Subgroups — D₃×#146488 #72255367

Order 3072.

At least 6900 conjugacy classes of subgroups; only the 1287 normal subgroups are shown.

The subgroup lattice has 589 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72255335	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×#34258	C₂	1	1	yes	maximal, characteristic
3	#72255328	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#146488	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×#12585	C₂	1	1	yes	maximal, characteristic, complemented
6	#72253980	C₂	1	1	yes	maximal, characteristic, complemented
7	D₃×#12575	C₂	1	2	yes	maximal, complemented
8	#72253938	C₂	1	2	yes	maximal, complemented
9	#72253910	C₂	1	2	yes	maximal, complemented
10	C₂×D₃×#1795	C₂	1	2	yes	maximal
11	D₃×#12581	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
13	C₂×D₃×#520	C₄	1	1	yes	characteristic, complemented
14	C₂×C₄×D₃×#41	C₄	1	1	yes	characteristic, complemented
15	C₂×D₃×#413	C₂²	1	2	yes	—
16	C₂×D₃×#410	C₂²	1	2	yes	—
17	#10956233	C₂²	1	1	yes	characteristic
18	#10956232	C₄	1	1	yes	characteristic, complemented
19	#10956231	C₂²	1	1	yes	characteristic
20	#10956229	C₄	1	1	yes	characteristic, complemented
21	#10956228	C₄	1	1	yes	characteristic, complemented
22	#10956227	C₄	1	1	yes	characteristic, complemented
23	#10956226	C₂²	1	1	yes	characteristic
24	D₃×#2311	C₂²	1	1	yes	characteristic
25	D₃×#2309	C₄	1	1	yes	characteristic, complemented
26	D₃×#2297	C₂²	1	1	yes	characteristic
27	C₂×D₃×#390	C₄	1	1	yes	characteristic, complemented
28	C₂×#70139	C₂²	1	2	yes	—
29	C₂×#72141	C₂²	1	2	yes	—
30	C₂×#70048	C₂²	1	2	yes	—
31	D₃×#1795	C₄	1	16	yes	complemented
32	#10710169	C₂²	1	1	yes	characteristic, complemented
33	#10710168	C₂²	1	2	yes	complemented
34	#10710157	C₂²	1	1	yes	characteristic, complemented
35	#10710156	C₂²	1	2	yes	complemented
36	#10710139	C₂²	1	2	yes	complemented
37	#10710138	C₂²	1	2	yes	complemented
38	#10710137	C₂²	1	2	yes	complemented
39	C₃×#34258	C₂²	1	1	yes	characteristic
40	C₂×C₃×#1795	C₂²	1	2	yes	—
41	C₃×#12585	C₂²	1	1	yes	characteristic, complemented
42	C₃×#12581	C₂²	1	1	yes	characteristic, complemented
43	C₃×#12575	C₂²	1	2	yes	complemented
44	#146488	D₃	1	1	yes	characteristic, direct product factor
45	C₂²×C₃×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
46	C₂×D₃×H(5,𝔽₂)	C₂×C₄	1	8	yes	—
47	C₂×D₃×H(5,𝔽₂)	D₄	1	4	yes	—
48	C₂×D₃×H(5,𝔽₂)	Q₈	1	4	yes	—
49	C₂²×#1009	C₂×C₄	1	1	yes	characteristic
50	C₂²×#1009	D₄	1	2	yes	—
51	C₂²×#1009	C₂³	1	1	yes	characteristic
52	C₂²×D₃×#41	C₂×C₄	1	1	yes	characteristic
53	C₂²×D₃×#41	D₄	1	2	yes	—
54	C₂²×D₃×#41	C₂³	1	1	yes	characteristic
55	C₂²×#1004	C₂×C₄	1	1	yes	characteristic
56	C₂²×#1004	D₄	1	2	yes	—
57	C₂³×D₃×D₄	C₂×C₄	1	1	yes	characteristic
58	C₂³×D₃×D₄	D₄	1	2	yes	—
59	C₂×C₃×#520	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×C₃×C₄×#41	C₂×C₄	1	1	yes	characteristic, complemented
61	C₂×#5827	C₂×C₄	1	1	yes	characteristic, complemented
62	C₂×Dic₃×#41	C₂×C₄	1	1	yes	characteristic, complemented
63	C₂×#5523	C₂×C₄	1	1	yes	characteristic, complemented
64	C₂×D₃×#117	C₂×C₄	1	1	yes	characteristic
65	C₂×D₃×#117	C₂×C₄	1	1	yes	characteristic
66	C₂×#5522	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂×#5504	C₂×C₄	1	1	yes	characteristic, complemented
