Subgroups — C₇×#24802 #13202018

Order 1792.

884 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#471	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3055	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×#465	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₇×#108	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2063	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2052	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2051	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1977	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1951	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1901	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1900	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1815	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#137	C₂²	1	1	yes	characteristic
17	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₇×#131	C₂²	1	1	yes	characteristic
20	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
22	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
23	C₇×#525	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#121	C₂²	1	1	yes	characteristic
26	C₇×#471	—	2	4	no	—
27	C₇×#470	—	2	1	no	—
28	C₇×#469	—	2	1	no	—
29	C₇×#468	—	2	1	no	—
30	C₇×#468	—	2	1	no	—
31	C₇×#467	—	2	1	no	—
32	C₇×#466	—	2	1	no	—
33	C₇×#465	—	2	1	no	—
34	C₇×#465	—	2	1	no	—
35	C₇×#465	—	2	1	no	—
36	C₇×#465	—	2	1	no	—
37	C₇×#465	—	2	1	no	—
38	C₇×#465	—	2	1	no	—
39	C₇×#435	—	2	1	no	—
40	C₇×#435	—	2	1	no	—
41	C₇×C₈×D₄	—	2	1	no	—
42	C₇×C₈×D₄	—	2	1	no	—
43	C₂×C₇×#108	—	2	4	no	—
44	C₂×C₇×#108	C₂²	1	1	yes	characteristic
45	C₂×C₇×#108	C₂²	1	1	yes	characteristic
46	C₂×C₇×#108	C₂²	1	1	yes	characteristic
47	C₂×C₇×#108	C₂²	1	1	yes	characteristic
48	C₇×#428	C₂²	1	1	yes	characteristic
49	C₇×#428	C₂²	1	1	yes	characteristic
50	C₂×C₇×#106	C₂²	1	1	yes	characteristic
51	C₇×#424	C₂²	1	1	yes	characteristic
52	C₇×#419	C₂²	1	1	yes	characteristic
53	C₇×#418	C₂²	1	1	yes	characteristic
54	C₇×#417	C₂²	1	1	yes	characteristic
55	C₇×#417	C₂²	1	1	yes	characteristic
56	C₂×C₇×#103	C₂²	1	1	yes	characteristic
57	C₂×C₇×#102	C₂²	1	1	yes	characteristic
58	C₂×C₇×#101	C₂²	1	1	yes	characteristic
59	C₂×C₇×#101	C₂²	1	1	yes	characteristic
60	C₂×C₇×#100	C₂²	1	1	yes	characteristic
61	C₂×C₇×#100	C₂²	1	1	yes	characteristic
62	C₇×#408	C₂²	1	1	yes	characteristic
63	C₇×#407	C₂²	1	1	yes	characteristic
64	C₇×#405	C₂²	1	1	yes	characteristic
65	C₇×#343	C₂²	1	1	yes	characteristic
66	C₇×#343	C₂²	1	1	yes	characteristic
67	C₇×#343	C₂²	1	1	yes	characteristic
68	C₇×#343	C₂²	1	1	yes	characteristic
69	#24802	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂×C₇×#41	C₂³	1	1	yes	characteristic
71	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇×D₄	—	2	1	no	—
73	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
