Subgroups — C₃×#90465 #13061116

Order 1344.

536 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#6548	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6513	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#1141	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6479	C₂	1	2	yes	maximal, complemented
7	C₃×#6477	C₂	1	2	yes	maximal, complemented
8	C₃×#6474	C₂	1	2	yes	maximal, complemented
9	C₃×D₇×D₈	C₂	1	2	yes	maximal, complemented
10	C₃×#6471	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#6470	C₂	1	1	yes	maximal, characteristic, complemented
12	#90465	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₇×#41	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₃×C₂²⋊D₇	—	2	2	no	—
16	C₃×#1161	C₂²	1	2	yes	complemented
17	C₃×#1159	—	2	1	no	—
18	C₃×#1159	C₂²	1	2	yes	complemented
19	C₃×D₄×D₇	—	2	2	no	—
20	C₃×D₄×D₇	—	2	1	no	—
21	C₃×D₄×D₇	C₂²	1	2	yes	complemented
22	C₃×D₄×D₇	C₂²	1	2	yes	complemented
23	C₃×#1157	—	2	1	no	—
24	C₃×#1157	C₂²	1	1	yes	characteristic
25	C₃×#1157	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×D₂₈	—	2	1	no	—
27	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₇×SD₁₆	C₂²	1	2	yes	complemented
29	C₃×C₇×D₈	C₂²	1	2	yes	complemented
30	C₃×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₃×#1144	C₂²	1	1	yes	characteristic, complemented
32	C₃×#1143	C₂²	1	1	yes	characteristic, complemented
33	C₃×#1142	C₂²	1	1	yes	characteristic, complemented
34	C₃×#1141	C₂²	1	1	yes	characteristic, complemented
35	C₃×#1141	C₂²	1	2	yes	complemented
36	C₃×#1141	C₂²	1	2	yes	complemented
37	C₂×C₃×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×D₅₆	C₂²	1	2	yes	complemented
39	C₃×#1132	C₂²	1	2	yes	complemented
40	C₃×#1131	C₂²	1	2	yes	complemented
41	C₃×C₈×D₇	C₂²	1	2	yes	complemented
42	#6553	C₂×C₃	1	1	yes	characteristic, complemented
43	#6548	C₂×C₃	1	1	yes	characteristic, complemented
44	C₇×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
45	#6513	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×#1141	C₂×C₃	1	1	yes	characteristic, complemented
47	#6479	C₂×C₃	1	2	yes	complemented
48	#6477	C₂×C₃	1	2	yes	complemented
49	#6474	C₂×C₃	1	2	yes	complemented
50	D₇×D₈	C₂×C₃	1	2	yes	complemented
51	#6471	C₂×C₃	1	1	yes	characteristic, complemented
52	#6470	C₂×C₃	1	1	yes	characteristic, complemented
53	C₃×#576	—	7	1	no	maximal, Hall
54	C₂³×C₃×C₇	—	2	1	no	—
55	C₂²×C₃×D₇	—	2	1	no	—
56	C₂²×C₃×D₇	—	2	2	no	—
57	C₂²×C₃×D₇	—	2	2	no	—
