Subgroups — C₃×#60797 #10679404

Order 768.

2062 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3225	C₂	1	4	yes	maximal, complemented
4	C₃×#3224	C₂	1	4	yes	maximal, complemented
5	C₃×#3223	C₂	1	2	yes	maximal, complemented
6	C₃×#3222	C₂	1	2	yes	maximal, complemented
7	C₃×#3221	C₂	1	2	yes	maximal, complemented
8	C₃×#3220	C₂	1	2	yes	maximal, complemented
9	C₃×#3150	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3035	C₂	1	4	yes	maximal, complemented
14	C₃×#3002	C₂	1	4	yes	maximal, complemented
15	C₂×C₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
16	#60797	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂²×C₃×#41	C₂²	1	2	yes	—
18	C₂×C₃×#135	C₂²	1	4	yes	complemented
19	C₂×C₃×#135	C₂²	1	4	yes	complemented
20	C₃×#542	C₂²	1	4	yes	complemented
21	C₃×#541	C₂²	1	2	yes	complemented
22	C₃×#540	C₂²	1	2	yes	complemented
23	C₃×#539	—	2	2	no	—
24	C₃×#538	—	2	2	no	—
25	C₃×#537	—	2	2	no	—
26	C₃×#536	C₂²	1	2	yes	—
27	C₃×#536	C₂²	1	2	yes	—
28	C₃×#535	C₂²	1	2	yes	—
29	C₃×#535	C₂²	1	2	yes	—
30	C₃×#534	—	2	2	no	—
31	C₃×#533	C₂²	1	1	yes	characteristic, complemented
32	C₃×#532	C₂²	1	1	yes	characteristic
33	C₃×#532	C₂²	1	1	yes	characteristic
34	C₃×#532	C₂²	1	2	yes	—
35	C₃×#532	C₂²	1	1	yes	characteristic, complemented
36	C₃×#529	—	2	4	no	—
37	C₃×#525	—	2	4	no	—
38	C₃×#525	C₂²	1	2	yes	—
39	C₃×C₄×#41	C₂²	1	2	yes	complemented
40	C₂×C₃×#117	C₂²	1	1	yes	characteristic
41	C₃×#497	C₂²	1	2	yes	complemented
42	C₃×#497	C₂²	1	2	yes	complemented
43	C₃×#496	C₂²	1	2	yes	complemented
44	C₃×#496	C₂²	1	2	yes	complemented
45	C₃×#495	C₂²	1	4	yes	complemented
46	C₃×#494	C₂²	1	1	yes	characteristic, complemented
47	C₃×#493	C₂²	1	1	yes	characteristic, complemented
48	C₃×#492	C₂²	1	1	yes	characteristic, complemented
49	C₃×#492	C₂²	1	1	yes	characteristic, complemented
50	C₃×#491	C₂²	1	2	yes	complemented
51	C₃×#490	C₂²	1	2	yes	complemented
52	C₃×#489	C₂²	1	4	yes	complemented
53	C₃×#488	C₂²	1	2	yes	complemented
54	C₃×#488	C₂²	1	2	yes	complemented
55	C₃×#487	C₂²	1	2	yes	complemented
56	C₃×#486	C₂²	1	2	yes	complemented
57	C₃×#464	C₂²	1	4	yes	complemented
58	C₃×#464	C₂²	1	4	yes	complemented
59	C₃×#463	C₂²	1	4	yes	complemented
60	C₃×#463	C₂²	1	4	yes	complemented
61	C₃×#462	C₂²	1	4	yes	complemented
62	C₃×#461	C₂²	1	4	yes	complemented
63	C₃×#460	C₂²	1	4	yes	complemented
64	C₃×#459	C₂²	1	4	yes	complemented
65	C₃×#452	C₂²	1	4	yes	—
66	C₃×#452	C₂²	1	4	yes	—
67	C₃×#451	C₂²	1	4	yes	complemented
68	C₃×#450	C₂²	1	4	yes	complemented
69	C₃×#449	C₂²	1	4	yes	—
70	C₃×#449	C₂²	1	4	yes	—
71	C₃×#448	C₂²	1	4	yes	complemented
72	C₃×#447	C₂²	1	4	yes	complemented
73	C₃×#433	C₂²	1	2	yes	complemented
74	C₃×#433	C₂²	1	2	yes	complemented
75	C₃×#433	C₂²	1	4	yes	complemented
76	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	complemented
77	C₃×#416	C₂²	1	4	yes	complemented
78	C₃×#416	C₂²	1	4	yes	complemented
79	C₂×C₃×C₂²⋊C₈	C₂²	1	2	yes	—
80	C₂×C₃×#97	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
82	#3455	C₂×C₃	1	1	yes	characteristic, complemented
83	#3449	C₂×C₃	1	1	yes	characteristic, complemented
