Subgroups — C₃×D₃×#534 #11900928

Order 1152.

4141 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₃×D₄	C₂	1	2	yes	maximal, complemented
2	C₃²×#534	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5804	C₂	1	2	yes	maximal, complemented
4	C₃×#5653	C₂	1	4	yes	maximal, complemented
5	C₃×D₃×#123	C₂	1	4	yes	maximal, complemented
6	C₃×#5605	C₂	1	4	yes	maximal, complemented
7	C₃×D₃×#121	C₂	1	4	yes	maximal, complemented
8	C₃×#5589	C₂	1	4	yes	maximal, complemented
9	C₃×D₃×#120	C₂	1	4	yes	maximal, complemented
10	C₃×#5493	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#534	—	3	1	no	maximal
13	D₃×#534	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₃×D₃	C₂²	1	2	yes	complemented
16	C₂²×C₃²×D₄	C₂²	1	2	yes	complemented
17	C₂²×C₃×#67	C₂²	1	2	yes	complemented
18	C₂²×C₃×#67	C₂²	1	2	yes	complemented
19	C₂×C₃×D₃×D₄	—	2	16	no	—
20	C₂×C₃×D₃×D₄	C₂²	1	4	yes	—
21	C₂×C₃×D₃×D₄	C₂²	1	4	yes	complemented
22	C₂×C₃×D₃×D₄	C₂²	1	4	yes	complemented
23	C₂×C₃×D₃×D₄	C₂²	1	4	yes	complemented
24	C₂×C₃×D₃×D₄	C₂²	1	4	yes	complemented
25	C₂²×C₃×D₁₂	C₂²	1	2	yes	complemented
26	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
27	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
28	C₃²×#123	C₂²	1	4	yes	complemented
29	C₃²×#121	C₂²	1	4	yes	complemented
30	C₃²×#120	C₂²	1	4	yes	complemented
31	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₃×#953	C₂²	1	4	yes	complemented
33	C₂×C₃×#217	C₂²	1	1	yes	characteristic, complemented
34	C₃×#939	C₂²	1	8	yes	complemented
35	C₃×#938	C₂²	1	4	yes	complemented
36	C₃×#937	C₂²	1	8	yes	complemented
37	C₃×#937	C₂²	1	4	yes	complemented
38	C₃×#935	C₂²	1	4	yes	complemented
39	C₃×#930	C₂²	1	4	yes	complemented
40	C₃×#929	C₂²	1	4	yes	complemented
41	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
42	C₃×#895	C₂²	1	4	yes	complemented
43	C₃×#894	C₂²	1	8	yes	complemented
44	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	complemented
45	C₃×#886	C₂²	1	4	yes	complemented
46	C₃×#884	C₂²	1	8	yes	complemented
47	C₃×#883	C₂²	1	8	yes	complemented
48	C₃×#882	C₂²	1	8	yes	complemented
49	C₃×#882	C₂²	1	4	yes	complemented
50	C₃×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
51	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
52	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
53	C₂³×C₃×D₄	—	3	2	no	—
54	C₂²×D₃×D₄	C₂×C₃	1	2	yes	complemented
55	C₃×#534	—	2	1	no	—
56	C₃×#534	—	3	2	no	—
57	C₃×#534	—	3	4	no	—
58	C₃×#534	—	3	4	no	—
59	C₃×#534	—	3	4	no	—
60	C₃×#534	—	3	1	no	—
61	C₃×#534	D₃	1	1	yes	characteristic, direct product factor
62	C₃×#534	C₂×C₃	1	1	yes	characteristic, complemented
63	C₂×C₃×#123	—	3	4	no	—
64	C₂×C₃×#121	—	3	4	no	—
65	C₂×C₃×#120	—	3	4	no	—
66	C₂²×C₃×C₂²⋊C₄	—	3	1	no	—
67	#5804	C₂×C₃	1	2	yes	complemented
68	#5653	C₂×C₃	1	4	yes	complemented
69	D₃×#123	C₂×C₃	1	4	yes	complemented
70	#5605	C₂×C₃	1	4	yes	complemented
71	D₃×#121	C₂×C₃	1	4	yes	complemented
72	#5589	C₂×C₃	1	4	yes	complemented
73	D₃×#120	C₂×C₃	1	4	yes	complemented
74	#5493	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×D₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
77	C₂⁴×C₃²	C₂³	1	2	yes	complemented
78	C₂³×C₃×D₃	—	2	8	no	—
79	C₂³×C₃×D₃	—	4	4	no	—
80	C₂³×C₃×D₃	—	4	8	no	—
81	C₂³×C₃×D₃	D₄	1	8	yes	complemented
82	C₂³×C₃×D₃	C₂³	1	4	yes	—
83	C₂³×C₃×D₃	C₂³	1	2	yes	—
84	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
85	C₂³×C₃×D₃	C₂³	1	2	yes	—
86	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
87	C₂³×C₃×D₃	C₂³	1	2	yes	complemented
88	C₂³×C₃×D₃	C₂³	1	4	yes	complemented
89	C₂×C₃²×D₄	—	2	8	no	—
90	C₂×C₃²×D₄	C₂³	1	4	yes	—
91	C₂×C₃²×D₄	C₂³	1	4	yes	complemented
92	C₂×C₃²×D₄	C₂³	1	4	yes	complemented
93	C₂²×C₃²×C₄	C₂³	1	2	yes	complemented
94	C₂²×C₃²×C₄	C₂³	1	2	yes	complemented
95	C₂×C₃×#67	—	2	8	no	—
96	C₂×C₃×#67	—	2	8	no	—
97	C₂×C₃×#67	C₂³	1	4	yes	—
98	C₂×C₃×#67	C₂³	1	4	yes	—
99	C₂×C₃×#67	C₂³	1	4	yes	complemented
100	C₂×C₃×#67	C₂³	1	4	yes	complemented
101	C₂×C₃×#67	C₂³	1	8	yes	complemented
102	C₂²×C₃×Dic₃	C₂³	1	2	yes	complemented
103	C₂²×C₃×Dic₃	C₂³	1	2	yes	complemented
