Subgroups — #10765249

Order 768.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3105	C₂	1	1	yes	maximal, characteristic
2	#83131	C₂	1	1	yes	maximal, characteristic, complemented
3	#82301	C₂	1	1	yes	maximal, characteristic, complemented
4	#71750	C₂	1	1	yes	maximal, characteristic, complemented
5	#71598	C₂	1	1	yes	maximal, characteristic, complemented
6	#70897	C₂	1	1	yes	maximal, characteristic, complemented
7	#70895	C₂	1	1	yes	maximal, characteristic, complemented
8	SD₁₆⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
9	SD₁₆×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#70880	C₂	1	1	yes	maximal, characteristic, complemented
11	#70879	C₂	1	1	yes	maximal, characteristic, complemented
12	#70878	C₂	1	1	yes	maximal, characteristic, complemented
13	D₈×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#70753	C₂	1	1	yes	maximal, characteristic, complemented
15	#70744	C₂	1	1	yes	maximal, characteristic, complemented
16	#17918	—	3	1	no	maximal, Sylow
17	C₃×#529	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
19	C₃×#484	C₄	1	1	yes	characteristic
20	C₃×#481	C₄	1	1	yes	characteristic
21	C₃×#478	C₄	1	1	yes	characteristic
22	C₃×#478	C₄	1	1	yes	characteristic
23	C₃×#463	C₄	1	1	yes	characteristic
24	C₃×#463	C₄	1	1	yes	characteristic
25	C₃×#450	C₄	1	1	yes	characteristic
26	C₃×#447	C₄	1	1	yes	characteristic
27	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
28	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
29	C₃×C₄×D₈	C₂²	1	1	yes	characteristic
30	C₃×C₄×D₈	C₂²	1	1	yes	characteristic
31	C₃×#431	C₂²	1	1	yes	characteristic
32	C₂×#830	—	2	1	no	—
33	C₂×#830	—	2	1	no	—
34	#5024	C₂²	1	1	yes	characteristic, complemented
35	Q₈×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
36	#5012	—	2	1	no	—
37	#5012	C₂²	1	1	yes	characteristic, complemented
38	#5011	—	2	1	no	—
39	D₄×C₃⋊C₈	—	2	1	no	—
40	D₄×C₃⋊C₈	—	2	1	no	—
41	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
42	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
43	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
44	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
45	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	#5000	—	2	1	no	—
47	#4999	—	2	1	no	—
48	#4925	C₂²	1	1	yes	characteristic
49	#4925	C₂²	1	1	yes	characteristic
50	#4925	C₂²	1	1	yes	characteristic
51	#4924	C₂²	1	1	yes	characteristic
52	#4535	C₂²	1	1	yes	characteristic, complemented
53	#4535	C₂²	1	1	yes	characteristic, complemented
54	D₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
55	D₄⋊(C₃⋊C₈)	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, complemented
59	D₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
60	#4458	C₂²	1	1	yes	characteristic, complemented
61	#4458	C₂²	1	1	yes	characteristic, complemented
