Subgroups — C₃×#35014 #10653621

Order 768.

1978 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2848	C₂	1	2	yes	maximal
4	C₃×#2646	C₂	1	2	yes	maximal, complemented
5	C₃×#2626	C₂	1	2	yes	maximal
6	C₃×#2589	C₂	1	4	yes	maximal, complemented
7	C₃×#2587	C₂	1	4	yes	maximal, complemented
8	C₃×#2497	C₂	1	2	yes	maximal, complemented
9	C₃×#2492	C₂	1	2	yes	maximal, complemented
10	C₃×#2429	C₂	1	2	yes	maximal, complemented
11	C₃×#2423	C₂	1	2	yes	maximal, complemented
12	C₃×#2329	C₂	1	2	yes	maximal, complemented
13	C₃×#2312	C₂	1	2	yes	maximal
14	C₃×C₄×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
15	C₂×C₃×C₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	#35014	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
25	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
28	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
29	C₃×#400	C₂²	1	4	yes	complemented
30	C₃×#400	C₂²	1	4	yes	complemented
31	C₃×#399	C₂²	1	4	yes	—
32	C₃×#398	C₂²	1	4	yes	complemented
33	C₃×#398	C₂²	1	4	yes	complemented
34	C₃×#396	C₂²	1	4	yes	—
35	C₃×#396	C₂²	1	4	yes	—
36	C₃×#393	C₂²	1	4	yes	—
37	C₃×#391	C₂²	1	2	yes	complemented
38	C₃×#391	C₂²	1	2	yes	complemented
39	C₃×#391	C₂²	1	4	yes	complemented
40	C₃×#391	C₂²	1	2	yes	complemented
41	C₃×#389	C₂²	1	2	yes	complemented
42	C₃×#389	C₂²	1	2	yes	complemented
43	C₃×#389	C₂²	1	4	yes	complemented
44	C₃×#389	C₂²	1	2	yes	complemented
45	C₃×#389	C₂²	1	2	yes	complemented
46	C₃×#389	C₂²	1	2	yes	complemented
47	C₃×#388	C₂²	1	4	yes	—
48	C₃×#388	C₂²	1	4	yes	—
49	C₃×#388	C₂²	1	4	yes	—
50	C₃×#388	C₂²	1	4	yes	—
51	C₃×#387	C₂²	1	4	yes	complemented
52	C₃×#387	C₂²	1	4	yes	complemented
53	C₃×#387	C₂²	1	4	yes	complemented
54	C₃×#385	C₂²	1	4	yes	—
55	C₃×#385	C₂²	1	4	yes	—
56	C₃×#385	C₂²	1	4	yes	—
57	C₃×#385	C₂²	1	4	yes	—
58	C₃×#384	C₂²	1	1	yes	characteristic, complemented
59	C₃×#384	C₂²	1	1	yes	characteristic, complemented
60	C₃×#380	C₂²	1	2	yes	—
61	C₃×#380	C₂²	1	2	yes	—
62	C₃×#380	C₂²	1	2	yes	—
63	C₃×#380	C₂²	1	2	yes	—
64	C₃×#380	C₂²	1	2	yes	—
65	C₃×#380	C₂²	1	2	yes	—
66	C₃×#379	C₂²	1	4	yes	—
67	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
68	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	complemented
69	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
70	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
71	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
73	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
74	C₂×C₃×#95	C₂²	1	1	yes	characteristic
75	C₂×C₃×#95	C₂²	1	1	yes	characteristic
76	#2857	C₂×C₃	1	1	yes	characteristic, complemented
77	#2857	C₂×C₃	1	1	yes	characteristic, complemented
78	#2848	C₂×C₃	1	2	yes	—
79	#2646	C₂×C₃	1	2	yes	complemented
80	#2626	C₂×C₃	1	2	yes	—
81	#2589	C₂×C₃	1	4	yes	complemented
