Subgroups — C₂×C₇×#3368 #13238524

Order 1792.

2122 conjugacy classes of subgroups.

The subgroup lattice has 548 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×#550	C₂	1	1	yes	maximal, characteristic
3	C₇×#3368	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#490	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#486	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#478	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#460	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#440	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	—	2	1	no	—
14	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
16	C₇×#557	—	2	4	no	—
17	C₇×#557	C₂²	1	8	yes	complemented
18	C₇×#550	—	2	4	no	—
19	C₇×#550	C₂²	1	8	yes	—
20	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
21	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×#127	C₂²	1	1	yes	characteristic
23	C₂×C₇×#127	C₂²	1	2	yes	—
24	C₂×C₇×#125	—	2	2	no	—
25	C₂×C₇×#125	C₂²	1	2	yes	—
26	C₂×C₇×#121	—	2	1	no	—
27	C₂×C₇×#121	—	2	2	no	—
28	C₂×C₄×C₇×Q₈	—	2	1	no	—
29	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
31	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
34	C₇×#490	C₂²	1	16	yes	complemented
35	C₇×#486	C₂²	1	8	yes	complemented
36	C₇×#478	C₂²	1	16	yes	complemented
37	C₇×#474	C₂²	1	8	yes	complemented
38	C₇×#460	C₂²	1	16	yes	complemented
39	C₇×#460	C₂²	1	8	yes	complemented
40	C₇×#446	C₂²	1	8	yes	complemented
41	C₇×#440	C₂²	1	16	yes	complemented
42	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
43	C₂×C₇×#107	C₂²	1	2	yes	—
44	C₂×C₇×#106	C₂²	1	1	yes	characteristic
45	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
47	C₂×C₇×#103	C₂²	1	1	yes	characteristic
48	C₂×C₇×#102	C₂²	1	1	yes	characteristic
49	C₂×C₇×#102	C₂²	1	2	yes	—
50	C₂×C₇×#102	C₂²	1	2	yes	—
51	C₂×C₇×#102	C₂²	1	2	yes	—
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×#3368	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	D₄	1	1	yes	characteristic
60	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇×D₄	—	2	2	no	—
62	C₂²×C₇×D₄	—	2	1	no	—
63	C₂²×C₇×D₄	—	2	2	no	—
64	C₂²×C₇×D₄	—	2	1	no	—
65	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
66	C₂²×C₇×D₄	C₂³	1	2	yes	—
67	C₂³×C₄×C₇	—	2	2	no	—
68	C₂³×C₄×C₇	—	2	1	no	—
69	C₂×C₇×SD₁₆	—	2	4	no	—
70	C₂×C₇×SD₁₆	—	2	8	no	—
71	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
72	C₂×C₇×SD₁₆	C₂³	1	8	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	2	yes	—
76	C₇×C₄⋊Q₈	—	2	8	no	—
77	C₇×C₄⋊Q₈	—	2	2	no	—
78	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
79	C₇×#127	—	2	4	no	—
80	C₇×#127	—	2	2	no	—
81	C₇×#127	C₂³	1	4	yes	—
82	C₇×#127	C₂³	1	8	yes	—
83	C₇×#125	—	2	16	no	—
84	C₇×#125	—	2	4	no	—
85	C₇×#125	C₂³	1	8	yes	—
86	C₇×#121	—	2	8	no	—
87	C₇×#121	—	2	16	no	—
88	C₄×C₇×Q₈	—	2	8	no	—
89	C₄×C₇×Q₈	—	2	4	no	—
90	C₄×C₇×Q₈	—	2	2	no	—
91	C₄×C₇×Q₈	D₄	1	4	yes	—
92	C₄×C₇×Q₈	C₂³	1	4	yes	—
93	C₄×C₇×Q₈	C₂³	1	8	yes	—
94	C₄×C₇×Q₈	C₂³	1	4	yes	—
95	C₄×C₇×D₄	—	2	4	no	—
