Subgroups — C₃×#90301 #13060954

Order 1344.

668 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#1159	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6502	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6500	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6500	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#6498	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×(C₂×D₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#6457	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#6448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#6447	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×(C₂²⋊D₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×D₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	#90301	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
18	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
30	C₃×#1159	—	2	4	no	—
31	C₃×D₄×D₇	—	2	4	no	—
32	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
43	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
44	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
45	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
46	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
54	C₂×#1159	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×D₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
56	C₇×#121	C₂×C₃	1	1	yes	characteristic, complemented
57	#6502	C₂×C₃	1	1	yes	characteristic, complemented
58	#6500	C₂×C₃	1	1	yes	characteristic, complemented
59	#6500	C₂×C₃	1	1	yes	characteristic, complemented
60	#6498	C₂×C₃	1	1	yes	characteristic, complemented
61	C₄×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
62	C₂×(C₂×D₇)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
63	#6459	C₂×C₃	1	1	yes	characteristic, complemented
64	#6457	C₂×C₃	1	1	yes	characteristic, complemented
65	#6448	C₂×C₃	1	1	yes	characteristic, complemented
66	#6447	C₂×C₃	1	1	yes	characteristic, complemented
67	(C₂²⋊D₇)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
68	D₇×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
69	C₃×#546	—	7	1	no	maximal, Hall
70	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
71	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
72	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
73	C₂²×C₃×D₇	—	2	2	no	—
74	C₂²×C₃×D₇	—	2	2	no	—
75	C₂²×C₃×D₇	—	2	2	no	—
76	C₂²×C₃×D₇	—	2	2	no	—
77	C₂²×C₃×D₇	—	4	1	no	—
78	C₂²×C₃×D₇	—	4	1	no	—
79	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
80	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
81	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
82	C₃×C₇×D₄	—	2	2	no	—
83	C₃×C₇×D₄	—	2	2	no	—
84	C₃×C₇×D₄	—	4	1	no	—
85	C₂×C₃×C₄×C₇	—	4	1	no	—
86	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
90	C₃×C₂²⋊D₇	—	2	2	no	—
91	C₃×C₂²⋊D₇	—	2	2	no	—
92	C₃×C₂²⋊D₇	—	2	2	no	—
93	C₃×C₂²⋊D₇	—	4	1	no	—
94	C₃×C₂²⋊D₇	D₄	1	4	yes	complemented
95	C₂×C₃×Dic₇	—	2	2	no	—
96	C₂×C₃×Dic₇	—	2	2	no	—
97	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
98	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
99	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
100	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
