Subgroups — C₇×C₃⋊D₃×#120 #72246741

Order 4032.

3972 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#64091	C₂	1	3	yes	maximal, complemented
2	C₇×#64162	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#64146	C₂	1	3	yes	maximal, complemented
4	C₃²×C₇×#120	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×C₂²⋊C₄×C₃⋊D₃	C₂	1	3	yes	maximal, complemented
6	C₂⁴×C₇×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×D₄×C₃⋊D₃	C₂	1	3	yes	maximal, complemented
8	D₃×C₇×#120	—	3	4	no	maximal
9	C₂⁴×C₃²×C₇	C₂²	1	1	yes	characteristic, complemented
10	C₂³×C₇×C₃⋊D₃	—	2	12	no	—
11	C₂³×C₇×C₃⋊D₃	C₂²	1	3	yes	—
12	C₂³×C₇×C₃⋊D₃	C₂²	1	3	yes	complemented
13	C₂³×C₇×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃²×C₇×D₄	C₂²	1	3	yes	complemented
15	C₂×C₇×#638	C₂²	1	3	yes	complemented
16	C₂×C₇×#638	C₂²	1	3	yes	complemented
17	C₇×D₄×C₃⋊D₃	—	2	12	no	—
18	C₂×C₇×C₄⋊(C₃⋊D₃)	C₂²	1	3	yes	complemented
19	C₂×C₄×C₇×C₃⋊D₃	C₂²	1	3	yes	complemented
20	C₃²×C₇×C₂²⋊C₄	C₂²	1	3	yes	complemented
21	C₇×#3757	C₂²	1	3	yes	complemented
22	C₇×#3752	C₂²	1	6	yes	complemented
23	C₂⁴×D₃×C₇	—	3	4	no	—
24	C₂×D₃×C₇×D₄	—	3	12	no	—
25	C₃×C₇×#120	D₃	1	4	yes	complemented
26	C₇×#953	—	3	4	no	—
27	C₇×#937	—	3	12	no	—
28	C₇×#882	—	3	12	no	—
29	D₃×C₇×C₂²⋊C₄	—	3	12	no	—
30	C₃⋊D₃×#120	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂³×C₃²×C₇	—	2	6	no	—
32	C₂³×C₃²×C₇	C₂³	1	3	yes	—
33	C₂³×C₃²×C₇	C₂³	1	1	yes	characteristic, complemented
34	C₂²×C₇×C₃⋊D₃	—	2	32	no	—
35	C₂²×C₇×C₃⋊D₃	—	2	6	no	—
36	C₂²×C₇×C₃⋊D₃	—	2	12	no	—
37	C₂²×C₇×C₃⋊D₃	—	2	12	no	—
38	C₂²×C₇×C₃⋊D₃	—	2	6	no	—
39	C₂²×C₇×C₃⋊D₃	D₄	1	12	yes	complemented
40	C₂²×C₇×C₃⋊D₃	C₂³	1	3	yes	—
41	C₂²×C₇×C₃⋊D₃	C₂³	1	1	yes	characteristic
42	C₂²×C₇×C₃⋊D₃	C₂³	1	1	yes	characteristic, complemented
43	C₃²×C₇×D₄	—	2	6	no	—
44	C₂×C₃²×C₄×C₇	C₂³	1	3	yes	complemented
45	C₇×#638	—	2	6	no	—
