Subgroups — C₃×#90469 #13061120

Order 1344.

516 conjugacy classes of subgroups.

The subgroup lattice has 364 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×#6551	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6513	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#1143	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6482	C₂	1	2	yes	maximal, complemented
7	C₃×#6481	C₂	1	2	yes	maximal, complemented
8	C₃×#6477	C₂	1	2	yes	maximal, complemented
9	C₃×D₇×SD₁₆	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	#90469	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₇×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₃×#1161	—	2	1	no	—
16	C₃×#1161	C₂²	1	2	yes	—
17	C₃×#1161	C₂²	1	2	yes	complemented
18	C₃×Q₈×D₇	—	2	1	no	—
19	C₃×Q₈×D₇	C₂²	1	2	yes	complemented
20	C₃×D₄×D₇	—	2	2	no	—
21	C₃×D₄×D₇	C₂²	1	2	yes	—
22	C₃×#1157	—	2	2	no	—
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
28	C₃×C₇×Q₁₆	C₂²	1	2	yes	complemented
29	C₃×C₇×SD₁₆	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	2	yes	complemented
33	C₃×#1143	C₂²	1	2	yes	complemented
34	C₃×#1143	C₂²	1	1	yes	characteristic, complemented
35	C₃×#1142	C₂²	1	1	yes	characteristic, complemented
36	C₃×#1141	C₂²	1	1	yes	characteristic, 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	#6551	C₂×C₃	1	1	yes	characteristic, complemented
44	C₇×#137	C₂×C₃	1	1	yes	characteristic, complemented
45	#6513	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×#1143	C₂×C₃	1	1	yes	characteristic, complemented
47	#6482	C₂×C₃	1	2	yes	complemented
48	#6481	C₂×C₃	1	2	yes	complemented
49	#6477	C₂×C₃	1	2	yes	complemented
50	D₇×SD₁₆	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×#577	—	7	1	no	maximal, Hall
54	C₂²×C₃×D₇	—	2	1	no	—
55	C₂²×C₃×D₇	—	2	2	no	—
56	C₃×C₇×Q₈	—	2	1	no	—
57	C₃×C₇×Q₈	C₂³	1	2	yes	—
58	C₃×C₇×Q₈	C₂³	1	1	yes	characteristic
59	C₃×C₇×D₄	—	2	1	no	—
60	C₃×C₇×D₄	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₄×C₇	—	2	1	no	—
62	C₂×C₃×C₄×C₇	—	2	1	no	—
63	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
64	C₃×C₂²⋊D₇	—	2	1	no	—
65	C₃×C₂²⋊D₇	—	2	2	no	—
66	C₃×C₂²⋊D₇	D₄	1	2	yes	—
67	C₃×D₂₈	—	2	2	no	—
68	C₃×D₂₈	—	2	2	no	—
69	C₃×D₂₈	—	2	1	no	—
70	C₃×D₂₈	D₄	1	1	yes	characteristic
71	C₃×D₂₈	C₂³	1	2	yes	—
72	C₃×D₂₈	C₂³	1	1	yes	characteristic
73	C₃×C₄×D₇	—	2	2	no	—
74	C₃×C₄×D₇	—	2	1	no	—
75	C₃×C₄×D₇	—	2	2	no	—
76	C₃×C₄×D₇	—	2	2	no	—
77	C₃×C₄×D₇	C₂³	1	2	yes	—
78	C₃×Dic₁₄	—	2	2	no	—
