Subgroups — D₃×D₄×Dic₇ #13059925

Order 1344.

852 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₇×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×D₃×Dic₇	C₂	1	2	yes	maximal, complemented
3	D₄×Dic₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₄×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#67⋊Dic₇	C₂	1	2	yes	maximal, complemented
6	D₃×C₂²⋊Dic₇	C₂	1	2	yes	maximal, complemented
7	#67×Dic₇	C₂	1	2	yes	maximal, complemented
8	#10620997	C₂	1	1	yes	maximal, characteristic, complemented
9	D₃×C₄⋊Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₂×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×D₃×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₄×Dic₇	—	3	1	no	maximal, Hall
13	C₂³×D₃×C₇	C₂²	1	2	yes	—
14	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂²×Dic₂₁	C₂²	1	2	yes	complemented
16	C₂×C₇×#67	C₂²	1	2	yes	—
17	D₃×C₇×D₄	C₄	1	8	yes	complemented
18	C₂×C₇×D₁₂	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₃×C₇	C₂²	1	1	yes	characteristic
20	C₂²×C₃×Dic₇	C₂²	1	2	yes	complemented
21	C₂×D₃×Dic₇	—	2	8	no	—
22	C₂×D₃×Dic₇	C₂²	1	1	yes	characteristic
23	C₂×D₃×Dic₇	C₂²	1	2	yes	—
24	C₂×D₃×Dic₇	C₂²	1	1	yes	characteristic
25	C₂×D₃×Dic₇	C₂²	1	2	yes	complemented
26	C₂×D₃×Dic₇	C₂²	1	2	yes	complemented
27	#66636	C₂²	1	2	yes	complemented
28	C₄⋊Dic₂₁	C₂²	1	1	yes	characteristic, complemented
29	C₄×Dic₂₁	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₂²⋊Dic₇	C₂²	1	2	yes	complemented
31	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
33	Dic₃⋊Dic₇	C₂²	1	2	yes	complemented
34	(C₂×D₃)⋊Dic₇	C₂²	1	2	yes	complemented
35	(C₂×D₃)⋊Dic₇	C₂²	1	2	yes	complemented
36	Dic₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
37	Dic₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₇×D₄	—	3	1	no	—
39	C₂³×Dic₇	—	3	2	no	—
40	C₂×C₂²⋊Dic₇	—	3	2	no	—
41	D₄×Dic₇	—	3	1	no	—
42	D₄×Dic₇	—	3	2	no	—
43	D₄×Dic₇	—	3	2	no	—
44	D₄×Dic₇	—	3	1	no	—
45	D₄×Dic₇	—	3	1	no	—
46	D₄×Dic₇	D₃	1	1	yes	characteristic, direct product factor
47	C₂×C₄⋊Dic₇	—	3	1	no	—
48	C₂×C₄×Dic₇	—	3	1	no	—
49	C₄×D₃×D₄	—	7	1	no	maximal, Hall
50	C₂³×C₃×C₇	C₂³	1	2	yes	—
51	C₂²×D₃×C₇	—	2	4	no	—
52	C₂²×D₃×C₇	—	2	4	no	—
53	C₂²×D₃×C₇	C₂×C₄	1	8	yes	complemented