84	#3225	C₂×C₃	1	4	yes	complemented
85	#3224	C₂×C₃	1	4	yes	complemented
86	#3223	C₂×C₃	1	2	yes	complemented
87	#3222	C₂×C₃	1	2	yes	complemented
88	#3221	C₂×C₃	1	2	yes	complemented
89	#3220	C₂×C₃	1	2	yes	complemented
90	#3150	C₂×C₃	1	1	yes	characteristic, complemented
91	#3147	C₂×C₃	1	1	yes	characteristic, complemented
92	#3135	C₂×C₃	1	1	yes	characteristic, complemented
93	#3131	C₂×C₃	1	1	yes	characteristic, complemented
94	#3035	C₂×C₃	1	4	yes	complemented
95	#3002	C₂×C₃	1	4	yes	complemented
96	C₂×#433	C₂×C₃	1	1	yes	characteristic, complemented
97	C₂×C₃×#41	—	2	2	no	—
98	C₂×C₃×#41	—	2	2	no	—
99	C₂×C₃×#41	—	4	8	no	—
100	C₂×C₃×#41	C₂³	1	2	yes	—
101	C₂×C₃×#41	C₂³	1	2	yes	—
102	C₂×C₃×#41	C₂³	1	2	yes	—
103	C₂×C₃×#41	C₂³	1	2	yes	—
104	C₂×C₃×#41	C₂³	1	2	yes	—
105	C₂²×C₃×Q₈	C₂³	1	2	yes	—
106	C₂²×C₃×D₄	—	2	2	no	—
107	C₂²×C₃×D₄	C₂³	1	2	yes	—
108	C₂³×C₃×C₄	—	2	2	no	—
109	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
110	C₃×#135	—	4	8	no	—
111	C₃×#135	—	4	8	no	—
112	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
113	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
114	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
115	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
116	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
117	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
118	C₂×C₃×D₈	C₂³	1	4	yes	—
119	C₂×C₃×D₈	C₂³	1	4	yes	—
120	C₂²×C₃×C₈	C₂³	1	2	yes	—
121	C₂²×C₃×C₈	C₂³	1	2	yes	—
122	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
123	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
127	C₃×#127	C₂³	1	2	yes	—
128	C₃×#127	C₂³	1	1	yes	characteristic
129	C₃×#127	C₂³	1	1	yes	characteristic
130	C₃×#127	C₂³	1	1	yes	characteristic
131	C₃×#126	—	2	4	no	—
132	C₃×#126	—	2	4	no	—
133	C₃×#125	—	2	4	no	—
134	C₃×#125	C₂³	1	2	yes	—
135	C₃×#124	—	2	4	no	—
136	C₃×#124	C₂³	1	2	yes	—
137	C₃×#124	C₂³	1	2	yes	—
138	C₃×#124	C₂³	1	2	yes	—
139	C₃×#124	C₂³	1	2	yes	—
140	C₃×#124	C₂³	1	2	yes	—
141	C₃×#123	—	2	2	no	—
142	C₃×#123	—	2	4	no	—
143	C₃×#123	—	2	4	no	—
144	C₃×#123	—	2	4	no	—
145	C₃×#123	—	2	4	no	—
146	C₃×C₂²⋊Q₈	—	2	2	no	—
147	C₃×C₂²⋊Q₈	—	2	4	no	—
148	C₃×C₂²⋊Q₈	—	2	4	no	—
149	C₃×C₂²⋊Q₈	—	2	4	no	—
150	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
151	C₃×#121	—	2	4	no	—
152	C₃×#121	—	2	2	no	—
153	C₃×#121	—	2	2	no	—
154	C₃×#121	—	2	2	no	—
155	C₃×#121	—	2	4	no	—
156	C₃×#121	—	2	4	no	—
157	C₃×#121	—	2	4	no	—
158	C₃×#121	C₂³	1	4	yes	—
159	C₃×#120	—	2	2	no	—
160	C₃×#120	—	2	4	no	—
161	C₃×#120	—	2	4	no	—
162	C₃×C₄×Q₈	—	2	2	no	—
163	C₃×C₄×Q₈	C₂³	1	4	yes	—
164	C₃×C₄×D₄	—	2	4	no	—
165	C₃×C₄×D₄	—	2	4	no	—
166	C₃×C₄×D₄	—	2	4	no	—
167	C₃×C₄×D₄	—	2	2	no	—
168	C₃×C₄×D₄	—	2	2	no	—
169	C₃×C₄×D₄	—	2	2	no	—
170	C₃×C₄×D₄	C₂³	1	4	yes	—
171	C₃×#117	—	2	2	no	—
172	C₃×#117	D₄	1	4	yes	—
173	C₃×#117	C₂³	1	2	yes	—
174	C₃×#117	C₂³	1	2	yes	—
175	C₃×#117	C₂³	1	2	yes	—
176	C₂×C₃×C₄⋊C₄	D₄	1	2	yes	—
177	C₂×C₃×C₂²⋊C₄	D₄	1	2	yes	—
178	C₂×C₃×C₄²	—	2	2	no	—
179	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
181	C₃×C₄⋊C₈	C₂³	1	4	yes	—
182	C₃×C₄⋊C₈	C₂³	1	4	yes	—
