Subgroups — C₃×#35291 #10653898

Order 768.

1650 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2857	C₂	1	1	yes	maximal, characteristic
4	C₃×#2857	C₂	1	1	yes	maximal, characteristic
5	C₃×#2645	C₂	1	2	yes	maximal, complemented
6	C₃×#2625	C₂	1	2	yes	maximal
7	C₃×#2514	C₂	1	2	yes	maximal, complemented
8	C₃×#2509	C₂	1	2	yes	maximal, complemented
9	C₃×#2508	C₂	1	2	yes	maximal, complemented
10	C₃×#2495	C₂	1	2	yes	maximal
11	C₃×#2494	C₂	1	2	yes	maximal
12	C₃×#2489	C₂	1	2	yes	maximal
13	C₃×#2453	C₂	1	2	yes	maximal, complemented
14	C₃×#2421	C₂	1	2	yes	maximal
15	C₃×#2323	C₂	1	2	yes	maximal
16	C₃×#2320	C₂	1	2	yes	maximal, complemented
17	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×C₄×#117	C₂	1	1	yes	maximal, characteristic
20	#35291	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₃×#125	C₂²	1	2	yes	—
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
27	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
28	C₂×C₃×#117	C₂²	1	1	yes	characteristic
29	C₂×C₃×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
31	C₃×#401	C₂²	1	4	yes	—
32	C₃×#400	C₂²	1	4	yes	—
33	C₃×#400	C₂²	1	4	yes	—
34	C₃×#400	C₂²	1	4	yes	—
35	C₃×#400	C₂²	1	4	yes	—
36	C₃×#398	C₂²	1	4	yes	—
37	C₃×#397	C₂²	1	4	yes	—
38	C₃×#397	C₂²	1	4	yes	—
39	C₃×#391	C₂²	1	2	yes	—
40	C₃×#391	C₂²	1	2	yes	—
41	C₃×#391	C₂²	1	2	yes	—
42	C₃×#391	C₂²	1	2	yes	—
43	C₃×#391	C₂²	1	2	yes	—
44	C₃×#391	C₂²	1	2	yes	—
45	C₃×#391	C₂²	1	2	yes	—
46	C₃×#391	C₂²	1	2	yes	—
47	C₃×#389	C₂²	1	2	yes	—
48	C₃×#389	C₂²	1	2	yes	—
49	C₃×#389	C₂²	1	2	yes	—
50	C₃×#389	C₂²	1	2	yes	—
51	C₃×#389	C₂²	1	2	yes	—
52	C₃×#389	C₂²	1	4	yes	—
53	C₃×#389	C₂²	1	2	yes	—
54	C₃×#389	C₂²	1	2	yes	—
55	C₃×#389	C₂²	1	2	yes	—
56	C₃×#389	C₂²	1	2	yes	—
57	C₃×#389	C₂²	1	2	yes	—
58	C₃×#389	C₂²	1	2	yes	—
59	C₃×#389	C₂²	1	2	yes	—
60	C₃×#388	C₂²	1	4	yes	—
61	C₃×#388	C₂²	1	4	yes	—
62	C₃×#387	C₂²	1	4	yes	—
63	C₃×#387	C₂²	1	4	yes	—
64	C₃×#387	C₂²	1	4	yes	—
65	C₃×#384	C₂²	1	1	yes	characteristic
66	C₃×#384	C₂²	1	1	yes	characteristic
67	C₃×#383	C₂²	1	4	yes	—
68	C₃×#382	C₂²	1	2	yes	—
69	C₃×#382	C₂²	1	4	yes	—
70	C₃×#382	C₂²	1	2	yes	—
71	C₃×#382	C₂²	1	2	yes	—
72	C₃×#380	C₂²	1	2	yes	—
73	C₃×#380	C₂²	1	2	yes	—
74	C₃×#380	C₂²	1	2	yes	—
75	C₃×#380	C₂²	1	2	yes	—
76	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
77	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
78	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
79	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
80	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
81	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
82	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
83	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
84	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
85	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
86	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
87	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
88	C₃×#376	C₂²	1	1	yes	characteristic
89	C₃×#376	C₂²	1	1	yes	characteristic