54	C₂²×D₃×C₇	C₂³	1	2	yes	—
55	C₂²×D₃×C₇	C₂³	1	1	yes	characteristic
56	C₃×C₇×D₄	C₂×C₄	1	4	yes	complemented
57	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
58	C₂×Dic₂₁	—	2	4	no	—
59	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
60	C₂×Dic₂₁	C₂³	1	2	yes	—
61	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
62	C₇×#67	C₂×C₄	1	8	yes	complemented
63	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
64	C₇×D₁₂	C₂×C₄	1	4	yes	complemented
65	C₄×D₃×C₇	C₂×C₄	1	4	yes	complemented
66	C₂×C₃×Dic₇	—	2	4	no	—
67	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
68	C₂×C₃×Dic₇	C₂³	1	2	yes	—
69	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
70	D₃×Dic₇	—	2	4	no	—
71	D₃×Dic₇	—	2	2	no	—
72	D₃×Dic₇	—	2	4	no	—
73	D₃×Dic₇	—	2	4	no	—
74	D₃×Dic₇	D₄	1	4	yes	direct product factor
75	C₂⁴×C₇	—	3	2	no	—
76	C₂×C₇×D₄	—	3	2	no	—
77	C₂×C₇×D₄	—	3	8	no	—
78	C₂×C₇×D₄	—	3	1	no	—
79	C₂×C₇×D₄	C₂×D₃	1	1	yes	characteristic
80	C₂²×C₄×C₇	—	3	1	no	—
81	C₂²×Dic₇	—	3	1	no	—
82	C₂²×Dic₇	—	3	2	no	—
83	C₂²×Dic₇	—	3	1	no	—
84	C₂²×Dic₇	—	3	2	no	—
85	C₂²×Dic₇	—	3	2	no	—
86	C₂²×Dic₇	—	3	2	no	—
87	C₂²×Dic₇	—	6	8	no	—
88	C₂²×Dic₇	C₂×D₃	1	2	yes	complemented
89	C₂²⋊Dic₇	—	3	2	no	—
90	C₂²⋊Dic₇	—	3	2	no	—
91	C₂²⋊Dic₇	—	3	2	no	—
92	C₂²⋊Dic₇	C₂×D₃	1	2	yes	complemented
93	C₄⋊Dic₇	—	3	1	no	—
94	C₄⋊Dic₇	—	3	2	no	—
95	C₄⋊Dic₇	C₂×D₃	1	1	yes	characteristic, complemented
96	C₄×Dic₇	—	3	1	no	—
97	C₄×Dic₇	—	3	1	no	—
98	C₄×Dic₇	—	3	1	no	—
99	C₄×Dic₇	C₂×D₃	1	1	yes	characteristic, complemented
100	C₂×D₃×D₄	D₇	1	1	yes	characteristic
101	C₂²×C₄×D₃	—	7	2	no	—
102	C₃×C₄×D₄	—	7	1	no	—
103	D₄×Dic₃	—	7	1	no	—
104	C₄×#67	—	7	2	no	—
105	#893	—	7	1	no	—
106	D₃×C₄⋊C₄	—	7	1	no	—
107	#67⋊C₄	—	7	2	no	—
108	D₃×C₂²⋊C₄	—	7	2	no	—
109	C₄×D₁₂	—	7	1	no	—
110	C₄²×D₃	—	7	1	no	—
111	C₂²×C₃×C₇	—	2	2	no	—
112	C₂²×C₃×C₇	—	2	2	no	—
113	C₂²×C₃×C₇	C₂²×C₄	1	4	yes	complemented
114	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
115	C₂×D₃×C₇	—	2	2	no	—
116	C₂×D₃×C₇	—	2	2	no	—
117	C₂×D₃×C₇	—	2	16	no	—
118	C₂×D₃×C₇	C₂²×C₄	1	2	yes	—
119	C₂×D₃×C₇	C₂²×C₄	1	4	yes	complemented
120	C₂×D₃×C₇	C₂×D₄	1	2	yes	—
121	C₂×D₃×C₇	#41	1	2	yes	—
122	C₃×C₄×C₇	C₂²×C₄	1	2	yes	complemented
123	Dic₂₁	—	2	2	no	—
