Subgroups — D₄×Dic₃×D₇ #13059915

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×C₃×D₄×D₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₃×D₇	C₂	1	2	yes	maximal, complemented
3	D₄×Dic₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	(C₂²⋊D₇)⋊Dic₃	C₂	1	2	yes	maximal, complemented
6	Dic₃×C₂²⋊D₇	C₂	1	2	yes	maximal, complemented
7	D₇×#217	C₂	1	2	yes	maximal, complemented
8	#10620996	C₂	1	1	yes	maximal, characteristic, complemented
9	Dic₃×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
10	D₇×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×Dic₃×D₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×D₄×D₇	—	3	1	no	maximal, Hall
13	C₂³×C₃×D₇	C₂²	1	2	yes	—
14	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂²×Dic₂₁	C₂²	1	2	yes	complemented
16	C₂²×C₇×Dic₃	C₂²	1	2	yes	complemented
17	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	—
18	C₃×D₄×D₇	C₄	1	8	yes	complemented
19	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
21	C₂×Dic₃×D₇	—	2	8	no	—
22	C₂×Dic₃×D₇	C₂²	1	1	yes	characteristic
23	C₂×Dic₃×D₇	C₂²	1	2	yes	—
24	C₂×Dic₃×D₇	C₂²	1	1	yes	characteristic
25	C₂×Dic₃×D₇	C₂²	1	2	yes	complemented
26	C₂×Dic₃×D₇	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	C₇×#217	C₂²	1	2	yes	complemented
31	C₇×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
32	C₄×C₇×Dic₃	C₂²	1	1	yes	characteristic, complemented
33	Dic₇⋊Dic₃	C₂²	1	2	yes	complemented
34	(C₂×D₇)⋊Dic₃	C₂²	1	2	yes	complemented
35	(C₂×D₇)⋊Dic₃	C₂²	1	2	yes	complemented
36	Dic₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
37	Dic₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×D₄×D₇	D₃	1	1	yes	characteristic
39	C₂²×C₄×D₇	—	3	2	no	—
40	C₄×C₇×D₄	—	3	1	no	—
41	D₄×Dic₇	—	3	1	no	—
42	C₄×C₂²⋊D₇	—	3	2	no	—
43	#6456	—	3	1	no	—
44	D₇×C₄⋊C₄	—	3	1	no	—
45	(C₂²⋊D₇)⋊C₄	—	3	2	no	—
46	D₇×C₂²⋊C₄	—	3	2	no	—
47	C₄×D₂₈	—	3	1	no	—
48	C₄²×D₇	—	3	1	no	—
49	C₂×D₄×Dic₃	—	7	1	no	maximal, Hall
50	C₂³×C₃×C₇	C₂³	1	2	yes	—
51	C₂²×C₃×D₇	—	2	4	no	—
52	C₂²×C₃×D₇	—	2	4	no	—
53	C₂²×C₃×D₇	C₂×C₄	1	8	yes	complemented
54	C₂²×C₃×D₇	C₂³	1	2	yes	—
55	C₂²×C₃×D₇	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	C₂×C₇×Dic₃	—	2	4	no	—
63	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
64	C₂×C₇×Dic₃	C₂³	1	2	yes	—
65	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
66	C₃×C₂²⋊D₇	C₂×C₄	1	8	yes	complemented
