Subgroups — D₃×C₇×AGL(1,ℤ/8) #13061488

Order 1344.

596 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#949	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#932	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#914	C₂	1	2	yes	maximal, complemented
7	D₃×C₇×SD₁₆	C₂	1	2	yes	maximal, complemented
8	C₇×#911	C₂	1	2	yes	maximal, complemented
9	D₃×C₇×D₈	C₂	1	2	yes	maximal, complemented
10	C₇×#908	C₂	1	1	yes	maximal, characteristic, complemented
11	D₃×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×AGL(1,ℤ/8)	—	3	1	no	maximal, Hall
13	C₂³×D₃×C₇	—	2	1	no	—
14	C₃×C₇×#41	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₇×#67	—	2	1	no	—
17	C₇×#239	C₂²	1	1	yes	characteristic, complemented
18	D₃×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₇×#237	—	2	1	no	—
20	C₇×#237	C₂²	1	1	yes	characteristic, complemented
21	D₃×C₇×D₄	—	2	1	no	—
22	D₃×C₇×D₄	—	2	1	no	—
23	D₃×C₇×D₄	—	2	1	no	—
24	D₃×C₇×D₄	C₂²	1	2	yes	—
25	D₃×C₇×D₄	C₂²	1	2	yes	complemented
26	D₃×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
27	C₇×#235	—	2	1	no	—
28	C₇×#235	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₇×D₁₂	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×D₃×C₇	—	2	1	no	—
31	C₂×C₄×D₃×C₇	C₂²	1	1	yes	characteristic
32	C₃×C₇×SD₁₆	C₂²	1	2	yes	complemented
33	C₃×C₇×D₈	C₂²	1	2	yes	complemented
34	C₃×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₇×#215	C₂²	1	2	yes	complemented
36	C₇×#214	C₂²	1	2	yes	complemented
37	C₇×#213	C₂²	1	2	yes	complemented
38	C₇×#213	C₂²	1	2	yes	complemented
39	C₇×#208	C₂²	1	1	yes	characteristic, complemented
40	C₇×D₂₄	C₂²	1	2	yes	complemented
41	C₇×#204	C₂²	1	2	yes	complemented
42	C₇×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
43	D₃×C₇×C₈	C₂²	1	2	yes	complemented
44	C₂×C₇×#41	—	3	1	no	—
45	C₂²×C₇×D₄	—	3	1	no	—
46	C₇×AGL(1,ℤ/8)	—	3	1	no	—
47	C₇×AGL(1,ℤ/8)	—	3	1	no	—
48	C₇×AGL(1,ℤ/8)	—	3	2	no	—
49	C₇×AGL(1,ℤ/8)	—	3	2	no	—
50	C₇×AGL(1,ℤ/8)	—	3	1	no	—
51	C₇×AGL(1,ℤ/8)	D₃	1	1	yes	characteristic, direct product factor
52	C₂×C₇×SD₁₆	—	3	2	no	—
53	C₂×C₇×D₈	—	3	2	no	—
54	C₂×C₇×M₁₆	—	3	1	no	—
