Subgroups — C₇×#19236 #13196452

Order 1792.

662 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3245	C₂	1	1	yes	maximal, characteristic
2	C₇×#3227	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1703	C₂	1	2	yes	maximal, complemented
6	C₇×#1697	C₂	1	2	yes	maximal, complemented
7	C₇×#1683	C₂	1	2	yes	maximal, complemented
8	C₇×#1677	C₂	1	2	yes	maximal, complemented
9	C₇×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#333	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1540	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#131	—	2	1	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	C₇×#498	—	2	1	no	—
17	C₇×#489	—	2	2	no	—
18	C₇×#487	C₂²	1	2	yes	—
19	C₇×#486	—	2	1	no	—
20	C₇×#486	C₂²	1	2	yes	—
21	C₇×#481	—	2	2	no	—
22	C₇×#476	C₂²	1	2	yes	—
23	C₇×#476	C₂²	1	2	yes	—
24	C₇×#474	—	2	1	no	—
25	C₇×#474	C₂²	1	2	yes	—
26	C₇×#466	—	2	2	no	—
27	C₇×#459	—	2	1	no	—
28	C₇×#459	C₂²	1	2	yes	—
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	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₇×#417	—	2	1	no	—
36	C₇×#417	—	2	1	no	—
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×#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	#19236	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	C₂×C₇×D₈	—	2	2	no	—
52	C₇×#131	—	4	4	no	—
53	C₂×C₇×M₁₆	—	2	2	no	—
54	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
55	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
56	C₂²×C₇×C₈	—	2	1	no	—
57	C₂²×C₇×C₈	—	2	1	no	—
58	C₂²×C₇×C₈	—	2	2	no	—
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	D₄	1	1	yes	characteristic
63	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₇×#127	D₄	1	1	yes	characteristic
66	C₇×#127	C₂³	1	1	yes	characteristic
67	C₇×#124	—	2	1	no	—
68	C₇×#124	—	2	1	no	—
69	C₇×#121	—	2	1	no	—
70	C₇×#121	—	2	1	no	—
71	C₇×#121	—	2	1	no	—
72	C₇×#121	D₄	1	2	yes	—
73	C₄×C₇×D₄	—	2	1	no	—
74	C₄×C₇×D₄	—	2	1	no	—
75	C₄×C₇×D₄	—	2	1	no	—
76	C₄×C₇×D₄	C₂³	1	2	yes	—
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×#106	—	2	2	no	—
82	C₇×#106	—	2	2	no	—
83	C₇×C₄⋊C₈	—	2	1	no	—
84	C₇×C₄⋊C₈	—	2	1	no	—
85	C₇×C₄⋊C₈	C₂³	1	2	yes	—
86	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
89	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
90	C₇×#103	—	2	2	no	—
91	C₇×#103	—	2	2	no	—
92	C₇×#102	—	2	2	no	—
93	C₇×#102	—	2	2	no	—
94	C₇×#102	—	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	#3245	C₂×C₇	1	1	yes	characteristic
105	#3227	C₂×C₇	1	1	yes	characteristic, complemented
106	#3141	C₂×C₇	1	1	yes	characteristic, complemented
107	#2935	C₂×C₇	1	1	yes	characteristic, complemented
108	#1703	C₂×C₇	1	2	yes	complemented
109	#1697	C₂×C₇	1	2	yes	complemented
110	#1683	C₂×C₇	1	2	yes	complemented
111	#1677	C₂×C₇	1	2	yes	complemented
112	#1565	C₂×C₇	1	1	yes	characteristic, complemented
113	C₂×#333	C₂×C₇	1	1	yes	characteristic, complemented
114	#1540	C₂×C₇	1	1	yes	characteristic, complemented
115	C₇×#41	—	4	2	no	—
