Subgroups — C₇×#19110 #13196326

Order 1792.

716 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3101	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3100	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1683	C₂	1	2	yes	maximal, complemented
6	C₇×#1681	C₂	1	2	yes	maximal, complemented
7	C₇×#1679	C₂	1	2	yes	maximal, complemented
8	C₇×#1677	C₂	1	2	yes	maximal, complemented
9	C₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1540	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₇×C₈	—	2	1	no	—
13	C₇×#533	C₂²	1	1	yes	characteristic
14	C₇×#532	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₇×#488	—	2	1	no	—
17	C₇×#488	—	2	1	no	—
18	C₇×#487	C₂²	1	1	yes	characteristic, complemented
19	C₇×#487	C₂²	1	1	yes	characteristic, complemented
20	C₇×#486	C₂²	1	1	yes	characteristic, complemented
21	C₇×#486	C₂²	1	1	yes	characteristic, complemented
22	C₇×#483	—	2	1	no	—
23	C₇×#480	—	2	1	no	—
24	C₇×#476	C₂²	1	2	yes	—
25	C₇×#474	C₂²	1	2	yes	—
26	C₇×#461	C₂²	1	2	yes	—
27	C₇×#459	C₂²	1	2	yes	—
28	C₇×#450	—	2	1	no	—
29	C₇×#447	—	2	1	no	—
30	C₄×C₇×SD₁₆	—	2	2	no	—
31	C₄×C₇×D₈	—	2	2	no	—
32	C₇×C₈×D₄	—	2	1	no	—
33	C₇×C₈×D₄	—	2	1	no	—
34	C₇×C₈×D₄	C₂²	1	2	yes	—
35	C₇×C₈×D₄	C₂²	1	2	yes	—
36	C₇×#431	C₂²	1	1	yes	characteristic
37	C₇×#431	C₂²	1	1	yes	characteristic
38	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₇×#416	—	2	1	no	—
40	C₇×#416	—	2	1	no	—
41	C₂×C₇×C₂²⋊C₈	—	2	1	no	—
42	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
43	C₇×#335	C₂²	1	2	yes	complemented
44	C₇×#334	C₂²	1	2	yes	complemented
45	C₇×#333	C₂²	1	2	yes	complemented
46	C₇×#332	C₂²	1	2	yes	complemented
47	C₇×#332	C₂²	1	2	yes	complemented
48	C₇×#331	C₂²	1	2	yes	complemented
49	#19110	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₇×#41	—	2	1	no	—
51	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₇	—	2	1	no	—
53	C₂×C₇×SD₁₆	—	2	2	no	—
54	C₂×C₇×D₈	—	2	2	no	—
55	C₂²×C₇×C₈	—	2	1	no	—
56	C₂²×C₇×C₈	—	2	2	no	—
57	C₂²×C₇×C₈	—	2	2	no	—
58	C₂²×C₇×C₈	—	4	4	no	—
59	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
60	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
61	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₇×#127	C₂³	1	1	yes	characteristic
65	C₇×#125	—	2	1	no	—
66	C₇×#124	—	2	1	no	—
67	C₇×C₂²⋊Q₈	—	2	1	no	—
68	C₇×C₂²⋊Q₈	—	2	1	no	—
69	C₇×#121	—	2	1	no	—
70	C₇×#121	—	2	1	no	—
71	C₄×C₇×Q₈	—	2	1	no	—
72	C₄×C₇×Q₈	—	2	1	no	—
73	C₄×C₇×D₄	—	2	1	no	—
74	C₄×C₇×D₄	—	2	1	no	—
75	C₄×C₇×D₄	—	2	1	no	—
76	C₄×C₇×D₄	—	2	1	no	—
77	C₄×C₇×D₄	D₄	1	2	yes	—
78	C₄×C₇×D₄	C₂³	1	2	yes	—
79	C₇×#117	—	2	1	no	—
80	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
82	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
83	C₇×#107	—	2	2	no	—
84	C₇×#106	—	2	2	no	—
85	C₇×C₄⋊C₈	—	2	1	no	—
86	C₇×C₄⋊C₈	C₂³	1	2	yes	—
87	C₇×C₄⋊C₈	C₂³	1	2	yes	—
88	C₇×C₄⋊C₈	C₂³	1	2	yes	—
89	C₇×#103	—	2	1	no	—
90	C₇×#103	—	2	1	no	—
91	C₇×#103	—	2	1	no	—
