Subgroups — C₂×C₄×C₇×AGL(1,ℤ/8) #13237372

Order 1792.

3242 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₇×AGL(1,ℤ/8)	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₇×#442	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#440	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₇×SD₁₆	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₇×D₈	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#428	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#417	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#418	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
14	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₇	—	2	1	no	—
16	C₂×C₇×AGL(1,ℤ/8)	C₄	1	16	yes	direct product factor
17	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	8	yes	—
18	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
19	C₂²×C₇×D₈	C₂²	1	2	yes	—
20	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
22	C₄×C₇×#41	—	2	4	no	—
23	C₄×C₇×#41	C₂²	1	8	yes	complemented
24	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×C₇×D₄	—	2	1	no	—
27	C₂×C₄×C₇×D₄	—	2	1	no	—
28	C₂×C₄×C₇×D₄	—	2	1	no	—
29	C₂×C₄×C₇×D₄	—	2	4	no	—
30	C₂×C₄×C₇×D₄	—	2	1	no	—
31	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
32	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
33	C₂×C₄×C₇×D₄	C₂²	1	8	yes	complemented
34	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₇×#117	—	2	1	no	—
37	C₂×C₇×#117	C₂²	1	1	yes	characteristic
38	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
40	C₂²×C₄²×C₇	—	2	1	no	—
41	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
42	C₇×#442	C₂²	1	16	yes	complemented
43	C₇×#440	C₂²	1	16	yes	complemented
44	C₄×C₇×SD₁₆	C₂²	1	16	yes	complemented
45	C₄×C₇×D₈	C₂²	1	16	yes	complemented
46	C₇×#428	C₂²	1	8	yes	complemented
47	C₂×C₇×#107	C₂²	1	2	yes	complemented
48	C₂×C₇×#106	C₂²	1	2	yes	complemented
49	C₇×#418	C₂²	1	8	yes	complemented
50	C₇×#417	C₂²	1	8	yes	complemented
51	C₂×C₇×#103	C₂²	1	2	yes	complemented
52	C₂×C₇×#102	C₂²	1	2	yes	—
53	C₂×C₇×#102	C₂²	1	2	yes	—
54	C₂×C₇×#102	C₂²	1	2	yes	complemented
55	C₄×C₇×M₁₆	C₂²	1	8	yes	complemented
56	C₂×C₇×#97	C₂²	1	2	yes	complemented
57	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
58	C₂×C₄×AGL(1,ℤ/8)	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
59	C₂⁵×C₇	—	2	1	no	—
60	C₂×C₇×#41	—	2	2	no	—
61	C₂×C₇×#41	—	2	4	no	—
62	C₂×C₇×#41	C₂×C₄	1	8	yes	complemented
63	C₂×C₇×#41	C₂³	1	4	yes	—
64	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×D₄	—	2	1	no	—
66	C₂²×C₇×D₄	—	2	1	no	—
67	C₂²×C₇×D₄	—	2	2	no	—
68	C₂²×C₇×D₄	—	2	4	no	—
69	C₂²×C₇×D₄	C₂×C₄	1	8	yes	complemented
70	C₂²×C₇×D₄	C₂³	1	2	yes	—
71	C₂²×C₇×D₄	C₂³	1	4	yes	—
72	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₇	—	2	1	no	—
74	C₂³×C₄×C₇	—	2	1	no	—
75	C₂³×C₄×C₇	—	2	1	no	—
76	C₂³×C₄×C₇	—	2	2	no	—
77	C₂³×C₄×C₇	—	2	8	no	—
78	C₂³×C₄×C₇	—	2	1	no	—
79	C₂³×C₄×C₇	—	2	2	no	—
80	C₂³×C₄×C₇	—	4	8	no	—
81	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
82	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
83	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
84	C₇×AGL(1,ℤ/8)	C₂×C₄	1	64	yes	direct product factor
85	C₂×C₇×SD₁₆	C₂×C₄	1	16	yes	complemented