183	C₃×#103	C₂³	1	4	yes	—
184	C₃×#103	C₂³	1	4	yes	—
185	C₃×#103	C₂³	1	4	yes	—
186	C₃×#103	C₂³	1	4	yes	—
187	C₃×#102	C₂³	1	4	yes	—
188	C₃×#102	C₂³	1	4	yes	—
189	C₃×#102	C₂³	1	4	yes	—
190	C₃×#102	C₂³	1	4	yes	—
191	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
192	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
193	C₃×#97	C₂³	1	2	yes	—
194	C₃×#97	C₂³	1	2	yes	—
195	C₃×C₄×C₈	C₂³	1	2	yes	—
196	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
197	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
198	C₂²×#41	C₂²×C₃	1	2	yes	—
199	C₂×#135	C₂²×C₃	1	4	yes	complemented
200	C₂×#135	C₂²×C₃	1	4	yes	complemented
201	#542	C₂²×C₃	1	4	yes	complemented
202	#541	C₂²×C₃	1	2	yes	complemented
203	#540	C₂²×C₃	1	2	yes	complemented
204	#539	—	2	2	no	—
205	#538	—	2	2	no	—
206	#537	—	2	2	no	—
207	#536	C₂²×C₃	1	2	yes	—
208	#536	C₂²×C₃	1	2	yes	—
209	#535	C₂²×C₃	1	2	yes	—
210	#535	C₂²×C₃	1	2	yes	—
211	#534	—	2	2	no	—
212	#533	C₂²×C₃	1	1	yes	characteristic, complemented
213	#532	C₂²×C₃	1	1	yes	characteristic
214	#532	C₂²×C₃	1	1	yes	characteristic
215	#532	C₂²×C₃	1	2	yes	—
216	#532	C₂²×C₃	1	1	yes	characteristic, complemented
217	#529	—	2	4	no	—
218	#525	—	2	4	no	—
219	#525	C₂²×C₃	1	2	yes	—
220	C₄×#41	C₂²×C₃	1	2	yes	complemented
221	C₂×#117	C₂²×C₃	1	1	yes	characteristic
222	#497	C₂²×C₃	1	2	yes	complemented
223	#497	C₂²×C₃	1	2	yes	complemented
224	#496	C₂²×C₃	1	2	yes	complemented
225	#496	C₂²×C₃	1	2	yes	complemented
226	#495	C₂²×C₃	1	4	yes	complemented
227	#494	C₂²×C₃	1	1	yes	characteristic, complemented
228	#493	C₂²×C₃	1	1	yes	characteristic, complemented
229	#492	C₂²×C₃	1	1	yes	characteristic, complemented
230	#492	C₂²×C₃	1	1	yes	characteristic, complemented
231	#491	C₂²×C₃	1	2	yes	complemented
232	#490	C₂²×C₃	1	2	yes	complemented
233	#489	C₂²×C₃	1	4	yes	complemented
234	#488	C₂²×C₃	1	2	yes	complemented
235	#488	C₂²×C₃	1	2	yes	complemented
236	#487	C₂²×C₃	1	2	yes	complemented
237	#486	C₂²×C₃	1	2	yes	complemented
238	#464	C₂²×C₃	1	4	yes	complemented
239	#464	C₂²×C₃	1	4	yes	complemented
240	#463	C₂²×C₃	1	4	yes	complemented
241	#463	C₂²×C₃	1	4	yes	complemented
242	#462	C₂²×C₃	1	4	yes	complemented
243	#461	C₂²×C₃	1	4	yes	complemented
244	#460	C₂²×C₃	1	4	yes	complemented
245	#459	C₂²×C₃	1	4	yes	complemented
246	#452	C₂²×C₃	1	4	yes	—
247	#452	C₂²×C₃	1	4	yes	—
248	#451	C₂²×C₃	1	4	yes	complemented
249	#450	C₂²×C₃	1	4	yes	complemented
250	#449	C₂²×C₃	1	4	yes	—
251	#449	C₂²×C₃	1	4	yes	—
252	#448	C₂²×C₃	1	4	yes	complemented
253	#447	C₂²×C₃	1	4	yes	complemented
254	#433	C₂²×C₃	1	2	yes	complemented
255	#433	C₂²×C₃	1	2	yes	complemented
256	#433	C₂²×C₃	1	4	yes	complemented
257	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
258	#416	C₂²×C₃	1	4	yes	complemented
259	#416	C₂²×C₃	1	4	yes	complemented
260	C₂×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
261	C₂×#97	C₂²×C₃	1	1	yes	characteristic, complemented
262	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
263	C₂⁴×C₃	—	2	2	no	—
264	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
265	C₃×#41	—	2	8	no	—
