Subgroups — C₂×C₃×#3076 #10679086

Order 768.

2162 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₄×#41	C₂	1	1	yes	maximal, characteristic
3	C₃×#3076	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#479	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#478	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#427	C₂	1	2	yes	maximal, complemented
11	C₂²×C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#416	C₂	1	2	yes	maximal
13	C₂×#3076	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₈	C₂²	1	2	yes	—
16	C₃×#533	—	2	4	no	—
17	C₃×#533	C₂²	1	8	yes	complemented
18	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×#125	C₂²	1	2	yes	—
21	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
22	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
23	C₃×C₄×#41	—	2	4	no	—
24	C₃×C₄×#41	C₂²	1	8	yes	—
25	C₂×C₃×C₄×Q₈	—	2	1	no	—
26	C₂×C₃×C₄×Q₈	—	2	1	no	—
27	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×D₄	—	2	1	no	—
30	C₂×C₃×C₄×D₄	—	2	1	no	—
31	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×#117	—	2	1	no	—
34	C₂×C₃×#117	C₂²	1	1	yes	characteristic
35	C₂×C₃×#117	C₂²	1	2	yes	—
36	C₂²×C₃×C₄²	—	2	1	no	—
37	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
38	C₃×#479	C₂²	1	16	yes	complemented
39	C₃×#478	C₂²	1	16	yes	complemented
40	C₃×#477	C₂²	1	8	yes	complemented
41	C₃×#476	C₂²	1	8	yes	complemented
42	C₃×#475	C₂²	1	8	yes	complemented
43	C₃×#474	C₂²	1	8	yes	complemented
44	C₃×#427	C₂²	1	16	yes	complemented
45	C₂×C₃×#107	C₂²	1	2	yes	—
46	C₂×C₃×#107	C₂²	1	2	yes	—
47	C₂×C₃×#106	C₂²	1	2	yes	—
48	C₂×C₃×#106	C₂²	1	2	yes	—
49	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	—
52	C₂×C₃×C₄⋊C₈	C₂²	1	8	yes	complemented
53	C₃×#416	C₂²	1	16	yes	—
54	C₂×C₃×#103	C₂²	1	2	yes	—
55	C₂×C₃×#103	C₂²	1	2	yes	—
56	C₂×C₃×#102	C₂²	1	2	yes	—
57	C₂×C₃×#102	C₂²	1	2	yes	—
58	C₂×#533	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₄×#41	C₂×C₃	1	1	yes	characteristic
60	#3076	C₂×C₃	1	16	yes	direct product factor
61	C₂×#479	C₂×C₃	1	2	yes	complemented
62	C₂×#477	C₂×C₃	1	1	yes	characteristic, complemented
63	C₂×#475	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂×#478	C₂×C₃	1	2	yes	complemented
65	C₂×#476	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂×#474	C₂×C₃	1	1	yes	characteristic, complemented
67	C₂×#427	C₂×C₃	1	2	yes	complemented
68	C₂²×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
69	C₂×#416	C₂×C₃	1	2	yes	—
70	C₂×C₃×#41	—	2	2	no	—
71	C₂×C₃×#41	—	2	4	no	—
72	C₂×C₃×#41	Q₈	1	8	yes	complemented
73	C₂×C₃×#41	C₂³	1	4	yes	—
74	C₂²×C₃×Q₈	—	2	1	no	—
75	C₂²×C₃×Q₈	—	2	1	no	—
76	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
77	C₂²×C₃×D₄	—	2	1	no	—
