Subgroups — C₃×#61802 #10680409

Order 768.

1860 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3354	C₂	1	2	yes	maximal, complemented
4	C₃×#3347	C₂	1	4	yes	maximal, complemented
5	C₃×#3341	C₂	1	2	yes	maximal, complemented
6	C₃×#3325	C₂	1	2	yes	maximal, complemented
7	C₃×#3318	C₂	1	4	yes	maximal, complemented
8	C₃×#3294	C₂	1	2	yes	maximal, complemented
9	C₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3199	C₂	1	4	yes	maximal, complemented
12	C₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3096	C₂	1	4	yes	maximal, complemented
15	C₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	#61802	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×H(3,𝔽₄)	—	2	2	no	—
18	C₃×#559	—	2	2	no	—
19	C₃×#556	—	2	1	no	—
20	C₃×#555	—	2	1	no	—
21	C₃×#555	C₂²	1	2	yes	complemented
22	C₃×#555	C₂²	1	2	yes	complemented
23	C₃×#555	C₂²	1	2	yes	complemented
24	C₃×#553	C₂²	1	4	yes	complemented
25	C₃×#550	—	2	1	no	—
26	C₃×#547	C₂²	1	2	yes	complemented
27	C₃×D₄²	—	2	1	no	—
28	C₃×D₄²	C₂²	1	2	yes	complemented
29	C₃×D₄²	C₂²	1	2	yes	complemented
30	C₃×#538	—	2	2	no	—
31	C₃×#535	—	2	2	no	—
32	C₃×#535	—	2	2	no	—
33	C₃×#535	C₂²	1	4	yes	—
34	C₃×#535	C₂²	1	2	yes	complemented
35	C₃×#533	C₂²	1	1	yes	characteristic, complemented
36	C₃×#532	C₂²	1	1	yes	characteristic
37	C₃×#532	C₂²	1	1	yes	characteristic
38	C₃×#532	C₂²	1	1	yes	characteristic
39	C₃×#525	—	2	2	no	—
40	C₃×#520	C₂²	1	2	yes	complemented
41	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
42	C₃×#501	C₂²	1	2	yes	complemented
43	C₃×#500	C₂²	1	1	yes	characteristic, complemented
44	C₃×#498	C₂²	1	1	yes	characteristic, complemented
45	C₃×#490	C₂²	1	2	yes	complemented
46	C₃×#486	C₂²	1	1	yes	characteristic, complemented
47	C₃×#486	C₂²	1	1	yes	characteristic, complemented
48	C₃×#482	C₂²	1	4	yes	complemented
49	C₃×#482	C₂²	1	4	yes	complemented
50	C₃×#482	C₂²	1	4	yes	complemented
51	C₃×#482	C₂²	1	4	yes	complemented
52	C₃×#482	C₂²	1	4	yes	complemented
53	C₃×#482	C₂²	1	4	yes	complemented
54	C₃×#481	C₂²	1	4	yes	complemented
55	C₃×#481	C₂²	1	2	yes	complemented
56	C₃×#480	C₂²	1	4	yes	complemented
57	C₃×#480	C₂²	1	2	yes	complemented
58	C₃×#478	C₂²	1	4	yes	complemented
59	C₃×#476	C₂²	1	2	yes	complemented
60	C₃×#476	C₂²	1	2	yes	complemented
61	C₃×#474	C₂²	1	2	yes	complemented
62	C₃×#474	C₂²	1	2	yes	complemented
63	C₃×#469	C₂²	1	4	yes	complemented
64	C₃×#469	C₂²	1	4	yes	complemented
65	C₃×#466	C₂²	1	4	yes	complemented
66	C₃×#466	C₂²	1	4	yes	complemented
67	C₃×#459	C₂²	1	2	yes	—
68	C₃×#459	C₂²	1	2	yes	—
69	C₃×#447	C₂²	1	2	yes	complemented
70	C₃×#447	C₂²	1	2	yes	complemented
71	C₃×#447	C₂²	1	4	yes	complemented
72	C₃×#447	C₂²	1	4	yes	complemented
73	C₃×#442	C₂²	1	4	yes	complemented
74	C₃×C₄×D₈	C₂²	1	2	yes	complemented
75	C₃×C₄×D₈	C₂²	1	2	yes	complemented
76	C₃×#436	C₂²	1	2	yes	complemented
77	C₃×#435	C₂²	1	4	yes	complemented
78	C₃×C₈×D₄	C₂²	1	2	yes	complemented
79	C₃×#432	C₂²	1	1	yes	characteristic, complemented
80	C₃×#431	C₂²	1	1	yes	characteristic, complemented
81	C₃×#428	C₂²	1	4	yes	complemented
82	C₃×#427	C₂²	1	4	yes	complemented
83	C₃×#418	C₂²	1	4	yes	complemented
84	C₂×C₃×#102	C₂²	1	4	yes	complemented
85	C₃×#408	C₂²	1	4	yes	complemented