116	C₇×#41	—	4	2	no	—
117	C₇×#41	—	4	2	no	—
118	C₇×#41	—	4	2	no	—
119	C₂×C₇×Q₈	—	2	1	no	—
120	C₂×C₇×Q₈	—	2	1	no	—
121	C₂×C₇×Q₈	—	2	2	no	—
122	C₂×C₇×Q₈	—	4	1	no	—
123	C₂×C₇×Q₈	—	8	2	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	—	2	1	no	—
128	C₂×C₇×D₄	—	2	1	no	—
129	C₂×C₇×D₄	—	2	1	no	—
130	C₂×C₇×D₄	—	4	1	no	—
131	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₇	—	2	2	no	—
133	C₂²×C₄×C₇	—	4	1	no	—
134	C₂²×C₄×C₇	—	4	1	no	—
135	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇	#41	1	1	yes	characteristic
138	C₇×D₈	—	8	2	no	—
139	C₇×M₁₆	—	2	2	no	—
140	C₇×M₁₆	—	2	2	no	—
141	C₇×M₁₆	—	4	4	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	1	no	—
146	C₂×C₇×C₈	—	2	2	no	—
147	C₂×C₇×C₈	—	4	4	no	—
148	C₂×C₇×C₈	—	4	2	no	—
149	C₂×C₇×C₈	—	8	1	no	—
150	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
151	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
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	1	no	—
156	C₇×C₄⋊C₄	—	2	1	no	—
157	C₇×C₄⋊C₄	—	4	1	no	—
158	C₇×C₄⋊C₄	—	4	1	no	—
159	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
160	C₇×C₂²⋊C₄	—	2	2	no	—
161	C₇×C₂²⋊C₄	—	2	2	no	—
162	C₇×C₂²⋊C₄	—	4	1	no	—
163	C₇×C₂²⋊C₄	—	4	1	no	—
164	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₇	#41	1	1	yes	characteristic
167	C₄²×C₇	C₂⁴	1	1	yes	characteristic
168	C₂×#131	—	2	1	no	—
169	#532	C₂²×C₇	1	1	yes	characteristic
170	#532	C₂²×C₇	1	1	yes	characteristic
171	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
172	#498	—	2	1	no	—
173	#489	—	2	2	no	—
174	#487	C₂²×C₇	1	2	yes	—
175	#486	—	2	1	no	—
176	#486	C₂²×C₇	1	2	yes	—
177	#481	—	2	2	no	—
178	#476	C₂²×C₇	1	2	yes	—
179	#476	C₂²×C₇	1	2	yes	—
180	#474	—	2	1	no	—
181	#474	C₂²×C₇	1	2	yes	—
182	#466	—	2	2	no	—
183	#459	—	2	1	no	—
184	#459	C₂²×C₇	1	2	yes	—
185	#436	C₂²×C₇	1	2	yes	—
186	#435	—	2	2	no	—
187	C₈×D₄	C₂²×C₇	1	2	yes	—
188	#431	C₂²×C₇	1	1	yes	characteristic
189	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
190	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
191	#417	—	2	1	no	—
192	#417	—	2	1	no	—
193	#408	—	2	1	no	—
194	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
195	#335	C₂²×C₇	1	2	yes	—
196	#334	C₂²×C₇	1	2	yes	—
197	#333	C₂²×C₇	1	2	yes	—
198	#333	C₂²×C₇	1	2	yes	—
199	#332	C₂²×C₇	1	1	yes	characteristic
200	#332	C₂²×C₇	1	1	yes	characteristic
201	#331	C₂²×C₇	1	1	yes	characteristic
202	#331	C₂²×C₇	1	1	yes	characteristic
203	C₂³×C₇	—	2	2	no	—
204	C₂³×C₇	—	4	1	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	1	no	—
209	C₇×Q₈	—	8	2	no	—
210	C₇×Q₈	—	8	2	no	—
211	C₇×D₄	—	2	2	no	—
212	C₇×D₄	—	2	2	no	—
213	C₇×D₄	—	4	4	no	—
214	C₇×D₄	—	4	1	no	—
215	C₇×D₄	—	4	1	no	—
216	C₇×D₄	—	4	1	no	—
217	C₇×D₄	—	4	1	no	—
218	C₇×D₄	—	4	2	no	—
219	C₇×D₄	—	8	1	no	—
220	C₇×D₄	—	8	1	no	—
221	C₇×D₄	—	8	2	no	—
222	C₂×C₄×C₇	—	2	1	no	—
223	C₂×C₄×C₇	—	2	1	no	—
224	C₂×C₄×C₇	—	2	2	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	—	4	1	no	—
229	C₂×C₄×C₇	—	4	2	no	—
