Subgroups — #11861368

Order 1152.

775 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10593926	C₂	1	1	yes	maximal, characteristic
2	#10592400	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#4708	C₂	1	1	yes	maximal, characteristic
4	C₃×#4701	C₂	1	1	yes	maximal, characteristic, complemented
5	#10590787	C₂	1	1	yes	maximal, characteristic, complemented
6	#10590784	C₂	1	1	yes	maximal, characteristic, complemented
7	#10590695	C₂	1	1	yes	maximal, characteristic
8	#10590693	C₂	1	1	yes	maximal, characteristic
9	#10590663	C₂	1	1	yes	maximal, characteristic
10	D₃×C₈×Dic₃	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	#10590324	C₂	1	1	yes	maximal, characteristic
14	#10590254	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	#78542	—	3	1	no	maximal
18	C₄×#634	C₂²	1	1	yes	characteristic
19	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
20	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
21	C₃×#872	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	#63899	C₄	1	1	yes	characteristic
26	#63896	C₄	1	1	yes	characteristic
27	#63893	C₄	1	1	yes	characteristic
28	#63887	C₄	1	1	yes	characteristic
29	C₄×D₃×Dic₃	C₂²	1	1	yes	characteristic
30	#63855	C₂²	1	1	yes	characteristic
31	#63846	C₄	1	1	yes	characteristic
32	#63845	C₄	1	1	yes	characteristic
33	#63840	C₄	1	1	yes	characteristic
34	#63839	C₄	1	1	yes	characteristic
35	C₂×#3711	C₂²	1	1	yes	characteristic
36	C₂×D₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
37	C₃²×#97	C₂²	1	1	yes	characteristic
38	#63642	C₂²	1	1	yes	characteristic
39	#63641	C₂²	1	1	yes	characteristic
40	#63641	C₂²	1	1	yes	characteristic
41	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
42	C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic
43	C₃×#815	C₂²	1	1	yes	characteristic
44	C₃×#815	C₂²	1	1	yes	characteristic
45	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
46	C₃×Dic₃⋊C₈	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×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
50	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
51	#63572	C₂²	1	1	yes	characteristic
52	#63572	C₂²	1	1	yes	characteristic
53	Dic₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
54	Dic₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
55	Dic₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
56	Dic₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
57	#63553	C₂²	1	1	yes	characteristic
58	#63553	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	#5517	—	3	1	no	—
63	C₃×#446	—	3	1	no	—
