Subgroups — C₃×D₇×#805 #72246662

Order 4032.

788 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#10620516	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#10620644	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#10620514	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×#805	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×C₄²×D₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×D₇×#235	C₂	1	1	yes	maximal, characteristic
7	C₃×D₇×#208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₇×#104	—	3	1	no	maximal
9	D₇×#805	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#66728	C₂²	1	1	yes	characteristic
11	C₃×C₇×#235	C₂²	1	1	yes	characteristic
12	C₂×C₃²×C₄×D₇	—	2	1	no	—
13	C₂×C₃²×C₄×D₇	C₂²	1	1	yes	characteristic
14	C₃×D₇×#67	—	2	1	no	—
15	C₃×#66686	—	2	1	no	—
16	C₃×D₇×D₁₂	C₄	1	1	yes	characteristic, complemented
17	C₃×C₄×D₃×D₇	—	2	1	no	—
18	C₃×#66677	C₄	1	1	yes	characteristic, complemented
19	C₃×#66676	C₄	1	1	yes	characteristic, complemented
20	C₃×#66675	—	2	1	no	—
21	C₃×D₇×Dic₆	C₄	1	1	yes	characteristic, complemented
22	C₃²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
23	C₃×#66627	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₇×#208	C₂²	1	1	yes	characteristic, complemented
25	C₃²×C₄×Dic₇	—	2	1	no	—
26	C₃²×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
27	C₃×#66557	—	2	1	no	—
28	C₃×D₇×C₃⋊C₈	—	2	1	no	—
29	C₃×D₇×#41	—	3	1	no	—
30	D₇×#235	C₂×C₃	1	1	yes	characteristic
31	C₃×D₇×M₁₆	—	3	1	no	—
32	C₃×C₄²×D₇	—	2	1	no	—
33	C₃×C₄²×D₇	D₃	1	1	yes	characteristic, complemented
34	C₃×C₄²×D₇	C₂×C₃	1	1	yes	characteristic, complemented
35	D₇×#208	C₂×C₃	1	1	yes	characteristic, complemented
36	C₃×C₇×#104	—	3	1	no	—
37	#10620644	C₂×C₃	1	1	yes	characteristic, complemented
38	C₇×#805	C₂×C₃	1	1	yes	characteristic, complemented
39	C₃×#6411	—	3	1	no	—
40	C₃×#6399	—	3	1	no	—
41	C₃×#6379	—	3	1	no	—
42	#10620516	C₂×C₃	1	1	yes	characteristic, complemented
43	#10620514	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×C₃×#805	—	7	1	no	maximal, Hall
45	C₂²×C₃²×D₇	D₄	1	1	yes	characteristic
46	C₂×C₃×D₃×D₇	—	2	1	no	—
47	C₂×C₃²×C₄×C₇	—	2	1	no	—
48	C₂×C₃²×C₄×C₇	C₂³	1	1	yes	characteristic
49	C₃×#4268	—	2	1	no	—
50	C₃×D₈₄	C₂×C₄	1	1	yes	characteristic, complemented
51	C₃×C₄×D₂₁	—	2	1	no	—
52	C₃×Dic₄₂	C₂×C₄	1	1	yes	characteristic, complemented
53	C₃×C₇×#67	—	2	1	no	—
54	C₃×C₇×D₁₂	C₂×C₄	1	1	yes	characteristic, complemented
55	C₃×C₄×D₃×C₇	—	2	1	no	—
56	C₃×C₇×Dic₆	C₂×C₄	1	1	yes	characteristic, complemented
57	C₂×C₃²×Dic₇	—	2	1	no	—
58	C₂×C₃²×Dic₇	D₄	1	1	yes	characteristic
59	C₃²×C₄×D₇	—	2	4	no	—
60	C₃²×C₄×D₇	C₂×C₄	1	1	yes	characteristic
61	C₃²×C₄×D₇	C₂×C₄	1	1	yes	characteristic
62	C₃²×C₄×D₇	D₄	1	1	yes	characteristic
63	C₃²×C₄×D₇	D₄	1	1	yes	characteristic
64	C₃×#4248	—	2	1	no	—
65	C₃×#4247	—	2	1	no	—
66	C₃×#4246	—	2	1	no	—
67	C₃×#4245	—	2	1	no	—
68	C₃×D₂₁⋊C₄	—	2	1	no	—
69	C₃×D₃×Dic₇	—	2	1	no	—
70	C₃×Dic₃×D₇	—	2	1	no	—
