Subgroups — C₂×C₇×#3356 #13238465

Order 1792.

1866 conjugacy classes of subgroups.

The subgroup lattice has 516 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
2	C₂×C₇×#554	C₂	1	1	yes	maximal, characteristic
3	C₇×#3356	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×#483	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#475	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#470	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×#428	C₂	1	2	yes	maximal, complemented
13	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
15	C₇×#556	—	2	4	no	—
16	C₇×#556	C₂²	1	8	yes	—
17	C₇×#554	—	2	4	no	—
18	C₇×#554	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×#125	—	2	1	no	—
23	C₂×C₇×#124	—	2	1	no	—
24	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
25	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₇×C₂²⋊Q₈	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×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×D₄	—	2	1	no	—
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×#498	C₂²	1	8	yes	complemented
35	C₇×#485	C₂²	1	16	yes	complemented
36	C₇×#483	C₂²	1	16	yes	complemented
37	C₇×#477	C₂²	1	8	yes	complemented
38	C₇×#475	C₂²	1	8	yes	complemented
39	C₇×#470	C₂²	1	16	yes	complemented
40	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
41	C₇×#436	C₂²	1	8	yes	—
42	C₇×#428	C₂²	1	16	yes	complemented
43	C₂×C₇×#107	C₂²	1	1	yes	characteristic
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	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	1	yes	characteristic
51	C₂×C₇×#103	C₂²	1	2	yes	—
52	C₂×C₇×#103	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×#3356	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×Q₈	C₂³	1	1	yes	characteristic
60	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₇	—	2	2	no	—
62	C₂³×C₄×C₇	C₂³	1	2	yes	—
63	C₂×C₇×Q₁₆	—	2	4	no	—
64	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
65	C₂×C₇×M₁₆	—	2	8	no	—
66	C₂×C₇×M₁₆	C₂³	1	8	yes	—
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂³	1	2	yes	—
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₇×C₄⋊Q₈	—	2	2	no	—
71	C₇×C₄⋊Q₈	—	2	2	no	—
72	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
73	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
74	C₇×#126	—	2	16	no	—
75	C₇×#125	—	2	8	no	—
76	C₇×#124	—	2	8	no	—
77	C₇×C₂²⋊Q₈	—	2	4	no	—
78	C₇×C₂²⋊Q₈	—	2	4	no	—
79	C₇×C₂²⋊Q₈	—	2	16	no	—
80	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
81	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
82	C₄×C₇×Q₈	—	2	8	no	—
83	C₄×C₇×Q₈	—	2	2	no	—
84	C₄×C₇×Q₈	—	2	2	no	—
85	C₄×C₇×Q₈	C₂³	1	4	yes	—
86	C₄×C₇×Q₈	C₂³	1	4	yes	—
87	C₄×C₇×D₄	—	2	8	no	—
88	C₄×C₇×D₄	D₄	1	4	yes	—
89	C₄×C₇×D₄	C₂³	1	4	yes	—
90	C₇×#117	—	2	4	no	—
91	C₇×#117	C₂³	1	8	yes	—
92	C₂×C₇×C₄⋊C₄	—	2	2	no	—
93	C₂×C₇×C₄⋊C₄	—	2	4	no	—
94	C₂×C₇×C₄⋊C₄	—	2	1	no	—
95	C₂×C₇×C₄⋊C₄	—	2	2	no	—
96	C₂×C₇×C₄⋊C₄	—	2	1	no	—
97	C₂×C₇×C₄⋊C₄	—	2	1	no	—
98	C₂×C₇×C₄⋊C₄	—	2	2	no	—
99	C₂×C₇×C₄⋊C₄	—	2	1	no	—
100	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
101	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
102	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