46	C₇×#638	—	2	6	no	—
47	C₂×C₇×C₃⋊Dic₃	C₂³	1	3	yes	complemented
48	C₇×C₄⋊(C₃⋊D₃)	—	2	6	no	—
49	C₄×C₇×C₃⋊D₃	—	2	6	no	—
50	C₂×C₇×#120	—	9	1	no	Hall
51	C₂⁴×C₃×C₇	C₂×D₃	1	4	yes	complemented
52	C₂³×D₃×C₇	—	3	12	no	—
53	C₂³×D₃×C₇	—	3	12	no	—
54	C₂³×D₃×C₇	—	3	4	no	—
55	C₂³×D₃×C₇	—	6	48	no	—
56	C₂×C₃×C₇×D₄	C₂×D₃	1	12	yes	complemented
57	C₂×C₇×#67	—	3	12	no	—
58	C₂×C₇×#67	—	3	12	no	—
59	D₃×C₇×D₄	—	6	48	no	—
60	C₂×C₇×D₁₂	—	3	12	no	—
61	C₂×C₄×D₃×C₇	—	3	12	no	—
62	C₃×C₇×C₂²⋊C₄	C₂×D₃	1	12	yes	complemented
63	C₇×#217	—	3	12	no	—
64	C₇×(C₂×D₃)⋊C₄	—	3	24	no	—
65	C₂⁴×C₃⋊D₃	C₂×C₇	1	1	yes	characteristic, complemented
66	C₂×D₄×C₃⋊D₃	C₂×C₇	1	3	yes	complemented
67	C₃²×#120	C₂×C₇	1	1	yes	characteristic, complemented
68	#64162	C₂×C₇	1	1	yes	characteristic, complemented
69	#64146	C₂×C₇	1	3	yes	complemented
70	#64091	C₂×C₇	1	3	yes	complemented
71	C₂²⋊C₄×C₃⋊D₃	C₂×C₇	1	3	yes	complemented
72	C₂²×C₃²×C₇	—	2	8	no	—
73	C₂²×C₃²×C₇	—	2	6	no	—
74	C₂²×C₃²×C₇	—	2	3	no	—
75	C₂²×C₃²×C₇	C₂×D₄	1	6	yes	complemented
76	C₂²×C₃²×C₇	C₂⁴	1	1	yes	characteristic
77	C₂×C₇×C₃⋊D₃	—	2	24	no	—
78	C₂×C₇×C₃⋊D₃	—	2	6	no	—
79	C₂×C₇×C₃⋊D₃	—	2	24	no	—
80	C₂×C₇×C₃⋊D₃	—	2	3	no	—
81	C₂×C₇×C₃⋊D₃	—	4	4	no	—
82	C₂×C₇×C₃⋊D₃	C₂×D₄	1	6	yes	—
83	C₂×C₇×C₃⋊D₃	C₂×D₄	1	6	yes	complemented
84	C₃²×C₄×C₇	—	2	3	no	—
85	C₇×C₃⋊Dic₃	—	2	3	no	—
86	C₂⁵×C₇	—	9	1	no	—
87	C₂²×C₇×D₄	—	9	3	no	—
88	C₇×#120	—	9	1	no	—
89	C₇×#120	—	9	3	no	—
90	C₇×#120	—	9	3	no	—
91	C₇×#120	C₃⋊D₃	1	1	yes	characteristic, direct product factor
92	C₂×C₇×C₂²⋊C₄	—	9	3	no	—
93	D₃×#120	—	3	4	no	—
94	C₂³×C₃×C₇	—	2	24	no	—
95	C₂³×C₃×C₇	C₂²×D₃	1	12	yes	—
96	C₂³×C₃×C₇	C₂²×D₃	1	4	yes	complemented
97	C₂²×D₃×C₇	—	3	4	no	—
98	C₂²×D₃×C₇	—	3	48	no	—
99	C₂²×D₃×C₇	—	3	12	no	—
100	C₂²×D₃×C₇	—	3	4	no	—
101	C₂²×D₃×C₇	—	6	48	no	—
102	C₂²×D₃×C₇	—	6	48	no	—
103	C₂²×D₃×C₇	—	6	24	no	—
104	C₂²×D₃×C₇	—	6	128	no	—