266	C₃×#41	—	2	8	no	—
267	C₃×#41	—	2	8	no	—
268	C₃×#41	—	4	4	no	—
269	C₃×#41	—	4	4	no	—
270	C₃×#41	—	4	8	no	—
271	C₃×#41	—	4	8	no	—
272	C₂×C₃×Q₈	—	2	2	no	—
273	C₂×C₃×Q₈	—	2	2	no	—
274	C₂×C₃×Q₈	—	4	4	no	—
275	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
276	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
277	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
278	C₂×C₃×D₄	—	2	2	no	—
279	C₂×C₃×D₄	—	2	2	no	—
280	C₂×C₃×D₄	—	2	2	no	—
281	C₂×C₃×D₄	—	2	2	no	—
282	C₂×C₃×D₄	—	2	2	no	—
283	C₂×C₃×D₄	—	2	4	no	—
284	C₂×C₃×D₄	—	2	2	no	—
285	C₂×C₃×D₄	—	2	4	no	—
286	C₂×C₃×D₄	—	2	2	no	—
287	C₂×C₃×D₄	—	2	2	no	—
288	C₂×C₃×D₄	—	2	2	no	—
289	C₂×C₃×D₄	—	4	4	no	—
290	C₂×C₃×D₄	—	4	8	no	—
291	C₂×C₃×D₄	C₂⁴	1	2	yes	—
292	C₂×C₃×D₄	C₂⁴	1	2	yes	—
293	C₂×C₃×D₄	C₂⁴	1	2	yes	—
294	C₂²×C₃×C₄	—	2	4	no	—
295	C₂²×C₃×C₄	—	2	2	no	—
296	C₂²×C₃×C₄	—	2	2	no	—
297	C₂²×C₃×C₄	—	2	2	no	—
298	C₂²×C₃×C₄	—	2	2	no	—
299	C₂²×C₃×C₄	—	2	2	no	—
300	C₂²×C₃×C₄	—	2	2	no	—
301	C₂²×C₃×C₄	—	2	4	no	—
302	C₂²×C₃×C₄	—	4	8	no	—
303	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
305	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
306	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
307	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
308	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
309	C₃×Q₁₆	—	4	4	no	—
310	C₃×Q₁₆	—	4	4	no	—
311	C₃×SD₁₆	—	4	4	no	—
312	C₃×SD₁₆	—	4	4	no	—
313	C₃×SD₁₆	—	4	4	no	—
314	C₃×SD₁₆	—	4	4	no	—
315	C₃×D₈	—	4	4	no	—
316	C₃×D₈	—	4	4	no	—
317	C₂×C₃×C₈	—	2	4	no	—
318	C₂×C₃×C₈	—	2	4	no	—
319	C₂×C₃×C₈	C₂⁴	1	2	yes	—
320	C₂×C₃×C₈	C₂⁴	1	2	yes	—
321	C₂×C₃×C₈	C₂⁴	1	4	yes	—
322	C₃×C₄⋊C₄	—	2	4	no	—
323	C₃×C₄⋊C₄	—	2	4	no	—
324	C₃×C₄⋊C₄	—	2	2	no	—
325	C₃×C₄⋊C₄	—	2	2	no	—
326	C₃×C₄⋊C₄	—	2	2	no	—
327	C₃×C₄⋊C₄	—	2	4	no	—
328	C₃×C₄⋊C₄	—	2	4	no	—
329	C₃×C₄⋊C₄	—	2	2	no	—
330	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
331	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
332	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
333	C₃×C₂²⋊C₄	—	2	2	no	—
334	C₃×C₂²⋊C₄	—	2	4	no	—
335	C₃×C₂²⋊C₄	—	2	4	no	—
336	C₃×C₂²⋊C₄	—	2	4	no	—
337	C₃×C₂²⋊C₄	—	2	4	no	—
338	C₃×C₂²⋊C₄	—	2	4	no	—
339	C₃×C₂²⋊C₄	—	2	4	no	—
340	C₃×C₂²⋊C₄	—	2	4	no	—
341	C₃×C₂²⋊C₄	—	2	4	no	—
342	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
343	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
344	C₃×C₄²	—	2	4	no	—
345	C₃×C₄²	—	2	2	no	—
346	C₃×C₄²	C₂×D₄	1	2	yes	—
347	C₃×C₄²	C₂×D₄	1	2	yes	—
348	C₃×C₄²	C₂⁴	1	1	yes	characteristic
349	C₃×C₄²	C₂⁴	1	1	yes	characteristic
350	C₃×C₄²	C₂⁴	1	2	yes	—
351	C₂×#41	—	2	2	no	—
352	C₂×#41	—	2	2	no	—
353	C₂×#41	—	4	8	no	—
354	C₂×#41	C₂³×C₃	1	2	yes	—
355	C₂×#41	C₂³×C₃	1	2	yes	—
356	C₂×#41	C₂³×C₃	1	2	yes	—
357	C₂×#41	C₂³×C₃	1	2	yes	—
358	C₂×#41	C₂³×C₃	1	2	yes	—
359	C₂²×Q₈	C₂³×C₃	1	2	yes	—
360	C₂²×D₄	—	2	2	no	—
361	C₂²×D₄	C₂³×C₃	1	2	yes	—
362	C₂³×C₄	—	2	2	no	—
363	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
364	#135	—	4	8	no	—
365	#135	—	4	8	no	—
366	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
367	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
