Subgroups — C₂²×#64307 #11919225

Order 1152.

13565 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#3828	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₃×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₃×#67	C₂	1	4	yes	maximal, complemented
5	C₂×#64307	C₂	1	48	yes	maximal, direct product factor
6	C₂²×#3802	C₂	1	2	yes	maximal, complemented
7	C₂²×D₃×D₁₂	C₂	1	2	yes	maximal, complemented
8	C₂²×#3796	C₂	1	2	yes	maximal, complemented
9	C₂²×#3795	C₂	1	2	yes	maximal, complemented
10	C₂²×#1009	—	3	1	no	maximal
11	C₂²×#1004	—	3	1	no	maximal
12	C₂⁴×C₃×D₃	C₂²	1	2	yes	complemented
13	C₂³×D₃²	C₂²	1	4	yes	complemented
14	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
15	C₂²×#638	C₂²	1	2	yes	complemented
16	C₂×#3828	C₂²	1	24	yes	complemented
17	C₂²×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₄×C₃⋊D₃	C₂²	1	2	yes	complemented
19	C₂²×#634	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃×#67	C₂²	1	2	yes	complemented
21	C₂×C₃×#235	C₂²	1	24	yes	complemented
22	C₂²×C₃×D₁₂	C₂²	1	2	yes	complemented
23	C₂²×C₃×D₁₂	C₂²	1	2	yes	complemented
24	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃×D₁₂	C₂²	1	24	yes	complemented
26	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
27	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic, complemented
28	C₂×D₃×#67	C₂²	1	96	yes	complemented
29	C₂²×#626	C₂²	1	4	yes	complemented
30	C₂²×#625	C₂²	1	4	yes	complemented
31	C₂²×D₃×Dic₃	C₂²	1	4	yes	complemented
32	#64307	C₂²	1	256	yes	direct product factor
33	C₂×#3802	C₂²	1	48	yes	complemented
34	C₂×D₃×D₁₂	C₂²	1	48	yes	complemented
35	C₂×#3796	C₂²	1	48	yes	complemented
36	C₂×#3795	C₂²	1	48	yes	complemented
37	C₂²×C₃×#41	—	3	1	no	—
38	C₂³×C₃×D₄	—	3	1	no	—
39	C₂³×#67	—	3	4	no	—
40	C₂×#1009	—	3	48	no	—
41	C₂²×#239	—	3	2	no	—
42	C₂×#1004	—	3	48	no	—
43	C₂²×#237	—	3	2	no	—
44	C₂²×#237	—	3	2	no	—
45	C₂²×D₃×D₄	—	3	4	no	—
46	C₂²×D₃×D₄	—	3	2	no	—
47	C₂²×D₃×D₄	—	3	2	no	—
48	C₂²×D₃×D₄	—	3	2	no	—
49	C₂²×#235	—	3	1	no	—
50	C₂²×#235	—	3	1	no	—
51	C₂²×#235	—	3	2	no	—
52	C₂²×#235	—	6	1	no	—
53	C₂²×#235	D₃	1	1	yes	characteristic, complemented
54	C₂³×D₁₂	—	3	2	no	—
55	C₂³×D₁₂	D₃	1	1	yes	characteristic, complemented
56	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
57	C₂³×C₃⋊D₃	C₂³	1	2	yes	—
58	C₂³×C₃×D₃	—	4	8	no	—
59	C₂³×C₃×D₃	C₂³	1	4	yes	—
60	C₂³×C₃×D₃	C₂³	1	2	yes	—
61	C₂³×C₃×D₃	C₂³	1	24	yes	complemented
62	C₂²×D₃²	—	4	16	no	—
63	C₂²×D₃²	C₂³	1	48	yes	complemented
