Subgroups — C₂×C₇×#3340 #13238447

Order 1792.

1918 conjugacy classes of subgroups.

The subgroup lattice has 532 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×#555	C₂	1	1	yes	maximal, characteristic
3	C₇×#3340	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#485	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#482	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#465	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#427	C₂	1	2	yes	maximal, complemented
13	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₇×C₈	C₂²	1	2	yes	—
15	C₇×#556	—	2	4	no	—
16	C₇×#556	C₂²	1	8	yes	complemented
17	C₇×#555	—	2	4	no	—
18	C₇×#555	C₂²	1	8	yes	—
19	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×#126	—	2	2	no	—
22	C₂×C₇×#124	—	2	1	no	—
23	C₂×C₇×#124	—	2	2	no	—
24	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₇×#121	—	2	1	no	—
26	C₂×C₇×#121	C₂²	1	2	yes	—
27	C₂×C₄×C₇×Q₈	—	2	1	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×C₇×#117	—	2	1	no	—
32	C₂×C₇×#117	C₂²	1	2	yes	—
33	C₂×C₇×#117	C₂²	1	2	yes	—
34	C₇×#498	C₂²	1	8	yes	complemented
35	C₇×#485	C₂²	1	16	yes	complemented
36	C₇×#482	C₂²	1	16	yes	complemented
37	C₇×#477	C₂²	1	8	yes	complemented
38	C₇×#474	C₂²	1	8	yes	complemented
39	C₇×#465	C₂²	1	16	yes	complemented
40	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
41	C₇×C₈×D₄	C₂²	1	8	yes	complemented
42	C₇×#427	C₂²	1	16	yes	complemented
43	C₂×C₇×#107	C₂²	1	2	yes	—
44	C₂×C₇×#107	C₂²	1	2	yes	—
45	C₂×C₇×#106	C₂²	1	2	yes	—
46	C₂×C₇×#106	C₂²	1	2	yes	—
47	C₂×C₇×#106	C₂²	1	1	yes	characteristic
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×#3340	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂²×C₇×Q₈	—	2	1	no	—
57	C₂²×C₇×Q₈	—	2	1	no	—
58	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
59	C₂²×C₇×D₄	—	2	2	no	—
60	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
61	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₇	—	2	1	no	—
63	C₂³×C₄×C₇	C₂³	1	2	yes	—
64	C₂×C₇×SD₁₆	—	2	4	no	—
65	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
66	C₂²×C₇×C₈	—	2	8	no	—
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂³	1	2	yes	—
69	C₂²×C₇×C₈	C₂³	1	8	yes	—
70	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
71	C₇×C₄⋊Q₈	—	2	2	no	—
72	C₇×C₄⋊Q₈	—	2	2	no	—
73	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
74	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
75	C₇×#126	—	2	16	no	—
76	C₇×#124	—	2	8	no	—
77	C₇×#124	—	2	16	no	—
78	C₇×C₂²⋊Q₈	—	2	4	no	—
79	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
80	C₇×#121	—	2	8	no	—
81	C₇×#121	—	2	4	no	—
82	C₇×#121	C₂³	1	8	yes	—
83	C₄×C₇×Q₈	—	2	8	no	—
84	C₄×C₇×Q₈	—	2	2	no	—
85	C₄×C₇×Q₈	C₂³	1	4	yes	—
86	C₄×C₇×D₄	—	2	2	no	—
87	C₄×C₇×D₄	D₄	1	4	yes	—
88	C₄×C₇×D₄	C₂³	1	4	yes	—
89	C₄×C₇×D₄	C₂³	1	4	yes	—
90	C₇×#117	—	2	4	no	—
