Subgroups — #11859111

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic
2	#10592625	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#4925	C₂	1	1	yes	maximal, characteristic, complemented
4	#10591145	C₂	1	2	yes	maximal
5	#10591056	C₂	1	2	yes	maximal, complemented
6	#10590336	C₂	1	1	yes	maximal, characteristic, complemented
7	D₃×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	#10590318	C₂	1	2	yes	maximal, complemented
9	#10590264	C₂	1	2	yes	maximal, complemented
10	#10590263	C₂	1	1	yes	maximal, characteristic, complemented
11	#10590248	C₂	1	1	yes	maximal, characteristic, complemented
12	#82515	—	3	1	no	maximal
13	#79285	—	3	1	no	maximal
14	C₂×C₃×#235	C₂²	1	1	yes	characteristic
15	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
16	C₃×C₄×#67	C₄	1	1	yes	characteristic
17	C₃×C₄×#67	C₄	1	1	yes	characteristic
18	C₃×C₄×#67	C₄	1	1	yes	characteristic
19	C₃×C₄×#67	C₄	1	1	yes	characteristic
20	C₃×#926	C₂²	1	1	yes	characteristic
21	C₃×C₄×D₁₂	C₄	1	1	yes	characteristic
22	C₃×C₄×D₁₂	C₄	1	1	yes	characteristic
23	C₃×#872	C₂²	1	1	yes	characteristic
24	C₃×#872	C₂²	1	1	yes	characteristic
25	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
26	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
27	C₃×C₄×Dic₆	C₄	1	1	yes	characteristic
28	C₃×C₄×Dic₆	C₄	1	1	yes	characteristic
29	C₂×#3711	C₂²	1	2	yes	—
30	C₂×D₃×C₃⋊C₈	C₂²	1	2	yes	—
31	#63657	C₂²	1	2	yes	—
32	C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic
33	C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic
34	#63630	C₂²	1	2	yes	—
35	C₃×#830	C₂²	1	2	yes	—
36	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
37	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
38	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	—
39	Dic₃⋊(C₃⋊C₈)	C₂²	1	2	yes	—
40	Dic₃⋊(C₃⋊C₈)	C₂²	1	2	yes	—
41	(C₂×D₃)⋊(C₃⋊C₈)	C₂²	1	2	yes	—
42	(C₂×D₃)⋊(C₃⋊C₈)	C₂²	1	2	yes	—
43	#63554	C₂²	1	2	yes	—
44	Dic₃×C₃⋊C₈	C₂²	1	2	yes	—
45	C₃×C₄×#41	—	3	1	no	—
46	C₄×#235	D₃	1	1	yes	characteristic
47	C₃×#431	—	3	1	no	—
48	#5234	—	3	2	no	—
49	#5000	—	3	2	no	—
50	#5000	—	3	2	no	—
51	#4997	—	3	2	no	—
52	#4926	—	3	1	no	—
53	#4926	—	3	1	no	—
54	#4926	—	3	1	no	—
55	#4926	—	6	1	no	—
56	#4925	—	3	1	no	—
57	#4925	D₃	1	1	yes	characteristic, complemented
58	#4924	—	3	1	no	—
59	C₂×C₄⋊(C₃⋊C₈)	—	3	1	no	—
60	#4837	—	3	1	no	—
61	#4835	—	3	1	no	—
62	#4833	—	3	1	no	—
63	D₃×C₄⋊C₈	—	3	1	no	—
64	#4727	—	3	2	no	—
65	#4720	—	3	2	no	—
