Subgroups — #11861366

Order 1152.

785 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10593935	C₂	1	1	yes	maximal, characteristic
2	#10592538	C₂	1	1	yes	maximal, characteristic
3	C₃×#4830	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4828	C₂	1	1	yes	maximal, characteristic, complemented
5	#10590910	C₂	1	1	yes	maximal, characteristic
6	#10590786	C₂	1	1	yes	maximal, characteristic, complemented
7	#10590785	C₂	1	1	yes	maximal, characteristic, complemented
8	#10590701	C₂	1	1	yes	maximal, characteristic
9	#10590666	C₂	1	1	yes	maximal, characteristic
10	C₈×#624	C₂	1	1	yes	maximal, characteristic
11	#10590644	C₂	1	1	yes	maximal, characteristic, complemented
12	#10590644	C₂	1	1	yes	maximal, characteristic, complemented
13	#10590321	C₂	1	1	yes	maximal, characteristic
14	#10590251	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃⋊C₈×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
16	#79958	—	3	1	no	maximal
17	#79917	—	3	1	no	maximal
18	C₂×#3743	C₂²	1	1	yes	characteristic
19	C₂×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
20	#64081	C₂²	1	1	yes	characteristic
21	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
22	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
23	C₄×#627	C₂²	1	1	yes	characteristic
24	C₄×#627	C₂²	1	1	yes	characteristic
25	#63895	C₄	1	1	yes	characteristic
26	#63895	C₄	1	1	yes	characteristic
27	#63888	C₄	1	1	yes	characteristic
28	#63888	C₄	1	1	yes	characteristic
29	C₄×#624	C₂²	1	1	yes	characteristic
30	#63874	C₂²	1	1	yes	characteristic
31	#63847	C₄	1	1	yes	characteristic
32	#63847	C₄	1	1	yes	characteristic
33	#63839	C₄	1	1	yes	characteristic
34	#63839	C₄	1	1	yes	characteristic
35	C₂×#3712	C₂²	1	1	yes	characteristic
36	C₂×#3710	C₂²	1	1	yes	characteristic
37	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	#63641	C₂²	1	1	yes	characteristic
39	#63641	C₂²	1	1	yes	characteristic
40	C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic
41	C₃×#815	C₂²	1	1	yes	characteristic
42	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
43	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
44	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
45	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
46	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
47	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
48	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
49	C₃×#803	C₂²	1	1	yes	characteristic
50	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
51	Dic₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
52	Dic₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
53	Dic₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
54	Dic₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
55	#63555	C₂²	1	1	yes	characteristic
