Subgroups — C₂×C₇×#3384 #13238574

Order 1792.

2082 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3384	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#501	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#478	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#476	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#442	C₂	1	2	yes	maximal
12	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic
13	C₂³×C₇×Q₈	—	2	1	no	—
14	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
15	C₇×#554	—	2	4	no	—
16	C₇×#554	C₂²	1	8	yes	complemented
17	C₇×D₄×Q₈	—	2	4	no	—
18	C₇×D₄×Q₈	C₂²	1	8	yes	complemented
19	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₇×#125	C₂²	1	2	yes	—
23	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
24	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
27	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
31	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
32	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
33	C₇×#501	C₂²	1	16	yes	complemented
34	C₇×#498	C₂²	1	8	yes	complemented
35	C₇×#478	C₂²	1	16	yes	complemented
36	C₇×#476	C₂²	1	16	yes	complemented
37	C₇×#476	C₂²	1	8	yes	complemented
38	C₇×#474	C₂²	1	8	yes	complemented
39	C₇×#446	C₂²	1	8	yes	complemented
40	C₇×#442	C₂²	1	16	yes	—
41	C₄×C₇×D₈	C₂²	1	8	yes	—
42	C₂×C₇×#107	C₂²	1	1	yes	characteristic
43	C₂×C₇×#107	C₂²	1	2	yes	—
44	C₂×C₇×#106	C₂²	1	2	yes	—
45	C₂×C₇×#106	C₂²	1	2	yes	—
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×#102	C₂²	1	1	yes	characteristic
50	C₂×C₇×#102	C₂²	1	1	yes	characteristic
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×#3384	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×D₄	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	C₂³×C₄×C₇	—	2	1	no	—
67	C₂³×C₄×C₇	—	2	2	no	—
68	C₂×C₇×D₈	Q₈	1	8	yes	complemented
69	C₂×C₇×D₈	C₂³	1	4	yes	—
70	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇×C₈	C₂³	1	2	yes	—
72	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
73	C₇×C₄⋊Q₈	—	2	4	no	—
74	C₇×C₄⋊Q₈	—	2	2	no	—
75	C₇×C₄⋊Q₈	—	2	2	no	—
76	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
77	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
78	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
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	8	no	—
83	C₇×C₂²⋊Q₈	—	2	16	no	—
84	C₇×C₂²⋊Q₈	—	2	16	no	—
85	C₄×C₇×Q₈	D₄	1	4	yes	—
86	C₄×C₇×Q₈	C₂³	1	4	yes	—
87	C₄×C₇×D₄	—	2	4	no	—
88	C₄×C₇×D₄	—	2	2	no	—
89	C₄×C₇×D₄	—	2	4	no	—
90	C₄×C₇×D₄	—	2	2	no	—
91	C₄×C₇×D₄	C₂³	1	4	yes	—
92	C₄×C₇×D₄	C₂³	1	4	yes	—
93	C₄×C₇×D₄	C₂³	1	8	yes	—
94	C₄×C₇×D₄	C₂³	1	8	yes	—
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	1	no	—
99	C₂×C₇×C₄⋊C₄	—	2	2	no	—
100	C₂×C₇×C₄⋊C₄	—	2	8	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	1	no	—
108	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
109	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₇×C₂²⋊C₄	—	2	2	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	4	yes	—
115	C₇×#106	C₂³	1	8	yes	—
116	C₇×#106	C₂³	1	8	yes	—
117	C₇×#106	C₂³	1	8	yes	—
118	C₇×C₄⋊C₈	C₂³	1	4	yes	—
119	C₇×C₄⋊C₈	C₂³	1	8	yes	—
120	C₇×#102	C₂³	1	8	yes	—
121	C₇×#102	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×#554	C₂×C₇	1	1	yes	characteristic, complemented
127	C₂×D₄×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
128	#3384	C₂×C₇	1	16	yes	direct product factor
129	C₂×#501	C₂×C₇	1	2	yes	complemented
