Subgroups — C₃×#90304 #13060957

Order 1344.

500 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#6502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#6501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6500	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6500	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6499	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#6498	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#6492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6461	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#6459	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#6448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×(C₂²⋊D₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×D₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#6442	C₂	1	1	yes	maximal, characteristic, complemented
16	#90304	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₇×D₄	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	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
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	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
29	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
34	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
35	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
36	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
39	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
41	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
42	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
43	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
44	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
45	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
46	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
52	C₇×#121	C₂×C₃	1	1	yes	characteristic, complemented
53	#6502	C₂×C₃	1	1	yes	characteristic, complemented
54	#6501	C₂×C₃	1	1	yes	characteristic, complemented
55	#6500	C₂×C₃	1	1	yes	characteristic, complemented
56	#6500	C₂×C₃	1	1	yes	characteristic, complemented
57	#6499	C₂×C₃	1	1	yes	characteristic, complemented
58	#6498	C₂×C₃	1	1	yes	characteristic, complemented
59	#6492	C₂×C₃	1	1	yes	characteristic, complemented
60	C₄×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
61	#6461	C₂×C₃	1	1	yes	characteristic, complemented
62	#6459	C₂×C₃	1	1	yes	characteristic, complemented
63	#6448	C₂×C₃	1	1	yes	characteristic, complemented
64	(C₂²⋊D₇)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
65	D₇×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
66	#6442	C₂×C₃	1	1	yes	characteristic, complemented
67	C₃×#538	—	7	1	no	maximal, Hall
68	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
69	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
70	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
71	C₂²×C₃×D₇	—	2	2	no	—
72	C₂²×C₃×D₇	—	4	1	no	—
73	C₂²×C₃×D₇	—	4	1	no	—
74	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
75	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
76	C₃×C₇×D₄	—	4	1	no	—
77	C₃×C₇×D₄	—	4	1	no	—
78	C₃×C₇×D₄	—	4	1	no	—
79	C₂×C₃×C₄×C₇	—	4	1	no	—
80	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
84	C₃×C₂²⋊D₇	—	2	2	no	—
85	C₃×C₂²⋊D₇	—	2	2	no	—
86	C₃×C₂²⋊D₇	—	4	1	no	—
87	C₃×C₂²⋊D₇	—	4	1	no	—
88	C₂×C₃×Dic₇	—	4	1	no	—
89	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
