Subgroups — C₂×C₃×C₄×C₂²⋊D₇ #13061130

Order 1344.

852 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄×C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₂²⋊Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₂²⋊D₇	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×(C₂×D₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×Dic₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×C₄×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×C₂²⋊D₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂⁴×C₃×C₇	C₂²	1	1	yes	characteristic
11	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×C₇	—	2	4	no	—
13	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₇	C₂²	1	4	yes	complemented
16	C₂×C₃×C₂²⋊D₇	C₄	1	8	yes	direct product factor
17	C₂×C₃×C₂²⋊D₇	C₂²	1	4	yes	—
18	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
19	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
20	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄×D₇	—	2	4	no	—
22	C₂×C₃×C₄×D₇	C₂²	1	4	yes	complemented
23	C₃×C₂²⋊Dic₇	C₂²	1	4	yes	complemented
24	C₃×(C₂×D₇)⋊C₄	C₂²	1	4	yes	complemented
25	C₃×Dic₇⋊C₄	C₂²	1	4	yes	complemented
26	C₃×C₄×Dic₇	C₂²	1	4	yes	complemented
27	C₂³×C₄×C₇	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic
29	C₂²×C₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₂²⋊Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
31	C₄×C₂²⋊D₇	C₂×C₃	1	8	yes	direct product factor
32	C₂×(C₂×D₇)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×Dic₇⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₄×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×C₃×C₄×D₄	—	7	1	no	maximal, Hall
36	C₂³×C₃×C₇	—	2	2	no	—
37	C₂³×C₃×C₇	—	2	2	no	—
38	C₂³×C₃×C₇	C₂×C₄	1	4	yes	complemented
39	C₂³×C₃×C₇	C₂³	1	2	yes	—
40	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
41	C₂²×C₃×D₇	—	2	2	no	—
42	C₂²×C₃×D₇	—	2	2	no	—
43	C₂²×C₃×D₇	C₂×C₄	1	4	yes	complemented
44	C₂²×C₃×D₇	C₂³	1	2	yes	—
45	C₂×C₃×C₄×C₇	—	2	2	no	—
46	C₂×C₃×C₄×C₇	—	2	8	no	—
47	C₂×C₃×C₄×C₇	D₄	1	4	yes	complemented
48	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
49	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
50	C₃×C₂²⋊D₇	C₂×C₄	1	16	yes	direct product factor
51	C₂×C₃×Dic₇	—	2	2	no	—
52	C₂×C₃×Dic₇	—	2	2	no	—
53	C₂×C₃×Dic₇	C₂×C₄	1	4	yes	complemented
54	C₂×C₃×Dic₇	C₂³	1	2	yes	—
55	C₂×C₃×Dic₇	C₂³	1	2	yes	—
56	C₂×C₃×Dic₇	C₂³	1	2	yes	—
57	C₃×C₄×D₇	—	2	8	no	—
58	C₂⁴×C₇	C₂²×C₃	1	1	yes	characteristic