56	#63554	C₂²	1	1	yes	characteristic
57	#63553	C₂²	1	1	yes	characteristic
58	Dic₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
59	Dic₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
60	Dic₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
61	#5578	—	3	1	no	—
62	#5578	—	3	1	no	—
63	C₃×#446	—	3	1	no	—
64	C₃×C₈×Q₈	—	3	1	no	—
65	#5024	—	3	1	no	—
66	Q₈×C₃⋊C₈	—	3	1	no	—
67	#4839	—	3	1	no	—
68	#4839	—	3	1	no	—
69	#4839	—	3	1	no	—
70	#4839	—	3	1	no	—
71	#4839	—	6	1	no	—
72	#4837	—	3	1	no	—
73	#4837	—	3	1	no	—
74	#4831	—	3	1	no	—
75	#4830	—	3	1	no	—
76	#4830	—	3	1	no	—
77	#4830	D₃	1	1	yes	characteristic, complemented
78	#4828	—	3	1	no	—
79	#4828	D₃	1	1	yes	characteristic, complemented
80	#4708	—	3	1	no	—
81	#4708	—	3	1	no	—
82	#4701	—	3	1	no	—
83	#4701	—	3	1	no	—
84	#4689	—	3	1	no	—
85	#4689	—	3	1	no	—
86	C₄×D₃×C₈	—	3	1	no	—
87	C₄×D₃×C₈	—	3	1	no	—
88	#4679	—	3	1	no	—
89	C₈×Dic₆	—	3	1	no	—
90	C₈×Dic₆	—	3	1	no	—
91	C₈×Dic₆	—	3	1	no	—
92	C₂×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
93	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
94	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
95	C₂×#627	C₂×C₄	1	1	yes	characteristic
96	C₂×#627	C₂×C₄	1	1	yes	characteristic
97	C₂×#624	C₂×C₄	1	1	yes	characteristic
98	C₂×#624	C₂×C₄	1	1	yes	characteristic
99	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
100	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
101	C₃²×C₄²	C₂³	1	1	yes	characteristic
102	#3752	C₂×C₄	1	1	yes	characteristic
103	#3752	C₂×C₄	1	1	yes	characteristic
104	#3750	C₂×C₄	1	1	yes	characteristic
105	#3750	C₂×C₄	1	1	yes	characteristic
106	C₄×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
107	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
108	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
109	#3743	—	2	2	no	—
110	C₈×C₃⋊D₃	—	2	2	no	—
111	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
112	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
113	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
118	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
119	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
120	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
121	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
122	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
123	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
125	#3724	C₂×C₄	1	1	yes	characteristic
126	#3724	C₂×C₄	1	1	yes	characteristic
127	#3724	C₂×C₄	1	1	yes	characteristic
128	#3724	C₂×C₄	1	1	yes	characteristic
129	Dic₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
130	Dic₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
131	Dic₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