104	C₃×D₃×D₄	—	2	16	no	—
105	C₃×D₃×D₄	—	2	16	no	—
106	C₃×D₃×D₄	—	2	16	no	—
107	C₃×D₃×D₄	—	2	16	no	—
108	C₃×D₃×D₄	—	4	8	no	—
109	C₂×C₃×D₁₂	—	2	8	no	—
110	C₂×C₃×D₁₂	C₂³	1	4	yes	—
111	C₂×C₃×D₁₂	C₂³	1	4	yes	complemented
112	C₂×C₃×D₁₂	C₂³	1	4	yes	complemented
113	C₂×C₃×C₄×D₃	—	2	8	no	—
114	C₂×C₃×C₄×D₃	—	4	4	no	—
115	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
116	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
117	C₂×C₃×C₄×D₃	C₂³	1	4	yes	complemented
118	C₂×C₃×C₄×D₃	C₂³	1	4	yes	complemented
119	C₃²×C₄⋊C₄	C₂³	1	4	yes	complemented
120	C₃²×C₂²⋊C₄	C₂³	1	4	yes	complemented
121	C₃²×C₂²⋊C₄	C₂³	1	8	yes	complemented
122	C₃×#217	C₂³	1	4	yes	complemented
123	C₃×#217	C₂³	1	8	yes	complemented
124	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
125	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
126	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
127	C₃×C₄⋊Dic₃	C₂³	1	4	yes	complemented
128	C₃×Dic₃⋊C₄	C₂³	1	8	yes	complemented
129	C₂×#534	—	3	1	no	Sylow
130	C₂⁵×C₃	—	3	1	no	—
131	C₂⁵×C₃	—	3	2	no	—
132	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic
133	C₂⁴×D₃	C₂²×C₃	1	2	yes	complemented
134	C₂²×C₃×D₄	—	2	2	no	—
135	C₂²×C₃×D₄	—	3	2	no	—
136	C₂²×C₃×D₄	—	3	2	no	—
137	C₂²×C₃×D₄	—	3	4	no	—
138	C₂²×C₃×D₄	—	3	4	no	—
139	C₂²×C₃×D₄	—	3	4	no	—
140	C₂²×C₃×D₄	—	3	4	no	—
141	C₂²×C₃×D₄	—	3	4	no	—
142	C₂²×C₃×D₄	—	3	2	no	—
143	C₂²×C₃×D₄	—	6	16	no	—
144	C₂²×C₃×D₄	C₂×D₃	1	2	yes	complemented
145	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	complemented
146	C₂³×C₃×C₄	—	3	2	no	—
147	C₂³×C₃×C₄	—	3	2	no	—
148	C₂²×#67	C₂²×C₃	1	2	yes	complemented
149	C₂²×#67	C₂²×C₃	1	2	yes	complemented
150	C₂×D₃×D₄	—	2	16	no	—
151	C₂×D₃×D₄	C₂²×C₃	1	4	yes	—
152	C₂×D₃×D₄	C₂²×C₃	1	4	yes	complemented
153	C₂×D₃×D₄	C₂²×C₃	1	4	yes	complemented
154	C₂×D₃×D₄	C₂²×C₃	1	4	yes	complemented
155	C₂×D₃×D₄	C₂²×C₃	1	4	yes	complemented
156	C₂²×D₁₂	C₂²×C₃	1	2	yes	complemented
157	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
158	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
159	C₃×#123	—	2	4	no	—
160	C₃×#123	—	3	4	no	—
161	C₃×#123	—	3	4	no	—
162	C₃×#123	—	3	8	no	—
163	C₃×#123	—	3	8	no	—
164	C₃×#123	—	3	4	no	—
165	C₃×#123	C₂×D₃	1	4	yes	complemented
166	C₃×#123	C₂²×C₃	1	4	yes	complemented
167	C₃×#121	—	2	4	no	—
168	C₃×#121	—	3	4	no	—
169	C₃×#121	—	3	8	no	—
170	C₃×#121	—	3	4	no	—
171	C₃×#121	—	3	4	no	—
172	C₃×#121	—	3	8	no	—
173	C₃×#121	C₂×D₃	1	4	yes	complemented
174	C₃×#121	C₂²×C₃	1	4	yes	complemented
175	C₃×#120	—	2	4	no	—
176	C₃×#120	—	3	4	no	—
177	C₃×#120	—	3	4	no	—
178	C₃×#120	—	3	8	no	—
179	C₃×#120	—	3	8	no	—
180	C₃×#120	—	3	4	no	—
181	C₃×#120	C₂×D₃	1	4	yes	complemented
182	C₃×#120	C₂²×C₃	1	4	yes	complemented
183	C₂×C₃×C₄⋊C₄	—	3	4	no	—
184	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
185	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
186	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
187	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
188	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
189	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
190	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
191	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
192	#953	C₂²×C₃	1	4	yes	complemented
193	C₂×#217	C₂²×C₃	1	1	yes	characteristic, complemented
194	#939	C₂²×C₃	1	8	yes	complemented
195	#938	C₂²×C₃	1	4	yes	complemented
196	#937	C₂²×C₃	1	8	yes	complemented
197	#937	C₂²×C₃	1	4	yes	complemented
198	#935	C₂²×C₃	1	4	yes	complemented
199	#930	C₂²×C₃	1	4	yes	complemented
200	#929	C₂²×C₃	1	4	yes	complemented
201	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
202	#895	C₂²×C₃	1	4	yes	complemented
203	#894	C₂²×C₃	1	8	yes	complemented
204	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
205	#886	C₂²×C₃	1	4	yes	complemented
206	#884	C₂²×C₃	1	8	yes	complemented
207	#883	C₂²×C₃	1	8	yes	complemented
208	#882	C₂²×C₃	1	8	yes	complemented
209	#882	C₂²×C₃	1	4	yes	complemented
210	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
211	D₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
