Subgroups — C₃×#3564 #87448

Order 384.

936 conjugacy classes of subgroups.

The subgroup lattice has 542 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×#563	C₂	1	2	yes	maximal, complemented
3	C₃×#556	C₂	1	2	yes	maximal, complemented
4	C₃×#554	C₂	1	2	yes	maximal, complemented
5	C₃×#552	C₂	1	2	yes	maximal, complemented
6	C₃×#552	C₂	1	2	yes	maximal, complemented
7	C₃×#551	C₂	1	2	yes	maximal, complemented
8	C₃×#551	C₂	1	2	yes	maximal, complemented
9	C₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#543	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#542	C₂	1	2	yes	maximal, complemented
12	C₃×#541	C₂	1	2	yes	maximal, complemented
13	C₃×#541	C₂	1	2	yes	maximal, complemented
14	C₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#539	C₂	1	2	yes	maximal, complemented
16	C₃×#538	C₂	1	1	yes	maximal, characteristic
17	C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃×#126	C₂	1	1	yes	maximal, characteristic, complemented
20	#3564	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
24	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
25	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
26	C₃×#126	C₂²	1	2	yes	—
27	C₃×#126	C₂²	1	2	yes	—
28	C₃×#126	C₂²	1	2	yes	—
29	C₃×#126	C₂²	1	2	yes	—
30	C₃×#126	C₂²	1	2	yes	—
31	C₃×#126	C₂²	1	2	yes	—
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	complemented
36	C₃×#126	C₂²	1	2	yes	complemented
37	C₃×#126	C₂²	1	2	yes	complemented
38	C₃×#126	C₂²	1	2	yes	complemented
39	C₃×#125	C₂²	1	2	yes	complemented
40	C₃×#125	C₂²	1	2	yes	complemented
41	C₃×#125	C₂²	1	2	yes	complemented
42	C₃×#125	C₂²	1	2	yes	complemented
43	C₃×#125	C₂²	1	1	yes	characteristic, complemented
44	C₃×#125	C₂²	1	2	yes	complemented
45	C₃×#125	C₂²	1	2	yes	complemented
46	C₃×#125	C₂²	1	2	yes	complemented
47	C₃×#125	C₂²	1	2	yes	complemented
48	C₃×#125	C₂²	1	2	yes	complemented
49	C₃×#124	C₂²	1	2	yes	—
50	C₃×#124	C₂²	1	2	yes	—
51	C₃×#124	C₂²	1	2	yes	—
52	C₃×#124	C₂²	1	1	yes	characteristic, complemented
53	C₃×#123	C₂²	1	2	yes	—
54	C₃×#123	C₂²	1	2	yes	—
55	C₃×#123	C₂²	1	2	yes	—
56	C₃×#123	C₂²	1	2	yes	—
57	C₃×#123	C₂²	1	2	yes	—
58	C₃×#123	C₂²	1	2	yes	—
59	C₃×#123	C₂²	1	2	yes	—
60	C₃×#123	C₂²	1	2	yes	complemented
61	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
62	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
63	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
64	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
65	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
66	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
67	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
68	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
69	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
70	C₃×C₂²⋊Q₈	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	complemented
74	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
75	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
76	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
77	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
78	C₃×#121	C₂²	1	1	yes	characteristic
79	C₃×#121	C₂²	1	2	yes	—
80	C₃×#120	C₂²	1	2	yes	—
81	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
82	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
83	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
