Subgroups — C₂×C₇×#3366 #13238520

Order 1792.

2198 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3366	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#490	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#486	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#478	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#459	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#442	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	—	2	1	no	—
14	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
15	C₂²×C₇×D₈	C₂²	1	2	yes	—
16	C₇×#554	—	2	4	no	—
17	C₇×#554	C₂²	1	8	yes	complemented
18	C₇×#550	—	2	4	no	—
19	C₇×#550	C₂²	1	8	yes	complemented
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×#127	C₂²	1	1	yes	characteristic
22	C₂×C₇×#127	C₂²	1	2	yes	—
23	C₂×C₇×#125	C₂²	1	2	yes	—
24	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₇×#121	—	2	1	no	—
27	C₂×C₇×#121	—	2	2	no	—
28	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
32	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
33	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
34	C₇×#490	C₂²	1	16	yes	complemented
35	C₇×#486	C₂²	1	8	yes	complemented
36	C₇×#478	C₂²	1	16	yes	complemented
37	C₇×#476	C₂²	1	8	yes	complemented
38	C₇×#459	C₂²	1	16	yes	complemented
39	C₇×#459	C₂²	1	8	yes	complemented
40	C₇×#446	C₂²	1	8	yes	complemented
41	C₇×#442	C₂²	1	16	yes	complemented
42	C₄×C₇×D₈	C₂²	1	8	yes	complemented
43	C₂×C₇×#107	C₂²	1	1	yes	characteristic
44	C₂×C₇×#106	C₂²	1	2	yes	—
45	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
47	C₂×C₇×#102	C₂²	1	1	yes	characteristic
48	C₂×C₇×#102	C₂²	1	1	yes	characteristic
49	C₂×C₇×#102	C₂²	1	2	yes	—
50	C₂×C₇×#102	C₂²	1	2	yes	—
51	C₂×C₇×#102	C₂²	1	2	yes	—
52	C₂×C₇×#102	C₂²	1	2	yes	—
53	C₂×C₇×#97	C₂²	1	2	yes	—
54	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
55	C₂×#3366	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂×C₇×#41	—	2	8	no	—
57	C₂×C₇×#41	—	4	8	no	—
58	C₂²×C₇×Q₈	—	2	1	no	—
59	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
60	C₂²×C₇×D₄	—	2	2	no	—
61	C₂²×C₇×D₄	—	2	1	no	—
62	C₂²×C₇×D₄	—	2	1	no	—
63	C₂²×C₇×D₄	—	2	2	no	—
64	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₇×D₄	C₂³	1	2	yes	—
66	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₇	—	2	2	no	—
68	C₂³×C₄×C₇	—	2	1	no	—
69	C₂³×C₄×C₇	—	2	1	no	—
70	C₂³×C₄×C₇	—	2	2	no	—
71	C₂×C₇×D₈	—	2	4	no	—
72	C₂×C₇×D₈	—	2	8	no	—
73	C₂×C₇×D₈	C₂³	1	4	yes	—
74	C₂×C₇×D₈	C₂³	1	8	yes	—
75	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₇×C₈	C₂³	1	2	yes	—
78	C₇×C₄⋊Q₈	—	2	2	no	—
79	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
80	C₇×#127	—	2	4	no	—
81	C₇×#127	—	2	2	no	—
82	C₇×#127	C₂³	1	4	yes	—
83	C₇×#127	C₂³	1	8	yes	—
84	C₇×#125	—	2	4	no	—
85	C₇×#125	C₂³	1	8	yes	—
86	C₇×C₂²⋊Q₈	—	2	8	no	—
87	C₇×C₂²⋊Q₈	—	2	16	no	—
88	C₇×#121	—	2	8	no	—
89	C₇×#121	—	2	16	no	—
90	C₄×C₇×Q₈	D₄	1	4	yes	—
91	C₄×C₇×Q₈	C₂³	1	4	yes	—
92	C₄×C₇×D₄	—	2	4	no	—
93	C₄×C₇×D₄	—	2	2	no	—