82	#2587	C₂×C₃	1	4	yes	complemented
83	#2497	C₂×C₃	1	2	yes	complemented
84	#2492	C₂×C₃	1	2	yes	complemented
85	#2429	C₂×C₃	1	2	yes	complemented
86	#2423	C₂×C₃	1	2	yes	complemented
87	#2329	C₂×C₃	1	2	yes	complemented
88	#2312	C₂×C₃	1	2	yes	—
89	C₄×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
90	C₂×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
91	C₂⁵×C₃	C₂³	1	1	yes	characteristic
92	C₂²×C₃×Q₈	C₂³	1	2	yes	—
93	C₂²×C₃×Q₈	C₂³	1	2	yes	—
94	C₂³×C₃×C₄	—	2	4	no	—
95	C₂³×C₃×C₄	—	4	2	no	—
96	C₂³×C₃×C₄	—	4	2	no	—
97	C₂³×C₃×C₄	C₂³	1	2	yes	—
98	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
99	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
100	C₂³×C₃×C₄	C₂³	1	2	yes	—
101	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
102	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
103	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
104	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
105	C₃×C₄⋊Q₈	—	4	2	no	—
106	C₃×C₄⋊Q₈	—	4	2	no	—
107	C₃×C₂²⋊Q₈	—	2	8	no	—
108	C₃×C₂²⋊Q₈	—	2	8	no	—
109	C₃×C₂²⋊Q₈	—	4	4	no	—
110	C₃×C₂²⋊Q₈	—	4	4	no	—
111	C₃×C₄×Q₈	—	4	4	no	—
112	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
126	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
127	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
128	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
129	C₂×C₃×C₂²⋊C₄	Q₈	1	8	yes	complemented
130	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂×C₃×C₄²	—	4	2	no	—
141	C₂×C₃×C₄²	—	4	2	no	—
142	C₂×C₃×C₄²	C₂³	1	2	yes	—
143	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
144	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
145	C₂×C₃×C₄²	C₂³	1	2	yes	—
146	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
147	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
148	C₂×C₃×C₄²	C₂³	1	4	yes	—
149	C₂×C₃×C₄²	C₂³	1	4	yes	—
150	C₃×#95	C₂³	1	2	yes	—
151	C₃×#95	C₂³	1	2	yes	—
152	C₃×#95	C₂³	1	2	yes	—
153	C₃×#95	C₂³	1	2	yes	—
154	C₃×#95	C₂³	1	4	yes	—
155	C₃×#95	C₂³	1	4	yes	—
156	C₃×#95	C₂³	1	4	yes	—
157	C₃×#95	C₂³	1	4	yes	—
158	C₃×#95	C₂³	1	4	yes	—
159	C₃×#95	C₂³	1	4	yes	—
160	C₃×#95	C₂³	1	4	yes	—
161	C₃×#95	C₂³	1	4	yes	—
162	C₃×#95	C₂³	1	4	yes	—
163	C₃×#95	C₂³	1	4	yes	—
164	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
165	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
167	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
168	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
169	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
170	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
171	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
172	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
173	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
