Subgroups — C₂×C₇×#3386 #13238576

Order 1792.

2006 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×D₄×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₇×#3386	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#501	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#500	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#477	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#475	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#478	C₂	1	2	yes	maximal
9	C₂×C₇×#474	C₂	1	1	yes	maximal, characteristic
10	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#440	C₂	1	2	yes	maximal
12	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic
13	C₂³×C₇×Q₈	—	2	1	no	—
14	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
15	C₇×#557	—	2	4	no	—
16	C₇×#557	C₂²	1	8	yes	complemented
17	C₇×D₄×Q₈	—	2	4	no	—
18	C₇×D₄×Q₈	C₂²	1	8	yes	—
19	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₇×#125	—	2	2	no	—
24	C₂×C₇×#125	C₂²	1	2	yes	—
25	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
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	2	yes	—
30	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
33	C₇×#501	C₂²	1	16	yes	complemented
34	C₇×#500	C₂²	1	8	yes	complemented
35	C₇×#478	C₂²	1	16	yes	—
36	C₇×#477	C₂²	1	16	yes	complemented
37	C₇×#475	C₂²	1	8	yes	complemented
38	C₇×#474	C₂²	1	8	yes	—
39	C₇×#446	C₂²	1	8	yes	complemented
40	C₇×#440	C₂²	1	16	yes	—
41	C₄×C₇×SD₁₆	C₂²	1	8	yes	—
42	C₂×C₇×#107	C₂²	1	2	yes	—
43	C₂×C₇×#107	C₂²	1	2	yes	—
44	C₂×C₇×#107	C₂²	1	2	yes	—
45	C₂×C₇×#106	C₂²	1	1	yes	characteristic
46	C₂×C₇×#106	C₂²	1	2	yes	—
47	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
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×#97	C₂²	1	2	yes	—
54	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
55	C₂×#3386	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂²×C₇×Q₈	—	2	8	no	—
57	C₂²×C₇×Q₈	—	2	2	no	—
58	C₂²×C₇×Q₈	—	2	1	no	—
59	C₂²×C₇×Q₈	—	2	1	no	—
60	C₂²×C₇×Q₈	—	4	8	no	—
61	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
62	C₂²×C₇×Q₈	C₂³	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	C₂×C₇×SD₁₆	Q₈	1	8	yes	complemented
67	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂³	1	2	yes	—
70	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
71	C₇×C₄⋊Q₈	—	2	8	no	—
72	C₇×C₄⋊Q₈	—	2	4	no	—
73	C₇×C₄⋊Q₈	—	2	2	no	—
74	C₇×C₄⋊Q₈	—	2	2	no	—
75	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
76	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
77	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
78	C₇×#125	—	2	16	no	—
79	C₇×#125	—	2	4	no	—
80	C₇×#125	C₂³	1	8	yes	—
81	C₇×C₂²⋊Q₈	—	2	8	no	—
82	C₇×C₂²⋊Q₈	—	2	16	no	—
83	C₄×C₇×Q₈	—	2	8	no	—
84	C₄×C₇×Q₈	—	2	4	no	—
85	C₄×C₇×Q₈	—	2	2	no	—
86	C₄×C₇×Q₈	D₄	1	4	yes	—
87	C₄×C₇×Q₈	C₂³	1	4	yes	—
88	C₄×C₇×Q₈	C₂³	1	8	yes	—
89	C₄×C₇×Q₈	C₂³	1	4	yes	—
90	C₄×C₇×D₄	—	2	4	no	—
91	C₄×C₇×D₄	—	2	2	no	—
92	C₄×C₇×D₄	C₂³	1	4	yes	—
93	C₄×C₇×D₄	C₂³	1	8	yes	—
94	C₂×C₇×C₄⋊C₄	—	2	2	no	—
95	C₂×C₇×C₄⋊C₄	—	2	1	no	—
96	C₂×C₇×C₄⋊C₄	—	2	2	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	2	no	—
101	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
102	C₂×C₇×C₄⋊C₄	D₄	1	2	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	1	no	—
109	C₂×C₄²×C₇	—	2	2	no	—
