Subgroups — C₇×#19672 #13196888

Order 1792.

798 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×#3226	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3169	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3152	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1723	C₂	1	2	yes	maximal, complemented
8	C₇×#1720	C₂	1	2	yes	maximal, complemented
9	C₇×#1715	C₂	1	2	yes	maximal, complemented
10	C₇×#1714	C₂	1	2	yes	maximal, complemented
11	C₇×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#137	—	2	2	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	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₇×#500	C₂²	1	2	yes	—
18	C₇×#500	C₂²	1	1	yes	characteristic
19	C₇×#498	—	2	2	no	—
20	C₇×#498	C₂²	1	2	yes	—
21	C₇×#498	C₂²	1	2	yes	—
22	C₇×#497	—	2	2	no	—
23	C₇×#494	C₂²	1	2	yes	—
24	C₇×#493	C₂²	1	1	yes	characteristic
25	C₇×#492	C₂²	1	2	yes	—
26	C₇×#492	C₂²	1	2	yes	—
27	C₇×#489	—	2	2	no	—
28	C₇×#487	C₂²	1	2	yes	—
29	C₇×#487	C₂²	1	2	yes	—
30	C₇×#486	C₂²	1	1	yes	characteristic
31	C₇×#486	C₂²	1	2	yes	—
32	C₇×#486	C₂²	1	2	yes	—
33	C₇×#486	C₂²	1	1	yes	characteristic
34	C₇×#480	—	2	2	no	—
35	C₇×#474	—	2	2	no	—
36	C₇×#466	—	2	2	no	—
37	C₇×#461	—	2	2	no	—
38	C₇×#448	—	2	2	no	—
39	C₄×C₇×D₈	—	2	2	no	—
40	C₇×#431	C₂²	1	1	yes	characteristic
41	C₂×C₇×#106	—	2	2	no	—
42	C₇×#417	—	2	2	no	—
43	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
45	C₇×#322	C₂²	1	2	yes	—
46	C₇×#322	C₂²	1	2	yes	—
47	#19672	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	C₂²×C₇×Q₈	—	2	1	no	—
52	C₇×#137	—	4	8	no	—
53	C₂×C₇×Q₁₆	—	2	4	no	—
54	C₂×C₇×SD₁₆	—	2	4	no	—
55	C₂×C₇×SD₁₆	—	2	4	no	—
56	C₂×C₇×D₈	—	2	2	no	—
57	C₂×C₇×M₁₆	D₄	1	2	yes	—
58	C₂²×C₇×C₈	D₄	1	2	yes	—
59	C₇×C₄⋊Q₈	—	2	1	no	—
60	C₇×C₄⋊Q₈	—	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	—	2	1	no	—
65	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₇×#127	C₂³	1	1	yes	characteristic
70	C₇×#127	C₂³	1	1	yes	characteristic
71	C₇×#124	—	2	1	no	—
72	C₇×#124	—	2	1	no	—
73	C₇×#121	—	2	1	no	—
74	C₇×#121	—	2	1	no	—
75	C₇×#121	—	2	1	no	—
76	C₇×#121	—	2	1	no	—
77	C₄×C₇×D₄	—	2	1	no	—
78	C₄×C₇×D₄	—	2	1	no	—
79	C₄×C₇×D₄	—	2	1	no	—
80	C₄×C₇×D₄	—	2	1	no	—
81	C₂×C₇×C₄⋊C₄	—	2	1	no	—
82	C₂×C₇×C₄⋊C₄	—	2	1	no	—
83	C₂×C₇×C₄⋊C₄	—	2	1	no	—
84	C₂×C₇×C₄⋊C₄	—	2	1	no	—
85	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
86	C₇×#107	—	2	2	no	—
87	C₇×#107	—	2	4	no	—
88	C₇×#106	—	2	4	no	—
89	C₇×#106	—	2	4	no	—
90	C₇×C₄⋊C₈	D₄	1	2	yes	—
91	C₇×#103	—	2	4	no	—
92	C₇×#103	—	2	4	no	—
93	C₇×#102	—	2	2	no	—
94	C₇×#102	—	2	2	no	—
95	C₇×#102	—	2	4	no	—
96	C₇×#102	—	2	4	no	—
97	C₇×C₂²⋊C₈	D₄	1	2	yes	—
98	C₇×#97	D₄	1	2	yes	—
99	C₄×C₇×C₈	D₄	1	2	yes	—
100	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
101	C₄×C₇×C₈	C₂³	1	2	yes	—
102	C₄×C₇×C₈	C₂³	1	2	yes	—
103	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
104	#3226	C₂×C₇	1	1	yes	characteristic, complemented
105	#3206	C₂×C₇	1	1	yes	characteristic, complemented
106	#3169	C₂×C₇	1	1	yes	characteristic