78	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
79	C₂³×C₃×C₄	—	2	1	no	—
80	C₂³×C₃×C₄	—	2	1	no	—
81	C₂³×C₃×C₄	—	2	1	no	—
82	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
83	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
84	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
85	C₂²×C₃×C₈	—	2	8	no	—
86	C₂²×C₃×C₈	C₂³	1	2	yes	—
87	C₂²×C₃×C₈	C₂³	1	2	yes	—
88	C₂²×C₃×C₈	C₂³	1	8	yes	—
89	C₃×C₄⋊Q₈	—	2	2	no	—
90	C₃×C₄⋊Q₈	—	2	2	no	—
91	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
92	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
93	C₃×#125	—	2	4	no	—
94	C₃×#125	C₂³	1	8	yes	—
95	C₃×C₂²⋊Q₈	—	2	8	no	—
96	C₃×C₂²⋊Q₈	—	2	8	no	—
97	C₃×C₄×Q₈	—	2	8	no	—
98	C₃×C₄×Q₈	—	2	8	no	—
99	C₃×C₄×Q₈	—	2	2	no	—
100	C₃×C₄×Q₈	—	2	2	no	—
101	C₃×C₄×Q₈	C₂³	1	4	yes	—
102	C₃×C₄×Q₈	C₂³	1	4	yes	—
103	C₃×C₄×D₄	—	2	8	no	—
104	C₃×C₄×D₄	—	2	8	no	—
105	C₃×C₄×D₄	—	2	2	no	—
106	C₃×C₄×D₄	—	2	2	no	—
107	C₃×C₄×D₄	C₂³	1	4	yes	—
108	C₃×C₄×D₄	C₂³	1	4	yes	—
109	C₃×#117	—	2	2	no	—
110	C₃×#117	—	2	4	no	—
111	C₃×#117	—	2	8	no	—
112	C₃×#117	C₂³	1	8	yes	—
113	C₃×#117	C₂³	1	4	yes	—
114	C₂×C₃×C₄⋊C₄	—	2	1	no	—
115	C₂×C₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₃×C₄⋊C₄	—	2	2	no	—
117	C₂×C₃×C₄⋊C₄	—	2	2	no	—
118	C₂×C₃×C₄⋊C₄	—	2	1	no	—
119	C₂×C₃×C₄⋊C₄	—	2	1	no	—
120	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
124	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
126	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
128	C₂×C₃×C₄²	—	2	1	no	—
129	C₂×C₃×C₄²	—	2	1	no	—
130	C₂×C₃×C₄²	—	2	1	no	—
131	C₂×C₃×C₄²	—	2	2	no	—
132	C₂×C₃×C₄²	—	2	8	no	—
133	C₂×C₃×C₄²	D₄	1	4	yes	—
134	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
135	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
136	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
137	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
138	C₂×C₃×C₄²	C₂³	1	4	yes	—
139	C₃×#107	C₂³	1	8	yes	—
140	C₃×#107	C₂³	1	8	yes	—
141	C₃×#106	C₂³	1	8	yes	—
142	C₃×#106	C₂³	1	8	yes	—
143	C₃×C₄⋊C₈	C₂³	1	4	yes	—
144	C₃×C₄⋊C₈	C₂³	1	4	yes	—
145	C₃×C₄⋊C₈	C₂³	1	8	yes	—
146	C₃×#103	C₂³	1	8	yes	—
147	C₃×#103	C₂³	1	8	yes	—
148	C₃×#102	C₂³	1	8	yes	—
149	C₃×#102	C₂³	1	8	yes	—
150	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
151	C₂³×C₈	C₂²×C₃	1	2	yes	—
152	#533	—	2	4	no	—
153	#533	C₂²×C₃	1	8	yes	complemented
154	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
156	C₂×#125	C₂²×C₃	1	2	yes	—
157	C₂×C₂²⋊Q₈	—	2	1	no	—
158	C₂×C₂²⋊Q₈	—	2	1	no	—
159	C₄×#41	—	2	4	no	—
160	C₄×#41	C₂²×C₃	1	8	yes	—
161	C₂×C₄×Q₈	—	2	1	no	—
162	C₂×C₄×Q₈	—	2	1	no	—
163	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
164	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
