Subgroups — C₂×C₇×#2409 #13211898

Order 1792.

5566 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₇×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic
4	C₇×#2409	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₇×#395	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#393	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#391	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#386	C₂	1	2	yes	maximal
9	C₂×C₇×#385	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#380	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×C₇×Q₈	—	2	16	no	—
12	C₂³×C₇×Q₈	—	2	8	no	—
13	C₂³×C₇×Q₈	C₂²	1	2	yes	—
14	C₂³×C₇×Q₈	C₂²	1	2	yes	—
15	C₂³×C₇×Q₈	C₂²	1	8	yes	complemented
16	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
18	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
20	C₂×C₇×C₂²⋊Q₈	—	2	16	no	—
21	C₂×C₇×C₂²⋊Q₈	C₂²	1	16	yes	complemented
22	C₂×C₄×C₇×D₄	—	2	8	no	—
23	C₂×C₄×C₇×D₄	C₂²	1	8	yes	—
24	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	—
26	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
30	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
32	C₇×#395	C₂²	1	16	yes	complemented
33	C₇×#393	C₂²	1	16	yes	complemented
34	C₇×#391	C₂²	1	16	yes	complemented
35	C₇×#386	C₂²	1	16	yes	—
36	C₇×#385	C₂²	1	16	yes	complemented
37	C₇×#380	C₂²	1	8	yes	complemented
38	C₂×C₇×#95	C₂²	1	2	yes	—
39	C₂×C₇×#95	C₂²	1	4	yes	—
40	C₂×C₇×#95	C₂²	1	4	yes	—
41	C₂×#2409	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂⁵×C₇	C₂³	1	1	yes	characteristic
43	C₂⁵×C₇	C₂³	1	1	yes	characteristic
44	C₂²×C₇×Q₈	—	2	128	no	—
45	C₂²×C₇×Q₈	—	2	64	no	—
46	C₂²×C₇×Q₈	—	2	16	no	—
47	C₂²×C₇×Q₈	—	2	8	no	—
48	C₂²×C₇×Q₈	—	2	8	no	—
49	C₂²×C₇×Q₈	—	2	8	no	—
50	C₂²×C₇×Q₈	—	2	32	no	—
51	C₂²×C₇×Q₈	D₄	1	16	yes	complemented
52	C₂²×C₇×Q₈	C₂³	1	8	yes	—
53	C₂²×C₇×Q₈	C₂³	1	8	yes	—
54	C₂²×C₇×D₄	—	2	4	no	—
55	C₂²×C₇×D₄	—	2	4	no	—
56	C₂²×C₇×D₄	Q₈	1	8	yes	complemented
57	C₂²×C₇×D₄	C₂³	1	4	yes	—
58	C₂³×C₄×C₇	—	2	8	no	—
59	C₂³×C₄×C₇	—	2	16	no	—
60	C₂³×C₄×C₇	—	2	8	no	—
61	C₂³×C₄×C₇	—	2	4	no	—
62	C₂³×C₄×C₇	—	2	8	no	—
63	C₂³×C₄×C₇	D₄	1	8	yes	—
64	C₂³×C₄×C₇	C₂³	1	8	yes	—
65	C₂³×C₄×C₇	C₂³	1	4	yes	—
66	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₇	C₂³	1	4	yes	—
68	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₇	C₂³	1	4	yes	—
70	C₂³×C₄×C₇	C₂³	1	4	yes	—
71	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
74	C₇×C₂²⋊Q₈	—	2	64	no	—
75	C₄×C₇×D₄	—	2	32	no	—
76	C₂×C₇×C₄⋊C₄	—	2	4	no	—
77	C₂×C₇×C₄⋊C₄	—	2	8	no	—
78	C₂×C₇×C₄⋊C₄	—	2	16	no	—
79	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
80	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
81	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
82	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
83	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
84	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
85	C₂×C₇×C₂²⋊C₄	—	2	16	no	—
86	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