368	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
369	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
370	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
371	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
372	C₂×D₈	C₂³×C₃	1	4	yes	—
373	C₂×D₈	C₂³×C₃	1	4	yes	—
374	C₂²×C₈	C₂³×C₃	1	2	yes	—
375	C₂²×C₈	C₂³×C₃	1	2	yes	—
376	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
377	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
378	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
379	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
380	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
381	#127	C₂³×C₃	1	2	yes	—
382	#127	C₂³×C₃	1	1	yes	characteristic
383	#127	C₂³×C₃	1	1	yes	characteristic
384	#127	C₂³×C₃	1	1	yes	characteristic
385	#126	—	2	4	no	—
386	#126	—	2	4	no	—
387	#125	—	2	4	no	—
388	#125	C₂³×C₃	1	2	yes	—
389	#124	—	2	4	no	—
390	#124	C₂³×C₃	1	2	yes	—
391	#124	C₂³×C₃	1	2	yes	—
392	#124	C₂³×C₃	1	2	yes	—
393	#124	C₂³×C₃	1	2	yes	—
394	#124	C₂³×C₃	1	2	yes	—
395	#123	—	2	2	no	—
396	#123	—	2	4	no	—
397	#123	—	2	4	no	—
398	#123	—	2	4	no	—
399	#123	—	2	4	no	—
400	C₂²⋊Q₈	—	2	2	no	—
401	C₂²⋊Q₈	—	2	4	no	—
402	C₂²⋊Q₈	—	2	4	no	—
403	C₂²⋊Q₈	—	2	4	no	—
404	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
405	#121	—	2	4	no	—
406	#121	—	2	2	no	—
407	#121	—	2	2	no	—
408	#121	—	2	2	no	—
409	#121	—	2	4	no	—
410	#121	—	2	4	no	—
411	#121	—	2	4	no	—
412	#121	C₂³×C₃	1	4	yes	—
413	#120	—	2	2	no	—
414	#120	—	2	4	no	—
415	#120	—	2	4	no	—
416	C₄×Q₈	—	2	2	no	—
417	C₄×Q₈	C₂³×C₃	1	4	yes	—
418	C₄×D₄	—	2	4	no	—
419	C₄×D₄	—	2	4	no	—
420	C₄×D₄	—	2	4	no	—
421	C₄×D₄	—	2	2	no	—
422	C₄×D₄	—	2	2	no	—
423	C₄×D₄	—	2	2	no	—
424	C₄×D₄	C₂³×C₃	1	4	yes	—
425	#117	—	2	2	no	—
426	#117	C₃×D₄	1	4	yes	—
427	#117	C₂³×C₃	1	2	yes	—
428	#117	C₂³×C₃	1	2	yes	—
429	#117	C₂³×C₃	1	2	yes	—
430	C₂×C₄⋊C₄	C₃×D₄	1	2	yes	—
431	C₂×C₂²⋊C₄	C₃×D₄	1	2	yes	—
432	C₂×C₄²	—	2	2	no	—
433	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
435	C₄⋊C₈	C₂³×C₃	1	4	yes	—
436	C₄⋊C₈	C₂³×C₃	1	4	yes	—
437	#103	C₂³×C₃	1	4	yes	—
438	#103	C₂³×C₃	1	4	yes	—
439	#103	C₂³×C₃	1	4	yes	—
440	#103	C₂³×C₃	1	4	yes	—
441	#102	C₂³×C₃	1	4	yes	—
442	#102	C₂³×C₃	1	4	yes	—
443	#102	C₂³×C₃	1	4	yes	—
444	#102	C₂³×C₃	1	4	yes	—
445	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
446	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
447	#97	C₂³×C₃	1	2	yes	—
448	#97	C₂³×C₃	1	2	yes	—
449	C₄×C₈	C₂³×C₃	1	2	yes	—
450	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
451	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
452	C₂³×C₃	—	2	2	no	—
453	C₂³×C₃	—	2	2	no	—
454	C₂³×C₃	—	2	2	no	—
455	C₂³×C₃	—	2	2	no	—
456	C₂³×C₃	—	4	2	no	—
457	C₂³×C₃	—	4	4	no	—
458	C₂³×C₃	—	8	4	no	—
459	C₂³×C₃	C₂²×D₄	1	2	yes	—
460	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
461	C₃×Q₈	—	2	4	no	—
462	C₃×Q₈	—	2	4	no	—
463	C₃×Q₈	—	2	4	no	—
464	C₃×Q₈	—	4	4	no	—
465	C₃×Q₈	—	8	2	no	—
466	C₃×D₄	—	2	4	no	—
467	C₃×D₄	—	2	4	no	—
468	C₃×D₄	—	2	4	no	—
469	C₃×D₄	—	4	4	no	—
470	C₃×D₄	—	4	4	no	—
471	C₃×D₄	—	4	4	no	—
