Subgroups — C₃×D₃×#550 #11902690

Order 1152.

3628 conjugacy classes of subgroups.

The subgroup lattice has 635 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×#41	C₂	1	2	yes	maximal, complemented
2	C₃²×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5834	C₂	1	2	yes	maximal, complemented
4	C₃×#5718	C₂	1	3	yes	maximal, complemented
5	C₃×D₃×#127	C₂	1	3	yes	maximal, complemented
6	C₃×D₃×#121	C₂	1	6	yes	maximal, complemented
7	C₃×#5599	C₂	1	6	yes	maximal, complemented
8	C₃×#5577	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5553	C₂	1	3	yes	maximal, complemented
11	C₃×C₄×D₃×D₄	C₂	1	3	yes	maximal, complemented
12	C₂×C₃×#550	—	3	1	no	maximal
13	D₃×#550	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃²×#41	C₂²	1	2	yes	complemented
15	C₃×D₃×#41	—	2	16	no	—
16	C₂×C₃×#239	C₂²	1	2	yes	complemented
17	C₂×C₃×D₃×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₃×#237	C₂²	1	6	yes	complemented
19	C₂×C₃×D₃×D₄	C₂²	1	3	yes	—
20	C₂×C₃×D₃×D₄	C₂²	1	6	yes	—
21	C₂×C₃×D₃×D₄	C₂²	1	6	yes	—
22	C₂×C₃×#235	C₂²	1	6	yes	complemented
23	C₂²×C₃×C₄×D₃	C₂²	1	6	yes	—
24	C₃²×#127	C₂²	1	3	yes	complemented
25	C₃²×#121	C₂²	1	6	yes	complemented
26	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₃²×C₄×D₄	C₂²	1	3	yes	complemented
28	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
29	C₃×#940	C₂²	1	6	yes	complemented
30	C₃×#940	C₂²	1	6	yes	complemented
31	C₃×#940	C₂²	1	6	yes	complemented
32	C₃×#939	C₂²	1	12	yes	complemented
33	C₃×#938	C₂²	1	6	yes	complemented
34	C₃×D₄×Dic₃	C₂²	1	3	yes	complemented
35	C₃×#930	C₂²	1	6	yes	complemented
36	C₃×C₄×#67	C₂²	1	6	yes	complemented
37	C₃×#895	C₂²	1	6	yes	complemented
38	C₃×#893	C₂²	1	3	yes	complemented
39	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×D₃×C₄⋊C₄	C₂²	1	3	yes	—
41	C₃×#887	C₂²	1	3	yes	complemented
42	C₃×#884	C₂²	1	12	yes	complemented
43	C₃×#67⋊C₄	C₂²	1	6	yes	complemented
44	C₃×D₃×C₂²⋊C₄	C₂²	1	6	yes	—
45	C₃×#874	C₂²	1	3	yes	complemented
46	C₃×C₄×D₁₂	C₂²	1	3	yes	complemented
47	C₃×C₄²×D₃	C₂²	1	3	yes	—
48	C₃×C₄×Dic₆	C₂²	1	3	yes	complemented
49	C₂²×C₃×#41	—	3	2	no	—
50	C₂×D₃×#41	C₂×C₃	1	2	yes	complemented
51	C₃×#550	—	2	1	no	—
52	C₃×#550	—	3	2	no	—
53	C₃×#550	—	3	3	no	—
54	C₃×#550	—	3	6	no	—
55	C₃×#550	—	3	1	no	—
56	C₃×#550	—	3	3	no	—
57	C₃×#550	D₃	1	1	yes	characteristic, direct product factor
58	C₃×#550	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₃×#127	—	3	3	no	—
60	C₂×C₃×#121	—	3	6	no	—
61	C₂×C₃×C₄×Q₈	—	3	1	no	—
62	C₂×C₃×C₄×D₄	—	3	3	no	—
63	#5834	C₂×C₃	1	2	yes	complemented
64	#5718	C₂×C₃	1	3	yes	complemented
65	D₃×#127	C₂×C₃	1	3	yes	complemented
66	D₃×#121	C₂×C₃	1	6	yes	complemented
67	#5599	C₂×C₃	1	6	yes	complemented
68	#5577	C₂×C₃	1	1	yes	characteristic, complemented
69	C₄×D₃×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
70	#5553	C₂×C₃	1	3	yes	complemented
71	C₄×D₃×D₄	C₂×C₃	1	3	yes	complemented
72	C₂³×C₃×D₃	C₂³	1	6	yes	—
73	C₃²×#41	—	2	8	no	—
74	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
