Subgroups — C₃×#86248 #11910349

Order 1152.

2271 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5832	C₂	1	2	yes	maximal, complemented
3	C₃×#5828	C₂	1	2	yes	maximal, complemented
4	C₃×#5735	C₂	1	2	yes	maximal, complemented
5	C₃×#5720	C₂	1	2	yes	maximal, complemented
6	C₃×#5684	C₂	1	2	yes	maximal, complemented
7	C₃×#5683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5672	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5621	C₂	1	4	yes	maximal, complemented
10	C₃×#5620	C₂	1	4	yes	maximal, complemented
11	C₃×#5547	C₂	1	4	yes	maximal, complemented
12	C₃×#5538	C₂	1	4	yes	maximal, complemented
13	C₃×#5479	C₂	1	2	yes	maximal, complemented
14	C₃×#3529	—	3	1	no	maximal
15	#86248	C₃	1	1	yes	maximal, characteristic, direct product factor
16	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
17	C₂×C₃²×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×#235	C₂²	1	2	yes	—
19	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
20	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₃²×#127	C₂²	1	1	yes	characteristic
22	C₃²×#124	C₂²	1	1	yes	characteristic
23	C₃²×#124	C₂²	1	1	yes	characteristic, complemented
24	C₃²×#121	C₂²	1	4	yes	complemented
25	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
26	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
27	C₃×#947	C₂²	1	2	yes	—
28	C₃×#946	C₂²	1	4	yes	complemented
29	C₃×#944	C₂²	1	2	yes	complemented
30	C₃×#940	C₂²	1	2	yes	—
31	C₃×#939	C₂²	1	4	yes	—
32	C₃×#939	C₂²	1	4	yes	—
33	C₃×#939	C₂²	1	4	yes	complemented
34	C₃×#939	C₂²	1	4	yes	complemented
35	C₃×#938	C₂²	1	4	yes	—
36	C₃×#937	C₂²	1	2	yes	—
37	C₃×#937	C₂²	1	4	yes	complemented
38	C₃×#937	C₂²	1	2	yes	complemented
39	C₃×#936	C₂²	1	2	yes	complemented
40	C₃×#935	C₂²	1	2	yes	—
41	C₃×#935	C₂²	1	4	yes	complemented
42	C₃×#935	C₂²	1	2	yes	complemented
43	C₃×#930	C₂²	1	2	yes	—
44	C₃×#929	C₂²	1	4	yes	complemented
45	C₃×C₄×#67	C₂²	1	4	yes	—
46	C₃×C₄×#67	C₂²	1	4	yes	complemented
47	C₃×C₄×#67	C₂²	1	4	yes	complemented
48	C₃×#926	C₂²	1	2	yes	complemented
49	C₃×#924	C₂²	1	2	yes	complemented
50	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	complemented
51	C₃×#898	C₂²	1	4	yes	complemented
52	C₃×#896	C₂²	1	4	yes	complemented
53	C₃×#894	C₂²	1	4	yes	—
54	C₃×#889	C₂²	1	4	yes	complemented
55	C₃×#886	C₂²	1	4	yes	complemented
56	C₃×#885	C₂²	1	4	yes	—
57	C₃×#884	C₂²	1	4	yes	—
58	C₃×#883	C₂²	1	4	yes	complemented
59	C₃×#882	C₂²	1	4	yes	—
60	C₃×#879	C₂²	1	4	yes	complemented
61	C₃×#878	C₂²	1	4	yes	complemented
62	C₃×#878	C₂²	1	4	yes	complemented
63	C₃×#876	C₂²	1	4	yes	complemented
64	C₃×#875	C₂²	1	2	yes	—
65	C₃×C₄×D₁₂	C₂²	1	2	yes	—
66	C₃×#872	C₂²	1	4	yes	complemented
67	C₃×#870	C₂²	1	2	yes	complemented
68	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
69	C₃×#563	—	3	2	no	—
70	C₃×#563	—	3	1	no	—
71	C₃×#562	—	3	2	no	—
72	C₃×#562	—	3	4	no	—
73	C₃×H(3,𝔽₄)	—	3	1	no	—
74	C₃×#560	—	3	2	no	—
75	C₃×#560	—	3	4	no	—
76	C₃×#532	—	2	1	no	—
77	C₃×#532	—	3	2	no	—
78	C₃×#532	D₃	1	1	yes	characteristic, complemented
79	C₃×#532	C₂×C₃	1	1	yes	characteristic, complemented
80	C₃×#529	—	3	4	no	—
81	C₃×#529	—	3	2	no	—
82	C₃×#525	—	3	2	no	—
83	C₃×#525	—	3	4	no	—
84	#5832	C₂×C₃	1	2	yes	complemented
85	#5828	C₂×C₃	1	2	yes	complemented
86	#5735	C₂×C₃	1	2	yes	complemented
87	#5720	C₂×C₃	1	2	yes	complemented
88	#5684	C₂×C₃	1	2	yes	complemented
89	#5683	C₂×C₃	1	1	yes	characteristic, complemented
90	#5672	C₂×C₃	1	1	yes	characteristic, complemented
91	#5621	C₂×C₃	1	4	yes	complemented
92	#5620	C₂×C₃	1	4	yes	complemented
93	#5547	C₂×C₃	1	4	yes	complemented
94	#5538	C₂×C₃	1	4	yes	complemented
95	#5479	C₂×C₃	1	2	yes	complemented
96	C₂³×C₃×D₃	C₂³	1	2	yes	—
97	C₃²×#41	—	4	2	no	—
98	C₃²×#41	—	4	2	no	—
99	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
100	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