84	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
85	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
86	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
87	C₃×C₄×D₄	C₂²	1	2	yes	—
88	C₃×C₄×D₄	C₂²	1	2	yes	—
89	C₃×C₄×D₄	C₂²	1	2	yes	—
90	C₃×C₄×D₄	C₂²	1	2	yes	—
91	C₃×C₄×D₄	C₂²	1	2	yes	—
92	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
93	C₃×#117	C₂²	1	2	yes	—
94	C₃×#117	C₂²	1	2	yes	—
95	C₃×#117	C₂²	1	2	yes	—
96	C₃×#117	C₂²	1	2	yes	—
97	C₃×#117	C₂²	1	2	yes	complemented
98	C₃×#117	C₂²	1	2	yes	complemented
99	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
100	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
103	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
106	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
107	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
108	#563	C₂×C₃	1	2	yes	complemented
109	#563	C₂×C₃	1	2	yes	complemented
110	#556	C₂×C₃	1	2	yes	complemented
111	#554	C₂×C₃	1	2	yes	complemented
112	#552	C₂×C₃	1	2	yes	complemented
113	#552	C₂×C₃	1	2	yes	complemented
114	#551	C₂×C₃	1	2	yes	complemented
115	#551	C₂×C₃	1	2	yes	complemented
116	#544	C₂×C₃	1	1	yes	characteristic, complemented
117	#543	C₂×C₃	1	1	yes	characteristic, complemented
118	#542	C₂×C₃	1	2	yes	complemented
119	#541	C₂×C₃	1	2	yes	complemented
120	#541	C₂×C₃	1	2	yes	complemented
121	#539	C₂×C₃	1	1	yes	characteristic, complemented
122	#539	C₂×C₃	1	2	yes	complemented
123	#538	C₂×C₃	1	1	yes	characteristic
124	#533	C₂×C₃	1	1	yes	characteristic, complemented
125	#529	C₂×C₃	1	1	yes	characteristic, complemented
126	C₂×#126	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂⁴×C₃	C₂³	1	1	yes	characteristic
128	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
129	C₂×C₃×Q₈	C₂³	1	2	yes	—
130	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
131	C₂×C₃×Q₈	C₂³	1	2	yes	—
132	C₂×C₃×Q₈	C₂³	1	2	yes	—
133	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
134	C₂×C₃×D₄	C₂³	1	2	yes	—
135	C₂×C₃×D₄	C₂³	1	2	yes	—
136	C₂×C₃×D₄	C₂³	1	2	yes	—
137	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
138	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
139	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
141	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
142	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
143	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂³	1	2	yes	—
145	C₂²×C₃×C₄	C₂³	1	2	yes	—
146	C₂²×C₃×C₄	C₂³	1	2	yes	—
147	C₂²×C₃×C₄	C₂³	1	2	yes	—
148	C₂²×C₃×C₄	C₂³	1	2	yes	—
149	C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
178	C₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₃×C₄²	C₂³	1	1	yes	characteristic
204	C₃×C₄²	C₂³	1	1	yes	characteristic
205	C₃×C₄²	C₂³	1	1	yes	characteristic
206	C₃×C₄²	C₂³	1	1	yes	characteristic
207	C₃×C₄²	C₂³	1	2	yes	—
208	C₃×C₄²	C₂³	1	2	yes	—
209	C₃×C₄²	C₂³	1	2	yes	—
210	C₃×C₄²	C₂³	1	2	yes	—
211	C₃×C₄²	C₂³	1	2	yes	—
212	C₃×C₄²	C₂³	1	2	yes	—
213	C₃×C₄²	C₂³	1	2	yes	—
214	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
215	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
216	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
217	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
218	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
219	#126	C₂²×C₃	1	2	yes	—
220	#126	C₂²×C₃	1	2	yes	—