66	#4690	—	3	2	no	—
67	#4689	—	3	2	no	—
68	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
71	C₂×C₃×#67	C₂×C₄	1	1	yes	characteristic
72	C₂×C₃×#67	C₂×C₄	1	1	yes	characteristic
73	C₃×#235	—	2	2	no	—
74	C₃×#235	—	2	2	no	—
75	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
76	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
82	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
83	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
84	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
85	C₃²×C₄²	C₂³	1	1	yes	characteristic
86	C₃²×C₄²	C₂³	1	1	yes	characteristic
87	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	—
88	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	—
89	C₃×#217	C₂×C₄	1	1	yes	characteristic
90	C₃×#217	C₂×C₄	1	1	yes	characteristic
91	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
96	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
97	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
102	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
103	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
104	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
105	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
106	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
107	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
108	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
109	#3711	—	2	4	no	—
110	D₃×C₃⋊C₈	—	2	4	no	—
111	#2925	—	9	1	no	Sylow
112	C₂×C₃×#41	—	3	1	no	—
113	C₂×#235	C₂×D₃	1	1	yes	characteristic
114	C₃×C₄×Q₈	—	3	1	no	—
115	C₃×C₄×Q₈	—	3	1	no	—
116	C₃×C₄×D₄	—	3	1	no	—
117	C₃×C₄×D₄	—	3	1	no	—
118	C₃×C₄×D₄	—	3	1	no	—
119	C₃×C₄×D₄	—	3	1	no	—
120	C₃×C₄×D₄	—	3	1	no	—
121	C₃×C₄×D₄	—	3	1	no	—
122	C₃×#117	—	3	1	no	—
123	C₃×#117	—	3	1	no	—
124	C₃×#117	—	3	1	no	—
125	C₂×C₃×C₄²	—	2	1	no	—
126	C₂×C₃×C₄²	—	3	1	no	—
127	C₂×C₃×C₄²	—	3	1	no	—
128	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
129	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
130	C₄×#67	Dic₃	1	1	yes	characteristic
131	C₄×#67	Dic₃	1	1	yes	characteristic
132	C₄×#67	Dic₃	1	1	yes	characteristic
133	C₄×#67	Dic₃	1	1	yes	characteristic
134	#926	C₂×D₃	1	1	yes	characteristic
135	C₂×#208	—	3	2	no	—
136	C₂²×C₃⋊C₈	—	3	2	no	—
137	C₂×ΓL(1,𝔽₂₅)	—	3	2	no	—
138	C₂×D₃×C₈	—	3	2	no	—
139	C₄×D₁₂	Dic₃	1	1	yes	characteristic
140	C₄×D₁₂	Dic₃	1	1	yes	characteristic
141	#872	C₂×D₃	1	1	yes	characteristic
142	#872	C₂×D₃	1	1	yes	characteristic