90	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
91	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
92	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
93	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
94	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
95	C₃×C₄×D₇	—	4	1	no	—
96	C₃×C₄×D₇	—	4	1	no	—
97	C₃×Dic₁₄	—	4	1	no	—
98	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
102	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
103	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
107	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
108	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
110	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic, complemented
111	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
112	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
114	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
115	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
116	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
117	C₂²⋊Dic₇	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	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
127	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
128	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
129	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
130	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
131	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
132	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
133	C₃×#126	—	7	1	no	—
134	C₃×#126	—	7	1	no	—
135	C₃×#124	—	7	1	no	—
136	C₃×#124	—	7	1	no	—
137	C₃×#123	—	7	1	no	—
138	C₃×#123	—	7	1	no	—
139	C₃×C₂²⋊Q₈	—	7	1	no	—
140	C₃×#121	—	7	1	no	—
141	C₃×#121	—	7	1	no	—
142	C₃×#121	D₇	1	1	yes	characteristic, complemented
143	C₃×#120	—	7	1	no	—
144	C₃×#120	—	7	1	no	—
145	C₃×C₄×D₄	—	7	1	no	—
146	C₃×C₄×D₄	—	7	1	no	—
147	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
148	C₂²×C₃×C₇	—	2	1	no	—
149	C₂²×C₃×C₇	—	2	1	no	—
150	C₂²×C₃×C₇	—	2	1	no	—
151	C₂²×C₃×C₇	—	2	1	no	—
152	C₂²×C₃×C₇	—	2	1	no	—
153	C₂²×C₃×C₇	—	2	1	no	—
154	C₂²×C₃×C₇	—	2	1	no	—
155	C₂²×C₃×C₇	—	2	1	no	—
156	C₂²×C₃×C₇	—	2	1	no	—
157	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
158	C₂×C₃×D₇	—	2	1	no	—
159	C₂×C₃×D₇	—	2	1	no	—
160	C₂×C₃×D₇	—	2	1	no	—
161	C₂×C₃×D₇	—	2	1	no	—
162	C₂×C₃×D₇	—	2	1	no	—
163	C₂×C₃×D₇	—	4	4	no	—
164	C₂×C₃×D₇	#41	1	2	yes	—
165	C₃×C₄×C₇	—	2	1	no	—
166	C₃×C₄×C₇	—	2	1	no	—
167	C₃×C₄×C₇	—	2	1	no	—
168	C₃×C₄×C₇	—	2	1	no	—
169	C₃×Dic₇	—	2	1	no	—
170	C₃×Dic₇	—	2	1	no	—
171	C₃×Dic₇	—	2	1	no	—
172	C₃×Dic₇	—	2	1	no	—
173	C₃×Dic₇	—	2	1	no	—
174	C₃×Dic₇	—	2	1	no	—
175	#538	—	7	1	no	Sylow
176	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
177	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
178	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
179	C₂²×D₇	—	2	2	no	—
180	C₂²×D₇	—	4	1	no	—
181	C₂²×D₇	—	4	1	no	—
182	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
183	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
184	C₇×D₄	—	4	1	no	—
185	C₇×D₄	—	4	1	no	—
186	C₇×D₄	—	4	1	no	—
187	C₂×C₄×C₇	—	4	1	no	—
188	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
192	C₂²⋊D₇	—	2	2	no	—
193	C₂²⋊D₇	—	2	2	no	—
194	C₂²⋊D₇	—	4	1	no	—
195	C₂²⋊D₇	—	4	1	no	—
196	C₂×Dic₇	—	4	1	no	—
197	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