64	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
65	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
66	C₂²×C₃²×C₄	C₂³	1	12	yes	complemented
67	C₂×#638	C₂³	1	24	yes	complemented
68	C₂²×C₃⋊Dic₃	C₂³	1	2	yes	—
69	#3828	C₂³	1	64	yes	complemented
70	C₂×C₄⋊(C₃⋊D₃)	C₂³	1	12	yes	complemented
71	C₂×C₄×C₃⋊D₃	C₂³	1	24	yes	complemented
72	C₂×#634	C₂³	1	12	yes	complemented
73	C₂×C₃×#67	C₂³	1	24	yes	complemented
74	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
75	C₃×#235	C₂³	1	64	yes	complemented
76	C₂×C₃×D₁₂	C₂³	1	24	yes	complemented
77	C₂×C₃×D₁₂	C₂³	1	24	yes	complemented
78	C₂×C₃×D₁₂	C₂³	1	12	yes	complemented
79	C₂×C₃×D₁₂	C₂³	1	64	yes	complemented
80	C₂×C₃×C₄×D₃	C₂³	1	24	yes	complemented
81	C₂×C₃×Dic₆	C₂³	1	12	yes	complemented
82	D₃×#67	C₂³	1	256	yes	complemented
83	C₂×#626	C₂³	1	48	yes	complemented
84	C₂×#625	C₂³	1	48	yes	complemented
85	C₂×D₃×Dic₃	C₂³	1	48	yes	complemented
86	#3802	C₂³	1	128	yes	complemented
87	D₃×D₁₂	C₂³	1	128	yes	complemented
88	#3796	C₂³	1	128	yes	complemented
89	#3795	C₂³	1	128	yes	complemented
90	C₂²×H(5,𝔽₂)	—	9	1	no	Sylow
91	C₂⁵×C₃	—	3	2	no	—
92	C₂⁴×D₃	—	3	4	no	—
93	C₂⁴×D₃	—	3	4	no	—
94	C₂⁴×D₃	C₂×D₃	1	2	yes	complemented
95	C₂×C₃×#41	—	3	24	no	—
96	C₂²×C₃×Q₈	—	3	1	no	—
97	C₂²×C₃×D₄	—	3	2	no	—
98	C₂²×C₃×D₄	—	3	1	no	—
99	C₂²×C₃×D₄	—	3	2	no	—
100	C₂²×C₃×D₄	—	3	2	no	—
101	C₂²×C₃×D₄	—	3	24	no	—
102	C₂³×C₃×C₄	—	2	1	no	—
103	C₂³×C₃×C₄	—	3	2	no	—
104	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
105	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
106	C₂²×#67	—	3	2	no	—
107	C₂²×#67	—	3	2	no	—
108	C₂²×#67	—	3	4	no	—
109	C₂²×#67	—	3	4	no	—
110	C₂²×#67	—	3	96	no	—
111	C₂²×#67	—	3	4	no	—
112	C₂²×#67	—	6	2	no	—
113	C₂²×#67	C₂×D₃	1	2	yes	complemented
114	C₂³×Dic₃	—	3	4	no	—
115	#1009	—	3	256	no	—
116	C₂×#239	—	3	48	no	—
117	#1004	—	3	256	no	—
118	C₂×#237	—	3	48	no	—
119	C₂×#237	—	3	48	no	—
120	C₂×D₃×D₄	—	3	96	no	—
121	C₂×D₃×D₄	—	3	48	no	—
122	C₂×D₃×D₄	—	3	48	no	—
123	C₂×D₃×D₄	—	3	48	no	—
124	C₂×#235	—	3	24	no	—
125	C₂×#235	—	3	24	no	—
126	C₂×#235	—	3	48	no	—
127	C₂×#235	—	6	24	no	—
128	C₂×#235	C₂×D₃	1	24	yes	complemented
129	C₂²×D₁₂	—	3	4	no	—
130	C₂²×D₁₂	—	3	1	no	—
131	C₂²×D₁₂	—	3	1	no	—
132	C₂²×D₁₂	—	3	48	no	—
133	C₂²×D₁₂	—	6	1	no	—
134	C₂²×D₁₂	C₂×D₃	1	2	yes	complemented
135	C₂²×D₁₂	C₂×D₃	1	2	yes	complemented
136	C₂²×D₁₂	C₂×D₃	1	1	yes	characteristic, complemented
137	C₂²×D₁₂	C₂×D₃	1	24	yes	complemented