110	C₂×C₄²×C₇	—	2	1	no	—
111	C₂×C₄²×C₇	C₂³	1	2	yes	—
112	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
113	C₇×#107	C₂³	1	8	yes	—
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	4	yes	—
118	C₇×C₄⋊C₈	C₂³	1	4	yes	—
119	C₇×C₄⋊C₈	C₂³	1	8	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×#97	C₂³	1	8	yes	—
125	C₄×C₇×C₈	C₂³	1	4	yes	—
126	C₂×#557	C₂×C₇	1	1	yes	characteristic, complemented
127	C₂×D₄×Q₈	C₂×C₇	1	1	yes	characteristic
128	#3386	C₂×C₇	1	16	yes	direct product factor
129	C₂×#501	C₂×C₇	1	2	yes	complemented
130	C₂×#500	C₂×C₇	1	1	yes	characteristic, complemented
131	C₂×#477	C₂×C₇	1	2	yes	complemented
132	C₂×#475	C₂×C₇	1	1	yes	characteristic, complemented
133	C₂×#478	C₂×C₇	1	2	yes	—
134	C₂×#474	C₂×C₇	1	1	yes	characteristic
135	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
136	C₂×#440	C₂×C₇	1	2	yes	—
137	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic
138	C₂⁴×C₇	—	2	1	no	—
139	C₂×C₇×Q₈	—	2	4	no	—
140	C₂×C₇×Q₈	—	2	1	no	—
141	C₂×C₇×Q₈	—	2	4	no	—
142	C₂×C₇×Q₈	—	2	8	no	—
143	C₂×C₇×Q₈	—	2	4	no	—
144	C₂×C₇×Q₈	—	2	2	no	—
145	C₂×C₇×Q₈	—	4	8	no	—
146	C₂×C₇×Q₈	—	4	32	no	—
147	C₂×C₇×Q₈	—	4	4	no	—
148	C₂×C₇×Q₈	—	4	4	no	—
149	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
150	C₂×C₇×Q₈	C₂×Q₈	1	4	yes	complemented
151	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
152	C₂×C₇×D₄	—	2	1	no	—
153	C₂×C₇×D₄	—	2	2	no	—
154	C₂×C₇×D₄	C₂×Q₈	1	4	yes	—
155	C₂×C₇×D₄	C₂⁴	1	2	yes	—
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	2	no	—
160	C₂²×C₄×C₇	—	2	1	no	—
161	C₂²×C₄×C₇	—	2	8	no	—
162	C₂²×C₄×C₇	—	2	4	no	—
163	C₂²×C₄×C₇	—	4	8	no	—
164	C₂²×C₄×C₇	—	4	4	no	—
165	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
170	C₇×SD₁₆	C₂×Q₈	1	16	yes	complemented
171	C₂×C₇×C₈	—	2	2	no	—
172	C₂×C₇×C₈	—	2	4	no	—
173	C₂×C₇×C₈	C₂×Q₈	1	4	yes	complemented
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	8	no	—
178	C₇×C₄⋊C₄	—	2	4	no	—
179	C₇×C₄⋊C₄	—	2	8	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	8	no	—
184	C₇×C₄⋊C₄	—	2	1	no	—
185	C₇×C₄⋊C₄	—	2	2	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	C₂×D₄	1	8	yes	—
190	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
191	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
192	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
193	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
194	C₇×C₂²⋊C₄	—	2	8	no	—
195	C₇×C₂²⋊C₄	—	2	4	no	—
196	C₄²×C₇	—	2	8	no	—
197	C₄²×C₇	—	2	4	no	—
198	C₄²×C₇	C₂×D₄	1	4	yes	—
199	C₄²×C₇	C₂×D₄	1	2	yes	—
200	C₄²×C₇	C₂⁴	1	2	yes	—
201	C₄²×C₇	C₂⁴	1	4	yes	—
202	C₂³×Q₈	—	2	1	no	—
203	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
204	#557	—	2	4	no	—
205	#557	C₂²×C₇	1	8	yes	complemented
206	D₄×Q₈	—	2	4	no	—
207	D₄×Q₈	C₂²×C₇	1	8	yes	—
208	C₂×C₄⋊Q₈	—	2	1	no	—
209	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
210	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
211	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
212	C₂×#125	—	2	2	no	—
213	C₂×#125	C₂²×C₇	1	2	yes	—
214	C₂×C₂²⋊Q₈	—	2	1	no	—
215	C₂×C₂²⋊Q₈	—	2	2	no	—
216	C₂×C₄×Q₈	—	2	1	no	—
217	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
218	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
219	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