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
85	C₂×C₇×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
86	#1161	—	2	1	no	—
87	#1161	C₂²×C₃	1	2	yes	—
88	#1161	C₂²×C₃	1	2	yes	complemented
89	Q₈×D₇	—	2	1	no	—
90	Q₈×D₇	C₂²×C₃	1	2	yes	complemented
91	D₄×D₇	—	2	2	no	—
92	D₄×D₇	C₂²×C₃	1	2	yes	—
93	#1157	—	2	2	no	—
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
99	C₇×Q₁₆	C₂²×C₃	1	2	yes	complemented
100	C₇×SD₁₆	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	2	yes	complemented
104	#1143	C₂²×C₃	1	2	yes	complemented
105	#1143	C₂²×C₃	1	1	yes	characteristic, complemented
106	#1142	C₂²×C₃	1	1	yes	characteristic, complemented
107	#1141	C₂²×C₃	1	1	yes	characteristic, 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	C₃×2₋¹⁺⁴	—	7	1	no	—
114	C₃×H(5,𝔽₂)	—	7	1	no	—
115	C₃×#137	—	7	2	no	—
116	C₃×#137	D₇	1	1	yes	characteristic, complemented
117	C₃×AGL(1,ℤ/8)	—	7	2	no	—
118	C₃×AGL(1,ℤ/8)	—	7	1	no	—
119	C₃×#135	—	7	1	no	—
120	C₃×#135	—	7	2	no	—
121	C₂×C₃×SD₁₆	—	7	1	no	—
122	C₂×C₃×SD₁₆	—	7	2	no	—
123	C₃×#131	—	7	1	no	—
124	C₂²×C₃×C₇	—	2	1	no	—
125	C₂²×C₃×C₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₃×D₇	—	2	1	no	—
127	C₂×C₃×D₇	—	2	2	no	—
128	C₂×C₃×D₇	—	8	2	no	—
129	C₂×C₃×D₇	—	8	1	no	—
130	C₂×C₃×D₇	C₂×D₄	1	2	yes	—
131	C₃×C₄×C₇	—	2	2	no	—
132	C₃×C₄×C₇	—	2	1	no	—
133	C₃×C₄×C₇	C₂×D₄	1	1	yes	characteristic
134	C₃×C₄×C₇	C₂⁴	1	1	yes	characteristic
135	C₃×Dic₇	—	2	1	no	—
136	C₃×Dic₇	C₂×D₄	1	2	yes	—
137	#577	—	7	1	no	Sylow
138	C₂²×D₇	—	2	1	no	—
139	C₂²×D₇	—	2	2	no	—
140	C₇×Q₈	—	2	1	no	—
141	C₇×Q₈	C₂³×C₃	1	2	yes	—
142	C₇×Q₈	C₂³×C₃	1	1	yes	characteristic
143	C₇×D₄	—	2	1	no	—
144	C₇×D₄	C₂³×C₃	1	1	yes	characteristic
145	C₂×C₄×C₇	—	2	1	no	—
146	C₂×C₄×C₇	—	2	1	no	—
147	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
148	C₂²⋊D₇	—	2	1	no	—
149	C₂²⋊D₇	—	2	2	no	—
150	C₂²⋊D₇	C₃×D₄	1	2	yes	—
151	D₂₈	—	2	2	no	—
152	D₂₈	—	2	2	no	—
153	D₂₈	—	2	1	no	—
154	D₂₈	C₃×D₄	1	1	yes	characteristic
155	D₂₈	C₂³×C₃	1	2	yes	—
156	D₂₈	C₂³×C₃	1	1	yes	characteristic
157	C₄×D₇	—	2	2	no	—
158	C₄×D₇	—	2	1	no	—
159	C₄×D₇	—	2	2	no	—
160	C₄×D₇	—	2	2	no	—
161	C₄×D₇	C₂³×C₃	1	2	yes	—
162	Dic₁₄	—	2	2	no	—
163	Dic₁₄	C₃×D₄	1	1	yes	characteristic
164	Dic₁₄	C₂³×C₃	1	1	yes	characteristic
165	C₇×C₈	C₂³×C₃	1	2	yes	—
166	C₇⋊C₈	C₂³×C₃	1	1	yes	characteristic
167	C₇⋊C₈	C₂³×C₃	1	1	yes	characteristic
168	C₃×#41	—	7	1	no	—
169	C₃×#41	—	7	2	no	—
170	C₃×#41	—	7	2	no	—
171	C₃×#41	—	7	1	no	—
