Subgroups — C₃×#35938 #10654545

Order 768.

2072 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#556	C₂	1	1	yes	maximal, characteristic
3	C₃×#2664	C₂	1	2	yes	maximal, complemented
4	C₃×#2658	C₂	1	1	yes	maximal, characteristic
5	C₃×#2611	C₂	1	2	yes	maximal, complemented
6	C₃×#2604	C₂	1	2	yes	maximal, complemented
7	C₃×#2592	C₂	1	1	yes	maximal, characteristic
8	C₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2556	C₂	1	4	yes	maximal, complemented
10	C₃×#2546	C₂	1	2	yes	maximal, complemented
11	C₃×#2545	C₂	1	2	yes	maximal
12	C₃×#2519	C₂	1	4	yes	maximal, complemented
13	C₃×#2399	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2396	C₂	1	2	yes	maximal, complemented
15	C₃×#2367	C₂	1	2	yes	maximal
16	C₃×#2365	C₂	1	2	yes	maximal, complemented
17	C₃×#2276	C₂	1	1	yes	maximal, characteristic, complemented
18	#35938	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃×#557	—	2	8	no	—
20	C₃×#556	—	2	8	no	—
21	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₃×#126	C₂²	1	2	yes	—
26	C₂×C₃×#126	C₂²	1	2	yes	—
27	C₂×C₃×#125	C₂²	1	2	yes	—
28	C₂×C₃×#125	C₂²	1	4	yes	—
29	C₂×C₃×#124	C₂²	1	2	yes	—
30	C₂×C₃×#124	C₂²	1	1	yes	characteristic
31	C₂×C₃×#124	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
35	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
36	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
39	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₃×#117	C₂²	1	2	yes	—
42	C₃×#400	C₂²	1	2	yes	—
43	C₃×#400	C₂²	1	2	yes	—
44	C₃×#399	C₂²	1	2	yes	—
45	C₃×#399	C₂²	1	4	yes	—
46	C₃×#399	C₂²	1	2	yes	—
47	C₃×#398	C₂²	1	4	yes	—
48	C₃×#398	C₂²	1	1	yes	characteristic
49	C₃×#398	C₂²	1	2	yes	—
50	C₃×#398	C₂²	1	1	yes	characteristic
51	C₃×#398	C₂²	1	4	yes	—
52	C₃×#397	C₂²	1	2	yes	—
53	C₃×#396	C₂²	1	4	yes	—
54	C₃×#396	C₂²	1	4	yes	—
55	C₃×#395	C₂²	1	1	yes	characteristic
56	C₃×#395	C₂²	1	2	yes	—
57	C₃×#395	C₂²	1	1	yes	characteristic
58	C₃×#393	C₂²	1	2	yes	—
59	C₃×#391	C₂²	1	2	yes	—
60	C₃×#391	C₂²	1	2	yes	—
61	C₃×#391	C₂²	1	2	yes	—
62	C₃×#391	C₂²	1	2	yes	—
63	C₃×#390	C₂²	1	2	yes	—
64	C₃×#389	C₂²	1	4	yes	—
65	C₃×#389	C₂²	1	4	yes	—
66	C₃×#389	C₂²	1	4	yes	—
67	C₃×#388	C₂²	1	4	yes	—
68	C₃×#388	C₂²	1	4	yes	—
69	C₃×#388	C₂²	1	4	yes	—
70	C₃×#388	C₂²	1	4	yes	—
71	C₃×#388	C₂²	1	4	yes	—
72	C₃×#387	C₂²	1	4	yes	—
73	C₃×#387	C₂²	1	4	yes	—
74	C₃×#385	C₂²	1	4	yes	—
75	C₃×#382	C₂²	1	2	yes	—
76	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
77	C₃×C₄×C₄⋊C₄	C₂²	1	4	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	2	yes	—
81	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
82	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
83	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
84	C₃×#376	C₂²	1	1	yes	characteristic
85	C₃×#376	C₂²	1	2	yes	—
86	C₂×#557	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂×#556	C₂×C₃	1	1	yes	characteristic
88	#2664	C₂×C₃	1	2	yes	complemented
89	#2658	C₂×C₃	1	1	yes	characteristic
90	#2611	C₂×C₃	1	2	yes	complemented
91	#2604	C₂×C₃	1	2	yes	complemented
92	#2592	C₂×C₃	1	1	yes	characteristic
93	#2568	C₂×C₃	1	1	yes	characteristic, complemented
94	#2556	C₂×C₃	1	4	yes	complemented
95	#2546	C₂×C₃	1	2	yes	complemented