86	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
87	C₂×C₇×D₈	C₂×C₄	1	16	yes	complemented
88	C₂×C₇×D₈	C₂³	1	8	yes	—
89	C₂×C₇×M₁₆	—	2	4	no	—
90	C₂×C₇×M₁₆	C₂×C₄	1	8	yes	complemented
91	C₂×C₇×M₁₆	C₂³	1	4	yes	—
92	C₂×C₇×M₁₆	C₂³	1	4	yes	—
93	C₂²×C₇×C₈	C₂³	1	2	yes	—
94	C₂²×C₇×C₈	C₂³	1	2	yes	—
95	C₄×C₇×Q₈	—	2	2	no	—
96	C₄×C₇×Q₈	—	2	2	no	—
97	C₄×C₇×Q₈	C₂³	1	4	yes	complemented
98	C₄×C₇×Q₈	C₂³	1	4	yes	complemented
99	C₄×C₇×D₄	—	2	8	no	—
100	C₄×C₇×D₄	—	2	8	no	—
101	C₄×C₇×D₄	—	2	4	no	—
102	C₄×C₇×D₄	—	2	4	no	—
103	C₄×C₇×D₄	—	2	8	no	—
104	C₄×C₇×D₄	—	2	8	no	—
105	C₄×C₇×D₄	—	2	2	no	—
106	C₄×C₇×D₄	—	2	2	no	—
107	C₄×C₇×D₄	C₂³	1	8	yes	—
108	C₄×C₇×D₄	C₂³	1	8	yes	—
109	C₄×C₇×D₄	C₂³	1	4	yes	complemented
110	C₄×C₇×D₄	C₂³	1	4	yes	complemented
111	C₇×#117	—	2	2	no	—
112	C₇×#117	—	2	8	no	—
113	C₇×#117	C₂³	1	4	yes	—
114	C₂×C₇×C₄⋊C₄	—	2	1	no	—
115	C₂×C₇×C₄⋊C₄	—	2	2	no	—
116	C₂×C₇×C₄⋊C₄	—	2	1	no	—
117	C₂×C₇×C₄⋊C₄	—	2	1	no	—
118	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
120	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
124	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
125	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
126	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
128	C₂×C₄²×C₇	—	2	1	no	—
129	C₂×C₄²×C₇	—	2	1	no	—
130	C₂×C₄²×C₇	—	2	1	no	—
131	C₂×C₄²×C₇	—	2	8	no	—
132	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
133	C₂×C₄²×C₇	D₄	1	4	yes	—
134	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
135	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₇	C₂³	1	4	yes	—
137	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
138	C₇×#107	C₂³	1	8	yes	complemented
139	C₇×#106	C₂³	1	8	yes	complemented
140	C₇×#103	C₂³	1	8	yes	complemented
141	C₇×#102	C₂³	1	8	yes	—
142	C₇×#102	C₂³	1	8	yes	—
143	C₇×#102	C₂³	1	8	yes	complemented
144	C₇×#97	C₂³	1	8	yes	complemented
145	C₄×C₇×C₈	C₂³	1	8	yes	complemented
146	C₂²×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic
147	C₂×C₄×#41	C₂×C₇	1	1	yes	characteristic, complemented
148	C₂²×C₄×D₄	C₂×C₇	1	1	yes	characteristic, complemented
149	C₄×AGL(1,ℤ/8)	C₂×C₇	1	16	yes	direct product factor
150	C₂×#442	C₂×C₇	1	2	yes	complemented
151	C₂×#440	C₂×C₇	1	2	yes	complemented
152	C₂×C₄×SD₁₆	C₂×C₇	1	2	yes	complemented
153	C₂×C₄×D₈	C₂×C₇	1	2	yes	complemented
154	C₂×#428	C₂×C₇	1	1	yes	characteristic, complemented
155	C₂×#417	C₂×C₇	1	1	yes	characteristic, complemented
156	C₂×#418	C₂×C₇	1	1	yes	characteristic, complemented
157	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
158	C₂⁴×C₇	—	2	8	no	—
159	C₂⁴×C₇	—	2	1	no	—
160	C₂⁴×C₇	—	2	2	no	—
161	C₂⁴×C₇	—	2	4	no	—
162	C₂⁴×C₇	—	4	4	no	—
163	C₂⁴×C₇	—	4	4	no	—
164	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
165	C₇×#41	—	2	16	no	—
166	C₇×#41	—	2	8	no	—
167	C₇×#41	C₂²×C₄	1	16	yes	complemented
168	C₂×C₇×Q₈	—	2	1	no	—
169	C₂×C₇×Q₈	—	2	2	no	—
170	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	complemented
171	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
172	C₂×C₇×D₄	—	2	8	no	—
173	C₂×C₇×D₄	—	2	4	no	—
174	C₂×C₇×D₄	—	2	8	no	—
175	C₂×C₇×D₄	—	2	16	no	—
176	C₂×C₇×D₄	—	2	4	no	—
177	C₂×C₇×D₄	—	2	2	no	—
178	C₂×C₇×D₄	—	2	1	no	—
179	C₂×C₇×D₄	—	2	4	no	—
