Subgroups — C₃×#42977 #10661584

Order 768.

2330 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2828	C₂	1	2	yes	maximal, complemented
2	C₃×#2678	C₂	1	4	yes	maximal, complemented
3	C₃×#2670	C₂	1	2	yes	maximal, complemented
4	C₃×#2668	C₂	1	2	yes	maximal, complemented
5	C₃×#2661	C₂	1	4	yes	maximal, complemented
6	C₃×#2619	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2555	C₂	1	2	yes	maximal, complemented
8	C₃×#2548	C₂	1	2	yes	maximal, complemented
9	C₃×#2541	C₂	1	2	yes	maximal, complemented
10	C₃×#2513	C₂	1	2	yes	maximal, complemented
11	C₃×#2445	C₂	1	2	yes	maximal, complemented
12	C₃×#2433	C₂	1	2	yes	maximal, complemented
13	C₃×#2396	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2363	C₂	1	2	yes	maximal, complemented
15	C₃×#2309	C₂	1	1	yes	maximal, characteristic, complemented
16	#42977	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×#127	C₂²	1	2	yes	—
19	C₂×C₃×#127	C₂²	1	2	yes	—
20	C₂×C₃×#127	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×#124	C₂²	1	4	yes	complemented
22	C₂×C₃×#123	C₂²	1	4	yes	complemented
23	C₂×C₃×#121	C₂²	1	2	yes	—
24	C₂×C₃×#121	C₂²	1	4	yes	complemented
25	C₂×C₃×#121	C₂²	1	4	yes	complemented
26	C₂×C₃×#120	C₂²	1	4	yes	—
27	C₂×C₃×#120	C₂²	1	4	yes	—
28	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
30	C₂×C₃×#117	C₂²	1	1	yes	characteristic
31	C₂×C₃×#117	C₂²	1	1	yes	characteristic
32	C₃×#400	C₂²	1	1	yes	characteristic, complemented
33	C₃×#399	C₂²	1	1	yes	characteristic
34	C₃×#398	C₂²	1	2	yes	complemented
35	C₃×#397	C₂²	1	4	yes	complemented
36	C₃×#397	C₂²	1	4	yes	complemented
37	C₃×#396	C₂²	1	2	yes	—
38	C₃×#395	C₂²	1	1	yes	characteristic, complemented
39	C₃×#394	C₂²	1	2	yes	complemented
40	C₃×#394	C₂²	1	2	yes	complemented
41	C₃×#394	C₂²	1	4	yes	complemented
42	C₃×#394	C₂²	1	4	yes	complemented
43	C₃×#394	C₂²	1	4	yes	complemented
44	C₃×#394	C₂²	1	4	yes	complemented
45	C₃×#393	C₂²	1	1	yes	characteristic
46	C₃×#392	C₂²	1	2	yes	—
47	C₃×#392	C₂²	1	2	yes	—
48	C₃×#392	C₂²	1	4	yes	—
49	C₃×#392	C₂²	1	4	yes	—
50	C₃×#392	C₂²	1	4	yes	complemented
51	C₃×#392	C₂²	1	4	yes	complemented
52	C₃×#390	C₂²	1	4	yes	—
53	C₃×#390	C₂²	1	2	yes	—
54	C₃×#390	C₂²	1	2	yes	—
55	C₃×#390	C₂²	1	2	yes	—
56	C₃×#390	C₂²	1	2	yes	—
57	C₃×#390	C₂²	1	2	yes	—
58	C₃×#390	C₂²	1	2	yes	—
59	C₃×#390	C₂²	1	2	yes	complemented
60	C₃×#390	C₂²	1	2	yes	complemented
61	C₃×#390	C₂²	1	4	yes	complemented
62	C₃×#389	C₂²	1	2	yes	complemented
63	C₃×#388	C₂²	1	4	yes	complemented
64	C₃×#388	C₂²	1	4	yes	complemented
65	C₃×#388	C₂²	1	4	yes	complemented
66	C₃×#386	C₂²	1	4	yes	—
67	C₃×#386	C₂²	1	4	yes	complemented
68	C₃×#382	C₂²	1	1	yes	characteristic, complemented
69	C₃×#379	C₂²	1	2	yes	—
70	C₃×#379	C₂²	1	2	yes	—
71	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
72	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
73	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