138	C₂²×C₄×D₃	—	3	4	no	—
139	C₂²×C₄×D₃	—	3	2	no	—
140	C₂²×C₄×D₃	—	3	2	no	—
141	C₂²×C₄×D₃	—	6	2	no	—
142	C₂²×C₄×D₃	C₂×D₃	1	2	yes	complemented
143	C₂²×Dic₆	—	3	1	no	—
144	C₂²×Dic₆	—	3	1	no	—
145	C₂²×Dic₆	—	6	1	no	—
146	C₂²×Dic₆	C₂×D₃	1	1	yes	characteristic, complemented
147	C₂³×C₃²	—	2	4	no	—
148	C₂³×C₃²	C₂⁴	1	6	yes	—
149	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
150	C₂²×C₃⋊D₃	—	2	8	no	—
151	C₂²×C₃⋊D₃	C₂⁴	1	12	yes	—
152	C₂²×C₃×D₃	—	2	8	no	—
153	C₂²×C₃×D₃	—	2	16	no	—
154	C₂²×C₃×D₃	—	4	48	no	—
155	C₂²×C₃×D₃	C₂⁴	1	12	yes	—
156	C₂²×C₃×D₃	C₂⁴	1	24	yes	—
157	C₂²×C₃×D₃	C₂⁴	1	32	yes	complemented
158	C₂×D₃²	—	4	96	no	—
159	C₂×D₃²	C₂⁴	1	64	yes	complemented
160	C₂×C₃²×C₄	C₂⁴	1	6	yes	—
161	C₂×C₃²×C₄	C₂⁴	1	6	yes	—
162	C₂×C₃²×C₄	C₂⁴	1	16	yes	complemented
163	#638	C₂⁴	1	32	yes	complemented
164	C₂×C₃⋊Dic₃	C₂⁴	1	12	yes	—
165	C₄⋊(C₃⋊D₃)	C₂⁴	1	16	yes	complemented
166	C₄×C₃⋊D₃	C₂⁴	1	32	yes	complemented
167	#634	C₂⁴	1	16	yes	complemented
168	C₃×#67	C₂⁴	1	32	yes	complemented
169	C₂×C₃×Dic₃	C₂⁴	1	12	yes	—
170	C₃×D₁₂	C₂⁴	1	32	yes	complemented
171	C₃×D₁₂	C₂⁴	1	32	yes	complemented
172	C₃×D₁₂	C₂⁴	1	16	yes	complemented
173	C₃×C₄×D₃	C₂⁴	1	32	yes	complemented
174	C₃×Dic₆	C₂⁴	1	16	yes	complemented
175	#626	C₂⁴	1	64	yes	complemented
176	#625	C₂⁴	1	64	yes	complemented
177	D₃×Dic₃	C₂⁴	1	64	yes	complemented
178	C₂×H(5,𝔽₂)	—	9	48	no	—
179	C₂²×#41	—	3	1	no	—
180	C₂²×#41	—	9	2	no	—
181	C₂²×#41	—	9	2	no	—
182	C₂²×#41	—	9	1	no	—
183	C₂³×D₄	—	3	1	no	—
184	C₂³×D₄	—	9	2	no	—
185	C₂³×D₄	—	9	2	no	—
186	C₂³×D₄	—	9	4	no	—
187	C₂⁴×C₃	—	2	1	no	—
188	C₂⁴×C₃	—	3	4	no	—
189	C₂⁴×C₃	—	3	2	no	—
190	C₂⁴×C₃	—	3	24	no	—
191	C₂⁴×C₃	—	12	8	no	—
192	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
193	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
194	C₂³×D₃	—	3	2	no	—
195	C₂³×D₃	—	3	2	no	—
196	C₂³×D₃	—	3	48	no	—
197	C₂³×D₃	—	3	48	no	—
198	C₂³×D₃	—	4	8	no	—
199	C₂³×D₃	—	6	2	no	—
200	C₂³×D₃	—	12	16	no	—
201	C₂³×D₃	—	12	16	no	—
202	C₂³×D₃	C₂²×D₃	1	4	yes	—
203	C₂³×D₃	C₂²×D₃	1	2	yes	—
204	C₂³×D₃	C₂²×D₃	1	24	yes	complemented
205	C₃×#41	—	3	64	no	—
206	C₂×C₃×Q₈	—	3	12	no	—
207	C₂×C₃×D₄	—	3	24	no	—
208	C₂×C₃×D₄	—	3	12	no	—
209	C₂×C₃×D₄	—	3	24	no	—
210	C₂×C₃×D₄	—	3	24	no	—
211	C₂×C₃×D₄	—	3	64	no	—
212	C₂²×C₃×C₄	—	2	1	no	—
213	C₂²×C₃×C₄	—	2	1	no	—
214	C₂²×C₃×C₄	—	2	12	no	—
215	C₂²×C₃×C₄	—	3	2	no	—
216	C₂²×C₃×C₄	—	3	24	no	—
217	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂²×D₃	1	12	yes	complemented