96	C₄×C₇×D₄	—	2	2	no	—
97	C₄×C₇×D₄	C₂³	1	4	yes	—
98	C₄×C₇×D₄	C₂³	1	8	yes	—
99	C₂×C₇×C₄⋊C₄	—	2	2	no	—
100	C₂×C₇×C₄⋊C₄	—	2	1	no	—
101	C₂×C₇×C₄⋊C₄	—	2	2	no	—
102	C₂×C₇×C₄⋊C₄	—	2	1	no	—
103	C₂×C₇×C₄⋊C₄	—	2	2	no	—
104	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
106	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₄²×C₇	—	2	2	no	—
112	C₂×C₄²×C₇	—	2	1	no	—
113	C₂×C₄²×C₇	C₂³	1	2	yes	—
114	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
115	C₇×#107	C₂³	1	8	yes	—
116	C₇×#106	C₂³	1	4	yes	—
117	C₇×C₄⋊C₈	C₂³	1	4	yes	—
118	C₇×C₄⋊C₈	C₂³	1	8	yes	—
119	C₇×#103	C₂³	1	4	yes	—
120	C₇×#102	C₂³	1	8	yes	—
121	C₇×#102	C₂³	1	8	yes	—
122	C₇×#102	C₂³	1	8	yes	—
123	C₇×#102	C₂³	1	8	yes	—
124	C₇×#102	C₂³	1	4	yes	—
125	C₇×#97	C₂³	1	8	yes	—
126	C₄×C₇×C₈	C₂³	1	4	yes	—
127	C₂×#557	C₂×C₇	1	1	yes	characteristic, complemented
128	C₂×#550	C₂×C₇	1	1	yes	characteristic
129	#3368	C₂×C₇	1	16	yes	direct product factor
130	C₂×#490	C₂×C₇	1	2	yes	complemented
131	C₂×#486	C₂×C₇	1	1	yes	characteristic, complemented
132	C₂×#478	C₂×C₇	1	2	yes	complemented
133	C₂×#474	C₂×C₇	1	1	yes	characteristic, complemented
134	C₂×#460	C₂×C₇	1	1	yes	characteristic, complemented
135	C₂×#460	C₂×C₇	1	2	yes	complemented
136	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂×#440	C₂×C₇	1	2	yes	complemented
138	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
139	C₂⁴×C₇	—	2	2	no	—
140	C₂⁴×C₇	—	2	1	no	—
141	C₇×#41	—	4	32	no	—
142	C₂×C₇×Q₈	—	2	4	no	—
143	C₂×C₇×Q₈	—	2	1	no	—
144	C₂×C₇×Q₈	—	2	4	no	—
145	C₂×C₇×Q₈	—	2	2	no	—
146	C₂×C₇×Q₈	—	4	4	no	—
147	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
148	C₂×C₇×Q₈	#41	1	4	yes	complemented
149	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
150	C₂×C₇×D₄	—	2	2	no	—
151	C₂×C₇×D₄	—	2	1	no	—
152	C₂×C₇×D₄	—	2	8	no	—
153	C₂×C₇×D₄	—	2	4	no	—
154	C₂×C₇×D₄	—	2	8	no	—
155	C₂×C₇×D₄	—	2	4	no	—
156	C₂×C₇×D₄	—	2	2	no	—
157	C₂×C₇×D₄	—	2	4	no	—
158	C₂×C₇×D₄	—	2	2	no	—
159	C₂×C₇×D₄	—	2	4	no	—
160	C₂×C₇×D₄	—	4	8	no	—
161	C₂×C₇×D₄	—	4	4	no	—
162	C₂×C₇×D₄	—	8	4	no	—
163	C₂×C₇×D₄	—	8	2	no	—
164	C₂×C₇×D₄	C₂⁴	1	2	yes	—
165	C₂×C₇×D₄	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₇	—	2	1	no	—
167	C₂²×C₄×C₇	—	2	1	no	—
168	C₂²×C₄×C₇	—	2	2	no	—
169	C₂²×C₄×C₇	—	2	1	no	—
170	C₂²×C₄×C₇	—	2	8	no	—
171	C₂²×C₄×C₇	—	2	4	no	—
172	C₂²×C₄×C₇	—	4	8	no	—
173	C₂²×C₄×C₇	—	4	4	no	—
174	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
179	C₇×SD₁₆	—	2	8	no	—
180	C₇×SD₁₆	—	2	16	no	—
181	C₂×C₇×C₈	—	2	2	no	—
182	C₂×C₇×C₈	—	2	4	no	—
183	C₂×C₇×C₈	—	2	2	no	—
184	C₂×C₇×C₈	C₂⁴	1	2	yes	—
185	C₂×C₇×C₈	C₂⁴	1	2	yes	—
186	C₂×C₇×C₈	C₂⁴	1	4	yes	—
187	C₇×C₄⋊C₄	—	2	8	no	—
188	C₇×C₄⋊C₄	—	2	4	no	—
189	C₇×C₄⋊C₄	—	2	8	no	—
190	C₇×C₄⋊C₄	—	2	4	no	—
191	C₇×C₄⋊C₄	—	2	8	no	—
192	C₇×C₄⋊C₄	—	2	1	no	—
193	C₇×C₄⋊C₄	—	2	1	no	—
194	C₇×C₄⋊C₄	—	2	2	no	—
195	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
196	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
197	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