86	#3549	C₂×C₃	1	1	yes	characteristic, complemented
87	#3506	C₂×C₃	1	1	yes	characteristic, complemented
88	#3354	C₂×C₃	1	2	yes	complemented
89	#3347	C₂×C₃	1	4	yes	complemented
90	#3341	C₂×C₃	1	2	yes	complemented
91	#3325	C₂×C₃	1	2	yes	complemented
92	#3318	C₂×C₃	1	4	yes	complemented
93	#3294	C₂×C₃	1	2	yes	complemented
94	#3235	C₂×C₃	1	1	yes	characteristic, complemented
95	#3228	C₂×C₃	1	1	yes	characteristic, complemented
96	#3199	C₂×C₃	1	4	yes	complemented
97	#3109	C₂×C₃	1	1	yes	characteristic, complemented
98	#3100	C₂×C₃	1	1	yes	characteristic, complemented
99	#3096	C₂×C₃	1	4	yes	complemented
100	#2981	C₂×C₃	1	1	yes	characteristic, complemented
101	C₂×C₃×#41	—	2	2	no	—
102	C₂×C₃×#41	—	2	1	no	—
103	C₂×C₃×#41	—	2	1	no	—
104	C₂×C₃×#41	C₂³	1	2	yes	—
105	C₂²×C₃×D₄	—	2	2	no	—
106	C₂²×C₃×D₄	—	2	2	no	—
107	C₂²×C₃×D₄	C₂³	1	4	yes	—
108	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
109	C₂³×C₃×C₄	—	2	1	no	—
110	C₂×C₃×D₈	C₂³	1	2	yes	—
111	C₂×C₃×D₈	C₂³	1	2	yes	—
112	C₂×C₃×D₈	C₂³	1	4	yes	—
113	C₂×C₃×M₁₆	C₂³	1	4	yes	—
114	C₂²×C₃×C₈	C₂³	1	4	yes	—
115	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
116	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₃×#127	—	2	2	no	—
121	C₃×#127	—	2	4	no	—
122	C₃×#127	D₄	1	1	yes	characteristic
123	C₃×#127	C₂³	1	1	yes	characteristic
124	C₃×#127	C₂³	1	1	yes	characteristic
125	C₃×#126	—	2	4	no	—
126	C₃×#125	C₂³	1	2	yes	—
127	C₃×#124	—	2	2	no	—
128	C₃×#124	—	2	4	no	—
129	C₃×#124	—	2	4	no	—
130	C₃×#124	—	2	4	no	—
131	C₃×#124	—	2	4	no	—
132	C₃×#124	—	2	1	no	—
133	C₃×#124	—	2	1	no	—
134	C₃×#124	D₄	1	2	yes	—
135	C₃×#123	—	2	4	no	—
136	C₃×#123	—	2	4	no	—
137	C₃×C₂²⋊Q₈	—	2	1	no	—
138	C₃×C₂²⋊Q₈	—	2	1	no	—
139	C₃×C₂²⋊Q₈	—	2	2	no	—
140	C₃×#121	—	2	2	no	—
141	C₃×#121	—	2	2	no	—
142	C₃×#121	—	2	2	no	—
143	C₃×#121	—	2	4	no	—
144	C₃×#121	—	2	1	no	—
145	C₃×#121	—	2	1	no	—
146	C₃×#121	—	2	2	no	—
147	C₃×#121	—	2	2	no	—
148	C₃×#121	D₄	1	2	yes	—
149	C₃×#121	D₄	1	2	yes	—
150	C₃×#121	C₂³	1	4	yes	—
151	C₃×#121	C₂³	1	4	yes	—
152	C₃×#121	C₂³	1	2	yes	—
153	C₃×#121	C₂³	1	2	yes	—
154	C₃×#121	C₂³	1	4	yes	—
155	C₃×#121	C₂³	1	4	yes	—
156	C₃×#120	—	2	4	no	—
157	C₃×#120	—	2	4	no	—
158	C₃×#120	—	2	4	no	—
159	C₃×#120	—	2	4	no	—
160	C₃×#120	—	2	4	no	—
161	C₃×C₄×Q₈	—	2	2	no	—
162	C₃×C₄×Q₈	—	2	1	no	—
163	C₃×C₄×Q₈	—	2	1	no	—
164	C₃×C₄×D₄	—	2	2	no	—
165	C₃×C₄×D₄	—	2	4	no	—
166	C₃×C₄×D₄	—	2	4	no	—
167	C₃×C₄×D₄	—	2	1	no	—
168	C₃×C₄×D₄	—	2	1	no	—
169	C₃×C₄×D₄	—	2	1	no	—
170	C₃×C₄×D₄	—	2	1	no	—
171	C₃×C₄×D₄	C₂³	1	2	yes	—
172	C₃×C₄×D₄	C₂³	1	2	yes	—
173	C₃×C₄×D₄	C₂³	1	2	yes	—
174	C₃×C₄×D₄	C₂³	1	2	yes	—
175	C₃×C₄×D₄	C₂³	1	2	yes	—
176	C₃×C₄×D₄	C₂³	1	2	yes	—
177	C₃×#117	—	2	2	no	—
178	C₃×#117	—	2	2	no	—
179	C₃×#117	—	2	2	no	—
180	C₃×#117	C₂³	1	4	yes	—
181	C₃×#117	C₂³	1	4	yes	—
182	C₃×#117	C₂³	1	2	yes	—
183	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
184	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
186	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
187	C₃×#107	C₂³	1	2	yes	—
188	C₃×#107	C₂³	1	4	yes	—
189	C₃×#107	C₂³	1	2	yes	—
190	C₃×#107	C₂³	1	4	yes	—
191	C₃×#106	C₂³	1	4	yes	—
192	C₃×#106	C₂³	1	4	yes	—
193	C₃×#106	C₂³	1	4	yes	—
194	C₃×C₄⋊C₈	C₂³	1	2	yes	—
195	C₃×C₄⋊C₈	C₂³	1	2	yes	—
196	C₃×#102	C₂³	1	2	yes	—