143	C₄²×D₃	C₂×D₃	1	1	yes	characteristic
144	C₄²×D₃	C₂×D₃	1	1	yes	characteristic
145	C₄×Dic₆	Dic₃	1	1	yes	characteristic
146	C₄×Dic₆	Dic₃	1	1	yes	characteristic
147	C₃×C₄⋊C₈	—	3	1	no	—
148	C₃×C₄⋊C₈	—	3	1	no	—
149	C₃×C₂²⋊C₈	—	3	2	no	—
150	C₃×C₄×C₈	—	3	2	no	—
151	#830	—	3	2	no	—
152	#830	—	3	2	no	—
153	#830	—	3	2	no	—
154	#830	—	3	2	no	—
155	#830	—	6	2	no	—
156	#830	C₂×D₃	1	2	yes	—
157	(C₂×D₃)⋊C₈	—	3	2	no	—
158	(C₂×D₃)⋊C₈	—	3	2	no	—
159	#815	—	3	2	no	—
160	Dic₃⋊C₈	—	3	2	no	—
161	Dic₃⋊C₈	—	3	2	no	—
162	C₈×Dic₃	—	3	2	no	—
163	C₄⋊(C₃⋊C₈)	—	3	1	no	—
164	C₄⋊(C₃⋊C₈)	—	3	1	no	—
165	C₄⋊(C₃⋊C₈)	—	3	1	no	—
166	C₄⋊(C₃⋊C₈)	—	3	1	no	—
167	C₄⋊(C₃⋊C₈)	—	3	2	no	—
168	C₄⋊(C₃⋊C₈)	—	3	2	no	—
169	C₄⋊(C₃⋊C₈)	—	6	1	no	—
170	C₄⋊(C₃⋊C₈)	—	6	1	no	—
171	C₄⋊(C₃⋊C₈)	C₂×D₃	1	1	yes	characteristic
172	C₄⋊(C₃⋊C₈)	C₂×D₃	1	1	yes	characteristic
173	#803	—	3	2	no	—
174	#803	—	3	2	no	—
175	#803	—	3	2	no	—
176	#803	—	6	2	no	—
177	C₄×C₃⋊C₈	—	3	2	no	—
178	C₄×C₃⋊C₈	C₂×D₃	1	2	yes	—
179	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₃²×C₄	—	2	2	no	—
183	C₂×C₃²×C₄	—	2	1	no	—
184	C₂×C₃²×C₄	—	2	1	no	—
185	C₂×C₃²×C₄	—	4	1	no	—
186	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
192	C₃×#67	—	2	2	no	—
193	C₃×#67	—	2	2	no	—
194	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
200	C₃×D₁₂	—	2	2	no	—
201	C₃×C₄×D₃	—	2	2	no	—
202	C₃×C₄×D₃	—	2	2	no	—
203	C₃×C₄×D₃	—	2	1	no	—
204	C₃×C₄×D₃	—	2	1	no	—
205	C₃×C₄×D₃	—	4	1	no	—
206	C₃×C₄×D₃	—	4	1	no	—
207	C₃×C₄×D₃	#41	1	2	yes	—
208	C₃×C₄×D₃	#41	1	2	yes	—
209	C₃×Dic₆	—	2	2	no	—
210	C₃⋊(C₃⋊C₈)	—	2	2	no	—
211	C₃⋊(C₃⋊C₈)	—	2	2	no	—
212	C₃×C₃⋊C₈	—	2	2	no	—
213	C₃×C₃⋊C₈	—	2	2	no	—
214	C₄×#41	—	3	1	no	—
215	#433	—	9	2	no	—
216	#433	—	9	2	no	—
217	#432	—	9	1	no	—
218	#432	—	9	1	no	—
219	#431	—	3	1	no	—
220	#431	—	9	1	no	—
221	#423	—	9	1	no	—
222	C₂×C₄⋊C₈	—	9	1	no	—
223	#408	—	9	2	no	—
224	#405	—	9	2	no	—
225	C₃×#41	—	6	2	no	—
226	C₃×#41	—	6	2	no	—
227	C₂×C₃×Q₈	—	3	1	no	—
228	C₂×C₃×D₄	—	3	1	no	—
229	C₂×C₃×D₄	—	3	1	no	—
230	C₂×C₃×D₄	—	3	1	no	—
231	C₂²×C₃×C₄	—	2	1	no	—
232	C₂²×C₃×C₄	—	2	1	no	—
233	C₂²×C₃×C₄	—	2	1	no	—
234	C₂²×C₃×C₄	—	3	1	no	—
235	C₂²×C₃×C₄	—	3	1	no	—
236	C₂²×C₃×C₄	—	3	1	no	—
237	C₂²×C₃×C₄	—	3	1	no	—
238	C₂²×C₃×C₄	—	3	1	no	—
239	C₂²×C₃×C₄	—	3	1	no	—
240	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
241	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
242	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
