Subgroups — C₂²×#64306 #11919199

Order 1152.

13721 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#235	C₂	1	2	yes	maximal, complemented
3	C₂²×#3811	C₂	1	2	yes	maximal, complemented
4	C₂²×#3805	C₂	1	2	yes	maximal, complemented
5	C₂×#64306	C₂	1	48	yes	maximal, direct product factor
6	C₂²×#3802	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄×D₃²	C₂	1	2	yes	maximal, complemented
8	C₂²×#3798	C₂	1	2	yes	maximal, complemented
9	C₂²×#3797	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#3796	C₂	1	2	yes	maximal, complemented
11	C₂²×D₃×#41	—	3	2	no	maximal
12	C₂⁴×C₃⋊D₃	C₂²	1	1	yes	characteristic
13	C₂³×D₃²	C₂²	1	2	yes	—
14	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
15	C₂³×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₃⋊D₃	C₂²	1	24	yes	complemented
19	C₂²×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×#67	C₂²	1	4	yes	complemented
22	C₂×C₃×#235	C₂²	1	48	yes	complemented
23	C₂²×C₃×D₁₂	C₂²	1	2	yes	complemented
24	C₂²×C₃×C₄×D₃	C₂²	1	4	yes	complemented
25	C₂²×C₃×Dic₆	C₂²	1	2	yes	complemented
26	C₂×#3811	C₂²	1	48	yes	complemented
27	C₂²×#627	C₂²	1	2	yes	complemented
28	C₂²×#626	C₂²	1	4	yes	complemented
29	C₂²×#625	C₂²	1	2	yes	complemented
30	C₂²×#624	C₂²	1	2	yes	—
31	C₂×#3805	C₂²	1	48	yes	complemented
32	C₂²×D₃×Dic₃	C₂²	1	4	yes	complemented
33	#64306	C₂²	1	256	yes	direct product factor
34	C₂×#3802	C₂²	1	24	yes	complemented
35	C₂×C₄×D₃²	C₂²	1	48	yes	complemented
36	C₂×#3798	C₂²	1	48	yes	complemented
37	C₂×#3797	C₂²	1	24	yes	complemented
38	C₂×#3796	C₂²	1	48	yes	complemented
39	C₂²×C₃×#41	—	3	2	no	—
40	C₂×D₃×#41	—	3	96	no	—
41	C₂²×#239	—	3	2	no	—
42	C₂²×D₃×Q₈	—	3	2	no	—
43	C₂²×#237	—	3	4	no	—
44	C₂²×#237	—	3	2	no	—
45	C₂²×D₃×D₄	—	3	4	no	—
46	C₂²×D₃×D₄	—	3	2	no	—
47	C₂²×#235	—	3	4	no	—
48	C₂²×#235	D₃	1	2	yes	complemented
49	C₂³×C₄×D₃	—	3	2	no	—
50	C₂³×C₄×D₃	—	3	4	no	—
51	C₂³×C₄×D₃	—	6	1	no	—
52	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
53	C₂³×C₃⋊D₃	—	2	8	no	—
54	C₂³×C₃⋊D₃	C₂³	1	1	yes	characteristic
55	C₂³×C₃⋊D₃	C₂³	1	12	yes	—
56	C₂³×C₃⋊D₃	C₂³	1	1	yes	characteristic
57	C₂³×C₃×D₃	C₂³	1	4	yes	—
58	C₂²×D₃²	—	2	16	no	—
59	C₂²×D₃²	C₂³	1	24	yes	—
