Subgroups — C₃×C₄×D₄×D₇ #13060888

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×C₃×C₄×D₇	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₄×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₂²⋊D₇	C₂	1	2	yes	maximal, complemented
6	C₃×#6456	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×D₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×(C₂²⋊D₇)⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₃×D₇×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄²×D₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×D₄×D₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×D₇	C₂²	1	2	yes	—
14	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₇	C₂²	1	2	yes	complemented
16	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	—
17	C₂²×C₃×Dic₇	C₂²	1	2	yes	complemented
18	C₃×D₄×D₇	C₄	1	8	yes	direct product factor
19	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄×D₇	—	2	8	no	—
21	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄×D₇	C₂²	1	2	yes	—
23	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×D₇	C₂²	1	2	yes	complemented
26	C₂×C₃×C₄×D₇	C₂²	1	2	yes	complemented
27	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
29	C₃×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₂²⋊Dic₇	C₂²	1	2	yes	complemented
31	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
32	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
33	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
34	C₃×Dic₇⋊C₄	C₂²	1	2	yes	complemented
35	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×D₄×D₇	C₂×C₃	1	1	yes	characteristic
39	C₂²×C₄×D₇	C₂×C₃	1	2	yes	complemented
40	C₄×C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
41	D₄×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
42	C₄×C₂²⋊D₇	C₂×C₃	1	2	yes	complemented
43	#6456	C₂×C₃	1	1	yes	characteristic, complemented
44	D₇×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
45	(C₂²⋊D₇)⋊C₄	C₂×C₃	1	2	yes	complemented
46	D₇×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
47	C₄×D₂₈	C₂×C₃	1	1	yes	characteristic, complemented
48	C₄²×D₇	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×C₃×C₄×D₄	—	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	—	2	4	no	—
58	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
60	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
62	C₃×C₂²⋊D₇	C₂×C₄	1	8	yes	complemented
63	C₂×C₃×Dic₇	—	2	4	no	—
64	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
65	C₂×C₃×Dic₇	C₂³	1	2	yes	—
66	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
67	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
68	C₃×D₂₈	C₂×C₄	1	4	yes	complemented
69	C₃×C₄×D₇	—	2	4	no	—
70	C₃×C₄×D₇	—	2	2	no	—
71	C₃×C₄×D₇	—	2	4	no	—