222	C₂²×C₃×C₄	C₂²×D₃	1	12	yes	complemented
223	C₂×#67	—	3	24	no	—
224	C₂×#67	—	3	24	no	—
225	C₂×#67	—	3	48	no	—
226	C₂×#67	—	3	48	no	—
227	C₂×#67	—	3	256	no	—
228	C₂×#67	—	3	48	no	—
229	C₂×#67	—	6	24	no	—
230	C₂×#67	C₂²×D₃	1	24	yes	complemented
231	C₂²×Dic₃	—	3	2	no	—
232	C₂²×Dic₃	—	3	2	no	—
233	C₂²×Dic₃	—	3	48	no	—
234	C₂²×Dic₃	—	6	2	no	—
235	C₂²×Dic₃	C₂²×D₃	1	2	yes	—
236	#239	—	3	128	no	—
237	#237	—	3	128	no	—
238	#237	—	3	128	no	—
239	D₃×D₄	—	3	256	no	—
240	D₃×D₄	—	3	128	no	—
241	D₃×D₄	—	3	128	no	—
242	D₃×D₄	—	3	128	no	—
243	#235	—	3	64	no	—
244	#235	—	3	64	no	—
245	#235	—	3	128	no	—
246	#235	—	6	64	no	—
247	#235	C₂²×D₃	1	64	yes	complemented
248	C₂×D₁₂	—	3	48	no	—
249	C₂×D₁₂	—	3	12	no	—
250	C₂×D₁₂	—	3	12	no	—
251	C₂×D₁₂	—	3	128	no	—
252	C₂×D₁₂	—	6	12	no	—
253	C₂×D₁₂	C₂²×D₃	1	24	yes	complemented
254	C₂×D₁₂	C₂²×D₃	1	24	yes	complemented
255	C₂×D₁₂	C₂²×D₃	1	12	yes	complemented
256	C₂×D₁₂	C₂²×D₃	1	64	yes	complemented
257	C₂×C₄×D₃	—	3	48	no	—
258	C₂×C₄×D₃	—	3	24	no	—
259	C₂×C₄×D₃	—	3	24	no	—
260	C₂×C₄×D₃	—	6	24	no	—
261	C₂×C₄×D₃	C₂²×D₃	1	24	yes	complemented
262	C₂×Dic₆	—	3	12	no	—
263	C₂×Dic₆	—	3	12	no	—
264	C₂×Dic₆	—	6	12	no	—
265	C₂×Dic₆	C₂²×D₃	1	12	yes	complemented
266	C₂²×C₃²	—	2	12	no	—
267	C₂²×C₃²	H(5,𝔽₂)	1	4	yes	complemented
268	C₂²×C₃²	C₂⁵	1	4	yes	—
269	C₂²×C₃²	C₂⁵	1	3	yes	—
270	C₂×C₃⋊D₃	—	2	24	no	—
271	C₂×C₃⋊D₃	C₂⁵	1	8	yes	—
272	C₂×C₃×D₃	—	2	24	no	—
273	C₂×C₃×D₃	—	2	48	no	—
274	C₂×C₃×D₃	—	4	32	no	—
275	C₂×C₃×D₃	C₂⁵	1	16	yes	—
276	C₂×C₃×D₃	C₂⁵	1	8	yes	—
277	D₃²	—	4	64	no	—
278	C₃²×C₄	C₂⁵	1	4	yes	—
279	C₃²×C₄	C₂⁵	1	4	yes	—
280	C₃⋊Dic₃	C₂⁵	1	8	yes	—
281	C₃×Dic₃	C₂⁵	1	8	yes	—
282	C₂⁵	—	3	2	no	—
283	C₂⁵	—	9	4	no	—
284	H(5,𝔽₂)	—	9	256	no	—
285	C₂×#41	—	3	24	no	—
286	C₂×#41	—	9	48	no	—
287	C₂×#41	—	9	48	no	—
288	C₂×#41	—	9	24	no	—
289	C₂²×Q₈	—	3	1	no	—
290	C₂²×Q₈	—	9	1	no	—
291	C₂²×D₄	—	3	2	no	—
292	C₂²×D₄	—	3	2	no	—
293	C₂²×D₄	—	3	2	no	—
294	C₂²×D₄	—	3	1	no	—
295	C₂²×D₄	—	3	24	no	—
296	C₂²×D₄	—	9	48	no	—
297	C₂²×D₄	—	9	4	no	—
298	C₂²×D₄	—	9	48	no	—
299	C₂²×D₄	—	9	96	no	—
300	C₂²×D₄	—	9	4	no	—
301	C₂²×D₄	—	9	2	no	—
302	C₂²×D₄	—	9	1	no	—
303	C₂³×C₄	—	3	2	no	—
304	C₂³×C₄	—	9	4	no	—
305	C₂³×C₄	—	9	2	no	—
306	C₂³×C₄	D₃²	1	1	yes	characteristic, complemented
307	C₂³×C₃	—	2	4	no	—
308	C₂³×C₃	—	2	4	no	—
309	C₂³×C₃	—	2	6	no	—
310	C₂³×C₃	—	2	1	no	—
311	C₂³×C₃	—	3	24	no	—
312	C₂³×C₃	—	3	12	no	—
313	C₂³×C₃	—	3	32	no	—
314	C₂³×C₃	—	4	4	no	—