124	Dic₂₁	—	2	1	no	—
125	Dic₂₁	C₂×D₄	1	2	yes	complemented
126	C₃×Dic₇	—	2	2	no	—
127	C₃×Dic₇	—	2	1	no	—
128	C₃×Dic₇	C₂×D₄	1	2	yes	complemented
129	C₇×Dic₃	C₂²×C₄	1	2	yes	complemented
130	C₂×C₄×D₄	—	21	1	no	Sylow
131	C₂³×C₇	—	3	1	no	—
132	C₂³×C₇	—	3	8	no	—
133	C₂³×C₇	—	3	2	no	—
134	C₂³×C₇	—	6	4	no	—
135	C₂³×C₇	—	6	4	no	—
136	C₂³×C₇	C₂²×D₃	1	2	yes	—
137	C₇×D₄	—	3	8	no	—
138	C₇×D₄	—	3	4	no	—
139	C₇×D₄	C₄×D₃	1	4	yes	complemented
140	C₂×C₄×C₇	—	3	1	no	—
141	C₂×C₄×C₇	—	3	4	no	—
142	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
143	C₂×Dic₇	—	2	4	no	—
144	C₂×Dic₇	—	3	1	no	—
145	C₂×Dic₇	—	3	4	no	—
146	C₂×Dic₇	—	3	1	no	—
147	C₂×Dic₇	—	3	2	no	—
148	C₂×Dic₇	—	6	4	no	—
149	C₂×Dic₇	—	6	4	no	—
150	C₂×Dic₇	—	6	2	no	—
151	C₂×Dic₇	—	6	4	no	—
152	C₂×Dic₇	—	6	4	no	—
153	C₂×Dic₇	C₂²×D₃	1	1	yes	characteristic
154	C₂×Dic₇	C₂²×D₃	1	2	yes	—
155	C₂×Dic₇	C₂²×D₃	1	1	yes	characteristic
156	C₂³×D₃	C₂×D₇	1	2	yes	—
157	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
158	C₂²×C₃×C₄	—	7	2	no	—
159	C₂×#67	C₂×D₇	1	2	yes	—
160	C₂²×Dic₃	—	7	2	no	—
161	D₃×D₄	Dic₇	1	8	yes	direct product factor
162	C₂×D₁₂	C₂×D₇	1	1	yes	characteristic
163	C₂×C₄×D₃	—	7	1	no	—
164	C₂×C₄×D₃	—	7	1	no	—
165	C₂×C₄×D₃	—	7	2	no	—
166	C₂×C₄×D₃	—	7	2	no	—
167	C₂×C₄×D₃	—	7	2	no	—
168	C₂×C₄×D₃	—	14	8	no	—
169	C₂×C₄×D₃	C₂×D₇	1	1	yes	characteristic
170	C₃×C₄⋊C₄	—	7	1	no	—
171	C₃×C₂²⋊C₄	—	7	2	no	—
172	C₃×C₄²	—	7	1	no	—
173	#217	—	7	2	no	—
174	(C₂×D₃)⋊C₄	—	7	2	no	—
175	(C₂×D₃)⋊C₄	—	7	2	no	—
176	C₄⋊Dic₃	—	7	1	no	—
177	Dic₃⋊C₄	—	7	2	no	—
178	C₄×Dic₃	—	7	1	no	—
179	C₄×Dic₃	—	7	1	no	—
180	C₄×Dic₃	—	7	1	no	—
181	C₂×C₃×C₇	—	2	4	no	—
182	C₂×C₃×C₇	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
185	D₃×C₇	—	2	4	no	—
186	D₃×C₇	C₄×D₄	1	4	yes	complemented
187	C₂²×D₄	—	3	1	no	—
188	C₂³×C₄	—	21	2	no	—
189	C₄×D₄	—	7	1	no	—
190	C₄×D₄	—	21	1	no	—
191	C₄×D₄	—	21	2	no	—
192	C₄×D₄	—	21	1	no	—
193	C₄×D₄	—	21	2	no	—
194	C₄×D₄	—	21	1	no	—
195	C₂×C₄⋊C₄	—	21	1	no	—
196	C₂×C₂²⋊C₄	—	21	2	no	—
197	C₂×C₄²	—	21	1	no	—
198	C₂²×C₇	—	2	2	no	—
199	C₂²×C₇	—	2	2	no	—
200	C₂²×C₇	—	3	2	no	—
201	C₂²×C₇	—	3	2	no	—
202	C₂²×C₇	—	3	2	no	—
203	C₂²×C₇	—	3	4	no	—
204	C₂²×C₇	—	6	16	no	—
205	C₂²×C₇	—	6	2	no	—