55	D₃×AGL(1,ℤ/8)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
56	C₂³×C₃×C₇	—	2	1	no	—
57	C₂²×D₃×C₇	—	2	1	no	—
58	C₂²×D₃×C₇	—	2	1	no	—
59	C₂²×D₃×C₇	—	2	2	no	—
60	C₂²×D₃×C₇	—	2	2	no	—
61	C₂²×D₃×C₇	—	4	4	no	—
62	C₂²×D₃×C₇	D₄	1	1	yes	characteristic
63	C₃×C₇×Q₈	C₂³	1	1	yes	characteristic, complemented
64	C₃×C₇×D₄	—	2	1	no	—
65	C₃×C₇×D₄	—	2	1	no	—
66	C₃×C₇×D₄	C₂³	1	2	yes	—
67	C₃×C₇×D₄	C₂³	1	1	yes	characteristic, complemented
68	C₂×C₃×C₄×C₇	—	2	1	no	—
69	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
70	C₇×#67	—	2	1	no	—
71	C₇×#67	—	2	1	no	—
72	C₇×#67	—	2	1	no	—
73	C₇×#67	—	2	2	no	—
74	C₇×#67	—	2	2	no	—
75	C₂×C₇×Dic₃	—	2	1	no	—
76	C₂×C₇×Dic₃	D₄	1	1	yes	characteristic
77	C₇×D₁₂	—	2	1	no	—
78	C₇×D₁₂	—	2	1	no	—
79	C₇×D₁₂	C₂³	1	2	yes	—
80	C₇×D₁₂	C₂³	1	1	yes	characteristic, complemented
81	C₄×D₃×C₇	—	2	1	no	—
82	C₄×D₃×C₇	—	2	1	no	—
83	C₄×D₃×C₇	—	2	1	no	—
84	C₄×D₃×C₇	D₄	1	1	yes	characteristic
85	C₄×D₃×C₇	D₄	1	1	yes	characteristic
86	C₄×D₃×C₇	C₂³	1	1	yes	characteristic
87	C₄×D₃×C₇	C₂³	1	1	yes	characteristic
88	C₇×Dic₆	—	2	1	no	—
89	C₇×Dic₆	C₂³	1	1	yes	characteristic, complemented
90	C₃×C₇×C₈	C₂³	1	2	yes	complemented
91	C₇×C₃⋊C₈	C₂³	1	2	yes	complemented
92	C₂⁴×C₇	—	6	1	no	—
93	C₇×#41	—	3	1	no	—
94	C₇×#41	—	3	1	no	—
95	C₇×#41	—	3	1	no	—
96	C₇×#41	—	6	1	no	—
97	C₇×#41	—	6	1	no	—
98	C₇×#41	C₂×D₃	1	1	yes	characteristic, complemented
99	C₂×C₇×Q₈	—	3	1	no	—
100	C₂×C₇×D₄	—	3	2	no	—
101	C₂×C₇×D₄	—	3	2	no	—
102	C₂×C₇×D₄	—	3	1	no	—
103	C₂×C₇×D₄	—	3	1	no	—
104	C₂×C₇×D₄	—	6	1	no	—
105	C₂×C₇×D₄	—	6	1	no	—
106	C₂×C₇×D₄	—	6	1	no	—
107	C₂×C₇×D₄	—	6	1	no	—
108	C₂×C₇×D₄	C₂×D₃	1	1	yes	characteristic, complemented
109	C₂²×C₄×C₇	—	3	1	no	—
110	C₂²×C₄×C₇	—	6	1	no	—
111	C₇×SD₁₆	—	3	2	no	—
112	C₇×SD₁₆	—	3	2	no	—
113	C₇×SD₁₆	—	3	2	no	—
114	C₇×SD₁₆	C₂×D₃	1	2	yes	complemented
115	C₇×D₈	—	3	2	no	—
116	C₇×D₈	—	3	2	no	—
117	C₇×D₈	—	3	2	no	—
118	C₇×D₈	C₂×D₃	1	2	yes	complemented
119	C₇×M₁₆	—	3	1	no	—
120	C₇×M₁₆	—	3	2	no	—
121	C₇×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
122	C₂×C₇×C₈	—	3	2	no	—
123	D₃×#41	C₂×C₇	1	1	yes	characteristic, complemented