58	C₃×C₇×Q₈	C₂³	1	1	yes	characteristic
59	C₃×C₇×D₄	—	2	1	no	—
60	C₃×C₇×D₄	—	2	1	no	—
61	C₃×C₇×D₄	C₂³	1	2	yes	—
62	C₃×C₇×D₄	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₇	—	2	1	no	—
64	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
65	C₃×C₂²⋊D₇	—	2	1	no	—
66	C₃×C₂²⋊D₇	—	2	2	no	—
67	C₃×C₂²⋊D₇	—	2	2	no	—
68	C₃×C₂²⋊D₇	—	2	2	no	—
69	C₃×C₂²⋊D₇	D₄	1	2	yes	—
70	C₂×C₃×Dic₇	—	2	2	no	—
71	C₃×D₂₈	—	2	2	no	—
72	C₃×D₂₈	—	2	1	no	—
73	C₃×D₂₈	D₄	1	1	yes	characteristic
74	C₃×D₂₈	C₂³	1	2	yes	—
75	C₃×D₂₈	C₂³	1	1	yes	characteristic
76	C₃×C₄×D₇	—	2	1	no	—
77	C₃×C₄×D₇	—	2	2	no	—
78	C₃×C₄×D₇	C₂³	1	2	yes	—
79	C₃×Dic₁₄	D₄	1	1	yes	characteristic
80	C₃×Dic₁₄	C₂³	1	1	yes	characteristic
81	C₃×C₇×C₈	C₂³	1	2	yes	—
82	C₃×C₇⋊C₈	C₂³	1	1	yes	characteristic
83	C₃×C₇⋊C₈	C₂³	1	1	yes	characteristic
84	C₇×#41	C₂²×C₃	1	1	yes	characteristic, complemented
85	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
86	C₂×C₂²⋊D₇	—	2	2	no	—
87	#1161	C₂²×C₃	1	2	yes	complemented
88	#1159	—	2	1	no	—
89	#1159	C₂²×C₃	1	2	yes	complemented
90	D₄×D₇	—	2	2	no	—
91	D₄×D₇	—	2	1	no	—
92	D₄×D₇	C₂²×C₃	1	2	yes	complemented
93	D₄×D₇	C₂²×C₃	1	2	yes	complemented
94	#1157	—	2	1	no	—
95	#1157	C₂²×C₃	1	1	yes	characteristic
96	#1157	C₂²×C₃	1	1	yes	characteristic, complemented
97	C₂×D₂₈	—	2	1	no	—
98	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₇×SD₁₆	C₂²×C₃	1	2	yes	complemented
100	C₇×D₈	C₂²×C₃	1	2	yes	complemented
101	C₇×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
102	#1144	C₂²×C₃	1	1	yes	characteristic, complemented
103	#1143	C₂²×C₃	1	1	yes	characteristic, complemented
104	#1142	C₂²×C₃	1	1	yes	characteristic, complemented
105	#1141	C₂²×C₃	1	1	yes	characteristic, complemented
106	#1141	C₂²×C₃	1	2	yes	complemented
107	#1141	C₂²×C₃	1	2	yes	complemented
108	C₂×C₇⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
109	D₅₆	C₂²×C₃	1	2	yes	complemented
110	#1132	C₂²×C₃	1	2	yes	complemented
111	#1131	C₂²×C₃	1	2	yes	complemented
112	C₈×D₇	C₂²×C₃	1	2	yes	complemented
113	C₃×H(5,𝔽₂)	—	7	1	no	—
114	C₃×H(5,𝔽₂)	—	7	1	no	—
115	C₃×AGL(1,ℤ/8)	—	7	2	no	—
116	C₃×AGL(1,ℤ/8)	—	7	2	no	—
117	C₃×AGL(1,ℤ/8)	—	7	1	no	—
118	C₃×AGL(1,ℤ/8)	D₇	1	1	yes	characteristic, complemented
119	C₃×#135	—	7	1	no	—
120	C₃×#135	—	7	2	no	—
121	C₂×C₃×D₈	—	7	1	no	—
122	C₂×C₃×D₈	—	7	2	no	—
123	C₃×#131	—	7	1	no	—
124	C₂²×C₃×C₇	—	2	2	no	—
125	C₂²×C₃×C₇	—	2	1	no	—
126	C₂²×C₃×C₇	—	8	1	no	—
