Subgroups — #10765677

Order 768.

590 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3102	C₂	1	1	yes	maximal, characteristic
2	#83131	C₂	1	1	yes	maximal, characteristic, complemented
3	#82521	C₂	1	1	yes	maximal, characteristic, complemented
4	#71751	C₂	1	1	yes	maximal, characteristic, complemented
5	#71641	C₂	1	1	yes	maximal, characteristic, complemented
6	#70905	C₂	1	1	yes	maximal, characteristic, complemented
7	#70903	C₂	1	1	yes	maximal, characteristic, complemented
8	#70900	C₂	1	1	yes	maximal, characteristic, complemented
9	#70900	C₂	1	1	yes	maximal, characteristic, complemented
10	#70898	C₂	1	1	yes	maximal, characteristic, complemented
11	#70897	C₂	1	1	yes	maximal, characteristic, complemented
12	#70881	C₂	1	1	yes	maximal, characteristic, complemented
13	#70879	C₂	1	1	yes	maximal, characteristic, complemented
14	#70750	C₂	1	1	yes	maximal, characteristic, complemented
15	#70743	C₂	1	1	yes	maximal, characteristic, complemented
16	#17954	—	3	1	no	maximal, Sylow
17	C₃×#529	C₂²	1	1	yes	characteristic
18	C₃×C₄×#41	C₂²	1	1	yes	characteristic
19	C₃×#485	C₄	1	1	yes	characteristic
20	C₃×#482	C₄	1	1	yes	characteristic
21	C₃×#479	C₄	1	1	yes	characteristic
22	C₃×#478	C₄	1	1	yes	characteristic
23	C₃×#464	C₄	1	1	yes	characteristic
24	C₃×#463	C₄	1	1	yes	characteristic
25	C₃×#452	C₄	1	1	yes	characteristic
26	C₃×#449	C₄	1	1	yes	characteristic
27	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic
28	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
29	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
30	C₃×C₄×D₈	C₂²	1	1	yes	characteristic
31	C₃×#431	C₂²	1	1	yes	characteristic
32	#5024	C₂²	1	1	yes	characteristic
33	#5024	C₂²	1	1	yes	characteristic
34	#5024	C₂²	1	1	yes	characteristic
35	Q₈×C₃⋊C₈	C₂²	1	1	yes	characteristic
36	#5012	—	2	1	no	—
37	#5012	C₂²	1	1	yes	characteristic
38	#5012	C₂²	1	1	yes	characteristic
39	#5012	C₂²	1	1	yes	characteristic
40	#5011	—	2	1	no	—
41	#5011	—	2	1	no	—
42	#5011	—	2	1	no	—
43	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
44	#5000	—	2	1	no	—
45	#4999	—	2	1	no	—
46	#4926	—	2	1	no	—
47	#4925	C₂²	1	1	yes	characteristic
48	#4924	—	2	1	no	—
49	#4924	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
51	C₄×#208	C₂²	1	1	yes	characteristic
52	#4535	C₂²	1	1	yes	characteristic
53	#4535	C₂²	1	1	yes	characteristic
54	#4535	C₂²	1	1	yes	characteristic
55	#4535	C₂²	1	1	yes	characteristic
56	D₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
57	D₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
58	D₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
59	D₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
60	#4458	C₂²	1	1	yes	characteristic
61	#4458	C₂²	1	1	yes	characteristic
62	#4458	C₂²	1	1	yes	characteristic
63	#4458	C₂²	1	1	yes	characteristic
64	#4455	C₂²	1	1	yes	characteristic
65	#4454	C₂²	1	1	yes	characteristic
66	#4454	C₂²	1	1	yes	characteristic
