Subgroups — C₂×C₃×#3054 #10679048

Order 768.

2918 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#525	C₂	1	2	yes	maximal, complemented
4	C₃×#3054	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#470	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#469	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#468	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#416	C₂	1	2	yes	maximal, complemented
10	C₂×#3054	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂²×C₃×#41	C₂²	1	2	yes	—
12	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×#135	—	2	8	no	—
14	C₂×C₃×#135	C₂²	1	8	yes	complemented
15	C₂²×C₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×SD₁₆	C₂²	1	2	yes	complemented
17	C₂²×C₃×D₈	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃×M₁₆	—	2	8	no	—
19	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
20	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
21	C₂²×C₃×M₁₆	C₂²	1	8	yes	complemented
22	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
23	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
24	C₃×#525	—	2	8	no	—
25	C₃×#525	C₂²	1	16	yes	complemented
26	C₂×C₃×#123	—	2	2	no	—
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
28	C₂×C₃×#121	C₂²	1	4	yes	—
29	C₂×C₃×#120	—	2	2	no	—
30	C₂×C₃×C₄×D₄	—	2	4	no	—
31	C₂×C₃×#117	C₂²	1	2	yes	—
32	C₃×#470	C₂²	1	16	yes	complemented
33	C₃×#469	C₂²	1	16	yes	complemented
34	C₃×#468	C₂²	1	32	yes	complemented
35	C₃×#427	C₂²	1	8	yes	complemented
36	C₂×C₃×#107	C₂²	1	2	yes	complemented
37	C₂×C₃×#106	C₂²	1	2	yes	complemented
38	C₃×#416	C₂²	1	16	yes	complemented
39	C₂×C₃×#103	C₂²	1	4	yes	complemented
40	C₂×C₃×#102	C₂²	1	4	yes	complemented
41	C₂²×#135	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂³×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×#525	C₂×C₃	1	2	yes	complemented
44	#3054	C₂×C₃	1	16	yes	direct product factor
45	C₂×#470	C₂×C₃	1	2	yes	complemented
46	C₂×#469	C₂×C₃	1	2	yes	complemented
47	C₂×#468	C₂×C₃	1	4	yes	complemented
48	C₂×#427	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×#416	C₂×C₃	1	2	yes	complemented
50	C₂⁵×C₃	D₄	1	1	yes	characteristic
51	C₂×C₃×#41	—	2	4	no	—
52	C₂×C₃×#41	—	2	8	no	—
53	C₂×C₃×#41	—	2	8	no	—
54	C₂×C₃×#41	C₂³	1	8	yes	—
55	C₂²×C₃×Q₈	C₂³	1	2	yes	—
56	C₂²×C₃×D₄	—	2	2	no	—
57	C₂²×C₃×D₄	—	2	4	no	—
58	C₂²×C₃×D₄	C₂³	1	2	yes	—
59	C₂³×C₃×C₄	—	2	4	no	—
60	C₂³×C₃×C₄	—	2	4	no	—
61	C₂³×C₃×C₄	—	2	2	no	—
62	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
63	C₂³×C₃×C₄	D₄	1	4	yes	—
64	C₂³×C₃×C₄	D₄	1	2	yes	—
65	C₂³×C₃×C₄	C₂³	1	2	yes	—
66	C₂³×C₃×C₄	C₂³	1	4	yes	—
67	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
68	C₃×#135	—	2	32	no	—
69	C₂×C₃×Q₁₆	—	2	4	no	—
70	C₂×C₃×Q₁₆	C₂³	1	4	yes	complemented
71	C₂×C₃×SD₁₆	—	2	8	no	—
72	C₂×C₃×SD₁₆	C₂³	1	8	yes	complemented