105	C₂²×D₃×C₇	—	6	24	no	—
106	C₃×C₇×D₄	—	2	24	no	—
107	C₂×C₃×C₄×C₇	C₂²×D₃	1	12	yes	complemented
108	C₇×#67	—	6	24	no	—
109	C₇×#67	—	6	24	no	—
110	C₂×C₇×Dic₃	—	3	12	no	—
111	C₇×D₁₂	—	6	24	no	—
112	C₄×D₃×C₇	—	6	24	no	—
113	C₂⁴×C₃²	C₂²×C₇	1	1	yes	characteristic, complemented
114	C₂³×C₃⋊D₃	—	2	12	no	—
115	C₂³×C₃⋊D₃	C₂²×C₇	1	3	yes	—
116	C₂³×C₃⋊D₃	C₂²×C₇	1	3	yes	complemented
117	C₂³×C₃⋊D₃	C₂²×C₇	1	1	yes	characteristic, complemented
118	C₂×C₃²×D₄	C₂²×C₇	1	3	yes	complemented
119	C₂×#638	C₂²×C₇	1	3	yes	complemented
120	C₂×#638	C₂²×C₇	1	3	yes	complemented
121	D₄×C₃⋊D₃	—	2	12	no	—
122	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₇	1	3	yes	complemented
123	C₂×C₄×C₃⋊D₃	C₂²×C₇	1	3	yes	complemented
124	C₃²×C₂²⋊C₄	C₂²×C₇	1	3	yes	complemented
125	#3757	C₂²×C₇	1	3	yes	complemented
126	#3752	C₂²×C₇	1	6	yes	complemented
127	C₂×C₃²×C₇	—	2	6	no	—
128	C₂×C₃²×C₇	—	4	1	no	—
129	C₂×C₃²×C₇	C₂²×D₄	1	3	yes	—
130	C₇×C₃⋊D₃	—	2	6	no	—
131	C₇×C₃⋊D₃	—	4	1	no	—
132	C₇×C₃⋊D₃	#120	1	4	yes	direct product factor
133	C₂⁴×C₇	—	9	3	no	—
134	C₂⁴×C₇	—	9	3	no	—
135	C₂⁴×C₇	—	9	1	no	—
136	C₂⁴×C₇	—	18	12	no	—
137	C₂⁴×C₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
138	C₂×C₇×D₄	—	9	3	no	—
139	C₂×C₇×D₄	—	9	3	no	—
140	C₂×C₇×D₄	—	9	3	no	—
141	C₂×C₇×D₄	—	18	12	no	—
142	C₂×C₇×D₄	C₂×C₃⋊D₃	1	3	yes	complemented
143	C₂²×C₄×C₇	—	9	3	no	—
144	C₇×C₂²⋊C₄	—	9	3	no	—
145	C₇×C₂²⋊C₄	—	9	6	no	—
146	C₇×C₂²⋊C₄	C₂×C₃⋊D₃	1	3	yes	complemented
147	C₂⁴×D₃	—	3	4	no	—
148	C₂×D₃×D₄	—	3	12	no	—
149	C₃×#120	D₃×C₇	1	4	yes	complemented
150	#953	—	3	4	no	—
151	#937	—	3	12	no	—
152	#882	—	3	12	no	—
153	D₃×C₂²⋊C₄	—	3	12	no	—
154	C₂²×C₃×C₇	—	2	32	no	—
155	C₂²×C₃×C₇	—	2	24	no	—
156	C₂²×C₃×C₇	—	2	12	no	—
157	C₂²×C₃×C₇	D₃×D₄	1	24	yes	complemented
158	C₂²×C₃×C₇	C₂³×D₃	1	4	yes	—
159	C₂×D₃×C₇	—	3	24	no	—
160	C₂×D₃×C₇	—	3	24	no	—