92	C₇×#103	—	2	1	no	—
93	C₇×#103	—	2	2	no	—
94	C₇×#102	—	2	2	no	—
95	C₇×#102	—	2	2	no	—
96	C₇×#102	—	2	1	no	—
97	C₇×#102	—	2	1	no	—
98	C₇×#102	—	2	1	no	—
99	C₇×#102	—	2	1	no	—
100	C₇×#102	—	2	2	no	—
101	C₇×C₂²⋊C₈	—	2	1	no	—
102	C₇×C₂²⋊C₈	—	2	1	no	—
103	C₇×C₂²⋊C₈	—	2	2	no	—
104	C₇×C₂²⋊C₈	—	2	2	no	—
105	C₄×C₇×C₈	—	2	1	no	—
106	C₄×C₇×C₈	—	2	1	no	—
107	C₄×C₇×C₈	D₄	1	1	yes	characteristic
108	C₄×C₇×C₈	D₄	1	1	yes	characteristic
109	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
110	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
111	#3131	C₂×C₇	1	1	yes	characteristic, complemented
112	#3101	C₂×C₇	1	1	yes	characteristic, complemented
113	#3100	C₂×C₇	1	1	yes	characteristic
114	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
115	#1683	C₂×C₇	1	2	yes	complemented
116	#1681	C₂×C₇	1	2	yes	complemented
117	#1679	C₂×C₇	1	2	yes	complemented
118	#1677	C₂×C₇	1	2	yes	complemented
119	#1564	C₂×C₇	1	1	yes	characteristic, complemented
120	#1542	C₂×C₇	1	1	yes	characteristic, complemented
121	#1540	C₂×C₇	1	1	yes	characteristic, complemented
122	C₂⁴×C₇	—	2	1	no	—
123	C₇×#41	—	4	2	no	—
124	C₇×#41	—	4	2	no	—
125	C₂×C₇×Q₈	—	2	1	no	—
126	C₂×C₇×Q₈	—	2	1	no	—
127	C₂×C₇×Q₈	—	2	1	no	—
128	C₂×C₇×D₄	—	2	4	no	—
129	C₂×C₇×D₄	—	2	1	no	—
130	C₂×C₇×D₄	—	2	1	no	—
131	C₂×C₇×D₄	—	2	1	no	—
132	C₂×C₇×D₄	—	2	1	no	—
133	C₂×C₇×D₄	—	4	1	no	—
134	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₇	—	2	1	no	—
136	C₂²×C₄×C₇	—	2	2	no	—
137	C₂²×C₄×C₇	—	2	2	no	—
138	C₂²×C₄×C₇	—	4	2	no	—
139	C₂²×C₄×C₇	—	4	2	no	—
140	C₂²×C₄×C₇	—	4	1	no	—
141	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇	#41	1	1	yes	characteristic
144	C₇×SD₁₆	—	4	4	no	—
145	C₇×D₈	—	4	4	no	—
146	C₂×C₇×C₈	—	2	2	no	—
147	C₂×C₇×C₈	—	2	2	no	—
148	C₂×C₇×C₈	—	2	2	no	—
149	C₂×C₇×C₈	—	2	2	no	—
150	C₂×C₇×C₈	—	2	2	no	—
151	C₂×C₇×C₈	—	4	4	no	—
152	C₂×C₇×C₈	—	4	4	no	—
153	C₂×C₇×C₈	—	4	2	no	—
154	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
157	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
158	C₇×C₄⋊C₄	—	2	1	no	—
159	C₇×C₄⋊C₄	—	2	1	no	—
160	C₇×C₄⋊C₄	—	2	1	no	—
161	C₇×C₄⋊C₄	—	2	1	no	—
162	C₇×C₄⋊C₄	—	2	1	no	—
163	C₇×C₄⋊C₄	—	2	1	no	—
164	C₇×C₄⋊C₄	—	2	1	no	—
165	C₇×C₄⋊C₄	—	4	1	no	—
166	C₇×C₄⋊C₄	—	4	1	no	—
167	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
168	C₇×C₂²⋊C₄	—	2	2	no	—
169	C₇×C₂²⋊C₄	—	2	2	no	—
170	C₇×C₂²⋊C₄	—	4	1	no	—
171	C₇×C₂²⋊C₄	—	4	1	no	—
172	C₇×C₂²⋊C₄	—	4	1	no	—
173	C₄²×C₇	—	4	1	no	—
174	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₇	#41	1	1	yes	characteristic
177	C₄²×C₇	C₂⁴	1	1	yes	characteristic
178	C₂³×C₈	—	2	1	no	—
179	#533	C₂²×C₇	1	1	yes	characteristic
180	#532	C₂²×C₇	1	1	yes	characteristic
181	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
182	#488	—	2	1	no	—
183	#488	—	2	1	no	—
184	#487	C₂²×C₇	1	1	yes	characteristic, complemented
185	#487	C₂²×C₇	1	1	yes	characteristic, complemented
186	#486	C₂²×C₇	1	1	yes	characteristic, complemented