107	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
109	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
110	C₂×C₄²×C₇	—	2	2	no	—
111	C₂×C₄²×C₇	—	2	1	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	4	yes	—
116	C₇×#106	C₂³	1	8	yes	—
117	C₇×#106	C₂³	1	8	yes	—
118	C₇×#106	C₂³	1	8	yes	—
119	C₇×C₄⋊C₈	C₂³	1	4	yes	—
120	C₇×#103	C₂³	1	8	yes	—
121	C₇×#103	C₂³	1	8	yes	—
122	C₇×#103	C₂³	1	4	yes	—
123	C₇×#103	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
127	C₂×#554	C₂×C₇	1	1	yes	characteristic
128	#3356	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×#483	C₂×C₇	1	2	yes	complemented
132	C₂×#477	C₂×C₇	1	1	yes	characteristic, complemented
133	C₂×#475	C₂×C₇	1	1	yes	characteristic, complemented
134	C₂×#470	C₂×C₇	1	2	yes	complemented
135	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
136	C₂×#436	C₂×C₇	1	1	yes	characteristic
137	C₂×#428	C₂×C₇	1	2	yes	complemented
138	C₂⁴×C₇	C₂×D₄	1	2	yes	—
139	C₂×C₇×Q₈	—	2	1	no	—
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	—	2	2	no	—
146	C₂×C₇×Q₈	—	2	2	no	—
147	C₂×C₇×Q₈	—	4	4	no	—
148	C₂×C₇×Q₈	—	8	2	no	—
149	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
150	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
151	C₂×C₇×D₄	—	2	4	no	—
152	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₇	—	2	4	no	—
154	C₂²×C₄×C₇	—	2	4	no	—
155	C₂²×C₄×C₇	—	2	1	no	—
156	C₂²×C₄×C₇	—	2	1	no	—
157	C₂²×C₄×C₇	—	2	1	no	—
158	C₂²×C₄×C₇	—	2	2	no	—
159	C₂²×C₄×C₇	—	2	1	no	—
160	C₂²×C₄×C₇	—	2	2	no	—
161	C₂²×C₄×C₇	—	2	8	no	—
162	C₂²×C₄×C₇	—	8	4	no	—
163	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
169	C₇×Q₁₆	—	2	8	no	—
170	C₇×M₁₆	—	2	16	no	—
171	C₂×C₇×C₈	—	2	4	no	—
172	C₂×C₇×C₈	—	2	2	no	—
173	C₂×C₇×C₈	#41	1	4	yes	—
174	C₂×C₇×C₈	C₂⁴	1	2	yes	—
175	C₂×C₇×C₈	C₂⁴	1	4	yes	—
176	C₂×C₇×C₈	C₂⁴	1	2	yes	—
177	C₇×C₄⋊C₄	—	2	1	no	—
178	C₇×C₄⋊C₄	—	2	8	no	—
179	C₇×C₄⋊C₄	—	2	2	no	—
180	C₇×C₄⋊C₄	—	2	4	no	—
181	C₇×C₄⋊C₄	—	2	8	no	—
182	C₇×C₄⋊C₄	—	2	4	no	—
183	C₇×C₄⋊C₄	—	2	4	no	—
184	C₇×C₄⋊C₄	—	2	8	no	—
185	C₇×C₄⋊C₄	—	2	4	no	—
186	C₇×C₄⋊C₄	—	2	1	no	—
187	C₇×C₄⋊C₄	—	2	2	no	—
188	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
189	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
190	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
191	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
192	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
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	C₂×D₄	1	8	yes	—
197	C₄²×C₇	—	2	8	no	—
198	C₄²×C₇	—	2	4	no	—
199	C₄²×C₇	—	2	4	no	—
200	C₄²×C₇	C₂×D₄	1	2	yes	—
201	C₄²×C₇	C₂⁴	1	2	yes	—
202	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
203	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
204	#556	—	2	4	no	—
205	#556	C₂²×C₇	1	8	yes	—
206	#554	—	2	4	no	—
207	#554	C₂²×C₇	1	8	yes	—
208	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
210	C₂×#126	—	2	2	no	—
211	C₂×#125	—	2	1	no	—
212	C₂×#124	—	2	1	no	—
213	C₂×C₂²⋊Q₈	—	2	2	no	—
214	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
215	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
216	C₂×C₄×Q₈	—	2	1	no	—