161	C₂×D₃×C₇	—	6	96	no	—
162	C₂×D₃×C₇	—	6	96	no	—
163	C₂×D₃×C₇	—	6	24	no	—
164	C₂×D₃×C₇	—	6	12	no	—
165	C₂×D₃×C₇	—	12	16	no	—
166	C₃×C₄×C₇	—	2	12	no	—
167	C₇×Dic₃	—	6	12	no	—
168	C₂³×C₃²	—	2	6	no	—
169	C₂³×C₃²	C₂³×C₇	1	3	yes	—
170	C₂³×C₃²	C₂³×C₇	1	1	yes	characteristic, complemented
171	C₂²×C₃⋊D₃	—	2	32	no	—
172	C₂²×C₃⋊D₃	—	2	6	no	—
173	C₂²×C₃⋊D₃	—	2	12	no	—
174	C₂²×C₃⋊D₃	—	2	12	no	—
175	C₂²×C₃⋊D₃	—	2	6	no	—
176	C₂²×C₃⋊D₃	C₇×D₄	1	12	yes	complemented
177	C₂²×C₃⋊D₃	C₂³×C₇	1	3	yes	—
178	C₂²×C₃⋊D₃	C₂³×C₇	1	1	yes	characteristic
179	C₂²×C₃⋊D₃	C₂³×C₇	1	1	yes	characteristic, complemented
180	C₃²×D₄	—	2	6	no	—
181	C₂×C₃²×C₄	C₂³×C₇	1	3	yes	complemented
182	#638	—	2	6	no	—
183	#638	—	2	6	no	—
184	C₂×C₃⋊Dic₃	C₂³×C₇	1	3	yes	complemented
185	C₄⋊(C₃⋊D₃)	—	2	6	no	—
186	C₄×C₃⋊D₃	—	2	6	no	—
187	C₂×#120	—	9	1	no	Sylow
188	C₃²×C₇	C₂×#120	1	1	yes	characteristic, complemented, Hall
189	C₂³×C₇	—	2	6	no	—
190	C₂³×C₇	—	9	1	no	—
191	C₂³×C₇	—	9	3	no	—
192	C₂³×C₇	—	9	12	no	—
193	C₂³×C₇	—	9	1	no	—
194	C₂³×C₇	—	18	12	no	—
195	C₂³×C₇	—	18	12	no	—
196	C₂³×C₇	—	18	6	no	—
197	C₂³×C₇	—	18	32	no	—
198	C₂³×C₇	—	18	6	no	—
199	C₂³×C₇	C₂²×C₃⋊D₃	1	3	yes	—
200	C₂³×C₇	C₂²×C₃⋊D₃	1	1	yes	characteristic, complemented
201	C₇×D₄	—	2	6	no	—
202	C₇×D₄	—	18	6	no	—
203	C₇×D₄	—	18	6	no	—
204	C₇×D₄	—	18	6	no	—
205	C₂×C₄×C₇	—	9	3	no	—
206	C₂×C₄×C₇	—	18	6	no	—
207	C₂×C₄×C₇	C₂²×C₃⋊D₃	1	3	yes	complemented
208	C₂⁴×C₃	C₂×D₃×C₇	1	4	yes	complemented
209	C₂³×D₃	—	3	12	no	—
210	C₂³×D₃	—	3	12	no	—
211	C₂³×D₃	—	3	4	no	—
212	C₂³×D₃	—	6	48	no	—
213	C₂×C₃×D₄	C₂×D₃×C₇	1	12	yes	complemented
214	C₂×#67	—	3	12	no	—
215	C₂×#67	—	3	12	no	—
216	D₃×D₄	—	6	48	no	—
217	C₂×D₁₂	—	3	12	no	—
218	C₂×C₄×D₃	—	3	12	no	—
219	C₃×C₂²⋊C₄	C₂×D₃×C₇	1	12	yes	complemented
220	#217	—	3	12	no	—
221	(C₂×D₃)⋊C₄	—	3	24	no	—
222	C₂×C₃×C₇	—	2	24	no	—
223	C₂×C₃×C₇	—	4	4	no	—