60	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
61	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
62	C₂²×C₃²×C₄	C₂³	1	12	yes	complemented
63	C₂²×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
64	C₂²×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
65	C₂²×C₃⋊Dic₃	C₂³	1	12	yes	complemented
66	C₂×C₄×C₃⋊D₃	C₂³	1	12	yes	—
67	C₂×C₄×C₃⋊D₃	C₂³	1	12	yes	—
68	C₂×C₄×C₃⋊D₃	C₂³	1	64	yes	complemented
69	C₂×C₄×C₃⋊D₃	C₂³	1	12	yes	complemented
70	C₂×C₄×C₃⋊D₃	C₂³	1	12	yes	complemented
71	C₂×C₃×#67	C₂³	1	48	yes	complemented
72	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
73	C₃×#235	C₂³	1	128	yes	complemented
74	C₂×C₃×D₁₂	C₂³	1	24	yes	complemented
75	C₂×C₃×C₄×D₃	C₂³	1	48	yes	complemented
76	C₂×C₃×Dic₆	C₂³	1	24	yes	complemented
77	#3811	C₂³	1	128	yes	complemented
78	C₂×#627	C₂³	1	24	yes	complemented
79	C₂×#626	C₂³	1	48	yes	complemented
80	C₂×#625	C₂³	1	24	yes	complemented
81	C₂×#624	C₂³	1	24	yes	—
82	#3805	C₂³	1	128	yes	complemented
83	C₂×D₃×Dic₃	C₂³	1	48	yes	complemented
84	#3802	C₂³	1	64	yes	complemented
85	C₄×D₃²	C₂³	1	128	yes	complemented
86	#3798	C₂³	1	128	yes	complemented
87	#3797	C₂³	1	64	yes	complemented
88	#3796	C₂³	1	128	yes	complemented
89	C₂³×#41	—	9	1	no	Sylow
90	C₂⁴×D₃	—	3	2	no	—
91	C₂⁴×D₃	—	3	4	no	—
92	C₂⁴×D₃	—	6	1	no	—
93	C₂×C₃×#41	—	3	48	no	—
94	C₂²×C₃×Q₈	—	3	2	no	—
95	C₂²×C₃×D₄	—	3	4	no	—
96	C₂²×C₃×D₄	—	3	2	no	—
97	C₂³×C₃×C₄	—	2	1	no	—
98	C₂³×C₃×C₄	—	3	4	no	—
99	C₂³×C₃×C₄	C₂×D₃	1	2	yes	complemented
100	C₂²×#67	—	3	4	no	—
101	C₂²×#67	—	3	4	no	—
102	C₂²×#67	C₂×D₃	1	4	yes	complemented
103	C₂³×Dic₃	—	3	2	no	—
104	C₂³×Dic₃	—	3	4	no	—
105	C₂³×Dic₃	—	6	1	no	—
106	D₃×#41	—	3	512	no	—
107	C₂×#239	—	3	48	no	—
108	C₂×D₃×Q₈	—	3	48	no	—
109	C₂×#237	—	3	96	no	—
110	C₂×#237	—	3	48	no	—
111	C₂×D₃×D₄	—	3	96	no	—
112	C₂×D₃×D₄	—	3	48	no	—
113	C₂×#235	—	3	96	no	—
114	C₂×#235	C₂×D₃	1	48	yes	complemented
115	C₂²×D₁₂	—	3	4	no	—
116	C₂²×D₁₂	C₂×D₃	1	2	yes	complemented
117	C₂²×C₄×D₃	—	3	4	no	—
118	C₂²×C₄×D₃	—	3	2	no	—
119	C₂²×C₄×D₃	—	3	2	no	—
120	C₂²×C₄×D₃	—	3	2	no	—
121	C₂²×C₄×D₃	—	3	2	no	—
122	C₂²×C₄×D₃	—	3	48	no	—
123	C₂²×C₄×D₃	—	3	4	no	—