94	C₄×C₇×D₄	—	2	4	no	—
95	C₄×C₇×D₄	—	2	2	no	—
96	C₄×C₇×D₄	C₂³	1	4	yes	—
97	C₄×C₇×D₄	C₂³	1	8	yes	—
98	C₄×C₇×D₄	C₂³	1	4	yes	—
99	C₄×C₇×D₄	C₂³	1	8	yes	—
100	C₂×C₇×C₄⋊C₄	—	2	2	no	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	—	2	2	no	—
103	C₂×C₇×C₄⋊C₄	—	2	8	no	—
104	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
106	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₄²×C₇	C₂³	1	2	yes	—
114	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
115	C₇×#107	C₂³	1	4	yes	—
116	C₇×#106	C₂³	1	8	yes	—
117	C₇×C₄⋊C₈	C₂³	1	4	yes	—
118	C₇×C₄⋊C₈	C₂³	1	8	yes	—
119	C₇×#102	C₂³	1	8	yes	—
120	C₇×#102	C₂³	1	8	yes	—
121	C₇×#102	C₂³	1	8	yes	—
122	C₇×#102	C₂³	1	8	yes	—
123	C₇×#102	C₂³	1	4	yes	—
124	C₇×#102	C₂³	1	4	yes	—
125	C₇×#97	C₂³	1	8	yes	—
126	C₄×C₇×C₈	C₂³	1	4	yes	—
127	C₂×#554	C₂×C₇	1	1	yes	characteristic, complemented
128	C₂×#550	C₂×C₇	1	1	yes	characteristic, complemented
129	#3366	C₂×C₇	1	16	yes	direct product factor
130	C₂×#490	C₂×C₇	1	2	yes	complemented
131	C₂×#486	C₂×C₇	1	1	yes	characteristic, complemented
132	C₂×#478	C₂×C₇	1	2	yes	complemented
133	C₂×#476	C₂×C₇	1	1	yes	characteristic, complemented
134	C₂×#459	C₂×C₇	1	1	yes	characteristic, complemented
135	C₂×#459	C₂×C₇	1	2	yes	complemented
136	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂×#442	C₂×C₇	1	2	yes	complemented
138	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
139	C₂⁴×C₇	—	2	1	no	—
140	C₂⁴×C₇	—	2	2	no	—
141	C₂⁴×C₇	—	2	1	no	—
142	C₇×#41	—	4	32	no	—
143	C₂×C₇×Q₈	—	2	4	no	—
144	C₂×C₇×Q₈	—	2	4	no	—
145	C₂×C₇×Q₈	—	8	2	no	—
146	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
147	C₂×C₇×D₄	—	2	1	no	—
148	C₂×C₇×D₄	—	2	2	no	—
149	C₂×C₇×D₄	—	2	1	no	—
150	C₂×C₇×D₄	—	2	8	no	—
151	C₂×C₇×D₄	—	2	4	no	—
152	C₂×C₇×D₄	—	2	4	no	—
153	C₂×C₇×D₄	—	2	8	no	—
154	C₂×C₇×D₄	—	2	2	no	—
155	C₂×C₇×D₄	—	2	4	no	—
156	C₂×C₇×D₄	—	2	2	no	—
157	C₂×C₇×D₄	—	2	2	no	—
158	C₂×C₇×D₄	—	2	4	no	—
159	C₂×C₇×D₄	—	4	8	no	—
160	C₂×C₇×D₄	—	4	4	no	—
161	C₂×C₇×D₄	—	8	4	no	—
162	C₂×C₇×D₄	—	8	2	no	—
163	C₂×C₇×D₄	#41	1	4	yes	complemented
164	C₂×C₇×D₄	C₂⁴	1	2	yes	—
165	C₂×C₇×D₄	C₂⁴	1	4	yes	—
166	C₂×C₇×D₄	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₇	—	2	1	no	—
168	C₂²×C₄×C₇	—	2	1	no	—
169	C₂²×C₄×C₇	—	2	2	no	—
170	C₂²×C₄×C₇	—	2	4	no	—
171	C₂²×C₄×C₇	—	2	8	no	—
172	C₂²×C₄×C₇	—	2	4	no	—
173	C₂²×C₄×C₇	—	2	8	no	—
174	C₂²×C₄×C₇	—	4	8	no	—
175	C₂²×C₄×C₇	—	4	4	no	—
176	C₂²×C₄×C₇	—	4	4	no	—
177	C₂²×C₄×C₇	—	8	4	no	—
178	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
183	C₇×D₈	—	2	8	no	—
184	C₇×D₈	—	2	16	no	—
185	C₂×C₇×C₈	—	2	2	no	—
186	C₂×C₇×C₈	—	2	4	no	—
187	C₂×C₇×C₈	—	2	2	no	—
188	C₂×C₇×C₈	C₂⁴	1	2	yes	—
189	C₂×C₇×C₈	C₂⁴	1	2	yes	—
190	C₂×C₇×C₈	C₂⁴	1	4	yes	—
191	C₇×C₄⋊C₄	—	2	8	no	—
192	C₇×C₄⋊C₄	—	2	4	no	—
193	C₇×C₄⋊C₄	—	2	8	no	—
194	C₇×C₄⋊C₄	—	2	1	no	—
195	C₇×C₄⋊C₄	—	2	1	no	—
196	C₇×C₄⋊C₄	—	2	2	no	—
197	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
198	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
