Subgroups — C₇×#19233 #13196449

Order 1792.

640 conjugacy classes of subgroups.

The subgroup lattice has 434 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×#3227	C₂	1	1	yes	maximal, characteristic
3	C₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2935	C₂	1	1	yes	maximal, characteristic
5	C₇×#1695	C₂	1	2	yes	maximal, complemented
6	C₇×#1691	C₂	1	2	yes	maximal, complemented
7	C₇×#1675	C₂	1	2	yes	maximal, complemented
8	C₇×#1671	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×#333	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×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₇×#501	—	2	2	no	—
17	C₇×#500	C₂²	1	2	yes	—
18	C₇×#498	—	2	1	no	—
19	C₇×#498	C₂²	1	2	yes	—
20	C₇×#486	—	2	1	no	—
21	C₇×#481	—	2	2	no	—
22	C₇×#476	C₂²	1	2	yes	—
23	C₇×#476	C₂²	1	2	yes	—
24	C₇×#476	C₂²	1	2	yes	—
25	C₇×#475	—	2	1	no	—
26	C₇×#465	—	2	2	no	—
27	C₇×#461	C₂²	1	2	yes	—
28	C₇×#460	—	2	1	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	C₇×#428	—	2	1	no	—
34	C₇×#428	—	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×#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×#333	C₂²	1	2	yes	—
42	C₇×#333	C₂²	1	2	yes	—
43	C₇×#333	C₂²	1	1	yes	characteristic
44	C₇×#333	C₂²	1	1	yes	characteristic
45	C₇×#332	C₂²	1	1	yes	characteristic
46	C₇×#332	C₂²	1	1	yes	characteristic
47	#19233	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	C₂×C₇×SD₁₆	—	2	2	no	—
51	C₇×#131	—	4	4	no	—
52	C₂×C₇×M₁₆	—	2	2	no	—
53	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
54	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
55	C₂²×C₇×C₈	—	2	1	no	—
56	C₂²×C₇×C₈	—	2	1	no	—
57	C₂²×C₇×C₈	—	2	2	no	—
58	C₇×C₄⋊Q₈	—	2	1	no	—
59	C₇×C₄⋊Q₈	—	2	1	no	—
60	C₇×C₄⋊Q₈	—	2	1	no	—
61	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
62	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₇×#127	D₄	1	1	yes	characteristic
66	C₇×#125	—	2	1	no	—
67	C₇×#124	—	2	1	no	—
68	C₇×C₂²⋊Q₈	—	2	1	no	—
69	C₇×C₂²⋊Q₈	—	2	1	no	—
70	C₇×#121	—	2	1	no	—
71	C₇×#121	D₄	1	2	yes	—
72	C₄×C₇×Q₈	—	2	1	no	—
73	C₄×C₇×Q₈	—	2	1	no	—
74	C₄×C₇×D₄	—	2	1	no	—
75	C₄×C₇×D₄	C₂³	1	2	yes	—
76	C₇×#117	—	2	1	no	—
77	C₂×C₇×C₄⋊C₄	—	2	1	no	—
78	C₂×C₇×C₄⋊C₄	—	2	1	no	—
79	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
80	C₇×#107	—	2	2	no	—
81	C₇×#107	—	2	2	no	—
82	C₇×#106	—	2	2	no	—
83	C₇×#106	—	2	2	no	—
84	C₇×#106	—	2	2	no	—
85	C₇×#106	—	2	2	no	—
86	C₇×#106	—	2	2	no	—
87	C₇×C₄⋊C₈	—	2	1	no	—
88	C₇×C₄⋊C₈	—	2	1	no	—
89	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
90	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₇×C₄⋊C₈	C₂³	1	2	yes	—
92	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
93	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
94	C₇×#103	—	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
105	#3227	C₂×C₇	1	1	yes	characteristic
106	#3165	C₂×C₇	1	1	yes	characteristic, complemented
107	#2935	C₂×C₇	1	1	yes	characteristic
108	#1695	C₂×C₇	1	2	yes	complemented