315	C₂³×C₃	—	6	8	no	—
316	C₂³×C₃	—	6	16	no	—
317	C₂³×C₃	—	12	48	no	—
318	C₂³×C₃	C₂³×D₃	1	6	yes	—
319	C₂³×C₃	C₂³×D₃	1	6	yes	—
320	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
321	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
322	C₂²×D₃	—	2	16	no	—
323	C₂²×D₃	—	2	8	no	—
324	C₂²×D₃	—	3	12	no	—
325	C₂²×D₃	—	3	12	no	—
326	C₂²×D₃	—	3	64	no	—
327	C₂²×D₃	—	3	64	no	—
328	C₂²×D₃	—	4	48	no	—
329	C₂²×D₃	—	6	12	no	—
330	C₂²×D₃	—	6	8	no	—
331	C₂²×D₃	—	6	8	no	—
332	C₂²×D₃	—	12	8	no	—
333	C₂²×D₃	—	12	96	no	—
334	C₂²×D₃	—	12	96	no	—
335	C₂²×D₃	C₂³×D₃	1	24	yes	—
336	C₂²×D₃	C₂³×D₃	1	12	yes	—
337	C₂²×D₃	C₂³×D₃	1	32	yes	complemented
338	C₃×Q₈	—	3	16	no	—
339	C₃×D₄	—	3	32	no	—
340	C₃×D₄	—	3	16	no	—
341	C₃×D₄	—	3	32	no	—
342	C₃×D₄	—	3	32	no	—
343	C₂×C₃×C₄	—	2	6	no	—
344	C₂×C₃×C₄	—	2	6	no	—
345	C₂×C₃×C₄	—	2	16	no	—
346	C₂×C₃×C₄	—	3	12	no	—
347	C₂×C₃×C₄	—	3	32	no	—
348	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
349	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
350	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
351	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
352	C₂×C₃×C₄	C₂³×D₃	1	16	yes	complemented
353	C₂×C₃×C₄	C₂³×D₃	1	16	yes	complemented
354	#67	—	3	32	no	—
355	#67	—	3	32	no	—
356	#67	—	3	64	no	—
357	#67	—	3	64	no	—
358	#67	—	3	64	no	—
359	#67	—	6	32	no	—
360	#67	C₂³×D₃	1	32	yes	complemented
361	C₂×Dic₃	—	3	12	no	—
362	C₂×Dic₃	—	3	12	no	—
363	C₂×Dic₃	—	3	64	no	—
364	C₂×Dic₃	—	6	12	no	—
365	C₂×Dic₃	C₂³×D₃	1	12	yes	—
366	D₁₂	—	3	64	no	—
367	D₁₂	—	3	16	no	—
368	D₁₂	—	3	16	no	—
369	D₁₂	—	6	16	no	—
370	D₁₂	C₂³×D₃	1	32	yes	complemented
371	D₁₂	C₂³×D₃	1	32	yes	complemented
372	D₁₂	C₂³×D₃	1	16	yes	complemented
373	C₄×D₃	—	3	64	no	—
374	C₄×D₃	—	3	32	no	—
375	C₄×D₃	—	3	32	no	—
376	C₄×D₃	—	6	32	no	—
377	C₄×D₃	C₂³×D₃	1	32	yes	complemented
378	Dic₆	—	3	16	no	—
379	Dic₆	—	3	16	no	—
380	Dic₆	—	6	16	no	—
381	Dic₆	C₂³×D₃	1	16	yes	complemented
382	C₂×C₃²	—	2	4	no	—
383	C₂×C₃²	C₂×H(5,𝔽₂)	1	6	yes	complemented
384	C₂×C₃²	C₂⁶	1	1	yes	characteristic
385	C₃⋊D₃	—	2	8	no	—
386	C₃×D₃	—	2	8	no	—
387	C₃×D₃	—	2	16	no	—
388	C₂⁴	—	3	2	no	—
389	C₂⁴	—	3	4	no	—
390	C₂⁴	—	3	24	no	—
391	C₂⁴	—	9	48	no	—
392	C₂⁴	—	9	2	no	—
393	C₂⁴	—	12	8	no	—
394	C₂⁴	—	36	16	no	—
395	C₂⁴	C₂×D₃²	1	1	yes	characteristic
396	#41	—	3	64	no	—
397	#41	—	9	128	no	—
398	#41	—	9	128	no	—
399	#41	—	9	64	no	—
400	C₂×Q₈	—	3	12	no	—
401	C₂×Q₈	—	9	12	no	—
402	C₂×D₄	—	3	24	no	—
