Subgroups — C₇×#23718 #13200934

Order 1792.

784 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2090	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2079	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
11	C₇×#2046	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2019	C₂	1	1	yes	maximal, characteristic
13	C₄×C₇×#108	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₇×#101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₇×#100	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	C₄×C₇×#41	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
22	C₇×#442	—	2	1	no	—
23	C₇×#441	—	2	1	no	—
24	C₇×#440	—	2	1	no	—
25	C₇×#440	—	2	1	no	—
26	C₄×C₇×Q₁₆	—	2	1	no	—
27	C₄×C₇×SD₁₆	—	2	1	no	—
28	C₄×C₇×SD₁₆	—	2	1	no	—
29	C₄×C₇×SD₁₆	—	2	2	no	—
30	C₄×C₇×SD₁₆	—	2	2	no	—
31	C₄×C₇×D₈	—	2	1	no	—
32	C₇×#433	—	2	2	no	—
33	C₇×#431	—	2	2	no	—
34	C₂×C₇×#108	C₂²	1	1	yes	characteristic
35	C₂×C₇×#108	C₂²	1	1	yes	characteristic
36	C₇×#428	C₂²	1	1	yes	characteristic
37	C₇×#428	C₂²	1	1	yes	characteristic
38	C₂×C₇×#106	C₂²	1	1	yes	characteristic
39	C₇×#424	C₂²	1	1	yes	characteristic
40	C₇×#424	C₂²	1	1	yes	characteristic
41	C₇×#419	C₂²	1	1	yes	characteristic
42	C₇×#418	C₂²	1	1	yes	characteristic
43	C₇×#417	C₂²	1	1	yes	characteristic
44	C₇×#417	C₂²	1	1	yes	characteristic
45	C₂×C₇×#103	C₂²	1	1	yes	characteristic
46	C₂×C₇×#102	C₂²	1	1	yes	characteristic
47	C₂×C₇×#101	C₂²	1	1	yes	characteristic
48	C₂×C₇×#101	C₂²	1	1	yes	characteristic
49	C₂×C₇×#100	C₂²	1	1	yes	characteristic
50	C₂×C₇×#100	C₂²	1	1	yes	characteristic
51	C₇×#408	C₂²	1	1	yes	characteristic
52	C₇×#408	C₂²	1	1	yes	characteristic
53	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
54	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
55	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
57	C₇×#343	C₂²	1	1	yes	characteristic
58	C₇×#343	C₂²	1	1	yes	characteristic
59	C₇×#343	C₂²	1	1	yes	characteristic
60	C₇×#343	C₂²	1	1	yes	characteristic
61	C₇×#341	C₂²	1	1	yes	characteristic
62	C₇×#341	C₂²	1	1	yes	characteristic
63	#23718	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂×C₇×#41	C₂³	1	1	yes	characteristic
65	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₇	—	2	1	no	—
68	C₇×#137	—	2	2	no	—
69	C₇×#137	—	2	2	no	—
70	C₇×AGL(1,ℤ/8)	—	2	2	no	—
71	C₇×AGL(1,ℤ/8)	—	2	2	no	—
72	C₂×C₇×Q₁₆	—	2	1	no	—
73	C₂×C₇×SD₁₆	—	2	1	no	—
74	C₂×C₇×SD₁₆	—	2	2	no	—
75	C₂×C₇×SD₁₆	—	2	1	no	—
76	C₂×C₇×SD₁₆	—	2	2	no	—
77	C₂×C₇×SD₁₆	—	2	2	no	—
78	C₂×C₇×D₈	—	2	1	no	—
79	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