180	C₂×C₇×D₄	—	2	8	no	—
181	C₂×C₇×D₄	—	2	2	no	—
182	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
183	C₂×C₇×D₄	C₂²×C₄	1	16	yes	complemented
184	C₂×C₇×D₄	C₂²×C₄	1	4	yes	complemented
185	C₂×C₇×D₄	C₂⁴	1	4	yes	—
186	C₂×C₇×D₄	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₇	—	2	1	no	—
188	C₂²×C₄×C₇	—	2	8	no	—
189	C₂²×C₄×C₇	—	2	4	no	—
190	C₂²×C₄×C₇	—	2	4	no	—
191	C₂²×C₄×C₇	—	2	1	no	—
192	C₂²×C₄×C₇	—	2	1	no	—
193	C₂²×C₄×C₇	—	2	4	no	—
194	C₂²×C₄×C₇	—	2	2	no	—
195	C₂²×C₄×C₇	—	2	4	no	—
196	C₂²×C₄×C₇	—	2	4	no	—
197	C₂²×C₄×C₇	—	2	8	no	—
198	C₂²×C₄×C₇	—	2	8	no	—
199	C₂²×C₄×C₇	—	4	2	no	—
200	C₂²×C₄×C₇	—	4	4	no	—
201	C₂²×C₄×C₇	—	4	8	no	—
202	C₂²×C₄×C₇	—	4	32	no	—
203	C₂²×C₄×C₇	—	4	4	no	—
204	C₂²×C₄×C₇	—	4	4	no	—
205	C₂²×C₄×C₇	—	4	8	no	—
206	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
207	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
211	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
212	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
214	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₇	#41	1	4	yes	—
216	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
218	C₇×SD₁₆	C₂²×C₄	1	32	yes	complemented
219	C₇×D₈	C₂²×C₄	1	32	yes	complemented
220	C₇×M₁₆	—	2	8	no	—
221	C₇×M₁₆	C₂²×C₄	1	16	yes	complemented
222	C₂×C₇×C₈	—	2	4	no	—
223	C₂×C₇×C₈	C₂²×C₄	1	8	yes	complemented
224	C₂×C₇×C₈	C₂⁴	1	4	yes	—
225	C₂×C₇×C₈	C₂⁴	1	4	yes	—
226	C₇×C₄⋊C₄	—	2	4	no	—
227	C₇×C₄⋊C₄	—	2	2	no	—
228	C₇×C₄⋊C₄	—	2	4	no	—
229	C₇×C₄⋊C₄	—	2	4	no	—
230	C₇×C₄⋊C₄	—	2	1	no	—
231	C₇×C₄⋊C₄	—	2	1	no	—
232	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
233	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
234	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
235	C₇×C₂²⋊C₄	—	2	4	no	—
236	C₇×C₂²⋊C₄	—	2	8	no	—
237	C₇×C₂²⋊C₄	—	2	8	no	—
238	C₇×C₂²⋊C₄	—	2	4	no	—
239	C₇×C₂²⋊C₄	—	2	4	no	—
240	C₄²×C₇	—	2	4	no	—
241	C₄²×C₇	—	2	4	no	—
242	C₄²×C₇	—	2	4	no	—
243	C₄²×C₇	C₂×D₄	1	4	yes	—
244	C₄²×C₇	C₂×D₄	1	4	yes	—
245	C₄²×C₇	C₂×D₄	1	2	yes	—
246	C₄²×C₇	C₂×D₄	1	2	yes	—
247	C₄²×C₇	C₂⁴	1	2	yes	—
248	C₄²×C₇	C₂⁴	1	2	yes	—
249	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
250	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
251	C₂⁴×C₄	—	2	1	no	—
252	C₂×AGL(1,ℤ/8)	C₄×C₇	1	16	yes	direct product factor
253	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	8	yes	—
254	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
255	C₂²×D₈	C₂²×C₇	1	2	yes	—
256	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
257	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
258	C₄×#41	—	2	4	no	—
259	C₄×#41	C₂²×C₇	1	8	yes	complemented
260	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
261	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
262	C₂×C₄×D₄	—	2	1	no	—
263	C₂×C₄×D₄	—	2	1	no	—
264	C₂×C₄×D₄	—	2	1	no	—
265	C₂×C₄×D₄	—	2	4	no	—
266	C₂×C₄×D₄	—	2	1	no	—
267	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
268	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
269	C₂×C₄×D₄	C₂²×C₇	1	8	yes	complemented
270	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
271	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
272	C₂×#117	—	2	1	no	—