172	C₃×#41	—	14	2	no	—
173	C₃×#41	—	14	1	no	—
174	C₃×#41	—	14	1	no	—
175	C₃×#41	C₂×D₇	1	1	yes	characteristic
176	C₂×C₃×Q₈	—	7	2	no	—
177	C₂×C₃×Q₈	—	14	1	no	—
178	C₂×C₃×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
179	C₂×C₃×D₄	—	7	2	no	—
180	C₂×C₃×D₄	—	7	1	no	—
181	C₂×C₃×D₄	—	14	1	no	—
182	C₂×C₃×D₄	—	14	2	no	—
183	C₃×Q₁₆	—	7	1	no	—
184	C₃×Q₁₆	C₂×D₇	1	2	yes	complemented
185	C₃×SD₁₆	—	7	2	no	—
186	C₃×SD₁₆	—	7	2	no	—
187	C₃×SD₁₆	—	7	1	no	—
188	C₃×SD₁₆	—	7	1	no	—
189	C₃×SD₁₆	—	7	2	no	—
190	C₃×SD₁₆	C₂×D₇	1	2	yes	complemented
191	C₃×D₈	—	7	1	no	—
192	C₃×D₈	—	7	2	no	—
193	C₃×M₁₆	—	7	2	no	—
194	C₃×M₁₆	C₂×D₇	1	1	yes	characteristic, complemented
195	C₂×C₃×C₈	—	7	1	no	—
196	C₂×C₃×C₈	—	7	2	no	—
197	C₂×C₃×C₇	—	2	1	no	—
198	C₂×C₃×C₇	—	4	1	no	—
199	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
200	C₃×D₇	—	2	2	no	—
201	C₃×D₇	—	4	1	no	—
202	C₃×D₇	—	4	2	no	—
203	2₋¹⁺⁴	—	7	1	no	—
204	H(5,𝔽₂)	—	7	1	no	—
205	#137	—	7	2	no	—
206	#137	C₃×D₇	1	1	yes	characteristic, complemented
207	AGL(1,ℤ/8)	—	7	2	no	—
208	AGL(1,ℤ/8)	—	7	1	no	—
209	#135	—	7	1	no	—
210	#135	—	7	2	no	—
211	C₂×SD₁₆	—	7	1	no	—
212	C₂×SD₁₆	—	7	2	no	—
213	#131	—	7	1	no	—
214	C₂²×C₇	—	2	1	no	—
215	C₂²×C₇	C₂×C₃×D₄	1	1	yes	characteristic
216	C₂×D₇	—	2	1	no	—
217	C₂×D₇	—	2	2	no	—
218	C₂×D₇	—	8	2	no	—
219	C₂×D₇	—	8	1	no	—
220	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
221	C₄×C₇	—	2	2	no	—
222	C₄×C₇	—	2	1	no	—
223	C₄×C₇	C₂×C₃×D₄	1	1	yes	characteristic
224	C₄×C₇	C₂⁴×C₃	1	1	yes	characteristic
225	Dic₇	—	2	1	no	—
226	Dic₇	C₂×C₃×D₄	1	2	yes	—
227	C₂³×C₃	—	14	2	no	—
228	C₂³×C₃	—	14	1	no	—
229	C₃×Q₈	—	2	1	no	—
230	C₃×Q₈	—	7	1	no	—
231	C₃×Q₈	—	7	1	no	—
232	C₃×Q₈	—	14	2	no	—
233	C₃×Q₈	C₂²×D₇	1	2	yes	—
234	C₃×Q₈	C₂²×D₇	1	1	yes	characteristic
235	C₃×D₄	—	2	1	no	—
236	C₃×D₄	—	7	2	no	—
237	C₃×D₄	—	7	1	no	—
238	C₃×D₄	—	7	1	no	—
239	C₃×D₄	—	7	2	no	—
240	C₃×D₄	—	14	2	no	—
241	C₃×D₄	—	14	2	no	—
242	C₃×D₄	—	14	2	no	—
243	C₃×D₄	—	14	1	no	—
244	C₃×D₄	—	14	1	no	—
245	C₃×D₄	C₂²×D₇	1	1	yes	characteristic
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	7	2	no	—
249	C₂×C₃×C₄	—	14	2	no	—
250	C₂×C₃×C₄	—	14	2	no	—
251	C₂×C₃×C₄	—	14	2	no	—
252	C₂×C₃×C₄	—	14	1	no	—
253	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
254	C₃×C₈	—	7	1	no	—
255	C₃×C₈	—	7	1	no	—
256	C₃×C₈	C₂²×D₇	1	2	yes	—
257	C₃×C₇	#577	1	1	yes	characteristic, complemented, Hall
258	#41	—	7	1	no	—
259	#41	—	7	2	no	—
260	#41	—	7	2	no	—
261	#41	—	7	1	no	—
