Subgroups — C₇×#22864 #13200080

Order 1792.

1274 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#450	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#418	C₂	1	1	yes	maximal, characteristic
4	C₇×#2362	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
6	C₇×#1968	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1936	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1925	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1864	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₇×#102	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
24	C₂×C₇×#117	C₂²	1	1	yes	characteristic
25	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
26	C₇×#450	C₄	1	8	yes	complemented
27	C₇×#440	—	2	4	no	—
28	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₇×#106	C₂²	1	1	yes	characteristic, complemented
30	C₇×#418	—	2	4	no	—
31	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₇×#102	C₂²	1	1	yes	characteristic
34	C₂×C₇×#102	C₂²	1	1	yes	characteristic
35	C₂×C₇×#102	C₂²	1	1	yes	characteristic
36	C₂×C₇×#102	C₂²	1	1	yes	characteristic
37	C₂×C₇×#102	C₂²	1	1	yes	characteristic
38	C₂×C₇×#102	C₂²	1	1	yes	characteristic
39	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
42	C₇×#391	C₂²	1	1	yes	characteristic, complemented
43	C₇×#390	C₂²	1	1	yes	characteristic
44	C₇×#390	C₂²	1	1	yes	characteristic
45	C₇×#389	C₂²	1	1	yes	characteristic, complemented
46	C₇×#388	—	2	1	no	—
47	C₇×#388	—	2	1	no	—
48	C₇×#387	—	2	1	no	—
49	C₇×#386	—	2	1	no	—
50	C₇×#386	—	2	1	no	—
51	C₇×#380	C₂²	1	1	yes	characteristic
52	C₇×#379	—	2	1	no	—
53	C₄×C₇×C₄⋊C₄	—	2	1	no	—
54	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
55	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
56	C₇×#340	C₂²	1	1	yes	characteristic, complemented
57	C₇×#340	C₂²	1	1	yes	characteristic, complemented
58	C₇×#340	C₂²	1	1	yes	characteristic, complemented
59	C₇×#340	C₂²	1	1	yes	characteristic, complemented
60	C₇×#336	C₂²	1	1	yes	characteristic, complemented
61	C₇×#336	C₂²	1	1	yes	characteristic, complemented
62	#22864	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂⁵×C₇	—	2	1	no	—
64	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×D₄	—	2	2	no	—
66	C₂²×C₇×D₄	—	2	2	no	—
67	C₂²×C₇×D₄	—	2	1	no	—
68	C₂²×C₇×D₄	—	2	2	no	—
69	C₂²×C₇×D₄	—	4	1	no	—
70	C₂²×C₇×D₄	—	4	1	no	—
71	C₂²×C₇×D₄	C₂×C₄	1	4	yes	—
72	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
73	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₇	—	2	1	no	—
75	C₂³×C₄×C₇	—	2	1	no	—
76	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
77	C₂×C₇×SD₁₆	—	2	2	no	—
78	C₂×C₇×SD₁₆	—	2	2	no	—
79	C₂×C₇×SD₁₆	—	4	1	no	—
80	C₂×C₇×SD₁₆	—	4	1	no	—
81	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
82	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	complemented
83	C₂×C₇×M₁₆	—	2	2	no	—
84	C₂×C₇×M₁₆	—	2	2	no	—
85	C₂×C₇×M₁₆	—	4	1	no	—
