Subgroups — C₃×#90312 #13060963

Order 1344.

440 conjugacy classes of subgroups.

The subgroup lattice has 440 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×#6502	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6499	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6498	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×#6487	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#6452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#6448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#6446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#6441	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#6441	C₂	1	1	yes	maximal, characteristic, complemented
16	#90312	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₇×D₄	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	C₂²×C₃×C₄×C₇	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	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
24	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
25	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
27	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic
29	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
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
37	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
38	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
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×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
43	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
44	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
45	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
46	C₃×Dic₇⋊C₄	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×C₄×Dic₇	C₂²	1	1	yes	characteristic
52	C₇×#121	C₂×C₃	1	1	yes	characteristic, complemented
53	#6502	C₂×C₃	1	1	yes	characteristic, complemented
54	#6502	C₂×C₃	1	1	yes	characteristic, complemented
55	#6501	C₂×C₃	1	1	yes	characteristic, complemented
56	#6499	C₂×C₃	1	1	yes	characteristic, complemented
57	#6498	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	#6487	C₂×C₃	1	1	yes	characteristic, complemented
61	#6459	C₂×C₃	1	1	yes	characteristic, complemented
62	#6452	C₂×C₃	1	1	yes	characteristic, complemented
63	#6448	C₂×C₃	1	1	yes	characteristic, complemented
64	#6446	C₂×C₃	1	1	yes	characteristic, complemented
65	#6441	C₂×C₃	1	1	yes	characteristic, complemented
66	#6441	C₂×C₃	1	1	yes	characteristic, complemented
67	C₃×#562	—	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	C₂³	1	1	yes	characteristic
72	C₃×C₇×D₄	—	4	1	no	—
73	C₃×C₇×D₄	—	4	1	no	—
74	C₃×C₇×D₄	—	4	1	no	—
75	C₂×C₃×C₄×C₇	—	4	1	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	C₃×C₂²⋊D₇	—	4	1	no	—
81	C₃×C₂²⋊D₇	—	4	1	no	—
82	C₃×C₂²⋊D₇	—	4	1	no	—
83	C₂×C₃×Dic₇	—	4	1	no	—
84	C₂×C₃×Dic₇	—	4	1	no	—
85	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
86	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
87	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
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	C₃×C₄×D₇	—	4	1	no	—
93	C₃×Dic₁₄	—	4	1	no	—
94	C₃×Dic₁₄	—	4	1	no	—
95	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
98	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
102	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
103	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
105	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic
106	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic
