Subgroups — C₇×#19239 #13196455

Order 1792.

658 conjugacy classes of subgroups.

The subgroup lattice has 446 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
2	C₇×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3152	C₂	1	1	yes	maximal, characteristic
4	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1690	C₂	1	2	yes	maximal, complemented
6	C₇×#1686	C₂	1	2	yes	maximal, complemented
7	C₇×#1670	C₂	1	2	yes	maximal, complemented
8	C₇×#1666	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
11	C₂×C₇×#332	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#137	—	2	1	no	—
13	C₂×C₇×#137	—	2	1	no	—
14	C₇×#533	C₂²	1	1	yes	characteristic
15	C₇×#532	C₂²	1	1	yes	characteristic
16	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₇×#498	—	2	1	no	—
18	C₇×#497	—	2	2	no	—
19	C₇×#494	C₂²	1	2	yes	—
20	C₇×#492	C₂²	1	2	yes	—
21	C₇×#487	—	2	1	no	—
22	C₇×#483	—	2	2	no	—
23	C₇×#476	—	2	1	no	—
24	C₇×#475	C₂²	1	2	yes	—
25	C₇×#475	C₂²	1	2	yes	—
26	C₇×#475	C₂²	1	2	yes	—
27	C₇×#465	—	2	2	no	—
28	C₇×#461	—	2	1	no	—
29	C₇×#460	C₂²	1	2	yes	—
30	C₇×#446	—	2	2	no	—
31	C₇×#446	C₂²	1	2	yes	—
32	C₇×C₈×Q₈	C₂²	1	2	yes	—
33	C₇×#431	C₂²	1	1	yes	characteristic
34	C₇×#424	—	2	1	no	—
35	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₇×#405	—	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	#19239	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	—	2	1	no	—
49	C₂²×C₇×Q₈	—	2	1	no	—
50	C₇×#137	—	4	4	no	—
51	C₇×#137	—	4	4	no	—
52	C₂×C₇×Q₁₆	—	2	2	no	—
53	C₂×C₇×Q₁₆	—	2	2	no	—
54	C₂×C₇×SD₁₆	—	2	2	no	—
55	C₂×C₇×SD₁₆	—	2	2	no	—
56	C₂×C₇×SD₁₆	—	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	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	D₄	1	1	yes	characteristic
66	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₇×#127	C₂³	1	1	yes	characteristic
69	C₇×#125	—	2	1	no	—
70	C₇×#124	—	2	1	no	—
71	C₇×C₂²⋊Q₈	—	2	1	no	—
72	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
73	C₇×#121	—	2	1	no	—
74	C₇×#121	—	2	1	no	—
75	C₄×C₇×Q₈	—	2	1	no	—
76	C₄×C₇×Q₈	C₂³	1	2	yes	—
77	C₄×C₇×D₄	—	2	1	no	—
78	C₄×C₇×D₄	—	2	1	no	—
79	C₇×#117	—	2	1	no	—
80	C₂×C₇×C₄⋊C₄	—	2	1	no	—
81	C₂×C₇×C₄⋊C₄	—	2	1	no	—
82	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
83	C₇×#106	—	2	2	no	—
84	C₇×#106	—	2	2	no	—
85	C₇×#106	—	2	2	no	—
86	C₇×C₄⋊C₈	—	2	2	no	—
87	C₇×C₄⋊C₈	—	2	2	no	—
88	C₇×C₄⋊C₈	—	2	1	no	—
89	C₇×C₄⋊C₈	—	2	1	no	—
90	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
92	C₇×C₄⋊C₈	C₂³	1	2	yes	—
93	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
94	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
95	C₇×#103	—	2	2	no	—
96	C₇×#103	—	2	2	no	—
97	C₇×#103	—	2	2	no	—
98	C₇×#102	—	2	2	no	—
99	C₇×C₂²⋊C₈	—	2	1	no	—
100	C₇×#97	—	2	2	no	—
101	C₇×#97	D₄	1	2	yes	—
102	C₄×C₇×C₈	—	2	2	no	—
103	C₄×C₇×C₈	—	2	1	no	—
104	C₄×C₇×C₈	C₂³	1	2	yes	—
105	#3246	C₂×C₇	1	1	yes	characteristic
106	#3229	C₂×C₇	1	1	yes	characteristic, complemented
107	#3152	C₂×C₇	1	1	yes	characteristic
108	#2962	C₂×C₇	1	1	yes	characteristic, complemented
109	#1690	C₂×C₇	1	2	yes	complemented
110	#1686	C₂×C₇	1	2	yes	complemented
