Subgroups — C₃×C₇×#546 #13061966

Order 1344.

668 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	C₂×C₃×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×#123	C₂	1	2	yes	maximal, complemented
5	C₃×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₇×#121	C₂	1	2	yes	maximal, complemented
7	C₃×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₇×#120	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₇×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₇×#546	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂⁴×C₃×C₇	C₂²	1	2	yes	—
14	C₃×C₇×#41	—	2	4	no	—
15	C₂×C₃×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₇×D₄	—	2	4	no	—
17	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₇×D₄	C₂²	1	2	yes	—
19	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₇×D₄	C₂²	1	2	yes	complemented
22	C₂×C₃×C₇×D₄	C₂²	1	2	yes	complemented
23	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃×C₄×C₇	C₂²	1	2	yes	complemented
26	C₂²×C₃×C₄×C₇	C₂²	1	2	yes	complemented
27	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
33	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
35	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
36	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
37	C₃×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₇×#41	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂²×C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
40	C₇×#124	C₂×C₃	1	1	yes	characteristic, complemented
41	C₇×#123	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, complemented
44	C₇×#121	C₂×C₃	1	2	yes	complemented
45	C₇×#120	C₂×C₃	1	2	yes	complemented
46	C₄×C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
47	C₄×C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×C₇×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
49	C₃×#546	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
50	C₂³×C₃×C₇	—	2	4	no	—
51	C₂³×C₃×C₇	—	2	4	no	—
52	C₂³×C₃×C₇	—	4	2	no	—
53	C₂³×C₃×C₇	C₂³	1	2	yes	—
54	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
55	C₂³×C₃×C₇	C₂³	1	2	yes	—
56	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
57	C₃×C₇×Q₈	—	2	2	no	—
58	C₃×C₇×D₄	—	2	4	no	—
59	C₃×C₇×D₄	—	2	4	no	—
60	C₃×C₇×D₄	—	2	2	no	—
61	C₃×C₇×D₄	—	2	2	no	—
62	C₃×C₇×D₄	—	4	2	no	—
63	C₃×C₇×D₄	D₄	1	4	yes	complemented
64	C₂×C₃×C₄×C₇	—	2	4	no	—
65	C₂×C₃×C₄×C₇	—	2	2	no	—
66	C₂×C₃×C₄×C₇	—	2	2	no	—
67	C₂×C₃×C₄×C₇	—	4	2	no	—
68	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
71	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
73	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
75	C₂⁴×C₇	C₂²×C₃	1	2	yes	—
76	C₇×#41	—	2	4	no	—
77	C₂×C₇×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
78	C₂×C₇×D₄	—	2	4	no	—
79	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₇×D₄	C₂²×C₃	1	2	yes	—
81	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₇×D₄	C₂²×C₃	1	2	yes	complemented