62	#4457	C₂²	1	1	yes	characteristic, complemented
63	#4457	C₂²	1	1	yes	characteristic, complemented
64	#4455	C₂²	1	1	yes	characteristic, complemented
65	#4454	C₂²	1	1	yes	characteristic, complemented
66	#4454	C₂²	1	1	yes	characteristic, complemented
67	C₈×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
68	#3105	D₃	1	1	yes	characteristic
69	#2993	—	3	1	no	—
70	#2972	—	3	1	no	—
71	#1586	—	3	1	no	—
72	#1585	—	3	1	no	—
73	#1582	—	3	1	no	—
74	#1581	—	3	1	no	—
75	#1580	—	3	1	no	—
76	SD₁₆⋊C₈	—	3	1	no	—
77	C₈×SD₁₆	—	3	1	no	—
78	C₈×D₈	—	3	1	no	—
79	#1574	—	3	1	no	—
80	#1486	—	3	1	no	—
81	#1482	—	3	1	no	—
82	#1454	—	3	1	no	—
83	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₃×C₄	—	2	1	no	—
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	C₂×C₃×D₈	C₂×C₄	1	1	yes	characteristic
89	C₃×#126	—	2	1	no	—
90	C₃×#125	C₂×C₄	1	1	yes	characteristic
91	C₃×#124	C₂×C₄	1	1	yes	characteristic
92	C₃×#123	—	2	1	no	—
93	C₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
94	C₃×#121	C₂×C₄	1	1	yes	characteristic
95	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
96	C₃×C₄×D₄	—	2	1	no	—
97	C₃×C₄×D₄	—	2	1	no	—
98	C₃×C₄×D₄	—	2	1	no	—
99	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
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×C₄×D₄	C₂³	1	1	yes	characteristic
104	C₃×#117	—	2	1	no	—
105	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₂×C₃×C₂²⋊C₄	—	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	C₂²×C₃⋊C₈	—	2	1	no	—
111	C₂²×C₃⋊C₈	—	2	1	no	—
112	C₂²×C₃⋊C₈	—	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×#102	C₂×C₄	1	1	yes	characteristic
124	C₃×#102	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	—	2	1	no	—
138	#830	—	2	1	no	—
139	#830	—	2	1	no	—
140	#830	—	2	1	no	—
141	#830	D₄	1	1	yes	characteristic
142	#830	D₄	1	1	yes	characteristic
143	C₄⋊(C₃⋊C₈)	—	2	1	no	—
144	C₄⋊(C₃⋊C₈)	—	2	1	no	—
145	C₄⋊(C₃⋊C₈)	—	2	1	no	—
146	C₄⋊(C₃⋊C₈)	—	2	1	no	—
147	C₄⋊(C₃⋊C₈)	D₄	1	1	yes	characteristic
148	C₄⋊(C₃⋊C₈)	D₄	1	1	yes	characteristic
149	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
150	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
151	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
152	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
153	#803	—	2	1	no	—
154	C₄×C₃⋊C₈	—	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	C₂×C₄×D₄	C₂×D₃	1	1	yes	characteristic
162	#484	Dic₃	1	1	yes	characteristic
163	#481	Dic₃	1	1	yes	characteristic
164	#478	Dic₃	1	1	yes	characteristic
165	#478	Dic₃	1	1	yes	characteristic
166	#463	Dic₃	1	1	yes	characteristic
167	#463	Dic₃	1	1	yes	characteristic
168	#450	Dic₃	1	1	yes	characteristic
169	#447	Dic₃	1	1	yes	characteristic
170	#446	—	3	1	no	—
171	C₈×Q₈	—	3	1	no	—
172	C₄×SD₁₆	C₂×D₃	1	1	yes	characteristic