109	#1691	C₂×C₇	1	2	yes	complemented
110	#1675	C₂×C₇	1	2	yes	complemented
111	#1671	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×#333	C₂×C₇	1	1	yes	characteristic, complemented
115	C₇×#41	—	4	2	no	—
116	C₇×#41	—	4	2	no	—
117	C₂×C₇×Q₈	—	2	1	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	—	8	2	no	—
123	C₂×C₇×D₄	—	2	2	no	—
124	C₂×C₇×D₄	—	2	1	no	—
125	C₂×C₇×D₄	—	2	1	no	—
126	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₇	—	2	2	no	—
128	C₂²×C₄×C₇	—	4	1	no	—
129	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇	#41	1	1	yes	characteristic
132	C₇×SD₁₆	—	8	2	no	—
133	C₇×M₁₆	—	2	2	no	—
134	C₇×M₁₆	—	4	4	no	—
135	C₇×M₁₆	SD₁₆	1	4	yes	complemented
136	C₂×C₇×C₈	—	2	1	no	—
137	C₂×C₇×C₈	—	2	1	no	—
138	C₂×C₇×C₈	—	2	1	no	—
139	C₂×C₇×C₈	—	2	1	no	—
140	C₂×C₇×C₈	—	2	2	no	—
141	C₂×C₇×C₈	—	4	2	no	—
142	C₂×C₇×C₈	—	4	4	no	—
143	C₂×C₇×C₈	—	8	1	no	—
144	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
145	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
146	C₇×C₄⋊C₄	—	2	1	no	—
147	C₇×C₄⋊C₄	—	2	2	no	—
148	C₇×C₄⋊C₄	—	2	1	no	—
149	C₇×C₄⋊C₄	—	2	1	no	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	—	2	1	no	—
152	C₇×C₄⋊C₄	—	2	1	no	—
153	C₇×C₄⋊C₄	—	4	1	no	—
154	C₇×C₄⋊C₄	—	4	1	no	—
155	C₇×C₄⋊C₄	—	4	1	no	—
156	C₇×C₄⋊C₄	—	4	1	no	—
157	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
158	C₇×C₂²⋊C₄	—	2	2	no	—
159	C₇×C₂²⋊C₄	—	2	2	no	—
160	C₇×C₂²⋊C₄	—	4	1	no	—
161	C₄²×C₇	—	4	1	no	—
162	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₇	#41	1	1	yes	characteristic
165	C₄²×C₇	C₂⁴	1	1	yes	characteristic
166	C₂×#131	—	2	1	no	—
167	#533	C₂²×C₇	1	1	yes	characteristic
168	#532	C₂²×C₇	1	1	yes	characteristic
169	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
170	#501	—	2	2	no	—
171	#500	C₂²×C₇	1	2	yes	—
172	#498	—	2	1	no	—
173	#498	C₂²×C₇	1	2	yes	—
174	#486	—	2	1	no	—
175	#481	—	2	2	no	—
176	#476	C₂²×C₇	1	2	yes	—
177	#476	C₂²×C₇	1	2	yes	—
178	#476	C₂²×C₇	1	2	yes	—
179	#475	—	2	1	no	—
180	#465	—	2	2	no	—
181	#461	C₂²×C₇	1	2	yes	—
182	#460	—	2	1	no	—
183	#436	C₂²×C₇	1	2	yes	—
184	#435	—	2	2	no	—
185	C₈×D₄	C₂²×C₇	1	2	yes	—
186	#431	C₂²×C₇	1	1	yes	characteristic
187	#428	—	2	1	no	—
188	#428	—	2	1	no	—
189	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
190	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
191	#408	—	2	1	no	—
192	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
193	#335	C₂²×C₇	1	2	yes	—
194	#334	C₂²×C₇	1	2	yes	—
195	#333	C₂²×C₇	1	2	yes	—
196	#333	C₂²×C₇	1	2	yes	—
197	#333	C₂²×C₇	1	1	yes	characteristic
198	#333	C₂²×C₇	1	1	yes	characteristic
199	#332	C₂²×C₇	1	1	yes	characteristic
200	#332	C₂²×C₇	1	1	yes	characteristic
201	C₂³×C₇	—	2	2	no	—
202	C₂³×C₇	#121	1	1	yes	characteristic
203	C₇×Q₈	—	4	2	no	—
204	C₇×Q₈	—	4	1	no	—
205	C₇×Q₈	—	4	1	no	—
206	C₇×Q₈	—	8	1	no	—
207	C₇×Q₈	—	8	2	no	—
208	C₇×Q₈	—	8	2	no	—
209	C₇×D₄	—	2	2	no	—
210	C₇×D₄	—	2	2	no	—
211	C₇×D₄	—	4	4	no	—