75	C₂×C₃²×D₄	C₂³	1	3	yes	—
76	C₂×C₃²×D₄	C₂³	1	6	yes	—
77	C₂×C₃²×D₄	C₂³	1	6	yes	—
78	C₂²×C₃²×C₄	C₂³	1	6	yes	—
79	C₂×C₃×#67	C₂³	1	6	yes	—
80	C₂×C₃×#67	C₂³	1	12	yes	—
81	C₂×C₃×#67	C₂³	1	12	yes	—
82	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
83	C₃×#239	—	2	8	no	—
84	C₃×D₃×Q₈	D₄	1	8	yes	complemented
85	C₃×#237	—	2	24	no	—
86	C₃×D₃×D₄	—	2	24	no	—
87	C₃×D₃×D₄	—	2	12	no	—
88	C₃×D₃×D₄	—	4	12	no	—
89	C₃×#235	—	2	24	no	—
90	C₂×C₃×D₁₂	C₂³	1	3	yes	—
91	C₂×C₃×D₁₂	C₂³	1	6	yes	—
92	C₂×C₃×D₁₂	C₂³	1	6	yes	—
93	C₂×C₃×C₄×D₃	—	2	24	no	—
94	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
95	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
96	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
97	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
98	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
99	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
100	C₂×C₃×Dic₆	C₂³	1	3	yes	—
101	C₃²×C₄⋊C₄	C₂³	1	3	yes	—
102	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₃²×C₂²⋊C₄	C₂³	1	6	yes	—
104	C₃²×C₄²	C₂³	1	3	yes	—
105	C₃×#217	C₂³	1	6	yes	—
106	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
107	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
108	C₃×C₄⋊Dic₃	C₂³	1	3	yes	—
109	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
110	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
111	C₃×Dic₃⋊C₄	C₂³	1	6	yes	—
112	C₃×C₄×Dic₃	C₂³	1	3	yes	—
113	C₃×C₄×Dic₃	C₂³	1	3	yes	—
114	C₃×C₄×Dic₃	C₂³	1	3	yes	—
115	C₂×#550	—	3	1	no	Sylow
116	C₂×C₃×#41	—	2	2	no	—
117	C₂×C₃×#41	—	3	2	no	—
118	C₂×C₃×#41	—	3	6	no	—
119	C₂×C₃×#41	—	3	6	no	—
120	C₂×C₃×#41	—	6	16	no	—
121	C₂×C₃×#41	C₂×D₃	1	2	yes	complemented
122	C₂×C₃×#41	C₂²×C₃	1	2	yes	complemented
123	C₂²×C₃×Q₈	—	3	1	no	—
124	C₂²×C₃×D₄	—	3	6	no	—
125	C₂²×C₃×D₄	—	3	3	no	—
126	C₂²×C₃×D₄	—	3	6	no	—
127	C₂³×C₃×C₄	—	3	6	no	—
128	D₃×#41	—	2	16	no	—
129	C₂×#239	C₂²×C₃	1	2	yes	complemented
130	C₂×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
131	C₂×#237	C₂²×C₃	1	6	yes	complemented
132	C₂×D₃×D₄	C₂²×C₃	1	6	yes	—
133	C₂×D₃×D₄	C₂²×C₃	1	3	yes	—
134	C₂×D₃×D₄	C₂²×C₃	1	6	yes	—
135	C₂×#235	C₂²×C₃	1	6	yes	complemented
136	C₂²×C₄×D₃	C₂²×C₃	1	6	yes	—
137	C₃×#127	—	2	3	no	—
138	C₃×#127	—	3	6	no	—
139	C₃×#127	—	3	6	no	—
140	C₃×#127	—	3	6	no	—
141	C₃×#127	—	3	3	no	—
142	C₃×#127	C₂×D₃	1	3	yes	complemented
143	C₃×#127	C₂²×C₃	1	3	yes	complemented
144	C₃×#121	—	2	6	no	—
145	C₃×#121	—	3	6	no	—
146	C₃×#121	—	3	12	no	—
147	C₃×#121	—	3	6	no	—
148	C₃×#121	—	3	6	no	—
149	C₃×#121	—	3	12	no	—
150	C₃×#121	C₂×D₃	1	6	yes	complemented
151	C₃×#121	C₂²×C₃	1	6	yes	complemented
152	C₃×C₄×Q₈	—	2	1	no	—
153	C₃×C₄×Q₈	—	3	1	no	—
154	C₃×C₄×Q₈	—	3	3	no	—
155	C₃×C₄×Q₈	—	3	3	no	—
156	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
157	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
158	C₃×C₄×D₄	—	2	3	no	—
159	C₃×C₄×D₄	—	3	3	no	—
160	C₃×C₄×D₄	—	3	6	no	—
161	C₃×C₄×D₄	—	3	3	no	—
162	C₃×C₄×D₄	—	3	6	no	—
163	C₃×C₄×D₄	—	3	3	no	—