124	C₂²×C₄×D₃	—	3	96	no	—
125	C₂²×C₄×D₃	—	6	1	no	—
126	C₂²×C₄×D₃	—	6	1	no	—
127	C₂²×C₄×D₃	—	6	1	no	—
128	C₂²×C₄×D₃	—	6	1	no	—
129	C₂²×C₄×D₃	—	6	24	no	—
130	C₂²×C₄×D₃	C₂×D₃	1	4	yes	complemented
131	C₂²×Dic₆	—	3	4	no	—
132	C₂²×Dic₆	C₂×D₃	1	2	yes	complemented
133	C₂³×C₃²	—	2	4	no	—
134	C₂³×C₃²	C₂⁴	1	6	yes	—
135	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
136	C₂²×C₃⋊D₃	—	2	4	no	—
137	C₂²×C₃⋊D₃	—	2	48	no	—
138	C₂²×C₃⋊D₃	#41	1	8	yes	complemented
139	C₂²×C₃⋊D₃	C₂⁴	1	6	yes	—
140	C₂²×C₃⋊D₃	C₂⁴	1	16	yes	—
141	C₂²×C₃⋊D₃	C₂⁴	1	6	yes	—
142	C₂²×C₃×D₃	—	2	16	no	—
143	C₂²×C₃×D₃	C₂⁴	1	24	yes	—
144	C₂×D₃²	—	2	96	no	—
145	C₂×D₃²	C₂⁴	1	32	yes	—
146	C₂×C₃²×C₄	C₂⁴	1	6	yes	—
147	C₂×C₃²×C₄	C₂⁴	1	6	yes	—
148	C₂×C₃²×C₄	C₂⁴	1	16	yes	complemented
149	C₂×C₃⋊Dic₃	C₂⁴	1	6	yes	—
150	C₂×C₃⋊Dic₃	C₂⁴	1	6	yes	—
151	C₂×C₃⋊Dic₃	C₂⁴	1	16	yes	complemented
152	C₄×C₃⋊D₃	C₂⁴	1	16	yes	—
153	C₄×C₃⋊D₃	C₂⁴	1	16	yes	—
154	C₄×C₃⋊D₃	C₂⁴	1	16	yes	complemented
155	C₄×C₃⋊D₃	C₂⁴	1	16	yes	complemented
156	C₃×#67	C₂⁴	1	64	yes	complemented
157	C₂×C₃×Dic₃	C₂⁴	1	24	yes	—
158	C₃×D₁₂	C₂⁴	1	32	yes	complemented
159	C₃×C₄×D₃	C₂⁴	1	64	yes	complemented
160	C₃×Dic₆	C₂⁴	1	32	yes	complemented
161	#627	C₂⁴	1	32	yes	complemented
162	#626	C₂⁴	1	64	yes	complemented
163	#625	C₂⁴	1	32	yes	complemented
164	#624	C₂⁴	1	32	yes	—
165	D₃×Dic₃	C₂⁴	1	64	yes	complemented
166	C₂²×#41	—	3	2	no	—
167	C₂²×#41	—	9	2	no	—
168	C₂²×#41	—	9	2	no	—
169	C₂²×#41	—	9	2	no	—
170	C₂²×#41	—	9	48	no	—
171	C₂³×Q₈	—	9	1	no	—
172	C₂³×D₄	—	9	2	no	—
173	C₂³×D₄	—	9	1	no	—
174	C₂⁴×C₄	—	9	2	no	—
175	C₂⁴×C₄	—	9	1	no	—
176	C₂⁴×C₃	—	2	1	no	—
177	C₂⁴×C₃	—	3	4	no	—
178	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
179	C₂³×D₃	—	3	2	no	—
180	C₂³×D₃	—	3	2	no	—
181	C₂³×D₃	—	3	24	no	—
182	C₂³×D₃	—	3	48	no	—
183	C₂³×D₃	—	6	1	no	—
184	C₂³×D₃	—	6	1	no	—
185	C₂³×D₃	—	6	12	no	—
186	C₂³×D₃	—	6	32	no	—
187	C₂³×D₃	—	6	16	no	—
188	C₂³×D₃	—	6	16	no	—
189	C₂³×D₃	C₂²×D₃	1	4	yes	—
190	C₃×#41	—	3	128	no	—
191	C₂×C₃×Q₈	—	3	24	no	—
192	C₂×C₃×D₄	—	3	48	no	—
193	C₂×C₃×D₄	—	3	24	no	—
194	C₂²×C₃×C₄	—	2	1	no	—
195	C₂²×C₃×C₄	—	2	1	no	—
196	C₂²×C₃×C₄	—	2	12	no	—
197	C₂²×C₃×C₄	—	3	4	no	—