107	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
108	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
109	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
110	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
111	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
112	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
113	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
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	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
118	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
121	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
122	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
130	C₃×#125	—	7	1	no	—
131	C₃×#124	—	7	1	no	—
132	C₃×#124	—	7	1	no	—
133	C₃×#123	—	7	1	no	—
134	C₃×#123	—	7	1	no	—
135	C₃×#123	—	7	1	no	—
136	C₃×#123	—	7	1	no	—
137	C₃×C₂²⋊Q₈	—	7	1	no	—
138	C₃×C₂²⋊Q₈	—	7	1	no	—
139	C₃×C₂²⋊Q₈	—	7	1	no	—
140	C₃×C₂²⋊Q₈	—	7	1	no	—
141	C₃×#121	—	7	1	no	—
142	C₃×#121	—	7	1	no	—
143	C₃×#121	—	7	1	no	—
144	C₃×#121	D₇	1	1	yes	characteristic, complemented
145	C₂²×C₃×C₇	—	2	1	no	—
146	C₂²×C₃×C₇	—	2	1	no	—
147	C₂²×C₃×C₇	—	2	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	C₂⁴	1	1	yes	characteristic
155	C₂×C₃×D₇	—	2	1	no	—
156	C₂×C₃×D₇	—	2	1	no	—
157	C₂×C₃×D₇	—	2	1	no	—
158	C₃×C₄×C₇	—	2	1	no	—
159	C₃×C₄×C₇	—	2	1	no	—
160	C₃×C₄×C₇	—	2	1	no	—
161	C₃×C₄×C₇	—	2	1	no	—
162	C₃×Dic₇	—	2	1	no	—
163	C₃×Dic₇	—	2	1	no	—
164	C₃×Dic₇	—	2	1	no	—
165	C₃×Dic₇	—	2	1	no	—
166	C₃×Dic₇	—	2	1	no	—
167	C₃×Dic₇	—	2	1	no	—
168	C₃×Dic₇	—	2	1	no	—
169	#562	—	7	1	no	Sylow
170	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
171	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
172	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
173	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
174	C₇×D₄	—	4	1	no	—
175	C₇×D₄	—	4	1	no	—
176	C₇×D₄	—	4	1	no	—
177	C₂×C₄×C₇	—	4	1	no	—
178	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
179	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
181	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
182	C₂²⋊D₇	—	4	1	no	—
183	C₂²⋊D₇	—	4	1	no	—
184	C₂²⋊D₇	—	4	1	no	—
185	C₂×Dic₇	—	4	1	no	—
186	C₂×Dic₇	—	4	1	no	—
187	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
188	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
189	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
190	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
191	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
192	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
193	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
194	C₄×D₇	—	4	1	no	—
195	Dic₁₄	—	4	1	no	—
196	Dic₁₄	—	4	1	no	—
197	C₂×C₃×Q₈	—	7	1	no	—
198	C₂×C₃×Q₈	—	7	1	no	—
199	C₂×C₃×D₄	—	7	1	no	—
200	C₂×C₃×D₄	—	7	1	no	—
201	C₂×C₃×D₄	—	7	1	no	—
202	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
203	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
204	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
205	C₂²×C₃×C₄	—	7	1	no	—
206	C₂²×C₃×C₄	—	7	1	no	—
207	C₂²×C₃×C₄	—	7	1	no	—
208	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
209	C₃×C₄⋊C₄	—	7	1	no	—
210	C₃×C₄⋊C₄	—	7	1	no	—
211	C₃×C₄⋊C₄	—	7	1	no	—
212	C₃×C₄⋊C₄	—	7	1	no	—
213	C₃×C₄⋊C₄	—	7	1	no	—
214	C₃×C₄⋊C₄	—	7	1	no	—
215	C₃×C₄⋊C₄	—	7	1	no	—
216	C₃×C₄⋊C₄	—	7	1	no	—
217	C₃×C₄⋊C₄	—	7	1	no	—
218	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
219	C₃×C₂²⋊C₄	—	7	1	no	—