75	C₇×#137	—	2	2	no	—
76	C₇×#137	—	4	1	no	—
77	C₇×AGL(1,ℤ/8)	—	2	2	no	—
78	C₇×AGL(1,ℤ/8)	—	4	1	no	—
79	C₂×C₇×Q₁₆	—	2	1	no	—
80	C₂×C₇×SD₁₆	—	2	1	no	—
81	C₂×C₇×SD₁₆	—	2	1	no	—
82	C₂×C₇×SD₁₆	—	2	2	no	—
83	C₂×C₇×SD₁₆	—	2	1	no	—
84	C₂×C₇×SD₁₆	—	2	1	no	—
85	C₂×C₇×SD₁₆	—	2	2	no	—
86	C₂×C₇×D₈	—	2	1	no	—
87	C₇×#131	—	2	2	no	—
88	C₇×#131	—	2	2	no	—
89	C₂×C₇×M₁₆	—	2	1	no	—
90	C₂×C₇×M₁₆	—	2	1	no	—
91	C₂×C₇×M₁₆	—	2	1	no	—
92	C₂×C₇×M₁₆	—	2	2	no	—
93	C₂×C₇×M₁₆	—	2	2	no	—
94	C₂×C₇×M₁₆	—	4	1	no	—
95	C₂×C₇×M₁₆	—	4	1	no	—
96	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
99	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
100	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
101	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
102	C₂²×C₇×C₈	—	2	2	no	—
103	C₂²×C₇×C₈	—	2	2	no	—
104	C₂²×C₇×C₈	—	2	1	no	—
105	C₂²×C₇×C₈	—	2	1	no	—
106	C₂²×C₇×C₈	—	2	1	no	—
107	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
108	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
109	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
110	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
111	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
112	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
113	C₇×#123	—	2	1	no	—
114	C₇×C₂²⋊Q₈	—	2	1	no	—
115	C₇×C₂²⋊Q₈	—	2	1	no	—
116	C₇×C₂²⋊Q₈	—	2	1	no	—
117	C₇×C₂²⋊Q₈	—	2	1	no	—
118	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
119	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
120	C₇×#121	—	2	1	no	—
121	C₇×#121	—	2	1	no	—
122	C₇×#121	—	2	1	no	—
123	C₇×#121	—	2	1	no	—
124	C₇×#121	D₄	1	1	yes	characteristic
125	C₇×#121	D₄	1	1	yes	characteristic
126	C₇×#120	—	2	1	no	—
127	C₄×C₇×D₄	—	2	1	no	—
128	C₄×C₇×D₄	—	2	1	no	—
129	C₇×#117	C₂³	1	1	yes	characteristic
130	C₂×C₇×C₄⋊C₄	—	2	1	no	—
131	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
134	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
135	C₇×#108	—	2	2	no	—
136	C₇×#108	—	2	2	no	—
137	C₇×#108	—	2	2	no	—
138	C₇×#108	D₄	1	4	yes	complemented
139	C₇×#107	—	2	1	no	—
140	C₇×#107	—	2	1	no	—
141	C₇×#106	—	2	1	no	—
142	C₇×#106	—	2	1	no	—
143	C₇×#106	—	2	1	no	—
144	C₇×#106	—	2	1	no	—
145	C₇×C₄⋊C₈	—	2	1	no	—
146	C₇×C₄⋊C₈	—	2	1	no	—
147	C₇×#103	—	2	1	no	—
148	C₇×#103	—	2	1	no	—
149	C₇×#103	—	2	1	no	—
150	C₇×#103	—	2	1	no	—
151	C₇×#103	—	2	1	no	—
152	C₇×#103	—	2	1	no	—
153	C₇×#102	—	2	1	no	—
154	C₇×#102	—	2	1	no	—
155	C₇×#102	—	2	1	no	—
156	C₇×#102	—	2	1	no	—
157	C₇×#102	—	2	1	no	—
158	C₇×#102	—	2	1	no	—
159	C₇×#101	—	2	2	no	—
160	C₇×#101	—	4	1	no	—
161	C₇×#100	—	2	2	no	—
162	C₇×#100	—	4	1	no	—
163	C₇×C₂²⋊C₈	—	2	1	no	—
164	C₇×C₂²⋊C₈	—	2	1	no	—
165	C₇×C₂²⋊C₈	—	2	1	no	—
166	C₇×C₂²⋊C₈	—	2	1	no	—
167	C₇×#97	—	2	1	no	—
168	C₄×C₇×C₈	—	2	1	no	—
169	C₂×#471	C₂×C₇	1	1	yes	characteristic, complemented