91	C₇×#117	—	2	4	no	—
92	C₇×#117	—	2	8	no	—
93	C₇×#117	C₂³	1	8	yes	—
94	C₇×#117	C₂³	1	8	yes	—
95	C₂×C₇×C₄⋊C₄	—	2	1	no	—
96	C₂×C₇×C₄⋊C₄	—	2	2	no	—
97	C₂×C₇×C₄⋊C₄	—	2	1	no	—
98	C₂×C₇×C₄⋊C₄	—	2	1	no	—
99	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
100	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
105	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
106	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
107	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
110	C₂×C₄²×C₇	—	2	2	no	—
111	C₂×C₄²×C₇	—	2	2	no	—
112	C₂×C₄²×C₇	—	2	1	no	—
113	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
114	C₇×#107	C₂³	1	8	yes	—
115	C₇×#107	C₂³	1	8	yes	—
116	C₇×#106	C₂³	1	8	yes	—
117	C₇×#106	C₂³	1	8	yes	—
118	C₇×#106	C₂³	1	4	yes	—
119	C₇×C₄⋊C₈	C₂³	1	4	yes	—
120	C₇×#103	C₂³	1	8	yes	—
121	C₇×#103	C₂³	1	4	yes	—
122	C₇×#102	C₂³	1	8	yes	—
123	C₇×#102	C₂³	1	4	yes	—
124	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
125	C₄×C₇×C₈	C₂³	1	4	yes	—
126	C₂×#556	C₂×C₇	1	1	yes	characteristic, complemented
127	C₂×#555	C₂×C₇	1	1	yes	characteristic
128	#3340	C₂×C₇	1	16	yes	direct product factor
129	C₂×#498	C₂×C₇	1	1	yes	characteristic, complemented
130	C₂×#485	C₂×C₇	1	2	yes	complemented
131	C₂×#482	C₂×C₇	1	2	yes	complemented
132	C₂×#477	C₂×C₇	1	1	yes	characteristic, complemented
133	C₂×#474	C₂×C₇	1	1	yes	characteristic, complemented
134	C₂×#465	C₂×C₇	1	2	yes	complemented
135	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
136	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂×#427	C₂×C₇	1	2	yes	complemented
138	C₂⁴×C₇	—	2	1	no	—
139	C₂⁴×C₇	C₂×D₄	1	2	yes	—
140	C₂×C₇×Q₈	—	2	1	no	—
141	C₂×C₇×Q₈	—	2	4	no	—
142	C₂×C₇×Q₈	—	2	4	no	—
143	C₂×C₇×Q₈	—	2	2	no	—
144	C₂×C₇×Q₈	—	2	2	no	—
145	C₂×C₇×Q₈	—	4	4	no	—
146	C₂×C₇×Q₈	—	8	2	no	—
147	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
148	C₂×C₇×D₄	—	2	8	no	—
149	C₂×C₇×D₄	—	2	4	no	—
150	C₂×C₇×D₄	—	2	1	no	—
151	C₂×C₇×D₄	—	2	2	no	—
152	C₂×C₇×D₄	—	2	2	no	—
153	C₂×C₇×D₄	—	8	4	no	—
154	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
155	C₂×C₇×D₄	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₇	—	2	4	no	—
157	C₂²×C₄×C₇	—	2	4	no	—
158	C₂²×C₄×C₇	—	2	1	no	—
159	C₂²×C₄×C₇	—	2	1	no	—
160	C₂²×C₄×C₇	—	2	1	no	—
161	C₂²×C₄×C₇	—	2	2	no	—
162	C₂²×C₄×C₇	—	2	2	no	—
163	C₂²×C₄×C₇	—	2	4	no	—
164	C₂²×C₄×C₇	—	4	4	no	—
165	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
166	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
171	C₇×SD₁₆	—	2	8	no	—
172	C₂×C₇×C₈	—	2	4	no	—
173	C₂×C₇×C₈	—	2	2	no	—
174	C₂×C₇×C₈	—	2	16	no	—
175	C₂×C₇×C₈	#41	1	4	yes	—
176	C₂×C₇×C₈	C₂⁴	1	2	yes	—
177	C₂×C₇×C₈	C₂⁴	1	4	yes	—
178	C₂×C₇×C₈	C₂⁴	1	2	yes	—
179	C₇×C₄⋊C₄	—	2	4	no	—
180	C₇×C₄⋊C₄	—	2	8	no	—
181	C₇×C₄⋊C₄	—	2	4	no	—
182	C₇×C₄⋊C₄	—	2	4	no	—
183	C₇×C₄⋊C₄	—	2	1	no	—
184	C₇×C₄⋊C₄	—	2	1	no	—