111	#1670	C₂×C₇	1	2	yes	complemented
112	#1666	C₂×C₇	1	2	yes	complemented
113	#1565	C₂×C₇	1	1	yes	characteristic, complemented
114	#1540	C₂×C₇	1	1	yes	characteristic
115	C₂×#332	C₂×C₇	1	1	yes	characteristic, complemented
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	2	no	—
121	C₂×C₇×Q₈	—	4	1	no	—
122	C₂×C₇×Q₈	—	4	2	no	—
123	C₂×C₇×Q₈	—	4	2	no	—
124	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
125	C₂×C₇×D₄	—	2	1	no	—
126	C₂×C₇×D₄	—	2	1	no	—
127	C₂×C₇×D₄	—	2	1	no	—
128	C₂×C₇×D₄	—	4	1	no	—
129	C₂²×C₄×C₇	—	4	1	no	—
130	C₂²×C₄×C₇	—	4	1	no	—
131	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇	#41	1	1	yes	characteristic
134	C₇×Q₁₆	—	4	4	no	—
135	C₇×Q₁₆	—	4	4	no	—
136	C₇×SD₁₆	—	4	4	no	—
137	C₇×SD₁₆	—	4	4	no	—
138	C₇×SD₁₆	—	8	2	no	—
139	C₇×M₁₆	—	2	2	no	—
140	C₇×M₁₆	SD₁₆	1	4	yes	complemented
141	C₂×C₇×C₈	—	2	1	no	—
142	C₂×C₇×C₈	—	2	1	no	—
143	C₂×C₇×C₈	—	2	1	no	—
144	C₂×C₇×C₈	—	2	1	no	—
145	C₂×C₇×C₈	—	2	2	no	—
146	C₂×C₇×C₈	—	4	2	no	—
147	C₂×C₇×C₈	—	8	1	no	—
148	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
149	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
150	C₇×C₄⋊C₄	—	2	1	no	—
151	C₇×C₄⋊C₄	—	2	1	no	—
152	C₇×C₄⋊C₄	—	2	1	no	—
153	C₇×C₄⋊C₄	—	2	2	no	—
154	C₇×C₄⋊C₄	—	2	2	no	—
155	C₇×C₄⋊C₄	—	2	2	no	—
156	C₇×C₄⋊C₄	—	2	1	no	—
157	C₇×C₄⋊C₄	—	2	2	no	—
158	C₇×C₄⋊C₄	—	2	1	no	—
159	C₇×C₄⋊C₄	—	4	1	no	—
160	C₇×C₄⋊C₄	—	4	1	no	—
161	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
162	C₇×C₂²⋊C₄	—	2	2	no	—
163	C₇×C₂²⋊C₄	—	4	1	no	—
164	C₇×C₂²⋊C₄	—	4	1	no	—
165	C₄²×C₇	—	2	2	no	—
166	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₇	#41	1	1	yes	characteristic
169	C₄²×C₇	C₂⁴	1	1	yes	characteristic
170	C₂×#137	—	2	1	no	—
171	C₂×#137	—	2	1	no	—
172	#533	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	#498	—	2	1	no	—
176	#497	—	2	2	no	—
177	#494	C₂²×C₇	1	2	yes	—
178	#492	C₂²×C₇	1	2	yes	—
179	#487	—	2	1	no	—
180	#483	—	2	2	no	—
181	#476	—	2	1	no	—
182	#475	C₂²×C₇	1	2	yes	—
183	#475	C₂²×C₇	1	2	yes	—
184	#475	C₂²×C₇	1	2	yes	—
185	#465	—	2	2	no	—
186	#461	—	2	1	no	—
187	#460	C₂²×C₇	1	2	yes	—
188	#446	—	2	2	no	—
189	#446	C₂²×C₇	1	2	yes	—
190	C₈×Q₈	C₂²×C₇	1	2	yes	—
191	#431	C₂²×C₇	1	1	yes	characteristic
192	#424	—	2	1	no	—
193	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
194	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
195	#405	—	2	1	no	—
196	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
197	#335	C₂²×C₇	1	2	yes	—
198	#334	C₂²×C₇	1	2	yes	—
199	#332	C₂²×C₇	1	2	yes	—
200	#332	C₂²×C₇	1	2	yes	—
201	#332	C₂²×C₇	1	1	yes	characteristic
202	#332	C₂²×C₇	1	1	yes	characteristic
203	#331	C₂²×C₇	1	1	yes	characteristic
204	#331	C₂²×C₇	1	1	yes	characteristic
205	C₂³×C₇	—	4	1	no	—
206	C₂³×C₇	#121	1	1	yes	characteristic
207	C₇×Q₈	—	2	2	no	—
208	C₇×Q₈	—	2	2	no	—
209	C₇×Q₈	—	4	2	no	—
210	C₇×Q₈	—	4	1	no	—
211	C₇×Q₈	—	4	2	no	—
212	C₇×Q₈	—	4	1	no	—
213	C₇×Q₈	—	8	1	no	—
214	C₇×Q₈	—	8	2	no	—
215	C₇×D₄	—	4	1	no	—
216	C₇×D₄	—	4	1	no	—
217	C₇×D₄	—	4	1	no	—
218	C₇×D₄	—	4	1	no	—
219	C₇×D₄	—	8	1	no	—
220	C₇×D₄	—	8	2	no	—
221	C₂×C₄×C₇	—	2	1	no	—
222	C₂×C₄×C₇	—	2	1	no	—