212	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
213	C₂³×C₃²	—	2	4	no	—
214	C₂³×C₃²	—	4	2	no	—
215	C₂³×C₃²	—	4	4	no	—
216	C₂³×C₃²	C₂×D₄	1	4	yes	complemented
217	C₂³×C₃²	C₂⁴	1	4	yes	—
218	C₂³×C₃²	C₂⁴	1	2	yes	—
219	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
220	C₂²×C₃×D₃	—	2	8	no	—
221	C₂²×C₃×D₃	—	2	4	no	—
222	C₂²×C₃×D₃	—	2	4	no	—
223	C₂²×C₃×D₃	—	2	8	no	—
224	C₂²×C₃×D₃	—	2	8	no	—
225	C₂²×C₃×D₃	—	2	16	no	—
226	C₂²×C₃×D₃	—	4	16	no	—
227	C₂²×C₃×D₃	—	4	4	no	—
228	C₂²×C₃×D₃	—	4	2	no	—
229	C₂²×C₃×D₃	—	4	8	no	—
230	C₂²×C₃×D₃	—	4	4	no	—
231	C₂²×C₃×D₃	—	4	32	no	—
232	C₂²×C₃×D₃	C₂×D₄	1	8	yes	—
233	C₂²×C₃×D₃	C₂×D₄	1	4	yes	—
234	C₂²×C₃×D₃	C₂×D₄	1	8	yes	complemented
235	C₂²×C₃×D₃	C₂×D₄	1	4	yes	complemented
236	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
237	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
238	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
239	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
240	C₃²×D₄	—	2	8	no	—
241	C₃²×D₄	—	2	8	no	—
242	C₃²×D₄	—	4	4	no	—
243	C₂×C₃²×C₄	—	2	4	no	—
244	C₂×C₃²×C₄	—	4	2	no	—
245	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
246	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
247	C₃×#67	—	2	8	no	—
248	C₃×#67	—	2	8	no	—
249	C₃×#67	—	2	8	no	—
250	C₃×#67	—	2	8	no	—
251	C₃×#67	—	4	8	no	—
252	C₂×C₃×Dic₃	—	2	4	no	—
253	C₂×C₃×Dic₃	—	4	2	no	—
254	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
255	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
256	C₃×D₁₂	—	2	8	no	—
257	C₃×D₁₂	—	2	8	no	—
258	C₃×D₁₂	—	4	4	no	—
259	C₃×C₄×D₃	—	2	8	no	—
260	C₃×C₄×D₃	—	2	8	no	—
261	C₃×C₄×D₃	—	2	8	no	—
262	C₃×C₄×D₃	—	4	4	no	—
263	C₂³×D₄	—	3	2	no	—
264	#534	—	3	2	no	—
265	#534	—	3	4	no	—
266	#534	—	3	4	no	—
267	#534	—	3	4	no	—
268	#534	—	3	1	no	—
269	#534	C₃×D₃	1	1	yes	characteristic, direct product factor
270	C₂×#123	—	3	4	no	—
271	C₂×#121	—	3	4	no	—
272	C₂×#120	—	3	4	no	—
273	C₂²×C₂²⋊C₄	—	3	1	no	—
274	C₂⁴×C₃	—	2	1	no	—
275	C₂⁴×C₃	—	2	2	no	—
276	C₂⁴×C₃	—	3	2	no	—
277	C₂⁴×C₃	—	3	1	no	—
278	C₂⁴×C₃	—	3	8	no	—
279	C₂⁴×C₃	—	3	1	no	—
280	C₂⁴×C₃	—	3	2	no	—
281	C₂⁴×C₃	—	3	4	no	—
282	C₂⁴×C₃	—	3	4	no	—
283	C₂⁴×C₃	—	3	2	no	—
284	C₂⁴×C₃	—	6	8	no	—
285	C₂⁴×C₃	—	12	4	no	—
286	C₂⁴×C₃	—	12	8	no	—
287	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
288	C₂⁴×C₃	C₂²×D₃	1	2	yes	complemented
289	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
290	C₂⁴×C₃	C₂³×C₃	1	2	yes	complemented
291	C₂³×D₃	—	2	8	no	—
292	C₂³×D₃	—	4	4	no	—
293	C₂³×D₃	—	4	8	no	—
294	C₂³×D₃	C₃×D₄	1	8	yes	complemented
295	C₂³×D₃	C₂³×C₃	1	4	yes	—
296	C₂³×D₃	C₂³×C₃	1	2	yes	—
297	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
298	C₂³×D₃	C₂³×C₃	1	2	yes	—
299	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
300	C₂³×D₃	C₂³×C₃	1	2	yes	complemented
301	C₂³×D₃	C₂³×C₃	1	4	yes	complemented
302	C₂×C₃×D₄	—	2	8	no	—
303	C₂×C₃×D₄	—	2	8	no	—
304	C₂×C₃×D₄	—	2	4	no	—
305	C₂×C₃×D₄	—	2	4	no	—
306	C₂×C₃×D₄	—	2	4	no	—
307	C₂×C₃×D₄	—	3	4	no	—
308	C₂×C₃×D₄	—	3	4	no	—
309	C₂×C₃×D₄	—	3	4	no	—
310	C₂×C₃×D₄	—	3	4	no	—
311	C₂×C₃×D₄	—	3	8	no	—
312	C₂×C₃×D₄	—	3	4	no	—
313	C₂×C₃×D₄	—	3	4	no	—
314	C₂×C₃×D₄	—	3	4	no	—
315	C₂×C₃×D₄	—	4	8	no	—
316	C₂×C₃×D₄	—	6	8	no	—
317	C₂×C₃×D₄	—	6	16	no	—
318	C₂×C₃×D₄	—	6	16	no	—
319	C₂×C₃×D₄	—	6	16	no	—
320	C₂×C₃×D₄	—	6	16	no	—
321	C₂×C₃×D₄	—	6	8	no	—
322	C₂×C₃×D₄	—	6	8	no	—
323	C₂×C₃×D₄	—	12	8	no	—
324	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
325	C₂×C₃×D₄	C₂²×D₃	1	4	yes	complemented
326	C₂×C₃×D₄	C₂²×D₃	1	4	yes	complemented
327	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
328	C₂×C₃×D₄	C₂³×C₃	1	4	yes	complemented
329	C₂×C₃×D₄	C₂³×C₃	1	4	yes	complemented
330	C₂²×C₃×C₄	—	2	2	no	—
331	C₂²×C₃×C₄	—	2	2	no	—
332	C₂²×C₃×C₄	—	3	2	no	—
333	C₂²×C₃×C₄	—	3	2	no	—
334	C₂²×C₃×C₄	—	3	4	no	—
335	C₂²×C₃×C₄	—	3	4	no	—
336	C₂²×C₃×C₄	—	3	4	no	—
337	C₂²×C₃×C₄	—	3	4	no	—
338	C₂²×C₃×C₄	—	6	8	no	—
339	C₂²×C₃×C₄	—	12	4	no	—
340	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	complemented
341	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	complemented