206	C₂²×C₇	—	6	2	no	—
207	C₂²×C₇	C₂×C₄×D₃	1	4	yes	complemented
208	C₂²×C₇	C₂³×D₃	1	1	yes	characteristic
209	C₄×C₇	—	3	2	no	—
210	C₄×C₇	C₂×C₄×D₃	1	2	yes	complemented
211	Dic₇	—	2	2	no	—
212	Dic₇	—	2	1	no	—
213	Dic₇	—	3	2	no	—
214	Dic₇	—	6	2	no	—
215	Dic₇	—	6	1	no	—
216	Dic₇	D₃×D₄	1	2	yes	direct product factor
217	C₂³×C₃	C₂²×D₇	1	2	yes	—
218	C₂²×D₃	—	2	4	no	—
219	C₂²×D₃	—	2	4	no	—
220	C₂²×D₃	C₂×Dic₇	1	8	yes	complemented
221	C₂²×D₃	C₂²×D₇	1	2	yes	—
222	C₂²×D₃	C₂²×D₇	1	1	yes	characteristic
223	C₃×D₄	C₂×Dic₇	1	4	yes	complemented
224	C₂×C₃×C₄	—	7	1	no	—
225	C₂×C₃×C₄	—	7	1	no	—
226	C₂×C₃×C₄	—	7	2	no	—
227	C₂×C₃×C₄	—	14	4	no	—
228	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
229	#67	C₂×Dic₇	1	8	yes	complemented
230	C₂×Dic₃	—	7	1	no	—
231	C₂×Dic₃	—	7	1	no	—
232	C₂×Dic₃	—	7	2	no	—
233	C₂×Dic₃	—	14	4	no	—
234	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
235	D₁₂	C₂×Dic₇	1	4	yes	complemented
236	C₄×D₃	—	7	4	no	—
237	C₄×D₃	—	14	4	no	—
238	C₄×D₃	—	14	4	no	—
239	C₄×D₃	—	14	4	no	—
240	C₄×D₃	—	14	2	no	—
241	C₄×D₃	C₂×Dic₇	1	4	yes	complemented
242	C₃×C₇	C₂×C₄×D₄	1	1	yes	characteristic, complemented, Hall
243	C₂⁴	—	3	2	no	—
244	C₂×D₄	—	3	2	no	—
245	C₂×D₄	—	3	8	no	—
246	C₂×D₄	—	3	1	no	—
247	C₂×D₄	D₃×D₇	1	1	yes	characteristic
248	C₂²×C₄	—	3	1	no	—
249	C₂²×C₄	—	7	2	no	—
250	C₂²×C₄	—	21	1	no	—
251	C₂²×C₄	—	21	1	no	—
252	C₂²×C₄	—	21	2	no	—
253	C₂²×C₄	—	21	2	no	—
254	C₂²×C₄	—	21	2	no	—
255	C₂²×C₄	—	21	2	no	—
256	C₂²×C₄	—	42	8	no	—
257	C₄⋊C₄	—	7	1	no	—
258	C₄⋊C₄	—	21	2	no	—
259	C₄⋊C₄	—	21	1	no	—
260	C₂²⋊C₄	—	7	2	no	—
261	C₂²⋊C₄	—	21	2	no	—
262	C₂²⋊C₄	—	21	2	no	—
263	C₂²⋊C₄	—	21	2	no	—
264	C₄²	—	7	1	no	—
265	C₄²	—	21	1	no	—
266	C₄²	—	21	1	no	—
267	C₄²	—	21	1	no	—
268	C₂×C₇	—	2	4	no	—
269	C₂×C₇	—	3	4	no	—
270	C₂×C₇	—	6	4	no	—
271	C₂×C₇	C₂²×C₄×D₃	1	1	yes	characteristic
272	C₂×C₇	C₂×D₃×D₄	1	1	yes	characteristic
273	C₂×C₇	D₃×#41	1	1	yes	characteristic
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	2	2	no	—
276	C₂²×C₃	C₂²×Dic₇	1	4	yes	complemented
277	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
278	C₂×D₃	—	2	2	no	—
279	C₂×D₃	—	2	2	no	—
280	C₂×D₃	—	2	16	no	—
281	C₂×D₃	D₄×D₇	1	2	yes	—
282	C₂×D₃	#1159	1	2	yes	—