132	Dic₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
133	#3722	C₂×C₄	1	1	yes	characteristic
134	#3722	C₂×C₄	1	1	yes	characteristic
135	Dic₃²	C₂×C₄	1	1	yes	characteristic
136	Dic₃²	C₂×C₄	1	1	yes	characteristic
137	#3712	—	2	2	no	—
138	#3710	Q₈	1	4	yes	complemented
139	#2960	—	9	1	no	Sylow
140	C₃×C₄×Q₈	—	3	1	no	—
141	C₃×C₄×Q₈	—	3	1	no	—
142	#946	—	3	1	no	—
143	#946	—	3	1	no	—
144	#944	—	3	1	no	—
145	#944	—	3	1	no	—
146	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
147	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
148	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
149	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
150	C₂×ΓL(1,𝔽₂₅)	—	6	1	no	—
151	C₂×D₃×C₈	—	3	1	no	—
152	C₂×D₃×C₈	—	3	1	no	—
153	C₂×D₃×C₈	—	3	1	no	—
154	C₂×D₃×C₈	—	3	1	no	—
155	C₂×D₃×C₈	—	6	1	no	—
156	#897	—	3	1	no	—
157	#897	—	3	1	no	—
158	#896	—	3	1	no	—
159	#896	—	3	1	no	—
160	#896	—	3	1	no	—
161	#896	—	3	1	no	—
162	#889	—	3	1	no	—
163	#889	—	3	1	no	—
164	#889	—	3	1	no	—
165	#889	—	3	1	no	—
166	#888	—	3	1	no	—
167	#888	—	3	1	no	—
168	#872	—	3	1	no	—
169	#872	—	3	1	no	—
170	#872	—	3	1	no	—
171	#872	—	3	1	no	—
172	#872	—	6	1	no	—
173	C₄²×D₃	—	3	1	no	—
174	C₄²×D₃	—	3	1	no	—
175	C₄×Dic₆	—	3	1	no	—
176	C₄×Dic₆	—	3	1	no	—
177	C₄×Dic₆	—	3	1	no	—
178	C₄×Dic₆	—	3	1	no	—
179	C₄×Dic₆	C₂×D₃	1	1	yes	characteristic
180	C₄×Dic₆	C₂×D₃	1	1	yes	characteristic
181	C₃×C₄⋊C₈	—	2	1	no	—
182	C₃×C₄⋊C₈	—	3	1	no	—
183	C₃×C₄⋊C₈	—	3	1	no	—
184	C₃×C₄⋊C₈	—	3	1	no	—
185	C₃×C₄⋊C₈	—	3	1	no	—
186	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
187	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
188	C₃×#97	—	3	1	no	—
189	C₃×#97	—	3	1	no	—
190	C₃×C₄×C₈	—	3	1	no	—
191	C₃×C₄×C₈	—	3	1	no	—
192	C₃×C₄×C₈	—	3	1	no	—
193	C₃×C₄×C₈	—	3	1	no	—
194	#815	—	3	1	no	—
195	#815	—	3	1	no	—
196	#815	—	3	1	no	—
197	#815	C₂×D₃	1	1	yes	characteristic
198	Dic₃⋊C₈	—	3	1	no	—
199	Dic₃⋊C₈	—	3	1	no	—
200	Dic₃⋊C₈	—	3	1	no	—
201	Dic₃⋊C₈	—	3	1	no	—
202	Dic₃⋊C₈	—	3	1	no	—
203	Dic₃⋊C₈	—	3	1	no	—
204	Dic₃⋊C₈	—	3	1	no	—
205	Dic₃⋊C₈	—	3	1	no	—
206	Dic₃⋊C₈	—	6	1	no	—
207	Dic₃⋊C₈	—	6	1	no	—
208	Dic₃⋊C₈	C₂×D₃	1	1	yes	characteristic
209	Dic₃⋊C₈	C₂×D₃	1	1	yes	characteristic
210	Dic₃⋊C₈	C₂×D₃	1	1	yes	characteristic
211	Dic₃⋊C₈	C₂×D₃	1	1	yes	characteristic
212	C₈×Dic₃	—	3	1	no	—
213	C₈×Dic₃	—	3	1	no	—
214	C₈×Dic₃	—	3	1	no	—
215	C₈×Dic₃	—	3	1	no	—
216	C₈×Dic₃	—	3	1	no	—
217	C₈×Dic₃	C₂×D₃	1	1	yes	characteristic
218	C₈×Dic₃	C₂×D₃	1	1	yes	characteristic
219	C₈×Dic₃	C₂×D₃	1	1	yes	characteristic
220	C₄⋊(C₃⋊C₈)	—	3	1	no	—
221	C₄⋊(C₃⋊C₈)	—	3	1	no	—
222	C₄⋊(C₃⋊C₈)	—	3	1	no	—
223	C₄⋊(C₃⋊C₈)	—	3	1	no	—
224	C₄⋊(C₃⋊C₈)	—	3	1	no	—
225	C₄⋊(C₃⋊C₈)	—	3	1	no	—
226	C₄⋊(C₃⋊C₈)	—	6	1	no	—
227	#803	—	3	1	no	—
228	#803	C₂×D₃	1	1	yes	characteristic