68	C₂²×D₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄²×D₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×#235	C₂×C₄	1	1	yes	characteristic, complemented
71	C₂×C₃×#413	C₂³	1	2	yes	—
72	C₂×C₃×#410	C₂³	1	2	yes	—
73	C₃×#2311	C₂³	1	1	yes	characteristic
74	C₃×#2309	C₂×C₄	1	1	yes	characteristic, complemented
75	C₃×#2297	C₂³	1	1	yes	characteristic
76	C₂×C₃×#390	C₂×C₄	1	1	yes	characteristic, complemented
77	#84087	C₂³	1	1	yes	characteristic
78	#84086	C₂³	1	1	yes	characteristic
79	C₂×#5240	C₂³	1	2	yes	—
80	C₂×#5237	C₂³	1	2	yes	—
81	#84044	C₂×C₄	1	1	yes	characteristic, complemented
82	C₂×#5221	C₂×C₄	1	1	yes	characteristic, complemented
83	#82270	C₂×C₄	1	1	yes	characteristic
84	#82269	C₂×C₄	1	1	yes	characteristic, complemented
85	#82269	C₂×C₄	1	1	yes	characteristic, complemented
86	#82228	C₂×C₄	1	1	yes	characteristic
87	#82186	C₂×C₄	1	1	yes	characteristic
88	C₂×#4988	C₂×C₄	1	1	yes	characteristic, complemented
89	#82070	C₂×C₄	1	1	yes	characteristic
90	C₂×#4939	C₂×C₄	1	1	yes	characteristic, complemented
91	D₃×#413	C₂×C₄	1	8	yes	complemented
92	D₃×#410	C₂×C₄	1	8	yes	complemented
93	D₃×#391	D₄	1	1	yes	characteristic
94	D₃×#391	D₄	1	1	yes	characteristic
95	#76478	D₄	1	1	yes	characteristic
96	#76478	D₄	1	1	yes	characteristic
97	D₃×#390	D₄	1	1	yes	characteristic
98	D₃×#390	D₄	1	1	yes	characteristic
99	#76290	D₄	1	1	yes	characteristic
100	#76290	D₄	1	1	yes	characteristic
101	D₃×#386	D₄	1	4	yes	—
102	#74662	D₄	1	4	yes	—
103	C₃×#1795	C₂×C₄	1	8	yes	complemented
104	#72141	C₂×C₄	1	8	yes	complemented
105	#70139	C₂×C₄	1	8	yes	complemented
106	#70048	C₂×C₄	1	8	yes	complemented
107	#34258	C₂×D₃	1	1	yes	characteristic
108	C₂×#1795	C₂×D₃	1	2	yes	—
109	#12585	C₂×D₃	1	1	yes	characteristic, complemented
110	#12581	C₂×D₃	1	1	yes	characteristic, complemented
111	#12575	C₂×D₃	1	2	yes	complemented
112	C₂×C₃×H(5,𝔽₂)	C₂²×C₄	1	4	yes	—
113	C₂×C₃×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
114	C₂×C₃×H(5,𝔽₂)	C₂×Q₈	1	2	yes	—
115	C₂²×C₃×#41	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₃×#41	C₂×D₄	1	2	yes	—
117	C₂²×C₃×#41	C₂⁴	1	1	yes	characteristic
118	C₂³×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
119	C₂³×C₃×D₄	C₂×D₄	1	2	yes	—
120	C₂×#1009	C₄²	1	4	yes	—
121	C₂×#1009	C₂²⋊C₄	1	8	yes	—
122	C₂×#1009	C₄⋊C₄	1	4	yes	—
123	C₂×#1009	C₄⋊C₄	1	8	yes	—
124	C₂×#1009	C₂²×C₄	1	4	yes	—
125	C₂×#1009	C₂×D₄	1	2	yes	—
126	C₂×#1009	C₂×Q₈	1	2	yes	—
127	C₂×D₃×#41	C₄²	1	4	yes	—
128	C₂×D₃×#41	C₂²⋊C₄	1	8	yes	—
129	C₂×D₃×#41	C₄⋊C₄	1	4	yes	—
130	C₂×D₃×#41	C₄⋊C₄	1	8	yes	—
131	C₂×D₃×#41	C₂²×C₄	1	4	yes	—
132	C₂×D₃×#41	C₂×D₄	1	2	yes	—
133	C₂×D₃×#41	C₂×Q₈	1	2	yes	—
134	C₂×D₃×#41	#41	1	2	yes	—
135	C₂×D₃×#41	#41	1	2	yes	—
136	C₂×D₃×#41	#41	1	4	yes	—
137	C₂²×#239	C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×#239	C₂²⋊C₄	1	2	yes	—
139	C₂²×#239	C₂×D₄	1	1	yes	characteristic
140	C₂²×D₃×Q₈	C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×D₃×Q₈	C₂×D₄	1	1	yes	characteristic
142	C₂×#1004	C₄²	1	4	yes	—
143	C₂×#1004	C₂²⋊C₄	1	8	yes	—
144	C₂×#1004	C₄⋊C₄	1	4	yes	—
145	C₂×#1004	C₄⋊C₄	1	8	yes	—
146	C₂²×#237	C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×#237	C₂²⋊C₄	1	2	yes	—