173	C₄×SD₁₆	C₂×D₃	1	1	yes	characteristic
174	C₄×D₈	C₂×D₃	1	1	yes	characteristic
175	C₄×D₈	C₂×D₃	1	1	yes	characteristic
176	#436	—	3	1	no	—
177	#436	—	6	1	no	—
178	#435	—	6	1	no	—
179	C₈×D₄	—	3	1	no	—
180	C₈×D₄	—	3	1	no	—
181	C₈×D₄	—	3	1	no	—
182	C₈×D₄	—	3	1	no	—
183	C₈×D₄	—	3	1	no	—
184	C₈×D₄	—	6	1	no	—
185	C₈×D₄	—	6	1	no	—
186	#433	—	6	1	no	—
187	#431	—	3	1	no	—
188	#431	—	3	1	no	—
189	#431	—	3	1	no	—
190	#431	C₂×D₃	1	1	yes	characteristic
191	#424	—	6	1	no	—
192	#423	—	3	1	no	—
193	C₂×C₂²⋊C₈	—	6	1	no	—
194	C₂×C₂²⋊C₈	—	6	1	no	—
195	#335	—	3	1	no	—
196	#335	—	3	1	no	—
197	#334	—	3	1	no	—
198	#334	—	3	1	no	—
199	Q₈⋊C₈	—	3	1	no	—
200	Q₈⋊C₈	—	3	1	no	—
201	D₄⋊C₈	—	3	1	no	—
202	D₄⋊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	C₂⁴×C₃	—	2	1	no	—
212	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
213	C₂×C₃×D₄	—	2	2	no	—
214	C₂×C₃×D₄	—	2	2	no	—
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	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
224	C₂²×C₃×C₄	—	2	1	no	—
225	C₂²×C₃×C₄	—	2	1	no	—
226	C₂²×C₃×C₄	—	8	1	no	—
227	C₂²×C₃×C₄	—	8	1	no	—
228	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₃×C₄	#41	1	1	yes	characteristic
231	C₃×SD₁₆	—	2	2	no	—
232	C₃×SD₁₆	—	2	2	no	—
233	C₃×D₈	—	2	2	no	—
234	C₃×D₈	—	2	2	no	—
235	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
236	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
237	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
238	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
239	C₃×C₄⋊C₄	—	2	1	no	—
240	C₃×C₄⋊C₄	—	2	1	no	—
241	C₃×C₄⋊C₄	—	2	1	no	—
242	C₃×C₄⋊C₄	—	2	1	no	—
243	C₃×C₄⋊C₄	—	2	1	no	—
244	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
245	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
246	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
247	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
253	C₃×C₂²⋊C₄	—	2	1	no	—
254	C₃×C₂²⋊C₄	—	2	1	no	—
255	C₃×C₂²⋊C₄	—	2	1	no	—
256	C₃×C₂²⋊C₄	—	2	1	no	—
257	C₃×C₄²	—	2	1	no	—
258	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
259	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
260	C₃×C₄²	#41	1	1	yes	characteristic
261	C₃×C₄²	C₂⁴	1	1	yes	characteristic
262	#208	—	8	1	no	—
263	#208	—	8	1	no	—
264	C₂×C₃⋊C₈	—	2	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	—	8	1	no	—
271	C₂×C₃⋊C₈	—	8	1	no	—
272	C₂×C₃⋊C₈	—	8	1	no	—
273	C₂×C₃⋊C₈	—	8	1	no	—
274	C₂×C₃⋊C₈	—	8	1	no	—
275	C₂×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
276	C₂×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
277	C₂×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
278	C₂×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
279	C₂²×D₄	C₂×Dic₃	1	1	yes	characteristic
280	C₂³×C₄	—	2	1	no	—
281	C₂×SD₁₆	C₂×Dic₃	1	1	yes	characteristic
