Subgroups — C₇×#19700 #13196916

Order 1792.

778 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×#3227	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3147	C₂	1	1	yes	maximal, characteristic
6	C₂×C₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1723	C₂	1	2	yes	maximal, complemented
8	C₇×#1719	C₂	1	2	yes	maximal, complemented
9	C₇×#1717	C₂	1	2	yes	maximal, complemented
10	C₇×#1714	C₂	1	2	yes	maximal, complemented
11	C₇×#1452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#135	—	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	2	yes	—
19	C₇×#498	C₂²	1	2	yes	—
20	C₇×#495	—	2	2	no	—
21	C₇×#494	C₂²	1	1	yes	characteristic
22	C₇×#493	C₂²	1	1	yes	characteristic
23	C₇×#492	C₂²	1	1	yes	characteristic
24	C₇×#492	C₂²	1	2	yes	—
25	C₇×#492	C₂²	1	1	yes	characteristic
26	C₇×#487	—	2	2	no	—
27	C₇×#487	C₂²	1	2	yes	—
28	C₇×#487	C₂²	1	2	yes	—
29	C₇×#487	C₂²	1	2	yes	—
30	C₇×#486	C₂²	1	2	yes	—
31	C₇×#486	C₂²	1	2	yes	—
32	C₇×#486	C₂²	1	2	yes	—
33	C₇×#481	—	2	2	no	—
34	C₇×#480	—	2	2	no	—
35	C₇×#480	—	2	2	no	—
36	C₇×#476	—	2	2	no	—
37	C₇×#474	—	2	2	no	—
38	C₇×#474	—	2	2	no	—
39	C₇×#461	—	2	2	no	—
40	C₇×#448	—	2	2	no	—
41	C₇×#431	C₂²	1	1	yes	characteristic
42	C₇×#431	C₂²	1	1	yes	characteristic
43	C₂×C₇×#103	—	2	2	no	—
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	#19700	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×#135	—	4	8	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	4	no	—
57	C₂×C₇×D₈	—	2	2	no	—
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	2	yes	—
67	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	4	no	—
87	C₇×#107	—	2	4	no	—
88	C₇×#106	—	2	4	no	—
89	C₇×C₄⋊C₈	D₄	1	2	yes	—
90	C₇×C₄⋊C₈	D₄	1	2	yes	—
91	C₇×#103	—	2	4	no	—
92	C₇×#103	—	2	4	no	—
93	C₇×#103	—	2	4	no	—
94	C₇×#102	—	2	4	no	—
95	C₇×#102	—	2	4	no	—
96	C₇×#102	—	2	4	no	—
97	C₇×C₂²⋊C₈	D₄	1	2	yes	—
98	C₇×C₂²⋊C₈	D₄	1	2	yes	—
99	C₄×C₇×C₈	D₄	1	2	yes	—
100	C₄×C₇×C₈	C₂³	1	2	yes	—
101	C₄×C₇×C₈	C₂³	1	2	yes	—
102	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
103	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
104	#3227	C₂×C₇	1	1	yes	characteristic, complemented
105	#3226	C₂×C₇	1	1	yes	characteristic, complemented
106	#3226	C₂×C₇	1	1	yes	characteristic, complemented
107	#3206	C₂×C₇	1	1	yes	characteristic, complemented
108	#3147	C₂×C₇	1	1	yes	characteristic
109	C₂×#487	C₂×C₇	1	1	yes	characteristic, complemented
110	#1723	C₂×C₇	1	2	yes	complemented
111	#1719	C₂×C₇	1	2	yes	complemented
112	#1717	C₂×C₇	1	2	yes	complemented
113	#1714	C₂×C₇	1	2	yes	complemented
114	#1452	C₂×C₇	1	1	yes	characteristic, complemented
115	C₇×#41	—	4	4	no	—
116	C₇×#41	—	4	4	no	—
117	C₂×C₇×Q₈	—	2	2	no	—
118	C₂×C₇×Q₈	—	2	2	no	—
119	C₂×C₇×Q₈	—	2	1	no	—
120	C₂×C₇×Q₈	—	2	1	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	4	no	—
141	C₇×SD₁₆	—	4	4	no	—
142	C₇×SD₁₆	—	4	4	no	—
143	C₇×SD₁₆	—	8	4	no	—
144	C₇×D₈	—	4	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	2	yes	—
148	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
149	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	—	2	2	no	—
152	C₇×C₄⋊C₄	—	2	2	no	—
153	C₇×C₄⋊C₄	—	2	2	no	—
154	C₇×C₄⋊C₄	—	2	1	no	—
155	C₇×C₄⋊C₄	—	2	1	no	—
156	C₇×C₄⋊C₄	—	2	1	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×#135	—	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	2	yes	—
176	#500	C₂²×C₇	1	2	yes	—
177	#498	C₂²×C₇	1	2	yes	—
178	#495	—	2	2	no	—
