Subgroups — C₃×C₃⋊D₃×AGL(1,ℤ/8) #13179523

Order 1728.

2060 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64158	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64141	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64123	C₂	1	2	yes	maximal, complemented
7	C₃×SD₁₆×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
8	C₃×#64120	C₂	1	2	yes	maximal, complemented
9	C₃×D₈×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
10	C₃×#64117	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×M₁₆×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃⋊D₃×AGL(1,ℤ/8)	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₃×D₃×AGL(1,ℤ/8)	—	3	4	no	maximal
14	C₂³×C₃×C₃⋊D₃	—	2	1	no	—
15	C₃³×#41	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃×#638	—	2	1	no	—
18	C₃×#3832	C₂²	1	1	yes	characteristic, complemented
19	C₃×Q₈×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
20	C₃×#3830	—	2	1	no	—
21	C₃×#3830	C₂²	1	1	yes	characteristic, complemented
22	C₃×D₄×C₃⋊D₃	—	2	1	no	—
23	C₃×D₄×C₃⋊D₃	—	2	1	no	—
24	C₃×D₄×C₃⋊D₃	—	2	1	no	—
25	C₃×D₄×C₃⋊D₃	C₂²	1	2	yes	—
26	C₃×D₄×C₃⋊D₃	C₂²	1	2	yes	complemented
27	C₃×D₄×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
28	C₃×#3828	—	2	1	no	—
29	C₃×#3828	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×C₄×C₃⋊D₃	—	2	1	no	—
32	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
33	C₃³×SD₁₆	C₂²	1	2	yes	complemented
34	C₃³×D₈	C₂²	1	2	yes	complemented
35	C₃³×M₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3755	C₂²	1	2	yes	complemented
37	C₃×#3754	C₂²	1	2	yes	complemented
38	C₃×#3753	C₂²	1	2	yes	complemented
39	C₃×#3753	C₂²	1	2	yes	complemented
40	C₃×#3748	C₂²	1	1	yes	characteristic, complemented
41	C₃×#3745	C₂²	1	2	yes	complemented
42	C₃×#3744	C₂²	1	2	yes	complemented
43	C₃×#3743	C₂²	1	2	yes	complemented
44	C₃×C₈×C₃⋊D₃	C₂²	1	2	yes	complemented
45	#41×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×D₄×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
47	C₃×D₃×#41	—	3	4	no	—
48	C₂×C₃×D₃×D₄	—	3	4	no	—
49	C₃²×AGL(1,ℤ/8)	—	2	4	no	—
50	C₃²×AGL(1,ℤ/8)	D₃	1	4	yes	complemented
51	C₃²×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
52	#64158	C₂×C₃	1	1	yes	characteristic, complemented
53	#64141	C₂×C₃	1	1	yes	characteristic, complemented
54	#64123	C₂×C₃	1	2	yes	complemented
55	SD₁₆×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
56	#64120	C₂×C₃	1	2	yes	complemented
57	D₈×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
58	#64117	C₂×C₃	1	1	yes	characteristic, complemented
59	M₁₆×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
60	C₃×#949	—	3	4	no	—
61	C₃×#932	—	3	4	no	—
62	C₃×#914	—	3	8	no	—
63	C₃×D₃×SD₁₆	—	3	8	no	—
64	C₃×#911	—	3	8	no	—
65	C₃×D₃×D₈	—	3	8	no	—
66	C₃×#908	—	3	4	no	—
67	C₃×D₃×M₁₆	—	3	4	no	—
68	C₂³×C₃³	—	2	1	no	—
69	C₂²×C₃×C₃⋊D₃	—	2	1	no	—
70	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
71	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
72	C₂²×C₃×C₃⋊D₃	—	2	1	no	—
73	C₂²×C₃×C₃⋊D₃	—	4	4	no	—
74	C₂²×C₃×C₃⋊D₃	D₄	1	1	yes	characteristic
75	C₃³×Q₈	C₂³	1	1	yes	characteristic, complemented
76	C₃³×D₄	—	2	1	no	—
77	C₃³×D₄	—	2	1	no	—
78	C₃³×D₄	C₂³	1	2	yes	—
79	C₃³×D₄	C₂³	1	1	yes	characteristic, complemented
