Subgroups — C₃×C₇×#542 #13061962

Order 1344.

432 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₇×#126	C₂	1	2	yes	maximal, complemented
3	C₃×C₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×#124	C₂	1	2	yes	maximal, complemented
5	C₃×C₇×#123	C₂	1	2	yes	maximal, complemented
6	C₃×C₇×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
7	C₃×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₇×#121	C₂	1	1	yes	maximal, characteristic
9	C₃×C₄×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#542	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₇×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₇×Q₈	C₂²	1	2	yes	—
15	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₇×D₄	C₂²	1	2	yes	—
17	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×C₇	C₂²	1	2	yes	—
19	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₃×C₇×C₄⋊C₄	C₂²	1	2	yes	—
24	C₃×C₇×C₄⋊C₄	C₂²	1	2	yes	—
25	C₃×C₇×C₄⋊C₄	C₂²	1	2	yes	—
26	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₃×C₄²×C₇	C₂²	1	1	yes	characteristic
34	C₃×C₄²×C₇	C₂²	1	1	yes	characteristic
35	C₃×C₄²×C₇	C₂²	1	2	yes	—
36	C₇×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
37	C₇×#126	C₂×C₃	1	2	yes	complemented
38	C₇×#124	C₂×C₃	1	1	yes	characteristic, complemented
39	C₇×#124	C₂×C₃	1	2	yes	complemented
40	C₇×#123	C₂×C₃	1	2	yes	complemented
41	C₇×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
42	C₇×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
43	C₇×#121	C₂×C₃	1	1	yes	characteristic
44	C₄×C₇×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
45	C₄×C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
46	C₇×#117	C₂×C₃	1	1	yes	characteristic, complemented
47	C₃×#542	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
48	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
49	C₂³×C₃×C₇	C₂³	1	2	yes	—
50	C₃×C₇×Q₈	—	2	2	no	—
51	C₃×C₇×Q₈	—	4	2	no	—
52	C₃×C₇×D₄	—	2	2	no	—
53	C₃×C₇×D₄	—	4	2	no	—
54	C₂×C₃×C₄×C₇	—	2	2	no	—
55	C₂×C₃×C₄×C₇	—	4	2	no	—
56	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
59	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
62	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
64	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
65	C₂×C₇×Q₈	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₇×Q₈	C₂²×C₃	1	2	yes	—
67	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₇×D₄	C₂²×C₃	1	2	yes	—
69	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₄×C₇	C₂²×C₃	1	2	yes	—
71	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
72	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
73	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
74	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
75	C₇×C₄⋊C₄	C₂²×C₃	1	2	yes	—
76	C₇×C₄⋊C₄	C₂²×C₃	1	2	yes	—
77	C₇×C₄⋊C₄	C₂²×C₃	1	2	yes	—
78	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
79	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
80	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
81	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
82	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
83	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