148	C₂²×#237	C₂×D₄	1	1	yes	characteristic
149	C₂²×#237	C₂×D₄	1	2	yes	—
150	C₂²×D₃×D₄	C₄²	1	4	yes	—
151	C₂²×D₃×D₄	C₂²⋊C₄	1	2	yes	—
152	C₂²×D₃×D₄	C₂²⋊C₄	1	2	yes	—
153	C₂²×D₃×D₄	C₂²⋊C₄	1	2	yes	—
154	C₂²×D₃×D₄	C₂²⋊C₄	1	8	yes	—
155	C₂²×D₃×D₄	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×D₃×D₄	C₂²⋊C₄	1	2	yes	—
157	C₂²×D₃×D₄	C₄⋊C₄	1	8	yes	—
158	C₂²×D₃×D₄	C₄⋊C₄	1	4	yes	—
159	C₂²×D₃×D₄	C₂×D₄	1	1	yes	characteristic
160	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
161	C₂²×#235	C₂²×C₄	1	1	yes	characteristic
162	C₂²×#235	C₂²×C₄	1	1	yes	characteristic
163	C₂²×#235	C₂×D₄	1	2	yes	—
164	C₂²×#235	C₂×D₄	1	2	yes	—
165	C₂³×D₁₂	C₂²×C₄	1	1	yes	characteristic
166	C₂³×D₁₂	C₂×D₄	1	2	yes	—
167	C₂³×C₄×D₃	C₂²⋊C₄	1	2	yes	—
168	C₂³×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
169	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
170	C₂×C₃×#117	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₃×#117	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
174	C₂×#926	C₂²×C₄	1	1	yes	characteristic
175	C₂×#926	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
177	C₂²×Dic₃⋊C₄	C₂²⋊C₄	1	2	yes	—
178	C₂²×C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
179	C₂×#892	C₂²⋊C₄	1	1	yes	characteristic
180	C₂×#892	C₂²⋊C₄	1	1	yes	characteristic
181	C₂×D₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
182	C₂×D₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
183	C₂×D₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
184	C₂×#877	C₂²⋊C₄	1	2	yes	—
185	C₂×C₄²×D₃	C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₄²×D₃	C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₄²×D₃	C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₄²×D₃	C₂²⋊C₄	1	1	yes	characteristic
189	C₃×#413	C₂²×C₄	1	4	yes	complemented
190	C₃×#410	C₂²×C₄	1	4	yes	complemented
191	C₃×#391	C₂×D₄	1	1	yes	characteristic
192	C₃×#391	C₂×D₄	1	1	yes	characteristic
193	C₃×#390	C₂×D₄	1	1	yes	characteristic
194	C₃×#390	C₂×D₄	1	1	yes	characteristic
195	C₃×#386	C₂×D₄	1	4	yes	—
196	#5240	C₂²×C₄	1	4	yes	complemented
197	#5237	C₂²×C₄	1	4	yes	complemented
198	#5229	C₂×D₄	1	1	yes	characteristic
199	#5229	C₂×D₄	1	1	yes	characteristic
200	#5221	C₂×D₄	1	1	yes	characteristic
201	#5221	C₂×D₄	1	1	yes	characteristic
202	#5220	C₂×D₄	1	4	yes	—
203	#5213	C₂²⋊C₄	1	4	yes	—
204	#4988	C₂²⋊C₄	1	1	yes	characteristic
205	#4988	C₂²⋊C₄	1	1	yes	characteristic
206	#4973	C₂²⋊C₄	1	1	yes	characteristic
207	#4973	C₂²⋊C₄	1	1	yes	characteristic
208	#4958	C₂²⋊C₄	1	4	yes	—
209	#4939	C₂²⋊C₄	1	1	yes	characteristic
210	#4939	C₂²⋊C₄	1	1	yes	characteristic
211	#4929	C₂²⋊C₄	1	1	yes	characteristic
212	#4929	C₂²⋊C₄	1	1	yes	characteristic
213	C₂²×H(5,𝔽₂)	C₂²×D₃	1	1	yes	characteristic
214	C₂×#520	C₄×D₃	1	1	yes	characteristic, complemented
215	C₂×C₄×#41	C₄×D₃	1	1	yes	characteristic, complemented
216	C₂×#413	C₂²×D₃	1	2	yes	—
217	C₂×#410	C₂²×D₃	1	2	yes	—
218	#2311	C₂²×D₃	1	1	yes	characteristic
219	#2309	C₄×D₃	1	1	yes	characteristic, complemented
220	#2297	C₂²×D₃	1	1	yes	characteristic
221	C₂×#390	C₄×D₃	1	1	yes	characteristic, complemented
222	#1795	C₄×D₃	1	8	yes	complemented
223	C₂⁴×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂⁴×D₃	#120	1	2	yes	—
225	C₂×C₃×#41	C₂×C₄²	1	2	yes	—