80	C₂×C₃³×C₄	—	2	1	no	—
81	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
82	C₃×#638	—	2	1	no	—
83	C₃×#638	—	2	1	no	—
84	C₃×#638	—	2	1	no	—
85	C₃×#638	—	2	2	no	—
86	C₃×#638	—	2	2	no	—
87	C₂×C₃×C₃⋊Dic₃	—	2	1	no	—
88	C₂×C₃×C₃⋊Dic₃	D₄	1	1	yes	characteristic
89	C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
90	C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
91	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	2	yes	—
92	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic, complemented
93	C₃×C₄×C₃⋊D₃	—	2	1	no	—
94	C₃×C₄×C₃⋊D₃	—	2	1	no	—
95	C₃×C₄×C₃⋊D₃	—	2	1	no	—
96	C₃×C₄×C₃⋊D₃	D₄	1	1	yes	characteristic
97	C₃×C₄×C₃⋊D₃	D₄	1	1	yes	characteristic
98	C₃×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
99	C₃×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
100	C₃×#634	—	2	1	no	—
101	C₃×#634	C₂³	1	1	yes	characteristic, complemented
102	C₃³×C₈	C₂³	1	2	yes	complemented
103	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	complemented
104	C₂×C₃×AGL(1,ℤ/8)	—	9	1	no	—
105	D₃×AGL(1,ℤ/8)	—	3	4	no	—
106	C₂³×C₃⋊D₃	—	2	1	no	—
107	C₂³×C₃×D₃	—	6	4	no	—
108	C₃²×#41	—	2	4	no	—
109	C₃²×#41	C₂×D₃	1	4	yes	complemented
110	C₃²×#41	C₂²×C₃	1	1	yes	characteristic, complemented
111	C₂×C₃²×D₄	—	2	4	no	—
112	C₂×C₃²×D₄	C₂×D₃	1	4	yes	complemented
113	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
114	C₂×#638	—	2	1	no	—
115	#3832	C₂²×C₃	1	1	yes	characteristic, complemented
116	Q₈×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic, complemented
117	#3830	—	2	1	no	—
118	#3830	C₂²×C₃	1	1	yes	characteristic, complemented
119	D₄×C₃⋊D₃	—	2	1	no	—
120	D₄×C₃⋊D₃	—	2	1	no	—
121	D₄×C₃⋊D₃	—	2	1	no	—
122	D₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
123	D₄×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
124	D₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic, complemented
125	#3828	—	2	1	no	—
126	#3828	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic, complemented
128	C₂×C₄×C₃⋊D₃	—	2	1	no	—
129	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₃×#67	—	6	4	no	—
131	C₃×#239	—	3	4	no	—
132	C₃×D₃×Q₈	—	3	4	no	—
133	C₃×#237	—	3	4	no	—
134	C₃×#237	—	6	4	no	—
135	C₃×D₃×D₄	—	3	8	no	—
136	C₃×D₃×D₄	—	3	8	no	—
137	C₃×D₃×D₄	—	3	4	no	—
138	C₃×D₃×D₄	—	6	4	no	—
139	C₃×D₃×D₄	—	6	4	no	—
140	C₃×D₃×D₄	—	6	4	no	—
141	C₃×#235	—	3	4	no	—
142	C₃×#235	—	6	4	no	—
143	C₂×C₃×D₁₂	—	3	4	no	—
144	C₂×C₃×C₄×D₃	—	3	4	no	—
145	C₂×C₃×C₄×D₃	—	6	4	no	—
146	C₃²×SD₁₆	—	2	8	no	—
147	C₃²×SD₁₆	C₂×D₃	1	8	yes	complemented
148	C₃²×SD₁₆	C₂²×C₃	1	2	yes	complemented
149	C₃²×D₈	—	2	8	no	—
150	C₃²×D₈	C₂×D₃	1	8	yes	complemented
151	C₃²×D₈	C₂²×C₃	1	2	yes	complemented
152	C₃²×M₁₆	—	2	4	no	—
153	C₃²×M₁₆	C₂×D₃	1	4	yes	complemented
154	C₃²×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
155	#3755	C₂²×C₃	1	2	yes	complemented
156	#3754	C₂²×C₃	1	2	yes	complemented
157	#3753	C₂²×C₃	1	2	yes	complemented
158	#3753	C₂²×C₃	1	2	yes	complemented
159	#3748	C₂²×C₃	1	1	yes	characteristic, complemented
160	#3745	C₂²×C₃	1	2	yes	complemented
161	#3744	C₂²×C₃	1	2	yes	complemented
162	#3743	C₂²×C₃	1	2	yes	complemented
163	C₈×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
164	C₃×#215	—	3	8	no	—
165	C₃×#214	—	3	8	no	—