170	#3056	C₂×C₇	1	1	yes	characteristic, complemented
171	#3055	C₂×C₇	1	1	yes	characteristic
172	C₂×#465	C₂×C₇	1	1	yes	characteristic, complemented
173	#2929	C₂×C₇	1	1	yes	characteristic, complemented
174	C₂²×#108	C₂×C₇	1	1	yes	characteristic, complemented
175	#2064	C₂×C₇	1	1	yes	characteristic, complemented
176	#2063	C₂×C₇	1	1	yes	characteristic, complemented
177	#2052	C₂×C₇	1	1	yes	characteristic, complemented
178	#2051	C₂×C₇	1	1	yes	characteristic, complemented
179	#1977	C₂×C₇	1	1	yes	characteristic, complemented
180	#1951	C₂×C₇	1	1	yes	characteristic, complemented
181	#1901	C₂×C₇	1	1	yes	characteristic, complemented
182	#1900	C₂×C₇	1	1	yes	characteristic, complemented
183	#1815	C₂×C₇	1	1	yes	characteristic, complemented
184	C₂⁴×C₇	—	2	1	no	—
185	C₂⁴×C₇	#41	1	1	yes	characteristic
186	C₇×#41	—	2	1	no	—
187	C₇×#41	—	2	1	no	—
188	C₇×#41	—	2	1	no	—
189	C₇×#41	—	2	1	no	—
190	C₂×C₇×Q₈	—	2	1	no	—
191	C₂×C₇×Q₈	—	2	1	no	—
192	C₂×C₇×Q₈	—	2	1	no	—
193	C₂×C₇×Q₈	—	2	1	no	—
194	C₂×C₇×Q₈	—	2	1	no	—
195	C₂×C₇×Q₈	—	2	1	no	—
196	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
197	C₂×C₇×D₄	—	2	1	no	—
198	C₂×C₇×D₄	—	2	1	no	—
199	C₂×C₇×D₄	—	2	1	no	—
200	C₂×C₇×D₄	—	2	1	no	—
201	C₂×C₇×D₄	—	2	1	no	—
202	C₂×C₇×D₄	—	2	1	no	—
203	C₂×C₇×D₄	—	2	1	no	—
204	C₂×C₇×D₄	—	2	1	no	—
205	C₂×C₇×D₄	—	2	1	no	—
206	C₂×C₇×D₄	—	4	1	no	—
207	C₂×C₇×D₄	—	4	1	no	—
208	C₂×C₇×D₄	—	8	2	no	—
209	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₇	—	2	1	no	—
211	C₂²×C₄×C₇	—	2	1	no	—
212	C₂²×C₄×C₇	—	2	1	no	—
213	C₂²×C₄×C₇	—	2	1	no	—
214	C₂²×C₄×C₇	—	2	1	no	—
215	C₂²×C₄×C₇	—	2	1	no	—
216	C₂²×C₄×C₇	—	2	1	no	—
217	C₂²×C₄×C₇	—	2	1	no	—
218	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₇	#41	1	1	yes	characteristic
223	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
224	C₇×Q₁₆	—	4	2	no	—
225	C₇×SD₁₆	—	4	2	no	—
226	C₇×SD₁₆	—	4	2	no	—
227	C₇×SD₁₆	—	4	2	no	—
228	C₇×SD₁₆	—	4	2	no	—
229	C₇×D₈	—	4	2	no	—
230	C₇×M₁₆	—	2	1	no	—
231	C₇×M₁₆	—	2	1	no	—
232	C₇×M₁₆	—	2	1	no	—
233	C₇×M₁₆	—	2	1	no	—
234	C₇×M₁₆	—	2	1	no	—
235	C₇×M₁₆	—	2	1	no	—
236	C₇×M₁₆	—	2	1	no	—
237	C₇×M₁₆	—	2	1	no	—
238	C₇×M₁₆	—	2	1	no	—
239	C₇×M₁₆	—	2	1	no	—
240	C₇×M₁₆	—	4	2	no	—
241	C₇×M₁₆	—	4	2	no	—
242	C₇×M₁₆	—	4	2	no	—
243	C₇×M₁₆	C₂×D₄	1	2	yes	—
244	C₇×M₁₆	C₂×D₄	1	2	yes	—
245	C₂×C₇×C₈	—	2	1	no	—
246	C₂×C₇×C₈	—	2	1	no	—
247	C₂×C₇×C₈	—	2	1	no	—
248	C₂×C₇×C₈	—	2	1	no	—
249	C₂×C₇×C₈	—	2	2	no	—
250	C₂×C₇×C₈	—	2	2	no	—
251	C₂×C₇×C₈	—	2	2	no	—
252	C₂×C₇×C₈	—	2	2	no	—
253	C₂×C₇×C₈	—	2	1	no	—
254	C₂×C₇×C₈	—	2	1	no	—
255	C₂×C₇×C₈	—	2	1	no	—
256	C₂×C₇×C₈	—	2	1	no	—
257	C₂×C₇×C₈	—	4	2	no	—
258	C₂×C₇×C₈	—	4	2	no	—
259	C₂×C₇×C₈	—	4	2	no	—
260	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
261	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
