Subgroups — #11859115

Order 1152.

832 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5522	C₂	1	1	yes	maximal, characteristic
2	#10592699	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5000	C₂	1	1	yes	maximal, characteristic, complemented
4	#10591145	C₂	1	1	yes	maximal, characteristic
5	#10591145	C₂	1	1	yes	maximal, characteristic
6	#10591063	C₂	1	1	yes	maximal, characteristic, complemented
7	#10591053	C₂	1	1	yes	maximal, characteristic, complemented
8	#10590336	C₂	1	1	yes	maximal, characteristic, complemented
9	D₃×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	#10590319	C₂	1	1	yes	maximal, characteristic, complemented
11	#10590318	C₂	1	1	yes	maximal, characteristic, complemented
12	#10590262	C₂	1	1	yes	maximal, characteristic, complemented
13	#10590261	C₂	1	1	yes	maximal, characteristic, complemented
14	#10590253	C₂	1	1	yes	maximal, characteristic, complemented
15	#10590253	C₂	1	1	yes	maximal, characteristic, complemented
16	#82515	—	3	1	no	maximal
17	#79375	—	3	1	no	maximal
18	C₂×C₃×#235	C₂²	1	1	yes	characteristic
19	C₃²×#117	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
21	C₃×#893	C₄	1	1	yes	characteristic
22	C₃×#893	C₄	1	1	yes	characteristic
23	C₃×#887	C₄	1	1	yes	characteristic
24	C₃×#887	C₄	1	1	yes	characteristic
25	C₃×#67⋊C₄	C₄	1	1	yes	characteristic
26	C₃×#67⋊C₄	C₄	1	1	yes	characteristic
27	C₃×#67⋊C₄	C₄	1	1	yes	characteristic
28	C₃×#67⋊C₄	C₄	1	1	yes	characteristic
29	C₃×#872	C₂²	1	1	yes	characteristic
30	C₃×#872	C₂²	1	1	yes	characteristic
31	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
32	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
33	C₂×#3711	C₂²	1	1	yes	characteristic
34	C₂×#3711	C₂²	1	1	yes	characteristic
35	C₂×D₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×D₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
37	#63657	C₂²	1	1	yes	characteristic
38	#63657	C₂²	1	1	yes	characteristic
39	C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic
40	C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic
41	#63630	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	#63554	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×C₄×#41	—	3	1	no	—
62	#5522	D₃	1	1	yes	characteristic
63	C₃×#433	—	3	1	no	—
64	#5234	—	3	1	no	—
65	#5234	—	3	1	no	—
66	#5000	—	3	1	no	—
67	#5000	—	3	1	no	—
68	#5000	—	3	1	no	—
69	#5000	—	3	1	no	—
70	#5000	—	6	1	no	—
71	#5000	D₃	1	1	yes	characteristic, complemented
72	#4997	—	3	1	no	—
73	#4997	—	3	1	no	—
74	#4926	—	3	1	no	—
75	#4926	—	3	1	no	—
76	#4925	—	3	1	no	—
77	#4925	—	3	1	no	—
78	#4924	—	3	1	no	—
79	C₂×C₄⋊(C₃⋊C₈)	—	3	1	no	—
80	#4840	—	3	1	no	—
81	#4840	—	3	1	no	—
82	#4837	—	3	1	no	—
