C₃×C₄×Q₈	C₂²	1	2	yes	—
96	C₃×C₄×Q₈	C₂²	1	2	yes	—
97	C₃×C₄×Q₈	C₂²	1	2	yes	—
98	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
99	C₃×C₄×Q₈	C₂²	1	2	yes	—
100	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
101	C₃×C₄×D₄	C₂²	1	2	yes	—
102	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
103	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
104	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
105	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
106	C₃×C₄×D₄	C₂²	1	2	yes	—
107	C₃×C₄×D₄	C₂²	1	2	yes	—
108	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
109	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
110	C₃×#117	C₂²	1	1	yes	characteristic
111	C₃×#117	C₂²	1	1	yes	characteristic
112	C₃×#117	C₂²	1	2	yes	—
113	C₃×#117	C₂²	1	1	yes	characteristic
114	C₃×#117	C₂²	1	1	yes	characteristic
115	C₃×#117	C₂²	1	2	yes	—
116	C₃×#117	C₂²	1	2	yes	—
117	C₃×#117	C₂²	1	2	yes	—
118	C₃×#117	C₂²	1	1	yes	characteristic
119	C₃×#117	C₂²	1	1	yes	characteristic
120	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
121	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
122	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
123	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
124	#563	C₂×C₃	1	2	yes	complemented
125	#562	C₂×C₃	1	2	yes	complemented
126	#557	C₂×C₃	1	1	yes	characteristic, complemented
127	#556	C₂×C₃	1	2	yes	complemented
128	#556	C₂×C₃	1	1	yes	characteristic, complemented
129	#555	C₂×C₃	1	1	yes	characteristic, complemented
130	#554	C₂×C₃	1	1	yes	characteristic, complemented
131	#553	C₂×C₃	1	1	yes	characteristic, complemented
132	#553	C₂×C₃	1	1	yes	characteristic, complemented
133	#552	C₂×C₃	1	2	yes	complemented
134	#552	C₂×C₃	1	1	yes	characteristic, complemented
135	#552	C₂×C₃	1	1	yes	characteristic, complemented
136	#544	C₂×C₃	1	1	yes	characteristic, complemented
137	#544	C₂×C₃	1	1	yes	characteristic, complemented
138	#542	C₂×C₃	1	1	yes	characteristic, complemented
139	#542	C₂×C₃	1	1	yes	characteristic, complemented
140	#542	C₂×C₃	1	2	yes	complemented
141	#542	C₂×C₃	1	2	yes	complemented
142	#541	C₂×C₃	1	2	yes	complemented
143	#539	C₂×C₃	1	2	yes	complemented
144	#533	C₂×C₃	1	1	yes	characteristic, complemented
145	#529	C₂×C₃	1	1	yes	characteristic, complemented
146	#529	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
148	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
149	C₂×C₃×Q₈	C₂³	1	2	yes	—
150	C₂×C₃×Q₈	C₂³	1	2	yes	—
151	C₂×C₃×Q₈	C₂³	1	2	yes	—
152	C₂×C₃×Q₈	C₂³	1	2	yes	—
153	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
154	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
155	C₂×C₃×D₄	C₂³	1	2	yes	—
156	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
157	C₂×C₃×D₄	C₂³	1	2	yes	—
158	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
159	C₂×C₃×D₄	C₂³	1	2	yes	—
160	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
161	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₂³	1	2	yes	—
166	C₂²×C₃×C₄	C₂³	1	2	yes	—
167	C₂²×C₃×C₄	C₂³	1	2	yes	—
168	C₂²×C₃×C₄	C₂³	1	2	yes	—
169	C₂²×C₃×C₄	C₂³	1	2	yes	—
170	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₃×C₄⋊C₄	C₂³	1	2	yes	—
201	C₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₃×C₄⋊C₄	C₂³	1	2	yes	—
206	C₃×C₄⋊C₄	C₂³	1	2	yes	—
207	C₃×C₄⋊C₄	C₂³	1	2	yes	—
208	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
210	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
212	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
219	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
220	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
224	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