74	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
75	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	complemented
76	#2828	C₂×C₃	1	2	yes	complemented
77	#2678	C₂×C₃	1	4	yes	complemented
78	#2670	C₂×C₃	1	2	yes	complemented
79	#2668	C₂×C₃	1	2	yes	complemented
80	#2661	C₂×C₃	1	4	yes	complemented
81	#2619	C₂×C₃	1	1	yes	characteristic, complemented
82	#2555	C₂×C₃	1	2	yes	complemented
83	#2548	C₂×C₃	1	2	yes	complemented
84	#2541	C₂×C₃	1	2	yes	complemented
85	#2513	C₂×C₃	1	2	yes	complemented
86	#2445	C₂×C₃	1	2	yes	complemented
87	#2433	C₂×C₃	1	2	yes	complemented
88	#2396	C₂×C₃	1	1	yes	characteristic, complemented
89	#2363	C₂×C₃	1	2	yes	complemented
90	#2309	C₂×C₃	1	1	yes	characteristic, complemented
91	C₂⁵×C₃	C₂³	1	2	yes	—
92	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
93	C₂²×C₃×D₄	—	2	4	no	—
94	C₂²×C₃×D₄	—	4	2	no	—
95	C₂²×C₃×D₄	—	4	2	no	—
96	C₂²×C₃×D₄	C₂³	1	2	yes	—
97	C₂²×C₃×D₄	C₂³	1	2	yes	—
98	C₂²×C₃×D₄	C₂³	1	2	yes	—
99	C₂²×C₃×D₄	C₂³	1	4	yes	—
100	C₂²×C₃×D₄	C₂³	1	4	yes	—
101	C₂²×C₃×D₄	C₂³	1	4	yes	—
102	C₂²×C₃×D₄	C₂³	1	4	yes	—
103	C₂²×C₃×D₄	C₂³	1	2	yes	—
104	C₂²×C₃×D₄	C₂³	1	2	yes	—
105	C₂²×C₃×D₄	C₂³	1	4	yes	—
106	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
107	C₂³×C₃×C₄	C₂³	1	4	yes	—
108	C₃×#127	—	4	4	no	—
109	C₃×#127	—	4	4	no	—
110	C₃×#127	—	4	2	no	—
111	C₃×#124	—	4	8	no	—
112	C₃×#123	—	4	8	no	—
113	C₃×#121	—	2	8	no	—
114	C₃×#121	—	4	8	no	—
115	C₃×#121	—	4	8	no	—
116	C₃×#120	—	4	8	no	—
117	C₃×#120	—	4	8	no	—
118	C₃×C₄×Q₈	—	4	2	no	—
119	C₃×C₄×D₄	—	4	4	no	—
120	C₃×#117	—	4	2	no	—
121	C₃×#117	—	4	2	no	—
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	2	yes	—
126	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
128	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₂×C₃×C₂²⋊C₄	C₂³	1	2	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	1	yes	characteristic
140	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₂×C₃×C₄²	C₂³	1	2	yes	—
152	C₂×C₃×C₄²	C₂³	1	2	yes	—
153	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
154	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
155	C₂×C₃×C₄²	C₂³	1	2	yes	—
156	C₂×C₃×C₄²	C₂³	1	4	yes	—
157	C₃×#95	C₂³	1	2	yes	—
158	C₃×#95	C₂³	1	2	yes	—
159	C₃×#95	C₂³	1	4	yes	—
160	C₃×#95	C₂³	1	4	yes	—
161	C₃×#95	C₂³	1	1	yes	characteristic
162	C₃×#95	C₂³	1	2	yes	—
163	C₃×#95	C₂³	1	2	yes	—
164	C₃×#95	C₂³	1	1	yes	characteristic
165	C₃×#95	C₂³	1	2	yes	—
166	C₃×#95	C₂³	1	2	yes	—
167	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
168	C₂×#127	C₂²×C₃	1	2	yes	—
169	C₂×#127	C₂²×C₃	1	2	yes	—
170	C₂×#127	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₂×#124	C₂²×C₃	1	4	yes	complemented
172	C₂×#123	C₂²×C₃	1	4	yes	complemented
173	C₂×#121	C₂²×C₃	1	2	yes	—
174	C₂×#121	C₂²×C₃	1	4	yes	complemented
175	C₂×#121	C₂²×C₃	1	4	yes	complemented
176	C₂×#120	C₂²×C₃	1	4	yes	—
