Subgroups — #10766179

Order 768.

594 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
2	#79918	C₂	1	1	yes	maximal, characteristic
3	#79722	C₂	1	1	yes	maximal, characteristic
4	C₃×#1579	C₂	1	1	yes	maximal, characteristic, complemented
5	#70935	C₂	1	1	yes	maximal, characteristic, complemented
6	#70935	C₂	1	1	yes	maximal, characteristic, complemented
7	#70904	C₂	1	1	yes	maximal, characteristic, complemented
8	#68532	C₂	1	1	yes	maximal, characteristic
9	#68522	C₂	1	1	yes	maximal, characteristic, complemented
10	#68240	C₂	1	1	yes	maximal, characteristic
11	D₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic
12	#68227	C₂	1	1	yes	maximal, characteristic, complemented
13	#68215	C₂	1	1	yes	maximal, characteristic, complemented
14	#68089	C₂	1	1	yes	maximal, characteristic, complemented
15	#68070	C₂	1	1	yes	maximal, characteristic
16	#18003	—	3	1	no	maximal, Sylow
17	#5578	C₂²	1	1	yes	characteristic
18	C₄×D₃×Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₈×Q₈	C₂²	1	1	yes	characteristic
20	C₃×C₈×Q₈	C₂²	1	1	yes	characteristic
21	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic
22	#5186	C₄	1	1	yes	characteristic
23	#5182	C₄	1	1	yes	characteristic
24	C₄×#216	C₂²	1	1	yes	characteristic
25	C₄×#216	C₂²	1	1	yes	characteristic
26	#5024	C₂²	1	1	yes	characteristic
27	Q₈×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	#4884	C₄	1	1	yes	characteristic
29	#4875	C₄	1	1	yes	characteristic
30	#4839	—	2	1	no	—
31	#4837	—	2	1	no	—
32	#4837	C₂²	1	1	yes	characteristic
33	D₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	#4831	—	2	1	no	—
35	#4831	C₂²	1	1	yes	characteristic
36	#4830	C₂²	1	1	yes	characteristic
37	#4828	—	2	1	no	—
38	#4811	C₄	1	1	yes	characteristic
39	#4809	C₄	1	1	yes	characteristic
40	#4795	C₄	1	1	yes	characteristic
41	#4793	C₄	1	1	yes	characteristic
42	C₄×Dic₁₂	C₂²	1	1	yes	characteristic
43	#4689	—	2	1	no	—
44	C₄×ΓL(1,𝔽₂₅)	—	2	1	no	—
45	C₄×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
46	#4685	C₂²	1	1	yes	characteristic
47	C₄×D₃×C₈	C₂²	1	1	yes	characteristic
48	#4679	—	2	1	no	—
49	#4679	—	2	1	no	—
50	#4679	C₂²	1	1	yes	characteristic
51	#4679	C₂²	1	1	yes	characteristic
52	C₃×#334	C₂²	1	1	yes	characteristic
53	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
54	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
55	C₃×#322	C₂²	1	1	yes	characteristic
56	#4535	C₂²	1	1	yes	characteristic
57	#4535	C₂²	1	1	yes	characteristic