59	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
60	C₂²×C₄×C₇	—	2	4	no	—
61	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
62	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₄×C₇	C₂²×C₃	1	4	yes	complemented
64	C₂×C₂²⋊D₇	C₃×C₄	1	8	yes	direct product factor
65	C₂×C₂²⋊D₇	C₂²×C₃	1	4	yes	—
66	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
67	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
68	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₄×D₇	—	2	4	no	—
70	C₂×C₄×D₇	C₂²×C₃	1	4	yes	complemented
71	C₂²⋊Dic₇	C₂²×C₃	1	4	yes	complemented
72	(C₂×D₇)⋊C₄	C₂²×C₃	1	4	yes	complemented
73	Dic₇⋊C₄	C₂²×C₃	1	4	yes	complemented
74	C₄×Dic₇	C₂²×C₃	1	4	yes	complemented
75	C₂²×C₃×D₄	—	7	1	no	—
76	C₂³×C₃×C₄	—	7	1	no	—
77	C₂³×C₃×C₄	D₇	1	1	yes	characteristic, complemented
78	C₃×C₄×D₄	—	7	8	no	—
79	C₂×C₃×C₄⋊C₄	—	7	1	no	—
80	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
81	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
82	C₂×C₃×C₄²	—	7	1	no	—
83	C₂²×C₃×C₇	—	2	8	no	—
84	C₂²×C₃×C₇	—	2	2	no	—
85	C₂²×C₃×C₇	—	2	2	no	—
86	C₂²×C₃×C₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₃×C₇	C₂²×C₄	1	4	yes	complemented
88	C₂²×C₃×C₇	C₂×D₄	1	2	yes	—
89	C₂²×C₃×C₇	#41	1	2	yes	—
90	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
91	C₂×C₃×D₇	—	2	8	no	—
92	C₂×C₃×D₇	—	2	2	no	—
93	C₂×C₃×D₇	—	2	2	no	—
94	C₂×C₃×D₇	C₂²×C₄	1	4	yes	complemented
95	C₃×C₄×C₇	—	2	2	no	—
96	C₃×C₄×C₇	C₂×D₄	1	4	yes	complemented
97	C₃×Dic₇	—	2	2	no	—
98	C₃×Dic₇	—	2	2	no	—
99	C₃×Dic₇	C₂²×C₄	1	4	yes	complemented
100	C₂×C₄×D₄	—	7	1	no	Sylow
101	C₂³×C₇	—	2	2	no	—
102	C₂³×C₇	—	2	2	no	—
103	C₂³×C₇	C₂×C₃×C₄	1	4	yes	complemented
104	C₂³×C₇	C₂³×C₃	1	2	yes	—
105	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
106	C₂²×D₇	—	2	2	no	—
107	C₂²×D₇	—	2	2	no	—
108	C₂²×D₇	C₂×C₃×C₄	1	4	yes	complemented
109	C₂²×D₇	C₂³×C₃	1	2	yes	—
110	C₂×C₄×C₇	—	2	2	no	—
111	C₂×C₄×C₇	—	2	8	no	—
112	C₂×C₄×C₇	C₃×D₄	1	4	yes	complemented
113	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
114	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
115	C₂²⋊D₇	C₂×C₃×C₄	1	16	yes	direct product factor
116	C₂×Dic₇	—	2	2	no	—
117	C₂×Dic₇	—	2	2	no	—
118	C₂×Dic₇	C₂×C₃×C₄	1	4	yes	complemented
119	C₂×Dic₇	C₂³×C₃	1	2	yes	—
120	C₂×Dic₇	C₂³×C₃	1	2	yes	—
121	C₂×Dic₇	C₂³×C₃	1	2	yes	—
122	C₄×D₇	—	2	8	no	—
123	C₂⁴×C₃	—	7	1	no	—
124	C₂⁴×C₃	C₂×D₇	1	1	yes	characteristic
125	C₂×C₃×D₄	—	7	8	no	—
126	C₂×C₃×D₄	—	7	4	no	—
127	C₂²×C₃×C₄	—	2	4	no	—
128	C₂²×C₃×C₄	—	7	1	no	—