71	C₃×C₃⋊(C₇⋊C₈)	—	2	1	no	—
72	C₃×C₇×C₃⋊C₈	—	2	1	no	—
73	D₇×#104	—	3	1	no	Hall
74	C₃×C₇×#41	—	3	1	no	—
75	#66728	C₂²×C₃	1	1	yes	characteristic
76	C₇×#235	C₂²×C₃	1	1	yes	characteristic
77	C₃×#1161	—	3	1	no	—
78	C₃×Q₈×D₇	—	3	1	no	—
79	C₃×#1159	—	3	1	no	—
80	C₃×#1159	—	6	1	no	—
81	C₃×D₄×D₇	—	3	1	no	—
82	C₃×D₄×D₇	—	6	1	no	—
83	C₃×#1157	—	3	1	no	—
84	C₃×#1157	—	6	1	no	—
85	C₂×C₃×C₄×D₇	—	2	1	no	—
86	C₂×C₃×C₄×D₇	—	2	1	no	—
87	C₂×C₃×C₄×D₇	—	2	1	no	—
88	C₂×C₃×C₄×D₇	—	2	1	no	—
89	C₂×C₃×C₄×D₇	—	2	1	no	—
90	C₂×C₃×C₄×D₇	—	6	1	no	—
91	C₂×C₃×C₄×D₇	C₂×D₃	1	1	yes	characteristic
92	C₂×C₃×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
93	D₇×#67	—	2	1	no	—
94	#66686	—	2	1	no	—
95	D₇×D₁₂	C₃×C₄	1	1	yes	characteristic, complemented
96	C₄×D₃×D₇	—	2	1	no	—
97	#66677	C₃×C₄	1	1	yes	characteristic, complemented
98	#66676	C₃×C₄	1	1	yes	characteristic, complemented
99	#66675	—	2	1	no	—
100	D₇×Dic₆	C₃×C₄	1	1	yes	characteristic, complemented
101	C₃×C₇×M₁₆	—	3	1	no	—
102	C₃×C₄²×C₇	—	2	1	no	—
103	C₃×C₄²×C₇	C₂×D₃	1	1	yes	characteristic, complemented
104	C₃×C₄²×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
105	#66627	C₂²×C₃	1	1	yes	characteristic, complemented
106	C₇×#208	C₂²×C₃	1	1	yes	characteristic, complemented
107	C₃×C₄×Dic₇	—	2	1	no	—
108	C₃×C₄×Dic₇	—	2	1	no	—
109	C₃×C₄×Dic₇	—	2	1	no	—
110	C₃×C₄×Dic₇	—	2	1	no	—
111	C₃×C₄×Dic₇	—	2	1	no	—
112	C₃×C₄×Dic₇	C₂×D₃	1	1	yes	characteristic, complemented
113	C₃×C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
114	C₃×#1136	—	3	1	no	—
115	C₃×#1131	—	6	1	no	—
116	C₃×C₈×D₇	—	6	1	no	—
117	#66557	—	2	1	no	—
118	D₇×C₃⋊C₈	—	2	1	no	—
119	C₂×C₃×#235	—	7	1	no	—
120	C₂×C₃²×C₄²	—	7	1	no	—
121	C₂×C₃×#208	—	7	1	no	—
122	C₃×#805	—	7	1	no	—
123	C₃×#805	—	7	1	no	—
124	C₃×#805	—	7	1	no	—
125	C₃×#805	D₇	1	1	yes	characteristic, direct product factor
126	C₂²×C₃²×C₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃×D₂₁	—	2	1	no	—
128	C₂×C₃×D₃×C₇	—	2	1	no	—
129	C₂×C₃²×D₇	—	2	2	no	—
130	C₂×C₃²×D₇	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₃²×D₇	C₂²⋊C₄	1	1	yes	characteristic
132	C₃×D₃×D₇	—	4	2	no	—
133	C₃²×C₄×C₇	—	2	2	no	—
134	C₃²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
135	C₃²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
136	C₃×Dic₂₁	—	2	1	no	—
137	C₃×C₇×Dic₃	—	2	1	no	—
138	C₃²×Dic₇	—	2	2	no	—
139	C₃²×Dic₇	C₂²⋊C₄	1	1	yes	characteristic
140	C₃²×Dic₇	C₂²⋊C₄	1	1	yes	characteristic
141	D₇×#41	—	3	1	no	—
142	D₇×M₁₆	—	3	1	no	—
143	C₄²×D₇	C₃×D₃	1	1	yes	characteristic, complemented
144	C₇×#104	—	3	1	no	—
145	#6411	—	3	1	no	—
146	#6399	—	3	1	no	—
147	#6379	—	3	1	no	—
148	C₂×C₃×#104	—	21	1	no	—
149	C₂×#805	—	7	1	no	—
150	C₂²×C₃×D₇	—	2	1	no	—
151	C₂²×C₃×D₇	—	6	1	no	—
152	C₂²×C₃×D₇	#67	1	1	yes	characteristic
153	C₂²×C₃×D₇	C₃×D₄	1	1	yes	characteristic
154	C₂×D₃×D₇	—	2	1	no	—
155	C₃×C₇×Q₈	—	3	1	no	—
156	C₃×C₇×D₄	—	3	1	no	—
157	C₃×C₇×D₄	—	6	1	no	—
158	C₂×C₃×C₄×C₇	—	2	1	no	—
159	C₂×C₃×C₄×C₇	—	2	1	no	—
160	C₂×C₃×C₄×C₇	—	2	1	no	—
