Subgroups — C₇×#19222 #13196438

Order 1792.

628 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×#3247	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×#1698	C₂	1	2	yes	maximal, complemented
5	C₇×#1697	C₂	1	2	yes	maximal, complemented
6	C₇×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1675	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	C₂×C₇×#335	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1551	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×#493	C₂²	1	1	yes	characteristic
16	C₇×#486	C₂²	1	2	yes	—
17	C₇×#478	—	2	2	no	—
18	C₇×#477	C₂²	1	2	yes	—
19	C₇×#476	C₂²	1	2	yes	—
20	C₇×#466	—	2	1	no	—
21	C₇×#466	—	2	1	no	—
22	C₇×#466	—	2	2	no	—
23	C₇×#465	—	2	2	no	—
24	C₇×#463	—	2	2	no	—
25	C₇×#460	C₂²	1	2	yes	—
26	C₇×#459	C₂²	1	2	yes	—
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	C₂×C₇×C₄⋊C₈	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×#335	C₂²	1	2	yes	—
43	C₇×#333	C₂²	1	2	yes	—
44	C₇×#333	C₂²	1	2	yes	—
45	C₇×#331	C₂²	1	2	yes	—
46	C₇×#331	C₂²	1	2	yes	—
47	#19222	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	—	2	2	no	—
49	C₂×C₇×SD₁₆	—	2	2	no	—
50	C₂×C₇×D₈	—	2	2	no	—
51	C₂×C₇×D₈	—	2	1	no	—
52	C₂×C₇×D₈	—	2	1	no	—
53	C₂×C₇×M₁₆	—	2	1	no	—
54	C₂²×C₇×C₈	—	2	2	no	—
55	C₂²×C₇×C₈	—	2	1	no	—
56	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
57	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
58	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₇×#127	C₂³	1	2	yes	—
60	C₇×#126	—	2	1	no	—
61	C₇×#125	D₄	1	1	yes	characteristic
62	C₇×#124	—	2	2	no	—
63	C₇×#124	D₄	1	1	yes	characteristic
64	C₇×#123	—	2	1	no	—
65	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
66	C₇×#121	—	2	2	no	—
67	C₇×#121	—	2	2	no	—
68	C₇×#121	D₄	1	1	yes	characteristic
69	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
70	C₄×C₇×D₄	—	2	1	no	—
71	C₄×C₇×D₄	—	2	2	no	—
72	C₄×C₇×D₄	—	2	2	no	—
73	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
74	C₇×#117	—	2	1	no	—
75	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
76	C₇×#107	—	2	1	no	—
77	C₇×#107	—	2	1	no	—
78	C₇×#107	—	2	2	no	—
79	C₇×#106	—	2	2	no	—
80	C₇×C₄⋊C₈	—	2	1	no	—
81	C₇×C₄⋊C₈	—	2	1	no	—
82	C₇×C₄⋊C₈	—	2	2	no	—
83	C₇×C₄⋊C₈	C₂³	1	2	yes	—
84	C₇×C₄⋊C₈	C₂³	1	2	yes	—
85	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₇×#103	—	2	2	no	—
88	C₇×#102	—	2	2	no	—
89	C₇×#102	—	2	2	no	—
90	C₇×#102	—	2	2	no	—
91	C₇×#102	—	2	2	no	—
92	C₇×#102	—	2	2	no	—
93	C₇×C₂²⋊C₈	—	2	1	no	—
94	C₇×C₂²⋊C₈	—	2	1	no	—
95	C₇×C₂²⋊C₈	—	2	1	no	—
96	C₇×#97	—	2	1	no	—
97	C₇×#97	—	2	1	no	—
98	C₄×C₇×C₈	—	2	1	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	#3247	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	#1698	C₂×C₇	1	2	yes	complemented
107	#1697	C₂×C₇	1	2	yes	complemented
108	#1676	C₂×C₇	1	1	yes	characteristic, complemented
109	#1675	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	C₂×#335	C₂×C₇	1	1	yes	characteristic, complemented
113	#1551	C₂×C₇	1	2	yes	complemented
114	C₇×#41	—	8	4	no	—
115	C₂×C₇×Q₈	—	2	2	no	—
116	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
117	C₂×C₇×D₄	—	2	1	no	—
118	C₂×C₇×D₄	—	2	2	no	—
119	C₂×C₇×D₄	—	2	2	no	—
120	C₂×C₇×D₄	—	2	2	no	—
121	C₂×C₇×D₄	—	4	2	no	—
122	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	—	2	1	no	—
124	C₂²×C₄×C₇	—	4	2	no	—
125	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇	#41	1	1	yes	characteristic
128	C₇×SD₁₆	—	8	2	no	—
129	C₇×D₈	—	4	2	no	—
130	C₇×D₈	—	4	2	no	—
131	C₇×D₈	—	8	2	no	—
132	C₇×M₁₆	—	4	2	no	—
133	C₂×C₇×C₈	—	2	2	no	—
134	C₂×C₇×C₈	—	2	1	no	—
135	C₂×C₇×C₈	—	2	1	no	—
136	C₂×C₇×C₈	—	2	2	no	—
137	C₂×C₇×C₈	—	2	2	no	—
138	C₂×C₇×C₈	—	4	1	no	—
139	C₂×C₇×C₈	—	4	2	no	—
140	C₂×C₇×C₈	—	8	2	no	—
141	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
142	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
143	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
145	C₇×C₄⋊C₄	—	2	1	no	—
146	C₇×C₄⋊C₄	—	2	1	no	—
147	C₇×C₄⋊C₄	—	2	1	no	—