244	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
246	C₂×#67	C₂×Dic₃	1	1	yes	characteristic
247	C₂×#67	C₂×Dic₃	1	1	yes	characteristic
248	#235	—	2	2	no	—
249	#235	—	2	2	no	—
250	C₂×D₁₂	C₂×Dic₃	1	1	yes	characteristic
251	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
252	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
253	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
254	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
255	C₂×C₄×D₃	C₂²×D₃	1	1	yes	characteristic
256	C₂×C₄×D₃	C₂²×D₃	1	1	yes	characteristic
257	C₂×Dic₆	C₂×Dic₃	1	1	yes	characteristic
258	C₂×C₃×C₈	—	3	2	no	—
259	C₂×C₃×C₈	—	3	2	no	—
260	C₃×C₄⋊C₄	—	3	1	no	—
261	C₃×C₄⋊C₄	—	3	1	no	—
262	C₃×C₄⋊C₄	—	3	1	no	—
263	C₃×C₄⋊C₄	—	3	1	no	—
264	C₃×C₄⋊C₄	—	3	1	no	—
265	C₃×C₄⋊C₄	—	3	1	no	—
266	C₃×C₂²⋊C₄	—	3	1	no	—
267	C₃×C₂²⋊C₄	—	3	1	no	—
268	C₃×C₂²⋊C₄	—	3	1	no	—
269	C₃×C₂²⋊C₄	—	3	1	no	—
270	C₃×C₂²⋊C₄	—	3	1	no	—
271	C₃×C₂²⋊C₄	—	3	1	no	—
272	C₃×C₄²	—	2	1	no	—
273	C₃×C₄²	—	2	1	no	—
274	C₃×C₄²	—	2	1	no	—
275	C₃×C₄²	—	2	1	no	—
276	C₃×C₄²	—	3	1	no	—
277	C₃×C₄²	—	3	1	no	—
278	C₃×C₄²	—	3	1	no	—
279	C₃×C₄²	—	3	1	no	—
280	C₃×C₄²	—	3	1	no	—
281	C₃×C₄²	—	3	1	no	—
282	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
283	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
284	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
285	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
286	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
287	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
288	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
289	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
290	#217	C₂×Dic₃	1	1	yes	characteristic
291	#217	C₂×Dic₃	1	1	yes	characteristic
292	(C₂×D₃)⋊C₄	C₂×Dic₃	1	1	yes	characteristic
293	(C₂×D₃)⋊C₄	C₂×Dic₃	1	1	yes	characteristic
294	(C₂×D₃)⋊C₄	C₂×Dic₃	1	1	yes	characteristic
295	(C₂×D₃)⋊C₄	C₂×Dic₃	1	1	yes	characteristic
296	C₄⋊Dic₃	C₂×Dic₃	1	1	yes	characteristic
297	C₄⋊Dic₃	C₂×Dic₃	1	1	yes	characteristic
298	Dic₃⋊C₄	C₂×Dic₃	1	1	yes	characteristic
299	Dic₃⋊C₄	C₂×Dic₃	1	1	yes	characteristic
300	Dic₃⋊C₄	C₂×Dic₃	1	1	yes	characteristic
301	Dic₃⋊C₄	C₂×Dic₃	1	1	yes	characteristic
302	C₄×Dic₃	C₂×Dic₃	1	1	yes	characteristic
303	C₄×Dic₃	C₂×Dic₃	1	1	yes	characteristic
304	C₄×Dic₃	C₂×Dic₃	1	1	yes	characteristic
305	C₄×Dic₃	C₂×Dic₃	1	1	yes	characteristic
306	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
307	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