64	C₃×#405	—	3	1	no	—
65	#5119	—	3	1	no	—
66	#5118	—	3	1	no	—
67	#5101	—	3	1	no	—
68	C₂×C₈×Dic₃	—	3	1	no	—
69	Q₈×C₃⋊C₈	—	3	1	no	—
70	#4999	—	3	1	no	—
71	#4839	—	3	1	no	—
72	#4839	—	3	1	no	—
73	#4837	—	3	1	no	—
74	#4830	—	3	1	no	—
75	#4830	—	3	1	no	—
76	#4830	—	3	1	no	—
77	#4708	—	3	1	no	—
78	#4708	D₃	1	1	yes	characteristic
79	#4701	—	3	1	no	—
80	#4701	—	3	1	no	—
81	#4701	—	3	1	no	—
82	#4701	—	3	1	no	—
83	#4701	—	3	1	no	—
84	#4701	—	6	1	no	—
85	#4701	D₃	1	1	yes	characteristic, complemented
86	C₄×D₃×C₈	—	3	1	no	—
87	#4679	—	3	1	no	—
88	C₈×Dic₆	—	3	1	no	—
89	C₈×Dic₆	—	3	1	no	—
90	C₈×Dic₆	—	3	1	no	—
91	C₈×Dic₆	—	3	1	no	—
92	C₂×#634	C₂×C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×D₃	C₂³	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×D₃×Dic₃	C₂×C₄	1	1	yes	characteristic
98	C₂×D₃×Dic₃	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	C₄⋊(C₃⋊Dic₃)	C₂×C₄	1	1	yes	characteristic
103	#3750	C₂×C₄	1	1	yes	characteristic
104	#3750	C₂×C₄	1	1	yes	characteristic
105	C₄×C₃⋊Dic₃	C₂³	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	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
112	C₃×Dic₃⋊C₄	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×C₄×Dic₃	C₂³	1	1	yes	characteristic
117	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
118	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
119	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
120	C₂×C₃×C₃⋊C₈	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	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
124	C₃×D₃×C₈	Q₈	1	4	yes	complemented
125	#3724	C₂×C₄	1	1	yes	characteristic
126	#3724	C₂×C₄	1	1	yes	characteristic
127	Dic₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
128	Dic₃⋊Dic₃	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	(C₂×D₃)⋊Dic₃	C₂×C₄	1	1	yes	characteristic
134	(C₂×D₃)⋊Dic₃	C₂×C₄	1	1	yes	characteristic
135	Dic₃²	C₂×C₄	1	1	yes	characteristic
136	Dic₃²	C₂×C₄	1	1	yes	characteristic
137	#3711	—	2	2	no	—
138	D₃×C₃⋊C₈	—	2	2	no	—
139	#2960	—	9	1	no	Sylow
140	C₂×C₃×M₁₆	—	3	1	no	—
141	C₂²×C₃×C₈	—	3	1	no	—
142	C₃×C₄×Q₈	—	3	1	no	—
143	C₃×#117	—	3	1	no	—
144	#946	—	3	1	no	—
145	#944	—	3	1	no	—
146	#926	—	3	1	no	—
147	C₂×C₄×Dic₃	—	3	1	no	—
148	C₂×#208	—	3	1	no	—
149	C₂²×C₃⋊C₈	—	3	1	no	—
150	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
151	C₂×ΓL(1,𝔽₂₅)	C₂×D₃	1	1	yes	characteristic
152	C₂×D₃×C₈	—	3	1	no	—
153	C₂×D₃×C₈	C₂×D₃	1	1	yes	characteristic
154	#897	—	3	1	no	—
155	#896	—	3	1	no	—
156	#896	—	3	1	no	—
157	#890	—	3	1	no	—