101	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
102	C₃×D₂₈	—	2	2	no	—
103	C₃×C₄×D₇	—	2	2	no	—
104	C₃×C₄×D₇	—	2	2	no	—
105	C₃×C₄×D₇	—	4	1	no	—
106	C₃×Dic₁₄	—	2	2	no	—
107	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
108	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
111	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
112	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic, complemented
117	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic, complemented
118	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
119	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
120	#1159	—	2	4	no	—
121	D₄×D₇	—	2	4	no	—
122	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
126	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
128	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
129	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
130	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
131	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
132	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
133	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
137	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
138	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
139	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
140	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
141	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
142	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
143	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
144	C₂×C₃×#41	—	7	1	no	—
145	C₂²×C₃×D₄	—	7	1	no	—
146	C₃×#124	—	7	1	no	—
147	C₃×#123	—	7	1	no	—
148	C₃×#123	—	7	1	no	—
149	C₃×C₂²⋊Q₈	—	7	1	no	—
150	C₃×#121	—	7	1	no	—
151	C₃×#121	—	7	1	no	—
152	C₃×#121	D₇	1	1	yes	characteristic, complemented
153	C₃×#120	—	7	1	no	—
154	C₃×#120	—	7	1	no	—
155	C₃×C₄×D₄	—	7	1	no	—
156	C₃×C₄×D₄	—	7	1	no	—
157	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
158	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
159	C₂²×C₃×C₇	—	2	1	no	—
160	C₂²×C₃×C₇	—	2	1	no	—
161	C₂²×C₃×C₇	—	2	1	no	—
162	C₂²×C₃×C₇	—	2	1	no	—
163	C₂²×C₃×C₇	—	2	1	no	—
164	C₂²×C₃×C₇	—	2	1	no	—
165	C₂²×C₃×C₇	—	2	1	no	—
166	C₂²×C₃×C₇	—	2	1	no	—
167	C₂²×C₃×C₇	C₂×D₄	1	2	yes	—
168	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
169	C₂×C₃×D₇	—	2	1	no	—
170	C₂×C₃×D₇	—	2	1	no	—
171	C₂×C₃×D₇	—	2	1	no	—
172	C₂×C₃×D₇	—	2	1	no	—
173	C₂×C₃×D₇	—	2	1	no	—
174	C₂×C₃×D₇	—	2	1	no	—
175	C₂×C₃×D₇	—	2	1	no	—
176	C₂×C₃×D₇	—	4	4	no	—
177	C₂×C₃×D₇	—	4	4	no	—
178	C₂×C₃×D₇	C₂×D₄	1	2	yes	—
179	C₂×C₃×D₇	#41	1	2	yes	complemented
180	C₃×C₄×C₇	—	2	1	no	—
181	C₃×C₄×C₇	—	2	1	no	—
182	C₃×C₄×C₇	—	2	1	no	—
183	C₃×C₄×C₇	—	2	1	no	—
184	C₃×Dic₇	—	2	1	no	—
185	C₃×Dic₇	—	2	1	no	—
186	C₃×Dic₇	—	2	1	no	—
187	C₃×Dic₇	—	2	1	no	—
188	C₃×Dic₇	C₂×D₄	1	2	yes	—
189	#546	—	7	1	no	Sylow
190	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
191	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
192	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
193	C₂²×D₇	—	2	2	no	—
194	C₂²×D₇	—	2	2	no	—
195	C₂²×D₇	—	2	2	no	—
196	C₂²×D₇	—	2	2	no	—
197	C₂²×D₇	—	4	1	no	—
198	C₂²×D₇	—	4	1	no	—
199	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