67	C₈×C₃⋊C₈	C₂²	1	1	yes	characteristic
68	#3102	D₃	1	1	yes	characteristic
69	#2993	—	3	1	no	—
70	#2989	—	3	1	no	—
71	#1592	—	3	1	no	—
72	#1592	—	3	1	no	—
73	#1591	—	3	1	no	—
74	#1589	—	3	1	no	—
75	#1588	—	3	1	no	—
76	#1585	—	3	1	no	—
77	#1584	—	3	1	no	—
78	#1581	—	3	1	no	—
79	#1571	—	3	1	no	—
80	#1489	—	3	1	no	—
81	#1483	—	3	1	no	—
82	#1453	—	3	1	no	—
83	C₂×C₃×#41	C₂×C₄	1	1	yes	characteristic
84	C₂×C₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
85	C₂×C₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
86	C₂×C₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
87	C₂×C₃×D₈	C₂×C₄	1	1	yes	characteristic
88	C₃×#126	—	2	1	no	—
89	C₃×#125	C₂×C₄	1	1	yes	characteristic
90	C₃×#124	C₂×C₄	1	1	yes	characteristic
91	C₃×#123	—	2	1	no	—
92	C₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
93	C₃×#121	C₂×C₄	1	1	yes	characteristic
94	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
95	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
96	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
97	C₃×C₄×D₄	—	2	1	no	—
98	C₃×C₄×D₄	—	2	1	no	—
99	C₃×C₄×D₄	—	2	1	no	—
100	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
101	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
102	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
103	C₃×#117	—	2	1	no	—
104	C₃×#117	—	2	1	no	—
105	C₃×#117	C₂×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄²	—	2	1	no	—
107	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
108	C₂×#208	—	2	1	no	—
109	C₂×#208	—	2	1	no	—
110	C₂×#208	—	2	1	no	—
111	C₂×#208	—	2	1	no	—
112	C₂×#208	—	2	1	no	—
113	C₂²×C₃⋊C₈	—	2	1	no	—
114	C₂²×C₃⋊C₈	—	2	1	no	—
115	C₃×#107	C₂×C₄	1	1	yes	characteristic
116	C₃×#107	C₂×C₄	1	1	yes	characteristic
117	C₃×#106	C₂×C₄	1	1	yes	characteristic
118	C₃×#106	C₂×C₄	1	1	yes	characteristic
119	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
120	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
121	C₃×#103	C₂×C₄	1	1	yes	characteristic
122	C₃×#103	C₂×C₄	1	1	yes	characteristic
123	C₃×#103	C₂×C₄	1	1	yes	characteristic
124	C₃×#103	C₂×C₄	1	1	yes	characteristic
125	C₃×#102	C₂×C₄	1	1	yes	characteristic
126	C₃×#102	C₂×C₄	1	1	yes	characteristic
127	C₃×#102	C₂×C₄	1	1	yes	characteristic
128	C₃×#102	C₂×C₄	1	1	yes	characteristic
129	C₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
130	C₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
131	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
132	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
133	#830	—	2	1	no	—
134	#830	—	2	1	no	—
135	#830	—	2	1	no	—
136	#830	—	2	1	no	—
137	#830	D₄	1	1	yes	characteristic
138	#830	D₄	1	1	yes	characteristic
139	C₄⋊(C₃⋊C₈)	—	2	1	no	—
140	C₄⋊(C₃⋊C₈)	—	2	1	no	—
141	C₄⋊(C₃⋊C₈)	—	2	1	no	—
142	C₄⋊(C₃⋊C₈)	—	2	1	no	—
143	C₄⋊(C₃⋊C₈)	—	2	1	no	—
144	C₄⋊(C₃⋊C₈)	—	2	1	no	—
145	C₄⋊(C₃⋊C₈)	D₄	1	1	yes	characteristic
146	C₄⋊(C₃⋊C₈)	D₄	1	1	yes	characteristic
147	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