72	C₃×C₄×D₇	—	2	4	no	—
73	C₃×C₄×D₇	C₂×C₄	1	4	yes	complemented
74	C₃×C₄×D₇	D₄	1	4	yes	direct product factor
75	C₂³×D₇	C₂²×C₃	1	2	yes	—
76	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₄×C₇	C₂²×C₃	1	2	yes	complemented
78	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
79	C₂²×Dic₇	C₂²×C₃	1	2	yes	complemented
80	D₄×D₇	C₃×C₄	1	8	yes	direct product factor
81	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄×D₇	—	2	8	no	—
83	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₄×D₇	C₂²×C₃	1	2	yes	—
85	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₄×D₇	C₂²×C₃	1	2	yes	complemented
88	C₂×C₄×D₇	C₂²×C₃	1	2	yes	complemented
89	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
90	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
91	C₄²×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
92	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	complemented
93	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
94	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
95	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
96	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
97	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
98	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
100	C₂²×C₃×D₄	—	7	1	no	—
101	C₂³×C₃×C₄	—	7	2	no	—
102	C₃×C₄×D₄	—	7	1	no	—
103	C₃×C₄×D₄	—	7	2	no	—
104	C₃×C₄×D₄	—	7	1	no	—
105	C₃×C₄×D₄	—	7	2	no	—
106	C₃×C₄×D₄	—	7	1	no	—
107	C₃×C₄×D₄	D₇	1	1	yes	characteristic, direct product factor
108	C₂×C₃×C₄⋊C₄	—	7	1	no	—
109	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
110	C₂×C₃×C₄²	—	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	—	2	2	no	—
123	C₃×C₄×C₇	—	2	1	no	—
124	C₃×C₄×C₇	C₂²×C₄	1	2	yes	complemented
125	C₃×C₄×C₇	C₂×D₄	1	2	yes	complemented
126	C₃×Dic₇	—	2	2	no	—
127	C₃×Dic₇	—	2	1	no	—
128	C₃×Dic₇	C₂²×C₄	1	2	yes	complemented
129	C₃×Dic₇	C₂×D₄	1	2	yes	complemented
130	C₂×C₄×D₄	—	7	1	no	Sylow
131	C₂³×C₇	C₂³×C₃	1	2	yes	—
132	C₂²×D₇	—	2	4	no	—
133	C₂²×D₇	—	2	4	no	—
134	C₂²×D₇	C₂×C₃×C₄	1	8	yes	complemented
135	C₂²×D₇	C₂³×C₃	1	2	yes	—
136	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
137	C₇×D₄	C₂×C₃×C₄	1	4	yes	complemented
138	C₂×C₄×C₇	—	2	4	no	—
139	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
140	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
141	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
142	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
143	C₂²⋊D₇	C₂×C₃×C₄	1	8	yes	complemented
144	C₂×Dic₇	—	2	4	no	—
145	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
146	C₂×Dic₇	C₂³×C₃	1	2	yes	—
147	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
148	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
149	D₂₈	C₂×C₃×C₄	1	4	yes	complemented