166	C₃×#213	—	3	8	no	—
167	C₃×#213	—	3	8	no	—
168	C₃×#208	—	3	4	no	—
169	C₃×D₂₄	—	3	8	no	—
170	C₃×#204	—	3	8	no	—
171	C₃×ΓL(1,𝔽₂₅)	—	3	8	no	—
172	C₃×D₃×C₈	—	3	8	no	—
173	C₂²×C₃³	—	2	1	no	—
174	C₂²×C₃³	—	2	2	no	—
175	C₂²×C₃³	—	4	2	no	—
176	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
177	C₂×C₃×C₃⋊D₃	—	2	2	no	—
178	C₂×C₃×C₃⋊D₃	—	2	1	no	—
179	C₂×C₃×C₃⋊D₃	—	2	2	no	—
180	C₂×C₃×C₃⋊D₃	—	4	4	no	—
181	C₂×C₃×C₃⋊D₃	—	4	2	no	—
182	C₂×C₃×C₃⋊D₃	—	4	2	no	—
183	C₂×C₃×C₃⋊D₃	—	4	4	no	—
184	C₂×C₃×C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
185	C₂×C₃×C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
186	C₃³×C₄	—	2	1	no	—
187	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
188	C₃³×C₄	C₂⁴	1	1	yes	characteristic
189	C₃×C₃⋊Dic₃	—	2	1	no	—
190	C₃×C₃⋊Dic₃	C₂×D₄	1	1	yes	characteristic
191	C₃×C₃⋊Dic₃	C₂×D₄	1	1	yes	characteristic
192	C₂×C₃×#41	—	9	1	no	—
193	C₂²×C₃×D₄	—	9	1	no	—
194	D₃×#41	—	3	4	no	—
195	C₂×D₃×D₄	—	3	4	no	—
196	C₃×AGL(1,ℤ/8)	—	2	4	no	—
197	C₃×AGL(1,ℤ/8)	—	9	1	no	—
198	C₃×AGL(1,ℤ/8)	—	9	1	no	—
199	C₃×AGL(1,ℤ/8)	—	9	2	no	—
200	C₃×AGL(1,ℤ/8)	—	9	2	no	—
201	C₃×AGL(1,ℤ/8)	—	9	1	no	—
202	C₃×AGL(1,ℤ/8)	C₃×D₃	1	4	yes	complemented
203	C₃×AGL(1,ℤ/8)	C₃⋊D₃	1	1	yes	characteristic, direct product factor
204	C₂×C₃×SD₁₆	—	9	2	no	—
205	C₂×C₃×D₈	—	9	2	no	—
206	C₂×C₃×M₁₆	—	9	1	no	—
207	#949	—	3	4	no	—
208	#932	—	3	4	no	—
209	#914	—	3	8	no	—
210	D₃×SD₁₆	—	3	8	no	—
211	#911	—	3	8	no	—
212	D₃×D₈	—	3	8	no	—
213	#908	—	3	4	no	—
214	D₃×M₁₆	—	3	4	no	—
215	C₂³×C₃²	—	2	1	no	—
216	C₂³×C₃²	—	2	4	no	—
217	C₂³×C₃²	—	4	4	no	—
218	C₂²×C₃⋊D₃	—	2	1	no	—
219	C₂²×C₃⋊D₃	—	2	2	no	—
220	C₂²×C₃⋊D₃	—	2	2	no	—
221	C₂²×C₃⋊D₃	—	2	1	no	—
222	C₂²×C₃⋊D₃	—	4	4	no	—
223	C₂²×C₃⋊D₃	C₃×D₄	1	1	yes	characteristic
224	C₂²×C₃×D₃	—	3	4	no	—
225	C₂²×C₃×D₃	—	6	8	no	—
226	C₂²×C₃×D₃	—	6	8	no	—
227	C₂²×C₃×D₃	—	6	4	no	—
228	C₂²×C₃×D₃	—	6	4	no	—
229	C₂²×C₃×D₃	—	12	16	no	—
230	C₃²×Q₈	—	2	4	no	—
231	C₃²×Q₈	C₂²×D₃	1	4	yes	complemented
232	C₃²×Q₈	C₂³×C₃	1	1	yes	characteristic, complemented
233	C₃²×D₄	—	2	1	no	—
234	C₃²×D₄	—	2	1	no	—
235	C₃²×D₄	—	2	8	no	—
236	C₃²×D₄	—	2	4	no	—
237	C₃²×D₄	—	2	4	no	—
238	C₃²×D₄	—	2	4	no	—
239	C₃²×D₄	—	4	4	no	—
240	C₃²×D₄	—	4	4	no	—
241	C₃²×D₄	C₂²×D₃	1	8	yes	—
242	C₃²×D₄	C₂²×D₃	1	4	yes	complemented
243	C₃²×D₄	C₂³×C₃	1	2	yes	—
244	C₃²×D₄	C₂³×C₃	1	1	yes	characteristic, complemented
245	C₂×C₃²×C₄	—	2	1	no	—
246	C₂×C₃²×C₄	—	2	4	no	—
247	C₂×C₃²×C₄	—	2	4	no	—
248	C₂×C₃²×C₄	—	4	4	no	—
249	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
250	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
251	#638	—	2	1	no	—
252	#638	—	2	1	no	—
253	#638	—	2	1	no	—
254	#638	—	2	2	no	—
255	#638	—	2	2	no	—
256	C₂×C₃⋊Dic₃	—	2	1	no	—
257	C₂×C₃⋊Dic₃	C₃×D₄	1	1	yes	characteristic
258	C₄⋊(C₃⋊D₃)	—	2	1	no	—
259	C₄⋊(C₃⋊D₃)	—	2	1	no	—
260	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	2	yes	—
261	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	1	yes	characteristic, complemented
262	C₄×C₃⋊D₃	—	2	1	no	—
263	C₄×C₃⋊D₃	—	2	1	no	—
264	C₄×C₃⋊D₃	—	2	1	no	—
265	C₄×C₃⋊D₃	C₃×D₄	1	1	yes	characteristic
266	C₄×C₃⋊D₃	C₃×D₄	1	1	yes	characteristic
267	C₄×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