107	C₂×#498	C₂×C₇	1	1	yes	characteristic, complemented
108	#3152	C₂×C₇	1	1	yes	characteristic, complemented
109	#3141	C₂×C₇	1	1	yes	characteristic, complemented
110	#1723	C₂×C₇	1	2	yes	complemented
111	#1720	C₂×C₇	1	2	yes	complemented
112	#1715	C₂×C₇	1	2	yes	complemented
113	#1714	C₂×C₇	1	2	yes	complemented
114	#1451	C₂×C₇	1	1	yes	characteristic, complemented
115	C₇×#41	—	4	4	no	—
116	C₇×#41	—	4	4	no	—
117	C₂×C₇×Q₈	—	2	1	no	—
118	C₂×C₇×Q₈	—	2	2	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	1	no	—
123	C₂×C₇×Q₈	—	4	4	no	—
124	C₂×C₇×Q₈	—	8	2	no	—
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	—	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	—	4	1	no	—
133	C₂²×C₄×C₇	—	4	1	no	—
134	C₂²×C₄×C₇	—	4	1	no	—
135	C₂²×C₄×C₇	—	4	1	no	—
136	C₂²×C₄×C₇	—	4	1	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	C₂×D₄	1	1	yes	characteristic
140	C₇×Q₁₆	—	4	8	no	—
141	C₇×SD₁₆	—	4	8	no	—
142	C₇×SD₁₆	—	8	4	no	—
143	C₇×D₈	—	4	4	no	—
144	C₇×M₁₆	—	2	4	no	—
145	C₂×C₇×C₈	—	2	4	no	—
146	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
147	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
148	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
149	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	—	2	2	no	—
152	C₇×C₄⋊C₄	—	2	1	no	—
153	C₇×C₄⋊C₄	—	2	1	no	—
154	C₇×C₄⋊C₄	—	2	1	no	—
155	C₇×C₄⋊C₄	—	2	2	no	—
156	C₇×C₄⋊C₄	—	2	2	no	—
157	C₇×C₄⋊C₄	—	2	1	no	—
158	C₇×C₄⋊C₄	—	4	1	no	—
159	C₇×C₄⋊C₄	—	4	1	no	—
160	C₇×C₄⋊C₄	—	4	1	no	—
161	C₇×C₄⋊C₄	—	4	1	no	—
162	C₇×C₂²⋊C₄	—	4	1	no	—
163	C₇×C₂²⋊C₄	—	4	1	no	—
164	C₇×C₂²⋊C₄	—	4	1	no	—
165	C₇×C₂²⋊C₄	—	4	1	no	—
166	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₇	C₂⁴	1	1	yes	characteristic
170	C₂×#137	—	2	2	no	—
171	#532	C₂²×C₇	1	1	yes	characteristic
172	#532	C₂²×C₇	1	1	yes	characteristic
173	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
174	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
175	#500	C₂²×C₇	1	1	yes	characteristic
176	#500	C₂²×C₇	1	2	yes	—
177	#498	—	2	2	no	—
178	#498	C₂²×C₇	1	2	yes	—
179	#498	C₂²×C₇	1	2	yes	—
180	#497	—	2	2	no	—
181	#494	C₂²×C₇	1	2	yes	—
182	#493	C₂²×C₇	1	1	yes	characteristic
183	#492	C₂²×C₇	1	2	yes	—
184	#492	C₂²×C₇	1	2	yes	—
185	#489	—	2	2	no	—
186	#487	C₂²×C₇	1	2	yes	—
187	#487	C₂²×C₇	1	2	yes	—
188	#486	C₂²×C₇	1	2	yes	—
189	#486	C₂²×C₇	1	1	yes	characteristic
190	#486	C₂²×C₇	1	1	yes	characteristic
191	#486	C₂²×C₇	1	2	yes	—
192	#480	—	2	2	no	—
193	#474	—	2	2	no	—
194	#466	—	2	2	no	—
195	#461	—	2	2	no	—
196	#448	—	2	2	no	—
197	C₄×D₈	—	2	2	no	—
198	#431	C₂²×C₇	1	1	yes	characteristic
199	C₂×#106	—	2	2	no	—
200	#417	—	2	2	no	—
201	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
202	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
203	#322	C₂²×C₇	1	2	yes	—
204	#322	C₂²×C₇	1	2	yes	—
205	C₂³×C₇	—	4	1	no	—
206	C₂³×C₇	—	4	1	no	—
207	C₂³×C₇	#127	1	1	yes	characteristic
208	C₇×Q₈	—	4	4	no	—
209	C₇×Q₈	—	4	2	no	—
210	C₇×Q₈	—	4	2	no	—
211	C₇×Q₈	—	4	4	no	—
212	C₇×Q₈	—	8	2	no	—
213	C₇×Q₈	—	8	2	no	—
214	C₇×D₄	—	4	2	no	—