308	#208	—	6	4	no	—
309	C₂×C₃⋊C₈	—	3	2	no	—
310	C₂×C₃⋊C₈	—	3	2	no	—
311	C₂×C₃⋊C₈	—	3	2	no	—
312	C₂×C₃⋊C₈	—	3	2	no	—
313	C₂×C₃⋊C₈	—	6	2	no	—
314	C₂×C₃⋊C₈	—	6	2	no	—
315	C₂×C₃⋊C₈	—	6	4	no	—
316	C₂×C₃⋊C₈	C₂²×D₃	1	2	yes	—
317	C₂×C₃⋊C₈	C₂²×D₃	1	2	yes	—
318	ΓL(1,𝔽₂₅)	—	6	4	no	—
319	D₃×C₈	—	6	4	no	—
320	C₂²×C₃²	—	2	1	no	—
321	C₂²×C₃²	—	2	1	no	—
322	C₂²×C₃²	—	2	1	no	—
323	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
324	C₂×C₃×D₃	—	2	1	no	—
325	C₂×C₃×D₃	—	2	1	no	—
326	C₂×C₃×D₃	—	2	1	no	—
327	C₂×C₃×D₃	—	2	1	no	—
328	C₂×C₃×D₃	—	2	1	no	—
329	C₂×C₃×D₃	#117	1	2	yes	—
330	C₃²×C₄	—	2	1	no	—
331	C₃²×C₄	—	2	1	no	—
332	C₃²×C₄	—	2	1	no	—
333	C₃²×C₄	—	2	1	no	—
334	C₃²×C₄	#131	1	2	yes	—
335	C₃²×C₄	C₂×#41	1	1	yes	characteristic
336	C₃²×C₄	C₂×#41	1	1	yes	characteristic
337	C₃×Dic₃	—	2	1	no	—
338	C₃×Dic₃	—	2	1	no	—
339	C₃×Dic₃	—	2	1	no	—
340	C₃×Dic₃	—	2	1	no	—
341	C₃×Dic₃	—	2	1	no	—
342	C₃×Dic₃	#117	1	2	yes	—
343	C₂×#41	—	3	1	no	—
344	C₂×M₁₆	—	9	2	no	—
345	C₂²×C₈	—	9	2	no	—
346	C₄×Q₈	—	3	1	no	—
347	C₄×Q₈	—	3	1	no	—
348	C₄×D₄	—	3	1	no	—
349	C₄×D₄	—	3	1	no	—
350	C₄×D₄	—	3	1	no	—
351	C₄×D₄	—	3	1	no	—
352	C₄×D₄	—	3	1	no	—
353	C₄×D₄	—	3	1	no	—
354	#117	—	3	1	no	—
355	#117	—	3	1	no	—
356	#117	—	3	1	no	—
357	C₂×C₄²	—	3	1	no	—
358	C₂×C₄²	—	3	1	no	—
359	C₂×C₄²	D₃²	1	1	yes	characteristic
360	C₄⋊C₈	—	3	1	no	—
361	C₄⋊C₈	—	3	1	no	—
362	C₄⋊C₈	—	9	2	no	—
363	C₄⋊C₈	—	9	2	no	—
364	C₄⋊C₈	—	9	1	no	—
365	C₄⋊C₈	—	9	1	no	—
366	C₂²⋊C₈	—	3	2	no	—
367	C₂²⋊C₈	—	9	2	no	—
368	C₂²⋊C₈	—	9	2	no	—
369	C₂²⋊C₈	—	9	2	no	—
370	#97	—	9	2	no	—
371	#97	—	9	2	no	—
372	C₄×C₈	—	3	2	no	—
373	C₄×C₈	—	9	2	no	—
374	C₂³×C₃	—	2	1	no	—
375	C₂³×C₃	—	3	1	no	—
376	C₂³×C₃	—	3	1	no	—
377	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
378	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
379	C₂²×D₃	C₂²×Dic₃	1	1	yes	characteristic
380	C₂²×D₃	C₂²×Dic₃	1	1	yes	characteristic
381	C₃×Q₈	—	6	2	no	—
382	C₃×D₄	—	6	2	no	—
383	C₃×D₄	—	6	2	no	—
384	C₃×D₄	—	6	2	no	—
385	C₂×C₃×C₄	—	2	2	no	—
386	C₂×C₃×C₄	—	2	2	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	1	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	3	1	no	—
398	C₂×C₃×C₄	—	3	2	no	—
399	C₂×C₃×C₄	—	3	2	no	—
400	C₂×C₃×C₄	—	3	1	no	—
401	C₂×C₃×C₄	—	3	1	no	—
402	C₂×C₃×C₄	—	3	1	no	—
403	C₂×C₃×C₄	—	3	1	no	—
404	C₂×C₃×C₄	—	3	1	no	—
405	C₂×C₃×C₄	—	4	1	no	—
406	C₂×C₃×C₄	—	4	1	no	—
407	C₂×C₃×C₄	—	4	2	no	—
408	C₂×C₃×C₄	—	4	1	no	—
409	C₂×C₃×C₄	—	4	1	no	—
