Subgroups — C₃×#60771 #10679378

Order 768.

2254 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3488	C₂	1	2	yes	maximal, complemented
2	C₃×#3204	C₂	1	2	yes	maximal, complemented
3	C₃×#3199	C₂	1	2	yes	maximal, complemented
4	C₃×#3198	C₂	1	4	yes	maximal, complemented
5	C₃×#3197	C₂	1	2	yes	maximal, complemented
6	C₃×#3194	C₂	1	4	yes	maximal, complemented
7	C₃×#3192	C₂	1	2	yes	maximal, complemented
8	C₃×#3099	C₂	1	2	yes	maximal, complemented
9	C₃×#3096	C₂	1	2	yes	maximal, complemented
10	C₃×#3055	C₂	1	2	yes	maximal, complemented
11	C₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3012	C₂	1	2	yes	maximal, complemented
14	C₃×#3008	C₂	1	2	yes	maximal, complemented
15	C₃×#2879	C₂	1	1	yes	maximal, characteristic, complemented
16	#60771	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×C₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
18	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
19	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
20	C₂×C₃×#135	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×D₈	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₃×#550	—	2	2	no	—
25	C₃×#548	—	2	2	no	—
26	C₃×#546	—	2	4	no	—
27	C₃×#546	—	2	2	no	—
28	C₃×D₄²	—	2	4	no	—
29	C₃×D₄²	—	2	2	no	—
30	C₃×#537	C₂²	1	2	yes	—
31	C₃×#537	C₂²	1	4	yes	complemented
32	C₃×#535	C₂²	1	2	yes	—
33	C₃×#535	C₂²	1	4	yes	complemented
34	C₃×#525	C₂²	1	4	yes	complemented
35	C₃×#525	C₂²	1	2	yes	complemented
36	C₂×C₃×#121	C₂²	1	4	yes	complemented
37	C₂×C₃×#121	C₂²	1	2	yes	complemented
38	C₃×#520	C₂²	1	2	yes	complemented
39	C₃×#485	C₂²	1	4	yes	complemented
40	C₃×#483	C₂²	1	4	yes	complemented
41	C₃×#482	C₂²	1	4	yes	complemented
42	C₃×#482	C₂²	1	4	yes	complemented
43	C₃×#482	C₂²	1	4	yes	complemented
44	C₃×#481	C₂²	1	4	yes	complemented
45	C₃×#481	C₂²	1	4	yes	complemented
46	C₃×#480	C₂²	1	4	yes	complemented
47	C₃×#470	C₂²	1	1	yes	characteristic, complemented
48	C₃×#470	C₂²	1	1	yes	characteristic, complemented
49	C₃×#469	C₂²	1	1	yes	characteristic, complemented
50	C₃×#469	C₂²	1	4	yes	complemented
51	C₃×#469	C₂²	1	2	yes	complemented
52	C₃×#469	C₂²	1	2	yes	complemented
53	C₃×#469	C₂²	1	2	yes	complemented
54	C₃×#469	C₂²	1	1	yes	characteristic, complemented
55	C₃×#469	C₂²	1	2	yes	complemented
56	C₃×#468	C₂²	1	2	yes	complemented
57	C₃×#468	C₂²	1	4	yes	complemented
58	C₃×#468	C₂²	1	2	yes	complemented
59	C₃×#466	C₂²	1	4	yes	complemented
60	C₃×#465	C₂²	1	4	yes	complemented
61	C₃×#452	C₂²	1	4	yes	complemented
62	C₃×#450	C₂²	1	4	yes	complemented
63	C₃×#449	C₂²	1	4	yes	complemented
64	C₃×#449	C₂²	1	4	yes	complemented
65	C₃×#449	C₂²	1	4	yes	complemented
66	C₃×#447	C₂²	1	4	yes	complemented
67	C₃×#447	C₂²	1	4	yes	complemented
68	C₃×#447	C₂²	1	4	yes	complemented
69	C₃×#428	C₂²	1	2	yes	complemented
70	C₃×#427	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₃×#106	C₂²	1	1	yes	characteristic, complemented
72	C₃×#418	C₂²	1	2	yes	complemented
73	C₃×#417	C₂²	1	2	yes	complemented
74	C₃×#416	C₂²	1	2	yes	complemented
75	C₂×C₃×#102	C₂²	1	2	yes	complemented
76	C₃×#408	C₂²	1	2	yes	complemented
77	C₃×#408	C₂²	1	2	yes	complemented
78	C₃×#408	C₂²	1	2	yes	complemented
79	C₃×#408	C₂²	1	2	yes	complemented
80	C₃×#407	C₂²	1	2	yes	complemented
81	C₃×#407	C₂²	1	2	yes	complemented
82	#3488	C₂×C₃	1	2	yes	complemented
83	#3204	C₂×C₃	1	2	yes	complemented
84	#3199	C₂×C₃	1	2	yes	complemented
85	#3198	C₂×C₃	1	4	yes	complemented
86	#3197	C₂×C₃	1	2	yes	complemented
87	#3194	C₂×C₃	1	4	yes	complemented
88	#3192	C₂×C₃	1	2	yes	complemented
89	#3099	C₂×C₃	1	2	yes	complemented