124	C₂×D₃×D₄	C₂×C₇	1	1	yes	characteristic, complemented
125	C₃×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic, complemented
126	#949	C₂×C₇	1	1	yes	characteristic, complemented
127	#932	C₂×C₇	1	1	yes	characteristic, complemented
128	#914	C₂×C₇	1	2	yes	complemented
129	D₃×SD₁₆	C₂×C₇	1	2	yes	complemented
130	#911	C₂×C₇	1	2	yes	complemented
131	D₃×D₈	C₂×C₇	1	2	yes	complemented
132	#908	C₂×C₇	1	1	yes	characteristic, complemented
133	D₃×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
134	C₂²×C₃×C₇	—	2	1	no	—
135	C₂²×C₃×C₇	—	2	2	no	—
136	C₂²×C₃×C₇	—	4	2	no	—
137	C₂²×C₃×C₇	C₂×D₄	1	1	yes	characteristic
138	C₂×D₃×C₇	—	2	2	no	—
139	C₂×D₃×C₇	—	2	1	no	—
140	C₂×D₃×C₇	—	2	2	no	—
141	C₂×D₃×C₇	—	4	4	no	—
142	C₂×D₃×C₇	—	4	2	no	—
143	C₂×D₃×C₇	—	4	2	no	—
144	C₂×D₃×C₇	—	4	4	no	—
145	C₂×D₃×C₇	C₂×D₄	1	1	yes	characteristic
146	C₂×D₃×C₇	C₂×D₄	1	1	yes	characteristic
147	C₃×C₄×C₇	—	2	1	no	—
148	C₃×C₄×C₇	C₂×D₄	1	1	yes	characteristic
149	C₃×C₄×C₇	C₂⁴	1	1	yes	characteristic
150	C₇×Dic₃	—	2	1	no	—
151	C₇×Dic₃	C₂×D₄	1	1	yes	characteristic
152	C₇×Dic₃	C₂×D₄	1	1	yes	characteristic
153	C₂×AGL(1,ℤ/8)	—	3	1	no	Sylow
154	C₂³×C₇	—	2	1	no	—
155	C₂³×C₇	—	3	1	no	—
156	C₂³×C₇	—	6	1	no	—
157	C₂³×C₇	—	6	2	no	—
158	C₂³×C₇	—	6	2	no	—
159	C₂³×C₇	—	6	1	no	—
160	C₂³×C₇	—	12	4	no	—
161	C₇×Q₈	—	3	1	no	—
162	C₇×Q₈	—	6	1	no	—
163	C₇×Q₈	C₂²×D₃	1	1	yes	characteristic, complemented
164	C₇×D₄	—	2	1	no	—
165	C₇×D₄	—	2	1	no	—
166	C₇×D₄	—	3	1	no	—
167	C₇×D₄	—	3	2	no	—
168	C₇×D₄	—	6	1	no	—
169	C₇×D₄	—	6	2	no	—
170	C₇×D₄	—	6	2	no	—
171	C₇×D₄	—	6	1	no	—
172	C₇×D₄	—	6	1	no	—
173	C₇×D₄	—	6	1	no	—
174	C₇×D₄	—	6	1	no	—
175	C₇×D₄	C₂²×D₃	1	2	yes	—
176	C₇×D₄	C₂²×D₃	1	1	yes	characteristic, complemented
177	C₂×C₄×C₇	—	2	1	no	—
178	C₂×C₄×C₇	—	3	1	no	—
179	C₂×C₄×C₇	—	3	1	no	—
180	C₂×C₄×C₇	—	3	1	no	—
181	C₂×C₄×C₇	—	3	1	no	—
182	C₂×C₄×C₇	—	3	1	no	—
183	C₂×C₄×C₇	—	6	1	no	—
184	C₂×C₄×C₇	—	6	1	no	—
185	C₂×C₄×C₇	—	6	1	no	—
186	C₂×C₄×C₇	—	6	1	no	—
187	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
188	C₇×C₈	—	3	2	no	—
189	C₇×C₈	C₂²×D₃	1	2	yes	complemented