58	#4484	C₂²	1	1	yes	characteristic
59	#4484	C₂²	1	1	yes	characteristic
60	#4480	C₂²	1	1	yes	characteristic
61	#4480	C₂²	1	1	yes	characteristic
62	#4457	C₂²	1	1	yes	characteristic
63	#4456	C₂²	1	1	yes	characteristic
64	#4456	C₂²	1	1	yes	characteristic
65	#4454	C₂²	1	1	yes	characteristic
66	#4454	C₂²	1	1	yes	characteristic
67	#4454	C₂²	1	1	yes	characteristic
68	#3104	—	3	1	no	—
69	Q₈×M₁₆	—	3	1	no	—
70	#2962	—	3	1	no	—
71	#1593	—	3	1	no	—
72	#1593	—	3	1	no	—
73	#1587	—	3	1	no	—
74	#1587	—	3	1	no	—
75	#1587	—	3	1	no	—
76	#1587	—	3	1	no	—
77	#1579	—	3	1	no	—
78	#1579	D₃	1	1	yes	characteristic, complemented
79	#1570	—	3	1	no	—
80	#1493	—	3	1	no	—
81	C₂×Q₈⋊C₈	—	3	1	no	—
82	#1451	—	3	1	no	—
83	C₂×D₃×Q₈	C₂×C₄	1	1	yes	characteristic
84	C₂×C₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
85	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
86	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
87	#946	C₂×C₄	1	1	yes	characteristic
88	Q₈×Dic₃	C₂×C₄	1	1	yes	characteristic
89	#944	C₂×C₄	1	1	yes	characteristic
90	C₂×#216	C₂×C₄	1	1	yes	characteristic
91	C₂×#216	C₂×C₄	1	1	yes	characteristic
92	C₂×Dic₁₂	C₂×C₄	1	1	yes	characteristic
93	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
94	C₂×ΓL(1,𝔽₂₅)	D₄	1	1	yes	characteristic
95	C₂×ΓL(1,𝔽₂₅)	D₄	1	1	yes	characteristic
96	C₂×D₃×C₈	—	2	1	no	—
97	C₂×D₃×C₈	—	2	1	no	—
98	#897	C₂×C₄	1	1	yes	characteristic
99	#896	—	2	1	no	—
100	D₃×C₄⋊C₄	—	2	1	no	—
101	D₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
102	#889	—	2	1	no	—
103	#888	C₂×C₄	1	1	yes	characteristic
104	#887	—	2	1	no	—
105	#887	C₂×C₄	1	1	yes	characteristic
106	#872	—	2	1	no	—
107	C₄²×D₃	—	2	1	no	—
108	C₄²×D₃	C₂³	1	1	yes	characteristic
109	C₄×Dic₆	—	2	1	no	—
110	C₄×Dic₆	—	2	1	no	—
111	C₄×Dic₆	C₂³	1	1	yes	characteristic
112	C₄×Dic₆	C₂³	1	1	yes	characteristic
113	C₃×#107	C₂×C₄	1	1	yes	characteristic
114	C₃×C₄⋊C₈	—	2	1	no	—
115	C₃×C₄⋊C₈	—	2	1	no	—
116	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₃×#103	C₂×C₄	1	1	yes	characteristic
119	C₃×#103	C₂×C₄	1	1	yes	characteristic
120	C₃×C₄×C₈	—	2	1	no	—
121	C₃×C₄×C₈	—	2	1	no	—
122	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
123	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
124	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
125	#835	C₂×C₄	1	1	yes	characteristic
126	#835	C₂×C₄	1	1	yes	characteristic
127	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
128	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