229	C₄×C₃⋊C₈	—	3	1	no	—
230	C₄×C₃⋊C₈	—	3	1	no	—
231	C₄×C₃⋊C₈	—	3	1	no	—
232	C₄×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
233	C₂²×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
234	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
235	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
236	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
237	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
238	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
239	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
240	C₄×C₃⋊D₃	C₂×Q₈	1	2	yes	—
241	C₄×C₃⋊D₃	#41	1	2	yes	—
242	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
243	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
244	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
245	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
246	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
247	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
248	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
249	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
250	C₃×Dic₆	—	2	2	no	—
251	C₃×Dic₆	—	2	2	no	—
252	#627	—	2	2	no	—
253	#627	—	2	2	no	—
254	#624	—	2	2	no	—
255	#624	—	2	2	no	—
256	C₃²×C₈	—	2	1	no	—
257	C₃²×C₈	—	2	1	no	—
258	C₃⋊(C₃⋊C₈)	—	2	1	no	—
259	C₃⋊(C₃⋊C₈)	—	2	1	no	—
260	C₃×C₃⋊C₈	—	2	1	no	—
261	C₃×C₃⋊C₈	—	2	1	no	—
262	C₃×C₃⋊C₈	C₂×Q₈	1	2	yes	—
263	C₃×C₃⋊C₈	C₂×Q₈	1	2	yes	—
264	#533	—	9	1	no	—
265	#446	—	3	1	no	—
266	#446	—	9	1	no	—
267	#446	—	9	1	no	—
268	#446	—	9	1	no	—
269	C₈×Q₈	—	3	1	no	—
270	C₈×Q₈	—	9	1	no	—
271	C₈×Q₈	—	9	1	no	—
272	C₈×Q₈	—	9	1	no	—
273	#424	—	9	1	no	—
274	#424	—	9	1	no	—
275	#423	—	9	1	no	—
276	#405	—	9	1	no	—
277	#405	—	9	1	no	—
278	C₂×C₄×C₈	—	9	1	no	—
279	C₂×C₃×Q₈	—	3	1	no	—
280	C₂×C₃×Q₈	—	3	1	no	—
281	C₂×C₄×D₃	—	3	1	no	—
282	C₂×C₄×D₃	—	3	1	no	—
283	C₂×C₄×D₃	—	3	1	no	—
284	C₂×C₄×D₃	—	3	1	no	—
285	C₂×C₄×D₃	—	3	1	no	—
286	C₂×C₄×D₃	—	3	1	no	—
287	C₂×C₄×D₃	—	6	1	no	—
288	C₂×Dic₆	—	3	1	no	—
289	C₂×Dic₆	—	3	1	no	—
290	C₂×Dic₆	—	3	1	no	—
291	C₂×Dic₆	—	3	1	no	—
292	C₂×Dic₆	C₄×D₃	1	1	yes	characteristic
293	C₂×Dic₆	C₄×D₃	1	1	yes	characteristic
294	C₂×C₃×C₈	—	2	1	no	—
295	C₂×C₃×C₈	—	2	1	no	—
296	C₂×C₃×C₈	—	3	1	no	—
297	C₂×C₃×C₈	—	3	1	no	—
298	C₂×C₃×C₈	—	3	1	no	—
299	C₂×C₃×C₈	—	3	1	no	—
300	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
301	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
302	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
303	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
304	C₃×C₄⋊C₄	—	3	1	no	—
305	C₃×C₄⋊C₄	—	3	1	no	—
306	C₃×C₄⋊C₄	—	3	1	no	—
307	C₃×C₄⋊C₄	—	3	1	no	—
308	C₃×C₄⋊C₄	—	3	1	no	—
309	C₃×C₄⋊C₄	—	3	1	no	—
310	C₃×C₄²	—	2	1	no	—
311	C₃×C₄²	—	3	1	no	—
312	C₃×C₄²	—	3	1	no	—
313	C₃×C₄²	—	3	1	no	—
314	C₃×C₄²	—	3	1	no	—