403	C₂×D₄	—	3	24	no	—
404	C₂×D₄	—	3	24	no	—
405	C₂×D₄	—	3	12	no	—
406	C₂×D₄	—	3	64	no	—
407	C₂×D₄	—	9	128	no	—
408	C₂×D₄	—	9	48	no	—
409	C₂×D₄	—	9	128	no	—
410	C₂×D₄	—	9	256	no	—
411	C₂×D₄	—	9	48	no	—
412	C₂×D₄	—	9	24	no	—
413	C₂×D₄	—	9	12	no	—
414	C₂²×C₄	—	3	2	no	—
415	C₂²×C₄	—	3	24	no	—
416	C₂²×C₄	—	9	48	no	—
417	C₂²×C₄	—	9	2	no	—
418	C₂²×C₄	—	9	24	no	—
419	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₃²	1	12	yes	complemented
422	C₂²×C₃	—	2	12	no	—
423	C₂²×C₃	—	2	12	no	—
424	C₂²×C₃	—	2	4	no	—
425	C₂²×C₃	—	2	3	no	—
426	C₂²×C₃	—	2	4	no	—
427	C₂²×C₃	—	3	16	no	—
428	C₂²×C₃	—	3	8	no	—
429	C₂²×C₃	—	4	12	no	—
430	C₂²×C₃	—	6	24	no	—
431	C₂²×C₃	—	6	48	no	—
432	C₂²×C₃	—	12	32	no	—
433	C₂²×C₃	#1004	1	4	yes	complemented
434	C₂²×C₃	#1009	1	4	yes	complemented
435	C₂²×C₃	C₂⁴×D₃	1	4	yes	—
436	C₂²×C₃	C₂⁴×D₃	1	4	yes	—
437	C₂²×C₃	C₂⁴×D₃	1	3	yes	—
438	C₂²×C₃	C₂⁴×D₃	1	3	yes	—
439	C₂×D₃	—	2	48	no	—
440	C₂×D₃	—	2	24	no	—
441	C₂×D₃	—	3	8	no	—
442	C₂×D₃	—	3	8	no	—
443	C₂×D₃	—	4	32	no	—
444	C₂×D₃	—	6	8	no	—
445	C₂×D₃	—	6	24	no	—
446	C₂×D₃	—	6	24	no	—
447	C₂×D₃	—	12	24	no	—
448	C₂×D₃	—	12	64	no	—
449	C₂×D₃	—	12	64	no	—
450	C₂×D₃	C₂⁴×D₃	1	16	yes	—
451	C₂×D₃	C₂⁴×D₃	1	8	yes	—
452	C₃×C₄	—	2	4	no	—
453	C₃×C₄	—	2	4	no	—
454	C₃×C₄	—	3	8	no	—
455	C₃×C₄	C₂⁴×D₃	1	4	yes	—
456	C₃×C₄	C₂⁴×D₃	1	4	yes	—
457	C₃×C₄	C₂⁴×D₃	1	4	yes	—
458	C₃×C₄	C₂⁴×D₃	1	4	yes	—
459	Dic₃	—	3	8	no	—
460	Dic₃	—	3	8	no	—
461	Dic₃	—	6	8	no	—
462	Dic₃	C₂⁴×D₃	1	8	yes	—
463	C₃²	C₂²×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
464	C₂³	—	2	4	no	—
465	C₂³	—	3	12	no	—
466	C₂³	—	3	24	no	—
467	C₂³	—	3	32	no	—
468	C₂³	—	6	16	no	—
469	C₂³	—	6	8	no	—
470	C₂³	—	9	64	no	—
471	C₂³	—	9	12	no	—
472	C₂³	—	12	48	no	—
473	C₂³	—	18	8	no	—
474	C₂³	—	36	96	no	—
475	C₂³	C₂²×D₃²	1	6	yes	—
476	C₂³	C₂²×D₃²	1	1	yes	characteristic
477	Q₈	—	3	16	no	—
478	Q₈	—	9	16	no	—
479	D₄	—	3	32	no	—
480	D₄	—	3	32	no	—
481	D₄	—	3	32	no	—
482	D₄	—	3	16	no	—
483	D₄	—	9	64	no	—
484	D₄	—	9	64	no	—
485	D₄	—	9	32	no	—
486	D₄	—	9	16	no	—
487	C₂×C₄	—	3	12	no	—
488	C₂×C₄	—	3	32	no	—
489	C₂×C₄	—	9	64	no	—
490	C₂×C₄	—	9	12	no	—
491	C₂×C₄	—	9	32	no	—
492	C₂×C₄	C₂²×D₃²	1	6	yes	—
493	C₂×C₄	C₂²×D₃²	1	6	yes	—
494	C₂×C₄	C₂²×D₃²	1	16	yes	complemented
495	C₂×C₃	—	2	4	no	—
496	C₂×C₃	—	2	4	no	—
497	C₂×C₃	—	2	6	no	—
498	C₂×C₃	—	2	1	no	—
499	C₂×C₃	—	4	4	no	—
500	C₂×C₃	—	6	8	no	—
501	C₂×C₃	—	6	16	no	—
502	C₂×C₃	C₂×#1004	1	6	yes	complemented
503	C₂×C₃	C₂×#1009	1	6	yes	complemented