96	#2545	C₂×C₃	1	2	yes	—
97	#2519	C₂×C₃	1	4	yes	complemented
98	#2399	C₂×C₃	1	1	yes	characteristic, complemented
99	#2396	C₂×C₃	1	2	yes	complemented
100	#2367	C₂×C₃	1	2	yes	—
101	#2365	C₂×C₃	1	2	yes	complemented
102	#2276	C₂×C₃	1	1	yes	characteristic, complemented
103	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
104	C₂²×C₃×Q₈	C₂³	1	2	yes	—
105	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
106	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
107	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
108	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
109	C₂³×C₃×C₄	C₂³	1	2	yes	—
110	C₃×C₄⋊Q₈	—	2	4	no	—
111	C₃×C₄⋊Q₈	—	2	8	no	—
112	C₃×C₄⋊Q₈	—	2	4	no	—
113	C₃×C₄⋊Q₈	—	2	8	no	—
114	C₃×#126	—	2	8	no	—
115	C₃×#126	—	2	8	no	—
116	C₃×#125	—	2	16	no	—
117	C₃×#125	—	2	8	no	—
118	C₃×#124	—	2	4	no	—
119	C₃×#124	—	2	4	no	—
120	C₃×#124	—	2	8	no	—
121	C₃×C₂²⋊Q₈	—	2	8	no	—
122	C₃×C₄×Q₈	—	2	4	no	—
123	C₃×C₄×Q₈	—	2	8	no	—
124	C₃×C₄×Q₈	—	2	4	no	—
125	C₃×C₄×Q₈	—	2	8	no	—
126	C₃×C₄×Q₈	—	2	4	no	—
127	C₃×C₄×Q₈	—	2	8	no	—
128	C₃×C₄×Q₈	D₄	1	8	yes	—
129	C₃×C₄×D₄	—	2	4	no	—
130	C₃×#117	—	2	8	no	—
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	4	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	4	yes	—
137	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
144	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
145	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
163	C₂×C₃×C₄²	C₂³	1	4	yes	—
164	C₂×C₃×C₄²	C₂³	1	4	yes	—
165	C₂×C₃×C₄²	C₂³	1	2	yes	—
166	C₂×C₃×C₄²	C₂³	1	2	yes	—
167	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
168	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
169	C₂×C₃×C₄²	C₂³	1	4	yes	—
170	C₂×C₃×C₄²	C₂³	1	2	yes	—
171	C₂×C₃×C₄²	C₂³	1	2	yes	—
172	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄²	C₂³	1	2	yes	—
174	C₃×#95	C₂³	1	1	yes	characteristic
175	C₃×#95	C₂³	1	4	yes	—
176	C₃×#95	C₂³	1	2	yes	—
177	C₃×#95	C₂³	1	1	yes	characteristic
178	C₃×#95	C₂³	1	2	yes	—
179	C₃×#95	C₂³	1	2	yes	—
180	C₃×#95	C₂³	1	4	yes	—
181	C₃×#95	C₂³	1	4	yes	—
182	C₃×#95	C₂³	1	2	yes	—
183	C₃×#95	C₂³	1	2	yes	—
184	C₃×#95	C₂³	1	4	yes	—
185	C₃×#95	C₂³	1	2	yes	—
186	C₃×#95	C₂³	1	4	yes	—
187	C₃×#95	C₂³	1	4	yes	—
188	C₃×#95	C₂³	1	4	yes	—
189	#557	—	2	8	no	—
190	#556	—	2	8	no	—
191	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
192	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
193	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
194	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
195	C₂×#126	C₂²×C₃	1	2	yes	—
196	C₂×#126	C₂²×C₃	1	2	yes	—
197	C₂×#125	C₂²×C₃	1	2	yes	—
198	C₂×#125	C₂²×C₃	1	4	yes	—
199	C₂×#124	C₂²×C₃	1	1	yes	characteristic
200	C₂×#124	C₂²×C₃	1	2	yes	—
201	C₂×#124	C₂²×C₃	1	1	yes	characteristic
202	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
203	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
204	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
205	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
206	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
207	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
208	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