342	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	complemented
343	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	complemented
344	C₂×#67	—	2	8	no	—
345	C₂×#67	—	2	8	no	—
346	C₂×#67	C₂³×C₃	1	4	yes	—
347	C₂×#67	C₂³×C₃	1	4	yes	—
348	C₂×#67	C₂³×C₃	1	4	yes	complemented
349	C₂×#67	C₂³×C₃	1	4	yes	complemented
350	C₂×#67	C₂³×C₃	1	8	yes	complemented
351	C₂²×Dic₃	C₂³×C₃	1	2	yes	complemented
352	C₂²×Dic₃	C₂³×C₃	1	2	yes	complemented
353	D₃×D₄	—	2	16	no	—
354	D₃×D₄	—	2	16	no	—
355	D₃×D₄	—	2	16	no	—
356	D₃×D₄	—	2	16	no	—
357	D₃×D₄	—	4	8	no	—
358	C₂×D₁₂	—	2	8	no	—
359	C₂×D₁₂	C₂³×C₃	1	4	yes	—
360	C₂×D₁₂	C₂³×C₃	1	4	yes	complemented
361	C₂×D₁₂	C₂³×C₃	1	4	yes	complemented
362	C₂×C₄×D₃	—	2	8	no	—
363	C₂×C₄×D₃	—	4	4	no	—
364	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
365	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
366	C₂×C₄×D₃	C₂³×C₃	1	4	yes	complemented
367	C₂×C₄×D₃	C₂³×C₃	1	4	yes	complemented
368	C₃×C₄⋊C₄	—	2	4	no	—
369	C₃×C₄⋊C₄	—	3	8	no	—
370	C₃×C₄⋊C₄	—	3	4	no	—
371	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
372	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
373	C₃×C₂²⋊C₄	—	2	4	no	—
374	C₃×C₂²⋊C₄	—	2	8	no	—
375	C₃×C₂²⋊C₄	—	3	4	no	—
376	C₃×C₂²⋊C₄	—	3	8	no	—
377	C₃×C₂²⋊C₄	—	3	8	no	—
378	C₃×C₂²⋊C₄	—	3	8	no	—
379	C₃×C₂²⋊C₄	—	3	8	no	—
380	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
381	C₃×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
382	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
383	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
384	#217	C₂³×C₃	1	4	yes	complemented
385	#217	C₂³×C₃	1	8	yes	complemented
386	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
387	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
388	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
389	C₄⋊Dic₃	C₂³×C₃	1	4	yes	complemented
390	Dic₃⋊C₄	C₂³×C₃	1	8	yes	complemented
391	C₂²×C₃²	—	2	2	no	—
392	C₂²×C₃²	—	2	4	no	—
393	C₂²×C₃²	—	2	4	no	—
394	C₂²×C₃²	—	2	8	no	—
395	C₂²×C₃²	—	4	4	no	—
396	C₂²×C₃²	—	4	8	no	—
397	C₂²×C₃²	C₂²×D₄	1	4	yes	—
398	C₂²×C₃²	C₂²×D₄	1	2	yes	—
399	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
400	C₂×C₃×D₃	—	2	2	no	—
401	C₂×C₃×D₃	—	2	4	no	—
402	C₂×C₃×D₃	—	2	16	no	—
403	C₂×C₃×D₃	—	2	8	no	—
404	C₂×C₃×D₃	—	2	4	no	—
405	C₂×C₃×D₃	—	2	8	no	—
406	C₂×C₃×D₃	—	4	4	no	—
407	C₂×C₃×D₃	—	4	8	no	—
408	C₂×C₃×D₃	—	4	16	no	—
409	C₂×C₃×D₃	—	4	8	no	—
410	C₂×C₃×D₃	—	4	16	no	—
411	C₂×C₃×D₃	C₂²×D₄	1	4	yes	—
412	C₂×C₃×D₃	C₂²×D₄	1	2	yes	—
413	C₂×C₃×D₃	C₂²×D₄	1	2	yes	—
414	C₂×C₃×D₃	H(5,𝔽₂)	1	4	yes	—
415	C₃²×C₄	—	2	4	no	—
416	C₃²×C₄	—	2	4	no	—
417	C₃×Dic₃	—	2	4	no	—
418	C₃×Dic₃	—	2	4	no	—
419	C₂⁵	—	3	1	no	—
420	C₂⁵	—	3	2	no	—
421	C₂²×D₄	—	3	2	no	—
422	C₂²×D₄	—	3	2	no	—
423	C₂²×D₄	—	3	4	no	—
424	C₂²×D₄	—	3	4	no	—
425	C₂²×D₄	—	3	4	no	—
426	C₂²×D₄	—	3	4	no	—
427	C₂²×D₄	—	3	4	no	—
428	C₂²×D₄	—	3	2	no	—
429	C₂²×D₄	—	6	16	no	—
430	C₂²×D₄	C₂×C₃×D₃	1	2	yes	complemented
431	C₂³×C₄	—	3	2	no	—
432	C₂³×C₄	—	3	2	no	—
433	#123	—	3	4	no	—
434	#123	—	3	4	no	—
435	#123	—	3	8	no	—
436	#123	—	3	8	no	—
437	#123	—	3	4	no	—
438	#123	C₂×C₃×D₃	1	4	yes	complemented
439	#121	—	3	4	no	—
440	#121	—	3	8	no	—
441	#121	—	3	4	no	—
442	#121	—	3	4	no	—
443	#121	—	3	8	no	—
444	#121	C₂×C₃×D₃	1	4	yes	complemented
445	#120	—	3	4	no	—
446	#120	—	3	4	no	—
447	#120	—	3	8	no	—
448	#120	—	3	8	no	—
449	#120	—	3	4	no	—
450	#120	C₂×C₃×D₃	1	4	yes	complemented
451	C₂×C₄⋊C₄	—	3	4	no	—
452	C₂×C₂²⋊C₄	—	3	1	no	—
453	C₂×C₂²⋊C₄	—	3	2	no	—
454	C₂×C₂²⋊C₄	—	3	4	no	—
455	C₂×C₂²⋊C₄	—	3	4	no	—
456	C₂×C₂²⋊C₄	—	3	8	no	—
457	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
458	C₂³×C₃	—	2	4	no	—
459	C₂³×C₃	—	2	4	no	—
460	C₂³×C₃	—	2	2	no	—
461	C₂³×C₃	—	2	1	no	—
462	C₂³×C₃	—	2	4	no	—
463	C₂³×C₃	—	2	4	no	—
464	C₂³×C₃	—	3	1	no	—
465	C₂³×C₃	—	3	8	no	—
466	C₂³×C₃	—	3	4	no	—
467	C₂³×C₃	—	3	2	no	—
468	C₂³×C₃	—	3	1	no	—
469	C₂³×C₃	—	3	4	no	—
470	C₂³×C₃	—	3	8	no	—
471	C₂³×C₃	—	3	4	no	—
472	C₂³×C₃	—	4	4	no	—
473	C₂³×C₃	—	4	2	no	—
474	C₂³×C₃	—	4	4	no	—
475	C₂³×C₃	—	4	2	no	—