177	C₂×#120	C₂²×C₃	1	4	yes	—
178	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
179	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
180	C₂×#117	C₂²×C₃	1	1	yes	characteristic
181	C₂×#117	C₂²×C₃	1	1	yes	characteristic
182	#400	C₂²×C₃	1	1	yes	characteristic, complemented
183	#399	C₂²×C₃	1	1	yes	characteristic
184	#398	C₂²×C₃	1	2	yes	complemented
185	#397	C₂²×C₃	1	4	yes	complemented
186	#397	C₂²×C₃	1	4	yes	complemented
187	#396	C₂²×C₃	1	2	yes	—
188	#395	C₂²×C₃	1	1	yes	characteristic, complemented
189	#394	C₂²×C₃	1	2	yes	complemented
190	#394	C₂²×C₃	1	4	yes	complemented
191	#394	C₂²×C₃	1	4	yes	complemented
192	#394	C₂²×C₃	1	2	yes	complemented
193	#394	C₂²×C₃	1	4	yes	complemented
194	#394	C₂²×C₃	1	4	yes	complemented
195	#393	C₂²×C₃	1	1	yes	characteristic
196	#392	C₂²×C₃	1	4	yes	—
197	#392	C₂²×C₃	1	2	yes	—
198	#392	C₂²×C₃	1	2	yes	—
199	#392	C₂²×C₃	1	4	yes	—
200	#392	C₂²×C₃	1	4	yes	complemented
201	#392	C₂²×C₃	1	4	yes	complemented
202	#390	C₂²×C₃	1	2	yes	—
203	#390	C₂²×C₃	1	2	yes	—
204	#390	C₂²×C₃	1	2	yes	—
205	#390	C₂²×C₃	1	2	yes	—
206	#390	C₂²×C₃	1	4	yes	—
207	#390	C₂²×C₃	1	2	yes	—
208	#390	C₂²×C₃	1	2	yes	—
209	#390	C₂²×C₃	1	2	yes	complemented
210	#390	C₂²×C₃	1	2	yes	complemented
211	#390	C₂²×C₃	1	4	yes	complemented
212	#389	C₂²×C₃	1	2	yes	complemented
213	#388	C₂²×C₃	1	4	yes	complemented
214	#388	C₂²×C₃	1	4	yes	complemented
215	#388	C₂²×C₃	1	4	yes	complemented
216	#386	C₂²×C₃	1	4	yes	—
217	#386	C₂²×C₃	1	4	yes	complemented
218	#382	C₂²×C₃	1	1	yes	characteristic, complemented
219	#379	C₂²×C₃	1	2	yes	—
220	#379	C₂²×C₃	1	2	yes	—
221	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
222	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
223	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
224	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
225	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
226	C₂⁴×C₃	—	2	4	no	—
227	C₂⁴×C₃	—	4	2	no	—
228	C₂⁴×C₃	—	4	2	no	—
229	C₂⁴×C₃	—	4	4	no	—
230	C₂⁴×C₃	—	4	4	no	—
231	C₂⁴×C₃	C₂⁴	1	4	yes	—
232	C₂⁴×C₃	C₂⁴	1	4	yes	—
233	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
234	C₂×C₃×Q₈	—	2	4	no	—
235	C₂×C₃×Q₈	—	4	1	no	—
236	C₂×C₃×D₄	—	2	8	no	—
237	C₂×C₃×D₄	—	2	4	no	—
238	C₂×C₃×D₄	—	2	4	no	—
239	C₂×C₃×D₄	—	2	4	no	—
240	C₂×C₃×D₄	—	2	4	no	—
241	C₂×C₃×D₄	—	2	4	no	—
242	C₂×C₃×D₄	—	2	4	no	—
243	C₂×C₃×D₄	—	2	4	no	—
244	C₂×C₃×D₄	—	2	8	no	—
245	C₂×C₃×D₄	—	2	8	no	—
246	C₂×C₃×D₄	—	4	2	no	—
247	C₂×C₃×D₄	—	4	2	no	—
248	C₂×C₃×D₄	—	4	16	no	—
249	C₂×C₃×D₄	—	4	4	no	—
250	C₂×C₃×D₄	—	4	4	no	—
251	C₂×C₃×D₄	—	4	4	no	—
252	C₂×C₃×D₄	—	4	4	no	—
253	C₂×C₃×D₄	—	4	4	no	—
254	C₂×C₃×D₄	—	4	4	no	—
255	C₂×C₃×D₄	—	4	4	no	—
256	C₂×C₃×D₄	—	4	4	no	—
257	C₂×C₃×D₄	—	4	4	no	—
258	C₂×C₃×D₄	—	4	4	no	—
259	C₂×C₃×D₄	—	4	4	no	—
260	C₂×C₃×D₄	—	4	4	no	—
261	C₂×C₃×D₄	—	4	4	no	—
262	C₂×C₃×D₄	—	4	2	no	—
263	C₂×C₃×D₄	—	4	2	no	—
