Subgroups — C₃×#90346 #13061001

Order 1344.

584 conjugacy classes of subgroups.

The subgroup lattice has 464 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×#1157	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6502	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×Dic₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6459	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#6457	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#6451	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6449	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#6447	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#6446	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×(C₂²⋊D₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×(C₂²⋊D₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#6441	C₂	1	1	yes	maximal, characteristic, complemented
16	#90346	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
23	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
24	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
25	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
26	C₃×#1159	—	2	4	no	—
27	C₃×#1157	—	2	4	no	—
28	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
33	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic
35	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×C₂²⋊Dic₇	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
46	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
47	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
48	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
49	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
50	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
51	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
52	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
53	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic
54	C₂×#1159	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×#1157	C₂×C₃	1	1	yes	characteristic, complemented
56	C₇×#123	C₂×C₃	1	1	yes	characteristic, complemented
57	#6502	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂×Dic₇⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
59	#6459	C₂×C₃	1	1	yes	characteristic, complemented
60	#6457	C₂×C₃	1	1	yes	characteristic, complemented
61	D₇×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
62	#6451	C₂×C₃	1	1	yes	characteristic, complemented
63	#6449	C₂×C₃	1	1	yes	characteristic, complemented
64	#6447	C₂×C₃	1	1	yes	characteristic, complemented
65	#6446	C₂×C₃	1	1	yes	characteristic, complemented
66	(C₂²⋊D₇)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
67	(C₂²⋊D₇)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
68	#6441	C₂×C₃	1	1	yes	characteristic, complemented
69	C₃×#547	—	7	1	no	maximal, Hall
70	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
71	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
72	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
73	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
74	C₃×C₇×D₄	—	2	2	no	—
75	C₂×C₃×C₄×C₇	—	2	2	no	—
76	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
81	C₃×C₂²⋊D₇	—	2	2	no	—
82	C₃×C₂²⋊D₇	—	2	2	no	—
83	C₃×C₂²⋊D₇	—	2	2	no	—
84	C₃×C₂²⋊D₇	D₄	1	4	yes	complemented
85	C₂×C₃×Dic₇	—	2	2	no	—
86	C₂×C₃×Dic₇	—	2	2	no	—
87	C₂×C₃×Dic₇	—	2	2	no	—
88	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
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	C₃×D₂₈	—	2	2	no	—
95	C₃×C₄×D₇	—	2	2	no	—
96	C₃×C₄×D₇	—	2	2	no	—