268	C₄×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
269	#634	—	2	1	no	—
270	#634	C₂³×C₃	1	1	yes	characteristic, complemented
271	C₃×#67	—	6	4	no	—
272	C₃×#67	—	6	8	no	—
273	C₃×#67	—	6	8	no	—
274	C₃×#67	—	6	4	no	—
275	C₃×#67	—	6	4	no	—
276	C₂×C₃×Dic₃	—	3	4	no	—
277	C₂×C₃×Dic₃	—	6	4	no	—
278	C₃×D₁₂	—	3	8	no	—
279	C₃×D₁₂	—	3	4	no	—
280	C₃×D₁₂	—	6	4	no	—
281	C₃×D₁₂	—	6	4	no	—
282	C₃×C₄×D₃	—	3	4	no	—
283	C₃×C₄×D₃	—	3	4	no	—
284	C₃×C₄×D₃	—	3	4	no	—
285	C₃×C₄×D₃	—	3	4	no	—
286	C₃×C₄×D₃	—	6	4	no	—
287	C₃×C₄×D₃	—	6	4	no	—
288	C₃×C₄×D₃	—	6	4	no	—
289	C₃×Dic₆	—	3	4	no	—
290	C₃×Dic₆	—	6	4	no	—
291	C₃²×C₈	—	2	8	no	—
292	C₃²×C₈	C₂²×D₃	1	8	yes	complemented
293	C₃²×C₈	C₂³×C₃	1	2	yes	complemented
294	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	2	yes	complemented
295	C₃×C₃⋊C₈	—	3	8	no	—
296	C₂×AGL(1,ℤ/8)	—	9	1	no	Sylow
297	C₂×C₃³	—	2	1	no	—
298	C₂×C₃³	—	4	2	no	—
299	C₂×C₃³	—	4	1	no	—
300	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
301	C₃×C₃⋊D₃	—	2	1	no	—
302	C₃×C₃⋊D₃	—	4	1	no	—
303	C₃×C₃⋊D₃	—	4	2	no	—
304	C₃×C₃⋊D₃	AGL(1,ℤ/8)	1	2	yes	direct product factor
305	C₂⁴×C₃	—	18	1	no	—
306	C₂³×D₃	—	6	4	no	—
307	C₃×#41	—	2	4	no	—
308	C₃×#41	—	9	1	no	—
309	C₃×#41	—	9	1	no	—
310	C₃×#41	—	9	1	no	—
311	C₃×#41	—	18	1	no	—
312	C₃×#41	—	18	1	no	—
313	C₃×#41	C₂×C₃×D₃	1	4	yes	complemented
314	C₃×#41	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
315	C₂×C₃×Q₈	—	9	1	no	—
316	C₂×C₃×D₄	—	2	4	no	—
317	C₂×C₃×D₄	—	9	2	no	—
318	C₂×C₃×D₄	—	9	2	no	—
319	C₂×C₃×D₄	—	9	1	no	—
320	C₂×C₃×D₄	—	9	1	no	—
321	C₂×C₃×D₄	—	18	1	no	—
322	C₂×C₃×D₄	—	18	1	no	—
323	C₂×C₃×D₄	—	18	1	no	—
324	C₂×C₃×D₄	—	18	1	no	—
325	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	complemented
326	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
327	C₂²×C₃×C₄	—	9	1	no	—
328	C₂²×C₃×C₄	—	18	1	no	—
329	C₂×#67	—	6	4	no	—
330	#239	—	3	4	no	—
331	D₃×Q₈	—	3	4	no	—
332	#237	—	3	4	no	—
333	#237	—	6	4	no	—
334	D₃×D₄	—	3	8	no	—
335	D₃×D₄	—	3	8	no	—
336	D₃×D₄	—	3	4	no	—
337	D₃×D₄	—	6	4	no	—
338	D₃×D₄	—	6	4	no	—
339	D₃×D₄	—	6	4	no	—
340	#235	—	3	4	no	—
341	#235	—	6	4	no	—
342	C₂×D₁₂	—	3	4	no	—
343	C₂×C₄×D₃	—	3	4	no	—
344	C₂×C₄×D₃	—	6	4	no	—
345	C₃×SD₁₆	—	2	8	no	—
346	C₃×SD₁₆	—	9	2	no	—
347	C₃×SD₁₆	—	9	2	no	—
348	C₃×SD₁₆	—	9	2	no	—
349	C₃×SD₁₆	C₂×C₃×D₃	1	8	yes	complemented
350	C₃×SD₁₆	C₂×C₃⋊D₃	1	2	yes	complemented
351	C₃×D₈	—	2	8	no	—
352	C₃×D₈	—	9	2	no	—
353	C₃×D₈	—	9	2	no	—
354	C₃×D₈	—	9	2	no	—
355	C₃×D₈	C₂×C₃×D₃	1	8	yes	complemented
356	C₃×D₈	C₂×C₃⋊D₃	1	2	yes	complemented
357	C₃×M₁₆	—	2	4	no	—
358	C₃×M₁₆	—	9	1	no	—
359	C₃×M₁₆	—	9	2	no	—
360	C₃×M₁₆	C₂×C₃×D₃	1	4	yes	complemented
361	C₃×M₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
362	C₂×C₃×C₈	—	9	2	no	—
363	#215	—	3	8	no	—
364	#214	—	3	8	no	—
365	#213	—	3	8	no	—
366	#213	—	3	8	no	—
367	#208	—	3	4	no	—
368	D₂₄	—	3	8	no	—
369	#204	—	3	8	no	—
370	ΓL(1,𝔽₂₅)	—	3	8	no	—
371	D₃×C₈	—	3	8	no	—
372	C₂²×C₃²	—	2	1	no	—
373	C₂²×C₃²	—	2	2	no	—
374	C₂²×C₃²	—	2	4	no	—
375	C₂²×C₃²	—	2	4	no	—
376	C₂²×C₃²	—	2	8	no	—
377	C₂²×C₃²	—	4	4	no	—
378	C₂²×C₃²	—	4	8	no	—
379	C₂²×C₃²	—	4	2	no	—
380	C₂²×C₃²	—	4	8	no	—
381	C₂²×C₃²	—	8	8	no	—
382	C₂²×C₃²	D₃×D₄	1	4	yes	—
383	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