90	C₃×C₄³	C₂²	1	1	yes	characteristic
91	C₃×C₄³	C₂²	1	1	yes	characteristic
92	#2862	C₂×C₃	1	1	yes	characteristic, complemented
93	#2859	C₂×C₃	1	1	yes	characteristic, complemented
94	#2857	C₂×C₃	1	1	yes	characteristic
95	#2857	C₂×C₃	1	1	yes	characteristic
96	#2645	C₂×C₃	1	2	yes	complemented
97	#2625	C₂×C₃	1	2	yes	—
98	#2514	C₂×C₃	1	2	yes	complemented
99	#2509	C₂×C₃	1	2	yes	complemented
100	#2508	C₂×C₃	1	2	yes	complemented
101	#2495	C₂×C₃	1	2	yes	—
102	#2494	C₂×C₃	1	2	yes	—
103	#2489	C₂×C₃	1	2	yes	—
104	#2453	C₂×C₃	1	2	yes	complemented
105	#2421	C₂×C₃	1	2	yes	—
106	#2323	C₂×C₃	1	2	yes	—
107	#2320	C₂×C₃	1	2	yes	complemented
108	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
109	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
110	C₄×#117	C₂×C₃	1	1	yes	characteristic
111	C₂²×C₃×Q₈	C₂³	1	2	yes	—
112	C₂²×C₃×Q₈	C₂³	1	2	yes	—
113	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
114	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
115	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
116	C₃×C₄⋊Q₈	—	2	4	no	—
117	C₃×C₄⋊Q₈	—	2	4	no	—
118	C₃×#125	—	4	4	no	—
119	C₃×C₂²⋊Q₈	—	2	8	no	—
120	C₃×C₂²⋊Q₈	—	4	4	no	—
121	C₃×C₄×Q₈	—	2	8	no	—
122	C₃×C₄×Q₈	—	4	4	no	—
123	C₃×#117	—	2	4	no	—
124	C₃×#117	—	2	4	no	—
125	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
140	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
141	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
143	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
144	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
145	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₂×C₃×C₄²	—	2	4	no	—
152	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
154	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
155	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
156	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
157	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
158	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
160	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
161	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
163	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
164	C₂×C₃×C₄²	C₂³	1	4	yes	—
165	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
166	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
167	C₂×C₃×C₄²	C₂³	1	4	yes	—
168	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
169	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
170	C₃×#95	C₂³	1	1	yes	characteristic
171	C₃×#95	C₂³	1	1	yes	characteristic
172	C₃×#95	C₂³	1	1	yes	characteristic
173	C₃×#95	C₂³	1	1	yes	characteristic
174	C₃×#95	C₂³	1	1	yes	characteristic
175	C₃×#95	C₂³	1	1	yes	characteristic
176	C₃×#95	C₂³	1	1	yes	characteristic
177	C₃×#95	C₂³	1	1	yes	characteristic
178	C₃×#95	C₂³	1	4	yes	—
179	C₃×#95	C₂³	1	4	yes	—
180	C₃×#95	C₂³	1	4	yes	—
181	C₃×#95	C₂³	1	4	yes	—
182	C₃×#95	C₂³	1	4	yes	—
183	C₃×#95	C₂³	1	4	yes	—
184	C₃×#95	C₂³	1	4	yes	—
185	C₃×#95	C₂³	1	4	yes	—
186	C₃×#95	C₂³	1	4	yes	—
187	C₃×#95	C₂³	1	4	yes	—