199	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
200	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
201	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
202	C₇×C₂²⋊C₄	—	2	4	no	—
203	C₇×C₂²⋊C₄	—	2	8	no	—
204	C₇×C₂²⋊C₄	—	2	4	no	—
205	C₇×C₂²⋊C₄	—	2	8	no	—
206	C₄²×C₇	C₂×D₄	1	4	yes	—
207	C₄²×C₇	C₂×D₄	1	2	yes	—
208	C₄²×C₇	C₂⁴	1	2	yes	—
209	C₄²×C₇	C₂⁴	1	4	yes	—
210	C₂²×#41	—	2	1	no	—
211	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
212	C₂²×D₈	C₂²×C₇	1	2	yes	—
213	#554	—	2	4	no	—
214	#554	C₂²×C₇	1	8	yes	complemented
215	#550	—	2	4	no	—
216	#550	C₂²×C₇	1	8	yes	complemented
217	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
218	C₂×#127	C₂²×C₇	1	1	yes	characteristic
219	C₂×#127	C₂²×C₇	1	2	yes	—
220	C₂×#125	C₂²×C₇	1	2	yes	—
221	C₂×C₂²⋊Q₈	—	2	1	no	—
222	C₂×C₂²⋊Q₈	—	2	2	no	—
223	C₂×#121	—	2	1	no	—
224	C₂×#121	—	2	2	no	—
225	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
226	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
227	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
228	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
230	C₂²×C₄⋊C₄	—	2	1	no	—
231	#490	C₂²×C₇	1	16	yes	complemented
232	#486	C₂²×C₇	1	8	yes	complemented
233	#478	C₂²×C₇	1	16	yes	complemented
234	#476	C₂²×C₇	1	8	yes	complemented
235	#459	C₂²×C₇	1	16	yes	complemented
236	#459	C₂²×C₇	1	8	yes	complemented
237	#446	C₂²×C₇	1	8	yes	complemented
238	#442	C₂²×C₇	1	16	yes	complemented
239	C₄×D₈	C₂²×C₇	1	8	yes	complemented
240	C₂×#107	C₂²×C₇	1	1	yes	characteristic
241	C₂×#106	C₂²×C₇	1	2	yes	—
242	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
243	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
244	C₂×#102	C₂²×C₇	1	2	yes	—
245	C₂×#102	C₂²×C₇	1	2	yes	—
246	C₂×#102	C₂²×C₇	1	2	yes	—
247	C₂×#102	C₂²×C₇	1	1	yes	characteristic
248	C₂×#102	C₂²×C₇	1	2	yes	—
249	C₂×#102	C₂²×C₇	1	1	yes	characteristic
250	C₂×#97	C₂²×C₇	1	2	yes	—
251	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
252	C₂³×C₇	—	2	4	no	—
253	C₂³×C₇	—	2	2	no	—
254	C₂³×C₇	—	2	4	no	—
255	C₂³×C₇	—	2	2	no	—
256	C₂³×C₇	—	4	2	no	—
257	C₂³×C₇	—	4	2	no	—
258	C₂³×C₇	—	4	4	no	—
259	C₂³×C₇	—	4	2	no	—
260	C₂³×C₇	—	4	4	no	—
261	C₂³×C₇	—	4	2	no	—
262	C₂³×C₇	—	4	2	no	—
263	C₂³×C₇	—	4	4	no	—
264	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
265	C₇×Q₈	—	2	8	no	—
266	C₇×Q₈	—	8	4	no	—
267	C₇×D₄	—	2	4	no	—
268	C₇×D₄	—	2	2	no	—
269	C₇×D₄	—	2	4	no	—
270	C₇×D₄	—	2	2	no	—
271	C₇×D₄	—	2	2	no	—
272	C₇×D₄	—	2	4	no	—
273	C₇×D₄	—	4	16	no	—
274	C₇×D₄	—	4	4	no	—
275	C₇×D₄	—	4	2	no	—
276	C₇×D₄	—	4	8	no	—
277	C₇×D₄	—	8	8	no	—
278	C₇×D₄	—	8	4	no	—
279	C₇×D₄	C₂×#41	1	4	yes	complemented
280	C₂×C₄×C₇	—	2	4	no	—
281	C₂×C₄×C₇	—	2	4	no	—
282	C₂×C₄×C₇	—	2	2	no	—
283	C₂×C₄×C₇	—	2	2	no	—
284	C₂×C₄×C₇	—	2	2	no	—
285	C₂×C₄×C₇	—	2	4	no	—
286	C₂×C₄×C₇	—	4	16	no	—
287	C₂×C₄×C₇	—	4	2	no	—
288	C₂×C₄×C₇	—	4	2	no	—
289	C₂×C₄×C₇	—	4	4	no	—
290	C₂×C₄×C₇	—	4	8	no	—
291	C₂×C₄×C₇	—	4	8	no	—
292	C₂×C₄×C₇	—	8	8	no	—