165	C₂×C₄×D₄	—	2	1	no	—
166	C₂×C₄×D₄	—	2	1	no	—
167	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
168	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
169	C₂×#117	—	2	1	no	—
170	C₂×#117	C₂²×C₃	1	2	yes	—
171	C₂×#117	C₂²×C₃	1	1	yes	characteristic
172	C₂²×C₄²	—	2	1	no	—
173	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
174	#479	C₂²×C₃	1	16	yes	complemented
175	#478	C₂²×C₃	1	16	yes	complemented
176	#477	C₂²×C₃	1	8	yes	complemented
177	#476	C₂²×C₃	1	8	yes	complemented
178	#475	C₂²×C₃	1	8	yes	complemented
179	#474	C₂²×C₃	1	8	yes	complemented
180	#427	C₂²×C₃	1	16	yes	complemented
181	C₂×#107	C₂²×C₃	1	2	yes	—
182	C₂×#107	C₂²×C₃	1	2	yes	—
183	C₂×#106	C₂²×C₃	1	2	yes	—
184	C₂×#106	C₂²×C₃	1	2	yes	—
185	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	—
186	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
187	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
188	C₂×C₄⋊C₈	C₂²×C₃	1	8	yes	complemented
189	#416	C₂²×C₃	1	16	yes	—
190	C₂×#103	C₂²×C₃	1	2	yes	—
191	C₂×#103	C₂²×C₃	1	2	yes	—
192	C₂×#102	C₂²×C₃	1	2	yes	—
193	C₂×#102	C₂²×C₃	1	2	yes	—
194	C₂⁴×C₃	—	2	1	no	—
195	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
196	C₃×#41	—	2	16	no	—
197	C₃×#41	—	2	8	no	—
198	C₃×#41	C₂×Q₈	1	16	yes	complemented
199	C₂×C₃×Q₈	—	2	1	no	—
200	C₂×C₃×Q₈	—	2	4	no	—
201	C₂×C₃×Q₈	—	2	4	no	—
202	C₂×C₃×Q₈	—	2	2	no	—
203	C₂×C₃×Q₈	—	4	4	no	—
204	C₂×C₃×Q₈	—	4	4	no	—
205	C₂×C₃×Q₈	C₂×Q₈	1	4	yes	—
206	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
207	C₂×C₃×D₄	—	2	8	no	—
208	C₂×C₃×D₄	—	2	4	no	—
209	C₂×C₃×D₄	—	2	1	no	—
210	C₂×C₃×D₄	—	2	2	no	—
211	C₂×C₃×D₄	C₂×Q₈	1	4	yes	—
212	C₂×C₃×D₄	C₂⁴	1	2	yes	—
213	C₂²×C₃×C₄	—	2	1	no	—
214	C₂²×C₃×C₄	—	2	8	no	—
215	C₂²×C₃×C₄	—	2	4	no	—
216	C₂²×C₃×C₄	—	2	4	no	—
217	C₂²×C₃×C₄	—	2	1	no	—
218	C₂²×C₃×C₄	—	2	1	no	—
219	C₂²×C₃×C₄	—	2	2	no	—
220	C₂²×C₃×C₄	—	2	2	no	—
221	C₂²×C₃×C₄	—	2	4	no	—
222	C₂²×C₃×C₄	—	2	4	no	—
223	C₂²×C₃×C₄	—	4	2	no	—
224	C₂²×C₃×C₄	—	4	4	no	—
225	C₂²×C₃×C₄	—	4	4	no	—
226	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
230	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
231	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
232	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
235	C₂²×C₃×C₄	#41	1	4	yes	—
236	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
237	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
238	C₂×C₃×C₈	—	2	4	no	—
239	C₂×C₃×C₈	—	2	4	no	—
240	C₂×C₃×C₈	—	2	16	no	—
241	C₂×C₃×C₈	C₂⁴	1	4	yes	—
242	C₂×C₃×C₈	C₂⁴	1	4	yes	—
243	C₃×C₄⋊C₄	—	2	4	no	—
244	C₃×C₄⋊C₄	—	2	4	no	—
245	C₃×C₄⋊C₄	—	2	8	no	—
246	C₃×C₄⋊C₄	—	2	8	no	—
247	C₃×C₄⋊C₄	—	2	4	no	—
248	C₃×C₄⋊C₄	—	2	4	no	—