101	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
102	C₂×C₃²×D₄	C₂³	1	2	yes	—
103	C₂×C₃²×D₄	C₂³	1	4	yes	—
104	C₂×C₃²×D₄	C₂³	1	2	yes	—
105	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
106	C₂²×C₃²×C₄	C₂³	1	2	yes	—
107	C₂²×C₃²×C₄	C₂³	1	2	yes	—
108	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
109	C₂²×C₃²×C₄	C₂³	1	2	yes	—
110	C₂×C₃×#67	C₂³	1	4	yes	—
111	C₂×C₃×#67	C₂³	1	4	yes	—
112	C₂×C₃×#67	C₂³	1	4	yes	—
113	C₂×C₃×#67	C₂³	1	4	yes	—
114	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
115	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
116	C₃×#235	—	4	4	no	—
117	C₂×C₃×D₁₂	C₂³	1	2	yes	—
118	C₂×C₃×D₁₂	C₂³	1	2	yes	—
119	C₂×C₃×C₄×D₃	—	4	4	no	—
120	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
121	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
122	C₂×C₃×Dic₆	C₂³	1	2	yes	—
123	C₂×C₃×Dic₆	C₂³	1	2	yes	—
124	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
125	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₃²×C₄²	C₂³	1	2	yes	—
128	C₃²×C₄²	C₂³	1	1	yes	characteristic
129	C₃²×C₄²	C₂³	1	1	yes	characteristic
130	C₃×#217	C₂³	1	4	yes	—
131	C₃×#217	C₂³	1	4	yes	—
132	C₃×#217	C₂³	1	2	yes	—
133	C₃×#217	C₂³	1	2	yes	—
134	C₃×#217	C₂³	1	4	yes	—
135	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
136	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
137	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
138	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
139	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
140	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
141	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
142	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
143	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
144	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
145	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
146	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
147	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
148	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
149	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
150	C₃×C₄×Dic₃	C₂³	1	2	yes	—
151	C₃×C₄×Dic₃	C₂³	1	2	yes	—
152	C₃×C₄×Dic₃	C₂³	1	4	yes	—
153	#3529	—	3	1	no	Sylow
154	C₂×C₃×#41	—	2	1	no	—
155	C₂×C₃×#41	—	2	1	no	—
156	C₂×C₃×#41	—	3	2	no	—
157	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
158	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic, complemented
159	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
160	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₂³×C₃×C₄	—	3	2	no	—
162	C₂×#235	C₂²×C₃	1	2	yes	—
163	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
164	C₃×C₄⋊Q₈	—	2	1	no	—
165	C₃×C₄⋊Q₈	—	3	2	no	—
166	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
167	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₃×#127	—	2	1	no	—
169	C₃×#127	—	3	2	no	—
170	C₃×#127	C₂×D₃	1	1	yes	characteristic
171	C₃×#127	C₂²×C₃	1	1	yes	characteristic
172	C₃×#126	—	3	4	no	—
173	C₃×#126	—	3	4	no	—
174	C₃×#126	—	3	4	no	—
175	C₃×#125	—	3	4	no	—
176	C₃×#125	—	3	2	no	—
177	C₃×#124	—	2	1	no	—
178	C₃×#124	—	2	1	no	—
179	C₃×#124	—	3	2	no	—
180	C₃×#124	—	3	2	no	—
181	C₃×#124	—	3	4	no	—
182	C₃×#124	—	3	2	no	—
183	C₃×#124	C₂×D₃	1	1	yes	characteristic
184	C₃×#124	C₂×D₃	1	1	yes	characteristic, complemented
185	C₃×#124	C₂²×C₃	1	1	yes	characteristic
186	C₃×#124	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₃×#123	—	3	4	no	—
188	C₃×#123	—	3	2	no	—
189	C₃×#123	—	3	2	no	—
190	C₃×#123	—	3	4	no	—
191	C₃×#123	—	3	4	no	—
192	C₃×#123	—	3	4	no	—
193	C₃×#123	—	3	4	no	—
194	C₃×C₂²⋊Q₈	—	3	4	no	—
195	C₃×C₂²⋊Q₈	—	3	2	no	—
196	C₃×C₂²⋊Q₈	—	3	4	no	—
197	C₃×C₂²⋊Q₈	—	3	4	no	—
198	C₃×C₂²⋊Q₈	—	3	4	no	—
199	C₃×#121	—	2	4	no	—
200	C₃×#121	—	3	4	no	—
201	C₃×#121	—	3	4	no	—
202	C₃×#121	—	3	4	no	—
203	C₃×#121	—	3	4	no	—
204	C₃×#121	—	3	4	no	—