164	C₃×C₄×D₄	C₂×D₃	1	3	yes	complemented
165	C₃×C₄×D₄	C₂²×C₃	1	3	yes	complemented
166	C₂×C₃×C₄⋊C₄	—	3	1	no	—
167	C₂×C₃×C₄⋊C₄	—	3	3	no	—
168	C₂×C₃×C₂²⋊C₄	—	3	6	no	—
169	C₂×C₃×C₄²	—	3	3	no	—
170	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
171	#940	C₂²×C₃	1	6	yes	complemented
172	#940	C₂²×C₃	1	6	yes	complemented
173	#940	C₂²×C₃	1	6	yes	complemented
174	#939	C₂²×C₃	1	12	yes	complemented
175	#938	C₂²×C₃	1	6	yes	complemented
176	D₄×Dic₃	C₂²×C₃	1	3	yes	complemented
177	#930	C₂²×C₃	1	6	yes	complemented
178	C₄×#67	C₂²×C₃	1	6	yes	complemented
179	#895	C₂²×C₃	1	6	yes	complemented
180	#893	C₂²×C₃	1	3	yes	complemented
181	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
182	D₃×C₄⋊C₄	C₂²×C₃	1	3	yes	—
183	#887	C₂²×C₃	1	3	yes	complemented
184	#884	C₂²×C₃	1	12	yes	complemented
185	#67⋊C₄	C₂²×C₃	1	6	yes	complemented
186	D₃×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
187	#874	C₂²×C₃	1	3	yes	complemented
188	C₄×D₁₂	C₂²×C₃	1	3	yes	complemented
189	C₄²×D₃	C₂²×C₃	1	3	yes	—
190	C₄×Dic₆	C₂²×C₃	1	3	yes	complemented
191	C₂³×C₃²	C₂⁴	1	6	yes	—
192	C₂²×C₃×D₃	—	2	12	no	—
193	C₂²×C₃×D₃	—	2	12	no	—
194	C₂²×C₃×D₃	—	2	12	no	—
195	C₂²×C₃×D₃	C₂⁴	1	6	yes	—
196	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
197	C₃²×Q₈	C₂×D₄	1	4	yes	complemented
198	C₃²×D₄	—	2	12	no	—
199	C₃²×D₄	—	2	6	no	—
200	C₃²×D₄	—	4	6	no	—
201	C₂×C₃²×C₄	—	2	12	no	—
202	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
203	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
204	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
205	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
206	C₃×#67	—	2	24	no	—
207	C₃×#67	—	2	12	no	—
208	C₃×#67	—	4	12	no	—
209	C₂×C₃×Dic₃	—	2	12	no	—
210	C₂×C₃×Dic₃	C₂⁴	1	3	yes	—
211	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
212	C₂×C₃×Dic₃	C₂⁴	1	3	yes	—
213	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
214	C₃×D₁₂	—	2	12	no	—
215	C₃×D₁₂	—	2	6	no	—
216	C₃×D₁₂	—	4	6	no	—
217	C₃×C₄×D₃	—	2	4	no	—
218	C₃×C₄×D₃	—	2	6	no	—
219	C₃×C₄×D₃	—	2	12	no	—
220	C₃×C₄×D₃	—	2	12	no	—
221	C₃×C₄×D₃	C₂×D₄	1	12	yes	—
222	C₃×C₄×D₃	#41	1	4	yes	complemented
223	C₃×Dic₆	C₂×D₄	1	12	yes	complemented
224	C₂²×#41	—	3	2	no	—
225	#550	—	3	2	no	—
226	#550	—	3	3	no	—
227	#550	—	3	6	no	—
228	#550	—	3	1	no	—
229	#550	—	3	3	no	—
230	#550	C₃×D₃	1	1	yes	characteristic, direct product factor
231	C₂×#127	—	3	3	no	—
232	C₂×#121	—	3	6	no	—
233	C₂×C₄×Q₈	—	3	1	no	—
234	C₂×C₄×D₄	—	3	3	no	—
235	C₂⁴×C₃	—	3	6	no	—
236	C₂³×D₃	C₂³×C₃	1	6	yes	—
237	C₃×#41	—	2	8	no	—
238	C₃×#41	—	2	8	no	—
239	C₃×#41	—	4	8	no	—
240	C₃×#41	—	6	24	no	—
241	C₃×#41	—	6	24	no	—
242	C₃×#41	—	6	8	no	—
243	C₂×C₃×Q₈	—	2	1	no	—
244	C₂×C₃×Q₈	—	3	8	no	—
245	C₂×C₃×Q₈	—	3	3	no	—
246	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
247	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
248	C₂×C₃×D₄	—	2	3	no	—
249	C₂×C₃×D₄	—	2	6	no	—
250	C₂×C₃×D₄	—	2	6	no	—
251	C₂×C₃×D₄	—	3	6	no	—
252	C₂×C₃×D₄	—	3	12	no	—