197	C₃×#102	C₂³	1	4	yes	—
198	C₃×#102	C₂³	1	4	yes	—
199	C₃×#102	C₂³	1	4	yes	—
200	C₃×#102	C₂³	1	2	yes	—
201	C₃×#102	C₂³	1	4	yes	—
202	C₃×#102	C₂³	1	4	yes	—
203	C₃×#102	C₂³	1	2	yes	—
204	C₃×#102	C₂³	1	2	yes	—
205	C₃×#102	C₂³	1	4	yes	—
206	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
207	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
209	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
210	C₃×#97	C₂³	1	2	yes	—
211	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
212	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
213	H(3,𝔽₄)	—	2	2	no	—
214	#559	—	2	2	no	—
215	#556	—	2	1	no	—
216	#555	—	2	1	no	—
217	#555	C₂²×C₃	1	2	yes	complemented
218	#555	C₂²×C₃	1	2	yes	complemented
219	#555	C₂²×C₃	1	2	yes	complemented
220	#553	C₂²×C₃	1	4	yes	complemented
221	#550	—	2	1	no	—
222	#547	C₂²×C₃	1	2	yes	complemented
223	D₄²	—	2	1	no	—
224	D₄²	C₂²×C₃	1	2	yes	complemented
225	D₄²	C₂²×C₃	1	2	yes	complemented
226	#538	—	2	2	no	—
227	#535	—	2	2	no	—
228	#535	—	2	2	no	—
229	#535	C₂²×C₃	1	4	yes	—
230	#535	C₂²×C₃	1	2	yes	complemented
231	#533	C₂²×C₃	1	1	yes	characteristic, complemented
232	#532	C₂²×C₃	1	1	yes	characteristic
233	#532	C₂²×C₃	1	1	yes	characteristic
234	#532	C₂²×C₃	1	1	yes	characteristic
235	#525	—	2	2	no	—
236	#520	C₂²×C₃	1	2	yes	complemented
237	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
238	#501	C₂²×C₃	1	2	yes	complemented
239	#500	C₂²×C₃	1	1	yes	characteristic, complemented
240	#498	C₂²×C₃	1	1	yes	characteristic, complemented
241	#490	C₂²×C₃	1	2	yes	complemented
242	#486	C₂²×C₃	1	1	yes	characteristic, complemented
243	#486	C₂²×C₃	1	1	yes	characteristic, complemented
244	#482	C₂²×C₃	1	4	yes	complemented
245	#482	C₂²×C₃	1	4	yes	complemented
246	#482	C₂²×C₃	1	4	yes	complemented
247	#482	C₂²×C₃	1	4	yes	complemented
248	#482	C₂²×C₃	1	4	yes	complemented
249	#482	C₂²×C₃	1	4	yes	complemented
250	#481	C₂²×C₃	1	2	yes	complemented
251	#481	C₂²×C₃	1	4	yes	complemented
252	#480	C₂²×C₃	1	4	yes	complemented
253	#480	C₂²×C₃	1	2	yes	complemented
254	#478	C₂²×C₃	1	4	yes	complemented
255	#476	C₂²×C₃	1	2	yes	complemented
256	#476	C₂²×C₃	1	2	yes	complemented
257	#474	C₂²×C₃	1	2	yes	complemented
258	#474	C₂²×C₃	1	2	yes	complemented
259	#469	C₂²×C₃	1	4	yes	complemented
260	#469	C₂²×C₃	1	4	yes	complemented
261	#466	C₂²×C₃	1	4	yes	complemented
262	#466	C₂²×C₃	1	4	yes	complemented
263	#459	C₂²×C₃	1	2	yes	—
264	#459	C₂²×C₃	1	2	yes	—
265	#447	C₂²×C₃	1	2	yes	complemented
266	#447	C₂²×C₃	1	2	yes	complemented
267	#447	C₂²×C₃	1	4	yes	complemented
268	#447	C₂²×C₃	1	4	yes	complemented
269	#442	C₂²×C₃	1	4	yes	complemented
270	C₄×D₈	C₂²×C₃	1	2	yes	complemented
271	C₄×D₈	C₂²×C₃	1	2	yes	complemented
272	#436	C₂²×C₃	1	2	yes	complemented
273	#435	C₂²×C₃	1	4	yes	complemented
274	C₈×D₄	C₂²×C₃	1	2	yes	complemented
275	#432	C₂²×C₃	1	1	yes	characteristic, complemented
276	#431	C₂²×C₃	1	1	yes	characteristic, complemented
277	#428	C₂²×C₃	1	4	yes	complemented
278	#427	C₂²×C₃	1	4	yes	complemented
279	#418	C₂²×C₃	1	4	yes	complemented
280	C₂×#102	C₂²×C₃	1	4	yes	complemented
281	#408	C₂²×C₃	1	4	yes	complemented
282	C₂⁴×C₃	—	2	1	no	—
283	C₂⁴×C₃	—	2	4	no	—
284	C₃×#41	—	4	4	no	—
285	C₃×#41	—	8	2	no	—