282	C₂×SD₁₆	C₂×Dic₃	1	1	yes	characteristic
283	C₂×D₈	C₂×Dic₃	1	1	yes	characteristic
284	C₂×D₈	C₂×Dic₃	1	1	yes	characteristic
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	C₂²×C₈	—	6	1	no	—
290	C₂²×C₈	—	6	1	no	—
291	C₂²×C₈	—	6	1	no	—
292	#126	—	2	1	no	—
293	#125	C₂×Dic₃	1	1	yes	characteristic
294	#124	C₂×Dic₃	1	1	yes	characteristic
295	#123	—	2	1	no	—
296	C₂²⋊Q₈	C₂×Dic₃	1	1	yes	characteristic
297	#121	C₂×Dic₃	1	1	yes	characteristic
298	C₄×Q₈	C₂²×D₃	1	1	yes	characteristic
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
303	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
304	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
305	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
306	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
307	#117	—	2	1	no	—
308	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
311	#107	C₂×Dic₃	1	1	yes	characteristic
312	#107	C₂×Dic₃	1	1	yes	characteristic
313	#106	C₂×Dic₃	1	1	yes	characteristic
314	#106	C₂×Dic₃	1	1	yes	characteristic
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	—	3	1	no	—
320	C₄⋊C₈	—	3	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	#102	C₂×Dic₃	1	1	yes	characteristic
330	#102	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	—	6	1	no	—
342	C₂²⋊C₈	—	6	1	no	—
343	C₂²⋊C₈	—	6	1	no	—
344	C₂²⋊C₈	—	6	1	no	—
345	C₂²⋊C₈	C₂×Dic₃	1	1	yes	characteristic
346	C₂²⋊C₈	C₂×Dic₃	1	1	yes	characteristic
347	#97	—	6	1	no	—
348	C₄×C₈	—	3	1	no	—
349	C₄×C₈	—	3	1	no	—
350	C₄×C₈	—	3	1	no	—
351	C₄×C₈	—	3	1	no	—
352	C₄×C₈	—	6	1	no	—
353	C₄×C₈	—	6	1	no	—
354	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
355	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
356	C₂³×C₃	—	2	4	no	—
357	C₂³×C₃	—	2	1	no	—
358	C₂³×C₃	—	2	1	no	—
359	C₂³×C₃	—	2	1	no	—
360	C₂³×C₃	—	8	1	no	—
361	C₂³×C₃	—	8	1	no	—
362	C₂³×C₃	C₄×D₄	1	1	yes	characteristic
363	C₃×Q₈	—	2	1	no	—
364	C₃×Q₈	—	2	1	no	—
365	C₃×D₄	—	2	4	no	—
366	C₃×D₄	—	2	1	no	—
367	C₃×D₄	—	2	1	no	—
368	C₃×D₄	—	2	1	no	—
369	C₃×D₄	—	2	1	no	—
370	C₃×D₄	—	8	1	no	—
371	C₃×D₄	#131	1	2	yes	—
372	C₃×D₄	#131	1	2	yes	—
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	—	2	1	no	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	4	1	no	—
383	C₂×C₃×C₄	—	4	1	no	—
384	C₂×C₃×C₄	—	4	1	no	—
385	C₂×C₃×C₄	—	4	1	no	—
386	C₂×C₃×C₄	—	4	1	no	—
387	C₂×C₃×C₄	—	4	1	no	—
388	C₂×C₃×C₄	—	4	1	no	—
389	C₂×C₃×C₄	—	8	1	no	—
390	C₂×C₃×C₄	—	8	1	no	—
391	C₂×C₃×C₄	—	8	1	no	—
392	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
393	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
394	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
395	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
396	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
398	C₃×C₈	—	2	1	no	—
