Subgroups — C₇×#19219 #13196435

Order 1792.

630 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3212	C₂	1	2	yes	maximal, complemented
2	C₇×#3169	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1702	C₂	1	2	yes	maximal, complemented
5	C₇×#1701	C₂	1	2	yes	maximal, complemented
6	C₇×#1674	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1673	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1668	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1667	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1553	C₂	1	2	yes	maximal, complemented
12	C₇×#532	C₂²	1	2	yes	—
13	C₇×#529	C₂²	1	1	yes	characteristic
14	C₇×#500	C₂²	1	1	yes	characteristic
15	C₇×#495	—	2	2	no	—
16	C₇×#493	C₂²	1	1	yes	characteristic
17	C₇×#488	—	2	2	no	—
18	C₇×#486	C₂²	1	2	yes	—
19	C₇×#466	—	2	1	no	—
20	C₇×#466	—	2	1	no	—
21	C₇×#462	C₂²	1	2	yes	—
22	C₇×#461	C₂²	1	2	yes	—
23	C₇×#460	C₂²	1	2	yes	—
24	C₇×#459	C₂²	1	2	yes	—
25	C₇×#452	—	2	2	no	—
26	C₇×#449	—	2	2	no	—
27	C₇×#446	C₂²	1	1	yes	characteristic
28	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
29	C₄×C₇×D₈	—	2	1	no	—
30	C₄×C₇×D₈	—	2	1	no	—
31	C₇×#436	C₂²	1	1	yes	characteristic
32	C₇×#435	—	2	1	no	—
33	C₇×C₈×D₄	—	2	1	no	—
34	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
35	C₇×#433	—	2	1	no	—
36	C₇×#432	C₂²	1	1	yes	characteristic
37	C₇×#431	C₂²	1	2	yes	—
38	C₇×#405	—	2	1	no	—
39	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
40	C₇×#335	C₂²	1	1	yes	characteristic
41	C₇×#335	C₂²	1	1	yes	characteristic
42	C₇×#334	C₂²	1	2	yes	—
43	C₇×#332	C₂²	1	2	yes	—
44	C₇×#332	C₂²	1	2	yes	—
45	C₇×#331	C₂²	1	2	yes	—
46	C₇×#331	C₂²	1	2	yes	—
47	#19219	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	—	2	2	no	—
49	C₂×C₇×Q₁₆	—	2	2	no	—
50	C₂×C₇×SD₁₆	—	2	2	no	—
51	C₂×C₇×SD₁₆	—	2	2	no	—
52	C₂×C₇×D₈	—	2	2	no	—
53	C₂×C₇×D₈	—	2	1	no	—
54	C₂×C₇×D₈	—	2	1	no	—
55	C₂×C₇×M₁₆	—	2	1	no	—
56	C₂²×C₇×C₈	—	2	1	no	—
57	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
58	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
59	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₇×#127	C₂³	1	2	yes	—
61	C₇×#126	—	2	1	no	—
62	C₇×#125	D₄	1	1	yes	characteristic
63	C₇×#124	—	2	2	no	—
64	C₇×#124	D₄	1	1	yes	characteristic
65	C₇×#123	—	2	1	no	—
66	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
67	C₇×#121	—	2	2	no	—
68	C₇×#121	—	2	2	no	—
69	C₇×#121	D₄	1	1	yes	characteristic
70	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
71	C₄×C₇×D₄	—	2	1	no	—
72	C₄×C₇×D₄	—	2	2	no	—
73	C₄×C₇×D₄	—	2	2	no	—
74	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
75	C₇×#117	—	2	1	no	—
76	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
77	C₇×#107	—	2	1	no	—
78	C₇×#107	—	2	1	no	—
79	C₇×C₄⋊C₈	—	2	1	no	—
80	C₇×C₄⋊C₈	—	2	1	no	—
81	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
82	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₇×C₄⋊C₈	C₂³	1	2	yes	—
84	C₇×C₄⋊C₈	C₂³	1	2	yes	—
85	C₇×#103	—	2	2	no	—
86	C₇×#103	—	2	2	no	—
87	C₇×#102	—	2	2	no	—
88	C₇×#102	—	2	2	no	—
89	C₇×#102	—	2	2	no	—
90	C₇×#102	—	2	2	no	—
91	C₇×C₂²⋊C₈	—	2	2	no	—
92	C₇×C₂²⋊C₈	—	2	1	no	—
93	C₇×C₂²⋊C₈	—	2	1	no	—
94	C₇×C₂²⋊C₈	—	2	1	no	—
95	C₇×#97	—	2	1	no	—
96	C₇×#97	—	2	1	no	—
97	C₄×C₇×C₈	—	2	1	no	—
98	C₄×C₇×C₈	—	2	2	no	—