220	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
221	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
222	#501	C₂²×C₇	1	16	yes	complemented
223	#500	C₂²×C₇	1	8	yes	complemented
224	#478	C₂²×C₇	1	16	yes	—
225	#477	C₂²×C₇	1	16	yes	complemented
226	#475	C₂²×C₇	1	8	yes	complemented
227	#474	C₂²×C₇	1	8	yes	—
228	#446	C₂²×C₇	1	8	yes	complemented
229	#440	C₂²×C₇	1	16	yes	—
230	C₄×SD₁₆	C₂²×C₇	1	8	yes	—
231	C₂×#107	C₂²×C₇	1	2	yes	—
232	C₂×#107	C₂²×C₇	1	2	yes	—
233	C₂×#107	C₂²×C₇	1	2	yes	—
234	C₂×#106	C₂²×C₇	1	2	yes	—
235	C₂×#106	C₂²×C₇	1	1	yes	characteristic
236	C₂×C₄⋊C₈	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	1	yes	characteristic
240	C₂×#102	C₂²×C₇	1	1	yes	characteristic
241	C₂×#102	C₂²×C₇	1	2	yes	—
242	C₂×#97	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	2	no	—
246	C₂³×C₇	—	4	2	no	—
247	C₂³×C₇	—	4	2	no	—
248	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
249	C₇×Q₈	—	2	4	no	—
250	C₇×Q₈	—	2	8	no	—
251	C₇×Q₈	—	2	2	no	—
252	C₇×Q₈	—	4	16	no	—
253	C₇×Q₈	—	4	8	no	—
254	C₇×Q₈	—	4	8	no	—
255	C₇×Q₈	C₂²×Q₈	1	4	yes	complemented
256	C₇×D₄	—	2	4	no	—
257	C₇×D₄	—	2	2	no	—
258	C₇×D₄	C₂²×Q₈	1	4	yes	—
259	C₂×C₄×C₇	—	2	4	no	—
260	C₂×C₄×C₇	—	2	4	no	—
261	C₂×C₄×C₇	—	2	4	no	—
262	C₂×C₄×C₇	—	2	2	no	—
263	C₂×C₄×C₇	—	2	2	no	—
264	C₂×C₄×C₇	—	2	2	no	—
265	C₂×C₄×C₇	—	2	4	no	—
266	C₂×C₄×C₇	—	2	4	no	—
267	C₂×C₄×C₇	—	2	2	no	—
268	C₂×C₄×C₇	—	4	16	no	—
269	C₂×C₄×C₇	—	4	4	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	8	no	—
274	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
275	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
276	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
277	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
278	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
281	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
282	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
283	C₇×C₈	—	2	2	no	—
284	C₇×C₈	—	2	4	no	—
285	C₇×C₈	C₂²×Q₈	1	4	yes	complemented
286	C₂²×Q₈	—	2	8	no	—
287	C₂²×Q₈	—	2	1	no	—
288	C₂²×Q₈	—	2	2	no	—
289	C₂²×Q₈	—	2	1	no	—
290	C₂²×Q₈	—	4	8	no	—
291	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
292	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
293	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
294	C₂³×C₄	—	2	2	no	—
295	C₂³×C₄	—	2	1	no	—
296	C₂×SD₁₆	C₇×Q₈	1	8	yes	complemented
297	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
298	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₇	1	2	yes	—
300	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
301	C₄⋊Q₈	—	2	8	no	—
302	C₄⋊Q₈	—	2	4	no	—
303	C₄⋊Q₈	—	2	2	no	—
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
306	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
307	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
308	#125	—	2	16	no	—
309	#125	—	2	4	no	—
310	#125	C₂³×C₇	1	8	yes	—
311	C₂²⋊Q₈	—	2	8	no	—
312	C₂²⋊Q₈	—	2	16	no	—
313	C₄×Q₈	—	2	8	no	—
314	C₄×Q₈	—	2	4	no	—
315	C₄×Q₈	—	2	2	no	—
316	C₄×Q₈	C₇×D₄	1	4	yes	—
317	C₄×Q₈	C₂³×C₇	1	4	yes	—
318	C₄×Q₈	C₂³×C₇	1	8	yes	—
319	C₄×Q₈	C₂³×C₇	1	4	yes	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	C₂³×C₇	1	4	yes	—
323	C₄×D₄	C₂³×C₇	1	8	yes	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	1	no	—