384	C₂×C₃⋊D₃	—	2	2	no	—
385	C₂×C₃⋊D₃	—	2	1	no	—
386	C₂×C₃⋊D₃	—	2	2	no	—
387	C₂×C₃⋊D₃	—	4	4	no	—
388	C₂×C₃⋊D₃	—	4	2	no	—
389	C₂×C₃⋊D₃	—	4	2	no	—
390	C₂×C₃⋊D₃	—	4	4	no	—
391	C₂×C₃⋊D₃	C₂×C₃×D₄	1	1	yes	characteristic
392	C₂×C₃⋊D₃	C₂×C₃×D₄	1	1	yes	characteristic
393	C₂×C₃×D₃	—	3	4	no	—
394	C₂×C₃×D₃	—	3	4	no	—
395	C₂×C₃×D₃	—	6	8	no	—
396	C₂×C₃×D₃	—	6	4	no	—
397	C₂×C₃×D₃	—	6	8	no	—
398	C₂×C₃×D₃	—	12	8	no	—
399	C₂×C₃×D₃	—	12	16	no	—
400	C₂×C₃×D₃	—	12	16	no	—
401	C₂×C₃×D₃	—	12	8	no	—
402	C₃²×C₄	—	2	1	no	—
403	C₃²×C₄	—	2	4	no	—
404	C₃²×C₄	—	2	4	no	—
405	C₃²×C₄	—	2	4	no	—
406	C₃²×C₄	—	4	4	no	—
407	C₃²×C₄	D₃×D₄	1	4	yes	—
408	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
409	C₃²×C₄	C₂³×D₃	1	4	yes	—
410	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
411	C₃⋊Dic₃	—	2	1	no	—
412	C₃⋊Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
413	C₃⋊Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
414	C₃×Dic₃	—	3	4	no	—
415	C₃×Dic₃	—	3	4	no	—
416	C₃×Dic₃	—	6	4	no	—
417	C₂×#41	—	9	1	no	—
418	C₂²×D₄	—	9	1	no	—
419	AGL(1,ℤ/8)	—	9	1	no	—
420	AGL(1,ℤ/8)	—	9	1	no	—
421	AGL(1,ℤ/8)	—	9	2	no	—
422	AGL(1,ℤ/8)	—	9	2	no	—
423	AGL(1,ℤ/8)	—	9	1	no	—
424	AGL(1,ℤ/8)	C₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
425	C₂×SD₁₆	—	9	2	no	—
426	C₂×D₈	—	9	2	no	—
427	C₂×M₁₆	—	9	1	no	—
428	C₃³	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
429	C₂³×C₃	—	2	4	no	—
430	C₂³×C₃	—	2	1	no	—
431	C₂³×C₃	—	4	4	no	—
432	C₂³×C₃	—	9	1	no	—
433	C₂³×C₃	—	18	1	no	—
434	C₂³×C₃	—	18	2	no	—
435	C₂³×C₃	—	18	2	no	—
436	C₂³×C₃	—	18	1	no	—
437	C₂³×C₃	—	36	4	no	—
438	C₂²×D₃	—	3	4	no	—
439	C₂²×D₃	—	6	4	no	—
440	C₂²×D₃	—	6	8	no	—
441	C₂²×D₃	—	6	8	no	—
442	C₂²×D₃	—	6	4	no	—
443	C₂²×D₃	—	12	16	no	—
444	C₃×Q₈	—	2	4	no	—
445	C₃×Q₈	—	9	1	no	—
446	C₃×Q₈	—	18	1	no	—
447	C₃×Q₈	C₂²×C₃×D₃	1	4	yes	complemented
448	C₃×Q₈	C₂²×C₃⋊D₃	1	1	yes	characteristic, complemented
449	C₃×D₄	—	2	4	no	—
450	C₃×D₄	—	2	1	no	—
451	C₃×D₄	—	2	4	no	—
452	C₃×D₄	—	2	1	no	—
453	C₃×D₄	—	2	8	no	—
454	C₃×D₄	—	2	4	no	—
455	C₃×D₄	—	4	4	no	—
456	C₃×D₄	—	4	4	no	—
457	C₃×D₄	—	9	1	no	—
458	C₃×D₄	—	9	2	no	—
459	C₃×D₄	—	18	1	no	—
460	C₃×D₄	—	18	2	no	—
461	C₃×D₄	—	18	2	no	—
462	C₃×D₄	—	18	1	no	—
463	C₃×D₄	—	18	1	no	—
464	C₃×D₄	—	18	1	no	—
465	C₃×D₄	—	18	1	no	—
466	C₃×D₄	C₂²×C₃×D₃	1	8	yes	—
467	C₃×D₄	C₂²×C₃×D₃	1	4	yes	complemented
468	C₃×D₄	C₂²×C₃⋊D₃	1	2	yes	—
469	C₃×D₄	C₂²×C₃⋊D₃	1	1	yes	characteristic, complemented
470	C₂×C₃×C₄	—	2	4	no	—
471	C₂×C₃×C₄	—	2	1	no	—
472	C₂×C₃×C₄	—	2	4	no	—
473	C₂×C₃×C₄	—	4	4	no	—
474	C₂×C₃×C₄	—	9	1	no	—
475	C₂×C₃×C₄	—	9	1	no	—
476	C₂×C₃×C₄	—	9	1	no	—
477	C₂×C₃×C₄	—	9	1	no	—
478	C₂×C₃×C₄	—	9	1	no	—
479	C₂×C₃×C₄	—	18	1	no	—
480	C₂×C₃×C₄	—	18	1	no	—
481	C₂×C₃×C₄	—	18	1	no	—
482	C₂×C₃×C₄	—	18	1	no	—
483	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
484	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
485	#67	—	6	4	no	—
486	#67	—	6	8	no	—
487	#67	—	6	8	no	—
488	#67	—	6	4	no	—
489	#67	—	6	4	no	—
490	C₂×Dic₃	—	3	4	no	—
491	C₂×Dic₃	—	6	4	no	—
492	D₁₂	—	3	8	no	—
493	D₁₂	—	3	4	no	—
494	D₁₂	—	6	4	no	—
495	D₁₂	—	6	4	no	—
496	C₄×D₃	—	3	4	no	—
497	C₄×D₃	—	3	4	no	—
498	C₄×D₃	—	3	4	no	—
499	C₄×D₃	—	3	4	no	—
500	C₄×D₃	—	6	4	no	—
501	C₄×D₃	—	6	4	no	—