130	C₂×#498	C₂×C₇	1	1	yes	characteristic, complemented
131	C₂×#478	C₂×C₇	1	2	yes	complemented
132	C₂×#476	C₂×C₇	1	1	yes	characteristic, complemented
133	C₂×#476	C₂×C₇	1	2	yes	complemented
134	C₂×#474	C₂×C₇	1	1	yes	characteristic, complemented
135	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
136	C₂×#442	C₂×C₇	1	2	yes	—
137	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic
138	C₂⁴×C₇	—	2	1	no	—
139	C₂⁴×C₇	—	2	1	no	—
140	C₂×C₇×Q₈	—	2	4	no	—
141	C₂×C₇×Q₈	—	2	8	no	—
142	C₂×C₇×Q₈	—	2	4	no	—
143	C₂×C₇×Q₈	—	2	4	no	—
144	C₂×C₇×Q₈	—	4	8	no	—
145	C₂×C₇×Q₈	—	4	32	no	—
146	C₂×C₇×Q₈	—	4	4	no	—
147	C₂×C₇×Q₈	—	8	2	no	—
148	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
149	C₂×C₇×D₄	—	2	1	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	C₂×Q₈	1	4	yes	—
154	C₂×C₇×D₄	C₂×Q₈	1	4	yes	complemented
155	C₂×C₇×D₄	C₂⁴	1	2	yes	—
156	C₂×C₇×D₄	C₂⁴	1	2	yes	—
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	4	no	—
162	C₂²×C₄×C₇	—	2	8	no	—
163	C₂²×C₄×C₇	—	2	4	no	—
164	C₂²×C₄×C₇	—	2	8	no	—
165	C₂²×C₄×C₇	—	4	8	no	—
166	C₂²×C₄×C₇	—	4	4	no	—
167	C₂²×C₄×C₇	—	4	4	no	—
168	C₂²×C₄×C₇	—	8	4	no	—
169	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
173	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
174	C₇×D₈	C₂×Q₈	1	16	yes	complemented
175	C₂×C₇×C₈	—	2	2	no	—
176	C₂×C₇×C₈	—	2	4	no	—
177	C₂×C₇×C₈	C₂×Q₈	1	4	yes	complemented
178	C₂×C₇×C₈	C₂⁴	1	2	yes	—
179	C₂×C₇×C₈	C₂⁴	1	4	yes	—
180	C₂×C₇×C₈	C₂⁴	1	2	yes	—
181	C₇×C₄⋊C₄	—	2	8	no	—
182	C₇×C₄⋊C₄	—	2	4	no	—
183	C₇×C₄⋊C₄	—	2	8	no	—
184	C₇×C₄⋊C₄	—	2	4	no	—
185	C₇×C₄⋊C₄	—	2	8	no	—
186	C₇×C₄⋊C₄	—	2	1	no	—
187	C₇×C₄⋊C₄	—	2	2	no	—
188	C₇×C₄⋊C₄	—	2	1	no	—
189	C₇×C₄⋊C₄	—	2	2	no	—
190	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
191	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
192	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
193	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
194	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
195	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
196	C₇×C₂²⋊C₄	—	2	4	no	—
197	C₇×C₂²⋊C₄	—	2	8	no	—
198	C₇×C₂²⋊C₄	—	2	4	no	—
199	C₇×C₂²⋊C₄	—	2	8	no	—
200	C₄²×C₇	C₂×D₄	1	4	yes	—
201	C₄²×C₇	C₂×D₄	1	2	yes	—
202	C₄²×C₇	C₂⁴	1	2	yes	—
203	C₄²×C₇	C₂⁴	1	4	yes	—
204	C₂³×Q₈	—	2	1	no	—
205	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
206	#554	—	2	4	no	—
207	#554	C₂²×C₇	1	8	yes	complemented
208	D₄×Q₈	—	2	4	no	—
209	D₄×Q₈	C₂²×C₇	1	8	yes	complemented
210	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
211	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
212	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
213	C₂×#125	C₂²×C₇	1	2	yes	—
214	C₂×C₂²⋊Q₈	—	2	1	no	—
215	C₂×C₂²⋊Q₈	—	2	1	no	—
216	C₂×C₂²⋊Q₈	—	2	2	no	—
217	C₂×C₂²⋊Q₈	—	2	2	no	—
218	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
219	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
220	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
222	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
223	C₂²×C₄⋊C₄	—	2	1	no	—
224	#501	C₂²×C₇	1	16	yes	complemented
225	#498	C₂²×C₇	1	8	yes	complemented
226	#478	C₂²×C₇	1	16	yes	complemented
227	#476	C₂²×C₇	1	16	yes	complemented
228	#476	C₂²×C₇	1	8	yes	complemented
229	#474	C₂²×C₇	1	8	yes	complemented
230	#446	C₂²×C₇	1	8	yes	complemented
231	#442	C₂²×C₇	1	16	yes	—
232	C₄×D₈	C₂²×C₇	1	8	yes	—
233	C₂×#107	C₂²×C₇	1	2	yes	—