339	C₂×C₄²	—	2	2	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	C₂³×C₇	1	2	yes	—
342	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
343	#107	C₂³×C₇	1	8	yes	—
344	#107	C₂³×C₇	1	8	yes	—
345	#107	C₂³×C₇	1	8	yes	—
346	#106	C₂³×C₇	1	4	yes	—
347	#106	C₂³×C₇	1	8	yes	—
348	C₄⋊C₈	C₂³×C₇	1	4	yes	—
349	C₄⋊C₈	C₂³×C₇	1	8	yes	—
350	#103	C₂³×C₇	1	4	yes	—
351	#103	C₂³×C₇	1	8	yes	—
352	#102	C₂³×C₇	1	4	yes	—
353	#102	C₂³×C₇	1	8	yes	—
354	#97	C₂³×C₇	1	8	yes	—
355	C₄×C₈	C₂³×C₇	1	4	yes	—
356	C₂²×C₇	—	2	4	no	—
357	C₂²×C₇	—	4	8	no	—
358	C₂²×C₇	—	4	2	no	—
359	C₂²×C₇	—	4	2	no	—
360	C₂²×C₇	D₄×Q₈	1	2	yes	—
361	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
362	C₂²×C₇	#578	1	2	yes	—
363	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
364	C₄×C₇	—	2	4	no	—
365	C₄×C₇	—	2	4	no	—
366	C₄×C₇	—	2	4	no	—
367	C₄×C₇	—	2	2	no	—
368	C₄×C₇	—	4	4	no	—
369	C₄×C₇	—	4	2	no	—
370	C₄×C₇	—	4	4	no	—
371	C₄×C₇	—	4	2	no	—
372	C₄×C₇	D₄×Q₈	1	2	yes	—
373	C₄×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
374	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
375	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
376	C₂⁴	—	2	1	no	—
377	C₂×Q₈	—	2	4	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	4	no	—
380	C₂×Q₈	—	2	8	no	—
381	C₂×Q₈	—	2	4	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	4	8	no	—
384	C₂×Q₈	—	4	32	no	—
385	C₂×Q₈	—	4	4	no	—
386	C₂×Q₈	—	4	4	no	—
387	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
388	C₂×Q₈	C₂×C₇×Q₈	1	4	yes	complemented
389	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	C₂×C₇×Q₈	1	4	yes	—
393	C₂×D₄	C₂⁴×C₇	1	2	yes	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	8	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	4	8	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
404	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
405	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
406	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
408	SD₁₆	C₂×C₇×Q₈	1	16	yes	complemented
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	4	no	—
411	C₂×C₈	C₂×C₇×Q₈	1	4	yes	complemented
412	C₂×C₈	C₂⁴×C₇	1	2	yes	—
413	C₂×C₈	C₂⁴×C₇	1	4	yes	—
414	C₂×C₈	C₂⁴×C₇	1	2	yes	—
415	C₄⋊C₄	—	2	8	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	8	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
427	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
428	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
429	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
430	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
431	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
432	C₂²⋊C₄	—	2	8	no	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₄²	—	2	8	no	—
435	C₄²	—	2	4	no	—
436	C₄²	C₂×C₇×D₄	1	4	yes	—
437	C₄²	C₂×C₇×D₄	1	2	yes	—
438	C₄²	C₂⁴×C₇	1	2	yes	—
439	C₄²	C₂⁴×C₇	1	4	yes	—
440	C₂×C₇	—	4	4	no	—
441	C₂×C₇	#3386	1	4	yes	direct product factor
442	C₂×C₇	C₂×D₄×Q₈	1	1	yes	characteristic
443	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
444	C₂×C₇	C₂×#578	1	1	yes	characteristic
445	C₂³	—	2	2	no	—
446	C₂³	—	2	4	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
450	Q₈	—	2	2	no	—
451	Q₈	—	2	4	no	—
452	Q₈	—	2	8	no	—
453	Q₈	—	4	16	no	—
454	Q₈	—	4	8	no	—
455	Q₈	—	4	8	no	—
456	Q₈	C₂²×C₇×Q₈	1	4	yes	complemented