83	D₃×C₄⋊C₈	—	3	1	no	—
84	#4727	—	3	1	no	—
85	#4727	—	3	1	no	—
86	#4719	—	3	1	no	—
87	#4718	—	3	1	no	—
88	#4708	—	3	1	no	—
89	#4705	—	3	1	no	—
90	#4689	—	3	1	no	—
91	#4685	—	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	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
96	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
97	C₃×#235	—	2	2	no	—
98	C₃×#235	—	2	2	no	—
99	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
102	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
103	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
106	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
107	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₃²×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₃²×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₃²×C₄²	C₂³	1	1	yes	characteristic
112	C₃²×C₄²	C₂³	1	1	yes	characteristic
113	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
114	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
115	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
116	C₂×C₃⋊(C₃⋊C₈)	C₂³	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×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
122	C₃×Dic₃⋊C₄	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×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
126	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
127	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
128	C₃×C₄×Dic₃	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	#3711	—	2	2	no	—
139	D₃×C₃⋊C₈	—	2	2	no	—
140	D₃×C₃⋊C₈	—	2	2	no	—
141	#2925	—	9	1	no	Sylow
142	C₂×C₃×#41	—	3	1	no	—
143	C₂×#235	C₂×D₃	1	1	yes	characteristic
144	C₃×C₄×Q₈	—	3	1	no	—
145	C₃×C₄×Q₈	—	3	1	no	—
146	C₃×C₄×D₄	—	3	1	no	—
147	C₃×C₄×D₄	—	3	1	no	—
148	C₃×C₄×D₄	—	3	1	no	—
149	C₃×C₄×D₄	—	3	1	no	—
150	C₃×C₄×D₄	—	3	1	no	—
151	C₃×C₄×D₄	—	3	1	no	—
152	C₃×#117	—	2	1	no	—
153	C₃×#117	—	3	1	no	—
154	C₃×#117	—	3	1	no	—
155	C₃×#117	C₂×D₃	1	1	yes	characteristic
156	C₃×#117	C₂×D₃	1	1	yes	characteristic
157	C₂×C₃×C₄²	—	3	1	no	—
158	C₂×C₃×C₄²	—	3	1	no	—
159	C₂×C₃×C₄²	—	3	1	no	—
160	C₂×C₄×Dic₃	C₂×D₃	1	1	yes	characteristic
161	C₂×#208	—	3	1	no	—
162	C₂×#208	—	3	1	no	—
163	C₂²×C₃⋊C₈	—	3	1	no	—
164	C₂²×C₃⋊C₈	—	3	1	no	—
165	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
166	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
167	C₂×D₃×C₈	—	3	1	no	—
168	C₂×D₃×C₈	—	3	1	no	—
169	#893	Dic₃	1	1	yes	characteristic
170	#893	Dic₃	1	1	yes	characteristic
171	#887	Dic₃	1	1	yes	characteristic
172	#887	Dic₃	1	1	yes	characteristic
173	#67⋊C₄	Dic₃	1	1	yes	characteristic
174	#67⋊C₄	Dic₃	1	1	yes	characteristic
175	#67⋊C₄	Dic₃	1	1	yes	characteristic