205	C₃×#121	—	3	2	no	—
206	C₃×#121	—	3	4	no	—
207	C₃×#121	C₂×D₃	1	4	yes	complemented
208	C₃×#121	C₂²×C₃	1	4	yes	complemented
209	C₃×#120	—	3	2	no	—
210	C₃×#120	—	3	4	no	—
211	C₃×#120	—	3	2	no	—
212	C₃×#120	—	3	4	no	—
213	C₃×C₄×Q₈	—	3	2	no	—
214	C₃×C₄×D₄	—	2	4	no	—
215	C₃×C₄×D₄	—	3	4	no	—
216	C₃×C₄×D₄	—	3	4	no	—
217	C₃×C₄×D₄	—	3	4	no	—
218	C₃×C₄×D₄	—	3	2	no	—
219	C₃×C₄×D₄	C₂×D₃	1	4	yes	complemented
220	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
221	C₃×#117	—	3	2	no	—
222	C₃×#117	—	3	4	no	—
223	C₂×C₃×C₄²	—	2	1	no	—
224	C₂×C₃×C₄²	—	3	2	no	—
225	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
226	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
227	#947	C₂²×C₃	1	2	yes	—
228	#946	C₂²×C₃	1	4	yes	complemented
229	#944	C₂²×C₃	1	2	yes	complemented
230	#940	C₂²×C₃	1	2	yes	—
231	#939	C₂²×C₃	1	4	yes	—
232	#939	C₂²×C₃	1	4	yes	—
233	#939	C₂²×C₃	1	4	yes	complemented
234	#939	C₂²×C₃	1	4	yes	complemented
235	#938	C₂²×C₃	1	4	yes	—
236	#937	C₂²×C₃	1	2	yes	—
237	#937	C₂²×C₃	1	4	yes	complemented
238	#937	C₂²×C₃	1	2	yes	complemented
239	#936	C₂²×C₃	1	2	yes	complemented
240	#935	C₂²×C₃	1	2	yes	—
241	#935	C₂²×C₃	1	4	yes	complemented
242	#935	C₂²×C₃	1	2	yes	complemented
243	#930	C₂²×C₃	1	2	yes	—
244	#929	C₂²×C₃	1	4	yes	complemented
245	C₄×#67	C₂²×C₃	1	4	yes	—
246	C₄×#67	C₂²×C₃	1	4	yes	complemented
247	C₄×#67	C₂²×C₃	1	4	yes	complemented
248	#926	C₂²×C₃	1	2	yes	complemented
249	#924	C₂²×C₃	1	2	yes	complemented
250	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	complemented
251	#898	C₂²×C₃	1	4	yes	complemented
252	#896	C₂²×C₃	1	4	yes	complemented
253	#894	C₂²×C₃	1	4	yes	—
254	#889	C₂²×C₃	1	4	yes	complemented
255	#886	C₂²×C₃	1	4	yes	complemented
256	#885	C₂²×C₃	1	4	yes	—
257	#884	C₂²×C₃	1	4	yes	—
258	#883	C₂²×C₃	1	4	yes	complemented
259	#882	C₂²×C₃	1	4	yes	—
260	#879	C₂²×C₃	1	4	yes	complemented
261	#878	C₂²×C₃	1	4	yes	complemented
262	#878	C₂²×C₃	1	4	yes	complemented
263	#876	C₂²×C₃	1	4	yes	complemented
264	#875	C₂²×C₃	1	2	yes	—
265	C₄×D₁₂	C₂²×C₃	1	2	yes	—
266	#872	C₂²×C₃	1	4	yes	complemented
267	#870	C₂²×C₃	1	2	yes	complemented
268	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
269	C₂³×C₃²	C₂⁴	1	2	yes	—
270	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
271	C₂³×C₃²	C₂⁴	1	2	yes	—
272	C₂²×C₃×D₃	—	4	4	no	—
273	C₂²×C₃×D₃	—	4	2	no	—
274	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
275	C₃²×Q₈	—	4	1	no	—
276	C₃²×Q₈	—	4	1	no	—
277	C₃²×D₄	—	4	4	no	—
278	C₃²×D₄	—	4	1	no	—
279	C₃²×D₄	—	4	1	no	—
280	C₃²×D₄	—	4	2	no	—
281	C₃²×D₄	—	4	2	no	—
282	C₂×C₃²×C₄	—	2	2	no	—
283	C₂×C₃²×C₄	—	2	4	no	—
284	C₂×C₃²×C₄	—	2	4	no	—
285	C₂×C₃²×C₄	—	4	2	no	—
286	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
287	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
288	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
289	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
290	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
291	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
292	C₃×#67	—	4	4	no	—
293	C₃×#67	—	4	4	no	—
294	C₃×#67	—	4	4	no	—
295	C₃×#67	—	4	4	no	—
296	C₂×C₃×Dic₃	—	4	2	no	—
297	C₂×C₃×Dic₃	—	4	4	no	—
298	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
299	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
300	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
301	C₃×D₁₂	—	4	2	no	—
302	C₃×D₁₂	—	4	2	no	—
303	C₃×C₄×D₃	—	2	8	no	—
304	C₃×C₄×D₃	—	4	4	no	—
305	C₃×Dic₆	—	4	2	no	—
306	C₃×Dic₆	—	4	2	no	—
307	#563	—	3	2	no	—
308	#563	—	3	1	no	—
309	#562	—	3	2	no	—
310	#562	—	3	4	no	—
311	H(3,𝔽₄)	—	3	1	no	—
312	#560	—	3	2	no	—
313	#560	—	3	4	no	—
314	#532	—	3	2	no	—
315	#532	C₃×D₃	1	1	yes	characteristic, complemented
316	#529	—	3	4	no	—
317	#529	—	3	2	no	—
318	#525	—	3	2	no	—
319	#525	—	3	4	no	—
320	C₂⁴×C₃	—	3	2	no	—
321	C₂³×D₃	C₂³×C₃	1	2	yes	—
322	C₃×#41	—	4	2	no	—