286	C₃×#41	—	8	2	no	—
287	C₃×#41	—	8	4	no	—
288	C₂×C₃×Q₈	—	2	1	no	—
289	C₂×C₃×Q₈	—	2	1	no	—
290	C₂×C₃×Q₈	—	2	1	no	—
291	C₂×C₃×Q₈	—	2	1	no	—
292	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
293	C₂×C₃×D₄	—	2	4	no	—
294	C₂×C₃×D₄	—	2	4	no	—
295	C₂×C₃×D₄	—	2	4	no	—
296	C₂×C₃×D₄	—	2	2	no	—
297	C₂×C₃×D₄	—	2	2	no	—
298	C₂×C₃×D₄	—	2	4	no	—
299	C₂×C₃×D₄	—	2	1	no	—
300	C₂×C₃×D₄	—	2	1	no	—
301	C₂×C₃×D₄	—	2	1	no	—
302	C₂×C₃×D₄	—	2	1	no	—
303	C₂×C₃×D₄	—	2	1	no	—
304	C₂×C₃×D₄	—	2	4	no	—
305	C₂×C₃×D₄	—	4	2	no	—
306	C₂×C₃×D₄	—	4	4	no	—
307	C₂×C₃×D₄	—	4	4	no	—
308	C₂×C₃×D₄	—	8	4	no	—
309	C₂×C₃×D₄	—	8	4	no	—
310	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
311	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
312	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
313	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
314	C₂×C₃×D₄	C₂⁴	1	2	yes	—
315	C₂×C₃×D₄	C₂⁴	1	2	yes	—
316	C₂×C₃×D₄	C₂⁴	1	2	yes	—
317	C₂²×C₃×C₄	—	2	1	no	—
318	C₂²×C₃×C₄	—	2	4	no	—
319	C₂²×C₃×C₄	—	2	2	no	—
320	C₂²×C₃×C₄	—	2	2	no	—
321	C₂²×C₃×C₄	—	2	2	no	—
322	C₂²×C₃×C₄	—	2	2	no	—
323	C₂²×C₃×C₄	—	8	2	no	—
324	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
327	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
328	C₃×D₈	—	4	2	no	—
329	C₃×D₈	—	4	4	no	—
330	C₃×D₈	—	4	2	no	—
331	C₃×M₁₆	—	4	4	no	—
332	C₂×C₃×C₈	—	4	4	no	—
333	C₂×C₃×C₈	C₂⁴	1	2	yes	—
334	C₂×C₃×C₈	C₂⁴	1	2	yes	—
335	C₂×C₃×C₈	C₂⁴	1	4	yes	—
336	C₃×C₄⋊C₄	—	2	1	no	—
337	C₃×C₄⋊C₄	—	2	4	no	—
338	C₃×C₄⋊C₄	—	2	1	no	—
339	C₃×C₄⋊C₄	—	2	1	no	—
340	C₃×C₄⋊C₄	—	2	1	no	—
341	C₃×C₄⋊C₄	—	2	2	no	—
342	C₃×C₄⋊C₄	—	2	2	no	—
343	C₃×C₄⋊C₄	—	2	1	no	—
344	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
345	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
346	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
347	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
348	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
349	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
350	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
351	C₃×C₂²⋊C₄	—	2	2	no	—
352	C₃×C₂²⋊C₄	—	2	4	no	—
353	C₃×C₂²⋊C₄	—	2	4	no	—
354	C₃×C₂²⋊C₄	—	2	2	no	—
355	C₃×C₂²⋊C₄	—	2	2	no	—
356	C₃×C₂²⋊C₄	—	2	4	no	—
357	C₃×C₂²⋊C₄	—	2	4	no	—
358	C₃×C₂²⋊C₄	—	2	4	no	—
359	C₃×C₂²⋊C₄	—	2	2	no	—
360	C₃×C₂²⋊C₄	—	2	2	no	—
361	C₃×C₂²⋊C₄	—	2	4	no	—
362	C₃×C₂²⋊C₄	—	2	2	no	—
363	C₃×C₂²⋊C₄	—	2	2	no	—
364	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
365	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
366	C₃×C₄²	—	2	4	no	—
367	C₃×C₄²	—	2	4	no	—
368	C₃×C₄²	—	2	2	no	—
369	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
370	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
371	C₃×C₄²	C₂⁴	1	1	yes	characteristic
372	C₃×C₄²	C₂⁴	1	1	yes	characteristic
373	C₂×#41	—	2	2	no	—
374	C₂×#41	—	2	1	no	—
375	C₂×#41	—	2	1	no	—
376	C₂×#41	C₂³×C₃	1	2	yes	—
377	C₂²×D₄	—	2	2	no	—
378	C₂²×D₄	—	2	2	no	—
379	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
380	C₂²×D₄	C₂³×C₃	1	4	yes	—
381	C₂³×C₄	—	2	1	no	—
382	C₂×D₈	C₂³×C₃	1	2	yes	—
383	C₂×D₈	C₂³×C₃	1	2	yes	—
384	C₂×D₈	C₂³×C₃	1	4	yes	—
385	C₂×M₁₆	C₂³×C₃	1	4	yes	—
386	C₂²×C₈	C₂³×C₃	1	4	yes	—
387	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