198	C₂²×C₃×C₄	—	3	48	no	—
199	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
200	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
201	C₂²×C₃×C₄	C₂²×D₃	1	24	yes	complemented
202	C₂×#67	—	3	48	no	—
203	C₂×#67	—	3	48	no	—
204	C₂×#67	C₂²×D₃	1	48	yes	complemented
205	C₂²×Dic₃	—	3	2	no	—
206	C₂²×Dic₃	—	3	2	no	—
207	C₂²×Dic₃	—	3	24	no	—
208	C₂²×Dic₃	—	3	48	no	—
209	C₂²×Dic₃	—	6	1	no	—
210	C₂²×Dic₃	—	6	1	no	—
211	C₂²×Dic₃	—	6	12	no	—
212	C₂²×Dic₃	C₂²×D₃	1	4	yes	—
213	#239	—	3	128	no	—
214	D₃×Q₈	—	3	128	no	—
215	#237	—	3	256	no	—
216	#237	—	3	128	no	—
217	D₃×D₄	—	3	256	no	—
218	D₃×D₄	—	3	128	no	—
219	#235	—	3	256	no	—
220	#235	C₂²×D₃	1	128	yes	complemented
221	C₂×D₁₂	—	3	48	no	—
222	C₂×D₁₂	C₂²×D₃	1	24	yes	complemented
223	C₂×C₄×D₃	—	3	48	no	—
224	C₂×C₄×D₃	—	3	24	no	—
225	C₂×C₄×D₃	—	3	24	no	—
226	C₂×C₄×D₃	—	3	24	no	—
227	C₂×C₄×D₃	—	3	24	no	—
228	C₂×C₄×D₃	—	3	128	no	—
229	C₂×C₄×D₃	—	3	48	no	—
230	C₂×C₄×D₃	—	3	256	no	—
231	C₂×C₄×D₃	—	6	12	no	—
232	C₂×C₄×D₃	—	6	12	no	—
233	C₂×C₄×D₃	—	6	12	no	—
234	C₂×C₄×D₃	—	6	12	no	—
235	C₂×C₄×D₃	—	6	64	no	—
236	C₂×C₄×D₃	C₂²×D₃	1	48	yes	complemented
237	C₂×Dic₆	—	3	48	no	—
238	C₂×Dic₆	C₂²×D₃	1	24	yes	complemented
239	C₂²×C₃²	—	2	12	no	—
240	C₂²×C₃²	C₂×#41	1	4	yes	complemented
241	C₂²×C₃²	C₂⁵	1	4	yes	—
242	C₂²×C₃²	C₂⁵	1	3	yes	—
243	C₂×C₃⋊D₃	—	2	12	no	—
244	C₂×C₃⋊D₃	—	2	32	no	—
245	C₂×C₃⋊D₃	C₂×#41	1	24	yes	complemented
246	C₂×C₃⋊D₃	C₂⁵	1	4	yes	—
247	C₂×C₃⋊D₃	C₂⁵	1	4	yes	—
248	C₂×C₃×D₃	—	2	48	no	—
249	C₂×C₃×D₃	C₂⁵	1	16	yes	—
250	D₃²	—	2	64	no	—
251	C₃²×C₄	C₂⁵	1	4	yes	—
252	C₃²×C₄	C₂⁵	1	4	yes	—
253	C₃⋊Dic₃	C₂⁵	1	4	yes	—
254	C₃⋊Dic₃	C₂⁵	1	4	yes	—
255	C₃×Dic₃	C₂⁵	1	16	yes	—
256	C₂⁵	—	9	2	no	—
257	C₂⁵	—	9	1	no	—
258	C₂×#41	—	3	48	no	—
259	C₂×#41	—	9	48	no	—
260	C₂×#41	—	9	48	no	—
261	C₂×#41	—	9	48	no	—
262	C₂×#41	—	9	256	no	—
263	C₂²×Q₈	—	3	2	no	—
264	C₂²×Q₈	—	9	2	no	—
265	C₂²×Q₈	—	9	24	no	—
266	C₂²×D₄	—	3	4	no	—
267	C₂²×D₄	—	3	2	no	—
268	C₂²×D₄	—	9	4	no	—
269	C₂²×D₄	—	9	48	no	—
270	C₂²×D₄	—	9	24	no	—
271	C₂²×D₄	—	9	2	no	—
272	C₂³×C₄	—	3	4	no	—
273	C₂³×C₄	—	9	2	no	—
274	C₂³×C₄	—	9	48	no	—
275	C₂³×C₄	—	9	4	no	—
276	C₂³×C₄	—	9	1	no	—
277	C₂³×C₄	—	9	1	no	—