176	#67⋊C₄	Dic₃	1	1	yes	characteristic
177	#872	C₂×D₃	1	1	yes	characteristic
178	#872	C₂×D₃	1	1	yes	characteristic
179	C₄²×D₃	C₂×D₃	1	1	yes	characteristic
180	C₄²×D₃	C₂×D₃	1	1	yes	characteristic
181	C₃×C₄⋊C₈	—	3	1	no	—
182	C₃×C₄⋊C₈	—	3	1	no	—
183	C₃×C₂²⋊C₈	—	3	1	no	—
184	C₃×C₂²⋊C₈	—	3	1	no	—
185	C₃×#97	—	3	1	no	—
186	C₃×C₄×C₈	—	3	1	no	—
187	#830	—	3	1	no	—
188	#830	—	3	1	no	—
189	#830	—	3	1	no	—
190	#830	—	3	1	no	—
191	#830	—	3	1	no	—
192	#830	—	3	1	no	—
193	#830	—	3	1	no	—
194	#830	—	3	1	no	—
195	#830	—	6	1	no	—
196	#830	—	6	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	#815	—	3	1	no	—
205	Dic₃⋊C₈	—	3	1	no	—
206	Dic₃⋊C₈	—	3	1	no	—
207	Dic₃⋊C₈	—	3	1	no	—
208	Dic₃⋊C₈	—	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)	—	3	1	no	—
216	C₄⋊(C₃⋊C₈)	—	3	1	no	—
217	C₄⋊(C₃⋊C₈)	—	3	1	no	—
218	C₄⋊(C₃⋊C₈)	—	3	1	no	—
219	C₄⋊(C₃⋊C₈)	—	6	1	no	—
220	C₄⋊(C₃⋊C₈)	—	6	1	no	—
221	C₄⋊(C₃⋊C₈)	C₂×D₃	1	1	yes	characteristic
222	C₄⋊(C₃⋊C₈)	C₂×D₃	1	1	yes	characteristic
223	#803	—	3	1	no	—
224	#803	—	3	1	no	—
225	#803	—	3	1	no	—
226	#803	—	3	1	no	—
227	#803	—	6	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	—	3	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	—	2	2	no	—
249	C₂×C₃×Dic₃	—	4	1	no	—
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	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
255	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
256	C₃×D₁₂	—	2	2	no	—
257	C₃×C₄×D₃	—	2	1	no	—
258	C₃×C₄×D₃	—	2	1	no	—
259	C₃×C₄×D₃	—	2	2	no	—
260	C₃×C₄×D₃	—	2	2	no	—
261	C₃×C₄×D₃	—	4	1	no	—
262	C₃×C₄×D₃	—	4	1	no	—
263	C₃×C₄×D₃	#41	1	2	yes	—
264	C₃×C₄×D₃	#41	1	2	yes	—
265	C₃×Dic₆	—	2	2	no	—
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	C₃×C₃⋊C₈	—	2	1	no	—
271	C₃×C₃⋊C₈	—	2	1	no	—
272	C₃×C₃⋊C₈	—	2	1	no	—
273	C₃×C₃⋊C₈	—	2	1	no	—
274	C₄×#41	—	3	1	no	—
275	#433	—	3	1	no	—
276	#433	—	9	1	no	—
277	#433	—	9	1	no	—
278	#433	—	9	1	no	—
279	#432	—	9	1	no	—
280	#432	—	9	1	no	—
281	#431	—	9	1	no	—
282	#431	—	9	1	no	—
283	#423	—	9	1	no	—
284	C₂×C₄⋊C₈	—	9	1	no	—
285	#408	—	9	1	no	—
286	#408	—	9	1	no	—
287	#405	—	9	1	no	—
288	#405	—	9	1	no	—
289	C₃×#41	—	6	2	no	—
290	C₃×#41	—	6	2	no	—
291	C₂×C₃×Q₈	—	3	1	no	—
292	C₂×C₃×D₄	—	3	1	no	—
293	C₂×C₃×D₄	—	3	1	no	—
294	C₂×C₃×D₄	—	3	1	no	—
295	C₂²×C₃×C₄	—	2	1	no	—
296	C₂²×C₃×C₄	—	3	1	no	—
297	C₂²×C₃×C₄	—	3	1	no	—
298	C₂²×C₃×C₄	—	3	1	no	—
299	C₂²×C₃×C₄	—	3	1	no	—
300	C₂²×C₃×C₄	—	3	1	no	—
301	C₂²×C₃×C₄	—	3	1	no	—
302	C₂²×C₃×C₄	—	3	1	no	—
303	C₂²×C₃×C₄	—	3	1	no	—
304	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
305	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
306	C₂×#67	C₂×Dic₃	1	1	yes	characteristic