86	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
87	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
88	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
89	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
90	C₇×C₂²⋊Q₈	—	2	2	no	—
91	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	complemented
92	C₄×C₇×Q₈	—	2	2	no	—
93	C₄×C₇×Q₈	—	4	1	no	—
94	C₄×C₇×D₄	—	2	2	no	—
95	C₄×C₇×D₄	—	2	2	no	—
96	C₄×C₇×D₄	—	4	1	no	—
97	C₄×C₇×D₄	—	4	1	no	—
98	C₇×#117	—	2	2	no	—
99	C₇×#117	—	4	1	no	—
100	C₂×C₇×C₄⋊C₄	—	2	1	no	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	—	2	1	no	—
103	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
118	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
119	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₇	—	2	1	no	—
121	C₂×C₄²×C₇	—	2	1	no	—
122	C₂×C₄²×C₇	—	2	1	no	—
123	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
125	C₇×#107	—	2	2	no	—
126	C₇×#106	—	4	1	no	—
127	C₇×#103	—	2	2	no	—
128	C₇×#103	—	4	1	no	—
129	C₇×#102	—	2	2	no	—
130	C₇×#102	—	2	2	no	—
131	C₇×#102	—	2	2	no	—
132	C₇×#102	C₂×C₄	1	4	yes	—
133	C₇×#102	C₂×C₄	1	4	yes	complemented
134	C₇×#102	D₄	1	4	yes	—
135	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
136	C₇×#97	—	2	2	no	—
137	C₄×C₇×C₈	—	4	1	no	—
138	C₇×#95	—	2	1	no	—
139	C₇×#95	—	2	1	no	—
140	C₇×#95	—	2	1	no	—
141	C₇×#95	—	2	1	no	—
142	C₇×#95	—	2	1	no	—
143	C₇×#95	D₄	1	1	yes	characteristic
144	C₇×#95	D₄	1	1	yes	characteristic
145	C₂×#450	C₂×C₇	1	1	yes	characteristic
146	C₂×#440	C₂×C₇	1	1	yes	characteristic, complemented
147	C₂×#418	C₂×C₇	1	1	yes	characteristic
148	#2362	C₂×C₇	1	1	yes	characteristic, complemented
149	D₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
150	#1968	C₂×C₇	1	1	yes	characteristic, complemented
151	#1936	C₂×C₇	1	1	yes	characteristic, complemented
152	#1925	C₂×C₇	1	1	yes	characteristic, complemented
153	#1894	C₂×C₇	1	1	yes	characteristic, complemented
154	#1880	C₂×C₇	1	1	yes	characteristic, complemented
155	#1877	C₂×C₇	1	1	yes	characteristic, complemented
156	#1864	C₂×C₇	1	1	yes	characteristic, complemented
157	#1854	C₂×C₇	1	1	yes	characteristic, complemented
158	C₄×#102	C₂×C₇	1	1	yes	characteristic, complemented
159	#1753	C₂×C₇	1	1	yes	characteristic, complemented
160	C₂⁴×C₇	—	2	1	no	—
161	C₂⁴×C₇	—	2	1	no	—
162	C₂⁴×C₇	—	2	4	no	—
163	C₂⁴×C₇	—	4	2	no	—
164	C₂⁴×C₇	—	4	2	no	—
165	C₂⁴×C₇	—	4	2	no	—
166	C₂⁴×C₇	—	4	2	no	—
167	C₂⁴×C₇	—	8	1	no	—
168	C₂⁴×C₇	—	8	1	no	—
169	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
170	C₂×C₇×Q₈	—	2	1	no	—
171	C₂×C₇×Q₈	—	2	1	no	—
172	C₂×C₇×Q₈	—	2	1	no	—
173	C₂×C₇×Q₈	—	2	1	no	—
174	C₂×C₇×Q₈	—	2	1	no	—
175	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
176	C₂×C₇×D₄	—	2	8	no	—
177	C₂×C₇×D₄	—	2	4	no	—
178	C₂×C₇×D₄	—	2	1	no	—
179	C₂×C₇×D₄	—	2	1	no	—
180	C₂×C₇×D₄	—	2	1	no	—
181	C₂×C₇×D₄	—	2	1	no	—
182	C₂×C₇×D₄	—	2	1	no	—