99	C₄×C₇×C₈	D₄	1	1	yes	characteristic
100	C₄×C₇×C₈	D₄	1	1	yes	characteristic
101	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
102	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
103	#3212	C₂×C₇	1	2	yes	complemented
104	#3169	C₂×C₇	1	1	yes	characteristic, complemented
105	#2966	C₂×C₇	1	1	yes	characteristic, complemented
106	#1702	C₂×C₇	1	2	yes	complemented
107	#1701	C₂×C₇	1	2	yes	complemented
108	#1674	C₂×C₇	1	1	yes	characteristic, complemented
109	#1673	C₂×C₇	1	1	yes	characteristic, complemented
110	#1668	C₂×C₇	1	1	yes	characteristic, complemented
111	#1667	C₂×C₇	1	1	yes	characteristic, complemented
112	#1564	C₂×C₇	1	1	yes	characteristic, complemented
113	#1553	C₂×C₇	1	2	yes	complemented
114	C₇×#41	—	8	2	no	—
115	C₇×#41	—	8	2	no	—
116	C₂×C₇×Q₈	—	2	2	no	—
117	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
118	C₂×C₇×D₄	—	2	1	no	—
119	C₂×C₇×D₄	—	2	2	no	—
120	C₂×C₇×D₄	—	2	2	no	—
121	C₂×C₇×D₄	—	2	2	no	—
122	C₂×C₇×D₄	—	4	2	no	—
123	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₇	—	2	1	no	—
125	C₂²×C₄×C₇	—	4	2	no	—
126	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇	#41	1	1	yes	characteristic
129	C₇×Q₁₆	—	8	2	no	—
130	C₇×SD₁₆	—	8	2	no	—
131	C₇×SD₁₆	—	8	2	no	—
132	C₇×D₈	—	4	2	no	—
133	C₇×D₈	—	4	2	no	—
134	C₇×D₈	—	8	2	no	—
135	C₇×M₁₆	—	4	2	no	—
136	C₂×C₇×C₈	—	2	2	no	—
137	C₂×C₇×C₈	—	2	1	no	—
138	C₂×C₇×C₈	—	2	2	no	—
139	C₂×C₇×C₈	—	2	2	no	—
140	C₂×C₇×C₈	—	2	1	no	—
141	C₂×C₇×C₈	—	4	1	no	—
142	C₂×C₇×C₈	—	4	2	no	—
143	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
145	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
146	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
147	C₇×C₄⋊C₄	—	2	1	no	—
148	C₇×C₄⋊C₄	—	2	1	no	—
149	C₇×C₄⋊C₄	—	2	1	no	—
150	C₇×C₄⋊C₄	—	2	1	no	—
151	C₇×C₄⋊C₄	—	2	2	no	—
152	C₇×C₄⋊C₄	—	2	2	no	—
153	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
154	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
155	C₇×C₂²⋊C₄	—	2	1	no	—
156	C₇×C₂²⋊C₄	—	2	1	no	—
157	C₇×C₂²⋊C₄	—	2	1	no	—
158	C₇×C₂²⋊C₄	—	2	1	no	—
159	C₇×C₂²⋊C₄	—	2	1	no	—
160	C₇×C₂²⋊C₄	—	4	2	no	—
161	C₇×C₂²⋊C₄	—	4	2	no	—
162	C₄²×C₇	—	2	1	no	—
163	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₇	#41	1	1	yes	characteristic
166	C₄²×C₇	C₂⁴	1	1	yes	characteristic
167	#532	C₂²×C₇	1	2	yes	—
168	#529	C₂²×C₇	1	1	yes	characteristic
169	#500	C₂²×C₇	1	1	yes	characteristic
170	#495	—	2	2	no	—
171	#493	C₂²×C₇	1	1	yes	characteristic
172	#488	—	2	2	no	—
173	#486	C₂²×C₇	1	2	yes	—
174	#466	—	2	1	no	—
175	#466	—	2	1	no	—
176	#462	C₂²×C₇	1	2	yes	—
177	#461	C₂²×C₇	1	2	yes	—
178	#460	C₂²×C₇	1	2	yes	—
179	#459	C₂²×C₇	1	2	yes	—
180	#452	—	2	2	no	—
181	#449	—	2	2	no	—
182	#446	C₂²×C₇	1	1	yes	characteristic
183	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
184	C₄×D₈	—	2	1	no	—
185	C₄×D₈	—	2	1	no	—
186	#436	C₂²×C₇	1	1	yes	characteristic
187	#435	—	2	1	no	—
188	C₈×D₄	—	2	1	no	—
189	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
190	#433	—	2	1	no	—
191	#432	C₂²×C₇	1	1	yes	characteristic
192	#431	C₂²×C₇	1	2	yes	—
193	#405	—	2	1	no	—
194	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
195	#335	C₂²×C₇	1	1	yes	characteristic
196	#335	C₂²×C₇	1	1	yes	characteristic
197	#334	C₂²×C₇	1	2	yes	—
198	#332	C₂²×C₇	1	2	yes	—
199	#332	C₂²×C₇	1	2	yes	—