198	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
199	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
200	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
201	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
202	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
203	C₄×D₇	—	4	1	no	—
204	C₄×D₇	—	4	1	no	—
205	Dic₁₄	—	4	1	no	—
206	C₂⁴×C₃	—	7	1	no	—
207	C₂×C₃×Q₈	—	7	1	no	—
208	C₂×C₃×D₄	—	7	1	no	—
209	C₂×C₃×D₄	—	7	1	no	—
210	C₂×C₃×D₄	—	7	1	no	—
211	C₂×C₃×D₄	—	7	1	no	—
212	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
213	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
214	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic, complemented
215	C₂²×C₃×C₄	—	7	1	no	—
216	C₂²×C₃×C₄	—	7	1	no	—
217	C₂²×C₃×C₄	—	7	1	no	—
218	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic, complemented
219	C₃×C₄⋊C₄	—	7	1	no	—
220	C₃×C₄⋊C₄	—	7	1	no	—
221	C₃×C₄⋊C₄	—	7	1	no	—
222	C₃×C₄⋊C₄	—	7	1	no	—
223	C₃×C₄⋊C₄	—	7	1	no	—
224	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
225	C₃×C₂²⋊C₄	—	7	1	no	—
226	C₃×C₂²⋊C₄	—	7	1	no	—
227	C₃×C₂²⋊C₄	—	7	1	no	—
228	C₃×C₂²⋊C₄	—	7	1	no	—
229	C₃×C₂²⋊C₄	—	7	1	no	—
230	C₃×C₂²⋊C₄	—	7	1	no	—
231	C₃×C₂²⋊C₄	—	7	1	no	—
232	C₃×C₂²⋊C₄	—	7	1	no	—
233	C₃×C₂²⋊C₄	—	7	1	no	—
234	C₃×C₂²⋊C₄	—	7	1	no	—
235	C₃×C₂²⋊C₄	—	7	1	no	—
236	C₃×C₂²⋊C₄	—	7	1	no	—
237	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
238	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
239	C₃×C₄²	—	7	1	no	—
240	C₃×C₄²	—	7	1	no	—
241	C₂×C₃×C₇	—	4	1	no	—
242	C₂×C₃×C₇	—	4	1	no	—
243	C₂×C₃×C₇	—	4	1	no	—
244	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
245	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
247	C₃×D₇	—	2	2	no	—
248	C₃×D₇	—	4	1	no	—
249	#126	—	7	1	no	—
250	#126	—	7	1	no	—
251	#124	—	7	1	no	—
252	#124	—	7	1	no	—
253	#123	—	7	1	no	—
254	#123	—	7	1	no	—
255	C₂²⋊Q₈	—	7	1	no	—
256	#121	—	7	1	no	—
257	#121	—	7	1	no	—
258	#121	C₃×D₇	1	1	yes	characteristic, complemented
259	#120	—	7	1	no	—
260	#120	—	7	1	no	—
261	C₄×D₄	—	7	1	no	—
262	C₄×D₄	—	7	1	no	—
263	C₂×C₂²⋊C₄	—	7	1	no	—
264	C₂²×C₇	—	2	1	no	—
265	C₂²×C₇	—	2	1	no	—
266	C₂²×C₇	—	2	1	no	—
267	C₂²×C₇	—	2	1	no	—
268	C₂²×C₇	—	2	1	no	—
269	C₂²×C₇	—	2	1	no	—
270	C₂²×C₇	—	2	1	no	—
271	C₂²×C₇	—	2	1	no	—
272	C₂²×C₇	—	2	1	no	—
273	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
274	C₂×D₇	—	2	1	no	—
275	C₂×D₇	—	2	1	no	—
276	C₂×D₇	—	2	1	no	—
277	C₂×D₇	—	2	1	no	—
278	C₂×D₇	—	2	1	no	—
279	C₂×D₇	—	4	4	no	—
280	C₂×D₇	C₃×#41	1	2	yes	—
281	C₄×C₇	—	2	1	no	—
282	C₄×C₇	—	2	1	no	—
283	C₄×C₇	—	2	1	no	—
284	C₄×C₇	—	2	1	no	—
285	Dic₇	—	2	1	no	—
286	Dic₇	—	2	1	no	—
287	Dic₇	—	2	1	no	—
288	Dic₇	—	2	1	no	—
289	Dic₇	—	2	1	no	—
290	Dic₇	—	2	1	no	—
291	C₂³×C₃	—	7	1	no	—
292	C₂³×C₃	—	7	1	no	—
293	C₂³×C₃	—	14	2	no	—
294	C₂³×C₃	—	28	1	no	—
295	C₂³×C₃	—	28	1	no	—
296	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
297	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
298	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
299	C₃×Q₈	—	28	1	no	—
300	C₃×D₄	—	4	1	no	—
301	C₃×D₄	—	4	1	no	—
302	C₃×D₄	—	4	1	no	—
303	C₃×D₄	—	14	2	no	—
304	C₃×D₄	—	14	2	no	—
305	C₃×D₄	—	28	1	no	—
306	C₃×D₄	—	28	1	no	—
307	C₂×C₃×C₄	—	4	1	no	—
308	C₂×C₃×C₄	—	7	1	no	—
309	C₂×C₃×C₄	—	7	1	no	—
310	C₂×C₃×C₄	—	7	1	no	—
311	C₂×C₃×C₄	—	7	1	no	—
312	C₂×C₃×C₄	—	7	1	no	—
313	C₂×C₃×C₄	—	7	1	no	—