476	C₂³×C₃	—	4	4	no	—
477	C₂³×C₃	—	6	4	no	—
478	C₂³×C₃	—	6	8	no	—
479	C₂³×C₃	—	6	8	no	—
480	C₂³×C₃	—	6	8	no	—
481	C₂³×C₃	—	6	16	no	—
482	C₂³×C₃	—	6	4	no	—
483	C₂³×C₃	—	8	2	no	—
484	C₂³×C₃	—	8	4	no	—
485	C₂³×C₃	—	12	2	no	—
486	C₂³×C₃	—	12	4	no	—
487	C₂³×C₃	—	12	4	no	—
488	C₂³×C₃	—	12	8	no	—
489	C₂³×C₃	—	12	16	no	—
490	C₂³×C₃	—	12	32	no	—
491	C₂³×C₃	D₃×D₄	1	4	yes	complemented
492	C₂³×C₃	C₂×C₃×D₄	1	4	yes	complemented
493	C₂³×C₃	C₂³×D₃	1	4	yes	—
494	C₂³×C₃	C₂³×D₃	1	2	yes	—
495	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
496	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
497	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
498	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
499	C₂²×D₃	—	2	4	no	—
500	C₂²×D₃	—	2	8	no	—
501	C₂²×D₃	—	2	4	no	—
502	C₂²×D₃	—	2	8	no	—
503	C₂²×D₃	—	2	8	no	—
504	C₂²×D₃	—	2	16	no	—
505	C₂²×D₃	—	4	16	no	—
506	C₂²×D₃	—	4	4	no	—
507	C₂²×D₃	—	4	2	no	—
508	C₂²×D₃	—	4	8	no	—
509	C₂²×D₃	—	4	4	no	—
510	C₂²×D₃	—	4	32	no	—
511	C₂²×D₃	C₂×C₃×D₄	1	8	yes	—
512	C₂²×D₃	C₂×C₃×D₄	1	4	yes	—
513	C₂²×D₃	C₂×C₃×D₄	1	8	yes	complemented
514	C₂²×D₃	C₂×C₃×D₄	1	4	yes	complemented
515	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
516	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
517	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
518	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
519	C₃×D₄	—	2	8	no	—
520	C₃×D₄	—	2	8	no	—
521	C₃×D₄	—	2	8	no	—
522	C₃×D₄	—	2	8	no	—
523	C₃×D₄	—	4	8	no	—
524	C₃×D₄	—	4	8	no	—
525	C₃×D₄	—	4	4	no	—
526	C₃×D₄	—	4	4	no	—
527	C₃×D₄	—	6	8	no	—
528	C₃×D₄	—	6	8	no	—
529	C₃×D₄	—	6	8	no	—
530	C₃×D₄	—	6	8	no	—
531	C₃×D₄	—	6	8	no	—
532	C₃×D₄	—	6	8	no	—
533	C₃×D₄	—	8	4	no	—
534	C₃×D₄	—	12	4	no	—
535	C₃×D₄	—	12	8	no	—
536	C₂×C₃×C₄	—	2	4	no	—
537	C₂×C₃×C₄	—	2	4	no	—
538	C₂×C₃×C₄	—	2	4	no	—
539	C₂×C₃×C₄	—	2	4	no	—
540	C₂×C₃×C₄	—	3	4	no	—
541	C₂×C₃×C₄	—	3	4	no	—
542	C₂×C₃×C₄	—	4	4	no	—
543	C₂×C₃×C₄	—	4	2	no	—
544	C₂×C₃×C₄	—	4	2	no	—
545	C₂×C₃×C₄	—	6	8	no	—
546	C₂×C₃×C₄	—	6	8	no	—
547	C₂×C₃×C₄	—	6	8	no	—
548	C₂×C₃×C₄	—	6	4	no	—
549	C₂×C₃×C₄	—	8	2	no	—
550	C₂×C₃×C₄	—	12	4	no	—
551	C₂×C₃×C₄	—	12	2	no	—
552	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
553	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
554	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
555	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
556	#67	—	2	8	no	—
557	#67	—	2	8	no	—
558	#67	—	2	8	no	—
559	#67	—	2	8	no	—
560	#67	—	4	8	no	—
561	C₂×Dic₃	—	2	4	no	—
562	C₂×Dic₃	—	4	2	no	—
563	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
564	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
565	D₁₂	—	2	8	no	—
566	D₁₂	—	2	8	no	—
567	D₁₂	—	4	4	no	—
568	C₄×D₃	—	2	8	no	—
569	C₄×D₃	—	2	8	no	—
570	C₄×D₃	—	2	8	no	—
571	C₄×D₃	—	4	4	no	—
572	C₂×C₃²	—	2	4	no	—
573	C₂×C₃²	—	2	2	no	—
574	C₂×C₃²	—	4	4	no	—
575	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
576	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
577	C₃×D₃	—	2	4	no	—
578	C₃×D₃	—	2	2	no	—
579	C₃×D₃	—	4	4	no	—
580	C₃×D₃	#534	1	4	yes	direct product factor
581	C₂⁴	—	3	2	no	—
582	C₂⁴	—	3	1	no	—
583	C₂⁴	—	3	1	no	—
584	C₂⁴	—	3	2	no	—
585	C₂⁴	—	3	8	no	—
586	C₂⁴	—	3	4	no	—
587	C₂⁴	—	3	4	no	—
588	C₂⁴	—	3	2	no	—
589	C₂⁴	—	6	8	no	—
590	C₂⁴	—	12	4	no	—
591	C₂⁴	—	12	8	no	—
592	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
593	C₂⁴	C₂²×C₃×D₃	1	2	yes	complemented
594	C₂×D₄	—	2	8	no	—
595	C₂×D₄	—	3	4	no	—
596	C₂×D₄	—	3	4	no	—
597	C₂×D₄	—	3	4	no	—
598	C₂×D₄	—	3	4	no	—
599	C₂×D₄	—	3	8	no	—
600	C₂×D₄	—	3	4	no	—
601	C₂×D₄	—	3	4	no	—
602	C₂×D₄	—	3	4	no	—
603	C₂×D₄	—	6	8	no	—
604	C₂×D₄	—	6	16	no	—
605	C₂×D₄	—	6	16	no	—
606	C₂×D₄	—	6	16	no	—
607	C₂×D₄	—	6	16	no	—
608	C₂×D₄	—	6	8	no	—
609	C₂×D₄	—	6	8	no	—
610	C₂×D₄	—	12	8	no	—
611	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
612	C₂×D₄	C₂²×C₃×D₃	1	4	yes	complemented
613	C₂×D₄	C₂²×C₃×D₃	1	4	yes	complemented
614	C₂²×C₄	—	3	2	no	—
615	C₂²×C₄	—	3	2	no	—
616	C₂²×C₄	—	3	4	no	—
617	C₂²×C₄	—	3	4	no	—
618	C₂²×C₄	—	3	4	no	—
619	C₂²×C₄	—	3	4	no	—
