Subgroups — C₂×C₇×#3353 #13238462

Order 1792.

2082 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#547	C₂	1	1	yes	maximal, characteristic
3	C₇×#3353	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#500	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#484	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#482	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#475	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#468	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#428	C₂	1	2	yes	maximal, complemented
13	C₂²×C₇×#41	—	2	1	no	—
14	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
16	C₇×#556	—	2	4	no	—
17	C₇×#556	C₂²	1	8	yes	complemented
18	C₇×#547	—	2	4	no	—
19	C₇×#547	C₂²	1	8	yes	—
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×#126	—	2	2	no	—
23	C₂×C₇×#124	—	2	1	no	—
24	C₂×C₇×#123	—	2	2	no	—
25	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₇×#121	C₂²	1	2	yes	—
28	C₂×C₄×C₇×Q₈	—	2	1	no	—
29	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₇×#117	C₂²	1	2	yes	—
33	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
34	C₇×#500	C₂²	1	8	yes	complemented
35	C₇×#484	C₂²	1	16	yes	complemented
36	C₇×#482	C₂²	1	16	yes	complemented
37	C₇×#475	C₂²	1	8	yes	complemented
38	C₇×#474	C₂²	1	8	yes	complemented
39	C₇×#468	C₂²	1	16	yes	complemented
40	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
41	C₇×#436	C₂²	1	8	yes	complemented
42	C₇×#428	C₂²	1	16	yes	complemented
43	C₂×C₇×#107	C₂²	1	2	yes	—
44	C₂×C₇×#107	C₂²	1	2	yes	—
45	C₂×C₇×#107	C₂²	1	2	yes	—
46	C₂×C₇×#106	C₂²	1	1	yes	characteristic
47	C₂×C₇×#106	C₂²	1	2	yes	—
48	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₇×#103	C₂²	1	1	yes	characteristic
50	C₂×C₇×#103	C₂²	1	2	yes	—
51	C₂×C₇×#102	C₂²	1	1	yes	characteristic
52	C₂×C₇×#102	C₂²	1	2	yes	—
53	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
54	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
55	C₂×#3353	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	—	2	1	no	—
60	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇×D₄	—	2	2	no	—
62	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
63	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₇	—	2	2	no	—
65	C₂³×C₄×C₇	—	2	1	no	—
66	C₂³×C₄×C₇	C₂³	1	2	yes	—
67	C₂×C₇×SD₁₆	—	2	4	no	—
68	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
69	C₂×C₇×M₁₆	—	2	8	no	—
70	C₂×C₇×M₁₆	C₂³	1	8	yes	—
71	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇×C₈	C₂³	1	2	yes	—
73	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
74	C₇×C₄⋊Q₈	—	2	2	no	—
75	C₇×C₄⋊Q₈	—	2	2	no	—
76	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
77	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
78	C₇×#126	—	2	16	no	—
79	C₇×#124	—	2	8	no	—
80	C₇×#123	—	2	16	no	—
81	C₇×C₂²⋊Q₈	—	2	4	no	—
82	C₇×C₂²⋊Q₈	—	2	8	no	—
83	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
84	C₇×#121	—	2	4	no	—
85	C₇×#121	C₂³	1	8	yes	—
86	C₄×C₇×Q₈	—	2	8	no	—