399	C₃×C₈	—	2	1	no	—
400	C₃×C₈	—	2	1	no	—
401	C₃×C₈	—	2	1	no	—
402	C₃⋊C₈	—	2	1	no	—
403	C₃⋊C₈	—	2	1	no	—
404	C₃⋊C₈	—	2	1	no	—
405	C₃⋊C₈	—	2	1	no	—
406	C₃⋊C₈	—	4	1	no	—
407	C₃⋊C₈	—	4	1	no	—
408	C₃⋊C₈	—	4	1	no	—
409	C₃⋊C₈	—	4	1	no	—
410	C₃⋊C₈	—	4	1	no	—
411	C₃⋊C₈	—	4	1	no	—
412	C₂⁴	—	2	1	no	—
413	C₂×Q₈	C₂²×Dic₃	1	1	yes	characteristic
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
419	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
420	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	8	1	no	—
428	C₂²×C₄	—	8	1	no	—
429	C₂²×C₄	D₃×D₄	1	1	yes	characteristic
430	C₂²×C₄	#237	1	1	yes	characteristic
431	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
432	SD₁₆	—	2	2	no	—
433	SD₁₆	—	2	2	no	—
434	D₈	—	2	2	no	—
435	D₈	—	2	2	no	—
436	M₁₆	—	24	1	no	—
437	M₁₆	—	24	1	no	—
438	C₂×C₈	—	3	1	no	—
439	C₂×C₈	—	3	1	no	—
440	C₂×C₈	—	3	1	no	—
441	C₂×C₈	—	3	1	no	—
442	C₂×C₈	—	6	1	no	—
443	C₂×C₈	—	6	1	no	—
444	C₂×C₈	—	6	1	no	—
445	C₂×C₈	—	6	1	no	—
446	C₂×C₈	—	6	1	no	—
447	C₂×C₈	—	6	1	no	—
448	C₂×C₈	—	24	1	no	—
449	C₂×C₈	—	24	1	no	—
450	C₂×C₈	—	24	1	no	—
451	C₂×C₈	—	24	1	no	—
452	C₂×C₈	—	24	1	no	—
453	C₂×C₈	C₂²×Dic₃	1	1	yes	characteristic
454	C₂×C₈	C₂²×Dic₃	1	1	yes	characteristic
455	C₂×C₈	C₂²×Dic₃	1	1	yes	characteristic
456	C₂×C₈	C₂²×Dic₃	1	1	yes	characteristic
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
463	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
464	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
465	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	D₃×D₄	1	1	yes	characteristic
477	C₄²	#237	1	1	yes	characteristic
478	C₄²	C₂²×Dic₃	1	1	yes	characteristic
479	C₄²	C₂³×D₃	1	1	yes	characteristic
480	C₂²×C₃	—	2	1	no	—
481	C₂²×C₃	—	2	2	no	—
482	C₂²×C₃	—	2	2	no	—
483	C₂²×C₃	—	2	1	no	—
484	C₂²×C₃	—	2	1	no	—
485	C₂²×C₃	—	4	1	no	—
486	C₂²×C₃	—	4	1	no	—
487	C₂²×C₃	—	4	1	no	—
488	C₂²×C₃	—	4	1	no	—
489	C₂²×C₃	—	4	1	no	—
490	C₂²×C₃	—	4	1	no	—
491	C₂²×C₃	—	4	1	no	—
492	C₂²×C₃	—	8	4	no	—
493	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
494	C₃×C₄	—	2	1	no	—
495	C₃×C₄	—	2	1	no	—
496	C₃×C₄	—	2	1	no	—
497	C₃×C₄	—	2	1	no	—
498	C₃×C₄	—	4	1	no	—
499	C₃×C₄	—	4	1	no	—
500	C₃×C₄	—	4	1	no	—
501	C₃×C₄	—	4	1	no	—
502	C₃×C₄	—	4	1	no	—
503	C₃×C₄	C₂×#131	1	1	yes	characteristic
504	C₃×C₄	C₂×#131	1	1	yes	characteristic
505	C₃×C₄	#576	1	1	yes	characteristic
506	C₃×C₄	#577	1	1	yes	characteristic
507	C₂³	—	2	4	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	1	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	8	1	no	—
512	C₂³	—	8	1	no	—
513	C₂³	D₄×Dic₃	1	1	yes	characteristic
514	Q₈	—	2	1	no	—
515	Q₈	—	2	1	no	—
516	D₄	—	2	4	no	—
517	D₄	—	2	1	no	—
518	D₄	—	2	1	no	—
519	D₄	—	2	1	no	—
520	D₄	—	2	1	no	—
521	D₄	—	8	1	no	—
522	D₄	#948	1	2	yes	—
