Subgroups — C₇×#19237 #13196453

Order 1792.

674 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3245	C₂	1	1	yes	maximal, characteristic
2	C₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3141	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×#1699	C₂	1	2	yes	maximal, complemented
7	C₇×#1681	C₂	1	2	yes	maximal, complemented
8	C₇×#1679	C₂	1	2	yes	maximal, complemented
9	C₇×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1540	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#332	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#131	—	2	1	no	—
13	C₇×#532	C₂²	1	1	yes	characteristic
14	C₇×#532	C₂²	1	1	yes	characteristic
15	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₇×#492	—	2	1	no	—
17	C₇×#489	—	2	2	no	—
18	C₇×#487	—	2	1	no	—
19	C₇×#487	C₂²	1	2	yes	—
20	C₇×#486	C₂²	1	2	yes	—
21	C₇×#474	—	2	1	no	—
22	C₇×#474	C₂²	1	2	yes	—
23	C₇×#466	—	2	2	no	—
24	C₇×#461	C₂²	1	2	yes	—
25	C₇×#461	C₂²	1	2	yes	—
26	C₇×#459	—	2	1	no	—
27	C₇×#459	C₂²	1	2	yes	—
28	C₇×#448	—	2	2	no	—
29	C₇×#436	C₂²	1	2	yes	—
30	C₇×#435	—	2	2	no	—
31	C₇×C₈×D₄	C₂²	1	2	yes	—
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×#417	—	2	1	no	—
36	C₇×#417	—	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	—
40	C₇×#334	C₂²	1	2	yes	—
41	C₇×#332	C₂²	1	2	yes	—
42	C₇×#332	C₂²	1	2	yes	—
43	C₇×#332	C₂²	1	1	yes	characteristic
44	C₇×#332	C₂²	1	1	yes	characteristic
45	C₇×#331	C₂²	1	1	yes	characteristic
46	C₇×#331	C₂²	1	1	yes	characteristic
47	#19237	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	—	2	1	no	—
49	C₂×C₇×#41	—	2	1	no	—
50	C₂²×C₇×Q₈	—	2	1	no	—
51	C₂×C₇×SD₁₆	—	2	2	no	—
52	C₂×C₇×SD₁₆	—	2	2	no	—
53	C₂×C₇×D₈	—	2	2	no	—
54	C₇×#131	—	4	4	no	—
55	C₂×C₇×M₁₆	—	2	2	no	—
56	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
57	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
58	C₂²×C₇×C₈	—	2	1	no	—
59	C₂²×C₇×C₈	—	2	1	no	—
60	C₂²×C₇×C₈	—	2	2	no	—
61	C₇×C₄⋊Q₈	—	2	1	no	—
62	C₇×C₄⋊Q₈	—	2	1	no	—
63	C₇×C₄⋊Q₈	—	2	1	no	—
64	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₇×#127	D₄	1	1	yes	characteristic
68	C₇×#127	C₂³	1	1	yes	characteristic
69	C₇×#124	—	2	1	no	—
70	C₇×#124	—	2	1	no	—
71	C₇×#121	—	2	1	no	—
72	C₇×#121	—	2	1	no	—
73	C₇×#121	—	2	1	no	—
74	C₇×#121	D₄	1	2	yes	—
75	C₄×C₇×D₄	—	2	1	no	—
76	C₄×C₇×D₄	—	2	1	no	—
77	C₄×C₇×D₄	—	2	1	no	—
78	C₄×C₇×D₄	C₂³	1	2	yes	—
79	C₂×C₇×C₄⋊C₄	—	2	1	no	—
80	C₂×C₇×C₄⋊C₄	—	2	1	no	—
81	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
82	C₇×#107	—	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×#103	—	2	2	no	—
92	C₇×#103	—	2	2	no	—
93	C₇×#103	—	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	#3245	C₂×C₇	1	1	yes	characteristic
105	#3206	C₂×C₇	1	1	yes	characteristic, complemented
106	#3141	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	#1699	C₂×C₇	1	2	yes	complemented
110	#1681	C₂×C₇	1	2	yes	complemented
111	#1679	C₂×C₇	1	2	yes	complemented
112	#1565	C₂×C₇	1	1	yes	characteristic, complemented
113	#1540	C₂×C₇	1	1	yes	characteristic, complemented
114	C₂×#332	C₂×C₇	1	1	yes	characteristic, complemented