73	C₂×C₃×D₈	—	2	4	no	—
74	C₂×C₃×D₈	C₂³	1	4	yes	complemented
75	C₂×C₃×M₁₆	—	2	8	no	—
76	C₂×C₃×M₁₆	—	2	8	no	—
77	C₂×C₃×M₁₆	—	2	32	no	—
78	C₂×C₃×M₁₆	C₂³	1	8	yes	—
79	C₂×C₃×M₁₆	C₂³	1	8	yes	—
80	C₂²×C₃×C₈	—	2	4	no	—
81	C₂²×C₃×C₈	D₄	1	8	yes	complemented
82	C₂²×C₃×C₈	C₂³	1	2	yes	—
83	C₂²×C₃×C₈	C₂³	1	4	yes	—
84	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₃×C₈	C₂³	1	4	yes	—
87	C₃×#123	—	2	16	no	—
88	C₃×C₂²⋊Q₈	—	2	8	no	—
89	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
90	C₃×#121	—	2	8	no	—
91	C₃×#121	C₂³	1	16	yes	—
92	C₃×#120	—	2	16	no	—
93	C₃×C₄×D₄	—	2	32	no	—
94	C₃×#117	—	2	4	no	—
95	C₃×#117	C₂³	1	8	yes	—
96	C₂×C₃×C₄⋊C₄	—	2	4	no	—
97	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
99	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
100	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
101	C₂×C₃×C₄²	—	2	2	no	—
102	C₃×#107	C₂³	1	8	yes	complemented
103	C₃×#106	C₂³	1	8	yes	complemented
104	C₃×#103	C₂³	1	16	yes	complemented
105	C₃×#102	C₂³	1	16	yes	complemented
106	C₂²×#41	C₂²×C₃	1	2	yes	—
107	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
108	C₂×#135	—	2	8	no	—
109	C₂×#135	C₂²×C₃	1	8	yes	complemented
110	C₂²×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
111	C₂²×SD₁₆	C₂²×C₃	1	2	yes	complemented
112	C₂²×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₂²×M₁₆	—	2	8	no	—
114	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
115	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
116	C₂²×M₁₆	C₂²×C₃	1	8	yes	complemented
117	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
118	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
119	#525	—	2	8	no	—
120	#525	C₂²×C₃	1	16	yes	complemented
121	C₂×#123	—	2	2	no	—
122	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
123	C₂×#121	C₂²×C₃	1	4	yes	—
124	C₂×#120	—	2	2	no	—
125	C₂×C₄×D₄	—	2	4	no	—
126	C₂×#117	C₂²×C₃	1	2	yes	—
127	#470	C₂²×C₃	1	16	yes	complemented
128	#469	C₂²×C₃	1	16	yes	complemented
129	#468	C₂²×C₃	1	32	yes	complemented
130	#427	C₂²×C₃	1	8	yes	complemented
131	C₂×#107	C₂²×C₃	1	2	yes	complemented
132	C₂×#106	C₂²×C₃	1	2	yes	complemented
133	#416	C₂²×C₃	1	16	yes	complemented
134	C₂×#103	C₂²×C₃	1	4	yes	complemented
135	C₂×#102	C₂²×C₃	1	4	yes	complemented
136	C₂⁴×C₃	—	2	4	no	—
137	C₂⁴×C₃	—	2	2	no	—
138	C₂⁴×C₃	—	4	4	no	—
139	C₂⁴×C₃	C₂×D₄	1	2	yes	—
140	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
141	C₂⁴×C₃	C₂×D₄	1	4	yes	—
142	C₃×#41	—	2	16	no	—
143	C₃×#41	—	2	16	no	—
144	C₃×#41	—	4	16	no	—
145	C₂×C₃×Q₈	—	2	2	no	—
146	C₂×C₃×Q₈	—	2	4	no	—
147	C₂×C₃×Q₈	—	2	4	no	—
148	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
149	C₂×C₃×D₄	—	2	16	no	—
150	C₂×C₃×D₄	—	2	8	no	—
151	C₂×C₃×D₄	—	2	4	no	—
152	C₂×C₃×D₄	—	2	2	no	—
153	C₂×C₃×D₄	—	2	4	no	—
154	C₂×C₃×D₄	—	4	16	no	—