262	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
263	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
264	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
265	C₂×C₇×C₈	#41	1	2	yes	—
266	C₇×C₄⋊C₄	—	2	1	no	—
267	C₇×C₄⋊C₄	—	2	1	no	—
268	C₇×C₄⋊C₄	—	2	1	no	—
269	C₇×C₄⋊C₄	—	2	1	no	—
270	C₇×C₄⋊C₄	—	2	1	no	—
271	C₇×C₄⋊C₄	—	2	1	no	—
272	C₇×C₄⋊C₄	—	4	1	no	—
273	C₇×C₄⋊C₄	—	4	1	no	—
274	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
275	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
276	C₇×C₂²⋊C₄	—	2	1	no	—
277	C₇×C₂²⋊C₄	—	2	1	no	—
278	C₇×C₂²⋊C₄	—	2	1	no	—
279	C₇×C₂²⋊C₄	—	2	1	no	—
280	C₇×C₂²⋊C₄	—	2	1	no	—
281	C₇×C₂²⋊C₄	—	4	1	no	—
282	C₇×C₂²⋊C₄	—	4	1	no	—
283	C₇×C₂²⋊C₄	—	4	1	no	—
284	C₇×C₂²⋊C₄	—	4	1	no	—
285	C₄²×C₇	—	2	1	no	—
286	C₂×#137	C₂²×C₇	1	1	yes	characteristic
287	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
288	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
289	C₂×#131	C₂²×C₇	1	1	yes	characteristic
290	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
291	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
292	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
293	#525	C₂²×C₇	1	1	yes	characteristic
294	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
295	C₂×#121	C₂²×C₇	1	1	yes	characteristic
296	#471	—	2	4	no	—
297	#470	—	2	1	no	—
298	#469	—	2	1	no	—
299	#468	—	2	1	no	—
300	#468	—	2	1	no	—
301	#467	—	2	1	no	—
302	#466	—	2	1	no	—
303	#465	—	2	1	no	—
304	#465	—	2	1	no	—
305	#465	—	2	1	no	—
306	#465	—	2	1	no	—
307	#465	—	2	1	no	—
308	#465	—	2	1	no	—
309	#435	—	2	1	no	—
310	#435	—	2	1	no	—
311	C₈×D₄	—	2	1	no	—
312	C₈×D₄	—	2	1	no	—
313	C₂×#108	—	2	4	no	—
314	C₂×#108	C₂²×C₇	1	1	yes	characteristic
315	C₂×#108	C₂²×C₇	1	1	yes	characteristic
316	C₂×#108	C₂²×C₇	1	1	yes	characteristic
317	C₂×#108	C₂²×C₇	1	1	yes	characteristic
318	#428	C₂²×C₇	1	1	yes	characteristic
319	#428	C₂²×C₇	1	1	yes	characteristic
320	C₂×#106	C₂²×C₇	1	1	yes	characteristic
321	#424	C₂²×C₇	1	1	yes	characteristic
322	#419	C₂²×C₇	1	1	yes	characteristic
323	#418	C₂²×C₇	1	1	yes	characteristic
324	#417	C₂²×C₇	1	1	yes	characteristic
325	#417	C₂²×C₇	1	1	yes	characteristic
326	C₂×#103	C₂²×C₇	1	1	yes	characteristic
327	C₂×#102	C₂²×C₇	1	1	yes	characteristic
328	C₂×#101	C₂²×C₇	1	1	yes	characteristic
329	C₂×#101	C₂²×C₇	1	1	yes	characteristic
330	C₂×#100	C₂²×C₇	1	1	yes	characteristic
331	C₂×#100	C₂²×C₇	1	1	yes	characteristic
332	#408	C₂²×C₇	1	1	yes	characteristic
333	#407	C₂²×C₇	1	1	yes	characteristic
334	#405	C₂²×C₇	1	1	yes	characteristic
335	#343	C₂²×C₇	1	1	yes	characteristic
336	#343	C₂²×C₇	1	1	yes	characteristic
337	#343	C₂²×C₇	1	1	yes	characteristic
338	#343	C₂²×C₇	1	1	yes	characteristic
339	C₂³×C₇	—	2	1	no	—
340	C₂³×C₇	—	2	1	no	—
341	C₂³×C₇	—	2	2	no	—
342	C₂³×C₇	—	2	1	no	—