87	C₄×C₇×Q₈	—	2	2	no	—
88	C₄×C₇×Q₈	C₂³	1	4	yes	—
89	C₄×C₇×D₄	—	2	2	no	—
90	C₄×C₇×D₄	D₄	1	4	yes	—
91	C₄×C₇×D₄	C₂³	1	4	yes	—
92	C₄×C₇×D₄	C₂³	1	4	yes	—
93	C₇×#117	—	2	4	no	—
94	C₇×#117	C₂³	1	8	yes	—
95	C₂×C₇×C₄⋊C₄	—	2	2	no	—
96	C₂×C₇×C₄⋊C₄	—	2	4	no	—
97	C₂×C₇×C₄⋊C₄	—	2	2	no	—
98	C₂×C₇×C₄⋊C₄	—	2	1	no	—
99	C₂×C₇×C₄⋊C₄	—	2	1	no	—
100	C₂×C₇×C₄⋊C₄	—	2	1	no	—
101	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
102	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
103	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
109	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
112	C₂×C₄²×C₇	—	2	2	no	—
113	C₂×C₄²×C₇	—	2	1	no	—
114	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
115	C₇×#107	C₂³	1	8	yes	—
116	C₇×#107	C₂³	1	8	yes	—
117	C₇×#107	C₂³	1	8	yes	—
118	C₇×#106	C₂³	1	8	yes	—
119	C₇×#106	C₂³	1	4	yes	—
120	C₇×C₄⋊C₈	C₂³	1	4	yes	—
121	C₇×#103	C₂³	1	8	yes	—
122	C₇×#103	C₂³	1	4	yes	—
123	C₇×#102	C₂³	1	8	yes	—
124	C₇×#102	C₂³	1	4	yes	—
125	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
126	C₄×C₇×C₈	C₂³	1	4	yes	—
127	C₂×#556	C₂×C₇	1	1	yes	characteristic, complemented
128	C₂×#547	C₂×C₇	1	1	yes	characteristic
129	#3353	C₂×C₇	1	16	yes	direct product factor
130	C₂×#500	C₂×C₇	1	1	yes	characteristic, complemented
131	C₂×#484	C₂×C₇	1	2	yes	complemented
132	C₂×#482	C₂×C₇	1	2	yes	complemented
133	C₂×#475	C₂×C₇	1	1	yes	characteristic, complemented
134	C₂×#474	C₂×C₇	1	1	yes	characteristic, complemented
135	C₂×#468	C₂×C₇	1	2	yes	complemented
136	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
138	C₂×#428	C₂×C₇	1	2	yes	complemented
139	C₂⁴×C₇	—	2	1	no	—
140	C₂⁴×C₇	C₂×D₄	1	2	yes	—
141	C₇×#41	—	4	32	no	—
142	C₂×C₇×Q₈	—	2	1	no	—
143	C₂×C₇×Q₈	—	2	4	no	—
144	C₂×C₇×Q₈	—	2	4	no	—
145	C₂×C₇×Q₈	—	2	2	no	—
146	C₂×C₇×Q₈	—	2	2	no	—
147	C₂×C₇×Q₈	—	4	4	no	—
148	C₂×C₇×Q₈	—	4	4	no	—
149	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
150	C₂×C₇×D₄	—	2	8	no	—
151	C₂×C₇×D₄	—	2	4	no	—
152	C₂×C₇×D₄	—	2	1	no	—
153	C₂×C₇×D₄	—	2	2	no	—
154	C₂×C₇×D₄	—	2	2	no	—
155	C₂×C₇×D₄	—	4	8	no	—
156	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
157	C₂×C₇×D₄	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₇	—	2	4	no	—
159	C₂²×C₄×C₇	—	2	4	no	—
160	C₂²×C₄×C₇	—	2	8	no	—
161	C₂²×C₄×C₇	—	2	1	no	—
162	C₂²×C₄×C₇	—	2	1	no	—
163	C₂²×C₄×C₇	—	2	2	no	—
164	C₂²×C₄×C₇	—	2	1	no	—
165	C₂²×C₄×C₇	—	2	2	no	—
166	C₂²×C₄×C₇	—	2	4	no	—
167	C₂²×C₄×C₇	—	4	8	no	—
168	C₂²×C₄×C₇	—	4	4	no	—
169	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
175	C₇×SD₁₆	—	2	8	no	—
176	C₇×M₁₆	—	2	16	no	—
177	C₂×C₇×C₈	—	2	4	no	—
178	C₂×C₇×C₈	—	2	2	no	—
179	C₂×C₇×C₈	#41	1	4	yes	complemented
180	C₂×C₇×C₈	C₂⁴	1	2	yes	—
181	C₂×C₇×C₈	C₂⁴	1	4	yes	—
182	C₂×C₇×C₈	C₂⁴	1	2	yes	—
183	C₇×C₄⋊C₄	—	2	1	no	—
184	C₇×C₄⋊C₄	—	2	2	no	—
185	C₇×C₄⋊C₄	—	2	8	no	—
186	C₇×C₄⋊C₄	—	2	8	no	—
187	C₇×C₄⋊C₄	—	2	4	no	—
188	C₇×C₄⋊C₄	—	2	4	no	—
189	C₇×C₄⋊C₄	—	2	4	no	—
190	C₇×C₄⋊C₄	—	2	1	no	—
191	C₇×C₄⋊C₄	—	2	2	no	—