472	C₃×D₄	—	4	4	no	—
473	C₃×D₄	—	4	4	no	—
474	C₃×D₄	—	4	4	no	—
475	C₃×D₄	—	8	4	no	—
476	C₃×D₄	—	8	2	no	—
477	C₃×D₄	—	8	2	no	—
478	C₃×D₄	—	8	2	no	—
479	C₃×D₄	—	8	4	no	—
480	C₂×C₃×C₄	—	2	2	no	—
481	C₂×C₃×C₄	—	2	4	no	—
482	C₂×C₃×C₄	—	2	4	no	—
483	C₂×C₃×C₄	—	2	2	no	—
484	C₂×C₃×C₄	—	2	4	no	—
485	C₂×C₃×C₄	—	2	2	no	—
486	C₂×C₃×C₄	—	2	2	no	—
487	C₂×C₃×C₄	—	4	2	no	—
488	C₂×C₃×C₄	—	4	2	no	—
489	C₂×C₃×C₄	—	4	4	no	—
490	C₂×C₃×C₄	—	4	4	no	—
491	C₂×C₃×C₄	—	4	4	no	—
492	C₂×C₃×C₄	—	4	4	no	—
493	C₂×C₃×C₄	—	4	4	no	—
494	C₂×C₃×C₄	—	4	4	no	—
495	C₂×C₃×C₄	—	8	4	no	—
496	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
497	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
498	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
499	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
500	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
502	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
503	C₃×C₈	—	2	2	no	—
504	C₃×C₈	—	2	4	no	—
505	C₃×C₈	—	2	2	no	—
506	C₂⁴	—	2	2	no	—
507	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
508	#41	—	2	8	no	—
509	#41	—	2	8	no	—
510	#41	—	2	8	no	—
511	#41	—	4	4	no	—
512	#41	—	4	4	no	—
513	#41	—	4	8	no	—
514	#41	—	4	8	no	—
515	C₂×Q₈	—	2	2	no	—
516	C₂×Q₈	—	2	2	no	—
517	C₂×Q₈	—	4	4	no	—
518	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
519	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
520	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
521	C₂×D₄	—	2	2	no	—
522	C₂×D₄	—	2	2	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	4	4	no	—
533	C₂×D₄	—	4	8	no	—
534	C₂×D₄	C₂⁴×C₃	1	2	yes	—
535	C₂×D₄	C₂⁴×C₃	1	2	yes	—
536	C₂×D₄	C₂⁴×C₃	1	2	yes	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	4	8	no	—
546	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
547	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
548	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
549	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
552	Q₁₆	—	4	4	no	—
553	Q₁₆	—	4	4	no	—
554	SD₁₆	—	4	4	no	—
555	SD₁₆	—	4	4	no	—
556	SD₁₆	—	4	4	no	—
557	SD₁₆	—	4	4	no	—
558	D₈	—	4	4	no	—
559	D₈	—	4	4	no	—
560	C₂×C₈	—	2	4	no	—
561	C₂×C₈	—	2	4	no	—
562	C₂×C₈	C₂⁴×C₃	1	2	yes	—
563	C₂×C₈	C₂⁴×C₃	1	2	yes	—
564	C₂×C₈	C₂⁴×C₃	1	4	yes	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
574	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
575	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
586	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
587	C₄²	—	2	2	no	—
588	C₄²	—	2	4	no	—
589	C₄²	C₂×C₃×D₄	1	2	yes	—
590	C₄²	C₂×C₃×D₄	1	2	yes	—
591	C₄²	C₂⁴×C₃	1	1	yes	characteristic
592	C₄²	C₂⁴×C₃	1	1	yes	characteristic
593	C₄²	C₂⁴×C₃	1	2	yes	—
594	C₂²×C₃	—	2	2	no	—
595	C₂²×C₃	—	2	4	no	—
596	C₂²×C₃	—	2	2	no	—
597	C₂²×C₃	—	4	4	no	—
598	C₂²×C₃	—	4	4	no	—
599	C₂²×C₃	—	4	4	no	—
600	C₂²×C₃	—	4	2	no	—
601	C₂²×C₃	—	4	2	no	—
602	C₂²×C₃	—	4	2	no	—
603	C₂²×C₃	—	8	2	no	—
604	C₂²×C₃	—	8	8	no	—
605	C₂²×C₃	#535	1	2	yes	—
606	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
607	C₃×C₄	—	2	4	no	—
608	C₃×C₄	—	2	2	no	—
609	C₃×C₄	—	2	2	no	—