343	C₂³×C₇	—	4	1	no	—
344	C₂³×C₇	—	4	1	no	—
345	C₂³×C₇	—	4	1	no	—
346	C₂³×C₇	—	4	1	no	—
347	C₂³×C₇	—	8	1	no	—
348	C₂³×C₇	—	8	1	no	—
349	C₂³×C₇	#121	1	1	yes	characteristic
350	C₂³×C₇	#121	1	1	yes	characteristic
351	C₂³×C₇	C₂×#41	1	1	yes	characteristic
352	C₇×Q₈	—	2	1	no	—
353	C₇×Q₈	—	2	1	no	—
354	C₇×Q₈	—	4	1	no	—
355	C₇×Q₈	—	4	1	no	—
356	C₇×Q₈	—	4	1	no	—
357	C₇×Q₈	—	4	1	no	—
358	C₇×D₄	—	2	1	no	—
359	C₇×D₄	—	2	1	no	—
360	C₇×D₄	—	4	2	no	—
361	C₇×D₄	—	4	1	no	—
362	C₇×D₄	—	4	1	no	—
363	C₇×D₄	—	4	2	no	—
364	C₇×D₄	—	4	1	no	—
365	C₇×D₄	—	4	1	no	—
366	C₇×D₄	—	4	1	no	—
367	C₇×D₄	—	4	1	no	—
368	C₇×D₄	—	8	2	no	—
369	C₇×D₄	—	8	2	no	—
370	C₂×C₄×C₇	—	2	1	no	—
371	C₂×C₄×C₇	—	2	1	no	—
372	C₂×C₄×C₇	—	2	1	no	—
373	C₂×C₄×C₇	—	2	1	no	—
374	C₂×C₄×C₇	—	2	1	no	—
375	C₂×C₄×C₇	—	2	1	no	—
376	C₂×C₄×C₇	—	2	1	no	—
377	C₂×C₄×C₇	—	2	1	no	—
378	C₂×C₄×C₇	—	2	1	no	—
379	C₂×C₄×C₇	—	2	1	no	—
380	C₂×C₄×C₇	—	2	1	no	—
381	C₂×C₄×C₇	—	2	1	no	—
382	C₂×C₄×C₇	—	2	1	no	—
383	C₂×C₄×C₇	—	4	1	no	—
384	C₂×C₄×C₇	—	4	1	no	—
385	C₂×C₄×C₇	—	4	1	no	—
386	C₂×C₄×C₇	—	4	1	no	—
387	C₂×C₄×C₇	—	4	1	no	—
388	C₂×C₄×C₇	—	4	1	no	—
389	C₂×C₄×C₇	—	4	1	no	—
390	C₂×C₄×C₇	—	8	1	no	—
391	C₂×C₄×C₇	—	8	1	no	—
392	C₂×C₄×C₇	#121	1	1	yes	characteristic
393	C₂×C₄×C₇	#121	1	1	yes	characteristic
394	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
398	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
399	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
400	C₇×C₈	—	2	1	no	—
401	C₇×C₈	—	2	1	no	—
402	C₇×C₈	—	2	2	no	—
403	C₇×C₈	—	2	2	no	—
404	C₇×C₈	—	4	1	no	—
405	C₇×C₈	—	4	1	no	—
406	C₇×C₈	—	4	1	no	—
407	C₇×C₈	—	4	1	no	—
408	C₇×C₈	#121	1	2	yes	—
409	C₇×C₈	#121	1	2	yes	—
410	C₂×#41	C₂³×C₇	1	1	yes	characteristic
411	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
412	C₂²×D₄	—	2	1	no	—
413	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
414	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
415	#137	—	2	2	no	—
416	#137	—	4	1	no	—
417	AGL(1,ℤ/8)	—	2	2	no	—
418	AGL(1,ℤ/8)	—	4	1	no	—
419	C₂×Q₁₆	—	2	1	no	—
420	C₂×SD₁₆	—	2	1	no	—
421	C₂×SD₁₆	—	2	1	no	—
422	C₂×SD₁₆	—	2	1	no	—
423	C₂×SD₁₆	—	2	1	no	—
424	C₂×SD₁₆	—	2	2	no	—
425	C₂×SD₁₆	—	2	2	no	—
426	C₂×D₈	—	2	1	no	—
427	#131	—	2	2	no	—
428	#131	—	2	2	no	—
429	C₂×M₁₆	—	2	1	no	—
430	C₂×M₁₆	—	2	1	no	—
431	C₂×M₁₆	—	2	1	no	—
432	C₂×M₁₆	—	2	2	no	—
433	C₂×M₁₆	—	2	2	no	—
434	C₂×M₁₆	—	4	1	no	—
435	C₂×M₁₆	—	4	1	no	—
436	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
437	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
438	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
439	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
440	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
441	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
442	C₂²×C₈	—	2	2	no	—
443	C₂²×C₈	—	2	2	no	—