174	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
175	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
176	#400	C₂²×C₃	1	4	yes	complemented
177	#400	C₂²×C₃	1	4	yes	complemented
178	#399	C₂²×C₃	1	4	yes	—
179	#398	C₂²×C₃	1	4	yes	complemented
180	#398	C₂²×C₃	1	4	yes	complemented
181	#396	C₂²×C₃	1	4	yes	—
182	#396	C₂²×C₃	1	4	yes	—
183	#393	C₂²×C₃	1	4	yes	—
184	#391	C₂²×C₃	1	4	yes	complemented
185	#391	C₂²×C₃	1	2	yes	complemented
186	#391	C₂²×C₃	1	2	yes	complemented
187	#391	C₂²×C₃	1	2	yes	complemented
188	#389	C₂²×C₃	1	4	yes	complemented
189	#389	C₂²×C₃	1	2	yes	complemented
190	#389	C₂²×C₃	1	2	yes	complemented
191	#389	C₂²×C₃	1	2	yes	complemented
192	#389	C₂²×C₃	1	2	yes	complemented
193	#389	C₂²×C₃	1	2	yes	complemented
194	#388	C₂²×C₃	1	4	yes	—
195	#388	C₂²×C₃	1	4	yes	—
196	#388	C₂²×C₃	1	4	yes	—
197	#388	C₂²×C₃	1	4	yes	—
198	#387	C₂²×C₃	1	4	yes	complemented
199	#387	C₂²×C₃	1	4	yes	complemented
200	#387	C₂²×C₃	1	4	yes	complemented
201	#385	C₂²×C₃	1	4	yes	—
202	#385	C₂²×C₃	1	4	yes	—
203	#385	C₂²×C₃	1	4	yes	—
204	#385	C₂²×C₃	1	4	yes	—
205	#384	C₂²×C₃	1	1	yes	characteristic, complemented
206	#384	C₂²×C₃	1	1	yes	characteristic, complemented
207	#380	C₂²×C₃	1	2	yes	—
208	#380	C₂²×C₃	1	2	yes	—
209	#380	C₂²×C₃	1	2	yes	—
210	#380	C₂²×C₃	1	2	yes	—
211	#380	C₂²×C₃	1	2	yes	—
212	#380	C₂²×C₃	1	2	yes	—
213	#379	C₂²×C₃	1	4	yes	—
214	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
215	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
216	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
217	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
218	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
219	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
220	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
221	C₂×#95	C₂²×C₃	1	1	yes	characteristic
222	C₂×#95	C₂²×C₃	1	1	yes	characteristic
223	C₂⁴×C₃	—	2	2	no	—
224	C₂⁴×C₃	—	2	2	no	—
225	C₂⁴×C₃	—	4	1	no	—
226	C₂⁴×C₃	—	4	1	no	—
227	C₂⁴×C₃	—	4	1	no	—
228	C₂⁴×C₃	—	4	1	no	—
229	C₂⁴×C₃	C₂×Q₈	1	4	yes	—
230	C₂⁴×C₃	C₂⁴	1	2	yes	—
231	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
232	C₂×C₃×Q₈	—	2	4	no	—
233	C₂×C₃×Q₈	—	2	4	no	—
234	C₂×C₃×Q₈	—	2	4	no	—
235	C₂×C₃×Q₈	—	2	4	no	—
236	C₂×C₃×Q₈	—	4	2	no	—
237	C₂×C₃×Q₈	—	4	2	no	—
238	C₂²×C₃×C₄	—	2	2	no	—
239	C₂²×C₃×C₄	—	2	2	no	—
240	C₂²×C₃×C₄	—	2	2	no	—
241	C₂²×C₃×C₄	—	2	2	no	—
242	C₂²×C₃×C₄	—	2	4	no	—
243	C₂²×C₃×C₄	—	2	4	no	—
244	C₂²×C₃×C₄	—	2	4	no	—
245	C₂²×C₃×C₄	—	2	4	no	—
246	C₂²×C₃×C₄	—	4	1	no	—
247	C₂²×C₃×C₄	—	4	1	no	—
248	C₂²×C₃×C₄	—	4	1	no	—
249	C₂²×C₃×C₄	—	4	1	no	—
250	C₂²×C₃×C₄	—	4	2	no	—
251	C₂²×C₃×C₄	—	4	2	no	—
252	C₂²×C₃×C₄	—	4	1	no	—
253	C₂²×C₃×C₄	—	4	1	no	—
254	C₂²×C₃×C₄	—	4	1	no	—
255	C₂²×C₃×C₄	—	4	1	no	—