200	#331	C₂²×C₇	1	2	yes	—
201	#331	C₂²×C₇	1	2	yes	—
202	C₂³×C₇	—	2	1	no	—
203	C₂³×C₇	—	4	2	no	—
204	C₂³×C₇	#121	1	1	yes	characteristic
205	C₇×Q₈	—	2	1	no	—
206	C₇×Q₈	—	2	1	no	—
207	C₇×Q₈	—	4	2	no	—
208	C₇×Q₈	—	4	2	no	—
209	C₇×D₄	—	2	1	no	—
210	C₇×D₄	—	2	1	no	—
211	C₇×D₄	—	4	2	no	—
212	C₇×D₄	—	4	2	no	—
213	C₇×D₄	—	4	2	no	—
214	C₇×D₄	—	4	2	no	—
215	C₇×D₄	—	4	2	no	—
216	C₇×D₄	—	8	2	no	—
217	C₇×D₄	—	8	4	no	—
218	C₂×C₄×C₇	—	2	1	no	—
219	C₂×C₄×C₇	—	2	1	no	—
220	C₂×C₄×C₇	—	2	1	no	—
221	C₂×C₄×C₇	—	2	1	no	—
222	C₂×C₄×C₇	—	2	1	no	—
223	C₂×C₄×C₇	—	2	1	no	—
224	C₂×C₄×C₇	—	2	1	no	—
225	C₂×C₄×C₇	—	4	1	no	—
226	C₂×C₄×C₇	—	4	1	no	—
227	C₂×C₄×C₇	—	4	1	no	—
228	C₂×C₄×C₇	—	4	2	no	—
229	C₂×C₄×C₇	—	8	4	no	—
230	C₂×C₄×C₇	#121	1	1	yes	characteristic
231	C₂×C₄×C₇	#121	1	1	yes	characteristic
232	C₂×C₄×C₇	#121	1	1	yes	characteristic
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	1	no	—
237	C₇×C₈	—	2	1	no	—
238	C₇×C₈	—	2	1	no	—
239	C₇×C₈	—	4	1	no	—
240	C₇×C₈	—	4	1	no	—
241	C₇×C₈	—	4	2	no	—
242	C₇×C₈	—	4	2	no	—
243	C₇×C₈	#135	1	2	yes	—
244	C₂×#41	—	2	2	no	—
245	C₂×Q₁₆	—	2	2	no	—
246	C₂×SD₁₆	—	2	2	no	—
247	C₂×SD₁₆	—	2	2	no	—
248	C₂×D₈	—	2	2	no	—
249	C₂×D₈	—	2	1	no	—
250	C₂×D₈	—	2	1	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
254	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
255	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
256	#127	C₂³×C₇	1	2	yes	—
257	#126	—	2	1	no	—
258	#125	C₇×D₄	1	1	yes	characteristic
259	#124	—	2	2	no	—
260	#124	C₇×D₄	1	1	yes	characteristic
261	#123	—	2	1	no	—
262	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
263	#121	—	2	2	no	—
264	#121	—	2	2	no	—
265	#121	C₇×D₄	1	1	yes	characteristic
266	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	—	2	2	no	—
269	C₄×D₄	—	2	2	no	—
270	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
271	#117	—	2	1	no	—
272	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
273	#107	—	2	1	no	—
274	#107	—	2	1	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
278	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
279	C₄⋊C₈	C₂³×C₇	1	2	yes	—
280	C₄⋊C₈	C₂³×C₇	1	2	yes	—
281	#103	—	2	2	no	—
282	#103	—	2	2	no	—
283	#102	—	2	2	no	—
284	#102	—	2	2	no	—
285	#102	—	2	2	no	—
286	#102	—	2	2	no	—
287	C₂²⋊C₈	—	2	2	no	—
288	C₂²⋊C₈	—	2	1	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	#97	—	2	1	no	—
292	#97	—	2	1	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	2	2	no	—
295	C₄×C₈	C₇×D₄	1	1	yes	characteristic
296	C₄×C₈	C₇×D₄	1	1	yes	characteristic
297	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
298	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
299	C₂²×C₇	—	2	1	no	—
300	C₂²×C₇	—	2	1	no	—
301	C₂²×C₇	—	2	1	no	—
302	C₂²×C₇	—	4	1	no	—
303	C₂²×C₇	—	4	1	no	—
304	C₂²×C₇	—	4	1	no	—
305	C₂²×C₇	—	8	2	no	—
306	C₂²×C₇	—	8	2	no	—
307	C₂²×C₇	—	8	2	no	—
308	C₂²×C₇	C₂×#121	1	1	yes	characteristic
309	C₄×C₇	—	2	1	no	—
310	C₄×C₇	—	2	1	no	—
311	C₄×C₇	—	2	1	no	—
312	C₄×C₇	—	2	1	no	—
313	C₄×C₇	—	4	1	no	—
314	C₄×C₇	—	4	1	no	—
315	C₄×C₇	—	4	1	no	—
316	C₄×C₇	—	8	2	no	—
317	C₄×C₇	C₂×#135	1	1	yes	characteristic
318	C₄×C₇	#575	1	1	yes	characteristic
319	C₄×C₇	#576	1	1	yes	characteristic
320	C₄×C₇	#576	1	1	yes	characteristic
321	#41	—	8	2	no	—