388	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
389	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
390	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
391	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
392	#127	—	2	4	no	—
393	#127	—	2	2	no	—
394	#127	C₃×D₄	1	1	yes	characteristic
395	#127	C₂³×C₃	1	1	yes	characteristic
396	#127	C₂³×C₃	1	1	yes	characteristic
397	#126	—	2	4	no	—
398	#125	C₂³×C₃	1	2	yes	—
399	#124	—	2	4	no	—
400	#124	—	2	2	no	—
401	#124	—	2	4	no	—
402	#124	—	2	4	no	—
403	#124	—	2	4	no	—
404	#124	—	2	1	no	—
405	#124	—	2	1	no	—
406	#124	C₃×D₄	1	2	yes	—
407	#123	—	2	4	no	—
408	#123	—	2	4	no	—
409	C₂²⋊Q₈	—	2	1	no	—
410	C₂²⋊Q₈	—	2	1	no	—
411	C₂²⋊Q₈	—	2	2	no	—
412	#121	—	2	2	no	—
413	#121	—	2	2	no	—
414	#121	—	2	2	no	—
415	#121	—	2	4	no	—
416	#121	—	2	1	no	—
417	#121	—	2	1	no	—
418	#121	—	2	2	no	—
419	#121	—	2	2	no	—
420	#121	C₃×D₄	1	2	yes	—
421	#121	C₃×D₄	1	2	yes	—
422	#121	C₂³×C₃	1	2	yes	—
423	#121	C₂³×C₃	1	2	yes	—
424	#121	C₂³×C₃	1	4	yes	—
425	#121	C₂³×C₃	1	4	yes	—
426	#121	C₂³×C₃	1	4	yes	—
427	#121	C₂³×C₃	1	4	yes	—
428	#120	—	2	4	no	—
429	#120	—	2	4	no	—
430	#120	—	2	4	no	—
431	#120	—	2	4	no	—
432	#120	—	2	4	no	—
433	C₄×Q₈	—	2	2	no	—
434	C₄×Q₈	—	2	1	no	—
435	C₄×Q₈	—	2	1	no	—
436	C₄×D₄	—	2	4	no	—
437	C₄×D₄	—	2	2	no	—
438	C₄×D₄	—	2	4	no	—
439	C₄×D₄	—	2	1	no	—
440	C₄×D₄	—	2	1	no	—
441	C₄×D₄	—	2	1	no	—
442	C₄×D₄	—	2	1	no	—
443	C₄×D₄	C₂³×C₃	1	2	yes	—
444	C₄×D₄	C₂³×C₃	1	2	yes	—
445	C₄×D₄	C₂³×C₃	1	2	yes	—
446	C₄×D₄	C₂³×C₃	1	2	yes	—
447	C₄×D₄	C₂³×C₃	1	2	yes	—
448	C₄×D₄	C₂³×C₃	1	2	yes	—
449	#117	—	2	2	no	—
450	#117	—	2	2	no	—
451	#117	—	2	2	no	—
452	#117	C₂³×C₃	1	2	yes	—
453	#117	C₂³×C₃	1	4	yes	—
454	#117	C₂³×C₃	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
459	#107	C₂³×C₃	1	2	yes	—
460	#107	C₂³×C₃	1	4	yes	—
461	#107	C₂³×C₃	1	2	yes	—
462	#107	C₂³×C₃	1	4	yes	—
463	#106	C₂³×C₃	1	4	yes	—
464	#106	C₂³×C₃	1	4	yes	—
465	#106	C₂³×C₃	1	4	yes	—
466	C₄⋊C₈	C₂³×C₃	1	2	yes	—
467	C₄⋊C₈	C₂³×C₃	1	2	yes	—
468	#102	C₂³×C₃	1	2	yes	—
469	#102	C₂³×C₃	1	4	yes	—
470	#102	C₂³×C₃	1	4	yes	—
471	#102	C₂³×C₃	1	4	yes	—
472	#102	C₂³×C₃	1	2	yes	—
473	#102	C₂³×C₃	1	4	yes	—
474	#102	C₂³×C₃	1	4	yes	—
475	#102	C₂³×C₃	1	2	yes	—
476	#102	C₂³×C₃	1	2	yes	—
477	#102	C₂³×C₃	1	4	yes	—
478	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
479	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
480	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
481	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
482	#97	C₂³×C₃	1	2	yes	—
483	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
484	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
485	C₂³×C₃	—	2	2	no	—
486	C₂³×C₃	—	2	2	no	—
487	C₂³×C₃	—	2	2	no	—
488	C₂³×C₃	—	4	2	no	—
489	C₂³×C₃	—	8	1	no	—
490	C₂³×C₃	—	8	1	no	—
491	C₂³×C₃	—	8	4	no	—
492	C₂³×C₃	—	8	4	no	—
493	C₂³×C₃	—	8	4	no	—
494	C₂³×C₃	C₂²×D₄	1	4	yes	—
495	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
496	C₃×Q₈	—	4	2	no	—
497	C₃×Q₈	—	4	2	no	—
498	C₃×Q₈	—	8	1	no	—
499	C₃×Q₈	—	8	1	no	—
500	C₃×Q₈	—	8	1	no	—
501	C₃×D₄	—	2	4	no	—
502	C₃×D₄	—	2	2	no	—
503	C₃×D₄	—	2	2	no	—
504	C₃×D₄	—	2	2	no	—
505	C₃×D₄	—	2	4	no	—
506	C₃×D₄	—	2	2	no	—
507	C₃×D₄	—	4	2	no	—
508	C₃×D₄	—	4	2	no	—