187	#486	C₂²×C₇	1	1	yes	characteristic, complemented
188	#483	—	2	1	no	—
189	#480	—	2	1	no	—
190	#476	C₂²×C₇	1	2	yes	—
191	#474	C₂²×C₇	1	2	yes	—
192	#461	C₂²×C₇	1	2	yes	—
193	#459	C₂²×C₇	1	2	yes	—
194	#450	—	2	1	no	—
195	#447	—	2	1	no	—
196	C₄×SD₁₆	—	2	2	no	—
197	C₄×D₈	—	2	2	no	—
198	C₈×D₄	—	2	1	no	—
199	C₈×D₄	—	2	1	no	—
200	C₈×D₄	C₂²×C₇	1	2	yes	—
201	C₈×D₄	C₂²×C₇	1	2	yes	—
202	#431	C₂²×C₇	1	1	yes	characteristic
203	#431	C₂²×C₇	1	1	yes	characteristic
204	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
205	#416	—	2	1	no	—
206	#416	—	2	1	no	—
207	C₂×C₂²⋊C₈	—	2	1	no	—
208	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
209	#335	C₂²×C₇	1	2	yes	complemented
210	#334	C₂²×C₇	1	2	yes	complemented
211	#333	C₂²×C₇	1	2	yes	complemented
212	#332	C₂²×C₇	1	2	yes	complemented
213	#332	C₂²×C₇	1	2	yes	complemented
214	#331	C₂²×C₇	1	2	yes	complemented
215	C₂³×C₇	—	2	4	no	—
216	C₂³×C₇	—	2	2	no	—
217	C₂³×C₇	—	4	2	no	—
218	C₂³×C₇	—	4	2	no	—
219	C₂³×C₇	—	4	1	no	—
220	C₂³×C₇	#121	1	1	yes	characteristic
221	C₇×Q₈	—	4	2	no	—
222	C₇×Q₈	—	4	1	no	—
223	C₇×Q₈	—	4	1	no	—
224	C₇×Q₈	—	8	1	no	—
225	C₇×D₄	—	2	4	no	—
226	C₇×D₄	—	2	2	no	—
227	C₇×D₄	—	4	2	no	—
228	C₇×D₄	—	4	1	no	—
229	C₇×D₄	—	4	1	no	—
230	C₇×D₄	—	8	1	no	—
231	C₇×D₄	—	8	2	no	—
232	C₇×D₄	#135	1	4	yes	—
233	C₂×C₄×C₇	—	2	2	no	—
234	C₂×C₄×C₇	—	2	2	no	—
235	C₂×C₄×C₇	—	4	1	no	—
236	C₂×C₄×C₇	—	4	2	no	—
237	C₂×C₄×C₇	—	4	2	no	—
238	C₂×C₄×C₇	—	4	2	no	—
239	C₂×C₄×C₇	—	4	4	no	—
240	C₂×C₄×C₇	—	4	1	no	—
241	C₂×C₄×C₇	—	4	1	no	—
242	C₂×C₄×C₇	—	4	1	no	—
243	C₂×C₄×C₇	—	8	2	no	—
244	C₂×C₄×C₇	#121	1	1	yes	characteristic
245	C₂×C₄×C₇	#121	1	1	yes	characteristic
246	C₂×C₄×C₇	#121	1	1	yes	characteristic
247	C₂×C₄×C₇	#135	1	2	yes	—
248	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
249	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
252	C₇×C₈	—	2	1	no	—
253	C₇×C₈	—	2	1	no	—
254	C₇×C₈	—	2	1	no	—
255	C₇×C₈	—	2	1	no	—
256	C₇×C₈	—	4	2	no	—
257	C₇×C₈	—	4	2	no	—
258	C₇×C₈	—	4	2	no	—
259	C₂×#41	—	2	1	no	—
260	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
261	C₂³×C₄	—	2	1	no	—
262	C₂×SD₁₆	—	2	2	no	—
263	C₂×D₈	—	2	2	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	—	2	2	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	4	4	no	—
268	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
269	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
270	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
271	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
272	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
273	#127	C₂³×C₇	1	1	yes	characteristic
274	#125	—	2	1	no	—
275	#124	—	2	1	no	—
276	C₂²⋊Q₈	—	2	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	#121	—	2	1	no	—
279	#121	—	2	1	no	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×D₄	—	2	1	no	—
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	C₇×D₄	1	2	yes	—
287	C₄×D₄	C₂³×C₇	1	2	yes	—
