Subgroups — #11709044

Order 768.

10894 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#87568	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
3	#87277	C₂	1	2	yes	maximal, complemented
4	#87204	C₂	1	16	yes	maximal, complemented
5	#87203	C₂	1	8	yes	maximal, complemented
6	D₃×#576	C₂	1	8	yes	maximal, complemented
7	#87192	C₂	1	12	yes	maximal, complemented
8	#87187	C₂	1	6	yes	maximal, complemented
9	C₂×#5757	C₂	1	6	yes	maximal, complemented
10	#87163	C₂	1	1	yes	maximal, characteristic, complemented
11	#87160	C₂	1	1	yes	maximal, characteristic, complemented
12	#63091	—	3	1	no	maximal, Sylow
13	C₂×C₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
14	#5966	—	2	8	no	—
15	#5966	C₂²	1	16	yes	complemented
16	D₃×H(5,𝔽₂)	—	2	8	no	—
17	D₃×H(5,𝔽₂)	C₂²	1	16	yes	complemented
18	#5964	—	2	4	no	—
19	#5964	C₂²	1	1	yes	characteristic
20	#5964	C₂²	1	12	yes	complemented
21	#5964	C₂²	1	2	yes	complemented
22	C₂×#1004	—	2	12	no	—
23	C₂×#1004	C₂²	1	12	yes	complemented
24	C₃×#576	C₂²	1	8	yes	complemented
25	C₃×#576	C₂²	1	8	yes	complemented
26	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
27	C₂×C₃×#135	C₂²	1	3	yes	complemented
28	C₂²×C₃×D₈	C₂²	1	3	yes	complemented
29	C₂×C₃×#131	C₂²	1	1	yes	characteristic, complemented
30	#5836	C₂²	1	16	yes	complemented
31	#5835	C₂²	1	16	yes	complemented
32	#5822	C₂²	1	12	yes	complemented
33	#5819	C₂²	1	1	yes	characteristic, complemented
34	C₂×#932	C₂²	1	12	yes	complemented
35	#5775	C₂²	1	48	yes	complemented
36	#5774	C₂²	1	48	yes	complemented
37	#5773	C₂²	1	48	yes	complemented
38	D₃×AGL(1,ℤ/8)	C₂²	1	48	yes	complemented
39	#5771	C₂²	1	12	yes	complemented
40	#5770	C₂²	1	24	yes	complemented
41	#5769	C₂²	1	12	yes	complemented
42	#5768	C₂²	1	24	yes	complemented
43	D₃×#135	C₂²	1	24	yes	complemented
44	#5766	C₂²	1	4	yes	complemented
45	#5762	C₂²	1	24	yes	complemented
46	#5757	C₂²	1	12	yes	complemented
47	#5757	C₂²	1	24	yes	complemented
48	#5757	C₂²	1	24	yes	complemented
49	#5757	C₂²	1	24	yes	complemented
50	C₂×#912	C₂²	1	12	yes	complemented
51	C₂×#911	C₂²	1	24	yes	complemented
52	C₂×D₃×D₈	C₂²	1	12	yes	complemented
53	#5753	C₂²	1	4	yes	complemented
54	#5752	C₂²	1	4	yes	complemented
55	#5751	C₂²	1	8	yes	complemented
56	#5750	C₂²	1	8	yes	complemented
57	D₃×#131	C₂²	1	8	yes	complemented
58	#5748	C₂²	1	6	yes	complemented
59	#5745	C₂²	1	6	yes	complemented
60	C₂×#904	C₂²	1	6	yes	complemented
61	C₂×#901	C₂²	1	6	yes	complemented
62	H(7,𝔽₂)	—	3	2	no	—
63	#3585	—	3	2	no	—
64	#3585	—	3	16	no	—
65	#3585	—	3	12	no	—
66	#3584	—	3	8	no	—
67	#3584	—	3	6	no	—
68	#3584	—	3	1	no	—
69	C₂×#576	—	3	8	no	—
70	C₂×#576	—	3	6	no	—
71	C₂×#576	D₃	1	1	yes	characteristic, complemented
72	#3573	—	3	1	no	—
73	C₃×H(5,𝔽₂)	—	2	8	no	—
74	C₃×H(5,𝔽₂)	C₂³	1	16	yes	complemented
75	C₂×C₃×#41	—	2	2	no	—
76	C₂×C₃×#41	C₂³	1	1	yes	characteristic
77	C₂×C₃×#41	C₂³	1	6	yes	complemented