293	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
294	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
296	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
297	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₇	C₂×#41	1	2	yes	—
300	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
301	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
302	C₇×C₈	—	2	2	no	—
303	C₇×C₈	—	2	4	no	—
304	C₇×C₈	—	2	2	no	—
305	C₂×#41	—	2	8	no	—
306	C₂×#41	—	4	8	no	—
307	C₂²×Q₈	—	2	1	no	—
308	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
309	C₂²×D₄	—	2	2	no	—
310	C₂²×D₄	—	2	1	no	—
311	C₂²×D₄	—	2	1	no	—
312	C₂²×D₄	—	2	2	no	—
313	C₂²×D₄	C₂³×C₇	1	2	yes	—
314	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
315	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
316	C₂³×C₄	—	2	1	no	—
317	C₂³×C₄	—	2	2	no	—
318	C₂³×C₄	—	2	1	no	—
319	C₂³×C₄	—	2	2	no	—
320	C₂×D₈	—	2	4	no	—
321	C₂×D₈	—	2	8	no	—
322	C₂×D₈	C₂³×C₇	1	4	yes	—
323	C₂×D₈	C₂³×C₇	1	8	yes	—
324	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₇	1	2	yes	—
326	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
327	C₄⋊Q₈	—	2	2	no	—
328	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
329	#127	—	2	4	no	—
330	#127	—	2	2	no	—
331	#127	C₂³×C₇	1	4	yes	—
332	#127	C₂³×C₇	1	8	yes	—
333	#125	—	2	4	no	—
334	#125	C₂³×C₇	1	8	yes	—
335	C₂²⋊Q₈	—	2	8	no	—
336	C₂²⋊Q₈	—	2	16	no	—
337	#121	—	2	8	no	—
338	#121	—	2	16	no	—
339	C₄×Q₈	C₇×D₄	1	4	yes	—
340	C₄×Q₈	C₂³×C₇	1	4	yes	—
341	C₄×D₄	—	2	4	no	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	—	2	4	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	C₂³×C₇	1	4	yes	—
346	C₄×D₄	C₂³×C₇	1	8	yes	—
347	C₄×D₄	C₂³×C₇	1	4	yes	—
348	C₄×D₄	C₂³×C₇	1	8	yes	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	8	no	—
353	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
355	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₄²	C₂³×C₇	1	2	yes	—
363	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
364	#107	C₂³×C₇	1	4	yes	—
365	#106	C₂³×C₇	1	8	yes	—
366	C₄⋊C₈	C₂³×C₇	1	4	yes	—
367	C₄⋊C₈	C₂³×C₇	1	8	yes	—
368	#102	C₂³×C₇	1	4	yes	—
369	#102	C₂³×C₇	1	4	yes	—
370	#102	C₂³×C₇	1	8	yes	—
371	#102	C₂³×C₇	1	8	yes	—
372	#102	C₂³×C₇	1	8	yes	—
373	#102	C₂³×C₇	1	8	yes	—
374	#97	C₂³×C₇	1	8	yes	—
375	C₄×C₈	C₂³×C₇	1	4	yes	—
376	C₂²×C₇	—	2	4	no	—
377	C₂²×C₇	—	4	8	no	—
378	C₂²×C₇	—	4	2	no	—
379	C₂²×C₇	—	4	2	no	—
380	C₂²×C₇	—	4	4	no	—
381	C₂²×C₇	—	4	2	no	—
382	C₂²×C₇	—	4	4	no	—
383	C₂²×C₇	—	4	2	no	—
384	C₂²×C₇	—	4	2	no	—
385	C₂²×C₇	—	4	4	no	—
386	C₂²×C₇	—	8	8	no	—
387	C₂²×C₇	—	8	4	no	—
388	C₂²×C₇	#548	1	2	yes	—
389	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
390	C₂²×C₇	#576	1	2	yes	—
391	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
392	C₄×C₇	—	2	4	no	—
393	C₄×C₇	—	2	4	no	—
394	C₄×C₇	—	2	2	no	—
395	C₄×C₇	—	4	2	no	—
396	C₄×C₇	—	4	2	no	—
397	C₄×C₇	—	4	4	no	—
398	C₄×C₇	#548	1	2	yes	—
399	C₄×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
400	C₄×C₇	C₂²×#41	1	1	yes	characteristic