84	C₂×C₇×D₄	C₂²×C₃	1	2	yes	complemented
85	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
86	C₂²×C₄×C₇	C₂²×C₃	1	2	yes	complemented
87	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
88	C₂²×C₄×C₇	C₂²×C₃	1	2	yes	complemented
89	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
90	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
91	C₇×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
92	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
94	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
95	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
96	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
97	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
98	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
99	C₄²×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
100	C₂×C₃×#41	C₂×C₇	1	1	yes	characteristic, complemented
101	C₂²×C₃×D₄	C₂×C₇	1	1	yes	characteristic, complemented
102	C₃×#124	C₂×C₇	1	1	yes	characteristic, complemented
103	C₃×#123	C₂×C₇	1	2	yes	complemented
104	C₃×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
105	C₃×#121	C₂×C₇	1	1	yes	characteristic, complemented
106	C₃×#121	C₂×C₇	1	2	yes	complemented
107	C₃×#120	C₂×C₇	1	2	yes	complemented
108	C₃×C₄×D₄	C₂×C₇	1	1	yes	characteristic, complemented
109	C₃×C₄×D₄	C₂×C₇	1	1	yes	characteristic, complemented
110	C₂×C₃×C₂²⋊C₄	C₂×C₇	1	2	yes	complemented
111	C₂²×C₃×C₇	—	2	1	no	—
112	C₂²×C₃×C₇	—	2	2	no	—
113	C₂²×C₃×C₇	—	2	2	no	—
114	C₂²×C₃×C₇	—	2	1	no	—
115	C₂²×C₃×C₇	—	2	1	no	—
116	C₂²×C₃×C₇	—	2	2	no	—
117	C₂²×C₃×C₇	—	2	1	no	—
118	C₂²×C₃×C₇	—	2	2	no	—
119	C₂²×C₃×C₇	—	2	1	no	—
120	C₂²×C₃×C₇	—	2	2	no	—
121	C₂²×C₃×C₇	—	4	8	no	—
122	C₂²×C₃×C₇	C₂×D₄	1	4	yes	—
123	C₂²×C₃×C₇	#41	1	2	yes	complemented
124	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
125	C₃×C₄×C₇	—	2	1	no	—
126	C₃×C₄×C₇	—	2	1	no	—
127	C₃×C₄×C₇	—	2	2	no	—
128	C₃×C₄×C₇	—	2	1	no	—
129	C₃×C₄×C₇	—	2	1	no	—
130	C₃×C₄×C₇	—	2	2	no	—
131	C₃×C₄×C₇	C₂×D₄	1	2	yes	—
132	#546	C₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
133	C₂³×C₇	—	2	4	no	—
134	C₂³×C₇	—	2	4	no	—
135	C₂³×C₇	—	4	2	no	—
136	C₂³×C₇	C₂³×C₃	1	2	yes	—
137	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
138	C₂³×C₇	C₂³×C₃	1	2	yes	—
139	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
140	C₇×Q₈	—	2	2	no	—
141	C₇×D₄	—	2	4	no	—
142	C₇×D₄	—	2	4	no	—
143	C₇×D₄	—	2	2	no	—
144	C₇×D₄	—	2	2	no	—
145	C₇×D₄	—	4	2	no	—
146	C₇×D₄	C₃×D₄	1	4	yes	complemented
147	C₂×C₄×C₇	—	2	4	no	—
148	C₂×C₄×C₇	—	2	2	no	—
149	C₂×C₄×C₇	—	2	2	no	—
150	C₂×C₄×C₇	—	4	2	no	—
151	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
152	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
153	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
154	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