158	#890	—	3	1	no	—
159	#889	—	3	1	no	—
160	#889	—	3	1	no	—
161	#888	—	3	1	no	—
162	#888	—	3	1	no	—
163	#888	—	3	1	no	—
164	#878	—	3	1	no	—
165	#878	—	3	1	no	—
166	#878	—	3	1	no	—
167	#878	—	3	1	no	—
168	#872	—	3	1	no	—
169	#872	C₂×D₃	1	1	yes	characteristic
170	C₄²×D₃	—	3	1	no	—
171	C₄×Dic₆	—	3	1	no	—
172	C₄×Dic₆	—	3	1	no	—
173	C₄×Dic₆	—	3	1	no	—
174	C₄×Dic₆	—	3	1	no	—
175	C₄×Dic₆	—	3	1	no	—
176	C₄×Dic₆	—	3	1	no	—
177	C₄×Dic₆	—	6	1	no	—
178	C₄×Dic₆	C₂×D₃	1	1	yes	characteristic
179	C₃×C₄⋊C₈	—	3	1	no	—
180	C₃×C₄⋊C₈	—	3	1	no	—
181	C₃×C₄⋊C₈	—	3	1	no	—
182	C₃×#97	—	2	1	no	—
183	C₃×#97	—	3	1	no	—
184	C₃×#97	—	3	1	no	—
185	C₃×#97	C₂×D₃	1	1	yes	characteristic
186	C₃×#97	C₂×D₃	1	1	yes	characteristic
187	C₃×C₄×C₈	—	3	1	no	—
188	C₃×C₄×C₈	—	3	1	no	—
189	C₃×C₄×C₈	—	3	1	no	—
190	#815	—	3	1	no	—
191	#815	—	3	1	no	—
192	#815	—	6	1	no	—
193	#815	C₂×D₃	1	1	yes	characteristic
194	#815	C₂×D₃	1	1	yes	characteristic
195	Dic₃⋊C₈	—	3	1	no	—
196	Dic₃⋊C₈	—	3	1	no	—
197	Dic₃⋊C₈	—	3	1	no	—
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	—	3	1	no	—
207	Dic₃⋊C₈	—	6	1	no	—
208	Dic₃⋊C₈	—	6	1	no	—
209	Dic₃⋊C₈	C₂×D₃	1	1	yes	characteristic
210	Dic₃⋊C₈	C₂×D₃	1	1	yes	characteristic
211	C₈×Dic₃	—	3	1	no	—
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	—	3	1	no	—
218	C₈×Dic₃	—	3	1	no	—
219	C₈×Dic₃	—	6	1	no	—
220	C₈×Dic₃	C₂×D₃	1	1	yes	characteristic
221	C₈×Dic₃	C₂×D₃	1	1	yes	characteristic
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)	—	3	1	no	—
227	C₄⋊(C₃⋊C₈)	—	3	1	no	—
228	C₄⋊(C₃⋊C₈)	—	6	1	no	—
229	C₄⋊(C₃⋊C₈)	C₂×D₃	1	1	yes	characteristic
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	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
241	#634	—	2	2	no	—
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	C₃×C₄×D₃	C₂×Q₈	1	2	yes	—
250	C₃×C₄×D₃	#41	1	2	yes	—
251	C₃×Dic₆	—	2	2	no	—
252	#627	—	2	2	no	—
253	#627	—	2	2	no	—
254	D₃×Dic₃	—	2	2	no	—
255	D₃×Dic₃	—	2	2	no	—
256	C₃²×C₈	—	2	1	no	—
257	C₃²×C₈	C₂×Q₈	1	2	yes	—
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	—	2	1	no	—
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	—	9	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	—	3	1	no	—
277	#405	—	9	1	no	—
278	C₂×C₄×C₈	—	9	1	no	—
279	C₂×C₃×Q₈	—	3	1	no	—
280	C₂²×C₃×C₄	—	3	1	no	—
281	C₂²×Dic₃	—	3	1	no	—
282	C₂²×Dic₃	—	3	1	no	—
283	C₂×C₄×D₃	—	3	1	no	—
284	C₂×C₄×D₃	—	3	1	no	—
285	C₂×C₄×D₃	C₂²×D₃	1	1	yes	characteristic
286	C₂×Dic₆	—	3	1	no	—
287	C₂×Dic₆	—	3	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	—	6	1	no	—