83	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
85	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
87	C₄×C₇×Q₈	—	2	1	no	—
88	C₄×C₇×Q₈	—	2	1	no	—
89	C₄×C₇×Q₈	—	2	1	no	—
90	C₄×C₇×Q₈	—	2	1	no	—
91	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
92	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
93	C₄×C₇×D₄	—	2	1	no	—
94	C₄×C₇×D₄	—	2	1	no	—
95	C₄×C₇×D₄	—	2	1	no	—
96	C₄×C₇×D₄	—	2	1	no	—
97	C₄×C₇×D₄	—	2	1	no	—
98	C₄×C₇×D₄	—	2	1	no	—
99	C₄×C₇×D₄	D₄	1	1	yes	characteristic
100	C₄×C₇×D₄	D₄	1	1	yes	characteristic
101	C₇×#117	—	2	1	no	—
102	C₇×#117	C₂³	1	1	yes	characteristic
103	C₂×C₇×C₄⋊C₄	—	2	1	no	—
104	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₄²×C₇	—	2	1	no	—
108	C₂×C₄²×C₇	—	2	1	no	—
109	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
110	C₇×#108	—	2	2	no	—
111	C₇×#108	—	2	2	no	—
112	C₇×#107	—	2	1	no	—
113	C₇×#107	—	2	1	no	—
114	C₇×#106	—	2	2	no	—
115	C₇×#106	—	2	1	no	—
116	C₇×#106	—	2	1	no	—
117	C₇×C₄⋊C₈	—	2	2	no	—
118	C₇×C₄⋊C₈	—	2	2	no	—
119	C₇×#103	—	2	1	no	—
120	C₇×#103	—	2	1	no	—
121	C₇×#103	—	2	2	no	—
122	C₇×#103	—	2	1	no	—
123	C₇×#103	—	2	1	no	—
124	C₇×#102	—	2	1	no	—
125	C₇×#102	—	2	1	no	—
126	C₇×#102	—	2	2	no	—
127	C₇×#102	—	2	1	no	—
128	C₇×#102	—	2	1	no	—
129	C₇×#101	—	2	2	no	—
130	C₇×#101	—	2	2	no	—
131	C₇×#100	—	2	2	no	—
132	C₇×#100	—	2	2	no	—
133	C₇×C₂²⋊C₈	—	2	2	no	—
134	C₇×C₂²⋊C₈	—	2	2	no	—
135	C₇×#97	—	2	1	no	—
136	C₇×#97	—	2	1	no	—
137	C₇×#97	—	2	1	no	—
138	C₄×C₇×C₈	—	2	1	no	—
139	C₄×C₇×C₈	—	2	1	no	—
140	C₄×C₇×C₈	—	2	1	no	—
141	C₄×C₇×C₈	D₄	1	2	yes	—
142	C₄×C₇×C₈	D₄	1	2	yes	—
143	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
144	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic
145	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
146	#2922	C₂×C₇	1	1	yes	characteristic, complemented
147	#2090	C₂×C₇	1	1	yes	characteristic, complemented
148	#2079	C₂×C₇	1	1	yes	characteristic, complemented
149	#2064	C₂×C₇	1	1	yes	characteristic, complemented
150	#2063	C₂×C₇	1	1	yes	characteristic, complemented
151	#2052	C₂×C₇	1	1	yes	characteristic, complemented
152	#2051	C₂×C₇	1	1	yes	characteristic
153	#2046	C₂×C₇	1	1	yes	characteristic, complemented
154	#2019	C₂×C₇	1	1	yes	characteristic
155	C₄×#108	C₂×C₇	1	1	yes	characteristic, complemented
156	C₄×#101	C₂×C₇	1	1	yes	characteristic, complemented
157	C₄×#100	C₂×C₇	1	1	yes	characteristic, complemented
158	C₂⁴×C₇	—	2	1	no	—
159	C₇×#41	—	2	1	no	—
160	C₇×#41	—	2	1	no	—
161	C₇×#41	—	2	1	no	—
162	C₇×#41	—	2	1	no	—
163	C₂×C₇×Q₈	—	2	1	no	—
164	C₂×C₇×Q₈	—	2	1	no	—
165	C₂×C₇×Q₈	—	2	1	no	—
166	C₂×C₇×Q₈	—	2	1	no	—