198	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
199	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
200	C₇×C₂²⋊C₄	—	2	8	no	—
201	C₇×C₂²⋊C₄	—	2	4	no	—
202	C₄²×C₇	—	2	8	no	—
203	C₄²×C₇	—	2	4	no	—
204	C₄²×C₇	C₂×D₄	1	4	yes	—
205	C₄²×C₇	C₂×D₄	1	2	yes	—
206	C₄²×C₇	C₂⁴	1	2	yes	—
207	C₄²×C₇	C₂⁴	1	4	yes	—
208	C₂²×#41	—	2	1	no	—
209	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
210	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
211	#557	—	2	4	no	—
212	#557	C₂²×C₇	1	8	yes	complemented
213	#550	—	2	4	no	—
214	#550	C₂²×C₇	1	8	yes	—
215	C₂×C₄⋊Q₈	—	2	1	no	—
216	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
217	C₂×#127	C₂²×C₇	1	1	yes	characteristic
218	C₂×#127	C₂²×C₇	1	2	yes	—
219	C₂×#125	—	2	2	no	—
220	C₂×#125	C₂²×C₇	1	2	yes	—
221	C₂×#121	—	2	1	no	—
222	C₂×#121	—	2	2	no	—
223	C₂×C₄×Q₈	—	2	1	no	—
224	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
226	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
227	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
228	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
229	#490	C₂²×C₇	1	16	yes	complemented
230	#486	C₂²×C₇	1	8	yes	complemented
231	#478	C₂²×C₇	1	16	yes	complemented
232	#474	C₂²×C₇	1	8	yes	complemented
233	#460	C₂²×C₇	1	16	yes	complemented
234	#460	C₂²×C₇	1	8	yes	complemented
235	#446	C₂²×C₇	1	8	yes	complemented
236	#440	C₂²×C₇	1	16	yes	complemented
237	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
238	C₂×#107	C₂²×C₇	1	2	yes	—
239	C₂×#106	C₂²×C₇	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
241	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
242	C₂×#103	C₂²×C₇	1	1	yes	characteristic
243	C₂×#102	C₂²×C₇	1	2	yes	—
244	C₂×#102	C₂²×C₇	1	2	yes	—
245	C₂×#102	C₂²×C₇	1	2	yes	—
246	C₂×#102	C₂²×C₇	1	1	yes	characteristic
247	C₂×#102	C₂²×C₇	1	2	yes	—
248	C₂×#97	C₂²×C₇	1	2	yes	—
249	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
250	C₂³×C₇	—	2	4	no	—
251	C₂³×C₇	—	2	2	no	—
252	C₂³×C₇	—	4	4	no	—
253	C₂³×C₇	—	4	2	no	—
254	C₂³×C₇	—	4	4	no	—
255	C₂³×C₇	—	4	2	no	—
256	C₂³×C₇	—	4	4	no	—
257	C₂³×C₇	—	4	2	no	—
258	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
259	C₇×Q₈	—	2	4	no	—
260	C₇×Q₈	—	2	8	no	—
261	C₇×Q₈	—	2	2	no	—
262	C₇×Q₈	—	4	8	no	—
263	C₇×Q₈	C₂×#41	1	4	yes	complemented
264	C₇×D₄	—	2	2	no	—
265	C₇×D₄	—	2	4	no	—
266	C₇×D₄	—	2	2	no	—
267	C₇×D₄	—	2	4	no	—
268	C₇×D₄	—	4	16	no	—
269	C₇×D₄	—	4	4	no	—
270	C₇×D₄	—	4	2	no	—
271	C₇×D₄	—	4	8	no	—
272	C₇×D₄	—	8	8	no	—
273	C₇×D₄	—	8	4	no	—
274	C₂×C₄×C₇	—	2	4	no	—
275	C₂×C₄×C₇	—	2	4	no	—
276	C₂×C₄×C₇	—	2	4	no	—
277	C₂×C₄×C₇	—	2	2	no	—
278	C₂×C₄×C₇	—	2	2	no	—
279	C₂×C₄×C₇	—	2	2	no	—
280	C₂×C₄×C₇	—	2	4	no	—
281	C₂×C₄×C₇	—	2	2	no	—
282	C₂×C₄×C₇	—	4	16	no	—
283	C₂×C₄×C₇	—	4	2	no	—
284	C₂×C₄×C₇	—	4	4	no	—
285	C₂×C₄×C₇	—	4	2	no	—
286	C₂×C₄×C₇	—	4	8	no	—
287	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
288	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
289	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