183	C₂×C₇×D₄	—	2	1	no	—
184	C₂×C₇×D₄	—	2	1	no	—
185	C₂×C₇×D₄	—	2	1	no	—
186	C₂×C₇×D₄	—	4	4	no	—
187	C₂×C₇×D₄	—	4	4	no	—
188	C₂×C₇×D₄	—	4	4	no	—
189	C₂×C₇×D₄	—	4	2	no	—
190	C₂×C₇×D₄	—	4	2	no	—
191	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
192	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
193	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
194	C₂×C₇×D₄	#41	1	2	yes	—
195	C₂²×C₄×C₇	—	2	1	no	—
196	C₂²×C₄×C₇	—	2	1	no	—
197	C₂²×C₄×C₇	—	2	1	no	—
198	C₂²×C₄×C₇	—	2	1	no	—
199	C₂²×C₄×C₇	—	2	1	no	—
200	C₂²×C₄×C₇	—	2	1	no	—
201	C₂²×C₄×C₇	—	2	1	no	—
202	C₂²×C₄×C₇	—	2	1	no	—
203	C₂²×C₄×C₇	—	2	1	no	—
204	C₂²×C₄×C₇	—	2	1	no	—
205	C₂²×C₄×C₇	—	4	2	no	—
206	C₂²×C₄×C₇	—	4	2	no	—
207	C₂²×C₄×C₇	—	4	2	no	—
208	C₂²×C₄×C₇	—	4	2	no	—
209	C₂²×C₄×C₇	—	8	1	no	—
210	C₂²×C₄×C₇	—	8	1	no	—
211	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
212	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₇	#41	1	2	yes	—
218	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
219	C₇×SD₁₆	—	2	8	no	—
220	C₇×SD₁₆	—	4	4	no	—
221	C₇×M₁₆	—	4	4	no	—
222	C₂×C₇×C₈	—	2	1	no	—
223	C₂×C₇×C₈	—	2	1	no	—
224	C₂×C₇×C₈	—	2	1	no	—
225	C₂×C₇×C₈	—	2	1	no	—
226	C₂×C₇×C₈	—	2	1	no	—
227	C₂×C₇×C₈	—	2	1	no	—
228	C₂×C₇×C₈	—	2	1	no	—
229	C₂×C₇×C₈	—	2	1	no	—
230	C₂×C₇×C₈	—	2	1	no	—
231	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
232	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
233	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
234	C₇×C₄⋊C₄	—	2	4	no	—
235	C₇×C₄⋊C₄	—	2	1	no	—
236	C₇×C₄⋊C₄	—	2	1	no	—
237	C₇×C₄⋊C₄	—	2	1	no	—
238	C₇×C₄⋊C₄	—	2	1	no	—
239	C₇×C₄⋊C₄	—	2	1	no	—
240	C₇×C₄⋊C₄	—	2	1	no	—
241	C₇×C₄⋊C₄	—	2	1	no	—
242	C₇×C₄⋊C₄	—	2	1	no	—
243	C₇×C₄⋊C₄	—	4	2	no	—
244	C₇×C₄⋊C₄	—	4	2	no	—
245	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
246	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
247	C₇×C₂²⋊C₄	—	2	4	no	—
248	C₇×C₂²⋊C₄	—	2	2	no	—
249	C₇×C₂²⋊C₄	—	4	1	no	—
250	C₇×C₂²⋊C₄	—	4	2	no	—
251	C₇×C₂²⋊C₄	—	4	2	no	—
252	C₇×C₂²⋊C₄	—	4	2	no	—
253	C₇×C₂²⋊C₄	—	4	2	no	—
254	C₇×C₂²⋊C₄	—	4	2	no	—
255	C₇×C₂²⋊C₄	—	4	2	no	—
256	C₇×C₂²⋊C₄	—	8	1	no	—
257	C₇×C₂²⋊C₄	—	8	1	no	—
258	C₄²×C₇	—	2	1	no	—
259	C₄²×C₇	—	2	1	no	—
260	C₄²×C₇	—	2	1	no	—
261	C₄²×C₇	—	2	1	no	—
262	C₄²×C₇	—	4	2	no	—
263	C₄²×C₇	—	4	2	no	—
264	C₄²×C₇	—	4	2	no	—
265	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
266	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
267	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
268	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
269	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
270	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
271	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
272	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
273	C₂×#117	C₂²×C₇	1	1	yes	characteristic
274	C₂²×C₂²⋊C₄	—	2	1	no	—
275	#450	C₄×C₇	1	8	yes	complemented