115	C₇×#41	—	4	2	no	—
116	C₇×#41	—	4	2	no	—
117	C₇×#41	—	4	2	no	—
118	C₇×#41	—	4	2	no	—
119	C₂×C₇×Q₈	—	2	1	no	—
120	C₂×C₇×Q₈	—	2	1	no	—
121	C₂×C₇×Q₈	—	2	2	no	—
122	C₂×C₇×Q₈	—	4	1	no	—
123	C₂×C₇×Q₈	—	8	1	no	—
124	C₂×C₇×Q₈	—	8	1	no	—
125	C₂×C₇×D₄	—	2	2	no	—
126	C₂×C₇×D₄	—	2	1	no	—
127	C₂×C₇×D₄	—	2	1	no	—
128	C₂×C₇×D₄	—	2	1	no	—
129	C₂×C₇×D₄	—	2	1	no	—
130	C₂×C₇×D₄	—	2	1	no	—
131	C₂×C₇×D₄	—	4	1	no	—
132	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₇	—	2	2	no	—
134	C₂²×C₄×C₇	—	4	1	no	—
135	C₂²×C₄×C₇	—	4	1	no	—
136	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇	#41	1	1	yes	characteristic
139	C₇×SD₁₆	—	8	2	no	—
140	C₇×SD₁₆	—	8	2	no	—
141	C₇×D₈	—	8	2	no	—
142	C₇×M₁₆	—	2	2	no	—
143	C₇×M₁₆	—	2	2	no	—
144	C₇×M₁₆	—	4	4	no	—
145	C₂×C₇×C₈	—	2	1	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	2	no	—
150	C₂×C₇×C₈	—	4	4	no	—
151	C₂×C₇×C₈	—	4	2	no	—
152	C₂×C₇×C₈	—	8	1	no	—
153	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
154	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
155	C₇×C₄⋊C₄	—	2	1	no	—
156	C₇×C₄⋊C₄	—	2	2	no	—
157	C₇×C₄⋊C₄	—	2	1	no	—
158	C₇×C₄⋊C₄	—	2	2	no	—
159	C₇×C₄⋊C₄	—	2	1	no	—
160	C₇×C₄⋊C₄	—	4	1	no	—
161	C₇×C₄⋊C₄	—	4	1	no	—
162	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
163	C₇×C₂²⋊C₄	—	2	2	no	—
164	C₇×C₂²⋊C₄	—	2	2	no	—
165	C₇×C₂²⋊C₄	—	4	1	no	—
166	C₇×C₂²⋊C₄	—	4	1	no	—
167	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₇	#41	1	1	yes	characteristic
170	C₄²×C₇	C₂⁴	1	1	yes	characteristic
171	C₂×#131	—	2	1	no	—
172	#532	C₂²×C₇	1	1	yes	characteristic
173	#532	C₂²×C₇	1	1	yes	characteristic
174	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
175	#492	—	2	1	no	—
176	#489	—	2	2	no	—
177	#487	—	2	1	no	—
178	#487	C₂²×C₇	1	2	yes	—
179	#486	C₂²×C₇	1	2	yes	—
180	#474	—	2	1	no	—
181	#474	C₂²×C₇	1	2	yes	—
182	#466	—	2	2	no	—
183	#461	C₂²×C₇	1	2	yes	—
184	#461	C₂²×C₇	1	2	yes	—
185	#459	—	2	1	no	—
186	#459	C₂²×C₇	1	2	yes	—
187	#448	—	2	2	no	—
188	#436	C₂²×C₇	1	2	yes	—
189	#435	—	2	2	no	—
190	C₈×D₄	C₂²×C₇	1	2	yes	—
191	#431	C₂²×C₇	1	1	yes	characteristic
192	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
193	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
194	#417	—	2	1	no	—
195	#417	—	2	1	no	—
196	#408	—	2	1	no	—
197	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
198	#335	C₂²×C₇	1	2	yes	—
199	#334	C₂²×C₇	1	2	yes	—
200	#332	C₂²×C₇	1	2	yes	—
201	#332	C₂²×C₇	1	2	yes	—
202	#332	C₂²×C₇	1	1	yes	characteristic
203	#332	C₂²×C₇	1	1	yes	characteristic
204	#331	C₂²×C₇	1	1	yes	characteristic
205	#331	C₂²×C₇	1	1	yes	characteristic
206	C₂³×C₇	—	2	2	no	—
207	C₂³×C₇	—	4	1	no	—
208	C₂³×C₇	#121	1	1	yes	characteristic
209	C₇×Q₈	—	4	2	no	—
210	C₇×Q₈	—	4	1	no	—
211	C₇×Q₈	—	4	1	no	—
212	C₇×Q₈	—	4	2	no	—
213	C₇×Q₈	—	4	2	no	—
214	C₇×Q₈	—	8	2	no	—
215	C₇×D₄	—	2	2	no	—
216	C₇×D₄	—	2	2	no	—
217	C₇×D₄	—	4	4	no	—
218	C₇×D₄	—	4	1	no	—
219	C₇×D₄	—	4	1	no	—
220	C₇×D₄	—	4	1	no	—
221	C₇×D₄	—	4	1	no	—
222	C₇×D₄	—	4	2	no	—
223	C₇×D₄	—	8	1	no	—
224	C₇×D₄	—	8	1	no	—
225	C₇×D₄	—	8	2	no	—
226	C₂×C₄×C₇	—	2	1	no	—