148	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
149	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
150	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
151	#803	—	2	1	no	—
152	#803	—	2	1	no	—
153	#803	—	2	1	no	—
154	#803	—	2	1	no	—
155	C₄×C₃⋊C₈	—	2	1	no	—
156	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
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	#529	C₂×D₃	1	1	yes	characteristic
161	C₄×#41	C₂×D₃	1	1	yes	characteristic
162	#485	Dic₃	1	1	yes	characteristic
163	#482	Dic₃	1	1	yes	characteristic
164	#479	Dic₃	1	1	yes	characteristic
165	#478	Dic₃	1	1	yes	characteristic
166	#464	Dic₃	1	1	yes	characteristic
167	#463	Dic₃	1	1	yes	characteristic
168	#452	Dic₃	1	1	yes	characteristic
169	#449	Dic₃	1	1	yes	characteristic
170	#446	—	3	1	no	—
171	#446	—	3	1	no	—
172	#446	—	3	1	no	—
173	C₈×Q₈	—	3	1	no	—
174	C₄×Q₁₆	C₂×D₃	1	1	yes	characteristic
175	C₄×SD₁₆	C₂×D₃	1	1	yes	characteristic
176	C₄×SD₁₆	C₂×D₃	1	1	yes	characteristic
177	C₄×D₈	C₂×D₃	1	1	yes	characteristic
178	#436	—	3	1	no	—
179	#436	—	3	1	no	—
180	#436	—	3	1	no	—
181	#436	—	6	1	no	—
182	#435	—	6	1	no	—
183	#435	—	6	1	no	—
184	#435	—	6	1	no	—
185	C₈×D₄	—	3	1	no	—
186	#433	—	6	1	no	—
187	#432	—	6	1	no	—
188	#431	—	3	1	no	—
189	#431	C₂×D₃	1	1	yes	characteristic
190	#424	—	6	1	no	—
191	#423	—	3	1	no	—
192	#423	—	6	1	no	—
193	C₂×C₄⋊C₈	—	3	1	no	—
194	C₄×M₁₆	—	3	1	no	—
195	#335	—	3	1	no	—
196	#335	—	3	1	no	—
197	#335	—	3	1	no	—
198	#335	—	3	1	no	—
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	D₄⋊C₈	—	3	1	no	—
204	D₄⋊C₈	—	3	1	no	—
205	D₄⋊C₈	—	3	1	no	—
206	D₄⋊C₈	—	3	1	no	—
207	#322	—	3	1	no	—
208	#322	—	3	1	no	—
209	#322	—	3	1	no	—
210	C₈²	—	3	1	no	—
211	C₃×#41	—	4	1	no	—
212	C₃×#41	—	4	1	no	—
213	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
214	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
215	C₂×C₃×D₄	—	2	1	no	—
216	C₂×C₃×D₄	—	2	1	no	—
217	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
219	C₂²×C₃×C₄	—	2	1	no	—
220	C₂²×C₃×C₄	—	2	1	no	—
221	C₂²×C₃×C₄	—	2	1	no	—
222	C₂²×C₃×C₄	—	2	1	no	—
223	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₃×C₄	#41	1	1	yes	characteristic
226	C₃×Q₁₆	—	4	1	no	—
227	C₃×SD₁₆	—	4	1	no	—
228	C₃×SD₁₆	—	4	1	no	—
229	C₃×D₈	—	4	1	no	—
230	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
231	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
232	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
233	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
234	C₃×C₄⋊C₄	—	2	1	no	—
235	C₃×C₄⋊C₄	—	2	1	no	—
236	C₃×C₄⋊C₄	—	2	1	no	—
237	C₃×C₄⋊C₄	—	2	1	no	—
238	C₃×C₄⋊C₄	—	2	1	no	—
239	C₃×C₄⋊C₄	—	2	1	no	—
240	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
241	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
242	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
243	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
244	C₃×C₂²⋊C₄	—	2	1	no	—
245	C₃×C₂²⋊C₄	—	2	1	no	—