307	C₂×#67	C₂×Dic₃	1	1	yes	characteristic
308	C₂²×Dic₃	C₂×Dic₃	1	1	yes	characteristic
309	C₂²×Dic₃	C₂×Dic₃	1	1	yes	characteristic
310	#235	—	2	2	no	—
311	#235	—	2	2	no	—
312	C₂×D₁₂	C₂×Dic₃	1	1	yes	characteristic
313	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
314	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
315	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
316	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
317	C₂×C₄×D₃	C₂²×D₃	1	1	yes	characteristic
318	C₂×C₄×D₃	C₂²×D₃	1	1	yes	characteristic
319	C₂×Dic₆	C₂×Dic₃	1	1	yes	characteristic
320	C₂×C₃×C₈	—	3	1	no	—
321	C₂×C₃×C₈	—	3	1	no	—
322	C₂×C₃×C₈	—	3	1	no	—
323	C₂×C₃×C₈	—	3	1	no	—
324	C₃×C₄⋊C₄	—	2	1	no	—
325	C₃×C₄⋊C₄	—	2	1	no	—
326	C₃×C₄⋊C₄	—	3	1	no	—
327	C₃×C₄⋊C₄	—	3	1	no	—
328	C₃×C₄⋊C₄	—	3	1	no	—
329	C₃×C₄⋊C₄	—	3	1	no	—
330	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
331	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
332	C₃×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
333	C₃×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
334	C₃×C₂²⋊C₄	—	2	1	no	—
335	C₃×C₂²⋊C₄	—	2	1	no	—
336	C₃×C₂²⋊C₄	—	3	1	no	—
337	C₃×C₂²⋊C₄	—	3	1	no	—
338	C₃×C₂²⋊C₄	—	3	1	no	—
339	C₃×C₂²⋊C₄	—	3	1	no	—
340	C₃×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
341	C₃×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
342	C₃×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
343	C₃×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
344	C₃×C₄²	—	2	1	no	—
345	C₃×C₄²	—	2	1	no	—
346	C₃×C₄²	—	3	1	no	—
347	C₃×C₄²	—	3	1	no	—
348	C₃×C₄²	—	3	1	no	—
349	C₃×C₄²	—	3	1	no	—
350	C₃×C₄²	—	3	1	no	—
351	C₃×C₄²	—	3	1	no	—
352	C₃×C₄²	—	3	1	no	—
353	C₃×C₄²	—	3	1	no	—
354	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
355	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
356	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
357	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
358	(C₂×D₃)⋊C₄	C₂×Dic₃	1	1	yes	characteristic
359	(C₂×D₃)⋊C₄	C₂×Dic₃	1	1	yes	characteristic
360	(C₂×D₃)⋊C₄	C₂×Dic₃	1	1	yes	characteristic
361	(C₂×D₃)⋊C₄	C₂×Dic₃	1	1	yes	characteristic
362	Dic₃⋊C₄	C₂×Dic₃	1	1	yes	characteristic
363	Dic₃⋊C₄	C₂×Dic₃	1	1	yes	characteristic
364	Dic₃⋊C₄	C₂×Dic₃	1	1	yes	characteristic
365	Dic₃⋊C₄	C₂×Dic₃	1	1	yes	characteristic
366	C₄×Dic₃	C₂×Dic₃	1	1	yes	characteristic
367	C₄×Dic₃	C₂×Dic₃	1	1	yes	characteristic
368	C₄×Dic₃	C₂×Dic₃	1	1	yes	characteristic
369	C₄×Dic₃	C₂×Dic₃	1	1	yes	characteristic
370	C₄×Dic₃	C₂×Dic₃	1	1	yes	characteristic
371	C₄×Dic₃	C₂×Dic₃	1	1	yes	characteristic
372	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
373	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