215	C₇×D₄	—	4	2	no	—
216	C₇×D₄	—	4	2	no	—
217	C₇×D₄	—	4	2	no	—
218	C₇×D₄	—	4	2	no	—
219	C₇×D₄	—	4	2	no	—
220	C₇×D₄	—	8	2	no	—
221	C₇×D₄	—	8	2	no	—
222	C₂×C₄×C₇	—	2	2	no	—
223	C₂×C₄×C₇	—	2	2	no	—
224	C₂×C₄×C₇	—	4	1	no	—
225	C₂×C₄×C₇	—	4	1	no	—
226	C₂×C₄×C₇	—	4	2	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	—	8	2	no	—
231	C₂×C₄×C₇	—	8	2	no	—
232	C₂×C₄×C₇	#127	1	1	yes	characteristic
233	C₂×C₄×C₇	#127	1	1	yes	characteristic
234	C₂×C₄×C₇	#127	1	1	yes	characteristic
235	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
236	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
239	C₇×C₈	—	2	4	no	—
240	C₇×C₈	—	2	2	no	—
241	C₇×C₈	—	2	4	no	—
242	C₇×C₈	#137	1	4	yes	complemented
243	C₂×#41	—	2	1	no	—
244	C₂×#41	—	2	1	no	—
245	C₂²×Q₈	—	2	1	no	—
246	C₂²×Q₈	—	2	1	no	—
247	#137	—	4	8	no	—
248	C₂×Q₁₆	—	2	4	no	—
249	C₂×SD₁₆	—	2	4	no	—
250	C₂×SD₁₆	—	2	4	no	—
251	C₂×D₈	—	2	2	no	—
252	C₂×M₁₆	C₇×D₄	1	2	yes	—
253	C₂²×C₈	C₇×D₄	1	2	yes	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	—	2	1	no	—
260	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
261	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
262	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
263	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
264	#127	C₂³×C₇	1	1	yes	characteristic
265	#127	C₂³×C₇	1	1	yes	characteristic
266	#124	—	2	1	no	—
267	#124	—	2	1	no	—
268	#121	—	2	1	no	—
269	#121	—	2	1	no	—
270	#121	—	2	1	no	—
271	#121	—	2	1	no	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
281	#107	—	2	2	no	—
282	#107	—	2	4	no	—
283	#106	—	2	4	no	—
284	#106	—	2	4	no	—
285	C₄⋊C₈	C₇×D₄	1	2	yes	—
286	#103	—	2	4	no	—
287	#103	—	2	4	no	—
288	#102	—	2	4	no	—
289	#102	—	2	2	no	—
290	#102	—	2	2	no	—
291	#102	—	2	4	no	—
292	C₂²⋊C₈	C₇×D₄	1	2	yes	—
293	#97	C₇×D₄	1	2	yes	—
294	C₄×C₈	C₇×D₄	1	2	yes	—
295	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
296	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
297	C₄×C₈	C₂³×C₇	1	2	yes	—
298	C₄×C₈	C₂³×C₇	1	2	yes	—
299	C₂²×C₇	—	2	1	no	—
300	C₂²×C₇	—	2	1	no	—
301	C₂²×C₇	—	8	1	no	—
302	C₂²×C₇	—	8	1	no	—
303	C₂²×C₇	—	8	1	no	—
304	C₂²×C₇	—	8	1	no	—
305	C₂²×C₇	—	8	1	no	—
306	C₂²×C₇	—	8	1	no	—
307	C₂²×C₇	#496	1	2	yes	—
308	C₂²×C₇	C₂×#127	1	1	yes	characteristic
309	C₄×C₇	—	2	1	no	—
310	C₄×C₇	—	2	1	no	—
311	C₄×C₇	—	8	1	no	—
312	C₄×C₇	—	8	1	no	—
313	C₄×C₇	—	8	2	no	—
314	C₄×C₇	—	8	2	no	—
315	C₄×C₇	#496	1	2	yes	—
316	C₄×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
317	C₄×C₇	C₂×#137	1	2	yes	—
318	C₄×C₇	#577	1	2	yes	—
319	#41	—	4	4	no	—
320	#41	—	4	4	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	4	1	no	—
326	C₂×Q₈	—	4	1	no	—
327	C₂×Q₈	—	4	4	no	—
328	C₂×Q₈	—	8	2	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	4	1	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
344	Q₁₆	—	4	8	no	—
345	SD₁₆	—	4	8	no	—
346	SD₁₆	—	8	4	no	—
347	D₈	—	4	4	no	—
348	M₁₆	—	2	4	no	—
349	C₂×C₈	—	2	4	no	—
350	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
