Subgroups — #11861708

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5528	C₂	1	1	yes	maximal, characteristic
2	#10592696	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5000	C₂	1	1	yes	maximal, characteristic, complemented
4	#10591151	C₂	1	1	yes	maximal, characteristic, complemented
5	#67⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#67⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	#10591067	C₂	1	1	yes	maximal, characteristic, complemented
8	#10590330	C₂	1	1	yes	maximal, characteristic, complemented
9	#10590329	C₂	1	1	yes	maximal, characteristic, complemented
10	#10590319	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×D₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#10590264	C₂	1	1	yes	maximal, characteristic, complemented
13	#10590262	C₂	1	1	yes	maximal, characteristic, complemented
14	#10590252	C₂	1	1	yes	maximal, characteristic, complemented
15	#10590250	C₂	1	1	yes	maximal, characteristic, complemented
16	#83126	—	3	1	no	maximal
17	#79366	—	3	1	no	maximal
18	C₃²×#117	C₂²	1	1	yes	characteristic
19	C₂×#3748	C₂²	1	1	yes	characteristic
20	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
21	C₃×C₄×#67	C₂²	1	1	yes	characteristic
22	C₃×C₄×#67	C₂²	1	1	yes	characteristic
23	C₃×#898	C₄	1	1	yes	characteristic
24	C₃×#896	C₄	1	1	yes	characteristic
25	C₃×#894	C₄	1	1	yes	characteristic
26	C₃×#889	C₄	1	1	yes	characteristic
27	C₃×#885	C₄	1	1	yes	characteristic
28	C₃×#884	C₄	1	1	yes	characteristic
29	C₃×#883	C₄	1	1	yes	characteristic
30	C₃×#879	C₄	1	1	yes	characteristic
31	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
32	C₃×#872	C₂²	1	1	yes	characteristic
33	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
34	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
35	C₂×#3711	C₂²	1	1	yes	characteristic
36	C₂×D₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×D₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×D₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
39	#63630	C₂²	1	1	yes	characteristic
40	#63630	C₂²	1	1	yes	characteristic
41	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
42	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
43	C₃×#830	C₂²	1	1	yes	characteristic
44	C₃×#830	C₂²	1	1	yes	characteristic
45	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
46	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
47	C₃×#803	C₂²	1	1	yes	characteristic
48	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
49	Dic₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
50	Dic₃⋊(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	(C₂×D₃)⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
54	(C₂×D₃)⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
55	(C₂×D₃)⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
56	(C₂×D₃)⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
57	#63554	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	C₃×#529	—	3	1	no	—
62	#5528	D₃	1	1	yes	characteristic
63	C₃×#433	—	3	1	no	—
64	#5024	—	3	1	no	—
