Subgroups — C₂×C₇×#3083 #13237703

Order 1792.

2094 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#520	C₂	1	1	yes	maximal, characteristic
3	C₇×#3083	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#479	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#477	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#478	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#474	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#428	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×#107	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#417	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×#416	C₂	1	1	yes	maximal, characteristic
13	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
15	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
16	C₇×#544	—	2	4	no	—
17	C₇×#544	C₂²	1	8	yes	complemented
18	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
19	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₇×#125	—	2	1	no	—
21	C₂×C₇×#125	C₂²	1	2	yes	—
22	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
23	C₇×#520	—	2	4	no	—
24	C₇×#520	C₂²	1	8	yes	—
25	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
26	C₂×C₄×C₇×D₄	—	2	2	no	—
27	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
28	C₂×C₇×#117	—	2	1	no	—
29	C₂×C₇×#117	C₂²	1	1	yes	characteristic
30	C₂×C₇×#117	C₂²	1	1	yes	characteristic
31	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
32	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₇×#479	C₂²	1	16	yes	complemented
35	C₇×#478	C₂²	1	16	yes	complemented
36	C₇×#477	C₂²	1	16	yes	complemented
37	C₇×#474	C₂²	1	16	yes	complemented
38	C₇×#428	C₂²	1	8	yes	complemented
39	C₂×C₇×#107	C₂²	1	2	yes	—
40	C₂×C₇×#107	C₂²	1	2	yes	—
41	C₂×C₇×#107	C₂²	1	2	yes	—
42	C₂×C₇×#107	C₂²	1	8	yes	complemented
43	C₂×C₇×#106	C₂²	1	2	yes	—
44	C₇×#424	C₂²	1	8	yes	complemented
45	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
46	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
47	C₇×#417	C₂²	1	8	yes	—
48	C₇×#416	C₂²	1	8	yes	—
49	C₂×C₇×#103	C₂²	1	1	yes	characteristic
50	C₂×C₇×#103	C₂²	1	2	yes	—
51	C₂×C₇×#103	C₂²	1	1	yes	characteristic
52	C₂×C₇×#102	C₂²	1	1	yes	characteristic
53	C₂×C₇×#102	C₂²	1	2	yes	—
54	C₂×C₇×#102	C₂²	1	1	yes	characteristic
55	C₂×#3083	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂×C₇×#41	—	2	2	no	—
57	C₂×C₇×#41	—	2	4	no	—
58	C₂×C₇×#41	Q₈	1	8	yes	complemented
59	C₂×C₇×#41	C₂³	1	4	yes	—
60	C₂²×C₇×Q₈	—	2	2	no	—
61	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
62	C₂²×C₇×D₄	—	2	1	no	—
63	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₇	—	2	1	no	—
65	C₂³×C₄×C₇	—	2	1	no	—
66	C₂³×C₄×C₇	—	2	1	no	—
67	C₂³×C₄×C₇	—	2	2	no	—
68	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
69	C₂×C₇×M₁₆	—	2	4	no	—
70	C₂×C₇×M₁₆	C₂³	1	4	yes	—
71	C₂²×C₇×C₈	—	2	4	no	—
72	C₂²×C₇×C₈	C₂³	1	2	yes	—
73	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₇×C₈	C₂³	1	4	yes	—
76	C₇×C₄⋊Q₈	—	2	8	no	—
77	C₇×C₄⋊Q₈	—	2	4	no	—