323	C₃×#41	—	4	2	no	—
324	C₃×#41	—	4	2	no	—
325	C₃×#41	—	4	2	no	—
326	C₃×#41	—	4	4	no	—
327	C₃×#41	—	4	4	no	—
328	C₃×#41	—	12	4	no	—
329	C₂×C₃×Q₈	—	2	1	no	—
330	C₂×C₃×Q₈	—	2	1	no	—
331	C₂×C₃×Q₈	—	3	2	no	—
332	C₂×C₃×Q₈	—	3	2	no	—
333	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
334	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
335	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
336	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
337	C₂×C₃×D₄	—	2	4	no	—
338	C₂×C₃×D₄	—	2	2	no	—
339	C₂×C₃×D₄	—	2	2	no	—
340	C₂×C₃×D₄	—	2	1	no	—
341	C₂×C₃×D₄	—	2	1	no	—
342	C₂×C₃×D₄	—	3	4	no	—
343	C₂×C₃×D₄	—	3	4	no	—
344	C₂×C₃×D₄	—	3	4	no	—
345	C₂×C₃×D₄	—	3	4	no	—
346	C₂×C₃×D₄	—	3	2	no	—
347	C₂×C₃×D₄	—	3	2	no	—
348	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
349	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
350	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
351	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
352	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
353	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
354	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
355	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
356	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
357	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
358	C₂²×C₃×C₄	—	2	1	no	—
359	C₂²×C₃×C₄	—	2	2	no	—
360	C₂²×C₃×C₄	—	2	2	no	—
361	C₂²×C₃×C₄	—	2	2	no	—
362	C₂²×C₃×C₄	—	3	4	no	—
363	C₂²×C₃×C₄	—	3	2	no	—
364	C₂²×C₃×C₄	—	3	4	no	—
365	C₂²×C₃×C₄	—	3	4	no	—
366	C₂²×C₃×C₄	—	12	4	no	—
367	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
368	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
369	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
370	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
371	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
372	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
373	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
374	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
375	C₂×#67	C₂³×C₃	1	4	yes	—
376	C₂×#67	C₂³×C₃	1	4	yes	—
377	C₂×#67	C₂³×C₃	1	4	yes	—
378	C₂×#67	C₂³×C₃	1	4	yes	—
379	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
380	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
381	#235	—	4	4	no	—
382	C₂×D₁₂	C₂³×C₃	1	2	yes	—
383	C₂×D₁₂	C₂³×C₃	1	2	yes	—
384	C₂×C₄×D₃	—	4	4	no	—
385	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
386	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
387	C₂×Dic₆	C₂³×C₃	1	2	yes	—
388	C₂×Dic₆	C₂³×C₃	1	2	yes	—
389	C₃×C₄⋊C₄	—	2	4	no	—
390	C₃×C₄⋊C₄	—	3	4	no	—
391	C₃×C₄⋊C₄	—	3	4	no	—
392	C₃×C₄⋊C₄	—	3	4	no	—
393	C₃×C₄⋊C₄	—	3	4	no	—
394	C₃×C₄⋊C₄	—	3	4	no	—
395	C₃×C₄⋊C₄	—	3	4	no	—
396	C₃×C₄⋊C₄	—	3	4	no	—
397	C₃×C₄⋊C₄	—	3	2	no	—
398	C₃×C₄⋊C₄	—	3	2	no	—
399	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
400	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
401	C₃×C₂²⋊C₄	—	2	4	no	—
402	C₃×C₂²⋊C₄	—	2	4	no	—
403	C₃×C₂²⋊C₄	—	3	2	no	—
404	C₃×C₂²⋊C₄	—	3	2	no	—
405	C₃×C₂²⋊C₄	—	3	4	no	—
406	C₃×C₂²⋊C₄	—	3	4	no	—
407	C₃×C₂²⋊C₄	—	3	4	no	—
408	C₃×C₂²⋊C₄	—	3	4	no	—
409	C₃×C₂²⋊C₄	—	3	4	no	—
410	C₃×C₂²⋊C₄	—	3	4	no	—
411	C₃×C₂²⋊C₄	—	3	4	no	—
412	C₃×C₂²⋊C₄	—	3	4	no	—
413	C₃×C₂²⋊C₄	—	3	4	no	—
414	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
415	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
416	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
417	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
418	C₃×C₄²	—	2	2	no	—
419	C₃×C₄²	—	2	1	no	—
420	C₃×C₄²	—	2	1	no	—
421	C₃×C₄²	—	3	2	no	—
422	C₃×C₄²	—	3	2	no	—
423	C₃×C₄²	—	3	4	no	—
424	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
425	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
426	C₃×C₄²	C₂²×D₃	1	2	yes	—
427	C₃×C₄²	C₂³×C₃	1	2	yes	—
428	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