87	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
88	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
89	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
90	C₂×C₄²×C₇	—	2	4	no	—
91	C₂×C₄²×C₇	C₂³	1	4	yes	—
92	C₇×#95	C₂³	1	8	yes	—
93	C₇×#95	C₂³	1	16	yes	—
94	C₇×#95	C₂³	1	16	yes	—
95	C₂⁴×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
96	C₂²×C₂²⋊Q₈	C₂×C₇	1	2	yes	complemented
97	C₂²×C₄×D₄	C₂×C₇	1	1	yes	characteristic
98	#2409	C₂×C₇	1	16	yes	direct product factor
99	C₂×#395	C₂×C₇	1	2	yes	complemented
100	C₂×#393	C₂×C₇	1	2	yes	complemented
101	C₂×#391	C₂×C₇	1	2	yes	complemented
102	C₂×#386	C₂×C₇	1	2	yes	—
103	C₂×#385	C₂×C₇	1	2	yes	complemented
104	C₂×#380	C₂×C₇	1	1	yes	characteristic, complemented
105	C₂⁴×C₇	—	2	4	no	—
106	C₂⁴×C₇	—	2	4	no	—
107	C₂⁴×C₇	—	2	4	no	—
108	C₂⁴×C₇	—	2	2	no	—
109	C₂⁴×C₇	—	2	2	no	—
110	C₂⁴×C₇	—	2	4	no	—
111	C₂⁴×C₇	C₂×D₄	1	4	yes	—
112	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
113	C₂⁴×C₇	C₂×Q₈	1	4	yes	complemented
114	C₂⁴×C₇	#41	1	4	yes	—
115	C₂⁴×C₇	C₂⁴	1	2	yes	—
116	C₂⁴×C₇	C₂⁴	1	2	yes	—
117	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
118	C₂×C₇×Q₈	—	2	256	no	—
119	C₂×C₇×Q₈	—	2	64	no	—
120	C₂×C₇×Q₈	—	2	64	no	—
121	C₂×C₇×Q₈	—	2	32	no	—
122	C₂×C₇×Q₈	—	2	16	no	—
123	C₂×C₇×Q₈	—	2	16	no	—
124	C₂×C₇×Q₈	—	2	16	no	—
125	C₂×C₇×Q₈	C₂×D₄	1	32	yes	complemented
126	C₂×C₇×D₄	—	2	32	no	—
127	C₂×C₇×D₄	—	2	8	no	—
128	C₂×C₇×D₄	—	2	8	no	—
129	C₂×C₇×D₄	C₂×Q₈	1	16	yes	complemented
130	C₂²×C₄×C₇	—	2	64	no	—
131	C₂²×C₄×C₇	—	2	2	no	—
132	C₂²×C₄×C₇	—	2	16	no	—
133	C₂²×C₄×C₇	—	2	8	no	—
134	C₂²×C₄×C₇	—	2	8	no	—
135	C₂²×C₄×C₇	—	2	4	no	—
136	C₂²×C₄×C₇	—	2	2	no	—
137	C₂²×C₄×C₇	—	2	32	no	—
138	C₂²×C₄×C₇	—	2	32	no	—
139	C₂²×C₄×C₇	—	2	16	no	—
140	C₂²×C₄×C₇	—	2	2	no	—
141	C₂²×C₄×C₇	—	2	8	no	—
142	C₂²×C₄×C₇	—	2	2	no	—
143	C₂²×C₄×C₇	—	2	4	no	—
144	C₂²×C₄×C₇	—	2	8	no	—
145	C₂²×C₄×C₇	—	2	4	no	—
146	C₂²×C₄×C₇	—	2	8	no	—
147	C₂²×C₄×C₇	—	2	8	no	—
148	C₂²×C₄×C₇	—	2	16	no	—
149	C₂²×C₄×C₇	—	4	16	no	—
150	C₂²×C₄×C₇	C₂×D₄	1	16	yes	—
151	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₇	C₂×D₄	1	16	yes	—
153	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
155	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	complemented
156	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
158	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
160	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
163	C₇×C₄⋊C₄	—	2	8	no	—
164	C₇×C₄⋊C₄	—	2	16	no	—
165	C₇×C₄⋊C₄	—	2	32	no	—
166	C₇×C₂²⋊C₄	—	2	8	no	—
167	C₇×C₂²⋊C₄	—	2	16	no	—
168	C₇×C₂²⋊C₄	—	2	8	no	—
169	C₇×C₂²⋊C₄	—	2	32	no	—
170	C₄²×C₇	—	2	8	no	—
171	C₂³×Q₈	—	2	16	no	—
172	C₂³×Q₈	—	2	8	no	—
173	C₂³×Q₈	C₂²×C₇	1	2	yes	—
174	C₂³×Q₈	C₂²×C₇	1	2	yes	—
175	C₂³×Q₈	C₂²×C₇	1	8	yes	complemented
176	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
177	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
178	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