293	C₂×Dic₆	C₄×D₃	1	1	yes	characteristic
294	C₃×M₁₆	—	6	2	no	—
295	C₂×C₃×C₈	—	2	1	no	—
296	C₂×C₃×C₈	—	2	1	no	—
297	C₂×C₃×C₈	—	3	1	no	—
298	C₂×C₃×C₈	—	3	4	no	—
299	C₂×C₃×C₈	—	3	1	no	—
300	C₂×C₃×C₈	—	3	1	no	—
301	C₂×C₃×C₈	—	3	1	no	—
302	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
303	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
304	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
305	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
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×C₄⋊C₄	—	3	1	no	—
311	C₃×C₂²⋊C₄	—	3	1	no	—
312	C₃×C₂²⋊C₄	—	3	1	no	—
313	C₃×C₄²	—	2	1	no	—
314	C₃×C₄²	—	3	1	no	—
315	C₃×C₄²	—	3	1	no	—
316	C₃×C₄²	—	3	1	no	—
317	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
318	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
319	#217	—	3	1	no	—
320	#217	—	3	1	no	—
321	(C₂×D₃)⋊C₄	—	3	1	no	—
322	(C₂×D₃)⋊C₄	—	3	1	no	—
323	(C₂×D₃)⋊C₄	C₄×D₃	1	1	yes	characteristic
324	(C₂×D₃)⋊C₄	C₄×D₃	1	1	yes	characteristic
325	C₄⋊Dic₃	—	3	1	no	—
326	C₄⋊Dic₃	—	3	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	—	3	1	no	—
332	C₄⋊Dic₃	—	3	1	no	—
333	C₄⋊Dic₃	—	6	1	no	—
334	C₄⋊Dic₃	C₄×D₃	1	1	yes	characteristic
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	—	3	1	no	—
362	C₄×Dic₃	—	3	1	no	—
363	C₄×Dic₃	—	6	1	no	—
364	C₄×Dic₃	—	6	1	no	—
365	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
366	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
367	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
368	#208	—	6	2	no	—
369	C₂×C₃⋊C₈	—	3	1	no	—
370	C₂×C₃⋊C₈	—	3	1	no	—
371	C₂×C₃⋊C₈	—	3	1	no	—
372	C₂×C₃⋊C₈	—	3	1	no	—
373	C₂×C₃⋊C₈	—	6	1	no	—
374	C₂×C₃⋊C₈	—	6	1	no	—
375	C₂×C₃⋊C₈	—	6	2	no	—
376	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
377	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
378	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
379	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
380	ΓL(1,𝔽₂₅)	—	2	2	no	—
381	ΓL(1,𝔽₂₅)	—	6	2	no	—
382	D₃×C₈	—	6	2	no	—
383	D₃×C₈	Dic₆	1	4	yes	complemented
384	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
385	C₂×C₃×D₃	—	2	1	no	—
386	C₂×C₃×D₃	—	2	1	no	—
387	C₂×C₃×D₃	C₄×Q₈	1	2	yes	—
388	C₃²×C₄	—	2	1	no	—
389	C₃²×C₄	—	2	1	no	—
390	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
391	C₃²×C₄	C₂×#41	1	1	yes	characteristic
392	C₃⋊Dic₃	—	2	1	no	—
393	C₃⋊Dic₃	—	2	1	no	—
394	C₃⋊Dic₃	—	2	1	no	—
395	C₃⋊Dic₃	#131	1	2	yes	—
396	C₃×Dic₃	—	2	1	no	—
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	C₄×Q₈	1	2	yes	—
402	C₃×Dic₃	#131	1	2	yes	—