315	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
316	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
317	(C₂×D₃)⋊C₄	—	3	1	no	—
318	(C₂×D₃)⋊C₄	—	3	1	no	—
319	(C₂×D₃)⋊C₄	—	3	1	no	—
320	(C₂×D₃)⋊C₄	—	3	1	no	—
321	(C₂×D₃)⋊C₄	—	3	1	no	—
322	(C₂×D₃)⋊C₄	—	3	1	no	—
323	(C₂×D₃)⋊C₄	—	3	1	no	—
324	(C₂×D₃)⋊C₄	—	3	1	no	—
325	(C₂×D₃)⋊C₄	—	6	1	no	—
326	(C₂×D₃)⋊C₄	—	6	1	no	—
327	C₄⋊Dic₃	—	3	1	no	—
328	C₄⋊Dic₃	—	3	1	no	—
329	C₄⋊Dic₃	—	3	1	no	—
330	C₄⋊Dic₃	—	3	1	no	—
331	C₄⋊Dic₃	C₄×D₃	1	1	yes	characteristic
332	C₄⋊Dic₃	C₄×D₃	1	1	yes	characteristic
333	Dic₃⋊C₄	—	3	1	no	—
334	Dic₃⋊C₄	—	3	1	no	—
335	Dic₃⋊C₄	—	3	1	no	—
336	Dic₃⋊C₄	—	3	1	no	—
337	Dic₃⋊C₄	—	3	1	no	—
338	Dic₃⋊C₄	—	3	1	no	—
339	Dic₃⋊C₄	—	3	1	no	—
340	Dic₃⋊C₄	—	3	1	no	—
341	Dic₃⋊C₄	—	3	1	no	—
342	Dic₃⋊C₄	—	3	1	no	—
343	Dic₃⋊C₄	—	3	1	no	—
344	Dic₃⋊C₄	—	3	1	no	—
345	Dic₃⋊C₄	—	3	1	no	—
346	Dic₃⋊C₄	—	3	1	no	—
347	Dic₃⋊C₄	—	3	1	no	—
348	Dic₃⋊C₄	—	3	1	no	—
349	Dic₃⋊C₄	—	6	1	no	—
350	Dic₃⋊C₄	—	6	1	no	—
351	Dic₃⋊C₄	C₄×D₃	1	1	yes	characteristic
352	Dic₃⋊C₄	C₄×D₃	1	1	yes	characteristic
353	Dic₃⋊C₄	C₄×D₃	1	1	yes	characteristic
354	Dic₃⋊C₄	C₄×D₃	1	1	yes	characteristic
355	C₄×Dic₃	—	3	1	no	—
356	C₄×Dic₃	—	3	1	no	—
357	C₄×Dic₃	—	3	1	no	—
358	C₄×Dic₃	—	3	1	no	—
359	C₄×Dic₃	—	3	1	no	—
360	C₄×Dic₃	—	3	1	no	—
361	C₄×Dic₃	—	6	1	no	—
362	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
363	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
364	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
365	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
366	C₂×C₃⋊C₈	—	3	1	no	—
367	C₂×C₃⋊C₈	—	3	1	no	—
368	C₂×C₃⋊C₈	—	3	1	no	—
369	C₂×C₃⋊C₈	—	3	1	no	—
370	C₂×C₃⋊C₈	—	6	1	no	—
371	C₂×C₃⋊C₈	—	6	1	no	—
372	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
373	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
374	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
375	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
376	ΓL(1,𝔽₂₅)	—	6	2	no	—
377	ΓL(1,𝔽₂₅)	—	6	2	no	—
378	ΓL(1,𝔽₂₅)	—	6	2	no	—
379	ΓL(1,𝔽₂₅)	—	6	2	no	—
380	ΓL(1,𝔽₂₅)	—	12	2	no	—
381	D₃×C₈	—	3	4	no	—
382	D₃×C₈	—	3	4	no	—
383	D₃×C₈	—	6	2	no	—
384	D₃×C₈	—	6	2	no	—
385	D₃×C₈	—	12	2	no	—
386	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
387	C₂×C₃⋊D₃	—	2	1	no	—
388	C₂×C₃⋊D₃	—	2	1	no	—
389	C₂×C₃⋊D₃	C₄×Q₈	1	2	yes	—
390	C₃²×C₄	—	2	1	no	—
391	C₃²×C₄	—	2	1	no	—
392	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
393	C₃²×C₄	C₂×#41	1	1	yes	characteristic
394	C₃⋊Dic₃	—	2	1	no	—
395	C₃⋊Dic₃	—	2	1	no	—
396	C₃⋊Dic₃	C₄×Q₈	1	2	yes	—
397	C₃×Dic₃	—	2	1	no	—
398	C₃×Dic₃	—	2	1	no	—
399	C₃×Dic₃	—	2	1	no	—
400	C₃×Dic₃	—	2	1	no	—
401	C₃×Dic₃	—	2	1	no	—
402	C₃×Dic₃	—	2	1	no	—
403	C₃×Dic₃	#131	1	2	yes	—
404	C₃×Dic₃	#131	1	2	yes	—
405	C₂×M₁₆	—	9	1	no	—
406	C₂×M₁₆	—	9	1	no	—