179	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
180	C₂×C₂²⋊Q₈	—	2	16	no	—
181	C₂×C₂²⋊Q₈	C₂²×C₇	1	16	yes	complemented
182	C₂×C₄×D₄	—	2	8	no	—
183	C₂×C₄×D₄	C₂²×C₇	1	8	yes	—
184	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
185	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	—
186	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
187	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
188	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
189	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
190	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
191	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
192	#395	C₂²×C₇	1	16	yes	complemented
193	#393	C₂²×C₇	1	16	yes	complemented
194	#391	C₂²×C₇	1	16	yes	complemented
195	#386	C₂²×C₇	1	16	yes	—
196	#385	C₂²×C₇	1	16	yes	complemented
197	#380	C₂²×C₇	1	8	yes	complemented
198	C₂×#95	C₂²×C₇	1	2	yes	—
199	C₂×#95	C₂²×C₇	1	4	yes	—
200	C₂×#95	C₂²×C₇	1	4	yes	—
201	C₂³×C₇	—	2	8	no	—
202	C₂³×C₇	—	2	8	no	—
203	C₂³×C₇	—	2	16	no	—
204	C₂³×C₇	—	2	16	no	—
205	C₂³×C₇	—	2	4	no	—
206	C₂³×C₇	—	2	4	no	—
207	C₂³×C₇	—	2	8	no	—
208	C₂³×C₇	—	2	16	no	—
209	C₂³×C₇	—	2	4	no	—
210	C₂³×C₇	—	2	2	no	—
211	C₂³×C₇	—	2	2	no	—
212	C₂³×C₇	—	2	4	no	—
213	C₂³×C₇	—	4	4	no	—
214	C₂³×C₇	—	4	4	no	—
215	C₂³×C₇	—	4	8	no	—
216	C₂³×C₇	C₂²⋊Q₈	1	16	yes	complemented
217	C₂³×C₇	C₂²×D₄	1	4	yes	—
218	C₂³×C₇	C₂²×D₄	1	2	yes	—
219	C₂³×C₇	C₂²×D₄	1	4	yes	—
220	C₂³×C₇	C₂²×Q₈	1	4	yes	—
221	C₂³×C₇	C₂²×Q₈	1	2	yes	—
222	C₂³×C₇	C₂²×Q₈	1	4	yes	complemented
223	C₂³×C₇	C₂×#41	1	4	yes	—
224	C₂³×C₇	C₂×#41	1	2	yes	—
225	C₂³×C₇	2₋¹⁺⁴	1	4	yes	—
226	C₂³×C₇	C₂⁵	1	1	yes	characteristic
227	C₇×Q₈	—	2	64	no	—
228	C₇×Q₈	—	2	64	no	—
229	C₇×D₄	—	2	32	no	—
230	C₂×C₄×C₇	—	2	64	no	—
231	C₂×C₄×C₇	—	2	32	no	—
232	C₂×C₄×C₇	—	2	8	no	—
233	C₂×C₄×C₇	—	2	8	no	—
234	C₂×C₄×C₇	—	2	2	no	—
235	C₂×C₄×C₇	—	2	8	no	—
236	C₂×C₄×C₇	—	2	8	no	—
237	C₂×C₄×C₇	—	2	4	no	—
238	C₂×C₄×C₇	—	2	2	no	—
239	C₂×C₄×C₇	—	2	32	no	—
240	C₂×C₄×C₇	—	2	2	no	—
241	C₂×C₄×C₇	—	2	8	no	—
242	C₂×C₄×C₇	—	2	2	no	—
243	C₂×C₄×C₇	—	2	4	no	—
244	C₂×C₄×C₇	—	2	8	no	—
245	C₂×C₄×C₇	—	2	4	no	—
246	C₂×C₄×C₇	—	2	8	no	—
247	C₂×C₄×C₇	—	4	4	no	—
248	C₂×C₄×C₇	—	4	4	no	—
249	C₂×C₄×C₇	—	4	16	no	—
250	C₂×C₄×C₇	—	4	16	no	—
251	C₂×C₄×C₇	#120	1	16	yes	—
252	C₂×C₄×C₇	C₂²×D₄	1	16	yes	—
253	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
254	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
255	C₂×C₄×C₇	C₂²×D₄	1	8	yes	—
256	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	complemented
257	C₂⁵	C₂³×C₇	1	1	yes	characteristic
258	C₂⁵	C₂³×C₇	1	1	yes	characteristic
259	C₂²×Q₈	—	2	128	no	—
260	C₂²×Q₈	—	2	64	no	—
261	C₂²×Q₈	—	2	16	no	—
262	C₂²×Q₈	—	2	8	no	—
263	C₂²×Q₈	—	2	8	no	—
264	C₂²×Q₈	—	2	8	no	—
265	C₂²×Q₈	—	2	32	no	—
266	C₂²×Q₈	C₇×D₄	1	16	yes	complemented
267	C₂²×Q₈	C₂³×C₇	1	8	yes	—
268	C₂²×Q₈	C₂³×C₇	1	8	yes	—
269	C₂²×D₄	—	2	4	no	—
270	C₂²×D₄	—	2	4	no	—
271	C₂²×D₄	C₇×Q₈	1	8	yes	complemented
272	C₂²×D₄	C₂³×C₇	1	4	yes	—