167	C₂×C₇×Q₈	—	2	1	no	—
168	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₇×Q₈	#41	1	2	yes	—
170	C₂×C₇×D₄	—	2	1	no	—
171	C₂×C₇×D₄	—	2	1	no	—
172	C₂×C₇×D₄	—	2	1	no	—
173	C₂×C₇×D₄	—	2	1	no	—
174	C₂×C₇×D₄	—	2	1	no	—
175	C₂×C₇×D₄	—	2	1	no	—
176	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
177	C₂×C₇×D₄	#41	1	2	yes	—
178	C₂²×C₄×C₇	—	2	1	no	—
179	C₂²×C₄×C₇	—	2	1	no	—
180	C₂²×C₄×C₇	—	2	1	no	—
181	C₂²×C₄×C₇	—	2	1	no	—
182	C₂²×C₄×C₇	—	2	1	no	—
183	C₂²×C₄×C₇	—	2	1	no	—
184	C₂²×C₄×C₇	—	4	1	no	—
185	C₂²×C₄×C₇	—	4	1	no	—
186	C₂²×C₄×C₇	—	8	2	no	—
187	C₂²×C₄×C₇	#41	1	1	yes	characteristic
188	C₂²×C₄×C₇	#41	1	1	yes	characteristic
189	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
190	C₇×Q₁₆	—	2	4	no	—
191	C₇×SD₁₆	—	2	8	no	—
192	C₇×SD₁₆	—	2	4	no	—
193	C₇×SD₁₆	—	2	4	no	—
194	C₇×D₈	—	2	4	no	—
195	C₇×M₁₆	—	2	1	no	—
196	C₇×M₁₆	—	2	1	no	—
197	C₇×M₁₆	—	2	1	no	—
198	C₇×M₁₆	—	2	1	no	—
199	C₇×M₁₆	—	2	1	no	—
200	C₇×M₁₆	—	2	1	no	—
201	C₇×M₁₆	—	2	1	no	—
202	C₇×M₁₆	—	2	1	no	—
203	C₇×M₁₆	—	2	1	no	—
204	C₇×M₁₆	—	2	1	no	—
205	C₇×M₁₆	#41	1	2	yes	—
206	C₇×M₁₆	#41	1	2	yes	—
207	C₂×C₇×C₈	—	2	1	no	—
208	C₂×C₇×C₈	—	2	1	no	—
209	C₂×C₇×C₈	—	2	1	no	—
210	C₂×C₇×C₈	—	2	1	no	—
211	C₂×C₇×C₈	—	2	1	no	—
212	C₂×C₇×C₈	—	2	1	no	—
213	C₂×C₇×C₈	—	2	1	no	—
214	C₂×C₇×C₈	—	2	1	no	—
215	C₂×C₇×C₈	—	2	1	no	—
216	C₂×C₇×C₈	—	2	1	no	—
217	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
218	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
219	C₇×C₄⋊C₄	—	2	1	no	—
220	C₇×C₄⋊C₄	—	2	1	no	—
221	C₇×C₄⋊C₄	—	2	1	no	—
222	C₇×C₄⋊C₄	—	2	1	no	—
223	C₇×C₄⋊C₄	—	2	1	no	—
224	C₇×C₄⋊C₄	—	2	1	no	—
225	C₇×C₄⋊C₄	—	4	1	no	—
226	C₇×C₄⋊C₄	—	4	1	no	—
227	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
228	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
229	C₇×C₂²⋊C₄	—	2	1	no	—
230	C₇×C₂²⋊C₄	—	2	1	no	—
231	C₇×C₂²⋊C₄	—	2	1	no	—
232	C₇×C₂²⋊C₄	—	4	1	no	—
233	C₇×C₂²⋊C₄	—	4	1	no	—
234	C₄²×C₇	—	2	1	no	—
235	C₄²×C₇	—	2	1	no	—
236	C₄²×C₇	—	2	1	no	—
237	C₄²×C₇	—	4	1	no	—
238	C₄²×C₇	—	4	1	no	—
239	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
240	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
241	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
242	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
243	C₂×#137	C₂²×C₇	1	1	yes	characteristic
244	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
245	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
246	C₄×#41	C₂²×C₇	1	1	yes	characteristic
247	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
249	#442	—	2	1	no	—
250	#441	—	2	1	no	—
251	#440	—	2	1	no	—