78	C₂²×C₃×D₄	—	2	6	no	—
79	C₂²×C₃×D₄	C₂³	1	6	yes	complemented
80	C₂²×#67	—	2	24	no	—
81	#1010	—	2	16	no	—
82	#1010	—	2	12	no	—
83	#1010	D₄	1	4	yes	—
84	#1010	C₂³	1	24	yes	complemented
85	#1010	C₂³	1	8	yes	complemented
86	#1009	—	2	16	no	—
87	#1009	—	2	12	no	—
88	#1009	D₄	1	4	yes	—
89	#1009	C₂³	1	24	yes	complemented
90	#1009	C₂³	1	8	yes	complemented
91	D₃×#41	—	2	8	no	—
92	D₃×#41	—	2	16	no	—
93	D₃×#41	—	2	16	no	—
94	D₃×#41	—	2	24	no	—
95	D₃×#41	C₂³	1	8	yes	—
96	D₃×#41	C₂³	1	48	yes	complemented
97	#1007	—	2	2	no	—
98	#1007	D₄	1	2	yes	—
99	#1007	C₂³	1	8	yes	complemented
100	#1004	—	2	6	no	—
101	#1004	—	2	24	no	—
102	#1004	—	2	48	no	—
103	#1004	—	2	48	no	—
104	#1004	—	2	24	no	—
105	#1004	—	2	24	no	—
106	#1004	D₄	1	6	yes	—
107	#1004	C₂³	1	24	yes	complemented
108	#1004	C₂³	1	48	yes	complemented
109	C₂×#237	—	2	48	no	—
110	C₂×#237	—	2	12	no	—
111	C₂×#237	C₂³	1	24	yes	complemented
112	C₂×D₃×D₄	—	2	48	no	—
113	C₂×D₃×D₄	—	2	12	no	—
114	C₂×D₃×D₄	C₂³	1	24	yes	complemented
115	C₂×#235	—	2	24	no	—
116	C₂×#235	C₂³	1	6	yes	—
117	C₂×#235	C₂³	1	12	yes	complemented
118	C₃×AGL(1,ℤ/8)	C₂³	1	48	yes	complemented
119	C₃×#135	C₂³	1	12	yes	complemented
120	C₃×#135	C₂³	1	12	yes	complemented
121	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic, complemented
122	C₂×C₃×SD₁₆	C₂³	1	6	yes	complemented
123	C₂×C₃×D₈	C₂³	1	3	yes	complemented
124	C₂×C₃×D₈	C₂³	1	6	yes	complemented
125	C₂×C₃×D₈	C₂³	1	12	yes	complemented
126	C₂×C₃×D₈	C₂³	1	12	yes	complemented
127	C₃×#131	C₂³	1	4	yes	complemented
128	C₃×#131	C₂³	1	4	yes	complemented
129	C₂×C₃×M₁₆	C₂³	1	3	yes	complemented
130	C₂²×C₃×C₈	C₂³	1	3	yes	complemented
131	#951	C₂³	1	24	yes	complemented
132	#950	C₂³	1	48	yes	complemented
133	#949	C₂³	1	24	yes	complemented
134	#948	C₂³	1	8	yes	complemented
135	#942	C₂³	1	8	yes	complemented
136	C₂×#214	C₂³	1	24	yes	complemented
137	#932	C₂³	1	24	yes	complemented
138	#932	C₂³	1	48	yes	complemented
139	C₂×#213	C₂³	1	24	yes	complemented
140	C₂×#208	C₂³	1	6	yes	complemented
141	#919	C₂³	1	8	yes	complemented
142	#918	C₂³	1	16	yes	complemented
143	D₃×Q₁₆	C₂³	1	8	yes	complemented
144	#916	C₂³	1	48	yes	complemented
145	#915	C₂³	1	48	yes	complemented
146	#914	C₂³	1	48	yes	complemented
147	D₃×SD₁₆	C₂³	1	48	yes	complemented
148	#912	C₂³	1	24	yes	complemented
149	#912	C₂³	1	48	yes	complemented
150	#911	C₂³	1	48	yes	complemented
151	#911	C₂³	1	96	yes	complemented
152	D₃×D₈	C₂³	1	24	yes	complemented
153	D₃×D₈	C₂³	1	48	yes	complemented
154	#909	C₂³	1	24	yes	complemented
155	#908	C₂³	1	24	yes	complemented
156	#907	C₂³	1	24	yes	complemented
157	D₃×M₁₆	C₂³	1	24	yes	complemented
158	C₂×Dic₁₂	C₂³	1	6	yes	complemented
159	#904	C₂³	1	4	yes	complemented
160	#904	C₂³	1	12	yes	complemented
161	#904	C₂³	1	12	yes	complemented
162	#904	C₂³	1	12	yes	complemented
163	C₂×D₂₄	C₂³	1	6	yes	complemented
164	C₂×#204	C₂³	1	12	yes	complemented