129	#818	C₂×C₄	1	1	yes	characteristic
130	#816	C₂×C₄	1	1	yes	characteristic
131	#816	C₂×C₄	1	1	yes	characteristic
132	#815	—	2	1	no	—
133	#815	—	2	1	no	—
134	#815	—	2	1	no	—
135	#815	D₄	1	1	yes	characteristic
136	#815	D₄	1	1	yes	characteristic
137	Dic₃⋊C₈	—	2	1	no	—
138	Dic₃⋊C₈	—	2	1	no	—
139	Dic₃⋊C₈	—	2	1	no	—
140	Dic₃⋊C₈	—	2	1	no	—
141	Dic₃⋊C₈	—	2	1	no	—
142	Dic₃⋊C₈	—	2	1	no	—
143	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
144	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
145	C₈×Dic₃	—	2	1	no	—
146	C₈×Dic₃	—	2	1	no	—
147	#810	C₂×C₄	1	1	yes	characteristic
148	#810	C₂×C₄	1	1	yes	characteristic
149	#807	C₂×C₄	1	1	yes	characteristic
150	#807	C₂×C₄	1	1	yes	characteristic
151	C₄⋊(C₃⋊C₈)	—	2	1	no	—
152	C₄⋊(C₃⋊C₈)	—	2	1	no	—
153	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
154	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
155	#803	—	2	1	no	—
156	C₄×C₃⋊C₈	—	2	1	no	—
157	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
158	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
159	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
160	#533	—	3	1	no	—
161	C₂×C₄×Q₈	—	3	1	no	—
162	#484	—	3	1	no	—
163	#484	—	3	1	no	—
164	#477	—	3	1	no	—
165	#477	—	3	1	no	—
166	#462	—	3	1	no	—
167	#462	—	3	1	no	—
168	#451	—	3	1	no	—
169	#451	—	3	1	no	—
170	#446	—	3	1	no	—
171	#446	—	3	1	no	—
172	#446	—	3	1	no	—
173	#446	—	3	1	no	—
174	#446	—	6	1	no	—
175	#446	—	6	1	no	—
176	#446	—	6	1	no	—
177	#446	—	6	1	no	—
178	C₈×Q₈	—	3	1	no	—
179	C₈×Q₈	—	3	1	no	—
180	C₈×Q₈	C₂×D₃	1	1	yes	characteristic
181	C₈×Q₈	C₂×D₃	1	1	yes	characteristic
182	C₄×Q₁₆	—	3	1	no	—
183	C₄×Q₁₆	—	3	1	no	—
184	C₄×Q₁₆	—	3	1	no	—
185	C₄×Q₁₆	C₂×D₃	1	1	yes	characteristic
186	#431	—	3	1	no	—
187	#424	—	6	1	no	—
188	#423	—	3	1	no	—
189	#423	—	6	1	no	—
190	C₂×C₄⋊C₈	—	3	1	no	—
191	#405	—	6	1	no	—
192	C₄×M₁₆	—	3	1	no	—
193	C₄×M₁₆	—	6	1	no	—
194	C₂×C₄×C₈	—	3	1	no	—
195	#334	—	3	1	no	—
196	#334	—	3	1	no	—
197	#334	—	3	1	no	—
198	#334	C₂×D₃	1	1	yes	characteristic
199	Q₈⋊C₈	—	3	1	no	—
200	Q₈⋊C₈	—	3	1	no	—
201	Q₈⋊C₈	—	3	1	no	—
202	Q₈⋊C₈	—	3	1	no	—
203	Q₈⋊C₈	—	3	1	no	—
204	Q₈⋊C₈	—	3	1	no	—
205	Q₈⋊C₈	C₂×D₃	1	1	yes	characteristic
206	Q₈⋊C₈	C₂×D₃	1	1	yes	characteristic
207	#322	—	3	1	no	—
208	#322	—	3	1	no	—
209	#322	—	3	1	no	—
210	#322	C₂×D₃	1	1	yes	characteristic
211	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
213	D₃×Q₈	—	2	2	no	—
214	D₃×Q₈	—	4	1	no	—
215	C₂×C₄×D₃	—	2	1	no	—