65	Q₈×C₃⋊C₈	—	3	1	no	—
66	#5012	—	3	1	no	—
67	#5011	—	3	1	no	—
68	#5011	—	3	1	no	—
69	D₄×C₃⋊C₈	—	3	1	no	—
70	D₄×C₃⋊C₈	—	3	1	no	—
71	D₄×C₃⋊C₈	—	3	1	no	—
72	#5000	—	3	1	no	—
73	#5000	D₃	1	1	yes	characteristic, complemented
74	#4997	—	3	1	no	—
75	#4997	—	3	1	no	—
76	#4997	—	3	1	no	—
77	#4997	—	6	1	no	—
78	#4926	—	3	1	no	—
79	C₂×C₄×C₃⋊C₈	—	3	1	no	—
80	#4836	—	3	1	no	—
81	#4834	—	3	1	no	—
82	#4830	—	3	1	no	—
83	#4828	—	3	1	no	—
84	#4729	—	3	1	no	—
85	#4728	—	3	1	no	—
86	#67⋊C₈	—	3	1	no	—
87	#67⋊C₈	—	3	1	no	—
88	#4708	—	3	1	no	—
89	#4705	—	3	1	no	—
90	#4690	—	3	1	no	—
91	C₄×D₃×C₈	—	3	1	no	—
92	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
93	C₂×C₃×#67	C₂×C₄	1	1	yes	characteristic
94	C₂×C₃×#67	C₂×C₄	1	1	yes	characteristic
95	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
100	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
101	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₃²×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₃²×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₃²×C₄²	C₂³	1	1	yes	characteristic
106	C₃²×C₄²	C₂³	1	1	yes	characteristic
107	#3748	—	2	2	no	—
108	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
109	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
110	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
111	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
112	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
113	C₃×#217	C₂×C₄	1	1	yes	characteristic
114	C₃×#217	C₂×C₄	1	1	yes	characteristic
115	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
118	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
119	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
120	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
121	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
122	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
123	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
124	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
125	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
126	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
127	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
128	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
129	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
130	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
131	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
132	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
133	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
134	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
135	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
136	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
137	#3711	—	2	2	no	—
138	D₃×C₃⋊C₈	—	2	2	no	—
139	D₃×C₃⋊C₈	—	2	2	no	—
140	D₃×C₃⋊C₈	—	2	2	no	—
141	#2966	—	9	1	no	Sylow
142	C₃×#126	—	3	1	no	—
143	C₃×#126	—	3	1	no	—
144	C₃×#125	—	3	1	no	—
145	C₃×#124	—	3	1	no	—
146	C₃×#123	—	3	1	no	—
147	C₃×#123	—	3	1	no	—
148	C₃×C₂²⋊Q₈	—	3	1	no	—
149	C₃×#121	—	3	1	no	—
150	C₃×C₄×Q₈	—	3	1	no	—