322	#41	—	8	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	4	2	no	—
330	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	4	2	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	Q₁₆	—	8	2	no	—
337	SD₁₆	—	8	2	no	—
338	SD₁₆	—	8	2	no	—
339	D₈	—	4	2	no	—
340	D₈	—	4	2	no	—
341	D₈	—	8	2	no	—
342	M₁₆	—	4	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
351	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
352	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
353	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
361	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	4	2	no	—
369	C₄²	—	2	1	no	—
370	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
371	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
372	C₄²	C₇×#41	1	1	yes	characteristic
373	C₄²	C₂⁴×C₇	1	1	yes	characteristic
374	C₂×C₇	—	4	1	no	—
375	C₂×C₇	—	8	1	no	—
376	C₂×C₇	—	16	2	no	—
377	C₂×C₇	#3035	1	1	yes	characteristic
378	C₂×C₇	#3058	1	1	yes	characteristic
379	C₂×C₇	#3067	1	1	yes	characteristic
380	C₂³	—	2	1	no	—
381	C₂³	—	4	2	no	—
382	C₂³	C₇×#121	1	1	yes	characteristic
383	Q₈	—	2	1	no	—
384	Q₈	—	2	1	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	2	no	—
387	D₄	—	2	1	no	—
388	D₄	—	2	1	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	—	8	2	no	—
395	D₄	—	8	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	8	4	no	—
408	C₂×C₄	C₇×#121	1	1	yes	characteristic
409	C₂×C₄	C₇×#121	1	1	yes	characteristic
410	C₂×C₄	C₇×#121	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
413	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
414	C₈	—	2	1	no	—
415	C₈	—	2	1	no	—
416	C₈	—	2	1	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	2	no	—
420	C₈	—	4	2	no	—
421	C₈	C₇×#135	1	2	yes	—
422	C₇	#19219	1	1	yes	characteristic, direct product factor, Sylow
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	C₂×C₇×#121	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	8	2	no	—
441	C₄	C₂×C₇×#135	1	1	yes	characteristic
442	C₄	C₇×#575	1	1	yes	characteristic
443	C₄	C₇×#576	1	1	yes	characteristic
444	C₄	C₇×#576	1	1	yes	characteristic
445	C₂	—	4	1	no	—
446	C₂	—	8	1	no	—
447	C₂	—	16	2	no	—
448	C₂	C₇×#3035	1	1	yes	characteristic
449	C₂	C₇×#3058	1	1	yes	characteristic
450	C₂	C₇×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
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×#3212	C₂	semidirect
2. C₇×#3169	C₂	semidirect
3. C₇×#2966	C₂	semidirect
4. C₇×#1702	C₂	semidirect
5. C₇×#1701	C₂	semidirect
6. C₇×#1674	C₂	semidirect
7. C₇×#1673	C₂	semidirect
8. C₇×#1668	C₂	semidirect
9. C₇×#1667	C₂	semidirect
10. C₇×#1564	C₂	semidirect
11. C₇×#1553	C₂	semidirect
47. #19219	C₇	direct (N × H)
103. #3212	C₂×C₇	semidirect
104. #3169	C₂×C₇	semidirect
105. #2966	C₂×C₇	semidirect
106. #1702	C₂×C₇	semidirect
107. #1701	C₂×C₇	semidirect
108. #1674	C₂×C₇	semidirect
109. #1673	C₂×C₇	semidirect
110. #1668	C₂×C₇	semidirect
111. #1667	C₂×C₇	semidirect
112. #1564	C₂×C₇	semidirect
113. #1553	C₂×C₇	semidirect
422. C₇	#19219	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×#3212	2
C₇×#3169	2
C₇×#2966	2
C₇×#1702	2
C₇×#1701	2
C₇×#1674	2
C₇×#1673	2
C₇×#1668	2
C₇×#1667	2
C₇×#1564	2
C₇×#1553	2
#19219	7

Subgroups — C7×#19219 #13196435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19219 #13196435