224	C₂×C₃×C₇	C₂×D₃×D₄	1	12	yes	—
225	D₃×C₇	—	3	16	no	—
226	D₃×C₇	—	6	24	no	—
227	D₃×C₇	—	12	4	no	—
228	C₂²×C₃²	—	2	8	no	—
229	C₂²×C₃²	—	2	6	no	—
230	C₂²×C₃²	—	2	3	no	—
231	C₂²×C₃²	C₂×C₇×D₄	1	6	yes	complemented
232	C₂²×C₃²	C₂⁴×C₇	1	1	yes	characteristic
233	C₂×C₃⋊D₃	—	2	24	no	—
234	C₂×C₃⋊D₃	—	2	6	no	—
235	C₂×C₃⋊D₃	—	2	24	no	—
236	C₂×C₃⋊D₃	—	2	3	no	—
237	C₂×C₃⋊D₃	—	4	4	no	—
238	C₂×C₃⋊D₃	C₂×C₇×D₄	1	6	yes	—
239	C₂×C₃⋊D₃	C₂×C₇×D₄	1	6	yes	complemented
240	C₃²×C₄	—	2	3	no	—
241	C₃⋊Dic₃	—	2	3	no	—
242	C₂⁵	—	9	1	no	—
243	C₂²×D₄	—	9	3	no	—
244	#120	—	9	1	no	—
245	#120	—	9	3	no	—
246	#120	—	9	3	no	—
247	#120	C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor
248	C₂×C₂²⋊C₄	—	9	3	no	—
249	C₂²×C₇	—	2	8	no	—
250	C₂²×C₇	—	2	6	no	—
251	C₂²×C₇	—	2	3	no	—
252	C₂²×C₇	—	9	6	no	—
253	C₂²×C₇	—	9	6	no	—
254	C₂²×C₇	—	18	24	no	—
255	C₂²×C₇	—	18	24	no	—
256	C₂²×C₇	—	18	6	no	—
257	C₂²×C₇	—	18	3	no	—
258	C₂²×C₇	—	36	4	no	—
259	C₂²×C₇	D₄×C₃⋊D₃	1	6	yes	complemented
260	C₂²×C₇	C₂³×C₃⋊D₃	1	1	yes	characteristic
261	C₄×C₇	—	2	3	no	—
262	C₄×C₇	—	18	3	no	—
263	C₂³×C₃	—	2	24	no	—
264	C₂³×C₃	C₂²×D₃×C₇	1	12	yes	—
265	C₂³×C₃	C₂²×D₃×C₇	1	4	yes	complemented
266	C₂²×D₃	—	3	4	no	—
267	C₂²×D₃	—	3	48	no	—
268	C₂²×D₃	—	3	12	no	—
269	C₂²×D₃	—	3	4	no	—
270	C₂²×D₃	—	6	48	no	—
271	C₂²×D₃	—	6	48	no	—
272	C₂²×D₃	—	6	24	no	—
273	C₂²×D₃	—	6	128	no	—
274	C₂²×D₃	—	6	24	no	—
275	C₃×D₄	—	2	24	no	—
276	C₂×C₃×C₄	C₂²×D₃×C₇	1	12	yes	complemented
277	#67	—	6	24	no	—
278	#67	—	6	24	no	—
279	C₂×Dic₃	—	3	12	no	—
280	D₁₂	—	6	24	no	—
281	C₄×D₃	—	6	24	no	—
282	C₃×C₇	D₃×#120	1	4	yes	complemented
283	C₂×C₃²	—	2	6	no	—
284	C₂×C₃²	—	4	1	no	—
285	C₂×C₃²	C₂²×C₇×D₄	1	3	yes	—
286	C₃⋊D₃	—	2	6	no	—
287	C₃⋊D₃	—	4	1	no	—
288	C₃⋊D₃	C₇×#120	1	4	yes	direct product factor
289	C₂⁴	—	9	3	no	—
290	C₂⁴	—	9	3	no	—
291	C₂⁴	—	9	1	no	—
292	C₂⁴	—	18	12	no	—