264	C₂×C₃×D₄	—	4	4	no	—
265	C₂²×C₃×C₄	—	2	2	no	—
266	C₂²×C₃×C₄	—	2	2	no	—
267	C₂²×C₃×C₄	—	2	8	no	—
268	C₂²×C₃×C₄	—	4	4	no	—
269	C₂²×C₃×C₄	—	4	4	no	—
270	C₂²×C₃×C₄	#41	1	4	yes	—
271	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
272	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
273	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
274	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
275	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
276	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
277	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
278	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
279	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
280	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
281	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
282	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
283	C₃×C₄⋊C₄	—	2	4	no	—
284	C₃×C₄⋊C₄	—	2	4	no	—
285	C₃×C₄⋊C₄	—	2	4	no	—
286	C₃×C₄⋊C₄	—	2	4	no	—
287	C₃×C₄⋊C₄	—	2	4	no	—
288	C₃×C₄⋊C₄	—	4	1	no	—
289	C₃×C₄⋊C₄	—	4	1	no	—
290	C₃×C₄⋊C₄	—	4	2	no	—
291	C₃×C₄⋊C₄	—	4	1	no	—
292	C₃×C₄⋊C₄	—	4	4	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	—	2	8	no	—
297	C₃×C₂²⋊C₄	—	2	8	no	—
298	C₃×C₂²⋊C₄	—	2	8	no	—
299	C₃×C₂²⋊C₄	—	4	1	no	—
300	C₃×C₂²⋊C₄	—	4	1	no	—
301	C₃×C₂²⋊C₄	—	4	2	no	—
302	C₃×C₂²⋊C₄	—	4	4	no	—
303	C₃×C₂²⋊C₄	—	4	4	no	—
304	C₃×C₂²⋊C₄	—	4	4	no	—
305	C₃×C₂²⋊C₄	—	4	4	no	—
306	C₃×C₂²⋊C₄	—	4	4	no	—
307	C₃×C₂²⋊C₄	—	4	4	no	—
308	C₃×C₂²⋊C₄	—	4	4	no	—
309	C₃×C₂²⋊C₄	—	4	4	no	—
310	C₃×C₂²⋊C₄	—	4	4	no	—
311	C₃×C₂²⋊C₄	—	4	4	no	—
312	C₃×C₄²	—	2	2	no	—
313	C₃×C₄²	—	2	2	no	—
314	C₃×C₄²	—	2	4	no	—
315	C₃×C₄²	—	2	4	no	—
316	C₃×C₄²	—	4	2	no	—
317	C₃×C₄²	—	4	4	no	—
318	C₂⁵	C₂³×C₃	1	2	yes	—
319	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
320	C₂²×D₄	—	2	4	no	—
321	C₂²×D₄	—	4	2	no	—
322	C₂²×D₄	—	4	2	no	—
323	C₂²×D₄	C₂³×C₃	1	2	yes	—
324	C₂²×D₄	C₂³×C₃	1	2	yes	—
325	C₂²×D₄	C₂³×C₃	1	4	yes	—
326	C₂²×D₄	C₂³×C₃	1	4	yes	—
327	C₂²×D₄	C₂³×C₃	1	4	yes	—
328	C₂²×D₄	C₂³×C₃	1	2	yes	—
329	C₂²×D₄	C₂³×C₃	1	4	yes	—
330	C₂²×D₄	C₂³×C₃	1	4	yes	—
331	C₂²×D₄	C₂³×C₃	1	2	yes	—
332	C₂²×D₄	C₂³×C₃	1	2	yes	—
333	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₃	1	4	yes	—
335	#127	—	4	4	no	—
336	#127	—	4	4	no	—
337	#127	—	4	2	no	—
338	#124	—	4	8	no	—
339	#123	—	4	8	no	—
340	#121	—	2	8	no	—
341	#121	—	4	8	no	—
342	#121	—	4	8	no	—
343	#120	—	4	8	no	—
344	#120	—	4	8	no	—
345	C₄×Q₈	—	4	2	no	—
346	C₄×D₄	—	4	4	no	—
347	#117	—	4	2	no	—
348	#117	—	4	2	no	—
349	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
357	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
362	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
363	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
368	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
378	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₃	1	2	yes	—