444	C₂²×C₈	—	2	1	no	—
445	C₂²×C₈	—	2	1	no	—
446	C₂²×C₈	—	2	1	no	—
447	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
448	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
449	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
450	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
451	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
453	#123	—	2	1	no	—
454	C₂²⋊Q₈	—	2	1	no	—
455	C₂²⋊Q₈	—	2	1	no	—
456	C₂²⋊Q₈	—	2	1	no	—
457	C₂²⋊Q₈	—	2	1	no	—
458	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
459	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
460	#121	—	2	1	no	—
461	#121	—	2	1	no	—
462	#121	—	2	1	no	—
463	#121	—	2	1	no	—
464	#121	C₇×D₄	1	1	yes	characteristic
465	#121	C₇×D₄	1	1	yes	characteristic
466	#120	—	2	1	no	—
467	C₄×D₄	—	2	1	no	—
468	C₄×D₄	—	2	1	no	—
469	#117	C₂³×C₇	1	1	yes	characteristic
470	C₂×C₄⋊C₄	—	2	1	no	—
471	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	#108	—	2	2	no	—
476	#108	—	2	2	no	—
477	#108	—	2	2	no	—
478	#108	C₇×D₄	1	4	yes	complemented
479	#107	—	2	1	no	—
480	#107	—	2	1	no	—
481	#106	—	2	1	no	—
482	#106	—	2	1	no	—
483	#106	—	2	1	no	—
484	#106	—	2	1	no	—
485	C₄⋊C₈	—	2	1	no	—
486	C₄⋊C₈	—	2	1	no	—
487	#103	—	2	1	no	—
488	#103	—	2	1	no	—
489	#103	—	2	1	no	—
490	#103	—	2	1	no	—
491	#103	—	2	1	no	—
492	#103	—	2	1	no	—
493	#102	—	2	1	no	—
494	#102	—	2	1	no	—
495	#102	—	2	1	no	—
496	#102	—	2	1	no	—
497	#102	—	2	1	no	—
498	#102	—	2	1	no	—
499	#101	—	2	2	no	—
500	#101	—	4	1	no	—
501	#100	—	2	2	no	—
502	#100	—	4	1	no	—
503	C₂²⋊C₈	—	2	1	no	—
504	C₂²⋊C₈	—	2	1	no	—
505	C₂²⋊C₈	—	2	1	no	—
506	C₂²⋊C₈	—	2	1	no	—
507	#97	—	2	1	no	—
508	C₄×C₈	—	2	1	no	—
509	C₂²×C₇	—	2	1	no	—
510	C₂²×C₇	—	2	1	no	—
511	C₂²×C₇	—	2	1	no	—
512	C₂²×C₇	—	2	1	no	—
513	C₂²×C₇	—	2	1	no	—
514	C₂²×C₇	—	2	1	no	—
515	C₂²×C₇	—	2	1	no	—
516	C₂²×C₇	—	4	2	no	—
517	C₂²×C₇	—	4	2	no	—
518	C₂²×C₇	—	4	1	no	—
519	C₂²×C₇	—	4	1	no	—
520	C₂²×C₇	—	4	1	no	—
521	C₂²×C₇	—	8	1	no	—
522	C₂²×C₇	—	8	1	no	—
523	C₂²×C₇	—	8	1	no	—
524	C₂²×C₇	—	16	1	no	—
525	C₂²×C₇	—	16	1	no	—
526	C₂²×C₇	#471	1	2	yes	complemented
527	C₂²×C₇	C₂×#121	1	1	yes	characteristic
528	C₂²×C₇	#548	1	1	yes	characteristic
529	C₂²×C₇	#553	1	1	yes	characteristic
530	C₄×C₇	—	2	1	no	—
531	C₄×C₇	—	2	1	no	—
532	C₄×C₇	—	4	1	no	—
533	C₄×C₇	—	4	1	no	—
534	C₄×C₇	—	4	1	no	—
535	C₄×C₇	—	8	1	no	—
536	C₄×C₇	—	8	1	no	—
537	C₄×C₇	—	8	1	no	—
538	C₄×C₇	C₂×#121	1	1	yes	characteristic
539	C₄×C₇	#537	1	1	yes	characteristic
540	C₄×C₇	D₄²	1	1	yes	characteristic
541	C₄×C₇	#547	1	1	yes	characteristic
542	C₂⁴	—	2	1	no	—
543	C₂⁴	C₇×#41	1	1	yes	characteristic
544	#41	—	2	1	no	—
545	#41	—	2	1	no	—
546	#41	—	2	1	no	—
547	#41	—	2	1	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	4	1	no	—
565	C₂×D₄	—	4	1	no	—
566	C₂×D₄	—	8	2	no	—