276	#440	—	2	4	no	—
277	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
278	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
279	#418	—	2	4	no	—
280	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
281	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
282	C₂×#102	C₂²×C₇	1	1	yes	characteristic
283	C₂×#102	C₂²×C₇	1	1	yes	characteristic
284	C₂×#102	C₂²×C₇	1	1	yes	characteristic
285	C₂×#102	C₂²×C₇	1	1	yes	characteristic
286	C₂×#102	C₂²×C₇	1	1	yes	characteristic
287	C₂×#102	C₂²×C₇	1	1	yes	characteristic
288	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
289	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
290	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
291	#391	C₂²×C₇	1	1	yes	characteristic, complemented
292	#390	C₂²×C₇	1	1	yes	characteristic
293	#390	C₂²×C₇	1	1	yes	characteristic
294	#389	C₂²×C₇	1	1	yes	characteristic, complemented
295	#388	—	2	1	no	—
296	#388	—	2	1	no	—
297	#387	—	2	1	no	—
298	#386	—	2	1	no	—
299	#386	—	2	1	no	—
300	#380	C₂²×C₇	1	1	yes	characteristic
301	#379	—	2	1	no	—
302	C₄×C₄⋊C₄	—	2	1	no	—
303	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
304	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
305	#340	C₂²×C₇	1	1	yes	characteristic, complemented
306	#340	C₂²×C₇	1	1	yes	characteristic, complemented
307	#340	C₂²×C₇	1	1	yes	characteristic, complemented
308	#340	C₂²×C₇	1	1	yes	characteristic, complemented
309	#336	C₂²×C₇	1	1	yes	characteristic, complemented
310	#336	C₂²×C₇	1	1	yes	characteristic, complemented
311	C₂³×C₇	—	2	2	no	—
312	C₂³×C₇	—	2	1	no	—
313	C₂³×C₇	—	2	2	no	—
314	C₂³×C₇	—	2	2	no	—
315	C₂³×C₇	—	2	1	no	—
316	C₂³×C₇	—	2	1	no	—
317	C₂³×C₇	—	2	1	no	—
318	C₂³×C₇	—	2	1	no	—
319	C₂³×C₇	—	2	1	no	—
320	C₂³×C₇	—	2	2	no	—
321	C₂³×C₇	—	4	8	no	—
322	C₂³×C₇	—	4	8	no	—
323	C₂³×C₇	—	4	1	no	—
324	C₂³×C₇	—	4	1	no	—
325	C₂³×C₇	—	4	1	no	—
326	C₂³×C₇	—	4	1	no	—
327	C₂³×C₇	—	4	1	no	—
328	C₂³×C₇	—	4	1	no	—
329	C₂³×C₇	—	4	1	no	—
330	C₂³×C₇	—	4	1	no	—
331	C₂³×C₇	—	4	1	no	—
332	C₂³×C₇	—	4	1	no	—
333	C₂³×C₇	—	8	4	no	—
334	C₂³×C₇	—	8	4	no	—
335	C₂³×C₇	—	8	4	no	—
336	C₂³×C₇	—	8	4	no	—
337	C₂³×C₇	—	8	4	no	—
338	C₂³×C₇	C₄×D₄	1	2	yes	—
339	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
340	C₇×Q₈	—	2	2	no	—
341	C₇×Q₈	—	2	2	no	—
342	C₇×Q₈	—	4	1	no	—
343	C₇×Q₈	—	4	1	no	—
344	C₇×D₄	—	2	2	no	—
345	C₇×D₄	—	2	2	no	—
346	C₇×D₄	—	2	2	no	—
347	C₇×D₄	—	2	2	no	—
348	C₇×D₄	—	2	2	no	—
349	C₇×D₄	—	4	8	no	—
350	C₇×D₄	—	4	1	no	—
351	C₇×D₄	—	4	1	no	—
352	C₇×D₄	C₄×D₄	1	4	yes	—
353	C₂×C₄×C₇	—	2	1	no	—
354	C₂×C₄×C₇	—	2	1	no	—
355	C₂×C₄×C₇	—	2	1	no	—
356	C₂×C₄×C₇	—	2	1	no	—
357	C₂×C₄×C₇	—	2	2	no	—
358	C₂×C₄×C₇	—	2	2	no	—
359	C₂×C₄×C₇	—	2	2	no	—
360	C₂×C₄×C₇	—	2	2	no	—
361	C₂×C₄×C₇	—	2	2	no	—
362	C₂×C₄×C₇	—	2	2	no	—
363	C₂×C₄×C₇	—	2	1	no	—
364	C₂×C₄×C₇	—	2	1	no	—
365	C₂×C₄×C₇	—	2	2	no	—
366	C₂×C₄×C₇	—	2	1	no	—
367	C₂×C₄×C₇	—	2	1	no	—