226	C₂×C₃×#41	C₂×C₂²⋊C₄	1	4	yes	—
227	C₂×C₃×#41	C₂×C₄⋊C₄	1	2	yes	—
228	C₂×C₃×#41	C₂×C₄⋊C₄	1	4	yes	—
229	C₂×C₃×#41	C₂³×C₄	1	2	yes	—
230	C₂×C₃×#41	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₃×#41	C₂²×Q₈	1	1	yes	characteristic
232	C₂×C₃×#41	C₂×#41	1	1	yes	characteristic
233	C₂×C₃×#41	C₂×#41	1	1	yes	characteristic
234	C₂×C₃×#41	C₂×#41	1	2	yes	—
235	C₂²×C₃×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂²×C₃×Q₈	C₂²×D₄	1	1	yes	characteristic
237	C₂²×C₃×D₄	C₂×C₄²	1	2	yes	—
238	C₂²×C₃×D₄	C₂×C₂²⋊C₄	1	2	yes	—
239	C₂²×C₃×D₄	C₂×C₂²⋊C₄	1	4	yes	—
240	C₂²×C₃×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂²×C₃×D₄	C₂×C₄⋊C₄	1	4	yes	—
242	C₂²×C₃×D₄	C₂×C₄⋊C₄	1	2	yes	—
243	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
244	C₂²×C₃×D₄	C₂²×D₄	1	2	yes	—
245	C₂³×C₃×C₄	C₂×C₂²⋊C₄	1	2	yes	—
246	C₂³×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
247	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	—
248	C₂²×#67	C₂×C₂²⋊C₄	1	2	yes	—
249	C₂²×#67	#120	1	2	yes	—
250	C₂²×#67	#120	1	2	yes	—
251	C₂³×Dic₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂³×Dic₃	C₂×C₂²⋊C₄	1	2	yes	—
253	C₂³×Dic₃	#120	1	2	yes	—
254	C₂×#239	#95	1	4	yes	—
255	C₂×#239	#95	1	8	yes	—
256	C₂×#239	C₄×D₄	1	4	yes	—
257	C₂×#239	#121	1	2	yes	—
258	C₂×#239	C₂²⋊Q₈	1	2	yes	—
259	C₂×D₃×Q₈	#95	1	4	yes	—
260	C₂×D₃×Q₈	#99	1	4	yes	—
261	C₂×D₃×Q₈	#99	1	2	yes	—
262	C₂×D₃×Q₈	#99	1	2	yes	—
263	C₂×D₃×Q₈	C₄×D₄	1	4	yes	—
264	C₂×D₃×Q₈	#121	1	2	yes	—
265	C₂×D₃×Q₈	C₂²⋊Q₈	1	2	yes	—
266	C₂×#237	#95	1	4	yes	—
267	C₂×#237	#95	1	8	yes	—
268	C₂×#237	C₄×D₄	1	4	yes	—
269	C₂×#237	C₄×D₄	1	4	yes	—
270	C₂×#237	C₄×D₄	1	4	yes	—
271	C₂×#237	#121	1	2	yes	—
272	C₂×#237	#121	1	4	yes	—
273	C₂×#237	C₂²⋊Q₈	1	2	yes	—
274	C₂×#237	C₂²⋊Q₈	1	4	yes	—
275	C₂×D₃×D₄	#95	1	8	yes	—
276	C₂×D₃×D₄	#95	1	8	yes	—
277	C₂×D₃×D₄	#95	1	8	yes	—
278	C₂×D₃×D₄	#95	1	4	yes	—
279	C₂×D₃×D₄	#95	1	8	yes	—
280	C₂×D₃×D₄	#99	1	4	yes	—
281	C₂×D₃×D₄	#99	1	2	yes	—
282	C₂×D₃×D₄	#99	1	2	yes	—
283	C₂×D₃×D₄	C₄×D₄	1	4	yes	—
284	C₂×D₃×D₄	C₄×D₄	1	4	yes	—
285	C₂×D₃×D₄	C₄×D₄	1	4	yes	—
286	C₂×D₃×D₄	#121	1	2	yes	—
287	C₂×D₃×D₄	#121	1	4	yes	—
288	C₂×D₃×D₄	C₂²⋊Q₈	1	2	yes	—
289	C₂×D₃×D₄	C₂²⋊Q₈	1	4	yes	—
290	C₂×#235	C₂×C₄²	1	2	yes	—
291	C₂×#235	C₂×C₄²	1	2	yes	—
292	C₂×#235	C₂×C₂²⋊C₄	1	4	yes	—
293	C₂×#235	C₂×C₂²⋊C₄	1	4	yes	—
294	C₂×#235	C₂×C₄⋊C₄	1	2	yes	—
295	C₂×#235	C₂×C₄⋊C₄	1	4	yes	—
296	C₂×#235	C₂×C₄⋊C₄	1	2	yes	—
297	C₂×#235	C₂×C₄⋊C₄	1	4	yes	—
298	C₂×#235	#117	1	2	yes	—
299	C₂×#235	#117	1	2	yes	—
300	C₂×#235	#123	1	4	yes	—
301	C₂×#235	#123	1	4	yes	—
302	C₂²×D₁₂	C₂×C₄²	1	2	yes	—
303	C₂²×D₁₂	C₂×C₂²⋊C₄	1	2	yes	—
304	C₂²×D₁₂	C₂×C₂²⋊C₄	1	4	yes	—
305	C₂²×D₁₂	C₂×C₂²⋊C₄	1	1	yes	characteristic
306	C₂²×D₁₂	C₂×C₂²⋊C₄	1	1	yes	characteristic
307	C₂²×D₁₂	C₂×C₄⋊C₄	1	4	yes	—
308	C₂²×D₁₂	C₂×C₄⋊C₄	1	2	yes	—
309	C₂²×D₁₂	#120	1	2	yes	—
310	C₂²×C₄×D₃	C₂×C₄²	1	2	yes	—
311	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
312	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	2	yes	—
313	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	4	yes	—
314	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
315	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
316	C₂²×C₄×D₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