190	C₂³×D₃	—	2	1	no	—
191	C₃×#41	C₂²×C₇	1	1	yes	characteristic, complemented
192	C₂×C₃×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
193	C₂×#67	—	2	1	no	—
194	#239	C₂²×C₇	1	1	yes	characteristic, complemented
195	D₃×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
196	#237	—	2	1	no	—
197	#237	C₂²×C₇	1	1	yes	characteristic, complemented
198	D₃×D₄	—	2	1	no	—
199	D₃×D₄	—	2	1	no	—
200	D₃×D₄	—	2	1	no	—
201	D₃×D₄	C₂²×C₇	1	2	yes	—
202	D₃×D₄	C₂²×C₇	1	2	yes	complemented
203	D₃×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
204	#235	—	2	1	no	—
205	#235	C₂²×C₇	1	1	yes	characteristic, complemented
206	C₂×D₁₂	C₂²×C₇	1	1	yes	characteristic, complemented
207	C₂×C₄×D₃	—	2	1	no	—
208	C₂×C₄×D₃	C₂²×C₇	1	1	yes	characteristic
209	C₃×SD₁₆	C₂²×C₇	1	2	yes	complemented
210	C₃×D₈	C₂²×C₇	1	2	yes	complemented
211	C₃×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
212	#215	C₂²×C₇	1	2	yes	complemented
213	#214	C₂²×C₇	1	2	yes	complemented
214	#213	C₂²×C₇	1	2	yes	complemented
215	#213	C₂²×C₇	1	2	yes	complemented
216	#208	C₂²×C₇	1	1	yes	characteristic, complemented
217	D₂₄	C₂²×C₇	1	2	yes	complemented
218	#204	C₂²×C₇	1	2	yes	complemented
219	ΓL(1,𝔽₂₅)	C₂²×C₇	1	2	yes	complemented
220	D₃×C₈	C₂²×C₇	1	2	yes	complemented
221	C₂×C₃×C₇	—	2	1	no	—
222	C₂×C₃×C₇	—	4	2	no	—
223	C₂×C₃×C₇	—	4	1	no	—
224	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
225	D₃×C₇	—	2	1	no	—
226	D₃×C₇	—	4	1	no	—
227	D₃×C₇	—	4	2	no	—
228	D₃×C₇	AGL(1,ℤ/8)	1	2	yes	direct product factor
229	C₂×#41	—	3	1	no	—
230	C₂²×D₄	—	3	1	no	—
231	AGL(1,ℤ/8)	—	3	1	no	—
232	AGL(1,ℤ/8)	—	3	1	no	—
233	AGL(1,ℤ/8)	—	3	2	no	—
234	AGL(1,ℤ/8)	—	3	2	no	—
235	AGL(1,ℤ/8)	—	3	1	no	—
236	AGL(1,ℤ/8)	D₃×C₇	1	1	yes	characteristic, direct product factor
237	C₂×SD₁₆	—	3	2	no	—
238	C₂×D₈	—	3	2	no	—
239	C₂×M₁₆	—	3	1	no	—
240	C₂²×C₇	—	2	1	no	—
241	C₂²×C₇	—	2	2	no	—
242	C₂²×C₇	—	3	1	no	—
243	C₂²×C₇	—	3	1	no	—
244	C₂²×C₇	—	4	2	no	—
245	C₂²×C₇	—	6	2	no	—
246	C₂²×C₇	—	6	1	no	—
247	C₂²×C₇	—	6	2	no	—
248	C₂²×C₇	—	12	2	no	—
249	C₂²×C₇	—	12	4	no	—
250	C₂²×C₇	—	12	2	no	—
251	C₂²×C₇	—	12	4	no	—