223	C₂×C₄×C₇	—	2	2	no	—
224	C₂×C₄×C₇	—	2	2	no	—
225	C₂×C₄×C₇	—	4	1	no	—
226	C₂×C₄×C₇	—	4	1	no	—
227	C₂×C₄×C₇	—	4	2	no	—
228	C₂×C₄×C₇	—	8	2	no	—
229	C₂×C₄×C₇	—	8	2	no	—
230	C₂×C₄×C₇	#121	1	1	yes	characteristic
231	C₂×C₄×C₇	#121	1	1	yes	characteristic
232	C₂×C₄×C₇	#121	1	1	yes	characteristic
233	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
234	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
235	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
238	C₇×C₈	—	2	2	no	—
239	C₇×C₈	—	4	1	no	—
240	C₇×C₈	—	4	1	no	—
241	C₇×C₈	—	4	1	no	—
242	C₇×C₈	—	4	2	no	—
243	C₇×C₈	—	4	1	no	—
244	C₇×C₈	C₂×SD₁₆	1	4	yes	—
245	C₂×#41	—	2	1	no	—
246	C₂²×Q₈	—	2	1	no	—
247	#137	—	4	4	no	—
248	#137	—	4	4	no	—
249	C₂×Q₁₆	—	2	2	no	—
250	C₂×Q₁₆	—	2	2	no	—
251	C₂×SD₁₆	—	2	2	no	—
252	C₂×SD₁₆	—	2	2	no	—
253	C₂×SD₁₆	—	2	2	no	—
254	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
255	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
256	C₂²×C₈	—	2	1	no	—
257	C₂²×C₈	—	2	1	no	—
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	—	2	1	no	—
260	C₄⋊Q₈	—	2	1	no	—
261	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
262	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
263	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
264	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
265	#127	C₂³×C₇	1	1	yes	characteristic
266	#125	—	2	1	no	—
267	#124	—	2	1	no	—
268	C₂²⋊Q₈	—	2	1	no	—
269	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
270	#121	—	2	1	no	—
271	#121	—	2	1	no	—
272	C₄×Q₈	—	2	1	no	—
273	C₄×Q₈	C₂³×C₇	1	2	yes	—
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	—	2	1	no	—
276	#117	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
280	#106	—	2	2	no	—
281	#106	—	2	2	no	—
282	#106	—	2	2	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	2	2	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
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	2	yes	—
292	#103	—	2	2	no	—
293	#103	—	2	2	no	—
294	#103	—	2	2	no	—
295	#102	—	2	2	no	—
296	C₂²⋊C₈	—	2	1	no	—
297	#97	—	2	2	no	—
298	#97	C₇×D₄	1	2	yes	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	C₂³×C₇	1	2	yes	—
302	C₂²×C₇	—	2	1	no	—
303	C₂²×C₇	—	2	1	no	—
304	C₂²×C₇	—	8	1	no	—
305	C₂²×C₇	—	8	1	no	—
306	C₂²×C₇	—	8	1	no	—
307	C₂²×C₇	#460	1	2	yes	—
308	C₂²×C₇	C₂×#121	1	1	yes	characteristic
309	C₄×C₇	—	2	1	no	—
310	C₄×C₇	—	2	1	no	—
311	C₄×C₇	—	2	1	no	—
312	C₄×C₇	—	4	2	no	—
313	C₄×C₇	—	4	2	no	—
314	C₄×C₇	—	8	1	no	—
315	C₄×C₇	—	8	2	no	—
316	C₄×C₇	#460	1	2	yes	—
317	C₄×C₇	C₂²×SD₁₆	1	1	yes	characteristic
318	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₄×C₇	#577	1	1	yes	characteristic
320	C₄×C₇	#578	1	1	yes	characteristic
321	#41	—	4	2	no	—
322	#41	—	4	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	4	1	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂²×C₄	—	4	1	no	—
335	C₂²×C₄	—	4	1	no	—
336	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
338	C₂²×C₄	C₇×#41	1	1	yes	characteristic
339	Q₁₆	—	4	4	no	—
340	Q₁₆	—	4	4	no	—
341	SD₁₆	—	4	4	no	—
342	SD₁₆	—	4	4	no	—