192	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
193	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
194	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
195	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
196	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
197	C₇×C₂²⋊C₄	—	2	8	no	—
198	C₇×C₂²⋊C₄	—	2	8	no	—
199	C₇×C₂²⋊C₄	—	2	4	no	—
200	C₇×C₂²⋊C₄	—	2	8	no	—
201	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
202	C₄²×C₇	—	2	8	no	—
203	C₄²×C₇	—	2	4	no	—
204	C₄²×C₇	C₂×D₄	1	2	yes	—
205	C₄²×C₇	C₂⁴	1	2	yes	—
206	C₂²×#41	—	2	1	no	—
207	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
208	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
209	#556	—	2	4	no	—
210	#556	C₂²×C₇	1	8	yes	complemented
211	#547	—	2	4	no	—
212	#547	C₂²×C₇	1	8	yes	—
213	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
214	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
215	C₂×#126	—	2	2	no	—
216	C₂×#124	—	2	1	no	—
217	C₂×#123	—	2	2	no	—
218	C₂×C₂²⋊Q₈	—	2	1	no	—
219	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
220	C₂×#121	C₂²×C₇	1	2	yes	—
221	C₂×C₄×Q₈	—	2	1	no	—
222	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
223	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
225	C₂×#117	C₂²×C₇	1	2	yes	—
226	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
227	#500	C₂²×C₇	1	8	yes	complemented
228	#484	C₂²×C₇	1	16	yes	complemented
229	#482	C₂²×C₇	1	16	yes	complemented
230	#475	C₂²×C₇	1	8	yes	complemented
231	#474	C₂²×C₇	1	8	yes	complemented
232	#468	C₂²×C₇	1	16	yes	complemented
233	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
234	#436	C₂²×C₇	1	8	yes	complemented
235	#428	C₂²×C₇	1	16	yes	complemented
236	C₂×#107	C₂²×C₇	1	2	yes	—
237	C₂×#107	C₂²×C₇	1	2	yes	—
238	C₂×#107	C₂²×C₇	1	2	yes	—
239	C₂×#106	C₂²×C₇	1	2	yes	—
240	C₂×#106	C₂²×C₇	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
242	C₂×#103	C₂²×C₇	1	2	yes	—
243	C₂×#103	C₂²×C₇	1	1	yes	characteristic
244	C₂×#102	C₂²×C₇	1	1	yes	characteristic
245	C₂×#102	C₂²×C₇	1	2	yes	—
246	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
247	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
248	C₂³×C₇	—	2	4	no	—
249	C₂³×C₇	—	2	4	no	—
250	C₂³×C₇	—	2	4	no	—
251	C₂³×C₇	—	2	2	no	—
252	C₂³×C₇	—	4	2	no	—
253	C₂³×C₇	—	4	2	no	—
254	C₂³×C₇	—	4	2	no	—
255	C₂³×C₇	C₂²×D₄	1	4	yes	—
256	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
257	C₇×Q₈	—	2	2	no	—
258	C₇×Q₈	—	2	2	no	—
259	C₇×Q₈	—	4	2	no	—
260	C₇×Q₈	—	4	8	no	—
261	C₇×Q₈	—	4	8	no	—
262	C₇×D₄	—	2	8	no	—
263	C₇×D₄	—	2	2	no	—
264	C₇×D₄	—	2	2	no	—
265	C₇×D₄	—	4	16	no	—
266	C₇×D₄	—	4	2	no	—
267	C₂×C₄×C₇	—	2	4	no	—
268	C₂×C₄×C₇	—	2	2	no	—
269	C₂×C₄×C₇	—	2	8	no	—
270	C₂×C₄×C₇	—	2	4	no	—
271	C₂×C₄×C₇	—	2	4	no	—
272	C₂×C₄×C₇	—	2	2	no	—
273	C₂×C₄×C₇	—	2	2	no	—
274	C₂×C₄×C₇	—	2	4	no	—
275	C₂×C₄×C₇	—	2	2	no	—
276	C₂×C₄×C₇	—	2	4	no	—
277	C₂×C₄×C₇	—	4	16	no	—
278	C₂×C₄×C₇	—	4	2	no	—
279	C₂×C₄×C₇	—	4	2	no	—