249	C₃×C₄⋊C₄	—	2	1	no	—
250	C₃×C₄⋊C₄	—	2	1	no	—
251	C₃×C₄⋊C₄	—	2	2	no	—
252	C₃×C₄⋊C₄	—	2	2	no	—
253	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
254	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
255	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
256	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
257	C₃×C₂²⋊C₄	—	2	4	no	—
258	C₃×C₂²⋊C₄	—	2	8	no	—
259	C₃×C₂²⋊C₄	—	2	4	no	—
260	C₃×C₂²⋊C₄	—	2	4	no	—
261	C₃×C₄²	—	2	4	no	—
262	C₃×C₄²	—	2	4	no	—
263	C₃×C₄²	—	2	4	no	—
264	C₃×C₄²	—	2	8	no	—
265	C₃×C₄²	C₂×D₄	1	4	yes	—
266	C₃×C₄²	C₂×D₄	1	4	yes	—
267	C₃×C₄²	C₂×D₄	1	2	yes	—
268	C₃×C₄²	C₂×D₄	1	2	yes	—
269	C₃×C₄²	C₂⁴	1	2	yes	—
270	C₃×C₄²	C₂⁴	1	2	yes	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	4	no	—
273	C₂×#41	C₃×Q₈	1	8	yes	complemented
274	C₂×#41	C₂³×C₃	1	4	yes	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
278	C₂²×D₄	—	2	1	no	—
279	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
280	C₂³×C₄	—	2	1	no	—
281	C₂³×C₄	—	2	1	no	—
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
284	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
286	C₂²×C₈	—	2	8	no	—
287	C₂²×C₈	C₂³×C₃	1	2	yes	—
288	C₂²×C₈	C₂³×C₃	1	2	yes	—
289	C₂²×C₈	C₂³×C₃	1	8	yes	—
290	C₄⋊Q₈	—	2	2	no	—
291	C₄⋊Q₈	—	2	2	no	—
292	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
293	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
294	#125	—	2	4	no	—
295	#125	C₂³×C₃	1	8	yes	—
296	C₂²⋊Q₈	—	2	8	no	—
297	C₂²⋊Q₈	—	2	8	no	—
298	C₄×Q₈	—	2	8	no	—
299	C₄×Q₈	—	2	8	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×Q₈	C₂³×C₃	1	4	yes	—
303	C₄×Q₈	C₂³×C₃	1	4	yes	—
304	C₄×D₄	—	2	8	no	—
305	C₄×D₄	—	2	8	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	C₂³×C₃	1	4	yes	—
309	C₄×D₄	C₂³×C₃	1	4	yes	—
310	#117	—	2	2	no	—
311	#117	—	2	4	no	—
312	#117	—	2	8	no	—
313	#117	C₂³×C₃	1	4	yes	—
314	#117	C₂³×C₃	1	8	yes	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	2	2	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	8	no	—
334	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
335	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
336	C₂×C₄²	C₃×D₄	1	4	yes	—
337	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₃	1	4	yes	—
340	#107	C₂³×C₃	1	8	yes	—
341	#107	C₂³×C₃	1	8	yes	—
342	#106	C₂³×C₃	1	8	yes	—
343	#106	C₂³×C₃	1	8	yes	—
344	C₄⋊C₈	C₂³×C₃	1	4	yes	—
345	C₄⋊C₈	C₂³×C₃	1	4	yes	—
346	C₄⋊C₈	C₂³×C₃	1	8	yes	—
347	#103	C₂³×C₃	1	8	yes	—
348	#103	C₂³×C₃	1	8	yes	—
349	#102	C₂³×C₃	1	8	yes	—
350	#102	C₂³×C₃	1	8	yes	—
351	C₂³×C₃	—	2	2	no	—
352	C₂³×C₃	—	2	2	no	—
353	C₂³×C₃	—	2	4	no	—
354	C₂³×C₃	—	2	2	no	—
355	C₂³×C₃	—	4	2	no	—
356	C₂³×C₃	—	4	2	no	—
357	C₂³×C₃	C₂²⋊Q₈	1	4	yes	—
358	C₂³×C₃	C₂²×D₄	1	2	yes	—