90	#3096	C₂×C₃	1	2	yes	complemented
91	#3055	C₂×C₃	1	2	yes	complemented
92	#3054	C₂×C₃	1	1	yes	characteristic, complemented
93	C₂×#469	C₂×C₃	1	1	yes	characteristic, complemented
94	#3012	C₂×C₃	1	2	yes	complemented
95	#3008	C₂×C₃	1	2	yes	complemented
96	#2879	C₂×C₃	1	1	yes	characteristic, complemented
97	C₃×H(5,𝔽₂)	—	4	4	no	—
98	C₃×H(5,𝔽₂)	—	4	4	no	—
99	C₂×C₃×#41	—	2	2	no	—
100	C₂×C₃×#41	—	4	2	no	—
101	C₂×C₃×#41	—	4	2	no	—
102	C₂×C₃×#41	D₄	1	2	yes	—
103	C₂×C₃×#41	D₄	1	2	yes	—
104	C₂×C₃×#41	C₂³	1	2	yes	—
105	C₂×C₃×#41	C₂³	1	4	yes	—
106	C₂×C₃×#41	C₂³	1	2	yes	—
107	C₂×C₃×#41	C₂³	1	2	yes	—
108	C₂²×C₃×Q₈	D₄	1	1	yes	characteristic
109	C₂²×C₃×D₄	—	2	2	no	—
110	C₂²×C₃×D₄	—	2	4	no	—
111	C₂²×C₃×D₄	—	2	4	no	—
112	C₂²×C₃×D₄	—	2	2	no	—
113	C₂²×C₃×D₄	D₄	1	1	yes	characteristic
114	C₂²×C₃×D₄	D₄	1	2	yes	—
115	C₂²×C₃×D₄	C₂³	1	2	yes	—
116	C₂²×C₃×D₄	C₂³	1	4	yes	—
117	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
118	C₂³×C₃×C₄	C₂³	1	2	yes	—
119	C₃×AGL(1,ℤ/8)	—	4	4	no	—
120	C₃×#135	—	4	2	no	—
121	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
123	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
124	C₂×C₃×D₈	—	4	2	no	—
125	C₂×C₃×D₈	C₂³	1	2	yes	—
126	C₂×C₃×D₈	C₂³	1	2	yes	—
127	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
128	C₂×C₃×D₈	C₂³	1	4	yes	—
129	C₂×C₃×M₁₆	—	4	2	no	—
130	C₂×C₃×M₁₆	—	4	2	no	—
131	C₂×C₃×M₁₆	C₂³	1	2	yes	—
132	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
133	C₂×C₃×M₁₆	C₂³	1	2	yes	—
134	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
135	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
136	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
137	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
138	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
139	C₂²×C₃×C₈	C₂³	1	2	yes	—
140	C₃×#127	—	2	2	no	—
141	C₃×#127	—	2	4	no	—
142	C₃×#124	—	2	2	no	—
143	C₃×#124	—	2	4	no	—
144	C₃×#123	—	2	2	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	C₂³	1	4	yes	—
149	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
150	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₃×#121	—	2	4	no	—
152	C₃×#121	—	2	2	no	—
153	C₃×#121	—	2	4	no	—
154	C₃×#121	—	2	4	no	—
155	C₃×#121	—	2	4	no	—
156	C₃×#121	—	2	2	no	—
157	C₃×#121	—	2	4	no	—
158	C₃×#121	—	2	2	no	—
159	C₃×#121	—	2	4	no	—
160	C₃×#121	C₂³	1	4	yes	—
161	C₃×#121	C₂³	1	4	yes	—
162	C₃×#121	C₂³	1	4	yes	—
163	C₃×#121	C₂³	1	4	yes	—
164	C₃×#121	C₂³	1	2	yes	—
165	C₃×#121	C₂³	1	2	yes	—
166	C₃×#121	C₂³	1	4	yes	—
167	C₃×#120	—	2	2	no	—
168	C₃×#120	—	2	4	no	—
169	C₃×#120	—	2	4	no	—
170	C₃×#120	—	2	4	no	—
171	C₃×#120	—	2	4	no	—
172	C₃×C₄×Q₈	—	2	2	no	—
173	C₃×C₄×D₄	—	2	4	no	—
174	C₃×C₄×D₄	—	2	2	no	—
175	C₃×C₄×D₄	—	2	2	no	—
176	C₃×C₄×D₄	—	2	4	no	—
177	C₃×C₄×D₄	—	2	2	no	—
178	C₃×C₄×D₄	—	2	4	no	—
179	C₃×#117	C₂³	1	2	yes	—
180	C₃×#117	C₂³	1	4	yes	—
181	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
183	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
184	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
185	C₃×#107	C₂³	1	2	yes	—
186	C₃×#107	C₂³	1	4	yes	—
187	C₃×#106	C₂³	1	2	yes	—
188	C₃×#106	C₂³	1	2	yes	—
189	C₃×#106	C₂³	1	1	yes	characteristic
190	C₃×#106	C₂³	1	1	yes	characteristic
191	C₃×#106	C₂³	1	4	yes	—
192	C₃×#103	C₂³	1	2	yes	—
193	C₃×#103	C₂³	1	2	yes	—
194	C₃×#103	C₂³	1	4	yes	—
195	C₃×#102	C₂³	1	4	yes	—
196	C₃×#102	C₂³	1	4	yes	—
197	C₃×#102	C₂³	1	2	yes	—
198	C₃×#102	C₂³	1	2	yes	—
199	C₃×#102	C₂³	1	4	yes	—
200	C₃×#102	C₂³	1	4	yes	—
201	C₃×#102	C₂³	1	4	yes	—
202	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