212	C₇×D₄	—	4	2	no	—
213	C₇×D₄	—	8	1	no	—
214	C₂×C₄×C₇	—	2	1	no	—
215	C₂×C₄×C₇	—	2	1	no	—
216	C₂×C₄×C₇	—	2	2	no	—
217	C₂×C₄×C₇	—	4	1	no	—
218	C₂×C₄×C₇	—	4	2	no	—
219	C₂×C₄×C₇	—	4	2	no	—
220	C₂×C₄×C₇	—	4	1	no	—
221	C₂×C₄×C₇	—	4	1	no	—
222	C₂×C₄×C₇	—	4	2	no	—
223	C₂×C₄×C₇	—	8	2	no	—
224	C₂×C₄×C₇	#121	1	1	yes	characteristic
225	C₂×C₄×C₇	#121	1	1	yes	characteristic
226	C₂×C₄×C₇	#121	1	1	yes	characteristic
227	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
228	C₂×C₄×C₇	#137	1	2	yes	—
229	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
232	C₇×C₈	—	2	2	no	—
233	C₇×C₈	—	4	1	no	—
234	C₇×C₈	—	4	1	no	—
235	C₇×C₈	—	4	1	no	—
236	C₇×C₈	—	4	2	no	—
237	C₇×C₈	—	4	1	no	—
238	C₇×C₈	C₂×SD₁₆	1	4	yes	—
239	C₂×#41	—	2	1	no	—
240	C₂²×Q₈	—	2	1	no	—
241	C₂×SD₁₆	—	2	2	no	—
242	#131	—	4	4	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
245	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
253	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
254	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
255	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
256	#127	C₇×D₄	1	1	yes	characteristic
257	#125	—	2	1	no	—
258	#124	—	2	1	no	—
259	C₂²⋊Q₈	—	2	1	no	—
260	C₂²⋊Q₈	—	2	1	no	—
261	#121	—	2	1	no	—
262	#121	C₇×D₄	1	2	yes	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×Q₈	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	C₂³×C₇	1	2	yes	—
267	#117	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
271	#107	—	2	2	no	—
272	#107	—	2	2	no	—
273	#106	—	2	2	no	—
274	#106	—	2	2	no	—
275	#106	—	2	2	no	—
276	#106	—	2	2	no	—
277	#106	—	2	2	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
281	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
282	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
283	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
284	C₄⋊C₈	C₂³×C₇	1	2	yes	—
285	#103	—	2	2	no	—
286	#102	—	2	2	no	—
287	#102	—	2	2	no	—
288	#102	—	2	2	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	2	2	no	—
291	C₂²⋊C₈	—	2	2	no	—
292	#97	C₇×D₄	1	2	yes	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	C₂³×C₇	1	2	yes	—
295	C₂²×C₇	—	2	1	no	—
296	C₂²×C₇	—	2	1	no	—
297	C₂²×C₇	—	4	2	no	—
298	C₂²×C₇	—	4	2	no	—
299	C₂²×C₇	—	4	2	no	—
300	C₂²×C₇	#461	1	2	yes	—
301	C₂²×C₇	C₂×#121	1	1	yes	characteristic
302	C₄×C₇	—	2	1	no	—
303	C₄×C₇	—	2	1	no	—
304	C₄×C₇	—	2	1	no	—
305	C₄×C₇	—	4	2	no	—
306	C₄×C₇	—	8	1	no	—
307	C₄×C₇	—	8	2	no	—
308	C₄×C₇	—	8	1	no	—
309	C₄×C₇	#461	1	2	yes	—
310	C₄×C₇	C₂²×SD₁₆	1	1	yes	characteristic
311	C₄×C₇	C₂×#137	1	1	yes	characteristic
312	C₄×C₇	#577	1	1	yes	characteristic
313	C₄×C₇	#578	1	1	yes	characteristic
314	#41	—	4	2	no	—
315	#41	—	4	2	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	4	1	no	—
321	C₂×Q₈	—	8	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
330	C₂²×C₄	C₇×#41	1	1	yes	characteristic
331	SD₁₆	—	8	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	4	4	no	—