509	C₃×D₄	—	4	4	no	—
510	C₃×D₄	—	4	2	no	—
511	C₃×D₄	—	4	2	no	—
512	C₃×D₄	—	4	2	no	—
513	C₃×D₄	—	8	4	no	—
514	C₃×D₄	—	8	1	no	—
515	C₃×D₄	—	8	1	no	—
516	C₃×D₄	—	8	4	no	—
517	C₃×D₄	—	8	4	no	—
518	C₃×D₄	—	8	4	no	—
519	C₃×D₄	—	8	2	no	—
520	C₃×D₄	—	8	2	no	—
521	C₃×D₄	—	8	4	no	—
522	C₂×C₃×C₄	—	2	2	no	—
523	C₂×C₃×C₄	—	2	4	no	—
524	C₂×C₃×C₄	—	2	4	no	—
525	C₂×C₃×C₄	—	2	2	no	—
526	C₂×C₃×C₄	—	2	2	no	—
527	C₂×C₃×C₄	—	2	2	no	—
528	C₂×C₃×C₄	—	2	2	no	—
529	C₂×C₃×C₄	—	2	2	no	—
530	C₂×C₃×C₄	—	2	2	no	—
531	C₂×C₃×C₄	—	4	1	no	—
532	C₂×C₃×C₄	—	4	4	no	—
533	C₂×C₃×C₄	—	4	4	no	—
534	C₂×C₃×C₄	—	4	4	no	—
535	C₂×C₃×C₄	—	8	2	no	—
536	C₂×C₃×C₄	—	8	1	no	—
537	C₂×C₃×C₄	—	8	4	no	—
538	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
540	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
545	C₃×C₈	—	2	2	no	—
546	C₃×C₈	—	2	4	no	—
547	C₃×C₈	—	2	2	no	—
548	C₂⁴	—	2	1	no	—
549	C₂⁴	—	2	4	no	—
550	#41	—	4	4	no	—
551	#41	—	8	2	no	—
552	#41	—	8	2	no	—
553	#41	—	8	4	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	4	2	no	—
572	C₂×D₄	—	4	4	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂×D₄	—	8	4	no	—
575	C₂×D₄	—	8	4	no	—
576	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
577	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
578	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
579	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
580	C₂×D₄	C₂⁴×C₃	1	2	yes	—
581	C₂×D₄	C₂⁴×C₃	1	2	yes	—
582	C₂×D₄	C₂⁴×C₃	1	2	yes	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	8	2	no	—
590	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
591	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
594	D₈	—	4	2	no	—
595	D₈	—	4	4	no	—
596	D₈	—	4	2	no	—
597	M₁₆	—	4	4	no	—
598	C₂×C₈	—	4	4	no	—
599	C₂×C₈	C₂⁴×C₃	1	2	yes	—
600	C₂×C₈	C₂⁴×C₃	1	2	yes	—
601	C₂×C₈	C₂⁴×C₃	1	4	yes	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
611	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
612	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
613	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
614	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
615	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
616	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
631	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	2	no	—
635	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
636	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
637	C₄²	C₂⁴×C₃	1	1	yes	characteristic
638	C₄²	C₂⁴×C₃	1	1	yes	characteristic
639	C₂²×C₃	—	2	1	no	—
640	C₂²×C₃	—	2	4	no	—
641	C₂²×C₃	—	2	1	no	—
642	C₂²×C₃	—	2	4	no	—
643	C₂²×C₃	—	2	1	no	—
644	C₂²×C₃	—	2	4	no	—
645	C₂²×C₃	—	4	2	no	—
646	C₂²×C₃	—	4	2	no	—
647	C₂²×C₃	—	4	2	no	—
648	C₂²×C₃	—	4	2	no	—
649	C₂²×C₃	—	4	2	no	—
650	C₂²×C₃	—	4	2	no	—
651	C₂²×C₃	—	4	2	no	—
652	C₂²×C₃	—	4	2	no	—
653	C₂²×C₃	—	4	2	no	—
654	C₂²×C₃	—	8	4	no	—
655	C₂²×C₃	—	16	8	no	—
656	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
657	C₃×C₄	—	2	1	no	—
658	C₃×C₄	—	2	1	no	—
659	C₃×C₄	—	2	1	no	—
660	C₃×C₄	—	2	4	no	—
661	C₃×C₄	—	2	1	no	—
662	C₃×C₄	—	4	2	no	—
663	C₃×C₄	—	4	2	no	—
664	C₃×C₄	—	4	2	no	—
665	C₃×C₄	—	4	2	no	—
666	C₃×C₄	—	4	2	no	—
667	C₃×C₄	#576	1	2	yes	—
668	C₃×C₄	#585	1	2	yes	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	4	2	no	—