165	#901	C₂³	1	4	yes	complemented
166	#901	C₂³	1	12	yes	complemented
167	#901	C₂³	1	12	yes	complemented
168	#901	C₂³	1	12	yes	complemented
169	C₂×ΓL(1,𝔽₂₅)	C₂³	1	12	yes	complemented
170	C₂×D₃×C₈	C₂³	1	12	yes	complemented
171	#585	—	3	1	no	—
172	#585	—	3	16	no	—
173	#585	—	3	2	no	—
174	#585	—	3	12	no	—
175	#585	—	6	4	no	—
176	#585	—	6	8	no	—
177	C₂×H(5,𝔽₂)	—	3	16	no	—
178	C₂×H(5,𝔽₂)	—	3	12	no	—
179	C₂×H(5,𝔽₂)	—	6	12	no	—
180	C₂×H(5,𝔽₂)	—	6	8	no	—
181	C₂×H(5,𝔽₂)	C₂×D₃	1	2	yes	complemented
182	#578	—	3	12	no	—
183	#578	—	3	4	no	—
184	#578	—	3	4	no	—
185	#577	—	3	16	no	—
186	#577	—	3	48	no	—
187	#577	—	3	24	no	—
188	#577	—	3	24	no	—
189	#577	—	3	8	no	—
190	#576	—	3	16	no	—
191	#576	—	3	48	no	—
192	#576	—	3	12	no	—
193	#576	—	3	24	no	—
194	#576	—	3	12	no	—
195	#576	—	3	24	no	—
196	#576	—	3	24	no	—
197	#576	—	3	4	no	—
198	#576	C₂×D₃	1	8	yes	complemented
199	#576	C₂×D₃	1	8	yes	complemented
200	#575	—	3	12	no	—
201	#575	—	3	48	no	—
202	#575	—	3	24	no	—
203	#575	—	3	6	no	—
204	C₂×AGL(1,ℤ/8)	—	3	12	no	—
205	C₂×AGL(1,ℤ/8)	—	3	48	no	—
206	C₂×AGL(1,ℤ/8)	—	3	24	no	—
207	C₂×AGL(1,ℤ/8)	C₂×D₃	1	6	yes	complemented
208	C₂×#135	—	3	24	no	—
209	C₂×#135	—	3	12	no	—
210	C₂×#135	—	3	6	no	—
211	C₂×#135	C₂×D₃	1	3	yes	complemented
212	C₂²×D₈	—	3	12	no	—
213	C₂²×D₈	C₂×D₃	1	3	yes	complemented
214	#568	—	3	1	no	—
215	#568	—	3	8	no	—
216	#568	—	3	6	no	—
217	C₂×#131	—	3	8	no	—
218	C₂×#131	—	3	6	no	—
219	C₂×#131	C₂×D₃	1	1	yes	characteristic, complemented
220	C₂⁴×C₃	—	2	6	no	—
221	C₂³×D₃	—	2	24	no	—
222	C₃×#41	—	2	16	no	—
223	C₃×#41	—	2	12	no	—
224	C₃×#41	C₂×D₄	1	4	yes	—
225	C₃×#41	C₂⁴	1	24	yes	—
226	C₃×#41	C₂⁴	1	4	yes	—
227	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
228	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
229	C₂×C₃×D₄	—	2	6	no	—
230	C₂×C₃×D₄	—	2	48	no	—
231	C₂×C₃×D₄	—	2	12	no	—
232	C₂×C₃×D₄	—	2	6	no	—
233	C₂×C₃×D₄	C₂×D₄	1	3	yes	—
234	C₂×C₃×D₄	C₂⁴	1	24	yes	—
235	C₂×C₃×D₄	C₂⁴	1	6	yes	—
236	C₂²×C₃×C₄	—	2	6	no	—
237	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
238	C₂×#67	—	2	12	no	—
239	C₂×#67	—	2	24	no	—
240	C₂×#67	—	2	48	no	—
241	C₂×#67	—	2	96	no	—
242	C₂×#67	—	2	24	no	—
243	C₂×#67	C₂×D₄	1	12	yes	—
244	C₂²×Dic₃	—	2	24	no	—
245	#239	—	2	8	no	—
246	#239	—	2	8	no	—
247	#239	C₂×D₄	1	8	yes	—
248	#239	C₂⁴	1	16	yes	—
249	D₃×Q₈	—	2	8	no	—
250	D₃×Q₈	—	2	8	no	—
251	D₃×Q₈	C₂×D₄	1	8	yes	—
252	D₃×Q₈	C₂⁴	1	16	yes	—
253	#237	—	2	24	no	—
254	#237	—	2	48	no	—
255	#237	—	2	48	no	—
256	#237	—	2	48	no	—
257	#237	—	2	48	no	—
258	#237	—	2	24	no	—
259	#237	C₂×D₄	1	24	yes	—
260	#237	C₂⁴	1	48	yes	—
261	D₃×D₄	—	2	48	no	—
262	D₃×D₄	—	2	24	no	—
263	D₃×D₄	—	2	48	no	—
264	D₃×D₄	—	2	48	no	—
265	D₃×D₄	—	2	24	no	—
266	D₃×D₄	—	2	48	no	—
267	D₃×D₄	C₂×D₄	1	24	yes	—
268	D₃×D₄	C₂⁴	1	48	yes	—
269	#235	—	2	12	no	—
270	#235	—	2	12	no	—
271	#235	—	2	16	no	—
272	#235	—	2	24	no	—