262	#41	—	14	2	no	—
263	#41	—	14	1	no	—
264	#41	—	14	1	no	—
265	#41	C₂×C₃×D₇	1	1	yes	characteristic
266	C₂×Q₈	—	7	2	no	—
267	C₂×Q₈	—	14	1	no	—
268	C₂×Q₈	C₂×C₃×D₇	1	1	yes	characteristic, complemented
269	C₂×D₄	—	7	2	no	—
270	C₂×D₄	—	7	1	no	—
271	C₂×D₄	—	14	1	no	—
272	C₂×D₄	—	14	2	no	—
273	Q₁₆	—	7	1	no	—
274	Q₁₆	C₂×C₃×D₇	1	2	yes	complemented
275	SD₁₆	—	7	2	no	—
276	SD₁₆	—	7	2	no	—
277	SD₁₆	—	7	1	no	—
278	SD₁₆	—	7	1	no	—
279	SD₁₆	—	7	2	no	—
280	SD₁₆	C₂×C₃×D₇	1	2	yes	complemented
281	D₈	—	7	1	no	—
282	D₈	—	7	2	no	—
283	M₁₆	—	7	2	no	—
284	M₁₆	C₂×C₃×D₇	1	1	yes	characteristic, complemented
285	C₂×C₈	—	7	1	no	—
286	C₂×C₈	—	7	2	no	—
287	C₂×C₇	—	2	1	no	—
288	C₂×C₇	—	4	1	no	—
289	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
290	D₇	—	2	2	no	—
291	D₇	—	4	2	no	—
292	D₇	—	4	1	no	—
293	C₂²×C₃	—	2	1	no	—
294	C₂²×C₃	—	7	2	no	—
295	C₂²×C₃	—	14	1	no	—
296	C₂²×C₃	—	14	2	no	—
297	C₂²×C₃	—	56	1	no	—
298	C₂²×C₃	—	56	2	no	—
299	C₂²×C₃	D₄×D₇	1	1	yes	characteristic
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	—	7	2	no	—
303	C₃×C₄	—	14	1	no	—
304	C₃×C₄	D₄×D₇	1	1	yes	characteristic
305	C₃×C₄	C₂³×D₇	1	1	yes	characteristic
306	C₂³	—	14	2	no	—
307	C₂³	—	14	1	no	—
308	Q₈	—	2	1	no	—
309	Q₈	—	7	1	no	—
310	Q₈	—	7	1	no	—
311	Q₈	—	14	2	no	—
312	Q₈	C₂²×C₃×D₇	1	2	yes	—
313	Q₈	C₂²×C₃×D₇	1	1	yes	characteristic
314	D₄	—	2	1	no	—
315	D₄	—	7	2	no	—
316	D₄	—	7	1	no	—
317	D₄	—	7	1	no	—
318	D₄	—	7	2	no	—
319	D₄	—	14	2	no	—
320	D₄	—	14	2	no	—
321	D₄	—	14	2	no	—
322	D₄	—	14	1	no	—
323	D₄	—	14	1	no	—
324	D₄	C₂²×C₃×D₇	1	1	yes	characteristic
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	7	2	no	—
328	C₂×C₄	—	14	2	no	—
329	C₂×C₄	—	14	2	no	—
330	C₂×C₄	—	14	2	no	—
331	C₂×C₄	—	14	1	no	—
332	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
333	C₈	—	7	1	no	—
334	C₈	—	7	1	no	—
335	C₈	C₂²×C₃×D₇	1	2	yes	—
336	C₇	C₃×#577	1	1	yes	characteristic, complemented, Sylow
337	C₂×C₃	—	2	1	no	—
338	C₂×C₃	—	4	1	no	—
339	C₂×C₃	—	14	2	no	—
340	C₂×C₃	—	28	2	no	—
341	C₂×C₃	—	28	1	no	—
342	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
343	C₂²	—	2	1	no	—
344	C₂²	—	7	2	no	—
345	C₂²	—	14	1	no	—
346	C₂²	—	14	2	no	—
347	C₂²	—	56	1	no	—
348	C₂²	—	56	2	no	—
349	C₂²	C₃×D₄×D₇	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	2	2	no	—
352	C₄	—	7	2	no	—
353	C₄	—	14	1	no	—
354	C₄	C₃×D₄×D₇	1	1	yes	characteristic
355	C₄	C₂³×C₃×D₇	1	1	yes	characteristic
356	C₃	#90469	1	1	yes	characteristic, direct product factor, Sylow