225	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
230	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
233	C₃×C₄²	C₂³	1	1	yes	characteristic
234	C₃×C₄²	C₂³	1	1	yes	characteristic
235	C₃×C₄²	C₂³	1	1	yes	characteristic
236	C₃×C₄²	C₂³	1	1	yes	characteristic
237	C₃×C₄²	C₂³	1	2	yes	—
238	C₃×C₄²	C₂³	1	2	yes	—
239	C₃×C₄²	C₂³	1	2	yes	—
240	C₃×C₄²	C₂³	1	2	yes	—
241	C₃×C₄²	C₂³	1	1	yes	characteristic
242	C₃×C₄²	C₂³	1	1	yes	characteristic
243	C₃×C₄²	C₂³	1	2	yes	—
244	C₃×C₄²	C₂³	1	2	yes	—
245	C₃×C₄²	C₂³	1	2	yes	—
246	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
247	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
248	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
249	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
250	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
251	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
252	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
253	#126	C₂²×C₃	1	2	yes	—
254	#126	C₂²×C₃	1	1	yes	characteristic
255	#126	C₂²×C₃	1	1	yes	characteristic
256	#126	C₂²×C₃	1	2	yes	—
257	#126	C₂²×C₃	1	2	yes	—
258	#126	C₂²×C₃	1	2	yes	—
259	#126	C₂²×C₃	1	2	yes	—
260	#126	C₂²×C₃	1	2	yes	—
261	#126	C₂²×C₃	1	2	yes	—
262	#126	C₂²×C₃	1	2	yes	—
263	#126	C₂²×C₃	1	2	yes	—
264	#125	C₂²×C₃	1	1	yes	characteristic
265	#125	C₂²×C₃	1	1	yes	characteristic
266	#125	C₂²×C₃	1	1	yes	characteristic
267	#125	C₂²×C₃	1	1	yes	characteristic
268	#125	C₂²×C₃	1	2	yes	—
269	#125	C₂²×C₃	1	2	yes	—
270	#125	C₂²×C₃	1	2	yes	—
271	#125	C₂²×C₃	1	2	yes	—
272	#125	C₂²×C₃	1	2	yes	—
273	#125	C₂²×C₃	1	1	yes	characteristic
274	#125	C₂²×C₃	1	2	yes	—
275	#125	C₂²×C₃	1	1	yes	characteristic
276	#124	C₂²×C₃	1	1	yes	characteristic
277	#124	C₂²×C₃	1	1	yes	characteristic
278	#124	C₂²×C₃	1	2	yes	—
279	#124	C₂²×C₃	1	2	yes	—
280	#124	C₂²×C₃	1	2	yes	—
281	#124	C₂²×C₃	1	2	yes	—
282	#124	C₂²×C₃	1	2	yes	—
283	#123	C₂²×C₃	1	1	yes	characteristic
284	#123	C₂²×C₃	1	1	yes	characteristic
285	#123	C₂²×C₃	1	2	yes	—
286	#123	C₂²×C₃	1	2	yes	—
287	#123	C₂²×C₃	1	2	yes	—
288	#123	C₂²×C₃	1	2	yes	—
289	#123	C₂²×C₃	1	2	yes	—
290	#123	C₂²×C₃	1	2	yes	—
291	#123	C₂²×C₃	1	2	yes	—
292	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
293	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
294	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
295	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
296	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
297	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
298	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
299	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
300	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
301	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
302	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
303	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
304	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
305	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
306	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
307	#121	C₂²×C₃	1	1	yes	characteristic
308	#121	C₂²×C₃	1	1	yes	characteristic
309	#121	C₂²×C₃	1	2	yes	—
310	#121	C₂²×C₃	1	1	yes	characteristic
311	#121	C₂²×C₃	1	1	yes	characteristic
312	#121	C₂²×C₃	1	2	yes	—
313	#121	C₂²×C₃	1	2	yes	—
314	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
315	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
316	C₄×Q₈	C₂²×C₃	1	2	yes	—
317	C₄×Q₈	C₂²×C₃	1	2	yes	—
318	C₄×Q₈	C₂²×C₃	1	2	yes	—
319	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
320	C₄×Q₈	C₂²×C₃	1	2	yes	—
321	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