273	#235	—	2	48	no	—
274	#235	—	2	24	no	—
275	#235	C₂×D₄	1	12	yes	—
276	#235	C₂×D₄	1	12	yes	—
277	#235	C₂⁴	1	4	yes	—
278	#235	C₂⁴	1	12	yes	—
279	#235	C₂⁴	1	8	yes	—
280	#235	C₂⁴	1	24	yes	—
281	C₂×D₁₂	—	2	24	no	—
282	C₂×D₁₂	C₂×D₄	1	6	yes	—
283	C₂×D₁₂	C₂⁴	1	12	yes	—
284	C₂×C₄×D₃	—	2	12	no	—
285	C₂×C₄×D₃	—	2	48	no	—
286	C₂×C₄×D₃	C₂⁴	1	12	yes	—
287	C₂×Dic₆	—	2	24	no	—
288	C₂×Dic₆	C₂×D₄	1	6	yes	—
289	C₂×Dic₆	C₂⁴	1	12	yes	—
290	C₃×Q₁₆	C₂⁴	1	2	yes	—
291	C₃×Q₁₆	C₂⁴	1	2	yes	—
292	C₃×SD₁₆	C₂⁴	1	24	yes	—
293	C₃×D₈	C₂⁴	1	6	yes	—
294	C₃×D₈	C₂⁴	1	24	yes	—
295	C₃×D₈	C₂⁴	1	6	yes	—
296	C₃×M₁₆	C₂⁴	1	12	yes	—
297	C₂×C₃×C₈	C₂⁴	1	6	yes	—
298	C₂×C₃×C₈	C₂⁴	1	6	yes	—
299	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
300	C₂×C₃×C₈	C₂⁴	1	3	yes	—
301	#216	C₂⁴	1	16	yes	—
302	#215	C₂⁴	1	16	yes	—
303	#214	C₂⁴	1	48	yes	—
304	#213	C₂⁴	1	48	yes	—
305	#208	C₂⁴	1	4	yes	—
306	#208	C₂⁴	1	12	yes	—
307	C₂×C₃⋊C₈	C₂⁴	1	12	yes	—
308	Dic₁₂	C₂⁴	1	4	yes	—
309	Dic₁₂	C₂⁴	1	12	yes	—
310	D₂₄	C₂⁴	1	4	yes	—
311	D₂₄	C₂⁴	1	12	yes	—
312	#204	C₂⁴	1	8	yes	—
313	#204	C₂⁴	1	24	yes	—
314	ΓL(1,𝔽₂₅)	C₂⁴	1	8	yes	—
315	ΓL(1,𝔽₂₅)	C₂⁴	1	24	yes	—
316	D₃×C₈	C₂⁴	1	8	yes	—
317	D₃×C₈	C₂⁴	1	24	yes	—
318	2₋¹⁺⁴	—	3	4	no	—
319	2₋¹⁺⁴	—	3	2	no	—
320	2₋¹⁺⁴	—	3	24	no	—
321	2₋¹⁺⁴	—	3	8	no	—
322	2₋¹⁺⁴	—	3	8	no	—
323	2₋¹⁺⁴	—	6	16	no	—
324	2₋¹⁺⁴	—	6	12	no	—
325	2₋¹⁺⁴	—	6	2	no	—
326	H(5,𝔽₂)	—	2	8	no	—
327	H(5,𝔽₂)	—	3	4	no	—
328	H(5,𝔽₂)	—	3	6	no	—
329	H(5,𝔽₂)	—	3	24	no	—
330	H(5,𝔽₂)	—	3	8	no	—
331	H(5,𝔽₂)	—	3	48	no	—
332	H(5,𝔽₂)	—	3	24	no	—
333	H(5,𝔽₂)	—	6	24	no	—
334	H(5,𝔽₂)	—	6	48	no	—
335	H(5,𝔽₂)	—	6	48	no	—
336	H(5,𝔽₂)	—	6	24	no	—
337	H(5,𝔽₂)	—	6	24	no	—
338	H(5,𝔽₂)	—	6	12	no	—
339	H(5,𝔽₂)	—	6	16	no	—
340	H(5,𝔽₂)	—	6	6	no	—
341	H(5,𝔽₂)	C₂²×D₃	1	16	yes	complemented
342	C₂×#41	—	2	2	no	—
343	C₂×#41	—	3	8	no	—
344	C₂×#41	—	3	6	no	—
345	C₂×#41	—	3	48	no	—
346	C₂×#41	—	3	24	no	—
347	C₂×#41	—	3	12	no	—
348	C₂×#41	—	6	24	no	—
349	C₂×#41	—	6	12	no	—
350	C₂×#41	—	6	48	no	—
351	C₂×#41	—	6	16	no	—
352	C₂×#41	—	6	16	no	—
353	C₂×#41	—	6	24	no	—
354	C₂×#41	—	6	8	no	—
355	C₂×#41	C₂²×D₃	1	1	yes	characteristic
356	C₂×#41	C₂²×D₃	1	6	yes	complemented
357	C₂²×D₄	—	2	6	no	—
358	C₂²×D₄	—	3	24	no	—
359	C₂²×D₄	—	6	48	no	—
360	C₂²×D₄	—	6	12	no	—
361	C₂²×D₄	—	6	24	no	—
362	C₂²×D₄	C₂²×D₃	1	6	yes	complemented
363	#137	—	3	24	no	—
364	#137	—	3	8	no	—
365	#137	—	3	16	no	—
366	#137	—	3	48	no	—
367	#137	—	3	24	no	—
368	AGL(1,ℤ/8)	—	3	24	no	—
369	AGL(1,ℤ/8)	—	3	48	no	—
370	AGL(1,ℤ/8)	—	3	24	no	—
371	AGL(1,ℤ/8)	—	3	48	no	—
372	AGL(1,ℤ/8)	—	3	96	no	—
373	AGL(1,ℤ/8)	—	3	48	no	—
374	AGL(1,ℤ/8)	—	3	24	no	—
375	AGL(1,ℤ/8)	C₂²×D₃	1	48	yes	complemented
376	#135	—	3	48	no	—
377	#135	—	3	8	no	—
378	#135	—	3	48	no	—
379	#135	—	3	24	no	—
380	#135	—	3	48	no	—
381	#135	—	3	12	no	—
382	#135	—	3	4	no	—
383	#135	—	3	12	no	—
384	#135	—	3	12	no	—
385	#135	C₂²×D₃	1	12	yes	complemented