502	C₄×D₃	—	6	4	no	—
503	Dic₆	—	3	4	no	—
504	Dic₆	—	6	4	no	—
505	C₃×C₈	—	2	8	no	—
506	C₃×C₈	—	9	2	no	—
507	C₃×C₈	C₂²×C₃×D₃	1	8	yes	complemented
508	C₃×C₈	C₂²×C₃⋊D₃	1	2	yes	complemented
509	C₃⋊C₈	—	3	8	no	—
510	C₂×C₃²	—	2	1	no	—
511	C₂×C₃²	—	2	4	no	—
512	C₂×C₃²	—	2	4	no	—
513	C₂×C₃²	—	4	4	no	—
514	C₂×C₃²	—	4	2	no	—
515	C₂×C₃²	—	4	1	no	—
516	C₂×C₃²	—	4	8	no	—
517	C₂×C₃²	—	4	4	no	—
518	C₂×C₃²	—	8	4	no	—
519	C₂×C₃²	—	8	8	no	—
520	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
521	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
522	C₃⋊D₃	—	2	1	no	—
523	C₃⋊D₃	—	4	1	no	—
524	C₃⋊D₃	—	4	2	no	—
525	C₃⋊D₃	C₃×AGL(1,ℤ/8)	1	2	yes	direct product factor
526	C₃×D₃	—	3	8	no	—
527	C₃×D₃	—	6	4	no	—
528	C₃×D₃	—	12	4	no	—
529	C₃×D₃	—	12	8	no	—
530	C₂⁴	—	18	1	no	—
531	#41	—	9	1	no	—
532	#41	—	9	1	no	—
533	#41	—	9	1	no	—
534	#41	—	18	1	no	—
535	#41	—	18	1	no	—
536	#41	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
537	C₂×Q₈	—	9	1	no	—
538	C₂×D₄	—	9	2	no	—
539	C₂×D₄	—	9	2	no	—
540	C₂×D₄	—	9	1	no	—
541	C₂×D₄	—	9	1	no	—
542	C₂×D₄	—	18	1	no	—
543	C₂×D₄	—	18	1	no	—
544	C₂×D₄	—	18	1	no	—
545	C₂×D₄	—	18	1	no	—
546	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
547	C₂²×C₄	—	9	1	no	—
548	C₂²×C₄	—	18	1	no	—
549	SD₁₆	—	9	2	no	—
550	SD₁₆	—	9	2	no	—
551	SD₁₆	—	9	2	no	—
552	SD₁₆	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
553	D₈	—	9	2	no	—
554	D₈	—	9	2	no	—
555	D₈	—	9	2	no	—
556	D₈	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
557	M₁₆	—	9	1	no	—
558	M₁₆	—	9	2	no	—
559	M₁₆	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
560	C₂×C₈	—	9	2	no	—
561	C₂²×C₃	—	2	4	no	—
562	C₂²×C₃	—	2	8	no	—
563	C₂²×C₃	—	2	1	no	—
564	C₂²×C₃	—	2	2	no	—
565	C₂²×C₃	—	2	4	no	—
566	C₂²×C₃	—	4	4	no	—
567	C₂²×C₃	—	4	8	no	—
568	C₂²×C₃	—	4	8	no	—
569	C₂²×C₃	—	4	2	no	—
570	C₂²×C₃	—	8	8	no	—
571	C₂²×C₃	—	9	1	no	—
572	C₂²×C₃	—	9	1	no	—
573	C₂²×C₃	—	18	2	no	—
574	C₂²×C₃	—	18	1	no	—
575	C₂²×C₃	—	18	2	no	—
576	C₂²×C₃	—	36	2	no	—
577	C₂²×C₃	—	36	4	no	—
578	C₂²×C₃	—	36	2	no	—
579	C₂²×C₃	—	36	4	no	—
580	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
581	C₂²×C₃	D₄×C₃⋊D₃	1	1	yes	characteristic
582	C₂×D₃	—	3	4	no	—
583	C₂×D₃	—	3	4	no	—
584	C₂×D₃	—	6	8	no	—
585	C₂×D₃	—	6	4	no	—
586	C₂×D₃	—	6	8	no	—
587	C₂×D₃	—	12	16	no	—
588	C₂×D₃	—	12	8	no	—
589	C₂×D₃	—	12	16	no	—
590	C₂×D₃	—	12	8	no	—
591	C₃×C₄	—	2	4	no	—
592	C₃×C₄	—	2	1	no	—
593	C₃×C₄	—	2	4	no	—
594	C₃×C₄	—	2	4	no	—
595	C₃×C₄	—	4	4	no	—
596	C₃×C₄	—	9	1	no	—
597	C₃×C₄	—	9	1	no	—
598	C₃×C₄	—	18	1	no	—
599	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
600	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
601	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
602	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
603	Dic₃	—	3	4	no	—
604	Dic₃	—	3	4	no	—
605	Dic₃	—	6	4	no	—
606	C₃²	—	2	4	no	—
607	C₃²	D₃×AGL(1,ℤ/8)	1	4	yes	complemented
608	C₃²	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented
609	C₂³	—	2	1	no	—
610	C₂³	—	9	1	no	—
611	C₂³	—	18	1	no	—
612	C₂³	—	18	2	no	—
613	C₂³	—	18	2	no	—
614	C₂³	—	18	1	no	—
615	C₂³	—	36	4	no	—
616	Q₈	—	9	1	no	—
617	Q₈	—	18	1	no	—
618	Q₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
619	D₄	—	2	1	no	—
620	D₄	—	2	1	no	—