127	C₂²×C₃×C₇	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃×D₇	—	2	2	no	—
129	C₂×C₃×D₇	—	2	1	no	—
130	C₂×C₃×D₇	—	8	2	no	—
131	C₂×C₃×D₇	—	8	2	no	—
132	C₂×C₃×D₇	—	8	1	no	—
133	C₂×C₃×D₇	C₂×D₄	1	2	yes	—
134	C₃×C₄×C₇	—	2	1	no	—
135	C₃×C₄×C₇	C₂×D₄	1	1	yes	characteristic
136	C₃×C₄×C₇	C₂⁴	1	1	yes	characteristic
137	C₃×Dic₇	—	2	1	no	—
138	C₃×Dic₇	C₂×D₄	1	2	yes	—
139	#576	—	7	1	no	Sylow
140	C₂³×C₇	—	2	1	no	—
141	C₂²×D₇	—	2	1	no	—
142	C₂²×D₇	—	2	2	no	—
143	C₂²×D₇	—	2	2	no	—
144	C₇×Q₈	C₂³×C₃	1	1	yes	characteristic
145	C₇×D₄	—	2	1	no	—
146	C₇×D₄	—	2	1	no	—
147	C₇×D₄	C₂³×C₃	1	2	yes	—
148	C₇×D₄	C₂³×C₃	1	1	yes	characteristic
149	C₂×C₄×C₇	—	2	1	no	—
150	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
151	C₂²⋊D₇	—	2	1	no	—
152	C₂²⋊D₇	—	2	2	no	—
153	C₂²⋊D₇	—	2	2	no	—
154	C₂²⋊D₇	—	2	2	no	—
155	C₂²⋊D₇	C₃×D₄	1	2	yes	—
156	C₂×Dic₇	—	2	2	no	—
157	D₂₈	—	2	2	no	—
158	D₂₈	—	2	1	no	—
159	D₂₈	C₃×D₄	1	1	yes	characteristic
160	D₂₈	C₂³×C₃	1	2	yes	—
161	D₂₈	C₂³×C₃	1	1	yes	characteristic
162	C₄×D₇	—	2	1	no	—
163	C₄×D₇	—	2	2	no	—
164	C₄×D₇	C₂³×C₃	1	2	yes	—
165	Dic₁₄	C₃×D₄	1	1	yes	characteristic
166	Dic₁₄	C₂³×C₃	1	1	yes	characteristic
167	C₇×C₈	C₂³×C₃	1	2	yes	—
168	C₇⋊C₈	C₂³×C₃	1	1	yes	characteristic
169	C₇⋊C₈	C₂³×C₃	1	1	yes	characteristic
170	C₃×#41	—	7	1	no	—
171	C₃×#41	—	7	2	no	—
172	C₃×#41	—	7	2	no	—
173	C₃×#41	—	7	1	no	—
174	C₃×#41	—	14	1	no	—
175	C₃×#41	—	14	1	no	—
176	C₃×#41	C₂×D₇	1	1	yes	characteristic, complemented
177	C₂×C₃×D₄	—	7	2	no	—
178	C₂×C₃×D₄	—	7	2	no	—
179	C₂×C₃×D₄	—	7	1	no	—
180	C₂×C₃×D₄	—	14	1	no	—
181	C₂×C₃×D₄	—	14	2	no	—
182	C₂×C₃×D₄	—	14	1	no	—
183	C₂×C₃×D₄	—	14	2	no	—
184	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic, complemented
185	C₃×Q₁₆	—	7	1	no	—
186	C₃×SD₁₆	—	7	1	no	—
187	C₃×SD₁₆	—	7	1	no	—
188	C₃×SD₁₆	—	7	2	no	—
189	C₃×SD₁₆	C₂×D₇	1	2	yes	complemented
190	C₃×D₈	—	7	2	no	—
191	C₃×D₈	—	7	1	no	—
192	C₃×D₈	—	7	2	no	—
193	C₃×D₈	—	7	2	no	—
194	C₃×D₈	C₂×D₇	1	2	yes	complemented
195	C₃×M₁₆	—	7	2	no	—
196	C₃×M₁₆	C₂×D₇	1	1	yes	characteristic, complemented
197	C₂×C₃×C₈	—	7	1	no	—
198	C₂×C₃×C₈	—	7	2	no	—
199	C₂×C₃×C₇	—	2	1	no	—
200	C₂×C₃×C₇	—	4	1	no	—
201	C₂×C₃×C₇	—	4	2	no	—
202	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
203	C₃×D₇	—	2	2	no	—
204	C₃×D₇	—	4	2	no	—
205	C₃×D₇	—	4	1	no	—
206	H(5,𝔽₂)	—	7	1	no	—
207	H(5,𝔽₂)	—	7	1	no	—
208	AGL(1,ℤ/8)	—	7	2	no	—
209	AGL(1,ℤ/8)	—	7	2	no	—
210	AGL(1,ℤ/8)	—	7	1	no	—
211	AGL(1,ℤ/8)	C₃×D₇	1	1	yes	characteristic, complemented