381	C₂×C₄²	C₂³×C₃	1	2	yes	—
382	C₂×C₄²	C₂³×C₃	1	2	yes	—
383	C₂×C₄²	C₂³×C₃	1	4	yes	—
384	#95	C₂³×C₃	1	2	yes	—
385	#95	C₂³×C₃	1	2	yes	—
386	#95	C₂³×C₃	1	4	yes	—
387	#95	C₂³×C₃	1	4	yes	—
388	#95	C₂³×C₃	1	1	yes	characteristic
389	#95	C₂³×C₃	1	2	yes	—
390	#95	C₂³×C₃	1	2	yes	—
391	#95	C₂³×C₃	1	1	yes	characteristic
392	#95	C₂³×C₃	1	2	yes	—
393	#95	C₂³×C₃	1	2	yes	—
394	C₂³×C₃	—	2	2	no	—
395	C₂³×C₃	—	2	2	no	—
396	C₂³×C₃	—	2	1	no	—
397	C₂³×C₃	—	2	1	no	—
398	C₂³×C₃	—	2	4	no	—
399	C₂³×C₃	—	2	4	no	—
400	C₂³×C₃	—	2	4	no	—
401	C₂³×C₃	—	2	4	no	—
402	C₂³×C₃	—	2	4	no	—
403	C₂³×C₃	—	2	4	no	—
404	C₂³×C₃	—	2	4	no	—
405	C₂³×C₃	—	2	4	no	—
406	C₂³×C₃	—	2	4	no	—
407	C₂³×C₃	—	2	4	no	—
408	C₂³×C₃	—	2	4	no	—
409	C₂³×C₃	—	2	4	no	—
410	C₂³×C₃	—	2	4	no	—
411	C₂³×C₃	—	2	4	no	—
412	C₂³×C₃	—	4	8	no	—
413	C₂³×C₃	—	8	8	no	—
414	C₂³×C₃	—	8	4	no	—
415	C₂³×C₃	—	8	8	no	—
416	C₂³×C₃	—	8	4	no	—
417	C₂³×C₃	C₂×#41	1	2	yes	—
418	C₂³×C₃	C₂⁵	1	1	yes	characteristic
419	C₃×Q₈	—	4	4	no	—
420	C₃×D₄	—	4	8	no	—
421	C₃×D₄	—	4	8	no	—
422	C₃×D₄	—	4	8	no	—
423	C₃×D₄	—	8	8	no	—
424	C₃×D₄	—	8	8	no	—
425	C₃×D₄	—	8	8	no	—
426	C₃×D₄	—	8	4	no	—
427	C₃×D₄	—	8	8	no	—
428	C₃×D₄	—	8	4	no	—
429	C₃×D₄	—	8	8	no	—
430	C₂×C₃×C₄	—	2	2	no	—
431	C₂×C₃×C₄	—	2	2	no	—
432	C₂×C₃×C₄	—	2	1	no	—
433	C₂×C₃×C₄	—	2	2	no	—
434	C₂×C₃×C₄	—	2	2	no	—
435	C₂×C₃×C₄	—	2	1	no	—
436	C₂×C₃×C₄	—	2	8	no	—
437	C₂×C₃×C₄	—	2	4	no	—
438	C₂×C₃×C₄	—	2	2	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	2	no	—
444	C₂×C₃×C₄	—	2	4	no	—
445	C₂×C₃×C₄	—	2	4	no	—
446	C₂×C₃×C₄	—	2	4	no	—
447	C₂×C₃×C₄	—	2	4	no	—
448	C₂×C₃×C₄	—	2	2	no	—
449	C₂×C₃×C₄	—	2	2	no	—
450	C₂×C₃×C₄	—	2	2	no	—
451	C₂×C₃×C₄	—	2	2	no	—
452	C₂×C₃×C₄	—	2	4	no	—
453	C₂×C₃×C₄	—	2	2	no	—
454	C₂×C₃×C₄	—	2	2	no	—
455	C₂×C₃×C₄	—	2	2	no	—
456	C₂×C₃×C₄	—	2	2	no	—
457	C₂×C₃×C₄	—	8	8	no	—
458	C₂×C₃×C₄	C₂×#41	1	2	yes	—
459	C₂×C₃×C₄	C₂×#41	1	2	yes	—
460	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
461	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
462	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
463	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
464	C₂⁴	—	2	4	no	—
465	C₂⁴	—	4	2	no	—
466	C₂⁴	—	4	2	no	—
467	C₂⁴	—	4	4	no	—
468	C₂⁴	—	4	4	no	—
469	C₂⁴	C₂⁴×C₃	1	4	yes	—
470	C₂⁴	C₂⁴×C₃	1	4	yes	—
471	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
472	C₂×Q₈	—	2	4	no	—
473	C₂×Q₈	—	4	1	no	—
474	C₂×D₄	—	2	8	no	—
475	C₂×D₄	—	2	4	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	4	no	—
478	C₂×D₄	—	2	4	no	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	8	no	—
483	C₂×D₄	—	2	8	no	—
484	C₂×D₄	—	4	2	no	—
485	C₂×D₄	—	4	2	no	—
486	C₂×D₄	—	4	16	no	—
487	C₂×D₄	—	4	4	no	—
488	C₂×D₄	—	4	4	no	—
489	C₂×D₄	—	4	4	no	—
490	C₂×D₄	—	4	4	no	—
491	C₂×D₄	—	4	4	no	—
492	C₂×D₄	—	4	4	no	—
493	C₂×D₄	—	4	4	no	—
494	C₂×D₄	—	4	4	no	—
495	C₂×D₄	—	4	4	no	—