621	D₄	—	9	1	no	—
622	D₄	—	9	2	no	—
623	D₄	—	18	1	no	—
624	D₄	—	18	2	no	—
625	D₄	—	18	2	no	—
626	D₄	—	18	1	no	—
627	D₄	—	18	1	no	—
628	D₄	—	18	1	no	—
629	D₄	—	18	1	no	—
630	D₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
631	D₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	9	1	no	—
634	C₂×C₄	—	9	1	no	—
635	C₂×C₄	—	9	1	no	—
636	C₂×C₄	—	9	1	no	—
637	C₂×C₄	—	9	1	no	—
638	C₂×C₄	—	18	1	no	—
639	C₂×C₄	—	18	1	no	—
640	C₂×C₄	—	18	1	no	—
641	C₂×C₄	—	18	1	no	—
642	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
643	C₈	—	9	2	no	—
644	C₈	C₂²×C₃×C₃⋊D₃	1	2	yes	complemented
645	C₂×C₃	—	2	4	no	—
646	C₂×C₃	—	2	1	no	—
647	C₂×C₃	—	2	4	no	—
648	C₂×C₃	—	4	4	no	—
649	C₂×C₃	—	4	8	no	—
650	C₂×C₃	—	4	4	no	—
651	C₂×C₃	—	4	2	no	—
652	C₂×C₃	—	4	1	no	—
653	C₂×C₃	—	8	8	no	—
654	C₂×C₃	—	8	4	no	—
655	C₂×C₃	—	9	2	no	—
656	C₂×C₃	—	18	1	no	—
657	C₂×C₃	—	36	2	no	—
658	C₂×C₃	—	36	1	no	—
659	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
660	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
661	D₃	—	3	8	no	—
662	D₃	—	6	4	no	—
663	D₃	—	12	8	no	—
664	D₃	—	12	4	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	9	1	no	—
669	C₂²	—	9	1	no	—
670	C₂²	—	18	2	no	—
671	C₂²	—	18	1	no	—
672	C₂²	—	18	2	no	—
673	C₂²	—	36	2	no	—
674	C₂²	—	36	4	no	—
675	C₂²	—	36	2	no	—
676	C₂²	—	36	4	no	—
677	C₂²	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
678	C₄	—	2	1	no	—
679	C₄	—	9	1	no	—
680	C₄	—	9	1	no	—
681	C₄	—	18	1	no	—
682	C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
683	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
684	C₃	—	2	4	no	—
685	C₃	C₃×D₃×AGL(1,ℤ/8)	1	4	yes	complemented
686	C₃	C₃⋊D₃×AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor
687	C₂	—	2	1	no	—
688	C₂	—	4	2	no	—
689	C₂	—	4	1	no	—
690	C₂	—	9	2	no	—
691	C₂	—	18	1	no	—
692	C₂	—	36	2	no	—
693	C₂	—	36	1	no	—
694	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄×C₃⋊D₃
commutator, cosocle	C₃²×C₄	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×AGL(1,ℤ/8)	C₂
socle	C₂×C₃³	C₂²×D₄
hypercenter	C₃×AGL(1,ℤ/8)	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×AGL(1,ℤ/8)
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₃×#41×C₃⋊D₃	C₂	semidirect
2. C₂×C₃×D₄×C₃⋊D₃	C₂	semidirect
3. C₃³×AGL(1,ℤ/8)	C₂	semidirect
4. C₃×#64158	C₂	semidirect
5. C₃×#64141	C₂	semidirect
6. C₃×#64123	C₂	semidirect
7. C₃×SD₁₆×C₃⋊D₃	C₂	semidirect
8. C₃×#64120	C₂	semidirect
9. C₃×D₈×C₃⋊D₃	C₂	semidirect
10. C₃×#64117	C₂	semidirect
11. C₃×M₁₆×C₃⋊D₃	C₂	semidirect
12. C₃⋊D₃×AGL(1,ℤ/8)	C₃	direct (N × H)
15. C₃³×#41	C₂²	semidirect
16. C₂×C₃³×D₄	C₂²	semidirect
18. C₃×#3832	C₂²	semidirect
19. C₃×Q₈×C₃⋊D₃	C₂²	semidirect
21. C₃×#3830	C₂²	semidirect
26. C₃×D₄×C₃⋊D₃	C₂²	semidirect
27. C₃×D₄×C₃⋊D₃	C₂²	semidirect
29. C₃×#3828	C₂²	semidirect
30. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
33. C₃³×SD₁₆	C₂²	semidirect
34. C₃³×D₈	C₂²	semidirect
35. C₃³×M₁₆	C₂²	semidirect
36. C₃×#3755	C₂²	semidirect
37. C₃×#3754	C₂²	semidirect
38. C₃×#3753	C₂²	semidirect
39. C₃×#3753	C₂²	semidirect
40. C₃×#3748	C₂²	semidirect
41. C₃×#3745	C₂²	semidirect
42. C₃×#3744	C₂²	semidirect
43. C₃×#3743	C₂²	semidirect
44. C₃×C₈×C₃⋊D₃	C₂²	semidirect
45. #41×C₃⋊D₃	C₂×C₃	semidirect