368	C₂×C₄×C₇	—	2	1	no	—
369	C₂×C₄×C₇	—	2	1	no	—
370	C₂×C₄×C₇	—	2	1	no	—
371	C₂×C₄×C₇	—	2	1	no	—
372	C₂×C₄×C₇	—	2	1	no	—
373	C₂×C₄×C₇	—	4	1	no	—
374	C₂×C₄×C₇	—	4	1	no	—
375	C₂×C₄×C₇	—	4	1	no	—
376	C₂×C₄×C₇	—	4	1	no	—
377	C₂×C₄×C₇	—	4	1	no	—
378	C₂×C₄×C₇	—	4	1	no	—
379	C₂×C₄×C₇	—	4	1	no	—
380	C₂×C₄×C₇	—	4	1	no	—
381	C₂×C₄×C₇	—	4	1	no	—
382	C₂×C₄×C₇	—	4	1	no	—
383	C₂×C₄×C₇	—	4	1	no	—
384	C₂×C₄×C₇	—	4	1	no	—
385	C₂×C₄×C₇	—	4	1	no	—
386	C₂×C₄×C₇	—	4	1	no	—
387	C₂×C₄×C₇	—	4	1	no	—
388	C₂×C₄×C₇	—	8	4	no	—
389	C₂×C₄×C₇	—	8	4	no	—
390	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
391	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
392	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
393	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
395	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
396	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
397	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
398	C₇×C₈	—	2	2	no	—
399	C₇×C₈	—	2	2	no	—
400	C₇×C₈	—	2	2	no	—
401	C₇×C₈	—	4	1	no	—
402	C₂⁵	—	2	1	no	—
403	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
404	C₂²×D₄	—	2	2	no	—
405	C₂²×D₄	—	2	2	no	—
406	C₂²×D₄	—	2	1	no	—
407	C₂²×D₄	—	2	2	no	—
408	C₂²×D₄	—	4	1	no	—
409	C₂²×D₄	—	4	1	no	—
410	C₂²×D₄	C₂×C₄×C₇	1	4	yes	—
411	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
412	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
413	C₂³×C₄	—	2	1	no	—
414	C₂³×C₄	—	2	1	no	—
415	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
416	C₂×SD₁₆	—	2	2	no	—
417	C₂×SD₁₆	—	2	2	no	—
418	C₂×SD₁₆	—	4	1	no	—
419	C₂×SD₁₆	—	4	1	no	—
420	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
421	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	complemented
422	C₂×M₁₆	—	2	2	no	—
423	C₂×M₁₆	—	2	2	no	—
424	C₂×M₁₆	—	4	1	no	—
425	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
426	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
427	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
428	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
429	C₂²⋊Q₈	—	2	2	no	—
430	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	complemented
431	C₄×Q₈	—	2	2	no	—
432	C₄×Q₈	—	4	1	no	—
433	C₄×D₄	—	2	2	no	—
434	C₄×D₄	—	2	2	no	—
435	C₄×D₄	—	4	1	no	—
436	C₄×D₄	—	4	1	no	—
437	#117	—	2	2	no	—
438	#117	—	4	1	no	—
439	C₂×C₄⋊C₄	—	2	1	no	—
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	4	4	no	—
457	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
458	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
459	C₂×C₄²	—	2	1	no	—
460	C₂×C₄²	—	2	1	no	—
461	C₂×C₄²	—	2	1	no	—
462	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
463	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
464	#107	—	2	2	no	—
465	#106	—	4	1	no	—
466	#103	—	2	2	no	—
467	#103	—	4	1	no	—
468	#102	—	2	2	no	—
469	#102	—	2	2	no	—
470	#102	—	2	2	no	—
471	#102	C₂×C₄×C₇	1	4	yes	—