273	C₂×#117	C₂²×C₇	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
275	C₂²×C₂²⋊C₄	—	2	1	no	—
276	C₂²×C₄²	—	2	1	no	—
277	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
278	#442	C₂²×C₇	1	16	yes	complemented
279	#440	C₂²×C₇	1	16	yes	complemented
280	C₄×SD₁₆	C₂²×C₇	1	16	yes	complemented
281	C₄×D₈	C₂²×C₇	1	16	yes	complemented
282	#428	C₂²×C₇	1	8	yes	complemented
283	C₂×#107	C₂²×C₇	1	2	yes	complemented
284	C₂×#106	C₂²×C₇	1	2	yes	complemented
285	#418	C₂²×C₇	1	8	yes	complemented
286	#417	C₂²×C₇	1	8	yes	complemented
287	C₂×#103	C₂²×C₇	1	2	yes	complemented
288	C₂×#102	C₂²×C₇	1	2	yes	—
289	C₂×#102	C₂²×C₇	1	2	yes	—
290	C₂×#102	C₂²×C₇	1	2	yes	complemented
291	C₄×M₁₆	C₂²×C₇	1	8	yes	complemented
292	C₂×#97	C₂²×C₇	1	2	yes	complemented
293	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
294	C₂³×C₇	—	2	2	no	—
295	C₂³×C₇	—	2	2	no	—
296	C₂³×C₇	—	2	4	no	—
297	C₂³×C₇	—	2	8	no	—
298	C₂³×C₇	—	2	16	no	—
299	C₂³×C₇	—	2	2	no	—
300	C₂³×C₇	—	2	4	no	—
301	C₂³×C₇	—	4	8	no	—
302	C₂³×C₇	—	4	32	no	—
303	C₂³×C₇	—	4	8	no	—
304	C₂³×C₇	—	4	4	no	—
305	C₂³×C₇	—	4	2	no	—
306	C₂³×C₇	—	4	2	no	—
307	C₂³×C₇	—	4	4	no	—
308	C₂³×C₇	C₄×D₄	1	4	yes	—
309	C₂³×C₇	C₂²×D₄	1	2	yes	—
310	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
311	C₇×Q₈	—	2	4	no	—
312	C₇×Q₈	—	2	2	no	—
313	C₇×Q₈	C₂³×C₄	1	4	yes	complemented
314	C₇×D₄	—	2	16	no	—
315	C₇×D₄	—	2	8	no	—
316	C₇×D₄	—	2	16	no	—
317	C₇×D₄	—	2	4	no	—
318	C₇×D₄	—	2	4	no	—
319	C₇×D₄	—	2	2	no	—
320	C₇×D₄	C₂³×C₄	1	8	yes	—
321	C₇×D₄	C₂³×C₄	1	4	yes	complemented
322	C₂×C₄×C₇	—	2	4	no	—
323	C₂×C₄×C₇	—	2	2	no	—
324	C₂×C₄×C₇	—	2	2	no	—
325	C₂×C₄×C₇	—	2	2	no	—
326	C₂×C₄×C₇	—	2	2	no	—
327	C₂×C₄×C₇	—	2	16	no	—
328	C₂×C₄×C₇	—	2	8	no	—
329	C₂×C₄×C₇	—	2	2	no	—
330	C₂×C₄×C₇	—	2	2	no	—
331	C₂×C₄×C₇	—	2	4	no	—
332	C₂×C₄×C₇	—	4	4	no	—
333	C₂×C₄×C₇	—	4	8	no	—
334	C₂×C₄×C₇	—	4	16	no	—
335	C₂×C₄×C₇	—	4	8	no	—
336	C₂×C₄×C₇	—	4	2	no	—
337	C₂×C₄×C₇	—	4	4	no	—
338	C₂×C₄×C₇	—	4	2	no	—
339	C₂×C₄×C₇	—	4	8	no	—
340	C₂×C₄×C₇	—	4	16	no	—
341	C₂×C₄×C₇	C₄×D₄	1	4	yes	—
342	C₂×C₄×C₇	C₄×D₄	1	8	yes	—
343	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	direct product factor
344	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
345	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
346	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₇	C₂×#41	1	2	yes	—
353	C₂×C₄×C₇	C₂×#41	1	4	yes	—
354	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
355	C₇×C₈	—	2	4	no	—
356	C₇×C₈	C₂³×C₄	1	8	yes	complemented
357	C₂⁵	—	2	1	no	—
358	C₂×#41	—	2	2	no	—
359	C₂×#41	—	2	4	no	—
360	C₂×#41	C₂×C₄×C₇	1	8	yes	complemented
361	C₂×#41	C₂³×C₇	1	4	yes	—
362	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
363	C₂²×D₄	—	2	1	no	—
364	C₂²×D₄	—	2	1	no	—
365	C₂²×D₄	—	2	2	no	—
366	C₂²×D₄	—	2	4	no	—
367	C₂²×D₄	C₂×C₄×C₇	1	8	yes	complemented
368	C₂²×D₄	C₂³×C₇	1	2	yes	—
369	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
370	C₂²×D₄	C₂³×C₇	1	4	yes	—
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	—	2	1	no	—
373	C₂³×C₄	—	2	2	no	—
374	C₂³×C₄	—	2	2	no	—
375	C₂³×C₄	—	2	8	no	—
376	C₂³×C₄	—	2	1	no	—
377	C₂³×C₄	—	2	1	no	—
378	C₂³×C₄	—	4	8	no	—
379	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