129	C₂²×C₃×C₄	—	7	1	no	—
130	C₂²×C₃×C₄	—	7	1	no	—
131	C₂²×C₃×C₄	—	7	4	no	—
132	C₂²×C₃×C₄	—	14	4	no	—
133	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
134	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
135	C₂²×C₃×C₄	C₂×D₇	1	4	yes	complemented
136	C₃×C₄⋊C₄	—	7	4	no	—
137	C₃×C₂²⋊C₄	—	7	4	no	—
138	C₃×C₂²⋊C₄	—	7	4	no	—
139	C₃×C₄²	—	7	4	no	—
140	C₂×C₃×C₇	—	2	4	no	—
141	C₂×C₃×C₇	C₄×D₄	1	4	yes	complemented
142	C₂×C₃×C₇	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
145	C₃×D₇	—	2	4	no	—
146	C₂²×D₄	—	7	1	no	—
147	C₂³×C₄	—	7	1	no	—
148	C₂³×C₄	C₃×D₇	1	1	yes	characteristic, complemented
149	C₄×D₄	—	7	8	no	—
150	C₂×C₄⋊C₄	—	7	1	no	—
151	C₂×C₂²⋊C₄	—	7	1	no	—
152	C₂×C₂²⋊C₄	—	7	1	no	—
153	C₂×C₄²	—	7	1	no	—
154	C₂²×C₇	—	2	8	no	—
155	C₂²×C₇	—	2	2	no	—
156	C₂²×C₇	—	2	2	no	—
157	C₂²×C₇	C₂²×C₃×C₄	1	2	yes	—
158	C₂²×C₇	C₂²×C₃×C₄	1	4	yes	complemented
159	C₂²×C₇	C₂×C₃×D₄	1	2	yes	—
160	C₂²×C₇	C₃×#41	1	2	yes	—
161	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
162	C₂×D₇	—	2	8	no	—
163	C₂×D₇	—	2	2	no	—
164	C₂×D₇	—	2	2	no	—
165	C₂×D₇	C₂²×C₃×C₄	1	4	yes	complemented
166	C₄×C₇	—	2	2	no	—
167	C₄×C₇	C₂×C₃×D₄	1	4	yes	complemented
168	Dic₇	—	2	2	no	—
169	Dic₇	—	2	2	no	—
170	Dic₇	C₂²×C₃×C₄	1	4	yes	complemented
171	C₂³×C₃	—	2	2	no	—
172	C₂³×C₃	—	2	2	no	—
173	C₂³×C₃	—	7	4	no	—
174	C₂³×C₃	—	7	2	no	—
175	C₂³×C₃	—	14	2	no	—
176	C₂³×C₃	—	14	2	no	—
177	C₂³×C₃	C₄×D₇	1	4	yes	complemented
178	C₂³×C₃	C₂²×D₇	1	2	yes	—
179	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
180	C₃×D₄	—	7	16	no	—
181	C₂×C₃×C₄	—	2	2	no	—
182	C₂×C₃×C₄	—	2	8	no	—
183	C₂×C₃×C₄	—	7	4	no	—
184	C₂×C₃×C₄	—	7	2	no	—
185	C₂×C₃×C₄	—	7	2	no	—
186	C₂×C₃×C₄	—	7	2	no	—
187	C₂×C₃×C₄	—	14	2	no	—
188	C₂×C₃×C₄	—	14	2	no	—
189	C₂×C₃×C₄	—	14	8	no	—
190	C₂×C₃×C₄	C₂²⋊D₇	1	4	yes	direct product factor
191	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
192	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
193	C₃×C₇	C₂×C₄×D₄	1	1	yes	characteristic, complemented, Hall
194	C₂⁴	—	7	1	no	—
195	C₂⁴	C₂×C₃×D₇	1	1	yes	characteristic
196	C₂×D₄	—	7	8	no	—
197	C₂×D₄	—	7	4	no	—
198	C₂²×C₄	—	2	4	no	—
199	C₂²×C₄	—	7	1	no	—
200	C₂²×C₄	—	7	1	no	—
201	C₂²×C₄	—	7	1	no	—
202	C₂²×C₄	—	7	4	no	—
203	C₂²×C₄	—	14	4	no	—
204	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic
205	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic
206	C₂²×C₄	C₂×C₃×D₇	1	4	yes	complemented
207	C₄⋊C₄	—	7	4	no	—
208	C₂²⋊C₄	—	7	4	no	—
209	C₂²⋊C₄	—	7	4	no	—
210	C₄²	—	7	4	no	—