256	C₂²×C₃×C₄	—	4	1	no	—
257	C₂²×C₃×C₄	—	4	1	no	—
258	C₂²×C₃×C₄	—	4	16	no	—
259	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
260	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
261	C₂²×C₃×C₄	#41	1	4	yes	—
262	C₂²×C₃×C₄	#41	1	4	yes	—
263	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
264	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
265	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
266	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
267	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
268	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
269	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
270	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
271	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
272	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
273	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
274	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
275	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
276	C₃×C₄⋊C₄	—	2	4	no	—
277	C₃×C₄⋊C₄	—	2	4	no	—
278	C₃×C₄⋊C₄	—	2	8	no	—
279	C₃×C₄⋊C₄	—	2	8	no	—
280	C₃×C₄⋊C₄	—	2	4	no	—
281	C₃×C₄⋊C₄	—	2	4	no	—
282	C₃×C₄⋊C₄	—	4	2	no	—
283	C₃×C₄⋊C₄	—	4	2	no	—
284	C₃×C₄⋊C₄	—	4	2	no	—
285	C₃×C₄⋊C₄	—	4	4	no	—
286	C₃×C₄⋊C₄	—	4	4	no	—
287	C₃×C₄⋊C₄	—	4	4	no	—
288	C₃×C₄⋊C₄	—	4	4	no	—
289	C₃×C₄⋊C₄	—	4	2	no	—
290	C₃×C₄⋊C₄	—	4	2	no	—
291	C₃×C₄⋊C₄	—	4	2	no	—
292	C₃×C₂²⋊C₄	—	2	8	no	—
293	C₃×C₂²⋊C₄	—	2	8	no	—
294	C₃×C₂²⋊C₄	—	2	4	no	—
295	C₃×C₂²⋊C₄	—	2	4	no	—
296	C₃×C₂²⋊C₄	—	4	4	no	—
297	C₃×C₂²⋊C₄	—	4	4	no	—
298	C₃×C₂²⋊C₄	—	4	4	no	—
299	C₃×C₂²⋊C₄	—	4	4	no	—
300	C₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
301	C₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
302	C₃×C₄²	—	2	4	no	—
303	C₃×C₄²	—	2	2	no	—
304	C₃×C₄²	—	2	2	no	—
305	C₃×C₄²	—	4	2	no	—
306	C₃×C₄²	—	4	1	no	—
307	C₃×C₄²	—	4	1	no	—
308	C₃×C₄²	—	4	4	no	—
309	C₃×C₄²	—	4	4	no	—
310	C₂⁵	C₂³×C₃	1	1	yes	characteristic
311	C₂²×Q₈	C₂³×C₃	1	2	yes	—
312	C₂²×Q₈	C₂³×C₃	1	2	yes	—
313	C₂³×C₄	—	2	4	no	—
314	C₂³×C₄	—	4	2	no	—
315	C₂³×C₄	—	4	2	no	—
316	C₂³×C₄	C₂³×C₃	1	2	yes	—
317	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
318	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₃	1	2	yes	—
321	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
324	C₄⋊Q₈	—	4	2	no	—
325	C₄⋊Q₈	—	4	2	no	—
326	C₂²⋊Q₈	—	2	8	no	—
327	C₂²⋊Q₈	—	2	8	no	—
328	C₂²⋊Q₈	—	4	4	no	—
329	C₂²⋊Q₈	—	4	4	no	—
330	C₄×Q₈	—	4	4	no	—
331	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
335	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
338	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
344	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
347	C₂×C₂²⋊C₄	—	2	4	no	—