78	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
79	C₇×#125	—	2	8	no	—
80	C₇×#125	—	2	4	no	—
81	C₇×#125	C₂³	1	8	yes	—
82	C₇×C₂²⋊Q₈	—	2	16	no	—
83	C₄×C₇×Q₈	—	2	4	no	—
84	C₄×C₇×Q₈	C₂³	1	8	yes	—
85	C₄×C₇×D₄	—	2	16	no	—
86	C₄×C₇×D₄	—	2	4	no	—
87	C₄×C₇×D₄	C₂³	1	8	yes	—
88	C₇×#117	—	2	2	no	—
89	C₇×#117	—	2	8	no	—
90	C₇×#117	D₄	1	4	yes	—
91	C₇×#117	C₂³	1	4	yes	—
92	C₇×#117	C₂³	1	4	yes	—
93	C₂×C₇×C₄⋊C₄	—	2	1	no	—
94	C₂×C₇×C₄⋊C₄	—	2	2	no	—
95	C₂×C₇×C₄⋊C₄	—	2	2	no	—
96	C₂×C₇×C₄⋊C₄	—	2	1	no	—
97	C₂×C₇×C₄⋊C₄	—	2	2	no	—
98	C₂×C₇×C₄⋊C₄	—	2	2	no	—
99	C₂×C₇×C₄⋊C₄	—	2	2	no	—
100	C₂×C₇×C₄⋊C₄	—	2	2	no	—
101	C₂×C₇×C₄⋊C₄	—	2	8	no	—
102	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
106	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
108	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
113	C₂×C₄²×C₇	—	2	2	no	—
114	C₂×C₄²×C₇	—	2	1	no	—
115	C₂×C₄²×C₇	C₂³	1	2	yes	—
116	C₇×#107	C₂³	1	8	yes	—
117	C₇×#107	C₂³	1	8	yes	—
118	C₇×#107	C₂³	1	8	yes	—
119	C₇×#106	C₂³	1	8	yes	—
120	C₇×C₄⋊C₈	C₂³	1	8	yes	—
121	C₇×C₄⋊C₈	C₂³	1	8	yes	—
122	C₇×#103	C₂³	1	4	yes	—
123	C₇×#103	C₂³	1	8	yes	—
124	C₇×#103	C₂³	1	4	yes	—
125	C₇×#102	C₂³	1	4	yes	—
126	C₇×#102	C₂³	1	8	yes	—
127	C₇×#102	C₂³	1	4	yes	—
128	C₂×#544	C₂×C₇	1	1	yes	characteristic, complemented
129	C₂×#520	C₂×C₇	1	1	yes	characteristic
130	#3083	C₂×C₇	1	16	yes	direct product factor
131	C₂×#479	C₂×C₇	1	2	yes	complemented
132	C₂×#477	C₂×C₇	1	2	yes	complemented
133	C₂×#478	C₂×C₇	1	2	yes	complemented
134	C₂×#474	C₂×C₇	1	2	yes	complemented
135	C₂×#428	C₂×C₇	1	1	yes	characteristic, complemented
136	C₂²×#107	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂×#424	C₂×C₇	1	1	yes	characteristic, complemented
138	C₂×#417	C₂×C₇	1	1	yes	characteristic
139	C₂×#416	C₂×C₇	1	1	yes	characteristic
140	C₂⁴×C₇	—	2	1	no	—
141	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
142	C₇×#41	—	2	16	no	—
143	C₇×#41	—	2	8	no	—
144	C₇×#41	C₂×Q₈	1	16	yes	complemented
145	C₂×C₇×Q₈	—	2	1	no	—
146	C₂×C₇×Q₈	—	2	8	no	—
147	C₂×C₇×Q₈	—	2	2	no	—
148	C₂×C₇×Q₈	—	8	4	no	—
149	C₂×C₇×Q₈	C₂×Q₈	1	4	yes	—
150	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
151	C₂×C₇×D₄	—	2	8	no	—
152	C₂×C₇×D₄	—	2	4	no	—
153	C₂×C₇×D₄	—	2	1	no	—
154	C₂×C₇×D₄	—	2	2	no	—
155	C₂×C₇×D₄	C₂×Q₈	1	4	yes	—
156	C₂×C₇×D₄	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₇	—	2	1	no	—
158	C₂²×C₄×C₇	—	2	8	no	—
159	C₂²×C₄×C₇	—	2	4	no	—
160	C₂²×C₄×C₇	—	2	1	no	—
161	C₂²×C₄×C₇	—	2	2	no	—
162	C₂²×C₄×C₇	—	2	1	no	—
163	C₂²×C₄×C₇	—	2	2	no	—
164	C₂²×C₄×C₇	—	2	4	no	—
165	C₂²×C₄×C₇	—	2	4	no	—
166	C₂²×C₄×C₇	—	2	8	no	—
167	C₂²×C₄×C₇	—	8	4	no	—
168	C₂²×C₄×C₇	—	8	2	no	—
169	C₂²×C₄×C₇	—	8	2	no	—
170	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
175	C₂²×C₄×C₇	#41	1	4	yes	—
176	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
178	C₇×M₁₆	—	2	8	no	—
179	C₂×C₇×C₈	—	2	2	no	—
180	C₂×C₇×C₈	—	2	2	no	—
181	C₂×C₇×C₈	—	2	8	no	—
182	C₂×C₇×C₈	—	2	4	no	—
183	C₂×C₇×C₈	C₂⁴	1	4	yes	—
184	C₂×C₇×C₈	C₂⁴	1	2	yes	—