386	#135	C₂²×D₃	1	12	yes	complemented
387	C₂×Q₁₆	—	3	8	no	—
388	C₂×Q₁₆	—	3	6	no	—
389	C₂×Q₁₆	C₂²×D₃	1	1	yes	characteristic, complemented
390	C₂×SD₁₆	—	3	24	no	—
391	C₂×SD₁₆	—	3	48	no	—
392	C₂×SD₁₆	—	3	12	no	—
393	C₂×SD₁₆	C₂²×D₃	1	6	yes	complemented
394	C₂×D₈	—	3	24	no	—
395	C₂×D₈	—	3	24	no	—
396	C₂×D₈	—	3	48	no	—
397	C₂×D₈	—	3	6	no	—
398	C₂×D₈	C₂²×D₃	1	12	yes	complemented
399	C₂×D₈	C₂²×D₃	1	3	yes	complemented
400	C₂×D₈	C₂²×D₃	1	12	yes	complemented
401	C₂×D₈	C₂²×D₃	1	6	yes	complemented
402	#131	—	3	8	no	—
403	#131	—	3	24	no	—
404	#131	—	3	12	no	—
405	#131	—	3	4	no	—
406	#131	—	3	12	no	—
407	#131	—	3	12	no	—
408	#131	C₂²×D₃	1	4	yes	complemented
409	#131	C₂²×D₃	1	4	yes	complemented
410	C₂×M₁₆	—	3	6	no	—
411	C₂×M₁₆	—	3	24	no	—
412	C₂×M₁₆	—	3	12	no	—
413	C₂×M₁₆	C₂²×D₃	1	3	yes	complemented
414	C₂²×C₈	—	3	12	no	—
415	C₂²×C₈	C₂²×D₃	1	3	yes	complemented
416	C₂³×C₃	—	2	24	no	—
417	C₂³×C₃	—	2	6	no	—
418	C₂³×C₃	—	16	6	no	—
419	C₂³×C₃	C₂²×D₄	1	3	yes	—
420	C₂²×D₃	—	2	12	no	—
421	C₂²×D₃	—	2	48	no	—
422	C₂²×D₃	—	16	24	no	—
423	C₂²×D₃	C₂²×D₄	1	12	yes	—
424	C₃×Q₈	—	2	2	no	—
425	C₃×Q₈	C₂²×D₄	1	4	yes	—
426	C₃×Q₈	C₂⁵	1	4	yes	—
427	C₃×D₄	—	2	24	no	—
428	C₃×D₄	—	2	24	no	—
429	C₃×D₄	—	2	6	no	—
430	C₃×D₄	C₂²×D₄	1	12	yes	—
431	C₃×D₄	C₂⁵	1	12	yes	—
432	C₂×C₃×C₄	—	2	2	no	—
433	C₂×C₃×C₄	—	2	24	no	—
434	C₂×C₃×C₄	C₂²×D₄	1	6	yes	—
435	C₂×C₃×C₄	C₂²×D₄	1	3	yes	—
436	C₂×C₃×C₄	C₂⁵	1	6	yes	—
437	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
438	#67	—	2	8	no	—
439	#67	—	2	24	no	—
440	#67	—	2	48	no	—
441	#67	—	2	48	no	—
442	#67	C₂²×D₄	1	8	yes	—
443	#67	C₂²×D₄	1	24	yes	—
444	C₂×Dic₃	—	2	12	no	—
445	C₂×Dic₃	—	2	48	no	—
446	C₂×Dic₃	C₂²×D₄	1	12	yes	—
447	D₁₂	—	2	16	no	—
448	D₁₂	—	2	12	no	—
449	D₁₂	C₂²×D₄	1	12	yes	—
450	D₁₂	C₂²×D₄	1	4	yes	—
451	D₁₂	C₂⁵	1	8	yes	—
452	C₄×D₃	—	2	16	no	—
453	C₄×D₃	—	2	24	no	—
454	C₄×D₃	—	2	8	no	—
455	C₄×D₃	—	2	16	no	—
456	C₄×D₃	C₂²×D₄	1	24	yes	—
457	C₄×D₃	C₂⁵	1	8	yes	—
458	Dic₆	—	2	12	no	—
459	Dic₆	—	2	16	no	—
460	Dic₆	C₂²×D₄	1	12	yes	—
461	Dic₆	C₂²×D₄	1	4	yes	—
462	Dic₆	C₂⁵	1	8	yes	—
463	C₃×C₈	C₂⁵	1	1	yes	characteristic
464	C₃×C₈	C₂⁵	1	6	yes	—
465	C₃×C₈	C₂⁵	1	1	yes	characteristic
466	C₃⋊C₈	C₂⁵	1	8	yes	—
467	C₂⁴	—	2	6	no	—
468	C₂⁴	—	6	24	no	—
469	#41	—	2	16	no	—
470	#41	—	2	12	no	—
471	#41	—	3	8	no	—
472	#41	—	3	24	no	—
473	#41	—	3	12	no	—
474	#41	—	3	12	no	—
475	#41	—	3	12	no	—
476	#41	—	3	4	no	—
477	#41	—	3	16	no	—
478	#41	—	3	48	no	—
479	#41	—	3	24	no	—
480	#41	—	3	8	no	—
481	#41	—	6	48	no	—
482	#41	—	6	16	no	—
483	#41	—	6	24	no	—
484	#41	—	6	24	no	—
485	#41	—	6	48	no	—
486	#41	—	6	48	no	—
487	#41	—	6	48	no	—
488	#41	—	6	24	no	—
489	#41	—	6	48	no	—
490	#41	—	6	8	no	—
491	#41	—	6	8	no	—
492	#41	—	6	24	no	—
493	#41	—	6	12	no	—
494	#41	—	6	12	no	—
495	#41	D₃×D₄	1	4	yes	—
496	#41	C₂³×D₃	1	24	yes	—
497	#41	C₂³×D₃	1	4	yes	—
498	C₂×Q₈	—	3	8	no	—