348	C₂×C₂²⋊C₄	C₃×Q₈	1	8	yes	complemented
349	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
359	C₂×C₄²	—	4	2	no	—
360	C₂×C₄²	—	4	2	no	—
361	C₂×C₄²	C₂³×C₃	1	2	yes	—
362	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₃	1	4	yes	—
365	C₂×C₄²	C₂³×C₃	1	2	yes	—
366	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₃	1	4	yes	—
369	#95	C₂³×C₃	1	2	yes	—
370	#95	C₂³×C₃	1	2	yes	—
371	#95	C₂³×C₃	1	2	yes	—
372	#95	C₂³×C₃	1	2	yes	—
373	#95	C₂³×C₃	1	4	yes	—
374	#95	C₂³×C₃	1	4	yes	—
375	#95	C₂³×C₃	1	4	yes	—
376	#95	C₂³×C₃	1	4	yes	—
377	#95	C₂³×C₃	1	4	yes	—
378	#95	C₂³×C₃	1	4	yes	—
379	#95	C₂³×C₃	1	4	yes	—
380	#95	C₂³×C₃	1	4	yes	—
381	#95	C₂³×C₃	1	4	yes	—
382	#95	C₂³×C₃	1	4	yes	—
383	C₂³×C₃	—	2	1	no	—
384	C₂³×C₃	—	2	1	no	—
385	C₂³×C₃	—	2	1	no	—
386	C₂³×C₃	—	2	1	no	—
387	C₂³×C₃	—	2	8	no	—
388	C₂³×C₃	—	2	2	no	—
389	C₂³×C₃	—	2	2	no	—
390	C₂³×C₃	—	2	2	no	—
391	C₂³×C₃	—	2	2	no	—
392	C₂³×C₃	—	2	2	no	—
393	C₂³×C₃	—	2	2	no	—
394	C₂³×C₃	—	4	4	no	—
395	C₂³×C₃	—	4	4	no	—
396	C₂³×C₃	—	4	4	no	—
397	C₂³×C₃	—	4	4	no	—
398	C₂³×C₃	—	4	4	no	—
399	C₂³×C₃	—	4	4	no	—
400	C₂³×C₃	C₂²×Q₈	1	4	yes	—
401	C₂³×C₃	C₂²×Q₈	1	2	yes	—
402	C₂³×C₃	C₂×#41	1	2	yes	—
403	C₂³×C₃	C₂×#41	1	2	yes	—
404	C₂³×C₃	C₂⁵	1	1	yes	characteristic
405	C₃×Q₈	—	4	8	no	—
406	C₃×Q₈	—	8	4	no	—
407	C₂×C₃×C₄	—	2	2	no	—
408	C₂×C₃×C₄	—	2	1	no	—
409	C₂×C₃×C₄	—	2	1	no	—
410	C₂×C₃×C₄	—	2	1	no	—
411	C₂×C₃×C₄	—	2	1	no	—
412	C₂×C₃×C₄	—	2	1	no	—
413	C₂×C₃×C₄	—	2	1	no	—
414	C₂×C₃×C₄	—	2	2	no	—
415	C₂×C₃×C₄	—	2	1	no	—
416	C₂×C₃×C₄	—	2	1	no	—
417	C₂×C₃×C₄	—	2	1	no	—
418	C₂×C₃×C₄	—	2	1	no	—
419	C₂×C₃×C₄	—	2	8	no	—
420	C₂×C₃×C₄	—	2	2	no	—
421	C₂×C₃×C₄	—	2	4	no	—
422	C₂×C₃×C₄	—	2	4	no	—
423	C₂×C₃×C₄	—	2	4	no	—
424	C₂×C₃×C₄	—	2	4	no	—
425	C₂×C₃×C₄	—	2	2	no	—
426	C₂×C₃×C₄	—	2	2	no	—
427	C₂×C₃×C₄	—	2	4	no	—
428	C₂×C₃×C₄	—	2	4	no	—
429	C₂×C₃×C₄	—	2	4	no	—
430	C₂×C₃×C₄	—	2	4	no	—
431	C₂×C₃×C₄	—	2	2	no	—
432	C₂×C₃×C₄	—	2	2	no	—
433	C₂×C₃×C₄	—	2	4	no	—
434	C₂×C₃×C₄	—	2	4	no	—
435	C₂×C₃×C₄	—	2	4	no	—
436	C₂×C₃×C₄	—	2	4	no	—
437	C₂×C₃×C₄	—	2	2	no	—
438	C₂×C₃×C₄	—	4	4	no	—
439	C₂×C₃×C₄	—	4	4	no	—
440	C₂×C₃×C₄	—	4	4	no	—
441	C₂×C₃×C₄	—	4	8	no	—
442	C₂×C₃×C₄	—	4	4	no	—
443	C₂×C₃×C₄	—	4	4	no	—
444	C₂×C₃×C₄	—	4	8	no	—
445	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
446	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
447	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
448	C₂×C₃×C₄	C₂×#41	1	2	yes	—
449	C₂×C₃×C₄	C₂×#41	1	2	yes	—
450	C₂×C₃×C₄	C₂×#41	1	2	yes	—
451	C₂×C₃×C₄	C₂×#41	1	2	yes	—
452	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
453	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
454	C₂⁴	—	2	2	no	—
455	C₂⁴	—	2	2	no	—
456	C₂⁴	—	4	1	no	—
457	C₂⁴	—	4	1	no	—
458	C₂⁴	—	4	1	no	—
459	C₂⁴	—	4	1	no	—