185	C₂×C₇×C₈	C₂⁴	1	2	yes	—
186	C₇×C₄⋊C₄	—	2	4	no	—
187	C₇×C₄⋊C₄	—	2	8	no	—
188	C₇×C₄⋊C₄	—	2	2	no	—
189	C₇×C₄⋊C₄	—	2	4	no	—
190	C₇×C₄⋊C₄	—	2	2	no	—
191	C₇×C₄⋊C₄	—	2	8	no	—
192	C₇×C₄⋊C₄	—	2	8	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	C₂×D₄	1	4	yes	—
197	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
198	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
199	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
200	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
201	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
202	C₇×C₂²⋊C₄	—	2	4	no	—
203	C₇×C₂²⋊C₄	—	2	8	no	—
204	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
205	C₄²×C₇	—	2	8	no	—
206	C₄²×C₇	—	2	4	no	—
207	C₄²×C₇	C₂×D₄	1	4	yes	—
208	C₄²×C₇	C₂⁴	1	4	yes	—
209	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
210	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
211	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
212	#544	—	2	4	no	—
213	#544	C₂²×C₇	1	8	yes	complemented
214	C₂×C₄⋊Q₈	—	2	1	no	—
215	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
216	C₂×#125	—	2	1	no	—
217	C₂×#125	C₂²×C₇	1	2	yes	—
218	C₂×C₂²⋊Q₈	—	2	2	no	—
219	#520	—	2	4	no	—
220	#520	C₂²×C₇	1	8	yes	—
221	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
222	C₂×C₄×D₄	—	2	2	no	—
223	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
224	C₂×#117	—	2	1	no	—
225	C₂×#117	C₂²×C₇	1	1	yes	characteristic
226	C₂×#117	C₂²×C₇	1	1	yes	characteristic
227	C₂²×C₄⋊C₄	—	2	1	no	—
228	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
230	#479	C₂²×C₇	1	16	yes	complemented
231	#478	C₂²×C₇	1	16	yes	complemented
232	#477	C₂²×C₇	1	16	yes	complemented
233	#474	C₂²×C₇	1	16	yes	complemented
234	#428	C₂²×C₇	1	8	yes	complemented
235	C₂×#107	C₂²×C₇	1	2	yes	—
236	C₂×#107	C₂²×C₇	1	2	yes	—
237	C₂×#107	C₂²×C₇	1	2	yes	—
238	C₂×#107	C₂²×C₇	1	8	yes	complemented
239	C₂×#106	C₂²×C₇	1	2	yes	—
240	#424	C₂²×C₇	1	8	yes	complemented
241	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
242	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
243	#417	C₂²×C₇	1	8	yes	—
244	#416	C₂²×C₇	1	8	yes	—
245	C₂×#103	C₂²×C₇	1	1	yes	characteristic
246	C₂×#103	C₂²×C₇	1	2	yes	—
247	C₂×#103	C₂²×C₇	1	1	yes	characteristic
248	C₂×#102	C₂²×C₇	1	1	yes	characteristic
249	C₂×#102	C₂²×C₇	1	2	yes	—
250	C₂×#102	C₂²×C₇	1	1	yes	characteristic
251	C₂³×C₇	—	2	2	no	—
252	C₂³×C₇	—	2	2	no	—
253	C₂³×C₇	—	2	4	no	—
254	C₂³×C₇	—	2	2	no	—
255	C₂³×C₇	—	4	2	no	—
256	C₂³×C₇	—	4	2	no	—
257	C₂³×C₇	C₂²⋊Q₈	1	4	yes	—
258	C₂³×C₇	C₂²×D₄	1	2	yes	—
259	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
260	C₇×Q₈	—	2	4	no	—
261	C₇×Q₈	—	2	2	no	—
262	C₇×Q₈	—	8	8	no	—
263	C₇×Q₈	C₂²×Q₈	1	4	yes	—
264	C₇×D₄	—	2	16	no	—
265	C₇×D₄	—	2	4	no	—
266	C₇×D₄	—	2	2	no	—
267	C₇×D₄	C₂²×Q₈	1	4	yes	—
268	C₂×C₄×C₇	—	2	4	no	—
269	C₂×C₄×C₇	—	2	4	no	—
270	C₂×C₄×C₇	—	2	4	no	—
271	C₂×C₄×C₇	—	2	2	no	—
272	C₂×C₄×C₇	—	2	16	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	4	no	—
278	C₂×C₄×C₇	—	4	4	no	—