610	C₃×C₄	—	2	2	no	—
611	C₃×C₄	—	4	4	no	—
612	C₃×C₄	—	4	2	no	—
613	C₃×C₄	—	4	2	no	—
614	C₃×C₄	—	4	2	no	—
615	C₃×C₄	#535	1	2	yes	—
616	C₃×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	4	2	no	—
622	C₂³	—	4	4	no	—
623	C₂³	—	8	4	no	—
624	C₂³	C₂²×C₃×D₄	1	2	yes	—
625	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
626	Q₈	—	2	4	no	—
627	Q₈	—	2	4	no	—
628	Q₈	—	2	4	no	—
629	Q₈	—	4	4	no	—
630	Q₈	—	8	2	no	—
631	D₄	—	2	4	no	—
632	D₄	—	2	4	no	—
633	D₄	—	2	4	no	—
634	D₄	—	4	4	no	—
635	D₄	—	4	4	no	—
636	D₄	—	4	4	no	—
637	D₄	—	4	4	no	—
638	D₄	—	4	4	no	—
639	D₄	—	4	4	no	—
640	D₄	—	8	4	no	—
641	D₄	—	8	2	no	—
642	D₄	—	8	2	no	—
643	D₄	—	8	2	no	—
644	D₄	—	8	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	4	2	no	—
653	C₂×C₄	—	4	2	no	—
654	C₂×C₄	—	4	4	no	—
655	C₂×C₄	—	4	4	no	—
656	C₂×C₄	—	4	4	no	—
657	C₂×C₄	—	4	4	no	—
658	C₂×C₄	—	4	4	no	—
659	C₂×C₄	—	4	4	no	—
660	C₂×C₄	—	8	4	no	—
661	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
662	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
663	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
664	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
665	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
666	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
667	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
668	C₈	—	2	2	no	—
669	C₈	—	2	4	no	—
670	C₈	—	2	2	no	—
671	C₂×C₃	—	2	2	no	—
672	C₂×C₃	—	4	2	no	—
673	C₂×C₃	—	8	2	no	—
674	C₂×C₃	—	8	2	no	—
675	C₂×C₃	—	8	2	no	—
676	C₂×C₃	C₂×#535	1	1	yes	characteristic
677	C₂×C₃	#3584	1	2	yes	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	4	no	—
681	C₂²	—	4	2	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	4	no	—
685	C₂²	—	4	4	no	—
686	C₂²	—	4	4	no	—
687	C₂²	—	8	2	no	—
688	C₂²	—	8	8	no	—
689	C₂²	C₃×#535	1	2	yes	—
690	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
691	C₄	—	2	2	no	—
692	C₄	—	2	4	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	4	2	no	—
696	C₄	—	4	2	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	4	no	—
699	C₄	C₃×#535	1	2	yes	—
700	C₄	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
701	C₃	#60797	1	1	yes	characteristic, direct product factor, Sylow
702	C₂	—	2	2	no	—
703	C₂	—	4	2	no	—
704	C₂	—	8	2	no	—
705	C₂	—	8	2	no	—
706	C₂	—	8	2	no	—
707	C₂	C₂×C₃×#535	1	1	yes	characteristic
708	C₂	C₃×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂²×C₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3455	C₂	semidirect
2. C₃×#3449	C₂	semidirect
3. C₃×#3225	C₂	semidirect
4. C₃×#3224	C₂	semidirect
5. C₃×#3223	C₂	semidirect
6. C₃×#3222	C₂	semidirect
7. C₃×#3221	C₂	semidirect
8. C₃×#3220	C₂	semidirect
9. C₃×#3150	C₂	semidirect
10. C₃×#3147	C₂	semidirect
11. C₃×#3135	C₂	semidirect
12. C₃×#3131	C₂	semidirect
13. C₃×#3035	C₂	semidirect
14. C₃×#3002	C₂	semidirect
15. C₂×C₃×#433	C₂	semidirect
16. #60797	C₃	direct (N × H)
18. C₂×C₃×#135	C₂²	semidirect
19. C₂×C₃×#135	C₂²	semidirect
20. C₃×#542	C₂²	semidirect
21. C₃×#541	C₂²	semidirect
22. C₃×#540	C₂²	semidirect
31. C₃×#533	C₂²	semidirect
35. C₃×#532	C₂²	semidirect