460	C₂⁴	C₂×C₃×Q₈	1	4	yes	—
461	C₂⁴	C₂⁴×C₃	1	2	yes	—
462	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
463	C₂×Q₈	—	2	4	no	—
464	C₂×Q₈	—	2	4	no	—
465	C₂×Q₈	—	2	4	no	—
466	C₂×Q₈	—	2	4	no	—
467	C₂×Q₈	—	4	2	no	—
468	C₂×Q₈	—	4	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	4	1	no	—
478	C₂²×C₄	—	4	1	no	—
479	C₂²×C₄	—	4	1	no	—
480	C₂²×C₄	—	4	1	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	4	1	no	—
484	C₂²×C₄	—	4	1	no	—
485	C₂²×C₄	—	4	1	no	—
486	C₂²×C₄	—	4	1	no	—
487	C₂²×C₄	—	4	1	no	—
488	C₂²×C₄	—	4	1	no	—
489	C₂²×C₄	—	4	16	no	—
490	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
491	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
492	C₂²×C₄	C₃×#41	1	4	yes	—
493	C₂²×C₄	C₃×#41	1	4	yes	—
494	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
495	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
497	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
498	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
500	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
502	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
503	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
504	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
505	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	2	8	no	—
510	C₄⋊C₄	—	2	8	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	4	no	—
513	C₄⋊C₄	—	4	4	no	—
514	C₄⋊C₄	—	4	4	no	—
515	C₄⋊C₄	—	4	4	no	—
516	C₄⋊C₄	—	4	2	no	—
517	C₄⋊C₄	—	4	2	no	—
518	C₄⋊C₄	—	4	2	no	—
519	C₄⋊C₄	—	4	2	no	—
520	C₄⋊C₄	—	4	2	no	—
521	C₄⋊C₄	—	4	2	no	—
522	C₄⋊C₄	—	4	4	no	—
523	C₂²⋊C₄	—	2	8	no	—
524	C₂²⋊C₄	—	2	8	no	—
525	C₂²⋊C₄	—	2	4	no	—
526	C₂²⋊C₄	—	2	4	no	—
527	C₂²⋊C₄	—	4	4	no	—
528	C₂²⋊C₄	—	4	4	no	—
529	C₂²⋊C₄	—	4	4	no	—
530	C₂²⋊C₄	—	4	4	no	—
531	C₂²⋊C₄	C₂×C₃×Q₈	1	8	yes	—
532	C₂²⋊C₄	C₂×C₃×Q₈	1	8	yes	—
533	C₄²	—	2	4	no	—
534	C₄²	—	2	2	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	4	2	no	—
537	C₄²	—	4	1	no	—
538	C₄²	—	4	1	no	—
539	C₄²	—	4	4	no	—
540	C₄²	—	4	4	no	—
541	C₂²×C₃	—	2	2	no	—
542	C₂²×C₃	—	2	2	no	—
543	C₂²×C₃	—	2	2	no	—
544	C₂²×C₃	—	2	2	no	—
545	C₂²×C₃	—	2	2	no	—
546	C₂²×C₃	—	2	2	no	—
547	C₂²×C₃	—	2	4	no	—
548	C₂²×C₃	—	2	4	no	—
549	C₂²×C₃	—	2	4	no	—
550	C₂²×C₃	—	4	16	no	—
551	C₂²×C₃	—	4	2	no	—
552	C₂²×C₃	—	4	2	no	—
553	C₂²×C₃	—	4	2	no	—
554	C₂²×C₃	—	4	2	no	—
555	C₂²×C₃	#533	1	4	yes	—
556	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
557	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
558	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
559	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
560	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂²×C₃	#585	1	1	yes	characteristic
562	C₂²×C₃	#585	1	1	yes	characteristic
563	C₃×C₄	—	2	2	no	—
564	C₃×C₄	—	2	4	no	—