246	C₃×C₂²⋊C₄	—	2	1	no	—
247	C₃×C₂²⋊C₄	—	2	1	no	—
248	C₃×C₂²⋊C₄	—	2	1	no	—
249	C₃×C₂²⋊C₄	—	2	1	no	—
250	C₃×C₂²⋊C₄	—	2	1	no	—
251	C₃×C₂²⋊C₄	—	2	1	no	—
252	C₃×C₄²	—	2	1	no	—
253	C₃×C₄²	—	2	1	no	—
254	C₃×C₄²	—	2	1	no	—
255	C₃×C₄²	—	2	1	no	—
256	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
257	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
258	C₃×C₄²	#41	1	1	yes	characteristic
259	C₃×C₄²	C₂⁴	1	1	yes	characteristic
260	#208	—	4	2	no	—
261	#208	—	8	1	no	—
262	#208	—	8	1	no	—
263	#208	—	8	1	no	—
264	#208	—	8	1	no	—
265	C₂×C₃⋊C₈	—	2	1	no	—
266	C₂×C₃⋊C₈	—	2	1	no	—
267	C₂×C₃⋊C₈	—	2	1	no	—
268	C₂×C₃⋊C₈	—	2	1	no	—
269	C₂×C₃⋊C₈	—	2	1	no	—
270	C₂×C₃⋊C₈	—	2	1	no	—
271	C₂×C₃⋊C₈	—	8	1	no	—
272	C₂×C₃⋊C₈	—	8	1	no	—
273	C₂×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
274	C₂×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
275	C₂×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
276	C₂×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
277	C₂×#41	C₂×Dic₃	1	1	yes	characteristic
278	C₂×Q₁₆	C₂×Dic₃	1	1	yes	characteristic
279	C₂×SD₁₆	C₂×Dic₃	1	1	yes	characteristic
280	C₂×SD₁₆	C₂×Dic₃	1	1	yes	characteristic
281	C₂×D₈	C₂×Dic₃	1	1	yes	characteristic
282	C₂×M₁₆	—	6	1	no	—
283	C₂×M₁₆	—	6	1	no	—
284	C₂×M₁₆	—	6	1	no	—
285	C₂×M₁₆	—	6	1	no	—
286	C₂×M₁₆	—	6	1	no	—
287	C₂²×C₈	—	6	1	no	—
288	C₂²×C₈	—	6	1	no	—
289	#126	—	2	1	no	—
290	#125	C₂×Dic₃	1	1	yes	characteristic
291	#124	C₂×Dic₃	1	1	yes	characteristic
292	#123	—	2	1	no	—
293	C₂²⋊Q₈	C₂×Dic₃	1	1	yes	characteristic
294	#121	C₂×Dic₃	1	1	yes	characteristic
295	C₄×Q₈	C₂×Dic₃	1	1	yes	characteristic
296	C₄×Q₈	C₂²×D₃	1	1	yes	characteristic
297	C₄×Q₈	C₂²×D₃	1	1	yes	characteristic
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
302	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
303	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
304	#117	—	2	1	no	—
305	#117	—	2	1	no	—
306	#117	C₂×Dic₃	1	1	yes	characteristic
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
309	#107	C₂×Dic₃	1	1	yes	characteristic
310	#107	C₂×Dic₃	1	1	yes	characteristic
311	#106	C₂×Dic₃	1	1	yes	characteristic
312	#106	C₂×Dic₃	1	1	yes	characteristic
313	C₄⋊C₈	—	3	1	no	—
314	C₄⋊C₈	—	3	1	no	—
315	C₄⋊C₈	—	3	1	no	—
316	C₄⋊C₈	—	3	1	no	—
317	C₄⋊C₈	—	3	1	no	—
318	C₄⋊C₈	—	3	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	—	6	1	no	—
324	C₄⋊C₈	—	6	1	no	—
325	C₄⋊C₈	C₂×Dic₃	1	1	yes	characteristic
326	C₄⋊C₈	C₂×Dic₃	1	1	yes	characteristic
327	#103	C₂×Dic₃	1	1	yes	characteristic
328	#103	C₂×Dic₃	1	1	yes	characteristic
329	#103	C₂×Dic₃	1	1	yes	characteristic
330	#103	C₂×Dic₃	1	1	yes	characteristic
331	#102	C₂×Dic₃	1	1	yes	characteristic
332	#102	C₂×Dic₃	1	1	yes	characteristic
333	#102	C₂×Dic₃	1	1	yes	characteristic
334	#102	C₂×Dic₃	1	1	yes	characteristic
335	C₂²⋊C₈	—	3	1	no	—
336	C₂²⋊C₈	—	3	1	no	—
337	C₂²⋊C₈	—	6	1	no	—
338	C₂²⋊C₈	—	6	1	no	—
339	C₂²⋊C₈	—	6	1	no	—
340	C₂²⋊C₈	—	6	1	no	—