150	C₄×D₇	—	2	4	no	—
151	C₄×D₇	—	2	2	no	—
152	C₄×D₇	—	2	4	no	—
153	C₄×D₇	—	2	4	no	—
154	C₄×D₇	C₂×C₃×C₄	1	4	yes	complemented
155	C₄×D₇	C₃×D₄	1	4	yes	direct product factor
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×C₃×C₄	—	7	1	no	—
163	C₂²×C₃×C₄	—	7	2	no	—
164	C₂²×C₃×C₄	—	7	1	no	—
165	C₂²×C₃×C₄	—	7	2	no	—
166	C₂²×C₃×C₄	—	7	2	no	—
167	C₂²×C₃×C₄	—	7	2	no	—
168	C₂²×C₃×C₄	—	14	8	no	—
169	C₂²×C₃×C₄	C₂×D₇	1	2	yes	complemented
170	C₃×C₄⋊C₄	—	7	2	no	—
171	C₃×C₄⋊C₄	—	7	1	no	—
172	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
173	C₃×C₂²⋊C₄	—	7	2	no	—
174	C₃×C₂²⋊C₄	—	7	2	no	—
175	C₃×C₂²⋊C₄	—	7	2	no	—
176	C₃×C₂²⋊C₄	C₂×D₇	1	2	yes	complemented
177	C₃×C₄²	—	7	1	no	—
178	C₃×C₄²	—	7	1	no	—
179	C₃×C₄²	—	7	1	no	—
180	C₃×C₄²	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	direct product factor
187	C₂²×D₄	—	7	1	no	—
188	C₂³×C₄	—	7	2	no	—
189	C₄×D₄	—	7	1	no	—
190	C₄×D₄	—	7	2	no	—
191	C₄×D₄	—	7	1	no	—
192	C₄×D₄	—	7	2	no	—
193	C₄×D₄	—	7	1	no	—
194	C₄×D₄	C₃×D₇	1	1	yes	characteristic, direct product factor
195	C₂×C₄⋊C₄	—	7	1	no	—
196	C₂×C₂²⋊C₄	—	7	2	no	—
197	C₂×C₄²	—	7	1	no	—
198	C₂²×C₇	—	2	2	no	—
199	C₂²×C₇	—	2	2	no	—
200	C₂²×C₇	C₂²×C₃×C₄	1	4	yes	complemented
201	C₂²×C₇	C₂⁴×C₃	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	C₂²×C₃×C₄	1	2	yes	—
206	C₂×D₇	C₂²×C₃×C₄	1	4	yes	complemented
207	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
208	C₂×D₇	C₃×#41	1	2	yes	—
209	C₄×C₇	—	2	2	no	—
210	C₄×C₇	—	2	1	no	—
211	C₄×C₇	C₂²×C₃×C₄	1	2	yes	complemented
212	C₄×C₇	C₂×C₃×D₄	1	2	yes	complemented
213	Dic₇	—	2	2	no	—
214	Dic₇	—	2	1	no	—
215	Dic₇	C₂²×C₃×C₄	1	2	yes	complemented
216	Dic₇	C₂×C₃×D₄	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	direct product factor
226	C₂×C₃×C₄	—	2	4	no	—
227	C₂×C₃×C₄	—	7	1	no	—
228	C₂×C₃×C₄	—	7	1	no	—
229	C₂×C₃×C₄	—	7	4	no	—
230	C₂×C₃×C₄	—	7	4	no	—
231	C₂×C₃×C₄	—	7	1	no	—
232	C₂×C₃×C₄	—	7	2	no	—
233	C₂×C₃×C₄	—	14	4	no	—
234	C₂×C₃×C₄	—	14	2	no	—
235	C₂×C₃×C₄	—	14	4	no	—
236	C₂×C₃×C₄	—	14	4	no	—
237	C₂×C₃×C₄	—	14	4	no	—
238	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
240	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
241	C₂×C₃×C₄	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	C₂×C₃×D₇	1	1	yes	characteristic
248	C₂²×C₄	—	7	1	no	—
249	C₂²×C₄	—	7	1	no	—
250	C₂²×C₄	—	7	2	no	—
251	C₂²×C₄	—	7	1	no	—
252	C₂²×C₄	—	7	2	no	—
253	C₂²×C₄	—	7	2	no	—
254	C₂²×C₄	—	7	2	no	—
255	C₂²×C₄	—	14	8	no	—
256	C₂²×C₄	C₂×C₃×D₇	1	2	yes	complemented
257	C₄⋊C₄	—	7	2	no	—
258	C₄⋊C₄	—	7	1	no	—
259	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
260	C₂²⋊C₄	—	7	2	no	—
261	C₂²⋊C₄	—	7	2	no	—
262	C₂²⋊C₄	—	7	2	no	—
263	C₂²⋊C₄	C₂×C₃×D₇	1	2	yes	complemented
264	C₄²	—	7	1	no	—
265	C₄²	—	7	1	no	—
266	C₄²	—	7	1	no	—