151	C₃×C₄×D₄	—	3	1	no	—
152	C₃×C₄×D₄	—	3	1	no	—
153	C₃×C₄×D₄	—	3	1	no	—
154	C₃×#117	—	2	1	no	—
155	C₃×#117	—	3	1	no	—
156	C₃×#117	C₂×D₃	1	1	yes	characteristic
157	C₃×#117	C₂×D₃	1	1	yes	characteristic
158	C₂×C₃×C₄²	—	3	1	no	—
159	C₄×#67	C₂×D₃	1	1	yes	characteristic
160	C₄×#67	C₂×D₃	1	1	yes	characteristic
161	C₂×#208	—	3	1	no	—
162	C₂×#208	—	3	1	no	—
163	C₂×#208	—	3	1	no	—
164	C₂×#208	—	6	1	no	—
165	C₂²×C₃⋊C₈	—	3	1	no	—
166	C₂²×C₃⋊C₈	—	3	1	no	—
167	C₂²×C₃⋊C₈	—	3	1	no	—
168	C₂²×C₃⋊C₈	—	3	1	no	—
169	C₂²×C₃⋊C₈	—	3	1	no	—
170	C₂²×C₃⋊C₈	—	6	1	no	—
171	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
172	C₂×D₃×C₈	—	3	1	no	—
173	C₂×D₃×C₈	—	3	1	no	—
174	C₂×D₃×C₈	—	3	1	no	—
175	#898	Dic₃	1	1	yes	characteristic
176	#896	Dic₃	1	1	yes	characteristic
177	#894	Dic₃	1	1	yes	characteristic
178	#889	Dic₃	1	1	yes	characteristic
179	#885	Dic₃	1	1	yes	characteristic
180	#884	Dic₃	1	1	yes	characteristic
181	#883	Dic₃	1	1	yes	characteristic
182	#879	Dic₃	1	1	yes	characteristic
183	C₄×D₁₂	C₂×D₃	1	1	yes	characteristic
184	#872	C₂×D₃	1	1	yes	characteristic
185	C₄²×D₃	C₂×D₃	1	1	yes	characteristic
186	C₄×Dic₆	C₂×D₃	1	1	yes	characteristic
187	C₃×C₄⋊C₈	—	3	1	no	—
188	C₃×C₄⋊C₈	—	3	1	no	—
189	C₃×C₂²⋊C₈	—	3	1	no	—
190	C₃×C₂²⋊C₈	—	3	1	no	—
191	C₃×#97	—	3	1	no	—
192	C₃×C₄×C₈	—	3	1	no	—
193	#830	—	3	1	no	—
194	#830	—	3	1	no	—
195	#830	—	3	1	no	—
196	#830	—	3	1	no	—
197	#830	C₂×D₃	1	1	yes	characteristic
198	#830	C₂×D₃	1	1	yes	characteristic
199	(C₂×D₃)⋊C₈	—	3	1	no	—
200	(C₂×D₃)⋊C₈	—	3	1	no	—
201	(C₂×D₃)⋊C₈	—	3	1	no	—
202	(C₂×D₃)⋊C₈	—	3	1	no	—
203	#815	—	3	1	no	—
204	Dic₃⋊C₈	—	3	1	no	—
205	Dic₃⋊C₈	—	3	1	no	—
206	Dic₃⋊C₈	—	3	1	no	—
207	Dic₃⋊C₈	—	3	1	no	—
208	C₈×Dic₃	—	3	1	no	—
209	C₈×Dic₃	—	3	1	no	—
210	C₈×Dic₃	—	3	1	no	—
211	C₄⋊(C₃⋊C₈)	—	3	1	no	—
212	C₄⋊(C₃⋊C₈)	—	3	1	no	—
213	C₄⋊(C₃⋊C₈)	—	3	1	no	—
214	C₄⋊(C₃⋊C₈)	—	3	1	no	—
215	C₄⋊(C₃⋊C₈)	C₂×D₃	1	1	yes	characteristic
216	C₄⋊(C₃⋊C₈)	C₂×D₃	1	1	yes	characteristic
217	#803	—	3	1	no	—
218	#803	—	3	1	no	—
219	#803	—	3	1	no	—
220	#803	—	3	1	no	—
221	#803	—	3	1	no	—
222	#803	—	6	1	no	—
223	#803	—	6	1	no	—
224	#803	C₂×D₃	1	1	yes	characteristic
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	—	3	1	no	—
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	—	6	1	no	—
233	C₄×C₃⋊C₈	—	6	1	no	—
234	C₄×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
235	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
236	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
237	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
238	C₂×C₃²×C₄	—	2	1	no	—
239	C₂×C₃²×C₄	—	2	1	no	—
240	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
241	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
242	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
243	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
244	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
245	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
246	C₃×#67	—	2	2	no	—
247	C₃×#67	—	2	2	no	—
248	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