314	C₂×C₃×C₄	—	28	1	no	—
315	C₂×C₃×C₄	—	28	1	no	—
316	C₂×C₃×C₄	—	28	1	no	—
317	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
319	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
321	C₃×C₇	#538	1	1	yes	characteristic, complemented, Hall
322	C₂⁴	—	7	1	no	—
323	C₂×Q₈	—	7	1	no	—
324	C₂×D₄	—	7	1	no	—
325	C₂×D₄	—	7	1	no	—
326	C₂×D₄	—	7	1	no	—
327	C₂×D₄	—	7	1	no	—
328	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic
329	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic
330	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
331	C₂²×C₄	—	7	1	no	—
332	C₂²×C₄	—	7	1	no	—
333	C₂²×C₄	—	7	1	no	—
334	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
335	C₄⋊C₄	—	7	1	no	—
336	C₄⋊C₄	—	7	1	no	—
337	C₄⋊C₄	—	7	1	no	—
338	C₄⋊C₄	—	7	1	no	—
339	C₄⋊C₄	—	7	1	no	—
340	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
341	C₂²⋊C₄	—	7	1	no	—
342	C₂²⋊C₄	—	7	1	no	—
343	C₂²⋊C₄	—	7	1	no	—
344	C₂²⋊C₄	—	7	1	no	—
345	C₂²⋊C₄	—	7	1	no	—
346	C₂²⋊C₄	—	7	1	no	—
347	C₂²⋊C₄	—	7	1	no	—
348	C₂²⋊C₄	—	7	1	no	—
349	C₂²⋊C₄	—	7	1	no	—
350	C₂²⋊C₄	—	7	1	no	—
351	C₂²⋊C₄	—	7	1	no	—
352	C₂²⋊C₄	—	7	1	no	—
353	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
354	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
355	C₄²	—	7	1	no	—
356	C₄²	—	7	1	no	—
357	C₂×C₇	—	4	1	no	—
358	C₂×C₇	—	4	1	no	—
359	C₂×C₇	—	4	1	no	—
360	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
361	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
363	D₇	—	2	2	no	—
364	D₇	—	4	1	no	—
365	C₂²×C₃	—	2	1	no	—
366	C₂²×C₃	—	2	1	no	—
367	C₂²×C₃	—	2	1	no	—
368	C₂²×C₃	—	2	1	no	—
369	C₂²×C₃	—	2	1	no	—
370	C₂²×C₃	—	2	1	no	—
371	C₂²×C₃	—	2	1	no	—
372	C₂²×C₃	—	2	1	no	—
373	C₂²×C₃	—	2	1	no	—
374	C₂²×C₃	—	7	2	no	—
375	C₂²×C₃	—	14	1	no	—
376	C₂²×C₃	—	14	1	no	—
377	C₂²×C₃	—	14	1	no	—
378	C₂²×C₃	—	14	1	no	—
379	C₂²×C₃	—	14	1	no	—
380	C₂²×C₃	—	28	4	no	—
381	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
382	C₃×C₄	—	2	1	no	—
383	C₃×C₄	—	2	1	no	—
384	C₃×C₄	—	2	1	no	—
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	14	1	no	—
387	C₃×C₄	—	14	1	no	—
388	C₃×C₄	—	14	1	no	—
389	C₃×C₄	—	14	1	no	—
390	C₃×C₄	—	14	1	no	—
391	C₃×C₄	—	14	1	no	—
392	C₂³	—	7	1	no	—
393	C₂³	—	7	1	no	—
394	C₂³	—	14	2	no	—
395	C₂³	—	28	1	no	—
396	C₂³	—	28	1	no	—
397	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
398	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
399	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
400	Q₈	—	28	1	no	—
401	D₄	—	4	1	no	—
402	D₄	—	4	1	no	—
403	D₄	—	4	1	no	—
404	D₄	—	14	2	no	—
405	D₄	—	14	2	no	—
406	D₄	—	28	1	no	—
407	D₄	—	28	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	7	1	no	—
410	C₂×C₄	—	7	1	no	—
411	C₂×C₄	—	7	1	no	—
412	C₂×C₄	—	7	1	no	—
413	C₂×C₄	—	7	1	no	—
414	C₂×C₄	—	7	1	no	—
415	C₂×C₄	—	28	1	no	—
416	C₂×C₄	—	28	1	no	—
417	C₂×C₄	—	28	1	no	—
418	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
419	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
420	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
422	C₇	C₃×#538	1	1	yes	characteristic, complemented, Sylow
423	C₂×C₃	—	4	1	no	—
424	C₂×C₃	—	4	1	no	—
425	C₂×C₃	—	4	1	no	—
426	C₂×C₃	—	14	2	no	—
427	C₂×C₃	—	28	1	no	—
428	C₂×C₃	#6548	1	1	yes	characteristic
429	C₂×C₃	#6548	1	1	yes	characteristic
430	C₂×C₃	D₇×#41	1	1	yes	characteristic
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	7	2	no	—