496	C₂×D₄	—	4	4	no	—
497	C₂×D₄	—	4	4	no	—
498	C₂×D₄	—	4	4	no	—
499	C₂×D₄	—	4	4	no	—
500	C₂×D₄	—	4	2	no	—
501	C₂×D₄	—	4	2	no	—
502	C₂×D₄	—	4	4	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	8	no	—
506	C₂²×C₄	—	4	4	no	—
507	C₂²×C₄	—	4	4	no	—
508	C₂²×C₄	C₃×#41	1	4	yes	—
509	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
510	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
511	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
512	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
513	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
514	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
515	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
516	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
517	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
518	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
519	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
521	C₄⋊C₄	—	2	4	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	4	no	—
525	C₄⋊C₄	—	2	4	no	—
526	C₄⋊C₄	—	4	1	no	—
527	C₄⋊C₄	—	4	1	no	—
528	C₄⋊C₄	—	4	2	no	—
529	C₄⋊C₄	—	4	1	no	—
530	C₄⋊C₄	—	4	4	no	—
531	C₂²⋊C₄	—	2	8	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	8	no	—
535	C₂²⋊C₄	—	2	8	no	—
536	C₂²⋊C₄	—	2	8	no	—
537	C₂²⋊C₄	—	4	1	no	—
538	C₂²⋊C₄	—	4	1	no	—
539	C₂²⋊C₄	—	4	2	no	—
540	C₂²⋊C₄	—	4	4	no	—
541	C₂²⋊C₄	—	4	4	no	—
542	C₂²⋊C₄	—	4	4	no	—
543	C₂²⋊C₄	—	4	4	no	—
544	C₂²⋊C₄	—	4	4	no	—
545	C₂²⋊C₄	—	4	4	no	—
546	C₂²⋊C₄	—	4	4	no	—
547	C₂²⋊C₄	—	4	4	no	—
548	C₂²⋊C₄	—	4	4	no	—
549	C₂²⋊C₄	—	4	4	no	—
550	C₄²	—	2	2	no	—
551	C₄²	—	2	2	no	—
552	C₄²	—	2	4	no	—
553	C₄²	—	2	4	no	—
554	C₄²	—	4	2	no	—
555	C₄²	—	4	4	no	—
556	C₂²×C₃	—	2	2	no	—
557	C₂²×C₃	—	2	4	no	—
558	C₂²×C₃	—	4	1	no	—
559	C₂²×C₃	—	4	2	no	—
560	C₂²×C₃	—	4	1	no	—
561	C₂²×C₃	—	4	4	no	—
562	C₂²×C₃	—	4	4	no	—
563	C₂²×C₃	—	4	4	no	—
564	C₂²×C₃	—	4	4	no	—
565	C₂²×C₃	—	4	4	no	—
566	C₂²×C₃	—	4	4	no	—
567	C₂²×C₃	—	4	4	no	—
568	C₂²×C₃	—	4	4	no	—
569	C₂²×C₃	—	4	4	no	—
570	C₂²×C₃	—	4	4	no	—
571	C₂²×C₃	—	4	4	no	—
572	C₂²×C₃	—	4	4	no	—
573	C₂²×C₃	—	4	4	no	—
574	C₂²×C₃	—	4	4	no	—
575	C₂²×C₃	—	8	16	no	—
576	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
577	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
578	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
579	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
580	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
581	C₃×C₄	—	2	2	no	—
582	C₃×C₄	—	2	4	no	—
583	C₃×C₄	—	2	4	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	2	no	—
589	C₃×C₄	—	4	1	no	—
590	C₃×C₄	—	4	1	no	—
591	C₃×C₄	—	4	2	no	—
592	C₃×C₄	#538	1	4	yes	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	4	no	—
598	C₂³	—	2	4	no	—
599	C₂³	—	2	4	no	—
600	C₂³	—	2	4	no	—
601	C₂³	—	2	4	no	—
602	C₂³	—	2	4	no	—
603	C₂³	—	2	4	no	—
604	C₂³	—	2	4	no	—
605	C₂³	—	2	4	no	—