185	C₇×C₄⋊C₄	—	2	2	no	—
186	C₇×C₄⋊C₄	—	2	2	no	—
187	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
188	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
189	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
190	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
191	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
192	C₇×C₂²⋊C₄	—	2	8	no	—
193	C₇×C₂²⋊C₄	—	2	8	no	—
194	C₇×C₂²⋊C₄	—	2	8	no	—
195	C₇×C₂²⋊C₄	—	2	8	no	—
196	C₇×C₂²⋊C₄	—	2	4	no	—
197	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
198	C₄²×C₇	—	2	8	no	—
199	C₄²×C₇	—	2	8	no	—
200	C₄²×C₇	—	2	4	no	—
201	C₄²×C₇	C₂×D₄	1	2	yes	—
202	C₄²×C₇	C₂⁴	1	2	yes	—
203	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
204	C₂³×C₈	C₂²×C₇	1	2	yes	—
205	#556	—	2	4	no	—
206	#556	C₂²×C₇	1	8	yes	complemented
207	#555	—	2	4	no	—
208	#555	C₂²×C₇	1	8	yes	—
209	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
210	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
211	C₂×#126	—	2	2	no	—
212	C₂×#124	—	2	1	no	—
213	C₂×#124	—	2	2	no	—
214	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
215	C₂×#121	—	2	1	no	—
216	C₂×#121	C₂²×C₇	1	2	yes	—
217	C₂×C₄×Q₈	—	2	1	no	—
218	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
219	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
220	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
221	C₂×#117	—	2	1	no	—
222	C₂×#117	C₂²×C₇	1	2	yes	—
223	C₂×#117	C₂²×C₇	1	2	yes	—
224	#498	C₂²×C₇	1	8	yes	complemented
225	#485	C₂²×C₇	1	16	yes	complemented
226	#482	C₂²×C₇	1	16	yes	complemented
227	#477	C₂²×C₇	1	8	yes	complemented
228	#474	C₂²×C₇	1	8	yes	complemented
229	#465	C₂²×C₇	1	16	yes	complemented
230	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
231	C₈×D₄	C₂²×C₇	1	8	yes	complemented
232	#427	C₂²×C₇	1	16	yes	complemented
233	C₂×#107	C₂²×C₇	1	2	yes	—
234	C₂×#107	C₂²×C₇	1	2	yes	—
235	C₂×#106	C₂²×C₇	1	2	yes	—
236	C₂×#106	C₂²×C₇	1	2	yes	—
237	C₂×#106	C₂²×C₇	1	1	yes	characteristic
238	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
239	C₂×#103	C₂²×C₇	1	2	yes	—
240	C₂×#103	C₂²×C₇	1	1	yes	characteristic
241	C₂×#102	C₂²×C₇	1	1	yes	characteristic
242	C₂×#102	C₂²×C₇	1	2	yes	—
243	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
244	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
245	C₂³×C₇	—	2	4	no	—
246	C₂³×C₇	—	2	4	no	—
247	C₂³×C₇	—	2	4	no	—
248	C₂³×C₇	—	2	2	no	—
249	C₂³×C₇	—	4	2	no	—
250	C₂³×C₇	—	4	2	no	—
251	C₂³×C₇	—	4	2	no	—
252	C₂³×C₇	C₂²×D₄	1	4	yes	—
253	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
254	C₇×Q₈	—	2	2	no	—
255	C₇×Q₈	—	2	2	no	—
256	C₇×Q₈	—	4	2	no	—
257	C₇×Q₈	—	4	8	no	—
258	C₇×Q₈	—	8	4	no	—
259	C₇×D₄	—	2	8	no	—
260	C₇×D₄	—	2	2	no	—
261	C₇×D₄	—	2	2	no	—
262	C₇×D₄	—	4	2	no	—
263	C₇×D₄	—	8	8	no	—
264	C₂×C₄×C₇	—	2	4	no	—
265	C₂×C₄×C₇	—	2	2	no	—
266	C₂×C₄×C₇	—	2	8	no	—