161	C₂×C₃×C₄×C₇	—	2	1	no	—
162	C₂×C₃×C₄×C₇	—	2	1	no	—
163	C₂×C₃×C₄×C₇	—	6	1	no	—
164	C₂×C₃×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
165	C₂×C₃×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
166	#4268	—	2	1	no	—
167	D₈₄	C₂×C₃×C₄	1	1	yes	characteristic, complemented
168	C₄×D₂₁	—	2	1	no	—
169	Dic₄₂	C₂×C₃×C₄	1	1	yes	characteristic, complemented
170	C₇×#67	—	2	1	no	—
171	C₇×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic, complemented
172	C₄×D₃×C₇	—	2	1	no	—
173	C₇×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic, complemented
174	C₃×C₂²⋊D₇	—	6	1	no	—
175	C₃×C₂²⋊D₇	—	6	1	no	—
176	C₃×C₂²⋊D₇	—	6	1	no	—
177	C₂×C₃×Dic₇	—	2	1	no	—
178	C₂×C₃×Dic₇	—	2	1	no	—
179	C₂×C₃×Dic₇	—	2	1	no	—
180	C₂×C₃×Dic₇	—	2	1	no	—
181	C₂×C₃×Dic₇	—	2	1	no	—
182	C₂×C₃×Dic₇	—	6	1	no	—
183	C₂×C₃×Dic₇	#67	1	1	yes	characteristic
184	C₂×C₃×Dic₇	C₃×D₄	1	1	yes	characteristic
185	C₃×D₂₈	—	3	1	no	—
186	C₃×D₂₈	—	6	1	no	—
187	C₃×C₄×D₇	—	2	4	no	—
188	C₃×C₄×D₇	—	2	4	no	—
189	C₃×C₄×D₇	—	2	4	no	—
190	C₃×C₄×D₇	—	2	4	no	—
191	C₃×C₄×D₇	—	2	1	no	—
192	C₃×C₄×D₇	—	2	1	no	—
193	C₃×C₄×D₇	—	2	1	no	—
194	C₃×C₄×D₇	—	2	1	no	—
195	C₃×C₄×D₇	—	6	1	no	—
196	C₃×C₄×D₇	—	6	1	no	—
197	C₃×C₄×D₇	—	6	1	no	—
198	C₃×C₄×D₇	C₄×D₃	1	1	yes	characteristic
199	C₃×C₄×D₇	C₄×D₃	1	1	yes	characteristic
200	C₃×C₄×D₇	D₁₂	1	1	yes	characteristic
201	C₃×C₄×D₇	D₁₂	1	1	yes	characteristic
202	C₃×C₄×D₇	C₂×C₃×C₄	1	1	yes	characteristic
203	C₃×C₄×D₇	C₂×C₃×C₄	1	1	yes	characteristic
204	C₃×C₄×D₇	C₃×D₄	1	1	yes	characteristic
205	C₃×C₄×D₇	C₃×D₄	1	1	yes	characteristic
206	C₃×Dic₁₄	—	3	1	no	—
207	C₃×Dic₁₄	—	6	1	no	—
208	#4248	—	2	1	no	—
209	#4247	—	2	1	no	—
210	#4246	—	2	1	no	—
211	#4245	—	2	1	no	—
212	D₂₁⋊C₄	—	2	1	no	—
213	D₃×Dic₇	—	2	1	no	—
214	Dic₃×D₇	—	2	1	no	—
215	C₃×C₇×C₈	—	6	1	no	—
216	C₃⋊(C₇⋊C₈)	—	2	1	no	—
217	C₃×C₇⋊C₈	—	6	1	no	—
218	C₇×C₃⋊C₈	—	2	1	no	—
219	C₂²×C₃²×C₄	—	7	1	no	—
220	C₂²×C₃²×C₄	—	14	1	no	—
221	C₂×C₃×#67	—	14	1	no	—
222	C₃×#235	—	7	1	no	—
223	C₃×#235	—	7	1	no	—
224	C₃×#235	—	7	1	no	—
225	C₃×#235	—	14	1	no	—
226	C₃×#235	—	14	1	no	—
227	C₃×#235	C₂×D₇	1	1	yes	characteristic
228	C₂×C₃×D₁₂	—	7	1	no	—
229	C₂×C₃×C₄×D₃	—	14	1	no	—
230	C₂×C₃×Dic₆	—	7	1	no	—
231	C₃²×C₄²	—	7	1	no	—
232	C₃²×C₄²	—	14	1	no	—
233	C₃²×C₄²	C₂×D₇	1	1	yes	characteristic, complemented
234	C₃×#208	—	7	1	no	—
235	C₃×#208	—	14	1	no	—
236	C₃×#208	C₂×D₇	1	1	yes	characteristic, complemented
237	C₂×C₃×C₃⋊C₈	—	14	1	no	—
238	C₂×C₃²×C₇	—	2	1	no	—
239	C₂×C₃²×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₃×D₂₁	—	4	1	no	—
241	C₃×D₃×C₇	—	4	1	no	—
242	C₃²×D₇	—	2	1	no	—
243	C₃²×D₇	#104	1	2	yes	complemented
244	C₇×#41	—	3	1	no	—
245	#1161	—	3	1	no	—
246	Q₈×D₇	—	3	1	no	—
247	#1159	—	3	1	no	—
248	#1159	—	6	1	no	—
249	D₄×D₇	—	3	1	no	—
250	D₄×D₇	—	6	1	no	—
251	#1157	—	3	1	no	—
252	#1157	—	6	1	no	—
253	C₂×C₄×D₇	—	2	1	no	—
254	C₂×C₄×D₇	—	6	1	no	—
255	C₂×C₄×D₇	C₂×C₃×D₃	1	1	yes	characteristic
256	C₇×M₁₆	—	3	1	no	—