280	C₂×C₄×C₇	—	4	4	no	—
281	C₂×C₄×C₇	—	4	4	no	—
282	C₂×C₄×C₇	—	4	2	no	—
283	C₂×C₄×C₇	—	4	8	no	—
284	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
285	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
286	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
287	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
289	C₂×C₄×C₇	C₂×#41	1	2	yes	—
290	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
291	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
292	C₇×C₈	—	2	4	no	—
293	C₇×C₈	—	2	2	no	—
294	C₇×C₈	C₂×#41	1	4	yes	complemented
295	C₂×#41	—	2	8	no	—
296	C₂×#41	—	4	8	no	—
297	C₂²×Q₈	—	2	1	no	—
298	C₂²×Q₈	—	2	1	no	—
299	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
300	C₂²×D₄	—	2	2	no	—
301	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
302	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
303	C₂³×C₄	—	2	2	no	—
304	C₂³×C₄	—	2	1	no	—
305	C₂³×C₄	C₂³×C₇	1	2	yes	—
306	C₂×SD₁₆	—	2	4	no	—
307	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
308	C₂×M₁₆	—	2	8	no	—
309	C₂×M₁₆	C₂³×C₇	1	8	yes	—
310	C₂²×C₈	C₂³×C₇	1	2	yes	—
311	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
313	C₄⋊Q₈	—	2	2	no	—
314	C₄⋊Q₈	—	2	2	no	—
315	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
316	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
317	#126	—	2	16	no	—
318	#124	—	2	8	no	—
319	#123	—	2	16	no	—
320	C₂²⋊Q₈	—	2	4	no	—
321	C₂²⋊Q₈	—	2	8	no	—
322	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
323	#121	—	2	4	no	—
324	#121	C₂³×C₇	1	8	yes	—
325	C₄×Q₈	—	2	8	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	C₂³×C₇	1	4	yes	—
328	C₄×D₄	—	2	2	no	—
329	C₄×D₄	C₇×D₄	1	4	yes	—
330	C₄×D₄	C₂³×C₇	1	4	yes	—
331	C₄×D₄	C₂³×C₇	1	4	yes	—
332	#117	—	2	4	no	—
333	#117	C₂³×C₇	1	8	yes	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	4	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
344	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
351	C₂×C₄²	—	2	2	no	—
352	C₂×C₄²	—	2	1	no	—
353	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
354	#107	C₂³×C₇	1	8	yes	—
355	#107	C₂³×C₇	1	8	yes	—
356	#107	C₂³×C₇	1	8	yes	—
357	#106	C₂³×C₇	1	4	yes	—
358	#106	C₂³×C₇	1	8	yes	—
359	C₄⋊C₈	C₂³×C₇	1	4	yes	—
360	#103	C₂³×C₇	1	4	yes	—
361	#103	C₂³×C₇	1	8	yes	—
362	#102	C₂³×C₇	1	4	yes	—
363	#102	C₂³×C₇	1	8	yes	—
364	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
365	C₄×C₈	C₂³×C₇	1	4	yes	—
366	C₂²×C₇	—	2	4	no	—
367	C₂²×C₇	—	2	4	no	—
368	C₂²×C₇	—	2	4	no	—
369	C₂²×C₇	—	4	8	no	—
370	C₂²×C₇	—	4	2	no	—
371	C₂²×C₇	—	4	2	no	—
372	C₂²×C₇	—	4	2	no	—
373	C₂²×C₇	—	8	4	no	—
374	C₂²×C₇	#547	1	2	yes	—
375	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
376	C₂²×C₇	#578	1	2	yes	—
377	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
378	C₄×C₇	—	2	4	no	—
379	C₄×C₇	—	2	2	no	—
380	C₄×C₇	—	4	2	no	—
381	C₄×C₇	—	4	2	no	—
382	C₄×C₇	—	4	4	no	—
383	C₄×C₇	—	4	4	no	—
384	C₄×C₇	—	4	2	no	—
385	C₄×C₇	#547	1	2	yes	—