155	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
156	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
157	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
158	C₂⁴×C₃	C₂²×C₇	1	2	yes	—
159	C₃×#41	—	2	4	no	—
160	C₂×C₃×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
161	C₂×C₃×D₄	—	2	4	no	—
162	C₂×C₃×D₄	C₂²×C₇	1	1	yes	characteristic
163	C₂×C₃×D₄	C₂²×C₇	1	2	yes	—
164	C₂×C₃×D₄	C₂²×C₇	1	1	yes	characteristic
165	C₂×C₃×D₄	C₂²×C₇	1	1	yes	characteristic
166	C₂×C₃×D₄	C₂²×C₇	1	2	yes	complemented
167	C₂×C₃×D₄	C₂²×C₇	1	2	yes	complemented
168	C₂²×C₃×C₄	C₂²×C₇	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₂²×C₇	1	2	yes	complemented
170	C₂²×C₃×C₄	C₂²×C₇	1	1	yes	characteristic, complemented
171	C₂²×C₃×C₄	C₂²×C₇	1	2	yes	complemented
172	C₃×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
173	C₃×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
174	C₃×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
175	C₃×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
176	C₃×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
177	C₃×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
178	C₃×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
179	C₃×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
180	C₃×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
181	C₃×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
182	C₃×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
183	C₂×C₃×C₇	—	2	2	no	—
184	C₂×C₃×C₇	—	2	4	no	—
185	C₂×C₃×C₇	—	4	1	no	—
186	C₂×C₃×C₇	—	4	2	no	—
187	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
189	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂×#41	C₂×C₃×C₇	1	1	yes	characteristic, complemented
191	C₂²×D₄	C₂×C₃×C₇	1	1	yes	characteristic, complemented
192	#124	C₂×C₃×C₇	1	1	yes	characteristic, complemented
193	#123	C₂×C₃×C₇	1	2	yes	complemented
194	C₂²⋊Q₈	C₂×C₃×C₇	1	1	yes	characteristic, complemented
195	#121	C₂×C₃×C₇	1	1	yes	characteristic, complemented
196	#121	C₂×C₃×C₇	1	2	yes	complemented
197	#120	C₂×C₃×C₇	1	2	yes	complemented
198	C₄×D₄	C₂×C₃×C₇	1	1	yes	characteristic, complemented
199	C₄×D₄	C₂×C₃×C₇	1	1	yes	characteristic, complemented
200	C₂×C₂²⋊C₄	C₂×C₃×C₇	1	2	yes	complemented
201	C₂²×C₇	—	2	1	no	—
202	C₂²×C₇	—	2	2	no	—
203	C₂²×C₇	—	2	2	no	—
204	C₂²×C₇	—	2	1	no	—
205	C₂²×C₇	—	2	1	no	—
206	C₂²×C₇	—	2	2	no	—
207	C₂²×C₇	—	2	1	no	—
208	C₂²×C₇	—	2	2	no	—
209	C₂²×C₇	—	2	1	no	—
210	C₂²×C₇	—	2	2	no	—
211	C₂²×C₇	—	4	8	no	—
212	C₂²×C₇	C₂×C₃×D₄	1	4	yes	—
213	C₂²×C₇	C₃×#41	1	2	yes	complemented
214	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
215	C₄×C₇	—	2	1	no	—
216	C₄×C₇	—	2	1	no	—
217	C₄×C₇	—	2	2	no	—
218	C₄×C₇	—	2	1	no	—
219	C₄×C₇	—	2	1	no	—
220	C₄×C₇	—	2	2	no	—
221	C₄×C₇	C₂×C₃×D₄	1	2	yes	—
222	C₂³×C₃	—	2	4	no	—
223	C₂³×C₃	—	2	4	no	—
224	C₂³×C₃	—	4	2	no	—
225	C₂³×C₃	C₂³×C₇	1	2	yes	—