257	C₄²×C₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented
258	C₄×Dic₇	—	2	1	no	—
259	C₄×Dic₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented
260	#1136	—	3	1	no	—
261	#1131	—	6	1	no	—
262	C₈×D₇	—	6	1	no	—
263	C₂×C₃×#41	—	21	1	no	—
264	C₂×#235	—	7	1	no	—
265	C₂×C₃×M₁₆	—	21	1	no	—
266	C₂×C₃×C₄²	—	7	1	no	—
267	C₂×C₃×C₄²	—	7	1	no	—
268	C₂×C₃×C₄²	—	14	1	no	—
269	C₂×#208	—	7	1	no	—
270	C₃×#104	—	3	1	no	—
271	C₃×#104	—	21	1	no	—
272	C₃×#104	—	21	1	no	—
273	C₃×#104	—	21	1	no	—
274	#805	—	7	1	no	—
275	#805	—	7	1	no	—
276	#805	—	7	1	no	—
277	#805	C₃×D₇	1	1	yes	characteristic, direct product factor
278	C₂²×C₃×C₇	—	2	1	no	—
279	C₂²×C₃×C₇	—	6	1	no	—
280	C₂²×C₃×C₇	C₂×#67	1	1	yes	characteristic
281	C₂²×C₃×C₇	C₂×C₃×D₄	1	1	yes	characteristic
282	C₂×D₂₁	—	2	1	no	—
283	C₂×D₃×C₇	—	2	1	no	—
284	C₂×C₃×D₇	—	2	2	no	—
285	C₂×C₃×D₇	—	2	2	no	—
286	C₂×C₃×D₇	—	2	2	no	—
287	C₂×C₃×D₇	—	2	2	no	—
288	C₂×C₃×D₇	—	2	1	no	—
289	C₂×C₃×D₇	—	2	1	no	—
290	C₂×C₃×D₇	—	6	1	no	—
291	C₂×C₃×D₇	—	12	2	no	—
292	C₂×C₃×D₇	(C₂×D₃)⋊C₄	1	1	yes	characteristic
293	C₂×C₃×D₇	(C₂×D₃)⋊C₄	1	1	yes	characteristic
294	C₂×C₃×D₇	C₃×C₂²⋊C₄	1	1	yes	characteristic
295	C₂×C₃×D₇	C₃×C₂²⋊C₄	1	1	yes	characteristic
296	D₃×D₇	—	4	2	no	—
297	C₃×C₄×C₇	—	2	2	no	—
298	C₃×C₄×C₇	—	2	2	no	—
299	C₃×C₄×C₇	—	2	2	no	—
300	C₃×C₄×C₇	—	2	2	no	—
301	C₃×C₄×C₇	—	2	1	no	—
302	C₃×C₄×C₇	—	2	1	no	—
303	C₃×C₄×C₇	—	6	1	no	—
304	C₃×C₄×C₇	C₂×C₄×D₃	1	1	yes	characteristic
305	C₃×C₄×C₇	C₂×D₁₂	1	1	yes	characteristic
306	C₃×C₄×C₇	C₂²×C₃×C₄	1	1	yes	characteristic
307	C₃×C₄×C₇	C₂×C₃×D₄	1	1	yes	characteristic
308	Dic₂₁	—	2	1	no	—
309	C₃×Dic₇	—	2	2	no	—
310	C₃×Dic₇	—	2	2	no	—
311	C₃×Dic₇	—	2	2	no	—
312	C₃×Dic₇	—	2	2	no	—
313	C₃×Dic₇	—	2	1	no	—
314	C₃×Dic₇	—	2	1	no	—
315	C₃×Dic₇	—	6	1	no	—
316	C₃×Dic₇	(C₂×D₃)⋊C₄	1	1	yes	characteristic
317	C₃×Dic₇	(C₂×D₃)⋊C₄	1	1	yes	characteristic
318	C₃×Dic₇	C₃×C₂²⋊C₄	1	1	yes	characteristic
319	C₃×Dic₇	C₃×C₂²⋊C₄	1	1	yes	characteristic
320	C₇×Dic₃	—	2	1	no	—
321	C₂³×C₃²	—	7	1	no	—
322	C₂²×C₃×D₃	—	14	1	no	—
323	C₂×C₃²×C₄	—	2	1	no	—
324	C₂×C₃²×C₄	—	7	1	no	—
325	C₂×C₃²×C₄	—	7	1	no	—
326	C₂×C₃²×C₄	—	7	1	no	—
327	C₂×C₃²×C₄	—	7	1	no	—
328	C₂×C₃²×C₄	—	7	1	no	—
329	C₂×C₃²×C₄	—	14	4	no	—
330	C₂×C₃²×C₄	—	14	1	no	—
331	C₂×C₃²×C₄	C₂²×D₇	1	1	yes	characteristic
332	C₃×#67	—	2	1	no	—
333	C₃×#67	—	14	1	no	—
334	C₃×#67	—	14	1	no	—
335	C₃×#67	—	14	1	no	—
336	C₂×C₃×Dic₃	—	14	1	no	—
337	C₃×D₁₂	—	7	1	no	—
338	C₃×D₁₂	—	14	1	no	—
339	C₃×D₁₂	C₄×D₇	1	1	yes	characteristic, complemented
340	C₃×C₄×D₃	—	2	1	no	—
341	C₃×C₄×D₃	—	14	1	no	—
342	C₃×C₄×D₃	—	14	1	no	—
343	C₃×C₄×D₃	—	14	1	no	—
344	C₃×Dic₆	—	7	1	no	—
345	C₃×Dic₆	—	14	1	no	—
346	C₃×Dic₆	C₄×D₇	1	1	yes	characteristic, complemented
347	C₃×C₃⋊C₈	—	2	1	no	—
348	C₃×C₃⋊C₈	—	14	1	no	—
349	C₂×#104	—	21	1	no	Sylow
350	C₃²×C₇	C₂×#104	1	1	yes	characteristic, complemented, Hall
351	C₂²×D₇	—	6	1	no	—
352	C₂²×D₇	C₃×#67	1	1	yes	characteristic
353	C₇×Q₈	—	3	1	no	—
354	C₇×D₄	—	3	1	no	—
355	C₇×D₄	—	6	1	no	—