249	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
250	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
251	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
252	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
253	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
254	C₃×D₁₂	—	2	2	no	—
255	C₃×C₄×D₃	—	2	2	no	—
256	C₃×C₄×D₃	—	2	1	no	—
257	C₃×C₄×D₃	—	2	1	no	—
258	C₃×C₄×D₃	—	2	1	no	—
259	C₃×C₄×D₃	—	2	1	no	—
260	C₃×C₄×D₃	—	2	2	no	—
261	C₃×Dic₆	—	2	2	no	—
262	C₃⋊(C₃⋊C₈)	—	2	1	no	—
263	C₃⋊(C₃⋊C₈)	—	2	1	no	—
264	C₃⋊(C₃⋊C₈)	#41	1	2	yes	—
265	C₃⋊(C₃⋊C₈)	#41	1	2	yes	—
266	C₃×C₃⋊C₈	—	2	1	no	—
267	C₃×C₃⋊C₈	—	2	1	no	—
268	C₃×C₃⋊C₈	—	2	1	no	—
269	C₃×C₃⋊C₈	—	2	1	no	—
270	#529	—	3	1	no	—
271	#446	—	9	1	no	—
272	C₈×Q₈	—	9	1	no	—
273	#436	—	9	1	no	—
274	#435	—	9	1	no	—
275	#435	—	9	1	no	—
276	C₈×D₄	—	9	1	no	—
277	C₈×D₄	—	9	1	no	—
278	C₈×D₄	—	9	1	no	—
279	#433	—	3	1	no	—
280	#433	—	9	1	no	—
281	#432	—	9	1	no	—
282	#405	—	9	1	no	—
283	#405	—	9	1	no	—
284	C₂×C₄×C₈	—	9	1	no	—
285	C₂×C₃×Q₈	—	3	1	no	—
286	C₂×C₃×D₄	—	3	1	no	—
287	C₂×C₃×D₄	—	3	1	no	—
288	C₂×C₃×D₄	—	3	1	no	—
289	C₂²×C₃×C₄	—	2	1	no	—
290	C₂²×C₃×C₄	—	3	1	no	—
291	C₂²×C₃×C₄	—	3	1	no	—
292	C₂²×C₃×C₄	—	3	1	no	—
293	C₂²×C₃×C₄	—	3	1	no	—
294	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
295	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
296	C₂×#67	C₂×Dic₃	1	1	yes	characteristic
297	C₂×#67	C₂×Dic₃	1	1	yes	characteristic
298	C₂×D₁₂	C₂×Dic₃	1	1	yes	characteristic
299	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
300	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
301	C₂×C₄×D₃	C₂²×D₃	1	1	yes	characteristic
302	C₂×C₄×D₃	C₂²×D₃	1	1	yes	characteristic
303	C₂×Dic₆	C₂×Dic₃	1	1	yes	characteristic
304	C₂×C₃×C₈	—	3	1	no	—
305	C₂×C₃×C₈	—	3	1	no	—
306	C₂×C₃×C₈	—	3	1	no	—
307	C₂×C₃×C₈	—	3	1	no	—
308	C₃×C₄⋊C₄	—	2	1	no	—
309	C₃×C₄⋊C₄	—	2	1	no	—
310	C₃×C₄⋊C₄	—	3	1	no	—
311	C₃×C₄⋊C₄	—	3	1	no	—
312	C₃×C₄⋊C₄	—	3	1	no	—
313	C₃×C₄⋊C₄	—	3	1	no	—
314	C₃×C₄⋊C₄	—	3	1	no	—
315	C₃×C₄⋊C₄	—	3	1	no	—
316	C₃×C₄⋊C₄	—	3	1	no	—
317	C₃×C₄⋊C₄	—	3	1	no	—
318	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
319	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
320	C₃×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
321	C₃×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
322	C₃×C₂²⋊C₄	—	2	1	no	—
323	C₃×C₂²⋊C₄	—	2	1	no	—
324	C₃×C₂²⋊C₄	—	3	1	no	—
325	C₃×C₂²⋊C₄	—	3	1	no	—
326	C₃×C₂²⋊C₄	—	3	1	no	—
327	C₃×C₂²⋊C₄	—	3	1	no	—
328	C₃×C₂²⋊C₄	—	3	1	no	—
329	C₃×C₂²⋊C₄	—	3	1	no	—
330	C₃×C₂²⋊C₄	—	3	1	no	—
331	C₃×C₂²⋊C₄	—	3	1	no	—
332	C₃×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
333	C₃×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
334	C₃×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
335	C₃×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
336	C₃×C₄²	—	2	1	no	—
337	C₃×C₄²	—	2	1	no	—
338	C₃×C₄²	—	3	1	no	—
339	C₃×C₄²	—	3	1	no	—
340	C₃×C₄²	—	3	1	no	—
341	C₃×C₄²	—	3	1	no	—
342	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