227	C₂×C₄×C₇	—	2	1	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	4	1	no	—
230	C₂×C₄×C₇	—	4	2	no	—
231	C₂×C₄×C₇	—	4	2	no	—
232	C₂×C₄×C₇	—	4	1	no	—
233	C₂×C₄×C₇	—	4	2	no	—
234	C₂×C₄×C₇	—	8	2	no	—
235	C₂×C₄×C₇	—	8	2	no	—
236	C₂×C₄×C₇	#121	1	1	yes	characteristic
237	C₂×C₄×C₇	#121	1	1	yes	characteristic
238	C₂×C₄×C₇	#121	1	1	yes	characteristic
239	C₂×C₄×C₇	#135	1	2	yes	—
240	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
241	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
244	C₇×C₈	—	2	2	no	—
245	C₇×C₈	—	2	2	no	—
246	C₇×C₈	—	4	1	no	—
247	C₇×C₈	—	4	1	no	—
248	C₇×C₈	—	4	2	no	—
249	C₇×C₈	—	4	1	no	—
250	C₇×C₈	—	4	1	no	—
251	C₂×#41	—	2	1	no	—
252	C₂×#41	—	2	1	no	—
253	C₂²×Q₈	—	2	1	no	—
254	C₂×SD₁₆	—	2	2	no	—
255	C₂×SD₁₆	—	2	2	no	—
256	C₂×D₈	—	2	2	no	—
257	#131	—	4	4	no	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
260	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	2	2	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
268	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
269	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
270	#127	C₇×D₄	1	1	yes	characteristic
271	#127	C₂³×C₇	1	1	yes	characteristic
272	#124	—	2	1	no	—
273	#124	—	2	1	no	—
274	#121	—	2	1	no	—
275	#121	—	2	1	no	—
276	#121	—	2	1	no	—
277	#121	C₇×D₄	1	2	yes	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	C₂³×C₇	1	2	yes	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
285	#107	—	2	2	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
289	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
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	#103	—	2	2	no	—
294	#103	—	2	2	no	—
295	#103	—	2	2	no	—
296	#103	—	2	2	no	—
297	#102	—	2	2	no	—
298	#102	—	2	2	no	—
299	#102	—	2	2	no	—
300	#102	—	2	2	no	—
301	C₂²⋊C₈	—	2	1	no	—
302	C₂²⋊C₈	—	2	2	no	—
303	C₂²⋊C₈	—	2	2	no	—
304	#97	C₇×D₄	1	2	yes	—
305	C₄×C₈	—	2	1	no	—
306	C₄×C₈	C₂³×C₇	1	2	yes	—
307	C₂²×C₇	—	2	1	no	—
308	C₂²×C₇	—	2	1	no	—
309	C₂²×C₇	—	4	2	no	—
310	C₂²×C₇	—	4	2	no	—
311	C₂²×C₇	—	4	2	no	—
312	C₂²×C₇	—	8	1	no	—
313	C₂²×C₇	—	8	1	no	—
314	C₂²×C₇	—	8	1	no	—
315	C₂²×C₇	#463	1	2	yes	—
316	C₂²×C₇	C₂×#121	1	1	yes	characteristic
317	C₄×C₇	—	2	1	no	—
318	C₄×C₇	—	2	1	no	—
319	C₄×C₇	—	2	1	no	—
320	C₄×C₇	—	4	2	no	—
321	C₄×C₇	—	8	1	no	—
322	C₄×C₇	—	8	2	no	—
323	C₄×C₇	#463	1	2	yes	—
324	C₄×C₇	C₂×#135	1	1	yes	characteristic
325	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
326	C₄×C₇	#576	1	1	yes	characteristic
327	C₄×C₇	#577	1	1	yes	characteristic
328	#41	—	4	2	no	—
329	#41	—	4	2	no	—
330	#41	—	4	2	no	—
331	#41	—	4	2	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	4	1	no	—
336	C₂×Q₈	—	8	1	no	—
337	C₂×Q₈	—	8	1	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
351	C₂²×C₄	C₇×#41	1	1	yes	characteristic
352	SD₁₆	—	8	2	no	—
353	SD₁₆	—	8	2	no	—
354	D₈	—	8	2	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	4	4	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	4	no	—
364	C₂×C₈	—	4	2	no	—
365	C₂×C₈	—	8	1	no	—
366	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
367	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	4	1	no	—