155	C₂×C₃×D₄	—	4	8	no	—
156	C₂×C₃×D₄	C₂⁴	1	4	yes	—
157	C₂²×C₃×C₄	—	2	4	no	—
158	C₂²×C₃×C₄	—	2	8	no	—
159	C₂²×C₃×C₄	—	2	16	no	—
160	C₂²×C₃×C₄	—	2	4	no	—
161	C₂²×C₃×C₄	—	2	8	no	—
162	C₂²×C₃×C₄	—	2	4	no	—
163	C₂²×C₃×C₄	—	2	8	no	—
164	C₂²×C₃×C₄	—	2	4	no	—
165	C₂²×C₃×C₄	—	2	2	no	—
166	C₂²×C₃×C₄	—	2	8	no	—
167	C₂²×C₃×C₄	—	4	8	no	—
168	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
169	C₂²×C₃×C₄	C₂×D₄	1	8	yes	—
170	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
171	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
172	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
173	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
174	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₃×C₄	#41	1	4	yes	—
176	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
177	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
179	C₃×Q₁₆	—	2	8	no	—
180	C₃×SD₁₆	—	2	16	no	—
181	C₃×D₈	—	2	8	no	—
182	C₃×M₁₆	—	2	16	no	—
183	C₃×M₁₆	—	2	16	no	—
184	C₂×C₃×C₈	—	2	4	no	—
185	C₂×C₃×C₈	—	2	8	no	—
186	C₂×C₃×C₈	C₂×D₄	1	4	yes	—
187	C₂×C₃×C₈	C₂×D₄	1	4	yes	—
188	C₂×C₃×C₈	C₂×D₄	1	16	yes	complemented
189	C₂×C₃×C₈	C₂⁴	1	4	yes	—
190	C₂×C₃×C₈	C₂⁴	1	2	yes	—
191	C₂×C₃×C₈	C₂⁴	1	2	yes	—
192	C₃×C₄⋊C₄	—	2	16	no	—
193	C₃×C₄⋊C₄	—	2	4	no	—
194	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
195	C₃×C₂²⋊C₄	—	2	8	no	—
196	C₃×C₂²⋊C₄	—	2	16	no	—
197	C₃×C₂²⋊C₄	—	2	16	no	—
198	C₃×C₄²	—	2	8	no	—
199	C₂⁵	C₃×D₄	1	1	yes	characteristic
200	C₂×#41	—	2	4	no	—
201	C₂×#41	—	2	8	no	—
202	C₂×#41	—	2	8	no	—
203	C₂×#41	C₂³×C₃	1	8	yes	—
204	C₂²×Q₈	C₂³×C₃	1	2	yes	—
205	C₂²×D₄	—	2	4	no	—
206	C₂²×D₄	—	2	2	no	—
207	C₂²×D₄	C₂³×C₃	1	2	yes	—
208	C₂³×C₄	—	2	4	no	—
209	C₂³×C₄	—	2	4	no	—
210	C₂³×C₄	—	2	2	no	—
211	C₂³×C₄	C₃×D₄	1	2	yes	—
212	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
213	C₂³×C₄	C₃×D₄	1	4	yes	—
214	C₂³×C₄	C₂³×C₃	1	2	yes	—
215	C₂³×C₄	C₂³×C₃	1	4	yes	—
216	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
217	#135	—	2	32	no	—
218	C₂×Q₁₆	—	2	4	no	—
219	C₂×Q₁₆	C₂³×C₃	1	4	yes	complemented
220	C₂×SD₁₆	—	2	8	no	—
221	C₂×SD₁₆	C₂³×C₃	1	8	yes	complemented
222	C₂×D₈	—	2	4	no	—
223	C₂×D₈	C₂³×C₃	1	4	yes	complemented
224	C₂×M₁₆	—	2	8	no	—
225	C₂×M₁₆	—	2	8	no	—
226	C₂×M₁₆	—	2	32	no	—
227	C₂×M₁₆	C₂³×C₃	1	8	yes	—
228	C₂×M₁₆	C₂³×C₃	1	8	yes	—
229	C₂²×C₈	—	2	4	no	—
230	C₂²×C₈	C₃×D₄	1	8	yes	complemented
231	C₂²×C₈	C₂³×C₃	1	2	yes	—
232	C₂²×C₈	C₂³×C₃	1	4	yes	—
233	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₃	1	4	yes	—
236	#123	—	2	16	no	—
237	C₂²⋊Q₈	—	2	8	no	—
238	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
239	#121	—	2	8	no	—
240	#121	C₂³×C₃	1	16	yes	—
241	#120	—	2	16	no	—
242	C₄×D₄	—	2	32	no	—
243	#117	—	2	4	no	—
244	#117	C₂³×C₃	1	8	yes	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₂²⋊C₄	—	2	4	no	—