343	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
344	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
345	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
346	#217	C₂×Dic₃	1	1	yes	characteristic
347	#217	C₂×Dic₃	1	1	yes	characteristic
348	(C₂×D₃)⋊C₄	C₂×Dic₃	1	1	yes	characteristic
349	(C₂×D₃)⋊C₄	C₂×Dic₃	1	1	yes	characteristic
350	(C₂×D₃)⋊C₄	C₂×Dic₃	1	1	yes	characteristic
351	(C₂×D₃)⋊C₄	C₂×Dic₃	1	1	yes	characteristic
352	(C₂×D₃)⋊C₄	C₂×Dic₃	1	1	yes	characteristic
353	(C₂×D₃)⋊C₄	C₂×Dic₃	1	1	yes	characteristic
354	C₄⋊Dic₃	C₂×Dic₃	1	1	yes	characteristic
355	C₄⋊Dic₃	C₂×Dic₃	1	1	yes	characteristic
356	Dic₃⋊C₄	C₂×Dic₃	1	1	yes	characteristic
357	Dic₃⋊C₄	C₂×Dic₃	1	1	yes	characteristic
358	Dic₃⋊C₄	C₂×Dic₃	1	1	yes	characteristic
359	Dic₃⋊C₄	C₂×Dic₃	1	1	yes	characteristic
360	Dic₃⋊C₄	C₂×Dic₃	1	1	yes	characteristic
361	Dic₃⋊C₄	C₂×Dic₃	1	1	yes	characteristic
362	C₄×Dic₃	C₂×Dic₃	1	1	yes	characteristic
363	C₄×Dic₃	C₂×Dic₃	1	1	yes	characteristic
364	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
365	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
366	#208	—	6	2	no	—
367	#208	—	6	2	no	—
368	#208	—	6	2	no	—
369	#208	—	6	4	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	—	3	1	no	—
374	C₂×C₃⋊C₈	—	3	1	no	—
375	C₂×C₃⋊C₈	—	3	1	no	—
376	C₂×C₃⋊C₈	—	3	1	no	—
377	C₂×C₃⋊C₈	—	3	1	no	—
378	C₂×C₃⋊C₈	—	6	1	no	—
379	C₂×C₃⋊C₈	—	6	1	no	—
380	C₂×C₃⋊C₈	—	6	1	no	—
381	C₂×C₃⋊C₈	—	6	1	no	—
382	C₂×C₃⋊C₈	—	6	2	no	—
383	C₂×C₃⋊C₈	—	6	2	no	—
384	C₂×C₃⋊C₈	—	6	2	no	—
385	C₂×C₃⋊C₈	—	6	2	no	—
386	C₂×C₃⋊C₈	—	6	2	no	—
387	C₂×C₃⋊C₈	—	6	4	no	—
388	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
389	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
390	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
391	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
392	ΓL(1,𝔽₂₅)	—	6	2	no	—
393	D₃×C₈	—	6	2	no	—
394	D₃×C₈	—	6	2	no	—
395	D₃×C₈	—	6	2	no	—
396	C₂²×C₃²	—	2	1	no	—
397	C₂²×C₃²	—	2	1	no	—
398	C₂²×C₃²	—	2	1	no	—
399	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
400	C₂×C₃×D₃	—	2	1	no	—
401	C₂×C₃×D₃	—	2	1	no	—
402	C₂×C₃×D₃	—	2	1	no	—
403	C₂×C₃×D₃	—	2	1	no	—
404	C₂×C₃×D₃	—	2	1	no	—
405	C₂×C₃×D₃	#131	1	2	yes	—
406	C₃²×C₄	—	2	1	no	—
407	C₃²×C₄	—	2	1	no	—
408	C₃²×C₄	—	2	1	no	—
409	C₃²×C₄	—	2	1	no	—
410	C₃²×C₄	—	2	1	no	—
411	C₃²×C₄	C₂×#41	1	1	yes	characteristic
412	C₃²×C₄	C₂×#41	1	1	yes	characteristic
413	C₃×Dic₃	—	2	1	no	—
414	C₃×Dic₃	—	2	1	no	—
415	C₃×Dic₃	—	2	1	no	—
416	C₃×Dic₃	—	2	1	no	—
417	C₃×Dic₃	—	2	1	no	—
418	C₃×Dic₃	#131	1	2	yes	—
419	C₂×M₁₆	—	9	1	no	—
420	C₂×M₁₆	—	9	1	no	—
421	C₂²×C₈	—	9	1	no	—
422	C₂²×C₈	—	9	1	no	—
423	C₂²×C₈	—	9	1	no	—
424	C₂²×C₈	—	9	1	no	—
425	#126	—	3	1	no	—
426	#126	—	3	1	no	—
427	#125	—	3	1	no	—
428	#124	—	3	1	no	—
429	#123	—	3	1	no	—
430	#123	—	3	1	no	—
431	C₂²⋊Q₈	—	3	1	no	—
432	#121	—	3	1	no	—
433	C₄×Q₈	—	3	1	no	—
434	C₄×D₄	—	3	1	no	—
435	C₄×D₄	—	3	1	no	—
436	C₄×D₄	—	3	1	no	—
437	#117	—	3	1	no	—
438	#117	D₃²	1	1	yes	characteristic
439	C₂×C₄²	—	3	1	no	—
440	C₄⋊C₈	—	3	1	no	—