97	C₃×C₄×D₇	—	2	2	no	—
98	C₃×C₄×D₇	—	2	2	no	—
99	C₃×Dic₁₄	—	2	2	no	—
100	C₃×Dic₁₄	—	2	2	no	—
101	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
102	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
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
108	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
109	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
110	#1159	—	2	4	no	—
111	#1157	—	2	4	no	—
112	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
117	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic
118	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic
119	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
125	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
130	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
131	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₃×#41	—	7	1	no	—
139	C₂×C₃×#41	—	7	1	no	—
140	C₃×C₄⋊Q₈	—	7	1	no	—
141	C₃×#123	—	7	1	no	—
142	C₃×#123	—	7	1	no	—
143	C₃×#123	—	7	1	no	—
144	C₃×#123	D₇	1	1	yes	characteristic, complemented
145	C₃×C₂²⋊Q₈	—	7	1	no	—
146	C₃×C₂²⋊Q₈	—	7	1	no	—
147	C₃×#121	—	7	1	no	—
148	C₃×#121	—	7	1	no	—
149	C₃×C₄×D₄	—	7	1	no	—
150	C₃×C₄×D₄	—	7	1	no	—
151	C₂×C₃×C₄⋊C₄	—	7	1	no	—
152	C₂×C₃×C₄⋊C₄	—	7	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	—	2	1	no	—
158	C₂²×C₃×C₇	C₂×D₄	1	2	yes	—
159	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
164	C₂×C₃×D₇	—	2	1	no	—
165	C₂×C₃×D₇	C₂×D₄	1	2	yes	—
166	C₃×C₄×C₇	—	2	1	no	—
167	C₃×C₄×C₇	—	2	1	no	—
168	C₃×C₄×C₇	—	2	1	no	—
169	C₃×C₄×C₇	—	2	1	no	—
170	C₃×C₄×C₇	—	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	C₃×Dic₇	C₂×D₄	1	2	yes	—
176	C₃×Dic₇	#41	1	2	yes	complemented
177	#547	—	7	1	no	Sylow
178	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
179	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
180	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
181	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
182	C₇×D₄	—	2	2	no	—
183	C₂×C₄×C₇	—	2	2	no	—
184	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
185	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
187	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
189	C₂²⋊D₇	—	2	2	no	—
190	C₂²⋊D₇	—	2	2	no	—
191	C₂²⋊D₇	—	2	2	no	—
192	C₂²⋊D₇	C₃×D₄	1	4	yes	complemented
193	C₂×Dic₇	—	2	2	no	—
194	C₂×Dic₇	—	2	2	no	—
195	C₂×Dic₇	—	2	2	no	—
196	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
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	D₂₈	—	2	2	no	—
203	C₄×D₇	—	2	2	no	—
204	C₄×D₇	—	2	2	no	—
205	C₄×D₇	—	2	2	no	—
206	C₄×D₇	—	2	2	no	—
207	Dic₁₄	—	2	2	no	—
208	Dic₁₄	—	2	2	no	—
209	C₃×#41	—	14	4	no	—
210	C₃×#41	—	14	4	no	—
211	C₂×C₃×Q₈	—	7	1	no	—
212	C₂×C₃×Q₈	—	7	1	no	—
213	C₂×C₃×D₄	—	7	1	no	—
214	C₂×C₃×D₄	—	7	1	no	—
215	C₂×C₃×D₄	—	7	1	no	—
216	C₂×C₃×D₄	—	7	1	no	—
217	C₂×C₃×D₄	—	7	1	no	—
218	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
219	C₂²×C₃×C₄	—	7	1	no	—
220	C₂²×C₃×C₄	—	7	1	no	—
221	C₂²×C₃×C₄	—	7	1	no	—
222	C₂²×C₃×C₄	—	7	1	no	—
223	C₂²×C₃×C₄	—	7	1	no	—
224	C₂²×C₃×C₄	—	7	1	no	—
225	C₂²×C₃×C₄	—	7	1	no	—
226	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
227	C₃×C₄⋊C₄	—	7	1	no	—
228	C₃×C₄⋊C₄	—	7	1	no	—
229	C₃×C₄⋊C₄	—	7	1	no	—
230	C₃×C₄⋊C₄	—	7	1	no	—
231	C₃×C₄⋊C₄	—	7	1	no	—
232	C₃×C₄⋊C₄	—	7	1	no	—
233	C₃×C₄⋊C₄	—	7	1	no	—
234	C₃×C₄⋊C₄	—	7	1	no	—
235	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
236	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
237	C₃×C₂²⋊C₄	—	7	1	no	—
238	C₃×C₂²⋊C₄	—	7	1	no	—