188	C₃×#95	C₂³	1	4	yes	—
189	C₃×#95	C₂³	1	4	yes	—
190	C₃×#95	C₂³	1	4	yes	—
191	C₃×#95	C₂³	1	4	yes	—
192	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
193	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
194	C₂×#125	C₂²×C₃	1	2	yes	—
195	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
196	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
197	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
198	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
199	C₂×#117	C₂²×C₃	1	1	yes	characteristic
200	C₂×#117	C₂²×C₃	1	1	yes	characteristic
201	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
202	#401	C₂²×C₃	1	4	yes	—
203	#400	C₂²×C₃	1	4	yes	—
204	#400	C₂²×C₃	1	4	yes	—
205	#400	C₂²×C₃	1	4	yes	—
206	#400	C₂²×C₃	1	4	yes	—
207	#398	C₂²×C₃	1	4	yes	—
208	#397	C₂²×C₃	1	4	yes	—
209	#397	C₂²×C₃	1	4	yes	—
210	#391	C₂²×C₃	1	2	yes	—
211	#391	C₂²×C₃	1	2	yes	—
212	#391	C₂²×C₃	1	2	yes	—
213	#391	C₂²×C₃	1	2	yes	—
214	#391	C₂²×C₃	1	2	yes	—
215	#391	C₂²×C₃	1	2	yes	—
216	#391	C₂²×C₃	1	2	yes	—
217	#391	C₂²×C₃	1	2	yes	—
218	#389	C₂²×C₃	1	2	yes	—
219	#389	C₂²×C₃	1	2	yes	—
220	#389	C₂²×C₃	1	2	yes	—
221	#389	C₂²×C₃	1	2	yes	—
222	#389	C₂²×C₃	1	2	yes	—
223	#389	C₂²×C₃	1	2	yes	—
224	#389	C₂²×C₃	1	2	yes	—
225	#389	C₂²×C₃	1	4	yes	—
226	#389	C₂²×C₃	1	2	yes	—
227	#389	C₂²×C₃	1	2	yes	—
228	#389	C₂²×C₃	1	2	yes	—
229	#389	C₂²×C₃	1	2	yes	—
230	#389	C₂²×C₃	1	2	yes	—
231	#388	C₂²×C₃	1	4	yes	—
232	#388	C₂²×C₃	1	4	yes	—
233	#387	C₂²×C₃	1	4	yes	—
234	#387	C₂²×C₃	1	4	yes	—
235	#387	C₂²×C₃	1	4	yes	—
236	#384	C₂²×C₃	1	1	yes	characteristic
237	#384	C₂²×C₃	1	1	yes	characteristic
238	#383	C₂²×C₃	1	4	yes	—
239	#382	C₂²×C₃	1	4	yes	—
240	#382	C₂²×C₃	1	2	yes	—
241	#382	C₂²×C₃	1	2	yes	—
242	#382	C₂²×C₃	1	2	yes	—
243	#380	C₂²×C₃	1	2	yes	—
244	#380	C₂²×C₃	1	2	yes	—
245	#380	C₂²×C₃	1	2	yes	—
246	#380	C₂²×C₃	1	2	yes	—
247	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
248	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
249	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
250	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
251	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
252	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
253	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
254	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
255	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
256	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
257	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
258	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
259	#376	C₂²×C₃	1	1	yes	characteristic
260	#376	C₂²×C₃	1	1	yes	characteristic
261	C₄³	C₂²×C₃	1	1	yes	characteristic
262	C₄³	C₂²×C₃	1	1	yes	characteristic
263	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
264	C₂×C₃×Q₈	—	2	4	no	—
265	C₂×C₃×Q₈	—	2	4	no	—
266	C₂×C₃×Q₈	—	2	4	no	—
267	C₂×C₃×Q₈	—	2	4	no	—
268	C₂×C₃×Q₈	—	2	4	no	—
269	C₂×C₃×Q₈	—	2	4	no	—
270	C₂²×C₃×C₄	—	2	2	no	—
271	C₂²×C₃×C₄	—	2	2	no	—
272	C₂²×C₃×C₄	—	2	2	no	—
273	C₂²×C₃×C₄	—	2	2	no	—