429	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
430	#217	C₂³×C₃	1	4	yes	—
431	#217	C₂³×C₃	1	4	yes	—
432	#217	C₂³×C₃	1	2	yes	—
433	#217	C₂³×C₃	1	2	yes	—
434	#217	C₂³×C₃	1	4	yes	—
435	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
436	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
437	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
438	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
439	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
440	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
441	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
442	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
443	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
444	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
445	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
446	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
447	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
448	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
449	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
450	C₄×Dic₃	C₂³×C₃	1	4	yes	—
451	C₄×Dic₃	C₂³×C₃	1	2	yes	—
452	C₄×Dic₃	C₂³×C₃	1	2	yes	—
453	C₂²×C₃²	—	2	1	no	—
454	C₂²×C₃²	—	2	2	no	—
455	C₂²×C₃²	—	2	2	no	—
456	C₂²×C₃²	—	2	4	no	—
457	C₂²×C₃²	—	2	2	no	—
458	C₂²×C₃²	—	2	4	no	—
459	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
460	C₂×C₃×D₃	—	2	4	no	—
461	C₂×C₃×D₃	—	2	4	no	—
462	C₂×C₃×D₃	—	2	4	no	—
463	C₂×C₃×D₃	—	4	8	no	—
464	C₃²×C₄	—	2	1	no	—
465	C₃²×C₄	—	2	2	no	—
466	C₃²×C₄	—	2	2	no	—
467	C₃²×C₄	—	2	2	no	—
468	C₃²×C₄	—	2	2	no	—
469	C₃²×C₄	H(5,𝔽₂)	1	2	yes	—
470	C₃×Dic₃	—	2	4	no	—
471	C₃×Dic₃	—	2	4	no	—
472	C₃×Dic₃	—	2	4	no	—
473	C₂×#41	—	3	2	no	—
474	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
475	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic, complemented
476	C₂³×C₄	—	3	2	no	—
477	C₄⋊Q₈	—	3	2	no	—
478	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
479	#127	—	3	2	no	—
480	#127	C₂×C₃×D₃	1	1	yes	characteristic
481	#126	—	3	4	no	—
482	#126	—	3	4	no	—
483	#126	—	3	4	no	—
484	#125	—	3	4	no	—
485	#125	—	3	2	no	—
486	#124	—	3	2	no	—
487	#124	—	3	2	no	—
488	#124	—	3	4	no	—
489	#124	—	3	2	no	—
490	#124	C₂×C₃×D₃	1	1	yes	characteristic
491	#124	C₂×C₃×D₃	1	1	yes	characteristic, complemented
492	#123	—	3	2	no	—
493	#123	—	3	2	no	—
494	#123	—	3	4	no	—
495	#123	—	3	4	no	—
496	#123	—	3	4	no	—
497	#123	—	3	4	no	—
498	#123	—	3	4	no	—
499	C₂²⋊Q₈	—	3	4	no	—
500	C₂²⋊Q₈	—	3	2	no	—
501	C₂²⋊Q₈	—	3	4	no	—
502	C₂²⋊Q₈	—	3	4	no	—
503	C₂²⋊Q₈	—	3	4	no	—
504	#121	—	3	4	no	—
505	#121	—	3	4	no	—
506	#121	—	3	4	no	—
507	#121	—	3	4	no	—
508	#121	—	3	4	no	—
509	#121	—	3	2	no	—
510	#121	—	3	4	no	—
511	#121	C₂×C₃×D₃	1	4	yes	complemented
512	#120	—	3	2	no	—
513	#120	—	3	4	no	—
514	#120	—	3	2	no	—
515	#120	—	3	4	no	—
516	C₄×Q₈	—	3	2	no	—
517	C₄×D₄	—	3	4	no	—
518	C₄×D₄	—	3	4	no	—
519	C₄×D₄	—	3	4	no	—
520	C₄×D₄	—	3	2	no	—
521	C₄×D₄	C₂×C₃×D₃	1	4	yes	complemented
522	#117	—	3	2	no	—
523	#117	—	3	4	no	—
524	C₂×C₄²	—	3	2	no	—
525	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
526	C₂³×C₃	—	2	1	no	—
527	C₂³×C₃	—	2	2	no	—
528	C₂³×C₃	—	2	2	no	—
529	C₂³×C₃	—	3	4	no	—
530	C₂³×C₃	—	12	2	no	—
531	C₂³×C₃	—	12	4	no	—
532	C₂³×C₃	C₂³×D₃	1	2	yes	—
533	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
534	C₂³×C₃	C₂³×D₃	1	2	yes	—
535	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
536	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
537	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
538	C₂²×D₃	—	4	2	no	—
539	C₂²×D₃	—	4	4	no	—
540	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
541	C₃×Q₈	—	4	1	no	—
542	C₃×Q₈	—	4	1	no	—
543	C₃×Q₈	—	4	1	no	—
544	C₃×Q₈	—	4	1	no	—
545	C₃×Q₈	—	4	2	no	—
546	C₃×Q₈	—	4	2	no	—
547	C₃×Q₈	—	12	2	no	—
548	C₃×Q₈	—	12	2	no	—
549	C₃×D₄	—	4	4	no	—
550	C₃×D₄	—	4	2	no	—
551	C₃×D₄	—	4	1	no	—