356	C₂×C₄×C₇	—	2	1	no	—
357	C₂×C₄×C₇	—	6	1	no	—
358	C₂×C₄×C₇	C₂²×C₃×D₃	1	1	yes	characteristic
359	C₂²⋊D₇	—	6	1	no	—
360	C₂²⋊D₇	—	6	1	no	—
361	C₂²⋊D₇	—	6	1	no	—
362	C₂×Dic₇	—	2	1	no	—
363	C₂×Dic₇	—	6	1	no	—
364	C₂×Dic₇	C₃×#67	1	1	yes	characteristic
365	D₂₈	—	3	1	no	—
366	D₂₈	—	6	1	no	—
367	C₄×D₇	—	2	4	no	—
368	C₄×D₇	—	6	1	no	—
369	C₄×D₇	—	6	1	no	—
370	C₄×D₇	—	6	1	no	—
371	C₄×D₇	C₃×C₄×D₃	1	1	yes	characteristic
372	C₄×D₇	C₃×C₄×D₃	1	1	yes	characteristic
373	C₄×D₇	C₃×D₁₂	1	1	yes	characteristic
374	C₄×D₇	C₃×D₁₂	1	1	yes	characteristic
375	Dic₁₄	—	3	1	no	—
376	Dic₁₄	—	6	1	no	—
377	C₇×C₈	—	6	1	no	—
378	C₇⋊C₈	—	6	1	no	—
379	C₃×#41	—	3	1	no	—
380	C₃×#41	—	21	1	no	—
381	C₃×#41	—	21	1	no	—
382	C₃×#41	—	21	1	no	—
383	C₃×#41	—	42	1	no	—
384	C₃×#41	—	42	1	no	—
385	C₂×C₃×Q₈	—	21	1	no	—
386	C₂×C₃×D₄	—	21	1	no	—
387	C₂×C₃×D₄	—	42	1	no	—
388	C₂²×C₃×C₄	—	7	1	no	—
389	C₂²×C₃×C₄	—	7	1	no	—
390	C₂²×C₃×C₄	—	14	1	no	—
391	C₂²×C₃×C₄	—	14	1	no	—
392	C₂²×C₃×C₄	—	14	1	no	—
393	C₂²×C₃×C₄	—	14	1	no	—
394	C₂²×C₃×C₄	—	14	1	no	—
395	C₂²×C₃×C₄	—	42	1	no	—
396	C₂×#67	—	14	1	no	—
397	#235	—	7	1	no	—
398	#235	—	7	1	no	—
399	#235	—	7	1	no	—
400	#235	—	14	1	no	—
401	#235	—	14	1	no	—
402	#235	C₂×C₃×D₇	1	1	yes	characteristic
403	C₂×D₁₂	—	7	1	no	—
404	C₂×C₄×D₃	—	14	1	no	—
405	C₂×Dic₆	—	7	1	no	—
406	C₃×M₁₆	—	3	1	no	—
407	C₃×M₁₆	—	21	1	no	—
408	C₃×M₁₆	—	42	1	no	—
409	C₂×C₃×C₈	—	42	1	no	—
410	C₃×C₄²	—	2	1	no	—
411	C₃×C₄²	—	7	1	no	—
412	C₃×C₄²	—	7	1	no	—
413	C₃×C₄²	—	14	1	no	—
414	C₃×C₄²	—	14	1	no	—
415	C₃×C₄²	—	14	1	no	—
416	C₃×C₄²	—	14	1	no	—
417	C₃×C₄²	—	14	1	no	—
418	C₃×C₄²	D₃×D₇	1	1	yes	characteristic, complemented
419	C₃×C₄²	C₂×C₃×D₇	1	1	yes	characteristic, complemented
420	#208	—	7	1	no	—
421	#208	—	14	1	no	—
422	#208	C₂×C₃×D₇	1	1	yes	characteristic, complemented
423	C₂×C₃⋊C₈	—	14	1	no	—
424	C₂×C₃×C₇	—	2	1	no	—
425	C₂×C₃×C₇	—	2	1	no	—
426	C₂×C₃×C₇	—	2	1	no	—
427	C₂×C₃×C₇	—	2	1	no	—
428	C₂×C₃×C₇	—	2	1	no	—
429	C₂×C₃×C₇	—	12	1	no	—
430	C₂×C₃×C₇	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
431	C₂×C₃×C₇	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
432	D₂₁	—	4	1	no	—
433	C₃×D₇	—	2	1	no	—
434	C₃×D₇	—	2	1	no	—
435	C₃×D₇	—	2	1	no	—
436	C₃×D₇	—	2	1	no	—
437	C₃×D₇	—	2	2	no	—
438	C₃×D₇	—	12	1	no	—
439	C₃×D₇	#805	1	2	yes	direct product factor
440	C₃×D₇	C₃×#104	1	2	yes	complemented
441	D₃×C₇	—	4	1	no	—
442	C₂²×C₃²	—	7	1	no	—
443	C₂²×C₃²	—	7	1	no	—
444	C₂²×C₃²	—	14	2	no	—
445	C₂²×C₃²	D₄×D₇	1	1	yes	characteristic
446	C₂×C₃×D₃	—	2	1	no	—
447	C₂×C₃×D₃	—	14	1	no	—
448	C₂×C₃×D₃	—	28	2	no	—
449	C₃²×C₄	—	2	2	no	—
450	C₃²×C₄	—	7	1	no	—
451	C₃²×C₄	—	7	1	no	—
452	C₃²×C₄	—	14	2	no	—
453	C₃²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
454	C₃²×C₄	D₄×D₇	1	1	yes	characteristic
455	C₃×Dic₃	—	2	1	no	—
456	C₃×Dic₃	—	14	1	no	—
457	C₂×#41	—	21	1	no	—
458	C₂×M₁₆	—	21	1	no	—
459	C₂×C₄²	—	7	1	no	—
460	#104	—	3	1	no	—
461	#104	—	21	1	no	—
462	#104	—	21	1	no	—
463	#104	—	21	1	no	—
