Subgroups — D₃²×C₇×D₄ #72246583

Order 2016.

998 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₃²×C₇	C₂	1	2	yes	maximal, complemented
2	C₇×D₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₇×D₄	C₂	1	2	yes	maximal, complemented
4	C₇×#3811	C₂	1	2	yes	maximal, complemented
5	D₃×C₇×#67	C₂	1	4	yes	maximal, complemented
6	C₇×#3802	C₂	1	1	yes	maximal, characteristic, complemented
7	D₃×C₇×D₁₂	C₂	1	2	yes	maximal, complemented
8	C₄×D₃²×C₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₃×C₇×D₄	—	3	2	no	maximal
10	C₂²×C₇×C₃⋊D₃	C₂²	1	2	yes	complemented
11	C₂²×C₃×D₃×C₇	C₂²	1	4	yes	complemented
12	C₂×D₃²×C₇	—	2	8	no	—
13	C₂×D₃²×C₇	C₂²	1	1	yes	characteristic
14	C₂×D₃²×C₇	C₂²	1	4	yes	complemented
15	C₂×D₃²×C₇	C₂²	1	2	yes	complemented
16	C₃²×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
17	C₇×#638	C₂²	1	2	yes	complemented
18	C₇×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
19	C₄×C₇×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₇×#67	C₂²	1	4	yes	complemented
21	C₃×C₇×D₁₂	C₂²	1	2	yes	complemented
22	C₃×C₄×D₃×C₇	C₂²	1	2	yes	complemented
23	C₇×#626	C₂²	1	4	yes	complemented
24	C₇×#625	C₂²	1	2	yes	complemented
25	C₇×#624	C₂²	1	1	yes	characteristic, complemented
26	D₃×C₇×Dic₃	C₂²	1	2	yes	complemented
27	C₂³×D₃×C₇	—	3	4	no	—
28	C₂×C₃×C₇×D₄	—	3	2	no	—
29	C₂×C₇×#67	—	3	4	no	—
30	D₃×C₇×D₄	—	3	4	no	—
31	D₃×C₇×D₄	—	3	2	no	—
32	D₃×C₇×D₄	—	3	4	no	—
33	D₃×C₇×D₄	—	3	2	no	—
34	D₃×C₇×D₄	—	3	2	no	—
35	D₃×C₇×D₄	—	6	1	no	—
36	D₃×C₇×D₄	D₃	1	2	yes	direct product factor
37	C₂×C₇×D₁₂	—	3	2	no	—
38	C₂×C₄×D₃×C₇	—	3	2	no	—
39	D₃²×D₄	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂²×C₃²×C₇	C₂³	1	2	yes	complemented
41	C₂×C₇×C₃⋊D₃	—	2	4	no	—
42	C₂×C₇×C₃⋊D₃	C₂³	1	1	yes	characteristic
43	C₂×C₇×C₃⋊D₃	C₂³	1	2	yes	complemented
44	C₂×C₃×D₃×C₇	—	2	8	no	—
45	C₂×C₃×D₃×C₇	C₂³	1	2	yes	—
46	C₂×C₃×D₃×C₇	C₂³	1	4	yes	complemented
47	D₃²×C₇	—	2	4	no	—
48	D₃²×C₇	—	2	8	no	—
49	D₃²×C₇	D₄	1	4	yes	direct product factor