67	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
68	C₃×D₂₈	C₂×C₄	1	4	yes	complemented
69	C₃×C₄×D₇	C₂×C₄	1	4	yes	complemented
70	Dic₃×D₇	—	2	4	no	—
71	Dic₃×D₇	—	2	2	no	—
72	Dic₃×D₇	—	2	4	no	—
73	Dic₃×D₇	—	2	4	no	—
74	Dic₃×D₇	D₄	1	4	yes	direct product factor
75	C₂³×D₇	C₂×D₃	1	2	yes	—
76	C₂×C₇×D₄	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₄×C₇	—	3	2	no	—
78	C₂×C₂²⋊D₇	C₂×D₃	1	2	yes	—
79	C₂²×Dic₇	—	3	2	no	—
80	D₄×D₇	Dic₃	1	8	yes	direct product factor
81	C₂×D₂₈	C₂×D₃	1	1	yes	characteristic
82	C₂×C₄×D₇	—	3	1	no	—
83	C₂×C₄×D₇	—	3	1	no	—
84	C₂×C₄×D₇	—	3	2	no	—
85	C₂×C₄×D₇	—	3	2	no	—
86	C₂×C₄×D₇	—	3	2	no	—
87	C₂×C₄×D₇	—	6	8	no	—
88	C₂×C₄×D₇	C₂×D₃	1	1	yes	characteristic
89	C₇×C₄⋊C₄	—	3	1	no	—
90	C₇×C₂²⋊C₄	—	3	2	no	—
91	C₄²×C₇	—	3	1	no	—
92	C₂²⋊Dic₇	—	3	2	no	—
93	(C₂×D₇)⋊C₄	—	3	2	no	—
94	(C₂×D₇)⋊C₄	—	3	2	no	—
95	C₄⋊Dic₇	—	3	1	no	—
96	Dic₇⋊C₄	—	3	2	no	—
97	C₄×Dic₇	—	3	1	no	—
98	C₄×Dic₇	—	3	1	no	—
99	C₄×Dic₇	—	3	1	no	—
100	C₂²×C₃×D₄	—	7	1	no	—
101	C₂³×Dic₃	—	7	2	no	—
102	C₂×#217	—	7	2	no	—
103	D₄×Dic₃	—	7	1	no	—
104	D₄×Dic₃	—	7	2	no	—
105	D₄×Dic₃	—	7	2	no	—
106	D₄×Dic₃	—	7	1	no	—
107	D₄×Dic₃	—	7	1	no	—
108	D₄×Dic₃	D₇	1	1	yes	characteristic, direct product factor
109	C₂×C₄⋊Dic₃	—	7	1	no	—
110	C₂×C₄×Dic₃	—	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×C₃×D₇	—	2	2	no	—
116	C₂×C₃×D₇	—	2	2	no	—
117	C₂×C₃×D₇	—	2	16	no	—
118	C₂×C₃×D₇	C₂²×C₄	1	2	yes	—
119	C₂×C₃×D₇	C₂²×C₄	1	4	yes	complemented
120	C₂×C₃×D₇	C₂×D₄	1	2	yes	—
121	C₂×C₃×D₇	#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	C₂²×C₄	1	2	yes	complemented
127	C₇×Dic₃	—	2	2	no	—
128	C₇×Dic₃	—	2	1	no	—
129	C₇×Dic₃	C₂×D₄	1	2	yes	complemented
130	C₂×C₄×D₄	—	21	1	no	Sylow
131	C₂³×C₇	C₂²×D₃	1	2	yes	—
132	C₂²×D₇	—	2	4	no	—
133	C₂²×D₇	—	2	4	no	—
134	C₂²×D₇	C₂×Dic₃	1	8	yes	complemented
135	C₂²×D₇	C₂²×D₃	1	2	yes	—
136	C₂²×D₇	C₂²×D₃	1	1	yes	characteristic
137	C₇×D₄	C₂×Dic₃	1	4	yes	complemented
138	C₂×C₄×C₇	—	3	1	no	—
139	C₂×C₄×C₇	—	3	1	no	—
140	C₂×C₄×C₇	—	3	2	no	—
141	C₂×C₄×C₇	—	6	4	no	—
142	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
143	C₂²⋊D₇	C₂×Dic₃	1	8	yes	complemented
144	C₂×Dic₇	—	3	1	no	—
145	C₂×Dic₇	—	3	1	no	—
146	C₂×Dic₇	—	3	2	no	—
147	C₂×Dic₇	—	6	4	no	—
148	C₂×Dic₇	C₂²×D₃	1	1	yes	characteristic
149	D₂₈	C₂×Dic₃	1	4	yes	complemented
150	C₄×D₇	—	3	4	no	—
151	C₄×D₇	—	6	4	no	—
152	C₄×D₇	—	6	4	no	—
153	C₄×D₇	—	6	4	no	—