606	C₂³	—	2	4	no	—
607	C₂³	—	2	4	no	—
608	C₂³	—	2	4	no	—
609	C₂³	—	2	4	no	—
610	C₂³	—	2	4	no	—
611	C₂³	—	4	8	no	—
612	C₂³	—	8	8	no	—
613	C₂³	—	8	4	no	—
614	C₂³	—	8	8	no	—
615	C₂³	—	8	4	no	—
616	C₂³	C₂×C₃×#41	1	2	yes	—
617	C₂³	C₂⁵×C₃	1	1	yes	characteristic
618	Q₈	—	4	4	no	—
619	D₄	—	4	8	no	—
620	D₄	—	4	8	no	—
621	D₄	—	4	8	no	—
622	D₄	—	8	8	no	—
623	D₄	—	8	8	no	—
624	D₄	—	8	8	no	—
625	D₄	—	8	4	no	—
626	D₄	—	8	8	no	—
627	D₄	—	8	4	no	—
628	D₄	—	8	8	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	8	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	2	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	2	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	8	8	no	—
657	C₂×C₄	C₂×C₃×#41	1	2	yes	—
658	C₂×C₄	C₂×C₃×#41	1	2	yes	—
659	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
660	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
661	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
662	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
663	C₂×C₃	—	4	2	no	—
664	C₂×C₃	—	8	4	no	—
665	C₂×C₃	—	8	4	no	—
666	C₂×C₃	C₂×#538	1	1	yes	characteristic
667	C₂×C₃	#3508	1	2	yes	—
668	C₂×C₃	#3537	1	1	yes	characteristic
669	C₂×C₃	#3543	1	2	yes	—
670	C₂×C₃	#3549	1	1	yes	characteristic
671	C₂²	—	2	2	no	—
672	C₂²	—	2	4	no	—
673	C₂²	—	4	1	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	1	no	—
676	C₂²	—	4	4	no	—
677	C₂²	—	4	4	no	—
678	C₂²	—	4	4	no	—
679	C₂²	—	4	4	no	—
680	C₂²	—	4	4	no	—
681	C₂²	—	4	4	no	—
682	C₂²	—	4	4	no	—
683	C₂²	—	4	4	no	—
684	C₂²	—	4	4	no	—
685	C₂²	—	4	4	no	—
686	C₂²	—	4	4	no	—
687	C₂²	—	4	4	no	—
688	C₂²	—	4	4	no	—
689	C₂²	—	4	4	no	—
690	C₂²	—	8	16	no	—
691	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
692	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
693	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
694	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
695	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
696	C₄	—	2	2	no	—
697	C₄	—	2	4	no	—
698	C₄	—	2	4	no	—
699	C₄	—	4	4	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	4	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	1	no	—
707	C₄	C₃×#538	1	4	yes	—
708	C₃	#42977	1	1	yes	characteristic, direct product factor, Sylow
709	C₂	—	4	2	no	—
710	C₂	—	8	4	no	—
711	C₂	—	8	4	no	—
712	C₂	C₂×C₃×#538	1	1	yes	characteristic
713	C₂	C₃×#3508	1	2	yes	—
714	C₂	C₃×#3537	1	1	yes	characteristic
715	C₂	C₃×#3543	1	2	yes	—
716	C₂	C₃×#3549	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
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×#2828	C₂	semidirect
2. C₃×#2678	C₂	semidirect
3. C₃×#2670	C₂	semidirect
4. C₃×#2668	C₂	semidirect
5. C₃×#2661	C₂	semidirect
6. C₃×#2619	C₂	semidirect
7. C₃×#2555	C₂	semidirect
8. C₃×#2548	C₂	semidirect
9. C₃×#2541	C₂	semidirect
10. C₃×#2513	C₂	semidirect
11. C₃×#2445	C₂	semidirect
12. C₃×#2433	C₂	semidirect