380	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
382	AGL(1,ℤ/8)	C₂×C₄×C₇	1	64	yes	direct product factor
383	C₂×SD₁₆	C₂×C₄×C₇	1	16	yes	complemented
384	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
385	C₂×D₈	C₂×C₄×C₇	1	16	yes	complemented
386	C₂×D₈	C₂³×C₇	1	8	yes	—
387	C₂×M₁₆	—	2	4	no	—
388	C₂×M₁₆	C₂×C₄×C₇	1	8	yes	complemented
389	C₂×M₁₆	C₂³×C₇	1	4	yes	—
390	C₂×M₁₆	C₂³×C₇	1	4	yes	—
391	C₂²×C₈	C₂³×C₇	1	2	yes	—
392	C₂²×C₈	C₂³×C₇	1	2	yes	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	C₂³×C₇	1	4	yes	complemented
396	C₄×Q₈	C₂³×C₇	1	4	yes	complemented
397	C₄×D₄	—	2	8	no	—
398	C₄×D₄	—	2	8	no	—
399	C₄×D₄	—	2	4	no	—
400	C₄×D₄	—	2	4	no	—
401	C₄×D₄	—	2	8	no	—
402	C₄×D₄	—	2	8	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	C₂³×C₇	1	8	yes	—
406	C₄×D₄	C₂³×C₇	1	8	yes	—
407	C₄×D₄	C₂³×C₇	1	4	yes	complemented
408	C₄×D₄	C₂³×C₇	1	4	yes	complemented
409	#117	—	2	2	no	—
410	#117	—	2	8	no	—
411	#117	C₂³×C₇	1	4	yes	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	2	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
418	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	2	no	—
422	C₂×C₂²⋊C₄	—	2	2	no	—
423	C₂×C₂²⋊C₄	—	2	8	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	—	2	8	no	—
430	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
431	C₂×C₄²	C₇×D₄	1	4	yes	—
432	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₇	1	4	yes	—
436	#107	C₂³×C₇	1	8	yes	complemented
437	#106	C₂³×C₇	1	8	yes	complemented
438	#103	C₂³×C₇	1	8	yes	complemented
439	#102	C₂³×C₇	1	8	yes	—
440	#102	C₂³×C₇	1	8	yes	—
441	#102	C₂³×C₇	1	8	yes	complemented
442	#97	C₂³×C₇	1	8	yes	complemented
443	C₄×C₈	C₂³×C₇	1	8	yes	complemented
444	C₂²×C₇	—	2	8	no	—
445	C₂²×C₇	—	2	2	no	—
446	C₂²×C₇	—	2	2	no	—
447	C₂²×C₇	—	2	4	no	—
448	C₂²×C₇	—	2	8	no	—
449	C₂²×C₇	—	4	32	no	—
450	C₂²×C₇	—	4	8	no	—
451	C₂²×C₇	—	4	16	no	—
452	C₂²×C₇	—	4	4	no	—
453	C₂²×C₇	—	4	2	no	—
454	C₂²×C₇	—	4	2	no	—
455	C₂²×C₇	—	4	4	no	—
456	C₂²×C₇	C₂×C₄×D₄	1	4	yes	—
457	C₂²×C₇	C₂×C₄×D₄	1	2	yes	—
458	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
459	C₂²×C₇	#575	1	2	yes	—
460	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
461	C₄×C₇	—	2	4	no	—
462	C₄×C₇	—	2	2	no	—
463	C₄×C₇	—	2	2	no	—
464	C₄×C₇	—	2	2	no	—
465	C₄×C₇	—	4	2	no	—
466	C₄×C₇	—	4	4	no	—
467	C₄×C₇	—	4	2	no	—
468	C₄×C₇	C₂×C₄×D₄	1	4	yes	—
469	C₄×C₇	C₂×C₄×D₄	1	2	yes	—
470	C₄×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	direct product factor
471	C₄×C₇	C₂⁴×C₄	1	1	yes	characteristic
472	C₄×C₇	C₂²×#41	1	1	yes	characteristic
473	C₂⁴	—	2	8	no	—
474	C₂⁴	—	2	1	no	—
475	C₂⁴	—	2	2	no	—
476	C₂⁴	—	2	4	no	—
477	C₂⁴	—	4	4	no	—
478	C₂⁴	—	4	4	no	—
479	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
480	#41	—	2	16	no	—
481	#41	—	2	8	no	—
482	#41	C₂²×C₄×C₇	1	16	yes	complemented
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	2	no	—
485	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	complemented
486	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
487	C₂×D₄	—	2	8	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	2	8	no	—
490	C₂×D₄	—	2	16	no	—
491	C₂×D₄	—	2	4	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	4	no	—