84	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
85	C₄²×C₇	C₂²×C₃	1	1	yes	characteristic
86	C₄²×C₇	C₂²×C₃	1	1	yes	characteristic
87	C₄²×C₇	C₂²×C₃	1	2	yes	—
88	C₃×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
89	C₃×#126	C₂×C₇	1	2	yes	complemented
90	C₃×#124	C₂×C₇	1	1	yes	characteristic, complemented
91	C₃×#124	C₂×C₇	1	2	yes	complemented
92	C₃×#123	C₂×C₇	1	2	yes	complemented
93	C₃×C₂²⋊Q₈	C₂×C₇	1	2	yes	complemented
94	C₃×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
95	C₃×#121	C₂×C₇	1	1	yes	characteristic
96	C₃×C₄×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
97	C₃×C₄×D₄	C₂×C₇	1	1	yes	characteristic, complemented
98	C₃×#117	C₂×C₇	1	1	yes	characteristic, complemented
99	C₂²×C₃×C₇	—	2	1	no	—
100	C₂²×C₃×C₇	—	2	2	no	—
101	C₂²×C₃×C₇	—	2	2	no	—
102	C₂²×C₃×C₇	—	2	1	no	—
103	C₂²×C₃×C₇	—	2	1	no	—
104	C₂²×C₃×C₇	—	2	2	no	—
105	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
106	C₃×C₄×C₇	—	2	1	no	—
107	C₃×C₄×C₇	—	2	2	no	—
108	C₃×C₄×C₇	—	2	1	no	—
109	C₃×C₄×C₇	—	2	2	no	—
110	C₃×C₄×C₇	—	2	2	no	—
111	C₃×C₄×C₇	—	2	1	no	—
112	C₃×C₄×C₇	—	2	1	no	—
113	C₃×C₄×C₇	—	2	1	no	—
114	C₃×C₄×C₇	#41	1	2	yes	—
115	#542	C₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
116	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
117	C₂³×C₇	C₂³×C₃	1	2	yes	—
118	C₇×Q₈	—	2	2	no	—
119	C₇×Q₈	—	4	2	no	—
120	C₇×D₄	—	2	2	no	—
121	C₇×D₄	—	4	2	no	—
122	C₂×C₄×C₇	—	2	2	no	—
123	C₂×C₄×C₇	—	4	2	no	—
124	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
125	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
126	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
127	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
128	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
129	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
130	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
131	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
132	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
133	C₂×C₃×Q₈	C₂²×C₇	1	1	yes	characteristic
134	C₂×C₃×Q₈	C₂²×C₇	1	2	yes	—
135	C₂×C₃×D₄	C₂²×C₇	1	1	yes	characteristic
136	C₂×C₃×D₄	C₂²×C₇	1	2	yes	—
137	C₂²×C₃×C₄	C₂²×C₇	1	1	yes	characteristic
138	C₂²×C₃×C₄	C₂²×C₇	1	2	yes	—
139	C₃×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
140	C₃×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
141	C₃×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
142	C₃×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
143	C₃×C₄⋊C₄	C₂²×C₇	1	2	yes	—
144	C₃×C₄⋊C₄	C₂²×C₇	1	2	yes	—
145	C₃×C₄⋊C₄	C₂²×C₇	1	2	yes	—
146	C₃×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
147	C₃×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
148	C₃×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
149	C₃×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
150	C₃×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
151	C₃×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
152	C₃×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
153	C₃×C₄²	C₂²×C₇	1	1	yes	characteristic
154	C₃×C₄²	C₂²×C₇	1	1	yes	characteristic
155	C₃×C₄²	C₂²×C₇	1	2	yes	—
156	C₂×C₃×C₇	—	4	1	no	—
157	C₂×C₃×C₇	—	4	2	no	—