211	C₂×C₇	—	2	4	no	—
212	C₂×C₇	C₃×C₄×D₄	1	4	yes	complemented
213	C₂×C₇	C₂³×C₃×C₄	1	1	yes	characteristic
214	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
215	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
216	D₇	—	2	4	no	—
217	C₂²×C₃	—	2	8	no	—
218	C₂²×C₃	—	2	2	no	—
219	C₂²×C₃	—	2	2	no	—
220	C₂²×C₃	—	7	4	no	—
221	C₂²×C₃	—	14	8	no	—
222	C₂²×C₃	—	14	2	no	—
223	C₂²×C₃	—	14	2	no	—
224	C₂²×C₃	C₂×C₄×D₇	1	2	yes	—
225	C₂²×C₃	C₂×C₄×D₇	1	4	yes	complemented
226	C₂²×C₃	#1157	1	2	yes	—
227	C₂²×C₃	C₂×C₂²⋊D₇	1	2	yes	—
228	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
229	C₃×C₄	—	2	2	no	—
230	C₃×C₄	—	7	4	no	—
231	C₃×C₄	—	14	2	no	—
232	C₃×C₄	—	14	2	no	—
233	C₃×C₄	C₂×C₂²⋊D₇	1	4	yes	direct product factor
234	C₂³	—	2	2	no	—
235	C₂³	—	2	2	no	—
236	C₂³	—	7	4	no	—
237	C₂³	—	7	2	no	—
238	C₂³	—	14	2	no	—
239	C₂³	—	14	2	no	—
240	C₂³	C₃×C₄×D₇	1	4	yes	complemented
241	C₂³	C₂²×C₃×D₇	1	2	yes	—
242	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
243	D₄	—	7	16	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	2	8	no	—
246	C₂×C₄	—	7	4	no	—
247	C₂×C₄	—	7	2	no	—
248	C₂×C₄	—	7	2	no	—
249	C₂×C₄	—	7	2	no	—
250	C₂×C₄	—	14	2	no	—
251	C₂×C₄	—	14	2	no	—
252	C₂×C₄	—	14	8	no	—
253	C₂×C₄	C₃×C₂²⋊D₇	1	4	yes	direct product factor
254	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
255	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
256	C₇	C₂×C₃×C₄×D₄	1	1	yes	characteristic, complemented, Sylow
257	C₂×C₃	—	2	4	no	—
258	C₂×C₃	—	14	4	no	—
259	C₂×C₃	C₄×C₂²⋊D₇	1	4	yes	direct product factor
260	C₂×C₃	C₂²×C₄×D₇	1	1	yes	characteristic
261	C₂×C₃	C₂×#1157	1	1	yes	characteristic
262	C₂×C₃	C₂²×C₂²⋊D₇	1	1	yes	characteristic
263	C₂²	—	2	8	no	—
264	C₂²	—	2	2	no	—
265	C₂²	—	2	2	no	—
266	C₂²	—	7	4	no	—
267	C₂²	—	14	8	no	—
268	C₂²	—	14	2	no	—
269	C₂²	—	14	2	no	—
270	C₂²	C₂×C₃×C₄×D₇	1	2	yes	—
271	C₂²	C₂×C₃×C₄×D₇	1	4	yes	complemented
272	C₂²	C₃×#1157	1	2	yes	—
273	C₂²	C₂×C₃×C₂²⋊D₇	1	2	yes	—
274	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
275	C₄	—	2	2	no	—
276	C₄	—	7	4	no	—
277	C₄	—	14	2	no	—
278	C₄	—	14	2	no	—
279	C₄	C₂×C₃×C₂²⋊D₇	1	4	yes	direct product factor
280	C₃	C₂×C₄×C₂²⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
281	C₂	—	2	4	no	—
282	C₂	—	14	4	no	—
283	C₂	C₃×C₄×C₂²⋊D₇	1	4	yes	direct product factor
284	C₂	C₂²×C₃×C₄×D₇	1	1	yes	characteristic
285	C₂	C₂×C₃×#1157	1	1	yes	characteristic
286	C₂	C₂²×C₃×C₂²⋊D₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₄×C₇	C₂	semidirect
3. C₂²×C₃×C₄×D₇	C₂	semidirect