274	C₂²×C₃×C₄	—	2	2	no	—
275	C₂²×C₃×C₄	—	2	2	no	—
276	C₂²×C₃×C₄	—	2	2	no	—
277	C₂²×C₃×C₄	—	2	2	no	—
278	C₂²×C₃×C₄	#41	1	4	yes	—
279	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
280	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
281	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
283	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
284	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
285	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
286	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
287	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
288	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
289	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
290	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
291	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
292	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
293	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
294	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
295	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
296	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
297	C₃×C₄⋊C₄	—	2	2	no	—
298	C₃×C₄⋊C₄	—	2	2	no	—
299	C₃×C₄⋊C₄	—	2	2	no	—
300	C₃×C₄⋊C₄	—	2	2	no	—
301	C₃×C₄⋊C₄	—	2	4	no	—
302	C₃×C₄⋊C₄	—	2	8	no	—
303	C₃×C₄⋊C₄	—	2	4	no	—
304	C₃×C₄⋊C₄	—	2	8	no	—
305	C₃×C₄⋊C₄	—	2	4	no	—
306	C₃×C₄⋊C₄	—	2	4	no	—
307	C₃×C₄⋊C₄	—	2	4	no	—
308	C₃×C₄⋊C₄	—	2	4	no	—
309	C₃×C₄⋊C₄	—	2	4	no	—
310	C₃×C₄⋊C₄	—	2	4	no	—
311	C₃×C₄⋊C₄	—	2	4	no	—
312	C₃×C₄⋊C₄	—	2	4	no	—
313	C₃×C₄⋊C₄	—	4	4	no	—
314	C₃×C₄⋊C₄	—	4	4	no	—
315	C₃×C₄⋊C₄	—	4	4	no	—
316	C₃×C₄⋊C₄	—	4	4	no	—
317	C₃×C₂²⋊C₄	—	2	2	no	—
318	C₃×C₂²⋊C₄	—	2	2	no	—
319	C₃×C₂²⋊C₄	—	2	8	no	—
320	C₃×C₂²⋊C₄	—	2	2	no	—
321	C₃×C₂²⋊C₄	—	2	2	no	—
322	C₃×C₂²⋊C₄	—	4	4	no	—
323	C₃×C₄²	—	2	2	no	—
324	C₃×C₄²	—	2	2	no	—
325	C₃×C₄²	—	2	2	no	—
326	C₃×C₄²	—	2	2	no	—
327	C₃×C₄²	—	2	2	no	—
328	C₃×C₄²	—	2	2	no	—
329	C₃×C₄²	—	2	8	no	—
330	C₃×C₄²	—	2	2	no	—
331	C₃×C₄²	—	2	2	no	—
332	C₃×C₄²	—	2	2	no	—
333	C₃×C₄²	—	2	2	no	—
334	C₃×C₄²	—	2	2	no	—
335	C₃×C₄²	—	2	2	no	—
336	C₃×C₄²	—	2	2	no	—
337	C₃×C₄²	—	2	2	no	—
338	C₃×C₄²	—	4	4	no	—
339	C₃×C₄²	#41	1	4	yes	—
340	C₃×C₄²	#41	1	4	yes	—
341	C₂²×Q₈	C₂³×C₃	1	2	yes	—
342	C₂²×Q₈	C₂³×C₃	1	2	yes	—
343	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
344	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
345	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
346	C₄⋊Q₈	—	2	4	no	—
347	C₄⋊Q₈	—	2	4	no	—
348	#125	—	4	4	no	—
349	C₂²⋊Q₈	—	2	8	no	—
350	C₂²⋊Q₈	—	4	4	no	—
351	C₄×Q₈	—	2	8	no	—
352	C₄×Q₈	—	4	4	no	—
353	#117	—	2	4	no	—
354	#117	—	2	4	no	—
355	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
365	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
372	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
373	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
378	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
379	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
381	C₂×C₄²	—	2	4	no	—