441	C₂²	—	14	1	no	—
442	C₂²	—	14	1	no	—
443	C₂²	—	14	1	no	—
444	C₂²	—	14	1	no	—
445	C₂²	—	14	1	no	—
446	C₂²	—	28	4	no	—
447	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	14	1	no	—
453	C₄	—	14	1	no	—
454	C₄	—	14	1	no	—
455	C₄	—	14	1	no	—
456	C₄	—	14	1	no	—
457	C₄	—	14	1	no	—
458	C₃	#90304	1	1	yes	characteristic, direct product factor, Sylow
459	C₂	—	4	1	no	—
460	C₂	—	4	1	no	—
461	C₂	—	4	1	no	—
462	C₂	—	14	2	no	—
463	C₂	—	28	1	no	—
464	C₂	C₃×#6548	1	1	yes	characteristic
465	C₂	C₃×#6548	1	1	yes	characteristic
466	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×#538
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. C₃×C₇×#121	C₂	semidirect
2. C₃×#6502	C₂	semidirect
3. C₃×#6501	C₂	semidirect
4. C₃×#6500	C₂	semidirect
5. C₃×#6500	C₂	semidirect
6. C₃×#6499	C₂	semidirect
7. C₃×#6498	C₂	semidirect
8. C₃×#6492	C₂	semidirect
9. C₃×C₄×C₂²⋊D₇	C₂	semidirect
10. C₃×#6461	C₂	semidirect
11. C₃×#6459	C₂	semidirect
12. C₃×#6448	C₂	semidirect
13. C₃×(C₂²⋊D₇)⋊C₄	C₂	semidirect
14. C₃×D₇×C₂²⋊C₄	C₂	semidirect
15. C₃×#6442	C₂	semidirect
16. #90304	C₃	direct (N × H)
20. C₂×C₃×C₇×D₄	C₂²	semidirect
21. C₂²×C₃×C₄×C₇	C₂²	semidirect
26. C₂²×C₃×Dic₇	C₂²	semidirect
29. C₂×C₃×Dic₁₄	C₂²	semidirect
30. C₃×C₇×C₄⋊C₄	C₂²	semidirect
32. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
36. C₃×C₂²⋊Dic₇	C₂²	semidirect
37. C₃×C₂²⋊Dic₇	C₂²	semidirect
38. C₃×C₂²⋊Dic₇	C₂²	semidirect
45. C₃×C₄⋊Dic₇	C₂²	semidirect
46. C₃×Dic₇⋊C₄	C₂²	semidirect
47. C₃×Dic₇⋊C₄	C₂²	semidirect
48. C₃×Dic₇⋊C₄	C₂²	semidirect
49. C₃×Dic₇⋊C₄	C₂²	semidirect
50. C₃×C₄×Dic₇	C₂²	semidirect
51. C₃×C₄×Dic₇	C₂²	semidirect
52. C₇×#121	C₂×C₃	semidirect
53. #6502	C₂×C₃	semidirect
54. #6501	C₂×C₃	semidirect
55. #6500	C₂×C₃	semidirect
56. #6500	C₂×C₃	semidirect
57. #6499	C₂×C₃	semidirect
58. #6498	C₂×C₃	semidirect
59. #6492	C₂×C₃	semidirect
60. C₄×C₂²⋊D₇	C₂×C₃	semidirect
61. #6461	C₂×C₃	semidirect
62. #6459	C₂×C₃	semidirect
63. #6448	C₂×C₃	semidirect
64. (C₂²⋊D₇)⋊C₄	C₂×C₃	semidirect
65. D₇×C₂²⋊C₄	C₂×C₃	semidirect
66. #6442	C₂×C₃	semidirect
101. C₂×C₇×D₄	C₂²×C₃	semidirect
102. C₂²×C₄×C₇	C₂²×C₃	semidirect
107. C₂²×Dic₇	C₂²×C₃	semidirect
110. C₂×Dic₁₄	C₂²×C₃	semidirect
111. C₇×C₄⋊C₄	C₂²×C₃	semidirect
113. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
117. C₂²⋊Dic₇	C₂²×C₃	semidirect
118. C₂²⋊Dic₇	C₂²×C₃	semidirect
119. C₂²⋊Dic₇	C₂²×C₃	semidirect
126. C₄⋊Dic₇	C₂²×C₃	semidirect
127. Dic₇⋊C₄	C₂²×C₃	semidirect
128. Dic₇⋊C₄	C₂²×C₃	semidirect
129. Dic₇⋊C₄	C₂²×C₃	semidirect
130. Dic₇⋊C₄	C₂²×C₃	semidirect
131. C₄×Dic₇	C₂²×C₃	semidirect
132. C₄×Dic₇	C₂²×C₃	semidirect
142. C₃×#121	D₇	semidirect
214. C₂×C₃×D₄	C₂×D₇	semidirect
218. C₂²×C₃×C₄	C₂×D₇	semidirect
224. C₃×C₄⋊C₄	C₂×D₇	semidirect
238. C₃×C₂²⋊C₄	C₂×D₇	semidirect
258. #121	C₃×D₇	semidirect
321. C₃×C₇	#538	semidirect
330. C₂×D₄	C₂×C₃×D₇	semidirect
334. C₂²×C₄	C₂×C₃×D₇	semidirect
340. C₄⋊C₄	C₂×C₃×D₇	semidirect
354. C₂²⋊C₄	C₂×C₃×D₇	semidirect
422. C₇	C₃×#538	semidirect
458. C₃	#90304	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×#121	2
C₃×#6502	2
C₃×#6501	2
C₃×#6500	2
C₃×#6499	2
C₃×#6498	2
C₃×#6492	2
C₃×C₄×C₂²⋊D₇	2
C₃×#6461	2
C₃×#6459	2
C₃×#6448	2
C₃×(C₂²⋊D₇)⋊C₄	2
C₃×D₇×C₂²⋊C₄	2
C₃×#6442	2
#90304	3
C₃×#538	7

Subgroups — C3×#90304 #13060957

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90304 #13060957