290	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
291	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
293	C₂×C₄×C₇	C₂×#41	1	2	yes	—
294	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
295	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
296	C₇×C₈	—	2	2	no	—
297	C₇×C₈	—	2	4	no	—
298	C₇×C₈	—	2	2	no	—
299	C₂×#41	—	2	8	no	—
300	C₂×#41	—	4	8	no	—
301	C₂²×Q₈	—	2	1	no	—
302	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
303	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
304	C₂²×D₄	—	2	2	no	—
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	—	2	2	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	C₂³×C₇	1	2	yes	—
309	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
310	C₂³×C₄	—	2	2	no	—
311	C₂³×C₄	—	2	1	no	—
312	C₂×SD₁₆	—	2	4	no	—
313	C₂×SD₁₆	—	2	8	no	—
314	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
315	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
316	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₇	1	2	yes	—
318	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
319	C₄⋊Q₈	—	2	8	no	—
320	C₄⋊Q₈	—	2	2	no	—
321	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
322	#127	—	2	4	no	—
323	#127	—	2	2	no	—
324	#127	C₂³×C₇	1	4	yes	—
325	#127	C₂³×C₇	1	8	yes	—
326	#125	—	2	16	no	—
327	#125	—	2	4	no	—
328	#125	C₂³×C₇	1	8	yes	—
329	#121	—	2	8	no	—
330	#121	—	2	16	no	—
331	C₄×Q₈	—	2	8	no	—
332	C₄×Q₈	—	2	4	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	C₇×D₄	1	4	yes	—
335	C₄×Q₈	C₂³×C₇	1	4	yes	—
336	C₄×Q₈	C₂³×C₇	1	8	yes	—
337	C₄×Q₈	C₂³×C₇	1	4	yes	—
338	C₄×D₄	—	2	4	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	C₂³×C₇	1	4	yes	—
341	C₄×D₄	C₂³×C₇	1	8	yes	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
349	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₄²	—	2	2	no	—
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	C₂³×C₇	1	2	yes	—
357	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
358	#107	C₂³×C₇	1	8	yes	—
359	#106	C₂³×C₇	1	4	yes	—
360	C₄⋊C₈	C₂³×C₇	1	4	yes	—
361	C₄⋊C₈	C₂³×C₇	1	8	yes	—
362	#103	C₂³×C₇	1	4	yes	—
363	#102	C₂³×C₇	1	4	yes	—
364	#102	C₂³×C₇	1	8	yes	—
365	#102	C₂³×C₇	1	8	yes	—
366	#102	C₂³×C₇	1	8	yes	—
367	#102	C₂³×C₇	1	8	yes	—
368	#97	C₂³×C₇	1	8	yes	—
369	C₄×C₈	C₂³×C₇	1	4	yes	—
370	C₂²×C₇	—	4	4	no	—
371	C₂²×C₇	—	4	2	no	—
372	C₂²×C₇	—	4	4	no	—
373	C₂²×C₇	—	4	2	no	—
374	C₂²×C₇	—	4	4	no	—
375	C₂²×C₇	—	4	2	no	—
376	C₂²×C₇	—	8	8	no	—
377	C₂²×C₇	—	8	4	no	—
378	C₂²×C₇	#548	1	2	yes	—
379	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
380	C₂²×C₇	#577	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	—	2	2	no	—
386	C₄×C₇	—	4	2	no	—
387	C₄×C₇	—	4	4	no	—
388	C₄×C₇	—	4	2	no	—
389	C₄×C₇	#548	1	2	yes	—
390	C₄×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
391	C₄×C₇	C₂²×#41	1	1	yes	characteristic
392	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
393	C₂⁴	—	2	2	no	—
394	C₂⁴	—	2	1	no	—