203	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
204	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
205	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
206	C₂×H(5,𝔽₂)	C₂²×C₃	1	2	yes	complemented
207	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
208	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	complemented
209	C₂×#135	C₂²×C₃	1	1	yes	characteristic, complemented
210	C₂²×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
211	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
212	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
213	#550	—	2	2	no	—
214	#548	—	2	2	no	—
215	#546	—	2	4	no	—
216	#546	—	2	2	no	—
217	D₄²	—	2	4	no	—
218	D₄²	—	2	2	no	—
219	#537	C₂²×C₃	1	2	yes	—
220	#537	C₂²×C₃	1	4	yes	complemented
221	#535	C₂²×C₃	1	2	yes	—
222	#535	C₂²×C₃	1	4	yes	complemented
223	#525	C₂²×C₃	1	4	yes	complemented
224	#525	C₂²×C₃	1	2	yes	complemented
225	C₂×#121	C₂²×C₃	1	4	yes	complemented
226	C₂×#121	C₂²×C₃	1	2	yes	complemented
227	#520	C₂²×C₃	1	2	yes	complemented
228	#485	C₂²×C₃	1	4	yes	complemented
229	#483	C₂²×C₃	1	4	yes	complemented
230	#482	C₂²×C₃	1	4	yes	complemented
231	#482	C₂²×C₃	1	4	yes	complemented
232	#482	C₂²×C₃	1	4	yes	complemented
233	#481	C₂²×C₃	1	4	yes	complemented
234	#481	C₂²×C₃	1	4	yes	complemented
235	#480	C₂²×C₃	1	4	yes	complemented
236	#470	C₂²×C₃	1	1	yes	characteristic, complemented
237	#470	C₂²×C₃	1	1	yes	characteristic, complemented
238	#469	C₂²×C₃	1	1	yes	characteristic, complemented
239	#469	C₂²×C₃	1	4	yes	complemented
240	#469	C₂²×C₃	1	2	yes	complemented
241	#469	C₂²×C₃	1	2	yes	complemented
242	#469	C₂²×C₃	1	2	yes	complemented
243	#469	C₂²×C₃	1	1	yes	characteristic, complemented
244	#469	C₂²×C₃	1	2	yes	complemented
245	#468	C₂²×C₃	1	2	yes	complemented
246	#468	C₂²×C₃	1	4	yes	complemented
247	#468	C₂²×C₃	1	2	yes	complemented
248	#466	C₂²×C₃	1	4	yes	complemented
249	#465	C₂²×C₃	1	4	yes	complemented
250	#452	C₂²×C₃	1	4	yes	complemented
251	#450	C₂²×C₃	1	4	yes	complemented
252	#449	C₂²×C₃	1	4	yes	complemented
253	#449	C₂²×C₃	1	4	yes	complemented
254	#449	C₂²×C₃	1	4	yes	complemented
255	#447	C₂²×C₃	1	4	yes	complemented
256	#447	C₂²×C₃	1	4	yes	complemented
257	#447	C₂²×C₃	1	4	yes	complemented
258	#428	C₂²×C₃	1	2	yes	complemented
259	#427	C₂²×C₃	1	1	yes	characteristic, complemented
260	C₂×#106	C₂²×C₃	1	1	yes	characteristic, complemented
261	#418	C₂²×C₃	1	2	yes	complemented
262	#417	C₂²×C₃	1	2	yes	complemented
263	#416	C₂²×C₃	1	2	yes	complemented
264	C₂×#102	C₂²×C₃	1	2	yes	complemented
265	#408	C₂²×C₃	1	2	yes	complemented
266	#408	C₂²×C₃	1	2	yes	complemented
267	#408	C₂²×C₃	1	2	yes	complemented
268	#408	C₂²×C₃	1	2	yes	complemented
269	#407	C₂²×C₃	1	2	yes	complemented
270	#407	C₂²×C₃	1	2	yes	complemented
271	C₂⁴×C₃	—	2	4	no	—
272	C₂⁴×C₃	—	2	2	no	—
273	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
274	C₂⁴×C₃	C₂×D₄	1	2	yes	—
275	C₃×#41	—	2	4	no	—
276	C₃×#41	—	2	4	no	—
277	C₃×#41	—	2	4	no	—
278	C₃×#41	—	2	4	no	—
279	C₃×#41	—	4	2	no	—
280	C₃×#41	—	4	2	no	—
281	C₃×#41	—	4	4	no	—
282	C₃×#41	—	4	4	no	—
283	C₃×#41	—	4	4	no	—
284	C₃×#41	—	4	4	no	—
285	C₃×#41	—	4	8	no	—
286	C₂×C₃×Q₈	—	4	2	no	—
287	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
288	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
289	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
290	C₂×C₃×D₄	—	2	2	no	—
291	C₂×C₃×D₄	—	2	4	no	—
292	C₂×C₃×D₄	—	2	4	no	—
293	C₂×C₃×D₄	—	2	2	no	—
294	C₂×C₃×D₄	—	2	4	no	—
295	C₂×C₃×D₄	—	2	2	no	—
296	C₂×C₃×D₄	—	2	4	no	—
297	C₂×C₃×D₄	—	2	4	no	—
298	C₂×C₃×D₄	—	2	4	no	—