403	C₂×M₁₆	—	3	1	no	—
404	C₂×M₁₆	—	9	1	no	—
405	C₂²×C₈	—	3	1	no	—
406	C₂²×C₈	—	9	1	no	—
407	C₄⋊Q₈	—	9	1	no	—
408	C₄⋊Q₈	—	9	1	no	—
409	#125	—	9	1	no	—
410	#125	—	9	1	no	—
411	C₂²⋊Q₈	—	9	1	no	—
412	C₂²⋊Q₈	—	9	1	no	—
413	C₂²⋊Q₈	—	9	1	no	—
414	C₂²⋊Q₈	—	9	1	no	—
415	C₄×Q₈	—	3	1	no	—
416	C₄×Q₈	—	9	1	no	—
417	C₄×Q₈	—	9	1	no	—
418	C₄×Q₈	—	9	1	no	—
419	#117	—	3	1	no	—
420	#117	—	9	1	no	—
421	C₂×C₄²	—	9	1	no	—
422	C₄⋊C₈	—	3	1	no	—
423	C₄⋊C₈	—	3	1	no	—
424	C₄⋊C₈	—	3	1	no	—
425	C₄⋊C₈	—	9	1	no	—
426	C₄⋊C₈	—	9	1	no	—
427	C₄⋊C₈	—	9	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	#97	—	3	1	no	—
435	#97	—	3	1	no	—
436	#97	—	9	1	no	—
437	#97	D₃²	1	1	yes	characteristic
438	C₄×C₈	—	3	1	no	—
439	C₄×C₈	—	3	1	no	—
440	C₄×C₈	—	3	1	no	—
441	C₄×C₈	—	9	1	no	—
442	C₄×C₈	—	9	1	no	—
443	C₄×C₈	—	9	1	no	—
444	C₄×C₈	—	9	1	no	—
445	C₄×C₈	—	9	1	no	—
446	C₂³×C₃	—	3	1	no	—
447	C₂²×D₃	C₂×C₄×D₃	1	1	yes	characteristic
448	C₃×Q₈	—	6	2	no	—
449	C₂×C₃×C₄	—	2	1	no	—
450	C₂×C₃×C₄	—	2	1	no	—
451	C₂×C₃×C₄	—	2	1	no	—
452	C₂×C₃×C₄	—	3	1	no	—
453	C₂×C₃×C₄	—	3	1	no	—
454	C₂×C₃×C₄	—	3	2	no	—
455	C₂×C₃×C₄	—	3	2	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	C₂×C₄×D₃	1	1	yes	characteristic
462	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
463	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
464	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
465	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
466	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
467	C₂×Dic₃	—	3	1	no	—
468	C₂×Dic₃	—	3	1	no	—
469	C₂×Dic₃	—	3	1	no	—
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	—	6	1	no	—
476	C₂×Dic₃	—	6	1	no	—
477	C₂×Dic₃	—	6	1	no	—
478	C₂×Dic₃	—	6	1	no	—
479	C₂×Dic₃	—	6	2	no	—
480	C₂×Dic₃	—	6	2	no	—
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	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
488	C₄×D₃	—	6	2	no	—
489	C₄×D₃	—	6	2	no	—
490	C₄×D₃	C₂×Dic₆	1	2	yes	—
491	C₄×D₃	#235	1	2	yes	—
492	Dic₆	—	2	2	no	—
493	Dic₆	—	6	2	no	—
494	Dic₆	—	6	2	no	—
495	Dic₆	—	6	2	no	—
496	Dic₆	—	6	2	no	—
497	Dic₆	—	6	2	no	—
498	Dic₆	—	6	2	no	—
499	Dic₆	—	12	2	no	—
500	C₃×C₈	—	2	1	no	—
501	C₃×C₈	—	2	1	no	—
502	C₃×C₈	—	2	2	no	—
503	C₃×C₈	—	3	2	no	—
504	C₃×C₈	—	4	1	no	—
505	C₃×C₈	—	6	1	no	—
506	C₃×C₈	—	6	1	no	—
507	C₃×C₈	—	6	1	no	—
508	C₃×C₈	C₂×Dic₆	1	2	yes	—
509	C₃×C₈	D₃×Q₈	1	2	yes	—
510	C₃⋊C₈	—	2	1	no	—
511	C₃⋊C₈	—	2	1	no	—
512	C₃⋊C₈	—	2	1	no	—
513	C₃⋊C₈	—	6	1	no	—
514	C₃⋊C₈	—	6	1	no	—
515	C₃⋊C₈	—	6	1	no	—
516	C₃⋊C₈	—	6	1	no	—
517	C₃⋊C₈	—	12	1	no	—
518	C₃⋊C₈	—	12	1	no	—