46. C₂×D₄×C₃⋊D₃	C₂×C₃	semidirect
50. C₃²×AGL(1,ℤ/8)	D₃	semidirect
51. C₃²×AGL(1,ℤ/8)	C₂×C₃	semidirect
52. #64158	C₂×C₃	semidirect
53. #64141	C₂×C₃	semidirect
54. #64123	C₂×C₃	semidirect
55. SD₁₆×C₃⋊D₃	C₂×C₃	semidirect
56. #64120	C₂×C₃	semidirect
57. D₈×C₃⋊D₃	C₂×C₃	semidirect
58. #64117	C₂×C₃	semidirect
59. M₁₆×C₃⋊D₃	C₂×C₃	semidirect
75. C₃³×Q₈	C₂³	semidirect
79. C₃³×D₄	C₂³	semidirect
92. C₃×C₄⋊(C₃⋊D₃)	C₂³	semidirect
101. C₃×#634	C₂³	semidirect
102. C₃³×C₈	C₂³	semidirect
103. C₃×C₃⋊(C₃⋊C₈)	C₂³	semidirect
109. C₃²×#41	C₂×D₃	semidirect
110. C₃²×#41	C₂²×C₃	semidirect
112. C₂×C₃²×D₄	C₂×D₃	semidirect
113. C₂×C₃²×D₄	C₂²×C₃	semidirect
115. #3832	C₂²×C₃	semidirect
116. Q₈×C₃⋊D₃	C₂²×C₃	semidirect
118. #3830	C₂²×C₃	semidirect
123. D₄×C₃⋊D₃	C₂²×C₃	semidirect
124. D₄×C₃⋊D₃	C₂²×C₃	semidirect
126. #3828	C₂²×C₃	semidirect
127. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
147. C₃²×SD₁₆	C₂×D₃	semidirect
148. C₃²×SD₁₆	C₂²×C₃	semidirect
150. C₃²×D₈	C₂×D₃	semidirect
151. C₃²×D₈	C₂²×C₃	semidirect
153. C₃²×M₁₆	C₂×D₃	semidirect
154. C₃²×M₁₆	C₂²×C₃	semidirect
155. #3755	C₂²×C₃	semidirect
156. #3754	C₂²×C₃	semidirect
157. #3753	C₂²×C₃	semidirect
158. #3753	C₂²×C₃	semidirect
159. #3748	C₂²×C₃	semidirect
160. #3745	C₂²×C₃	semidirect
161. #3744	C₂²×C₃	semidirect
162. #3743	C₂²×C₃	semidirect
163. C₈×C₃⋊D₃	C₂²×C₃	semidirect
202. C₃×AGL(1,ℤ/8)	C₃×D₃	semidirect
203. C₃×AGL(1,ℤ/8)	C₃⋊D₃	direct (N × H)
231. C₃²×Q₈	C₂²×D₃	semidirect
232. C₃²×Q₈	C₂³×C₃	semidirect
242. C₃²×D₄	C₂²×D₃	semidirect
244. C₃²×D₄	C₂³×C₃	semidirect
261. C₄⋊(C₃⋊D₃)	C₂³×C₃	semidirect
270. #634	C₂³×C₃	semidirect
292. C₃²×C₈	C₂²×D₃	semidirect
293. C₃²×C₈	C₂³×C₃	semidirect
294. C₃⋊(C₃⋊C₈)	C₂³×C₃	semidirect
304. C₃×C₃⋊D₃	AGL(1,ℤ/8)	direct (N × H)
313. C₃×#41	C₂×C₃×D₃	semidirect
314. C₃×#41	C₂×C₃⋊D₃	semidirect
325. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
326. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
349. C₃×SD₁₆	C₂×C₃×D₃	semidirect
350. C₃×SD₁₆	C₂×C₃⋊D₃	semidirect
355. C₃×D₈	C₂×C₃×D₃	semidirect
356. C₃×D₈	C₂×C₃⋊D₃	semidirect
360. C₃×M₁₆	C₂×C₃×D₃	semidirect
361. C₃×M₁₆	C₂×C₃⋊D₃	semidirect
424. AGL(1,ℤ/8)	C₃×C₃⋊D₃	direct (N × H)
428. C₃³	C₂×AGL(1,ℤ/8)	semidirect
447. C₃×Q₈	C₂²×C₃×D₃	semidirect
448. C₃×Q₈	C₂²×C₃⋊D₃	semidirect
467. C₃×D₄	C₂²×C₃×D₃	semidirect
469. C₃×D₄	C₂²×C₃⋊D₃	semidirect
507. C₃×C₈	C₂²×C₃×D₃	semidirect
508. C₃×C₈	C₂²×C₃⋊D₃	semidirect
525. C₃⋊D₃	C₃×AGL(1,ℤ/8)	direct (N × H)
536. #41	C₂×C₃×C₃⋊D₃	semidirect
546. C₂×D₄	C₂×C₃×C₃⋊D₃	semidirect
552. SD₁₆	C₂×C₃×C₃⋊D₃	semidirect
556. D₈	C₂×C₃×C₃⋊D₃	semidirect
559. M₁₆	C₂×C₃×C₃⋊D₃	semidirect
607. C₃²	D₃×AGL(1,ℤ/8)	semidirect
608. C₃²	C₂×C₃×AGL(1,ℤ/8)	semidirect
618. Q₈	C₂²×C₃×C₃⋊D₃	semidirect
631. D₄	C₂²×C₃×C₃⋊D₃	semidirect
644. C₈	C₂²×C₃×C₃⋊D₃	semidirect
685. C₃	C₃×D₃×AGL(1,ℤ/8)	semidirect
686. C₃	C₃⋊D₃×AGL(1,ℤ/8)	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×#41×C₃⋊D₃	2
C₂×C₃×D₄×C₃⋊D₃	2
C₃³×AGL(1,ℤ/8)	2
C₃×#64158	2
C₃×#64141	2
C₃×#64123	2
C₃×SD₁₆×C₃⋊D₃	2
C₃×#64120	2
C₃×D₈×C₃⋊D₃	2
C₃×#64117	2
C₃×M₁₆×C₃⋊D₃	2
C₃⋊D₃×AGL(1,ℤ/8)	3
C₃×D₃×AGL(1,ℤ/8)	3

Subgroups — C3×C3⋊D3×AGL(1,ℤ/8) #13179523

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊D₃×AGL(1,ℤ/8) #13179523