299	C₂×C₃×D₄	—	2	4	no	—
300	C₂×C₃×D₄	—	2	2	no	—
301	C₂×C₃×D₄	—	2	4	no	—
302	C₂×C₃×D₄	—	2	4	no	—
303	C₂×C₃×D₄	—	4	2	no	—
304	C₂×C₃×D₄	—	4	4	no	—
305	C₂×C₃×D₄	—	4	4	no	—
306	C₂×C₃×D₄	—	4	4	no	—
307	C₂×C₃×D₄	—	4	16	no	—
308	C₂×C₃×D₄	—	4	8	no	—
309	C₂×C₃×D₄	—	8	4	no	—
310	C₂×C₃×D₄	—	8	8	no	—
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	C₂×D₄	1	4	yes	—
315	C₂×C₃×D₄	C₂⁴	1	4	yes	—
316	C₂×C₃×D₄	C₂⁴	1	2	yes	—
317	C₂²×C₃×C₄	—	2	2	no	—
318	C₂²×C₃×C₄	—	2	2	no	—
319	C₂²×C₃×C₄	—	2	4	no	—
320	C₂²×C₃×C₄	—	2	2	no	—
321	C₂²×C₃×C₄	—	2	4	no	—
322	C₂²×C₃×C₄	—	2	2	no	—
323	C₂²×C₃×C₄	—	4	2	no	—
324	C₂²×C₃×C₄	—	4	2	no	—
325	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
328	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
329	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
330	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
331	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
332	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
333	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
334	C₃×Q₁₆	—	4	1	no	—
335	C₃×SD₁₆	—	4	2	no	—
336	C₃×SD₁₆	—	4	4	no	—
337	C₃×D₈	—	4	2	no	—
338	C₃×D₈	—	4	2	no	—
339	C₃×D₈	—	4	1	no	—
340	C₃×D₈	—	4	4	no	—
341	C₃×M₁₆	—	2	4	no	—
342	C₃×M₁₆	—	4	1	no	—
343	C₃×M₁₆	—	4	1	no	—
344	C₃×M₁₆	—	4	1	no	—
345	C₃×M₁₆	—	4	1	no	—
346	C₃×M₁₆	—	4	2	no	—
347	C₂×C₃×C₈	—	2	2	no	—
348	C₂×C₃×C₈	—	2	2	no	—
349	C₂×C₃×C₈	—	4	2	no	—
350	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
351	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
352	C₂×C₃×C₈	C₂⁴	1	4	yes	—
353	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
354	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
355	C₃×C₄⋊C₄	—	2	4	no	—
356	C₃×C₄⋊C₄	—	2	2	no	—
357	C₃×C₄⋊C₄	—	2	2	no	—
358	C₃×C₄⋊C₄	—	2	4	no	—
359	C₃×C₄⋊C₄	—	2	2	no	—
360	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
361	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
362	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
363	C₃×C₂²⋊C₄	—	2	4	no	—
364	C₃×C₂²⋊C₄	—	2	2	no	—
365	C₃×C₂²⋊C₄	—	2	2	no	—
366	C₃×C₂²⋊C₄	—	2	4	no	—
367	C₃×C₂²⋊C₄	—	2	2	no	—
368	C₃×C₂²⋊C₄	—	2	4	no	—
369	C₃×C₂²⋊C₄	—	2	2	no	—
370	C₃×C₂²⋊C₄	—	2	4	no	—
371	C₃×C₂²⋊C₄	—	2	4	no	—
372	C₃×C₂²⋊C₄	—	2	4	no	—
373	C₃×C₂²⋊C₄	—	2	4	no	—
374	C₃×C₂²⋊C₄	—	2	2	no	—
375	C₃×C₄²	—	2	4	no	—
376	C₃×C₄²	—	2	2	no	—
377	H(5,𝔽₂)	—	4	4	no	—
378	H(5,𝔽₂)	—	4	4	no	—
379	C₂×#41	—	2	2	no	—
380	C₂×#41	—	4	2	no	—
381	C₂×#41	—	4	2	no	—
382	C₂×#41	C₃×D₄	1	2	yes	—
383	C₂×#41	C₃×D₄	1	2	yes	—
384	C₂×#41	C₂³×C₃	1	2	yes	—
385	C₂×#41	C₂³×C₃	1	4	yes	—
386	C₂×#41	C₂³×C₃	1	2	yes	—
387	C₂×#41	C₂³×C₃	1	2	yes	—
388	C₂²×Q₈	C₃×D₄	1	1	yes	characteristic
389	C₂²×D₄	—	2	2	no	—
390	C₂²×D₄	—	2	4	no	—
391	C₂²×D₄	—	2	4	no	—
392	C₂²×D₄	—	2	2	no	—
393	C₂²×D₄	C₃×D₄	1	1	yes	characteristic
394	C₂²×D₄	C₃×D₄	1	2	yes	—
395	C₂²×D₄	C₂³×C₃	1	2	yes	—
396	C₂²×D₄	C₂³×C₃	1	4	yes	—
397	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₃	1	2	yes	—
399	AGL(1,ℤ/8)	—	4	4	no	—
400	#135	—	4	2	no	—
401	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
402	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
403	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
404	C₂×D₈	—	4	2	no	—
405	C₂×D₈	C₂³×C₃	1	2	yes	—
406	C₂×D₈	C₂³×C₃	1	2	yes	—
407	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
408	C₂×D₈	C₂³×C₃	1	4	yes	—
409	C₂×M₁₆	—	4	2	no	—
410	C₂×M₁₆	—	4	2	no	—
411	C₂×M₁₆	C₂³×C₃	1	2	yes	—
412	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
413	C₂×M₁₆	C₂³×C₃	1	2	yes	—
414	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