472	#102	C₂×C₄×C₇	1	4	yes	complemented
473	#102	C₇×D₄	1	4	yes	—
474	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
475	#97	—	2	2	no	—
476	C₄×C₈	—	4	1	no	—
477	#95	—	2	1	no	—
478	#95	—	2	1	no	—
479	#95	—	2	1	no	—
480	#95	—	2	1	no	—
481	#95	—	2	1	no	—
482	#95	C₇×D₄	1	1	yes	characteristic
483	#95	C₇×D₄	1	1	yes	characteristic
484	C₂²×C₇	—	2	2	no	—
485	C₂²×C₇	—	2	4	no	—
486	C₂²×C₇	—	2	2	no	—
487	C₂²×C₇	—	2	2	no	—
488	C₂²×C₇	—	4	2	no	—
489	C₂²×C₇	—	4	2	no	—
490	C₂²×C₇	—	4	2	no	—
491	C₂²×C₇	—	4	1	no	—
492	C₂²×C₇	—	4	1	no	—
493	C₂²×C₇	—	4	2	no	—
494	C₂²×C₇	—	4	2	no	—
495	C₂²×C₇	—	4	1	no	—
496	C₂²×C₇	—	4	1	no	—
497	C₂²×C₇	—	4	2	no	—
498	C₂²×C₇	—	4	2	no	—
499	C₂²×C₇	—	4	2	no	—
500	C₂²×C₇	—	4	2	no	—
501	C₂²×C₇	—	8	16	no	—
502	C₂²×C₇	—	8	1	no	—
503	C₂²×C₇	—	8	1	no	—
504	C₂²×C₇	—	8	1	no	—
505	C₂²×C₇	—	8	1	no	—
506	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
507	C₂²×C₇	D₄²	1	1	yes	characteristic
508	C₂²×C₇	#546	1	1	yes	characteristic
509	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
510	C₂²×C₇	#575	1	1	yes	characteristic
511	C₂²×C₇	#577	1	1	yes	characteristic
512	C₂²×C₇	#577	1	1	yes	characteristic
513	C₄×C₇	—	2	2	no	—
514	C₄×C₇	—	2	2	no	—
515	C₄×C₇	—	4	2	no	—
516	C₄×C₇	—	4	2	no	—
517	C₄×C₇	—	4	1	no	—
518	C₄×C₇	—	4	2	no	—
519	C₄×C₇	—	4	1	no	—
520	C₄×C₇	—	4	1	no	—
521	C₄×C₇	—	8	1	no	—
522	C₄×C₇	—	8	1	no	—
523	C₄×C₇	—	8	1	no	—
524	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
525	C₄×C₇	#518	1	1	yes	characteristic
526	C₄×C₇	#546	1	1	yes	characteristic
527	C₄×C₇	#551	1	1	yes	characteristic
528	C₂⁴	—	2	1	no	—
529	C₂⁴	—	2	1	no	—
530	C₂⁴	—	2	4	no	—
531	C₂⁴	—	4	2	no	—
532	C₂⁴	—	4	2	no	—
533	C₂⁴	—	4	2	no	—
534	C₂⁴	—	4	2	no	—
535	C₂⁴	—	8	1	no	—
536	C₂⁴	—	8	1	no	—
537	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
544	C₂×D₄	—	2	8	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂×D₄	—	4	2	no	—
558	C₂×D₄	—	4	2	no	—
559	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
560	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
561	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
562	C₂×D₄	C₇×#41	1	2	yes	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	—	4	2	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	4	2	no	—
577	C₂²×C₄	—	8	1	no	—
578	C₂²×C₄	—	8	1	no	—
579	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
580	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
581	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
582	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
583	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
584	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
585	C₂²×C₄	C₇×#41	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
587	SD₁₆	—	2	8	no	—
588	SD₁₆	—	4	4	no	—
589	M₁₆	—	4	4	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
600	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