252	#440	—	2	1	no	—
253	C₄×Q₁₆	—	2	1	no	—
254	C₄×SD₁₆	—	2	1	no	—
255	C₄×SD₁₆	—	2	1	no	—
256	C₄×SD₁₆	—	2	2	no	—
257	C₄×SD₁₆	—	2	2	no	—
258	C₄×D₈	—	2	1	no	—
259	#433	—	2	2	no	—
260	#431	—	2	2	no	—
261	C₂×#108	C₂²×C₇	1	1	yes	characteristic
262	C₂×#108	C₂²×C₇	1	1	yes	characteristic
263	#428	C₂²×C₇	1	1	yes	characteristic
264	#428	C₂²×C₇	1	1	yes	characteristic
265	C₂×#106	C₂²×C₇	1	1	yes	characteristic
266	#424	C₂²×C₇	1	1	yes	characteristic
267	#424	C₂²×C₇	1	1	yes	characteristic
268	#419	C₂²×C₇	1	1	yes	characteristic
269	#418	C₂²×C₇	1	1	yes	characteristic
270	#417	C₂²×C₇	1	1	yes	characteristic
271	#417	C₂²×C₇	1	1	yes	characteristic
272	C₂×#103	C₂²×C₇	1	1	yes	characteristic
273	C₂×#102	C₂²×C₇	1	1	yes	characteristic
274	C₂×#101	C₂²×C₇	1	1	yes	characteristic
275	C₂×#101	C₂²×C₇	1	1	yes	characteristic
276	C₂×#100	C₂²×C₇	1	1	yes	characteristic
277	C₂×#100	C₂²×C₇	1	1	yes	characteristic
278	#408	C₂²×C₇	1	1	yes	characteristic
279	#408	C₂²×C₇	1	1	yes	characteristic
280	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
281	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
282	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
283	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
284	#343	C₂²×C₇	1	1	yes	characteristic
285	#343	C₂²×C₇	1	1	yes	characteristic
286	#343	C₂²×C₇	1	1	yes	characteristic
287	#343	C₂²×C₇	1	1	yes	characteristic
288	#341	C₂²×C₇	1	1	yes	characteristic
289	#341	C₂²×C₇	1	1	yes	characteristic
290	C₂³×C₇	—	2	1	no	—
291	C₂³×C₇	—	2	2	no	—
292	C₂³×C₇	—	4	1	no	—
293	C₂³×C₇	—	4	1	no	—
294	C₂³×C₇	—	8	1	no	—
295	C₂³×C₇	—	8	1	no	—
296	C₂³×C₇	C₂×#41	1	1	yes	characteristic
297	C₇×Q₈	—	2	2	no	—
298	C₇×Q₈	—	2	1	no	—
299	C₇×Q₈	—	2	2	no	—
300	C₇×Q₈	—	2	1	no	—
301	C₇×Q₈	—	4	1	no	—
302	C₇×Q₈	—	4	1	no	—
303	C₇×D₄	—	2	1	no	—
304	C₇×D₄	—	2	2	no	—
305	C₇×D₄	—	2	2	no	—
306	C₇×D₄	—	2	1	no	—
307	C₇×D₄	—	4	1	no	—
308	C₇×D₄	—	4	1	no	—
309	C₇×D₄	—	4	1	no	—
310	C₇×D₄	—	4	1	no	—
311	C₂×C₄×C₇	—	2	2	no	—
312	C₂×C₄×C₇	—	2	1	no	—
313	C₂×C₄×C₇	—	2	1	no	—
314	C₂×C₄×C₇	—	2	1	no	—
315	C₂×C₄×C₇	—	2	2	no	—
316	C₂×C₄×C₇	—	4	1	no	—
317	C₂×C₄×C₇	—	4	2	no	—
318	C₂×C₄×C₇	—	4	1	no	—
319	C₂×C₄×C₇	—	4	1	no	—
320	C₂×C₄×C₇	—	4	1	no	—
321	C₂×C₄×C₇	—	4	1	no	—
322	C₂×C₄×C₇	—	4	2	no	—
323	C₂×C₄×C₇	—	4	1	no	—
324	C₂×C₄×C₇	—	4	1	no	—
325	C₂×C₄×C₇	—	8	2	no	—
326	C₂×C₄×C₇	—	8	2	no	—
327	C₂×C₄×C₇	—	8	1	no	—
328	C₂×C₄×C₇	—	8	1	no	—
329	C₂×C₄×C₇	#121	1	1	yes	characteristic
330	C₂×C₄×C₇	#121	1	1	yes	characteristic
331	C₂×C₄×C₇	#121	1	1	yes	characteristic
332	C₂×C₄×C₇	#121	1	1	yes	characteristic