252	C₂²×C₇	D₃×D₄	1	1	yes	characteristic
253	C₄×C₇	—	2	1	no	—
254	C₄×C₇	—	3	1	no	—
255	C₄×C₇	—	3	1	no	—
256	C₄×C₇	—	6	1	no	—
257	C₄×C₇	D₃×D₄	1	1	yes	characteristic
258	C₄×C₇	C₂³×D₃	1	1	yes	characteristic
259	C₂³×C₃	—	2	1	no	—
260	C₂²×D₃	—	2	1	no	—
261	C₂²×D₃	—	2	1	no	—
262	C₂²×D₃	—	2	2	no	—
263	C₂²×D₃	—	2	2	no	—
264	C₂²×D₃	—	4	4	no	—
265	C₂²×D₃	C₇×D₄	1	1	yes	characteristic
266	C₃×Q₈	C₂³×C₇	1	1	yes	characteristic, complemented
267	C₃×D₄	—	2	1	no	—
268	C₃×D₄	—	2	1	no	—
269	C₃×D₄	C₂³×C₇	1	2	yes	—
270	C₃×D₄	C₂³×C₇	1	1	yes	characteristic, complemented
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	C₂³×C₇	1	1	yes	characteristic
273	#67	—	2	1	no	—
274	#67	—	2	1	no	—
275	#67	—	2	1	no	—
276	#67	—	2	2	no	—
277	#67	—	2	2	no	—
278	C₂×Dic₃	—	2	1	no	—
279	C₂×Dic₃	C₇×D₄	1	1	yes	characteristic
280	D₁₂	—	2	1	no	—
281	D₁₂	—	2	1	no	—
282	D₁₂	C₂³×C₇	1	2	yes	—
283	D₁₂	C₂³×C₇	1	1	yes	characteristic, complemented
284	C₄×D₃	—	2	1	no	—
285	C₄×D₃	—	2	1	no	—
286	C₄×D₃	—	2	1	no	—
287	C₄×D₃	C₇×D₄	1	1	yes	characteristic
288	C₄×D₃	C₇×D₄	1	1	yes	characteristic
289	C₄×D₃	C₂³×C₇	1	1	yes	characteristic
290	C₄×D₃	C₂³×C₇	1	1	yes	characteristic
291	Dic₆	—	2	1	no	—
292	Dic₆	C₂³×C₇	1	1	yes	characteristic, complemented
293	C₃×C₈	C₂³×C₇	1	2	yes	complemented
294	C₃⋊C₈	C₂³×C₇	1	2	yes	complemented
295	C₃×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Hall
296	C₂⁴	—	6	1	no	—
297	#41	—	3	1	no	—
298	#41	—	3	1	no	—
299	#41	—	3	1	no	—
300	#41	—	6	1	no	—
301	#41	—	6	1	no	—
302	#41	C₂×D₃×C₇	1	1	yes	characteristic, complemented
303	C₂×Q₈	—	3	1	no	—
304	C₂×D₄	—	3	2	no	—
305	C₂×D₄	—	3	2	no	—
306	C₂×D₄	—	3	1	no	—
307	C₂×D₄	—	3	1	no	—
308	C₂×D₄	—	6	1	no	—
309	C₂×D₄	—	6	1	no	—
310	C₂×D₄	—	6	1	no	—
311	C₂×D₄	—	6	1	no	—
312	C₂×D₄	C₂×D₃×C₇	1	1	yes	characteristic, complemented
313	C₂²×C₄	—	3	1	no	—
314	C₂²×C₄	—	6	1	no	—
315	SD₁₆	—	3	2	no	—
316	SD₁₆	—	3	2	no	—
317	SD₁₆	—	3	2	no	—
318	SD₁₆	C₂×D₃×C₇	1	2	yes	complemented
319	D₈	—	3	2	no	—
320	D₈	—	3	2	no	—
321	D₈	—	3	2	no	—
322	D₈	C₂×D₃×C₇	1	2	yes	complemented
323	M₁₆	—	3	1	no	—
324	M₁₆	—	3	2	no	—
325	M₁₆	C₂×D₃×C₇	1	1	yes	characteristic, complemented