221	#126	C₂²×C₃	1	2	yes	—
222	#126	C₂²×C₃	1	2	yes	—
223	#126	C₂²×C₃	1	2	yes	—
224	#126	C₂²×C₃	1	2	yes	—
225	#126	C₂²×C₃	1	2	yes	—
226	#126	C₂²×C₃	1	2	yes	—
227	#126	C₂²×C₃	1	2	yes	—
228	#126	C₂²×C₃	1	2	yes	complemented
229	#126	C₂²×C₃	1	2	yes	complemented
230	#126	C₂²×C₃	1	2	yes	complemented
231	#126	C₂²×C₃	1	2	yes	complemented
232	#125	C₂²×C₃	1	1	yes	characteristic, complemented
233	#125	C₂²×C₃	1	2	yes	complemented
234	#125	C₂²×C₃	1	2	yes	complemented
235	#125	C₂²×C₃	1	2	yes	complemented
236	#125	C₂²×C₃	1	2	yes	complemented
237	#125	C₂²×C₃	1	2	yes	complemented
238	#125	C₂²×C₃	1	2	yes	complemented
239	#125	C₂²×C₃	1	2	yes	complemented
240	#125	C₂²×C₃	1	2	yes	complemented
241	#125	C₂²×C₃	1	2	yes	complemented
242	#124	C₂²×C₃	1	2	yes	—
243	#124	C₂²×C₃	1	2	yes	—
244	#124	C₂²×C₃	1	2	yes	—
245	#124	C₂²×C₃	1	1	yes	characteristic, complemented
246	#123	C₂²×C₃	1	2	yes	—
247	#123	C₂²×C₃	1	2	yes	—
248	#123	C₂²×C₃	1	2	yes	—
249	#123	C₂²×C₃	1	2	yes	—
250	#123	C₂²×C₃	1	2	yes	—
251	#123	C₂²×C₃	1	2	yes	—
252	#123	C₂²×C₃	1	2	yes	—
253	#123	C₂²×C₃	1	2	yes	complemented
254	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
255	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
256	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
257	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
258	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
259	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
260	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
261	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
262	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
263	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
264	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
265	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
266	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
267	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
268	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
269	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
270	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
271	#121	C₂²×C₃	1	1	yes	characteristic
272	#121	C₂²×C₃	1	2	yes	—
273	#120	C₂²×C₃	1	2	yes	—
274	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
275	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
276	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
277	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
278	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
279	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
280	C₄×D₄	C₂²×C₃	1	2	yes	—
281	C₄×D₄	C₂²×C₃	1	2	yes	—
282	C₄×D₄	C₂²×C₃	1	2	yes	—
283	C₄×D₄	C₂²×C₃	1	2	yes	—
284	C₄×D₄	C₂²×C₃	1	2	yes	—
285	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
286	#117	C₂²×C₃	1	2	yes	—
287	#117	C₂²×C₃	1	2	yes	—
288	#117	C₂²×C₃	1	2	yes	—
289	#117	C₂²×C₃	1	2	yes	—
290	#117	C₂²×C₃	1	2	yes	complemented
291	#117	C₂²×C₃	1	2	yes	complemented
292	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
296	C₂×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
300	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
301	C₂³×C₃	—	2	2	no	—
302	C₂³×C₃	—	4	1	no	—
303	C₂³×C₃	—	4	1	no	—
304	C₂³×C₃	C₂⁴	1	2	yes	—
305	C₂³×C₃	C₂⁴	1	2	yes	—
306	C₂³×C₃	C₂⁴	1	1	yes	characteristic
307	C₃×Q₈	—	4	1	no	—
308	C₃×Q₈	—	4	2	no	—