288	#117	—	2	1	no	—
289	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
292	#107	—	2	2	no	—
293	#106	—	2	2	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	C₂³×C₇	1	2	yes	—
296	C₄⋊C₈	C₂³×C₇	1	2	yes	—
297	C₄⋊C₈	C₂³×C₇	1	2	yes	—
298	#103	—	2	1	no	—
299	#103	—	2	1	no	—
300	#103	—	2	1	no	—
301	#103	—	2	1	no	—
302	#103	—	2	2	no	—
303	#102	—	2	2	no	—
304	#102	—	2	2	no	—
305	#102	—	2	1	no	—
306	#102	—	2	1	no	—
307	#102	—	2	1	no	—
308	#102	—	2	1	no	—
309	#102	—	2	2	no	—
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	2	no	—
313	C₂²⋊C₈	—	2	2	no	—
314	C₄×C₈	—	2	1	no	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	C₇×D₄	1	1	yes	characteristic
317	C₄×C₈	C₇×D₄	1	1	yes	characteristic
318	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
319	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
320	C₂²×C₇	—	2	1	no	—
321	C₂²×C₇	—	2	1	no	—
322	C₂²×C₇	—	2	4	no	—
323	C₂²×C₇	—	4	8	no	—
324	C₂²×C₇	—	4	2	no	—
325	C₂²×C₇	—	4	2	no	—
326	C₂²×C₇	—	8	1	no	—
327	C₂²×C₇	—	8	1	no	—
328	C₂²×C₇	—	8	1	no	—
329	C₂²×C₇	#463	1	2	yes	—
330	C₂²×C₇	C₂×#121	1	1	yes	characteristic
331	C₄×C₇	—	2	1	no	—
332	C₄×C₇	—	2	1	no	—
333	C₄×C₇	—	2	1	no	—
334	C₄×C₇	—	4	2	no	—
335	C₄×C₇	—	8	1	no	—
336	C₄×C₇	—	8	1	no	—
337	C₄×C₇	—	8	1	no	—
338	C₄×C₇	#463	1	2	yes	—
339	C₄×C₇	C₂×#135	1	1	yes	characteristic
340	C₄×C₇	C₂×#135	1	2	yes	—
341	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
342	C₂⁴	—	2	1	no	—
343	#41	—	4	2	no	—
344	#41	—	4	2	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
362	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
363	C₂²×C₄	C₇×#41	1	1	yes	characteristic
364	SD₁₆	—	4	4	no	—
365	D₈	—	4	4	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	4	4	no	—
372	C₂×C₈	—	4	4	no	—
373	C₂×C₈	—	4	2	no	—
374	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
375	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
376	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
377	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	4	1	no	—
386	C₄⋊C₄	—	4	1	no	—
387	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	4	1	no	—
391	C₂²⋊C₄	—	4	1	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₄²	—	4	1	no	—
394	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
395	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
396	C₄²	C₇×#41	1	1	yes	characteristic
397	C₄²	C₂⁴×C₇	1	1	yes	characteristic
398	C₂×C₇	—	2	2	no	—
399	C₂×C₇	—	4	4	no	—
400	C₂×C₇	—	16	1	no	—
401	C₂×C₇	C₂×#463	1	1	yes	characteristic
402	C₂×C₇	#3050	1	1	yes	characteristic
403	C₂×C₇	#3067	1	1	yes	characteristic
404	C₂³	—	2	4	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	1	no	—
409	C₂³	C₇×#121	1	1	yes	characteristic
410	Q₈	—	4	2	no	—
411	Q₈	—	4	1	no	—
412	Q₈	—	4	1	no	—
413	Q₈	—	8	1	no	—
414	D₄	—	2	4	no	—
415	D₄	—	2	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	1	no	—
418	D₄	—	4	1	no	—
419	D₄	—	8	1	no	—
420	D₄	—	8	2	no	—