357	C₂	—	2	1	no	—
358	C₂	—	4	1	no	—
359	C₂	—	14	2	no	—
360	C₂	—	28	2	no	—
361	C₂	—	28	1	no	—
362	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×#137	C₂
socle	C₂×C₃×C₇	C₂²×D₄
hypercenter	C₃×#137	D₇
hypocenter	C₇	C₃×#577
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#137

Complements

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

N	H ≅ G/N	type
1. C₃×#6553	C₂	semidirect
2. C₃×#6551	C₂	semidirect
3. C₃×C₇×#137	C₂	semidirect
4. C₃×#6513	C₂	semidirect
5. C₂×C₃×#1143	C₂	semidirect
6. C₃×#6482	C₂	semidirect
7. C₃×#6481	C₂	semidirect
8. C₃×#6477	C₂	semidirect
9. C₃×D₇×SD₁₆	C₂	semidirect
10. C₃×#6471	C₂	semidirect
11. C₃×#6470	C₂	semidirect
12. #90469	C₃	direct (N × H)
14. C₂×C₃×C₇×Q₈	C₂²	semidirect
17. C₃×#1161	C₂²	semidirect
19. C₃×Q₈×D₇	C₂²	semidirect
25. C₃×#1157	C₂²	semidirect
28. C₃×C₇×Q₁₆	C₂²	semidirect
29. C₃×C₇×SD₁₆	C₂²	semidirect
30. C₃×C₇×M₁₆	C₂²	semidirect
31. C₃×#1144	C₂²	semidirect
32. C₃×#1143	C₂²	semidirect
33. C₃×#1143	C₂²	semidirect
34. C₃×#1143	C₂²	semidirect
35. C₃×#1142	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. #6551	C₂×C₃	semidirect
44. C₇×#137	C₂×C₃	semidirect
45. #6513	C₂×C₃	semidirect
46. C₂×#1143	C₂×C₃	semidirect
47. #6482	C₂×C₃	semidirect
48. #6481	C₂×C₃	semidirect
49. #6477	C₂×C₃	semidirect
50. D₇×SD₁₆	C₂×C₃	semidirect
51. #6471	C₂×C₃	semidirect
52. #6470	C₂×C₃	semidirect
85. C₂×C₇×Q₈	C₂²×C₃	semidirect
88. #1161	C₂²×C₃	semidirect
90. Q₈×D₇	C₂²×C₃	semidirect
96. #1157	C₂²×C₃	semidirect
99. C₇×Q₁₆	C₂²×C₃	semidirect
100. C₇×SD₁₆	C₂²×C₃	semidirect
101. C₇×M₁₆	C₂²×C₃	semidirect
102. #1144	C₂²×C₃	semidirect
103. #1143	C₂²×C₃	semidirect
104. #1143	C₂²×C₃	semidirect
105. #1143	C₂²×C₃	semidirect
106. #1142	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
116. C₃×#137	D₇	semidirect
178. C₂×C₃×Q₈	C₂×D₇	semidirect
184. C₃×Q₁₆	C₂×D₇	semidirect
190. C₃×SD₁₆	C₂×D₇	semidirect
194. C₃×M₁₆	C₂×D₇	semidirect
206. #137	C₃×D₇	semidirect
257. C₃×C₇	#577	semidirect
268. C₂×Q₈	C₂×C₃×D₇	semidirect
274. Q₁₆	C₂×C₃×D₇	semidirect
280. SD₁₆	C₂×C₃×D₇	semidirect
284. M₁₆	C₂×C₃×D₇	semidirect
336. C₇	C₃×#577	semidirect
356. C₃	#90469	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×#6551	2
C₃×C₇×#137	2
C₃×#6513	2
C₂×C₃×#1143	2
C₃×#6482	2
C₃×#6481	2
C₃×#6477	2
C₃×D₇×SD₁₆	2
C₃×#6471	2
C₃×#6470	2
#90469	3
C₃×#577	7

Subgroups — C3×#90469 #13061120

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90469 #13061120