410	C₂×C₃×C₄	—	4	2	no	—
411	C₂×C₃×C₄	—	6	2	no	—
412	C₂×C₃×C₄	—	6	2	no	—
413	C₂×C₃×C₄	—	6	1	no	—
414	C₂×C₃×C₄	—	6	1	no	—
415	C₂×C₃×C₄	—	12	1	no	—
416	C₂×C₃×C₄	—	12	1	no	—
417	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
419	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
420	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
421	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
422	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
423	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
424	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
425	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
426	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
427	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
428	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
429	#67	—	2	2	no	—
430	#67	—	2	2	no	—
431	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
432	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
433	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
434	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
435	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
436	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
437	D₁₂	—	2	2	no	—
438	C₄×D₃	—	2	2	no	—
439	C₄×D₃	—	2	2	no	—
440	C₄×D₃	—	2	1	no	—
441	C₄×D₃	—	2	1	no	—
442	C₄×D₃	—	4	1	no	—
443	C₄×D₃	—	4	1	no	—
444	C₄×D₃	#235	1	2	yes	—
445	C₄×D₃	#235	1	2	yes	—
446	Dic₆	—	2	2	no	—
447	C₃×C₈	—	6	2	no	—
448	C₃×C₈	—	6	2	no	—
449	C₃⋊C₈	—	2	2	no	—
450	C₃⋊C₈	—	2	2	no	—
451	C₃⋊C₈	—	6	2	no	—
452	C₃⋊C₈	—	6	2	no	—
453	C₃⋊C₈	—	6	2	no	—
454	C₃⋊C₈	—	6	2	no	—
455	C₃⋊C₈	—	12	2	no	—
456	C₃⋊C₈	—	12	2	no	—
457	C₂×C₃²	—	4	1	no	—
458	C₂×C₃²	C₂×#117	1	1	yes	characteristic
459	C₂×C₃²	C₂×#131	1	1	yes	characteristic
460	C₂×C₃²	#568	1	1	yes	characteristic
461	C₃×D₃	—	2	2	no	—
462	C₃×D₃	—	4	1	no	—
463	#41	—	6	2	no	—
464	#41	—	6	2	no	—
465	C₂×Q₈	—	3	1	no	—
466	C₂×D₄	—	3	1	no	—
467	C₂×D₄	—	3	1	no	—
468	C₂×D₄	—	3	1	no	—
469	C₂²×C₄	—	3	1	no	—
470	C₂²×C₄	—	3	1	no	—
471	C₂²×C₄	—	3	1	no	—
472	C₂²×C₄	—	3	1	no	—
473	C₂²×C₄	—	3	1	no	—
474	C₂²×C₄	—	3	1	no	—
475	C₂²×C₄	D₃×Dic₃	1	1	yes	characteristic
476	C₂²×C₄	D₃×Dic₃	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
478	M₁₆	—	18	4	no	—
479	C₂×C₈	—	3	2	no	—
480	C₂×C₈	—	3	2	no	—
481	C₂×C₈	—	9	2	no	—
482	C₂×C₈	—	9	2	no	—
483	C₂×C₈	—	18	4	no	—
484	C₄⋊C₄	—	3	1	no	—
485	C₄⋊C₄	—	3	1	no	—
486	C₄⋊C₄	—	3	1	no	—
487	C₄⋊C₄	—	3	1	no	—
488	C₄⋊C₄	—	3	1	no	—