359	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
360	C₃×Q₈	—	2	4	no	—
361	C₃×Q₈	—	2	2	no	—
362	C₃×Q₈	—	4	8	no	—
363	C₃×Q₈	—	4	8	no	—
364	C₃×Q₈	C₂²×Q₈	1	4	yes	—
365	C₃×D₄	—	2	16	no	—
366	C₃×D₄	—	2	4	no	—
367	C₃×D₄	—	2	2	no	—
368	C₃×D₄	C₂²×Q₈	1	4	yes	—
369	C₂×C₃×C₄	—	2	4	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	16	no	—
375	C₂×C₃×C₄	—	2	8	no	—
376	C₂×C₃×C₄	—	2	2	no	—
377	C₂×C₃×C₄	—	2	2	no	—
378	C₂×C₃×C₄	—	2	4	no	—
379	C₂×C₃×C₄	—	2	4	no	—
380	C₂×C₃×C₄	—	4	4	no	—
381	C₂×C₃×C₄	—	4	8	no	—
382	C₂×C₃×C₄	—	4	2	no	—
383	C₂×C₃×C₄	—	4	4	no	—
384	C₂×C₃×C₄	—	4	2	no	—
385	C₂×C₃×C₄	—	4	4	no	—
386	C₂×C₃×C₄	—	4	8	no	—
387	C₂×C₃×C₄	C₂²⋊Q₈	1	4	yes	—
388	C₂×C₃×C₄	C₂²⋊Q₈	1	8	yes	—
389	C₂×C₃×C₄	#135	1	4	yes	—
390	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
391	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
392	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
393	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
394	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
396	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
397	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
398	C₂×C₃×C₄	C₂×#41	1	2	yes	—
399	C₂×C₃×C₄	C₂×#41	1	4	yes	—
400	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
401	C₃×C₈	—	2	4	no	—
402	C₃×C₈	—	2	4	no	—
403	C₂⁴	—	2	1	no	—
404	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
405	#41	—	2	16	no	—
406	#41	—	2	8	no	—
407	#41	C₂×C₃×Q₈	1	16	yes	complemented
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	2	4	no	—
410	C₂×Q₈	—	2	4	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	4	4	no	—
413	C₂×Q₈	—	4	4	no	—
414	C₂×Q₈	C₂×C₃×Q₈	1	4	yes	—
415	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	C₂×C₃×Q₈	1	4	yes	—
421	C₂×D₄	C₂⁴×C₃	1	2	yes	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	8	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
439	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
440	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
441	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
442	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
443	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
444	C₂²×C₄	C₃×#41	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
446	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
447	C₂×C₈	—	2	4	no	—
448	C₂×C₈	—	2	4	no	—
449	C₂×C₈	—	2	16	no	—
450	C₂×C₈	C₂⁴×C₃	1	4	yes	—
451	C₂×C₈	C₂⁴×C₃	1	4	yes	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	8	no	—
455	C₄⋊C₄	—	2	8	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
463	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
464	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
