Subgroups — C₇×#19234 #13196450

Order 1792.

704 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3246	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3205	C₂	1	1	yes	maximal, characteristic
3	C₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1701	C₂	1	2	yes	maximal, complemented
6	C₇×#1697	C₂	1	2	yes	maximal, complemented
7	C₇×#1681	C₂	1	2	yes	maximal, complemented
8	C₇×#1677	C₂	1	2	yes	maximal, complemented
9	C₇×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#131	—	2	1	no	—
13	C₇×#533	C₂²	1	1	yes	characteristic
14	C₇×#532	C₂²	1	1	yes	characteristic
15	C₂×C₇×#127	C₂²	1	1	yes	characteristic
16	C₇×#493	—	2	1	no	—
17	C₇×#490	—	2	2	no	—
18	C₇×#486	—	2	1	no	—
19	C₇×#486	C₂²	1	2	yes	—
20	C₇×#486	C₂²	1	2	yes	—
21	C₇×#476	C₂²	1	2	yes	complemented
22	C₇×#475	—	2	1	no	—
23	C₇×#465	—	2	2	no	—
24	C₇×#461	C₂²	1	2	yes	complemented
25	C₇×#460	—	2	1	no	—
26	C₇×#459	C₂²	1	2	yes	—
27	C₇×#459	C₂²	1	2	yes	—
28	C₇×#447	—	2	2	no	—
29	C₇×#436	C₂²	1	2	yes	complemented
30	C₇×#435	—	2	2	no	—
31	C₇×C₈×D₄	C₂²	1	2	yes	complemented
32	C₇×#431	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₇×#418	—	2	1	no	—
36	C₇×#418	—	2	1	no	—
37	C₇×#408	—	2	1	no	—
38	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
39	C₇×#335	C₂²	1	2	yes	complemented
40	C₇×#334	C₂²	1	2	yes	complemented
41	C₇×#333	C₂²	1	1	yes	characteristic, complemented
42	C₇×#333	C₂²	1	1	yes	characteristic, complemented
43	C₇×#332	C₂²	1	1	yes	characteristic, complemented
44	C₇×#332	C₂²	1	1	yes	characteristic, complemented
45	C₇×#331	C₂²	1	2	yes	—
46	C₇×#331	C₂²	1	2	yes	—
47	#19234	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	—	2	1	no	—
49	C₂²×C₇×D₄	—	2	1	no	—
50	C₂²×C₇×D₄	—	2	1	no	—
51	C₂²×C₇×D₄	—	2	1	no	—
52	C₂×C₇×SD₁₆	—	2	2	no	—
53	C₂×C₇×D₈	—	2	2	no	—
54	C₂×C₇×D₈	—	2	2	no	—
55	C₇×#131	—	4	4	no	—
56	C₂×C₇×M₁₆	—	2	2	no	—
57	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
58	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
59	C₂²×C₇×C₈	—	2	1	no	—
60	C₂²×C₇×C₈	—	2	1	no	—
61	C₂²×C₇×C₈	—	2	2	no	—
62	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
63	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₇×#127	—	2	1	no	—
66	C₇×#127	—	2	1	no	—
67	C₇×#127	—	2	1	no	—
68	C₇×#127	D₄	1	1	yes	characteristic
69	C₇×#127	C₂³	1	2	yes	—
70	C₇×#125	—	2	1	no	—
71	C₇×#124	—	2	1	no	—
72	C₇×C₂²⋊Q₈	—	2	1	no	—
73	C₇×C₂²⋊Q₈	—	2	1	no	—
74	C₇×#121	—	2	1	no	—
75	C₇×#121	D₄	1	2	yes	—
76	C₄×C₇×Q₈	—	2	1	no	—
77	C₄×C₇×Q₈	—	2	1	no	—
78	C₄×C₇×D₄	—	2	1	no	—
79	C₄×C₇×D₄	C₂³	1	2	yes	—
80	C₇×#117	—	2	1	no	—
81	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
82	C₇×#106	—	2	2	no	—
83	C₇×C₄⋊C₈	—	2	1	no	—
84	C₇×C₄⋊C₈	—	2	1	no	—
85	C₇×C₄⋊C₈	C₂³	1	2	yes	—
86	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