552	C₃×D₄	—	4	1	no	—
553	C₃×D₄	—	4	2	no	—
554	C₃×D₄	—	4	4	no	—
555	C₃×D₄	—	4	2	no	—
556	C₃×D₄	—	4	2	no	—
557	C₃×D₄	—	4	1	no	—
558	C₃×D₄	—	4	1	no	—
559	C₃×D₄	—	4	8	no	—
560	C₃×D₄	—	4	2	no	—
561	C₃×D₄	—	4	2	no	—
562	C₃×D₄	—	4	4	no	—
563	C₃×D₄	—	4	4	no	—
564	C₃×D₄	—	12	2	no	—
565	C₃×D₄	—	12	2	no	—
566	C₃×D₄	—	12	4	no	—
567	C₃×D₄	—	12	4	no	—
568	C₃×D₄	—	12	4	no	—
569	C₃×D₄	—	12	4	no	—
570	C₂×C₃×C₄	—	2	4	no	—
571	C₂×C₃×C₄	—	2	4	no	—
572	C₂×C₃×C₄	—	2	2	no	—
573	C₂×C₃×C₄	—	2	4	no	—
574	C₂×C₃×C₄	—	2	4	no	—
575	C₂×C₃×C₄	—	2	4	no	—
576	C₂×C₃×C₄	—	2	2	no	—
577	C₂×C₃×C₄	—	2	2	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	—	2	1	no	—
580	C₂×C₃×C₄	—	2	2	no	—
581	C₂×C₃×C₄	—	2	2	no	—
582	C₂×C₃×C₄	—	2	2	no	—
583	C₂×C₃×C₄	—	3	4	no	—
584	C₂×C₃×C₄	—	3	4	no	—
585	C₂×C₃×C₄	—	3	4	no	—
586	C₂×C₃×C₄	—	4	4	no	—
587	C₂×C₃×C₄	—	4	4	no	—
588	C₂×C₃×C₄	—	4	2	no	—
589	C₂×C₃×C₄	—	4	2	no	—
590	C₂×C₃×C₄	—	4	4	no	—
591	C₂×C₃×C₄	—	6	8	no	—
592	C₂×C₃×C₄	—	12	4	no	—
593	C₂×C₃×C₄	—	12	4	no	—
594	C₂×C₃×C₄	—	12	2	no	—
595	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
596	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
597	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
598	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
599	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
600	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
601	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
602	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
603	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
604	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
605	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
606	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
607	#67	—	4	4	no	—
608	#67	—	4	4	no	—
609	#67	—	4	4	no	—
610	#67	—	4	4	no	—
611	C₂×Dic₃	—	4	2	no	—
612	C₂×Dic₃	—	4	4	no	—
613	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
614	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
615	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
616	D₁₂	—	4	2	no	—
617	D₁₂	—	4	2	no	—
618	C₄×D₃	—	2	8	no	—
619	C₄×D₃	—	4	4	no	—
620	Dic₆	—	4	2	no	—
621	Dic₆	—	4	2	no	—
622	C₂×C₃²	—	4	1	no	—
623	C₂×C₃²	—	4	2	no	—
624	C₂×C₃²	—	4	2	no	—
625	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
626	C₂×C₃²	#585	1	2	yes	—
627	C₃×D₃	—	4	4	no	—
628	C₂⁴	—	3	2	no	—
629	#41	—	4	2	no	—
630	#41	—	4	2	no	—
631	#41	—	12	4	no	—
632	C₂×Q₈	—	3	2	no	—
633	C₂×Q₈	—	3	2	no	—
634	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
635	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
636	C₂×D₄	—	3	4	no	—
637	C₂×D₄	—	3	4	no	—
638	C₂×D₄	—	3	4	no	—
639	C₂×D₄	—	3	4	no	—
640	C₂×D₄	—	3	2	no	—
641	C₂×D₄	—	3	2	no	—
642	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
643	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
644	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
645	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
646	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
647	C₂²×C₄	—	3	4	no	—
648	C₂²×C₄	—	3	2	no	—
649	C₂²×C₄	—	3	4	no	—
650	C₂²×C₄	—	3	4	no	—
651	C₂²×C₄	—	12	4	no	—
652	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
653	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
654	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
655	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
656	C₄⋊C₄	—	3	4	no	—
657	C₄⋊C₄	—	3	4	no	—
658	C₄⋊C₄	—	3	4	no	—
659	C₄⋊C₄	—	3	4	no	—
660	C₄⋊C₄	—	3	4	no	—
661	C₄⋊C₄	—	3	4	no	—
662	C₄⋊C₄	—	3	2	no	—
663	C₄⋊C₄	—	3	4	no	—
664	C₄⋊C₄	—	3	2	no	—
665	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
666	C₂²⋊C₄	—	3	2	no	—
667	C₂²⋊C₄	—	3	2	no	—
668	C₂²⋊C₄	—	3	4	no	—
669	C₂²⋊C₄	—	3	4	no	—
670	C₂²⋊C₄	—	3	4	no	—
671	C₂²⋊C₄	—	3	4	no	—
672	C₂²⋊C₄	—	3	4	no	—
673	C₂²⋊C₄	—	3	4	no	—
674	C₂²⋊C₄	—	3	4	no	—
675	C₂²⋊C₄	—	3	4	no	—