249	C₂×C₂²⋊C₄	—	2	4	no	—
250	C₂×C₄²	—	2	2	no	—
251	#107	C₂³×C₃	1	8	yes	complemented
252	#106	C₂³×C₃	1	8	yes	complemented
253	#103	C₂³×C₃	1	16	yes	complemented
254	#102	C₂³×C₃	1	16	yes	complemented
255	C₂³×C₃	—	2	4	no	—
256	C₂³×C₃	—	2	8	no	—
257	C₂³×C₃	—	2	4	no	—
258	C₂³×C₃	—	2	8	no	—
259	C₂³×C₃	—	2	4	no	—
260	C₂³×C₃	—	4	8	no	—
261	C₂³×C₃	—	4	16	no	—
262	C₂³×C₃	—	4	4	no	—
263	C₂³×C₃	—	4	8	no	—
264	C₂³×C₃	#121	1	4	yes	—
265	C₂³×C₃	C₂²×D₄	1	4	yes	—
266	C₂³×C₃	C₂²×D₄	1	2	yes	—
267	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
268	C₃×Q₈	—	2	4	no	—
269	C₃×Q₈	—	2	4	no	—
270	C₃×Q₈	—	4	4	no	—
271	C₃×D₄	—	2	4	no	—
272	C₃×D₄	—	2	4	no	—
273	C₃×D₄	—	4	32	no	—
274	C₃×D₄	—	4	16	no	—
275	C₃×D₄	—	4	4	no	—
276	C₂×C₃×C₄	—	2	8	no	—
277	C₂×C₃×C₄	—	2	4	no	—
278	C₂×C₃×C₄	—	2	16	no	—
279	C₂×C₃×C₄	—	2	8	no	—
280	C₂×C₃×C₄	—	2	4	no	—
281	C₂×C₃×C₄	—	2	4	no	—
282	C₂×C₃×C₄	—	2	8	no	—
283	C₂×C₃×C₄	—	2	4	no	—
284	C₂×C₃×C₄	—	4	4	no	—
285	C₂×C₃×C₄	—	4	8	no	—
286	C₂×C₃×C₄	—	4	16	no	—
287	C₂×C₃×C₄	#121	1	4	yes	—
288	C₂×C₃×C₄	#121	1	8	yes	—
289	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
290	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
291	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
293	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
294	C₂×C₃×C₄	C₂×#41	1	2	yes	—
295	C₂×C₃×C₄	C₂×#41	1	4	yes	—
296	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
297	C₃×C₈	—	2	4	no	—
298	C₃×C₈	C₂²×D₄	1	4	yes	—
299	C₃×C₈	C₂²×D₄	1	4	yes	—
300	C₂⁴	—	2	4	no	—
301	C₂⁴	—	2	2	no	—
302	C₂⁴	—	4	4	no	—
303	C₂⁴	C₂×C₃×D₄	1	2	yes	—
304	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
305	C₂⁴	C₂×C₃×D₄	1	4	yes	—
306	#41	—	2	16	no	—
307	#41	—	2	16	no	—
308	#41	—	4	16	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
313	C₂×D₄	—	2	16	no	—
314	C₂×D₄	—	2	8	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	4	16	no	—
319	C₂×D₄	—	4	8	no	—
320	C₂×D₄	C₂⁴×C₃	1	4	yes	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	16	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	8	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	4	8	no	—
332	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
333	C₂²×C₄	C₂×C₃×D₄	1	8	yes	—
334	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
335	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
336	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
338	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
339	C₂²×C₄	C₃×#41	1	4	yes	—
340	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
341	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
343	Q₁₆	—	2	8	no	—
344	SD₁₆	—	2	16	no	—
345	D₈	—	2	8	no	—
346	M₁₆	—	2	16	no	—
347	M₁₆	—	2	16	no	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	8	no	—
350	C₂×C₈	C₂×C₃×D₄	1	4	yes	—
351	C₂×C₈	C₂×C₃×D₄	1	4	yes	—