209	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
210	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
211	C₂×#117	C₂²×C₃	1	2	yes	—
212	#400	C₂²×C₃	1	2	yes	—
213	#400	C₂²×C₃	1	2	yes	—
214	#399	C₂²×C₃	1	2	yes	—
215	#399	C₂²×C₃	1	2	yes	—
216	#399	C₂²×C₃	1	4	yes	—
217	#398	C₂²×C₃	1	1	yes	characteristic
218	#398	C₂²×C₃	1	4	yes	—
219	#398	C₂²×C₃	1	1	yes	characteristic
220	#398	C₂²×C₃	1	2	yes	—
221	#398	C₂²×C₃	1	4	yes	—
222	#397	C₂²×C₃	1	2	yes	—
223	#396	C₂²×C₃	1	4	yes	—
224	#396	C₂²×C₃	1	4	yes	—
225	#395	C₂²×C₃	1	1	yes	characteristic
226	#395	C₂²×C₃	1	1	yes	characteristic
227	#395	C₂²×C₃	1	2	yes	—
228	#393	C₂²×C₃	1	2	yes	—
229	#391	C₂²×C₃	1	2	yes	—
230	#391	C₂²×C₃	1	2	yes	—
231	#391	C₂²×C₃	1	2	yes	—
232	#391	C₂²×C₃	1	2	yes	—
233	#390	C₂²×C₃	1	2	yes	—
234	#389	C₂²×C₃	1	4	yes	—
235	#389	C₂²×C₃	1	4	yes	—
236	#389	C₂²×C₃	1	4	yes	—
237	#388	C₂²×C₃	1	4	yes	—
238	#388	C₂²×C₃	1	4	yes	—
239	#388	C₂²×C₃	1	4	yes	—
240	#388	C₂²×C₃	1	4	yes	—
241	#388	C₂²×C₃	1	4	yes	—
242	#387	C₂²×C₃	1	4	yes	—
243	#387	C₂²×C₃	1	4	yes	—
244	#385	C₂²×C₃	1	4	yes	—
245	#382	C₂²×C₃	1	2	yes	—
246	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
247	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
248	C₄×C₄⋊C₄	C₂²×C₃	1	4	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	2	yes	—
252	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
253	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
254	#376	C₂²×C₃	1	2	yes	—
255	#376	C₂²×C₃	1	1	yes	characteristic
256	C₂⁴×C₃	C₂⁴	1	2	yes	—
257	C₂×C₃×Q₈	—	2	2	no	—
258	C₂×C₃×Q₈	—	2	2	no	—
259	C₂×C₃×Q₈	—	2	2	no	—
260	C₂×C₃×Q₈	—	2	4	no	—
261	C₂×C₃×Q₈	—	2	4	no	—
262	C₂×C₃×Q₈	—	2	4	no	—
263	C₂×C₃×Q₈	—	2	4	no	—
264	C₂×C₃×Q₈	—	2	4	no	—
265	C₂×C₃×Q₈	—	2	4	no	—
266	C₂×C₃×Q₈	—	2	2	no	—
267	C₂×C₃×Q₈	—	4	1	no	—
268	C₂×C₃×Q₈	C₂×D₄	1	4	yes	—
269	C₂×C₃×D₄	—	2	2	no	—
270	C₂×C₃×D₄	—	2	4	no	—
271	C₂²×C₃×C₄	—	2	4	no	—
272	C₂²×C₃×C₄	—	2	4	no	—
273	C₂²×C₃×C₄	—	4	2	no	—
274	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
275	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
276	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
277	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
278	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
279	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
280	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
281	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
283	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
284	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
285	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
286	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
287	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
288	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
289	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
290	C₃×C₄⋊C₄	—	2	2	no	—
291	C₃×C₄⋊C₄	—	2	4	no	—
292	C₃×C₄⋊C₄	—	2	4	no	—
293	C₃×C₄⋊C₄	—	2	4	no	—
294	C₃×C₄⋊C₄	—	2	2	no	—
295	C₃×C₄⋊C₄	—	2	8	no	—
296	C₃×C₄⋊C₄	—	2	8	no	—
297	C₃×C₄⋊C₄	—	2	4	no	—
298	C₃×C₄⋊C₄	—	2	2	no	—
299	C₃×C₄⋊C₄	—	2	2	no	—
300	C₃×C₄⋊C₄	—	2	8	no	—
301	C₃×C₄⋊C₄	—	2	4	no	—
302	C₃×C₄⋊C₄	—	2	4	no	—
303	C₃×C₄⋊C₄	—	2	8	no	—
304	C₃×C₄⋊C₄	—	2	4	no	—