234	C₂×#107	C₂²×C₇	1	1	yes	characteristic
235	C₂×#106	C₂²×C₇	1	2	yes	—
236	C₂×#106	C₂²×C₇	1	2	yes	—
237	C₂×#106	C₂²×C₇	1	2	yes	—
238	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
239	C₂×C₄⋊C₈	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×#102	C₂²×C₇	1	1	yes	characteristic
243	C₂×#102	C₂²×C₇	1	2	yes	—
244	C₂×#97	C₂²×C₇	1	2	yes	—
245	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
246	C₂³×C₇	—	2	4	no	—
247	C₂³×C₇	—	2	4	no	—
248	C₂³×C₇	—	2	2	no	—
249	C₂³×C₇	—	2	2	no	—
250	C₂³×C₇	—	4	2	no	—
251	C₂³×C₇	—	4	2	no	—
252	C₂³×C₇	—	4	2	no	—
253	C₂³×C₇	—	4	2	no	—
254	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
255	C₇×Q₈	—	2	8	no	—
256	C₇×Q₈	—	4	16	no	—
257	C₇×Q₈	—	4	8	no	—
258	C₇×Q₈	—	8	4	no	—
259	C₇×D₄	—	2	4	no	—
260	C₇×D₄	—	2	4	no	—
261	C₇×D₄	—	2	2	no	—
262	C₇×D₄	—	2	2	no	—
263	C₇×D₄	C₂²×Q₈	1	4	yes	—
264	C₇×D₄	C₂²×Q₈	1	4	yes	complemented
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	—	2	2	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	—	4	16	no	—
273	C₂×C₄×C₇	—	4	2	no	—
274	C₂×C₄×C₇	—	4	4	no	—
275	C₂×C₄×C₇	—	4	2	no	—
276	C₂×C₄×C₇	—	4	4	no	—
277	C₂×C₄×C₇	—	4	8	no	—
278	C₂×C₄×C₇	—	4	8	no	—
279	C₂×C₄×C₇	—	8	8	no	—
280	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
281	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
282	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
283	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
284	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
286	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
287	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
288	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
289	C₇×C₈	—	2	2	no	—
290	C₇×C₈	—	2	4	no	—
291	C₇×C₈	C₂²×Q₈	1	4	yes	complemented
292	C₂²×Q₈	—	2	8	no	—
293	C₂²×Q₈	—	2	2	no	—
294	C₂²×Q₈	—	2	1	no	—
295	C₂²×Q₈	—	2	1	no	—
296	C₂²×Q₈	—	4	8	no	—
297	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
298	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
299	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
300	C₂³×C₄	—	2	1	no	—
301	C₂³×C₄	—	2	2	no	—
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	—	2	2	no	—
304	C₂×D₈	C₇×Q₈	1	8	yes	complemented
305	C₂×D₈	C₂³×C₇	1	4	yes	—
306	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₇	1	2	yes	—
308	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
309	C₄⋊Q₈	—	2	4	no	—
310	C₄⋊Q₈	—	2	2	no	—
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
313	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
314	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
315	#125	—	2	4	no	—
316	#125	C₂³×C₇	1	8	yes	—
317	C₂²⋊Q₈	—	2	8	no	—
318	C₂²⋊Q₈	—	2	8	no	—
319	C₂²⋊Q₈	—	2	16	no	—
320	C₂²⋊Q₈	—	2	16	no	—
321	C₄×Q₈	C₇×D₄	1	4	yes	—
322	C₄×Q₈	C₂³×C₇	1	4	yes	—
323	C₄×D₄	—	2	4	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	4	no	—
326	C₄×D₄	—	2	2	no	—
327	C₄×D₄	C₂³×C₇	1	4	yes	—
328	C₄×D₄	C₂³×C₇	1	8	yes	—
329	C₄×D₄	C₂³×C₇	1	4	yes	—
330	C₄×D₄	C₂³×C₇	1	8	yes	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	8	no	—
337	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
339	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₄²	C₂³×C₇	1	2	yes	—
348	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
349	#107	C₂³×C₇	1	4	yes	—
350	#107	C₂³×C₇	1	8	yes	—
351	#106	C₂³×C₇	1	8	yes	—
352	#106	C₂³×C₇	1	8	yes	—
353	#106	C₂³×C₇	1	8	yes	—
354	C₄⋊C₈	C₂³×C₇	1	4	yes	—