441	C₄⋊C₈	—	3	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	C₂²⋊C₈	—	3	1	no	—
447	C₂²⋊C₈	—	3	1	no	—
448	C₂²⋊C₈	—	9	1	no	—
449	C₂²⋊C₈	—	9	1	no	—
450	C₂²⋊C₈	—	9	1	no	—
451	C₂²⋊C₈	—	9	1	no	—
452	#97	—	3	1	no	—
453	#97	—	9	1	no	—
454	#97	—	9	1	no	—
455	#97	—	9	1	no	—
456	C₄×C₈	—	3	1	no	—
457	C₄×C₈	—	9	1	no	—
458	C₄×C₈	—	9	1	no	—
459	C₄×C₈	—	9	1	no	—
460	C₄×C₈	—	9	1	no	—
461	C₄×C₈	—	9	1	no	—
462	C₂³×C₃	—	2	1	no	—
463	C₂³×C₃	—	3	1	no	—
464	C₂³×C₃	—	3	1	no	—
465	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
466	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
467	C₂²×D₃	C₂²×Dic₃	1	1	yes	characteristic
468	C₂²×D₃	C₂²×Dic₃	1	1	yes	characteristic
469	C₃×Q₈	—	6	2	no	—
470	C₃×D₄	—	6	2	no	—
471	C₃×D₄	—	6	2	no	—
472	C₃×D₄	—	6	2	no	—
473	C₂×C₃×C₄	—	2	2	no	—
474	C₂×C₃×C₄	—	2	2	no	—
475	C₂×C₃×C₄	—	2	1	no	—
476	C₂×C₃×C₄	—	2	1	no	—
477	C₂×C₃×C₄	—	2	1	no	—
478	C₂×C₃×C₄	—	2	1	no	—
479	C₂×C₃×C₄	—	2	1	no	—
480	C₂×C₃×C₄	—	2	1	no	—
481	C₂×C₃×C₄	—	2	1	no	—
482	C₂×C₃×C₄	—	2	1	no	—
483	C₂×C₃×C₄	—	2	1	no	—
484	C₂×C₃×C₄	—	2	1	no	—
485	C₂×C₃×C₄	—	3	1	no	—
486	C₂×C₃×C₄	—	3	1	no	—
487	C₂×C₃×C₄	—	3	1	no	—
488	C₂×C₃×C₄	—	3	1	no	—
489	C₂×C₃×C₄	—	3	1	no	—
490	C₂×C₃×C₄	—	3	1	no	—
491	C₂×C₃×C₄	—	6	2	no	—
492	C₂×C₃×C₄	—	6	2	no	—
493	C₂×C₃×C₄	—	6	1	no	—
494	C₂×C₃×C₄	—	6	1	no	—
495	C₂×C₃×C₄	—	6	1	no	—
496	C₂×C₃×C₄	—	6	1	no	—
497	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
498	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
499	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
500	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
501	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
502	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
503	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
504	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
505	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
506	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
507	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
508	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
509	#67	—	2	2	no	—
510	#67	—	2	2	no	—
511	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
512	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
513	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
514	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
515	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
516	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
517	D₁₂	—	2	2	no	—
518	C₄×D₃	—	2	2	no	—
519	C₄×D₃	—	2	1	no	—
520	C₄×D₃	—	2	1	no	—
521	C₄×D₃	—	2	1	no	—
522	C₄×D₃	—	2	1	no	—
523	C₄×D₃	—	2	2	no	—
524	Dic₆	—	2	2	no	—
525	C₃×C₈	—	6	1	no	—
526	C₃×C₈	—	6	1	no	—
527	C₃×C₈	—	6	1	no	—
528	C₃×C₈	—	6	1	no	—
529	C₃⋊C₈	—	2	1	no	—
530	C₃⋊C₈	—	2	1	no	—
531	C₃⋊C₈	—	2	1	no	—
532	C₃⋊C₈	—	2	1	no	—
533	C₃⋊C₈	—	3	2	no	—
534	C₃⋊C₈	—	3	2	no	—
535	C₃⋊C₈	—	3	2	no	—
536	C₃⋊C₈	—	3	2	no	—
537	C₃⋊C₈	—	6	2	no	—
538	C₃⋊C₈	—	6	2	no	—
539	C₃⋊C₈	—	6	2	no	—
540	C₃⋊C₈	—	6	2	no	—
541	C₃⋊C₈	—	6	1	no	—
542	C₃⋊C₈	—	6	1	no	—
543	C₃⋊C₈	—	6	1	no	—
544	C₃⋊C₈	—	6	1	no	—