465	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	8	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₄²	—	2	4	no	—
471	C₄²	—	2	4	no	—
472	C₄²	—	2	4	no	—
473	C₄²	—	2	8	no	—
474	C₄²	C₂×C₃×D₄	1	4	yes	—
475	C₄²	C₂×C₃×D₄	1	4	yes	—
476	C₄²	C₂×C₃×D₄	1	2	yes	—
477	C₄²	C₂×C₃×D₄	1	2	yes	—
478	C₄²	C₂⁴×C₃	1	2	yes	—
479	C₄²	C₂⁴×C₃	1	2	yes	—
480	C₂²×C₃	—	2	8	no	—
481	C₂²×C₃	—	2	2	no	—
482	C₂²×C₃	—	2	2	no	—
483	C₂²×C₃	—	2	4	no	—
484	C₂²×C₃	—	4	8	no	—
485	C₂²×C₃	—	4	2	no	—
486	C₂²×C₃	—	4	2	no	—
487	C₂²×C₃	C₂×C₂²⋊Q₈	1	4	yes	—
488	C₂²×C₃	C₂×C₂²⋊Q₈	1	2	yes	—
489	C₂²×C₃	C₂×#135	1	2	yes	—
490	C₂²×C₃	#575	1	2	yes	—
491	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
492	C₃×C₄	—	2	4	no	—
493	C₃×C₄	—	2	2	no	—
494	C₃×C₄	—	2	2	no	—
495	C₃×C₄	—	2	2	no	—
496	C₃×C₄	—	4	2	no	—
497	C₃×C₄	—	4	4	no	—
498	C₃×C₄	—	4	2	no	—
499	C₃×C₄	—	4	4	no	—
500	C₃×C₄	C₂×C₂²⋊Q₈	1	4	yes	—
501	C₃×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
502	C₃×C₄	C₂×#135	1	4	yes	—
503	C₃×C₄	C₂³×Q₈	1	1	yes	characteristic
504	C₃×C₄	C₂²×#41	1	1	yes	characteristic
505	C₂³	—	2	2	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	4	2	no	—
511	C₂³	C₃×C₂²⋊Q₈	1	4	yes	—
512	C₂³	C₂²×C₃×D₄	1	2	yes	—
513	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
514	Q₈	—	2	2	no	—
515	Q₈	—	2	4	no	—
516	Q₈	—	4	8	no	—
517	Q₈	—	4	8	no	—
518	Q₈	C₂²×C₃×Q₈	1	4	yes	—
519	D₄	—	2	16	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	4	no	—
522	D₄	C₂²×C₃×Q₈	1	4	yes	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	16	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	4	8	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	4	no	—
540	C₂×C₄	—	4	8	no	—
541	C₂×C₄	C₃×C₂²⋊Q₈	1	4	yes	—
542	C₂×C₄	C₃×C₂²⋊Q₈	1	8	yes	—
543	C₂×C₄	C₃×#135	1	4	yes	—
544	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
545	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
546	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
547	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
548	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
549	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
550	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
551	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
552	C₂×C₄	C₂×C₃×#41	1	2	yes	—
553	C₂×C₄	C₂×C₃×#41	1	4	yes	—
554	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
555	C₈	—	2	4	no	—
556	C₈	—	2	4	no	—
557	C₂×C₃	—	2	4	no	—
558	C₂×C₃	—	4	4	no	—
559	C₂×C₃	#3076	1	4	yes	direct product factor
560	C₂×C₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
561	C₂×C₃	C₂²×#135	1	1	yes	characteristic
562	C₂×C₃	C₂×#575	1	1	yes	characteristic
563	C₂²	—	2	2	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	8	no	—