676	C₂²⋊C₄	—	3	4	no	—
677	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
678	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
679	C₄²	—	3	4	no	—
680	C₄²	—	3	2	no	—
681	C₄²	—	3	2	no	—
682	C₄²	C₂²×C₃×D₃	1	2	yes	—
683	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
684	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
685	C₂²×C₃	—	2	2	no	—
686	C₂²×C₃	—	2	2	no	—
687	C₂²×C₃	—	2	1	no	—
688	C₂²×C₃	—	2	2	no	—
689	C₂²×C₃	—	2	2	no	—
690	C₂²×C₃	—	2	4	no	—
691	C₂²×C₃	—	2	4	no	—
692	C₂²×C₃	—	2	2	no	—
693	C₂²×C₃	—	2	2	no	—
694	C₂²×C₃	—	2	1	no	—
695	C₂²×C₃	—	2	4	no	—
696	C₂²×C₃	—	2	2	no	—
697	C₂²×C₃	—	2	4	no	—
698	C₂²×C₃	—	2	1	no	—
699	C₂²×C₃	—	4	2	no	—
700	C₂²×C₃	—	4	2	no	—
701	C₂²×C₃	—	4	2	no	—
702	C₂²×C₃	—	4	4	no	—
703	C₂²×C₃	—	4	4	no	—
704	C₂²×C₃	—	6	4	no	—
705	C₂²×C₃	—	6	4	no	—
706	C₂²×C₃	—	6	4	no	—
707	C₂²×C₃	—	12	8	no	—
708	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
709	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
710	C₂×D₃	—	2	4	no	—
711	C₂×D₃	—	2	4	no	—
712	C₂×D₃	—	2	4	no	—
713	C₂×D₃	—	4	8	no	—
714	C₃×C₄	—	2	2	no	—
715	C₃×C₄	—	2	4	no	—
716	C₃×C₄	—	2	2	no	—
717	C₃×C₄	—	2	1	no	—
718	C₃×C₄	—	2	2	no	—
719	C₃×C₄	—	2	2	no	—
720	C₃×C₄	—	2	2	no	—
721	C₃×C₄	—	2	2	no	—
722	C₃×C₄	—	2	2	no	—
723	C₃×C₄	—	2	1	no	—
724	C₃×C₄	—	2	2	no	—
725	C₃×C₄	—	2	2	no	—
726	C₃×C₄	—	2	2	no	—
727	C₃×C₄	—	4	2	no	—
728	C₃×C₄	—	4	2	no	—
729	C₃×C₄	—	4	2	no	—
730	C₃×C₄	—	6	4	no	—
731	C₃×C₄	—	6	4	no	—
732	C₃×C₄	—	6	4	no	—
733	C₃×C₄	#1004	1	2	yes	—
734	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
735	Dic₃	—	2	4	no	—
736	Dic₃	—	2	4	no	—
737	Dic₃	—	2	4	no	—
738	C₃²	#3529	1	1	yes	characteristic, complemented, Sylow
739	C₂³	—	3	4	no	—
740	C₂³	—	12	2	no	—
741	C₂³	—	12	4	no	—
742	C₂³	C₂³×C₃×D₃	1	2	yes	—
743	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
744	C₂³	C₂³×C₃×D₃	1	2	yes	—
745	Q₈	—	4	1	no	—
746	Q₈	—	4	1	no	—
747	Q₈	—	12	2	no	—
748	Q₈	—	12	2	no	—
749	D₄	—	4	2	no	—
750	D₄	—	4	1	no	—
751	D₄	—	4	1	no	—
752	D₄	—	4	2	no	—
753	D₄	—	4	4	no	—
754	D₄	—	12	2	no	—
755	D₄	—	12	2	no	—
756	D₄	—	12	4	no	—
757	D₄	—	12	4	no	—
758	D₄	—	12	4	no	—
759	D₄	—	12	4	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	3	4	no	—
764	C₂×C₄	—	3	4	no	—
765	C₂×C₄	—	3	4	no	—
766	C₂×C₄	—	4	2	no	—
767	C₂×C₄	—	6	8	no	—
768	C₂×C₄	—	12	4	no	—
769	C₂×C₄	—	12	2	no	—
770	C₂×C₄	—	12	4	no	—
771	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
772	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
773	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
774	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
775	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
776	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
777	C₂×C₃	—	2	1	no	—
778	C₂×C₃	—	2	2	no	—
779	C₂×C₃	—	4	2	no	—
780	C₂×C₃	—	4	2	no	—
781	C₂×C₃	—	4	1	no	—
782	C₂×C₃	—	4	2	no	—
783	C₂×C₃	—	4	2	no	—
784	C₂×C₃	—	4	1	no	—
785	C₂×C₃	—	4	2	no	—
786	C₂×C₃	—	8	2	no	—
787	C₂×C₃	—	8	2	no	—
788	C₂×C₃	—	12	4	no	—
789	C₂×C₃	C₂×#1004	1	1	yes	characteristic
790	C₂×C₃	#5964	1	2	yes	—
791	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
792	C₂×C₃	C₃×#585	1	2	yes	—
793	D₃	—	4	4	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	4	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	6	4	no	—
801	C₂²	—	6	4	no	—
802	C₂²	—	6	4	no	—
803	C₂²	—	12	8	no	—
804	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
805	C₄	—	2	2	no	—
806	C₄	—	2	1	no	—
807	C₄	—	2	2	no	—
808	C₄	—	2	2	no	—
809	C₄	—	2	2	no	—
810	C₄	—	6	4	no	—
811	C₄	—	6	4	no	—
812	C₄	—	6	4	no	—
813	C₄	C₃×#1004	1	2	yes	—
814	C₃	—	2	1	no	—
815	C₃	#86248	1	1	yes	characteristic, direct product factor
816	C₃	C₃×#3529	1	1	yes	characteristic, complemented
817	C₂	—	4	2	no	—
818	C₂	—	4	1	no	—
819	C₂	—	4	2	no	—
820	C₂	—	12	4	no	—
821	C₂	C₂×C₃×#1004	1	1	yes	characteristic