464	C₂²×C₇	—	6	1	no	—
465	C₂²×C₇	C₂×C₃×#67	1	1	yes	characteristic
466	C₂×D₇	—	2	2	no	—
467	C₂×D₇	—	6	1	no	—
468	C₂×D₇	—	12	2	no	—
469	C₂×D₇	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
470	C₂×D₇	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
471	C₄×C₇	—	2	2	no	—
472	C₄×C₇	—	6	1	no	—
473	C₄×C₇	C₂×C₃×C₄×D₃	1	1	yes	characteristic
474	C₄×C₇	C₂×C₃×D₁₂	1	1	yes	characteristic
475	Dic₇	—	2	2	no	—
476	Dic₇	—	6	1	no	—
477	Dic₇	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
478	Dic₇	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
479	C₂³×C₃	—	7	1	no	—
480	C₂³×C₃	—	7	1	no	—
481	C₂³×C₃	—	14	1	no	—
482	C₂³×C₃	—	42	1	no	—
483	C₂²×D₃	—	14	1	no	—
484	C₃×Q₈	—	3	1	no	—
485	C₃×Q₈	—	21	1	no	—
486	C₃×Q₈	—	42	1	no	—
487	C₃×D₄	—	3	1	no	—
488	C₃×D₄	—	6	1	no	—
489	C₃×D₄	—	21	1	no	—
490	C₃×D₄	—	42	1	no	—
491	C₃×D₄	—	42	1	no	—
492	C₃×D₄	—	42	1	no	—
493	C₃×D₄	—	42	1	no	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	1	no	—
496	C₂×C₃×C₄	—	2	1	no	—
497	C₂×C₃×C₄	—	2	1	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	6	1	no	—
500	C₂×C₃×C₄	—	7	1	no	—
501	C₂×C₃×C₄	—	7	1	no	—
502	C₂×C₃×C₄	—	7	1	no	—
503	C₂×C₃×C₄	—	7	1	no	—
504	C₂×C₃×C₄	—	7	1	no	—
505	C₂×C₃×C₄	—	7	1	no	—
506	C₂×C₃×C₄	—	7	1	no	—
507	C₂×C₃×C₄	—	7	1	no	—
508	C₂×C₃×C₄	—	7	1	no	—
509	C₂×C₃×C₄	—	7	1	no	—
510	C₂×C₃×C₄	—	14	1	no	—
511	C₂×C₃×C₄	—	14	1	no	—
512	C₂×C₃×C₄	—	14	1	no	—
513	C₂×C₃×C₄	—	14	1	no	—
514	C₂×C₃×C₄	—	14	1	no	—
515	C₂×C₃×C₄	—	14	4	no	—
516	C₂×C₃×C₄	—	14	4	no	—
517	C₂×C₃×C₄	—	14	4	no	—
518	C₂×C₃×C₄	—	14	4	no	—
519	C₂×C₃×C₄	—	14	1	no	—
520	C₂×C₃×C₄	—	14	1	no	—
521	C₂×C₃×C₄	—	14	1	no	—
522	C₂×C₃×C₄	—	14	1	no	—
523	C₂×C₃×C₄	—	42	1	no	—
524	C₂×C₃×C₄	—	42	1	no	—
525	C₂×C₃×C₄	—	42	1	no	—
526	C₂×C₃×C₄	—	42	1	no	—
527	C₂×C₃×C₄	C₂×D₃×D₇	1	1	yes	characteristic
528	C₂×C₃×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
529	#67	—	2	1	no	—
530	#67	—	14	1	no	—
531	#67	—	14	1	no	—
532	#67	—	14	1	no	—
533	C₂×Dic₃	—	14	1	no	—
534	D₁₂	—	7	1	no	—
535	D₁₂	—	14	1	no	—
536	D₁₂	C₃×C₄×D₇	1	1	yes	characteristic, complemented
537	C₄×D₃	—	2	1	no	—
538	C₄×D₃	—	14	1	no	—
539	C₄×D₃	—	14	1	no	—
540	C₄×D₃	—	14	1	no	—
541	Dic₆	—	7	1	no	—
542	Dic₆	—	14	1	no	—
543	Dic₆	C₃×C₄×D₇	1	1	yes	characteristic, complemented
544	C₃×C₈	—	6	1	no	—
545	C₃×C₈	—	42	1	no	—
546	C₃⋊C₈	—	2	1	no	—
547	C₃⋊C₈	—	14	1	no	—
548	C₃×C₇	—	2	1	no	—
549	C₃×C₇	C₂×#805	1	1	yes	characteristic, complemented
550	C₃×C₇	C₂×C₃×#104	1	1	yes	characteristic, complemented
551	C₂×C₃²	—	2	1	no	—
552	C₂×C₃²	—	7	2	no	—
553	C₂×C₃²	—	14	1	no	—
554	C₂×C₃²	D₇×C₂²⋊C₄	1	1	yes	characteristic
555	C₃×D₃	—	4	1	no	—
556	C₃×D₃	—	28	1	no	—
557	#41	—	3	1	no	—
558	#41	—	21	1	no	—
559	#41	—	21	1	no	—
560	#41	—	21	1	no	—
561	#41	—	42	1	no	—
562	#41	—	42	1	no	—
563	C₂×Q₈	—	21	1	no	—
564	C₂×D₄	—	21	1	no	—
565	C₂×D₄	—	42	1	no	—
566	C₂²×C₄	—	7	1	no	—
567	C₂²×C₄	—	14	1	no	—
568	C₂²×C₄	—	42	1	no	—
569	M₁₆	—	3	1	no	—
570	M₁₆	—	21	1	no	—
571	M₁₆	—	42	1	no	—