89	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
90	C₇×#103	—	2	2	no	—
91	C₇×#102	—	2	2	no	—
92	C₇×#102	—	2	2	no	—
93	C₇×#102	—	2	2	no	—
94	C₇×#102	—	2	2	no	—
95	C₇×#102	—	2	2	no	—
96	C₇×#102	—	2	2	no	—
97	C₇×#102	—	2	2	no	—
98	C₇×C₂²⋊C₈	—	2	1	no	—
99	C₇×C₂²⋊C₈	—	2	2	no	—
100	C₇×C₂²⋊C₈	—	2	2	no	—
101	C₇×#97	D₄	1	2	yes	—
102	C₄×C₇×C₈	—	2	1	no	—
103	C₄×C₇×C₈	C₂³	1	2	yes	—
104	#3246	C₂×C₇	1	1	yes	characteristic, complemented
105	#3205	C₂×C₇	1	1	yes	characteristic
106	#3138	C₂×C₇	1	1	yes	characteristic, complemented
107	#2935	C₂×C₇	1	1	yes	characteristic, complemented
108	#1701	C₂×C₇	1	2	yes	complemented
109	#1697	C₂×C₇	1	2	yes	complemented
110	#1681	C₂×C₇	1	2	yes	complemented
111	#1677	C₂×C₇	1	2	yes	complemented
112	#1565	C₂×C₇	1	1	yes	characteristic, complemented
113	#1542	C₂×C₇	1	1	yes	characteristic, complemented
114	C₂×#331	C₂×C₇	1	1	yes	characteristic, complemented
115	C₂⁴×C₇	—	4	1	no	—
116	C₇×#41	—	4	2	no	—
117	C₇×#41	—	4	2	no	—
118	C₂×C₇×Q₈	—	2	1	no	—
119	C₂×C₇×Q₈	—	2	1	no	—
120	C₂×C₇×Q₈	—	2	1	no	—
121	C₂×C₇×D₄	—	2	2	no	—
122	C₂×C₇×D₄	—	2	1	no	—
123	C₂×C₇×D₄	—	2	1	no	—
124	C₂×C₇×D₄	—	2	2	no	—
125	C₂×C₇×D₄	—	2	2	no	—
126	C₂×C₇×D₄	—	2	2	no	—
127	C₂×C₇×D₄	—	4	1	no	—
128	C₂×C₇×D₄	—	4	1	no	—
129	C₂×C₇×D₄	—	4	1	no	—
130	C₂×C₇×D₄	—	4	2	no	—
131	C₂×C₇×D₄	—	4	2	no	—
132	C₂×C₇×D₄	—	8	1	no	—
133	C₂×C₇×D₄	—	8	1	no	—
134	C₂×C₇×D₄	—	8	2	no	—
135	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₇	—	2	2	no	—
137	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇	#41	1	1	yes	characteristic
140	C₇×SD₁₆	—	8	2	no	—
141	C₇×D₈	—	8	2	no	—
142	C₇×D₈	—	8	2	no	—
143	C₇×M₁₆	—	2	2	no	—
144	C₇×M₁₆	—	2	2	no	—
145	C₇×M₁₆	—	4	4	no	—
146	C₂×C₇×C₈	—	2	1	no	—
147	C₂×C₇×C₈	—	2	1	no	—
148	C₂×C₇×C₈	—	2	1	no	—
149	C₂×C₇×C₈	—	2	1	no	—
150	C₂×C₇×C₈	—	2	2	no	—
151	C₂×C₇×C₈	—	4	4	no	—
152	C₂×C₇×C₈	—	4	2	no	—
153	C₂×C₇×C₈	—	8	1	no	—
154	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
155	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
156	C₇×C₄⋊C₄	—	2	1	no	—
157	C₇×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
162	C₇×C₄⋊C₄	—	4	1	no	—
163	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
164	C₇×C₂²⋊C₄	—	2	2	no	—
165	C₇×C₂²⋊C₄	—	2	2	no	—
166	C₇×C₂²⋊C₄	—	4	1	no	—
167	C₄²×C₇	—	4	1	no	—
168	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₇	#41	1	1	yes	characteristic
171	C₄²×C₇	C₂⁴	1	1	yes	characteristic
172	C₂×#131	—	2	1	no	—
173	#533	C₂²×C₇	1	1	yes	characteristic
174	#532	C₂²×C₇	1	1	yes	characteristic
175	C₂×#127	C₂²×C₇	1	1	yes	characteristic
176	#493	—	2	1	no	—
177	#490	—	2	2	no	—
178	#486	—	2	1	no	—
179	#486	C₂²×C₇	1	2	yes	—
180	#486	C₂²×C₇	1	2	yes	—
181	#476	C₂²×C₇	1	2	yes	complemented
182	#475	—	2	1	no	—
183	#465	—	2	2	no	—