253	C₂×C₃×D₄	—	3	12	no	—
254	C₂×C₃×D₄	—	3	3	no	—
255	C₂×C₃×D₄	—	3	6	no	—
256	C₂×C₃×D₄	—	3	6	no	—
257	C₂×C₃×D₄	—	6	12	no	—
258	C₂×C₃×D₄	—	6	24	no	—
259	C₂×C₃×D₄	—	12	12	no	—
260	C₂×C₃×D₄	C₂²×D₃	1	3	yes	—
261	C₂×C₃×D₄	C₂²×D₃	1	6	yes	—
262	C₂×C₃×D₄	C₂²×D₃	1	6	yes	—
263	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
264	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
265	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
266	C₂²×C₃×C₄	—	2	6	no	—
267	C₂²×C₃×C₄	—	3	1	no	—
268	C₂²×C₃×C₄	—	3	3	no	—
269	C₂²×C₃×C₄	—	3	6	no	—
270	C₂²×C₃×C₄	—	3	3	no	—
271	C₂²×C₃×C₄	—	3	2	no	—
272	C₂²×C₃×C₄	—	3	6	no	—
273	C₂²×C₃×C₄	—	3	6	no	—
274	C₂²×C₃×C₄	—	6	24	no	—
275	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
276	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
277	C₂×#67	C₂³×C₃	1	6	yes	—
278	C₂×#67	C₂³×C₃	1	12	yes	—
279	C₂×#67	C₂³×C₃	1	12	yes	—
280	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
281	#239	—	2	8	no	—
282	D₃×Q₈	C₃×D₄	1	8	yes	complemented
283	#237	—	2	24	no	—
284	D₃×D₄	—	2	24	no	—
285	D₃×D₄	—	2	12	no	—
286	D₃×D₄	—	4	12	no	—
287	#235	—	2	24	no	—
288	C₂×D₁₂	C₂³×C₃	1	3	yes	—
289	C₂×D₁₂	C₂³×C₃	1	6	yes	—
290	C₂×D₁₂	C₂³×C₃	1	6	yes	—
291	C₂×C₄×D₃	—	2	24	no	—
292	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
293	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
294	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
295	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
296	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
297	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
298	C₂×Dic₆	C₂³×C₃	1	3	yes	—
299	C₃×C₄⋊C₄	—	2	1	no	—
300	C₃×C₄⋊C₄	—	2	3	no	—
301	C₃×C₄⋊C₄	—	3	2	no	—
302	C₃×C₄⋊C₄	—	3	6	no	—
303	C₃×C₄⋊C₄	—	3	1	no	—
304	C₃×C₄⋊C₄	—	3	3	no	—
305	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
306	C₃×C₄⋊C₄	C₂²×D₃	1	3	yes	—
307	C₃×C₄⋊C₄	C₂³×C₃	1	3	yes	—
308	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
309	C₃×C₂²⋊C₄	—	2	6	no	—
310	C₃×C₂²⋊C₄	—	3	6	no	—
311	C₃×C₂²⋊C₄	—	3	6	no	—
312	C₃×C₂²⋊C₄	—	3	6	no	—
313	C₃×C₂²⋊C₄	C₂²×D₃	1	6	yes	—
314	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
315	C₃×C₄²	—	2	3	no	—
316	C₃×C₄²	—	3	3	no	—
317	C₃×C₄²	—	3	3	no	—
318	C₃×C₄²	—	3	3	no	—
319	C₃×C₄²	C₂²×D₃	1	3	yes	—
320	C₃×C₄²	C₂³×C₃	1	3	yes	—
321	#217	C₂³×C₃	1	6	yes	—
322	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
323	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
324	C₄⋊Dic₃	C₂³×C₃	1	3	yes	—
325	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
326	Dic₃⋊C₄	C₂³×C₃	1	6	yes	—
327	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
328	C₄×Dic₃	C₂³×C₃	1	3	yes	—
329	C₄×Dic₃	C₂³×C₃	1	3	yes	—
330	C₄×Dic₃	C₂³×C₃	1	3	yes	—
331	C₂²×C₃²	—	2	6	no	—
332	C₂²×C₃²	—	2	6	no	—
333	C₂²×C₃²	—	2	6	no	—
334	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
335	C₂×C₃×D₃	—	2	6	no	—
336	C₂×C₃×D₃	—	2	6	no	—
337	C₂×C₃×D₃	—	2	6	no	—
338	C₂×C₃×D₃	—	4	24	no	—
339	C₂×C₃×D₃	C₂²×D₄	1	2	yes	—
340	C₂×C₃×D₃	C₂×#41	1	2	yes	—