13. C₃×#2396	C₂	semidirect
14. C₃×#2363	C₂	semidirect
15. C₃×#2309	C₂	semidirect
16. #42977	C₃	direct (N × H)
20. C₂×C₃×#127	C₂²	semidirect
21. C₂×C₃×#124	C₂²	semidirect
22. C₂×C₃×#123	C₂²	semidirect
24. C₂×C₃×#121	C₂²	semidirect
25. C₂×C₃×#121	C₂²	semidirect
28. C₂×C₃×C₄×Q₈	C₂²	semidirect
29. C₂×C₃×C₄×D₄	C₂²	semidirect
32. C₃×#400	C₂²	semidirect
34. C₃×#398	C₂²	semidirect
35. C₃×#397	C₂²	semidirect
36. C₃×#397	C₂²	semidirect
38. C₃×#395	C₂²	semidirect
39. C₃×#394	C₂²	semidirect
40. C₃×#394	C₂²	semidirect
41. C₃×#394	C₂²	semidirect
42. C₃×#394	C₂²	semidirect
43. C₃×#394	C₂²	semidirect
44. C₃×#394	C₂²	semidirect
50. C₃×#392	C₂²	semidirect
51. C₃×#392	C₂²	semidirect
59. C₃×#390	C₂²	semidirect
60. C₃×#390	C₂²	semidirect
61. C₃×#390	C₂²	semidirect
62. C₃×#389	C₂²	semidirect
63. C₃×#388	C₂²	semidirect
64. C₃×#388	C₂²	semidirect
65. C₃×#388	C₂²	semidirect
67. C₃×#386	C₂²	semidirect
68. C₃×#382	C₂²	semidirect
71. C₃×C₄×C₄⋊C₄	C₂²	semidirect
72. C₃×C₄×C₄⋊C₄	C₂²	semidirect
73. C₃×C₄×C₄⋊C₄	C₂²	semidirect
75. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
76. #2828	C₂×C₃	semidirect
77. #2678	C₂×C₃	semidirect
78. #2670	C₂×C₃	semidirect
79. #2668	C₂×C₃	semidirect
80. #2661	C₂×C₃	semidirect
81. #2619	C₂×C₃	semidirect
82. #2555	C₂×C₃	semidirect
83. #2548	C₂×C₃	semidirect
84. #2541	C₂×C₃	semidirect
85. #2513	C₂×C₃	semidirect
86. #2445	C₂×C₃	semidirect
87. #2433	C₂×C₃	semidirect
88. #2396	C₂×C₃	semidirect
89. #2363	C₂×C₃	semidirect
90. #2309	C₂×C₃	semidirect
170. C₂×#127	C₂²×C₃	semidirect
171. C₂×#124	C₂²×C₃	semidirect
172. C₂×#123	C₂²×C₃	semidirect
174. C₂×#121	C₂²×C₃	semidirect
175. C₂×#121	C₂²×C₃	semidirect
178. C₂×C₄×Q₈	C₂²×C₃	semidirect
179. C₂×C₄×D₄	C₂²×C₃	semidirect
182. #400	C₂²×C₃	semidirect
184. #398	C₂²×C₃	semidirect
185. #397	C₂²×C₃	semidirect
186. #397	C₂²×C₃	semidirect
188. #395	C₂²×C₃	semidirect
189. #394	C₂²×C₃	semidirect
190. #394	C₂²×C₃	semidirect
191. #394	C₂²×C₃	semidirect
192. #394	C₂²×C₃	semidirect
193. #394	C₂²×C₃	semidirect
194. #394	C₂²×C₃	semidirect
200. #392	C₂²×C₃	semidirect
201. #392	C₂²×C₃	semidirect
209. #390	C₂²×C₃	semidirect
210. #390	C₂²×C₃	semidirect
211. #390	C₂²×C₃	semidirect
212. #389	C₂²×C₃	semidirect
213. #388	C₂²×C₃	semidirect
214. #388	C₂²×C₃	semidirect
215. #388	C₂²×C₃	semidirect
217. #386	C₂²×C₃	semidirect
218. #382	C₂²×C₃	semidirect
221. C₄×C₄⋊C₄	C₂²×C₃	semidirect
222. C₄×C₄⋊C₄	C₂²×C₃	semidirect
223. C₄×C₄⋊C₄	C₂²×C₃	semidirect
225. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
708. C₃	#42977	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×#2828	2
C₃×#2678	2
C₃×#2670	2
C₃×#2668	2
C₃×#2661	2
C₃×#2619	2
C₃×#2555	2
C₃×#2548	2
C₃×#2541	2
C₃×#2513	2
C₃×#2445	2
C₃×#2433	2
C₃×#2396	2
C₃×#2363	2
C₃×#2309	2
#42977	3

Subgroups — C3×#42977 #10661584

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#42977 #10661584