407	C₂²×C₈	—	9	1	no	—
408	C₂²×C₈	—	9	1	no	—
409	C₄⋊Q₈	—	9	1	no	—
410	C₄⋊Q₈	—	9	1	no	—
411	#125	—	9	1	no	—
412	#125	—	9	1	no	—
413	C₂²⋊Q₈	—	9	1	no	—
414	C₂²⋊Q₈	—	9	1	no	—
415	C₂²⋊Q₈	—	9	1	no	—
416	C₂²⋊Q₈	—	9	1	no	—
417	C₄×Q₈	—	3	1	no	—
418	C₄×Q₈	—	3	1	no	—
419	C₄×Q₈	—	9	1	no	—
420	C₄×Q₈	—	9	1	no	—
421	#117	—	9	1	no	—
422	#117	—	9	1	no	—
423	C₂×C₄²	—	9	1	no	—
424	C₄⋊C₈	—	3	1	no	—
425	C₄⋊C₈	—	3	1	no	—
426	C₄⋊C₈	—	3	1	no	—
427	C₄⋊C₈	—	3	1	no	—
428	C₄⋊C₈	—	9	1	no	—
429	C₄⋊C₈	—	9	1	no	—
430	C₄⋊C₈	—	9	1	no	—
431	C₄⋊C₈	—	9	1	no	—
432	C₄⋊C₈	—	9	1	no	—
433	C₄⋊C₈	—	9	1	no	—
434	C₄⋊C₈	—	9	1	no	—
435	C₄⋊C₈	D₃²	1	1	yes	characteristic
436	#97	—	3	1	no	—
437	#97	—	3	1	no	—
438	#97	—	9	1	no	—
439	#97	—	9	1	no	—
440	C₄×C₈	—	3	1	no	—
441	C₄×C₈	—	3	1	no	—
442	C₄×C₈	—	3	1	no	—
443	C₄×C₈	—	3	1	no	—
444	C₄×C₈	—	9	1	no	—
445	C₄×C₈	—	9	1	no	—
446	C₄×C₈	—	9	1	no	—
447	C₄×C₈	—	9	1	no	—
448	C₂²×D₃	—	3	1	no	—
449	C₂²×D₃	—	3	1	no	—
450	C₂²×D₃	—	6	1	no	—
451	C₃×Q₈	—	6	2	no	—
452	C₃×Q₈	—	6	2	no	—
453	C₂×C₃×C₄	—	2	1	no	—
454	C₂×C₃×C₄	—	2	1	no	—
455	C₂×C₃×C₄	—	2	1	no	—
456	C₂×C₃×C₄	—	3	1	no	—
457	C₂×C₃×C₄	—	3	1	no	—
458	C₂×C₃×C₄	—	3	1	no	—
459	C₂×C₃×C₄	—	3	1	no	—
460	C₂×C₃×C₄	—	3	1	no	—
461	C₂×C₃×C₄	—	3	1	no	—
462	C₂×C₃×C₄	—	3	1	no	—
463	C₂×C₃×C₄	—	3	1	no	—
464	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
465	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
466	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
467	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
468	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
469	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
470	C₂×Dic₃	—	3	1	no	—
471	C₂×Dic₃	—	3	1	no	—
472	C₂×Dic₃	—	3	1	no	—
473	C₂×Dic₃	—	3	1	no	—
474	C₂×Dic₃	—	3	1	no	—
475	C₂×Dic₃	—	3	1	no	—
476	C₂×Dic₃	—	6	1	no	—
477	C₂×Dic₃	—	6	1	no	—
478	C₂×Dic₃	—	6	1	no	—
479	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
480	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
481	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
482	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
483	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
484	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
485	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
486	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
487	C₄×D₃	—	3	2	no	—
488	C₄×D₃	—	3	2	no	—
489	C₄×D₃	—	3	2	no	—
490	C₄×D₃	—	3	2	no	—
491	C₄×D₃	—	6	2	no	—
492	C₄×D₃	—	6	2	no	—
493	C₄×D₃	—	6	2	no	—
494	C₄×D₃	—	6	2	no	—
495	C₄×D₃	—	6	2	no	—
496	C₄×D₃	—	6	2	no	—
497	Dic₆	—	2	2	no	—
498	Dic₆	—	2	2	no	—
499	Dic₆	—	6	2	no	—
500	Dic₆	—	6	2	no	—
501	Dic₆	—	6	2	no	—
502	Dic₆	—	6	2	no	—
503	C₃×C₈	—	2	1	no	—
504	C₃×C₈	—	2	1	no	—
505	C₃×C₈	—	2	1	no	—
506	C₃×C₈	—	2	1	no	—
507	C₃×C₈	—	3	2	no	—
508	C₃×C₈	—	3	2	no	—