220	C₃×C₂²⋊C₄	—	7	1	no	—
221	C₃×C₂²⋊C₄	—	7	1	no	—
222	C₃×C₂²⋊C₄	—	7	1	no	—
223	C₃×C₂²⋊C₄	—	7	1	no	—
224	C₃×C₂²⋊C₄	—	7	1	no	—
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	C₂×D₇	1	1	yes	characteristic
230	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
231	C₃×C₄²	—	7	1	no	—
232	C₂×C₃×C₇	—	4	1	no	—
233	C₂×C₃×C₇	—	4	1	no	—
234	C₂×C₃×C₇	—	4	1	no	—
235	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
236	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₃×C₇	2₋¹⁺⁴	1	1	yes	characteristic
238	C₃×D₇	—	4	1	no	—
239	#125	—	7	1	no	—
240	#124	—	7	1	no	—
241	#124	—	7	1	no	—
242	#123	—	7	1	no	—
243	#123	—	7	1	no	—
244	#123	—	7	1	no	—
245	#123	—	7	1	no	—
246	C₂²⋊Q₈	—	7	1	no	—
247	C₂²⋊Q₈	—	7	1	no	—
248	C₂²⋊Q₈	—	7	1	no	—
249	C₂²⋊Q₈	—	7	1	no	—
250	#121	—	7	1	no	—
251	#121	—	7	1	no	—
252	#121	—	7	1	no	—
253	#121	C₃×D₇	1	1	yes	characteristic, complemented
254	C₂²×C₇	—	2	1	no	—
255	C₂²×C₇	—	2	1	no	—
256	C₂²×C₇	—	2	1	no	—
257	C₂²×C₇	—	2	1	no	—
258	C₂²×C₇	—	2	1	no	—
259	C₂²×C₇	—	2	1	no	—
260	C₂²×C₇	—	2	1	no	—
261	C₂²×C₇	—	2	1	no	—
262	C₂²×C₇	—	2	1	no	—
263	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
264	C₂×D₇	—	2	1	no	—
265	C₂×D₇	—	2	1	no	—
266	C₂×D₇	—	2	1	no	—
267	C₄×C₇	—	2	1	no	—
268	C₄×C₇	—	2	1	no	—
269	C₄×C₇	—	2	1	no	—
270	C₄×C₇	—	2	1	no	—
271	Dic₇	—	2	1	no	—
272	Dic₇	—	2	1	no	—
273	Dic₇	—	2	1	no	—
274	Dic₇	—	2	1	no	—
275	Dic₇	—	2	1	no	—
276	Dic₇	—	2	1	no	—
277	Dic₇	—	2	1	no	—
278	C₂³×C₃	—	7	1	no	—
279	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
280	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
281	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
282	C₃×Q₈	—	28	1	no	—
283	C₃×Q₈	—	28	1	no	—
284	C₃×D₄	—	4	1	no	—
285	C₃×D₄	—	4	1	no	—
286	C₃×D₄	—	4	1	no	—
287	C₃×D₄	—	28	1	no	—
288	C₃×D₄	—	28	1	no	—
289	C₃×D₄	—	28	1	no	—
290	C₂×C₃×C₄	—	4	1	no	—
291	C₂×C₃×C₄	—	7	1	no	—
292	C₂×C₃×C₄	—	7	1	no	—
293	C₂×C₃×C₄	—	7	1	no	—
294	C₂×C₃×C₄	—	7	1	no	—
295	C₂×C₃×C₄	—	7	1	no	—
296	C₂×C₃×C₄	—	7	1	no	—
297	C₂×C₃×C₄	—	7	1	no	—
298	C₂×C₃×C₄	—	28	1	no	—
299	C₂×C₃×C₄	—	28	1	no	—
300	C₂×C₃×C₄	—	28	1	no	—
301	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
305	C₃×C₇	#562	1	1	yes	characteristic, complemented, Hall
306	C₂×Q₈	—	7	1	no	—
307	C₂×Q₈	—	7	1	no	—
308	C₂×D₄	—	7	1	no	—
309	C₂×D₄	—	7	1	no	—
310	C₂×D₄	—	7	1	no	—
311	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic
312	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic
313	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic
314	C₂²×C₄	—	7	1	no	—
315	C₂²×C₄	—	7	1	no	—
316	C₂²×C₄	—	7	1	no	—
317	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic
318	C₄⋊C₄	—	7	1	no	—
319	C₄⋊C₄	—	7	1	no	—
320	C₄⋊C₄	—	7	1	no	—
321	C₄⋊C₄	—	7	1	no	—
322	C₄⋊C₄	—	7	1	no	—
323	C₄⋊C₄	—	7	1	no	—
324	C₄⋊C₄	—	7	1	no	—
325	C₄⋊C₄	—	7	1	no	—
326	C₄⋊C₄	—	7	1	no	—
327	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
328	C₂²⋊C₄	—	7	1	no	—
329	C₂²⋊C₄	—	7	1	no	—
330	C₂²⋊C₄	—	7	1	no	—
331	C₂²⋊C₄	—	7	1	no	—
332	C₂²⋊C₄	—	7	1	no	—
333	C₂²⋊C₄	—	7	1	no	—
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	C₂×C₃×D₇	1	1	yes	characteristic
339	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
340	C₄²	—	7	1	no	—
341	C₂×C₇	—	4	1	no	—
342	C₂×C₇	—	4	1	no	—
343	C₂×C₇	—	4	1	no	—
344	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₇	C₃×2₋¹⁺⁴	1	1	yes	characteristic
347	D₇	—	4	1	no	—
348	C₂²×C₃	—	2	1	no	—
349	C₂²×C₃	—	2	1	no	—
350	C₂²×C₃	—	2	1	no	—
351	C₂²×C₃	—	2	1	no	—
352	C₂²×C₃	—	2	1	no	—