226	C₂³×C₃	C₂³×C₇	1	1	yes	characteristic
227	C₂³×C₃	C₂³×C₇	1	2	yes	—
228	C₂³×C₃	C₂³×C₇	1	1	yes	characteristic
229	C₃×Q₈	—	2	2	no	—
230	C₃×D₄	—	2	4	no	—
231	C₃×D₄	—	2	4	no	—
232	C₃×D₄	—	2	2	no	—
233	C₃×D₄	—	2	2	no	—
234	C₃×D₄	—	4	2	no	—
235	C₃×D₄	C₇×D₄	1	4	yes	complemented
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	4	2	no	—
240	C₂×C₃×C₄	C₂³×C₇	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂³×C₇	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂³×C₇	1	2	yes	—
243	C₂×C₃×C₄	C₂³×C₇	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂³×C₇	1	2	yes	—
245	C₂×C₃×C₄	C₂³×C₇	1	1	yes	characteristic
246	C₂×C₃×C₄	C₂³×C₇	1	1	yes	characteristic
247	C₃×C₇	#546	1	1	yes	characteristic, direct product factor, Hall
248	C₂⁴	C₂²×C₃×C₇	1	2	yes	—
249	#41	—	2	4	no	—
250	C₂×Q₈	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
251	C₂×D₄	—	2	4	no	—
252	C₂×D₄	C₂²×C₃×C₇	1	1	yes	characteristic
253	C₂×D₄	C₂²×C₃×C₇	1	2	yes	—
254	C₂×D₄	C₂²×C₃×C₇	1	1	yes	characteristic
255	C₂×D₄	C₂²×C₃×C₇	1	1	yes	characteristic
256	C₂×D₄	C₂²×C₃×C₇	1	2	yes	complemented
257	C₂×D₄	C₂²×C₃×C₇	1	2	yes	complemented
258	C₂²×C₄	C₂²×C₃×C₇	1	1	yes	characteristic
259	C₂²×C₄	C₂²×C₃×C₇	1	2	yes	complemented
260	C₂²×C₄	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
261	C₂²×C₄	C₂²×C₃×C₇	1	2	yes	complemented
262	C₄⋊C₄	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
263	C₄⋊C₄	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
264	C₄⋊C₄	C₂²×C₃×C₇	1	2	yes	complemented
265	C₂²⋊C₄	C₂²×C₃×C₇	1	1	yes	characteristic
266	C₂²⋊C₄	C₂²×C₃×C₇	1	2	yes	—
267	C₂²⋊C₄	C₂²×C₃×C₇	1	2	yes	complemented
268	C₂²⋊C₄	C₂²×C₃×C₇	1	2	yes	complemented
269	C₂²⋊C₄	C₂²×C₃×C₇	1	2	yes	complemented
270	C₂²⋊C₄	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
271	C₂²⋊C₄	C₂²×C₃×C₇	1	2	yes	complemented
272	C₄²	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
273	C₂×C₇	—	2	2	no	—
274	C₂×C₇	—	2	4	no	—
275	C₂×C₇	—	4	2	no	—
276	C₂×C₇	—	4	1	no	—
277	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
278	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
279	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
280	C₂²×C₃	—	2	1	no	—
281	C₂²×C₃	—	2	2	no	—
282	C₂²×C₃	—	2	2	no	—
283	C₂²×C₃	—	2	1	no	—
284	C₂²×C₃	—	2	1	no	—
285	C₂²×C₃	—	2	2	no	—
286	C₂²×C₃	—	2	1	no	—
287	C₂²×C₃	—	2	2	no	—
288	C₂²×C₃	—	2	1	no	—
289	C₂²×C₃	—	2	2	no	—
290	C₂²×C₃	—	4	8	no	—
291	C₂²×C₃	C₂×C₇×D₄	1	4	yes	—
292	C₂²×C₃	C₇×#41	1	2	yes	complemented
293	C₂²×C₃	C₂⁴×C₇	1	1	yes	characteristic
294	C₃×C₄	—	2	1	no	—
295	C₃×C₄	—	2	1	no	—
296	C₃×C₄	—	2	2	no	—
297	C₃×C₄	—	2	1	no	—
298	C₃×C₄	—	2	1	no	—
299	C₃×C₄	—	2	2	no	—
300	C₃×C₄	C₂×C₇×D₄	1	2	yes	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	4	2	no	—
304	C₂³	C₂³×C₃×C₇	1	2	yes	—
305	C₂³	C₂³×C₃×C₇	1	1	yes	characteristic
306	C₂³	C₂³×C₃×C₇	1	2	yes	—
307	C₂³	C₂³×C₃×C₇	1	1	yes	characteristic
308	Q₈	—	2	2	no	—