305	C₃×C₄⋊C₄	—	2	8	no	—
306	C₃×C₄⋊C₄	—	2	8	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	—	4	2	no	—
311	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
312	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
313	C₃×C₂²⋊C₄	—	2	4	no	—
314	C₃×C₂²⋊C₄	—	2	4	no	—
315	C₃×C₂²⋊C₄	—	2	4	no	—
316	C₃×C₂²⋊C₄	—	2	4	no	—
317	C₃×C₂²⋊C₄	—	2	4	no	—
318	C₃×C₂²⋊C₄	—	2	8	no	—
319	C₃×C₂²⋊C₄	—	2	8	no	—
320	C₃×C₂²⋊C₄	—	2	8	no	—
321	C₃×C₂²⋊C₄	—	4	4	no	—
322	C₃×C₄²	—	2	4	no	—
323	C₃×C₄²	—	2	2	no	—
324	C₃×C₄²	—	2	2	no	—
325	C₃×C₄²	—	2	8	no	—
326	C₃×C₄²	—	2	4	no	—
327	C₃×C₄²	—	2	8	no	—
328	C₃×C₄²	—	4	4	no	—
329	C₃×C₄²	—	4	2	no	—
330	C₃×C₄²	C₂×D₄	1	8	yes	—
331	C₃×C₄²	C₂×D₄	1	4	yes	—
332	C₃×C₄²	#41	1	8	yes	—
333	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
334	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
335	C₂²×Q₈	C₂³×C₃	1	2	yes	—
336	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
337	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
338	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₃	1	2	yes	—
340	C₄⋊Q₈	—	2	4	no	—
341	C₄⋊Q₈	—	2	8	no	—
342	C₄⋊Q₈	—	2	4	no	—
343	C₄⋊Q₈	—	2	8	no	—
344	#126	—	2	8	no	—
345	#126	—	2	8	no	—
346	#125	—	2	16	no	—
347	#125	—	2	8	no	—
348	#124	—	2	4	no	—
349	#124	—	2	4	no	—
350	#124	—	2	8	no	—
351	C₂²⋊Q₈	—	2	8	no	—
352	C₄×Q₈	—	2	4	no	—
353	C₄×Q₈	—	2	8	no	—
354	C₄×Q₈	—	2	4	no	—
355	C₄×Q₈	—	2	8	no	—
356	C₄×Q₈	—	2	4	no	—
357	C₄×Q₈	—	2	8	no	—
358	C₄×Q₈	C₃×D₄	1	8	yes	—
359	C₄×D₄	—	2	4	no	—
360	#117	—	2	8	no	—
361	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
368	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
373	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
374	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
375	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
377	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
381	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
393	C₂×C₄²	C₂³×C₃	1	2	yes	—
394	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
396	C₂×C₄²	C₂³×C₃	1	4	yes	—
397	C₂×C₄²	C₂³×C₃	1	2	yes	—
398	C₂×C₄²	C₂³×C₃	1	4	yes	—
399	C₂×C₄²	C₂³×C₃	1	4	yes	—
400	C₂×C₄²	C₂³×C₃	1	2	yes	—
401	C₂×C₄²	C₂³×C₃	1	2	yes	—
402	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₃	1	2	yes	—
404	#95	C₂³×C₃	1	1	yes	characteristic
405	#95	C₂³×C₃	1	4	yes	—
406	#95	C₂³×C₃	1	2	yes	—
407	#95	C₂³×C₃	1	1	yes	characteristic
408	#95	C₂³×C₃	1	2	yes	—
409	#95	C₂³×C₃	1	2	yes	—
410	#95	C₂³×C₃	1	4	yes	—
411	#95	C₂³×C₃	1	4	yes	—
412	#95	C₂³×C₃	1	2	yes	—
413	#95	C₂³×C₃	1	2	yes	—
414	#95	C₂³×C₃	1	4	yes	—
415	#95	C₂³×C₃	1	2	yes	—
416	#95	C₂³×C₃	1	4	yes	—
417	#95	C₂³×C₃	1	4	yes	—
418	#95	C₂³×C₃	1	4	yes	—
419	C₂³×C₃	—	2	2	no	—
420	C₂³×C₃	—	2	4	no	—
421	C₂³×C₃	—	2	4	no	—
422	C₂³×C₃	—	2	2	no	—
423	C₂³×C₃	—	2	2	no	—
424	C₂³×C₃	C₂⁵	1	1	yes	characteristic
425	C₃×Q₈	—	2	8	no	—
426	C₃×Q₈	—	2	8	no	—
427	C₃×Q₈	—	4	4	no	—
428	C₃×Q₈	—	4	4	no	—
429	C₃×Q₈	—	4	8	no	—
430	C₃×D₄	—	4	4	no	—
431	C₂×C₃×C₄	—	2	2	no	—
432	C₂×C₃×C₄	—	2	1	no	—
433	C₂×C₃×C₄	—	2	4	no	—
434	C₂×C₃×C₄	—	2	2	no	—
435	C₂×C₃×C₄	—	2	2	no	—
436	C₂×C₃×C₄	—	2	2	no	—
437	C₂×C₃×C₄	—	2	2	no	—
438	C₂×C₃×C₄	—	2	2	no	—
439	C₂×C₃×C₄	—	2	2	no	—
440	C₂×C₃×C₄	—	2	1	no	—