216	C₂×C₄×D₃	—	2	1	no	—
217	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₄×D₃	C₂×D₄	1	1	yes	characteristic
219	C₂×C₄×D₃	#41	1	1	yes	characteristic
220	C₂×Dic₆	—	2	1	no	—
221	C₂×Dic₆	—	2	1	no	—
222	C₂×Dic₆	C₂²×C₄	1	1	yes	characteristic
223	C₂×Dic₆	C₂²×C₄	1	1	yes	characteristic
224	C₃×Q₁₆	—	2	2	no	—
225	C₂×C₃×C₈	—	2	1	no	—
226	C₂×C₃×C₈	—	2	1	no	—
227	C₂×C₃×C₈	—	2	1	no	—
228	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
229	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
230	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
231	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
232	C₃×C₄⋊C₄	—	2	1	no	—
233	C₃×C₄⋊C₄	—	2	1	no	—
234	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
235	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
236	C₃×C₄²	—	2	1	no	—
237	C₃×C₄²	—	2	1	no	—
238	C₃×C₄²	C₂⁴	1	1	yes	characteristic
239	#216	—	2	2	no	—
240	#216	—	4	1	no	—
241	(C₂×D₃)⋊C₄	—	2	1	no	—
242	(C₂×D₃)⋊C₄	—	2	1	no	—
243	C₄⋊Dic₃	—	2	1	no	—
244	C₄⋊Dic₃	—	2	1	no	—
245	C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
246	C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
247	Dic₃⋊C₄	—	2	1	no	—
248	Dic₃⋊C₄	—	2	1	no	—
249	Dic₃⋊C₄	—	2	1	no	—
250	Dic₃⋊C₄	—	2	1	no	—
251	Dic₃⋊C₄	—	2	1	no	—
252	Dic₃⋊C₄	—	2	1	no	—
253	Dic₃⋊C₄	—	2	1	no	—
254	Dic₃⋊C₄	—	2	1	no	—
255	C₄×Dic₃	—	2	1	no	—
256	C₄×Dic₃	—	2	1	no	—
257	C₄×Dic₃	—	2	1	no	—
258	C₄×Dic₃	—	2	1	no	—
259	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
260	C₄×Dic₃	C₂×D₄	1	1	yes	characteristic
261	C₄×Dic₃	#41	1	1	yes	characteristic
262	C₂×C₃⋊C₈	—	2	1	no	—
263	C₂×C₃⋊C₈	—	2	1	no	—
264	C₂×C₃⋊C₈	—	2	1	no	—
265	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
266	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
267	C₂×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
268	C₂×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
269	Dic₁₂	—	4	1	no	—
270	ΓL(1,𝔽₂₅)	—	2	2	no	—
271	ΓL(1,𝔽₂₅)	—	2	2	no	—
272	ΓL(1,𝔽₂₅)	—	4	2	no	—
273	D₃×C₈	—	4	2	no	—
274	D₃×C₈	—	4	2	no	—
275	C₂²×Q₈	—	3	1	no	—
276	C₂×Q₁₆	—	3	1	no	—
277	C₂×Q₁₆	—	3	1	no	—
278	C₂×Q₁₆	—	3	1	no	—
279	C₂×Q₁₆	C₄×D₃	1	1	yes	characteristic
280	C₂×M₁₆	—	3	1	no	—
281	C₂×M₁₆	—	3	1	no	—
282	C₂×M₁₆	—	6	1	no	—
283	C₂²×C₈	—	6	1	no	—
284	C₂²×C₈	—	6	1	no	—
285	C₄⋊Q₈	—	3	1	no	—
286	C₄⋊Q₈	—	3	1	no	—
287	#125	—	6	1	no	—
288	C₂²⋊Q₈	—	3	1	no	—
289	C₂²⋊Q₈	—	3	1	no	—
290	C₂²⋊Q₈	—	6	1	no	—
291	C₄×Q₈	—	3	1	no	—
292	C₄×Q₈	—	3	1	no	—
293	C₄×Q₈	—	3	1	no	—
294	C₄×Q₈	—	3	1	no	—