620	C₂²×C₄	—	6	8	no	—
621	C₂²×C₄	—	12	4	no	—
622	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	complemented
623	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	complemented
624	C₄⋊C₄	—	3	8	no	—
625	C₄⋊C₄	—	3	4	no	—
626	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	complemented
627	C₂²⋊C₄	—	3	4	no	—
628	C₂²⋊C₄	—	3	8	no	—
629	C₂²⋊C₄	—	3	8	no	—
630	C₂²⋊C₄	—	3	8	no	—
631	C₂²⋊C₄	—	3	8	no	—
632	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	complemented
633	C₂²⋊C₄	C₂²×C₃×D₃	1	8	yes	complemented
634	C₂²×C₃	—	2	2	no	—
635	C₂²×C₃	—	2	4	no	—
636	C₂²×C₃	—	2	2	no	—
637	C₂²×C₃	—	2	4	no	—
638	C₂²×C₃	—	2	4	no	—
639	C₂²×C₃	—	2	8	no	—
640	C₂²×C₃	—	2	4	no	—
641	C₂²×C₃	—	2	8	no	—
642	C₂²×C₃	—	2	4	no	—
643	C₂²×C₃	—	2	2	no	—
644	C₂²×C₃	—	2	1	no	—
645	C₂²×C₃	—	3	2	no	—
646	C₂²×C₃	—	3	4	no	—
647	C₂²×C₃	—	3	4	no	—
648	C₂²×C₃	—	3	2	no	—
649	C₂²×C₃	—	4	2	no	—
650	C₂²×C₃	—	4	4	no	—
651	C₂²×C₃	—	4	4	no	—
652	C₂²×C₃	—	4	8	no	—
653	C₂²×C₃	—	4	4	no	—
654	C₂²×C₃	—	4	4	no	—
655	C₂²×C₃	—	4	8	no	—
656	C₂²×C₃	—	4	8	no	—
657	C₂²×C₃	—	6	16	no	—
658	C₂²×C₃	—	6	8	no	—
659	C₂²×C₃	—	6	2	no	—
660	C₂²×C₃	—	6	4	no	—
661	C₂²×C₃	—	6	4	no	—
662	C₂²×C₃	—	6	8	no	—
663	C₂²×C₃	—	8	4	no	—
664	C₂²×C₃	—	8	8	no	—
665	C₂²×C₃	—	12	8	no	—
666	C₂²×C₃	—	12	4	no	—
667	C₂²×C₃	—	12	8	no	—
668	C₂²×C₃	—	12	16	no	—
669	C₂²×C₃	—	12	16	no	—
670	C₂²×C₃	C₂×D₃×D₄	1	4	yes	—
671	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
672	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
673	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
674	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
675	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
676	C₂×D₃	—	2	2	no	—
677	C₂×D₃	—	2	4	no	—
678	C₂×D₃	—	2	16	no	—
679	C₂×D₃	—	2	8	no	—
680	C₂×D₃	—	2	4	no	—
681	C₂×D₃	—	2	8	no	—
682	C₂×D₃	—	4	4	no	—
683	C₂×D₃	—	4	8	no	—
684	C₂×D₃	—	4	16	no	—
685	C₂×D₃	—	4	8	no	—
686	C₂×D₃	—	4	16	no	—
687	C₂×D₃	C₂²×C₃×D₄	1	4	yes	—
688	C₂×D₃	C₂²×C₃×D₄	1	2	yes	—
689	C₂×D₃	C₂²×C₃×D₄	1	2	yes	—
690	C₂×D₃	C₃×H(5,𝔽₂)	1	4	yes	—
691	C₃×C₄	—	2	4	no	—
692	C₃×C₄	—	2	4	no	—
693	C₃×C₄	—	2	4	no	—
694	C₃×C₄	—	2	4	no	—
695	C₃×C₄	—	4	4	no	—
696	C₃×C₄	—	4	4	no	—
697	C₃×C₄	—	6	4	no	—
698	C₃×C₄	—	6	4	no	—
699	Dic₃	—	2	4	no	—
700	Dic₃	—	2	4	no	—
701	C₃²	C₂×#534	1	1	yes	characteristic, complemented, Sylow
702	C₂³	—	2	4	no	—
703	C₂³	—	3	1	no	—
704	C₂³	—	3	8	no	—
705	C₂³	—	3	4	no	—
706	C₂³	—	3	2	no	—
707	C₂³	—	3	1	no	—
708	C₂³	—	3	4	no	—
709	C₂³	—	3	8	no	—
710	C₂³	—	3	4	no	—
711	C₂³	—	4	2	no	—
712	C₂³	—	4	4	no	—
713	C₂³	—	6	4	no	—
714	C₂³	—	6	8	no	—
715	C₂³	—	6	8	no	—
716	C₂³	—	6	8	no	—
717	C₂³	—	6	16	no	—
718	C₂³	—	6	4	no	—
719	C₂³	—	12	2	no	—
720	C₂³	—	12	4	no	—
721	C₂³	—	12	4	no	—
722	C₂³	—	12	8	no	—
723	C₂³	—	12	16	no	—
724	C₂³	—	12	32	no	—
725	C₂³	C₃×D₃×D₄	1	4	yes	complemented
726	C₂³	C₂³×C₃×D₃	1	4	yes	—
727	C₂³	C₂³×C₃×D₃	1	2	yes	—
728	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
729	D₄	—	2	8	no	—
730	D₄	—	2	8	no	—
731	D₄	—	4	4	no	—
732	D₄	—	6	8	no	—
733	D₄	—	6	8	no	—
734	D₄	—	6	8	no	—
735	D₄	—	6	8	no	—
736	D₄	—	6	8	no	—
737	D₄	—	6	8	no	—
738	D₄	—	12	4	no	—
739	D₄	—	12	8	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	3	4	no	—
742	C₂×C₄	—	3	4	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	6	8	no	—
745	C₂×C₄	—	6	8	no	—
746	C₂×C₄	—	6	8	no	—
747	C₂×C₄	—	6	4	no	—
748	C₂×C₄	—	12	4	no	—
749	C₂×C₄	—	12	2	no	—
750	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
751	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
752	C₂×C₃	—	2	4	no	—
753	C₂×C₃	—	2	2	no	—
754	C₂×C₃	—	2	4	no	—
755	C₂×C₃	—	2	2	no	—
756	C₂×C₃	—	2	1	no	—
757	C₂×C₃	—	2	2	no	—
758	C₂×C₃	—	3	4	no	—
759	C₂×C₃	—	4	4	no	—
760	C₂×C₃	—	4	2	no	—
761	C₂×C₃	—	4	4	no	—
762	C₂×C₃	—	4	4	no	—
763	C₂×C₃	—	6	4	no	—
764	C₂×C₃	—	6	2	no	—
765	C₂×C₃	—	8	4	no	—
766	C₂×C₃	—	12	4	no	—
767	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
768	C₂×C₃	D₃×H(5,𝔽₂)	1	2	yes	—
769	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
770	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
771	D₃	—	2	4	no	—