495	C₂×D₄	—	2	8	no	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
498	C₂×D₄	C₂²×C₄×C₇	1	16	yes	complemented
499	C₂×D₄	C₂²×C₄×C₇	1	4	yes	complemented
500	C₂×D₄	C₂⁴×C₇	1	4	yes	—
501	C₂×D₄	C₂⁴×C₇	1	2	yes	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	8	no	—
504	C₂²×C₄	—	2	4	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	8	no	—
513	C₂²×C₄	—	2	8	no	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	—	4	8	no	—
516	C₂²×C₄	—	4	32	no	—
517	C₂²×C₄	—	4	4	no	—
518	C₂²×C₄	—	4	4	no	—
519	C₂²×C₄	—	4	8	no	—
520	C₂²×C₄	—	4	4	no	—
521	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
522	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
523	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
524	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
525	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
526	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
527	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
528	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
529	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
530	C₂²×C₄	C₇×#41	1	4	yes	—
531	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
533	SD₁₆	C₂²×C₄×C₇	1	32	yes	complemented
534	D₈	C₂²×C₄×C₇	1	32	yes	complemented
535	M₁₆	—	2	8	no	—
536	M₁₆	C₂²×C₄×C₇	1	16	yes	complemented
537	C₂×C₈	—	2	4	no	—
538	C₂×C₈	C₂²×C₄×C₇	1	8	yes	complemented
539	C₂×C₈	C₂⁴×C₇	1	4	yes	—
540	C₂×C₈	C₂⁴×C₇	1	4	yes	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
548	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
549	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
550	C₂²⋊C₄	—	2	4	no	—
551	C₂²⋊C₄	—	2	8	no	—
552	C₂²⋊C₄	—	2	8	no	—
553	C₂²⋊C₄	—	2	4	no	—
554	C₂²⋊C₄	—	2	4	no	—
555	C₄²	—	2	4	no	—
556	C₄²	—	2	4	no	—
557	C₄²	—	2	4	no	—
558	C₄²	C₂×C₇×D₄	1	4	yes	—
559	C₄²	C₂×C₇×D₄	1	4	yes	—
560	C₄²	C₂×C₇×D₄	1	2	yes	—
561	C₄²	C₂×C₇×D₄	1	2	yes	—
562	C₄²	C₂⁴×C₇	1	2	yes	—
563	C₄²	C₂⁴×C₇	1	2	yes	—
564	C₂×C₇	—	2	4	no	—
565	C₂×C₇	—	4	4	no	—
566	C₂×C₇	—	4	8	no	—
567	C₂×C₇	C₄×AGL(1,ℤ/8)	1	4	yes	direct product factor
568	C₂×C₇	C₂²×C₄×D₄	1	1	yes	characteristic
569	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
570	C₂×C₇	C₂×#575	1	1	yes	characteristic
571	C₂³	—	2	2	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	4	no	—
575	C₂³	—	2	4	no	—
576	C₂³	—	2	8	no	—
577	C₂³	—	2	16	no	—
578	C₂³	—	4	8	no	—
579	C₂³	—	4	8	no	—
580	C₂³	—	4	32	no	—
581	C₂³	—	4	4	no	—
582	C₂³	—	4	2	no	—
583	C₂³	—	4	2	no	—
584	C₂³	—	4	4	no	—
585	C₂³	C₄×C₇×D₄	1	4	yes	—
586	C₂³	C₂²×C₇×D₄	1	2	yes	—
587	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
588	Q₈	—	2	2	no	—
589	Q₈	—	2	4	no	—
590	Q₈	C₂³×C₄×C₇	1	4	yes	complemented
591	D₄	—	2	16	no	—
592	D₄	—	2	4	no	—
593	D₄	—	2	2	no	—
594	D₄	—	2	8	no	—
595	D₄	—	2	16	no	—
596	D₄	—	2	4	no	—
597	D₄	C₂³×C₄×C₇	1	8	yes	—
598	D₄	C₂³×C₄×C₇	1	4	yes	complemented
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	16	no	—
605	C₂×C₄	—	2	8	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	4	4	no	—
610	C₂×C₄	—	4	8	no	—
611	C₂×C₄	—	4	16	no	—
612	C₂×C₄	—	4	8	no	—
613	C₂×C₄	—	4	2	no	—
614	C₂×C₄	—	4	4	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	8	no	—
617	C₂×C₄	—	4	16	no	—
618	C₂×C₄	C₄×C₇×D₄	1	4	yes	—