295	C₄×Q₈	—	6	1	no	—
296	C₄×Q₈	—	6	1	no	—
297	C₄×Q₈	—	6	1	no	—
298	C₄×Q₈	C₂²×D₃	1	1	yes	characteristic
299	C₄×Q₈	C₂²×D₃	1	1	yes	characteristic
300	#117	—	6	1	no	—
301	C₂×C₄⋊C₄	—	3	1	no	—
302	C₂×C₄⋊C₄	—	6	1	no	—
303	C₂×C₄²	—	3	1	no	—
304	C₂×C₄²	—	6	1	no	—
305	#107	—	3	1	no	—
306	#107	—	3	1	no	—
307	#107	—	3	1	no	—
308	#107	C₄×D₃	1	1	yes	characteristic
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	3	1	no	—
312	C₄⋊C₈	—	3	1	no	—
313	C₄⋊C₈	—	3	1	no	—
314	C₄⋊C₈	—	3	1	no	—
315	C₄⋊C₈	—	6	1	no	—
316	C₄⋊C₈	—	6	1	no	—
317	C₄⋊C₈	—	6	1	no	—
318	C₄⋊C₈	—	6	1	no	—
319	C₄⋊C₈	—	6	1	no	—
320	C₄⋊C₈	—	6	1	no	—
321	C₄⋊C₈	—	6	1	no	—
322	C₄⋊C₈	—	6	1	no	—
323	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
324	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
325	#103	—	3	1	no	—
326	#103	—	3	1	no	—
327	#103	—	3	1	no	—
328	#103	—	3	1	no	—
329	#103	—	3	1	no	—
330	#103	—	3	1	no	—
331	#103	C₄×D₃	1	1	yes	characteristic
332	#103	C₄×D₃	1	1	yes	characteristic
333	C₂²⋊C₈	—	3	1	no	—
334	C₂²⋊C₈	—	3	1	no	—
335	#97	—	3	1	no	—
336	#97	—	3	1	no	—
337	#97	—	6	1	no	—
338	#97	—	6	1	no	—
339	#97	—	6	1	no	—
340	#97	—	6	1	no	—
341	C₄×C₈	—	2	1	no	—
342	C₄×C₈	—	2	1	no	—
343	C₄×C₈	—	3	1	no	—
344	C₄×C₈	—	3	1	no	—
345	C₄×C₈	—	3	1	no	—
346	C₄×C₈	—	6	1	no	—
347	C₄×C₈	—	6	1	no	—
348	C₄×C₈	—	6	1	no	—
349	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
350	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
351	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
352	C₂²×D₃	C₄×D₄	1	1	yes	characteristic
353	C₃×Q₈	—	2	1	no	—
354	C₃×Q₈	—	2	1	no	—
355	C₃×Q₈	—	2	1	no	—
356	C₃×Q₈	#131	1	2	yes	—
357	C₂×C₃×C₄	—	2	1	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	—	2	1	no	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
362	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
364	C₂×Dic₃	—	2	1	no	—
365	C₂×Dic₃	—	2	1	no	—
366	C₂×Dic₃	—	2	1	no	—
367	C₂×Dic₃	—	2	1	no	—
368	C₂×Dic₃	C₄×D₄	1	1	yes	characteristic
369	C₂×Dic₃	C₄×D₄	1	1	yes	characteristic
370	C₂×Dic₃	C₄×D₄	1	1	yes	characteristic
371	C₄×D₃	—	2	1	no	—
372	C₄×D₃	—	2	1	no	—
373	C₄×D₃	—	4	1	no	—
374	C₄×D₃	—	4	2	no	—
375	C₄×D₃	—	8	1	no	—
376	C₄×D₃	#137	1	2	yes	—
377	C₄×D₃	#137	1	2	yes	—
378	Dic₆	—	2	1	no	—
379	Dic₆	—	2	1	no	—
380	Dic₆	—	2	1	no	—
381	Dic₆	—	2	1	no	—
382	Dic₆	—	4	2	no	—
383	Dic₆	—	8	1	no	—
384	C₃×C₈	—	2	1	no	—
385	C₃×C₈	—	2	1	no	—
386	C₃×C₈	—	2	1	no	—
387	C₃×C₈	—	2	1	no	—
388	C₃×C₈	—	4	1	no	—
389	C₃×C₈	—	4	1	no	—