382	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
384	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₃	1	4	yes	—
387	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
396	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
397	C₂×C₄²	C₂³×C₃	1	4	yes	—
398	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
400	#95	C₂³×C₃	1	1	yes	characteristic
401	#95	C₂³×C₃	1	1	yes	characteristic
402	#95	C₂³×C₃	1	1	yes	characteristic
403	#95	C₂³×C₃	1	1	yes	characteristic
404	#95	C₂³×C₃	1	1	yes	characteristic
405	#95	C₂³×C₃	1	1	yes	characteristic
406	#95	C₂³×C₃	1	1	yes	characteristic
407	#95	C₂³×C₃	1	1	yes	characteristic
408	#95	C₂³×C₃	1	4	yes	—
409	#95	C₂³×C₃	1	4	yes	—
410	#95	C₂³×C₃	1	4	yes	—
411	#95	C₂³×C₃	1	4	yes	—
412	#95	C₂³×C₃	1	4	yes	—
413	#95	C₂³×C₃	1	4	yes	—
414	#95	C₂³×C₃	1	4	yes	—
415	#95	C₂³×C₃	1	4	yes	—
416	#95	C₂³×C₃	1	4	yes	—
417	#95	C₂³×C₃	1	4	yes	—
418	#95	C₂³×C₃	1	4	yes	—
419	#95	C₂³×C₃	1	4	yes	—
420	#95	C₂³×C₃	1	4	yes	—
421	#95	C₂³×C₃	1	4	yes	—
422	C₂³×C₃	—	2	1	no	—
423	C₂³×C₃	—	2	1	no	—
424	C₂³×C₃	—	2	1	no	—
425	C₂³×C₃	—	2	1	no	—
426	C₂³×C₃	—	2	1	no	—
427	C₂³×C₃	—	2	1	no	—
428	C₂³×C₃	C₂×#41	1	2	yes	—
429	C₂³×C₃	C₂⁵	1	1	yes	characteristic
430	C₃×Q₈	—	4	8	no	—
431	C₃×Q₈	—	4	8	no	—
432	C₂×C₃×C₄	—	2	1	no	—
433	C₂×C₃×C₄	—	2	1	no	—
434	C₂×C₃×C₄	—	2	1	no	—
435	C₂×C₃×C₄	—	2	1	no	—
436	C₂×C₃×C₄	—	2	1	no	—
437	C₂×C₃×C₄	—	2	1	no	—
438	C₂×C₃×C₄	—	2	8	no	—
439	C₂×C₃×C₄	—	2	1	no	—
440	C₂×C₃×C₄	—	2	1	no	—
441	C₂×C₃×C₄	—	2	1	no	—
442	C₂×C₃×C₄	—	2	1	no	—
443	C₂×C₃×C₄	—	2	1	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	2	1	no	—
446	C₂×C₃×C₄	—	2	1	no	—
447	C₂×C₃×C₄	—	2	4	no	—
448	C₂×C₃×C₄	—	2	4	no	—
449	C₂×C₃×C₄	—	2	4	no	—
450	C₂×C₃×C₄	—	2	4	no	—
451	C₂×C₃×C₄	—	2	4	no	—
452	C₂×C₃×C₄	—	2	4	no	—
453	C₂×C₃×C₄	—	2	1	no	—
454	C₂×C₃×C₄	—	2	1	no	—
455	C₂×C₃×C₄	—	2	1	no	—
456	C₂×C₃×C₄	—	2	4	no	—
457	C₂×C₃×C₄	—	2	4	no	—
458	C₂×C₃×C₄	—	2	4	no	—
459	C₂×C₃×C₄	—	2	1	no	—
460	C₂×C₃×C₄	—	2	1	no	—
461	C₂×C₃×C₄	—	2	1	no	—
462	C₂×C₃×C₄	—	2	1	no	—
463	C₂×C₃×C₄	—	2	1	no	—
464	C₂×C₃×C₄	—	2	1	no	—
465	C₂×C₃×C₄	—	2	1	no	—
466	C₂×C₃×C₄	—	2	1	no	—
467	C₂×C₃×C₄	—	2	1	no	—
468	C₂×C₃×C₄	—	2	1	no	—
469	C₂×C₃×C₄	—	2	4	no	—
470	C₂×C₃×C₄	—	2	4	no	—
471	C₂×C₃×C₄	—	2	1	no	—
472	C₂×C₃×C₄	—	2	1	no	—
473	C₂×C₃×C₄	—	2	1	no	—
474	C₂×C₃×C₄	—	2	4	no	—
475	C₂×C₃×C₄	—	4	4	no	—
476	C₂×C₃×C₄	—	4	4	no	—
477	C₂×C₃×C₄	C₂×#41	1	2	yes	—
478	C₂×C₃×C₄	C₂×#41	1	2	yes	—
479	C₂×C₃×C₄	C₂×#41	1	2	yes	—
480	C₂×C₃×C₄	C₂×#41	1	2	yes	—
481	C₂×C₃×C₄	C₂×#41	1	2	yes	—
482	C₂×C₃×C₄	C₂×#41	1	2	yes	—
483	C₂×C₃×C₄	C₂×#41	1	2	yes	—
484	C₂×C₃×C₄	C₂×#41	1	2	yes	—
485	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
486	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
487	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
488	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
489	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
490	C₂×Q₈	—	2	4	no	—
491	C₂×Q₈	—	2	4	no	—
492	C₂×Q₈	—	2	4	no	—
493	C₂×Q₈	—	2	4	no	—
494	C₂×Q₈	—	2	4	no	—