230	C₂×C₄×C₇	—	8	2	no	—
231	C₂×C₄×C₇	—	8	2	no	—
232	C₂×C₄×C₇	#121	1	1	yes	characteristic
233	C₂×C₄×C₇	#121	1	1	yes	characteristic
234	C₂×C₄×C₇	#121	1	1	yes	characteristic
235	C₂×C₄×C₇	#135	1	2	yes	—
236	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
237	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
240	C₇×C₈	—	2	2	no	—
241	C₇×C₈	—	2	2	no	—
242	C₇×C₈	—	4	1	no	—
243	C₇×C₈	—	4	1	no	—
244	C₇×C₈	—	4	1	no	—
245	C₇×C₈	—	4	2	no	—
246	C₇×C₈	—	4	1	no	—
247	C₂×#41	—	2	1	no	—
248	C₂×#41	—	2	1	no	—
249	C₂²×Q₈	—	2	1	no	—
250	C₂×D₈	—	2	2	no	—
251	#131	—	4	4	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
254	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
255	C₂²×C₈	—	2	1	no	—
256	C₂²×C₈	—	2	1	no	—
257	C₂²×C₈	—	2	2	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	C₂³×C₇	1	2	yes	—
263	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
264	#127	C₇×D₄	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	C₇×D₄	1	2	yes	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	C₂³×C₇	1	2	yes	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
279	#107	—	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	1	yes	characteristic
287	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
288	C₄⋊C₈	C₂³×C₇	1	2	yes	—
289	#103	—	2	2	no	—
290	#103	—	2	2	no	—
291	#102	—	2	2	no	—
292	#102	—	2	2	no	—
293	#102	—	2	2	no	—
294	#102	—	2	2	no	—
295	#102	—	2	2	no	—
296	#102	—	2	2	no	—
297	C₂²⋊C₈	—	2	1	no	—
298	C₂²⋊C₈	—	2	2	no	—
299	C₂²⋊C₈	—	2	2	no	—
300	#97	C₇×D₄	1	2	yes	—
301	C₄×C₈	—	2	1	no	—
302	C₄×C₈	C₂³×C₇	1	2	yes	—
303	C₂²×C₇	—	2	1	no	—
304	C₂²×C₇	—	2	1	no	—
305	C₂²×C₇	—	4	2	no	—
306	C₂²×C₇	—	4	2	no	—
307	C₂²×C₇	—	4	2	no	—
308	C₂²×C₇	—	8	1	no	—
309	C₂²×C₇	—	8	1	no	—
310	C₂²×C₇	—	8	1	no	—
311	C₂²×C₇	#463	1	2	yes	—
312	C₂²×C₇	C₂×#121	1	1	yes	characteristic
313	C₄×C₇	—	2	1	no	—
314	C₄×C₇	—	2	1	no	—
315	C₄×C₇	—	2	1	no	—
316	C₄×C₇	—	4	2	no	—
317	C₄×C₇	—	8	1	no	—
318	C₄×C₇	—	8	2	no	—
319	C₄×C₇	#463	1	2	yes	—
320	C₄×C₇	C₂×#135	1	1	yes	characteristic
321	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
322	C₄×C₇	#577	1	1	yes	characteristic
323	C₄×C₇	#578	1	1	yes	characteristic
324	#41	—	4	2	no	—
325	#41	—	4	2	no	—
326	#41	—	4	2	no	—
327	#41	—	4	2	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	4	1	no	—
332	C₂×Q₈	—	8	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
346	C₂²×C₄	C₇×#41	1	1	yes	characteristic
347	D₈	—	8	2	no	—
348	M₁₆	—	2	2	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	4	4	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	4	4	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	8	1	no	—
359	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
360	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	4	1	no	—
372	C₂²⋊C₄	—	4	1	no	—
373	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
374	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
375	C₄²	C₇×#41	1	1	yes	characteristic