351	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
352	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
353	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	4	1	no	—
364	C₄⋊C₄	—	4	1	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	4	1	no	—
368	C₂²⋊C₄	—	4	1	no	—
369	C₂²⋊C₄	—	4	1	no	—
370	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
371	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
372	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
373	C₄²	C₂⁴×C₇	1	1	yes	characteristic
374	C₂×C₇	—	2	2	no	—
375	C₂×C₇	—	16	1	no	—
376	C₂×C₇	—	16	1	no	—
377	C₂×C₇	C₂×#496	1	1	yes	characteristic
378	C₂×C₇	#3152	1	1	yes	characteristic
379	C₂×C₇	#3154	1	1	yes	characteristic
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	C₇×#127	1	1	yes	characteristic
383	Q₈	—	4	4	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	4	no	—
387	Q₈	—	8	2	no	—
388	Q₈	—	8	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	8	2	no	—
396	D₄	—	8	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	—	8	2	no	—
407	C₂×C₄	C₇×#127	1	1	yes	characteristic
408	C₂×C₄	C₇×#127	1	1	yes	characteristic
409	C₂×C₄	C₇×#127	1	1	yes	characteristic
410	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
411	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
414	C₈	—	2	4	no	—
415	C₈	—	2	2	no	—
416	C₈	—	2	4	no	—
417	C₈	C₇×#137	1	4	yes	complemented
418	C₇	#19672	1	1	yes	characteristic, direct product factor, Sylow
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	C₇×#496	1	2	yes	—
428	C₂²	C₂×C₇×#127	1	1	yes	characteristic
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	1	no	—
433	C₄	—	8	2	no	—
434	C₄	—	8	2	no	—
435	C₄	C₇×#496	1	2	yes	—
436	C₄	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
437	C₄	C₂×C₇×#137	1	2	yes	—
438	C₄	C₇×#577	1	2	yes	—
439	C₂	—	2	2	no	—
440	C₂	—	16	1	no	—
441	C₂	—	16	1	no	—
442	C₂	C₂×C₇×#496	1	1	yes	characteristic
443	C₂	C₇×#3152	1	1	yes	characteristic
444	C₂	C₇×#3154	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#3169	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×#3226	C₂	semidirect
2. C₇×#3206	C₂	semidirect
4. C₂×C₇×#498	C₂	semidirect
5. C₇×#3152	C₂	semidirect
6. C₇×#3141	C₂	semidirect
7. C₇×#1723	C₂	semidirect
8. C₇×#1720	C₂	semidirect
9. C₇×#1715	C₂	semidirect
10. C₇×#1714	C₂	semidirect
11. C₇×#1451	C₂	semidirect
47. #19672	C₇	direct (N × H)
104. #3226	C₂×C₇	semidirect
105. #3206	C₂×C₇	semidirect
107. C₂×#498	C₂×C₇	semidirect
108. #3152	C₂×C₇	semidirect
109. #3141	C₂×C₇	semidirect
110. #1723	C₂×C₇	semidirect
111. #1720	C₂×C₇	semidirect
112. #1715	C₂×C₇	semidirect
113. #1714	C₂×C₇	semidirect
114. #1451	C₂×C₇	semidirect
242. C₇×C₈	#137	semidirect
417. C₈	C₇×#137	semidirect
418. C₇	#19672	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×#3226	2
C₇×#3206	2
C₇×#3169	2
C₂×C₇×#498	2
C₇×#3152	2
C₇×#3141	2
C₇×#1723	2
C₇×#1720	2
C₇×#1715	2
C₇×#1714	2
C₇×#1451	2
#19672	7

Subgroups — C7×#19672 #13196888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19672 #13196888