279	C₂×C₄×C₇	—	4	2	no	—
280	C₂×C₄×C₇	—	4	2	no	—
281	C₂×C₄×C₇	—	8	8	no	—
282	C₂×C₄×C₇	—	8	4	no	—
283	C₂×C₄×C₇	—	8	4	no	—
284	C₂×C₄×C₇	C₂²⋊Q₈	1	4	yes	—
285	C₂×C₄×C₇	C₂²⋊Q₈	1	8	yes	—
286	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
287	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
288	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
289	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
291	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
292	C₂×C₄×C₇	C₂×#41	1	2	yes	—
293	C₂×C₄×C₇	C₂×#41	1	4	yes	—
294	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
295	C₇×C₈	—	2	2	no	—
296	C₇×C₈	—	2	2	no	—
297	C₇×C₈	—	2	4	no	—
298	C₂×#41	—	2	2	no	—
299	C₂×#41	—	2	4	no	—
300	C₂×#41	C₇×Q₈	1	8	yes	complemented
301	C₂×#41	C₂³×C₇	1	4	yes	—
302	C₂²×Q₈	—	2	2	no	—
303	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
304	C₂²×D₄	—	2	1	no	—
305	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	—	2	1	no	—
308	C₂³×C₄	—	2	1	no	—
309	C₂³×C₄	—	2	2	no	—
310	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
311	C₂×M₁₆	—	2	4	no	—
312	C₂×M₁₆	C₂³×C₇	1	4	yes	—
313	C₂²×C₈	—	2	4	no	—
314	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₇	1	4	yes	—
317	C₂²×C₈	C₂³×C₇	1	2	yes	—
318	C₄⋊Q₈	—	2	8	no	—
319	C₄⋊Q₈	—	2	4	no	—
320	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
321	#125	—	2	8	no	—
322	#125	—	2	4	no	—
323	#125	C₂³×C₇	1	8	yes	—
324	C₂²⋊Q₈	—	2	16	no	—
325	C₄×Q₈	—	2	4	no	—
326	C₄×Q₈	C₂³×C₇	1	8	yes	—
327	C₄×D₄	—	2	16	no	—
328	C₄×D₄	—	2	4	no	—
329	C₄×D₄	C₂³×C₇	1	8	yes	—
330	#117	—	2	2	no	—
331	#117	—	2	8	no	—
332	#117	C₇×D₄	1	4	yes	—
333	#117	C₂³×C₇	1	4	yes	—
334	#117	C₂³×C₇	1	4	yes	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	8	no	—
344	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
348	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
349	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
350	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
355	C₂×C₄²	—	2	2	no	—
356	C₂×C₄²	—	2	1	no	—
357	C₂×C₄²	C₂³×C₇	1	2	yes	—
358	#107	C₂³×C₇	1	8	yes	—
359	#107	C₂³×C₇	1	8	yes	—
360	#107	C₂³×C₇	1	8	yes	—
361	#106	C₂³×C₇	1	8	yes	—
362	C₄⋊C₈	C₂³×C₇	1	8	yes	—
363	C₄⋊C₈	C₂³×C₇	1	8	yes	—
364	#103	C₂³×C₇	1	4	yes	—
365	#103	C₂³×C₇	1	4	yes	—
366	#103	C₂³×C₇	1	8	yes	—
367	#102	C₂³×C₇	1	4	yes	—
368	#102	C₂³×C₇	1	4	yes	—
369	#102	C₂³×C₇	1	8	yes	—
370	C₂²×C₇	—	2	8	no	—
371	C₂²×C₇	—	2	2	no	—
372	C₂²×C₇	—	2	2	no	—
373	C₂²×C₇	—	2	4	no	—
374	C₂²×C₇	—	4	8	no	—
375	C₂²×C₇	—	4	2	no	—
376	C₂²×C₇	—	4	2	no	—
377	C₂²×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
378	C₂²×C₇	C₂×C₂²⋊Q₈	1	2	yes	—
379	C₂²×C₇	#576	1	2	yes	—
380	C₂²×C₇	#578	1	2	yes	—
381	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
382	C₄×C₇	—	2	4	no	—
383	C₄×C₇	—	2	4	no	—
384	C₄×C₇	—	2	4	no	—
385	C₄×C₇	—	4	4	no	—
386	C₄×C₇	—	4	4	no	—
387	C₄×C₇	—	4	2	no	—
388	C₄×C₇	—	4	2	no	—
389	C₄×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
390	C₄×C₇	C₂×C₂²⋊Q₈	1	2	yes	—