267	C₂×C₄×C₇	—	2	4	no	—
268	C₂×C₄×C₇	—	2	4	no	—
269	C₂×C₄×C₇	—	2	2	no	—
270	C₂×C₄×C₇	—	2	2	no	—
271	C₂×C₄×C₇	—	2	2	no	—
272	C₂×C₄×C₇	—	2	4	no	—
273	C₂×C₄×C₇	—	2	4	no	—
274	C₂×C₄×C₇	—	4	2	no	—
275	C₂×C₄×C₇	—	4	2	no	—
276	C₂×C₄×C₇	—	4	4	no	—
277	C₂×C₄×C₇	—	4	2	no	—
278	C₂×C₄×C₇	—	4	4	no	—
279	C₂×C₄×C₇	—	4	8	no	—
280	C₂×C₄×C₇	#135	1	4	yes	—
281	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
282	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
283	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
285	C₂×C₄×C₇	C₂×#41	1	2	yes	—
286	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
287	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
288	C₇×C₈	—	2	4	no	—
289	C₇×C₈	—	2	2	no	—
290	C₇×C₈	C₂×#41	1	4	yes	—
291	C₂²×Q₈	—	2	1	no	—
292	C₂²×Q₈	—	2	1	no	—
293	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
294	C₂²×D₄	—	2	2	no	—
295	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
296	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
297	C₂³×C₄	—	2	1	no	—
298	C₂³×C₄	C₂³×C₇	1	2	yes	—
299	C₂×SD₁₆	—	2	4	no	—
300	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
301	C₂²×C₈	—	2	8	no	—
302	C₂²×C₈	C₂³×C₇	1	2	yes	—
303	C₂²×C₈	C₂³×C₇	1	8	yes	—
304	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
306	C₄⋊Q₈	—	2	2	no	—
307	C₄⋊Q₈	—	2	2	no	—
308	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
309	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
310	#126	—	2	16	no	—
311	#124	—	2	8	no	—
312	#124	—	2	16	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
315	#121	—	2	8	no	—
316	#121	—	2	4	no	—
317	#121	C₂³×C₇	1	8	yes	—
318	C₄×Q₈	—	2	8	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	C₂³×C₇	1	4	yes	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	C₇×D₄	1	4	yes	—
323	C₄×D₄	C₂³×C₇	1	4	yes	—
324	C₄×D₄	C₂³×C₇	1	4	yes	—
325	#117	—	2	4	no	—
326	#117	—	2	4	no	—
327	#117	—	2	8	no	—
328	#117	C₂³×C₇	1	8	yes	—
329	#117	C₂³×C₇	1	8	yes	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
345	C₂×C₄²	—	2	2	no	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
349	#107	C₂³×C₇	1	8	yes	—
350	#107	C₂³×C₇	1	8	yes	—
351	#106	C₂³×C₇	1	4	yes	—
352	#106	C₂³×C₇	1	8	yes	—
353	#106	C₂³×C₇	1	8	yes	—
354	C₄⋊C₈	C₂³×C₇	1	4	yes	—
355	#103	C₂³×C₇	1	4	yes	—
356	#103	C₂³×C₇	1	8	yes	—
357	#102	C₂³×C₇	1	4	yes	—
358	#102	C₂³×C₇	1	8	yes	—
359	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
360	C₄×C₈	C₂³×C₇	1	4	yes	—
361	C₂²×C₇	—	2	4	no	—
362	C₂²×C₇	—	2	4	no	—
363	C₂²×C₇	—	2	4	no	—
364	C₂²×C₇	—	4	8	no	—
365	C₂²×C₇	—	4	2	no	—
366	C₂²×C₇	—	4	2	no	—
367	C₂²×C₇	—	4	2	no	—
368	C₂²×C₇	—	8	4	no	—
369	C₂²×C₇	#547	1	2	yes	—
370	C₂²×C₇	C₂×#135	1	2	yes	—
371	C₂²×C₇	#577	1	2	yes	—
372	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
373	C₄×C₇	—	2	4	no	—
374	C₄×C₇	—	2	2	no	—
375	C₄×C₇	—	4	2	no	—
376	C₄×C₇	—	4	2	no	—