158	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
159	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
160	C₂×C₃×C₇	2₋¹⁺⁴	1	1	yes	characteristic
161	C₄⋊Q₈	C₂×C₃×C₇	1	1	yes	characteristic, complemented
162	#126	C₂×C₃×C₇	1	2	yes	complemented
163	#124	C₂×C₃×C₇	1	1	yes	characteristic, complemented
164	#124	C₂×C₃×C₇	1	2	yes	complemented
165	#123	C₂×C₃×C₇	1	2	yes	complemented
166	C₂²⋊Q₈	C₂×C₃×C₇	1	2	yes	complemented
167	C₂²⋊Q₈	C₂×C₃×C₇	1	1	yes	characteristic, complemented
168	#121	C₂×C₃×C₇	1	1	yes	characteristic
169	C₄×Q₈	C₂×C₃×C₇	1	1	yes	characteristic, complemented
170	C₄×D₄	C₂×C₃×C₇	1	1	yes	characteristic, complemented
171	#117	C₂×C₃×C₇	1	1	yes	characteristic, complemented
172	C₂²×C₇	—	2	1	no	—
173	C₂²×C₇	—	2	2	no	—
174	C₂²×C₇	—	2	2	no	—
175	C₂²×C₇	—	2	1	no	—
176	C₂²×C₇	—	2	1	no	—
177	C₂²×C₇	—	2	2	no	—
178	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
179	C₄×C₇	—	2	1	no	—
180	C₄×C₇	—	2	2	no	—
181	C₄×C₇	—	2	1	no	—
182	C₄×C₇	—	2	2	no	—
183	C₄×C₇	—	2	2	no	—
184	C₄×C₇	—	2	1	no	—
185	C₄×C₇	—	2	1	no	—
186	C₄×C₇	—	2	1	no	—
187	C₄×C₇	C₃×#41	1	2	yes	—
188	C₂³×C₃	C₂³×C₇	1	1	yes	characteristic
189	C₂³×C₃	C₂³×C₇	1	2	yes	—
190	C₃×Q₈	—	2	2	no	—
191	C₃×Q₈	—	4	2	no	—
192	C₃×D₄	—	2	2	no	—
193	C₃×D₄	—	4	2	no	—
194	C₂×C₃×C₄	—	2	2	no	—
195	C₂×C₃×C₄	—	4	2	no	—
196	C₂×C₃×C₄	C₂³×C₇	1	1	yes	characteristic
197	C₂×C₃×C₄	C₂³×C₇	1	1	yes	characteristic
198	C₂×C₃×C₄	C₂³×C₇	1	2	yes	—
199	C₂×C₃×C₄	C₂³×C₇	1	1	yes	characteristic
200	C₂×C₃×C₄	C₂³×C₇	1	1	yes	characteristic
201	C₂×C₃×C₄	C₂³×C₇	1	2	yes	—
202	C₂×C₃×C₄	C₂³×C₇	1	1	yes	characteristic
203	C₂×C₃×C₄	C₂³×C₇	1	2	yes	—
204	C₂×C₃×C₄	C₂³×C₇	1	1	yes	characteristic
205	C₃×C₇	#542	1	1	yes	characteristic, direct product factor, Hall
206	C₂×Q₈	C₂²×C₃×C₇	1	1	yes	characteristic
207	C₂×Q₈	C₂²×C₃×C₇	1	2	yes	—
208	C₂×D₄	C₂²×C₃×C₇	1	1	yes	characteristic
209	C₂×D₄	C₂²×C₃×C₇	1	2	yes	—
210	C₂²×C₄	C₂²×C₃×C₇	1	1	yes	characteristic
211	C₂²×C₄	C₂²×C₃×C₇	1	2	yes	—
212	C₄⋊C₄	C₂²×C₃×C₇	1	1	yes	characteristic
213	C₄⋊C₄	C₂²×C₃×C₇	1	1	yes	characteristic
214	C₄⋊C₄	C₂²×C₃×C₇	1	1	yes	characteristic
215	C₄⋊C₄	C₂²×C₃×C₇	1	1	yes	characteristic
216	C₄⋊C₄	C₂²×C₃×C₇	1	2	yes	—
217	C₄⋊C₄	C₂²×C₃×C₇	1	2	yes	—
218	C₄⋊C₄	C₂²×C₃×C₇	1	2	yes	—
219	C₂²⋊C₄	C₂²×C₃×C₇	1	1	yes	characteristic
220	C₂²⋊C₄	C₂²×C₃×C₇	1	1	yes	characteristic
221	C₂²⋊C₄	C₂²×C₃×C₇	1	2	yes	—
222	C₂²⋊C₄	C₂²×C₃×C₇	1	2	yes	—
223	C₂²⋊C₄	C₂²×C₃×C₇	1	2	yes	—
224	C₂²⋊C₄	C₂²×C₃×C₇	1	2	yes	—
225	C₂²⋊C₄	C₂²×C₃×C₇	1	2	yes	—
226	C₄²	C₂²×C₃×C₇	1	1	yes	characteristic
227	C₄²	C₂²×C₃×C₇	1	1	yes	characteristic
228	C₄²	C₂²×C₃×C₇	1	2	yes	—
229	C₂×C₇	—	4	1	no	—
230	C₂×C₇	—	4	2	no	—
231	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
232	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₇	C₃×2₋¹⁺⁴	1	1	yes	characteristic
234	C₂²×C₃	—	2	1	no	—
235	C₂²×C₃	—	2	2	no	—
236	C₂²×C₃	—	2	2	no	—
237	C₂²×C₃	—	2	1	no	—
238	C₂²×C₃	—	2	1	no	—
239	C₂²×C₃	—	2	2	no	—
240	C₂²×C₃	C₂⁴×C₇	1	1	yes	characteristic
241	C₃×C₄	—	2	1	no	—
242	C₃×C₄	—	2	2	no	—
243	C₃×C₄	—	2	1	no	—
244	C₃×C₄	—	2	2	no	—
245	C₃×C₄	—	2	2	no	—
246	C₃×C₄	—	2	1	no	—
247	C₃×C₄	—	2	1	no	—
248	C₃×C₄	—	2	1	no	—
249	C₃×C₄	C₇×#41	1	2	yes	—