317	C₂²×C₄×D₃	C₂×C₄⋊C₄	1	2	yes	—
318	C₂²×C₄×D₃	C₂×C₄⋊C₄	1	4	yes	—
319	C₂²×C₄×D₃	#117	1	2	yes	—
320	C₂²×C₄×D₃	#117	1	2	yes	—
321	C₂²×C₄×D₃	#120	1	2	yes	—
322	C₂²×C₄×D₃	#120	1	2	yes	—
323	C₂²×C₄×D₃	#123	1	4	yes	—
324	C₂²×C₄×D₃	#123	1	4	yes	—
325	C₂²×Dic₆	C₂×C₂²⋊C₄	1	1	yes	characteristic
326	C₂²×Dic₆	C₂×C₂²⋊C₄	1	1	yes	characteristic
327	C₂²×Dic₆	#120	1	2	yes	—
328	C₂×C₃×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
329	C₂×C₃×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
330	C₂×C₃×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
331	C₂×C₃×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
332	C₂×C₃×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
333	C₂×#217	C₂×C₂²⋊C₄	1	2	yes	—
334	C₂×C₄⋊Dic₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
335	C₂×C₄⋊Dic₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
336	C₂×C₄×Dic₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
337	C₂×C₄×Dic₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
338	C₂×H(5,𝔽₂)	C₂×C₄×D₃	1	4	yes	—
339	C₂×H(5,𝔽₂)	D₃×D₄	1	2	yes	—
340	C₂×H(5,𝔽₂)	D₃×Q₈	1	2	yes	—
341	C₂²×#41	C₂×C₄×D₃	1	1	yes	characteristic
342	C₂²×#41	D₃×D₄	1	2	yes	—
343	C₂²×#41	C₂³×D₃	1	1	yes	characteristic
344	C₂³×D₄	C₂×C₄×D₃	1	1	yes	characteristic
345	C₂³×D₄	D₃×D₄	1	2	yes	—
346	C₂×#117	C₂×C₄×D₃	1	1	yes	characteristic
347	C₂×#117	C₂×C₄×D₃	1	1	yes	characteristic
348	C₂²×C₄⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
349	C₂²×C₄²	C₂×C₄×D₃	1	1	yes	characteristic
350	#413	C₂×C₄×D₃	1	4	yes	complemented
351	#410	C₂×C₄×D₃	1	4	yes	complemented
352	#391	D₃×D₄	1	1	yes	characteristic
353	#391	D₃×D₄	1	1	yes	characteristic
354	#390	D₃×D₄	1	1	yes	characteristic
355	#390	D₃×D₄	1	1	yes	characteristic
356	#386	D₃×D₄	1	4	yes	—
357	C₂⁴×C₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
358	C₂⁴×C₃	C₂×#120	1	2	yes	—
359	C₂³×D₃	C₄×C₂²⋊C₄	1	2	yes	—
360	C₂³×D₃	#379	1	1	yes	characteristic
361	C₂³×D₃	#379	1	2	yes	—
362	C₂³×D₃	#379	1	1	yes	characteristic
363	C₂³×D₃	#380	1	2	yes	—
364	C₂³×D₃	#385	1	4	yes	—
365	C₂³×D₃	#386	1	4	yes	—
366	C₂×C₃×Q₈	C₂×#95	1	2	yes	—
367	C₂×C₃×Q₈	C₂×#99	1	2	yes	—
368	C₂×C₃×Q₈	C₂×#99	1	2	yes	—
369	C₂×C₃×Q₈	C₂×C₄×D₄	1	2	yes	—
370	C₂×C₃×Q₈	C₂×#121	1	1	yes	characteristic
371	C₂×C₃×Q₈	C₂×C₂²⋊Q₈	1	1	yes	characteristic
372	C₂×C₃×D₄	C₂×#95	1	4	yes	—
373	C₂×C₃×D₄	C₂×#95	1	2	yes	—
374	C₂×C₃×D₄	C₂×#99	1	2	yes	—
375	C₂×C₃×D₄	C₂×#99	1	2	yes	—
376	C₂×C₃×D₄	C₂×C₄×D₄	1	2	yes	—
377	C₂×C₃×D₄	C₂×C₄×D₄	1	2	yes	—
378	C₂×C₃×D₄	C₂×C₄×D₄	1	2	yes	—
379	C₂×C₃×D₄	C₂×#121	1	1	yes	characteristic
380	C₂×C₃×D₄	C₂×#121	1	2	yes	—
381	C₂×C₃×D₄	C₂×C₂²⋊Q₈	1	1	yes	characteristic
382	C₂×C₃×D₄	C₂×C₂²⋊Q₈	1	2	yes	—
383	C₂²×C₃×C₄	C₂²×C₄²	1	1	yes	characteristic
384	C₂²×C₃×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
385	C₂²×C₃×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
386	C₂²×C₃×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
387	C₂²×C₃×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
388	C₂²×C₃×C₄	C₂²×C₄⋊C₄	1	2	yes	—
389	C₂²×C₃×C₄	C₂×#117	1	1	yes	characteristic
390	C₂²×C₃×C₄	C₂×#117	1	1	yes	characteristic
391	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
392	C₂²×C₃×C₄	C₂×#123	1	2	yes	—