322	C₄×D₄	C₂²×C₃	1	2	yes	—
323	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
324	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
325	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
326	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
327	C₄×D₄	C₂²×C₃	1	2	yes	—
328	C₄×D₄	C₂²×C₃	1	2	yes	—
329	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
330	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
331	#117	C₂²×C₃	1	1	yes	characteristic
332	#117	C₂²×C₃	1	1	yes	characteristic
333	#117	C₂²×C₃	1	2	yes	—
334	#117	C₂²×C₃	1	1	yes	characteristic
335	#117	C₂²×C₃	1	1	yes	characteristic
336	#117	C₂²×C₃	1	2	yes	—
337	#117	C₂²×C₃	1	2	yes	—
338	#117	C₂²×C₃	1	2	yes	—
339	#117	C₂²×C₃	1	1	yes	characteristic
340	#117	C₂²×C₃	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
342	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
344	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
345	C₂³×C₃	C₂⁴	1	1	yes	characteristic
346	C₂³×C₃	C₂⁴	1	1	yes	characteristic
347	C₂³×C₃	C₂⁴	1	1	yes	characteristic
348	C₂³×C₃	C₂⁴	1	2	yes	—
349	C₃×Q₈	—	2	2	no	—
350	C₃×Q₈	—	4	1	no	—
351	C₃×Q₈	—	4	2	no	—
352	C₃×Q₈	—	4	2	no	—
353	C₃×Q₈	—	4	2	no	—
354	C₃×Q₈	—	4	2	no	—
355	C₃×D₄	—	2	2	no	—
356	C₃×D₄	—	4	1	no	—
357	C₃×D₄	—	4	1	no	—
358	C₃×D₄	—	4	2	no	—
359	C₃×D₄	—	4	2	no	—
360	C₃×D₄	—	4	1	no	—
361	C₃×D₄	—	4	2	no	—
362	C₂×C₃×C₄	—	2	2	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	4	2	no	—
366	C₂×C₃×C₄	—	4	1	no	—
367	C₂×C₃×C₄	—	4	2	no	—
368	C₂×C₃×C₄	—	4	2	no	—
369	C₂×C₃×C₄	—	4	2	no	—
370	C₂×C₃×C₄	—	4	2	no	—
371	C₂×C₃×C₄	—	4	1	no	—
372	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂⁴	1	2	yes	—
375	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂⁴	1	2	yes	—
377	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂⁴	1	2	yes	—
383	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	C₂×C₃×C₄	C₂⁴	1	2	yes	—
385	C₂×C₃×C₄	C₂⁴	1	2	yes	—
386	C₂×C₃×C₄	C₂⁴	1	2	yes	—
387	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂⁴	1	2	yes	—
389	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
391	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
392	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
393	C₂×Q₈	C₂³×C₃	1	2	yes	—
394	C₂×Q₈	C₂³×C₃	1	2	yes	—
395	C₂×Q₈	C₂³×C₃	1	2	yes	—
396	C₂×Q₈	C₂³×C₃	1	2	yes	—
397	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
398	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
399	C₂×D₄	C₂³×C₃	1	2	yes	—
400	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
401	C₂×D₄	C₂³×C₃	1	2	yes	—
402	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
403	C₂×D₄	C₂³×C₃	1	2	yes	—
404	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
405	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
406	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
407	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
408	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
409	C₂²×C₄	C₂³×C₃	1	2	yes	—
410	C₂²×C₄	C₂³×C₃	1	2	yes	—
411	C₂²×C₄	C₂³×C₃	1	2	yes	—
412	C₂²×C₄	C₂³×C₃	1	2	yes	—
413	C₂²×C₄	C₂³×C₃	1	2	yes	—
414	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
415	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
416	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
417	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
418	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
419	C₄⋊C₄	C₂³×C₃	1	2	yes	—
420	C₄⋊C₄	C₂³×C₃	1	2	yes	—
421	C₄⋊C₄	C₂³×C₃	1	2	yes	—
422	C₄⋊C₄	C₂³×C₃	1	2	yes	—
423	C₄⋊C₄	C₂³×C₃	1	2	yes	—
424	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
425	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
426	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