353	C₂²×C₃	—	2	1	no	—
354	C₂²×C₃	—	2	1	no	—
355	C₂²×C₃	—	2	1	no	—
356	C₂²×C₃	—	2	1	no	—
357	C₂²×C₃	—	14	1	no	—
358	C₂²×C₃	—	14	1	no	—
359	C₂²×C₃	—	14	1	no	—
360	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
361	C₃×C₄	—	2	1	no	—
362	C₃×C₄	—	2	1	no	—
363	C₃×C₄	—	2	1	no	—
364	C₃×C₄	—	2	1	no	—
365	C₃×C₄	—	14	1	no	—
366	C₃×C₄	—	14	1	no	—
367	C₃×C₄	—	14	1	no	—
368	C₃×C₄	—	14	1	no	—
369	C₃×C₄	—	14	1	no	—
370	C₃×C₄	—	14	1	no	—
371	C₃×C₄	—	14	1	no	—
372	C₂³	—	7	1	no	—
373	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
374	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
375	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
376	Q₈	—	28	1	no	—
377	Q₈	—	28	1	no	—
378	D₄	—	4	1	no	—
379	D₄	—	4	1	no	—
380	D₄	—	4	1	no	—
381	D₄	—	28	1	no	—
382	D₄	—	28	1	no	—
383	D₄	—	28	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	7	1	no	—
386	C₂×C₄	—	7	1	no	—
387	C₂×C₄	—	7	1	no	—
388	C₂×C₄	—	7	1	no	—
389	C₂×C₄	—	7	1	no	—
390	C₂×C₄	—	7	1	no	—
391	C₂×C₄	—	7	1	no	—
392	C₂×C₄	—	28	1	no	—
393	C₂×C₄	—	28	1	no	—
394	C₂×C₄	—	28	1	no	—
395	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
396	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
397	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
398	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
399	C₇	C₃×#562	1	1	yes	characteristic, complemented, Sylow
400	C₂×C₃	—	4	1	no	—
401	C₂×C₃	—	4	1	no	—
402	C₂×C₃	—	4	1	no	—
403	C₂×C₃	—	28	1	no	—
404	C₂×C₃	#6548	1	1	yes	characteristic
405	C₂×C₃	#6548	1	1	yes	characteristic
406	C₂×C₃	#6554	1	1	yes	characteristic
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	14	1	no	—
417	C₂²	—	14	1	no	—
418	C₂²	—	14	1	no	—
419	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	14	1	no	—
425	C₄	—	14	1	no	—
426	C₄	—	14	1	no	—
427	C₄	—	14	1	no	—
428	C₄	—	14	1	no	—
429	C₄	—	14	1	no	—
430	C₄	—	14	1	no	—
431	C₃	#90312	1	1	yes	characteristic, direct product factor, Sylow
432	C₂	—	4	1	no	—
433	C₂	—	4	1	no	—
434	C₂	—	4	1	no	—
435	C₂	—	28	1	no	—
436	C₂	C₃×#6548	1	1	yes	characteristic
437	C₂	C₃×#6548	1	1	yes	characteristic
438	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×#121	C₂
socle	C₂²×C₃×C₇	C₂⁴
hypercenter	C₃×#121	D₇
hypocenter	C₇	C₃×#562
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×#6502	C₂	semidirect
4. C₃×#6501	C₂	semidirect
5. C₃×#6499	C₂	semidirect
6. C₃×#6498	C₂	semidirect
7. C₃×#6498	C₂	semidirect
8. C₃×#6492	C₂	semidirect
9. C₃×#6487	C₂	semidirect
10. C₃×#6459	C₂	semidirect
11. C₃×#6452	C₂	semidirect
12. C₃×#6448	C₂	semidirect
13. C₃×#6446	C₂	semidirect
14. C₃×#6441	C₂	semidirect
15. C₃×#6441	C₂	semidirect
16. #90312	C₃	direct (N × H)
52. C₇×#121	C₂×C₃	semidirect
53. #6502	C₂×C₃	semidirect
54. #6502	C₂×C₃	semidirect
55. #6501	C₂×C₃	semidirect
56. #6499	C₂×C₃	semidirect
57. #6498	C₂×C₃	semidirect
58. #6498	C₂×C₃	semidirect
59. #6492	C₂×C₃	semidirect
60. #6487	C₂×C₃	semidirect
61. #6459	C₂×C₃	semidirect
62. #6452	C₂×C₃	semidirect
63. #6448	C₂×C₃	semidirect
64. #6446	C₂×C₃	semidirect
65. #6441	C₂×C₃	semidirect
66. #6441	C₂×C₃	semidirect
144. C₃×#121	D₇	semidirect
253. #121	C₃×D₇	semidirect
305. C₃×C₇	#562	semidirect
399. C₇	C₃×#562	semidirect
431. C₃	#90312	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×#6499	2
C₃×#6498	2
C₃×#6492	2
C₃×#6487	2
C₃×#6459	2
C₃×#6452	2
C₃×#6448	2
C₃×#6446	2
C₃×#6441	2
#90312	3
C₃×#562	7

Subgroups — C3×#90312 #13060963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90312 #13060963