278	C₂³×C₄	—	9	1	no	—
279	C₂³×C₄	—	9	1	no	—
280	C₂³×C₄	—	9	1	no	—
281	C₂³×C₄	—	9	24	no	—
282	C₂³×C₄	D₃²	1	1	yes	characteristic, complemented
283	C₂³×C₃	—	2	8	no	—
284	C₂³×C₃	—	2	8	no	—
285	C₂³×C₃	—	2	6	no	—
286	C₂³×C₃	—	2	1	no	—
287	C₂³×C₃	—	3	24	no	—
288	C₂³×C₃	—	6	16	no	—
289	C₂³×C₃	C₂³×D₃	1	12	yes	—
290	C₂³×C₃	C₂³×D₃	1	2	yes	—
291	C₂²×D₃	—	2	16	no	—
292	C₂²×D₃	—	3	16	no	—
293	C₂²×D₃	—	3	12	no	—
294	C₂²×D₃	—	3	12	no	—
295	C₂²×D₃	—	3	32	no	—
296	C₂²×D₃	—	3	64	no	—
297	C₂²×D₃	—	6	8	no	—
298	C₂²×D₃	—	6	6	no	—
299	C₂²×D₃	—	6	6	no	—
300	C₂²×D₃	—	6	16	no	—
301	C₂²×D₃	—	6	192	no	—
302	C₂²×D₃	—	6	96	no	—
303	C₂²×D₃	—	6	96	no	—
304	C₂²×D₃	—	6	8	no	—
305	C₂²×D₃	—	6	8	no	—
306	C₂²×D₃	C₂³×D₃	1	24	yes	—
307	C₃×Q₈	—	3	32	no	—
308	C₃×D₄	—	3	64	no	—
309	C₃×D₄	—	3	32	no	—
310	C₂×C₃×C₄	—	2	6	no	—
311	C₂×C₃×C₄	—	2	6	no	—
312	C₂×C₃×C₄	—	2	16	no	—
313	C₂×C₃×C₄	—	3	24	no	—
314	C₂×C₃×C₄	—	3	64	no	—
315	C₂×C₃×C₄	C₂³×D₃	1	12	yes	—
316	C₂×C₃×C₄	C₂³×D₃	1	12	yes	—
317	C₂×C₃×C₄	C₂³×D₃	1	32	yes	complemented
318	#67	—	3	64	no	—
319	#67	—	3	64	no	—
320	#67	C₂³×D₃	1	64	yes	complemented
321	C₂×Dic₃	—	3	12	no	—
322	C₂×Dic₃	—	3	12	no	—
323	C₂×Dic₃	—	3	32	no	—
324	C₂×Dic₃	—	3	64	no	—
325	C₂×Dic₃	—	6	6	no	—
326	C₂×Dic₃	—	6	6	no	—
327	C₂×Dic₃	—	6	16	no	—
328	C₂×Dic₃	C₂³×D₃	1	24	yes	—
329	D₁₂	—	3	64	no	—
330	D₁₂	C₂³×D₃	1	32	yes	complemented
331	C₄×D₃	—	3	64	no	—
332	C₄×D₃	—	3	32	no	—
333	C₄×D₃	—	3	32	no	—
334	C₄×D₃	—	3	32	no	—
335	C₄×D₃	—	3	32	no	—
336	C₄×D₃	—	3	64	no	—
337	C₄×D₃	—	6	16	no	—
338	C₄×D₃	—	6	16	no	—
339	C₄×D₃	—	6	16	no	—
340	C₄×D₃	—	6	16	no	—
341	C₄×D₃	C₂³×D₃	1	64	yes	complemented
342	Dic₆	—	3	64	no	—
343	Dic₆	C₂³×D₃	1	32	yes	complemented
344	C₂×C₃²	—	2	4	no	—
345	C₂×C₃²	C₂²×#41	1	6	yes	complemented
346	C₂×C₃²	C₂⁶	1	1	yes	characteristic
347	C₃⋊D₃	—	2	4	no	—
348	C₃⋊D₃	C₂²×#41	1	8	yes	complemented
349	C₃×D₃	—	2	16	no	—
350	C₂⁴	—	3	4	no	—
351	C₂⁴	—	9	24	no	—
352	C₂⁴	—	9	1	no	—
353	C₂⁴	—	9	12	no	—
354	C₂⁴	—	9	1	no	—
355	C₂⁴	—	18	8	no	—
356	C₂⁴	—	18	16	no	—
357	C₂⁴	C₂×D₃²	1	1	yes	characteristic
358	#41	—	3	128	no	—
359	#41	—	9	128	no	—
360	#41	—	9	128	no	—
361	#41	—	9	128	no	—
362	C₂×Q₈	—	3	24	no	—