427	C₄⋊C₄	C₂³×C₃	1	2	yes	—
428	C₄⋊C₄	C₂³×C₃	1	2	yes	—
429	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
430	C₄⋊C₄	C₂³×C₃	1	2	yes	—
431	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
432	C₄⋊C₄	C₂³×C₃	1	2	yes	—
433	C₄⋊C₄	C₂³×C₃	1	2	yes	—
434	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
435	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
436	C₄⋊C₄	C₂³×C₃	1	2	yes	—
437	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
438	C₄⋊C₄	C₂³×C₃	1	2	yes	—
439	C₄⋊C₄	C₂³×C₃	1	2	yes	—
440	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
441	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
442	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
443	C₄⋊C₄	C₂³×C₃	1	2	yes	—
444	C₄⋊C₄	C₂³×C₃	1	2	yes	—
445	C₄⋊C₄	C₂³×C₃	1	2	yes	—
446	C₄⋊C₄	C₂³×C₃	1	2	yes	—
447	C₄⋊C₄	C₂³×C₃	1	2	yes	—
448	C₄⋊C₄	C₂³×C₃	1	2	yes	—
449	C₄⋊C₄	C₂³×C₃	1	2	yes	—
450	C₄⋊C₄	C₂³×C₃	1	2	yes	—
451	C₄⋊C₄	C₂³×C₃	1	2	yes	—
452	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
453	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
454	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
455	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
456	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
457	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
458	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
459	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
460	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
461	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
462	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
463	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
464	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
465	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
466	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
467	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
468	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
469	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
470	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
471	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
472	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
473	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
474	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
475	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
476	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
477	C₄²	C₂³×C₃	1	1	yes	characteristic
478	C₄²	C₂³×C₃	1	1	yes	characteristic
479	C₄²	C₂³×C₃	1	1	yes	characteristic
480	C₄²	C₂³×C₃	1	1	yes	characteristic
481	C₄²	C₂³×C₃	1	2	yes	—
482	C₄²	C₂³×C₃	1	2	yes	—
483	C₄²	C₂³×C₃	1	2	yes	—
484	C₄²	C₂³×C₃	1	2	yes	—
485	C₄²	C₂³×C₃	1	1	yes	characteristic
486	C₄²	C₂³×C₃	1	1	yes	characteristic
487	C₄²	C₂³×C₃	1	2	yes	—
488	C₄²	C₂³×C₃	1	2	yes	—
489	C₄²	C₂³×C₃	1	2	yes	—
490	C₂²×C₃	—	2	1	no	—
491	C₂²×C₃	—	2	1	no	—
492	C₂²×C₃	—	2	1	no	—
493	C₂²×C₃	—	2	2	no	—
494	C₂²×C₃	—	2	1	no	—
495	C₂²×C₃	—	2	1	no	—
496	C₂²×C₃	—	2	2	no	—
497	C₂²×C₃	—	2	1	no	—
498	C₂²×C₃	—	2	1	no	—
499	C₂²×C₃	—	2	2	no	—
500	C₂²×C₃	—	2	1	no	—
501	C₂²×C₃	—	2	1	no	—
502	C₂²×C₃	C₂⁵	1	1	yes	characteristic
503	C₃×C₄	—	2	1	no	—
504	C₃×C₄	—	2	1	no	—
505	C₃×C₄	—	2	1	no	—
506	C₃×C₄	—	2	2	no	—
507	C₃×C₄	—	2	1	no	—
508	C₃×C₄	—	2	1	no	—
509	C₃×C₄	—	2	2	no	—
510	C₃×C₄	—	2	1	no	—
511	C₃×C₄	—	2	2	no	—
512	C₃×C₄	—	2	2	no	—
513	C₃×C₄	—	2	2	no	—
514	C₃×C₄	—	2	1	no	—
515	C₃×C₄	—	2	1	no	—
516	C₃×C₄	—	2	2	no	—
517	C₃×C₄	—	2	1	no	—
518	C₃×C₄	—	2	1	no	—
519	C₃×C₄	—	2	2	no	—
520	C₃×C₄	—	2	1	no	—
521	C₃×C₄	2₋¹⁺⁴	1	2	yes	—
522	C₂³	C₂⁴×C₃	1	1	yes	characteristic
523	C₂³	C₂⁴×C₃	1	1	yes	characteristic