489	C₄⋊C₄	—	3	1	no	—
490	C₂²⋊C₄	—	3	1	no	—
491	C₂²⋊C₄	—	3	1	no	—
492	C₂²⋊C₄	—	3	1	no	—
493	C₂²⋊C₄	—	3	1	no	—
494	C₂²⋊C₄	—	3	1	no	—
495	C₂²⋊C₄	—	3	1	no	—
496	C₄²	—	3	1	no	—
497	C₄²	—	3	1	no	—
498	C₄²	—	3	1	no	—
499	C₄²	—	3	1	no	—
500	C₄²	—	3	1	no	—
501	C₄²	—	3	1	no	—
502	C₄²	D₃×Dic₃	1	1	yes	characteristic
503	C₄²	D₃×Dic₃	1	1	yes	characteristic
504	C₄²	C₂×D₃²	1	1	yes	characteristic
505	C₄²	C₂×D₃²	1	1	yes	characteristic
506	C₂²×C₃	—	2	2	no	—
507	C₂²×C₃	—	2	1	no	—
508	C₂²×C₃	—	2	1	no	—
509	C₂²×C₃	—	2	1	no	—
510	C₂²×C₃	—	2	1	no	—
511	C₂²×C₃	—	2	1	no	—
512	C₂²×C₃	—	2	1	no	—
513	C₂²×C₃	—	2	1	no	—
514	C₂²×C₃	—	3	2	no	—
515	C₂²×C₃	—	4	1	no	—
516	C₂²×C₃	—	4	1	no	—
517	C₂²×C₃	—	6	1	no	—
518	C₂²×C₃	—	6	1	no	—
519	C₂²×C₃	—	6	1	no	—
520	C₂²×C₃	—	6	1	no	—
521	C₂²×C₃	—	6	1	no	—
522	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
523	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
524	C₂×D₃	—	2	1	no	—
525	C₂×D₃	—	2	1	no	—
526	C₂×D₃	—	2	1	no	—
527	C₂×D₃	—	2	1	no	—
528	C₂×D₃	—	2	1	no	—
529	C₂×D₃	#926	1	2	yes	—
530	C₃×C₄	—	2	1	no	—
531	C₃×C₄	—	2	1	no	—
532	C₃×C₄	—	2	1	no	—
533	C₃×C₄	—	2	1	no	—
534	C₃×C₄	—	2	1	no	—
535	C₃×C₄	—	2	1	no	—
536	C₃×C₄	—	2	1	no	—
537	C₃×C₄	—	2	1	no	—
538	C₃×C₄	—	2	1	no	—
539	C₃×C₄	—	2	1	no	—
540	C₃×C₄	—	2	2	no	—
541	C₃×C₄	—	3	2	no	—
542	C₃×C₄	—	4	1	no	—
543	C₃×C₄	—	4	1	no	—
544	C₃×C₄	—	4	1	no	—
545	C₃×C₄	—	4	1	no	—
546	C₃×C₄	—	6	1	no	—
547	C₃×C₄	—	6	1	no	—
548	C₃×C₄	—	6	1	no	—
549	C₃×C₄	—	6	1	no	—
550	C₃×C₄	—	6	1	no	—
551	C₃×C₄	#901	1	2	yes	—
552	C₃×C₄	#948	1	2	yes	—
553	C₃×C₄	C₂×#235	1	1	yes	characteristic
554	C₃×C₄	C₂×#235	1	1	yes	characteristic
555	C₃×C₄	D₃×#41	1	1	yes	characteristic
556	C₃×C₄	D₃×#41	1	1	yes	characteristic
557	Dic₃	—	2	1	no	—
558	Dic₃	—	2	1	no	—
559	Dic₃	—	2	1	no	—
560	Dic₃	—	2	1	no	—
561	Dic₃	—	2	1	no	—
562	Dic₃	#926	1	2	yes	—
563	C₃²	#2925	1	1	yes	characteristic, complemented, Sylow
564	C₂³	—	3	1	no	—
565	C₂³	—	3	1	no	—
566	C₂³	C₂×D₃×Dic₃	1	1	yes	characteristic
567	Q₈	—	6	2	no	—
568	D₄	—	6	2	no	—
569	D₄	—	6	2	no	—
570	D₄	—	6	2	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	3	1	no	—
575	C₂×C₄	—	3	2	no	—
576	C₂×C₄	—	3	2	no	—
577	C₂×C₄	—	3	1	no	—
578	C₂×C₄	—	3	1	no	—
579	C₂×C₄	—	3	1	no	—
580	C₂×C₄	—	3	1	no	—
581	C₂×C₄	—	3	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	6	1	no	—
584	C₂×C₄	—	6	1	no	—
585	C₂×C₄	—	6	2	no	—
586	C₂×C₄	—	6	2	no	—
587	C₂×C₄	—	12	1	no	—
588	C₂×C₄	—	12	1	no	—