504	C₂×C₃	C₂⁵×D₃	1	1	yes	characteristic
505	C₂×C₃	C₂⁵×D₃	1	1	yes	characteristic
506	D₃	—	2	16	no	—
507	D₃	—	2	8	no	—
508	D₃	—	6	8	no	—
509	D₃	—	6	8	no	—
510	D₃	—	12	8	no	—
511	C₂²	—	2	12	no	—
512	C₂²	—	3	8	no	—
513	C₂²	—	3	16	no	—
514	C₂²	—	6	48	no	—
515	C₂²	—	6	24	no	—
516	C₂²	—	9	8	no	—
517	C₂²	—	12	32	no	—
518	C₂²	—	18	24	no	—
519	C₂²	—	36	64	no	—
520	C₂²	#64307	1	4	yes	direct product factor
521	C₂²	C₂³×D₃²	1	4	yes	—
522	C₂²	C₂³×D₃²	1	3	yes	—
523	C₄	—	3	8	no	—
524	C₄	—	9	8	no	—
525	C₄	C₂³×D₃²	1	4	yes	—
526	C₄	C₂³×D₃²	1	4	yes	—
527	C₃	—	2	1	no	—
528	C₃	C₂²×#1004	1	1	yes	characteristic, complemented
529	C₃	C₂²×#1009	1	1	yes	characteristic, complemented
530	C₂	—	2	4	no	—
531	C₂	—	6	16	no	—
532	C₂	—	6	8	no	—
533	C₂	—	18	8	no	—
534	C₂	C₂×#64307	1	6	yes	direct product factor
535	C₂	C₂⁴×D₃²	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×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	C₂²×H(5,𝔽₂)
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#3828	C₂	semidirect
2. C₂²×C₃×#235	C₂	semidirect
3. C₂³×C₃×D₁₂	C₂	semidirect
4. C₂²×D₃×#67	C₂	semidirect
5. C₂×#64307	C₂	direct (N × H)
6. C₂²×#3802	C₂	semidirect
7. C₂²×D₃×D₁₂	C₂	semidirect
8. C₂²×#3796	C₂	semidirect
9. C₂²×#3795	C₂	semidirect
12. C₂⁴×C₃×D₃	C₂²	semidirect
13. C₂³×D₃²	C₂²	semidirect
14. C₂³×C₃²×C₄	C₂²	semidirect
15. C₂²×#638	C₂²	semidirect
16. C₂×#3828	C₂²	semidirect
17. C₂²×C₄⋊(C₃⋊D₃)	C₂²	semidirect
18. C₂²×C₄×C₃⋊D₃	C₂²	semidirect
19. C₂²×#634	C₂²	semidirect
20. C₂²×C₃×#67	C₂²	semidirect
21. C₂×C₃×#235	C₂²	semidirect
22. C₂²×C₃×D₁₂	C₂²	semidirect
23. C₂²×C₃×D₁₂	C₂²	semidirect
24. C₂²×C₃×D₁₂	C₂²	semidirect
25. C₂²×C₃×D₁₂	C₂²	semidirect
26. C₂²×C₃×C₄×D₃	C₂²	semidirect
27. C₂²×C₃×Dic₆	C₂²	semidirect
28. C₂×D₃×#67	C₂²	semidirect
29. C₂²×#626	C₂²	semidirect
30. C₂²×#625	C₂²	semidirect
31. C₂²×D₃×Dic₃	C₂²	semidirect
32. #64307	C₂²	direct (N × H)
33. C₂×#3802	C₂²	semidirect
34. C₂×D₃×D₁₂	C₂²	semidirect
35. C₂×#3796	C₂²	semidirect
36. C₂×#3795	C₂²	semidirect
53. C₂²×#235	D₃	semidirect
55. C₂³×D₁₂	D₃	semidirect
61. C₂³×C₃×D₃	C₂³	semidirect
63. C₂²×D₃²	C₂³	semidirect
66. C₂²×C₃²×C₄	C₂³	semidirect
67. C₂×#638	C₂³	semidirect
69. #3828	C₂³	semidirect
70. C₂×C₄⋊(C₃⋊D₃)	C₂³	semidirect
71. C₂×C₄×C₃⋊D₃	C₂³	semidirect
72. C₂×#634	C₂³	semidirect
73. C₂×C₃×#67	C₂³	semidirect
75. C₃×#235	C₂³	semidirect
76. C₂×C₃×D₁₂	C₂³	semidirect
77. C₂×C₃×D₁₂	C₂³	semidirect
78. C₂×C₃×D₁₂	C₂³	semidirect