619	C₂×C₄	C₄×C₇×D₄	1	8	yes	—
620	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	direct product factor
621	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
622	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
623	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
624	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
625	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
626	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
627	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
628	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
629	C₂×C₄	C₂×C₇×#41	1	2	yes	—
630	C₂×C₄	C₂×C₇×#41	1	4	yes	—
631	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
632	C₈	—	2	4	no	—
633	C₈	C₂³×C₄×C₇	1	8	yes	complemented
634	C₇	C₂×C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor, Sylow
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	8	no	—
638	C₂²	—	2	4	no	—
639	C₂²	—	2	8	no	—
640	C₂²	—	4	32	no	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	4	4	no	—
645	C₂²	—	4	16	no	—
646	C₂²	—	4	8	no	—
647	C₂²	C₂×C₄×C₇×D₄	1	4	yes	—
648	C₂²	C₂×C₄×C₇×D₄	1	2	yes	—
649	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
650	C₂²	C₇×#575	1	2	yes	—
651	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	4	no	—
656	C₄	—	4	4	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	2	no	—
659	C₄	C₂×C₄×C₇×D₄	1	4	yes	—
660	C₄	C₂×C₄×C₇×D₄	1	2	yes	—
661	C₄	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	direct product factor
662	C₄	C₂⁴×C₄×C₇	1	1	yes	characteristic
663	C₄	C₂²×C₇×#41	1	1	yes	characteristic
664	C₂	—	2	4	no	—
665	C₂	—	4	8	no	—
666	C₂	—	4	4	no	—
667	C₂	C₄×C₇×AGL(1,ℤ/8)	1	4	yes	direct product factor
668	C₂	C₂²×C₄×C₇×D₄	1	1	yes	characteristic
669	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
670	C₂	C₂×C₇×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂×D₄
commutator	C₄	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂³×C₇	C₂²×D₄
prime radical	C₂²×C₇×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₇×#41	C₂	semidirect
3. C₂²×C₄×C₇×D₄	C₂	semidirect
4. C₄×C₇×AGL(1,ℤ/8)	C₂	direct (N × H)
5. C₂×C₇×#442	C₂	semidirect
6. C₂×C₇×#440	C₂	semidirect
7. C₂×C₄×C₇×SD₁₆	C₂	semidirect
8. C₂×C₄×C₇×D₈	C₂	semidirect
9. C₂×C₇×#428	C₂	semidirect
10. C₂×C₇×#417	C₂	semidirect
11. C₂×C₇×#418	C₂	semidirect
12. C₂×C₄×C₇×M₁₆	C₂	semidirect
16. C₂×C₇×AGL(1,ℤ/8)	C₄	direct (N × H)
23. C₄×C₇×#41	C₂²	semidirect
24. C₂×C₄×C₇×Q₈	C₂²	semidirect
25. C₂×C₄×C₇×Q₈	C₂²	semidirect
33. C₂×C₄×C₇×D₄	C₂²	semidirect
34. C₂×C₄×C₇×D₄	C₂²	semidirect
35. C₂×C₄×C₇×D₄	C₂²	semidirect
42. C₇×#442	C₂²	semidirect
43. C₇×#440	C₂²	semidirect
44. C₄×C₇×SD₁₆	C₂²	semidirect
45. C₄×C₇×D₈	C₂²	semidirect
46. C₇×#428	C₂²	semidirect
47. C₂×C₇×#107	C₂²	semidirect
48. C₂×C₇×#106	C₂²	semidirect
49. C₇×#418	C₂²	semidirect
50. C₇×#417	C₂²	semidirect
51. C₂×C₇×#103	C₂²	semidirect
54. C₂×C₇×#102	C₂²	semidirect
55. C₄×C₇×M₁₆	C₂²	semidirect
56. C₂×C₇×#97	C₂²	semidirect
57. C₂×C₄×C₇×C₈	C₂²	semidirect
58. C₂×C₄×AGL(1,ℤ/8)	C₇	direct (N × H)
62. C₂×C₇×#41	C₂×C₄	semidirect
69. C₂²×C₇×D₄	C₂×C₄	semidirect
84. C₇×AGL(1,ℤ/8)	C₂×C₄	direct (N × H)
85. C₂×C₇×SD₁₆	C₂×C₄	semidirect