50	C₃²×C₄×C₇	C₂³	1	1	yes	characteristic, complemented
51	C₇×C₃⋊Dic₃	C₂³	1	1	yes	characteristic, complemented
52	C₃×C₇×Dic₃	C₂³	1	2	yes	complemented
53	C₂²×C₇×D₄	—	9	1	no	Hall
54	C₂³×C₃×C₇	—	3	4	no	—
55	C₂²×D₃×C₇	—	3	2	no	—
56	C₂²×D₃×C₇	—	3	4	no	—
57	C₂²×D₃×C₇	—	3	4	no	—
58	C₂²×D₃×C₇	—	3	4	no	—
59	C₂²×D₃×C₇	—	3	4	no	—
60	C₂²×D₃×C₇	—	6	2	no	—
61	C₂²×D₃×C₇	—	6	16	no	—
62	C₂²×D₃×C₇	C₂×D₃	1	4	yes	complemented
63	C₃×C₇×D₄	—	2	1	no	—
64	C₃×C₇×D₄	—	3	4	no	—
65	C₃×C₇×D₄	—	3	2	no	—
66	C₃×C₇×D₄	C₂×D₃	1	2	yes	complemented
67	C₂×C₃×C₄×C₇	—	3	2	no	—
68	C₇×#67	—	3	4	no	—
69	C₇×#67	—	3	4	no	—
70	C₇×#67	—	3	4	no	—
71	C₇×#67	—	6	2	no	—
72	C₇×#67	C₂×D₃	1	4	yes	complemented
73	C₂×C₇×Dic₃	—	3	2	no	—
74	C₇×D₁₂	—	3	4	no	—
75	C₇×D₁₂	—	3	2	no	—
76	C₇×D₁₂	—	6	1	no	—
77	C₇×D₁₂	C₂×D₃	1	2	yes	complemented
78	C₄×D₃×C₇	—	3	2	no	—
79	C₄×D₃×C₇	—	3	2	no	—
80	C₄×D₃×C₇	—	3	2	no	—
81	C₄×D₃×C₇	—	6	1	no	—
82	C₄×D₃×C₇	C₂×D₃	1	2	yes	complemented
83	C₂²×D₃²	C₂×C₇	1	2	yes	complemented
84	D₄×C₃⋊D₃	C₂×C₇	1	1	yes	characteristic, complemented
85	C₃×D₃×D₄	C₂×C₇	1	2	yes	complemented
86	#3811	C₂×C₇	1	2	yes	complemented
87	D₃×#67	C₂×C₇	1	4	yes	complemented
88	#3802	C₂×C₇	1	1	yes	characteristic, complemented
89	D₃×D₁₂	C₂×C₇	1	2	yes	complemented
90	C₄×D₃²	C₂×C₇	1	1	yes	characteristic, complemented
91	C₂×C₃²×C₇	—	2	2	no	—
92	C₂×C₃²×C₇	C₂⁴	1	1	yes	characteristic
93	C₇×C₃⋊D₃	—	2	2	no	—
94	C₇×C₃⋊D₃	C₂×D₄	1	2	yes	complemented
95	C₃×D₃×C₇	—	2	4	no	—
96	C₃×D₃×C₇	C₂×D₄	1	4	yes	complemented
97	C₂⁴×C₇	—	9	2	no	—
98	C₂×C₇×D₄	—	3	2	no	—
99	C₂×C₇×D₄	—	9	2	no	—
100	C₂×C₇×D₄	—	9	2	no	—
101	C₂×C₇×D₄	—	9	1	no	—
102	C₂×C₇×D₄	—	9	4	no	—
103	C₂×C₇×D₄	—	9	1	no	—
104	C₂²×C₄×C₇	—	9	1	no	—
105	C₂×D₃×D₄	—	3	2	no	—
106	C₂²×C₃×C₇	—	2	2	no	—
107	C₂²×C₃×C₇	—	3	2	no	—
108	C₂²×C₃×C₇	—	3	4	no	—
109	C₂²×C₃×C₇	—	6	8	no	—
110	C₂²×C₃×C₇	C₂²×D₃	1	4	yes	complemented
111	C₂×D₃×C₇	—	2	8	no	—
112	C₂×D₃×C₇	—	3	2	no	—
113	C₂×D₃×C₇	—	3	8	no	—
114	C₂×D₃×C₇	—	3	4	no	—
115	C₂×D₃×C₇	—	6	1	no	—