200	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
201	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
202	C₇×D₄	—	2	2	no	—
203	C₇×D₄	—	2	2	no	—
204	C₇×D₄	—	4	1	no	—
205	C₂×C₄×C₇	—	4	1	no	—
206	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
208	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
210	C₂²⋊D₇	—	2	2	no	—
211	C₂²⋊D₇	—	2	2	no	—
212	C₂²⋊D₇	—	2	2	no	—
213	C₂²⋊D₇	—	4	1	no	—
214	C₂²⋊D₇	C₃×D₄	1	4	yes	complemented
215	C₂×Dic₇	—	2	2	no	—
216	C₂×Dic₇	—	2	2	no	—
217	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
218	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
219	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
220	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
221	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
222	D₂₈	—	2	2	no	—
223	C₄×D₇	—	2	2	no	—
224	C₄×D₇	—	2	2	no	—
225	C₄×D₇	—	4	1	no	—
226	Dic₁₄	—	2	2	no	—
227	C₂⁴×C₃	—	7	1	no	—
228	C₂⁴×C₃	—	7	1	no	—
229	C₃×#41	—	14	4	no	—
230	C₂×C₃×Q₈	—	7	1	no	—
231	C₂×C₃×D₄	—	7	1	no	—
232	C₂×C₃×D₄	—	7	1	no	—
233	C₂×C₃×D₄	—	7	1	no	—
234	C₂×C₃×D₄	—	7	1	no	—
235	C₂×C₃×D₄	—	7	1	no	—
236	C₂×C₃×D₄	—	7	1	no	—
237	C₂×C₃×D₄	—	14	4	no	—
238	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
239	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic, complemented
240	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic, complemented
241	C₂²×C₃×C₄	—	7	1	no	—
242	C₂²×C₃×C₄	—	7	1	no	—
243	C₂²×C₃×C₄	—	7	1	no	—
244	C₂²×C₃×C₄	—	7	1	no	—
245	C₂²×C₃×C₄	—	7	1	no	—
246	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic, complemented
247	C₃×C₄⋊C₄	—	7	1	no	—
248	C₃×C₄⋊C₄	—	7	1	no	—
249	C₃×C₄⋊C₄	—	7	1	no	—
250	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
251	C₃×C₂²⋊C₄	—	7	1	no	—
252	C₃×C₂²⋊C₄	—	7	1	no	—
253	C₃×C₂²⋊C₄	—	7	1	no	—
254	C₃×C₂²⋊C₄	—	7	1	no	—
255	C₃×C₂²⋊C₄	—	7	1	no	—
256	C₃×C₂²⋊C₄	—	7	1	no	—
257	C₃×C₂²⋊C₄	—	7	1	no	—
258	C₃×C₂²⋊C₄	—	7	1	no	—
259	C₃×C₂²⋊C₄	—	7	1	no	—
260	C₃×C₂²⋊C₄	—	7	1	no	—
261	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
262	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
263	C₃×C₄²	—	7	1	no	—
264	C₂×C₃×C₇	—	2	2	no	—
265	C₂×C₃×C₇	—	4	1	no	—
266	C₂×C₃×C₇	—	4	1	no	—
267	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
269	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
270	C₃×D₇	—	2	2	no	—
271	C₃×D₇	—	2	2	no	—
272	C₃×D₇	—	4	1	no	—
273	C₂×#41	—	7	1	no	—
274	C₂²×D₄	—	7	1	no	—
275	#124	—	7	1	no	—
276	#123	—	7	1	no	—
277	#123	—	7	1	no	—
278	C₂²⋊Q₈	—	7	1	no	—
279	#121	—	7	1	no	—
280	#121	—	7	1	no	—
281	#121	C₃×D₇	1	1	yes	characteristic, complemented
282	#120	—	7	1	no	—
283	#120	—	7	1	no	—
284	C₄×D₄	—	7	1	no	—
285	C₄×D₄	—	7	1	no	—
286	C₂×C₂²⋊C₄	—	7	1	no	—
287	C₂×C₂²⋊C₄	—	7	1	no	—
288	C₂²×C₇	—	2	1	no	—
289	C₂²×C₇	—	2	1	no	—
290	C₂²×C₇	—	2	1	no	—
291	C₂²×C₇	—	2	1	no	—
292	C₂²×C₇	—	2	1	no	—
293	C₂²×C₇	—	2	1	no	—
294	C₂²×C₇	—	2	1	no	—
295	C₂²×C₇	—	2	1	no	—
296	C₂²×C₇	C₂×C₃×D₄	1	2	yes	—
297	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
298	C₂×D₇	—	2	1	no	—
299	C₂×D₇	—	2	1	no	—
300	C₂×D₇	—	2	1	no	—
301	C₂×D₇	—	2	1	no	—
302	C₂×D₇	—	2	1	no	—
303	C₂×D₇	—	2	1	no	—
304	C₂×D₇	—	2	1	no	—
305	C₂×D₇	—	4	4	no	—
306	C₂×D₇	—	4	4	no	—