519	C₃⋊C₈	C₂×Dic₆	1	2	yes	—
520	C₂×C₃²	C₂×C₄×Q₈	1	1	yes	characteristic
521	C₂×C₃²	C₂×#131	1	1	yes	characteristic
522	C₂×C₃²	C₂×#131	1	1	yes	characteristic
523	C₃×D₃	—	2	2	no	—
524	C₂×Q₈	—	3	1	no	—
525	C₂×Q₈	—	9	1	no	—
526	C₂×Q₈	—	9	1	no	—
527	C₂×Q₈	—	9	1	no	—
528	C₂²×C₄	—	3	1	no	—
529	C₂²×C₄	—	9	1	no	—
530	C₂²×C₄	—	9	1	no	—
531	M₁₆	—	6	2	no	—
532	M₁₆	—	18	2	no	—
533	C₂×C₈	—	3	1	no	—
534	C₂×C₈	—	3	4	no	—
535	C₂×C₈	—	3	1	no	—
536	C₂×C₈	—	3	1	no	—
537	C₂×C₈	—	3	1	no	—
538	C₂×C₈	—	9	1	no	—
539	C₂×C₈	—	9	1	no	—
540	C₂×C₈	—	18	2	no	—
541	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
542	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
543	C₄⋊C₄	—	3	1	no	—
544	C₄⋊C₄	—	3	1	no	—
545	C₄⋊C₄	—	3	1	no	—
546	C₄⋊C₄	—	3	1	no	—
547	C₄⋊C₄	—	3	1	no	—
548	C₄⋊C₄	—	9	1	no	—
549	C₄⋊C₄	—	9	1	no	—
550	C₄⋊C₄	—	9	1	no	—
551	C₄⋊C₄	—	9	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	C₂²⋊C₄	—	3	1	no	—
560	C₂²⋊C₄	—	3	1	no	—
561	C₂²⋊C₄	—	9	1	no	—
562	C₂²⋊C₄	—	9	1	no	—
563	C₄²	—	3	1	no	—
564	C₄²	—	3	1	no	—
565	C₄²	—	3	1	no	—
566	C₄²	—	9	1	no	—
567	C₄²	—	9	1	no	—
568	C₄²	—	9	1	no	—
569	C₄²	—	9	1	no	—
570	C₄²	C₂×D₃²	1	1	yes	characteristic
571	C₂²×C₃	—	2	1	no	—
572	C₂²×C₃	—	3	2	no	—
573	C₂²×C₃	—	6	1	no	—
574	C₂²×C₃	—	6	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	—	2	1	no	—
578	C₂×D₃	—	2	1	no	—
579	C₂×D₃	C₄×Dic₆	1	2	yes	—
580	C₃×C₄	—	2	1	no	—
581	C₃×C₄	—	2	1	no	—
582	C₃×C₄	—	2	1	no	—
583	C₃×C₄	—	2	1	no	—
584	C₃×C₄	—	2	1	no	—
585	C₃×C₄	—	2	1	no	—
586	C₃×C₄	—	3	2	no	—
587	C₃×C₄	—	3	2	no	—
588	C₃×C₄	—	4	1	no	—
589	C₃×C₄	—	4	1	no	—
590	C₃×C₄	—	6	1	no	—
591	C₃×C₄	—	6	1	no	—
592	C₃×C₄	—	6	1	no	—
593	C₃×C₄	—	6	1	no	—
594	C₃×C₄	—	6	1	no	—
595	C₃×C₄	C₂²×Dic₆	1	1	yes	characteristic
596	C₃×C₄	C₂×#235	1	1	yes	characteristic
597	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
598	C₃×C₄	D₃×#41	1	1	yes	characteristic
599	Dic₃	—	2	1	no	—
600	Dic₃	—	2	1	no	—
601	Dic₃	—	2	1	no	—
602	Dic₃	—	2	1	no	—
603	Dic₃	—	2	1	no	—
604	Dic₃	—	3	2	no	—
605	Dic₃	—	3	2	no	—
606	Dic₃	—	6	2	no	—
607	Dic₃	—	6	1	no	—
608	Dic₃	—	6	1	no	—
609	Dic₃	—	6	1	no	—
610	Dic₃	—	6	1	no	—
611	Dic₃	—	6	1	no	—
612	Dic₃	—	6	1	no	—
613	Dic₃	—	12	1	no	—
614	Dic₃	—	12	1	no	—
615	Dic₃	—	12	1	no	—
616	Dic₃	C₄×Dic₆	1	2	yes	—
617	Dic₃	#907	1	2	yes	—
618	C₃²	#2960	1	1	yes	characteristic, complemented, Sylow
619	C₂³	—	3	1	no	—
620	Q₈	—	6	2	no	—
621	Q₈	—	18	2	no	—
622	Q₈	—	18	2	no	—
623	Q₈	—	18	2	no	—
624	C₂×C₄	—	3	1	no	—
625	C₂×C₄	—	3	1	no	—
626	C₂×C₄	—	3	2	no	—
627	C₂×C₄	—	3	2	no	—