309	C₃×Q₈	—	4	2	no	—
310	C₃×Q₈	—	4	1	no	—
311	C₃×Q₈	—	4	2	no	—
312	C₃×Q₈	—	4	1	no	—
313	C₃×D₄	—	2	4	no	—
314	C₃×D₄	—	4	2	no	—
315	C₃×D₄	—	4	1	no	—
316	C₃×D₄	—	4	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	4	2	no	—
320	C₂×C₃×C₄	—	4	1	no	—
321	C₂×C₃×C₄	—	4	1	no	—
322	C₂×C₃×C₄	—	4	1	no	—
323	C₂×C₃×C₄	—	4	2	no	—
324	C₂×C₃×C₄	—	4	2	no	—
325	C₂×C₃×C₄	—	4	2	no	—
326	C₂×C₃×C₄	—	4	2	no	—
327	C₂×C₃×C₄	—	4	1	no	—
328	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂⁴	1	2	yes	—
331	C₂×C₃×C₄	C₂⁴	1	2	yes	—
332	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂⁴	1	2	yes	—
334	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂⁴	1	2	yes	—
337	C₂×C₃×C₄	C₂⁴	1	2	yes	—
338	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂⁴	1	2	yes	—
340	C₂×C₃×C₄	C₂⁴	1	2	yes	—
341	C₂×C₃×C₄	C₂⁴	1	2	yes	—
342	C₂×C₃×C₄	C₂⁴	1	2	yes	—
343	C₂×C₃×C₄	C₂⁴	1	2	yes	—
344	C₂⁴	C₂³×C₃	1	1	yes	characteristic
345	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
346	C₂×Q₈	C₂³×C₃	1	2	yes	—
347	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
348	C₂×Q₈	C₂³×C₃	1	2	yes	—
349	C₂×Q₈	C₂³×C₃	1	2	yes	—
350	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
351	C₂×D₄	C₂³×C₃	1	2	yes	—
352	C₂×D₄	C₂³×C₃	1	2	yes	—
353	C₂×D₄	C₂³×C₃	1	2	yes	—
354	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
355	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
356	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
357	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
358	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
359	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
360	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
361	C₂²×C₄	C₂³×C₃	1	2	yes	—
362	C₂²×C₄	C₂³×C₃	1	2	yes	—
363	C₂²×C₄	C₂³×C₃	1	2	yes	—
364	C₂²×C₄	C₂³×C₃	1	2	yes	—
365	C₂²×C₄	C₂³×C₃	1	2	yes	—
366	C₄⋊C₄	C₂³×C₃	1	2	yes	—
367	C₄⋊C₄	C₂³×C₃	1	2	yes	—
368	C₄⋊C₄	C₂³×C₃	1	2	yes	—
369	C₄⋊C₄	C₂³×C₃	1	2	yes	—
370	C₄⋊C₄	C₂³×C₃	1	2	yes	—
371	C₄⋊C₄	C₂³×C₃	1	2	yes	—
372	C₄⋊C₄	C₂³×C₃	1	2	yes	—
373	C₄⋊C₄	C₂³×C₃	1	2	yes	—
374	C₄⋊C₄	C₂³×C₃	1	2	yes	—
375	C₄⋊C₄	C₂³×C₃	1	2	yes	—
376	C₄⋊C₄	C₂³×C₃	1	2	yes	—
377	C₄⋊C₄	C₂³×C₃	1	2	yes	—
378	C₄⋊C₄	C₂³×C₃	1	2	yes	—
379	C₄⋊C₄	C₂³×C₃	1	2	yes	—
380	C₄⋊C₄	C₂³×C₃	1	2	yes	—
381	C₄⋊C₄	C₂³×C₃	1	2	yes	—
382	C₄⋊C₄	C₂³×C₃	1	2	yes	—
383	C₄⋊C₄	C₂³×C₃	1	2	yes	—
384	C₄⋊C₄	C₂³×C₃	1	2	yes	—
385	C₄⋊C₄	C₂³×C₃	1	2	yes	—
386	C₄⋊C₄	C₂³×C₃	1	2	yes	—
387	C₄⋊C₄	C₂³×C₃	1	2	yes	—
388	C₄⋊C₄	C₂³×C₃	1	2	yes	—
389	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
390	C₄⋊C₄	C₂³×C₃	1	2	yes	—
391	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
392	C₄⋊C₄	C₂³×C₃	1	2	yes	—
393	C₄⋊C₄	C₂³×C₃	1	2	yes	—
394	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
395	C₄⋊C₄	C₂³×C₃	1	2	yes	—
396	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
397	C₄⋊C₄	C₂³×C₃	1	2	yes	—
398	C₄⋊C₄	C₂³×C₃	1	2	yes	—
399	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
400	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
401	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
402	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
403	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
404	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
405	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
406	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