333	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
336	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
338	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
339	C₇×C₈	—	2	2	no	—
340	C₇×C₈	—	2	2	no	—
341	C₇×C₈	—	2	2	no	—
342	C₇×C₈	—	2	2	no	—
343	C₇×C₈	—	4	1	no	—
344	C₇×C₈	—	4	1	no	—
345	C₇×C₈	—	4	1	no	—
346	C₇×C₈	—	4	1	no	—
347	C₂×#41	C₂³×C₇	1	1	yes	characteristic
348	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
349	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
350	C₂³×C₄	—	2	1	no	—
351	#137	—	2	2	no	—
352	#137	—	2	2	no	—
353	AGL(1,ℤ/8)	—	2	2	no	—
354	AGL(1,ℤ/8)	—	2	2	no	—
355	C₂×Q₁₆	—	2	1	no	—
356	C₂×SD₁₆	—	2	1	no	—
357	C₂×SD₁₆	—	2	2	no	—
358	C₂×SD₁₆	—	2	1	no	—
359	C₂×SD₁₆	—	2	2	no	—
360	C₂×SD₁₆	—	2	2	no	—
361	C₂×D₈	—	2	1	no	—
362	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
363	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
364	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
365	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
366	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
367	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
375	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	C₇×D₄	1	1	yes	characteristic
383	C₄×D₄	C₇×D₄	1	1	yes	characteristic
384	#117	—	2	1	no	—
385	#117	C₂³×C₇	1	1	yes	characteristic
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
393	#108	—	2	2	no	—
394	#108	—	2	2	no	—
395	#107	—	2	1	no	—
396	#107	—	2	1	no	—
397	#106	—	2	2	no	—
398	#106	—	2	1	no	—
399	#106	—	2	1	no	—
400	C₄⋊C₈	—	2	2	no	—
401	C₄⋊C₈	—	2	2	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#103	—	2	2	no	—
405	#103	—	2	1	no	—
406	#103	—	2	1	no	—
407	#102	—	2	1	no	—
408	#102	—	2	1	no	—
409	#102	—	2	2	no	—
410	#102	—	2	1	no	—
411	#102	—	2	1	no	—
412	#101	—	2	2	no	—
413	#101	—	2	2	no	—
414	#100	—	2	2	no	—
415	#100	—	2	2	no	—
416	C₂²⋊C₈	—	2	2	no	—
417	C₂²⋊C₈	—	2	2	no	—
418	#97	—	2	1	no	—
419	#97	—	2	1	no	—
420	#97	—	2	1	no	—
421	C₄×C₈	—	2	1	no	—
422	C₄×C₈	—	2	1	no	—
423	C₄×C₈	—	2	1	no	—
424	C₄×C₈	C₇×D₄	1	2	yes	—
425	C₄×C₈	C₇×D₄	1	2	yes	—
426	C₂²×C₇	—	2	1	no	—
427	C₂²×C₇	—	2	1	no	—
428	C₂²×C₇	—	4	1	no	—
429	C₂²×C₇	—	4	2	no	—
430	C₂²×C₇	—	4	1	no	—
431	C₂²×C₇	—	4	1	no	—
432	C₂²×C₇	—	8	2	no	—
433	C₂²×C₇	—	8	2	no	—
434	C₂²×C₇	—	8	1	no	—
435	C₂²×C₇	—	8	1	no	—
436	C₂²×C₇	C₂×#121	1	1	yes	characteristic
437	C₂²×C₇	#529	1	1	yes	characteristic
438	C₂²×C₇	#529	1	1	yes	characteristic
439	C₄×C₇	—	2	1	no	—
440	C₄×C₇	—	2	1	no	—
441	C₄×C₇	—	2	1	no	—
442	C₄×C₇	—	4	1	no	—
443	C₄×C₇	—	4	2	no	—
444	C₄×C₇	—	4	1	no	—
445	C₄×C₇	—	4	1	no	—
446	C₄×C₇	—	8	1	no	—