415	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
416	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
417	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
418	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
419	C₂²×C₈	C₂³×C₃	1	2	yes	—
420	#127	—	2	2	no	—
421	#127	—	2	4	no	—
422	#124	—	2	2	no	—
423	#124	—	2	4	no	—
424	#123	—	2	2	no	—
425	#123	—	2	4	no	—
426	C₂²⋊Q₈	—	2	2	no	—
427	C₂²⋊Q₈	—	2	4	no	—
428	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
429	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
430	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
431	#121	—	2	4	no	—
432	#121	—	2	2	no	—
433	#121	—	2	4	no	—
434	#121	—	2	4	no	—
435	#121	—	2	4	no	—
436	#121	—	2	2	no	—
437	#121	—	2	4	no	—
438	#121	—	2	2	no	—
439	#121	—	2	4	no	—
440	#121	C₂³×C₃	1	2	yes	—
441	#121	C₂³×C₃	1	4	yes	—
442	#121	C₂³×C₃	1	4	yes	—
443	#121	C₂³×C₃	1	4	yes	—
444	#121	C₂³×C₃	1	4	yes	—
445	#121	C₂³×C₃	1	4	yes	—
446	#121	C₂³×C₃	1	2	yes	—
447	#120	—	2	2	no	—
448	#120	—	2	4	no	—
449	#120	—	2	4	no	—
450	#120	—	2	4	no	—
451	#120	—	2	4	no	—
452	C₄×Q₈	—	2	2	no	—
453	C₄×D₄	—	2	4	no	—
454	C₄×D₄	—	2	2	no	—
455	C₄×D₄	—	2	2	no	—
456	C₄×D₄	—	2	4	no	—
457	C₄×D₄	—	2	2	no	—
458	C₄×D₄	—	2	4	no	—
459	#117	C₂³×C₃	1	2	yes	—
460	#117	C₂³×C₃	1	4	yes	—
461	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
463	C₂×C₂²⋊C₄	—	2	2	no	—
464	C₂×C₂²⋊C₄	—	2	4	no	—
465	#107	C₂³×C₃	1	2	yes	—
466	#107	C₂³×C₃	1	4	yes	—
467	#106	C₂³×C₃	1	2	yes	—
468	#106	C₂³×C₃	1	2	yes	—
469	#106	C₂³×C₃	1	1	yes	characteristic
470	#106	C₂³×C₃	1	1	yes	characteristic
471	#106	C₂³×C₃	1	4	yes	—
472	#103	C₂³×C₃	1	2	yes	—
473	#103	C₂³×C₃	1	2	yes	—
474	#103	C₂³×C₃	1	4	yes	—
475	#102	C₂³×C₃	1	4	yes	—
476	#102	C₂³×C₃	1	4	yes	—
477	#102	C₂³×C₃	1	2	yes	—
478	#102	C₂³×C₃	1	2	yes	—
479	#102	C₂³×C₃	1	4	yes	—
480	#102	C₂³×C₃	1	4	yes	—
481	#102	C₂³×C₃	1	4	yes	—
482	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
483	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
484	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
485	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
486	C₂³×C₃	—	2	2	no	—
487	C₂³×C₃	—	2	4	no	—
488	C₂³×C₃	—	2	2	no	—
489	C₂³×C₃	—	4	2	no	—
490	C₂³×C₃	—	4	2	no	—
491	C₂³×C₃	—	4	4	no	—
492	C₂³×C₃	—	4	8	no	—
493	C₂³×C₃	—	4	4	no	—
494	C₂³×C₃	—	8	2	no	—
495	C₂³×C₃	—	8	4	no	—
496	C₂³×C₃	—	8	2	no	—
497	C₂³×C₃	—	8	4	no	—
498	C₂³×C₃	C₂²×D₄	1	4	yes	—
499	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
500	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
501	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
502	C₃×Q₈	—	2	4	no	—
503	C₃×Q₈	—	2	2	no	—
504	C₃×Q₈	—	2	2	no	—
505	C₃×Q₈	—	4	2	no	—
506	C₃×D₄	—	2	8	no	—
507	C₃×D₄	—	2	4	no	—
508	C₃×D₄	—	2	4	no	—
509	C₃×D₄	—	2	2	no	—
510	C₃×D₄	—	2	4	no	—
511	C₃×D₄	—	2	2	no	—
512	C₃×D₄	—	4	2	no	—
513	C₃×D₄	—	4	4	no	—
514	C₃×D₄	—	4	8	no	—
515	C₃×D₄	—	4	8	no	—
516	C₃×D₄	—	4	8	no	—
517	C₃×D₄	—	4	4	no	—
518	C₃×D₄	—	4	4	no	—
519	C₃×D₄	—	4	4	no	—
520	C₃×D₄	—	8	4	no	—
521	C₃×D₄	—	8	2	no	—
522	C₃×D₄	—	8	4	no	—
523	C₃×D₄	—	8	4	no	—
524	C₃×D₄	—	8	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	1	no	—
529	C₂×C₃×C₄	—	2	1	no	—
530	C₂×C₃×C₄	—	2	1	no	—
531	C₂×C₃×C₄	—	2	1	no	—
532	C₂×C₃×C₄	—	2	4	no	—
533	C₂×C₃×C₄	—	2	4	no	—
534	C₂×C₃×C₄	—	2	2	no	—
535	C₂×C₃×C₄	—	2	4	no	—
536	C₂×C₃×C₄	—	2	2	no	—
537	C₂×C₃×C₄	—	2	2	no	—
538	C₂×C₃×C₄	—	4	2	no	—
539	C₂×C₃×C₄	—	4	4	no	—
540	C₂×C₃×C₄	—	4	8	no	—
541	C₂×C₃×C₄	—	4	4	no	—
542	C₂×C₃×C₄	—	8	2	no	—
543	C₂×C₃×C₄	—	8	4	no	—
544	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