374	#208	—	6	2	no	—
375	#208	—	6	2	no	—
376	C₂×C₃⋊C₈	—	3	1	no	—
377	C₂×C₃⋊C₈	—	3	1	no	—
378	C₂×C₃⋊C₈	—	3	1	no	—
379	C₂×C₃⋊C₈	—	3	1	no	—
380	C₂×C₃⋊C₈	—	3	1	no	—
381	C₂×C₃⋊C₈	—	3	1	no	—
382	C₂×C₃⋊C₈	—	3	1	no	—
383	C₂×C₃⋊C₈	—	3	1	no	—
384	C₂×C₃⋊C₈	—	6	1	no	—
385	C₂×C₃⋊C₈	—	6	1	no	—
386	C₂×C₃⋊C₈	—	6	1	no	—
387	C₂×C₃⋊C₈	—	6	1	no	—
388	C₂×C₃⋊C₈	—	6	2	no	—
389	C₂×C₃⋊C₈	—	6	2	no	—
390	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
391	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
392	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
393	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
394	ΓL(1,𝔽₂₅)	—	6	2	no	—
395	ΓL(1,𝔽₂₅)	—	6	2	no	—
396	D₃×C₈	—	6	2	no	—
397	D₃×C₈	—	6	2	no	—
398	C₂²×C₃²	—	2	1	no	—
399	C₂²×C₃²	—	2	1	no	—
400	C₂²×C₃²	—	2	1	no	—
401	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
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	—	2	1	no	—
406	C₂×C₃×D₃	—	2	1	no	—
407	C₂×C₃×D₃	#117	1	2	yes	—
408	C₃²×C₄	—	2	1	no	—
409	C₃²×C₄	—	2	1	no	—
410	C₃²×C₄	—	2	1	no	—
411	C₃²×C₄	—	2	1	no	—
412	C₃²×C₄	—	2	1	no	—
413	C₃²×C₄	C₂×#41	1	1	yes	characteristic
414	C₃²×C₄	C₂×#41	1	1	yes	characteristic
415	C₃×Dic₃	—	2	1	no	—
416	C₃×Dic₃	—	2	1	no	—
417	C₃×Dic₃	—	2	1	no	—
418	C₃×Dic₃	—	2	1	no	—
419	C₃×Dic₃	#117	1	2	yes	—
420	C₃×Dic₃	#131	1	2	yes	—
421	C₂×#41	—	3	1	no	—
422	C₂×M₁₆	—	9	1	no	—
423	C₂×M₁₆	—	9	1	no	—
424	C₂²×C₈	—	9	1	no	—
425	C₂²×C₈	—	9	1	no	—
426	C₄×Q₈	—	3	1	no	—
427	C₄×Q₈	—	3	1	no	—
428	C₄×D₄	—	3	1	no	—
429	C₄×D₄	—	3	1	no	—
430	C₄×D₄	—	3	1	no	—
431	C₄×D₄	—	3	1	no	—
432	C₄×D₄	—	3	1	no	—
433	C₄×D₄	—	3	1	no	—
434	#117	—	3	1	no	—
435	#117	—	3	1	no	—
436	#117	D₃²	1	1	yes	characteristic
437	C₂×C₄²	—	3	1	no	—
438	C₂×C₄²	—	3	1	no	—
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	C₄⋊C₈	—	9	1	no	—
447	C₄⋊C₈	—	9	1	no	—
448	C₂²⋊C₈	—	3	1	no	—
449	C₂²⋊C₈	—	3	1	no	—
450	C₂²⋊C₈	—	9	1	no	—
451	C₂²⋊C₈	—	9	1	no	—
452	C₂²⋊C₈	—	9	1	no	—
453	C₂²⋊C₈	—	9	1	no	—
454	C₂²⋊C₈	—	9	1	no	—
455	C₂²⋊C₈	—	9	1	no	—
456	#97	—	3	1	no	—
457	#97	—	9	1	no	—
458	#97	—	9	1	no	—
459	#97	—	9	1	no	—
460	C₄×C₈	—	3	1	no	—
461	C₄×C₈	—	9	1	no	—
462	C₄×C₈	—	9	1	no	—
463	C₄×C₈	—	9	1	no	—
464	C₂³×C₃	—	2	1	no	—
465	C₂³×C₃	—	3	1	no	—
466	C₂³×C₃	—	3	1	no	—
467	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
468	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
469	C₂²×D₃	C₂²×Dic₃	1	1	yes	characteristic
470	C₂²×D₃	C₂²×Dic₃	1	1	yes	characteristic
471	C₃×Q₈	—	6	2	no	—
472	C₃×D₄	—	6	2	no	—
473	C₃×D₄	—	6	2	no	—
474	C₃×D₄	—	6	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	2	no	—
488	C₂×C₃×C₄	—	3	2	no	—
489	C₂×C₃×C₄	—	3	1	no	—
490	C₂×C₃×C₄	—	3	1	no	—
491	C₂×C₃×C₄	—	3	1	no	—