572	C₂×C₈	—	42	1	no	—
573	C₄²	—	7	1	no	—
574	C₄²	—	14	1	no	—
575	C₄²	C₃×D₃×D₇	1	1	yes	characteristic, complemented
576	C₂×C₇	—	2	1	no	—
577	C₂×C₇	—	12	1	no	—
578	C₂×C₇	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
579	D₇	—	2	1	no	—
580	D₇	—	12	1	no	—
581	D₇	C₃×#805	1	2	yes	direct product factor
582	C₂²×C₃	—	2	1	no	—
583	C₂²×C₃	—	6	1	no	—
584	C₂²×C₃	—	7	1	no	—
585	C₂²×C₃	—	7	1	no	—
586	C₂²×C₃	—	7	1	no	—
587	C₂²×C₃	—	7	1	no	—
588	C₂²×C₃	—	14	1	no	—
589	C₂²×C₃	—	14	1	no	—
590	C₂²×C₃	—	14	2	no	—
591	C₂²×C₃	—	14	2	no	—
592	C₂²×C₃	—	14	2	no	—
593	C₂²×C₃	—	14	2	no	—
594	C₂²×C₃	—	42	1	no	—
595	C₂²×C₃	—	84	2	no	—
596	C₂²×C₃	D₇×#67	1	1	yes	characteristic
597	C₂²×C₃	C₃×D₄×D₇	1	1	yes	characteristic
598	C₂×D₃	—	2	1	no	—
599	C₂×D₃	—	14	1	no	—
600	C₂×D₃	—	28	2	no	—
601	C₃×C₄	—	2	2	no	—
602	C₃×C₄	—	2	2	no	—
603	C₃×C₄	—	2	2	no	—
604	C₃×C₄	—	2	2	no	—
605	C₃×C₄	—	2	1	no	—
606	C₃×C₄	—	2	1	no	—
607	C₃×C₄	—	6	1	no	—
608	C₃×C₄	—	7	1	no	—
609	C₃×C₄	—	7	1	no	—
610	C₃×C₄	—	7	1	no	—
611	C₃×C₄	—	7	1	no	—
612	C₃×C₄	—	14	1	no	—
613	C₃×C₄	—	14	1	no	—
614	C₃×C₄	—	14	2	no	—
615	C₃×C₄	—	14	2	no	—
616	C₃×C₄	—	14	2	no	—
617	C₃×C₄	—	14	2	no	—
618	C₃×C₄	—	42	1	no	—
619	C₃×C₄	C₄×D₃×D₇	1	1	yes	characteristic
620	C₃×C₄	D₇×D₁₂	1	1	yes	characteristic
621	C₃×C₄	C₂×C₃×C₄×D₇	1	1	yes	characteristic
622	C₃×C₄	C₃×D₄×D₇	1	1	yes	characteristic
623	Dic₃	—	2	1	no	—
624	Dic₃	—	14	1	no	—
625	C₃²	D₇×#104	1	1	yes	characteristic, complemented, Sylow
626	C₂³	—	7	1	no	—
627	C₂³	—	42	1	no	—
628	Q₈	—	3	1	no	—
629	Q₈	—	21	1	no	—
630	Q₈	—	42	1	no	—
631	D₄	—	3	1	no	—
632	D₄	—	6	1	no	—
633	D₄	—	21	1	no	—
634	D₄	—	42	1	no	—
635	D₄	—	42	1	no	—
636	D₄	—	42	1	no	—
637	D₄	—	42	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	6	1	no	—
640	C₂×C₄	—	7	1	no	—
641	C₂×C₄	—	7	1	no	—
642	C₂×C₄	—	7	1	no	—
643	C₂×C₄	—	7	1	no	—
644	C₂×C₄	—	7	1	no	—
645	C₂×C₄	—	14	4	no	—
646	C₂×C₄	—	14	1	no	—
647	C₂×C₄	—	42	1	no	—
648	C₂×C₄	—	42	1	no	—
649	C₂×C₄	—	42	1	no	—
650	C₂×C₄	—	42	1	no	—
651	C₂×C₄	C₂×C₃×D₃×D₇	1	1	yes	characteristic
652	C₈	—	6	1	no	—
653	C₈	—	42	1	no	—
654	C₇	C₂×C₃×#805	1	1	yes	characteristic, complemented, Sylow
655	C₂×C₃	—	2	1	no	—
656	C₂×C₃	—	2	1	no	—
657	C₂×C₃	—	2	1	no	—
658	C₂×C₃	—	2	1	no	—
659	C₂×C₃	—	2	1	no	—
660	C₂×C₃	—	7	2	no	—
661	C₂×C₃	—	7	2	no	—
662	C₂×C₃	—	12	1	no	—
663	C₂×C₃	—	14	2	no	—
664	C₂×C₃	—	14	1	no	—
665	C₂×C₃	—	14	1	no	—
666	C₂×C₃	—	14	1	no	—
667	C₂×C₃	—	14	1	no	—
668	C₂×C₃	—	84	1	no	—
669	C₂×C₃	D₇×(C₂×D₃)⋊C₄	1	1	yes	characteristic
670	C₂×C₃	C₃×D₇×C₂²⋊C₄	1	1	yes	characteristic
671	D₃	—	4	1	no	—
672	D₃	—	28	1	no	—
673	C₂²	—	6	1	no	—
674	C₂²	—	7	1	no	—
675	C₂²	—	7	1	no	—
676	C₂²	—	14	2	no	—
677	C₂²	—	42	1	no	—
678	C₂²	—	84	2	no	—
679	C₂²	C₃×D₇×#67	1	1	yes	characteristic
680	C₄	—	2	2	no	—
681	C₄	—	6	1	no	—
682	C₄	—	7	1	no	—
683	C₄	—	7	1	no	—
684	C₄	—	14	2	no	—
685	C₄	—	42	1	no	—
686	C₄	C₃×C₄×D₃×D₇	1	1	yes	characteristic
687	C₄	C₃×D₇×D₁₂	1	1	yes	characteristic
688	C₃	—	2	1	no	—