293	C₂⁴	C₂×C₇×C₃⋊D₃	1	1	yes	characteristic, complemented
294	C₂×D₄	—	9	3	no	—
295	C₂×D₄	—	9	3	no	—
296	C₂×D₄	—	9	3	no	—
297	C₂×D₄	—	18	12	no	—
298	C₂×D₄	C₂×C₇×C₃⋊D₃	1	3	yes	complemented
299	C₂²×C₄	—	9	3	no	—
300	C₂²⋊C₄	—	9	3	no	—
301	C₂²⋊C₄	—	9	6	no	—
302	C₂²⋊C₄	C₂×C₇×C₃⋊D₃	1	3	yes	complemented
303	C₂×C₇	—	2	6	no	—
304	C₂×C₇	—	4	1	no	—
305	C₂×C₇	—	9	4	no	—
306	C₂×C₇	—	18	6	no	—
307	C₂×C₇	—	36	1	no	—
308	C₂×C₇	C₂×D₄×C₃⋊D₃	1	3	yes	—
309	C₂²×C₃	—	2	32	no	—
310	C₂²×C₃	—	2	24	no	—
311	C₂²×C₃	—	2	12	no	—
312	C₂²×C₃	D₃×C₇×D₄	1	24	yes	complemented
313	C₂²×C₃	C₂³×D₃×C₇	1	4	yes	—
314	C₂×D₃	—	3	24	no	—
315	C₂×D₃	—	3	24	no	—
316	C₂×D₃	—	6	96	no	—
317	C₂×D₃	—	6	96	no	—
318	C₂×D₃	—	6	24	no	—
319	C₂×D₃	—	6	12	no	—
320	C₂×D₃	—	12	16	no	—
321	C₃×C₄	—	2	12	no	—
322	Dic₃	—	6	12	no	—
323	C₃²	C₂×C₇×#120	1	1	yes	characteristic, complemented, Sylow
324	C₂³	—	2	6	no	—
325	C₂³	—	9	1	no	—
326	C₂³	—	9	12	no	—
327	C₂³	—	9	3	no	—
328	C₂³	—	9	1	no	—
329	C₂³	—	18	12	no	—
330	C₂³	—	18	12	no	—
331	C₂³	—	18	6	no	—
332	C₂³	—	18	32	no	—
333	C₂³	—	18	6	no	—
334	C₂³	C₂²×C₇×C₃⋊D₃	1	3	yes	—
335	C₂³	C₂²×C₇×C₃⋊D₃	1	1	yes	characteristic, complemented
336	D₄	—	2	6	no	—
337	D₄	—	18	6	no	—
338	D₄	—	18	6	no	—
339	D₄	—	18	6	no	—
340	C₂×C₄	—	9	3	no	—
341	C₂×C₄	—	18	6	no	—
342	C₂×C₄	C₂²×C₇×C₃⋊D₃	1	3	yes	complemented
343	C₇	C₃⋊D₃×#120	1	1	yes	characteristic, direct product factor, Sylow
344	C₂×C₃	—	2	24	no	—
345	C₂×C₃	—	4	4	no	—
346	C₂×C₃	C₂×D₃×C₇×D₄	1	12	yes	—
347	D₃	—	3	16	no	—
348	D₃	—	6	24	no	—
349	D₃	—	12	4	no	—
350	C₂²	—	2	8	no	—
351	C₂²	—	2	6	no	—
352	C₂²	—	2	3	no	—
353	C₂²	—	9	6	no	—
354	C₂²	—	9	6	no	—
355	C₂²	—	18	24	no	—
356	C₂²	—	18	24	no	—
357	C₂²	—	18	6	no	—
358	C₂²	—	18	3	no	—
359	C₂²	—	36	4	no	—
360	C₂²	C₇×D₄×C₃⋊D₃	1	6	yes	complemented
361	C₂²	C₂³×C₇×C₃⋊D₃	1	1	yes	characteristic
362	C₄	—	2	3	no	—
363	C₄	—	18	3	no	—