393	C₂²×C₃×C₄	C₂×#123	1	2	yes	—
394	C₂×#67	C₄×C₂²⋊C₄	1	4	yes	—
395	C₂×#67	#380	1	4	yes	—
396	C₂×#67	#385	1	4	yes	—
397	C₂×#67	#385	1	4	yes	—
398	C₂×#67	#386	1	4	yes	—
399	C₂×#67	#386	1	4	yes	—
400	C₂²×Dic₃	C₄×C₂²⋊C₄	1	2	yes	—
401	C₂²×Dic₃	#379	1	2	yes	—
402	C₂²×Dic₃	#379	1	1	yes	characteristic
403	C₂²×Dic₃	#379	1	1	yes	characteristic
404	C₂²×Dic₃	#380	1	2	yes	—
405	C₂²×Dic₃	#385	1	4	yes	—
406	C₂²×Dic₃	#386	1	4	yes	—
407	D₃×Q₈	#342	1	8	yes	—
408	D₃×Q₈	#342	1	8	yes	—
409	D₃×D₄	#342	1	8	yes	—
410	D₃×D₄	#342	1	8	yes	—
411	C₂×D₁₂	C₂×#95	1	4	yes	—
412	C₂×D₁₂	C₂×#95	1	2	yes	—
413	C₂×D₁₂	C₄×C₂²⋊C₄	1	2	yes	—
414	C₂×D₁₂	#380	1	2	yes	—
415	C₂×D₁₂	#385	1	4	yes	—
416	C₂×D₁₂	#386	1	4	yes	—
417	C₂×D₁₂	C₂×#99	1	2	yes	—
418	C₂×D₁₂	C₂×#99	1	2	yes	—
419	C₂×C₄×D₃	C₂×#95	1	2	yes	—
420	C₂×C₄×D₃	C₂×#95	1	4	yes	—
421	C₂×C₄×D₃	C₂×#95	1	2	yes	—
422	C₂×C₄×D₃	C₄×C₂²⋊C₄	1	2	yes	—
423	C₂×C₄×D₃	C₄×C₂²⋊C₄	1	2	yes	—
424	C₂×C₄×D₃	#380	1	2	yes	—
425	C₂×C₄×D₃	#380	1	2	yes	—
426	C₂×C₄×D₃	#381	1	2	yes	—
427	C₂×C₄×D₃	#381	1	4	yes	—
428	C₂×C₄×D₃	#381	1	2	yes	—
429	C₂×C₄×D₃	#385	1	4	yes	—
430	C₂×C₄×D₃	#385	1	4	yes	—
431	C₂×C₄×D₃	#386	1	4	yes	—
432	C₂×C₄×D₃	#386	1	4	yes	—
433	C₂×C₄×D₃	C₂×#99	1	2	yes	—
434	C₂×C₄×D₃	C₂×#99	1	1	yes	characteristic
435	C₂×C₄×D₃	C₂×#99	1	1	yes	characteristic
436	C₂×C₄×D₃	C₂×#99	1	2	yes	—
437	C₂×C₄×D₃	C₂×#99	1	1	yes	characteristic
438	C₂×C₄×D₃	C₂×#99	1	1	yes	characteristic
439	C₂×Dic₆	C₂×#95	1	2	yes	—
440	C₂×Dic₆	C₄×C₂²⋊C₄	1	2	yes	—
441	C₂×Dic₆	#380	1	2	yes	—
442	C₂×Dic₆	#385	1	4	yes	—
443	C₂×Dic₆	#386	1	4	yes	—
444	C₂×Dic₆	C₂×#99	1	2	yes	—
445	C₂×Dic₆	C₂×#99	1	2	yes	—
446	C₂×#41	C₄²×D₃	1	2	yes	—
447	C₂×#41	D₃×C₂²⋊C₄	1	4	yes	—
448	C₂×#41	D₃×C₄⋊C₄	1	2	yes	—
449	C₂×#41	D₃×C₄⋊C₄	1	4	yes	—
450	C₂×#41	C₂²×C₄×D₃	1	2	yes	—
451	C₂×#41	C₂×D₃×D₄	1	1	yes	characteristic
452	C₂×#41	C₂×D₃×Q₈	1	1	yes	characteristic
453	C₂×#41	D₃×#41	1	1	yes	characteristic
454	C₂×#41	D₃×#41	1	1	yes	characteristic
455	C₂×#41	D₃×#41	1	2	yes	—
456	C₂²×Q₈	D₃×C₂²⋊C₄	1	1	yes	characteristic
457	C₂²×Q₈	C₂×D₃×D₄	1	1	yes	characteristic
458	C₂²×D₄	C₄²×D₃	1	2	yes	—
459	C₂²×D₄	D₃×C₂²⋊C₄	1	4	yes	—
460	C₂²×D₄	D₃×C₂²⋊C₄	1	2	yes	—
461	C₂²×D₄	D₃×C₂²⋊C₄	1	1	yes	characteristic
462	C₂²×D₄	D₃×C₄⋊C₄	1	4	yes	—
463	C₂²×D₄	D₃×C₄⋊C₄	1	2	yes	—
464	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
465	C₂²×D₄	C₂×D₃×D₄	1	2	yes	—
466	C₂³×C₄	D₃×C₂²⋊C₄	1	2	yes	—
467	C₂³×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
468	C₂³×C₄	C₂×D₃×D₄	1	2	yes	—
469	C₂×C₄⋊C₄	D₃×C₂²⋊C₄	1	1	yes	characteristic
470	C₂×C₄⋊C₄	D₃×C₂²⋊C₄	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	D₃×C₂²⋊C₄	1	2	yes	—
472	C₂×C₄²	D₃×C₂²⋊C₄	1	1	yes	characteristic
473	C₂×C₄²	D₃×C₂²⋊C₄	1	1	yes	characteristic
474	C₂³×C₃	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
475	C₂³×C₃	C₂×#379	1	1	yes	characteristic
476	C₂³×C₃	C₂×#380	1	1	yes	characteristic
477	C₂³×C₃	C₂×#385	1	2	yes	—
478	C₂³×C₃	C₂×#386	1	2	yes	—
479	C₂²×D₃	C₂²⋊#95	1	2	yes	—
480	C₂²×D₃	C₂²⋊#95	1	2	yes	—
481	C₂²×D₃	C₂²⋊#95	1	4	yes	—
482	C₂²×D₃	#1781	1	2	yes	—
483	C₂²×D₃	#1781	1	1	yes	characteristic
484	C₂²×D₃	#1781	1	1	yes	characteristic
485	C₃×Q₈	C₂×#342	1	4	yes	—
486	C₃×D₄	C₂×#342	1	4	yes	—
487	C₂×C₃×C₄	C₂²×#95	1	1	yes	characteristic