212	#135	—	7	1	no	—
213	#135	—	7	2	no	—
214	C₂×D₈	—	7	1	no	—
215	C₂×D₈	—	7	2	no	—
216	#131	—	7	1	no	—
217	C₂²×C₇	—	2	2	no	—
218	C₂²×C₇	—	2	1	no	—
219	C₂²×C₇	—	8	1	no	—
220	C₂²×C₇	C₂×C₃×D₄	1	1	yes	characteristic
221	C₂×D₇	—	2	2	no	—
222	C₂×D₇	—	2	1	no	—
223	C₂×D₇	—	8	2	no	—
224	C₂×D₇	—	8	2	no	—
225	C₂×D₇	—	8	1	no	—
226	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
227	C₄×C₇	—	2	1	no	—
228	C₄×C₇	C₂×C₃×D₄	1	1	yes	characteristic
229	C₄×C₇	C₂⁴×C₃	1	1	yes	characteristic
230	Dic₇	—	2	1	no	—
231	Dic₇	C₂×C₃×D₄	1	2	yes	—
232	C₂³×C₃	—	2	1	no	—
233	C₂³×C₃	—	14	2	no	—
234	C₂³×C₃	—	14	2	no	—
235	C₂³×C₃	—	14	1	no	—
236	C₃×Q₈	—	7	1	no	—
237	C₃×Q₈	—	7	1	no	—
238	C₃×Q₈	C₂²×D₇	1	1	yes	characteristic
239	C₃×D₄	—	2	1	no	—
240	C₃×D₄	—	2	1	no	—
241	C₃×D₄	—	7	2	no	—
242	C₃×D₄	—	7	1	no	—
243	C₃×D₄	—	7	2	no	—
244	C₃×D₄	—	7	1	no	—
245	C₃×D₄	—	14	2	no	—
246	C₃×D₄	—	14	2	no	—
247	C₃×D₄	—	14	2	no	—
248	C₃×D₄	—	14	2	no	—
249	C₃×D₄	—	14	1	no	—
250	C₃×D₄	—	14	1	no	—
251	C₃×D₄	C₂²×D₇	1	2	yes	—
252	C₃×D₄	C₂²×D₇	1	1	yes	characteristic
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	7	2	no	—
255	C₂×C₃×C₄	—	14	2	no	—
256	C₂×C₃×C₄	—	14	2	no	—
257	C₂×C₃×C₄	—	14	1	no	—
258	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
259	C₃×C₈	—	7	1	no	—
260	C₃×C₈	—	7	1	no	—
261	C₃×C₈	C₂²×D₇	1	2	yes	—
262	C₃×C₇	#576	1	1	yes	characteristic, complemented, Hall
263	#41	—	7	1	no	—
264	#41	—	7	2	no	—
265	#41	—	7	2	no	—
266	#41	—	7	1	no	—
267	#41	—	14	1	no	—
268	#41	—	14	1	no	—
269	#41	C₂×C₃×D₇	1	1	yes	characteristic, complemented
270	C₂×D₄	—	7	2	no	—
271	C₂×D₄	—	7	2	no	—
272	C₂×D₄	—	7	1	no	—
273	C₂×D₄	—	14	1	no	—
274	C₂×D₄	—	14	2	no	—
275	C₂×D₄	—	14	1	no	—
276	C₂×D₄	—	14	2	no	—
277	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
278	Q₁₆	—	7	1	no	—
279	SD₁₆	—	7	1	no	—
280	SD₁₆	—	7	1	no	—
281	SD₁₆	—	7	2	no	—
282	SD₁₆	C₂×C₃×D₇	1	2	yes	complemented
283	D₈	—	7	2	no	—
284	D₈	—	7	1	no	—
285	D₈	—	7	2	no	—
286	D₈	—	7	2	no	—
287	D₈	C₂×C₃×D₇	1	2	yes	complemented
288	M₁₆	—	7	2	no	—
289	M₁₆	C₂×C₃×D₇	1	1	yes	characteristic, complemented
290	C₂×C₈	—	7	1	no	—
291	C₂×C₈	—	7	2	no	—
292	C₂×C₇	—	2	1	no	—
293	C₂×C₇	—	4	1	no	—
294	C₂×C₇	—	4	2	no	—
295	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
296	D₇	—	2	2	no	—
297	D₇	—	4	2	no	—
298	D₇	—	4	1	no	—
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	2	2	no	—
301	C₂²×C₃	—	7	2	no	—
302	C₂²×C₃	—	8	1	no	—
303	C₂²×C₃	—	14	2	no	—