179	#494	C₂²×C₇	1	1	yes	characteristic
180	#493	C₂²×C₇	1	1	yes	characteristic
181	#492	C₂²×C₇	1	1	yes	characteristic
182	#492	C₂²×C₇	1	1	yes	characteristic
183	#492	C₂²×C₇	1	2	yes	—
184	#487	—	2	2	no	—
185	#487	C₂²×C₇	1	2	yes	—
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	2	yes	—
190	#486	C₂²×C₇	1	2	yes	—
191	#481	—	2	2	no	—
192	#480	—	2	2	no	—
193	#480	—	2	2	no	—
194	#476	—	2	2	no	—
195	#474	—	2	2	no	—
196	#474	—	2	2	no	—
197	#461	—	2	2	no	—
198	#448	—	2	2	no	—
199	#431	C₂²×C₇	1	1	yes	characteristic
200	#431	C₂²×C₇	1	1	yes	characteristic
201	C₂×#103	—	2	2	no	—
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	2	no	—
209	C₇×Q₈	—	4	2	no	—
210	C₇×Q₈	—	4	4	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	2	no	—
240	C₇×C₈	—	2	2	no	—
241	C₇×C₈	—	2	4	no	—
242	C₇×C₈	—	2	4	no	—
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	#135	—	4	8	no	—
248	C₂×Q₁₆	—	2	2	no	—
249	C₂×SD₁₆	—	2	2	no	—
250	C₂×SD₁₆	—	2	2	no	—
251	C₂×SD₁₆	—	2	4	no	—
252	C₂×D₈	—	2	2	no	—
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	4	no	—
282	#107	—	2	4	no	—
283	#106	—	2	4	no	—
284	C₄⋊C₈	C₇×D₄	1	2	yes	—
285	C₄⋊C₈	C₇×D₄	1	2	yes	—
286	#103	—	2	4	no	—
287	#103	—	2	4	no	—
288	#103	—	2	4	no	—
289	#102	—	2	4	no	—
290	#102	—	2	4	no	—
291	#102	—	2	4	no	—
292	C₂²⋊C₈	C₇×D₄	1	2	yes	—
293	C₂²⋊C₈	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	#577	1	2	yes	—
318	C₄×C₇	#578	1	2	yes	—
319	#41	—	4	4	no	—
320	#41	—	4	4	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	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	4	no	—
345	SD₁₆	—	4	4	no	—
346	SD₁₆	—	4	4	no	—
347	SD₁₆	—	8	4	no	—
348	D₈	—	4	4	no	—
349	C₂×C₈	—	2	4	no	—
350	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
351	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
352	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
353	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	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	#3154	1	1	yes	characteristic
379	C₂×C₇	#3156	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	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	4	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	2	no	—
415	C₈	—	2	2	no	—
416	C₈	—	2	4	no	—
417	C₈	—	2	4	no	—
418	C₇	#19700	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	C₇×#577	1	2	yes	—
438	C₄	C₇×#578	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×#3154	1	1	yes	characteristic
444	C₂	C₇×#3156	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#3147	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×#3227	C₂	semidirect
2. C₇×#3226	C₂	semidirect
3. C₇×#3226	C₂	semidirect
4. C₇×#3206	C₂	semidirect
6. C₂×C₇×#487	C₂	semidirect
7. C₇×#1723	C₂	semidirect
8. C₇×#1719	C₂	semidirect
9. C₇×#1717	C₂	semidirect
10. C₇×#1714	C₂	semidirect
11. C₇×#1452	C₂	semidirect
47. #19700	C₇	direct (N × H)
104. #3227	C₂×C₇	semidirect
105. #3226	C₂×C₇	semidirect
106. #3226	C₂×C₇	semidirect
107. #3206	C₂×C₇	semidirect
109. C₂×#487	C₂×C₇	semidirect
110. #1723	C₂×C₇	semidirect
111. #1719	C₂×C₇	semidirect
112. #1717	C₂×C₇	semidirect
113. #1714	C₂×C₇	semidirect
114. #1452	C₂×C₇	semidirect
418. C₇	#19700	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×#3227	2
C₇×#3226	2
C₇×#3206	2
C₇×#3147	2
C₂×C₇×#487	2
C₇×#1723	2
C₇×#1719	2
C₇×#1717	2
C₇×#1714	2
C₇×#1452	2
#19700	7

Subgroups — C7×#19700 #13196916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19700 #13196916