772	D₃	—	2	2	no	—
773	D₃	—	4	4	no	—
774	D₃	C₃×#534	1	4	yes	direct product factor
775	C₂²	—	2	2	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	2	8	no	—
779	C₂²	—	3	2	no	—
780	C₂²	—	3	4	no	—
781	C₂²	—	3	4	no	—
782	C₂²	—	3	2	no	—
783	C₂²	—	4	4	no	—
784	C₂²	—	4	8	no	—
785	C₂²	—	6	16	no	—
786	C₂²	—	6	8	no	—
787	C₂²	—	6	2	no	—
788	C₂²	—	6	4	no	—
789	C₂²	—	6	4	no	—
790	C₂²	—	6	8	no	—
791	C₂²	—	12	8	no	—
792	C₂²	—	12	4	no	—
793	C₂²	—	12	8	no	—
794	C₂²	—	12	16	no	—
795	C₂²	—	12	16	no	—
796	C₂²	C₂×C₃×D₃×D₄	1	4	yes	—
797	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
798	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
799	C₄	—	2	4	no	—
800	C₄	—	2	4	no	—
801	C₄	—	6	4	no	—
802	C₄	—	6	4	no	—
803	C₃	—	2	1	no	—
804	C₃	D₃×#534	1	1	yes	characteristic, direct product factor
805	C₃	C₂×C₃×#534	1	1	yes	characteristic, complemented
806	C₂	—	2	4	no	—
807	C₂	—	2	2	no	—
808	C₂	—	3	4	no	—
809	C₂	—	4	4	no	—
810	C₂	—	6	4	no	—
811	C₂	—	6	2	no	—
812	C₂	—	12	4	no	—
813	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
814	C₂	C₃×D₃×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#534	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#534	D₃
hypocenter	C₃	C₂×C₃×#534
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#534

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₃×D₄	C₂	semidirect
2. C₃²×#534	C₂	semidirect
3. C₃×#5804	C₂	semidirect
4. C₃×#5653	C₂	semidirect
5. C₃×D₃×#123	C₂	semidirect
6. C₃×#5605	C₂	semidirect
7. C₃×D₃×#121	C₂	semidirect
8. C₃×#5589	C₂	semidirect
9. C₃×D₃×#120	C₂	semidirect
10. C₃×#5493	C₂	semidirect
11. C₂×C₃×D₃×C₂²⋊C₄	C₂	semidirect
13. D₃×#534	C₃	direct (N × H)
15. C₂⁴×C₃×D₃	C₂²	semidirect
16. C₂²×C₃²×D₄	C₂²	semidirect
17. C₂²×C₃×#67	C₂²	semidirect
18. C₂²×C₃×#67	C₂²	semidirect
21. C₂×C₃×D₃×D₄	C₂²	semidirect
22. C₂×C₃×D₃×D₄	C₂²	semidirect
23. C₂×C₃×D₃×D₄	C₂²	semidirect
24. C₂×C₃×D₃×D₄	C₂²	semidirect
25. C₂²×C₃×D₁₂	C₂²	semidirect
26. C₂²×C₃×C₄×D₃	C₂²	semidirect
27. C₂²×C₃×C₄×D₃	C₂²	semidirect
28. C₃²×#123	C₂²	semidirect
29. C₃²×#121	C₂²	semidirect
30. C₃²×#120	C₂²	semidirect
31. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
32. C₃×#953	C₂²	semidirect
33. C₂×C₃×#217	C₂²	semidirect
34. C₃×#939	C₂²	semidirect
35. C₃×#938	C₂²	semidirect
36. C₃×#937	C₂²	semidirect
37. C₃×#937	C₂²	semidirect
38. C₃×#935	C₂²	semidirect
39. C₃×#930	C₂²	semidirect
40. C₃×#929	C₂²	semidirect
41. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
42. C₃×#895	C₂²	semidirect
43. C₃×#894	C₂²	semidirect
44. C₃×D₃×C₄⋊C₄	C₂²	semidirect
45. C₃×#886	C₂²	semidirect
46. C₃×#884	C₂²	semidirect
47. C₃×#883	C₂²	semidirect
48. C₃×#882	C₂²	semidirect
49. C₃×#882	C₂²	semidirect
50. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
51. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
52. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
54. C₂²×D₃×D₄	C₂×C₃	semidirect
61. C₃×#534	D₃	direct (N × H)
62. C₃×#534	C₂×C₃	semidirect
67. #5804	C₂×C₃	semidirect
68. #5653	C₂×C₃	semidirect
69. D₃×#123	C₂×C₃	semidirect
70. #5605	C₂×C₃	semidirect
71. D₃×#121	C₂×C₃	semidirect
72. #5589	C₂×C₃	semidirect
73. D₃×#120	C₂×C₃	semidirect
74. #5493	C₂×C₃	semidirect
75. C₂×D₃×C₂²⋊C₄	C₂×C₃	semidirect
77. C₂⁴×C₃²	C₂³	semidirect
81. C₂³×C₃×D₃	D₄	semidirect
87. C₂³×C₃×D₃	C₂³	semidirect
88. C₂³×C₃×D₃	C₂³	semidirect
91. C₂×C₃²×D₄	C₂³	semidirect
92. C₂×C₃²×D₄	C₂³	semidirect
93. C₂²×C₃²×C₄	C₂³	semidirect
94. C₂²×C₃²×C₄	C₂³	semidirect
99. C₂×C₃×#67	C₂³	semidirect
100. C₂×C₃×#67	C₂³	semidirect
101. C₂×C₃×#67	C₂³	semidirect
102. C₂²×C₃×Dic₃	C₂³	semidirect
103. C₂²×C₃×Dic₃	C₂³	semidirect
111. C₂×C₃×D₁₂	C₂³	semidirect
112. C₂×C₃×D₁₂	C₂³	semidirect
117. C₂×C₃×C₄×D₃	C₂³	semidirect
118. C₂×C₃×C₄×D₃	C₂³	semidirect
119. C₃²×C₄⋊C₄	C₂³	semidirect
120. C₃²×C₂²⋊C₄	C₂³	semidirect
121. C₃²×C₂²⋊C₄	C₂³	semidirect
122. C₃×#217	C₂³	semidirect
123. C₃×#217	C₂³	semidirect
124. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
125. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
126. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