239	C₃×C₂²⋊C₄	—	7	1	no	—
240	C₃×C₂²⋊C₄	—	7	1	no	—
241	C₃×C₂²⋊C₄	—	7	1	no	—
242	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
243	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
244	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
245	C₃×C₄²	—	7	1	no	—
246	C₂×C₃×C₇	—	2	2	no	—
247	C₂×C₃×C₇	—	4	1	no	—
248	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
250	C₂×C₃×C₇	2₋¹⁺⁴	1	1	yes	characteristic
251	C₃×D₇	—	2	2	no	—
252	C₃×D₇	—	4	1	no	—
253	C₂×#41	—	7	1	no	—
254	C₂×#41	—	7	1	no	—
255	C₄⋊Q₈	—	7	1	no	—
256	#123	—	7	1	no	—
257	#123	—	7	1	no	—
258	#123	—	7	1	no	—
259	#123	C₃×D₇	1	1	yes	characteristic, complemented
260	C₂²⋊Q₈	—	7	1	no	—
261	C₂²⋊Q₈	—	7	1	no	—
262	#121	—	7	1	no	—
263	#121	—	7	1	no	—
264	C₄×D₄	—	7	1	no	—
265	C₄×D₄	—	7	1	no	—
266	C₂×C₄⋊C₄	—	7	1	no	—
267	C₂×C₄⋊C₄	—	7	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	C₂×C₃×D₄	1	2	yes	—
274	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
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	—	2	1	no	—
280	C₂×D₇	C₂×C₃×D₄	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	C₄×C₇	—	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	C₂×C₃×D₄	1	2	yes	—
291	Dic₇	C₃×#41	1	2	yes	complemented
292	C₂³×C₃	—	7	1	no	—
293	C₂³×C₃	—	7	1	no	—
294	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
295	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
296	C₃×Q₈	—	14	2	no	—
297	C₃×Q₈	—	14	2	no	—
298	C₃×D₄	—	2	2	no	—
299	C₃×D₄	—	7	4	no	—
300	C₃×D₄	—	14	2	no	—
301	C₃×D₄	—	14	2	no	—
302	C₃×D₄	—	14	2	no	—
303	C₃×D₄	—	14	2	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	7	1	no	—
306	C₂×C₃×C₄	—	7	1	no	—
307	C₂×C₃×C₄	—	7	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	—	14	2	no	—
312	C₂×C₃×C₄	—	14	2	no	—
313	C₂×C₃×C₄	—	14	2	no	—
314	C₂×C₃×C₄	—	14	2	no	—
315	C₂×C₃×C₄	—	14	2	no	—
316	C₂×C₃×C₄	—	14	2	no	—
317	C₂×C₃×C₄	—	14	2	no	—
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	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
323	C₃×C₇	#547	1	1	yes	characteristic, complemented, Hall
324	#41	—	14	4	no	—
325	#41	—	14	4	no	—
326	C₂×Q₈	—	7	1	no	—
327	C₂×Q₈	—	7	1	no	—
328	C₂×D₄	—	7	1	no	—
329	C₂×D₄	—	7	1	no	—
330	C₂×D₄	—	7	1	no	—
331	C₂×D₄	—	7	1	no	—
332	C₂×D₄	—	7	1	no	—
333	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic
334	C₂²×C₄	—	7	1	no	—
335	C₂²×C₄	—	7	1	no	—
336	C₂²×C₄	—	7	1	no	—
337	C₂²×C₄	—	7	1	no	—
338	C₂²×C₄	—	7	1	no	—
339	C₂²×C₄	—	7	1	no	—
340	C₂²×C₄	—	7	1	no	—
341	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic
342	C₄⋊C₄	—	7	1	no	—
343	C₄⋊C₄	—	7	1	no	—
344	C₄⋊C₄	—	7	1	no	—
345	C₄⋊C₄	—	7	1	no	—
346	C₄⋊C₄	—	7	1	no	—
347	C₄⋊C₄	—	7	1	no	—
348	C₄⋊C₄	—	7	1	no	—
349	C₄⋊C₄	—	7	1	no	—
350	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
351	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
352	C₂²⋊C₄	—	7	1	no	—
353	C₂²⋊C₄	—	7	1	no	—
354	C₂²⋊C₄	—	7	1	no	—
355	C₂²⋊C₄	—	7	1	no	—
356	C₂²⋊C₄	—	7	1	no	—
357	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
358	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
359	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
360	C₄²	—	7	1	no	—
361	C₂×C₇	—	2	2	no	—
362	C₂×C₇	—	4	1	no	—
363	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
364	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
365	C₂×C₇	C₃×2₋¹⁺⁴	1	1	yes	characteristic
366	D₇	—	2	2	no	—
367	D₇	—	4	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	—	7	2	no	—
374	C₂²×C₃	—	14	1	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	D₄×D₇	1	2	yes	—