391	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
392	C₄×C₇	C₂²×#41	1	1	yes	characteristic
393	C₂⁴	—	2	1	no	—
394	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
395	#41	—	2	16	no	—
396	#41	—	2	8	no	—
397	#41	C₂×C₇×Q₈	1	16	yes	complemented
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	8	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	8	4	no	—
402	C₂×Q₈	C₂×C₇×Q₈	1	4	yes	—
403	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
404	C₂×D₄	—	2	8	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	C₂×C₇×Q₈	1	4	yes	—
409	C₂×D₄	C₂⁴×C₇	1	2	yes	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	8	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	8	no	—
420	C₂²×C₄	—	8	4	no	—
421	C₂²×C₄	—	8	2	no	—
422	C₂²×C₄	—	8	2	no	—
423	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
424	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
425	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
426	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
427	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
428	C₂²×C₄	C₇×#41	1	4	yes	—
429	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
430	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
431	M₁₆	—	2	8	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	8	no	—
435	C₂×C₈	—	2	4	no	—
436	C₂×C₈	C₂⁴×C₇	1	4	yes	—
437	C₂×C₈	C₂⁴×C₇	1	2	yes	—
438	C₂×C₈	C₂⁴×C₇	1	2	yes	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	8	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	8	no	—
445	C₄⋊C₄	—	2	8	no	—
446	C₄⋊C₄	—	2	8	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
450	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
451	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
452	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
453	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
454	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
458	C₄²	—	2	8	no	—
459	C₄²	—	2	4	no	—
460	C₄²	C₂×C₇×D₄	1	4	yes	—
461	C₄²	C₂⁴×C₇	1	4	yes	—
462	C₂×C₇	—	2	4	no	—
463	C₂×C₇	—	4	4	no	—
464	C₂×C₇	#3083	1	4	yes	direct product factor
465	C₂×C₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
466	C₂×C₇	C₂×#576	1	1	yes	characteristic
467	C₂×C₇	C₂×#578	1	1	yes	characteristic
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	4	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	C₇×C₂²⋊Q₈	1	4	yes	—
475	C₂³	C₂²×C₇×D₄	1	2	yes	—
476	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
477	Q₈	—	2	2	no	—
478	Q₈	—	2	4	no	—
479	Q₈	—	8	8	no	—
480	Q₈	C₂²×C₇×Q₈	1	4	yes	—
481	D₄	—	2	16	no	—
482	D₄	—	2	2	no	—
483	D₄	—	2	4	no	—
484	D₄	C₂²×C₇×Q₈	1	4	yes	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	16	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	8	8	no	—
499	C₂×C₄	—	8	4	no	—
500	C₂×C₄	—	8	4	no	—
501	C₂×C₄	C₇×C₂²⋊Q₈	1	4	yes	—
502	C₂×C₄	C₇×C₂²⋊Q₈	1	8	yes	—
503	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
504	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