309	D₄	—	2	4	no	—
310	D₄	—	2	4	no	—
311	D₄	—	2	2	no	—
312	D₄	—	2	2	no	—
313	D₄	—	4	2	no	—
314	D₄	C₃×C₇×D₄	1	4	yes	complemented
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	C₂³×C₃×C₇	1	1	yes	characteristic
320	C₂×C₄	C₂³×C₃×C₇	1	1	yes	characteristic
321	C₂×C₄	C₂³×C₃×C₇	1	2	yes	—
322	C₂×C₄	C₂³×C₃×C₇	1	1	yes	characteristic
323	C₂×C₄	C₂³×C₃×C₇	1	2	yes	—
324	C₂×C₄	C₂³×C₃×C₇	1	1	yes	characteristic
325	C₂×C₄	C₂³×C₃×C₇	1	1	yes	characteristic
326	C₇	C₃×#546	1	1	yes	characteristic, direct product factor, Sylow
327	C₂×C₃	—	2	2	no	—
328	C₂×C₃	—	2	4	no	—
329	C₂×C₃	—	4	2	no	—
330	C₂×C₃	—	4	1	no	—
331	C₂×C₃	C₂²×C₇×D₄	1	1	yes	characteristic
332	C₂×C₃	C₂×C₇×#41	1	1	yes	characteristic
333	C₂×C₃	C₇×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂²	—	2	1	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	2	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	4	8	no	—
345	C₂²	C₂×C₃×C₇×D₄	1	4	yes	—
346	C₂²	C₃×C₇×#41	1	2	yes	complemented
347	C₂²	C₂⁴×C₃×C₇	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	2	no	—
354	C₄	C₂×C₃×C₇×D₄	1	2	yes	—
355	C₃	C₇×#546	1	1	yes	characteristic, direct product factor, Sylow
356	C₂	—	2	2	no	—
357	C₂	—	2	4	no	—
358	C₂	—	4	2	no	—
359	C₂	—	4	1	no	—
360	C₂	C₂²×C₃×C₇×D₄	1	1	yes	characteristic
361	C₂	C₂×C₃×C₇×#41	1	1	yes	characteristic
362	C₂	C₃×C₇×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃×C₇
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. C₂×C₃×C₇×#41	C₂	semidirect
2. C₂²×C₃×C₇×D₄	C₂	semidirect
3. C₃×C₇×#124	C₂	semidirect
4. C₃×C₇×#123	C₂	semidirect
5. C₃×C₇×C₂²⋊Q₈	C₂	semidirect
6. C₃×C₇×#121	C₂	semidirect
7. C₃×C₇×#121	C₂	semidirect
8. C₃×C₇×#120	C₂	semidirect
9. C₃×C₄×C₇×D₄	C₂	semidirect
10. C₃×C₄×C₇×D₄	C₂	semidirect
11. C₂×C₃×C₇×C₂²⋊C₄	C₂	semidirect
12. C₇×#546	C₃	direct (N × H)
15. C₂×C₃×C₇×Q₈	C₂²	semidirect
21. C₂×C₃×C₇×D₄	C₂²	semidirect
22. C₂×C₃×C₇×D₄	C₂²	semidirect
24. C₂²×C₃×C₄×C₇	C₂²	semidirect
25. C₂²×C₃×C₄×C₇	C₂²	semidirect
26. C₂²×C₃×C₄×C₇	C₂²	semidirect
27. C₃×C₇×C₄⋊C₄	C₂²	semidirect
28. C₃×C₇×C₄⋊C₄	C₂²	semidirect
29. C₃×C₇×C₄⋊C₄	C₂²	semidirect
32. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
33. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
34. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
35. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
36. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
37. C₃×C₄²×C₇	C₂²	semidirect
38. C₂×C₇×#41	C₂×C₃	semidirect
39. C₂²×C₇×D₄	C₂×C₃	semidirect
40. C₇×#124	C₂×C₃	semidirect
41. C₇×#123	C₂×C₃	semidirect
42. C₇×C₂²⋊Q₈	C₂×C₃	semidirect
43. C₇×#121	C₂×C₃	semidirect
44. C₇×#121	C₂×C₃	semidirect
45. C₇×#120	C₂×C₃	semidirect
46. C₄×C₇×D₄	C₂×C₃	semidirect
47. C₄×C₇×D₄	C₂×C₃	semidirect
48. C₂×C₇×C₂²⋊C₄	C₂×C₃	semidirect
49. C₃×#546	C₇	direct (N × H)
63. C₃×C₇×D₄	D₄	semidirect
77. C₂×C₇×Q₈	C₂²×C₃	semidirect
83. C₂×C₇×D₄	C₂²×C₃	semidirect