524	C₂³	C₂⁴×C₃	1	1	yes	characteristic
525	C₂³	C₂⁴×C₃	1	2	yes	—
526	Q₈	—	2	2	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	2	no	—
529	Q₈	—	4	2	no	—
530	Q₈	—	4	2	no	—
531	Q₈	—	4	2	no	—
532	D₄	—	2	2	no	—
533	D₄	—	4	1	no	—
534	D₄	—	4	1	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	1	no	—
538	D₄	—	4	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
550	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
551	C₂×C₄	C₂⁴×C₃	1	2	yes	—
552	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
553	C₂×C₄	C₂⁴×C₃	1	2	yes	—
554	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
555	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
556	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
557	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
558	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
559	C₂×C₄	C₂⁴×C₃	1	2	yes	—
560	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
561	C₂×C₄	C₂⁴×C₃	1	2	yes	—
562	C₂×C₄	C₂⁴×C₃	1	2	yes	—
563	C₂×C₄	C₂⁴×C₃	1	2	yes	—
564	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
565	C₂×C₄	C₂⁴×C₃	1	2	yes	—
566	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
567	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
568	C₂×C₃	—	4	1	no	—
569	C₂×C₃	—	4	1	no	—
570	C₂×C₃	—	4	1	no	—
571	C₂×C₃	—	4	2	no	—
572	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
573	C₂×C₃	#585	1	1	yes	characteristic
574	C₂×C₃	#585	1	1	yes	characteristic
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	2	1	no	—
587	C₂²	C₂⁵×C₃	1	1	yes	characteristic
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	2	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	2	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	1	no	—
606	C₄	C₃×2₋¹⁺⁴	1	2	yes	—
607	C₃	#3565	1	1	yes	characteristic, direct product factor, Sylow
608	C₂	—	4	1	no	—
609	C₂	—	4	1	no	—
610	C₂	—	4	1	no	—
611	C₂	—	4	2	no	—
612	C₂	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
613	C₂	C₃×#585	1	1	yes	characteristic
614	C₂	C₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#563	C₂	semidirect
2. C₃×#562	C₂	semidirect
3. C₃×#557	C₂	semidirect
4. C₃×#556	C₂	semidirect
5. C₃×#556	C₂	semidirect
6. C₃×#555	C₂	semidirect
7. C₃×#554	C₂	semidirect
8. C₃×#553	C₂	semidirect
9. C₃×#553	C₂	semidirect
10. C₃×#552	C₂	semidirect
11. C₃×#552	C₂	semidirect
12. C₃×#552	C₂	semidirect
13. C₃×#544	C₂	semidirect
14. C₃×#544	C₂	semidirect
15. C₃×#542	C₂	semidirect
16. C₃×#542	C₂	semidirect
17. C₃×#542	C₂	semidirect
18. C₃×#542	C₂	semidirect
19. C₃×#541	C₂	semidirect
20. C₃×#539	C₂	semidirect
21. C₃×#533	C₂	semidirect
22. C₃×#529	C₂	semidirect
23. C₃×#529	C₂	semidirect
24. #3565	C₃	direct (N × H)
124. #563	C₂×C₃	semidirect
125. #562	C₂×C₃	semidirect
126. #557	C₂×C₃	semidirect
127. #556	C₂×C₃	semidirect
128. #556	C₂×C₃	semidirect
129. #555	C₂×C₃	semidirect
130. #554	C₂×C₃	semidirect
131. #553	C₂×C₃	semidirect
132. #553	C₂×C₃	semidirect
133. #552	C₂×C₃	semidirect
134. #552	C₂×C₃	semidirect
135. #552	C₂×C₃	semidirect
136. #544	C₂×C₃	semidirect
137. #544	C₂×C₃	semidirect
138. #542	C₂×C₃	semidirect
139. #542	C₂×C₃	semidirect
140. #542	C₂×C₃	semidirect
141. #542	C₂×C₃	semidirect
142. #541	C₂×C₃	semidirect
143. #539	C₂×C₃	semidirect
144. #533	C₂×C₃	semidirect
145. #529	C₂×C₃	semidirect
146. #529	C₂×C₃	semidirect
607. C₃	#3565	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#563	2
C₃×#562	2
C₃×#557	2
C₃×#556	2
C₃×#555	2
C₃×#554	2
C₃×#553	2
C₃×#552	2
C₃×#544	2
C₃×#542	2
C₃×#541	2
C₃×#539	2
C₃×#533	2
C₃×#529	2
#3565	3

Subgroups — C3×#3565 #87449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3565 #87449