Subgroups — C₇×#19232 #13196448

Order 1792.

652 conjugacy classes of subgroups.

The subgroup lattice has 442 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×#3206	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×#1693	C₂	1	2	yes	maximal, complemented
6	C₇×#1691	C₂	1	2	yes	maximal, complemented
7	C₇×#1673	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×#332	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	C₂²	1	2	yes	—
19	C₇×#492	—	2	1	no	—
20	C₇×#487	—	2	1	no	—
21	C₇×#476	C₂²	1	2	yes	—
22	C₇×#475	—	2	1	no	—
23	C₇×#465	—	2	2	no	—
24	C₇×#461	C₂²	1	2	yes	—
25	C₇×#461	C₂²	1	2	yes	—
26	C₇×#461	C₂²	1	2	yes	—
27	C₇×#460	—	2	1	no	—
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	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	1	yes	characteristic
42	C₇×#333	C₂²	1	1	yes	characteristic
43	C₇×#332	C₂²	1	2	yes	—
44	C₇×#332	C₂²	1	2	yes	—
45	C₇×#332	C₂²	1	1	yes	characteristic
46	C₇×#332	C₂²	1	1	yes	characteristic
47	#19232	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	C₂×C₇×SD₁₆	—	2	2	no	—
52	C₂×C₇×SD₁₆	—	2	2	no	—
53	C₇×#131	—	4	4	no	—
54	C₂×C₇×M₁₆	—	2	2	no	—
55	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
56	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
57	C₂²×C₇×C₈	—	2	1	no	—
58	C₂²×C₇×C₈	—	2	1	no	—
59	C₂²×C₇×C₈	—	2	2	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	D₄	1	1	yes	characteristic
64	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₇×#127	D₄	1	1	yes	characteristic
68	C₇×#125	—	2	1	no	—
69	C₇×#124	—	2	1	no	—
70	C₇×C₂²⋊Q₈	—	2	1	no	—
71	C₇×C₂²⋊Q₈	—	2	1	no	—
72	C₇×#121	—	2	1	no	—
73	C₇×#121	D₄	1	2	yes	—
74	C₄×C₇×Q₈	—	2	1	no	—
75	C₄×C₇×Q₈	—	2	1	no	—
76	C₄×C₇×D₄	—	2	1	no	—
77	C₄×C₇×D₄	C₂³	1	2	yes	—
78	C₇×#117	—	2	1	no	—
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×#107	—	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	2	yes	—
90	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#103	—	2	2	no	—
96	C₇×#103	—	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	#3206	C₂×C₇	1	1	yes	characteristic
106	#3165	C₂×C₇	1	1	yes	characteristic, complemented
107	#2935	C₂×C₇	1	1	yes	characteristic
108	#1693	C₂×C₇	1	2	yes	complemented
109	#1691	C₂×C₇	1	2	yes	complemented
110	#1673	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×#332	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	2	no	—
120	C₂×C₇×Q₈	—	2	1	no	—
121	C₂×C₇×Q₈	—	4	1	no	—
122	C₂×C₇×Q₈	—	8	1	no	—
123	C₂×C₇×Q₈	—	8	1	no	—
124	C₂×C₇×D₄	—	2	2	no	—
125	C₂×C₇×D₄	—	2	1	no	—
126	C₂×C₇×D₄	—	2	1	no	—
127	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₇	—	2	2	no	—
129	C₂²×C₄×C₇	—	4	1	no	—
130	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇	#41	1	1	yes	characteristic
133	C₇×SD₁₆	—	8	2	no	—
134	C₇×SD₁₆	—	8	2	no	—
135	C₇×SD₁₆	—	8	2	no	—
136	C₇×M₁₆	—	2	2	no	—
137	C₇×M₁₆	—	4	4	no	—
138	C₇×M₁₆	SD₁₆	1	4	yes	complemented
139	C₂×C₇×C₈	—	2	1	no	—
140	C₂×C₇×C₈	—	2	1	no	—
141	C₂×C₇×C₈	—	2	1	no	—
142	C₂×C₇×C₈	—	2	1	no	—
143	C₂×C₇×C₈	—	2	2	no	—
144	C₂×C₇×C₈	—	4	2	no	—
145	C₂×C₇×C₈	—	4	4	no	—
146	C₂×C₇×C₈	—	8	1	no	—
147	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
148	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
149	C₇×C₄⋊C₄	—	2	1	no	—
150	C₇×C₄⋊C₄	—	2	1	no	—
151	C₇×C₄⋊C₄	—	2	1	no	—
152	C₇×C₄⋊C₄	—	2	2	no	—
153	C₇×C₄⋊C₄	—	2	1	no	—
154	C₇×C₄⋊C₄	—	2	2	no	—
155	C₇×C₄⋊C₄	—	2	1	no	—
156	C₇×C₄⋊C₄	—	4	1	no	—
157	C₇×C₄⋊C₄	—	4	1	no	—
158	C₇×C₄⋊C₄	—	4	1	no	—
159	C₇×C₄⋊C₄	—	4	1	no	—
160	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
161	C₇×C₂²⋊C₄	—	2	2	no	—
162	C₇×C₂²⋊C₄	—	2	2	no	—
163	C₇×C₂²⋊C₄	—	4	1	no	—
164	C₄²×C₇	—	4	1	no	—