390	C₃×C₈	—	4	1	no	—
391	C₃⋊C₈	—	2	2	no	—
392	C₃⋊C₈	—	2	1	no	—
393	C₃⋊C₈	—	2	1	no	—
394	C₃⋊C₈	—	2	1	no	—
395	C₃⋊C₈	—	2	1	no	—
396	C₃⋊C₈	—	4	1	no	—
397	C₃⋊C₈	—	4	1	no	—
398	C₂×Q₈	—	3	1	no	—
399	C₂×Q₈	—	3	1	no	—
400	C₂×Q₈	—	6	1	no	—
401	C₂×Q₈	—	6	1	no	—
402	C₂×Q₈	—	6	2	no	—
403	C₂×Q₈	—	12	1	no	—
404	C₂×Q₈	C₂×C₄×D₃	1	1	yes	characteristic
405	C₂×Q₈	C₂×C₄×D₃	1	1	yes	characteristic
406	C₂²×C₄	—	3	1	no	—
407	C₂²×C₄	—	3	1	no	—
408	C₂²×C₄	—	3	1	no	—
409	C₂²×C₄	—	6	1	no	—
410	C₂²×C₄	—	6	1	no	—
411	Q₁₆	—	2	2	no	—
412	Q₁₆	—	6	2	no	—
413	Q₁₆	—	12	1	no	—
414	Q₁₆	—	12	1	no	—
415	M₁₆	—	6	2	no	—
416	M₁₆	—	6	2	no	—
417	M₁₆	—	12	2	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	3	1	no	—
422	C₂×C₈	—	3	1	no	—
423	C₂×C₈	—	3	1	no	—
424	C₂×C₈	—	3	1	no	—
425	C₂×C₈	—	6	1	no	—
426	C₂×C₈	—	6	1	no	—
427	C₂×C₈	—	6	1	no	—
428	C₂×C₈	—	12	2	no	—
429	C₂×C₈	—	12	2	no	—
430	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
431	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
432	C₂×C₈	D₃×D₄	1	1	yes	characteristic
433	C₂×C₈	D₃×D₄	1	1	yes	characteristic
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	3	1	no	—
437	C₄⋊C₄	—	3	1	no	—
438	C₄⋊C₄	—	6	1	no	—
439	C₄⋊C₄	—	6	1	no	—
440	C₄⋊C₄	—	6	1	no	—
441	C₄⋊C₄	—	6	1	no	—
442	C₄⋊C₄	—	6	1	no	—
443	C₄⋊C₄	—	6	1	no	—
444	C₄⋊C₄	—	6	1	no	—
445	C₄⋊C₄	—	6	1	no	—
446	C₄⋊C₄	—	6	1	no	—
447	C₄⋊C₄	—	6	1	no	—
448	C₄⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
449	C₄⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
450	C₂²⋊C₄	—	6	1	no	—
451	C₂²⋊C₄	—	6	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	3	1	no	—
455	C₄²	—	3	1	no	—
456	C₄²	—	3	1	no	—
457	C₄²	—	6	1	no	—
458	C₄²	—	6	1	no	—
459	C₄²	—	6	1	no	—
460	C₄²	—	6	1	no	—
461	C₄²	C₂³×D₃	1	1	yes	characteristic
462	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
463	C₂×D₃	—	2	1	no	—
464	C₂×D₃	—	2	1	no	—
465	C₂×D₃	#441	1	2	yes	—
466	C₃×C₄	—	2	2	no	—
467	C₃×C₄	—	2	1	no	—
468	C₃×C₄	—	4	1	no	—
469	C₃×C₄	—	4	1	no	—
470	C₃×C₄	—	4	1	no	—
471	C₃×C₄	C₂×#131	1	1	yes	characteristic
472	C₃×C₄	#568	1	1	yes	characteristic
473	C₃×C₄	C₂×#137	1	1	yes	characteristic
474	C₃×C₄	C₂×#137	1	1	yes	characteristic
475	Dic₃	—	2	1	no	—
476	Dic₃	—	2	1	no	—
477	Dic₃	—	4	1	no	—
478	Dic₃	—	4	1	no	—
479	Dic₃	—	4	1	no	—
480	Dic₃	—	4	1	no	—
481	Dic₃	#441	1	2	yes	—
482	C₂³	—	3	1	no	—
483	Q₈	—	2	1	no	—
484	Q₈	—	2	1	no	—
485	Q₈	—	2	1	no	—
486	Q₈	—	6	1	no	—
487	Q₈	—	6	1	no	—
488	Q₈	—	6	1	no	—
489	Q₈	—	6	1	no	—
490	Q₈	—	12	2	no	—