116	C₂×D₃×C₇	—	6	2	no	—
117	C₂×D₃×C₇	—	6	8	no	—
118	C₂×D₃×C₇	—	6	8	no	—
119	C₂×D₃×C₇	—	6	8	no	—
120	C₂×D₃×C₇	—	6	8	no	—
121	C₂×D₃×C₇	—	12	4	no	—
122	C₂×D₃×C₇	C₂²×D₃	1	2	yes	—
123	C₂×D₃×C₇	C₂²×D₃	1	4	yes	complemented
124	C₃×C₄×C₇	—	2	1	no	—
125	C₃×C₄×C₇	—	3	2	no	—
126	C₃×C₄×C₇	C₂²×D₃	1	2	yes	complemented
127	C₇×Dic₃	—	3	2	no	—
128	C₇×Dic₃	—	6	1	no	—
129	C₇×Dic₃	C₂²×D₃	1	2	yes	complemented
130	C₂²×C₃⋊D₃	C₂²×C₇	1	2	yes	complemented
131	C₂²×C₃×D₃	C₂²×C₇	1	4	yes	complemented
132	C₂×D₃²	—	2	8	no	—
133	C₂×D₃²	C₂²×C₇	1	1	yes	characteristic
134	C₂×D₃²	C₂²×C₇	1	4	yes	complemented
135	C₂×D₃²	C₂²×C₇	1	2	yes	complemented
136	C₃²×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
137	#638	C₂²×C₇	1	2	yes	complemented
138	C₄⋊(C₃⋊D₃)	C₂²×C₇	1	1	yes	characteristic, complemented
139	C₄×C₃⋊D₃	C₂²×C₇	1	1	yes	characteristic, complemented
140	C₃×#67	C₂²×C₇	1	4	yes	complemented
141	C₃×D₁₂	C₂²×C₇	1	2	yes	complemented
142	C₃×C₄×D₃	C₂²×C₇	1	2	yes	complemented
143	#626	C₂²×C₇	1	4	yes	complemented
144	#625	C₂²×C₇	1	2	yes	complemented
145	#624	C₂²×C₇	1	1	yes	characteristic, complemented
146	D₃×Dic₃	C₂²×C₇	1	2	yes	complemented
147	C₃²×C₇	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
148	C₂³×C₇	—	3	4	no	—
149	C₂³×C₇	—	9	1	no	—
150	C₂³×C₇	—	9	4	no	—
151	C₂³×C₇	—	9	2	no	—
152	C₂³×C₇	—	9	2	no	—
153	C₂³×C₇	—	18	8	no	—
154	C₇×D₄	—	3	4	no	—
155	C₇×D₄	—	3	2	no	—
156	C₇×D₄	—	9	4	no	—
157	C₇×D₄	—	9	2	no	—
158	C₇×D₄	—	9	2	no	—
159	C₇×D₄	—	9	1	no	—
160	C₇×D₄	D₃²	1	1	yes	characteristic, direct product factor
161	C₂×C₄×C₇	—	3	2	no	—
162	C₂×C₄×C₇	—	9	1	no	—
163	C₂×C₄×C₇	—	9	2	no	—
164	C₂×C₄×C₇	—	9	1	no	—
165	C₂³×D₃	—	3	4	no	—
166	C₂×C₃×D₄	—	3	2	no	—
167	C₂×#67	—	3	4	no	—
168	D₃×D₄	—	3	4	no	—
169	D₃×D₄	—	3	2	no	—
170	D₃×D₄	—	3	4	no	—
171	D₃×D₄	—	3	2	no	—
172	D₃×D₄	—	3	2	no	—
173	D₃×D₄	—	6	1	no	—
174	D₃×D₄	D₃×C₇	1	2	yes	direct product factor
175	C₂×D₁₂	—	3	2	no	—
176	C₂×C₄×D₃	—	3	2	no	—
177	C₂×C₃×C₇	—	2	4	no	—
178	C₂×C₃×C₇	—	2	1	no	—