343	SD₁₆	—	8	2	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	C₇×SD₁₆	1	4	yes	complemented
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	4	2	no	—
352	C₂×C₈	—	8	1	no	—
353	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
354	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	4	1	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	4	1	no	—
369	C₂²⋊C₄	—	4	1	no	—
370	C₄²	—	2	2	no	—
371	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
372	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
373	C₄²	C₇×#41	1	1	yes	characteristic
374	C₄²	C₂⁴×C₇	1	1	yes	characteristic
375	C₂×C₇	—	2	2	no	—
376	C₂×C₇	—	16	1	no	—
377	C₂×C₇	C₂×#460	1	1	yes	characteristic
378	C₂×C₇	#3063	1	1	yes	characteristic
379	C₂×C₇	#3069	1	1	yes	characteristic
380	C₂³	—	4	1	no	—
381	C₂³	C₇×#121	1	1	yes	characteristic
382	Q₈	—	2	2	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	1	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	1	no	—
388	Q₈	—	8	1	no	—
389	Q₈	—	8	2	no	—
390	D₄	—	4	1	no	—
391	D₄	—	4	1	no	—
392	D₄	—	4	1	no	—
393	D₄	—	4	1	no	—
394	D₄	—	8	1	no	—
395	D₄	—	8	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	C₇×#121	1	1	yes	characteristic
406	C₂×C₄	C₇×#121	1	1	yes	characteristic
407	C₂×C₄	C₇×#121	1	1	yes	characteristic
408	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
409	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
410	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
412	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	1	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	2	no	—
418	C₈	—	4	1	no	—
419	C₈	C₂×C₇×SD₁₆	1	4	yes	—
420	C₇	#19239	1	1	yes	characteristic, direct product factor, Sylow
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	C₇×#460	1	2	yes	—
427	C₂²	C₂×C₇×#121	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	8	1	no	—
434	C₄	—	8	2	no	—
435	C₄	C₇×#460	1	2	yes	—
436	C₄	C₂²×C₇×SD₁₆	1	1	yes	characteristic
437	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
438	C₄	C₇×#577	1	1	yes	characteristic
439	C₄	C₇×#578	1	1	yes	characteristic
440	C₂	—	2	2	no	—
441	C₂	—	16	1	no	—
442	C₂	C₂×C₇×#460	1	1	yes	characteristic
443	C₂	C₇×#3063	1	1	yes	characteristic
444	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×#532	C₂²
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×#3229	C₂	semidirect
4. C₇×#2962	C₂	semidirect
5. C₇×#1690	C₂	semidirect
6. C₇×#1686	C₂	semidirect
7. C₇×#1670	C₂	semidirect
8. C₇×#1666	C₂	semidirect
9. C₇×#1565	C₂	semidirect
11. C₂×C₇×#332	C₂	semidirect
47. #19239	C₇	direct (N × H)
106. #3229	C₂×C₇	semidirect
108. #2962	C₂×C₇	semidirect
109. #1690	C₂×C₇	semidirect
110. #1686	C₂×C₇	semidirect
111. #1670	C₂×C₇	semidirect
112. #1666	C₂×C₇	semidirect
113. #1565	C₂×C₇	semidirect
115. C₂×#332	C₂×C₇	semidirect
140. C₇×M₁₆	SD₁₆	semidirect
345. M₁₆	C₇×SD₁₆	semidirect
420. C₇	#19239	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×#3229	2
C₇×#3152	2
C₇×#2962	2
C₇×#1690	2
C₇×#1686	2
C₇×#1670	2
C₇×#1666	2
C₇×#1565	2
C₇×#1540	2
C₂×C₇×#332	2
#19239	7

Subgroups — C7×#19239 #13196455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19239 #13196455