601	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
614	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	4	1	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₂²⋊C₄	—	4	2	no	—
620	C₂²⋊C₄	—	4	2	no	—
621	C₂²⋊C₄	—	4	2	no	—
622	C₂²⋊C₄	—	4	2	no	—
623	C₂²⋊C₄	—	4	2	no	—
624	C₂²⋊C₄	—	8	1	no	—
625	C₂²⋊C₄	—	8	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₄²	—	2	1	no	—
629	C₄²	—	2	1	no	—
630	C₄²	—	4	2	no	—
631	C₄²	—	4	2	no	—
632	C₄²	—	4	2	no	—
633	C₂×C₇	—	4	2	no	—
634	C₂×C₇	—	4	4	no	—
635	C₂×C₇	—	8	2	no	—
636	C₂×C₇	#2358	1	1	yes	characteristic
637	C₂×C₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
638	C₂×C₇	#2949	1	1	yes	characteristic
639	C₂×C₇	#3272	1	1	yes	characteristic
640	C₂×C₇	#3275	1	1	yes	characteristic
641	C₂×C₇	#3310	1	1	yes	characteristic
642	C₂×C₇	#3311	1	1	yes	characteristic
643	C₂³	—	2	2	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	4	8	no	—
654	C₂³	—	4	8	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	8	4	no	—
666	C₂³	—	8	4	no	—
667	C₂³	—	8	4	no	—
668	C₂³	—	8	4	no	—
669	C₂³	—	8	4	no	—
670	C₂³	C₄×C₇×D₄	1	2	yes	—
671	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
672	Q₈	—	2	2	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	4	1	no	—
675	Q₈	—	4	1	no	—
676	D₄	—	2	2	no	—
677	D₄	—	2	2	no	—
678	D₄	—	2	2	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	2	no	—
681	D₄	—	4	8	no	—
682	D₄	—	4	1	no	—
683	D₄	—	4	1	no	—
684	D₄	C₄×C₇×D₄	1	4	yes	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	8	4	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
723	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
724	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
725	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
726	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
727	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
728	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
729	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
730	C₈	—	2	2	no	—
731	C₈	—	2	2	no	—
732	C₈	—	2	2	no	—
733	C₈	—	4	1	no	—
734	C₇	#22864	1	1	yes	characteristic, direct product factor, Sylow
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	8	16	no	—
753	C₂²	—	8	1	no	—
754	C₂²	—	8	1	no	—
755	C₂²	—	8	1	no	—
756	C₂²	—	8	1	no	—
757	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
758	C₂²	C₇×D₄²	1	1	yes	characteristic
759	C₂²	C₇×#546	1	1	yes	characteristic
760	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
761	C₂²	C₇×#575	1	1	yes	characteristic
762	C₂²	C₇×#577	1	1	yes	characteristic
763	C₂²	C₇×#577	1	1	yes	characteristic
764	C₄	—	2	2	no	—
765	C₄	—	2	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	1	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	1	no	—
770	C₄	—	4	1	no	—
771	C₄	—	4	2	no	—
772	C₄	—	8	1	no	—
773	C₄	—	8	1	no	—
774	C₄	—	8	1	no	—
775	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