273	C₂³×C₄	—	2	8	no	—
274	C₂³×C₄	—	2	16	no	—
275	C₂³×C₄	—	2	8	no	—
276	C₂³×C₄	—	2	4	no	—
277	C₂³×C₄	—	2	8	no	—
278	C₂³×C₄	C₇×D₄	1	8	yes	—
279	C₂³×C₄	C₂³×C₇	1	4	yes	—
280	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
281	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
282	C₂³×C₄	C₂³×C₇	1	4	yes	—
283	C₂³×C₄	C₂³×C₇	1	8	yes	—
284	C₂³×C₄	C₂³×C₇	1	4	yes	—
285	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₇	1	4	yes	—
287	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
289	C₂²⋊Q₈	—	2	64	no	—
290	C₄×D₄	—	2	32	no	—
291	C₂×C₄⋊C₄	—	2	4	no	—
292	C₂×C₄⋊C₄	—	2	8	no	—
293	C₂×C₄⋊C₄	—	2	16	no	—
294	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
295	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
296	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
297	C₂×C₂²⋊C₄	—	2	4	no	—
298	C₂×C₂²⋊C₄	—	2	8	no	—
299	C₂×C₂²⋊C₄	—	2	4	no	—
300	C₂×C₂²⋊C₄	—	2	16	no	—
301	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
305	C₂×C₄²	—	2	4	no	—
306	C₂×C₄²	C₂³×C₇	1	4	yes	—
307	#95	C₂³×C₇	1	8	yes	—
308	#95	C₂³×C₇	1	16	yes	—
309	#95	C₂³×C₇	1	16	yes	—
310	C₂²×C₇	—	2	4	no	—
311	C₂²×C₇	—	2	32	no	—
312	C₂²×C₇	—	2	4	no	—
313	C₂²×C₇	—	2	8	no	—
314	C₂²×C₇	—	2	8	no	—
315	C₂²×C₇	—	2	4	no	—
316	C₂²×C₇	—	2	8	no	—
317	C₂²×C₇	—	4	2	no	—
318	C₂²×C₇	—	4	16	no	—
319	C₂²×C₇	—	4	2	no	—
320	C₂²×C₇	—	4	4	no	—
321	C₂²×C₇	C₂×#120	1	4	yes	—
322	C₂²×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
323	C₂²×C₇	C₂×C₂²⋊Q₈	1	8	yes	complemented
324	C₂²×C₇	#536	1	4	yes	—
325	C₂²×C₇	#548	1	8	yes	—
326	C₂²×C₇	D₄×Q₈	1	8	yes	—
327	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
328	C₂²×C₇	C₂³×D₄	1	2	yes	—
329	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
330	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
331	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
332	C₄×C₇	—	2	16	no	—
333	C₄×C₇	—	2	4	no	—
334	C₄×C₇	—	2	4	no	—
335	C₄×C₇	—	4	2	no	—
336	C₄×C₇	—	4	2	no	—
337	C₄×C₇	—	4	8	no	—
338	C₄×C₇	C₂×#120	1	8	yes	—
339	C₂⁴	—	2	4	no	—
340	C₂⁴	—	2	4	no	—
341	C₂⁴	—	2	4	no	—
342	C₂⁴	—	2	2	no	—
343	C₂⁴	—	2	2	no	—
344	C₂⁴	—	2	4	no	—
345	C₂⁴	C₂×C₇×D₄	1	4	yes	—
346	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
347	C₂⁴	C₂×C₇×Q₈	1	4	yes	complemented
348	C₂⁴	C₇×#41	1	4	yes	—
349	C₂⁴	C₂⁴×C₇	1	2	yes	—
350	C₂⁴	C₂⁴×C₇	1	2	yes	—
351	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
352	C₂×Q₈	—	2	256	no	—
353	C₂×Q₈	—	2	64	no	—
354	C₂×Q₈	—	2	64	no	—
355	C₂×Q₈	—	2	32	no	—
356	C₂×Q₈	—	2	16	no	—
357	C₂×Q₈	—	2	16	no	—
358	C₂×Q₈	—	2	16	no	—
359	C₂×Q₈	C₂×C₇×D₄	1	32	yes	complemented
360	C₂×D₄	—	2	32	no	—
361	C₂×D₄	—	2	8	no	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	C₂×C₇×Q₈	1	16	yes	complemented
364	C₂²×C₄	—	2	64	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	16	no	—
367	C₂²×C₄	—	2	8	no	—
368	C₂²×C₄	—	2	8	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	32	no	—
372	C₂²×C₄	—	2	32	no	—