447	C₄×C₇	—	8	1	no	—
448	C₄×C₇	#471	1	2	yes	—
449	C₄×C₇	#525	1	1	yes	characteristic
450	C₄×C₇	#525	1	1	yes	characteristic
451	C₄×C₇	#525	1	1	yes	characteristic
452	C₄×C₇	#532	1	1	yes	characteristic
453	C₂⁴	—	2	1	no	—
454	#41	—	2	1	no	—
455	#41	—	2	1	no	—
456	#41	—	2	1	no	—
457	#41	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
464	C₂×Q₈	C₇×#41	1	2	yes	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
472	C₂×D₄	C₇×#41	1	2	yes	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	4	1	no	—
480	C₂²×C₄	—	4	1	no	—
481	C₂²×C₄	—	8	2	no	—
482	C₂²×C₄	C₇×#41	1	1	yes	characteristic
483	C₂²×C₄	C₇×#41	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
485	Q₁₆	—	2	4	no	—
486	SD₁₆	—	2	8	no	—
487	SD₁₆	—	2	4	no	—
488	SD₁₆	—	2	4	no	—
489	D₈	—	2	4	no	—
490	M₁₆	—	2	1	no	—
491	M₁₆	—	2	1	no	—
492	M₁₆	—	2	1	no	—
493	M₁₆	—	2	1	no	—
494	M₁₆	—	2	1	no	—
495	M₁₆	—	2	1	no	—
496	M₁₆	—	2	1	no	—
497	M₁₆	—	2	1	no	—
498	M₁₆	—	2	1	no	—
499	M₁₆	—	2	1	no	—
500	M₁₆	C₇×#41	1	2	yes	—
501	M₁₆	C₇×#41	1	2	yes	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
513	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	4	1	no	—
521	C₄⋊C₄	—	4	1	no	—
522	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
523	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
524	C₂²⋊C₄	—	2	1	no	—
525	C₂²⋊C₄	—	2	1	no	—
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	4	1	no	—
528	C₂²⋊C₄	—	4	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	4	1	no	—
533	C₄²	—	4	1	no	—
534	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
535	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
536	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
537	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
538	C₂×C₇	—	2	1	no	—
539	C₂×C₇	—	2	1	no	—
540	C₂×C₇	—	8	1	no	—
541	C₂×C₇	—	8	2	no	—
542	C₂×C₇	#2392	1	1	yes	characteristic
543	C₂×C₇	C₂×#471	1	1	yes	characteristic
544	C₂×C₇	#3067	1	1	yes	characteristic
545	C₂³	—	2	1	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	4	1	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	8	1	no	—
550	C₂³	—	8	1	no	—
551	C₂³	C₂×C₇×#41	1	1	yes	characteristic
552	Q₈	—	2	2	no	—
553	Q₈	—	2	1	no	—
554	Q₈	—	2	2	no	—
555	Q₈	—	2	1	no	—
556	Q₈	—	4	1	no	—
557	Q₈	—	4	1	no	—
558	D₄	—	2	1	no	—
559	D₄	—	2	2	no	—
560	D₄	—	2	2	no	—
561	D₄	—	2	1	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	1	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	8	2	no	—
581	C₂×C₄	—	8	2	no	—
582	C₂×C₄	—	8	1	no	—
583	C₂×C₄	—	8	1	no	—
584	C₂×C₄	C₇×#121	1	1	yes	characteristic
585	C₂×C₄	C₇×#121	1	1	yes	characteristic