509	C₃×C₈	—	4	1	no	—
510	C₃×C₈	—	4	1	no	—
511	C₃×C₈	—	6	1	no	—
512	C₃×C₈	—	6	1	no	—
513	C₃⋊C₈	—	2	1	no	—
514	C₃⋊C₈	—	2	1	no	—
515	C₃⋊C₈	—	6	1	no	—
516	C₃⋊C₈	—	6	1	no	—
517	C₃⋊C₈	—	6	1	no	—
518	C₃⋊C₈	—	6	1	no	—
519	C₃⋊C₈	—	12	1	no	—
520	C₃⋊C₈	—	12	1	no	—
521	C₃⋊C₈	D₃×Q₈	1	2	yes	—
522	C₃⋊C₈	D₃×Q₈	1	2	yes	—
523	C₂×C₃²	C₂×C₄×Q₈	1	1	yes	characteristic
524	C₂×C₃²	C₂×#131	1	1	yes	characteristic
525	C₂×C₃²	C₂×#131	1	1	yes	characteristic
526	C₃⋊D₃	—	2	2	no	—
527	C₂×Q₈	—	3	1	no	—
528	C₂×Q₈	—	3	1	no	—
529	C₂×Q₈	—	9	1	no	—
530	C₂×Q₈	—	9	1	no	—
531	C₂²×C₄	—	9	1	no	—
532	C₂²×C₄	—	9	1	no	—
533	C₂²×C₄	—	9	1	no	—
534	M₁₆	—	18	2	no	—
535	M₁₆	—	18	2	no	—
536	C₂×C₈	—	3	1	no	—
537	C₂×C₈	—	3	1	no	—
538	C₂×C₈	—	3	1	no	—
539	C₂×C₈	—	3	1	no	—
540	C₂×C₈	—	9	4	no	—
541	C₂×C₈	—	9	1	no	—
542	C₂×C₈	—	9	1	no	—
543	C₂×C₈	—	18	2	no	—
544	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
545	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
546	C₄⋊C₄	—	3	1	no	—
547	C₄⋊C₄	—	3	1	no	—
548	C₄⋊C₄	—	3	1	no	—
549	C₄⋊C₄	—	3	1	no	—
550	C₄⋊C₄	—	3	1	no	—
551	C₄⋊C₄	—	3	1	no	—
552	C₄⋊C₄	—	9	1	no	—
553	C₄⋊C₄	—	9	1	no	—
554	C₄⋊C₄	—	9	1	no	—
555	C₄⋊C₄	—	9	1	no	—
556	C₄⋊C₄	—	9	1	no	—
557	C₄⋊C₄	—	9	1	no	—
558	C₄⋊C₄	—	9	1	no	—
559	C₄⋊C₄	—	9	1	no	—
560	C₄⋊C₄	—	9	1	no	—
561	C₄⋊C₄	—	9	1	no	—
562	C₂²⋊C₄	—	9	1	no	—
563	C₂²⋊C₄	—	9	1	no	—
564	C₂²⋊C₄	—	9	1	no	—
565	C₂²⋊C₄	—	9	1	no	—
566	C₄²	—	3	1	no	—
567	C₄²	—	3	1	no	—
568	C₄²	—	3	1	no	—
569	C₄²	—	3	1	no	—
570	C₄²	—	9	1	no	—
571	C₄²	—	9	1	no	—
572	C₄²	—	9	1	no	—
573	C₄²	C₂×D₃²	1	1	yes	characteristic
574	C₂²×C₃	—	2	1	no	—
575	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
576	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
577	C₂×D₃	—	3	2	no	—
578	C₂×D₃	—	3	2	no	—
579	C₂×D₃	—	6	2	no	—
580	C₂×D₃	—	6	1	no	—
581	C₂×D₃	—	6	1	no	—
582	C₂×D₃	—	6	1	no	—
583	C₂×D₃	—	6	1	no	—
584	C₂×D₃	—	12	1	no	—
585	C₂×D₃	—	12	1	no	—
586	C₃×C₄	—	2	1	no	—
587	C₃×C₄	—	2	1	no	—
588	C₃×C₄	—	2	1	no	—
589	C₃×C₄	—	2	1	no	—
590	C₃×C₄	—	2	1	no	—
591	C₃×C₄	—	2	1	no	—
592	C₃×C₄	—	3	2	no	—
593	C₃×C₄	—	3	2	no	—
594	C₃×C₄	—	4	1	no	—
595	C₃×C₄	—	4	1	no	—
596	C₃×C₄	—	6	1	no	—
597	C₃×C₄	—	6	1	no	—
598	C₃×C₄	—	6	1	no	—
599	C₃×C₄	—	6	1	no	—
600	C₃×C₄	—	6	1	no	—
601	C₃×C₄	—	6	1	no	—
602	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
603	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
604	C₃×C₄	D₃×#41	1	1	yes	characteristic
605	C₃×C₄	D₃×#41	1	1	yes	characteristic
606	Dic₃	—	2	1	no	—
607	Dic₃	—	2	1	no	—
608	Dic₃	—	2	1	no	—
609	Dic₃	—	2	1	no	—
610	Dic₃	—	2	1	no	—
611	Dic₃	—	2	1	no	—
612	Dic₃	—	3	2	no	—
613	Dic₃	—	3	2	no	—
614	Dic₃	—	6	2	no	—
615	Dic₃	—	6	1	no	—
616	Dic₃	—	6	1	no	—
617	Dic₃	—	6	1	no	—
618	Dic₃	—	6	1	no	—
619	Dic₃	—	12	1	no	—
620	Dic₃	—	12	1	no	—
621	Dic₃	#901	1	2	yes	—