373	C₂²×C₄	—	2	16	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	8	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	8	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	2	8	no	—
382	C₂²×C₄	—	2	16	no	—
383	C₂²×C₄	—	4	16	no	—
384	C₂²×C₄	C₂×C₇×D₄	1	16	yes	—
385	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
386	C₂²×C₄	C₂×C₇×D₄	1	16	yes	—
387	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
388	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
389	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	complemented
390	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
391	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
392	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
393	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
394	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
395	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
396	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	16	no	—
399	C₄⋊C₄	—	2	32	no	—
400	C₂²⋊C₄	—	2	8	no	—
401	C₂²⋊C₄	—	2	16	no	—
402	C₂²⋊C₄	—	2	8	no	—
403	C₂²⋊C₄	—	2	32	no	—
404	C₄²	—	2	8	no	—
405	C₂×C₇	—	2	8	no	—
406	C₂×C₇	—	4	4	no	—
407	C₂×C₇	#2409	1	8	yes	direct product factor
408	C₂×C₇	C₂²×#120	1	1	yes	characteristic
409	C₂×C₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
410	C₂×C₇	C₂×#536	1	1	yes	characteristic
411	C₂×C₇	C₂×#548	1	2	yes	—
412	C₂×C₇	C₂×D₄×Q₈	1	2	yes	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	8	no	—
416	C₂³	—	2	8	no	—
417	C₂³	—	2	16	no	—
418	C₂³	—	2	16	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	4	no	—
423	C₂³	—	2	8	no	—
424	C₂³	—	2	16	no	—
425	C₂³	—	4	4	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	8	no	—
428	C₂³	C₇×C₂²⋊Q₈	1	16	yes	complemented
429	C₂³	C₂²×C₇×D₄	1	4	yes	—
430	C₂³	C₂²×C₇×D₄	1	2	yes	—
431	C₂³	C₂²×C₇×D₄	1	4	yes	—
432	C₂³	C₂²×C₇×Q₈	1	4	yes	—
433	C₂³	C₂²×C₇×Q₈	1	2	yes	—
434	C₂³	C₂²×C₇×Q₈	1	4	yes	complemented
435	C₂³	C₂×C₇×#41	1	4	yes	—
436	C₂³	C₂×C₇×#41	1	2	yes	—
437	C₂³	C₇×2₋¹⁺⁴	1	4	yes	—
438	C₂³	C₂⁵×C₇	1	1	yes	characteristic
439	Q₈	—	2	64	no	—
440	Q₈	—	2	64	no	—
441	D₄	—	2	32	no	—
442	C₂×C₄	—	2	64	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	8	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	32	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	32	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	16	no	—
462	C₂×C₄	—	4	16	no	—
463	C₂×C₄	C₇×#120	1	16	yes	—
464	C₂×C₄	C₂²×C₇×D₄	1	16	yes	—
465	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
466	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
467	C₂×C₄	C₂²×C₇×D₄	1	8	yes	—
468	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	complemented
469	C₇	C₂×#2409	1	1	yes	characteristic, direct product factor, Sylow
470	C₂²	—	2	32	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	2	8	no	—
474	C₂²	—	2	8	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	8	no	—
477	C₂²	—	4	16	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	4	no	—
481	C₂²	C₂×C₇×#120	1	4	yes	—