326	C₂×C₈	—	3	2	no	—
327	C₂×C₇	—	2	1	no	—
328	C₂×C₇	—	3	2	no	—
329	C₂×C₇	—	4	2	no	—
330	C₂×C₇	—	4	1	no	—
331	C₂×C₇	—	6	1	no	—
332	C₂×C₇	—	12	2	no	—
333	C₂×C₇	—	12	1	no	—
334	C₂×C₇	C₂×D₃×D₄	1	1	yes	characteristic
335	C₂²×C₃	—	2	1	no	—
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	4	2	no	—
338	C₂²×C₃	C₂×C₇×D₄	1	1	yes	characteristic
339	C₂×D₃	—	2	2	no	—
340	C₂×D₃	—	2	1	no	—
341	C₂×D₃	—	2	2	no	—
342	C₂×D₃	—	4	4	no	—
343	C₂×D₃	—	4	2	no	—
344	C₂×D₃	—	4	4	no	—
345	C₂×D₃	—	4	2	no	—
346	C₂×D₃	C₂×C₇×D₄	1	1	yes	characteristic
347	C₂×D₃	C₂×C₇×D₄	1	1	yes	characteristic
348	C₃×C₄	—	2	1	no	—
349	C₃×C₄	C₂×C₇×D₄	1	1	yes	characteristic
350	C₃×C₄	C₂⁴×C₇	1	1	yes	characteristic
351	Dic₃	—	2	1	no	—
352	Dic₃	C₂×C₇×D₄	1	1	yes	characteristic
353	Dic₃	C₂×C₇×D₄	1	1	yes	characteristic
354	C₂³	—	2	1	no	—
355	C₂³	—	3	1	no	—
356	C₂³	—	6	1	no	—
357	C₂³	—	6	2	no	—
358	C₂³	—	6	2	no	—
359	C₂³	—	6	1	no	—
360	C₂³	—	12	4	no	—
361	Q₈	—	3	1	no	—
362	Q₈	—	6	1	no	—
363	Q₈	C₂²×D₃×C₇	1	1	yes	characteristic, complemented
364	D₄	—	2	1	no	—
365	D₄	—	2	1	no	—
366	D₄	—	3	1	no	—
367	D₄	—	3	2	no	—
368	D₄	—	6	1	no	—
369	D₄	—	6	2	no	—
370	D₄	—	6	2	no	—
371	D₄	—	6	1	no	—
372	D₄	—	6	1	no	—
373	D₄	—	6	1	no	—
374	D₄	—	6	1	no	—
375	D₄	C₂²×D₃×C₇	1	2	yes	—
376	D₄	C₂²×D₃×C₇	1	1	yes	characteristic, complemented
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	3	1	no	—
379	C₂×C₄	—	3	1	no	—
380	C₂×C₄	—	3	1	no	—
381	C₂×C₄	—	3	1	no	—
382	C₂×C₄	—	3	1	no	—
383	C₂×C₄	—	6	1	no	—
384	C₂×C₄	—	6	1	no	—
385	C₂×C₄	—	6	1	no	—
386	C₂×C₄	—	6	1	no	—
387	C₂×C₄	C₂²×D₃×C₇	1	1	yes	characteristic
388	C₈	—	3	2	no	—
389	C₈	C₂²×D₃×C₇	1	2	yes	complemented
390	C₇	D₃×AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor, Sylow
391	C₂×C₃	—	2	1	no	—
392	C₂×C₃	—	4	2	no	—
393	C₂×C₃	—	4	1	no	—
394	C₂×C₃	C₂²×C₇×D₄	1	1	yes	characteristic
395	D₃	—	2	1	no	—
396	D₃	—	4	2	no	—
397	D₃	—	4	1	no	—
398	D₃	C₇×AGL(1,ℤ/8)	1	2	yes	direct product factor
399	C₂²	—	2	1	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	3	1	no	—
402	C₂²	—	3	1	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	6	2	no	—