822	C₂	C₃×#5964	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#532	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#532	D₃
hypocenter	C₃	C₃×#3529
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#532

Complements

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

N	H ≅ G/N	type
1. C₃²×#532	C₂	semidirect
2. C₃×#5832	C₂	semidirect
3. C₃×#5828	C₂	semidirect
4. C₃×#5735	C₂	semidirect
5. C₃×#5720	C₂	semidirect
6. C₃×#5684	C₂	semidirect
7. C₃×#5683	C₂	semidirect
8. C₃×#5672	C₂	semidirect
9. C₃×#5621	C₂	semidirect
10. C₃×#5620	C₂	semidirect
11. C₃×#5547	C₂	semidirect
12. C₃×#5538	C₂	semidirect
13. C₃×#5479	C₂	semidirect
15. #86248	C₃	direct (N × H)
17. C₂×C₃²×#41	C₂²	semidirect
19. C₂²×C₃×C₄×D₃	C₂²	semidirect
20. C₃²×C₄⋊Q₈	C₂²	semidirect
23. C₃²×#124	C₂²	semidirect
24. C₃²×#121	C₂²	semidirect
25. C₃²×C₄×D₄	C₂²	semidirect
26. C₂×C₃²×C₄²	C₂²	semidirect
28. C₃×#946	C₂²	semidirect
29. C₃×#944	C₂²	semidirect
33. C₃×#939	C₂²	semidirect
34. C₃×#939	C₂²	semidirect
37. C₃×#937	C₂²	semidirect
38. C₃×#937	C₂²	semidirect
39. C₃×#936	C₂²	semidirect
41. C₃×#935	C₂²	semidirect
42. C₃×#935	C₂²	semidirect
44. C₃×#929	C₂²	semidirect
46. C₃×C₄×#67	C₂²	semidirect
47. C₃×C₄×#67	C₂²	semidirect
48. C₃×#926	C₂²	semidirect
49. C₃×#924	C₂²	semidirect
50. C₂×C₃×C₄×Dic₃	C₂²	semidirect
51. C₃×#898	C₂²	semidirect
52. C₃×#896	C₂²	semidirect
54. C₃×#889	C₂²	semidirect
55. C₃×#886	C₂²	semidirect
58. C₃×#883	C₂²	semidirect
60. C₃×#879	C₂²	semidirect
61. C₃×#878	C₂²	semidirect
62. C₃×#878	C₂²	semidirect
63. C₃×#876	C₂²	semidirect
66. C₃×#872	C₂²	semidirect
67. C₃×#870	C₂²	semidirect
68. C₃×C₄×Dic₆	C₂²	semidirect
78. C₃×#532	D₃	semidirect
79. C₃×#532	C₂×C₃	semidirect
84. #5832	C₂×C₃	semidirect
85. #5828	C₂×C₃	semidirect
86. #5735	C₂×C₃	semidirect
87. #5720	C₂×C₃	semidirect
88. #5684	C₂×C₃	semidirect
89. #5683	C₂×C₃	semidirect
90. #5672	C₂×C₃	semidirect
91. #5621	C₂×C₃	semidirect
92. #5620	C₂×C₃	semidirect
93. #5547	C₂×C₃	semidirect
94. #5538	C₂×C₃	semidirect
95. #5479	C₂×C₃	semidirect
158. C₂×C₃×#41	C₂×D₃	semidirect
160. C₂×C₃×#41	C₂²×C₃	semidirect
163. C₂²×C₄×D₃	C₂²×C₃	semidirect
166. C₃×C₄⋊Q₈	C₂×D₃	semidirect
167. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
184. C₃×#124	C₂×D₃	semidirect
186. C₃×#124	C₂²×C₃	semidirect
207. C₃×#121	C₂×D₃	semidirect
208. C₃×#121	C₂²×C₃	semidirect
219. C₃×C₄×D₄	C₂×D₃	semidirect
220. C₃×C₄×D₄	C₂²×C₃	semidirect
225. C₂×C₃×C₄²	C₂×D₃	semidirect
226. C₂×C₃×C₄²	C₂²×C₃	semidirect
228. #946	C₂²×C₃	semidirect
229. #944	C₂²×C₃	semidirect
233. #939	C₂²×C₃	semidirect
234. #939	C₂²×C₃	semidirect
237. #937	C₂²×C₃	semidirect
238. #937	C₂²×C₃	semidirect
239. #936	C₂²×C₃	semidirect
241. #935	C₂²×C₃	semidirect
242. #935	C₂²×C₃	semidirect
244. #929	C₂²×C₃	semidirect
246. C₄×#67	C₂²×C₃	semidirect
247. C₄×#67	C₂²×C₃	semidirect
248. #926	C₂²×C₃	semidirect
249. #924	C₂²×C₃	semidirect
250. C₂×C₄×Dic₃	C₂²×C₃	semidirect
251. #898	C₂²×C₃	semidirect
252. #896	C₂²×C₃	semidirect
254. #889	C₂²×C₃	semidirect
255. #886	C₂²×C₃	semidirect
258. #883	C₂²×C₃	semidirect
260. #879	C₂²×C₃	semidirect
261. #878	C₂²×C₃	semidirect
262. #878	C₂²×C₃	semidirect
263. #876	C₂²×C₃	semidirect
266. #872	C₂²×C₃	semidirect
267. #870	C₂²×C₃	semidirect
268. C₄×Dic₆	C₂²×C₃	semidirect
315. #532	C₃×D₃	semidirect
475. C₂×#41	C₂×C₃×D₃	semidirect
478. C₄⋊Q₈	C₂×C₃×D₃	semidirect
491. #124	C₂×C₃×D₃	semidirect
511. #121	C₂×C₃×D₃	semidirect
521. C₄×D₄	C₂×C₃×D₃	semidirect
525. C₂×C₄²	C₂×C₃×D₃	semidirect
738. C₃²	#3529	semidirect
815. C₃	#86248	direct (N × H)
816. C₃	C₃×#3529	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#532	2
C₃×#5832	2
C₃×#5828	2
C₃×#5735	2
C₃×#5720	2
C₃×#5684	2
C₃×#5683	2
C₃×#5672	2
C₃×#5621	2
C₃×#5620	2
C₃×#5547	2
C₃×#5538	2
C₃×#5479	2
C₃×#3529	3
#86248	3

Subgroups — C3×#86248 #11910349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86248 #11910349