492	C₂×C₃×C₄	—	3	1	no	—
493	C₂×C₃×C₄	—	4	1	no	—
494	C₂×C₃×C₄	—	4	1	no	—
495	C₂×C₃×C₄	—	6	2	no	—
496	C₂×C₃×C₄	—	6	2	no	—
497	C₂×C₃×C₄	—	6	2	no	—
498	C₂×C₃×C₄	—	6	1	no	—
499	C₂×C₃×C₄	—	6	1	no	—
500	C₂×C₃×C₄	—	12	1	no	—
501	C₂×C₃×C₄	—	12	1	no	—
502	C₂×C₃×C₄	—	12	1	no	—
503	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
504	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
505	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
506	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
507	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
508	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
509	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
510	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
511	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
512	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
513	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
514	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
515	#67	—	2	2	no	—
516	#67	—	2	2	no	—
517	C₂×Dic₃	—	2	2	no	—
518	C₂×Dic₃	—	4	1	no	—
519	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
520	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
521	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
522	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
523	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
524	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
525	D₁₂	—	2	2	no	—
526	C₄×D₃	—	2	1	no	—
527	C₄×D₃	—	2	1	no	—
528	C₄×D₃	—	2	2	no	—
529	C₄×D₃	—	2	2	no	—
530	C₄×D₃	—	4	1	no	—
531	C₄×D₃	—	4	1	no	—
532	C₄×D₃	#235	1	2	yes	—
533	C₄×D₃	#235	1	2	yes	—
534	Dic₆	—	2	2	no	—
535	C₃×C₈	—	6	1	no	—
536	C₃×C₈	—	6	1	no	—
537	C₃×C₈	—	6	1	no	—
538	C₃×C₈	—	6	1	no	—
539	C₃⋊C₈	—	2	1	no	—
540	C₃⋊C₈	—	2	1	no	—
541	C₃⋊C₈	—	2	1	no	—
542	C₃⋊C₈	—	2	1	no	—
543	C₃⋊C₈	—	6	1	no	—
544	C₃⋊C₈	—	6	1	no	—
545	C₃⋊C₈	—	6	1	no	—
546	C₃⋊C₈	—	6	1	no	—
547	C₃⋊C₈	—	6	1	no	—
548	C₃⋊C₈	—	6	1	no	—
549	C₃⋊C₈	—	6	1	no	—
550	C₃⋊C₈	—	6	1	no	—
551	C₃⋊C₈	—	12	1	no	—
552	C₃⋊C₈	—	12	1	no	—
553	C₃⋊C₈	—	12	1	no	—
554	C₃⋊C₈	—	12	1	no	—
555	C₂×C₃²	—	4	1	no	—
556	C₂×C₃²	C₂×#117	1	1	yes	characteristic
557	C₂×C₃²	C₂×#131	1	1	yes	characteristic
558	C₂×C₃²	#568	1	1	yes	characteristic
559	C₃×D₃	—	2	2	no	—
560	C₃×D₃	—	4	1	no	—
561	#41	—	6	2	no	—
562	#41	—	6	2	no	—
563	C₂×Q₈	—	3	1	no	—
564	C₂×D₄	—	3	1	no	—
565	C₂×D₄	—	3	1	no	—
566	C₂×D₄	—	3	1	no	—
567	C₂²×C₄	—	3	1	no	—
568	C₂²×C₄	—	3	1	no	—
569	C₂²×C₄	—	3	1	no	—
570	C₂²×C₄	—	3	1	no	—
571	C₂²×C₄	—	3	1	no	—
572	C₂²×C₄	—	3	1	no	—
573	C₂²×C₄	—	3	1	no	—
574	C₂²×C₄	—	3	1	no	—
575	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
576	M₁₆	—	18	2	no	—
577	M₁₆	—	18	2	no	—