380	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
381	C₃×C₄	—	2	1	no	—
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	—	7	2	no	—
387	C₃×C₄	—	7	2	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	C₂²×C₃×D₇	1	1	yes	characteristic
395	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
396	Q₈	—	14	2	no	—
397	Q₈	—	14	2	no	—
398	D₄	—	2	2	no	—
399	D₄	—	7	4	no	—
400	D₄	—	14	2	no	—
401	D₄	—	14	2	no	—
402	D₄	—	14	2	no	—
403	D₄	—	14	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	7	1	no	—
406	C₂×C₄	—	7	1	no	—
407	C₂×C₄	—	7	1	no	—
408	C₂×C₄	—	7	1	no	—
409	C₂×C₄	—	7	1	no	—
410	C₂×C₄	—	7	1	no	—
411	C₂×C₄	—	14	2	no	—
412	C₂×C₄	—	14	2	no	—
413	C₂×C₄	—	14	2	no	—
414	C₂×C₄	—	14	2	no	—
415	C₂×C₄	—	14	2	no	—
416	C₂×C₄	—	14	2	no	—
417	C₂×C₄	—	14	2	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	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
423	C₇	C₃×#547	1	1	yes	characteristic, complemented, Sylow
424	C₂×C₃	—	2	2	no	—
425	C₂×C₃	—	4	1	no	—
426	C₂×C₃	—	14	2	no	—
427	C₂×C₃	—	28	1	no	—
428	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
429	C₂×C₃	D₇×#41	1	1	yes	characteristic
430	C₂×C₃	#6554	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	—	7	2	no	—
437	C₂²	—	14	1	no	—
438	C₂²	—	14	1	no	—
439	C₂²	—	14	1	no	—
440	C₂²	—	14	1	no	—
441	C₂²	—	14	1	no	—
442	C₂²	C₃×D₄×D₇	1	2	yes	—
443	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	7	2	no	—
450	C₄	—	7	2	no	—
451	C₄	—	14	1	no	—
452	C₄	—	14	1	no	—
453	C₄	—	14	1	no	—
454	C₄	—	14	1	no	—
455	C₃	#90346	1	1	yes	characteristic, direct product factor, Sylow
456	C₂	—	2	2	no	—
457	C₂	—	4	1	no	—
458	C₂	—	14	2	no	—
459	C₂	—	28	1	no	—
460	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
461	C₂	C₃×D₇×#41	1	1	yes	characteristic
462	C₂	C₃×#6554	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×#123	C₂
socle	C₂²×C₃×C₇	C₂⁴
hypercenter	C₃×#123	D₇
hypocenter	C₇	C₃×#547
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#123

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×#1157	C₂	semidirect
3. C₃×C₇×#123	C₂	semidirect
4. C₃×#6502	C₂	semidirect
5. C₂×C₃×Dic₇⋊C₄	C₂	semidirect
6. C₃×#6459	C₂	semidirect
7. C₃×#6457	C₂	semidirect
8. C₃×D₇×C₄⋊C₄	C₂	semidirect
9. C₃×#6451	C₂	semidirect
10. C₃×#6449	C₂	semidirect
11. C₃×#6447	C₂	semidirect
12. C₃×#6446	C₂	semidirect
13. C₃×(C₂²⋊D₇)⋊C₄	C₂	semidirect
14. C₃×(C₂²⋊D₇)⋊C₄	C₂	semidirect
15. C₃×#6441	C₂	semidirect
16. #90346	C₃	direct (N × H)
54. C₂×#1159	C₂×C₃	semidirect
55. C₂×#1157	C₂×C₃	semidirect
56. C₇×#123	C₂×C₃	semidirect
57. #6502	C₂×C₃	semidirect
58. C₂×Dic₇⋊C₄	C₂×C₃	semidirect
59. #6459	C₂×C₃	semidirect
60. #6457	C₂×C₃	semidirect
61. D₇×C₄⋊C₄	C₂×C₃	semidirect
62. #6451	C₂×C₃	semidirect
63. #6449	C₂×C₃	semidirect
64. #6447	C₂×C₃	semidirect
65. #6446	C₂×C₃	semidirect
66. (C₂²⋊D₇)⋊C₄	C₂×C₃	semidirect
67. (C₂²⋊D₇)⋊C₄	C₂×C₃	semidirect
68. #6441	C₂×C₃	semidirect
84. C₃×C₂²⋊D₇	D₄	semidirect
144. C₃×#123	D₇	semidirect
176. C₃×Dic₇	#41	semidirect
192. C₂²⋊D₇	C₃×D₄	semidirect
259. #123	C₃×D₇	semidirect
291. Dic₇	C₃×#41	semidirect
323. C₃×C₇	#547	semidirect
423. C₇	C₃×#547	semidirect
455. C₃	#90346	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×#1157	2
C₃×C₇×#123	2
C₃×#6502	2
C₂×C₃×Dic₇⋊C₄	2
C₃×#6459	2
C₃×#6457	2
C₃×D₇×C₄⋊C₄	2
C₃×#6451	2
C₃×#6449	2
C₃×#6447	2
C₃×#6446	2
C₃×(C₂²⋊D₇)⋊C₄	2
C₃×#6441	2
#90346	3
C₃×#547	7

Subgroups — C3×#90346 #13061001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90346 #13061001