567	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
577	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
578	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
579	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
580	C₂²×C₄	C₇×#41	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
582	Q₁₆	—	4	2	no	—
583	SD₁₆	—	4	2	no	—
584	SD₁₆	—	4	2	no	—
585	SD₁₆	—	4	2	no	—
586	SD₁₆	—	4	2	no	—
587	D₈	—	4	2	no	—
588	M₁₆	—	2	1	no	—
589	M₁₆	—	2	1	no	—
590	M₁₆	—	2	1	no	—
591	M₁₆	—	2	1	no	—
592	M₁₆	—	2	1	no	—
593	M₁₆	—	2	1	no	—
594	M₁₆	—	2	1	no	—
595	M₁₆	—	2	1	no	—
596	M₁₆	—	2	1	no	—
597	M₁₆	—	2	1	no	—
598	M₁₆	—	4	2	no	—
599	M₁₆	—	4	2	no	—
600	M₁₆	—	4	2	no	—
601	M₁₆	C₂×C₇×D₄	1	2	yes	—
602	M₁₆	C₂×C₇×D₄	1	2	yes	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	2	no	—
608	C₂×C₈	—	2	2	no	—
609	C₂×C₈	—	2	2	no	—
610	C₂×C₈	—	2	2	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	4	2	no	—
616	C₂×C₈	—	4	2	no	—
617	C₂×C₈	—	4	2	no	—
618	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
619	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
620	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
621	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
622	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
623	C₂×C₈	C₇×#41	1	2	yes	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	4	1	no	—
631	C₄⋊C₄	—	4	1	no	—
632	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
633	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
634	C₂²⋊C₄	—	2	1	no	—
635	C₂²⋊C₄	—	2	1	no	—
636	C₂²⋊C₄	—	2	1	no	—
637	C₂²⋊C₄	—	2	1	no	—
638	C₂²⋊C₄	—	2	1	no	—
639	C₂²⋊C₄	—	4	1	no	—
640	C₂²⋊C₄	—	4	1	no	—
641	C₂²⋊C₄	—	4	1	no	—
642	C₂²⋊C₄	—	4	1	no	—
643	C₄²	—	2	1	no	—
644	C₂×C₇	—	2	1	no	—
645	C₂×C₇	—	2	1	no	—
646	C₂×C₇	—	2	2	no	—
647	C₂×C₇	—	4	1	no	—
648	C₂×C₇	—	8	1	no	—
649	C₂×C₇	—	16	1	no	—
650	C₂×C₇	#2416	1	1	yes	characteristic
651	C₂×C₇	C₂×#471	1	1	yes	characteristic
652	C₂×C₇	#3067	1	1	yes	characteristic
653	C₂³	—	2	2	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	8	1	no	—
662	C₂³	—	8	1	no	—
663	C₂³	C₇×#121	1	1	yes	characteristic
664	C₂³	C₇×#121	1	1	yes	characteristic
665	C₂³	C₂×C₇×#41	1	1	yes	characteristic
666	Q₈	—	2	1	no	—
667	Q₈	—	2	1	no	—
668	Q₈	—	4	1	no	—
669	Q₈	—	4	1	no	—
670	Q₈	—	4	1	no	—
671	Q₈	—	4	1	no	—
672	D₄	—	2	1	no	—
673	D₄	—	2	1	no	—
674	D₄	—	4	2	no	—
675	D₄	—	4	2	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	4	1	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	no	—
682	D₄	—	8	2	no	—
683	D₄	—	8	2	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	8	1	no	—
705	C₂×C₄	—	8	1	no	—
706	C₂×C₄	C₇×#121	1	1	yes	characteristic
707	C₂×C₄	C₇×#121	1	1	yes	characteristic
708	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
709	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