395	#41	—	4	32	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	4	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	4	4	no	—
401	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
402	C₂×Q₈	C₇×#41	1	4	yes	complemented
403	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	8	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	2	8	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	4	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	4	8	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	8	4	no	—
417	C₂×D₄	—	8	2	no	—
418	C₂×D₄	C₂⁴×C₇	1	2	yes	—
419	C₂×D₄	C₂⁴×C₇	1	4	yes	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	8	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	4	8	no	—
427	C₂²×C₄	—	4	4	no	—
428	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
429	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
431	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
432	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
433	SD₁₆	—	2	8	no	—
434	SD₁₆	—	2	16	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	4	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	C₂⁴×C₇	1	2	yes	—
439	C₂×C₈	C₂⁴×C₇	1	2	yes	—
440	C₂×C₈	C₂⁴×C₇	1	4	yes	—
441	C₄⋊C₄	—	2	8	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	8	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	8	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
450	C₄⋊C₄	C₂×C₇×D₄	1	8	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	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₄²	—	2	8	no	—
457	C₄²	—	2	4	no	—
458	C₄²	C₂×C₇×D₄	1	4	yes	—
459	C₄²	C₂×C₇×D₄	1	2	yes	—
460	C₄²	C₂⁴×C₇	1	2	yes	—
461	C₄²	C₂⁴×C₇	1	4	yes	—
462	C₂×C₇	—	8	4	no	—
463	C₂×C₇	—	8	2	no	—
464	C₂×C₇	#3368	1	4	yes	direct product factor
465	C₂×C₇	C₂×#548	1	1	yes	characteristic
466	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
467	C₂×C₇	C₂×#577	1	1	yes	characteristic
468	C₂³	—	2	4	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	4	4	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	4	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	4	no	—
475	C₂³	—	4	2	no	—
476	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
477	Q₈	—	2	2	no	—
478	Q₈	—	2	4	no	—
479	Q₈	—	2	8	no	—
480	Q₈	—	4	8	no	—
481	Q₈	C₂×C₇×#41	1	4	yes	complemented
482	D₄	—	2	2	no	—
483	D₄	—	2	4	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	4	no	—
486	D₄	—	4	16	no	—
487	D₄	—	4	4	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	8	no	—
490	D₄	—	8	8	no	—
491	D₄	—	8	4	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	4	16	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	4	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	8	no	—
505	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
506	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
507	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
508	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
509	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