154	C₄×D₇	—	6	2	no	—
155	C₄×D₇	C₂×Dic₃	1	4	yes	complemented
156	C₂⁴×C₃	—	7	2	no	—
157	C₂×C₃×D₄	—	7	2	no	—
158	C₂×C₃×D₄	—	7	8	no	—
159	C₂×C₃×D₄	—	7	1	no	—
160	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
161	C₂²×C₃×C₄	—	7	1	no	—
162	C₂²×Dic₃	—	7	1	no	—
163	C₂²×Dic₃	—	7	2	no	—
164	C₂²×Dic₃	—	7	1	no	—
165	C₂²×Dic₃	—	7	2	no	—
166	C₂²×Dic₃	—	7	2	no	—
167	C₂²×Dic₃	—	7	2	no	—
168	C₂²×Dic₃	—	14	8	no	—
169	C₂²×Dic₃	C₂×D₇	1	2	yes	complemented
170	#217	—	7	2	no	—
171	#217	—	7	2	no	—
172	#217	—	7	2	no	—
173	#217	C₂×D₇	1	2	yes	complemented
174	C₄⋊Dic₃	—	7	1	no	—
175	C₄⋊Dic₃	—	7	2	no	—
176	C₄⋊Dic₃	C₂×D₇	1	1	yes	characteristic, complemented
177	C₄×Dic₃	—	7	1	no	—
178	C₄×Dic₃	—	7	1	no	—
179	C₄×Dic₃	—	7	1	no	—
180	C₄×Dic₃	C₂×D₇	1	1	yes	characteristic, complemented
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	C₃×D₇	—	2	4	no	—
186	C₃×D₇	C₄×D₄	1	4	yes	complemented
187	C₂²×D₄	—	7	1	no	—
188	C₂³×C₄	—	21	2	no	—
189	C₄×D₄	—	3	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	C₂²×Dic₃	1	4	yes	complemented
201	C₂²×C₇	C₂³×D₃	1	1	yes	characteristic
202	C₂×D₇	—	2	2	no	—
203	C₂×D₇	—	2	2	no	—
204	C₂×D₇	—	2	16	no	—
205	C₂×D₇	D₃×D₄	1	2	yes	—
206	C₂×D₇	#237	1	2	yes	—
207	C₂×D₇	C₂²×Dic₃	1	2	yes	—
208	C₂×D₇	C₂²×Dic₃	1	4	yes	complemented
209	C₄×C₇	—	3	2	no	—
210	C₄×C₇	—	6	2	no	—
211	C₄×C₇	—	6	1	no	—
212	C₄×C₇	C₂²×Dic₃	1	2	yes	complemented
213	Dic₇	—	3	2	no	—
214	Dic₇	—	6	2	no	—
215	Dic₇	—	6	1	no	—
216	Dic₇	C₂²×Dic₃	1	2	yes	complemented
217	C₂³×C₃	—	7	1	no	—
218	C₂³×C₃	—	7	8	no	—
219	C₂³×C₃	—	7	2	no	—
220	C₂³×C₃	—	14	4	no	—
221	C₂³×C₃	—	14	4	no	—
222	C₂³×C₃	C₂²×D₇	1	2	yes	—
223	C₃×D₄	—	7	8	no	—
224	C₃×D₄	—	7	4	no	—
225	C₃×D₄	C₄×D₇	1	4	yes	complemented
226	C₂×C₃×C₄	—	7	1	no	—
227	C₂×C₃×C₄	—	7	4	no	—
228	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
229	C₂×Dic₃	—	2	4	no	—
230	C₂×Dic₃	—	7	1	no	—
231	C₂×Dic₃	—	7	4	no	—
232	C₂×Dic₃	—	7	1	no	—
233	C₂×Dic₃	—	7	2	no	—
234	C₂×Dic₃	—	14	4	no	—
235	C₂×Dic₃	—	14	2	no	—
236	C₂×Dic₃	—	14	4	no	—
237	C₂×Dic₃	—	14	4	no	—
238	C₂×Dic₃	—	14	4	no	—
239	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
240	C₂×Dic₃	C₂²×D₇	1	2	yes	—
241	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
242	C₃×C₇	C₂×C₄×D₄	1	1	yes	characteristic, complemented, Hall
243	C₂⁴	—	7	2	no	—
244	C₂×D₄	—	7	2	no	—
245	C₂×D₄	—	7	8	no	—
246	C₂×D₄	—	7	1	no	—
247	C₂×D₄	D₃×D₇	1	1	yes	characteristic