184	#461	C₂²×C₇	1	2	yes	complemented
185	#460	—	2	1	no	—
186	#459	C₂²×C₇	1	2	yes	—
187	#459	C₂²×C₇	1	2	yes	—
188	#447	—	2	2	no	—
189	#436	C₂²×C₇	1	2	yes	complemented
190	#435	—	2	2	no	—
191	C₈×D₄	C₂²×C₇	1	2	yes	complemented
192	#431	C₂²×C₇	1	1	yes	characteristic
193	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
194	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
195	#418	—	2	1	no	—
196	#418	—	2	1	no	—
197	#408	—	2	1	no	—
198	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
199	#335	C₂²×C₇	1	2	yes	complemented
200	#334	C₂²×C₇	1	2	yes	complemented
201	#333	C₂²×C₇	1	1	yes	characteristic, complemented
202	#333	C₂²×C₇	1	1	yes	characteristic, complemented
203	#332	C₂²×C₇	1	1	yes	characteristic, complemented
204	#332	C₂²×C₇	1	1	yes	characteristic, complemented
205	#331	C₂²×C₇	1	2	yes	—
206	#331	C₂²×C₇	1	2	yes	—
207	C₂³×C₇	—	2	2	no	—
208	C₂³×C₇	—	4	2	no	—
209	C₂³×C₇	—	8	2	no	—
210	C₂³×C₇	—	8	2	no	—
211	C₂³×C₇	—	8	2	no	—
212	C₂³×C₇	#121	1	1	yes	characteristic
213	C₇×Q₈	—	4	2	no	—
214	C₇×Q₈	—	4	1	no	—
215	C₇×Q₈	—	4	1	no	—
216	C₇×Q₈	—	8	1	no	—
217	C₇×D₄	—	2	2	no	—
218	C₇×D₄	—	2	2	no	—
219	C₇×D₄	—	4	4	no	—
220	C₇×D₄	—	4	2	no	—
221	C₇×D₄	—	4	2	no	—
222	C₇×D₄	—	4	2	no	—
223	C₇×D₄	—	4	2	no	—
224	C₇×D₄	—	4	2	no	—
225	C₇×D₄	—	8	1	no	—
226	C₇×D₄	—	8	2	no	—
227	C₇×D₄	—	8	2	no	—
228	C₇×D₄	—	8	2	no	—
229	C₇×D₄	—	8	2	no	—
230	C₂×C₄×C₇	—	2	1	no	—
231	C₂×C₄×C₇	—	2	1	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	4	1	no	—
234	C₂×C₄×C₇	—	4	2	no	—
235	C₂×C₄×C₇	—	4	2	no	—
236	C₂×C₄×C₇	—	4	1	no	—
237	C₂×C₄×C₇	—	4	1	no	—
238	C₂×C₄×C₇	#121	1	1	yes	characteristic
239	C₂×C₄×C₇	#121	1	1	yes	characteristic
240	C₂×C₄×C₇	#121	1	1	yes	characteristic
241	C₂×C₄×C₇	#135	1	2	yes	—
242	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
243	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
246	C₇×C₈	—	2	2	no	—
247	C₇×C₈	—	2	2	no	—
248	C₇×C₈	—	4	1	no	—
249	C₇×C₈	—	4	1	no	—
250	C₇×C₈	—	4	2	no	—
251	C₇×C₈	—	4	1	no	—
252	C₇×C₈	—	4	1	no	—
253	C₂×#41	—	2	1	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂×SD₁₆	—	2	2	no	—
258	C₂×D₈	—	2	2	no	—
259	C₂×D₈	—	2	2	no	—
260	#131	—	4	4	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
263	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
268	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
269	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
270	#127	—	2	1	no	—
271	#127	—	2	1	no	—
272	#127	—	2	1	no	—
273	#127	C₇×D₄	1	1	yes	characteristic
274	#127	C₂³×C₇	1	2	yes	—
275	#125	—	2	1	no	—
276	#124	—	2	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	C₂²⋊Q₈	—	2	1	no	—
279	#121	—	2	1	no	—
280	#121	C₇×D₄	1	2	yes	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	C₂³×C₇	1	2	yes	—
285	#117	—	2	1	no	—