545	C₂×C₃²	—	4	1	no	—
546	C₂×C₃²	C₄×#41	1	1	yes	characteristic
547	C₂×C₃²	C₂×#131	1	1	yes	characteristic
548	C₂×C₃²	C₂×#131	1	1	yes	characteristic
549	C₃×D₃	—	2	2	no	—
550	C₃×D₃	—	4	1	no	—
551	C₂×Q₈	—	3	1	no	—
552	C₂×D₄	—	3	1	no	—
553	C₂×D₄	—	3	1	no	—
554	C₂×D₄	—	3	1	no	—
555	C₂²×C₄	—	3	1	no	—
556	C₂²×C₄	—	3	1	no	—
557	C₂²×C₄	—	3	1	no	—
558	C₂²×C₄	—	3	1	no	—
559	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
560	M₁₆	—	18	2	no	—
561	M₁₆	—	18	2	no	—
562	C₂×C₈	—	3	1	no	—
563	C₂×C₈	—	3	1	no	—
564	C₂×C₈	—	3	1	no	—
565	C₂×C₈	—	3	1	no	—
566	C₂×C₈	—	9	1	no	—
567	C₂×C₈	—	9	1	no	—
568	C₂×C₈	—	9	1	no	—
569	C₂×C₈	—	9	1	no	—
570	C₂×C₈	—	18	2	no	—
571	C₂×C₈	—	18	2	no	—
572	C₂×C₈	—	18	2	no	—
573	C₂×C₈	—	18	2	no	—
574	C₄⋊C₄	—	3	1	no	—
575	C₄⋊C₄	—	3	1	no	—
576	C₄⋊C₄	—	3	1	no	—
577	C₄⋊C₄	—	3	1	no	—
578	C₄⋊C₄	—	3	1	no	—
579	C₄⋊C₄	—	3	1	no	—
580	C₄⋊C₄	—	3	1	no	—
581	C₄⋊C₄	—	3	1	no	—
582	C₄⋊C₄	D₃×Dic₃	1	1	yes	characteristic
583	C₄⋊C₄	D₃×Dic₃	1	1	yes	characteristic
584	C₂²⋊C₄	—	3	1	no	—
585	C₂²⋊C₄	—	3	1	no	—
586	C₂²⋊C₄	—	3	1	no	—
587	C₂²⋊C₄	—	3	1	no	—
588	C₂²⋊C₄	—	3	1	no	—
589	C₂²⋊C₄	—	3	1	no	—
590	C₂²⋊C₄	—	3	1	no	—
591	C₂²⋊C₄	—	3	1	no	—
592	C₂²⋊C₄	D₃×Dic₃	1	1	yes	characteristic
593	C₂²⋊C₄	D₃×Dic₃	1	1	yes	characteristic
594	C₄²	—	3	1	no	—
595	C₄²	—	3	1	no	—
596	C₄²	—	3	1	no	—
597	C₄²	—	3	1	no	—
598	C₄²	C₂×D₃²	1	1	yes	characteristic
599	C₄²	C₂×D₃²	1	1	yes	characteristic
600	C₂²×C₃	—	2	2	no	—
601	C₂²×C₃	—	2	1	no	—
602	C₂²×C₃	—	2	1	no	—
603	C₂²×C₃	—	2	1	no	—
604	C₂²×C₃	—	2	1	no	—
605	C₂²×C₃	—	2	1	no	—
606	C₂²×C₃	—	2	1	no	—
607	C₂²×C₃	—	2	1	no	—
608	C₂²×C₃	—	3	2	no	—
609	C₂²×C₃	—	4	1	no	—
610	C₂²×C₃	—	4	1	no	—
611	C₂²×C₃	—	6	1	no	—
612	C₂²×C₃	—	6	1	no	—
613	C₂²×C₃	—	6	1	no	—
614	C₂²×C₃	—	6	1	no	—
615	C₂²×C₃	—	6	1	no	—
616	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
617	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
618	C₂×D₃	—	2	1	no	—
619	C₂×D₃	—	2	1	no	—
620	C₂×D₃	—	2	1	no	—
621	C₂×D₃	—	2	1	no	—
622	C₂×D₃	—	2	1	no	—
623	C₂×D₃	#948	1	2	yes	—
624	C₃×C₄	—	2	2	no	—
625	C₃×C₄	—	2	1	no	—
626	C₃×C₄	—	2	1	no	—
627	C₃×C₄	—	2	1	no	—
628	C₃×C₄	—	2	1	no	—
629	C₃×C₄	—	2	1	no	—
630	C₃×C₄	—	2	1	no	—
631	C₃×C₄	—	2	1	no	—
632	C₃×C₄	—	2	1	no	—
633	C₃×C₄	—	2	1	no	—
634	C₃×C₄	—	2	1	no	—
635	C₃×C₄	—	2	1	no	—
636	C₃×C₄	—	2	1	no	—
637	C₃×C₄	—	3	2	no	—
638	C₃×C₄	—	4	1	no	—
639	C₃×C₄	—	4	1	no	—
640	C₃×C₄	—	4	1	no	—
641	C₃×C₄	—	4	1	no	—
642	C₃×C₄	—	6	1	no	—
643	C₃×C₄	—	6	1	no	—
644	C₃×C₄	—	6	1	no	—
645	C₃×C₄	—	6	1	no	—
646	C₃×C₄	—	6	1	no	—
647	C₃×C₄	D₃×#41	1	1	yes	characteristic
648	C₃×C₄	D₃×#41	1	1	yes	characteristic
649	C₃×C₄	D₃×#41	1	1	yes	characteristic
650	C₃×C₄	D₃×#41	1	1	yes	characteristic
651	Dic₃	—	2	1	no	—
652	Dic₃	—	2	1	no	—
653	Dic₃	—	2	1	no	—
654	Dic₃	—	2	1	no	—
655	Dic₃	—	2	1	no	—
656	Dic₃	#948	1	2	yes	—
657	C₃²	#2966	1	1	yes	characteristic, complemented, Sylow
658	C₂³	—	3	1	no	—
659	C₂³	—	3	1	no	—
660	C₂³	C₂×D₃×Dic₃	1	1	yes	characteristic
661	Q₈	—	6	2	no	—
662	D₄	—	6	2	no	—
663	D₄	—	6	2	no	—
664	D₄	—	6	2	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	3	1	no	—