363	C₂×Q₈	—	9	24	no	—
364	C₂×Q₈	—	9	64	no	—
365	C₂×D₄	—	3	48	no	—
366	C₂×D₄	—	3	24	no	—
367	C₂×D₄	—	9	48	no	—
368	C₂×D₄	—	9	128	no	—
369	C₂×D₄	—	9	64	no	—
370	C₂×D₄	—	9	24	no	—
371	C₂²×C₄	—	3	4	no	—
372	C₂²×C₄	—	3	48	no	—
373	C₂²×C₄	—	9	24	no	—
374	C₂²×C₄	—	9	128	no	—
375	C₂²×C₄	—	9	48	no	—
376	C₂²×C₄	—	9	1	no	—
377	C₂²×C₄	—	9	1	no	—
378	C₂²×C₄	—	9	12	no	—
379	C₂²×C₄	—	9	12	no	—
380	C₂²×C₄	—	9	12	no	—
381	C₂²×C₄	—	9	12	no	—
382	C₂²×C₄	—	9	12	no	—
383	C₂²×C₄	—	9	64	no	—
384	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₃²	1	12	yes	complemented
387	C₂²×C₃	—	2	24	no	—
388	C₂²×C₃	—	2	24	no	—
389	C₂²×C₃	—	2	4	no	—
390	C₂²×C₃	—	2	4	no	—
391	C₂²×C₃	—	2	3	no	—
392	C₂²×C₃	—	3	16	no	—
393	C₂²×C₃	—	6	48	no	—
394	C₂²×C₃	D₃×#41	1	8	yes	complemented
395	C₂²×C₃	C₂⁴×D₃	1	8	yes	—
396	C₂²×C₃	C₂⁴×D₃	1	6	yes	—
397	C₂×D₃	—	2	48	no	—
398	C₂×D₃	—	3	48	no	—
399	C₂×D₃	—	3	8	no	—
400	C₂×D₃	—	3	8	no	—
401	C₂×D₃	—	6	4	no	—
402	C₂×D₃	—	6	4	no	—
403	C₂×D₃	—	6	24	no	—
404	C₂×D₃	—	6	128	no	—
405	C₂×D₃	—	6	64	no	—
406	C₂×D₃	—	6	64	no	—
407	C₂×D₃	—	6	24	no	—
408	C₂×D₃	—	6	24	no	—
409	C₂×D₃	C₂⁴×D₃	1	16	yes	—
410	C₃×C₄	—	2	4	no	—
411	C₃×C₄	—	2	4	no	—
412	C₃×C₄	—	3	16	no	—
413	C₃×C₄	C₂⁴×D₃	1	8	yes	—
414	C₃×C₄	C₂⁴×D₃	1	8	yes	—
415	Dic₃	—	3	8	no	—
416	Dic₃	—	3	8	no	—
417	Dic₃	—	6	4	no	—
418	Dic₃	—	6	4	no	—
419	Dic₃	C₂⁴×D₃	1	16	yes	—
420	C₃²	C₂³×#41	1	1	yes	characteristic, complemented, Sylow
421	C₂³	—	2	4	no	—
422	C₂³	—	3	24	no	—
423	C₂³	—	6	16	no	—
424	C₂³	—	9	32	no	—
425	C₂³	—	9	8	no	—
426	C₂³	—	9	6	no	—
427	C₂³	—	9	16	no	—
428	C₂³	—	9	6	no	—
429	C₂³	—	18	48	no	—
430	C₂³	—	18	96	no	—
431	C₂³	—	18	4	no	—
432	C₂³	C₂²×D₃²	1	6	yes	—
433	C₂³	C₂²×D₃²	1	1	yes	characteristic
434	Q₈	—	3	32	no	—
435	Q₈	—	9	32	no	—
436	D₄	—	3	64	no	—
437	D₄	—	3	32	no	—
438	D₄	—	9	64	no	—
439	D₄	—	9	32	no	—
440	C₂×C₄	—	3	24	no	—
441	C₂×C₄	—	3	64	no	—
442	C₂×C₄	—	9	32	no	—
443	C₂×C₄	—	9	64	no	—
444	C₂×C₄	—	9	6	no	—
445	C₂×C₄	—	9	6	no	—
446	C₂×C₄	—	9	16	no	—
447	C₂×C₄	—	9	16	no	—
448	C₂×C₄	—	9	16	no	—
449	C₂×C₄	—	9	16	no	—
450	C₂×C₄	—	9	16	no	—
451	C₂×C₄	C₂²×D₃²	1	6	yes	—
452	C₂×C₄	C₂²×D₃²	1	6	yes	—
453	C₂×C₄	C₂²×D₃²	1	16	yes	complemented