179	C₂×C₃×C₇	—	3	4	no	—
180	C₂×C₃×C₇	—	4	2	no	—
181	C₂×C₃×C₇	—	6	4	no	—
182	C₂×C₃×C₇	C₂³×D₃	1	2	yes	—
183	D₃×C₇	—	2	4	no	—
184	D₃×C₇	—	3	4	no	—
185	D₃×C₇	—	6	2	no	—
186	D₃×C₇	—	6	4	no	—
187	D₃×C₇	—	12	2	no	—
188	D₃×C₇	D₃×D₄	1	4	yes	direct product factor
189	C₂²×C₃²	C₂³×C₇	1	2	yes	complemented
190	C₂×C₃⋊D₃	—	2	4	no	—
191	C₂×C₃⋊D₃	C₂³×C₇	1	1	yes	characteristic
192	C₂×C₃⋊D₃	C₂³×C₇	1	2	yes	complemented
193	C₂×C₃×D₃	—	2	8	no	—
194	C₂×C₃×D₃	C₂³×C₇	1	2	yes	—
195	C₂×C₃×D₃	C₂³×C₇	1	4	yes	complemented
196	D₃²	—	2	4	no	—
197	D₃²	—	2	8	no	—
198	D₃²	C₇×D₄	1	4	yes	direct product factor
199	C₃²×C₄	C₂³×C₇	1	1	yes	characteristic, complemented
200	C₃⋊Dic₃	C₂³×C₇	1	1	yes	characteristic, complemented
201	C₃×Dic₃	C₂³×C₇	1	2	yes	complemented
202	C₂²×D₄	—	9	1	no	Sylow
203	C₂²×C₇	—	3	2	no	—
204	C₂²×C₇	—	3	4	no	—
205	C₂²×C₇	—	6	8	no	—
206	C₂²×C₇	—	9	4	no	—
207	C₂²×C₇	—	9	1	no	—
208	C₂²×C₇	—	9	2	no	—
209	C₂²×C₇	—	18	4	no	—
210	C₂²×C₇	—	18	8	no	—
211	C₂²×C₇	—	18	4	no	—
212	C₂²×C₇	C₂×D₃²	1	2	yes	complemented
213	C₄×C₇	—	3	2	no	—
214	C₄×C₇	—	9	1	no	—
215	C₄×C₇	C₂×D₃²	1	1	yes	characteristic, complemented
216	C₂³×C₃	—	3	4	no	—
217	C₂²×D₃	—	3	2	no	—
218	C₂²×D₃	—	3	4	no	—
219	C₂²×D₃	—	3	4	no	—
220	C₂²×D₃	—	3	4	no	—
221	C₂²×D₃	—	3	4	no	—
222	C₂²×D₃	—	6	2	no	—
223	C₂²×D₃	—	6	16	no	—
224	C₂²×D₃	C₂×D₃×C₇	1	4	yes	complemented
225	C₃×D₄	—	2	1	no	—
226	C₃×D₄	—	3	4	no	—
227	C₃×D₄	—	3	2	no	—
228	C₃×D₄	C₂×D₃×C₇	1	2	yes	complemented
229	C₂×C₃×C₄	—	3	2	no	—
230	#67	—	3	4	no	—
231	#67	—	3	4	no	—
232	#67	—	3	4	no	—
233	#67	—	6	2	no	—
234	#67	C₂×D₃×C₇	1	4	yes	complemented
235	C₂×Dic₃	—	3	2	no	—
236	D₁₂	—	3	4	no	—
237	D₁₂	—	3	2	no	—
238	D₁₂	—	6	1	no	—
239	D₁₂	C₂×D₃×C₇	1	2	yes	complemented
240	C₄×D₃	—	3	2	no	—
241	C₄×D₃	—	3	2	no	—
242	C₄×D₃	—	3	2	no	—
243	C₄×D₃	—	6	1	no	—
244	C₄×D₃	C₂×D₃×C₇	1	2	yes	complemented
245	C₃×C₇	—	2	1	no	—
246	C₃×C₇	C₂×D₃×D₄	1	2	yes	complemented
247	C₂×C₃²	—	2	2	no	—
248	C₂×C₃²	C₂⁴×C₇	1	1	yes	characteristic