307	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
308	C₂×D₇	C₃×#41	1	2	yes	complemented
309	C₄×C₇	—	2	1	no	—
310	C₄×C₇	—	2	1	no	—
311	C₄×C₇	—	2	1	no	—
312	C₄×C₇	—	2	1	no	—
313	Dic₇	—	2	1	no	—
314	Dic₇	—	2	1	no	—
315	Dic₇	—	2	1	no	—
316	Dic₇	—	2	1	no	—
317	Dic₇	C₂×C₃×D₄	1	2	yes	—
318	C₂³×C₃	—	7	1	no	—
319	C₂³×C₃	—	7	1	no	—
320	C₂³×C₃	—	7	1	no	—
321	C₂³×C₃	—	14	2	no	—
322	C₂³×C₃	—	14	2	no	—
323	C₂³×C₃	—	14	2	no	—
324	C₂³×C₃	—	14	2	no	—
325	C₂³×C₃	—	28	1	no	—
326	C₂³×C₃	—	28	1	no	—
327	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
328	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
329	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
330	C₃×Q₈	—	14	2	no	—
331	C₃×D₄	—	2	2	no	—
332	C₃×D₄	—	2	2	no	—
333	C₃×D₄	—	4	1	no	—
334	C₃×D₄	—	7	4	no	—
335	C₃×D₄	—	14	2	no	—
336	C₃×D₄	—	14	2	no	—
337	C₃×D₄	—	14	2	no	—
338	C₃×D₄	—	14	2	no	—
339	C₃×D₄	—	28	1	no	—
340	C₂×C₃×C₄	—	4	1	no	—
341	C₂×C₃×C₄	—	7	1	no	—
342	C₂×C₃×C₄	—	7	1	no	—
343	C₂×C₃×C₄	—	7	1	no	—
344	C₂×C₃×C₄	—	7	1	no	—
345	C₂×C₃×C₄	—	7	1	no	—
346	C₂×C₃×C₄	—	14	2	no	—
347	C₂×C₃×C₄	—	14	2	no	—
348	C₂×C₃×C₄	—	14	2	no	—
349	C₂×C₃×C₄	—	14	2	no	—
350	C₂×C₃×C₄	—	28	1	no	—
351	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
355	C₃×C₇	#546	1	1	yes	characteristic, complemented, Hall
356	C₂⁴	—	7	1	no	—
357	C₂⁴	—	7	1	no	—
358	#41	—	14	4	no	—
359	C₂×Q₈	—	7	1	no	—
360	C₂×D₄	—	7	1	no	—
361	C₂×D₄	—	7	1	no	—
362	C₂×D₄	—	7	1	no	—
363	C₂×D₄	—	7	1	no	—
364	C₂×D₄	—	7	1	no	—
365	C₂×D₄	—	7	1	no	—
366	C₂×D₄	—	14	4	no	—
367	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic
368	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
369	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
370	C₂²×C₄	—	7	1	no	—
371	C₂²×C₄	—	7	1	no	—
372	C₂²×C₄	—	7	1	no	—
373	C₂²×C₄	—	7	1	no	—
374	C₂²×C₄	—	7	1	no	—
375	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
376	C₄⋊C₄	—	7	1	no	—
377	C₄⋊C₄	—	7	1	no	—
378	C₄⋊C₄	—	7	1	no	—
379	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
380	C₂²⋊C₄	—	7	1	no	—
381	C₂²⋊C₄	—	7	1	no	—
382	C₂²⋊C₄	—	7	1	no	—
383	C₂²⋊C₄	—	7	1	no	—
384	C₂²⋊C₄	—	7	1	no	—
385	C₂²⋊C₄	—	7	1	no	—
386	C₂²⋊C₄	—	7	1	no	—
387	C₂²⋊C₄	—	7	1	no	—
388	C₂²⋊C₄	—	7	1	no	—
389	C₂²⋊C₄	—	7	1	no	—
390	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
391	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
392	C₄²	—	7	1	no	—
393	C₂×C₇	—	2	2	no	—
394	C₂×C₇	—	4	1	no	—
395	C₂×C₇	—	4	1	no	—
396	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
397	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
398	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
399	D₇	—	2	2	no	—
400	D₇	—	2	2	no	—
401	D₇	—	4	1	no	—
402	C₂²×C₃	—	2	1	no	—
403	C₂²×C₃	—	2	1	no	—
404	C₂²×C₃	—	2	1	no	—
405	C₂²×C₃	—	2	1	no	—
406	C₂²×C₃	—	2	1	no	—
407	C₂²×C₃	—	2	1	no	—
408	C₂²×C₃	—	2	1	no	—
409	C₂²×C₃	—	2	1	no	—
410	C₂²×C₃	—	7	2	no	—
411	C₂²×C₃	—	7	2	no	—
412	C₂²×C₃	—	14	1	no	—
413	C₂²×C₃	—	14	1	no	—
414	C₂²×C₃	—	14	1	no	—
415	C₂²×C₃	—	14	1	no	—
416	C₂²×C₃	—	14	1	no	—
417	C₂²×C₃	—	14	1	no	—
418	C₂²×C₃	—	14	1	no	—
419	C₂²×C₃	—	28	4	no	—
420	C₂²×C₃	—	28	4	no	—
421	C₂²×C₃	D₄×D₇	1	2	yes	—
422	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	—	2	1	no	—
426	C₃×C₄	—	2	1	no	—
427	C₃×C₄	—	7	2	no	—