622	Dic₃	#907	1	2	yes	—
623	C₃²	#2960	1	1	yes	characteristic, complemented, Sylow
624	C₂³	—	9	1	no	—
625	Q₈	—	6	2	no	—
626	Q₈	—	6	2	no	—
627	Q₈	—	18	2	no	—
628	Q₈	—	18	2	no	—
629	C₂×C₄	—	3	1	no	—
630	C₂×C₄	—	3	1	no	—
631	C₂×C₄	—	3	1	no	—
632	C₂×C₄	—	3	1	no	—
633	C₂×C₄	—	3	1	no	—
634	C₂×C₄	—	3	1	no	—
635	C₂×C₄	—	3	1	no	—
636	C₂×C₄	—	3	1	no	—
637	C₂×C₄	—	9	1	no	—
638	C₂×C₄	—	9	2	no	—
639	C₂×C₄	—	9	2	no	—
640	C₂×C₄	—	9	1	no	—
641	C₂×C₄	—	9	1	no	—
642	C₂×C₄	—	18	2	no	—
643	C₂×C₄	—	18	2	no	—
644	C₂×C₄	C₄×D₃²	1	1	yes	characteristic
645	C₂×C₄	C₄×D₃²	1	1	yes	characteristic
646	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
647	C₈	—	2	1	no	—
648	C₈	—	2	1	no	—
649	C₈	—	3	2	no	—
650	C₈	—	3	2	no	—
651	C₈	—	6	1	no	—
652	C₈	—	6	1	no	—
653	C₈	—	18	1	no	—
654	C₈	—	18	1	no	—
655	C₂×C₃	—	2	1	no	—
656	C₂×C₃	—	2	1	no	—
657	C₂×C₃	—	2	1	no	—
658	C₂×C₃	C₄×D₃×Q₈	1	1	yes	characteristic
659	C₂×C₃	C₄×D₃×Q₈	1	1	yes	characteristic
660	C₂×C₃	C₂×#901	1	1	yes	characteristic
661	C₂×C₃	C₂×#907	1	1	yes	characteristic
662	C₂×C₃	D₃×#131	1	1	yes	characteristic
663	C₂×C₃	D₃×#131	1	1	yes	characteristic
664	D₃	—	6	2	no	—
665	D₃	—	6	2	no	—
666	D₃	—	12	2	no	—
667	C₂²	—	9	2	no	—
668	C₂²	—	18	1	no	—
669	C₂²	—	18	1	no	—
670	C₂²	C₂×C₄×D₃²	1	1	yes	characteristic
671	C₄	—	2	1	no	—
672	C₄	—	2	1	no	—
673	C₄	—	3	2	no	—
674	C₄	—	3	2	no	—
675	C₄	—	6	1	no	—
676	C₄	—	6	1	no	—
677	C₄	—	6	1	no	—
678	C₄	—	6	1	no	—
679	C₄	—	6	1	no	—
680	C₄	—	6	1	no	—
681	C₄	—	9	2	no	—
682	C₄	—	18	1	no	—
683	C₄	—	18	1	no	—
684	C₄	#64312	1	1	yes	characteristic
685	C₄	D₃²×Q₈	1	1	yes	characteristic
686	C₃	—	2	1	no	—
687	C₃	#79917	1	1	yes	characteristic, complemented
688	C₃	#79958	1	1	yes	characteristic, complemented
689	C₂	—	18	2	no	—
690	C₂	#10594363	1	1	yes	characteristic
691	C₂	D₃×#901	1	1	yes	characteristic
692	C₂	D₃×#907	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃²
commutator, socle	C₂²×C₃²	C₂³×C₄
Fitting	C₃²×C₄⋊C₈	C₂²
prime radical	C₂²×C₃⋊D₃	C₂²×C₄
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	C₄⋊C₈	D₃²
hypocenter	C₃²	#2960
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. C₃×#4830	C₂	semidirect
4. C₃×#4828	C₂	semidirect
6. #10590786	C₂	semidirect
7. #10590785	C₂	semidirect
11. #10590644	C₂	semidirect
12. #10590644	C₂	semidirect
14. #10590251	C₂	semidirect
15. C₃⋊C₈×Dic₆	C₂	semidirect
77. #4830	D₃	semidirect
79. #4828	D₃	semidirect
138. #3710	Q₈	semidirect
623. C₃²	#2960	semidirect
687. C₃	#79917	semidirect
688. C₃	#79958	semidirect

Maximal subgroups

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

subgroup	index
#10593935	2
#10592538	2
C₃×#4830	2
C₃×#4828	2
#10590910	2
#10590786	2
#10590785	2
#10590701	2
#10590666	2
C₈×#624	2
#10590644	2
#10590321	2
#10590251	2
C₃⋊C₈×Dic₆	2
#79958	3
#79917	3