267	C₄²	C₂×C₃×D₇	1	1	yes	characteristic, complemented
268	C₂×C₇	—	2	4	no	—
269	C₂×C₇	C₂³×C₃×C₄	1	1	yes	characteristic
270	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
271	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
272	D₇	—	2	4	no	—
273	D₇	C₃×C₄×D₄	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	—	2	2	no	—
286	C₃×C₄	—	2	1	no	—
287	C₃×C₄	—	7	2	no	—
288	C₃×C₄	—	7	2	no	—
289	C₃×C₄	—	14	2	no	—
290	C₃×C₄	—	14	1	no	—
291	C₃×C₄	C₂×C₄×D₇	1	2	yes	complemented
292	C₃×C₄	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	C₂²×C₃×D₇	1	2	yes	—
299	D₄	—	7	8	no	—
300	D₄	—	7	4	no	—
301	D₄	C₃×C₄×D₇	1	4	yes	direct product factor
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	7	1	no	—
304	C₂×C₄	—	7	1	no	—
305	C₂×C₄	—	7	4	no	—
306	C₂×C₄	—	7	4	no	—
307	C₂×C₄	—	7	1	no	—
308	C₂×C₄	—	7	2	no	—
309	C₂×C₄	—	14	4	no	—
310	C₂×C₄	—	14	4	no	—
311	C₂×C₄	—	14	2	no	—
312	C₂×C₄	—	14	4	no	—
313	C₂×C₄	—	14	4	no	—
314	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
315	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
316	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
317	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
318	C₇	C₂×C₃×C₄×D₄	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×C₃×C₄×D₇	1	4	yes	complemented
335	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
336	C₄	—	2	2	no	—
337	C₄	—	2	1	no	—
338	C₄	—	7	2	no	—
339	C₄	—	7	2	no	—
340	C₄	—	14	2	no	—
341	C₄	—	14	1	no	—
342	C₄	C₂×C₃×C₄×D₇	1	2	yes	complemented
343	C₄	C₃×D₄×D₇	1	2	yes	direct product factor
344	C₃	C₄×D₄×D₇	1	1	yes	characteristic, direct product factor, Sylow
345	C₂	—	2	4	no	—
346	C₂	—	7	4	no	—
347	C₂	—	14	4	no	—
348	C₂	C₂²×C₃×C₄×D₇	1	1	yes	characteristic
349	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
350	C₂	C₃×D₇×#41	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₄×D₇	C₂	semidirect
3. C₃×C₄×C₇×D₄	C₂	semidirect
4. C₃×D₄×Dic₇	C₂	semidirect
5. C₃×C₄×C₂²⋊D₇	C₂	semidirect
6. C₃×#6456	C₂	semidirect
7. C₃×D₇×C₄⋊C₄	C₂	semidirect
8. C₃×(C₂²⋊D₇)⋊C₄	C₂	semidirect
9. C₃×D₇×C₂²⋊C₄	C₂	semidirect
10. C₃×C₄×D₂₈	C₂	semidirect
11. C₃×C₄²×D₇	C₂	semidirect
12. C₄×D₄×D₇	C₃	direct (N × H)
15. C₂²×C₃×C₄×C₇	C₂²	semidirect
17. C₂²×C₃×Dic₇	C₂²	semidirect
18. C₃×D₄×D₇	C₄	direct (N × H)
25. C₂×C₃×C₄×D₇	C₂²	semidirect
26. C₂×C₃×C₄×D₇	C₂²	semidirect
27. C₃×C₇×C₄⋊C₄	C₂²	semidirect
28. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
29. C₃×C₄²×C₇	C₂²	semidirect
30. C₃×C₂²⋊Dic₇	C₂²	semidirect
31. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
32. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
33. C₃×C₄⋊Dic₇	C₂²	semidirect
34. C₃×Dic₇⋊C₄	C₂²	semidirect
35. C₃×C₄×Dic₇	C₂²	semidirect
36. C₃×C₄×Dic₇	C₂²	semidirect