510	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
511	C₂×C₄	C₂×C₇×#41	1	2	yes	—
512	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
513	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
514	C₈	—	2	2	no	—
515	C₈	—	2	4	no	—
516	C₈	—	2	2	no	—
517	C₇	C₂×#3368	1	1	yes	characteristic, direct product factor, Sylow
518	C₂²	—	4	4	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	8	8	no	—
525	C₂²	—	8	4	no	—
526	C₂²	C₇×#548	1	2	yes	—
527	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
528	C₂²	C₇×#577	1	2	yes	—
529	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
530	C₄	—	2	4	no	—
531	C₄	—	2	4	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	4	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	4	no	—
536	C₄	—	4	2	no	—
537	C₄	C₇×#548	1	2	yes	—
538	C₄	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
539	C₄	C₂²×C₇×#41	1	1	yes	characteristic
540	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
541	C₂	—	8	4	no	—
542	C₂	—	8	2	no	—
543	C₂	C₇×#3368	1	4	yes	direct product factor
544	C₂	C₂×C₇×#548	1	1	yes	characteristic
545	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
546	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×#550	C₂
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×#3368	C₂	direct (N × H)
4. C₂×C₇×#490	C₂	semidirect
5. C₂×C₇×#486	C₂	semidirect
6. C₂×C₇×#478	C₂	semidirect
7. C₂×C₇×#474	C₂	semidirect
8. C₂×C₇×#460	C₂	semidirect
9. C₂×C₇×#460	C₂	semidirect
10. C₂×C₇×#446	C₂	semidirect
11. C₂×C₇×#440	C₂	semidirect
12. C₂×C₄×C₇×SD₁₆	C₂	semidirect
17. C₇×#557	C₂²	semidirect
34. C₇×#490	C₂²	semidirect
35. C₇×#486	C₂²	semidirect
36. C₇×#478	C₂²	semidirect
37. C₇×#474	C₂²	semidirect
38. C₇×#460	C₂²	semidirect
39. C₇×#460	C₂²	semidirect
40. C₇×#446	C₂²	semidirect
41. C₇×#440	C₂²	semidirect
42. C₄×C₇×SD₁₆	C₂²	semidirect
55. C₂×#3368	C₇	direct (N × H)
127. C₂×#557	C₂×C₇	semidirect
129. #3368	C₂×C₇	direct (N × H)
130. C₂×#490	C₂×C₇	semidirect
131. C₂×#486	C₂×C₇	semidirect
132. C₂×#478	C₂×C₇	semidirect
133. C₂×#474	C₂×C₇	semidirect
134. C₂×#460	C₂×C₇	semidirect
135. C₂×#460	C₂×C₇	semidirect
136. C₂×#446	C₂×C₇	semidirect
137. C₂×#440	C₂×C₇	semidirect
138. C₂×C₄×SD₁₆	C₂×C₇	semidirect
148. C₂×C₇×Q₈	#41	semidirect
212. #557	C₂²×C₇	semidirect
229. #490	C₂²×C₇	semidirect
230. #486	C₂²×C₇	semidirect
231. #478	C₂²×C₇	semidirect
232. #474	C₂²×C₇	semidirect
233. #460	C₂²×C₇	semidirect
234. #460	C₂²×C₇	semidirect
235. #446	C₂²×C₇	semidirect
236. #440	C₂²×C₇	semidirect
237. C₄×SD₁₆	C₂²×C₇	semidirect
263. C₇×Q₈	C₂×#41	semidirect
402. C₂×Q₈	C₇×#41	semidirect
464. C₂×C₇	#3368	direct (N × H)
481. Q₈	C₂×C₇×#41	semidirect
517. C₇	C₂×#3368	direct (N × H)
543. C₂	C₇×#3368	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×#550	2
C₇×#3368	2
C₂×C₇×#490	2
C₂×C₇×#486	2
C₂×C₇×#478	2
C₂×C₇×#474	2
C₂×C₇×#460	2
C₂×C₇×#446	2
C₂×C₇×#440	2
C₂×C₄×C₇×SD₁₆	2
C₂×#3368	7

Subgroups — C2×C7×#3368 #13238524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3368 #13238524