341	C₂×C₃×D₃	H(5,𝔽₂)	1	2	yes	—
342	C₃²×C₄	—	2	2	no	—
343	C₃²×C₄	—	2	3	no	—
344	C₃²×C₄	C₂²×D₄	1	6	yes	—
345	C₃²×C₄	C₂×#41	1	2	yes	complemented
346	C₃×Dic₃	—	2	2	no	—
347	C₃×Dic₃	—	2	3	no	—
348	C₃×Dic₃	C₂²×D₄	1	6	yes	—
349	C₃×Dic₃	C₂×#41	1	2	yes	complemented
350	C₂×#41	—	3	2	no	—
351	C₂×#41	—	3	6	no	—
352	C₂×#41	—	3	6	no	—
353	C₂×#41	—	6	16	no	—
354	C₂×#41	C₂×C₃×D₃	1	2	yes	complemented
355	C₂²×Q₈	—	3	1	no	—
356	C₂²×D₄	—	3	3	no	—
357	C₂²×D₄	—	3	6	no	—
358	C₂²×D₄	—	3	6	no	—
359	C₂³×C₄	—	3	6	no	—
360	#127	—	3	6	no	—
361	#127	—	3	6	no	—
362	#127	—	3	6	no	—
363	#127	—	3	3	no	—
364	#127	C₂×C₃×D₃	1	3	yes	complemented
365	#121	—	3	6	no	—
366	#121	—	3	12	no	—
367	#121	—	3	6	no	—
368	#121	—	3	6	no	—
369	#121	—	3	12	no	—
370	#121	C₂×C₃×D₃	1	6	yes	complemented
371	C₄×Q₈	—	3	1	no	—
372	C₄×Q₈	—	3	3	no	—
373	C₄×Q₈	—	3	3	no	—
374	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
375	C₄×D₄	—	3	3	no	—
376	C₄×D₄	—	3	6	no	—
377	C₄×D₄	—	3	3	no	—
378	C₄×D₄	—	3	6	no	—
379	C₄×D₄	—	3	3	no	—
380	C₄×D₄	C₂×C₃×D₃	1	3	yes	complemented
381	C₂×C₄⋊C₄	—	3	1	no	—
382	C₂×C₄⋊C₄	—	3	3	no	—
383	C₂×C₂²⋊C₄	—	3	6	no	—
384	C₂×C₄²	—	3	3	no	—
385	C₂³×C₃	—	2	6	no	—
386	C₂³×C₃	—	3	1	no	—
387	C₂³×C₃	—	3	6	no	—
388	C₂³×C₃	—	6	12	no	—
389	C₂³×C₃	—	6	12	no	—
390	C₂³×C₃	—	6	12	no	—
391	C₂³×C₃	C₂³×D₃	1	6	yes	—
392	C₂³×C₃	C₂⁴×C₃	1	6	yes	—
393	C₂²×D₃	—	2	12	no	—
394	C₂²×D₃	—	2	12	no	—
395	C₂²×D₃	—	2	12	no	—
396	C₂²×D₃	C₂⁴×C₃	1	6	yes	—
397	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
398	C₃×Q₈	—	2	4	no	—
399	C₃×Q₈	—	3	12	no	—
400	C₃×Q₈	D₃×D₄	1	4	yes	complemented
401	C₃×Q₈	C₂×C₃×D₄	1	4	yes	complemented
402	C₃×D₄	—	2	12	no	—
403	C₃×D₄	—	2	6	no	—
404	C₃×D₄	—	2	12	no	—
405	C₃×D₄	—	2	6	no	—
406	C₃×D₄	—	4	6	no	—
407	C₃×D₄	—	4	12	no	—
408	C₃×D₄	—	4	6	no	—
409	C₃×D₄	—	4	6	no	—
410	C₃×D₄	—	6	12	no	—
411	C₃×D₄	—	6	24	no	—
412	C₃×D₄	—	6	12	no	—
413	C₃×D₄	—	6	6	no	—
414	C₃×D₄	—	8	6	no	—
415	C₃×D₄	—	12	6	no	—
416	C₃×D₄	—	12	12	no	—
417	C₂×C₃×C₄	—	2	12	no	—
418	C₂×C₃×C₄	—	2	12	no	—
419	C₂×C₃×C₄	—	2	1	no	—
420	C₂×C₃×C₄	—	2	3	no	—
421	C₂×C₃×C₄	—	2	3	no	—
422	C₂×C₃×C₄	—	2	2	no	—
423	C₂×C₃×C₄	—	3	1	no	—
424	C₂×C₃×C₄	—	3	3	no	—
425	C₂×C₃×C₄	—	3	12	no	—
426	C₂×C₃×C₄	—	3	4	no	—
427	C₂×C₃×C₄	—	3	3	no	—
428	C₂×C₃×C₄	—	3	2	no	—
429	C₂×C₃×C₄	—	4	12	no	—
430	C₂×C₃×C₄	—	6	12	no	—
431	C₂×C₃×C₄	—	6	4	no	—
432	C₂×C₃×C₄	—	6	6	no	—
433	C₂×C₃×C₄	—	6	12	no	—
434	C₂×C₃×C₄	—	6	12	no	—
435	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
436	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
437	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
438	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
439	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
440	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
441	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
442	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
443	#67	—	2	24	no	—
444	#67	—	2	12	no	—
445	#67	—	4	12	no	—
446	C₂×Dic₃	—	2	12	no	—
447	C₂×Dic₃	C₂⁴×C₃	1	3	yes	—