364	C₃	D₃×C₇×#120	1	4	yes	complemented
365	C₂	—	2	6	no	—
366	C₂	—	4	1	no	—
367	C₂	—	9	4	no	—
368	C₂	—	18	6	no	—
369	C₂	—	36	1	no	—
370	C₂	C₂×C₇×D₄×C₃⋊D₃	1	3	yes	—

	subgroup	G/H
center	C₂²×C₇	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₇
Frattini	C₂²	C₂³×C₇×C₃⋊D₃
Fitting	C₃²×C₇×#120	C₂
socle	C₂²×C₃²×C₇	C₂⁴
hypercenter	C₇×#120	C₃⋊D₃
hypocenter	C₃²	C₂×C₇×#120
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#120

Complements

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

N	H ≅ G/N	type
1. C₇×#64091	C₂	semidirect
2. C₇×#64162	C₂	semidirect
3. C₇×#64146	C₂	semidirect
4. C₃²×C₇×#120	C₂	semidirect
5. C₇×C₂²⋊C₄×C₃⋊D₃	C₂	semidirect
6. C₂⁴×C₇×C₃⋊D₃	C₂	semidirect
7. C₂×C₇×D₄×C₃⋊D₃	C₂	semidirect
9. C₂⁴×C₃²×C₇	C₂²	semidirect
12. C₂³×C₇×C₃⋊D₃	C₂²	semidirect
13. C₂³×C₇×C₃⋊D₃	C₂²	semidirect
14. C₂×C₃²×C₇×D₄	C₂²	semidirect
15. C₂×C₇×#638	C₂²	semidirect
16. C₂×C₇×#638	C₂²	semidirect
18. C₂×C₇×C₄⋊(C₃⋊D₃)	C₂²	semidirect
19. C₂×C₄×C₇×C₃⋊D₃	C₂²	semidirect
20. C₃²×C₇×C₂²⋊C₄	C₂²	semidirect
21. C₇×#3757	C₂²	semidirect
22. C₇×#3752	C₂²	semidirect
25. C₃×C₇×#120	D₃	semidirect
30. C₃⋊D₃×#120	C₇	direct (N × H)
33. C₂³×C₃²×C₇	C₂³	semidirect
39. C₂²×C₇×C₃⋊D₃	D₄	semidirect
42. C₂²×C₇×C₃⋊D₃	C₂³	semidirect
44. C₂×C₃²×C₄×C₇	C₂³	semidirect
47. C₂×C₇×C₃⋊Dic₃	C₂³	semidirect
51. C₂⁴×C₃×C₇	C₂×D₃	semidirect
56. C₂×C₃×C₇×D₄	C₂×D₃	semidirect
62. C₃×C₇×C₂²⋊C₄	C₂×D₃	semidirect
65. C₂⁴×C₃⋊D₃	C₂×C₇	semidirect
66. C₂×D₄×C₃⋊D₃	C₂×C₇	semidirect
67. C₃²×#120	C₂×C₇	semidirect
68. #64162	C₂×C₇	semidirect
69. #64146	C₂×C₇	semidirect
70. #64091	C₂×C₇	semidirect
71. C₂²⋊C₄×C₃⋊D₃	C₂×C₇	semidirect
75. C₂²×C₃²×C₇	C₂×D₄	semidirect
83. C₂×C₇×C₃⋊D₃	C₂×D₄	semidirect
91. C₇×#120	C₃⋊D₃	direct (N × H)
96. C₂³×C₃×C₇	C₂²×D₃	semidirect
107. C₂×C₃×C₄×C₇	C₂²×D₃	semidirect
113. C₂⁴×C₃²	C₂²×C₇	semidirect
116. C₂³×C₃⋊D₃	C₂²×C₇	semidirect