286	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
287	#106	—	2	2	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
291	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
292	C₄⋊C₈	C₂³×C₇	1	2	yes	—
293	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
294	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
295	#103	—	2	2	no	—
296	#102	—	2	2	no	—
297	#102	—	2	2	no	—
298	#102	—	2	2	no	—
299	#102	—	2	2	no	—
300	#102	—	2	2	no	—
301	#102	—	2	2	no	—
302	#102	—	2	2	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	—	2	2	no	—
305	C₂²⋊C₈	—	2	2	no	—
306	#97	C₇×D₄	1	2	yes	—
307	C₄×C₈	—	2	1	no	—
308	C₄×C₈	C₂³×C₇	1	2	yes	—
309	C₂²×C₇	—	2	1	no	—
310	C₂²×C₇	—	2	1	no	—
311	C₂²×C₇	—	4	2	no	—
312	C₂²×C₇	—	4	2	no	—
313	C₂²×C₇	—	4	2	no	—
314	C₂²×C₇	—	8	2	no	—
315	C₂²×C₇	—	8	2	no	—
316	C₂²×C₇	—	8	2	no	—
317	C₂²×C₇	—	16	4	no	—
318	C₂²×C₇	#463	1	2	yes	—
319	C₂²×C₇	C₂×#121	1	1	yes	characteristic
320	C₄×C₇	—	2	1	no	—
321	C₄×C₇	—	2	1	no	—
322	C₄×C₇	—	2	1	no	—
323	C₄×C₇	—	4	2	no	—
324	C₄×C₇	—	8	1	no	—
325	C₄×C₇	—	8	1	no	—
326	C₄×C₇	#463	1	2	yes	—
327	C₄×C₇	C₂×#135	1	1	yes	characteristic
328	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
329	C₄×C₇	#576	1	1	yes	characteristic
330	C₄×C₇	#577	1	1	yes	characteristic
331	C₂⁴	—	4	1	no	—
332	#41	—	4	2	no	—
333	#41	—	4	2	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	8	1	no	—
349	C₂×D₄	—	8	1	no	—
350	C₂×D₄	—	8	2	no	—
351	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
355	C₂²×C₄	C₇×#41	1	1	yes	characteristic
356	SD₁₆	—	8	2	no	—
357	D₈	—	8	2	no	—
358	D₈	—	8	2	no	—
359	M₁₆	—	2	2	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	4	4	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	4	4	no	—
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	—	8	1	no	—
370	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
371	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	4	1	no	—
383	C₄²	—	4	1	no	—
384	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
385	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
386	C₄²	C₇×#41	1	1	yes	characteristic
387	C₄²	C₂⁴×C₇	1	1	yes	characteristic
388	C₂×C₇	—	2	2	no	—
389	C₂×C₇	—	8	2	no	—
390	C₂×C₇	—	16	2	no	—
391	C₂×C₇	C₂×#463	1	1	yes	characteristic
392	C₂×C₇	#3062	1	1	yes	characteristic
393	C₂×C₇	#3068	1	1	yes	characteristic
394	C₂³	—	2	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	8	2	no	—
397	C₂³	—	8	2	no	—
398	C₂³	—	8	2	no	—
399	C₂³	C₇×#121	1	1	yes	characteristic
400	Q₈	—	4	2	no	—
401	Q₈	—	4	1	no	—
402	Q₈	—	4	1	no	—
403	Q₈	—	8	1	no	—
404	D₄	—	2	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	4	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	8	1	no	—
413	D₄	—	8	2	no	—
414	D₄	—	8	2	no	—
415	D₄	—	8	2	no	—