355	C₄⋊C₈	C₂³×C₇	1	8	yes	—
356	#102	C₂³×C₇	1	4	yes	—
357	#102	C₂³×C₇	1	4	yes	—
358	#102	C₂³×C₇	1	8	yes	—
359	#102	C₂³×C₇	1	8	yes	—
360	#97	C₂³×C₇	1	8	yes	—
361	C₄×C₈	C₂³×C₇	1	4	yes	—
362	C₂²×C₇	—	2	4	no	—
363	C₂²×C₇	—	2	4	no	—
364	C₂²×C₇	—	4	8	no	—
365	C₂²×C₇	—	4	8	no	—
366	C₂²×C₇	—	4	2	no	—
367	C₂²×C₇	—	4	2	no	—
368	C₂²×C₇	—	4	2	no	—
369	C₂²×C₇	—	4	2	no	—
370	C₂²×C₇	D₄×Q₈	1	2	yes	—
371	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
372	C₂²×C₇	#577	1	2	yes	—
373	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
374	C₄×C₇	—	2	4	no	—
375	C₄×C₇	—	2	4	no	—
376	C₄×C₇	—	2	2	no	—
377	C₄×C₇	—	4	2	no	—
378	C₄×C₇	—	4	4	no	—
379	C₄×C₇	—	4	2	no	—
380	C₄×C₇	—	4	4	no	—
381	C₄×C₇	D₄×Q₈	1	2	yes	—
382	C₄×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
383	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
384	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
385	C₂⁴	—	2	1	no	—
386	C₂⁴	—	2	1	no	—
387	C₂×Q₈	—	2	4	no	—
388	C₂×Q₈	—	2	8	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	4	8	no	—
392	C₂×Q₈	—	4	32	no	—
393	C₂×Q₈	—	4	4	no	—
394	C₂×Q₈	—	8	2	no	—
395	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	C₂×C₇×Q₈	1	4	yes	—
401	C₂×D₄	C₂×C₇×Q₈	1	4	yes	complemented
402	C₂×D₄	C₂⁴×C₇	1	2	yes	—
403	C₂×D₄	C₂⁴×C₇	1	2	yes	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	8	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	8	no	—
412	C₂²×C₄	—	4	8	no	—
413	C₂²×C₄	—	4	4	no	—
414	C₂²×C₄	—	4	4	no	—
415	C₂²×C₄	—	8	4	no	—
416	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
417	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
418	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
419	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
421	D₈	C₂×C₇×Q₈	1	16	yes	complemented
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	4	no	—
424	C₂×C₈	C₂×C₇×Q₈	1	4	yes	complemented
425	C₂×C₈	C₂⁴×C₇	1	2	yes	—
426	C₂×C₈	C₂⁴×C₇	1	4	yes	—
427	C₂×C₈	C₂⁴×C₇	1	2	yes	—
428	C₄⋊C₄	—	2	8	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	8	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
438	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
439	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
440	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
441	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
442	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	8	no	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₂²⋊C₄	—	2	8	no	—
447	C₄²	C₂×C₇×D₄	1	4	yes	—
448	C₄²	C₂×C₇×D₄	1	2	yes	—
449	C₄²	C₂⁴×C₇	1	2	yes	—
450	C₄²	C₂⁴×C₇	1	4	yes	—
451	C₂×C₇	—	4	4	no	—
452	C₂×C₇	—	4	4	no	—
453	C₂×C₇	#3384	1	4	yes	direct product factor
454	C₂×C₇	C₂×D₄×Q₈	1	1	yes	characteristic
455	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
456	C₂×C₇	C₂×#577	1	1	yes	characteristic
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	4	no	—
460	C₂³	—	2	4	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
466	Q₈	—	2	8	no	—
467	Q₈	—	4	16	no	—
468	Q₈	—	4	8	no	—
469	Q₈	—	8	4	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	4	no	—
473	D₄	—	2	4	no	—
474	D₄	C₂²×C₇×Q₈	1	4	yes	—
475	D₄	C₂²×C₇×Q₈	1	4	yes	complemented
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	4	16	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	8	no	—
489	C₂×C₄	—	4	8	no	—
490	C₂×C₄	—	8	8	no	—
491	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