495	C₂×Q₈	—	2	4	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	C₃×#41	1	4	yes	—
505	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
507	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
508	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
509	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
510	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
511	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
512	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
513	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
514	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
515	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
516	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
517	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
518	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
519	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
520	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
521	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
522	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	8	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	8	no	—
531	C₄⋊C₄	—	2	4	no	—
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	4	4	no	—
540	C₄⋊C₄	—	4	4	no	—
541	C₄⋊C₄	—	4	4	no	—
542	C₄⋊C₄	—	4	4	no	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	2	8	no	—
546	C₂²⋊C₄	—	2	2	no	—
547	C₂²⋊C₄	—	2	2	no	—
548	C₂²⋊C₄	—	4	4	no	—
549	C₄²	—	2	2	no	—
550	C₄²	—	2	2	no	—
551	C₄²	—	2	2	no	—
552	C₄²	—	2	2	no	—
553	C₄²	—	2	2	no	—
554	C₄²	—	2	2	no	—
555	C₄²	—	2	8	no	—
556	C₄²	—	2	2	no	—
557	C₄²	—	2	2	no	—
558	C₄²	—	2	2	no	—
559	C₄²	—	2	2	no	—
560	C₄²	—	2	2	no	—
561	C₄²	—	2	2	no	—
562	C₄²	—	2	2	no	—
563	C₄²	—	2	2	no	—
564	C₄²	—	4	4	no	—
565	C₄²	C₃×#41	1	4	yes	—
566	C₄²	C₃×#41	1	4	yes	—
567	C₂²×C₃	—	2	2	no	—
568	C₂²×C₃	—	2	2	no	—
569	C₂²×C₃	—	2	2	no	—
570	C₂²×C₃	—	4	1	no	—
571	C₂²×C₃	—	4	1	no	—
572	C₂²×C₃	—	4	1	no	—
573	C₂²×C₃	—	4	1	no	—
574	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
575	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
576	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
577	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
578	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
579	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
580	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
581	C₃×C₄	—	2	2	no	—
582	C₃×C₄	—	2	2	no	—
583	C₃×C₄	—	2	2	no	—
584	C₃×C₄	—	4	4	no	—
585	C₃×C₄	—	4	1	no	—
586	C₃×C₄	—	4	1	no	—
587	C₃×C₄	—	4	4	no	—
588	C₃×C₄	—	4	1	no	—
589	C₃×C₄	—	4	1	no	—
590	C₃×C₄	—	4	1	no	—
591	C₃×C₄	—	4	1	no	—
592	C₃×C₄	—	4	4	no	—
593	C₃×C₄	—	4	1	no	—
594	C₃×C₄	—	4	1	no	—
595	C₃×C₄	—	4	4	no	—
596	C₃×C₄	#529	1	4	yes	—
597	C₃×C₄	#541	1	4	yes	—
598	C₃×C₄	#542	1	4	yes	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	C₂×C₃×#41	1	2	yes	—
606	C₂³	C₂⁵×C₃	1	1	yes	characteristic
607	Q₈	—	4	8	no	—
608	Q₈	—	4	8	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	8	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	4	4	no	—