499	C₂×Q₈	—	3	6	no	—
500	C₂×Q₈	—	3	16	no	—
501	C₂×Q₈	—	3	12	no	—
502	C₂×Q₈	—	6	24	no	—
503	C₂×Q₈	—	6	8	no	—
504	C₂×Q₈	—	6	8	no	—
505	C₂×Q₈	D₃×D₄	1	1	yes	characteristic
506	C₂×Q₈	C₂³×D₃	1	2	yes	—
507	C₂×D₄	—	2	6	no	—
508	C₂×D₄	—	2	48	no	—
509	C₂×D₄	—	2	6	no	—
510	C₂×D₄	—	2	12	no	—
511	C₂×D₄	—	3	12	no	—
512	C₂×D₄	—	3	24	no	—
513	C₂×D₄	—	3	48	no	—
514	C₂×D₄	—	3	6	no	—
515	C₂×D₄	—	3	12	no	—
516	C₂×D₄	—	6	24	no	—
517	C₂×D₄	—	6	48	no	—
518	C₂×D₄	—	6	24	no	—
519	C₂×D₄	—	6	48	no	—
520	C₂×D₄	—	6	48	no	—
521	C₂×D₄	—	6	24	no	—
522	C₂×D₄	—	6	48	no	—
523	C₂×D₄	—	6	48	no	—
524	C₂×D₄	—	6	96	no	—
525	C₂×D₄	—	6	24	no	—
526	C₂×D₄	—	6	12	no	—
527	C₂×D₄	—	6	24	no	—
528	C₂×D₄	D₃×D₄	1	3	yes	—
529	C₂×D₄	C₂³×D₃	1	24	yes	—
530	C₂×D₄	C₂³×D₃	1	6	yes	—
531	C₂²×C₄	—	2	6	no	—
532	C₂²×C₄	—	3	12	no	—
533	C₂²×C₄	—	6	48	no	—
534	C₂²×C₄	—	6	24	no	—
535	C₂²×C₄	—	6	12	no	—
536	C₂²×C₄	C₂³×D₃	1	3	yes	—
537	Q₁₆	—	3	16	no	—
538	Q₁₆	—	3	4	no	—
539	Q₁₆	—	3	12	no	—
540	Q₁₆	C₂³×D₃	1	2	yes	—
541	Q₁₆	C₂³×D₃	1	2	yes	—
542	SD₁₆	—	3	16	no	—
543	SD₁₆	—	3	48	no	—
544	SD₁₆	—	3	24	no	—
545	SD₁₆	—	3	8	no	—
546	SD₁₆	C₂³×D₃	1	24	yes	—
547	D₈	—	3	48	no	—
548	D₈	—	3	4	no	—
549	D₈	—	3	12	no	—
550	D₈	C₂³×D₃	1	6	yes	—
551	D₈	C₂³×D₃	1	24	yes	—
552	D₈	C₂³×D₃	1	6	yes	—
553	M₁₆	—	3	12	no	—
554	M₁₆	—	3	4	no	—
555	M₁₆	—	3	24	no	—
556	M₁₆	—	3	8	no	—
557	M₁₆	C₂³×D₃	1	12	yes	—
558	C₂×C₈	—	3	12	no	—
559	C₂×C₈	—	3	8	no	—
560	C₂×C₈	—	3	24	no	—
561	C₂×C₈	C₂³×D₃	1	6	yes	—
562	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
563	C₂×C₈	C₂³×D₃	1	6	yes	—
564	C₂×C₈	C₂³×D₃	1	3	yes	—
565	C₂²×C₃	—	2	12	no	—
566	C₂²×C₃	—	4	3	no	—
567	C₂²×C₃	—	8	24	no	—
568	C₂²×C₃	—	8	6	no	—
569	C₂²×C₃	C₂³×D₄	1	6	yes	—
570	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
571	C₂×D₃	—	2	8	no	—
572	C₂×D₃	—	4	12	no	—
573	C₂×D₃	—	8	48	no	—
574	C₂×D₃	—	8	12	no	—
575	C₂×D₃	C₂³×D₄	1	8	yes	—
576	C₃×C₄	—	2	4	no	—
577	C₃×C₄	C₂³×D₄	1	6	yes	—
578	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
579	C₃×C₄	C₂⁶	1	1	yes	characteristic
580	Dic₃	—	2	8	no	—
581	Dic₃	C₂³×D₄	1	8	yes	—
582	C₂³	—	2	6	no	—
583	C₂³	—	2	24	no	—
584	C₂³	—	3	12	no	—
585	C₂³	—	6	48	no	—
586	C₂³	—	6	12	no	—
587	C₂³	—	16	6	no	—
588	C₂³	—	48	24	no	—
589	C₂³	C₂×D₃×D₄	1	3	yes	—
590	Q₈	—	2	2	no	—
591	Q₈	—	3	12	no	—
592	Q₈	—	3	4	no	—
593	Q₈	—	3	8	no	—
594	Q₈	—	6	16	no	—
595	Q₈	—	6	12	no	—
596	Q₈	C₂×D₃×D₄	1	4	yes	—
597	Q₈	C₂⁴×D₃	1	4	yes	—
598	D₄	—	2	24	no	—
599	D₄	—	2	24	no	—
600	D₄	—	2	6	no	—
601	D₄	—	3	8	no	—
602	D₄	—	3	24	no	—
603	D₄	—	3	12	no	—
604	D₄	—	3	4	no	—
605	D₄	—	3	8	no	—
606	D₄	—	6	16	no	—
607	D₄	—	6	48	no	—
608	D₄	—	6	48	no	—
609	D₄	—	6	8	no	—
610	D₄	—	6	24	no	—
611	D₄	—	6	12	no	—
612	D₄	C₂×D₃×D₄	1	12	yes	—
613	D₄	C₂⁴×D₃	1	12	yes	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	24	no	—
616	C₂×C₄	—	3	12	no	—
617	C₂×C₄	—	3	24	no	—
618	C₂×C₄	—	3	8	no	—
619	C₂×C₄	—	6	16	no	—
620	C₂×C₄	—	6	16	no	—