39. C₃×C₄×#41	C₂²	semidirect
41. C₃×#497	C₂²	semidirect
42. C₃×#497	C₂²	semidirect
43. C₃×#496	C₂²	semidirect
44. C₃×#496	C₂²	semidirect
45. C₃×#495	C₂²	semidirect
46. C₃×#494	C₂²	semidirect
47. C₃×#493	C₂²	semidirect
48. C₃×#492	C₂²	semidirect
49. C₃×#492	C₂²	semidirect
50. C₃×#491	C₂²	semidirect
51. C₃×#490	C₂²	semidirect
52. C₃×#489	C₂²	semidirect
53. C₃×#488	C₂²	semidirect
54. C₃×#488	C₂²	semidirect
55. C₃×#487	C₂²	semidirect
56. C₃×#486	C₂²	semidirect
57. C₃×#464	C₂²	semidirect
58. C₃×#464	C₂²	semidirect
59. C₃×#463	C₂²	semidirect
60. C₃×#463	C₂²	semidirect
61. C₃×#462	C₂²	semidirect
62. C₃×#461	C₂²	semidirect
63. C₃×#460	C₂²	semidirect
64. C₃×#459	C₂²	semidirect
67. C₃×#451	C₂²	semidirect
68. C₃×#450	C₂²	semidirect
71. C₃×#448	C₂²	semidirect
72. C₃×#447	C₂²	semidirect
73. C₃×#433	C₂²	semidirect
74. C₃×#433	C₂²	semidirect
75. C₃×#433	C₂²	semidirect
76. C₂×C₃×C₄⋊C₈	C₂²	semidirect
77. C₃×#416	C₂²	semidirect
78. C₃×#416	C₂²	semidirect
80. C₂×C₃×#97	C₂²	semidirect
81. C₂×C₃×C₄×C₈	C₂²	semidirect
82. #3455	C₂×C₃	semidirect
83. #3449	C₂×C₃	semidirect
84. #3225	C₂×C₃	semidirect
85. #3224	C₂×C₃	semidirect
86. #3223	C₂×C₃	semidirect
87. #3222	C₂×C₃	semidirect
88. #3221	C₂×C₃	semidirect
89. #3220	C₂×C₃	semidirect
90. #3150	C₂×C₃	semidirect
91. #3147	C₂×C₃	semidirect
92. #3135	C₂×C₃	semidirect
93. #3131	C₂×C₃	semidirect
94. #3035	C₂×C₃	semidirect
95. #3002	C₂×C₃	semidirect
96. C₂×#433	C₂×C₃	semidirect
199. C₂×#135	C₂²×C₃	semidirect
200. C₂×#135	C₂²×C₃	semidirect
201. #542	C₂²×C₃	semidirect
202. #541	C₂²×C₃	semidirect
203. #540	C₂²×C₃	semidirect
212. #533	C₂²×C₃	semidirect
216. #532	C₂²×C₃	semidirect
220. C₄×#41	C₂²×C₃	semidirect
222. #497	C₂²×C₃	semidirect
223. #497	C₂²×C₃	semidirect
224. #496	C₂²×C₃	semidirect
225. #496	C₂²×C₃	semidirect
226. #495	C₂²×C₃	semidirect
227. #494	C₂²×C₃	semidirect
228. #493	C₂²×C₃	semidirect
229. #492	C₂²×C₃	semidirect
230. #492	C₂²×C₃	semidirect
231. #491	C₂²×C₃	semidirect
232. #490	C₂²×C₃	semidirect
233. #489	C₂²×C₃	semidirect
234. #488	C₂²×C₃	semidirect
235. #488	C₂²×C₃	semidirect
236. #487	C₂²×C₃	semidirect
237. #486	C₂²×C₃	semidirect
238. #464	C₂²×C₃	semidirect
239. #464	C₂²×C₃	semidirect
240. #463	C₂²×C₃	semidirect
241. #463	C₂²×C₃	semidirect
242. #462	C₂²×C₃	semidirect
243. #461	C₂²×C₃	semidirect
244. #460	C₂²×C₃	semidirect
245. #459	C₂²×C₃	semidirect
248. #451	C₂²×C₃	semidirect
249. #450	C₂²×C₃	semidirect
252. #448	C₂²×C₃	semidirect
253. #447	C₂²×C₃	semidirect
254. #433	C₂²×C₃	semidirect
255. #433	C₂²×C₃	semidirect
256. #433	C₂²×C₃	semidirect
257. C₂×C₄⋊C₈	C₂²×C₃	semidirect
258. #416	C₂²×C₃	semidirect
259. #416	C₂²×C₃	semidirect
261. C₂×#97	C₂²×C₃	semidirect
262. C₂×C₄×C₈	C₂²×C₃	semidirect
701. C₃	#60797	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×#3455	2
C₃×#3449	2
C₃×#3225	2
C₃×#3224	2
C₃×#3223	2
C₃×#3222	2
C₃×#3221	2
C₃×#3220	2
C₃×#3150	2
C₃×#3147	2
C₃×#3135	2
C₃×#3131	2
C₃×#3035	2
C₃×#3002	2
C₂×C₃×#433	2
#60797	3

Subgroups — C3×#60797 #10679404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60797 #10679404