586	C₂×C₄	C₇×#121	1	1	yes	characteristic
587	C₂×C₄	C₇×#121	1	1	yes	characteristic
588	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
589	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
590	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
591	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
592	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
593	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
594	C₈	—	2	2	no	—
595	C₈	—	2	2	no	—
596	C₈	—	2	2	no	—
597	C₈	—	2	2	no	—
598	C₈	—	4	1	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₈	—	4	1	no	—
602	C₇	#23718	1	1	yes	characteristic, direct product factor, Sylow
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	8	2	no	—
610	C₂²	—	8	2	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	C₂×C₇×#121	1	1	yes	characteristic
614	C₂²	C₇×#529	1	1	yes	characteristic
615	C₂²	C₇×#529	1	1	yes	characteristic
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	8	1	no	—
624	C₄	—	8	1	no	—
625	C₄	C₇×#471	1	2	yes	—
626	C₄	C₇×#525	1	1	yes	characteristic
627	C₄	C₇×#525	1	1	yes	characteristic
628	C₄	C₇×#525	1	1	yes	characteristic
629	C₄	C₇×#532	1	1	yes	characteristic
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	8	1	no	—
633	C₂	—	8	2	no	—
634	C₂	C₇×#2392	1	1	yes	characteristic
635	C₂	C₂×C₇×#471	1	1	yes	characteristic
636	C₂	C₇×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂×#121
prime radical	C₂×C₇×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×C₇×#137	C₂	semidirect
3. C₂×C₄×C₇×SD₁₆	C₂	semidirect
4. C₇×#2922	C₂	semidirect
5. C₇×#2090	C₂	semidirect
6. C₇×#2079	C₂	semidirect
7. C₇×#2064	C₂	semidirect
8. C₇×#2063	C₂	semidirect
9. C₇×#2052	C₂	semidirect
11. C₇×#2046	C₂	semidirect
13. C₄×C₇×#108	C₂	semidirect
14. C₄×C₇×#101	C₂	semidirect
15. C₄×C₇×#100	C₂	semidirect
63. #23718	C₇	direct (N × H)
143. C₄×#137	C₂×C₇	semidirect
145. C₂×C₄×SD₁₆	C₂×C₇	semidirect
146. #2922	C₂×C₇	semidirect
147. #2090	C₂×C₇	semidirect
148. #2079	C₂×C₇	semidirect
149. #2064	C₂×C₇	semidirect
150. #2063	C₂×C₇	semidirect
151. #2052	C₂×C₇	semidirect
153. #2046	C₂×C₇	semidirect
155. C₄×#108	C₂×C₇	semidirect
156. C₄×#101	C₂×C₇	semidirect
157. C₄×#100	C₂×C₇	semidirect
602. C₇	#23718	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₇×#137	2
C₄×C₇×AGL(1,ℤ/8)	2
C₂×C₄×C₇×SD₁₆	2
C₇×#2922	2
C₇×#2090	2
C₇×#2079	2
C₇×#2064	2
C₇×#2063	2
C₇×#2052	2
C₇×#2051	2
C₇×#2046	2
C₇×#2019	2
C₄×C₇×#108	2
C₄×C₇×#101	2
C₄×C₇×#100	2
#23718	7

Subgroups — C7×#23718 #13200934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23718 #13200934