689	C₃	D₇×#805	1	1	yes	characteristic, direct product factor
690	C₃	C₃×D₇×#104	1	1	yes	characteristic, complemented
691	C₂	—	2	1	no	—
692	C₂	—	7	2	no	—
693	C₂	—	12	1	no	—
694	C₂	—	14	1	no	—
695	C₂	—	84	1	no	—
696	C₂	C₃×D₇×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	D₇×D₁₂
commutator	C₃×C₄×C₇	C₂²×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₃×D₇
Fitting	C₃²×C₄²×C₇	C₂²
socle	C₂×C₃²×C₇	C₂×C₂²⋊C₄
prime radical	C₃×D₇×#235	C₂
cosocle	C₂×C₃×C₄×C₇	C₂³×C₃
hypercenter	C₃×C₄²	D₃×D₇
hypocenter	C₃×C₇	C₂×C₃×#104
LCS	G ▷ C₃×C₄×C₇ ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
1. C₃×#10620516	C₂	semidirect
2. C₃×#10620644	C₂	semidirect
3. C₃×#10620514	C₂	semidirect
4. C₃×C₇×#805	C₂	semidirect
5. C₃²×C₄²×D₇	C₂	semidirect
7. C₃×D₇×#208	C₂	semidirect
9. D₇×#805	C₃	direct (N × H)
16. C₃×D₇×D₁₂	C₄	semidirect
18. C₃×#66677	C₄	semidirect
19. C₃×#66676	C₄	semidirect
21. C₃×D₇×Dic₆	C₄	semidirect
22. C₃²×C₄²×C₇	C₂²	semidirect
23. C₃×#66627	C₂²	semidirect
24. C₃×C₇×#208	C₂²	semidirect
26. C₃²×C₄×Dic₇	C₂²	semidirect
33. C₃×C₄²×D₇	D₃	semidirect
34. C₃×C₄²×D₇	C₂×C₃	semidirect
35. D₇×#208	C₂×C₃	semidirect
37. #10620644	C₂×C₃	semidirect
38. C₇×#805	C₂×C₃	semidirect
42. #10620516	C₂×C₃	semidirect
43. #10620514	C₂×C₃	semidirect
50. C₃×D₈₄	C₂×C₄	semidirect
52. C₃×Dic₄₂	C₂×C₄	semidirect
54. C₃×C₇×D₁₂	C₂×C₄	semidirect
56. C₃×C₇×Dic₆	C₂×C₄	semidirect
95. D₇×D₁₂	C₃×C₄	semidirect
97. #66677	C₃×C₄	semidirect
98. #66676	C₃×C₄	semidirect
100. D₇×Dic₆	C₃×C₄	semidirect
103. C₃×C₄²×C₇	C₂×D₃	semidirect
104. C₃×C₄²×C₇	C₂²×C₃	semidirect
105. #66627	C₂²×C₃	semidirect
106. C₇×#208	C₂²×C₃	semidirect
112. C₃×C₄×Dic₇	C₂×D₃	semidirect
113. C₃×C₄×Dic₇	C₂²×C₃	semidirect
125. C₃×#805	D₇	direct (N × H)
143. C₄²×D₇	C₃×D₃	semidirect
167. D₈₄	C₂×C₃×C₄	semidirect
169. Dic₄₂	C₂×C₃×C₄	semidirect
171. C₇×D₁₂	C₂×C₃×C₄	semidirect
173. C₇×Dic₆	C₂×C₃×C₄	semidirect
233. C₃²×C₄²	C₂×D₇	semidirect
236. C₃×#208	C₂×D₇	semidirect
243. C₃²×D₇	#104	semidirect
257. C₄²×C₇	C₂×C₃×D₃	semidirect
259. C₄×Dic₇	C₂×C₃×D₃	semidirect
277. #805	C₃×D₇	direct (N × H)
339. C₃×D₁₂	C₄×D₇	semidirect
346. C₃×Dic₆	C₄×D₇	semidirect
350. C₃²×C₇	C₂×#104	semidirect
418. C₃×C₄²	D₃×D₇	semidirect
419. C₃×C₄²	C₂×C₃×D₇	semidirect
422. #208	C₂×C₃×D₇	semidirect
439. C₃×D₇	#805	direct (N × H)
440. C₃×D₇	C₃×#104	semidirect
536. D₁₂	C₃×C₄×D₇	semidirect
543. Dic₆	C₃×C₄×D₇	semidirect
549. C₃×C₇	C₂×#805	semidirect
550. C₃×C₇	C₂×C₃×#104	semidirect
575. C₄²	C₃×D₃×D₇	semidirect
581. D₇	C₃×#805	direct (N × H)
625. C₃²	D₇×#104	semidirect
654. C₇	C₂×C₃×#805	semidirect
689. C₃	D₇×#805	direct (N × H)
690. C₃	C₃×D₇×#104	semidirect

Maximal subgroups

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

subgroup	index
C₃×#10620516	2
C₃×#10620644	2
C₃×#10620514	2
C₃×C₇×#805	2
C₃²×C₄²×D₇	2
C₃×D₇×#235	2
C₃×D₇×#208	2
C₃×D₇×#104	3
D₇×#805	3
C₂×C₃×#805	7

Subgroups — C3×D7×#805 #72246662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₇×#805 #72246662