454	C₂×C₃	—	2	8	no	—
455	C₂×C₃	—	2	8	no	—
456	C₂×C₃	—	2	6	no	—
457	C₂×C₃	—	2	1	no	—
458	C₂×C₃	—	6	16	no	—
459	C₂×C₃	C₂×D₃×#41	1	12	yes	complemented
460	C₂×C₃	C₂⁵×D₃	1	2	yes	—
461	D₃	—	2	16	no	—
462	D₃	—	3	16	no	—
463	D₃	—	6	8	no	—
464	D₃	—	6	8	no	—
465	D₃	—	6	8	no	—
466	C₂²	—	2	12	no	—
467	C₂²	—	3	16	no	—
468	C₂²	—	6	48	no	—
469	C₂²	—	9	24	no	—
470	C₂²	—	9	4	no	—
471	C₂²	—	9	4	no	—
472	C₂²	—	18	32	no	—
473	C₂²	—	18	64	no	—
474	C₂²	—	18	12	no	—
475	C₂²	#64306	1	4	yes	direct product factor
476	C₂²	C₂³×D₃²	1	4	yes	—
477	C₂²	C₂³×D₃²	1	3	yes	—
478	C₄	—	3	16	no	—
479	C₄	—	9	4	no	—
480	C₄	—	9	4	no	—
481	C₄	C₂³×D₃²	1	4	yes	—
482	C₄	C₂³×D₃²	1	4	yes	—
483	C₃	—	2	1	no	—
484	C₃	C₂²×D₃×#41	1	2	yes	complemented
485	C₂	—	2	4	no	—
486	C₂	—	6	16	no	—
487	C₂	—	9	8	no	—
488	C₂	—	18	4	no	—
489	C₂	C₂×#64306	1	6	yes	direct product factor
490	C₂	C₂⁴×D₃²	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃²
commutator, cosocle	C₂×C₃²	C₂⁶
Frattini	C₂	C₂⁴×D₃²
Fitting	C₂³×C₃²×C₄	C₂²
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂³×C₄	D₃²
hypocenter	C₃²	C₂³×#41
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₄×C₃⋊D₃	C₂	semidirect
2. C₂²×C₃×#235	C₂	semidirect
3. C₂²×#3811	C₂	semidirect
4. C₂²×#3805	C₂	semidirect
5. C₂×#64306	C₂	direct (N × H)
6. C₂²×#3802	C₂	semidirect
7. C₂²×C₄×D₃²	C₂	semidirect
8. C₂²×#3798	C₂	semidirect
9. C₂²×#3797	C₂	semidirect
10. C₂²×#3796	C₂	semidirect
14. C₂³×C₃²×C₄	C₂²	semidirect
15. C₂³×C₃⋊Dic₃	C₂²	semidirect
18. C₂²×C₄×C₃⋊D₃	C₂²	semidirect
19. C₂²×C₄×C₃⋊D₃	C₂²	semidirect
20. C₂²×C₄×C₃⋊D₃	C₂²	semidirect
21. C₂²×C₃×#67	C₂²	semidirect
22. C₂×C₃×#235	C₂²	semidirect
23. C₂²×C₃×D₁₂	C₂²	semidirect
24. C₂²×C₃×C₄×D₃	C₂²	semidirect
25. C₂²×C₃×Dic₆	C₂²	semidirect
26. C₂×#3811	C₂²	semidirect
27. C₂²×#627	C₂²	semidirect
28. C₂²×#626	C₂²	semidirect
29. C₂²×#625	C₂²	semidirect
31. C₂×#3805	C₂²	semidirect
32. C₂²×D₃×Dic₃	C₂²	semidirect
33. #64306	C₂²	direct (N × H)
34. C₂×#3802	C₂²	semidirect
35. C₂×C₄×D₃²	C₂²	semidirect
36. C₂×#3798	C₂²	semidirect
37. C₂×#3797	C₂²	semidirect
38. C₂×#3796	C₂²	semidirect
48. C₂²×#235	D₃	semidirect
62. C₂²×C₃²×C₄	C₂³	semidirect