377	C₄×C₇	—	4	4	no	—
378	C₄×C₇	—	4	2	no	—
379	C₄×C₇	—	4	4	no	—
380	C₄×C₇	#547	1	2	yes	—
381	C₄×C₇	C₂×#135	1	4	yes	—
382	C₄×C₇	C₂²×#41	1	1	yes	characteristic
383	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
384	C₂⁴	—	2	1	no	—
385	C₂⁴	C₂×C₇×D₄	1	2	yes	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	4	no	—
388	C₂×Q₈	—	2	4	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	4	4	no	—
392	C₂×Q₈	—	8	2	no	—
393	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
394	C₂×D₄	—	2	8	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	8	4	no	—
400	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
401	C₂×D₄	C₂⁴×C₇	1	2	yes	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	4	4	no	—
411	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
412	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
413	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
414	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
415	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
416	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
417	SD₁₆	—	2	8	no	—
418	C₂×C₈	—	2	4	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	16	no	—
421	C₂×C₈	C₇×#41	1	4	yes	—
422	C₂×C₈	C₂⁴×C₇	1	2	yes	—
423	C₂×C₈	C₂⁴×C₇	1	4	yes	—
424	C₂×C₈	C₂⁴×C₇	1	2	yes	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	8	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
434	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
435	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
436	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
437	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
438	C₂²⋊C₄	—	2	8	no	—
439	C₂²⋊C₄	—	2	8	no	—
440	C₂²⋊C₄	—	2	8	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
444	C₄²	—	2	8	no	—
445	C₄²	—	2	8	no	—
446	C₄²	—	2	4	no	—
447	C₄²	C₂×C₇×D₄	1	2	yes	—
448	C₄²	C₂⁴×C₇	1	2	yes	—
449	C₂×C₇	—	4	4	no	—
450	C₂×C₇	—	8	2	no	—
451	C₂×C₇	#3340	1	4	yes	direct product factor
452	C₂×C₇	C₂×#547	1	1	yes	characteristic
453	C₂×C₇	C₂²×#135	1	1	yes	characteristic
454	C₂×C₇	C₂×#577	1	1	yes	characteristic
455	C₂³	—	2	4	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	C₂²×C₇×D₄	1	4	yes	—
463	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
464	Q₈	—	2	2	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	4	8	no	—
468	Q₈	—	8	4	no	—
469	D₄	—	2	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	8	no	—
472	D₄	—	4	2	no	—
473	D₄	—	8	8	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	8	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	8	no	—
490	C₂×C₄	C₇×#135	1	4	yes	—
491	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
492	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
493	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
494	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