386	C₄×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
387	C₄×C₇	C₂²×#41	1	1	yes	characteristic
388	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
389	C₂⁴	—	2	1	no	—
390	C₂⁴	C₂×C₇×D₄	1	2	yes	—
391	#41	—	4	32	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	4	no	—
394	C₂×Q₈	—	2	4	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	4	4	no	—
398	C₂×Q₈	—	4	4	no	—
399	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
400	C₂×D₄	—	2	8	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	4	8	no	—
406	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
407	C₂×D₄	C₂⁴×C₇	1	2	yes	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	4	8	no	—
418	C₂²×C₄	—	4	4	no	—
419	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
420	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
421	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
422	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
424	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
425	SD₁₆	—	2	8	no	—
426	M₁₆	—	2	16	no	—
427	C₂×C₈	—	2	4	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	C₇×#41	1	4	yes	complemented
430	C₂×C₈	C₂⁴×C₇	1	2	yes	—
431	C₂×C₈	C₂⁴×C₇	1	4	yes	—
432	C₂×C₈	C₂⁴×C₇	1	2	yes	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	2	8	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
443	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
444	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
445	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
446	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
447	C₂²⋊C₄	—	2	8	no	—
448	C₂²⋊C₄	—	2	8	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	8	no	—
451	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
452	C₄²	—	2	8	no	—
453	C₄²	—	2	4	no	—
454	C₄²	C₂×C₇×D₄	1	2	yes	—
455	C₄²	C₂⁴×C₇	1	2	yes	—
456	C₂×C₇	—	4	4	no	—
457	C₂×C₇	—	8	2	no	—
458	C₂×C₇	#3353	1	4	yes	direct product factor
459	C₂×C₇	C₂×#547	1	1	yes	characteristic
460	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
461	C₂×C₇	C₂×#578	1	1	yes	characteristic
462	C₂³	—	2	4	no	—
463	C₂³	—	2	4	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	C₂²×C₇×D₄	1	4	yes	—
470	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
471	Q₈	—	2	2	no	—
472	Q₈	—	2	2	no	—
473	Q₈	—	4	2	no	—
474	Q₈	—	4	8	no	—
475	Q₈	—	4	8	no	—
476	D₄	—	2	2	no	—
477	D₄	—	2	2	no	—
478	D₄	—	2	8	no	—
479	D₄	—	4	16	no	—
480	D₄	—	4	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	8	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	4	16	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	8	no	—
498	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
499	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
500	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
501	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
502	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
503	C₂×C₄	C₂×C₇×#41	1	2	yes	—
504	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