621	C₂×C₄	—	6	48	no	—
622	C₂×C₄	—	6	12	no	—
623	C₂×C₄	—	6	24	no	—
624	C₂×C₄	—	6	8	no	—
625	C₂×C₄	C₂×D₃×D₄	1	3	yes	—
626	C₂×C₄	C₂×D₃×D₄	1	6	yes	—
627	C₂×C₄	C₂⁴×D₃	1	6	yes	—
628	C₂×C₄	C₂⁴×D₃	1	1	yes	characteristic
629	C₈	—	3	8	no	—
630	C₈	C₂⁴×D₃	1	1	yes	characteristic
631	C₈	C₂⁴×D₃	1	6	yes	—
632	C₈	C₂⁴×D₃	1	1	yes	characteristic
633	C₂×C₃	—	2	6	no	—
634	C₂×C₃	—	2	1	no	—
635	C₂×C₃	—	4	12	no	—
636	C₂×C₃	C₂⁴×D₄	1	1	yes	characteristic
637	D₃	—	2	8	no	—
638	D₃	—	4	8	no	—
639	C₂²	—	2	12	no	—
640	C₂²	—	3	8	no	—
641	C₂²	—	4	3	no	—
642	C₂²	—	6	8	no	—
643	C₂²	—	8	6	no	—
644	C₂²	—	8	24	no	—
645	C₂²	—	12	12	no	—
646	C₂²	—	24	12	no	—
647	C₂²	—	24	48	no	—
648	C₂²	C₂²×D₃×D₄	1	1	yes	characteristic
649	C₂²	C₂²×D₃×D₄	1	6	yes	—
650	C₄	—	2	4	no	—
651	C₄	—	3	8	no	—
652	C₄	—	6	8	no	—
653	C₄	C₂²×D₃×D₄	1	6	yes	—
654	C₄	C₂²×D₃×D₄	1	1	yes	characteristic
655	C₄	C₂⁵×D₃	1	1	yes	characteristic
656	C₃	#63091	1	1	yes	characteristic, complemented, Sylow
657	C₂	—	2	1	no	—
658	C₂	—	2	6	no	—
659	C₂	—	4	12	no	—
660	C₂	—	6	8	no	—
661	C₂	—	12	8	no	—
662	C₂	C₂³×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂³×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁶
Frattini	C₄	C₂⁵×D₃
Fitting	C₂×C₃×#576	C₂
socle	C₂×C₃	C₂⁴×D₄
hypercenter	C₂×#576	D₃
hypocenter	C₃	#63091
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ C₂×#576

Complements

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

N	H ≅ G/N	type
1. #87568	C₂	semidirect
2. C₂×C₃×#576	C₂	semidirect
3. #87277	C₂	semidirect
4. #87204	C₂	semidirect
5. #87203	C₂	semidirect
6. D₃×#576	C₂	semidirect
7. #87192	C₂	semidirect
8. #87187	C₂	semidirect
9. C₂×#5757	C₂	semidirect
10. #87163	C₂	semidirect
11. #87160	C₂	semidirect
13. C₂×C₃×H(5,𝔽₂)	C₂²	semidirect
15. #5966	C₂²	semidirect
17. D₃×H(5,𝔽₂)	C₂²	semidirect
20. #5964	C₂²	semidirect
21. #5964	C₂²	semidirect
23. C₂×#1004	C₂²	semidirect
24. C₃×#576	C₂²	semidirect
25. C₃×#576	C₂²	semidirect
26. C₂×C₃×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×C₃×#135	C₂²	semidirect
28. C₂²×C₃×D₈	C₂²	semidirect
29. C₂×C₃×#131	C₂²	semidirect
30. #5836	C₂²	semidirect
31. #5835	C₂²	semidirect
32. #5822	C₂²	semidirect
33. #5819	C₂²	semidirect
34. C₂×#932	C₂²	semidirect
35. #5775	C₂²	semidirect
36. #5774	C₂²	semidirect
37. #5773	C₂²	semidirect
38. D₃×AGL(1,ℤ/8)	C₂²	semidirect
39. #5771	C₂²	semidirect
40. #5770	C₂²	semidirect
41. #5769	C₂²	semidirect
42. #5768	C₂²	semidirect
43. D₃×#135	C₂²	semidirect
44. #5766	C₂²	semidirect
45. #5762	C₂²	semidirect
46. #5757	C₂²	semidirect
47. #5757	C₂²	semidirect
48. #5757	C₂²	semidirect
49. #5757	C₂²	semidirect
50. C₂×#912	C₂²	semidirect
51. C₂×#911	C₂²	semidirect
52. C₂×D₃×D₈	C₂²	semidirect
53. #5753	C₂²	semidirect
54. #5752	C₂²	semidirect
55. #5751	C₂²	semidirect
56. #5750	C₂²	semidirect
57. D₃×#131	C₂²	semidirect
58. #5748	C₂²	semidirect
59. #5745	C₂²	semidirect