428	C₃×C₄	—	14	1	no	—
429	C₃×C₄	—	14	1	no	—
430	C₃×C₄	—	14	1	no	—
431	C₃×C₄	—	14	1	no	—
432	C₂³	—	7	1	no	—
433	C₂³	—	7	1	no	—
434	C₂³	—	7	1	no	—
435	C₂³	—	14	2	no	—
436	C₂³	—	14	2	no	—
437	C₂³	—	14	2	no	—
438	C₂³	—	14	2	no	—
439	C₂³	—	28	1	no	—
440	C₂³	—	28	1	no	—
441	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
442	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
443	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
444	Q₈	—	14	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	4	1	no	—
448	D₄	—	7	4	no	—
449	D₄	—	14	2	no	—
450	D₄	—	14	2	no	—
451	D₄	—	14	2	no	—
452	D₄	—	14	2	no	—
453	D₄	—	28	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	7	1	no	—
456	C₂×C₄	—	7	1	no	—
457	C₂×C₄	—	7	1	no	—
458	C₂×C₄	—	7	1	no	—
459	C₂×C₄	—	7	1	no	—
460	C₂×C₄	—	14	2	no	—
461	C₂×C₄	—	14	2	no	—
462	C₂×C₄	—	14	2	no	—
463	C₂×C₄	—	14	2	no	—
464	C₂×C₄	—	28	1	no	—
465	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
466	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
467	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
468	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
469	C₇	C₃×#546	1	1	yes	characteristic, complemented, Sylow
470	C₂×C₃	—	2	2	no	—
471	C₂×C₃	—	4	1	no	—
472	C₂×C₃	—	4	1	no	—
473	C₂×C₃	—	14	2	no	—
474	C₂×C₃	—	14	2	no	—
475	C₂×C₃	—	28	1	no	—
476	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
477	C₂×C₃	#6548	1	1	yes	characteristic
478	C₂×C₃	D₇×#41	1	1	yes	characteristic
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	7	2	no	—
488	C₂²	—	7	2	no	—
489	C₂²	—	14	1	no	—
490	C₂²	—	14	1	no	—
491	C₂²	—	14	1	no	—
492	C₂²	—	14	1	no	—
493	C₂²	—	14	1	no	—
494	C₂²	—	14	1	no	—
495	C₂²	—	14	1	no	—
496	C₂²	—	28	4	no	—
497	C₂²	—	28	4	no	—
498	C₂²	C₃×D₄×D₇	1	2	yes	—
499	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
500	C₄	—	2	1	no	—
501	C₄	—	2	1	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	7	2	no	—
505	C₄	—	14	1	no	—
506	C₄	—	14	1	no	—
507	C₄	—	14	1	no	—
508	C₄	—	14	1	no	—
509	C₃	#90301	1	1	yes	characteristic, direct product factor, Sylow
510	C₂	—	2	2	no	—
511	C₂	—	4	1	no	—
512	C₂	—	4	1	no	—
513	C₂	—	14	2	no	—
514	C₂	—	14	2	no	—
515	C₂	—	28	1	no	—
516	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
517	C₂	C₃×#6548	1	1	yes	characteristic
518	C₂	C₃×D₇×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₇
commutator, cosocle	C₂²×C₇	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₇
Fitting	C₃×C₇×#121	C₂
socle	C₂²×C₃×C₇	C₂⁴
hypercenter	C₃×#121	D₇
hypocenter	C₇	C₃×#546
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#1159	C₂	semidirect
2. C₂×C₃×D₄×D₇	C₂	semidirect
3. C₃×C₇×#121	C₂	semidirect
4. C₃×#6502	C₂	semidirect
5. C₃×#6500	C₂	semidirect
6. C₃×#6500	C₂	semidirect
7. C₃×#6498	C₂	semidirect
8. C₃×C₄×C₂²⋊D₇	C₂	semidirect
9. C₂×C₃×(C₂×D₇)⋊C₄	C₂	semidirect
10. C₃×#6459	C₂	semidirect
11. C₃×#6457	C₂	semidirect
12. C₃×#6448	C₂	semidirect
13. C₃×#6447	C₂	semidirect
14. C₃×(C₂²⋊D₇)⋊C₄	C₂	semidirect
15. C₃×D₇×C₂²⋊C₄	C₂	semidirect
16. #90301	C₃	direct (N × H)
20. C₂×C₃×C₇×D₄	C₂²	semidirect
21. C₂×C₃×C₇×D₄	C₂²	semidirect
22. C₂²×C₃×C₄×C₇	C₂²	semidirect
26. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
27. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