628	C₂×C₄	—	3	1	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	—	9	1	no	—
634	C₂×C₄	—	9	1	no	—
635	C₂×C₄	—	9	1	no	—
636	C₂×C₄	—	9	1	no	—
637	C₂×C₄	—	18	2	no	—
638	C₂×C₄	—	18	2	no	—
639	C₂×C₄	C₄×D₃²	1	1	yes	characteristic
640	C₂×C₄	C₄×D₃²	1	1	yes	characteristic
641	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
642	C₈	—	2	1	no	—
643	C₈	—	3	2	no	—
644	C₈	—	6	1	no	—
645	C₈	—	6	1	no	—
646	C₈	—	6	1	no	—
647	C₈	—	18	1	no	—
648	C₈	—	18	1	no	—
649	C₈	D₃×Dic₆	1	2	yes	—
650	C₂×C₃	—	2	1	no	—
651	C₂×C₃	—	2	1	no	—
652	C₂×C₃	—	2	1	no	—
653	C₂×C₃	—	6	2	no	—
654	C₂×C₃	C₂×C₄×Dic₆	1	1	yes	characteristic
655	C₂×C₃	C₄×D₃×Q₈	1	1	yes	characteristic
656	C₂×C₃	C₂×#907	1	1	yes	characteristic
657	C₂×C₃	D₃×#131	1	1	yes	characteristic
658	C₂×C₃	D₃×#131	1	1	yes	characteristic
659	C₂×C₃	D₃×#131	1	1	yes	characteristic
660	D₃	—	2	2	no	—
661	C₂²	—	3	2	no	—
662	C₂²	—	6	1	no	—
663	C₂²	—	6	1	no	—
664	C₂²	C₂×C₄×D₃²	1	1	yes	characteristic
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	3	2	no	—
668	C₄	—	3	2	no	—
669	C₄	—	6	1	no	—
670	C₄	—	6	1	no	—
671	C₄	—	6	1	no	—
672	C₄	—	6	1	no	—
673	C₄	—	6	1	no	—
674	C₄	—	9	2	no	—
675	C₄	—	18	1	no	—
676	C₄	—	18	1	no	—
677	C₄	—	18	1	no	—
678	C₄	C₂×D₃×Dic₆	1	1	yes	characteristic
679	C₄	D₃×#235	1	1	yes	characteristic
680	C₃	—	2	1	no	—
681	C₃	#78542	1	1	yes	characteristic, complemented
682	C₃	#79958	1	1	yes	characteristic, complemented
683	C₂	—	6	2	no	—
684	C₂	C₄×D₃×Dic₆	1	1	yes	characteristic
685	C₂	D₃×#907	1	1	yes	characteristic
686	C₂	#10594707	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃²
commutator, socle	C₂²×C₃²	C₂³×C₄
Fitting	C₃²×#97	C₂²
prime radical	C₂²×C₃×D₃	C₂²×C₄
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	#97	D₃²
hypocenter	C₃²	#2960
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ #97

Complements

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

N	H ≅ G/N	type
2. #10592400	C₂	semidirect
4. C₃×#4701	C₂	semidirect
5. #10590787	C₂	semidirect
6. #10590784	C₂	semidirect
11. #10590644	C₂	semidirect
12. #10590644	C₂	semidirect
14. #10590254	C₂	semidirect
15. C₃⋊C₈×Dic₆	C₂	semidirect
85. #4701	D₃	semidirect
124. C₃×D₃×C₈	Q₈	semidirect
383. D₃×C₈	Dic₆	semidirect
618. C₃²	#2960	semidirect
681. C₃	#78542	semidirect
682. C₃	#79958	semidirect

Maximal subgroups

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

subgroup	index
#10593926	2
#10592400	2
C₃×#4708	2
C₃×#4701	2
#10590787	2
#10590784	2
#10590695	2
#10590693	2
#10590663	2
D₃×C₈×Dic₃	2
#10590644	2
#10590324	2
#10590254	2
C₃⋊C₈×Dic₆	2
#79958	3
#78542	3