87. C₂×C₇×D₈	C₂×C₄	semidirect
90. C₂×C₇×M₁₆	C₂×C₄	semidirect
97. C₄×C₇×Q₈	C₂³	semidirect
98. C₄×C₇×Q₈	C₂³	semidirect
109. C₄×C₇×D₄	C₂³	semidirect
110. C₄×C₇×D₄	C₂³	semidirect
138. C₇×#107	C₂³	semidirect
139. C₇×#106	C₂³	semidirect
140. C₇×#103	C₂³	semidirect
143. C₇×#102	C₂³	semidirect
144. C₇×#97	C₂³	semidirect
145. C₄×C₇×C₈	C₂³	semidirect
147. C₂×C₄×#41	C₂×C₇	semidirect
148. C₂²×C₄×D₄	C₂×C₇	semidirect
149. C₄×AGL(1,ℤ/8)	C₂×C₇	direct (N × H)
150. C₂×#442	C₂×C₇	semidirect
151. C₂×#440	C₂×C₇	semidirect
152. C₂×C₄×SD₁₆	C₂×C₇	semidirect
153. C₂×C₄×D₈	C₂×C₇	semidirect
154. C₂×#428	C₂×C₇	semidirect
155. C₂×#417	C₂×C₇	semidirect
156. C₂×#418	C₂×C₇	semidirect
157. C₂×C₄×M₁₆	C₂×C₇	semidirect
167. C₇×#41	C₂²×C₄	semidirect
170. C₂×C₇×Q₈	C₂²×C₄	semidirect
183. C₂×C₇×D₄	C₂²×C₄	semidirect
184. C₂×C₇×D₄	C₂²×C₄	semidirect
218. C₇×SD₁₆	C₂²×C₄	semidirect
219. C₇×D₈	C₂²×C₄	semidirect
221. C₇×M₁₆	C₂²×C₄	semidirect
223. C₂×C₇×C₈	C₂²×C₄	semidirect
252. C₂×AGL(1,ℤ/8)	C₄×C₇	direct (N × H)
259. C₄×#41	C₂²×C₇	semidirect
260. C₂×C₄×Q₈	C₂²×C₇	semidirect
261. C₂×C₄×Q₈	C₂²×C₇	semidirect
269. C₂×C₄×D₄	C₂²×C₇	semidirect
270. C₂×C₄×D₄	C₂²×C₇	semidirect
271. C₂×C₄×D₄	C₂²×C₇	semidirect
278. #442	C₂²×C₇	semidirect
279. #440	C₂²×C₇	semidirect
280. C₄×SD₁₆	C₂²×C₇	semidirect
281. C₄×D₈	C₂²×C₇	semidirect
282. #428	C₂²×C₇	semidirect
283. C₂×#107	C₂²×C₇	semidirect
284. C₂×#106	C₂²×C₇	semidirect
285. #418	C₂²×C₇	semidirect
286. #417	C₂²×C₇	semidirect
287. C₂×#103	C₂²×C₇	semidirect
290. C₂×#102	C₂²×C₇	semidirect
291. C₄×M₁₆	C₂²×C₇	semidirect
292. C₂×#97	C₂²×C₇	semidirect
293. C₂×C₄×C₈	C₂²×C₇	semidirect
313. C₇×Q₈	C₂³×C₄	semidirect
321. C₇×D₄	C₂³×C₄	semidirect
343. C₂×C₄×C₇	AGL(1,ℤ/8)	direct (N × H)
356. C₇×C₈	C₂³×C₄	semidirect
360. C₂×#41	C₂×C₄×C₇	semidirect
367. C₂²×D₄	C₂×C₄×C₇	semidirect
382. AGL(1,ℤ/8)	C₂×C₄×C₇	direct (N × H)
383. C₂×SD₁₆	C₂×C₄×C₇	semidirect
385. C₂×D₈	C₂×C₄×C₇	semidirect
388. C₂×M₁₆	C₂×C₄×C₇	semidirect
395. C₄×Q₈	C₂³×C₇	semidirect
396. C₄×Q₈	C₂³×C₇	semidirect
407. C₄×D₄	C₂³×C₇	semidirect
408. C₄×D₄	C₂³×C₇	semidirect
436. #107	C₂³×C₇	semidirect
437. #106	C₂³×C₇	semidirect
438. #103	C₂³×C₇	semidirect
441. #102	C₂³×C₇	semidirect
442. #97	C₂³×C₇	semidirect
443. C₄×C₈	C₂³×C₇	semidirect
470. C₄×C₇	C₂×AGL(1,ℤ/8)	direct (N × H)
482. #41	C₂²×C₄×C₇	semidirect
485. C₂×Q₈	C₂²×C₄×C₇	semidirect
498. C₂×D₄	C₂²×C₄×C₇	semidirect
499. C₂×D₄	C₂²×C₄×C₇	semidirect
533. SD₁₆	C₂²×C₄×C₇	semidirect
534. D₈	C₂²×C₄×C₇	semidirect
536. M₁₆	C₂²×C₄×C₇	semidirect
538. C₂×C₈	C₂²×C₄×C₇	semidirect
567. C₂×C₇	C₄×AGL(1,ℤ/8)	direct (N × H)
590. Q₈	C₂³×C₄×C₇	semidirect
598. D₄	C₂³×C₄×C₇	semidirect
620. C₂×C₄	C₇×AGL(1,ℤ/8)	direct (N × H)
633. C₈	C₂³×C₄×C₇	semidirect
634. C₇	C₂×C₄×AGL(1,ℤ/8)	direct (N × H)
661. C₄	C₂×C₇×AGL(1,ℤ/8)	direct (N × H)
667. C₂	C₄×C₇×AGL(1,ℤ/8)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₇×AGL(1,ℤ/8)	2
C₂×C₄×C₇×#41	2
C₂²×C₄×C₇×D₄	2
C₄×C₇×AGL(1,ℤ/8)	2
C₂×C₇×#442	2
C₂×C₇×#440	2
C₂×C₄×C₇×SD₁₆	2
C₂×C₄×C₇×D₈	2
C₂×C₇×#428	2
C₂×C₇×#417	2
C₂×C₇×#418	2
C₂×C₄×C₇×M₁₆	2
C₂×C₄×AGL(1,ℤ/8)	7

Subgroups — C2×C4×C7×AGL(1,ℤ/8) #13237372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₇×AGL(1,ℤ/8) #13237372