117. C₂³×C₃⋊D₃	C₂²×C₇	semidirect
118. C₂×C₃²×D₄	C₂²×C₇	semidirect
119. C₂×#638	C₂²×C₇	semidirect
120. C₂×#638	C₂²×C₇	semidirect
122. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₇	semidirect
123. C₂×C₄×C₃⋊D₃	C₂²×C₇	semidirect
124. C₃²×C₂²⋊C₄	C₂²×C₇	semidirect
125. #3757	C₂²×C₇	semidirect
126. #3752	C₂²×C₇	semidirect
132. C₇×C₃⋊D₃	#120	direct (N × H)
137. C₂⁴×C₇	C₂×C₃⋊D₃	semidirect
142. C₂×C₇×D₄	C₂×C₃⋊D₃	semidirect
146. C₇×C₂²⋊C₄	C₂×C₃⋊D₃	semidirect
149. C₃×#120	D₃×C₇	semidirect
157. C₂²×C₃×C₇	D₃×D₄	semidirect
170. C₂³×C₃²	C₂³×C₇	semidirect
176. C₂²×C₃⋊D₃	C₇×D₄	semidirect
179. C₂²×C₃⋊D₃	C₂³×C₇	semidirect
181. C₂×C₃²×C₄	C₂³×C₇	semidirect
184. C₂×C₃⋊Dic₃	C₂³×C₇	semidirect
188. C₃²×C₇	C₂×#120	semidirect
200. C₂³×C₇	C₂²×C₃⋊D₃	semidirect
207. C₂×C₄×C₇	C₂²×C₃⋊D₃	semidirect
208. C₂⁴×C₃	C₂×D₃×C₇	semidirect
213. C₂×C₃×D₄	C₂×D₃×C₇	semidirect
219. C₃×C₂²⋊C₄	C₂×D₃×C₇	semidirect
231. C₂²×C₃²	C₂×C₇×D₄	semidirect
239. C₂×C₃⋊D₃	C₂×C₇×D₄	semidirect
247. #120	C₇×C₃⋊D₃	direct (N × H)
259. C₂²×C₇	D₄×C₃⋊D₃	semidirect
265. C₂³×C₃	C₂²×D₃×C₇	semidirect
276. C₂×C₃×C₄	C₂²×D₃×C₇	semidirect
282. C₃×C₇	D₃×#120	semidirect
288. C₃⋊D₃	C₇×#120	direct (N × H)
293. C₂⁴	C₂×C₇×C₃⋊D₃	semidirect
298. C₂×D₄	C₂×C₇×C₃⋊D₃	semidirect
302. C₂²⋊C₄	C₂×C₇×C₃⋊D₃	semidirect
312. C₂²×C₃	D₃×C₇×D₄	semidirect
323. C₃²	C₂×C₇×#120	semidirect
335. C₂³	C₂²×C₇×C₃⋊D₃	semidirect
342. C₂×C₄	C₂²×C₇×C₃⋊D₃	semidirect
343. C₇	C₃⋊D₃×#120	direct (N × H)
360. C₂²	C₇×D₄×C₃⋊D₃	semidirect
364. C₃	D₃×C₇×#120	semidirect

Maximal subgroups

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

subgroup	index
C₇×#64091	2
C₇×#64162	2
C₇×#64146	2
C₃²×C₇×#120	2
C₇×C₂²⋊C₄×C₃⋊D₃	2
C₂⁴×C₇×C₃⋊D₃	2
C₂×C₇×D₄×C₃⋊D₃	2
D₃×C₇×#120	3
C₃⋊D₃×#120	7

Subgroups — C7×C3⋊D3×#120 #72246741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃⋊D₃×#120 #72246741