589	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
590	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
591	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
592	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
593	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
594	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
595	C₈	—	6	2	no	—
596	C₈	—	6	2	no	—
597	C₈	—	18	2	no	—
598	C₈	—	18	2	no	—
599	C₂×C₃	—	2	1	no	—
600	C₂×C₃	—	2	1	no	—
601	C₂×C₃	—	2	1	no	—
602	C₂×C₃	—	4	2	no	—
603	C₂×C₃	—	4	1	no	—
604	C₂×C₃	—	4	1	no	—
605	C₂×C₃	—	6	2	no	—
606	C₂×C₃	—	12	1	no	—
607	C₂×C₃	D₃×#117	1	1	yes	characteristic
608	C₂×C₃	C₂×#901	1	1	yes	characteristic
609	C₂×C₃	#5745	1	1	yes	characteristic
610	C₂×C₃	C₂×#926	1	1	yes	characteristic
611	C₂×C₃	C₂×#948	1	1	yes	characteristic
612	C₂×C₃	#5819	1	1	yes	characteristic
613	D₃	—	2	2	no	—
614	D₃	—	4	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	3	2	no	—
619	C₂²	—	6	1	no	—
620	C₂²	—	6	1	no	—
621	C₂²	—	6	1	no	—
622	C₂²	—	6	1	no	—
623	C₂²	—	6	1	no	—
624	C₂²	C₂²×D₃×Dic₃	1	1	yes	characteristic
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	3	2	no	—
630	C₄	—	6	1	no	—
631	C₄	—	6	1	no	—
632	C₄	—	6	1	no	—
633	C₄	—	6	1	no	—
634	C₄	—	6	1	no	—
635	C₄	#63814	1	2	yes	—
636	C₄	D₃×#235	1	1	yes	characteristic
637	C₄	D₃×#235	1	1	yes	characteristic
638	C₃	—	2	1	no	—
639	C₃	#79285	1	1	yes	characteristic, complemented
640	C₃	#82515	1	1	yes	characteristic, complemented
641	C₂	—	4	1	no	—
642	C₂	—	6	2	no	—
643	C₂	—	12	1	no	—
644	C₂	C₂×#63814	1	1	yes	characteristic
645	C₂	#10594776	1	1	yes	characteristic
646	C₂	D₃×#926	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃²
commutator, socle	C₂²×C₃²	C₂³×C₄
Fitting	C₂×C₃²×C₄²	C₂²
prime radical	C₂×C₃×#235	C₂²
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	C₂×C₄²	D₃²
hypocenter	C₃²	#2925
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #10592625	C₂	semidirect
3. C₃×#4925	C₂	semidirect
5. #10591056	C₂	semidirect
6. #10590336	C₂	semidirect
7. D₃×C₄⋊(C₃⋊C₈)	C₂	semidirect
8. #10590318	C₂	semidirect
9. #10590264	C₂	semidirect
10. #10590263	C₂	semidirect
11. #10590248	C₂	semidirect
57. #4925	D₃	semidirect
563. C₃²	#2925	semidirect
639. C₃	#79285	semidirect
640. C₃	#82515	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×#235	2
#10592625	2
C₃×#4925	2
#10591145	2
#10591056	2
#10590336	2
D₃×C₄⋊(C₃⋊C₈)	2
#10590318	2
#10590264	2
#10590263	2
#10590248	2
#82515	3
#79285	3