565	C₃×C₄	—	2	2	no	—
566	C₃×C₄	—	2	2	no	—
567	C₃×C₄	—	2	2	no	—
568	C₃×C₄	—	2	2	no	—
569	C₃×C₄	—	4	2	no	—
570	C₃×C₄	—	4	4	no	—
571	C₃×C₄	—	4	4	no	—
572	C₃×C₄	—	4	4	no	—
573	C₃×C₄	—	4	4	no	—
574	C₃×C₄	—	4	2	no	—
575	C₃×C₄	#538	1	4	yes	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	8	no	—
587	C₂³	—	4	4	no	—
588	C₂³	—	4	4	no	—
589	C₂³	—	4	4	no	—
590	C₂³	—	4	4	no	—
591	C₂³	—	4	4	no	—
592	C₂³	—	4	4	no	—
593	C₂³	C₂²×C₃×Q₈	1	4	yes	—
594	C₂³	C₂²×C₃×Q₈	1	2	yes	—
595	C₂³	C₂×C₃×#41	1	2	yes	—
596	C₂³	C₂×C₃×#41	1	2	yes	—
597	C₂³	C₂⁵×C₃	1	1	yes	characteristic
598	Q₈	—	4	8	no	—
599	Q₈	—	8	4	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	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	8	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	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	2	no	—
631	C₂×C₄	—	4	4	no	—
632	C₂×C₄	—	4	4	no	—
633	C₂×C₄	—	4	4	no	—
634	C₂×C₄	—	4	8	no	—
635	C₂×C₄	—	4	4	no	—
636	C₂×C₄	—	4	4	no	—
637	C₂×C₄	—	4	8	no	—
638	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
639	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
640	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
641	C₂×C₄	C₂×C₃×#41	1	2	yes	—
642	C₂×C₄	C₂×C₃×#41	1	2	yes	—
643	C₂×C₄	C₂×C₃×#41	1	2	yes	—
644	C₂×C₄	C₂×C₃×#41	1	2	yes	—
645	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
646	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
647	C₂×C₃	—	2	4	no	—
648	C₂×C₃	—	4	4	no	—
649	C₂×C₃	C₂×#533	1	1	yes	characteristic
650	C₂×C₃	C₂×#538	1	1	yes	characteristic
651	C₂×C₃	#3455	1	1	yes	characteristic
652	C₂×C₃	#3501	1	1	yes	characteristic
653	C₂×C₃	#3501	1	1	yes	characteristic
654	C₂×C₃	#3505	1	1	yes	characteristic
655	C₂×C₃	#3506	1	1	yes	characteristic
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	4	16	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	4	2	no	—
670	C₂²	C₃×#533	1	4	yes	—
671	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
672	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
673	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
674	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
675	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
676	C₂²	C₃×#585	1	1	yes	characteristic
677	C₂²	C₃×#585	1	1	yes	characteristic
678	C₄	—	2	2	no	—
679	C₄	—	2	4	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	4	no	—
686	C₄	—	4	4	no	—
687	C₄	—	4	4	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	4	no	—
690	C₄	C₃×#538	1	4	yes	—
691	C₃	#35014	1	1	yes	characteristic, direct product factor, Sylow
692	C₂	—	2	4	no	—
693	C₂	—	4	4	no	—
694	C₂	C₂×C₃×#533	1	1	yes	characteristic
695	C₂	C₂×C₃×#538	1	1	yes	characteristic
696	C₂	C₃×#3455	1	1	yes	characteristic
697	C₂	C₃×#3501	1	1	yes	characteristic