492	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
493	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
494	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
495	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
496	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
497	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
498	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
499	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
500	C₈	—	2	2	no	—
501	C₈	—	2	4	no	—
502	C₈	C₂²×C₇×Q₈	1	4	yes	complemented
503	C₇	C₂×#3384	1	1	yes	characteristic, direct product factor, Sylow
504	C₂²	—	2	4	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	8	no	—
511	C₂²	—	4	8	no	—
512	C₂²	C₇×D₄×Q₈	1	2	yes	—
513	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
514	C₂²	C₇×#577	1	2	yes	—
515	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
516	C₄	—	2	4	no	—
517	C₄	—	2	4	no	—
518	C₄	—	2	2	no	—
519	C₄	—	4	4	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	4	no	—
523	C₄	C₇×D₄×Q₈	1	2	yes	—
524	C₄	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
525	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
526	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
527	C₂	—	4	4	no	—
528	C₂	—	4	4	no	—
529	C₂	C₇×#3384	1	4	yes	direct product factor
530	C₂	C₂×C₇×D₄×Q₈	1	1	yes	characteristic
531	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
532	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×D₈	C₂²
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×#554	C₂	semidirect
2. C₂×C₇×D₄×Q₈	C₂	semidirect
3. C₇×#3384	C₂	direct (N × H)
4. C₂×C₇×#501	C₂	semidirect
5. C₂×C₇×#498	C₂	semidirect
6. C₂×C₇×#478	C₂	semidirect
7. C₂×C₇×#476	C₂	semidirect
8. C₂×C₇×#476	C₂	semidirect
9. C₂×C₇×#474	C₂	semidirect
10. C₂×C₇×#446	C₂	semidirect
16. C₇×#554	C₂²	semidirect
18. C₇×D₄×Q₈	C₂²	semidirect
33. C₇×#501	C₂²	semidirect
34. C₇×#498	C₂²	semidirect
35. C₇×#478	C₂²	semidirect
36. C₇×#476	C₂²	semidirect
37. C₇×#476	C₂²	semidirect
38. C₇×#474	C₂²	semidirect
39. C₇×#446	C₂²	semidirect
55. C₂×#3384	C₇	direct (N × H)
68. C₂×C₇×D₈	Q₈	semidirect
126. C₂×#554	C₂×C₇	semidirect
127. C₂×D₄×Q₈	C₂×C₇	semidirect
128. #3384	C₂×C₇	direct (N × H)
129. C₂×#501	C₂×C₇	semidirect
130. C₂×#498	C₂×C₇	semidirect
131. C₂×#478	C₂×C₇	semidirect
132. C₂×#476	C₂×C₇	semidirect
133. C₂×#476	C₂×C₇	semidirect
134. C₂×#474	C₂×C₇	semidirect
135. C₂×#446	C₂×C₇	semidirect
154. C₂×C₇×D₄	C₂×Q₈	semidirect
174. C₇×D₈	C₂×Q₈	semidirect
177. C₂×C₇×C₈	C₂×Q₈	semidirect
207. #554	C₂²×C₇	semidirect
209. D₄×Q₈	C₂²×C₇	semidirect
224. #501	C₂²×C₇	semidirect
225. #498	C₂²×C₇	semidirect
226. #478	C₂²×C₇	semidirect
227. #476	C₂²×C₇	semidirect
228. #476	C₂²×C₇	semidirect
229. #474	C₂²×C₇	semidirect
230. #446	C₂²×C₇	semidirect
264. C₇×D₄	C₂²×Q₈	semidirect
291. C₇×C₈	C₂²×Q₈	semidirect
304. C₂×D₈	C₇×Q₈	semidirect
401. C₂×D₄	C₂×C₇×Q₈	semidirect
421. D₈	C₂×C₇×Q₈	semidirect
424. C₂×C₈	C₂×C₇×Q₈	semidirect
453. C₂×C₇	#3384	direct (N × H)
475. D₄	C₂²×C₇×Q₈	semidirect
502. C₈	C₂²×C₇×Q₈	semidirect
503. C₇	C₂×#3384	direct (N × H)
529. C₂	C₇×#3384	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×#554	2
C₂×C₇×D₄×Q₈	2
C₇×#3384	2
C₂×C₇×#501	2
C₂×C₇×#498	2
C₂×C₇×#478	2
C₂×C₇×#476	2
C₂×C₇×#474	2
C₂×C₇×#446	2
C₂×C₇×#442	2
C₂×C₄×C₇×D₈	2
C₂×#3384	7

Subgroups — C2×C7×#3384 #13238574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3384 #13238574