653	C₂×C₄	—	4	4	no	—
654	C₂×C₄	C₂×C₃×#41	1	2	yes	—
655	C₂×C₄	C₂×C₃×#41	1	2	yes	—
656	C₂×C₄	C₂×C₃×#41	1	2	yes	—
657	C₂×C₄	C₂×C₃×#41	1	2	yes	—
658	C₂×C₄	C₂×C₃×#41	1	2	yes	—
659	C₂×C₄	C₂×C₃×#41	1	2	yes	—
660	C₂×C₄	C₂×C₃×#41	1	2	yes	—
661	C₂×C₄	C₂×C₃×#41	1	2	yes	—
662	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
663	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
664	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
665	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
666	C₂×C₃	—	4	2	no	—
667	C₂×C₃	C₂×#529	1	1	yes	characteristic
668	C₂×C₃	C₂×#541	1	1	yes	characteristic
669	C₂×C₃	C₂×#542	1	1	yes	characteristic
670	C₂×C₃	#3509	1	1	yes	characteristic
671	C₂×C₃	#3509	1	1	yes	characteristic
672	C₂×C₃	#3511	1	1	yes	characteristic
673	C₂×C₃	#3511	1	1	yes	characteristic
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	4	1	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
682	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
683	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
684	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
685	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
686	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
687	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
688	C₄	—	2	2	no	—
689	C₄	—	2	2	no	—
690	C₄	—	2	2	no	—
691	C₄	—	4	4	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	4	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	4	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	4	no	—
703	C₄	C₃×#529	1	4	yes	—
704	C₄	C₃×#541	1	4	yes	—
705	C₄	C₃×#542	1	4	yes	—
706	C₃	#35291	1	1	yes	characteristic, direct product factor, Sylow
707	C₂	—	4	2	no	—
708	C₂	C₂×C₃×#529	1	1	yes	characteristic
709	C₂	C₂×C₃×#541	1	1	yes	characteristic
710	C₂	C₂×C₃×#542	1	1	yes	characteristic
711	C₂	C₃×#3509	1	1	yes	characteristic
712	C₂	C₃×#3509	1	1	yes	characteristic
713	C₂	C₃×#3511	1	1	yes	characteristic
714	C₂	C₃×#3511	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂⁴×C₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#2862	C₂	semidirect
2. C₃×#2859	C₂	semidirect
5. C₃×#2645	C₂	semidirect
7. C₃×#2514	C₂	semidirect
8. C₃×#2509	C₂	semidirect
9. C₃×#2508	C₂	semidirect
13. C₃×#2453	C₂	semidirect
16. C₃×#2320	C₂	semidirect
17. C₃×C₄×C₄⋊Q₈	C₂	semidirect
18. C₃×C₄×C₄⋊Q₈	C₂	semidirect
20. #35291	C₃	direct (N × H)
92. #2862	C₂×C₃	semidirect
93. #2859	C₂×C₃	semidirect
96. #2645	C₂×C₃	semidirect
98. #2514	C₂×C₃	semidirect
99. #2509	C₂×C₃	semidirect
100. #2508	C₂×C₃	semidirect
104. #2453	C₂×C₃	semidirect
107. #2320	C₂×C₃	semidirect
108. C₄×C₄⋊Q₈	C₂×C₃	semidirect
109. C₄×C₄⋊Q₈	C₂×C₃	semidirect
706. C₃	#35291	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#2862	2
C₃×#2859	2
C₃×#2857	2
C₃×#2645	2
C₃×#2625	2
C₃×#2514	2
C₃×#2509	2
C₃×#2508	2
C₃×#2495	2
C₃×#2494	2
C₃×#2489	2
C₃×#2453	2
C₃×#2421	2
C₃×#2323	2
C₃×#2320	2
C₃×C₄×C₄⋊Q₈	2
C₃×C₄×#117	2
#35291	3

Subgroups — C3×#35291 #10653898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35291 #10653898