698	C₂	C₃×#3501	1	1	yes	characteristic
699	C₂	C₃×#3505	1	1	yes	characteristic
700	C₂	C₃×#3506	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂⁵×C₃	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. C₃×#2857	C₂	semidirect
2. C₃×#2857	C₂	semidirect
4. C₃×#2646	C₂	semidirect
6. C₃×#2589	C₂	semidirect
7. C₃×#2587	C₂	semidirect
8. C₃×#2497	C₂	semidirect
9. C₃×#2492	C₂	semidirect
10. C₃×#2429	C₂	semidirect
11. C₃×#2423	C₂	semidirect
12. C₃×#2329	C₂	semidirect
14. C₃×C₄×C₂²⋊Q₈	C₂	semidirect
16. #35014	C₃	direct (N × H)
18. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
19. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₃×C₄×Q₈	C₂²	semidirect
29. C₃×#400	C₂²	semidirect
30. C₃×#400	C₂²	semidirect
32. C₃×#398	C₂²	semidirect
33. C₃×#398	C₂²	semidirect
37. C₃×#391	C₂²	semidirect
38. C₃×#391	C₂²	semidirect
39. C₃×#391	C₂²	semidirect
40. C₃×#391	C₂²	semidirect
41. C₃×#389	C₂²	semidirect
42. C₃×#389	C₂²	semidirect
43. C₃×#389	C₂²	semidirect
44. C₃×#389	C₂²	semidirect
45. C₃×#389	C₂²	semidirect
46. C₃×#389	C₂²	semidirect
51. C₃×#387	C₂²	semidirect
52. C₃×#387	C₂²	semidirect
53. C₃×#387	C₂²	semidirect
58. C₃×#384	C₂²	semidirect
59. C₃×#384	C₂²	semidirect
67. C₃×C₄×C₄⋊C₄	C₂²	semidirect
68. C₃×C₄×C₄⋊C₄	C₂²	semidirect
76. #2857	C₂×C₃	semidirect
77. #2857	C₂×C₃	semidirect
79. #2646	C₂×C₃	semidirect
81. #2589	C₂×C₃	semidirect
82. #2587	C₂×C₃	semidirect
83. #2497	C₂×C₃	semidirect
84. #2492	C₂×C₃	semidirect
85. #2429	C₂×C₃	semidirect
86. #2423	C₂×C₃	semidirect
87. #2329	C₂×C₃	semidirect
89. C₄×C₂²⋊Q₈	C₂×C₃	semidirect
129. C₂×C₃×C₂²⋊C₄	Q₈	semidirect
165. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
166. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
171. C₂×C₄×Q₈	C₂²×C₃	semidirect
176. #400	C₂²×C₃	semidirect
177. #400	C₂²×C₃	semidirect
179. #398	C₂²×C₃	semidirect
180. #398	C₂²×C₃	semidirect
184. #391	C₂²×C₃	semidirect
185. #391	C₂²×C₃	semidirect
186. #391	C₂²×C₃	semidirect
187. #391	C₂²×C₃	semidirect
188. #389	C₂²×C₃	semidirect
189. #389	C₂²×C₃	semidirect
190. #389	C₂²×C₃	semidirect
191. #389	C₂²×C₃	semidirect
192. #389	C₂²×C₃	semidirect
193. #389	C₂²×C₃	semidirect
198. #387	C₂²×C₃	semidirect
199. #387	C₂²×C₃	semidirect
200. #387	C₂²×C₃	semidirect
205. #384	C₂²×C₃	semidirect
206. #384	C₂²×C₃	semidirect
214. C₄×C₄⋊C₄	C₂²×C₃	semidirect
215. C₄×C₄⋊C₄	C₂²×C₃	semidirect
348. C₂×C₂²⋊C₄	C₃×Q₈	semidirect
691. C₃	#35014	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×#2857	2
C₃×#2848	2
C₃×#2646	2
C₃×#2626	2
C₃×#2589	2
C₃×#2587	2
C₃×#2497	2
C₃×#2492	2
C₃×#2429	2
C₃×#2423	2
C₃×#2329	2
C₃×#2312	2
C₃×C₄×C₂²⋊Q₈	2
C₂×C₃×C₄×C₂²⋊C₄	2
#35014	3

Subgroups — C3×#35014 #10653621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35014 #10653621