416	D₄	—	8	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	C₇×#121	1	1	yes	characteristic
426	C₂×C₄	C₇×#121	1	1	yes	characteristic
427	C₂×C₄	C₇×#121	1	1	yes	characteristic
428	C₂×C₄	C₇×#135	1	2	yes	—
429	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
430	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
431	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
432	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	—	4	1	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	2	no	—
438	C₈	—	4	1	no	—
439	C₈	—	4	1	no	—
440	C₇	#19234	1	1	yes	characteristic, direct product factor, Sylow
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	16	4	no	—
450	C₂²	C₇×#463	1	2	yes	—
451	C₂²	C₂×C₇×#121	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	4	2	no	—
456	C₄	—	8	1	no	—
457	C₄	—	8	1	no	—
458	C₄	C₇×#463	1	2	yes	—
459	C₄	C₂×C₇×#135	1	1	yes	characteristic
460	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
461	C₄	C₇×#576	1	1	yes	characteristic
462	C₄	C₇×#577	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	8	2	no	—
465	C₂	—	16	2	no	—
466	C₂	C₂×C₇×#463	1	1	yes	characteristic
467	C₂	C₇×#3062	1	1	yes	characteristic
468	C₂	C₇×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#3205	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3246	C₂	semidirect
3. C₇×#3138	C₂	semidirect
4. C₇×#2935	C₂	semidirect
5. C₇×#1701	C₂	semidirect
6. C₇×#1697	C₂	semidirect
7. C₇×#1681	C₂	semidirect
8. C₇×#1677	C₂	semidirect
9. C₇×#1565	C₂	semidirect
10. C₇×#1542	C₂	semidirect
11. C₂×C₇×#331	C₂	semidirect
21. C₇×#476	C₂²	semidirect
24. C₇×#461	C₂²	semidirect
29. C₇×#436	C₂²	semidirect
31. C₇×C₈×D₄	C₂²	semidirect
39. C₇×#335	C₂²	semidirect
40. C₇×#334	C₂²	semidirect
41. C₇×#333	C₂²	semidirect
42. C₇×#333	C₂²	semidirect
43. C₇×#332	C₂²	semidirect
44. C₇×#332	C₂²	semidirect
47. #19234	C₇	direct (N × H)
104. #3246	C₂×C₇	semidirect
106. #3138	C₂×C₇	semidirect
107. #2935	C₂×C₇	semidirect
108. #1701	C₂×C₇	semidirect
109. #1697	C₂×C₇	semidirect
110. #1681	C₂×C₇	semidirect
111. #1677	C₂×C₇	semidirect
112. #1565	C₂×C₇	semidirect
113. #1542	C₂×C₇	semidirect
114. C₂×#331	C₂×C₇	semidirect
181. #476	C₂²×C₇	semidirect
184. #461	C₂²×C₇	semidirect
189. #436	C₂²×C₇	semidirect
191. C₈×D₄	C₂²×C₇	semidirect
199. #335	C₂²×C₇	semidirect
200. #334	C₂²×C₇	semidirect
201. #333	C₂²×C₇	semidirect
202. #333	C₂²×C₇	semidirect
203. #332	C₂²×C₇	semidirect
204. #332	C₂²×C₇	semidirect
440. C₇	#19234	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×#3246	2
C₇×#3205	2
C₇×#3138	2
C₇×#2935	2
C₇×#1701	2
C₇×#1697	2
C₇×#1681	2
C₇×#1677	2
C₇×#1565	2
C₇×#1542	2
C₂×C₇×#331	2
#19234	7

Subgroups — C7×#19234 #13196450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19234 #13196450