376	C₄²	C₂⁴×C₇	1	1	yes	characteristic
377	C₂×C₇	—	2	2	no	—
378	C₂×C₇	—	8	2	no	—
379	C₂×C₇	—	16	1	no	—
380	C₂×C₇	C₂×#463	1	1	yes	characteristic
381	C₂×C₇	#3063	1	1	yes	characteristic
382	C₂×C₇	#3068	1	1	yes	characteristic
383	C₂³	—	2	2	no	—
384	C₂³	—	4	1	no	—
385	C₂³	C₇×#121	1	1	yes	characteristic
386	Q₈	—	4	2	no	—
387	Q₈	—	4	1	no	—
388	Q₈	—	4	1	no	—
389	Q₈	—	8	2	no	—
390	Q₈	—	8	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	2	2	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	1	no	—
395	D₄	—	4	1	no	—
396	D₄	—	4	1	no	—
397	D₄	—	4	1	no	—
398	D₄	—	4	2	no	—
399	D₄	—	8	1	no	—
400	D₄	—	8	1	no	—
401	D₄	—	8	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	8	2	no	—
411	C₂×C₄	—	8	2	no	—
412	C₂×C₄	C₇×#121	1	1	yes	characteristic
413	C₂×C₄	C₇×#121	1	1	yes	characteristic
414	C₂×C₄	C₇×#121	1	1	yes	characteristic
415	C₂×C₄	C₇×#135	1	2	yes	—
416	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
417	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
418	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
419	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	2	2	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	1	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	2	no	—
426	C₈	—	4	1	no	—
427	C₇	#19236	1	1	yes	characteristic, direct product factor, Sylow
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	8	1	no	—
434	C₂²	—	8	1	no	—
435	C₂²	—	8	1	no	—
436	C₂²	C₇×#463	1	2	yes	—
437	C₂²	C₂×C₇×#121	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	4	2	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	2	no	—
444	C₄	C₇×#463	1	2	yes	—
445	C₄	C₂×C₇×#135	1	1	yes	characteristic
446	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
447	C₄	C₇×#577	1	1	yes	characteristic
448	C₄	C₇×#578	1	1	yes	characteristic
449	C₂	—	2	2	no	—
450	C₂	—	8	2	no	—
451	C₂	—	16	1	no	—
452	C₂	C₂×C₇×#463	1	1	yes	characteristic
453	C₂	C₇×#3063	1	1	yes	characteristic
454	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×#3245	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
2. C₇×#3227	C₂	semidirect
3. C₇×#3141	C₂	semidirect
4. C₇×#2935	C₂	semidirect
5. C₇×#1703	C₂	semidirect
6. C₇×#1697	C₂	semidirect
7. C₇×#1683	C₂	semidirect
8. C₇×#1677	C₂	semidirect
9. C₇×#1565	C₂	semidirect
10. C₂×C₇×#333	C₂	semidirect
11. C₇×#1540	C₂	semidirect
47. #19236	C₇	direct (N × H)
105. #3227	C₂×C₇	semidirect
106. #3141	C₂×C₇	semidirect
107. #2935	C₂×C₇	semidirect
108. #1703	C₂×C₇	semidirect
109. #1697	C₂×C₇	semidirect
110. #1683	C₂×C₇	semidirect
111. #1677	C₂×C₇	semidirect
112. #1565	C₂×C₇	semidirect
113. C₂×#333	C₂×C₇	semidirect
114. #1540	C₂×C₇	semidirect
427. C₇	#19236	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×#3245	2
C₇×#3227	2
C₇×#3141	2
C₇×#2935	2
C₇×#1703	2
C₇×#1697	2
C₇×#1683	2
C₇×#1677	2
C₇×#1565	2
C₂×C₇×#333	2
C₇×#1540	2
#19236	7

Subgroups — C7×#19236 #13196452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19236 #13196452