545	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
549	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
550	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
551	C₃×C₈	—	2	1	no	—
552	C₃×C₈	—	2	1	no	—
553	C₃×C₈	—	2	1	no	—
554	C₃×C₈	—	2	1	no	—
555	C₃×C₈	—	2	4	no	—
556	C₂⁴	—	2	4	no	—
557	C₂⁴	—	2	2	no	—
558	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
559	C₂⁴	C₂×C₃×D₄	1	2	yes	—
560	#41	—	2	4	no	—
561	#41	—	2	4	no	—
562	#41	—	2	4	no	—
563	#41	—	2	4	no	—
564	#41	—	4	2	no	—
565	#41	—	4	2	no	—
566	#41	—	4	4	no	—
567	#41	—	4	4	no	—
568	#41	—	4	4	no	—
569	#41	—	4	4	no	—
570	#41	—	4	8	no	—
571	C₂×Q₈	—	4	2	no	—
572	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
573	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
574	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	4	2	no	—
589	C₂×D₄	—	4	4	no	—
590	C₂×D₄	—	4	4	no	—
591	C₂×D₄	—	4	4	no	—
592	C₂×D₄	—	4	16	no	—
593	C₂×D₄	—	4	8	no	—
594	C₂×D₄	—	8	4	no	—
595	C₂×D₄	—	8	8	no	—
596	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
597	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
598	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
599	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
600	C₂×D₄	C₂⁴×C₃	1	4	yes	—
601	C₂×D₄	C₂⁴×C₃	1	2	yes	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	4	2	no	—
609	C₂²×C₄	—	4	2	no	—
610	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
611	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
612	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
613	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
614	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
616	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
619	Q₁₆	—	4	1	no	—
620	SD₁₆	—	4	2	no	—
621	SD₁₆	—	4	4	no	—
622	D₈	—	4	2	no	—
623	D₈	—	4	2	no	—
624	D₈	—	4	1	no	—
625	D₈	—	4	4	no	—
626	M₁₆	—	2	4	no	—
627	M₁₆	—	4	1	no	—
628	M₁₆	—	4	1	no	—
629	M₁₆	—	4	1	no	—
630	M₁₆	—	4	1	no	—
631	M₁₆	—	4	2	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	—	2	2	no	—
634	C₂×C₈	—	4	2	no	—
635	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
636	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
637	C₂×C₈	C₂⁴×C₃	1	4	yes	—
638	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
639	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
646	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
647	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₄²	—	2	4	no	—
661	C₄²	—	2	2	no	—
662	C₂²×C₃	—	2	2	no	—
663	C₂²×C₃	—	2	4	no	—
664	C₂²×C₃	—	2	2	no	—
665	C₂²×C₃	—	2	2	no	—
666	C₂²×C₃	—	2	4	no	—
667	C₂²×C₃	—	2	1	no	—
668	C₂²×C₃	—	2	1	no	—
669	C₂²×C₃	—	2	4	no	—
670	C₂²×C₃	—	4	4	no	—
671	C₂²×C₃	—	4	2	no	—
672	C₂²×C₃	—	4	4	no	—
673	C₂²×C₃	—	4	2	no	—
674	C₂²×C₃	—	4	4	no	—
675	C₂²×C₃	—	4	2	no	—
676	C₂²×C₃	—	8	2	no	—
677	C₂²×C₃	—	8	4	no	—
678	C₂²×C₃	—	16	4	no	—
679	C₂²×C₃	—	16	8	no	—
680	C₂²×C₃	#534	1	2	yes	—
681	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
682	C₃×C₄	—	2	1	no	—
683	C₃×C₄	—	2	1	no	—
684	C₃×C₄	—	2	4	no	—
685	C₃×C₄	—	4	4	no	—
686	C₃×C₄	—	4	2	no	—
687	C₃×C₄	—	4	2	no	—
688	C₃×C₄	—	4	2	no	—
689	C₃×C₄	#534	1	2	yes	—
690	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
691	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
692	C₂³	—	2	2	no	—
693	C₂³	—	2	4	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	4	2	no	—
697	C₂³	—	4	4	no	—
698	C₂³	—	4	8	no	—
699	C₂³	—	4	4	no	—
700	C₂³	—	8	2	no	—
701	C₂³	—	8	4	no	—
702	C₂³	—	8	2	no	—
703	C₂³	—	8	4	no	—
704	C₂³	C₂²×C₃×D₄	1	4	yes	—
705	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