165	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₇	#41	1	1	yes	characteristic
168	C₄²×C₇	C₂⁴	1	1	yes	characteristic
169	C₂×#131	—	2	1	no	—
170	#533	C₂²×C₇	1	1	yes	characteristic
171	#532	C₂²×C₇	1	1	yes	characteristic
172	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
173	#501	—	2	2	no	—
174	#500	C₂²×C₇	1	2	yes	—
175	#498	C₂²×C₇	1	2	yes	—
176	#492	—	2	1	no	—
177	#487	—	2	1	no	—
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	#461	C₂²×C₇	1	2	yes	—
183	#461	C₂²×C₇	1	2	yes	—
184	#460	—	2	1	no	—
185	#448	—	2	2	no	—
186	#436	C₂²×C₇	1	2	yes	—
187	#435	—	2	2	no	—
188	C₈×D₄	C₂²×C₇	1	2	yes	—
189	#431	C₂²×C₇	1	1	yes	characteristic
190	#428	—	2	1	no	—
191	#428	—	2	1	no	—
192	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
193	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
194	#408	—	2	1	no	—
195	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
196	#335	C₂²×C₇	1	2	yes	—
197	#334	C₂²×C₇	1	2	yes	—
198	#333	C₂²×C₇	1	1	yes	characteristic
199	#333	C₂²×C₇	1	1	yes	characteristic
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	C₂³×C₇	—	2	2	no	—
205	C₂³×C₇	#121	1	1	yes	characteristic
206	C₇×Q₈	—	4	2	no	—
207	C₇×Q₈	—	4	1	no	—
208	C₇×Q₈	—	4	2	no	—
209	C₇×Q₈	—	4	2	no	—
210	C₇×Q₈	—	4	1	no	—
211	C₇×Q₈	—	8	1	no	—
212	C₇×Q₈	—	8	2	no	—
213	C₇×D₄	—	2	2	no	—
214	C₇×D₄	—	2	2	no	—
215	C₇×D₄	—	4	4	no	—
216	C₇×D₄	—	4	2	no	—
217	C₇×D₄	—	8	1	no	—
218	C₂×C₄×C₇	—	2	1	no	—
219	C₂×C₄×C₇	—	2	1	no	—
220	C₂×C₄×C₇	—	2	2	no	—
221	C₂×C₄×C₇	—	4	1	no	—
222	C₂×C₄×C₇	—	4	2	no	—
223	C₂×C₄×C₇	—	4	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	—	8	2	no	—
228	C₂×C₄×C₇	#121	1	1	yes	characteristic
229	C₂×C₄×C₇	#121	1	1	yes	characteristic
230	C₂×C₄×C₇	#121	1	1	yes	characteristic
231	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
232	C₂×C₄×C₇	#137	1	2	yes	—
233	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
236	C₇×C₈	—	2	2	no	—
237	C₇×C₈	—	4	1	no	—
238	C₇×C₈	—	4	1	no	—
239	C₇×C₈	—	4	2	no	—
240	C₇×C₈	—	4	1	no	—
241	C₇×C₈	—	4	1	no	—
242	C₇×C₈	C₂×SD₁₆	1	4	yes	—
243	C₂×#41	—	2	1	no	—
244	C₂²×Q₈	—	2	1	no	—
245	C₂×SD₁₆	—	2	2	no	—
246	C₂×SD₁₆	—	2	2	no	—
247	C₂×SD₁₆	—	2	2	no	—
248	#131	—	4	4	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
251	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
259	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
260	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
261	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
262	#127	C₇×D₄	1	1	yes	characteristic
263	#125	—	2	1	no	—
264	#124	—	2	1	no	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	—	2	1	no	—
267	#121	—	2	1	no	—
268	#121	C₇×D₄	1	2	yes	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×Q₈	—	2	1	no	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	C₂³×C₇	1	2	yes	—
273	#117	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
277	#107	—	2	2	no	—
278	#107	—	2	2	no	—
279	#106	—	2	2	no	—
280	#106	—	2	2	no	—
281	#106	—	2	2	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
285	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
286	C₄⋊C₈	C₂³×C₇	1	2	yes	—
287	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
288	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
289	#103	—	2	2	no	—
290	#103	—	2	2	no	—
291	#103	—	2	2	no	—
292	#102	—	2	2	no	—
293	C₂²⋊C₈	—	2	1	no	—
294	C₂²⋊C₈	—	2	2	no	—
295	C₂²⋊C₈	—	2	2	no	—
296	#97	C₇×D₄	1	2	yes	—
297	C₄×C₈	—	2	1	no	—
298	C₄×C₈	C₂³×C₇	1	2	yes	—
299	C₂²×C₇	—	2	1	no	—
300	C₂²×C₇	—	2	1	no	—
301	C₂²×C₇	—	4	2	no	—
302	C₂²×C₇	—	4	2	no	—
303	C₂²×C₇	—	4	2	no	—
304	C₂²×C₇	#461	1	2	yes	—
305	C₂²×C₇	C₂×#121	1	1	yes	characteristic
306	C₄×C₇	—	2	1	no	—