352	C₂×C₈	C₂×C₃×D₄	1	16	yes	complemented
353	C₂×C₈	C₂⁴×C₃	1	4	yes	—
354	C₂×C₈	C₂⁴×C₃	1	2	yes	—
355	C₂×C₈	C₂⁴×C₃	1	2	yes	—
356	C₄⋊C₄	—	2	16	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
359	C₂²⋊C₄	—	2	8	no	—
360	C₂²⋊C₄	—	2	16	no	—
361	C₂²⋊C₄	—	2	16	no	—
362	C₄²	—	2	8	no	—
363	C₂²×C₃	—	2	8	no	—
364	C₂²×C₃	—	2	4	no	—
365	C₂²×C₃	—	2	4	no	—
366	C₂²×C₃	—	2	8	no	—
367	C₂²×C₃	—	4	16	no	—
368	C₂²×C₃	—	4	8	no	—
369	C₂²×C₃	—	4	4	no	—
370	C₂²×C₃	—	4	8	no	—
371	C₂²×C₃	—	8	8	no	—
372	C₂²×C₃	C₂×#121	1	4	yes	—
373	C₂²×C₃	C₂×#121	1	2	yes	—
374	C₂²×C₃	#575	1	4	yes	—
375	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
376	C₃×C₄	—	2	4	no	—
377	C₃×C₄	—	4	4	no	—
378	C₃×C₄	—	4	8	no	—
379	C₃×C₄	C₂×#121	1	4	yes	—
380	C₃×C₄	C₂×#121	1	2	yes	—
381	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
382	C₃×C₄	C₂²×#41	1	1	yes	characteristic
383	C₂³	—	2	4	no	—
384	C₂³	—	2	8	no	—
385	C₂³	—	2	8	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	4	8	no	—
389	C₂³	—	4	16	no	—
390	C₂³	—	4	8	no	—
391	C₂³	—	4	4	no	—
392	C₂³	C₃×#121	1	4	yes	—
393	C₂³	C₂²×C₃×D₄	1	4	yes	—
394	C₂³	C₂²×C₃×D₄	1	2	yes	—
395	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
396	Q₈	—	2	4	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	4	4	no	—
399	D₄	—	2	4	no	—
400	D₄	—	2	4	no	—
401	D₄	—	4	32	no	—
402	D₄	—	4	16	no	—
403	D₄	—	4	4	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	16	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	4	8	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	16	no	—
415	C₂×C₄	C₃×#121	1	4	yes	—
416	C₂×C₄	C₃×#121	1	8	yes	—
417	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
418	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
419	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
420	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
421	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
422	C₂×C₄	C₂×C₃×#41	1	2	yes	—
423	C₂×C₄	C₂×C₃×#41	1	4	yes	—
424	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
425	C₈	—	2	4	no	—
426	C₈	C₂²×C₃×D₄	1	4	yes	—
427	C₈	C₂²×C₃×D₄	1	4	yes	—
428	C₂×C₃	—	2	4	no	—
429	C₂×C₃	—	4	4	no	—
430	C₂×C₃	—	8	4	no	—
431	C₂×C₃	#3054	1	4	yes	direct product factor
432	C₂×C₃	C₂²×#121	1	1	yes	characteristic
433	C₂×C₃	C₂×#575	1	2	yes	—
434	C₂²	—	2	4	no	—
435	C₂²	—	2	8	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	8	no	—
438	C₂²	—	4	16	no	—
439	C₂²	—	4	8	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	4	8	no	—
442	C₂²	—	8	8	no	—
443	C₂²	C₂×C₃×#121	1	4	yes	—
444	C₂²	C₂×C₃×#121	1	2	yes	—
445	C₂²	C₃×#575	1	4	yes	—
446	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
447	C₄	—	2	4	no	—
448	C₄	—	4	4	no	—
449	C₄	—	4	8	no	—
450	C₄	C₂×C₃×#121	1	4	yes	—
451	C₄	C₂×C₃×#121	1	2	yes	—
452	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