505	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
506	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
507	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
508	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
509	C₂×C₄	C₂×C₇×#41	1	2	yes	—
510	C₂×C₄	C₂×C₇×#41	1	4	yes	—
511	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
512	C₈	—	2	2	no	—
513	C₈	—	2	2	no	—
514	C₈	—	2	4	no	—
515	C₇	C₂×#3083	1	1	yes	characteristic, direct product factor, Sylow
516	C₂²	—	2	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	8	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	8	no	—
523	C₂²	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
524	C₂²	C₂×C₇×C₂²⋊Q₈	1	2	yes	—
525	C₂²	C₇×#576	1	2	yes	—
526	C₂²	C₇×#578	1	2	yes	—
527	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
528	C₄	—	2	4	no	—
529	C₄	—	2	4	no	—
530	C₄	—	2	4	no	—
531	C₄	—	4	4	no	—
532	C₄	—	4	4	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	2	no	—
535	C₄	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
536	C₄	C₂×C₇×C₂²⋊Q₈	1	2	yes	—
537	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
538	C₄	C₂²×C₇×#41	1	1	yes	characteristic
539	C₂	—	2	4	no	—
540	C₂	—	4	4	no	—
541	C₂	C₇×#3083	1	4	yes	direct product factor
542	C₂	C₂²×C₇×C₂²⋊Q₈	1	1	yes	characteristic
543	C₂	C₂×C₇×#576	1	1	yes	characteristic
544	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	C₂²×C₇×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#544	C₂	semidirect
3. C₇×#3083	C₂	direct (N × H)
4. C₂×C₇×#479	C₂	semidirect
5. C₂×C₇×#477	C₂	semidirect
6. C₂×C₇×#478	C₂	semidirect
7. C₂×C₇×#474	C₂	semidirect
8. C₂×C₇×#428	C₂	semidirect
9. C₂²×C₇×#107	C₂	semidirect
10. C₂×C₇×#424	C₂	semidirect
17. C₇×#544	C₂²	semidirect
34. C₇×#479	C₂²	semidirect
35. C₇×#478	C₂²	semidirect
36. C₇×#477	C₂²	semidirect
37. C₇×#474	C₂²	semidirect
38. C₇×#428	C₂²	semidirect
42. C₂×C₇×#107	C₂²	semidirect
44. C₇×#424	C₂²	semidirect
55. C₂×#3083	C₇	direct (N × H)
58. C₂×C₇×#41	Q₈	semidirect
128. C₂×#544	C₂×C₇	semidirect
130. #3083	C₂×C₇	direct (N × H)
131. C₂×#479	C₂×C₇	semidirect
132. C₂×#477	C₂×C₇	semidirect
133. C₂×#478	C₂×C₇	semidirect
134. C₂×#474	C₂×C₇	semidirect
135. C₂×#428	C₂×C₇	semidirect
136. C₂²×#107	C₂×C₇	semidirect
137. C₂×#424	C₂×C₇	semidirect
144. C₇×#41	C₂×Q₈	semidirect
213. #544	C₂²×C₇	semidirect
230. #479	C₂²×C₇	semidirect
231. #478	C₂²×C₇	semidirect
232. #477	C₂²×C₇	semidirect
233. #474	C₂²×C₇	semidirect
234. #428	C₂²×C₇	semidirect
238. C₂×#107	C₂²×C₇	semidirect
240. #424	C₂²×C₇	semidirect
300. C₂×#41	C₇×Q₈	semidirect
397. #41	C₂×C₇×Q₈	semidirect
464. C₂×C₇	#3083	direct (N × H)
515. C₇	C₂×#3083	direct (N × H)
541. C₂	C₇×#3083	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×#544	2
C₂×C₇×#520	2
C₇×#3083	2
C₂×C₇×#479	2
C₂×C₇×#477	2
C₂×C₇×#478	2
C₂×C₇×#474	2
C₂×C₇×#428	2
C₂²×C₇×#107	2
C₂×C₇×#424	2
C₂×C₇×#417	2
C₂×C₇×#416	2
C₂×#3083	7

Subgroups — C2×C7×#3083 #13237703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3083 #13237703