401	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
402	C₂⁴	—	2	1	no	—
403	C₂⁴	—	2	2	no	—
404	C₂⁴	—	2	1	no	—
405	#41	—	4	32	no	—
406	C₂×Q₈	—	2	4	no	—
407	C₂×Q₈	—	2	4	no	—
408	C₂×Q₈	—	8	2	no	—
409	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	4	8	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂×D₄	—	8	4	no	—
425	C₂×D₄	—	8	2	no	—
426	C₂×D₄	C₇×#41	1	4	yes	complemented
427	C₂×D₄	C₂⁴×C₇	1	2	yes	—
428	C₂×D₄	C₂⁴×C₇	1	4	yes	—
429	C₂×D₄	C₂⁴×C₇	1	2	yes	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	8	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	8	no	—
437	C₂²×C₄	—	4	8	no	—
438	C₂²×C₄	—	4	4	no	—
439	C₂²×C₄	—	4	4	no	—
440	C₂²×C₄	—	8	4	no	—
441	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
443	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
444	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
445	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
446	D₈	—	2	8	no	—
447	D₈	—	2	16	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	4	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	C₂⁴×C₇	1	2	yes	—
452	C₂×C₈	C₂⁴×C₇	1	2	yes	—
453	C₂×C₈	C₂⁴×C₇	1	4	yes	—
454	C₄⋊C₄	—	2	8	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	8	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
461	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
462	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
463	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
464	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₄²	C₂×C₇×D₄	1	4	yes	—
470	C₄²	C₂×C₇×D₄	1	2	yes	—
471	C₄²	C₂⁴×C₇	1	2	yes	—
472	C₄²	C₂⁴×C₇	1	4	yes	—
473	C₂×C₇	—	4	4	no	—
474	C₂×C₇	—	8	4	no	—
475	C₂×C₇	—	8	2	no	—
476	C₂×C₇	#3366	1	4	yes	direct product factor
477	C₂×C₇	C₂×#548	1	1	yes	characteristic
478	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
479	C₂×C₇	C₂×#576	1	1	yes	characteristic
480	C₂³	—	2	2	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	4	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	4	no	—
492	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
493	Q₈	—	2	8	no	—
494	Q₈	—	8	4	no	—
495	D₄	—	2	2	no	—
496	D₄	—	2	4	no	—
497	D₄	—	2	2	no	—
498	D₄	—	2	2	no	—
499	D₄	—	2	4	no	—
500	D₄	—	2	4	no	—
501	D₄	—	4	16	no	—
502	D₄	—	4	4	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	8	no	—
505	D₄	—	8	8	no	—
506	D₄	—	8	4	no	—
507	D₄	C₂×C₇×#41	1	4	yes	complemented
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	4	16	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	8	no	—
519	C₂×C₄	—	4	8	no	—
520	C₂×C₄	—	8	8	no	—
521	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
522	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
523	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
524	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
525	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
526	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
527	C₂×C₄	C₂×C₇×#41	1	2	yes	—
528	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