421	D₄	C₇×#135	1	4	yes	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	8	2	no	—
433	C₂×C₄	C₇×#121	1	1	yes	characteristic
434	C₂×C₄	C₇×#121	1	1	yes	characteristic
435	C₂×C₄	C₇×#121	1	1	yes	characteristic
436	C₂×C₄	C₇×#135	1	2	yes	—
437	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
438	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
439	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
440	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
441	C₈	—	2	1	no	—
442	C₈	—	2	1	no	—
443	C₈	—	2	1	no	—
444	C₈	—	2	1	no	—
445	C₈	—	4	2	no	—
446	C₈	—	4	2	no	—
447	C₈	—	4	2	no	—
448	C₇	#19110	1	1	yes	characteristic, direct product factor, Sylow
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	4	8	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	1	no	—
458	C₂²	C₇×#463	1	2	yes	—
459	C₂²	C₂×C₇×#121	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	8	1	no	—
465	C₄	—	8	1	no	—
466	C₄	—	8	1	no	—
467	C₄	C₇×#463	1	2	yes	—
468	C₄	C₂×C₇×#135	1	1	yes	characteristic
469	C₄	C₂×C₇×#135	1	2	yes	—
470	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
471	C₂	—	2	2	no	—
472	C₂	—	4	4	no	—
473	C₂	—	16	1	no	—
474	C₂	C₂×C₇×#463	1	1	yes	characteristic
475	C₂	C₇×#3050	1	1	yes	characteristic
476	C₂	C₇×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
socle	C₂²×C₇	C₂×#121
prime radical	C₇×#3100	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ 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. C₇×#3131	C₂	semidirect
2. C₇×#3101	C₂	semidirect
4. C₂×C₇×C₈×D₄	C₂	semidirect
5. C₇×#1683	C₂	semidirect
6. C₇×#1681	C₂	semidirect
7. C₇×#1679	C₂	semidirect
8. C₇×#1677	C₂	semidirect
9. C₇×#1564	C₂	semidirect
10. C₇×#1542	C₂	semidirect
11. C₇×#1540	C₂	semidirect
18. C₇×#487	C₂²	semidirect
19. C₇×#487	C₂²	semidirect
20. C₇×#486	C₂²	semidirect
21. C₇×#486	C₂²	semidirect
43. C₇×#335	C₂²	semidirect
44. C₇×#334	C₂²	semidirect
45. C₇×#333	C₂²	semidirect
46. C₇×#332	C₂²	semidirect
47. C₇×#332	C₂²	semidirect
48. C₇×#331	C₂²	semidirect
49. #19110	C₇	direct (N × H)
111. #3131	C₂×C₇	semidirect
112. #3101	C₂×C₇	semidirect
114. C₂×C₈×D₄	C₂×C₇	semidirect
115. #1683	C₂×C₇	semidirect
116. #1681	C₂×C₇	semidirect
117. #1679	C₂×C₇	semidirect
118. #1677	C₂×C₇	semidirect
119. #1564	C₂×C₇	semidirect
120. #1542	C₂×C₇	semidirect
121. #1540	C₂×C₇	semidirect
184. #487	C₂²×C₇	semidirect
185. #487	C₂²×C₇	semidirect
186. #486	C₂²×C₇	semidirect
187. #486	C₂²×C₇	semidirect
209. #335	C₂²×C₇	semidirect
210. #334	C₂²×C₇	semidirect
211. #333	C₂²×C₇	semidirect
212. #332	C₂²×C₇	semidirect
213. #332	C₂²×C₇	semidirect
214. #331	C₂²×C₇	semidirect
448. C₇	#19110	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3131	2
C₇×#3101	2
C₇×#3100	2
C₂×C₇×C₈×D₄	2
C₇×#1683	2
C₇×#1681	2
C₇×#1679	2
C₇×#1677	2
C₇×#1564	2
C₇×#1542	2
C₇×#1540	2
#19110	7

Subgroups — C7×#19110 #13196326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19110 #13196326