304	C₂²×C₃	—	14	1	no	—
305	C₂²×C₃	—	56	1	no	—
306	C₂²×C₃	—	56	2	no	—
307	C₂²×C₃	—	56	2	no	—
308	C₂²×C₃	D₄×D₇	1	1	yes	characteristic
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	7	2	no	—
311	C₃×C₄	—	14	1	no	—
312	C₃×C₄	D₄×D₇	1	1	yes	characteristic
313	C₃×C₄	C₂³×D₇	1	1	yes	characteristic
314	C₂³	—	2	1	no	—
315	C₂³	—	14	2	no	—
316	C₂³	—	14	2	no	—
317	C₂³	—	14	1	no	—
318	Q₈	—	7	1	no	—
319	Q₈	—	7	1	no	—
320	Q₈	C₂²×C₃×D₇	1	1	yes	characteristic
321	D₄	—	2	1	no	—
322	D₄	—	2	1	no	—
323	D₄	—	7	2	no	—
324	D₄	—	7	1	no	—
325	D₄	—	7	2	no	—
326	D₄	—	7	1	no	—
327	D₄	—	14	2	no	—
328	D₄	—	14	2	no	—
329	D₄	—	14	2	no	—
330	D₄	—	14	2	no	—
331	D₄	—	14	1	no	—
332	D₄	—	14	1	no	—
333	D₄	C₂²×C₃×D₇	1	2	yes	—
334	D₄	C₂²×C₃×D₇	1	1	yes	characteristic
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	7	2	no	—
337	C₂×C₄	—	14	2	no	—
338	C₂×C₄	—	14	2	no	—
339	C₂×C₄	—	14	1	no	—
340	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
341	C₈	—	7	1	no	—
342	C₈	—	7	1	no	—
343	C₈	C₂²×C₃×D₇	1	2	yes	—
344	C₇	C₃×#576	1	1	yes	characteristic, complemented, Sylow
345	C₂×C₃	—	2	1	no	—
346	C₂×C₃	—	4	2	no	—
347	C₂×C₃	—	4	1	no	—
348	C₂×C₃	—	14	2	no	—
349	C₂×C₃	—	28	2	no	—
350	C₂×C₃	—	28	1	no	—
351	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
352	C₂²	—	2	1	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	7	2	no	—
355	C₂²	—	8	1	no	—
356	C₂²	—	14	2	no	—
357	C₂²	—	14	1	no	—
358	C₂²	—	56	1	no	—
359	C₂²	—	56	2	no	—
360	C₂²	—	56	2	no	—
361	C₂²	C₃×D₄×D₇	1	1	yes	characteristic
362	C₄	—	2	1	no	—
363	C₄	—	7	2	no	—
364	C₄	—	14	1	no	—
365	C₄	C₃×D₄×D₇	1	1	yes	characteristic
366	C₄	C₂³×C₃×D₇	1	1	yes	characteristic
367	C₃	#90465	1	1	yes	characteristic, direct product factor, Sylow
368	C₂	—	2	1	no	—
369	C₂	—	4	2	no	—
370	C₂	—	4	1	no	—
371	C₂	—	14	2	no	—
372	C₂	—	28	2	no	—
373	C₂	—	28	1	no	—
374	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄×D₇
commutator, cosocle	C₄×C₇	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×D₇
Fitting	C₃×C₇×AGL(1,ℤ/8)	C₂
socle	C₂×C₃×C₇	C₂²×D₄
hypercenter	C₃×AGL(1,ℤ/8)	D₇
hypocenter	C₇	C₃×#576
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
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×#6553	C₂	semidirect
2. C₃×#6548	C₂	semidirect
3. C₃×C₇×AGL(1,ℤ/8)	C₂	semidirect
4. C₃×#6513	C₂	semidirect
5. C₂×C₃×#1141	C₂	semidirect
6. C₃×#6479	C₂	semidirect
7. C₃×#6477	C₂	semidirect
8. C₃×#6474	C₂	semidirect
9. C₃×D₇×D₈	C₂	semidirect