217	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
218	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
219	C₂×C₄×D₄	—	2	1	no	—
220	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
221	C₂×#117	C₂²×C₇	1	2	yes	—
222	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
223	#498	C₂²×C₇	1	8	yes	complemented
224	#485	C₂²×C₇	1	16	yes	complemented
225	#483	C₂²×C₇	1	16	yes	complemented
226	#477	C₂²×C₇	1	8	yes	complemented
227	#475	C₂²×C₇	1	8	yes	complemented
228	#470	C₂²×C₇	1	16	yes	complemented
229	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
230	#436	C₂²×C₇	1	8	yes	—
231	#428	C₂²×C₇	1	16	yes	complemented
232	C₂×#107	C₂²×C₇	1	2	yes	—
233	C₂×#107	C₂²×C₇	1	1	yes	characteristic
234	C₂×#106	C₂²×C₇	1	2	yes	—
235	C₂×#106	C₂²×C₇	1	2	yes	—
236	C₂×#106	C₂²×C₇	1	2	yes	—
237	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
238	C₂×#103	C₂²×C₇	1	2	yes	—
239	C₂×#103	C₂²×C₇	1	2	yes	—
240	C₂×#103	C₂²×C₇	1	1	yes	characteristic
241	C₂×#103	C₂²×C₇	1	1	yes	characteristic
242	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
243	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
244	C₂³×C₇	—	2	4	no	—
245	C₂³×C₇	—	2	4	no	—
246	C₂³×C₇	—	2	4	no	—
247	C₂³×C₇	C₂²×D₄	1	4	yes	—
248	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
249	C₇×Q₈	—	2	2	no	—
250	C₇×Q₈	—	2	2	no	—
251	C₇×Q₈	—	2	2	no	—
252	C₇×Q₈	—	2	2	no	—
253	C₇×Q₈	—	4	2	no	—
254	C₇×Q₈	—	4	2	no	—
255	C₇×Q₈	—	4	8	no	—
256	C₇×Q₈	—	8	4	no	—
257	C₇×D₄	—	2	8	no	—
258	C₂×C₄×C₇	—	2	4	no	—
259	C₂×C₄×C₇	—	2	2	no	—
260	C₂×C₄×C₇	—	2	8	no	—
261	C₂×C₄×C₇	—	2	4	no	—
262	C₂×C₄×C₇	—	2	4	no	—
263	C₂×C₄×C₇	—	2	2	no	—
264	C₂×C₄×C₇	—	2	2	no	—
265	C₂×C₄×C₇	—	2	2	no	—
266	C₂×C₄×C₇	—	2	4	no	—
267	C₂×C₄×C₇	—	2	2	no	—
268	C₂×C₄×C₇	—	2	4	no	—
269	C₂×C₄×C₇	—	4	2	no	—
270	C₂×C₄×C₇	—	4	2	no	—
271	C₂×C₄×C₇	—	4	4	no	—
272	C₂×C₄×C₇	—	4	2	no	—
273	C₂×C₄×C₇	—	4	2	no	—
274	C₂×C₄×C₇	—	4	4	no	—
275	C₂×C₄×C₇	—	8	8	no	—
276	C₂×C₄×C₇	#137	1	4	yes	—
277	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
278	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
279	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
281	C₂×C₄×C₇	C₂×#41	1	2	yes	—
282	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
283	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
284	C₇×C₈	—	2	4	no	—
285	C₇×C₈	—	2	2	no	—
286	C₇×C₈	C₂×#41	1	4	yes	—
287	C₂²×Q₈	—	2	1	no	—
288	C₂²×Q₈	—	2	1	no	—
289	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
290	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
291	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
292	C₂³×C₄	—	2	2	no	—
293	C₂³×C₄	C₂³×C₇	1	2	yes	—
294	C₂×Q₁₆	—	2	4	no	—
295	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
296	C₂×M₁₆	—	2	8	no	—
297	C₂×M₁₆	C₂³×C₇	1	8	yes	—
298	C₂²×C₈	C₂³×C₇	1	2	yes	—
299	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	—	2	2	no	—
303	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
304	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
305	#126	—	2	16	no	—
306	#125	—	2	8	no	—
307	#124	—	2	8	no	—
308	C₂²⋊Q₈	—	2	4	no	—
309	C₂²⋊Q₈	—	2	4	no	—
310	C₂²⋊Q₈	—	2	16	no	—
311	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