79. C₂×C₃×D₁₂	C₂³	semidirect
80. C₂×C₃×C₄×D₃	C₂³	semidirect
81. C₂×C₃×Dic₆	C₂³	semidirect
82. D₃×#67	C₂³	semidirect
83. C₂×#626	C₂³	semidirect
84. C₂×#625	C₂³	semidirect
85. C₂×D₃×Dic₃	C₂³	semidirect
86. #3802	C₂³	semidirect
87. D₃×D₁₂	C₂³	semidirect
88. #3796	C₂³	semidirect
89. #3795	C₂³	semidirect
94. C₂⁴×D₃	C₂×D₃	semidirect
104. C₂³×C₃×C₄	C₂×D₃	semidirect
105. C₂³×C₃×C₄	C₂×D₃	semidirect
113. C₂²×#67	C₂×D₃	semidirect
128. C₂×#235	C₂×D₃	semidirect
134. C₂²×D₁₂	C₂×D₃	semidirect
135. C₂²×D₁₂	C₂×D₃	semidirect
136. C₂²×D₁₂	C₂×D₃	semidirect
137. C₂²×D₁₂	C₂×D₃	semidirect
142. C₂²×C₄×D₃	C₂×D₃	semidirect
146. C₂²×Dic₆	C₂×D₃	semidirect
157. C₂²×C₃×D₃	C₂⁴	semidirect
159. C₂×D₃²	C₂⁴	semidirect
162. C₂×C₃²×C₄	C₂⁴	semidirect
163. #638	C₂⁴	semidirect
165. C₄⋊(C₃⋊D₃)	C₂⁴	semidirect
166. C₄×C₃⋊D₃	C₂⁴	semidirect
167. #634	C₂⁴	semidirect
168. C₃×#67	C₂⁴	semidirect
170. C₃×D₁₂	C₂⁴	semidirect
171. C₃×D₁₂	C₂⁴	semidirect
172. C₃×D₁₂	C₂⁴	semidirect
173. C₃×C₄×D₃	C₂⁴	semidirect
174. C₃×Dic₆	C₂⁴	semidirect
175. #626	C₂⁴	semidirect
176. #625	C₂⁴	semidirect
177. D₃×Dic₃	C₂⁴	semidirect
204. C₂³×D₃	C₂²×D₃	semidirect
221. C₂²×C₃×C₄	C₂²×D₃	semidirect
222. C₂²×C₃×C₄	C₂²×D₃	semidirect
230. C₂×#67	C₂²×D₃	semidirect
247. #235	C₂²×D₃	semidirect
253. C₂×D₁₂	C₂²×D₃	semidirect
254. C₂×D₁₂	C₂²×D₃	semidirect
255. C₂×D₁₂	C₂²×D₃	semidirect
256. C₂×D₁₂	C₂²×D₃	semidirect
261. C₂×C₄×D₃	C₂²×D₃	semidirect
265. C₂×Dic₆	C₂²×D₃	semidirect
267. C₂²×C₃²	H(5,𝔽₂)	semidirect
306. C₂³×C₄	D₃²	semidirect
337. C₂²×D₃	C₂³×D₃	semidirect
352. C₂×C₃×C₄	C₂³×D₃	semidirect
353. C₂×C₃×C₄	C₂³×D₃	semidirect
360. #67	C₂³×D₃	semidirect
370. D₁₂	C₂³×D₃	semidirect
371. D₁₂	C₂³×D₃	semidirect
372. D₁₂	C₂³×D₃	semidirect
377. C₄×D₃	C₂³×D₃	semidirect
381. Dic₆	C₂³×D₃	semidirect
383. C₂×C₃²	C₂×H(5,𝔽₂)	semidirect
421. C₂²×C₄	C₂×D₃²	semidirect
433. C₂²×C₃	#1004	semidirect
434. C₂²×C₃	#1009	semidirect
463. C₃²	C₂²×H(5,𝔽₂)	semidirect
494. C₂×C₄	C₂²×D₃²	semidirect
502. C₂×C₃	C₂×#1004	semidirect
503. C₂×C₃	C₂×#1009	semidirect
520. C₂²	#64307	direct (N × H)
528. C₃	C₂²×#1004	semidirect
529. C₃	C₂²×#1009	semidirect
534. C₂	C₂×#64307	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×#3828	2
C₂²×C₃×#235	2
C₂³×C₃×D₁₂	2
C₂²×D₃×#67	2
C₂×#64307	2
C₂²×#3802	2
C₂²×D₃×D₁₂	2
C₂²×#3796	2
C₂²×#3795	2
C₂²×#1009	3
C₂²×#1004	3

Subgroups — C22×#64307 #11919225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#64307 #11919225