453	C₄	C₂²×C₃×#41	1	1	yes	characteristic
454	C₃	C₂×#3054	1	1	yes	characteristic, direct product factor, Sylow
455	C₂	—	2	4	no	—
456	C₂	—	4	4	no	—
457	C₂	—	8	4	no	—
458	C₂	C₃×#3054	1	4	yes	direct product factor
459	C₂	C₂²×C₃×#121	1	1	yes	characteristic
460	C₂	C₂×C₃×#575	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂³×C₃	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂⁴×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#135	C₂	semidirect
2. C₂³×C₃×M₁₆	C₂	semidirect
3. C₂×C₃×#525	C₂	semidirect
4. C₃×#3054	C₂	direct (N × H)
5. C₂×C₃×#470	C₂	semidirect
6. C₂×C₃×#469	C₂	semidirect
7. C₂×C₃×#468	C₂	semidirect
8. C₂×C₃×#427	C₂	semidirect
9. C₂×C₃×#416	C₂	semidirect
10. C₂×#3054	C₃	direct (N × H)
14. C₂×C₃×#135	C₂²	semidirect
15. C₂²×C₃×Q₁₆	C₂²	semidirect
16. C₂²×C₃×SD₁₆	C₂²	semidirect
17. C₂²×C₃×D₈	C₂²	semidirect
21. C₂²×C₃×M₁₆	C₂²	semidirect
25. C₃×#525	C₂²	semidirect
32. C₃×#470	C₂²	semidirect
33. C₃×#469	C₂²	semidirect
34. C₃×#468	C₂²	semidirect
35. C₃×#427	C₂²	semidirect
36. C₂×C₃×#107	C₂²	semidirect
37. C₂×C₃×#106	C₂²	semidirect
38. C₃×#416	C₂²	semidirect
39. C₂×C₃×#103	C₂²	semidirect
40. C₂×C₃×#102	C₂²	semidirect
41. C₂²×#135	C₂×C₃	semidirect
42. C₂³×M₁₆	C₂×C₃	semidirect
43. C₂×#525	C₂×C₃	semidirect
44. #3054	C₂×C₃	direct (N × H)
45. C₂×#470	C₂×C₃	semidirect
46. C₂×#469	C₂×C₃	semidirect
47. C₂×#468	C₂×C₃	semidirect
48. C₂×#427	C₂×C₃	semidirect
49. C₂×#416	C₂×C₃	semidirect
70. C₂×C₃×Q₁₆	C₂³	semidirect
72. C₂×C₃×SD₁₆	C₂³	semidirect
74. C₂×C₃×D₈	C₂³	semidirect
81. C₂²×C₃×C₈	D₄	semidirect
102. C₃×#107	C₂³	semidirect
103. C₃×#106	C₂³	semidirect
104. C₃×#103	C₂³	semidirect
105. C₃×#102	C₂³	semidirect
109. C₂×#135	C₂²×C₃	semidirect
110. C₂²×Q₁₆	C₂²×C₃	semidirect
111. C₂²×SD₁₆	C₂²×C₃	semidirect
112. C₂²×D₈	C₂²×C₃	semidirect
116. C₂²×M₁₆	C₂²×C₃	semidirect
120. #525	C₂²×C₃	semidirect
127. #470	C₂²×C₃	semidirect
128. #469	C₂²×C₃	semidirect
129. #468	C₂²×C₃	semidirect
130. #427	C₂²×C₃	semidirect
131. C₂×#107	C₂²×C₃	semidirect
132. C₂×#106	C₂²×C₃	semidirect
133. #416	C₂²×C₃	semidirect
134. C₂×#103	C₂²×C₃	semidirect
135. C₂×#102	C₂²×C₃	semidirect
188. C₂×C₃×C₈	C₂×D₄	semidirect
219. C₂×Q₁₆	C₂³×C₃	semidirect
221. C₂×SD₁₆	C₂³×C₃	semidirect
223. C₂×D₈	C₂³×C₃	semidirect
230. C₂²×C₈	C₃×D₄	semidirect
251. #107	C₂³×C₃	semidirect
252. #106	C₂³×C₃	semidirect
253. #103	C₂³×C₃	semidirect
254. #102	C₂³×C₃	semidirect
352. C₂×C₈	C₂×C₃×D₄	semidirect
431. C₂×C₃	#3054	direct (N × H)
454. C₃	C₂×#3054	direct (N × H)
458. C₂	C₃×#3054	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×#135	2
C₂³×C₃×M₁₆	2
C₂×C₃×#525	2
C₃×#3054	2
C₂×C₃×#470	2
C₂×C₃×#469	2
C₂×C₃×#468	2
C₂×C₃×#427	2
C₂×C₃×#416	2
C₂×#3054	3

Subgroups — C2×C3×#3054 #10679048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#3054 #10679048