10. C₃×#6471	C₂	semidirect
11. C₃×#6470	C₂	semidirect
12. #90465	C₃	direct (N × H)
13. C₃×C₇×#41	C₂²	semidirect
14. C₂×C₃×C₇×D₄	C₂²	semidirect
16. C₃×#1161	C₂²	semidirect
18. C₃×#1159	C₂²	semidirect
21. C₃×D₄×D₇	C₂²	semidirect
22. C₃×D₄×D₇	C₂²	semidirect
25. C₃×#1157	C₂²	semidirect
27. C₂×C₃×D₂₈	C₂²	semidirect
28. C₃×C₇×SD₁₆	C₂²	semidirect
29. C₃×C₇×D₈	C₂²	semidirect
30. C₃×C₇×M₁₆	C₂²	semidirect
31. C₃×#1144	C₂²	semidirect
32. C₃×#1143	C₂²	semidirect
33. C₃×#1142	C₂²	semidirect
34. C₃×#1141	C₂²	semidirect
35. C₃×#1141	C₂²	semidirect
36. C₃×#1141	C₂²	semidirect
37. C₂×C₃×C₇⋊C₈	C₂²	semidirect
38. C₃×D₅₆	C₂²	semidirect
39. C₃×#1132	C₂²	semidirect
40. C₃×#1131	C₂²	semidirect
41. C₃×C₈×D₇	C₂²	semidirect
42. #6553	C₂×C₃	semidirect
43. #6548	C₂×C₃	semidirect
44. C₇×AGL(1,ℤ/8)	C₂×C₃	semidirect
45. #6513	C₂×C₃	semidirect
46. C₂×#1141	C₂×C₃	semidirect
47. #6479	C₂×C₃	semidirect
48. #6477	C₂×C₃	semidirect
49. #6474	C₂×C₃	semidirect
50. D₇×D₈	C₂×C₃	semidirect
51. #6471	C₂×C₃	semidirect
52. #6470	C₂×C₃	semidirect
84. C₇×#41	C₂²×C₃	semidirect
85. C₂×C₇×D₄	C₂²×C₃	semidirect
87. #1161	C₂²×C₃	semidirect
89. #1159	C₂²×C₃	semidirect
92. D₄×D₇	C₂²×C₃	semidirect
93. D₄×D₇	C₂²×C₃	semidirect
96. #1157	C₂²×C₃	semidirect
98. C₂×D₂₈	C₂²×C₃	semidirect
99. C₇×SD₁₆	C₂²×C₃	semidirect
100. C₇×D₈	C₂²×C₃	semidirect
101. C₇×M₁₆	C₂²×C₃	semidirect
102. #1144	C₂²×C₃	semidirect
103. #1143	C₂²×C₃	semidirect
104. #1142	C₂²×C₃	semidirect
105. #1141	C₂²×C₃	semidirect
106. #1141	C₂²×C₃	semidirect
107. #1141	C₂²×C₃	semidirect
108. C₂×C₇⋊C₈	C₂²×C₃	semidirect
109. D₅₆	C₂²×C₃	semidirect
110. #1132	C₂²×C₃	semidirect
111. #1131	C₂²×C₃	semidirect
112. C₈×D₇	C₂²×C₃	semidirect
118. C₃×AGL(1,ℤ/8)	D₇	semidirect
176. C₃×#41	C₂×D₇	semidirect
184. C₂×C₃×D₄	C₂×D₇	semidirect
189. C₃×SD₁₆	C₂×D₇	semidirect
194. C₃×D₈	C₂×D₇	semidirect
196. C₃×M₁₆	C₂×D₇	semidirect
211. AGL(1,ℤ/8)	C₃×D₇	semidirect
262. C₃×C₇	#576	semidirect
269. #41	C₂×C₃×D₇	semidirect
277. C₂×D₄	C₂×C₃×D₇	semidirect
282. SD₁₆	C₂×C₃×D₇	semidirect
287. D₈	C₂×C₃×D₇	semidirect
289. M₁₆	C₂×C₃×D₇	semidirect
344. C₇	C₃×#576	semidirect
367. C₃	#90465	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×#6553	2
C₃×#6548	2
C₃×C₇×AGL(1,ℤ/8)	2
C₃×#6513	2
C₂×C₃×#1141	2
C₃×#6479	2
C₃×#6477	2
C₃×#6474	2
C₃×D₇×D₈	2
C₃×#6471	2
C₃×#6470	2
#90465	3
C₃×#576	7

Subgroups — C3×#90465 #13061116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90465 #13061116