776	C₄	C₇×#518	1	1	yes	characteristic
777	C₄	C₇×#546	1	1	yes	characteristic
778	C₄	C₇×#551	1	1	yes	characteristic
779	C₂	—	4	2	no	—
780	C₂	—	4	4	no	—
781	C₂	—	8	2	no	—
782	C₂	C₇×#2358	1	1	yes	characteristic
783	C₂	C₄×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
784	C₂	C₇×#2949	1	1	yes	characteristic
785	C₂	C₇×#3272	1	1	yes	characteristic
786	C₂	C₇×#3275	1	1	yes	characteristic
787	C₂	C₇×#3310	1	1	yes	characteristic
788	C₂	C₇×#3311	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#440	C₂	semidirect
4. C₇×#2362	C₂	semidirect
6. C₇×#1968	C₂	semidirect
7. C₇×#1936	C₂	semidirect
8. C₇×#1925	C₂	semidirect
9. C₇×#1894	C₂	semidirect
10. C₇×#1880	C₂	semidirect
11. C₇×#1877	C₂	semidirect
12. C₇×#1864	C₂	semidirect
13. C₇×#1854	C₂	semidirect
14. C₄×C₇×#102	C₂	semidirect
15. C₇×#1753	C₂	semidirect
21. C₂×C₄×C₇×Q₈	C₂²	semidirect
26. C₇×#450	C₄	semidirect
28. C₂×C₇×#107	C₂²	semidirect
29. C₂×C₇×#106	C₂²	semidirect
31. C₂×C₇×#103	C₂²	semidirect
32. C₂×C₇×#103	C₂²	semidirect
40. C₂×C₇×#97	C₂²	semidirect
41. C₂×C₄×C₇×C₈	C₂²	semidirect
42. C₇×#391	C₂²	semidirect
45. C₇×#389	C₂²	semidirect
54. C₄×C₇×C₄⋊C₄	C₂²	semidirect
56. C₇×#340	C₂²	semidirect
57. C₇×#340	C₂²	semidirect
58. C₇×#340	C₂²	semidirect
59. C₇×#340	C₂²	semidirect
60. C₇×#336	C₂²	semidirect
61. C₇×#336	C₂²	semidirect
62. #22864	C₇	direct (N × H)
82. C₂×C₇×SD₁₆	C₂×C₄	semidirect
91. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
133. C₇×#102	C₂×C₄	semidirect
135. C₇×C₂²⋊C₈	C₂×C₄	semidirect
146. C₂×#440	C₂×C₇	semidirect
148. #2362	C₂×C₇	semidirect
150. #1968	C₂×C₇	semidirect
151. #1936	C₂×C₇	semidirect
152. #1925	C₂×C₇	semidirect
153. #1894	C₂×C₇	semidirect
154. #1880	C₂×C₇	semidirect
155. #1877	C₂×C₇	semidirect
156. #1864	C₂×C₇	semidirect
157. #1854	C₂×C₇	semidirect
158. C₄×#102	C₂×C₇	semidirect
159. #1753	C₂×C₇	semidirect
270. C₂×C₄×Q₈	C₂²×C₇	semidirect
275. #450	C₄×C₇	semidirect
277. C₂×#107	C₂²×C₇	semidirect
278. C₂×#106	C₂²×C₇	semidirect
280. C₂×#103	C₂²×C₇	semidirect
281. C₂×#103	C₂²×C₇	semidirect
289. C₂×#97	C₂²×C₇	semidirect
290. C₂×C₄×C₈	C₂²×C₇	semidirect
291. #391	C₂²×C₇	semidirect
294. #389	C₂²×C₇	semidirect
303. C₄×C₄⋊C₄	C₂²×C₇	semidirect
305. #340	C₂²×C₇	semidirect
306. #340	C₂²×C₇	semidirect
307. #340	C₂²×C₇	semidirect
308. #340	C₂²×C₇	semidirect
309. #336	C₂²×C₇	semidirect
310. #336	C₂²×C₇	semidirect
421. C₂×SD₁₆	C₂×C₄×C₇	semidirect
430. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
472. #102	C₂×C₄×C₇	semidirect
474. C₂²⋊C₈	C₂×C₄×C₇	semidirect
734. C₇	#22864	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×C₇×#450	2
C₂×C₇×#440	2
C₂×C₇×#418	2
C₇×#2362	2
C₇×D₄×C₂²⋊C₄	2
C₇×#1968	2
C₇×#1936	2
C₇×#1925	2
C₇×#1894	2
C₇×#1880	2
C₇×#1877	2
C₇×#1864	2
C₇×#1854	2
C₄×C₇×#102	2
C₇×#1753	2
#22864	7

Subgroups — C7×#22864 #13200080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22864 #13200080