312	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
313	C₄×Q₈	—	2	8	no	—
314	C₄×Q₈	—	2	2	no	—
315	C₄×Q₈	—	2	2	no	—
316	C₄×Q₈	C₂³×C₇	1	4	yes	—
317	C₄×Q₈	C₂³×C₇	1	4	yes	—
318	C₄×D₄	—	2	8	no	—
319	C₄×D₄	C₇×D₄	1	4	yes	—
320	C₄×D₄	C₂³×C₇	1	4	yes	—
321	#117	—	2	4	no	—
322	#117	C₂³×C₇	1	8	yes	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	4	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
335	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
341	C₂×C₄²	—	2	2	no	—
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
345	#107	C₂³×C₇	1	4	yes	—
346	#107	C₂³×C₇	1	8	yes	—
347	#106	C₂³×C₇	1	8	yes	—
348	#106	C₂³×C₇	1	8	yes	—
349	#106	C₂³×C₇	1	8	yes	—
350	C₄⋊C₈	C₂³×C₇	1	4	yes	—
351	#103	C₂³×C₇	1	4	yes	—
352	#103	C₂³×C₇	1	4	yes	—
353	#103	C₂³×C₇	1	8	yes	—
354	#103	C₂³×C₇	1	8	yes	—
355	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
356	C₄×C₈	C₂³×C₇	1	4	yes	—
357	C₂²×C₇	—	2	4	no	—
358	C₂²×C₇	—	2	4	no	—
359	C₂²×C₇	—	2	4	no	—
360	C₂²×C₇	—	4	8	no	—
361	C₂²×C₇	#547	1	2	yes	—
362	C₂²×C₇	C₂×#137	1	2	yes	—
363	C₂²×C₇	#577	1	2	yes	—
364	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
365	C₄×C₇	—	2	4	no	—
366	C₄×C₇	—	2	2	no	—
367	C₄×C₇	—	4	2	no	—
368	C₄×C₇	—	4	2	no	—
369	C₄×C₇	—	4	4	no	—
370	C₄×C₇	—	4	2	no	—
371	C₄×C₇	—	4	2	no	—
372	C₄×C₇	—	4	4	no	—
373	C₄×C₇	#547	1	2	yes	—
374	C₄×C₇	C₂×#137	1	4	yes	—
375	C₄×C₇	C₂²×#41	1	1	yes	characteristic
376	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
377	C₂⁴	C₂×C₇×D₄	1	2	yes	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	—	2	4	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	4	4	no	—
387	C₂×Q₈	—	8	2	no	—
388	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
389	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	8	no	—
401	C₂²×C₄	—	8	4	no	—
402	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
403	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
404	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
405	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
406	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
407	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
408	Q₁₆	—	2	8	no	—
409	M₁₆	—	2	16	no	—
410	C₂×C₈	—	2	4	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	C₇×#41	1	4	yes	—
413	C₂×C₈	C₂⁴×C₇	1	2	yes	—
414	C₂×C₈	C₂⁴×C₇	1	4	yes	—
415	C₂×C₈	C₂⁴×C₇	1	2	yes	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	8	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
428	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
429	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
430	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
431	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
432	C₂²⋊C₄	—	2	8	no	—
433	C₂²⋊C₄	—	2	8	no	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
436	C₄²	—	2	8	no	—
437	C₄²	—	2	4	no	—
438	C₄²	—	2	4	no	—
439	C₄²	C₂×C₇×D₄	1	2	yes	—
440	C₄²	C₂⁴×C₇	1	2	yes	—
441	C₂×C₇	—	4	4	no	—
442	C₂×C₇	#3356	1	4	yes	direct product factor
443	C₂×C₇	C₂×#547	1	1	yes	characteristic
444	C₂×C₇	C₂²×#137	1	1	yes	characteristic
445	C₂×C₇	C₂×#577	1	1	yes	characteristic
446	C₂³	—	2	4	no	—
447	C₂³	—	2	4	no	—