28. C₂²×C₃×Dic₇	C₂²	semidirect
29. C₂²×C₃×Dic₇	C₂²	semidirect
34. C₂×C₃×C₄×D₇	C₂²	semidirect
35. C₂×C₃×C₄×D₇	C₂²	semidirect
36. C₂×C₃×Dic₁₄	C₂²	semidirect
37. C₃×C₇×C₄⋊C₄	C₂²	semidirect
38. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
39. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
40. C₃×C₂²⋊Dic₇	C₂²	semidirect
41. C₃×C₂²⋊Dic₇	C₂²	semidirect
42. C₃×C₂²⋊Dic₇	C₂²	semidirect
46. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
47. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
48. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
49. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
50. C₃×Dic₇⋊C₄	C₂²	semidirect
51. C₃×Dic₇⋊C₄	C₂²	semidirect
52. C₃×Dic₇⋊C₄	C₂²	semidirect
53. C₃×C₄×Dic₇	C₂²	semidirect
54. C₂×#1159	C₂×C₃	semidirect
55. C₂×D₄×D₇	C₂×C₃	semidirect
56. C₇×#121	C₂×C₃	semidirect
57. #6502	C₂×C₃	semidirect
58. #6500	C₂×C₃	semidirect
59. #6500	C₂×C₃	semidirect
60. #6498	C₂×C₃	semidirect
61. C₄×C₂²⋊D₇	C₂×C₃	semidirect
62. C₂×(C₂×D₇)⋊C₄	C₂×C₃	semidirect
63. #6459	C₂×C₃	semidirect
64. #6457	C₂×C₃	semidirect
65. #6448	C₂×C₃	semidirect
66. #6447	C₂×C₃	semidirect
67. (C₂²⋊D₇)⋊C₄	C₂×C₃	semidirect
68. D₇×C₂²⋊C₄	C₂×C₃	semidirect
94. C₃×C₂²⋊D₇	D₄	semidirect
110. C₂×C₇×D₄	C₂²×C₃	semidirect
111. C₂×C₇×D₄	C₂²×C₃	semidirect
112. C₂²×C₄×C₇	C₂²×C₃	semidirect
116. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
117. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
118. C₂²×Dic₇	C₂²×C₃	semidirect
119. C₂²×Dic₇	C₂²×C₃	semidirect
124. C₂×C₄×D₇	C₂²×C₃	semidirect
125. C₂×C₄×D₇	C₂²×C₃	semidirect
126. C₂×Dic₁₄	C₂²×C₃	semidirect
127. C₇×C₄⋊C₄	C₂²×C₃	semidirect
128. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
129. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
130. C₂²⋊Dic₇	C₂²×C₃	semidirect
131. C₂²⋊Dic₇	C₂²×C₃	semidirect
132. C₂²⋊Dic₇	C₂²×C₃	semidirect
136. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
137. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
138. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
139. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
140. Dic₇⋊C₄	C₂²×C₃	semidirect
141. Dic₇⋊C₄	C₂²×C₃	semidirect
142. Dic₇⋊C₄	C₂²×C₃	semidirect
143. C₄×Dic₇	C₂²×C₃	semidirect
152. C₃×#121	D₇	semidirect
179. C₂×C₃×D₇	#41	semidirect
214. C₂²⋊D₇	C₃×D₄	semidirect
239. C₂×C₃×D₄	C₂×D₇	semidirect
240. C₂×C₃×D₄	C₂×D₇	semidirect
246. C₂²×C₃×C₄	C₂×D₇	semidirect
250. C₃×C₄⋊C₄	C₂×D₇	semidirect
261. C₃×C₂²⋊C₄	C₂×D₇	semidirect
262. C₃×C₂²⋊C₄	C₂×D₇	semidirect
281. #121	C₃×D₇	semidirect
308. C₂×D₇	C₃×#41	semidirect
355. C₃×C₇	#546	semidirect
368. C₂×D₄	C₂×C₃×D₇	semidirect
369. C₂×D₄	C₂×C₃×D₇	semidirect
375. C₂²×C₄	C₂×C₃×D₇	semidirect
379. C₄⋊C₄	C₂×C₃×D₇	semidirect
390. C₂²⋊C₄	C₂×C₃×D₇	semidirect
391. C₂²⋊C₄	C₂×C₃×D₇	semidirect
469. C₇	C₃×#546	semidirect
509. C₃	#90301	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×#1159	2
C₂×C₃×D₄×D₇	2
C₃×C₇×#121	2
C₃×#6502	2
C₃×#6500	2
C₃×#6498	2
C₃×C₄×C₂²⋊D₇	2
C₂×C₃×(C₂×D₇)⋊C₄	2
C₃×#6459	2
C₃×#6457	2
C₃×#6448	2
C₃×#6447	2
C₃×(C₂²⋊D₇)⋊C₄	2
C₃×D₇×C₂²⋊C₄	2
#90301	3
C₃×#546	7

Subgroups — C3×#90301 #13060954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90301 #13060954