405	C₂²	—	6	1	no	—
406	C₂²	—	6	2	no	—
407	C₂²	—	12	2	no	—
408	C₂²	—	12	4	no	—
409	C₂²	—	12	2	no	—
410	C₂²	—	12	4	no	—
411	C₂²	D₃×C₇×D₄	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	3	1	no	—
414	C₄	—	3	1	no	—
415	C₄	—	6	1	no	—
416	C₄	D₃×C₇×D₄	1	1	yes	characteristic
417	C₄	C₂³×D₃×C₇	1	1	yes	characteristic
418	C₃	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
419	C₂	—	2	1	no	—
420	C₂	—	3	2	no	—
421	C₂	—	4	2	no	—
422	C₂	—	4	1	no	—
423	C₂	—	6	1	no	—
424	C₂	—	12	2	no	—
425	C₂	—	12	1	no	—
426	C₂	C₂×D₃×C₇×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₇	C₂×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁴×C₇
Frattini	C₄	C₂³×D₃×C₇
Fitting	C₃×C₇×AGL(1,ℤ/8)	C₂
socle	C₂×C₃×C₇	C₂²×D₄
hypercenter	C₇×AGL(1,ℤ/8)	D₃
hypocenter	C₃	C₂×C₇×AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₇ ◁ C₂×C₄×C₇ ◁ C₇×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. D₃×C₇×#41	C₂	semidirect
2. C₂×D₃×C₇×D₄	C₂	semidirect
3. C₃×C₇×AGL(1,ℤ/8)	C₂	semidirect
4. C₇×#949	C₂	semidirect
5. C₇×#932	C₂	semidirect
6. C₇×#914	C₂	semidirect
7. D₃×C₇×SD₁₆	C₂	semidirect
8. C₇×#911	C₂	semidirect
9. D₃×C₇×D₈	C₂	semidirect
10. C₇×#908	C₂	semidirect
11. D₃×C₇×M₁₆	C₂	semidirect
14. C₃×C₇×#41	C₂²	semidirect
15. C₂×C₃×C₇×D₄	C₂²	semidirect
17. C₇×#239	C₂²	semidirect
18. D₃×C₇×Q₈	C₂²	semidirect
20. C₇×#237	C₂²	semidirect
25. D₃×C₇×D₄	C₂²	semidirect
26. D₃×C₇×D₄	C₂²	semidirect
28. C₇×#235	C₂²	semidirect
29. C₂×C₇×D₁₂	C₂²	semidirect
32. C₃×C₇×SD₁₆	C₂²	semidirect
33. C₃×C₇×D₈	C₂²	semidirect
34. C₃×C₇×M₁₆	C₂²	semidirect
35. C₇×#215	C₂²	semidirect
36. C₇×#214	C₂²	semidirect
37. C₇×#213	C₂²	semidirect
38. C₇×#213	C₂²	semidirect
39. C₇×#208	C₂²	semidirect
40. C₇×D₂₄	C₂²	semidirect
41. C₇×#204	C₂²	semidirect
42. C₇×ΓL(1,𝔽₂₅)	C₂²	semidirect
43. D₃×C₇×C₈	C₂²	semidirect
51. C₇×AGL(1,ℤ/8)	D₃	direct (N × H)
55. D₃×AGL(1,ℤ/8)	C₇	direct (N × H)
63. C₃×C₇×Q₈	C₂³	semidirect
67. C₃×C₇×D₄	C₂³	semidirect
80. C₇×D₁₂	C₂³	semidirect
89. C₇×Dic₆	C₂³	semidirect
90. C₃×C₇×C₈	C₂³	semidirect
91. C₇×C₃⋊C₈	C₂³	semidirect
98. C₇×#41	C₂×D₃	semidirect