283	C₂×D₃	C₂²×Dic₇	1	2	yes	—
284	C₂×D₃	C₂²×Dic₇	1	4	yes	complemented
285	C₃×C₄	—	7	2	no	—
286	C₃×C₄	—	14	2	no	—
287	C₃×C₄	—	14	1	no	—
288	C₃×C₄	C₂²×Dic₇	1	2	yes	complemented
289	Dic₃	—	7	2	no	—
290	Dic₃	—	14	2	no	—
291	Dic₃	—	14	1	no	—
292	Dic₃	C₂²×Dic₇	1	2	yes	complemented
293	C₂³	—	3	1	no	—
294	C₂³	—	3	8	no	—
295	C₂³	—	3	2	no	—
296	C₂³	—	6	4	no	—
297	C₂³	—	6	4	no	—
298	C₂³	C₂×D₃×D₇	1	2	yes	—
299	D₄	—	3	8	no	—
300	D₄	—	3	4	no	—
301	D₄	D₃×Dic₇	1	4	yes	direct product factor
302	C₂×C₄	—	3	1	no	—
303	C₂×C₄	—	3	4	no	—
304	C₂×C₄	—	7	1	no	—
305	C₂×C₄	—	7	1	no	—
306	C₂×C₄	—	7	2	no	—
307	C₂×C₄	—	14	4	no	—
308	C₂×C₄	—	21	4	no	—
309	C₂×C₄	—	21	1	no	—
310	C₂×C₄	—	21	1	no	—
311	C₂×C₄	—	21	2	no	—
312	C₂×C₄	—	42	4	no	—
313	C₂×C₄	—	42	4	no	—
314	C₂×C₄	—	42	4	no	—
315	C₂×C₄	—	42	2	no	—
316	C₂×C₄	—	42	4	no	—
317	C₂×C₄	C₂×D₃×D₇	1	1	yes	characteristic
318	C₇	C₄×D₃×D₄	1	1	yes	characteristic, complemented, Sylow
319	C₂×C₃	—	2	4	no	—
320	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
321	C₂×C₃	C₂×#1159	1	1	yes	characteristic
322	C₂×C₃	C₂³×Dic₇	1	1	yes	characteristic
323	D₃	—	2	4	no	—
324	D₃	D₄×Dic₇	1	4	yes	direct product factor
325	C₂²	—	2	2	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	3	2	no	—
328	C₂²	—	3	2	no	—
329	C₂²	—	3	2	no	—
330	C₂²	—	3	4	no	—
331	C₂²	—	6	16	no	—
332	C₂²	—	6	2	no	—
333	C₂²	—	6	2	no	—
334	C₂²	C₂×D₃×Dic₇	1	4	yes	complemented
335	C₂²	C₂²×D₃×D₇	1	1	yes	characteristic
336	C₄	—	3	2	no	—
337	C₄	—	7	2	no	—
338	C₄	—	14	2	no	—
339	C₄	—	14	1	no	—
340	C₄	—	21	2	no	—
341	C₄	—	42	2	no	—
342	C₄	—	42	1	no	—
343	C₄	C₂×D₃×Dic₇	1	2	yes	complemented
344	C₃	C₂×D₄×Dic₇	1	1	yes	characteristic, complemented, Sylow
345	C₂	—	2	4	no	—
346	C₂	—	3	4	no	—
347	C₂	—	6	4	no	—
348	C₂	D₃×D₄×D₇	1	1	yes	characteristic
349	C₂	D₃×#1159	1	1	yes	characteristic
350	C₂	C₂²×D₃×Dic₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃×D₇
commutator	C₂×C₃×C₇	C₂³×C₄
Fitting	C₂×C₃×C₇×D₄	C₂²
socle, cosocle	C₂²×C₃×C₇	C₂⁴
prime radical	C₂×D₃×C₇×D₄	C₂
hypercenter	C₂×D₄	D₃×D₇
hypocenter	C₃×C₇	C₂×C₄×D₄
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂² ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×D₃×Dic₇	C₂	semidirect
3. D₄×Dic₂₁	C₂	semidirect