668	C₂×C₄	—	3	1	no	—
669	C₂×C₄	—	3	1	no	—
670	C₂×C₄	—	3	1	no	—
671	C₂×C₄	—	3	1	no	—
672	C₂×C₄	—	3	1	no	—
673	C₂×C₄	—	6	2	no	—
674	C₂×C₄	—	6	2	no	—
675	C₂×C₄	—	6	1	no	—
676	C₂×C₄	—	6	1	no	—
677	C₂×C₄	—	6	1	no	—
678	C₂×C₄	—	6	1	no	—
679	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
680	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
681	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
682	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
683	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
684	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
685	C₈	—	6	1	no	—
686	C₈	—	6	1	no	—
687	C₈	—	6	1	no	—
688	C₈	—	6	1	no	—
689	C₈	—	9	2	no	—
690	C₈	—	9	2	no	—
691	C₈	—	18	1	no	—
692	C₈	—	18	1	no	—
693	C₂×C₃	—	2	1	no	—
694	C₂×C₃	—	2	1	no	—
695	C₂×C₃	—	2	1	no	—
696	C₂×C₃	—	4	2	no	—
697	C₂×C₃	—	4	1	no	—
698	C₂×C₃	—	4	1	no	—
699	C₂×C₃	—	6	2	no	—
700	C₂×C₃	—	12	1	no	—
701	C₂×C₃	#5522	1	1	yes	characteristic
702	C₂×C₃	D₃×#131	1	1	yes	characteristic
703	C₂×C₃	D₃×#131	1	1	yes	characteristic
704	C₂×C₃	C₂×#948	1	1	yes	characteristic
705	C₂×C₃	C₂×#948	1	1	yes	characteristic
706	C₂×C₃	Dic₃×#41	1	1	yes	characteristic
707	D₃	—	2	2	no	—
708	D₃	—	4	1	no	—
709	C₂²	—	2	1	no	—
710	C₂²	—	2	1	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	3	2	no	—
713	C₂²	—	6	1	no	—
714	C₂²	—	6	1	no	—
715	C₂²	—	6	1	no	—
716	C₂²	—	6	1	no	—
717	C₂²	—	6	1	no	—
718	C₂²	C₂²×D₃×Dic₃	1	1	yes	characteristic
719	C₄	—	2	1	no	—
720	C₄	—	2	1	no	—
721	C₄	—	2	1	no	—
722	C₄	—	2	1	no	—
723	C₄	—	2	1	no	—
724	C₄	—	3	2	no	—
725	C₄	—	6	1	no	—
726	C₄	—	6	1	no	—
727	C₄	—	6	1	no	—
728	C₄	—	6	1	no	—
729	C₄	—	6	1	no	—
730	C₄	#64306	1	1	yes	characteristic
731	C₄	#64306	1	1	yes	characteristic
732	C₃	—	2	1	no	—
733	C₃	#79366	1	1	yes	characteristic, complemented
734	C₃	#83126	1	1	yes	characteristic, complemented
735	C₂	—	4	1	no	—
736	C₂	—	6	2	no	—
737	C₂	—	12	1	no	—
738	C₂	#10594958	1	1	yes	characteristic
739	C₂	D₃×#948	1	1	yes	characteristic
740	C₂	D₃×#948	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃²
commutator, socle	C₂²×C₃²	C₂³×C₄
Fitting	C₃²×#117	C₂²
prime radical	C₃×#884	C₄
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	#117	D₃²
hypocenter	C₃²	#2966
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
2. #10592696	C₂	semidirect
3. C₃×#5000	C₂	semidirect
4. #10591151	C₂	semidirect
5. #67⋊(C₃⋊C₈)	C₂	semidirect
6. #67⋊(C₃⋊C₈)	C₂	semidirect
7. #10591067	C₂	semidirect
8. #10590330	C₂	semidirect
9. #10590329	C₂	semidirect
10. #10590319	C₂	semidirect
11. C₄×D₃×C₃⋊C₈	C₂	semidirect
12. #10590264	C₂	semidirect
13. #10590262	C₂	semidirect
14. #10590252	C₂	semidirect
15. #10590250	C₂	semidirect
73. #5000	D₃	semidirect
657. C₃²	#2966	semidirect
733. C₃	#79366	semidirect
734. C₃	#83126	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5528	2
#10592696	2
C₃×#5000	2
#10591151	2
#67⋊(C₃⋊C₈)	2
#10591067	2
#10590330	2
#10590329	2
#10590319	2
C₄×D₃×C₃⋊C₈	2
#10590264	2
#10590262	2
#10590252	2
#10590250	2
#83126	3
#79366	3