108. C₂×C₇×D₄	C₂×D₃	semidirect
114. C₇×SD₁₆	C₂×D₃	semidirect
118. C₇×D₈	C₂×D₃	semidirect
121. C₇×M₁₆	C₂×D₃	semidirect
123. D₃×#41	C₂×C₇	semidirect
124. C₂×D₃×D₄	C₂×C₇	semidirect
125. C₃×AGL(1,ℤ/8)	C₂×C₇	semidirect
126. #949	C₂×C₇	semidirect
127. #932	C₂×C₇	semidirect
128. #914	C₂×C₇	semidirect
129. D₃×SD₁₆	C₂×C₇	semidirect
130. #911	C₂×C₇	semidirect
131. D₃×D₈	C₂×C₇	semidirect
132. #908	C₂×C₇	semidirect
133. D₃×M₁₆	C₂×C₇	semidirect
163. C₇×Q₈	C₂²×D₃	semidirect
176. C₇×D₄	C₂²×D₃	semidirect
189. C₇×C₈	C₂²×D₃	semidirect
191. C₃×#41	C₂²×C₇	semidirect
192. C₂×C₃×D₄	C₂²×C₇	semidirect
194. #239	C₂²×C₇	semidirect
195. D₃×Q₈	C₂²×C₇	semidirect
197. #237	C₂²×C₇	semidirect
202. D₃×D₄	C₂²×C₇	semidirect
203. D₃×D₄	C₂²×C₇	semidirect
205. #235	C₂²×C₇	semidirect
206. C₂×D₁₂	C₂²×C₇	semidirect
209. C₃×SD₁₆	C₂²×C₇	semidirect
210. C₃×D₈	C₂²×C₇	semidirect
211. C₃×M₁₆	C₂²×C₇	semidirect
212. #215	C₂²×C₇	semidirect
213. #214	C₂²×C₇	semidirect
214. #213	C₂²×C₇	semidirect
215. #213	C₂²×C₇	semidirect
216. #208	C₂²×C₇	semidirect
217. D₂₄	C₂²×C₇	semidirect
218. #204	C₂²×C₇	semidirect
219. ΓL(1,𝔽₂₅)	C₂²×C₇	semidirect
220. D₃×C₈	C₂²×C₇	semidirect
228. D₃×C₇	AGL(1,ℤ/8)	direct (N × H)
236. AGL(1,ℤ/8)	D₃×C₇	direct (N × H)
266. C₃×Q₈	C₂³×C₇	semidirect
270. C₃×D₄	C₂³×C₇	semidirect
283. D₁₂	C₂³×C₇	semidirect
292. Dic₆	C₂³×C₇	semidirect
293. C₃×C₈	C₂³×C₇	semidirect
294. C₃⋊C₈	C₂³×C₇	semidirect
295. C₃×C₇	C₂×AGL(1,ℤ/8)	semidirect
302. #41	C₂×D₃×C₇	semidirect
312. C₂×D₄	C₂×D₃×C₇	semidirect
318. SD₁₆	C₂×D₃×C₇	semidirect
322. D₈	C₂×D₃×C₇	semidirect
325. M₁₆	C₂×D₃×C₇	semidirect
363. Q₈	C₂²×D₃×C₇	semidirect
376. D₄	C₂²×D₃×C₇	semidirect
389. C₈	C₂²×D₃×C₇	semidirect
390. C₇	D₃×AGL(1,ℤ/8)	direct (N × H)
398. D₃	C₇×AGL(1,ℤ/8)	direct (N × H)
418. C₃	C₂×C₇×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
D₃×C₇×#41	2
C₂×D₃×C₇×D₄	2
C₃×C₇×AGL(1,ℤ/8)	2
C₇×#949	2
C₇×#932	2
C₇×#914	2
D₃×C₇×SD₁₆	2
C₇×#911	2
D₃×C₇×D₈	2
C₇×#908	2
D₃×C₇×M₁₆	2
C₂×C₇×AGL(1,ℤ/8)	3
D₃×AGL(1,ℤ/8)	7

Subgroups — D3×C7×AGL(1,ℤ/8) #13061488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×AGL(1,ℤ/8) #13061488