37. C₃×C₄×Dic₇	C₂²	semidirect
39. C₂²×C₄×D₇	C₂×C₃	semidirect
40. C₄×C₇×D₄	C₂×C₃	semidirect
41. D₄×Dic₇	C₂×C₃	semidirect
42. C₄×C₂²⋊D₇	C₂×C₃	semidirect
43. #6456	C₂×C₃	semidirect
44. D₇×C₄⋊C₄	C₂×C₃	semidirect
45. (C₂²⋊D₇)⋊C₄	C₂×C₃	semidirect
46. D₇×C₂²⋊C₄	C₂×C₃	semidirect
47. C₄×D₂₈	C₂×C₃	semidirect
48. C₄²×D₇	C₂×C₃	semidirect
53. C₂²×C₃×D₇	C₂×C₄	semidirect
56. C₃×C₇×D₄	C₂×C₄	semidirect
62. C₃×C₂²⋊D₇	C₂×C₄	semidirect
68. C₃×D₂₈	C₂×C₄	semidirect
73. C₃×C₄×D₇	C₂×C₄	semidirect
74. C₃×C₄×D₇	D₄	direct (N × H)
77. C₂²×C₄×C₇	C₂²×C₃	semidirect
79. C₂²×Dic₇	C₂²×C₃	semidirect
80. D₄×D₇	C₃×C₄	direct (N × H)
87. C₂×C₄×D₇	C₂²×C₃	semidirect
88. C₂×C₄×D₇	C₂²×C₃	semidirect
89. C₇×C₄⋊C₄	C₂²×C₃	semidirect
90. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
91. C₄²×C₇	C₂²×C₃	semidirect
92. C₂²⋊Dic₇	C₂²×C₃	semidirect
93. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
94. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
95. C₄⋊Dic₇	C₂²×C₃	semidirect
96. Dic₇⋊C₄	C₂²×C₃	semidirect
97. C₄×Dic₇	C₂²×C₃	semidirect
98. C₄×Dic₇	C₂²×C₃	semidirect
99. C₄×Dic₇	C₂²×C₃	semidirect
107. C₃×C₄×D₄	D₇	direct (N × H)
113. C₂²×C₃×C₇	C₂²×C₄	semidirect
119. C₂×C₃×D₇	C₂²×C₄	semidirect
124. C₃×C₄×C₇	C₂²×C₄	semidirect
125. C₃×C₄×C₇	C₂×D₄	semidirect
128. C₃×Dic₇	C₂²×C₄	semidirect
129. C₃×Dic₇	C₂×D₄	semidirect
134. C₂²×D₇	C₂×C₃×C₄	semidirect
137. C₇×D₄	C₂×C₃×C₄	semidirect
143. C₂²⋊D₇	C₂×C₃×C₄	semidirect
149. D₂₈	C₂×C₃×C₄	semidirect
154. C₄×D₇	C₂×C₃×C₄	semidirect
155. C₄×D₇	C₃×D₄	direct (N × H)
169. C₂²×C₃×C₄	C₂×D₇	semidirect
172. C₃×C₄⋊C₄	C₂×D₇	semidirect
176. C₃×C₂²⋊C₄	C₂×D₇	semidirect
180. C₃×C₄²	C₂×D₇	semidirect
186. C₃×D₇	C₄×D₄	direct (N × H)
194. C₄×D₄	C₃×D₇	direct (N × H)
200. C₂²×C₇	C₂²×C₃×C₄	semidirect
206. C₂×D₇	C₂²×C₃×C₄	semidirect
211. C₄×C₇	C₂²×C₃×C₄	semidirect
212. C₄×C₇	C₂×C₃×D₄	semidirect
215. Dic₇	C₂²×C₃×C₄	semidirect
216. Dic₇	C₂×C₃×D₄	semidirect
225. C₃×D₄	C₄×D₇	direct (N × H)
242. C₃×C₇	C₂×C₄×D₄	semidirect
256. C₂²×C₄	C₂×C₃×D₇	semidirect
259. C₄⋊C₄	C₂×C₃×D₇	semidirect
263. C₂²⋊C₄	C₂×C₃×D₇	semidirect
267. C₄²	C₂×C₃×D₇	semidirect
273. D₇	C₃×C₄×D₄	direct (N × H)
283. C₂²×C₃	C₂×C₄×D₇	semidirect
291. C₃×C₄	C₂×C₄×D₇	semidirect
292. C₃×C₄	D₄×D₇	direct (N × H)
301. D₄	C₃×C₄×D₇	direct (N × H)
318. C₇	C₂×C₃×C₄×D₄	semidirect
334. C₂²	C₂×C₃×C₄×D₇	semidirect
342. C₄	C₂×C₃×C₄×D₇	semidirect
343. C₄	C₃×D₄×D₇	direct (N × H)
344. C₃	C₄×D₄×D₇	direct (N × H)

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×C₃×C₄×D₇	2
C₃×C₄×C₇×D₄	2
C₃×D₄×Dic₇	2
C₃×C₄×C₂²⋊D₇	2
C₃×#6456	2
C₃×D₇×C₄⋊C₄	2
C₃×(C₂²⋊D₇)⋊C₄	2
C₃×D₇×C₂²⋊C₄	2
C₃×C₄×D₂₈	2
C₃×C₄²×D₇	2
C₄×D₄×D₇	3
C₂×C₃×C₄×D₄	7

Subgroups — C3×C4×D4×D7 #13060888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×D₄×D₇ #13060888