523	D₄	#948	1	2	yes	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	8	1	no	—
541	C₂×C₄	—	8	1	no	—
542	C₂×C₄	—	8	1	no	—
543	C₂×C₄	D₄×Dic₃	1	1	yes	characteristic
544	C₂×C₄	D₄×Dic₃	1	1	yes	characteristic
545	C₂×C₄	D₄×Dic₃	1	1	yes	characteristic
546	C₂×C₄	C₂×D₃×D₄	1	1	yes	characteristic
547	C₂×C₄	C₂×#237	1	1	yes	characteristic
548	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
549	C₈	—	2	1	no	—
550	C₈	—	2	1	no	—
551	C₈	—	2	1	no	—
552	C₈	—	2	1	no	—
553	C₈	—	6	1	no	—
554	C₈	—	6	1	no	—
555	C₈	—	6	1	no	—
556	C₈	—	6	1	no	—
557	C₈	—	12	1	no	—
558	C₈	—	12	1	no	—
559	C₈	—	12	1	no	—
560	C₈	—	12	1	no	—
561	C₈	—	12	1	no	—
562	C₈	—	12	1	no	—
563	C₂×C₃	—	4	1	no	—
564	C₂×C₃	—	4	2	no	—
565	C₂×C₃	—	4	2	no	—
566	C₂×C₃	—	8	1	no	—
567	C₂×C₃	#2929	1	1	yes	characteristic
568	C₂×C₃	#2946	1	1	yes	characteristic
569	C₂×C₃	#2957	1	1	yes	characteristic
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	8	4	no	—
583	C₂²	C₂×D₄×Dic₃	1	1	yes	characteristic
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	#5774	1	1	yes	characteristic
594	C₄	#5775	1	1	yes	characteristic
595	C₄	C₂×#948	1	1	yes	characteristic
596	C₄	C₂×#948	1	1	yes	characteristic
597	C₃	#17918	1	1	yes	characteristic, complemented, Sylow
598	C₂	—	4	1	no	—
599	C₂	—	4	2	no	—
600	C₂	—	4	2	no	—
601	C₂	—	8	1	no	—
602	C₂	#82916	1	1	yes	characteristic
603	C₂	#83910	1	1	yes	characteristic
604	C₂	#83930	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×#3105	C₂
socle	C₂²×C₃	C₂×C₄×D₄
prime radical	C₃×#447	C₄
cosocle	C₃×C₄²	C₂⁴
hypercenter	#3105	D₃
hypocenter	C₃	#17918
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3105

Complements

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

N	H ≅ G/N	type
2. #83131	C₂	semidirect
3. #82301	C₂	semidirect
4. #71750	C₂	semidirect
5. #71598	C₂	semidirect
6. #70897	C₂	semidirect
7. #70895	C₂	semidirect
8. SD₁₆⋊(C₃⋊C₈)	C₂	semidirect
9. SD₁₆×C₃⋊C₈	C₂	semidirect
10. #70880	C₂	semidirect
11. #70879	C₂	semidirect
12. #70878	C₂	semidirect
13. D₈×C₃⋊C₈	C₂	semidirect
14. #70753	C₂	semidirect
15. #70744	C₂	semidirect
34. #5024	C₂²	semidirect
35. Q₈×C₃⋊C₈	C₂²	semidirect
37. #5012	C₂²	semidirect
45. D₄×C₃⋊C₈	C₂²	semidirect
52. #4535	C₂²	semidirect
53. #4535	C₂²	semidirect
58. D₄⋊(C₃⋊C₈)	C₂²	semidirect
59. D₄⋊(C₃⋊C₈)	C₂²	semidirect
60. #4458	C₂²	semidirect
61. #4458	C₂²	semidirect
62. #4457	C₂²	semidirect
63. #4457	C₂²	semidirect
64. #4455	C₂²	semidirect
65. #4454	C₂²	semidirect
66. #4454	C₂²	semidirect
67. C₈×C₃⋊C₈	C₂²	semidirect
597. C₃	#17918	semidirect

Maximal subgroups

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

subgroup	index
C₃×#3105	2
#83131	2
#82301	2
#71750	2
#71598	2
#70897	2
#70895	2
SD₁₆⋊(C₃⋊C₈)	2
SD₁₆×C₃⋊C₈	2
#70880	2
#70879	2
#70878	2
D₈×C₃⋊C₈	2
#70753	2
#70744	2
#17918	3