673	C₂³	—	8	1	no	—
674	C₂³	—	8	1	no	—
675	C₂³	—	8	4	no	—
676	C₂³	—	8	4	no	—
677	C₂³	—	8	4	no	—
678	C₂³	C₂²×C₃×D₄	1	4	yes	—
679	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
680	Q₈	—	4	2	no	—
681	Q₈	—	4	2	no	—
682	Q₈	—	8	1	no	—
683	Q₈	—	8	1	no	—
684	Q₈	—	8	1	no	—
685	D₄	—	2	4	no	—
686	D₄	—	2	2	no	—
687	D₄	—	2	2	no	—
688	D₄	—	2	2	no	—
689	D₄	—	2	4	no	—
690	D₄	—	2	2	no	—
691	D₄	—	4	2	no	—
692	D₄	—	4	2	no	—
693	D₄	—	4	4	no	—
694	D₄	—	4	2	no	—
695	D₄	—	4	2	no	—
696	D₄	—	4	2	no	—
697	D₄	—	8	4	no	—
698	D₄	—	8	1	no	—
699	D₄	—	8	1	no	—
700	D₄	—	8	4	no	—
701	D₄	—	8	4	no	—
702	D₄	—	8	2	no	—
703	D₄	—	8	4	no	—
704	D₄	—	8	2	no	—
705	D₄	—	8	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	8	2	no	—
720	C₂×C₄	—	8	1	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
723	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
724	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
725	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
726	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
727	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
728	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
729	C₈	—	2	2	no	—
730	C₈	—	2	4	no	—
731	C₈	—	2	2	no	—
732	C₂×C₃	—	4	1	no	—
733	C₂×C₃	—	4	4	no	—
734	C₂×C₃	—	8	2	no	—
735	C₂×C₃	—	8	2	no	—
736	C₂×C₃	—	8	2	no	—
737	C₂×C₃	#3485	1	1	yes	characteristic
738	C₂×C₃	C₂×#576	1	1	yes	characteristic
739	C₂×C₃	#3585	1	1	yes	characteristic
740	C₂²	—	2	1	no	—
741	C₂²	—	2	4	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	4	no	—
744	C₂²	—	2	1	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	8	4	no	—
756	C₂²	—	16	8	no	—
757	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
758	C₄	—	2	1	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	1	no	—
761	C₄	—	2	1	no	—
762	C₄	—	2	1	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	C₃×#576	1	2	yes	—
769	C₄	C₃×#585	1	2	yes	—
770	C₃	#61802	1	1	yes	characteristic, direct product factor, Sylow
771	C₂	—	4	1	no	—
772	C₂	—	4	4	no	—
773	C₂	—	8	2	no	—
774	C₂	—	8	2	no	—
775	C₂	—	8	2	no	—
776	C₂	C₃×#3485	1	1	yes	characteristic
777	C₂	C₂×C₃×#576	1	1	yes	characteristic
778	C₂	C₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3549	C₂	semidirect
2. C₃×#3506	C₂	semidirect
3. C₃×#3354	C₂	semidirect
4. C₃×#3347	C₂	semidirect
5. C₃×#3341	C₂	semidirect
6. C₃×#3325	C₂	semidirect
7. C₃×#3318	C₂	semidirect
8. C₃×#3294	C₂	semidirect
9. C₃×#3235	C₂	semidirect
10. C₃×#3228	C₂	semidirect
11. C₃×#3199	C₂	semidirect
12. C₃×#3109	C₂	semidirect
13. C₃×#3100	C₂	semidirect
14. C₃×#3096	C₂	semidirect
15. C₃×#2981	C₂	semidirect
16. #61802	C₃	direct (N × H)
21. C₃×#555	C₂²	semidirect
22. C₃×#555	C₂²	semidirect
23. C₃×#555	C₂²	semidirect
24. C₃×#553	C₂²	semidirect
26. C₃×#547	C₂²	semidirect
28. C₃×D₄²	C₂²	semidirect
29. C₃×D₄²	C₂²	semidirect
34. C₃×#535	C₂²	semidirect
35. C₃×#533	C₂²	semidirect
40. C₃×#520	C₂²	semidirect
41. C₂×C₃×C₄×D₄	C₂²	semidirect
42. C₃×#501	C₂²	semidirect
43. C₃×#500	C₂²	semidirect
44. C₃×#498	C₂²	semidirect
45. C₃×#490	C₂²	semidirect
46. C₃×#486	C₂²	semidirect
47. C₃×#486	C₂²	semidirect
48. C₃×#482	C₂²	semidirect
49. C₃×#482	C₂²	semidirect
50. C₃×#482	C₂²	semidirect