4. C₂×C₃×C₂²⋊Dic₇	C₂	semidirect
5. C₃×C₄×C₂²⋊D₇	C₂	direct (N × H)
6. C₂×C₃×(C₂×D₇)⋊C₄	C₂	semidirect
7. C₂×C₃×Dic₇⋊C₄	C₂	semidirect
8. C₂×C₃×C₄×Dic₇	C₂	semidirect
9. C₂×C₄×C₂²⋊D₇	C₃	direct (N × H)
15. C₂²×C₃×C₄×C₇	C₂²	semidirect
16. C₂×C₃×C₂²⋊D₇	C₄	direct (N × H)
22. C₂×C₃×C₄×D₇	C₂²	semidirect
23. C₃×C₂²⋊Dic₇	C₂²	semidirect
24. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
25. C₃×Dic₇⋊C₄	C₂²	semidirect
26. C₃×C₄×Dic₇	C₂²	semidirect
27. C₂³×C₄×C₇	C₂×C₃	semidirect
29. C₂²×C₄×D₇	C₂×C₃	semidirect
30. C₂×C₂²⋊Dic₇	C₂×C₃	semidirect
31. C₄×C₂²⋊D₇	C₂×C₃	direct (N × H)
32. C₂×(C₂×D₇)⋊C₄	C₂×C₃	semidirect
33. C₂×Dic₇⋊C₄	C₂×C₃	semidirect
34. C₂×C₄×Dic₇	C₂×C₃	semidirect
38. C₂³×C₃×C₇	C₂×C₄	semidirect
43. C₂²×C₃×D₇	C₂×C₄	semidirect
47. C₂×C₃×C₄×C₇	D₄	semidirect
50. C₃×C₂²⋊D₇	C₂×C₄	direct (N × H)
53. C₂×C₃×Dic₇	C₂×C₄	semidirect
63. C₂²×C₄×C₇	C₂²×C₃	semidirect
64. C₂×C₂²⋊D₇	C₃×C₄	direct (N × H)
70. C₂×C₄×D₇	C₂²×C₃	semidirect
71. C₂²⋊Dic₇	C₂²×C₃	semidirect
72. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
73. Dic₇⋊C₄	C₂²×C₃	semidirect
74. C₄×Dic₇	C₂²×C₃	semidirect
77. C₂³×C₃×C₄	D₇	semidirect
87. C₂²×C₃×C₇	C₂²×C₄	semidirect
94. C₂×C₃×D₇	C₂²×C₄	semidirect
96. C₃×C₄×C₇	C₂×D₄	semidirect
99. C₃×Dic₇	C₂²×C₄	semidirect
103. C₂³×C₇	C₂×C₃×C₄	semidirect
108. C₂²×D₇	C₂×C₃×C₄	semidirect
112. C₂×C₄×C₇	C₃×D₄	semidirect
115. C₂²⋊D₇	C₂×C₃×C₄	direct (N × H)
118. C₂×Dic₇	C₂×C₃×C₄	semidirect
135. C₂²×C₃×C₄	C₂×D₇	semidirect
141. C₂×C₃×C₇	C₄×D₄	semidirect
148. C₂³×C₄	C₃×D₇	semidirect
158. C₂²×C₇	C₂²×C₃×C₄	semidirect
165. C₂×D₇	C₂²×C₃×C₄	semidirect
167. C₄×C₇	C₂×C₃×D₄	semidirect
170. Dic₇	C₂²×C₃×C₄	semidirect
177. C₂³×C₃	C₄×D₇	semidirect
190. C₂×C₃×C₄	C₂²⋊D₇	direct (N × H)
193. C₃×C₇	C₂×C₄×D₄	semidirect
206. C₂²×C₄	C₂×C₃×D₇	semidirect
212. C₂×C₇	C₃×C₄×D₄	semidirect
225. C₂²×C₃	C₂×C₄×D₇	semidirect
233. C₃×C₄	C₂×C₂²⋊D₇	direct (N × H)
240. C₂³	C₃×C₄×D₇	semidirect
253. C₂×C₄	C₃×C₂²⋊D₇	direct (N × H)
256. C₇	C₂×C₃×C₄×D₄	semidirect
259. C₂×C₃	C₄×C₂²⋊D₇	direct (N × H)
271. C₂²	C₂×C₃×C₄×D₇	semidirect
279. C₄	C₂×C₃×C₂²⋊D₇	direct (N × H)
280. C₃	C₂×C₄×C₂²⋊D₇	direct (N × H)
283. C₂	C₃×C₄×C₂²⋊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
C₂³×C₃×C₄×C₇	2
C₂²×C₃×C₂²⋊D₇	2
C₂²×C₃×C₄×D₇	2
C₂×C₃×C₂²⋊Dic₇	2
C₃×C₄×C₂²⋊D₇	2
C₂×C₃×(C₂×D₇)⋊C₄	2
C₂×C₃×Dic₇⋊C₄	2
C₂×C₃×C₄×Dic₇	2
C₂×C₄×C₂²⋊D₇	3
C₂×C₃×C₄×D₄	7

Subgroups — C2×C3×C4×C22⋊D7 #13061130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×C₂²⋊D₇ #13061130