4. C₃×D₄×Dic₇	C₂	semidirect
5. #67⋊Dic₇	C₂	semidirect
6. D₃×C₂²⋊Dic₇	C₂	semidirect
7. #67×Dic₇	C₂	semidirect
8. #10620997	C₂	semidirect
9. D₃×C₄⋊Dic₇	C₂	semidirect
10. D₁₂×Dic₇	C₂	semidirect
11. C₄×D₃×Dic₇	C₂	semidirect
15. C₂²×Dic₂₁	C₂²	semidirect
17. D₃×C₇×D₄	C₄	semidirect
20. C₂²×C₃×Dic₇	C₂²	semidirect
25. C₂×D₃×Dic₇	C₂²	semidirect
26. C₂×D₃×Dic₇	C₂²	semidirect
27. #66636	C₂²	semidirect
28. C₄⋊Dic₂₁	C₂²	semidirect
29. C₄×Dic₂₁	C₂²	semidirect
30. C₃×C₂²⋊Dic₇	C₂²	semidirect
31. C₃×C₄⋊Dic₇	C₂²	semidirect
32. C₃×C₄×Dic₇	C₂²	semidirect
33. Dic₃⋊Dic₇	C₂²	semidirect
34. (C₂×D₃)⋊Dic₇	C₂²	semidirect
35. (C₂×D₃)⋊Dic₇	C₂²	semidirect
36. Dic₃×Dic₇	C₂²	semidirect
37. Dic₃×Dic₇	C₂²	semidirect
46. D₄×Dic₇	D₃	direct (N × H)
53. C₂²×D₃×C₇	C₂×C₄	semidirect
56. C₃×C₇×D₄	C₂×C₄	semidirect
62. C₇×#67	C₂×C₄	semidirect
64. C₇×D₁₂	C₂×C₄	semidirect
65. C₄×D₃×C₇	C₂×C₄	semidirect
74. D₃×Dic₇	D₄	direct (N × H)
88. C₂²×Dic₇	C₂×D₃	semidirect
92. C₂²⋊Dic₇	C₂×D₃	semidirect
95. C₄⋊Dic₇	C₂×D₃	semidirect
99. C₄×Dic₇	C₂×D₃	semidirect
113. C₂²×C₃×C₇	C₂²×C₄	semidirect
119. C₂×D₃×C₇	C₂²×C₄	semidirect
122. C₃×C₄×C₇	C₂²×C₄	semidirect
125. Dic₂₁	C₂×D₄	semidirect
128. C₃×Dic₇	C₂×D₄	semidirect
129. C₇×Dic₃	C₂²×C₄	semidirect
139. C₇×D₄	C₄×D₃	semidirect
161. D₃×D₄	Dic₇	direct (N × H)
186. D₃×C₇	C₄×D₄	semidirect
207. C₂²×C₇	C₂×C₄×D₃	semidirect
210. C₄×C₇	C₂×C₄×D₃	semidirect
216. Dic₇	D₃×D₄	direct (N × H)
220. C₂²×D₃	C₂×Dic₇	semidirect
223. C₃×D₄	C₂×Dic₇	semidirect
229. #67	C₂×Dic₇	semidirect
235. D₁₂	C₂×Dic₇	semidirect
241. C₄×D₃	C₂×Dic₇	semidirect
242. C₃×C₇	C₂×C₄×D₄	semidirect
276. C₂²×C₃	C₂²×Dic₇	semidirect
284. C₂×D₃	C₂²×Dic₇	semidirect
288. C₃×C₄	C₂²×Dic₇	semidirect
292. Dic₃	C₂²×Dic₇	semidirect
301. D₄	D₃×Dic₇	direct (N × H)
318. C₇	C₄×D₃×D₄	semidirect
324. D₃	D₄×Dic₇	direct (N × H)
334. C₂²	C₂×D₃×Dic₇	semidirect
343. C₄	C₂×D₃×Dic₇	semidirect
344. C₃	C₂×D₄×Dic₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×C₇×D₄	2
C₂²×D₃×Dic₇	2
D₄×Dic₂₁	2
C₃×D₄×Dic₇	2
#67⋊Dic₇	2
D₃×C₂²⋊Dic₇	2
#67×Dic₇	2
#10620997	2
D₃×C₄⋊Dic₇	2
D₁₂×Dic₇	2
C₄×D₃×Dic₇	2
C₂×D₄×Dic₇	3
C₄×D₃×D₄	7

Subgroups — D3×D4×Dic7 #13059925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₄×Dic₇ #13059925