334	M₁₆	C₇×SD₁₆	1	4	yes	complemented
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	4	2	no	—
341	C₂×C₈	—	4	4	no	—
342	C₂×C₈	—	8	1	no	—
343	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
344	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₄²	—	4	1	no	—
361	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
362	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
363	C₄²	C₇×#41	1	1	yes	characteristic
364	C₄²	C₂⁴×C₇	1	1	yes	characteristic
365	C₂×C₇	—	2	2	no	—
366	C₂×C₇	—	8	2	no	—
367	C₂×C₇	C₂×#461	1	1	yes	characteristic
368	C₂×C₇	#3063	1	1	yes	characteristic
369	C₂×C₇	#3068	1	1	yes	characteristic
370	C₂³	—	2	2	no	—
371	C₂³	C₇×#121	1	1	yes	characteristic
372	Q₈	—	4	2	no	—
373	Q₈	—	4	1	no	—
374	Q₈	—	4	1	no	—
375	Q₈	—	8	1	no	—
376	Q₈	—	8	2	no	—
377	Q₈	—	8	2	no	—
378	D₄	—	2	2	no	—
379	D₄	—	2	2	no	—
380	D₄	—	4	4	no	—
381	D₄	—	4	2	no	—
382	D₄	—	8	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	C₇×#121	1	1	yes	characteristic
394	C₂×C₄	C₇×#121	1	1	yes	characteristic
395	C₂×C₄	C₇×#121	1	1	yes	characteristic
396	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
397	C₂×C₄	C₇×#137	1	2	yes	—
398	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
400	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
401	C₈	—	2	2	no	—
402	C₈	—	4	1	no	—
403	C₈	—	4	1	no	—
404	C₈	—	4	1	no	—
405	C₈	—	4	2	no	—
406	C₈	—	4	1	no	—
407	C₈	C₂×C₇×SD₁₆	1	4	yes	—
408	C₇	#19233	1	1	yes	characteristic, direct product factor, Sylow
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	C₇×#461	1	2	yes	—
415	C₂²	C₂×C₇×#121	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	4	2	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	1	no	—
423	C₄	C₇×#461	1	2	yes	—
424	C₄	C₂²×C₇×SD₁₆	1	1	yes	characteristic
425	C₄	C₂×C₇×#137	1	1	yes	characteristic
426	C₄	C₇×#577	1	1	yes	characteristic
427	C₄	C₇×#578	1	1	yes	characteristic
428	C₂	—	2	2	no	—
429	C₂	—	8	2	no	—
430	C₂	C₂×C₇×#461	1	1	yes	characteristic
431	C₂	C₇×#3063	1	1	yes	characteristic
432	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×#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
3. C₇×#3165	C₂	semidirect
5. C₇×#1695	C₂	semidirect
6. C₇×#1691	C₂	semidirect
7. C₇×#1675	C₂	semidirect
8. C₇×#1671	C₂	semidirect
9. C₇×#1565	C₂	semidirect
10. C₇×#1542	C₂	semidirect
11. C₂×C₇×#333	C₂	semidirect
47. #19233	C₇	direct (N × H)
106. #3165	C₂×C₇	semidirect
108. #1695	C₂×C₇	semidirect
109. #1691	C₂×C₇	semidirect
110. #1675	C₂×C₇	semidirect
111. #1671	C₂×C₇	semidirect
112. #1565	C₂×C₇	semidirect
113. #1542	C₂×C₇	semidirect
114. C₂×#333	C₂×C₇	semidirect
135. C₇×M₁₆	SD₁₆	semidirect
334. M₁₆	C₇×SD₁₆	semidirect
408. C₇	#19233	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×#3227	2
C₇×#3165	2
C₇×#2935	2
C₇×#1695	2
C₇×#1691	2
C₇×#1675	2
C₇×#1671	2
C₇×#1565	2
C₇×#1542	2
C₂×C₇×#333	2
#19233	7

Subgroups — C7×#19233 #13196449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19233 #13196449