491	Q₈	—	24	1	no	—
492	Q₈	#901	1	2	yes	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	3	1	no	—
498	C₂×C₄	—	3	2	no	—
499	C₂×C₄	—	3	2	no	—
500	C₂×C₄	—	3	1	no	—
501	C₂×C₄	—	3	1	no	—
502	C₂×C₄	—	6	1	no	—
503	C₂×C₄	—	6	1	no	—
504	C₂×C₄	—	6	1	no	—
505	C₂×C₄	—	6	1	no	—
506	C₂×C₄	—	6	1	no	—
507	C₂×C₄	—	6	1	no	—
508	C₂×C₄	—	12	1	no	—
509	C₂×C₄	—	12	2	no	—
510	C₂×C₄	—	24	1	no	—
511	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
512	C₂×C₄	C₂×D₃×D₄	1	1	yes	characteristic
513	C₂×C₄	D₃×#41	1	1	yes	characteristic
514	C₈	—	2	1	no	—
515	C₈	—	2	1	no	—
516	C₈	—	2	1	no	—
517	C₈	—	2	1	no	—
518	C₈	—	4	1	no	—
519	C₈	—	4	1	no	—
520	C₈	—	4	1	no	—
521	C₈	—	6	2	no	—
522	C₈	—	6	1	no	—
523	C₈	—	6	1	no	—
524	C₈	—	6	1	no	—
525	C₈	—	6	1	no	—
526	C₈	—	12	1	no	—
527	C₈	—	12	1	no	—
528	C₂×C₃	#2933	1	1	yes	characteristic
529	C₂×C₃	C₂×#441	1	1	yes	characteristic
530	C₂×C₃	#2956	1	1	yes	characteristic
531	D₃	—	2	2	no	—
532	C₂²	—	3	2	no	—
533	C₂²	—	6	1	no	—
534	C₂²	—	6	1	no	—
535	C₂²	C₄×D₃×D₄	1	1	yes	characteristic
536	C₄	—	2	1	no	—
537	C₄	—	2	2	no	—
538	C₄	—	3	2	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	1	no	—
542	C₄	—	6	1	no	—
543	C₄	—	6	1	no	—
544	C₄	—	12	1	no	—
545	C₄	—	12	1	no	—
546	C₄	—	12	1	no	—
547	C₄	—	12	1	no	—
548	C₄	C₂×#901	1	1	yes	characteristic
549	C₄	#5750	1	1	yes	characteristic
550	C₄	D₃×#137	1	1	yes	characteristic
551	C₄	D₃×#137	1	1	yes	characteristic
552	C₃	#18003	1	1	yes	characteristic, complemented, Sylow
553	C₂	—	6	2	no	—
554	C₂	#79423	1	1	yes	characteristic
555	C₂	D₃×#441	1	1	yes	characteristic
556	C₂	#79898	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃×D₄
commutator	C₂×C₃×C₄	C₂³×C₄
Frattini	C₄²	C₂³×D₃
Fitting	C₃×#1579	C₂
socle	C₂²×C₃	C₂×C₄×D₄
prime radical	C₂²×D₃	C₄×D₄
cosocle	C₃×C₄²	C₂⁴
hypercenter	#1579	D₃
hypocenter	C₃	#18003
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1579

Complements

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

N	H ≅ G/N	type
4. C₃×#1579	C₂	semidirect
5. #70935	C₂	semidirect
6. #70935	C₂	semidirect
7. #70904	C₂	semidirect
9. #68522	C₂	semidirect
12. #68227	C₂	semidirect
13. #68215	C₂	semidirect
14. #68089	C₂	semidirect
78. #1579	D₃	semidirect
552. C₃	#18003	semidirect

Maximal subgroups

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

subgroup	index
Q₈×ΓL(1,𝔽₂₅)	2
#79918	2
#79722	2
C₃×#1579	2
#70935	2
#70904	2
#68532	2
#68522	2
#68240	2
D₃×Q₈⋊C₈	2
#68227	2
#68215	2
#68089	2
#68070	2
#18003	3