407	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
408	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
415	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
416	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
417	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
418	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
419	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
420	C₄²	C₂³×C₃	1	1	yes	characteristic
421	C₄²	C₂³×C₃	1	1	yes	characteristic
422	C₄²	C₂³×C₃	1	1	yes	characteristic
423	C₄²	C₂³×C₃	1	1	yes	characteristic
424	C₄²	C₂³×C₃	1	2	yes	—
425	C₄²	C₂³×C₃	1	2	yes	—
426	C₄²	C₂³×C₃	1	2	yes	—
427	C₄²	C₂³×C₃	1	2	yes	—
428	C₄²	C₂³×C₃	1	2	yes	—
429	C₄²	C₂³×C₃	1	2	yes	—
430	C₄²	C₂³×C₃	1	2	yes	—
431	C₂²×C₃	—	2	1	no	—
432	C₂²×C₃	—	2	1	no	—
433	C₂²×C₃	—	2	2	no	—
434	C₂²×C₃	—	2	2	no	—
435	C₂²×C₃	—	2	2	no	—
436	C₂²×C₃	—	2	2	no	—
437	C₂²×C₃	—	2	2	no	—
438	C₂²×C₃	—	2	2	no	—
439	C₂²×C₃	—	8	2	no	—
440	C₂²×C₃	2₋¹⁺⁴	1	2	yes	—
441	C₂²×C₃	C₂⁵	1	1	yes	characteristic
442	C₃×C₄	—	2	1	no	—
443	C₃×C₄	—	2	1	no	—
444	C₃×C₄	—	2	2	no	—
445	C₃×C₄	—	2	2	no	—
446	C₃×C₄	—	2	1	no	—
447	C₃×C₄	—	2	2	no	—
448	C₃×C₄	—	2	2	no	—
449	C₃×C₄	—	2	2	no	—
450	C₃×C₄	—	2	2	no	—
451	C₃×C₄	—	2	2	no	—
452	C₃×C₄	—	2	1	no	—
453	C₃×C₄	—	2	1	no	—
454	C₃×C₄	—	2	2	no	—
455	C₃×C₄	—	2	2	no	—
456	C₃×C₄	—	2	1	no	—
457	C₃×C₄	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	4	1	no	—
460	C₂³	—	4	1	no	—
461	C₂³	C₂⁴×C₃	1	2	yes	—
462	C₂³	C₂⁴×C₃	1	2	yes	—
463	C₂³	C₂⁴×C₃	1	1	yes	characteristic
464	Q₈	—	4	1	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	4	1	no	—
468	Q₈	—	4	2	no	—
469	Q₈	—	4	1	no	—
470	D₄	—	2	4	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
486	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
487	C₂×C₄	C₂⁴×C₃	1	2	yes	—
488	C₂×C₄	C₂⁴×C₃	1	2	yes	—
489	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
490	C₂×C₄	C₂⁴×C₃	1	2	yes	—
491	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
492	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
493	C₂×C₄	C₂⁴×C₃	1	2	yes	—
494	C₂×C₄	C₂⁴×C₃	1	2	yes	—
495	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
496	C₂×C₄	C₂⁴×C₃	1	2	yes	—
497	C₂×C₄	C₂⁴×C₃	1	2	yes	—
498	C₂×C₄	C₂⁴×C₃	1	2	yes	—
499	C₂×C₄	C₂⁴×C₃	1	2	yes	—
500	C₂×C₄	C₂⁴×C₃	1	2	yes	—
501	C₂×C₃	—	2	2	no	—
502	C₂×C₃	—	4	2	no	—
503	C₂×C₃	—	4	2	no	—
504	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
505	C₂×C₃	#585	1	1	yes	characteristic
506	C₂×C₃	#585	1	1	yes	characteristic
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	8	2	no	—
516	C₂²	C₃×2₋¹⁺⁴	1	2	yes	—
517	C₂²	C₂⁵×C₃	1	1	yes	characteristic
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	2	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	2	no	—
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	1	no	—
529	C₄	—	2	1	no	—
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	2	no	—
534	C₃	#3564	1	1	yes	characteristic, direct product factor, Sylow
535	C₂	—	2	2	no	—
536	C₂	—	4	2	no	—
537	C₂	—	4	2	no	—
538	C₂	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
539	C₂	C₃×#585	1	1	yes	characteristic
540	C₂	C₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃
prime radical	C₃×#538	C₂
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×#563	C₂	semidirect
3. C₃×#556	C₂	semidirect