84. C₂×C₇×D₄	C₂²×C₃	semidirect
86. C₂²×C₄×C₇	C₂²×C₃	semidirect
87. C₂²×C₄×C₇	C₂²×C₃	semidirect
88. C₂²×C₄×C₇	C₂²×C₃	semidirect
89. C₇×C₄⋊C₄	C₂²×C₃	semidirect
90. C₇×C₄⋊C₄	C₂²×C₃	semidirect
91. C₇×C₄⋊C₄	C₂²×C₃	semidirect
94. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
95. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
96. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
97. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
98. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
99. C₄²×C₇	C₂²×C₃	semidirect
100. C₂×C₃×#41	C₂×C₇	semidirect
101. C₂²×C₃×D₄	C₂×C₇	semidirect
102. C₃×#124	C₂×C₇	semidirect
103. C₃×#123	C₂×C₇	semidirect
104. C₃×C₂²⋊Q₈	C₂×C₇	semidirect
105. C₃×#121	C₂×C₇	semidirect
106. C₃×#121	C₂×C₇	semidirect
107. C₃×#120	C₂×C₇	semidirect
108. C₃×C₄×D₄	C₂×C₇	semidirect
109. C₃×C₄×D₄	C₂×C₇	semidirect
110. C₂×C₃×C₂²⋊C₄	C₂×C₇	semidirect
123. C₂²×C₃×C₇	#41	semidirect
132. #546	C₃×C₇	direct (N × H)
146. C₇×D₄	C₃×D₄	semidirect
160. C₂×C₃×Q₈	C₂²×C₇	semidirect
166. C₂×C₃×D₄	C₂²×C₇	semidirect
167. C₂×C₃×D₄	C₂²×C₇	semidirect
169. C₂²×C₃×C₄	C₂²×C₇	semidirect
170. C₂²×C₃×C₄	C₂²×C₇	semidirect
171. C₂²×C₃×C₄	C₂²×C₇	semidirect
172. C₃×C₄⋊C₄	C₂²×C₇	semidirect
173. C₃×C₄⋊C₄	C₂²×C₇	semidirect
174. C₃×C₄⋊C₄	C₂²×C₇	semidirect
177. C₃×C₂²⋊C₄	C₂²×C₇	semidirect
178. C₃×C₂²⋊C₄	C₂²×C₇	semidirect
179. C₃×C₂²⋊C₄	C₂²×C₇	semidirect
180. C₃×C₂²⋊C₄	C₂²×C₇	semidirect
181. C₃×C₂²⋊C₄	C₂²×C₇	semidirect
182. C₃×C₄²	C₂²×C₇	semidirect
190. C₂×#41	C₂×C₃×C₇	semidirect
191. C₂²×D₄	C₂×C₃×C₇	semidirect
192. #124	C₂×C₃×C₇	semidirect
193. #123	C₂×C₃×C₇	semidirect
194. C₂²⋊Q₈	C₂×C₃×C₇	semidirect
195. #121	C₂×C₃×C₇	semidirect
196. #121	C₂×C₃×C₇	semidirect
197. #120	C₂×C₃×C₇	semidirect
198. C₄×D₄	C₂×C₃×C₇	semidirect
199. C₄×D₄	C₂×C₃×C₇	semidirect
200. C₂×C₂²⋊C₄	C₂×C₃×C₇	semidirect
213. C₂²×C₇	C₃×#41	semidirect
235. C₃×D₄	C₇×D₄	semidirect
247. C₃×C₇	#546	direct (N × H)
250. C₂×Q₈	C₂²×C₃×C₇	semidirect
256. C₂×D₄	C₂²×C₃×C₇	semidirect
257. C₂×D₄	C₂²×C₃×C₇	semidirect
259. C₂²×C₄	C₂²×C₃×C₇	semidirect
260. C₂²×C₄	C₂²×C₃×C₇	semidirect
261. C₂²×C₄	C₂²×C₃×C₇	semidirect
262. C₄⋊C₄	C₂²×C₃×C₇	semidirect
263. C₄⋊C₄	C₂²×C₃×C₇	semidirect
264. C₄⋊C₄	C₂²×C₃×C₇	semidirect
267. C₂²⋊C₄	C₂²×C₃×C₇	semidirect
268. C₂²⋊C₄	C₂²×C₃×C₇	semidirect
269. C₂²⋊C₄	C₂²×C₃×C₇	semidirect
270. C₂²⋊C₄	C₂²×C₃×C₇	semidirect
271. C₂²⋊C₄	C₂²×C₃×C₇	semidirect
272. C₄²	C₂²×C₃×C₇	semidirect
292. C₂²×C₃	C₇×#41	semidirect
314. D₄	C₃×C₇×D₄	semidirect
326. C₇	C₃×#546	direct (N × H)
346. C₂²	C₃×C₇×#41	semidirect
355. C₃	C₇×#546	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₇×#41	2
C₂²×C₃×C₇×D₄	2
C₃×C₇×#124	2
C₃×C₇×#123	2
C₃×C₇×C₂²⋊Q₈	2
C₃×C₇×#121	2
C₃×C₇×#120	2
C₃×C₄×C₇×D₄	2
C₂×C₃×C₇×C₂²⋊C₄	2
C₇×#546	3
C₃×#546	7

Subgroups — C3×C7×#546 #13061966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×#546 #13061966