441	C₂×C₃×C₄	—	2	2	no	—
442	C₂×C₃×C₄	—	2	2	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	2	no	—
448	C₂×C₃×C₄	—	2	1	no	—
449	C₂×C₃×C₄	—	2	2	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	4	no	—
454	C₂×C₃×C₄	—	2	4	no	—
455	C₂×C₃×C₄	—	2	4	no	—
456	C₂×C₃×C₄	—	2	2	no	—
457	C₂×C₃×C₄	—	2	2	no	—
458	C₂×C₃×C₄	—	2	2	no	—
459	C₂×C₃×C₄	—	2	1	no	—
460	C₂×C₃×C₄	—	2	4	no	—
461	C₂×C₃×C₄	—	2	2	no	—
462	C₂×C₃×C₄	—	2	1	no	—
463	C₂×C₃×C₄	—	4	8	no	—
464	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
465	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
466	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
467	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
468	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
469	C₂×C₃×C₄	C₂×#41	1	4	yes	—
470	C₂×C₃×C₄	C₂×#41	1	4	yes	—
471	C₂×C₃×C₄	C₂×#41	1	4	yes	—
472	C₂×C₃×C₄	2₋¹⁺⁴	1	4	yes	—
473	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
474	C₂⁴	C₂⁴×C₃	1	2	yes	—
475	C₂×Q₈	—	2	2	no	—
476	C₂×Q₈	—	2	2	no	—
477	C₂×Q₈	—	2	2	no	—
478	C₂×Q₈	—	2	4	no	—
479	C₂×Q₈	—	2	4	no	—
480	C₂×Q₈	—	2	4	no	—
481	C₂×Q₈	—	2	4	no	—
482	C₂×Q₈	—	2	4	no	—
483	C₂×Q₈	—	2	4	no	—
484	C₂×Q₈	—	2	2	no	—
485	C₂×Q₈	—	4	1	no	—
486	C₂×Q₈	C₂×C₃×D₄	1	4	yes	—
487	C₂×D₄	—	2	2	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
493	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
494	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
495	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
496	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
502	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
504	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	4	no	—
510	C₄⋊C₄	—	2	4	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	8	no	—
514	C₄⋊C₄	—	2	8	no	—
515	C₄⋊C₄	—	2	4	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	8	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	8	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	8	no	—
524	C₄⋊C₄	—	2	8	no	—
525	C₄⋊C₄	—	2	4	no	—
526	C₄⋊C₄	—	2	4	no	—
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	4	2	no	—
529	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
530	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
531	C₂²⋊C₄	—	2	4	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	2	8	no	—
537	C₂²⋊C₄	—	2	8	no	—
538	C₂²⋊C₄	—	2	8	no	—
539	C₂²⋊C₄	—	4	4	no	—
540	C₄²	—	2	4	no	—
541	C₄²	—	2	2	no	—
542	C₄²	—	2	2	no	—
543	C₄²	—	2	8	no	—
544	C₄²	—	2	4	no	—
545	C₄²	—	2	8	no	—
546	C₄²	—	4	4	no	—
547	C₄²	—	4	2	no	—
548	C₄²	C₂×C₃×D₄	1	8	yes	—
549	C₄²	C₂×C₃×D₄	1	4	yes	—
550	C₄²	C₃×#41	1	8	yes	—
551	C₂²×C₃	—	4	2	no	—
552	C₂²×C₃	—	4	2	no	—
553	C₂²×C₃	—	4	2	no	—
554	C₂²×C₃	—	4	4	no	—
555	C₂²×C₃	—	4	4	no	—
556	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
557	C₂²×C₃	C₂²×#41	1	2	yes	—
558	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
559	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
560	C₂²×C₃	#585	1	1	yes	characteristic
561	C₃×C₄	—	2	4	no	—
562	C₃×C₄	—	2	2	no	—
563	C₃×C₄	—	2	4	no	—
564	C₃×C₄	—	2	2	no	—
565	C₃×C₄	—	2	4	no	—
566	C₃×C₄	—	2	2	no	—
567	C₃×C₄	—	2	4	no	—
568	C₃×C₄	—	2	4	no	—
569	C₃×C₄	—	4	2	no	—
570	C₃×C₄	—	4	4	no	—
571	C₃×C₄	—	4	1	no	—