4. C₃×#554	C₂	semidirect
5. C₃×#552	C₂	semidirect
6. C₃×#552	C₂	semidirect
7. C₃×#551	C₂	semidirect
8. C₃×#551	C₂	semidirect
9. C₃×#544	C₂	semidirect
10. C₃×#543	C₂	semidirect
11. C₃×#542	C₂	semidirect
12. C₃×#541	C₂	semidirect
13. C₃×#541	C₂	semidirect
14. C₃×#539	C₂	semidirect
15. C₃×#539	C₂	semidirect
17. C₃×#533	C₂	semidirect
18. C₃×#529	C₂	semidirect
19. C₂×C₃×#126	C₂	semidirect
20. #3564	C₃	direct (N × H)
21. C₃×C₄⋊Q₈	C₂²	semidirect
22. C₃×C₄⋊Q₈	C₂²	semidirect
23. C₃×C₄⋊Q₈	C₂²	semidirect
24. C₃×C₄⋊Q₈	C₂²	semidirect
25. C₃×C₄⋊Q₈	C₂²	semidirect
35. C₃×#126	C₂²	semidirect
36. C₃×#126	C₂²	semidirect
37. C₃×#126	C₂²	semidirect
38. C₃×#126	C₂²	semidirect
39. C₃×#125	C₂²	semidirect
40. C₃×#125	C₂²	semidirect
41. C₃×#125	C₂²	semidirect
42. C₃×#125	C₂²	semidirect
43. C₃×#125	C₂²	semidirect
44. C₃×#125	C₂²	semidirect
45. C₃×#125	C₂²	semidirect
46. C₃×#125	C₂²	semidirect
47. C₃×#125	C₂²	semidirect
48. C₃×#125	C₂²	semidirect
52. C₃×#124	C₂²	semidirect
60. C₃×#123	C₂²	semidirect
73. C₃×C₂²⋊Q₈	C₂²	semidirect
74. C₃×C₂²⋊Q₈	C₂²	semidirect
75. C₃×C₂²⋊Q₈	C₂²	semidirect
76. C₃×C₂²⋊Q₈	C₂²	semidirect
77. C₃×C₂²⋊Q₈	C₂²	semidirect
81. C₃×C₄×Q₈	C₂²	semidirect
82. C₃×C₄×Q₈	C₂²	semidirect
83. C₃×C₄×Q₈	C₂²	semidirect
84. C₃×C₄×Q₈	C₂²	semidirect
85. C₃×C₄×Q₈	C₂²	semidirect
86. C₃×C₄×Q₈	C₂²	semidirect
92. C₃×C₄×D₄	C₂²	semidirect
97. C₃×#117	C₂²	semidirect
98. C₃×#117	C₂²	semidirect
102. C₂×C₃×C₄⋊C₄	C₂²	semidirect
108. #563	C₂×C₃	semidirect
109. #563	C₂×C₃	semidirect
110. #556	C₂×C₃	semidirect
111. #554	C₂×C₃	semidirect
112. #552	C₂×C₃	semidirect
113. #552	C₂×C₃	semidirect
114. #551	C₂×C₃	semidirect
115. #551	C₂×C₃	semidirect
116. #544	C₂×C₃	semidirect
117. #543	C₂×C₃	semidirect
118. #542	C₂×C₃	semidirect
119. #541	C₂×C₃	semidirect
120. #541	C₂×C₃	semidirect
121. #539	C₂×C₃	semidirect
122. #539	C₂×C₃	semidirect
124. #533	C₂×C₃	semidirect
125. #529	C₂×C₃	semidirect
126. C₂×#126	C₂×C₃	semidirect
214. C₄⋊Q₈	C₂²×C₃	semidirect
215. C₄⋊Q₈	C₂²×C₃	semidirect
216. C₄⋊Q₈	C₂²×C₃	semidirect
217. C₄⋊Q₈	C₂²×C₃	semidirect
218. C₄⋊Q₈	C₂²×C₃	semidirect
228. #126	C₂²×C₃	semidirect
229. #126	C₂²×C₃	semidirect
230. #126	C₂²×C₃	semidirect
231. #126	C₂²×C₃	semidirect
232. #125	C₂²×C₃	semidirect
233. #125	C₂²×C₃	semidirect
234. #125	C₂²×C₃	semidirect
235. #125	C₂²×C₃	semidirect
236. #125	C₂²×C₃	semidirect
237. #125	C₂²×C₃	semidirect
238. #125	C₂²×C₃	semidirect
239. #125	C₂²×C₃	semidirect
240. #125	C₂²×C₃	semidirect
241. #125	C₂²×C₃	semidirect
245. #124	C₂²×C₃	semidirect
253. #123	C₂²×C₃	semidirect
266. C₂²⋊Q₈	C₂²×C₃	semidirect
267. C₂²⋊Q₈	C₂²×C₃	semidirect
268. C₂²⋊Q₈	C₂²×C₃	semidirect
269. C₂²⋊Q₈	C₂²×C₃	semidirect
270. C₂²⋊Q₈	C₂²×C₃	semidirect
274. C₄×Q₈	C₂²×C₃	semidirect
275. C₄×Q₈	C₂²×C₃	semidirect
276. C₄×Q₈	C₂²×C₃	semidirect
277. C₄×Q₈	C₂²×C₃	semidirect
278. C₄×Q₈	C₂²×C₃	semidirect
279. C₄×Q₈	C₂²×C₃	semidirect
285. C₄×D₄	C₂²×C₃	semidirect
290. #117	C₂²×C₃	semidirect
291. #117	C₂²×C₃	semidirect
295. C₂×C₄⋊C₄	C₂²×C₃	semidirect
534. C₃	#3564	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×#556	2
C₃×#554	2
C₃×#552	2
C₃×#551	2
C₃×#544	2
C₃×#543	2
C₃×#542	2
C₃×#541	2
C₃×#539	2
C₃×#538	2
C₃×#533	2
C₃×#529	2
C₂×C₃×#126	2
#3564	3

Subgroups — C3×#3564 #87448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3564 #87448