248	C₂²×C₄	—	3	2	no	—
249	C₂²×C₄	—	7	1	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	—	3	1	no	—
258	C₄⋊C₄	—	21	2	no	—
259	C₄⋊C₄	—	21	1	no	—
260	C₂²⋊C₄	—	3	2	no	—
261	C₂²⋊C₄	—	21	2	no	—
262	C₂²⋊C₄	—	21	2	no	—
263	C₂²⋊C₄	—	21	2	no	—
264	C₄²	—	3	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	C₂×D₃×D₄	1	1	yes	characteristic
270	C₂×C₇	C₂×#237	1	1	yes	characteristic
271	C₂×C₇	C₂³×Dic₃	1	1	yes	characteristic
272	D₇	—	2	4	no	—
273	D₇	D₄×Dic₃	1	4	yes	direct product factor
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	2	2	no	—
276	C₂²×C₃	—	7	2	no	—
277	C₂²×C₃	—	7	2	no	—
278	C₂²×C₃	—	7	2	no	—
279	C₂²×C₃	—	7	4	no	—
280	C₂²×C₃	—	14	16	no	—
281	C₂²×C₃	—	14	2	no	—
282	C₂²×C₃	—	14	2	no	—
283	C₂²×C₃	C₂×C₄×D₇	1	4	yes	complemented
284	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
285	C₃×C₄	—	7	2	no	—
286	C₃×C₄	C₂×C₄×D₇	1	2	yes	complemented
287	Dic₃	—	2	2	no	—
288	Dic₃	—	2	1	no	—
289	Dic₃	—	7	2	no	—
290	Dic₃	—	14	2	no	—
291	Dic₃	—	14	1	no	—
292	Dic₃	D₄×D₇	1	2	yes	direct product factor
293	C₂³	—	7	1	no	—
294	C₂³	—	7	8	no	—
295	C₂³	—	7	2	no	—
296	C₂³	—	14	4	no	—
297	C₂³	—	14	4	no	—
298	C₂³	C₂×D₃×D₇	1	2	yes	—
299	D₄	—	7	8	no	—
300	D₄	—	7	4	no	—
301	D₄	Dic₃×D₇	1	4	yes	direct product factor
302	C₂×C₄	—	3	1	no	—
303	C₂×C₄	—	3	1	no	—
304	C₂×C₄	—	3	2	no	—
305	C₂×C₄	—	6	4	no	—
306	C₂×C₄	—	7	1	no	—
307	C₂×C₄	—	7	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	C₂×D₄×Dic₃	1	1	yes	characteristic, complemented, Sylow
319	C₂×C₃	—	2	4	no	—
320	C₂×C₃	—	7	4	no	—
321	C₂×C₃	—	14	4	no	—
322	C₂×C₃	C₂²×C₄×D₇	1	1	yes	characteristic
323	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
324	C₂×C₃	D₇×#41	1	1	yes	characteristic
325	C₂²	—	2	2	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	7	2	no	—
328	C₂²	—	7	2	no	—
329	C₂²	—	7	2	no	—
330	C₂²	—	7	4	no	—
331	C₂²	—	14	16	no	—
332	C₂²	—	14	2	no	—
333	C₂²	—	14	2	no	—
334	C₂²	C₂×Dic₃×D₇	1	4	yes	complemented
335	C₂²	C₂²×D₃×D₇	1	1	yes	characteristic
336	C₄	—	3	2	no	—
337	C₄	—	6	2	no	—
338	C₄	—	6	1	no	—
339	C₄	—	7	2	no	—
340	C₄	—	21	2	no	—
341	C₄	—	42	2	no	—
342	C₄	—	42	1	no	—
343	C₄	C₂×Dic₃×D₇	1	2	yes	complemented
344	C₃	C₄×D₄×D₇	1	1	yes	characteristic, complemented, Sylow
345	C₂	—	2	4	no	—
346	C₂	—	7	4	no	—
347	C₂	—	14	4	no	—
348	C₂	D₃×D₄×D₇	1	1	yes	characteristic
349	C₂	D₇×#237	1	1	yes	characteristic