457	D₄	—	2	2	no	—
458	D₄	—	2	4	no	—
459	D₄	C₂²×C₇×Q₈	1	4	yes	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	4	16	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	8	no	—
475	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
476	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
477	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
478	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
479	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
480	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
481	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
482	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
483	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
484	C₈	—	2	2	no	—
485	C₈	—	2	4	no	—
486	C₈	C₂²×C₇×Q₈	1	4	yes	complemented
487	C₇	C₂×#3386	1	1	yes	characteristic, direct product factor, Sylow
488	C₂²	—	2	4	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	8	no	—
492	C₂²	C₇×D₄×Q₈	1	2	yes	—
493	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
494	C₂²	C₇×#578	1	2	yes	—
495	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
496	C₄	—	2	4	no	—
497	C₄	—	2	4	no	—
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	C₇×D₄×Q₈	1	2	yes	—
505	C₄	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
506	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
507	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
508	C₂	—	4	4	no	—
509	C₂	C₇×#3386	1	4	yes	direct product factor
510	C₂	C₂×C₇×D₄×Q₈	1	1	yes	characteristic
511	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
512	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×D₄	C₂³
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×#557	C₂	semidirect
3. C₇×#3386	C₂	direct (N × H)
4. C₂×C₇×#501	C₂	semidirect
5. C₂×C₇×#500	C₂	semidirect
6. C₂×C₇×#477	C₂	semidirect
7. C₂×C₇×#475	C₂	semidirect
10. C₂×C₇×#446	C₂	semidirect
16. C₇×#557	C₂²	semidirect
33. C₇×#501	C₂²	semidirect
34. C₇×#500	C₂²	semidirect
36. C₇×#477	C₂²	semidirect
37. C₇×#475	C₂²	semidirect
39. C₇×#446	C₂²	semidirect
55. C₂×#3386	C₇	direct (N × H)
66. C₂×C₇×SD₁₆	Q₈	semidirect
126. C₂×#557	C₂×C₇	semidirect
128. #3386	C₂×C₇	direct (N × H)
129. C₂×#501	C₂×C₇	semidirect
130. C₂×#500	C₂×C₇	semidirect
131. C₂×#477	C₂×C₇	semidirect
132. C₂×#475	C₂×C₇	semidirect
135. C₂×#446	C₂×C₇	semidirect
150. C₂×C₇×Q₈	C₂×Q₈	semidirect
170. C₇×SD₁₆	C₂×Q₈	semidirect
173. C₂×C₇×C₈	C₂×Q₈	semidirect
205. #557	C₂²×C₇	semidirect
222. #501	C₂²×C₇	semidirect
223. #500	C₂²×C₇	semidirect
225. #477	C₂²×C₇	semidirect
226. #475	C₂²×C₇	semidirect
228. #446	C₂²×C₇	semidirect
255. C₇×Q₈	C₂²×Q₈	semidirect
285. C₇×C₈	C₂²×Q₈	semidirect
296. C₂×SD₁₆	C₇×Q₈	semidirect
388. C₂×Q₈	C₂×C₇×Q₈	semidirect
408. SD₁₆	C₂×C₇×Q₈	semidirect
411. C₂×C₈	C₂×C₇×Q₈	semidirect
441. C₂×C₇	#3386	direct (N × H)
456. Q₈	C₂²×C₇×Q₈	semidirect
486. C₈	C₂²×C₇×Q₈	semidirect
487. C₇	C₂×#3386	direct (N × H)
509. C₂	C₇×#3386	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×#557	2
C₂×C₇×D₄×Q₈	2
C₇×#3386	2
C₂×C₇×#501	2
C₂×C₇×#500	2
C₂×C₇×#477	2
C₂×C₇×#475	2
C₂×C₇×#478	2
C₂×C₇×#474	2
C₂×C₇×#446	2
C₂×C₇×#440	2
C₂×C₄×C₇×SD₁₆	2
C₂×#3386	7

Subgroups — C2×C7×#3386 #13238576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3386 #13238576