60. C₂×#904	C₂²	semidirect
61. C₂×#901	C₂²	semidirect
71. C₂×#576	D₃	semidirect
74. C₃×H(5,𝔽₂)	C₂³	semidirect
77. C₂×C₃×#41	C₂³	semidirect
79. C₂²×C₃×D₄	C₂³	semidirect
84. #1010	C₂³	semidirect
85. #1010	C₂³	semidirect
89. #1009	C₂³	semidirect
90. #1009	C₂³	semidirect
96. D₃×#41	C₂³	semidirect
99. #1007	C₂³	semidirect
107. #1004	C₂³	semidirect
108. #1004	C₂³	semidirect
111. C₂×#237	C₂³	semidirect
114. C₂×D₃×D₄	C₂³	semidirect
117. C₂×#235	C₂³	semidirect
118. C₃×AGL(1,ℤ/8)	C₂³	semidirect
119. C₃×#135	C₂³	semidirect
120. C₃×#135	C₂³	semidirect
121. C₂×C₃×Q₁₆	C₂³	semidirect
122. C₂×C₃×SD₁₆	C₂³	semidirect
123. C₂×C₃×D₈	C₂³	semidirect
124. C₂×C₃×D₈	C₂³	semidirect
125. C₂×C₃×D₈	C₂³	semidirect
126. C₂×C₃×D₈	C₂³	semidirect
127. C₃×#131	C₂³	semidirect
128. C₃×#131	C₂³	semidirect
129. C₂×C₃×M₁₆	C₂³	semidirect
130. C₂²×C₃×C₈	C₂³	semidirect
131. #951	C₂³	semidirect
132. #950	C₂³	semidirect
133. #949	C₂³	semidirect
134. #948	C₂³	semidirect
135. #942	C₂³	semidirect
136. C₂×#214	C₂³	semidirect
137. #932	C₂³	semidirect
138. #932	C₂³	semidirect
139. C₂×#213	C₂³	semidirect
140. C₂×#208	C₂³	semidirect
141. #919	C₂³	semidirect
142. #918	C₂³	semidirect
143. D₃×Q₁₆	C₂³	semidirect
144. #916	C₂³	semidirect
145. #915	C₂³	semidirect
146. #914	C₂³	semidirect
147. D₃×SD₁₆	C₂³	semidirect
148. #912	C₂³	semidirect
149. #912	C₂³	semidirect
150. #911	C₂³	semidirect
151. #911	C₂³	semidirect
152. D₃×D₈	C₂³	semidirect
153. D₃×D₈	C₂³	semidirect
154. #909	C₂³	semidirect
155. #908	C₂³	semidirect
156. #907	C₂³	semidirect
157. D₃×M₁₆	C₂³	semidirect
158. C₂×Dic₁₂	C₂³	semidirect
159. #904	C₂³	semidirect
160. #904	C₂³	semidirect
161. #904	C₂³	semidirect
162. #904	C₂³	semidirect
163. C₂×D₂₄	C₂³	semidirect
164. C₂×#204	C₂³	semidirect
165. #901	C₂³	semidirect
166. #901	C₂³	semidirect
167. #901	C₂³	semidirect
168. #901	C₂³	semidirect
169. C₂×ΓL(1,𝔽₂₅)	C₂³	semidirect
170. C₂×D₃×C₈	C₂³	semidirect
181. C₂×H(5,𝔽₂)	C₂×D₃	semidirect
198. #576	C₂×D₃	semidirect
199. #576	C₂×D₃	semidirect
207. C₂×AGL(1,ℤ/8)	C₂×D₃	semidirect
211. C₂×#135	C₂×D₃	semidirect
213. C₂²×D₈	C₂×D₃	semidirect
219. C₂×#131	C₂×D₃	semidirect
341. H(5,𝔽₂)	C₂²×D₃	semidirect
356. C₂×#41	C₂²×D₃	semidirect
362. C₂²×D₄	C₂²×D₃	semidirect
375. AGL(1,ℤ/8)	C₂²×D₃	semidirect
385. #135	C₂²×D₃	semidirect
386. #135	C₂²×D₃	semidirect
389. C₂×Q₁₆	C₂²×D₃	semidirect
393. C₂×SD₁₆	C₂²×D₃	semidirect
398. C₂×D₈	C₂²×D₃	semidirect
399. C₂×D₈	C₂²×D₃	semidirect
400. C₂×D₈	C₂²×D₃	semidirect
401. C₂×D₈	C₂²×D₃	semidirect
408. #131	C₂²×D₃	semidirect
409. #131	C₂²×D₃	semidirect
413. C₂×M₁₆	C₂²×D₃	semidirect
415. C₂²×C₈	C₂²×D₃	semidirect
656. C₃	#63091	semidirect

Maximal subgroups

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

subgroup	index
#87568	2
C₂×C₃×#576	2
#87277	2
#87204	2
#87203	2
D₃×#576	2
#87192	2
#87187	2
C₂×#5757	2
#87163	2
#87160	2
#63091	3