505	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
506	C₈	—	2	4	no	—
507	C₈	—	2	2	no	—
508	C₈	C₂×C₇×#41	1	4	yes	complemented
509	C₇	C₂×#3353	1	1	yes	characteristic, direct product factor, Sylow
510	C₂²	—	2	4	no	—
511	C₂²	—	2	4	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	4	8	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	8	4	no	—
518	C₂²	C₇×#547	1	2	yes	—
519	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
520	C₂²	C₇×#578	1	2	yes	—
521	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	2	4	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	4	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	2	no	—
529	C₄	C₇×#547	1	2	yes	—
530	C₄	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
531	C₄	C₂²×C₇×#41	1	1	yes	characteristic
532	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
533	C₂	—	4	4	no	—
534	C₂	—	8	2	no	—
535	C₂	C₇×#3353	1	4	yes	direct product factor
536	C₂	C₂×C₇×#547	1	1	yes	characteristic
537	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
538	C₂	C₂×C₇×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#547	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#556	C₂	semidirect
3. C₇×#3353	C₂	direct (N × H)
4. C₂×C₇×#500	C₂	semidirect
5. C₂×C₇×#484	C₂	semidirect
6. C₂×C₇×#482	C₂	semidirect
7. C₂×C₇×#475	C₂	semidirect
8. C₂×C₇×#474	C₂	semidirect
9. C₂×C₇×#468	C₂	semidirect
10. C₂×C₄×C₇×SD₁₆	C₂	semidirect
11. C₂×C₇×#436	C₂	semidirect
12. C₂×C₇×#428	C₂	semidirect
17. C₇×#556	C₂²	semidirect
34. C₇×#500	C₂²	semidirect
35. C₇×#484	C₂²	semidirect
36. C₇×#482	C₂²	semidirect
37. C₇×#475	C₂²	semidirect
38. C₇×#474	C₂²	semidirect
39. C₇×#468	C₂²	semidirect
40. C₄×C₇×SD₁₆	C₂²	semidirect
41. C₇×#436	C₂²	semidirect
42. C₇×#428	C₂²	semidirect
55. C₂×#3353	C₇	direct (N × H)
127. C₂×#556	C₂×C₇	semidirect
129. #3353	C₂×C₇	direct (N × H)
130. C₂×#500	C₂×C₇	semidirect
131. C₂×#484	C₂×C₇	semidirect
132. C₂×#482	C₂×C₇	semidirect
133. C₂×#475	C₂×C₇	semidirect
134. C₂×#474	C₂×C₇	semidirect
135. C₂×#468	C₂×C₇	semidirect
136. C₂×C₄×SD₁₆	C₂×C₇	semidirect
137. C₂×#436	C₂×C₇	semidirect
138. C₂×#428	C₂×C₇	semidirect
179. C₂×C₇×C₈	#41	semidirect
210. #556	C₂²×C₇	semidirect
227. #500	C₂²×C₇	semidirect
228. #484	C₂²×C₇	semidirect
229. #482	C₂²×C₇	semidirect
230. #475	C₂²×C₇	semidirect
231. #474	C₂²×C₇	semidirect
232. #468	C₂²×C₇	semidirect
233. C₄×SD₁₆	C₂²×C₇	semidirect
234. #436	C₂²×C₇	semidirect
235. #428	C₂²×C₇	semidirect
294. C₇×C₈	C₂×#41	semidirect
429. C₂×C₈	C₇×#41	semidirect
458. C₂×C₇	#3353	direct (N × H)
508. C₈	C₂×C₇×#41	semidirect
509. C₇	C₂×#3353	direct (N × H)
535. C₂	C₇×#3353	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×#556	2
C₂×C₇×#547	2
C₇×#3353	2
C₂×C₇×#500	2
C₂×C₇×#484	2
C₂×C₇×#482	2
C₂×C₇×#475	2
C₂×C₇×#474	2
C₂×C₇×#468	2
C₂×C₄×C₇×SD₁₆	2
C₂×C₇×#436	2
C₂×C₇×#428	2
C₂×#3353	7

Subgroups — C2×C7×#3353 #13238462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3353 #13238462