495	C₂×C₄	C₂×C₇×#41	1	2	yes	—
496	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
497	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
498	C₈	—	2	4	no	—
499	C₈	—	2	2	no	—
500	C₈	C₂×C₇×#41	1	4	yes	—
501	C₇	C₂×#3340	1	1	yes	characteristic, direct product factor, Sylow
502	C₂²	—	2	4	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	4	8	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	8	4	no	—
510	C₂²	C₇×#547	1	2	yes	—
511	C₂²	C₂×C₇×#135	1	2	yes	—
512	C₂²	C₇×#577	1	2	yes	—
513	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
514	C₄	—	2	2	no	—
515	C₄	—	2	4	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	4	no	—
518	C₄	—	4	4	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	2	no	—
521	C₄	C₇×#547	1	2	yes	—
522	C₄	C₂×C₇×#135	1	4	yes	—
523	C₄	C₂²×C₇×#41	1	1	yes	characteristic
524	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
525	C₂	—	4	4	no	—
526	C₂	—	8	2	no	—
527	C₂	C₇×#3340	1	4	yes	direct product factor
528	C₂	C₂×C₇×#547	1	1	yes	characteristic
529	C₂	C₂²×C₇×#135	1	1	yes	characteristic
530	C₂	C₂×C₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#555	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×#3340	C₂	direct (N × H)
4. C₂×C₇×#498	C₂	semidirect
5. C₂×C₇×#485	C₂	semidirect
6. C₂×C₇×#482	C₂	semidirect
7. C₂×C₇×#477	C₂	semidirect
8. C₂×C₇×#474	C₂	semidirect
9. C₂×C₇×#465	C₂	semidirect
10. C₂×C₄×C₇×SD₁₆	C₂	semidirect
11. C₂×C₇×C₈×D₄	C₂	semidirect
12. C₂×C₇×#427	C₂	semidirect
16. C₇×#556	C₂²	semidirect
34. C₇×#498	C₂²	semidirect
35. C₇×#485	C₂²	semidirect
36. C₇×#482	C₂²	semidirect
37. C₇×#477	C₂²	semidirect
38. C₇×#474	C₂²	semidirect
39. C₇×#465	C₂²	semidirect
40. C₄×C₇×SD₁₆	C₂²	semidirect
41. C₇×C₈×D₄	C₂²	semidirect
42. C₇×#427	C₂²	semidirect
55. C₂×#3340	C₇	direct (N × H)
126. C₂×#556	C₂×C₇	semidirect
128. #3340	C₂×C₇	direct (N × H)
129. C₂×#498	C₂×C₇	semidirect
130. C₂×#485	C₂×C₇	semidirect
131. C₂×#482	C₂×C₇	semidirect
132. C₂×#477	C₂×C₇	semidirect
133. C₂×#474	C₂×C₇	semidirect
134. C₂×#465	C₂×C₇	semidirect
135. C₂×C₄×SD₁₆	C₂×C₇	semidirect
136. C₂×C₈×D₄	C₂×C₇	semidirect
137. C₂×#427	C₂×C₇	semidirect
206. #556	C₂²×C₇	semidirect
224. #498	C₂²×C₇	semidirect
225. #485	C₂²×C₇	semidirect
226. #482	C₂²×C₇	semidirect
227. #477	C₂²×C₇	semidirect
228. #474	C₂²×C₇	semidirect
229. #465	C₂²×C₇	semidirect
230. C₄×SD₁₆	C₂²×C₇	semidirect
231. C₈×D₄	C₂²×C₇	semidirect
232. #427	C₂²×C₇	semidirect
451. C₂×C₇	#3340	direct (N × H)
501. C₇	C₂×#3340	direct (N × H)
527. C₂	C₇×#3340	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×#555	2
C₇×#3340	2
C₂×C₇×#498	2
C₂×C₇×#485	2
C₂×C₇×#482	2
C₂×C₇×#477	2
C₂×C₇×#474	2
C₂×C₇×#465	2
C₂×C₄×C₇×SD₁₆	2
C₂×C₇×C₈×D₄	2
C₂×C₇×#427	2
C₂×#3340	7

Subgroups — C2×C7×#3340 #13238447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3340 #13238447