448	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
449	C₂×Dic₃	C₂⁴×C₃	1	3	yes	—
450	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
451	D₁₂	—	2	12	no	—
452	D₁₂	—	2	6	no	—
453	D₁₂	—	4	6	no	—
454	C₄×D₃	—	2	4	no	—
455	C₄×D₃	—	2	6	no	—
456	C₄×D₃	—	2	12	no	—
457	C₄×D₃	—	2	12	no	—
458	C₄×D₃	C₂×C₃×D₄	1	12	yes	—
459	C₄×D₃	C₃×#41	1	4	yes	complemented
460	Dic₆	C₂×C₃×D₄	1	12	yes	complemented
461	C₂×C₃²	—	4	6	no	—
462	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
463	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
464	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
465	C₃×D₃	—	4	6	no	—
466	C₃×D₃	#550	1	4	yes	direct product factor
467	C₂⁴	—	3	6	no	—
468	#41	—	2	8	no	—
469	#41	—	6	24	no	—
470	#41	—	6	24	no	—
471	#41	—	6	8	no	—
472	C₂×Q₈	—	3	8	no	—
473	C₂×Q₈	—	3	3	no	—
474	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
475	C₂×D₄	—	3	6	no	—
476	C₂×D₄	—	3	12	no	—
477	C₂×D₄	—	3	12	no	—
478	C₂×D₄	—	3	3	no	—
479	C₂×D₄	—	3	6	no	—
480	C₂×D₄	—	3	6	no	—
481	C₂×D₄	—	6	24	no	—
482	C₂×D₄	—	6	12	no	—
483	C₂×D₄	—	12	12	no	—
484	C₂×D₄	C₂²×C₃×D₃	1	3	yes	—
485	C₂×D₄	C₂²×C₃×D₃	1	6	yes	—
486	C₂×D₄	C₂²×C₃×D₃	1	6	yes	—
487	C₂²×C₄	—	3	1	no	—
488	C₂²×C₄	—	3	3	no	—
489	C₂²×C₄	—	3	6	no	—
490	C₂²×C₄	—	3	3	no	—
491	C₂²×C₄	—	3	2	no	—
492	C₂²×C₄	—	3	6	no	—
493	C₂²×C₄	—	3	6	no	—
494	C₂²×C₄	—	6	24	no	—
495	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
496	C₄⋊C₄	—	3	2	no	—
497	C₄⋊C₄	—	3	1	no	—
498	C₄⋊C₄	—	3	6	no	—
499	C₄⋊C₄	—	3	3	no	—
500	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×C₃×D₃	1	3	yes	—
502	C₂²⋊C₄	—	3	6	no	—
503	C₂²⋊C₄	—	3	6	no	—
504	C₂²⋊C₄	—	3	6	no	—
505	C₂²⋊C₄	C₂²×C₃×D₃	1	6	yes	—
506	C₄²	—	3	3	no	—
507	C₄²	—	3	3	no	—
508	C₄²	—	3	3	no	—
509	C₄²	C₂²×C₃×D₃	1	3	yes	—
510	C₂²×C₃	—	2	6	no	—
511	C₂²×C₃	—	2	6	no	—
512	C₂²×C₃	—	2	6	no	—
513	C₂²×C₃	—	2	6	no	—
514	C₂²×C₃	—	2	6	no	—
515	C₂²×C₃	—	2	6	no	—
516	C₂²×C₃	—	2	1	no	—
517	C₂²×C₃	—	3	2	no	—
518	C₂²×C₃	—	3	2	no	—
519	C₂²×C₃	—	3	2	no	—
520	C₂²×C₃	—	4	6	no	—
521	C₂²×C₃	—	4	6	no	—
522	C₂²×C₃	—	4	6	no	—
523	C₂²×C₃	—	6	6	no	—
524	C₂²×C₃	—	6	6	no	—
525	C₂²×C₃	—	6	6	no	—
526	C₂²×C₃	—	12	24	no	—
527	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
528	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
529	C₂×D₃	—	2	6	no	—
530	C₂×D₃	—	2	6	no	—
531	C₂×D₃	—	2	6	no	—
532	C₂×D₃	—	4	24	no	—
533	C₂×D₃	C₂²×C₃×D₄	1	2	yes	—
534	C₂×D₃	C₂×C₃×#41	1	2	yes	—
535	C₂×D₃	C₃×H(5,𝔽₂)	1	2	yes	—
536	C₃×C₄	—	2	2	no	—
537	C₃×C₄	—	2	3	no	—
538	C₃×C₄	—	2	2	no	—
539	C₃×C₄	—	2	3	no	—
540	C₃×C₄	—	2	6	no	—
541	C₃×C₄	—	2	2	no	—
542	C₃×C₄	—	3	6	no	—
543	C₃×C₄	—	3	2	no	—
544	C₃×C₄	—	4	2	no	—
545	C₃×C₄	—	4	3	no	—
546	C₃×C₄	—	6	2	no	—
547	C₃×C₄	—	6	3	no	—
548	C₃×C₄	C₂×D₃×D₄	1	6	yes	—
549	C₃×C₄	D₃×#41	1	2	yes	complemented
550	C₃×C₄	C₂²×C₃×D₄	1	6	yes	—
551	C₃×C₄	C₂×C₃×#41	1	2	yes	complemented
552	Dic₃	—	2	2	no	—
553	Dic₃	—	2	3	no	—
554	Dic₃	C₂²×C₃×D₄	1	6	yes	—
555	Dic₃	C₂×C₃×#41	1	2	yes	complemented