307	C₄×C₇	—	2	1	no	—
308	C₄×C₇	—	2	1	no	—
309	C₄×C₇	—	4	2	no	—
310	C₄×C₇	—	8	2	no	—
311	C₄×C₇	—	8	1	no	—
312	C₄×C₇	—	8	1	no	—
313	C₄×C₇	#461	1	2	yes	—
314	C₄×C₇	C₂²×SD₁₆	1	1	yes	characteristic
315	C₄×C₇	C₂×#137	1	1	yes	characteristic
316	C₄×C₇	#576	1	1	yes	characteristic
317	C₄×C₇	#577	1	1	yes	characteristic
318	#41	—	4	2	no	—
319	#41	—	4	2	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	4	1	no	—
325	C₂×Q₈	—	8	1	no	—
326	C₂×Q₈	—	8	1	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
335	C₂²×C₄	C₇×#41	1	1	yes	characteristic
336	SD₁₆	—	8	2	no	—
337	SD₁₆	—	8	2	no	—
338	SD₁₆	—	8	2	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	4	4	no	—
341	M₁₆	C₇×SD₁₆	1	4	yes	complemented
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	4	2	no	—
348	C₂×C₈	—	4	4	no	—
349	C₂×C₈	—	8	1	no	—
350	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
351	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₄²	—	4	1	no	—
368	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
369	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
370	C₄²	C₇×#41	1	1	yes	characteristic
371	C₄²	C₂⁴×C₇	1	1	yes	characteristic
372	C₂×C₇	—	2	2	no	—
373	C₂×C₇	—	8	2	no	—
374	C₂×C₇	C₂×#461	1	1	yes	characteristic
375	C₂×C₇	#3062	1	1	yes	characteristic
376	C₂×C₇	#3069	1	1	yes	characteristic
377	C₂³	—	2	2	no	—
378	C₂³	C₇×#121	1	1	yes	characteristic
379	Q₈	—	4	2	no	—
380	Q₈	—	4	1	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	4	1	no	—
384	Q₈	—	8	1	no	—
385	Q₈	—	8	2	no	—
386	D₄	—	2	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	2	no	—
390	D₄	—	8	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	C₇×#121	1	1	yes	characteristic
402	C₂×C₄	C₇×#121	1	1	yes	characteristic
403	C₂×C₄	C₇×#121	1	1	yes	characteristic
404	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
405	C₂×C₄	C₇×#137	1	2	yes	—
406	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
407	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
408	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	4	1	no	—
411	C₈	—	4	1	no	—
412	C₈	—	4	2	no	—
413	C₈	—	4	1	no	—
414	C₈	—	4	1	no	—
415	C₈	C₂×C₇×SD₁₆	1	4	yes	—
416	C₇	#19232	1	1	yes	characteristic, direct product factor, Sylow
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	C₇×#461	1	2	yes	—
423	C₂²	C₂×C₇×#121	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	4	2	no	—
428	C₄	—	8	2	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	1	no	—
431	C₄	C₇×#461	1	2	yes	—
432	C₄	C₂²×C₇×SD₁₆	1	1	yes	characteristic
433	C₄	C₂×C₇×#137	1	1	yes	characteristic
434	C₄	C₇×#576	1	1	yes	characteristic
435	C₄	C₇×#577	1	1	yes	characteristic
436	C₂	—	2	2	no	—
437	C₂	—	8	2	no	—
438	C₂	C₂×C₇×#461	1	1	yes	characteristic
439	C₂	C₇×#3062	1	1	yes	characteristic
440	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
3. C₇×#3165	C₂	semidirect
5. C₇×#1693	C₂	semidirect
6. C₇×#1691	C₂	semidirect
7. C₇×#1673	C₂	semidirect
8. C₇×#1671	C₂	semidirect
9. C₇×#1565	C₂	semidirect
10. C₇×#1542	C₂	semidirect
11. C₂×C₇×#332	C₂	semidirect
47. #19232	C₇	direct (N × H)
106. #3165	C₂×C₇	semidirect
108. #1693	C₂×C₇	semidirect
109. #1691	C₂×C₇	semidirect
110. #1673	C₂×C₇	semidirect
111. #1671	C₂×C₇	semidirect
112. #1565	C₂×C₇	semidirect
113. #1542	C₂×C₇	semidirect
114. C₂×#332	C₂×C₇	semidirect
138. C₇×M₁₆	SD₁₆	semidirect
341. M₁₆	C₇×SD₁₆	semidirect
416. C₇	#19232	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×#3206	2
C₇×#3165	2
C₇×#2935	2
C₇×#1693	2
C₇×#1691	2
C₇×#1673	2
C₇×#1671	2
C₇×#1565	2
C₇×#1542	2
C₂×C₇×#332	2
#19232	7

Subgroups — C7×#19232 #13196448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19232 #13196448