706	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
707	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
708	Q₈	—	2	4	no	—
709	Q₈	—	2	2	no	—
710	Q₈	—	2	2	no	—
711	Q₈	—	4	2	no	—
712	D₄	—	2	8	no	—
713	D₄	—	2	4	no	—
714	D₄	—	2	2	no	—
715	D₄	—	2	4	no	—
716	D₄	—	2	2	no	—
717	D₄	—	2	4	no	—
718	D₄	—	4	2	no	—
719	D₄	—	4	4	no	—
720	D₄	—	4	8	no	—
721	D₄	—	4	8	no	—
722	D₄	—	4	8	no	—
723	D₄	—	4	4	no	—
724	D₄	—	4	4	no	—
725	D₄	—	4	4	no	—
726	D₄	—	8	4	no	—
727	D₄	—	8	4	no	—
728	D₄	—	8	4	no	—
729	D₄	—	8	4	no	—
730	D₄	—	8	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	4	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	4	2	no	—
745	C₂×C₄	—	4	4	no	—
746	C₂×C₄	—	4	8	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	8	2	no	—
749	C₂×C₄	—	8	4	no	—
750	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
751	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
752	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
753	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
754	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
755	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
756	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
757	C₈	—	2	1	no	—
758	C₈	—	2	1	no	—
759	C₈	—	2	1	no	—
760	C₈	—	2	1	no	—
761	C₈	—	2	4	no	—
762	C₂×C₃	—	2	2	no	—
763	C₂×C₃	—	4	1	no	—
764	C₂×C₃	—	4	1	no	—
765	C₂×C₃	—	4	4	no	—
766	C₂×C₃	—	8	4	no	—
767	C₂×C₃	—	8	2	no	—
768	C₂×C₃	C₂×#534	1	1	yes	characteristic
769	C₂×C₃	#3585	1	2	yes	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	1	no	—
772	C₂²	—	2	1	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	2	4	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	4	4	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	4	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	4	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	8	2	no	—
785	C₂²	—	8	4	no	—
786	C₂²	—	16	4	no	—
787	C₂²	—	16	8	no	—
788	C₂²	C₃×#534	1	2	yes	—
789	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
790	C₄	—	2	1	no	—
791	C₄	—	2	1	no	—
792	C₄	—	2	4	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	4	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	C₃×#534	1	2	yes	—
798	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
799	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
800	C₃	#60771	1	1	yes	characteristic, direct product factor, Sylow
801	C₂	—	2	2	no	—
802	C₂	—	4	1	no	—
803	C₂	—	4	4	no	—
804	C₂	—	4	1	no	—
805	C₂	—	8	4	no	—
806	C₂	—	8	2	no	—
807	C₂	C₂×C₃×#534	1	1	yes	characteristic
808	C₂	C₃×#3585	1	2	yes	—

	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 ◁ C₂²×C₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3488	C₂	semidirect
2. C₃×#3204	C₂	semidirect
3. C₃×#3199	C₂	semidirect
4. C₃×#3198	C₂	semidirect
5. C₃×#3197	C₂	semidirect
6. C₃×#3194	C₂	semidirect
7. C₃×#3192	C₂	semidirect
8. C₃×#3099	C₂	semidirect
9. C₃×#3096	C₂	semidirect
10. C₃×#3055	C₂	semidirect
11. C₃×#3054	C₂	semidirect
12. C₂×C₃×#469	C₂	semidirect
13. C₃×#3012	C₂	semidirect
14. C₃×#3008	C₂	semidirect
15. C₃×#2879	C₂	semidirect
16. #60771	C₃	direct (N × H)
17. C₂×C₃×H(5,𝔽₂)	C₂²	semidirect
19. C₂×C₃×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂×C₃×#135	C₂²	semidirect
21. C₂²×C₃×D₈	C₂²	semidirect
22. C₂²×C₃×M₁₆	C₂²	semidirect
23. C₂²×C₃×M₁₆	C₂²	semidirect
31. C₃×#537	C₂²	semidirect
33. C₃×#535	C₂²	semidirect
34. C₃×#525	C₂²	semidirect
35. C₃×#525	C₂²	semidirect
36. C₂×C₃×#121	C₂²	semidirect
37. C₂×C₃×#121	C₂²	semidirect
38. C₃×#520	C₂²	semidirect
39. C₃×#485	C₂²	semidirect
40. C₃×#483	C₂²	semidirect