578	C₂×C₈	—	3	1	no	—
579	C₂×C₈	—	3	1	no	—
580	C₂×C₈	—	3	1	no	—
581	C₂×C₈	—	3	1	no	—
582	C₂×C₈	—	9	1	no	—
583	C₂×C₈	—	9	1	no	—
584	C₂×C₈	—	9	1	no	—
585	C₂×C₈	—	9	1	no	—
586	C₂×C₈	—	18	2	no	—
587	C₂×C₈	—	18	2	no	—
588	C₄⋊C₄	—	3	1	no	—
589	C₄⋊C₄	—	3	1	no	—
590	C₄⋊C₄	—	3	1	no	—
591	C₄⋊C₄	—	3	1	no	—
592	C₄⋊C₄	D₃×Dic₃	1	1	yes	characteristic
593	C₄⋊C₄	D₃×Dic₃	1	1	yes	characteristic
594	C₂²⋊C₄	—	3	1	no	—
595	C₂²⋊C₄	—	3	1	no	—
596	C₂²⋊C₄	—	3	1	no	—
597	C₂²⋊C₄	—	3	1	no	—
598	C₂²⋊C₄	D₃×Dic₃	1	1	yes	characteristic
599	C₂²⋊C₄	D₃×Dic₃	1	1	yes	characteristic
600	C₄²	—	3	1	no	—
601	C₄²	—	3	1	no	—
602	C₄²	—	3	1	no	—
603	C₄²	—	3	1	no	—
604	C₄²	—	3	1	no	—
605	C₄²	—	3	1	no	—
606	C₄²	—	3	1	no	—
607	C₄²	—	3	1	no	—
608	C₄²	C₂×D₃²	1	1	yes	characteristic
609	C₄²	C₂×D₃²	1	1	yes	characteristic
610	C₂²×C₃	—	2	1	no	—
611	C₂²×C₃	—	2	1	no	—
612	C₂²×C₃	—	2	1	no	—
613	C₂²×C₃	—	2	1	no	—
614	C₂²×C₃	—	2	1	no	—
615	C₂²×C₃	—	2	1	no	—
616	C₂²×C₃	—	2	1	no	—
617	C₂²×C₃	—	3	2	no	—
618	C₂²×C₃	—	4	1	no	—
619	C₂²×C₃	—	4	1	no	—
620	C₂²×C₃	—	4	1	no	—
621	C₂²×C₃	—	6	1	no	—
622	C₂²×C₃	—	6	1	no	—
623	C₂²×C₃	—	6	1	no	—
624	C₂²×C₃	—	6	1	no	—
625	C₂²×C₃	—	6	1	no	—
626	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
627	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
628	C₂×D₃	—	2	1	no	—
629	C₂×D₃	—	2	1	no	—
630	C₂×D₃	—	2	1	no	—
631	C₂×D₃	—	2	1	no	—
632	C₂×D₃	—	2	1	no	—
633	C₂×D₃	#926	1	2	yes	—
634	C₃×C₄	—	2	1	no	—
635	C₃×C₄	—	2	1	no	—
636	C₃×C₄	—	2	1	no	—
637	C₃×C₄	—	2	1	no	—
638	C₃×C₄	—	2	1	no	—
639	C₃×C₄	—	2	1	no	—
640	C₃×C₄	—	2	1	no	—
641	C₃×C₄	—	2	1	no	—
642	C₃×C₄	—	2	1	no	—
643	C₃×C₄	—	2	1	no	—
644	C₃×C₄	—	2	1	no	—
645	C₃×C₄	—	2	1	no	—
646	C₃×C₄	—	3	2	no	—
647	C₃×C₄	—	3	2	no	—
648	C₃×C₄	—	4	1	no	—
649	C₃×C₄	—	4	1	no	—
650	C₃×C₄	—	4	1	no	—
651	C₃×C₄	—	4	1	no	—
652	C₃×C₄	—	4	1	no	—
653	C₃×C₄	—	6	1	no	—
654	C₃×C₄	—	6	1	no	—
655	C₃×C₄	—	6	1	no	—
656	C₃×C₄	—	6	1	no	—
657	C₃×C₄	C₂×#235	1	1	yes	characteristic
658	C₃×C₄	C₂×#235	1	1	yes	characteristic
659	C₃×C₄	D₃×#41	1	1	yes	characteristic
660	C₃×C₄	D₃×#41	1	1	yes	characteristic
661	Dic₃	—	2	1	no	—
662	Dic₃	—	2	1	no	—
663	Dic₃	—	2	1	no	—
664	Dic₃	—	2	1	no	—
665	Dic₃	#926	1	2	yes	—
666	Dic₃	#948	1	2	yes	—
667	C₃²	#2925	1	1	yes	characteristic, complemented, Sylow
668	C₂³	—	3	1	no	—
669	C₂³	—	3	1	no	—
670	C₂³	C₂×D₃×Dic₃	1	1	yes	characteristic
671	Q₈	—	6	2	no	—
672	D₄	—	6	2	no	—
673	D₄	—	6	2	no	—
674	D₄	—	6	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	3	1	no	—
678	C₂×C₄	—	3	1	no	—
679	C₂×C₄	—	3	2	no	—
680	C₂×C₄	—	3	2	no	—
681	C₂×C₄	—	3	1	no	—
682	C₂×C₄	—	3	1	no	—
683	C₂×C₄	—	3	1	no	—
684	C₂×C₄	—	3	1	no	—
685	C₂×C₄	—	6	2	no	—
686	C₂×C₄	—	6	2	no	—