341	C₂²⋊C₈	C₂×Dic₃	1	1	yes	characteristic
342	C₂²⋊C₈	C₂×Dic₃	1	1	yes	characteristic
343	#97	—	6	1	no	—
344	#97	—	6	1	no	—
345	#97	—	6	1	no	—
346	#97	—	6	1	no	—
347	C₄×C₈	—	3	1	no	—
348	C₄×C₈	—	3	1	no	—
349	C₄×C₈	—	3	1	no	—
350	C₄×C₈	—	3	1	no	—
351	C₄×C₈	—	6	1	no	—
352	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
353	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
354	C₂³×C₃	—	2	1	no	—
355	C₂³×C₃	—	2	1	no	—
356	C₂³×C₃	C₄×D₄	1	1	yes	characteristic
357	C₃×Q₈	—	2	1	no	—
358	C₃×Q₈	—	2	1	no	—
359	C₃×Q₈	—	2	1	no	—
360	C₃×Q₈	—	2	1	no	—
361	C₃×D₄	—	2	1	no	—
362	C₃×D₄	—	2	1	no	—
363	C₃×D₄	—	2	1	no	—
364	C₃×D₄	—	2	1	no	—
365	C₃×D₄	—	4	2	no	—
366	C₃×D₄	—	8	1	no	—
367	C₂×C₃×C₄	—	2	1	no	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	2	1	no	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	4	1	no	—
378	C₂×C₃×C₄	—	4	2	no	—
379	C₂×C₃×C₄	—	4	1	no	—
380	C₂×C₃×C₄	—	4	1	no	—
381	C₂×C₃×C₄	—	4	1	no	—
382	C₂×C₃×C₄	—	4	1	no	—
383	C₂×C₃×C₄	—	8	1	no	—
384	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
385	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
386	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
390	C₃×C₈	—	2	1	no	—
391	C₃×C₈	—	2	1	no	—
392	C₃×C₈	—	2	1	no	—
393	C₃×C₈	—	2	1	no	—
394	C₃⋊C₈	—	2	2	no	—
395	C₃⋊C₈	—	2	1	no	—
396	C₃⋊C₈	—	2	1	no	—
397	C₃⋊C₈	—	2	1	no	—
398	C₃⋊C₈	—	2	1	no	—
399	C₃⋊C₈	—	4	1	no	—
400	C₃⋊C₈	—	4	1	no	—
401	C₃⋊C₈	—	4	1	no	—
402	C₃⋊C₈	—	4	1	no	—
403	C₃⋊C₈	—	4	1	no	—
404	#41	—	4	1	no	—
405	#41	—	4	1	no	—
406	C₂×Q₈	C₂²×Dic₃	1	1	yes	characteristic
407	C₂×Q₈	C₂²×Dic₃	1	1	yes	characteristic
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
411	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	D₃×D₄	1	1	yes	characteristic
417	C₂²×C₄	#237	1	1	yes	characteristic
418	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
419	Q₁₆	—	4	1	no	—
420	SD₁₆	—	4	1	no	—
421	SD₁₆	—	4	1	no	—
422	D₈	—	4	1	no	—
423	M₁₆	—	12	2	no	—
424	M₁₆	—	24	1	no	—
425	M₁₆	—	24	1	no	—
426	M₁₆	—	24	1	no	—
427	M₁₆	—	24	1	no	—
428	C₂×C₈	—	3	1	no	—
429	C₂×C₈	—	3	1	no	—
430	C₂×C₈	—	3	1	no	—
431	C₂×C₈	—	3	1	no	—
432	C₂×C₈	—	6	1	no	—
433	C₂×C₈	—	6	1	no	—
434	C₂×C₈	—	6	1	no	—
435	C₂×C₈	—	6	1	no	—
436	C₂×C₈	—	6	1	no	—
437	C₂×C₈	—	6	1	no	—
438	C₂×C₈	—	24	1	no	—
439	C₂×C₈	—	24	1	no	—
440	C₂×C₈	C₂²×Dic₃	1	1	yes	characteristic
441	C₂×C₈	C₂²×Dic₃	1	1	yes	characteristic
442	C₂×C₈	C₂²×Dic₃	1	1	yes	characteristic
443	C₂×C₈	C₂²×Dic₃	1	1	yes	characteristic
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
451	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
452	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
453	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	D₃×D₄	1	1	yes	characteristic
467	C₄²	#237	1	1	yes	characteristic
468	C₄²	C₂²×Dic₃	1	1	yes	characteristic
469	C₄²	C₂³×D₃	1	1	yes	characteristic
470	C₂²×C₃	—	2	1	no	—
471	C₂²×C₃	—	2	1	no	—
472	C₂²×C₃	—	2	1	no	—
473	C₂²×C₃	—	4	1	no	—
474	C₂²×C₃	—	4	1	no	—