65. C₂²×C₃⋊Dic₃	C₂³	semidirect
68. C₂×C₄×C₃⋊D₃	C₂³	semidirect
69. C₂×C₄×C₃⋊D₃	C₂³	semidirect
70. C₂×C₄×C₃⋊D₃	C₂³	semidirect
71. C₂×C₃×#67	C₂³	semidirect
73. C₃×#235	C₂³	semidirect
74. C₂×C₃×D₁₂	C₂³	semidirect
75. C₂×C₃×C₄×D₃	C₂³	semidirect
76. C₂×C₃×Dic₆	C₂³	semidirect
77. #3811	C₂³	semidirect
78. C₂×#627	C₂³	semidirect
79. C₂×#626	C₂³	semidirect
80. C₂×#625	C₂³	semidirect
82. #3805	C₂³	semidirect
83. C₂×D₃×Dic₃	C₂³	semidirect
84. #3802	C₂³	semidirect
85. C₄×D₃²	C₂³	semidirect
86. #3798	C₂³	semidirect
87. #3797	C₂³	semidirect
88. #3796	C₂³	semidirect
99. C₂³×C₃×C₄	C₂×D₃	semidirect
102. C₂²×#67	C₂×D₃	semidirect
114. C₂×#235	C₂×D₃	semidirect
116. C₂²×D₁₂	C₂×D₃	semidirect
130. C₂²×C₄×D₃	C₂×D₃	semidirect
132. C₂²×Dic₆	C₂×D₃	semidirect
138. C₂²×C₃⋊D₃	#41	semidirect
148. C₂×C₃²×C₄	C₂⁴	semidirect
151. C₂×C₃⋊Dic₃	C₂⁴	semidirect
154. C₄×C₃⋊D₃	C₂⁴	semidirect
155. C₄×C₃⋊D₃	C₂⁴	semidirect
156. C₃×#67	C₂⁴	semidirect
158. C₃×D₁₂	C₂⁴	semidirect
159. C₃×C₄×D₃	C₂⁴	semidirect
160. C₃×Dic₆	C₂⁴	semidirect
161. #627	C₂⁴	semidirect
162. #626	C₂⁴	semidirect
163. #625	C₂⁴	semidirect
165. D₃×Dic₃	C₂⁴	semidirect
201. C₂²×C₃×C₄	C₂²×D₃	semidirect
204. C₂×#67	C₂²×D₃	semidirect
220. #235	C₂²×D₃	semidirect
222. C₂×D₁₂	C₂²×D₃	semidirect
236. C₂×C₄×D₃	C₂²×D₃	semidirect
238. C₂×Dic₆	C₂²×D₃	semidirect
240. C₂²×C₃²	C₂×#41	semidirect
245. C₂×C₃⋊D₃	C₂×#41	semidirect
282. C₂³×C₄	D₃²	semidirect
317. C₂×C₃×C₄	C₂³×D₃	semidirect
320. #67	C₂³×D₃	semidirect
330. D₁₂	C₂³×D₃	semidirect
341. C₄×D₃	C₂³×D₃	semidirect
343. Dic₆	C₂³×D₃	semidirect
345. C₂×C₃²	C₂²×#41	semidirect
348. C₃⋊D₃	C₂²×#41	semidirect
386. C₂²×C₄	C₂×D₃²	semidirect
394. C₂²×C₃	D₃×#41	semidirect
420. C₃²	C₂³×#41	semidirect
453. C₂×C₄	C₂²×D₃²	semidirect
459. C₂×C₃	C₂×D₃×#41	semidirect
475. C₂²	#64306	direct (N × H)
484. C₃	C₂²×D₃×#41	semidirect
489. C₂	C₂×#64306	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₃⋊D₃	2
C₂²×C₃×#235	2
C₂²×#3811	2
C₂²×#3805	2
C₂×#64306	2
C₂²×#3802	2
C₂²×C₄×D₃²	2
C₂²×#3798	2
C₂²×#3797	2
C₂²×#3796	2
C₂²×D₃×#41	3

Subgroups — C22×#64306 #11919199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#64306 #11919199