249	C₃⋊D₃	—	2	2	no	—
250	C₃⋊D₃	C₂×C₇×D₄	1	2	yes	complemented
251	C₃×D₃	—	2	4	no	—
252	C₃×D₃	C₂×C₇×D₄	1	4	yes	complemented
253	C₂⁴	—	9	2	no	—
254	C₂×D₄	—	3	2	no	—
255	C₂×D₄	—	9	2	no	—
256	C₂×D₄	—	9	2	no	—
257	C₂×D₄	—	9	1	no	—
258	C₂×D₄	—	9	4	no	—
259	C₂×D₄	—	9	1	no	—
260	C₂²×C₄	—	9	1	no	—
261	C₂×C₇	—	2	2	no	—
262	C₂×C₇	—	3	4	no	—
263	C₂×C₇	—	6	4	no	—
264	C₂×C₇	—	9	2	no	—
265	C₂×C₇	—	18	2	no	—
266	C₂×C₇	C₂²×D₃²	1	1	yes	characteristic
267	C₂²×C₃	—	2	2	no	—
268	C₂²×C₃	—	3	2	no	—
269	C₂²×C₃	—	3	4	no	—
270	C₂²×C₃	—	6	8	no	—
271	C₂²×C₃	C₂²×D₃×C₇	1	4	yes	complemented
272	C₂×D₃	—	2	8	no	—
273	C₂×D₃	—	3	2	no	—
274	C₂×D₃	—	3	8	no	—
275	C₂×D₃	—	3	4	no	—
276	C₂×D₃	—	6	1	no	—
277	C₂×D₃	—	6	2	no	—
278	C₂×D₃	—	6	8	no	—
279	C₂×D₃	—	6	8	no	—
280	C₂×D₃	—	6	8	no	—
281	C₂×D₃	—	6	8	no	—
282	C₂×D₃	—	12	4	no	—
283	C₂×D₃	C₂²×D₃×C₇	1	2	yes	—
284	C₂×D₃	C₂²×D₃×C₇	1	4	yes	complemented
285	C₃×C₄	—	2	1	no	—
286	C₃×C₄	—	3	2	no	—
287	C₃×C₄	C₂²×D₃×C₇	1	2	yes	complemented
288	Dic₃	—	3	2	no	—
289	Dic₃	—	6	1	no	—
290	Dic₃	C₂²×D₃×C₇	1	2	yes	complemented
291	C₃²	C₂²×C₇×D₄	1	1	yes	characteristic, complemented, Sylow
292	C₂³	—	3	4	no	—
293	C₂³	—	9	1	no	—
294	C₂³	—	9	4	no	—
295	C₂³	—	9	2	no	—
296	C₂³	—	9	2	no	—
297	C₂³	—	18	8	no	—
298	D₄	—	3	4	no	—
299	D₄	—	3	2	no	—
300	D₄	—	9	4	no	—
301	D₄	—	9	2	no	—
302	D₄	—	9	2	no	—
303	D₄	—	9	1	no	—
304	D₄	D₃²×C₇	1	1	yes	characteristic, direct product factor
305	C₂×C₄	—	3	2	no	—
306	C₂×C₄	—	9	1	no	—
307	C₂×C₄	—	9	2	no	—
308	C₂×C₄	—	9	1	no	—
309	C₇	D₃²×D₄	1	1	yes	characteristic, direct product factor, Sylow
310	C₂×C₃	—	2	4	no	—
311	C₂×C₃	—	2	1	no	—
312	C₂×C₃	—	3	4	no	—
313	C₂×C₃	—	4	2	no	—
314	C₂×C₃	—	6	4	no	—
315	C₂×C₃	C₂³×D₃×C₇	1	2	yes	—
316	D₃	—	2	4	no	—
317	D₃	—	3	4	no	—
318	D₃	—	6	2	no	—
319	D₃	—	6	4	no	—
320	D₃	—	12	2	no	—
321	D₃	D₃×C₇×D₄	1	4	yes	direct product factor
322	C₂²	—	3	2	no	—
323	C₂²	—	3	4	no	—
324	C₂²	—	6	8	no	—
325	C₂²	—	9	4	no	—
326	C₂²	—	9	1	no	—
327	C₂²	—	9	2	no	—
328	C₂²	—	18	4	no	—