687	C₂×C₄	—	6	2	no	—
688	C₂×C₄	—	6	1	no	—
689	C₂×C₄	—	6	1	no	—
690	C₂×C₄	—	12	1	no	—
691	C₂×C₄	—	12	1	no	—
692	C₂×C₄	—	12	1	no	—
693	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
694	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
695	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
696	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
697	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
698	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
699	C₈	—	6	1	no	—
700	C₈	—	6	1	no	—
701	C₈	—	6	1	no	—
702	C₈	—	6	1	no	—
703	C₈	—	18	1	no	—
704	C₈	—	18	1	no	—
705	C₈	—	18	1	no	—
706	C₈	—	18	1	no	—
707	C₂×C₃	—	2	1	no	—
708	C₂×C₃	—	2	1	no	—
709	C₂×C₃	—	2	1	no	—
710	C₂×C₃	—	4	1	no	—
711	C₂×C₃	—	4	1	no	—
712	C₂×C₃	—	6	2	no	—
713	C₂×C₃	—	8	1	no	—
714	C₂×C₃	—	12	1	no	—
715	C₂×C₃	D₃×#117	1	1	yes	characteristic
716	C₂×C₃	D₃×#131	1	1	yes	characteristic
717	C₂×C₃	#5750	1	1	yes	characteristic
718	C₂×C₃	C₂×#926	1	1	yes	characteristic
719	C₂×C₃	C₂×#948	1	1	yes	characteristic
720	C₂×C₃	#5819	1	1	yes	characteristic
721	D₃	—	2	2	no	—
722	D₃	—	4	1	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	3	2	no	—
727	C₂²	—	6	1	no	—
728	C₂²	—	6	1	no	—
729	C₂²	—	6	1	no	—
730	C₂²	—	6	1	no	—
731	C₂²	—	6	1	no	—
732	C₂²	C₂²×D₃×Dic₃	1	1	yes	characteristic
733	C₄	—	2	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	3	2	no	—
739	C₄	—	3	2	no	—
740	C₄	—	6	1	no	—
741	C₄	—	6	1	no	—
742	C₄	—	6	1	no	—
743	C₄	—	6	1	no	—
744	C₄	D₃×#235	1	1	yes	characteristic
745	C₄	D₃×#235	1	1	yes	characteristic
746	C₃	—	2	1	no	—
747	C₃	#79375	1	1	yes	characteristic, complemented
748	C₃	#82515	1	1	yes	characteristic, complemented
749	C₂	—	4	1	no	—
750	C₂	—	6	2	no	—
751	C₂	—	12	1	no	—
752	C₂	D₃×#926	1	1	yes	characteristic
753	C₂	D₃×#948	1	1	yes	characteristic
754	C₂	#10595441	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	C₂×C₃×#235	C₂²
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	#117	D₃²
hypocenter	C₃²	#2925
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. #10592699	C₂	semidirect
3. C₃×#5000	C₂	semidirect
6. #10591063	C₂	semidirect
7. #10591053	C₂	semidirect
8. #10590336	C₂	semidirect
9. D₃×C₄⋊(C₃⋊C₈)	C₂	semidirect
10. #10590319	C₂	semidirect
11. #10590318	C₂	semidirect
12. #10590262	C₂	semidirect
13. #10590261	C₂	semidirect
14. #10590253	C₂	semidirect
15. #10590253	C₂	semidirect
71. #5000	D₃	semidirect
667. C₃²	#2925	semidirect
747. C₃	#79375	semidirect
748. 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×#5522	2
#10592699	2
C₃×#5000	2
#10591145	2
#10591063	2
#10591053	2
#10590336	2
D₃×C₄⋊(C₃⋊C₈)	2
#10590319	2
#10590318	2
#10590262	2
#10590261	2
#10590253	2
#82515	3
#79375	3