448	C₂³	—	2	4	no	—
449	C₂³	C₂²×C₇×D₄	1	4	yes	—
450	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
451	Q₈	—	2	2	no	—
452	Q₈	—	2	2	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	2	2	no	—
455	Q₈	—	4	2	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	8	no	—
458	Q₈	—	8	4	no	—
459	D₄	—	2	8	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	8	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	8	8	no	—
478	C₂×C₄	C₇×#137	1	4	yes	—
479	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
480	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
481	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
482	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
483	C₂×C₄	C₂×C₇×#41	1	2	yes	—
484	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
485	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
486	C₈	—	2	4	no	—
487	C₈	—	2	2	no	—
488	C₈	C₂×C₇×#41	1	4	yes	—
489	C₇	C₂×#3356	1	1	yes	characteristic, direct product factor, Sylow
490	C₂²	—	2	4	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	4	8	no	—
494	C₂²	C₇×#547	1	2	yes	—
495	C₂²	C₂×C₇×#137	1	2	yes	—
496	C₂²	C₇×#577	1	2	yes	—
497	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	2	4	no	—
500	C₄	—	4	4	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	C₇×#547	1	2	yes	—
507	C₄	C₂×C₇×#137	1	4	yes	—
508	C₄	C₂²×C₇×#41	1	1	yes	characteristic
509	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
510	C₂	—	4	4	no	—
511	C₂	C₇×#3356	1	4	yes	direct product factor
512	C₂	C₂×C₇×#547	1	1	yes	characteristic
513	C₂	C₂²×C₇×#137	1	1	yes	characteristic
514	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	C₂²×C₇×D₄	D₄
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
3. C₇×#3356	C₂	direct (N × H)
4. C₂×C₇×#498	C₂	semidirect
5. C₂×C₇×#485	C₂	semidirect
6. C₂×C₇×#483	C₂	semidirect
7. C₂×C₇×#477	C₂	semidirect
8. C₂×C₇×#475	C₂	semidirect
9. C₂×C₇×#470	C₂	semidirect
10. C₂×C₄×C₇×Q₁₆	C₂	semidirect
12. C₂×C₇×#428	C₂	semidirect
34. C₇×#498	C₂²	semidirect
35. C₇×#485	C₂²	semidirect
36. C₇×#483	C₂²	semidirect
37. C₇×#477	C₂²	semidirect
38. C₇×#475	C₂²	semidirect
39. C₇×#470	C₂²	semidirect
40. C₄×C₇×Q₁₆	C₂²	semidirect
42. C₇×#428	C₂²	semidirect
55. C₂×#3356	C₇	direct (N × H)
128. #3356	C₂×C₇	direct (N × H)
129. C₂×#498	C₂×C₇	semidirect
130. C₂×#485	C₂×C₇	semidirect
131. C₂×#483	C₂×C₇	semidirect
132. C₂×#477	C₂×C₇	semidirect
133. C₂×#475	C₂×C₇	semidirect
134. C₂×#470	C₂×C₇	semidirect
135. C₂×C₄×Q₁₆	C₂×C₇	semidirect
137. C₂×#428	C₂×C₇	semidirect
223. #498	C₂²×C₇	semidirect
224. #485	C₂²×C₇	semidirect
225. #483	C₂²×C₇	semidirect
226. #477	C₂²×C₇	semidirect
227. #475	C₂²×C₇	semidirect
228. #470	C₂²×C₇	semidirect
229. C₄×Q₁₆	C₂²×C₇	semidirect
231. #428	C₂²×C₇	semidirect
442. C₂×C₇	#3356	direct (N × H)
489. C₇	C₂×#3356	direct (N × H)
511. C₂	C₇×#3356	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×#554	2
C₇×#3356	2
C₂×C₇×#498	2
C₂×C₇×#485	2
C₂×C₇×#483	2
C₂×C₇×#477	2
C₂×C₇×#475	2
C₂×C₇×#470	2
C₂×C₄×C₇×Q₁₆	2
C₂×C₇×#436	2
C₂×C₇×#428	2
C₂×#3356	7

Subgroups — C2×C7×#3356 #13238465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3356 #13238465