127. C₃×C₄⋊Dic₃	C₂³	semidirect
128. C₃×Dic₃⋊C₄	C₂³	semidirect
133. C₂⁴×D₃	C₂²×C₃	semidirect
144. C₂²×C₃×D₄	C₂×D₃	semidirect
145. C₂²×C₃×D₄	C₂²×C₃	semidirect
148. C₂²×#67	C₂²×C₃	semidirect
149. C₂²×#67	C₂²×C₃	semidirect
152. C₂×D₃×D₄	C₂²×C₃	semidirect
153. C₂×D₃×D₄	C₂²×C₃	semidirect
154. C₂×D₃×D₄	C₂²×C₃	semidirect
155. C₂×D₃×D₄	C₂²×C₃	semidirect
156. C₂²×D₁₂	C₂²×C₃	semidirect
157. C₂²×C₄×D₃	C₂²×C₃	semidirect
158. C₂²×C₄×D₃	C₂²×C₃	semidirect
165. C₃×#123	C₂×D₃	semidirect
166. C₃×#123	C₂²×C₃	semidirect
173. C₃×#121	C₂×D₃	semidirect
174. C₃×#121	C₂²×C₃	semidirect
181. C₃×#120	C₂×D₃	semidirect
182. C₃×#120	C₂²×C₃	semidirect
190. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
191. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
192. #953	C₂²×C₃	semidirect
193. C₂×#217	C₂²×C₃	semidirect
194. #939	C₂²×C₃	semidirect
195. #938	C₂²×C₃	semidirect
196. #937	C₂²×C₃	semidirect
197. #937	C₂²×C₃	semidirect
198. #935	C₂²×C₃	semidirect
199. #930	C₂²×C₃	semidirect
200. #929	C₂²×C₃	semidirect
201. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
202. #895	C₂²×C₃	semidirect
203. #894	C₂²×C₃	semidirect
204. D₃×C₄⋊C₄	C₂²×C₃	semidirect
205. #886	C₂²×C₃	semidirect
206. #884	C₂²×C₃	semidirect
207. #883	C₂²×C₃	semidirect
208. #882	C₂²×C₃	semidirect
209. #882	C₂²×C₃	semidirect
210. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
211. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
212. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
216. C₂³×C₃²	C₂×D₄	semidirect
234. C₂²×C₃×D₃	C₂×D₄	semidirect
235. C₂²×C₃×D₃	C₂×D₄	semidirect
269. #534	C₃×D₃	direct (N × H)
288. C₂⁴×C₃	C₂²×D₃	semidirect
290. C₂⁴×C₃	C₂³×C₃	semidirect
294. C₂³×D₃	C₃×D₄	semidirect
300. C₂³×D₃	C₂³×C₃	semidirect
301. C₂³×D₃	C₂³×C₃	semidirect
325. C₂×C₃×D₄	C₂²×D₃	semidirect
326. C₂×C₃×D₄	C₂²×D₃	semidirect
328. C₂×C₃×D₄	C₂³×C₃	semidirect
329. C₂×C₃×D₄	C₂³×C₃	semidirect
340. C₂²×C₃×C₄	C₂²×D₃	semidirect
341. C₂²×C₃×C₄	C₂²×D₃	semidirect
342. C₂²×C₃×C₄	C₂³×C₃	semidirect
343. C₂²×C₃×C₄	C₂³×C₃	semidirect
348. C₂×#67	C₂³×C₃	semidirect
349. C₂×#67	C₂³×C₃	semidirect
350. C₂×#67	C₂³×C₃	semidirect
351. C₂²×Dic₃	C₂³×C₃	semidirect
352. C₂²×Dic₃	C₂³×C₃	semidirect
360. C₂×D₁₂	C₂³×C₃	semidirect
361. C₂×D₁₂	C₂³×C₃	semidirect
366. C₂×C₄×D₃	C₂³×C₃	semidirect
367. C₂×C₄×D₃	C₂³×C₃	semidirect
371. C₃×C₄⋊C₄	C₂²×D₃	semidirect
372. C₃×C₄⋊C₄	C₂³×C₃	semidirect
380. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
381. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
382. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
383. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
384. #217	C₂³×C₃	semidirect
385. #217	C₂³×C₃	semidirect
386. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
387. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
388. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
389. C₄⋊Dic₃	C₂³×C₃	semidirect
390. Dic₃⋊C₄	C₂³×C₃	semidirect
430. C₂²×D₄	C₂×C₃×D₃	semidirect
438. #123	C₂×C₃×D₃	semidirect
444. #121	C₂×C₃×D₃	semidirect
450. #120	C₂×C₃×D₃	semidirect
457. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
491. C₂³×C₃	D₃×D₄	semidirect
492. C₂³×C₃	C₂×C₃×D₄	semidirect
513. C₂²×D₃	C₂×C₃×D₄	semidirect
514. C₂²×D₃	C₂×C₃×D₄	semidirect
580. C₃×D₃	#534	direct (N × H)
593. C₂⁴	C₂²×C₃×D₃	semidirect
612. C₂×D₄	C₂²×C₃×D₃	semidirect
613. C₂×D₄	C₂²×C₃×D₃	semidirect
622. C₂²×C₄	C₂²×C₃×D₃	semidirect
623. C₂²×C₄	C₂²×C₃×D₃	semidirect
626. C₄⋊C₄	C₂²×C₃×D₃	semidirect
632. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
633. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
701. C₃²	C₂×#534	semidirect
725. C₂³	C₃×D₃×D₄	semidirect
774. D₃	C₃×#534	direct (N × H)
804. C₃	D₃×#534	direct (N × H)
805. C₃	C₂×C₃×#534	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₃×D₄	2
C₃²×#534	2
C₃×#5804	2
C₃×#5653	2
C₃×D₃×#123	2
C₃×#5605	2
C₃×D₃×#121	2
C₃×#5589	2
C₃×D₃×#120	2
C₃×#5493	2
C₂×C₃×D₃×C₂²⋊C₄	2
C₂×C₃×#534	3
D₃×#534	3

Subgroups — C3×D3×#534 #11900928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#534 #11900928