329	C₂²	—	18	8	no	—
330	C₂²	—	18	4	no	—
331	C₂²	C₂×D₃²×C₇	1	2	yes	complemented
332	C₄	—	3	2	no	—
333	C₄	—	9	1	no	—
334	C₄	C₂×D₃²×C₇	1	1	yes	characteristic, complemented
335	C₃	—	2	1	no	—
336	C₃	C₂×D₃×C₇×D₄	1	2	yes	complemented
337	C₂	—	2	2	no	—
338	C₂	—	3	4	no	—
339	C₂	—	6	4	no	—
340	C₂	—	9	2	no	—
341	C₂	—	18	2	no	—
342	C₂	C₂²×D₃²×C₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₇	C₂²×D₃²
commutator, cosocle	C₂×C₃²	C₂⁴×C₇
Frattini	C₂	C₂²×D₃²×C₇
Fitting	C₃²×C₇×D₄	C₂²
socle	C₂×C₃²×C₇	C₂⁴
hypercenter	C₇×D₄	D₃²
hypocenter	C₃²	C₂²×C₇×D₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₇ ◁ C₇×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×D₃²×C₇	C₂	semidirect
2. C₇×D₄×C₃⋊D₃	C₂	semidirect
3. C₃×D₃×C₇×D₄	C₂	semidirect
4. C₇×#3811	C₂	semidirect
5. D₃×C₇×#67	C₂	semidirect
6. C₇×#3802	C₂	semidirect
7. D₃×C₇×D₁₂	C₂	semidirect
8. C₄×D₃²×C₇	C₂	semidirect
10. C₂²×C₇×C₃⋊D₃	C₂²	semidirect
11. C₂²×C₃×D₃×C₇	C₂²	semidirect
14. C₂×D₃²×C₇	C₂²	semidirect
15. C₂×D₃²×C₇	C₂²	semidirect
16. C₃²×C₇×D₄	C₂²	semidirect
17. C₇×#638	C₂²	semidirect
18. C₇×C₄⋊(C₃⋊D₃)	C₂²	semidirect
19. C₄×C₇×C₃⋊D₃	C₂²	semidirect
20. C₃×C₇×#67	C₂²	semidirect
21. C₃×C₇×D₁₂	C₂²	semidirect
22. C₃×C₄×D₃×C₇	C₂²	semidirect
23. C₇×#626	C₂²	semidirect
24. C₇×#625	C₂²	semidirect
25. C₇×#624	C₂²	semidirect
26. D₃×C₇×Dic₃	C₂²	semidirect
36. D₃×C₇×D₄	D₃	direct (N × H)
39. D₃²×D₄	C₇	direct (N × H)
40. C₂²×C₃²×C₇	C₂³	semidirect
43. C₂×C₇×C₃⋊D₃	C₂³	semidirect
46. C₂×C₃×D₃×C₇	C₂³	semidirect
49. D₃²×C₇	D₄	direct (N × H)
50. C₃²×C₄×C₇	C₂³	semidirect
51. C₇×C₃⋊Dic₃	C₂³	semidirect
52. C₃×C₇×Dic₃	C₂³	semidirect
62. C₂²×D₃×C₇	C₂×D₃	semidirect
66. C₃×C₇×D₄	C₂×D₃	semidirect
72. C₇×#67	C₂×D₃	semidirect
77. C₇×D₁₂	C₂×D₃	semidirect
82. C₄×D₃×C₇	C₂×D₃	semidirect
83. C₂²×D₃²	C₂×C₇	semidirect
84. D₄×C₃⋊D₃	C₂×C₇	semidirect
85. C₃×D₃×D₄	C₂×C₇	semidirect
86. #3811	C₂×C₇	semidirect
87. D₃×#67	C₂×C₇	semidirect
88. #3802	C₂×C₇	semidirect
89. D₃×D₁₂	C₂×C₇	semidirect