482	C₂²	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
483	C₂²	C₂×C₇×C₂²⋊Q₈	1	8	yes	complemented
484	C₂²	C₇×#536	1	4	yes	—
485	C₂²	C₇×#548	1	8	yes	—
486	C₂²	C₇×D₄×Q₈	1	8	yes	—
487	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
488	C₂²	C₂³×C₇×D₄	1	2	yes	—
489	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
490	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
491	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
492	C₄	—	2	16	no	—
493	C₄	—	2	4	no	—
494	C₄	—	2	4	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	8	no	—
498	C₄	C₂×C₇×#120	1	8	yes	—
499	C₂	—	2	8	no	—
500	C₂	—	4	4	no	—
501	C₂	C₇×#2409	1	8	yes	direct product factor
502	C₂	C₂²×C₇×#120	1	1	yes	characteristic
503	C₂	C₂²×C₇×C₂²⋊Q₈	1	1	yes	characteristic
504	C₂	C₂×C₇×#536	1	1	yes	characteristic
505	C₂	C₂×C₇×#548	1	2	yes	—
506	C₂	C₂×C₇×D₄×Q₈	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂³×C₇×D₄	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂⁴×C₇×Q₈	C₂	semidirect
2. C₂²×C₇×C₂²⋊Q₈	C₂	semidirect
4. C₇×#2409	C₂	direct (N × H)
5. C₂×C₇×#395	C₂	semidirect
6. C₂×C₇×#393	C₂	semidirect
7. C₂×C₇×#391	C₂	semidirect
9. C₂×C₇×#385	C₂	semidirect
10. C₂×C₇×#380	C₂	semidirect
15. C₂³×C₇×Q₈	C₂²	semidirect
21. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
32. C₇×#395	C₂²	semidirect
33. C₇×#393	C₂²	semidirect
34. C₇×#391	C₂²	semidirect
36. C₇×#385	C₂²	semidirect
37. C₇×#380	C₂²	semidirect
41. C₂×#2409	C₇	direct (N × H)
51. C₂²×C₇×Q₈	D₄	semidirect
56. C₂²×C₇×D₄	Q₈	semidirect
95. C₂⁴×Q₈	C₂×C₇	semidirect
96. C₂²×C₂²⋊Q₈	C₂×C₇	semidirect
98. #2409	C₂×C₇	direct (N × H)
99. C₂×#395	C₂×C₇	semidirect
100. C₂×#393	C₂×C₇	semidirect
101. C₂×#391	C₂×C₇	semidirect
103. C₂×#385	C₂×C₇	semidirect
104. C₂×#380	C₂×C₇	semidirect
113. C₂⁴×C₇	C₂×Q₈	semidirect
125. C₂×C₇×Q₈	C₂×D₄	semidirect
129. C₂×C₇×D₄	C₂×Q₈	semidirect
155. C₂²×C₄×C₇	C₂×Q₈	semidirect
175. C₂³×Q₈	C₂²×C₇	semidirect
181. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
192. #395	C₂²×C₇	semidirect
193. #393	C₂²×C₇	semidirect
194. #391	C₂²×C₇	semidirect
196. #385	C₂²×C₇	semidirect
197. #380	C₂²×C₇	semidirect
216. C₂³×C₇	C₂²⋊Q₈	semidirect
222. C₂³×C₇	C₂²×Q₈	semidirect
256. C₂×C₄×C₇	C₂²×Q₈	semidirect
266. C₂²×Q₈	C₇×D₄	semidirect
271. C₂²×D₄	C₇×Q₈	semidirect
323. C₂²×C₇	C₂×C₂²⋊Q₈	semidirect
347. C₂⁴	C₂×C₇×Q₈	semidirect
359. C₂×Q₈	C₂×C₇×D₄	semidirect
363. C₂×D₄	C₂×C₇×Q₈	semidirect
389. C₂²×C₄	C₂×C₇×Q₈	semidirect
407. C₂×C₇	#2409	direct (N × H)
428. C₂³	C₇×C₂²⋊Q₈	semidirect
434. C₂³	C₂²×C₇×Q₈	semidirect
468. C₂×C₄	C₂²×C₇×Q₈	semidirect
469. C₇	C₂×#2409	direct (N × H)
483. C₂²	C₂×C₇×C₂²⋊Q₈	semidirect
501. C₂	C₇×#2409	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁴×C₇×Q₈	2
C₂²×C₇×C₂²⋊Q₈	2
C₂²×C₄×C₇×D₄	2
C₇×#2409	2
C₂×C₇×#395	2
C₂×C₇×#393	2
C₂×C₇×#391	2
C₂×C₇×#386	2
C₂×C₇×#385	2
C₂×C₇×#380	2
C₂×#2409	7

Subgroups — C2×C7×#2409 #13211898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2409 #13211898