572	C₃×C₄	—	4	1	no	—
573	C₃×C₄	—	4	2	no	—
574	C₃×C₄	—	4	1	no	—
575	C₃×C₄	—	4	4	no	—
576	C₃×C₄	#532	1	4	yes	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	4	no	—
579	C₂³	—	2	4	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	C₂⁵×C₃	1	1	yes	characteristic
583	Q₈	—	2	8	no	—
584	Q₈	—	2	8	no	—
585	Q₈	—	4	4	no	—
586	Q₈	—	4	4	no	—
587	Q₈	—	4	8	no	—
588	D₄	—	4	4	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	4	8	no	—
622	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
623	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
624	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
625	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
626	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
627	C₂×C₄	C₂×C₃×#41	1	4	yes	—
628	C₂×C₄	C₂×C₃×#41	1	4	yes	—
629	C₂×C₄	C₂×C₃×#41	1	4	yes	—
630	C₂×C₄	C₃×2₋¹⁺⁴	1	4	yes	—
631	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
632	C₂×C₃	—	8	2	no	—
633	C₂×C₃	C₂×#532	1	1	yes	characteristic
634	C₂×C₃	#3486	1	1	yes	characteristic
635	C₂×C₃	#3489	1	1	yes	characteristic
636	C₂×C₃	#3507	1	2	yes	—
637	C₂×C₃	#3509	1	2	yes	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	4	no	—
643	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
644	C₂²	C₂²×C₃×#41	1	2	yes	—
645	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
646	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
647	C₂²	C₃×#585	1	1	yes	characteristic
648	C₄	—	2	4	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	4	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	4	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	4	no	—
655	C₄	—	2	4	no	—
656	C₄	—	4	2	no	—
657	C₄	—	4	4	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	4	no	—
663	C₄	C₃×#532	1	4	yes	—
664	C₃	#35938	1	1	yes	characteristic, direct product factor, Sylow
665	C₂	—	8	2	no	—
666	C₂	C₂×C₃×#532	1	1	yes	characteristic
667	C₂	C₃×#3486	1	1	yes	characteristic
668	C₂	C₃×#3489	1	1	yes	characteristic
669	C₂	C₃×#3507	1	2	yes	—
670	C₂	C₃×#3509	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×D₄	C₂³
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. C₂×C₃×#557	C₂	semidirect
3. C₃×#2664	C₂	semidirect
5. C₃×#2611	C₂	semidirect
6. C₃×#2604	C₂	semidirect
8. C₃×#2568	C₂	semidirect
9. C₃×#2556	C₂	semidirect
10. C₃×#2546	C₂	semidirect
12. C₃×#2519	C₂	semidirect
13. C₃×#2399	C₂	semidirect
14. C₃×#2396	C₂	semidirect
16. C₃×#2365	C₂	semidirect
17. C₃×#2276	C₂	semidirect
18. #35938	C₃	direct (N × H)
86. C₂×#557	C₂×C₃	semidirect
88. #2664	C₂×C₃	semidirect
90. #2611	C₂×C₃	semidirect
91. #2604	C₂×C₃	semidirect
93. #2568	C₂×C₃	semidirect
94. #2556	C₂×C₃	semidirect
95. #2546	C₂×C₃	semidirect
97. #2519	C₂×C₃	semidirect
98. #2399	C₂×C₃	semidirect
99. #2396	C₂×C₃	semidirect
101. #2365	C₂×C₃	semidirect
102. #2276	C₂×C₃	semidirect
664. C₃	#35938	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#557	2
C₂×C₃×#556	2
C₃×#2664	2
C₃×#2658	2
C₃×#2611	2
C₃×#2604	2
C₃×#2592	2
C₃×#2568	2
C₃×#2556	2
C₃×#2546	2
C₃×#2545	2
C₃×#2519	2
C₃×#2399	2
C₃×#2396	2
C₃×#2367	2
C₃×#2365	2
C₃×#2276	2
#35938	3

Subgroups — C3×#35938 #10654545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35938 #10654545