556	C₃²	C₂×#550	1	1	yes	characteristic, complemented, Sylow
557	C₂³	—	3	1	no	—
558	C₂³	—	3	6	no	—
559	C₂³	—	6	12	no	—
560	C₂³	—	6	12	no	—
561	C₂³	—	6	12	no	—
562	C₂³	C₂³×C₃×D₃	1	6	yes	—
563	Q₈	—	3	12	no	—
564	Q₈	C₃×D₃×D₄	1	4	yes	complemented
565	D₄	—	2	12	no	—
566	D₄	—	2	6	no	—
567	D₄	—	4	6	no	—
568	D₄	—	6	24	no	—
569	D₄	—	6	12	no	—
570	D₄	—	6	12	no	—
571	D₄	—	6	6	no	—
572	D₄	—	12	6	no	—
573	D₄	—	12	12	no	—
574	C₂×C₄	—	2	12	no	—
575	C₂×C₄	—	3	1	no	—
576	C₂×C₄	—	3	3	no	—
577	C₂×C₄	—	3	12	no	—
578	C₂×C₄	—	3	4	no	—
579	C₂×C₄	—	3	3	no	—
580	C₂×C₄	—	3	2	no	—
581	C₂×C₄	—	6	12	no	—
582	C₂×C₄	—	6	4	no	—
583	C₂×C₄	—	6	6	no	—
584	C₂×C₄	—	6	12	no	—
585	C₂×C₄	—	6	12	no	—
586	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
587	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
588	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
589	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
590	C₂×C₃	—	2	1	no	—
591	C₂×C₃	—	2	1	no	—
592	C₂×C₃	—	2	1	no	—
593	C₂×C₃	—	3	4	no	—
594	C₂×C₃	—	4	6	no	—
595	C₂×C₃	—	4	6	no	—
596	C₂×C₃	—	8	6	no	—
597	C₂×C₃	—	12	6	no	—
598	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
599	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
600	C₂×C₃	D₃×H(5,𝔽₂)	1	1	yes	characteristic
601	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
602	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
603	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
604	D₃	—	4	6	no	—
605	D₃	C₃×#550	1	4	yes	direct product factor
606	C₂²	—	2	6	no	—
607	C₂²	—	2	6	no	—
608	C₂²	—	2	6	no	—
609	C₂²	—	3	2	no	—
610	C₂²	—	3	2	no	—
611	C₂²	—	3	2	no	—
612	C₂²	—	6	6	no	—
613	C₂²	—	6	6	no	—
614	C₂²	—	6	6	no	—
615	C₂²	—	12	24	no	—
616	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
617	C₄	—	2	2	no	—
618	C₄	—	2	3	no	—
619	C₄	—	3	6	no	—
620	C₄	—	3	2	no	—
621	C₄	—	6	2	no	—
622	C₄	—	6	3	no	—
623	C₄	C₂×C₃×D₃×D₄	1	6	yes	—
624	C₄	C₃×D₃×#41	1	2	yes	complemented
625	C₃	—	2	1	no	—
626	C₃	D₃×#550	1	1	yes	characteristic, direct product factor
627	C₃	C₂×C₃×#550	1	1	yes	characteristic, complemented
628	C₂	—	3	4	no	—
629	C₂	—	4	6	no	—
630	C₂	—	12	6	no	—
631	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
632	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
633	C₂	C₃×D₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#550	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#550	D₃
hypocenter	C₃	C₂×C₃×#550
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#550

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₃×#41	C₂	semidirect
2. C₃²×#550	C₂	semidirect
3. C₃×#5834	C₂	semidirect
4. C₃×#5718	C₂	semidirect
5. C₃×D₃×#127	C₂	semidirect
6. C₃×D₃×#121	C₂	semidirect
7. C₃×#5599	C₂	semidirect
8. C₃×#5577	C₂	semidirect
9. C₃×C₄×D₃×Q₈	C₂	semidirect
10. C₃×#5553	C₂	semidirect
11. C₃×C₄×D₃×D₄	C₂	semidirect
13. D₃×#550	C₃	direct (N × H)
14. C₂×C₃²×#41	C₂²	semidirect
16. C₂×C₃×#239	C₂²	semidirect
18. C₂×C₃×#237	C₂²	semidirect
22. C₂×C₃×#235	C₂²	semidirect
24. C₃²×#127	C₂²	semidirect