529	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
530	C₈	—	2	2	no	—
531	C₈	—	2	4	no	—
532	C₈	—	2	2	no	—
533	C₇	C₂×#3366	1	1	yes	characteristic, direct product factor, Sylow
534	C₂²	—	2	4	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	8	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	8	8	no	—
545	C₂²	—	8	4	no	—
546	C₂²	C₇×#548	1	2	yes	—
547	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
548	C₂²	C₇×#576	1	2	yes	—
549	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
550	C₄	—	2	4	no	—
551	C₄	—	2	4	no	—
552	C₄	—	2	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	4	no	—
556	C₄	C₇×#548	1	2	yes	—
557	C₄	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
558	C₄	C₂²×C₇×#41	1	1	yes	characteristic
559	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
560	C₂	—	4	4	no	—
561	C₂	—	8	4	no	—
562	C₂	—	8	2	no	—
563	C₂	C₇×#3366	1	4	yes	direct product factor
564	C₂	C₂×C₇×#548	1	1	yes	characteristic
565	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
566	C₂	C₂×C₇×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#554	C₂	semidirect
2. C₂×C₇×#550	C₂	semidirect
3. C₇×#3366	C₂	direct (N × H)
4. C₂×C₇×#490	C₂	semidirect
5. C₂×C₇×#486	C₂	semidirect
6. C₂×C₇×#478	C₂	semidirect
7. C₂×C₇×#476	C₂	semidirect
8. C₂×C₇×#459	C₂	semidirect
9. C₂×C₇×#459	C₂	semidirect
10. C₂×C₇×#446	C₂	semidirect
11. C₂×C₇×#442	C₂	semidirect
12. C₂×C₄×C₇×D₈	C₂	semidirect
17. C₇×#554	C₂²	semidirect
19. C₇×#550	C₂²	semidirect
34. C₇×#490	C₂²	semidirect
35. C₇×#486	C₂²	semidirect
36. C₇×#478	C₂²	semidirect
37. C₇×#476	C₂²	semidirect
38. C₇×#459	C₂²	semidirect
39. C₇×#459	C₂²	semidirect
40. C₇×#446	C₂²	semidirect
41. C₇×#442	C₂²	semidirect
42. C₄×C₇×D₈	C₂²	semidirect
55. C₂×#3366	C₇	direct (N × H)
127. C₂×#554	C₂×C₇	semidirect
128. C₂×#550	C₂×C₇	semidirect
129. #3366	C₂×C₇	direct (N × H)
130. C₂×#490	C₂×C₇	semidirect
131. C₂×#486	C₂×C₇	semidirect
132. C₂×#478	C₂×C₇	semidirect
133. C₂×#476	C₂×C₇	semidirect
134. C₂×#459	C₂×C₇	semidirect
135. C₂×#459	C₂×C₇	semidirect
136. C₂×#446	C₂×C₇	semidirect
137. C₂×#442	C₂×C₇	semidirect
138. C₂×C₄×D₈	C₂×C₇	semidirect
163. C₂×C₇×D₄	#41	semidirect
214. #554	C₂²×C₇	semidirect
216. #550	C₂²×C₇	semidirect
231. #490	C₂²×C₇	semidirect
232. #486	C₂²×C₇	semidirect
233. #478	C₂²×C₇	semidirect
234. #476	C₂²×C₇	semidirect
235. #459	C₂²×C₇	semidirect
236. #459	C₂²×C₇	semidirect
237. #446	C₂²×C₇	semidirect
238. #442	C₂²×C₇	semidirect
239. C₄×D₈	C₂²×C₇	semidirect
279. C₇×D₄	C₂×#41	semidirect
426. C₂×D₄	C₇×#41	semidirect
476. C₂×C₇	#3366	direct (N × H)
507. D₄	C₂×C₇×#41	semidirect
533. C₇	C₂×#3366	direct (N × H)
563. C₂	C₇×#3366	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×#554	2
C₂×C₇×#550	2
C₇×#3366	2
C₂×C₇×#490	2
C₂×C₇×#486	2
C₂×C₇×#478	2
C₂×C₇×#476	2
C₂×C₇×#459	2
C₂×C₇×#446	2
C₂×C₇×#442	2
C₂×C₄×C₇×D₈	2
C₂×#3366	7

Subgroups — C2×C7×#3366 #13238520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3366 #13238520