350	C₂	C₂²×Dic₃×D₇	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×C₃×D₄×D₇	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×Dic₃×D₇	C₂	semidirect
3. D₄×Dic₂₁	C₂	semidirect
4. C₇×D₄×Dic₃	C₂	semidirect
5. (C₂²⋊D₇)⋊Dic₃	C₂	semidirect
6. Dic₃×C₂²⋊D₇	C₂	semidirect
7. D₇×#217	C₂	semidirect
8. #10620996	C₂	semidirect
9. Dic₃×D₂₈	C₂	semidirect
10. D₇×C₄⋊Dic₃	C₂	semidirect
11. C₄×Dic₃×D₇	C₂	semidirect
15. C₂²×Dic₂₁	C₂²	semidirect
16. C₂²×C₇×Dic₃	C₂²	semidirect
18. C₃×D₄×D₇	C₄	semidirect
25. C₂×Dic₃×D₇	C₂²	semidirect
26. C₂×Dic₃×D₇	C₂²	semidirect
27. #66636	C₂²	semidirect
28. C₄⋊Dic₂₁	C₂²	semidirect
29. C₄×Dic₂₁	C₂²	semidirect
30. C₇×#217	C₂²	semidirect
31. C₇×C₄⋊Dic₃	C₂²	semidirect
32. C₄×C₇×Dic₃	C₂²	semidirect
33. Dic₇⋊Dic₃	C₂²	semidirect
34. (C₂×D₇)⋊Dic₃	C₂²	semidirect
35. (C₂×D₇)⋊Dic₃	C₂²	semidirect
36. Dic₃×Dic₇	C₂²	semidirect
37. Dic₃×Dic₇	C₂²	semidirect
53. C₂²×C₃×D₇	C₂×C₄	semidirect
56. C₃×C₇×D₄	C₂×C₄	semidirect
66. C₃×C₂²⋊D₇	C₂×C₄	semidirect
68. C₃×D₂₈	C₂×C₄	semidirect
69. C₃×C₄×D₇	C₂×C₄	semidirect
74. Dic₃×D₇	D₄	direct (N × H)
80. D₄×D₇	Dic₃	direct (N × H)
108. D₄×Dic₃	D₇	direct (N × H)
113. C₂²×C₃×C₇	C₂²×C₄	semidirect
119. C₂×C₃×D₇	C₂²×C₄	semidirect
122. C₃×C₄×C₇	C₂²×C₄	semidirect
125. Dic₂₁	C₂×D₄	semidirect
126. C₃×Dic₇	C₂²×C₄	semidirect
129. C₇×Dic₃	C₂×D₄	semidirect
134. C₂²×D₇	C₂×Dic₃	semidirect
137. C₇×D₄	C₂×Dic₃	semidirect
143. C₂²⋊D₇	C₂×Dic₃	semidirect
149. D₂₈	C₂×Dic₃	semidirect
155. C₄×D₇	C₂×Dic₃	semidirect
169. C₂²×Dic₃	C₂×D₇	semidirect
173. #217	C₂×D₇	semidirect
176. C₄⋊Dic₃	C₂×D₇	semidirect
180. C₄×Dic₃	C₂×D₇	semidirect
186. C₃×D₇	C₄×D₄	semidirect
200. C₂²×C₇	C₂²×Dic₃	semidirect
208. C₂×D₇	C₂²×Dic₃	semidirect
212. C₄×C₇	C₂²×Dic₃	semidirect
216. Dic₇	C₂²×Dic₃	semidirect
225. C₃×D₄	C₄×D₇	semidirect
242. C₃×C₇	C₂×C₄×D₄	semidirect
273. D₇	D₄×Dic₃	direct (N × H)
283. C₂²×C₃	C₂×C₄×D₇	semidirect
286. C₃×C₄	C₂×C₄×D₇	semidirect
292. Dic₃	D₄×D₇	direct (N × H)
301. D₄	Dic₃×D₇	direct (N × H)
318. C₇	C₂×D₄×Dic₃	semidirect
334. C₂²	C₂×Dic₃×D₇	semidirect
343. C₄	C₂×Dic₃×D₇	semidirect
344. C₃	C₄×D₄×D₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₄×D₇	2
C₂²×Dic₃×D₇	2
D₄×Dic₂₁	2
C₇×D₄×Dic₃	2
(C₂²⋊D₇)⋊Dic₃	2
Dic₃×C₂²⋊D₇	2
D₇×#217	2
#10620996	2
Dic₃×D₂₈	2
D₇×C₄⋊Dic₃	2
C₄×Dic₃×D₇	2
C₄×D₄×D₇	3
C₂×D₄×Dic₃	7

Subgroups — D4×Dic3×D7 #13059915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×Dic₃×D₇ #13059915