25. C₃²×#121	C₂²	semidirect
26. C₃²×C₄×Q₈	C₂²	semidirect
27. C₃²×C₄×D₄	C₂²	semidirect
28. C₃×Q₈×Dic₃	C₂²	semidirect
29. C₃×#940	C₂²	semidirect
30. C₃×#940	C₂²	semidirect
31. C₃×#940	C₂²	semidirect
32. C₃×#939	C₂²	semidirect
33. C₃×#938	C₂²	semidirect
34. C₃×D₄×Dic₃	C₂²	semidirect
35. C₃×#930	C₂²	semidirect
36. C₃×C₄×#67	C₂²	semidirect
37. C₃×#895	C₂²	semidirect
38. C₃×#893	C₂²	semidirect
41. C₃×#887	C₂²	semidirect
42. C₃×#884	C₂²	semidirect
43. C₃×#67⋊C₄	C₂²	semidirect
45. C₃×#874	C₂²	semidirect
46. C₃×C₄×D₁₂	C₂²	semidirect
48. C₃×C₄×Dic₆	C₂²	semidirect
50. C₂×D₃×#41	C₂×C₃	semidirect
57. C₃×#550	D₃	direct (N × H)
58. C₃×#550	C₂×C₃	semidirect
63. #5834	C₂×C₃	semidirect
64. #5718	C₂×C₃	semidirect
65. D₃×#127	C₂×C₃	semidirect
66. D₃×#121	C₂×C₃	semidirect
67. #5599	C₂×C₃	semidirect
68. #5577	C₂×C₃	semidirect
69. C₄×D₃×Q₈	C₂×C₃	semidirect
70. #5553	C₂×C₃	semidirect
71. C₄×D₃×D₄	C₂×C₃	semidirect
84. C₃×D₃×Q₈	D₄	semidirect
121. C₂×C₃×#41	C₂×D₃	semidirect
122. C₂×C₃×#41	C₂²×C₃	semidirect
129. C₂×#239	C₂²×C₃	semidirect
131. C₂×#237	C₂²×C₃	semidirect
135. C₂×#235	C₂²×C₃	semidirect
142. C₃×#127	C₂×D₃	semidirect
143. C₃×#127	C₂²×C₃	semidirect
150. C₃×#121	C₂×D₃	semidirect
151. C₃×#121	C₂²×C₃	semidirect
156. C₃×C₄×Q₈	C₂×D₃	semidirect
157. C₃×C₄×Q₈	C₂²×C₃	semidirect
164. C₃×C₄×D₄	C₂×D₃	semidirect
165. C₃×C₄×D₄	C₂²×C₃	semidirect
170. Q₈×Dic₃	C₂²×C₃	semidirect
171. #940	C₂²×C₃	semidirect
172. #940	C₂²×C₃	semidirect
173. #940	C₂²×C₃	semidirect
174. #939	C₂²×C₃	semidirect
175. #938	C₂²×C₃	semidirect
176. D₄×Dic₃	C₂²×C₃	semidirect
177. #930	C₂²×C₃	semidirect
178. C₄×#67	C₂²×C₃	semidirect
179. #895	C₂²×C₃	semidirect
180. #893	C₂²×C₃	semidirect
183. #887	C₂²×C₃	semidirect
184. #884	C₂²×C₃	semidirect
185. #67⋊C₄	C₂²×C₃	semidirect
187. #874	C₂²×C₃	semidirect
188. C₄×D₁₂	C₂²×C₃	semidirect
190. C₄×Dic₆	C₂²×C₃	semidirect
197. C₃²×Q₈	C₂×D₄	semidirect
222. C₃×C₄×D₃	#41	semidirect
223. C₃×Dic₆	C₂×D₄	semidirect
230. #550	C₃×D₃	direct (N × H)
282. D₃×Q₈	C₃×D₄	semidirect
345. C₃²×C₄	C₂×#41	semidirect
349. C₃×Dic₃	C₂×#41	semidirect
354. C₂×#41	C₂×C₃×D₃	semidirect
364. #127	C₂×C₃×D₃	semidirect
370. #121	C₂×C₃×D₃	semidirect
374. C₄×Q₈	C₂×C₃×D₃	semidirect
380. C₄×D₄	C₂×C₃×D₃	semidirect
400. C₃×Q₈	D₃×D₄	semidirect
401. C₃×Q₈	C₂×C₃×D₄	semidirect
459. C₄×D₃	C₃×#41	semidirect
460. Dic₆	C₂×C₃×D₄	semidirect
466. C₃×D₃	#550	direct (N × H)
549. C₃×C₄	D₃×#41	semidirect
551. C₃×C₄	C₂×C₃×#41	semidirect
555. Dic₃	C₂×C₃×#41	semidirect
556. C₃²	C₂×#550	semidirect
564. Q₈	C₃×D₃×D₄	semidirect
605. D₃	C₃×#550	direct (N × H)
624. C₄	C₃×D₃×#41	semidirect
626. C₃	D₃×#550	direct (N × H)
627. C₃	C₂×C₃×#550	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×#41	2
C₃²×#550	2
C₃×#5834	2
C₃×#5718	2
C₃×D₃×#127	2
C₃×D₃×#121	2
C₃×#5599	2
C₃×#5577	2
C₃×C₄×D₃×Q₈	2
C₃×#5553	2
C₃×C₄×D₃×D₄	2
C₂×C₃×#550	3
D₃×#550	3

Subgroups — C3×D3×#550 #11902690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#550 #11902690