90. C₄×D₃²	C₂×C₇	semidirect
94. C₇×C₃⋊D₃	C₂×D₄	semidirect
96. C₃×D₃×C₇	C₂×D₄	semidirect
110. C₂²×C₃×C₇	C₂²×D₃	semidirect
123. C₂×D₃×C₇	C₂²×D₃	semidirect
126. C₃×C₄×C₇	C₂²×D₃	semidirect
129. C₇×Dic₃	C₂²×D₃	semidirect
130. C₂²×C₃⋊D₃	C₂²×C₇	semidirect
131. C₂²×C₃×D₃	C₂²×C₇	semidirect
134. C₂×D₃²	C₂²×C₇	semidirect
135. C₂×D₃²	C₂²×C₇	semidirect
136. C₃²×D₄	C₂²×C₇	semidirect
137. #638	C₂²×C₇	semidirect
138. C₄⋊(C₃⋊D₃)	C₂²×C₇	semidirect
139. C₄×C₃⋊D₃	C₂²×C₇	semidirect
140. C₃×#67	C₂²×C₇	semidirect
141. C₃×D₁₂	C₂²×C₇	semidirect
142. C₃×C₄×D₃	C₂²×C₇	semidirect
143. #626	C₂²×C₇	semidirect
144. #625	C₂²×C₇	semidirect
145. #624	C₂²×C₇	semidirect
146. D₃×Dic₃	C₂²×C₇	semidirect
147. C₃²×C₇	C₂²×D₄	semidirect
160. C₇×D₄	D₃²	direct (N × H)
174. D₃×D₄	D₃×C₇	direct (N × H)
188. D₃×C₇	D₃×D₄	direct (N × H)
189. C₂²×C₃²	C₂³×C₇	semidirect
192. C₂×C₃⋊D₃	C₂³×C₇	semidirect
195. C₂×C₃×D₃	C₂³×C₇	semidirect
198. D₃²	C₇×D₄	direct (N × H)
199. C₃²×C₄	C₂³×C₇	semidirect
200. C₃⋊Dic₃	C₂³×C₇	semidirect
201. C₃×Dic₃	C₂³×C₇	semidirect
212. C₂²×C₇	C₂×D₃²	semidirect
215. C₄×C₇	C₂×D₃²	semidirect
224. C₂²×D₃	C₂×D₃×C₇	semidirect
228. C₃×D₄	C₂×D₃×C₇	semidirect
234. #67	C₂×D₃×C₇	semidirect
239. D₁₂	C₂×D₃×C₇	semidirect
244. C₄×D₃	C₂×D₃×C₇	semidirect
246. C₃×C₇	C₂×D₃×D₄	semidirect
250. C₃⋊D₃	C₂×C₇×D₄	semidirect
252. C₃×D₃	C₂×C₇×D₄	semidirect
271. C₂²×C₃	C₂²×D₃×C₇	semidirect
284. C₂×D₃	C₂²×D₃×C₇	semidirect
287. C₃×C₄	C₂²×D₃×C₇	semidirect
290. Dic₃	C₂²×D₃×C₇	semidirect
291. C₃²	C₂²×C₇×D₄	semidirect
304. D₄	D₃²×C₇	direct (N × H)
309. C₇	D₃²×D₄	direct (N × H)
321. D₃	D₃×C₇×D₄	direct (N × H)
331. C₂²	C₂×D₃²×C₇	semidirect
334. C₄	C₂×D₃²×C₇	semidirect
336. C₃	C₂×D₃×C₇×D₄	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₃²×C₇	2
C₇×D₄×C₃⋊D₃	2
C₃×D₃×C₇×D₄	2
C₇×#3811	2
D₃×C₇×#67	2
C₇×#3802	2
D₃×C₇×D₁₂	2
C₄×D₃²×C₇	2
C₂×D₃×C₇×D₄	3
D₃²×D₄	7

Subgroups — D32×C7×D4 #72246583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃²×C₇×D₄ #72246583