488	C₂×C₃×C₄	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
489	C₂×C₃×C₄	C₂×#380	1	1	yes	characteristic
490	C₂×C₃×C₄	C₂×#381	1	1	yes	characteristic
491	C₂×C₃×C₄	C₂×#385	1	2	yes	—
492	C₂×C₃×C₄	C₂×#386	1	2	yes	—
493	C₂×C₃×C₄	C₂²×#99	1	1	yes	characteristic
494	C₂×C₃×C₄	C₂²×#99	1	1	yes	characteristic
495	C₂×C₃×C₄	C₂²×#99	1	1	yes	characteristic
496	C₂×C₃×C₄	C₂²×#99	1	1	yes	characteristic
497	C₂×Dic₃	C₂²⋊#95	1	4	yes	—
498	C₂×Dic₃	C₂²⋊#95	1	2	yes	—
499	C₂×Dic₃	C₂²⋊#95	1	2	yes	—
500	C₂×Dic₃	#1781	1	2	yes	—
501	C₂×Dic₃	#1781	1	1	yes	characteristic
502	C₂×Dic₃	#1781	1	1	yes	characteristic
503	D₁₂	C₂×#342	1	4	yes	—
504	C₄×D₃	C₂×#342	1	2	yes	—
505	C₄×D₃	C₂×#342	1	2	yes	—
506	C₄×D₃	C₂×#342	1	2	yes	—
507	C₄×D₃	C₂×#342	1	2	yes	—
508	C₄×D₃	#1819	1	2	yes	—
509	C₄×D₃	#1819	1	2	yes	—
510	C₄×D₃	#1819	1	2	yes	—
511	C₄×D₃	#1819	1	2	yes	—
512	Dic₆	C₂×#342	1	4	yes	—
513	C₂⁴	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
514	C₂⁴	D₃×#120	1	2	yes	—
515	C₂×Q₈	D₃×#95	1	2	yes	—
516	C₂×Q₈	D₃×#99	1	2	yes	—
517	C₂×Q₈	D₃×#99	1	2	yes	—
518	C₂×Q₈	C₄×D₃×D₄	1	2	yes	—
519	C₂×Q₈	D₃×#121	1	1	yes	characteristic
520	C₂×Q₈	D₃×C₂²⋊Q₈	1	1	yes	characteristic
521	C₂×D₄	D₃×#95	1	4	yes	—
522	C₂×D₄	D₃×#95	1	2	yes	—
523	C₂×D₄	D₃×#99	1	2	yes	—
524	C₂×D₄	D₃×#99	1	2	yes	—
525	C₂×D₄	C₄×D₃×D₄	1	2	yes	—
526	C₂×D₄	C₄×D₃×D₄	1	2	yes	—
527	C₂×D₄	C₄×D₃×D₄	1	2	yes	—
528	C₂×D₄	D₃×#121	1	1	yes	characteristic
529	C₂×D₄	D₃×#121	1	2	yes	—
530	C₂×D₄	D₃×C₂²⋊Q₈	1	1	yes	characteristic
531	C₂×D₄	D₃×C₂²⋊Q₈	1	2	yes	—
532	C₂²×C₄	C₂×C₄²×D₃	1	1	yes	characteristic
533	C₂²×C₄	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
534	C₂²×C₄	C₂×D₃×C₂²⋊C₄	1	2	yes	—
535	C₂²×C₄	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₃×C₄⋊C₄	1	2	yes	—
538	C₂²×C₄	D₃×#117	1	1	yes	characteristic
539	C₂²×C₄	D₃×#117	1	1	yes	characteristic
540	C₂²×C₄	D₃×#120	1	2	yes	—
541	C₂²×C₄	D₃×#123	1	2	yes	—
542	C₂²×C₄	D₃×#123	1	2	yes	—
543	C₂²×C₃	C₂×C₂²⋊#95	1	1	yes	characteristic
544	C₂²×C₃	C₂×#1781	1	1	yes	characteristic
545	C₂²×C₃	C₂×#1781	1	1	yes	characteristic
546	C₂×D₃	#10725	1	2	yes	—
547	C₂×D₃	#10725	1	2	yes	—
548	C₂×D₃	#12716	1	2	yes	—
549	C₂×D₃	#12718	1	2	yes	—
550	C₃×C₄	C₂²×#342	1	1	yes	characteristic
551	C₃×C₄	C₂²×#342	1	1	yes	characteristic
552	C₃×C₄	C₂×#1819	1	1	yes	characteristic
553	C₃×C₄	C₂×#1819	1	1	yes	characteristic
554	Dic₃	#10725	1	2	yes	—
555	Dic₃	#10725	1	2	yes	—
556	C₂³	C₄×D₃×C₂²⋊C₄	1	1	yes	characteristic
557	C₂³	D₃×#379	1	1	yes	characteristic
558	C₂³	D₃×#380	1	1	yes	characteristic
559	C₂³	D₃×#385	1	2	yes	—
560	C₂³	D₃×#386	1	2	yes	—
561	Q₈	D₃×#342	1	4	yes	—
562	D₄	D₃×#342	1	4	yes	—
563	C₂×C₄	C₂×D₃×#95	1	1	yes	characteristic
564	C₂×C₄	C₄×D₃×C₂²⋊C₄	1	1	yes	characteristic
565	C₂×C₄	D₃×#380	1	1	yes	characteristic
566	C₂×C₄	D₃×#381	1	1	yes	characteristic
567	C₂×C₄	D₃×#385	1	2	yes	—
568	C₂×C₄	D₃×#386	1	2	yes	—
569	C₂×C₄	C₂×D₃×#99	1	1	yes	characteristic
570	C₂×C₄	C₂×D₃×#99	1	1	yes	characteristic
571	C₂×C₄	C₂×D₃×#99	1	1	yes	characteristic
572	C₂×C₄	C₂×D₃×#99	1	1	yes	characteristic
573	C₂×C₃	C₂×#10725	1	1	yes	characteristic
574	C₂×C₃	C₂×#12716	1	1	yes	characteristic
575	C₂×C₃	C₂×#12718	1	1	yes	characteristic
576	D₃	#146488	1	4	yes	direct product factor