566	C₂²	—	2	4	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	8	no	—
570	C₂²	C₂×C₃×C₂²⋊Q₈	1	4	yes	—
571	C₂²	C₂×C₃×C₂²⋊Q₈	1	2	yes	—
572	C₂²	C₂×C₃×#135	1	2	yes	—
573	C₂²	C₃×#575	1	2	yes	—
574	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
575	C₄	—	2	4	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	2	no	—
579	C₄	—	4	2	no	—
580	C₄	—	4	4	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	4	no	—
583	C₄	C₂×C₃×C₂²⋊Q₈	1	4	yes	—
584	C₄	C₂×C₃×C₂²⋊Q₈	1	2	yes	—
585	C₄	C₂×C₃×#135	1	4	yes	—
586	C₄	C₂³×C₃×Q₈	1	1	yes	characteristic
587	C₄	C₂²×C₃×#41	1	1	yes	characteristic
588	C₃	C₂×#3076	1	1	yes	characteristic, direct product factor, Sylow
589	C₂	—	2	4	no	—
590	C₂	—	4	4	no	—
591	C₂	C₃×#3076	1	4	yes	direct product factor
592	C₂	C₂²×C₃×C₂²⋊Q₈	1	1	yes	characteristic
593	C₂	C₂²×C₃×#135	1	1	yes	characteristic
594	C₂	C₂×C₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂³×C₃	C₂²×D₄
prime radical	C₂²×C₃×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#533	C₂	semidirect
3. C₃×#3076	C₂	direct (N × H)
4. C₂×C₃×#479	C₂	semidirect
5. C₂×C₃×#477	C₂	semidirect
6. C₂×C₃×#475	C₂	semidirect
7. C₂×C₃×#478	C₂	semidirect
8. C₂×C₃×#476	C₂	semidirect
9. C₂×C₃×#474	C₂	semidirect
10. C₂×C₃×#427	C₂	semidirect
11. C₂²×C₃×C₄⋊C₈	C₂	semidirect
13. C₂×#3076	C₃	direct (N × H)
17. C₃×#533	C₂²	semidirect
38. C₃×#479	C₂²	semidirect
39. C₃×#478	C₂²	semidirect
40. C₃×#477	C₂²	semidirect
41. C₃×#476	C₂²	semidirect
42. C₃×#475	C₂²	semidirect
43. C₃×#474	C₂²	semidirect
44. C₃×#427	C₂²	semidirect
52. C₂×C₃×C₄⋊C₈	C₂²	semidirect
58. C₂×#533	C₂×C₃	semidirect
60. #3076	C₂×C₃	direct (N × H)
61. C₂×#479	C₂×C₃	semidirect
62. C₂×#477	C₂×C₃	semidirect
63. C₂×#475	C₂×C₃	semidirect
64. C₂×#478	C₂×C₃	semidirect
65. C₂×#476	C₂×C₃	semidirect
66. C₂×#474	C₂×C₃	semidirect
67. C₂×#427	C₂×C₃	semidirect
68. C₂²×C₄⋊C₈	C₂×C₃	semidirect
72. C₂×C₃×#41	Q₈	semidirect
153. #533	C₂²×C₃	semidirect
174. #479	C₂²×C₃	semidirect
175. #478	C₂²×C₃	semidirect
176. #477	C₂²×C₃	semidirect
177. #476	C₂²×C₃	semidirect
178. #475	C₂²×C₃	semidirect
179. #474	C₂²×C₃	semidirect
180. #427	C₂²×C₃	semidirect
188. C₂×C₄⋊C₈	C₂²×C₃	semidirect
198. C₃×#41	C₂×Q₈	semidirect
273. C₂×#41	C₃×Q₈	semidirect
407. #41	C₂×C₃×Q₈	semidirect
559. C₂×C₃	#3076	direct (N × H)
588. C₃	C₂×#3076	direct (N × H)
591. C₂	C₃×#3076	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#533	2
C₂×C₃×C₄×#41	2
C₃×#3076	2
C₂×C₃×#479	2
C₂×C₃×#477	2
C₂×C₃×#475	2
C₂×C₃×#478	2
C₂×C₃×#476	2
C₂×C₃×#474	2
C₂×C₃×#427	2
C₂²×C₃×C₄⋊C₈	2
C₂×C₃×#416	2
C₂×#3076	3

Subgroups — C2×C3×#3076 #10679086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#3076 #10679086