41. C₃×#482	C₂²	semidirect
42. C₃×#482	C₂²	semidirect
43. C₃×#482	C₂²	semidirect
44. C₃×#481	C₂²	semidirect
45. C₃×#481	C₂²	semidirect
46. C₃×#480	C₂²	semidirect
47. C₃×#470	C₂²	semidirect
48. C₃×#470	C₂²	semidirect
49. C₃×#469	C₂²	semidirect
50. C₃×#469	C₂²	semidirect
51. C₃×#469	C₂²	semidirect
52. C₃×#469	C₂²	semidirect
53. C₃×#469	C₂²	semidirect
54. C₃×#469	C₂²	semidirect
55. C₃×#469	C₂²	semidirect
56. C₃×#468	C₂²	semidirect
57. C₃×#468	C₂²	semidirect
58. C₃×#468	C₂²	semidirect
59. C₃×#466	C₂²	semidirect
60. C₃×#465	C₂²	semidirect
61. C₃×#452	C₂²	semidirect
62. C₃×#450	C₂²	semidirect
63. C₃×#449	C₂²	semidirect
64. C₃×#449	C₂²	semidirect
65. C₃×#449	C₂²	semidirect
66. C₃×#447	C₂²	semidirect
67. C₃×#447	C₂²	semidirect
68. C₃×#447	C₂²	semidirect
69. C₃×#428	C₂²	semidirect
70. C₃×#427	C₂²	semidirect
71. C₂×C₃×#106	C₂²	semidirect
72. C₃×#418	C₂²	semidirect
73. C₃×#417	C₂²	semidirect
74. C₃×#416	C₂²	semidirect
75. C₂×C₃×#102	C₂²	semidirect
76. C₃×#408	C₂²	semidirect
77. C₃×#408	C₂²	semidirect
78. C₃×#408	C₂²	semidirect
79. C₃×#408	C₂²	semidirect
80. C₃×#407	C₂²	semidirect
81. C₃×#407	C₂²	semidirect
82. #3488	C₂×C₃	semidirect
83. #3204	C₂×C₃	semidirect
84. #3199	C₂×C₃	semidirect
85. #3198	C₂×C₃	semidirect
86. #3197	C₂×C₃	semidirect
87. #3194	C₂×C₃	semidirect
88. #3192	C₂×C₃	semidirect
89. #3099	C₂×C₃	semidirect
90. #3096	C₂×C₃	semidirect
91. #3055	C₂×C₃	semidirect
92. #3054	C₂×C₃	semidirect
93. C₂×#469	C₂×C₃	semidirect
94. #3012	C₂×C₃	semidirect
95. #3008	C₂×C₃	semidirect
96. #2879	C₂×C₃	semidirect
206. C₂×H(5,𝔽₂)	C₂²×C₃	semidirect
208. C₂×AGL(1,ℤ/8)	C₂²×C₃	semidirect
209. C₂×#135	C₂²×C₃	semidirect
210. C₂²×D₈	C₂²×C₃	semidirect
211. C₂²×M₁₆	C₂²×C₃	semidirect
212. C₂²×M₁₆	C₂²×C₃	semidirect
220. #537	C₂²×C₃	semidirect
222. #535	C₂²×C₃	semidirect
223. #525	C₂²×C₃	semidirect
224. #525	C₂²×C₃	semidirect
225. C₂×#121	C₂²×C₃	semidirect
226. C₂×#121	C₂²×C₃	semidirect
227. #520	C₂²×C₃	semidirect
228. #485	C₂²×C₃	semidirect
229. #483	C₂²×C₃	semidirect
230. #482	C₂²×C₃	semidirect
231. #482	C₂²×C₃	semidirect
232. #482	C₂²×C₃	semidirect
233. #481	C₂²×C₃	semidirect
234. #481	C₂²×C₃	semidirect
235. #480	C₂²×C₃	semidirect
236. #470	C₂²×C₃	semidirect
237. #470	C₂²×C₃	semidirect
238. #469	C₂²×C₃	semidirect
239. #469	C₂²×C₃	semidirect
240. #469	C₂²×C₃	semidirect
241. #469	C₂²×C₃	semidirect
242. #469	C₂²×C₃	semidirect
243. #469	C₂²×C₃	semidirect
244. #469	C₂²×C₃	semidirect
245. #468	C₂²×C₃	semidirect
246. #468	C₂²×C₃	semidirect
247. #468	C₂²×C₃	semidirect
248. #466	C₂²×C₃	semidirect
249. #465	C₂²×C₃	semidirect
250. #452	C₂²×C₃	semidirect
251. #450	C₂²×C₃	semidirect
252. #449	C₂²×C₃	semidirect
253. #449	C₂²×C₃	semidirect
254. #449	C₂²×C₃	semidirect
255. #447	C₂²×C₃	semidirect
256. #447	C₂²×C₃	semidirect
257. #447	C₂²×C₃	semidirect
258. #428	C₂²×C₃	semidirect
259. #427	C₂²×C₃	semidirect
260. C₂×#106	C₂²×C₃	semidirect
261. #418	C₂²×C₃	semidirect
262. #417	C₂²×C₃	semidirect
263. #416	C₂²×C₃	semidirect
264. C₂×#102	C₂²×C₃	semidirect
265. #408	C₂²×C₃	semidirect
266. #408	C₂²×C₃	semidirect
267. #408	C₂²×C₃	semidirect
268. #408	C₂²×C₃	semidirect
269. #407	C₂²×C₃	semidirect
270. #407	C₂²×C₃	semidirect
800. C₃	#60771	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×#3488	2
C₃×#3204	2
C₃×#3199	2
C₃×#3198	2
C₃×#3197	2
C₃×#3194	2
C₃×#3192	2
C₃×#3099	2
C₃×#3096	2
C₃×#3055	2
C₃×#3054	2
C₂×C₃×#469	2
C₃×#3012	2
C₃×#3008	2
C₃×#2879	2
#60771	3

Subgroups — C3×#60771 #10679378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60771 #10679378