475	C₂²×C₃	—	4	1	no	—
476	C₂²×C₃	—	4	1	no	—
477	C₂²×C₃	—	4	1	no	—
478	C₂²×C₃	—	4	1	no	—
479	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
480	C₃×C₄	—	2	1	no	—
481	C₃×C₄	—	2	1	no	—
482	C₃×C₄	—	2	1	no	—
483	C₃×C₄	—	2	1	no	—
484	C₃×C₄	—	4	1	no	—
485	C₃×C₄	—	4	1	no	—
486	C₃×C₄	—	4	1	no	—
487	C₃×C₄	—	4	1	no	—
488	C₃×C₄	—	4	1	no	—
489	C₃×C₄	—	4	1	no	—
490	C₃×C₄	#568	1	1	yes	characteristic
491	C₃×C₄	#568	1	1	yes	characteristic
492	C₃×C₄	#576	1	1	yes	characteristic
493	C₃×C₄	#578	1	1	yes	characteristic
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	D₄×Dic₃	1	1	yes	characteristic
497	Q₈	—	2	1	no	—
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	2	1	no	—
501	D₄	—	2	1	no	—
502	D₄	—	2	1	no	—
503	D₄	—	2	1	no	—
504	D₄	—	2	1	no	—
505	D₄	—	4	2	no	—
506	D₄	—	8	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	8	1	no	—
524	C₂×C₄	D₄×Dic₃	1	1	yes	characteristic
525	C₂×C₄	D₄×Dic₃	1	1	yes	characteristic
526	C₂×C₄	D₄×Dic₃	1	1	yes	characteristic
527	C₂×C₄	C₂×D₃×D₄	1	1	yes	characteristic
528	C₂×C₄	C₂×#237	1	1	yes	characteristic
529	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	1	no	—
534	C₈	—	6	2	no	—
535	C₈	—	6	1	no	—
536	C₈	—	6	1	no	—
537	C₈	—	6	1	no	—
538	C₈	—	6	1	no	—
539	C₈	—	12	1	no	—
540	C₈	—	12	1	no	—
541	C₈	—	12	1	no	—
542	C₈	—	12	1	no	—
543	C₈	—	12	1	no	—
544	C₂×C₃	—	4	1	no	—
545	C₂×C₃	—	8	1	no	—
546	C₂×C₃	—	8	1	no	—
547	C₂×C₃	#2930	1	1	yes	characteristic
548	C₂×C₃	#2951	1	1	yes	characteristic
549	C₂×C₃	#2956	1	1	yes	characteristic
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	C₂×D₄×Dic₃	1	1	yes	characteristic
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	#5769	1	1	yes	characteristic
571	C₄	#5771	1	1	yes	characteristic
572	C₄	#5819	1	1	yes	characteristic
573	C₄	#5819	1	1	yes	characteristic
574	C₃	#17954	1	1	yes	characteristic, complemented, Sylow
575	C₂	—	4	1	no	—
576	C₂	—	8	1	no	—
577	C₂	—	8	1	no	—
578	C₂	#82917	1	1	yes	characteristic
579	C₂	#83898	1	1	yes	characteristic
580	C₂	#84000	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×#3102	C₂
socle	C₂²×C₃	C₂×C₄×D₄
prime radical	C₃×#449	C₄
cosocle	C₃×C₄²	C₂⁴
hypercenter	#3102	D₃
hypocenter	C₃	#17954
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3102

Complements

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

N	H ≅ G/N	type
2. #83131	C₂	semidirect
3. #82521	C₂	semidirect
4. #71751	C₂	semidirect
5. #71641	C₂	semidirect
6. #70905	C₂	semidirect
7. #70903	C₂	semidirect
8. #70900	C₂	semidirect
9. #70900	C₂	semidirect
10. #70898	C₂	semidirect
11. #70897	C₂	semidirect
12. #70881	C₂	semidirect
13. #70879	C₂	semidirect
14. #70750	C₂	semidirect
15. #70743	C₂	semidirect
574. C₃	#17954	semidirect

Maximal subgroups

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

subgroup	index
C₃×#3102	2
#83131	2
#82521	2
#71751	2
#71641	2
#70905	2
#70903	2
#70900	2
#70898	2
#70897	2
#70881	2
#70879	2
#70750	2
#70743	2
#17954	3