250	C₂³	C₂³×C₃×C₇	1	1	yes	characteristic
251	C₂³	C₂³×C₃×C₇	1	2	yes	—
252	Q₈	—	2	2	no	—
253	Q₈	—	4	2	no	—
254	D₄	—	2	2	no	—
255	D₄	—	4	2	no	—
256	C₂×C₄	—	2	2	no	—
257	C₂×C₄	—	4	2	no	—
258	C₂×C₄	C₂³×C₃×C₇	1	1	yes	characteristic
259	C₂×C₄	C₂³×C₃×C₇	1	1	yes	characteristic
260	C₂×C₄	C₂³×C₃×C₇	1	2	yes	—
261	C₂×C₄	C₂³×C₃×C₇	1	1	yes	characteristic
262	C₂×C₄	C₂³×C₃×C₇	1	1	yes	characteristic
263	C₂×C₄	C₂³×C₃×C₇	1	2	yes	—
264	C₂×C₄	C₂³×C₃×C₇	1	1	yes	characteristic
265	C₂×C₄	C₂³×C₃×C₇	1	2	yes	—
266	C₂×C₄	C₂³×C₃×C₇	1	1	yes	characteristic
267	C₇	C₃×#542	1	1	yes	characteristic, direct product factor, Sylow
268	C₂×C₃	—	4	1	no	—
269	C₂×C₃	—	4	2	no	—
270	C₂×C₃	C₂×C₇×#41	1	1	yes	characteristic
271	C₂×C₃	C₇×H(5,𝔽₂)	1	1	yes	characteristic
272	C₂×C₃	C₇×2₋¹⁺⁴	1	1	yes	characteristic
273	C₂²	—	2	1	no	—
274	C₂²	—	2	2	no	—
275	C₂²	—	2	2	no	—
276	C₂²	—	2	1	no	—
277	C₂²	—	2	1	no	—
278	C₂²	—	2	2	no	—
279	C₂²	C₂⁴×C₃×C₇	1	1	yes	characteristic
280	C₄	—	2	1	no	—
281	C₄	—	2	2	no	—
282	C₄	—	2	1	no	—
283	C₄	—	2	2	no	—
284	C₄	—	2	2	no	—
285	C₄	—	2	1	no	—
286	C₄	—	2	1	no	—
287	C₄	—	2	1	no	—
288	C₄	C₃×C₇×#41	1	2	yes	—
289	C₃	C₇×#542	1	1	yes	characteristic, direct product factor, Sylow
290	C₂	—	4	1	no	—
291	C₂	—	4	2	no	—
292	C₂	C₂×C₃×C₇×#41	1	1	yes	characteristic
293	C₂	C₃×C₇×H(5,𝔽₂)	1	1	yes	characteristic
294	C₂	C₃×C₇×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃×C₇
prime radical	C₃×C₇×#121	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₄⋊Q₈	C₂	semidirect
2. C₃×C₇×#126	C₂	semidirect
3. C₃×C₇×#124	C₂	semidirect
4. C₃×C₇×#124	C₂	semidirect
5. C₃×C₇×#123	C₂	semidirect
6. C₃×C₇×C₂²⋊Q₈	C₂	semidirect
7. C₃×C₇×C₂²⋊Q₈	C₂	semidirect
9. C₃×C₄×C₇×Q₈	C₂	semidirect
10. C₃×C₄×C₇×D₄	C₂	semidirect
11. C₃×C₇×#117	C₂	semidirect
12. C₇×#542	C₃	direct (N × H)
36. C₇×C₄⋊Q₈	C₂×C₃	semidirect
37. C₇×#126	C₂×C₃	semidirect
38. C₇×#124	C₂×C₃	semidirect
39. C₇×#124	C₂×C₃	semidirect
40. C₇×#123	C₂×C₃	semidirect
41. C₇×C₂²⋊Q₈	C₂×C₃	semidirect
42. C₇×C₂²⋊Q₈	C₂×C₃	semidirect
44. C₄×C₇×Q₈	C₂×C₃	semidirect
45. C₄×C₇×D₄	C₂×C₃	semidirect
46. C₇×#117	C₂×C₃	semidirect
47. C₃×#542	C₇	direct (N × H)
88. C₃×C₄⋊Q₈	C₂×C₇	semidirect
89. C₃×#126	C₂×C₇	semidirect
90. C₃×#124	C₂×C₇	semidirect
91. C₃×#124	C₂×C₇	semidirect
92. C₃×#123	C₂×C₇	semidirect
93. C₃×C₂²⋊Q₈	C₂×C₇	semidirect
94. C₃×C₂²⋊Q₈	C₂×C₇	semidirect
96. C₃×C₄×Q₈	C₂×C₇	semidirect
97. C₃×C₄×D₄	C₂×C₇	semidirect
98. C₃×#117	C₂×C₇	semidirect
115. #542	C₃×C₇	direct (N × H)
161. C₄⋊Q₈	C₂×C₃×C₇	semidirect
162. #126	C₂×C₃×C₇	semidirect
163. #124	C₂×C₃×C₇	semidirect
164. #124	C₂×C₃×C₇	semidirect
165. #123	C₂×C₃×C₇	semidirect
166. C₂²⋊Q₈	C₂×C₃×C₇	semidirect
167. C₂²⋊Q₈	C₂×C₃×C₇	semidirect
169. C₄×Q₈	C₂×C₃×C₇	semidirect
170. C₄×D₄	C₂×C₃×C₇	semidirect
171. #117	C₂×C₃×C₇	semidirect
205. C₃×C₇	#542	direct (N × H)
267. C₇	C₃×#542	direct (N × H)
289. C₃	C₇×#542	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×C₇×C₄⋊Q₈	2
C₃×C₇×#126	2
C₃×C₇×#124	2
C₃×C₇×#123	2
C₃×C₇×C₂²⋊Q₈	2
C₃×C₇×#121	2
C₃×C₄×C₇×Q₈	2
C₃×C₄×C₇×D₄	2
C₃×C₇×#117	2
C₇×#542	3
C₃×#542	7

Subgroups — C3×C7×#542 #13061962

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×#542 #13061962