51. C₃×#482	C₂²	semidirect
52. C₃×#482	C₂²	semidirect
53. C₃×#482	C₂²	semidirect
54. C₃×#481	C₂²	semidirect
55. C₃×#481	C₂²	semidirect
56. C₃×#480	C₂²	semidirect
57. C₃×#480	C₂²	semidirect
58. C₃×#478	C₂²	semidirect
59. C₃×#476	C₂²	semidirect
60. C₃×#476	C₂²	semidirect
61. C₃×#474	C₂²	semidirect
62. C₃×#474	C₂²	semidirect
63. C₃×#469	C₂²	semidirect
64. C₃×#469	C₂²	semidirect
65. C₃×#466	C₂²	semidirect
66. C₃×#466	C₂²	semidirect
69. C₃×#447	C₂²	semidirect
70. C₃×#447	C₂²	semidirect
71. C₃×#447	C₂²	semidirect
72. C₃×#447	C₂²	semidirect
73. C₃×#442	C₂²	semidirect
74. C₃×C₄×D₈	C₂²	semidirect
75. C₃×C₄×D₈	C₂²	semidirect
76. C₃×#436	C₂²	semidirect
77. C₃×#435	C₂²	semidirect
78. C₃×C₈×D₄	C₂²	semidirect
79. C₃×#432	C₂²	semidirect
80. C₃×#431	C₂²	semidirect
81. C₃×#428	C₂²	semidirect
82. C₃×#427	C₂²	semidirect
83. C₃×#418	C₂²	semidirect
84. C₂×C₃×#102	C₂²	semidirect
85. C₃×#408	C₂²	semidirect
86. #3549	C₂×C₃	semidirect
87. #3506	C₂×C₃	semidirect
88. #3354	C₂×C₃	semidirect
89. #3347	C₂×C₃	semidirect
90. #3341	C₂×C₃	semidirect
91. #3325	C₂×C₃	semidirect
92. #3318	C₂×C₃	semidirect
93. #3294	C₂×C₃	semidirect
94. #3235	C₂×C₃	semidirect
95. #3228	C₂×C₃	semidirect
96. #3199	C₂×C₃	semidirect
97. #3109	C₂×C₃	semidirect
98. #3100	C₂×C₃	semidirect
99. #3096	C₂×C₃	semidirect
100. #2981	C₂×C₃	semidirect
217. #555	C₂²×C₃	semidirect
218. #555	C₂²×C₃	semidirect
219. #555	C₂²×C₃	semidirect
220. #553	C₂²×C₃	semidirect
222. #547	C₂²×C₃	semidirect
224. D₄²	C₂²×C₃	semidirect
225. D₄²	C₂²×C₃	semidirect
230. #535	C₂²×C₃	semidirect
231. #533	C₂²×C₃	semidirect
236. #520	C₂²×C₃	semidirect
237. C₂×C₄×D₄	C₂²×C₃	semidirect
238. #501	C₂²×C₃	semidirect
239. #500	C₂²×C₃	semidirect
240. #498	C₂²×C₃	semidirect
241. #490	C₂²×C₃	semidirect
242. #486	C₂²×C₃	semidirect
243. #486	C₂²×C₃	semidirect
244. #482	C₂²×C₃	semidirect
245. #482	C₂²×C₃	semidirect
246. #482	C₂²×C₃	semidirect
247. #482	C₂²×C₃	semidirect
248. #482	C₂²×C₃	semidirect
249. #482	C₂²×C₃	semidirect
250. #481	C₂²×C₃	semidirect
251. #481	C₂²×C₃	semidirect
252. #480	C₂²×C₃	semidirect
253. #480	C₂²×C₃	semidirect
254. #478	C₂²×C₃	semidirect
255. #476	C₂²×C₃	semidirect
256. #476	C₂²×C₃	semidirect
257. #474	C₂²×C₃	semidirect
258. #474	C₂²×C₃	semidirect
259. #469	C₂²×C₃	semidirect
260. #469	C₂²×C₃	semidirect
261. #466	C₂²×C₃	semidirect
262. #466	C₂²×C₃	semidirect
265. #447	C₂²×C₃	semidirect
266. #447	C₂²×C₃	semidirect
267. #447	C₂²×C₃	semidirect
268. #447	C₂²×C₃	semidirect
269. #442	C₂²×C₃	semidirect
270. C₄×D₈	C₂²×C₃	semidirect
271. C₄×D₈	C₂²×C₃	semidirect
272. #436	C₂²×C₃	semidirect
273. #435	C₂²×C₃	semidirect
274. C₈×D₄	C₂²×C₃	semidirect
275. #432	C₂²×C₃	semidirect
276. #431	C₂²×C₃	semidirect
277. #428	C₂²×C₃	semidirect
278. #427	C₂²×C₃	semidirect
279. #418	C₂²×C₃	semidirect
280. C₂×#102	C₂²×C₃	semidirect
281. #408	C₂²×C₃	semidirect
770. C₃	#61802	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×#3549	2
C₃×#3506	2
C₃×#3354	2
C₃×#3347	2
C₃×#3341	2
C₃×#3325	2
C₃×#3318	2
C₃×#3294	2
C₃×#3235	2
C₃×#3228	2
C₃×#3199	2
C₃×#3109	2
C₃×#3100	2
C₃×#3096	2
C₃×#2981	2
#61802	3

Subgroups — C3×#61802 #10680409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61802 #10680409