710	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
711	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
712	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
713	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
714	C₈	—	2	1	no	—
715	C₈	—	2	1	no	—
716	C₈	—	2	2	no	—
717	C₈	—	2	2	no	—
718	C₈	—	4	1	no	—
719	C₈	—	4	1	no	—
720	C₈	—	4	1	no	—
721	C₈	—	4	1	no	—
722	C₈	C₇×#121	1	2	yes	—
723	C₈	C₇×#121	1	2	yes	—
724	C₇	#24802	1	1	yes	characteristic, direct product factor, Sylow
725	C₂²	—	2	1	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	8	1	no	—
738	C₂²	—	8	1	no	—
739	C₂²	—	8	1	no	—
740	C₂²	—	16	1	no	—
741	C₂²	—	16	1	no	—
742	C₂²	C₇×#471	1	2	yes	complemented
743	C₂²	C₂×C₇×#121	1	1	yes	characteristic
744	C₂²	C₇×#548	1	1	yes	characteristic
745	C₂²	C₇×#553	1	1	yes	characteristic
746	C₄	—	2	1	no	—
747	C₄	—	2	1	no	—
748	C₄	—	4	1	no	—
749	C₄	—	4	1	no	—
750	C₄	—	4	1	no	—
751	C₄	—	8	1	no	—
752	C₄	—	8	1	no	—
753	C₄	—	8	1	no	—
754	C₄	C₂×C₇×#121	1	1	yes	characteristic
755	C₄	C₇×#537	1	1	yes	characteristic
756	C₄	C₇×D₄²	1	1	yes	characteristic
757	C₄	C₇×#547	1	1	yes	characteristic
758	C₂	—	2	1	no	—
759	C₂	—	2	1	no	—
760	C₂	—	2	2	no	—
761	C₂	—	4	1	no	—
762	C₂	—	8	1	no	—
763	C₂	—	16	1	no	—
764	C₂	C₇×#2416	1	1	yes	characteristic
765	C₂	C₂×C₇×#471	1	1	yes	characteristic
766	C₂	C₇×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₇×#3055	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂³×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#471	C₂	semidirect
2. C₇×#3056	C₂	semidirect
4. C₂×C₇×#465	C₂	semidirect
5. C₇×#2929	C₂	semidirect
6. C₂²×C₇×#108	C₂	semidirect
7. C₇×#2064	C₂	semidirect
8. C₇×#2063	C₂	semidirect
9. C₇×#2052	C₂	semidirect
10. C₇×#2051	C₂	semidirect
11. C₇×#1977	C₂	semidirect
12. C₇×#1951	C₂	semidirect
13. C₇×#1901	C₂	semidirect
14. C₇×#1900	C₂	semidirect
15. C₇×#1815	C₂	semidirect
69. #24802	C₇	direct (N × H)
138. C₇×#108	D₄	semidirect
169. C₂×#471	C₂×C₇	semidirect
170. #3056	C₂×C₇	semidirect
172. C₂×#465	C₂×C₇	semidirect
173. #2929	C₂×C₇	semidirect
174. C₂²×#108	C₂×C₇	semidirect
175. #2064	C₂×C₇	semidirect
176. #2063	C₂×C₇	semidirect
177. #2052	C₂×C₇	semidirect
178. #2051	C₂×C₇	semidirect
179. #1977	C₂×C₇	semidirect
180. #1951	C₂×C₇	semidirect
181. #1901	C₂×C₇	semidirect
182. #1900	C₂×C₇	semidirect
183. #1815	C₂×C₇	semidirect
478. #108	C₇×D₄	semidirect
526. C₂²×C₇	#471	semidirect
724. C₇	#24802	direct (N × H)
742. C₂²	C₇×#471	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#471	2
C₇×#3056	2
C₇×#3055	2
C₂×C₇×#465	2
C₇×#2929	2
C₂²×C₇×#108	2
C₇×#2064	2
C₇×#2063	2
C₇×#2052	2
C₇×#2051	2
C₇×#1977	2
C₇×#1951	2
C₇×#1901	2
C₇×#1900	2
C₇×#1815	2
#24802	7

Subgroups — C7×#24802 #13202018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#24802 #13202018