577	C₂²	D₃×C₂²⋊#95	1	1	yes	characteristic
578	C₂²	D₃×#1781	1	1	yes	characteristic
579	C₂²	D₃×#1781	1	1	yes	characteristic
580	C₄	C₂×D₃×#342	1	1	yes	characteristic
581	C₄	C₂×D₃×#342	1	1	yes	characteristic
582	C₄	D₃×#1819	1	1	yes	characteristic
583	C₄	D₃×#1819	1	1	yes	characteristic
584	C₃	C₂×#146488	1	1	yes	characteristic, complemented, Sylow
585	C₂	D₃×#12718	1	1	yes	characteristic
586	C₂	D₃×#10725	1	1	yes	characteristic
587	C₂	D₃×#12716	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×#1781
commutator	C₂²×C₃×C₄	C₂²×C₄²
Frattini	C₂²×#41	C₂³×D₃
Fitting	C₃×#146488	C₂
socle	C₂²×C₃	C₂×#1781
prime radical	C₂²×D₃×H(5,𝔽₂)	C₂²
cosocle	C₂²×C₃×#41	C₂⁴
hypercenter	#146488	D₃
hypocenter	C₃	C₂×#146488
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×H(5,𝔽₂) ◁ #146488

Complements

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

N	H ≅ G/N	type
1. #72255335	C₂	semidirect
3. #72255328	C₂	semidirect
4. C₃×#146488	C₂	semidirect
5. D₃×#12585	C₂	semidirect
6. #72253980	C₂	semidirect
7. D₃×#12575	C₂	semidirect
8. #72253938	C₂	semidirect
9. #72253910	C₂	semidirect
11. D₃×#12581	C₂	semidirect
13. C₂×D₃×#520	C₄	semidirect
14. C₂×C₄×D₃×#41	C₄	semidirect
18. #10956232	C₄	semidirect
20. #10956229	C₄	semidirect
21. #10956228	C₄	semidirect
22. #10956227	C₄	semidirect
25. D₃×#2309	C₄	semidirect
27. C₂×D₃×#390	C₄	semidirect
31. D₃×#1795	C₄	semidirect
32. #10710169	C₂²	semidirect
33. #10710168	C₂²	semidirect
34. #10710157	C₂²	semidirect
35. #10710156	C₂²	semidirect
36. #10710139	C₂²	semidirect
37. #10710138	C₂²	semidirect
38. #10710137	C₂²	semidirect
41. C₃×#12585	C₂²	semidirect
42. C₃×#12581	C₂²	semidirect
43. C₃×#12575	C₂²	semidirect
44. #146488	D₃	direct (N × H)
59. C₂×C₃×#520	C₂×C₄	semidirect
60. C₂×C₃×C₄×#41	C₂×C₄	semidirect
61. C₂×#5827	C₂×C₄	semidirect
62. C₂×Dic₃×#41	C₂×C₄	semidirect
63. C₂×#5523	C₂×C₄	semidirect
66. C₂×#5522	C₂×C₄	semidirect
67. C₂×#5504	C₂×C₄	semidirect
70. C₂×C₄×#235	C₂×C₄	semidirect
74. C₃×#2309	C₂×C₄	semidirect
76. C₂×C₃×#390	C₂×C₄	semidirect
81. #84044	C₂×C₄	semidirect
82. C₂×#5221	C₂×C₄	semidirect
84. #82269	C₂×C₄	semidirect
85. #82269	C₂×C₄	semidirect
88. C₂×#4988	C₂×C₄	semidirect
90. C₂×#4939	C₂×C₄	semidirect
91. D₃×#413	C₂×C₄	semidirect
92. D₃×#410	C₂×C₄	semidirect
103. C₃×#1795	C₂×C₄	semidirect
104. #72141	C₂×C₄	semidirect
105. #70139	C₂×C₄	semidirect
106. #70048	C₂×C₄	semidirect
109. #12585	C₂×D₃	semidirect
110. #12581	C₂×D₃	semidirect
111. #12575	C₂×D₃	semidirect
189. C₃×#413	C₂²×C₄	semidirect
190. C₃×#410	C₂²×C₄	semidirect
196. #5240	C₂²×C₄	semidirect
197. #5237	C₂²×C₄	semidirect
214. C₂×#520	C₄×D₃	semidirect
215. C₂×C₄×#41	C₄×D₃	semidirect
219. #2309	C₄×D₃	semidirect
221. C₂×#390	C₄×D₃	semidirect
222. #1795	C₄×D₃	semidirect
350. #413	C₂×C₄×D₃	semidirect
351. #410	C₂×C₄×D₃	semidirect
576. D₃	#146488	direct (N × H)
584. C₃	C₂×#146488	semidirect

Maximal subgroups

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

subgroup	index
#72255335	2
D₃×#34258	2
#72255328	2
C₃×#146488	2
C₂×#146488	3
D₃×#12585	2
#72253980	2
D₃×#12575	2
#72253938	2
#72253910	2
C₂×D₃×#1795	2
D₃×#12581	2

Subgroups — D3×#146488 #72255367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#146488 #72255367