379	C₂²⋊C₄	—	4	1	no	—
380	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
381	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
382	C₄²	C₇×#41	1	1	yes	characteristic
383	C₄²	C₂⁴×C₇	1	1	yes	characteristic
384	C₂×C₇	—	2	2	no	—
385	C₂×C₇	—	8	2	no	—
386	C₂×C₇	—	16	1	no	—
387	C₂×C₇	C₂×#463	1	1	yes	characteristic
388	C₂×C₇	#3062	1	1	yes	characteristic
389	C₂×C₇	#3069	1	1	yes	characteristic
390	C₂³	—	2	2	no	—
391	C₂³	—	4	1	no	—
392	C₂³	C₇×#121	1	1	yes	characteristic
393	Q₈	—	4	2	no	—
394	Q₈	—	4	1	no	—
395	Q₈	—	4	1	no	—
396	Q₈	—	4	2	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	8	2	no	—
399	D₄	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	4	4	no	—
402	D₄	—	4	1	no	—
403	D₄	—	4	1	no	—
404	D₄	—	4	1	no	—
405	D₄	—	4	1	no	—
406	D₄	—	4	2	no	—
407	D₄	—	8	1	no	—
408	D₄	—	8	1	no	—
409	D₄	—	8	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	—	8	2	no	—
420	C₂×C₄	C₇×#121	1	1	yes	characteristic
421	C₂×C₄	C₇×#121	1	1	yes	characteristic
422	C₂×C₄	C₇×#121	1	1	yes	characteristic
423	C₂×C₄	C₇×#135	1	2	yes	—
424	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
425	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
427	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
428	C₈	—	2	2	no	—
429	C₈	—	2	2	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	1	no	—
432	C₈	—	4	2	no	—
433	C₈	—	4	1	no	—
434	C₈	—	4	1	no	—
435	C₇	#19237	1	1	yes	characteristic, direct product factor, Sylow
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	8	1	no	—
442	C₂²	—	8	1	no	—
443	C₂²	—	8	1	no	—
444	C₂²	C₇×#463	1	2	yes	—
445	C₂²	C₂×C₇×#121	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	1	no	—
451	C₄	—	8	2	no	—
452	C₄	C₇×#463	1	2	yes	—
453	C₄	C₂×C₇×#135	1	1	yes	characteristic
454	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
455	C₄	C₇×#576	1	1	yes	characteristic
456	C₄	C₇×#577	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	8	2	no	—
459	C₂	—	16	1	no	—
460	C₂	C₂×C₇×#463	1	1	yes	characteristic
461	C₂	C₇×#3062	1	1	yes	characteristic
462	C₂	C₇×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#3245	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
2. C₇×#3206	C₂	semidirect
3. C₇×#3141	C₂	semidirect
4. C₇×#2935	C₂	semidirect
5. C₇×#1701	C₂	semidirect
6. C₇×#1699	C₂	semidirect
7. C₇×#1681	C₂	semidirect
8. C₇×#1679	C₂	semidirect
9. C₇×#1565	C₂	semidirect
10. C₇×#1540	C₂	semidirect
11. C₂×C₇×#332	C₂	semidirect
47. #19237	C₇	direct (N × H)
105. #3206	C₂×C₇	semidirect
106. #3141	C₂×C₇	semidirect
107. #2935	C₂×C₇	semidirect
108. #1701	C₂×C₇	semidirect
109. #1699	C₂×C₇	semidirect
110. #1681	C₂×C₇	semidirect
111. #1679	C₂×C₇	semidirect
112. #1565	C₂×C₇	semidirect
113. #1540	C₂×C₇	semidirect
114. C₂×#332	C₂×C₇	semidirect
435. C₇	#19237	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×#3245	2
C₇×#3206	2
C₇×#3141	2
C₇×#2935	2
C₇×#1701	2
C₇×#1699	2
C₇×#1681	2
C₇×#1679	2
C₇×#1565	2
C₇×#1540	2
C₂×C₇×#332	2
#19237	7

Subgroups — C7×#19237 #13196453

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19237 #13196453