148	C₇×C₄⋊C₄	—	2	1	no	—
149	C₇×C₄⋊C₄	—	2	2	no	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
152	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
153	C₇×C₂²⋊C₄	—	2	1	no	—
154	C₇×C₂²⋊C₄	—	2	1	no	—
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	—	4	2	no	—
159	C₇×C₂²⋊C₄	—	4	2	no	—
160	C₄²×C₇	—	2	1	no	—
161	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₇	#41	1	1	yes	characteristic
164	C₄²×C₇	C₂⁴	1	1	yes	characteristic
165	#532	C₂²×C₇	1	2	yes	—
166	#529	C₂²×C₇	1	1	yes	characteristic
167	#500	C₂²×C₇	1	1	yes	characteristic
168	#493	C₂²×C₇	1	1	yes	characteristic
169	#486	C₂²×C₇	1	2	yes	—
170	#478	—	2	2	no	—
171	#477	C₂²×C₇	1	2	yes	—
172	#476	C₂²×C₇	1	2	yes	—
173	#466	—	2	1	no	—
174	#466	—	2	1	no	—
175	#466	—	2	2	no	—
176	#465	—	2	2	no	—
177	#463	—	2	2	no	—
178	#460	C₂²×C₇	1	2	yes	—
179	#459	C₂²×C₇	1	2	yes	—
180	#446	C₂²×C₇	1	1	yes	characteristic
181	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
182	C₄×D₈	—	2	1	no	—
183	C₄×D₈	—	2	1	no	—
184	#436	C₂²×C₇	1	1	yes	characteristic
185	#435	—	2	1	no	—
186	C₈×D₄	—	2	1	no	—
187	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
188	#433	—	2	1	no	—
189	#432	C₂²×C₇	1	1	yes	characteristic
190	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
191	#405	—	2	1	no	—
192	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
193	#335	C₂²×C₇	1	1	yes	characteristic
194	#335	C₂²×C₇	1	1	yes	characteristic
195	#335	C₂²×C₇	1	2	yes	—
196	#333	C₂²×C₇	1	2	yes	—
197	#333	C₂²×C₇	1	2	yes	—
198	#331	C₂²×C₇	1	2	yes	—
199	#331	C₂²×C₇	1	2	yes	—
200	C₂³×C₇	—	2	1	no	—
201	C₂³×C₇	—	4	2	no	—
202	C₂³×C₇	#121	1	1	yes	characteristic
203	C₇×Q₈	—	2	1	no	—
204	C₇×Q₈	—	2	1	no	—
205	C₇×Q₈	—	8	2	no	—
206	C₇×D₄	—	2	1	no	—
207	C₇×D₄	—	2	1	no	—
208	C₇×D₄	—	4	2	no	—
209	C₇×D₄	—	4	2	no	—
210	C₇×D₄	—	4	2	no	—
211	C₇×D₄	—	4	2	no	—
212	C₇×D₄	—	4	2	no	—
213	C₇×D₄	—	8	2	no	—
214	C₇×D₄	—	8	4	no	—
215	C₂×C₄×C₇	—	2	2	no	—
216	C₂×C₄×C₇	—	2	1	no	—
217	C₂×C₄×C₇	—	2	1	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	—	4	1	no	—
224	C₂×C₄×C₇	—	4	1	no	—
225	C₂×C₄×C₇	—	4	2	no	—
226	C₂×C₄×C₇	—	8	4	no	—
227	C₂×C₄×C₇	#121	1	1	yes	characteristic
228	C₂×C₄×C₇	#121	1	1	yes	characteristic
229	C₂×C₄×C₇	#121	1	1	yes	characteristic
230	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
233	C₇×C₈	—	2	1	no	—
234	C₇×C₈	—	2	1	no	—
235	C₇×C₈	—	2	1	no	—
236	C₇×C₈	—	4	1	no	—
237	C₇×C₈	—	4	1	no	—
238	C₇×C₈	—	4	2	no	—
239	C₇×C₈	—	4	2	no	—
240	C₇×C₈	#135	1	2	yes	—
241	C₂×#41	—	2	2	no	—
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×D₈	—	2	2	no	—
244	C₂×D₈	—	2	1	no	—
245	C₂×D₈	—	2	1	no	—
246	C₂×M₁₆	—	2	1	no	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
250	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
251	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
252	#127	C₂³×C₇	1	2	yes	—
253	#126	—	2	1	no	—
254	#125	C₇×D₄	1	1	yes	characteristic
255	#124	—	2	2	no	—
256	#124	C₇×D₄	1	1	yes	characteristic
257	#123	—	2	1	no	—
258	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
259	#121	—	2	2	no	—
260	#121	—	2	2	no	—
261	#121	C₇×D₄	1	1	yes	characteristic
262	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
267	#117	—	2	1	no	—
268	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
269	#107	—	2	1	no	—
270	#107	—	2	1	no	—
271	#107	—	2	2	no	—
272	#106	—	2	2	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
277	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
278	C₄⋊C₈	C₂³×C₇	1	2	yes	—
279	C₄⋊C₈	C₂³×C₇	1	2	yes	—
280	#103	—	2	2	no	—
281	#102	—	2	2	no	—
282	#102	—	2	2	no	—
283	#102	—	2	2	no	—
284	#102	—	2	2	no	—
285	#102	—	2	2	no	—
286	C₂²⋊C₈	—	2	1	no	—
287	C₂²⋊C₈	—	2	1	no	—
288	C₂²⋊C₈	—	2	1	no	—
289	#97	—	2	1	no	—
290	#97	—	2	1	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	C₇×D₄	1	1	yes	characteristic
293	C₄×C₈	C₇×D₄	1	1	yes	characteristic
294	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
295	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
296	C₂²×C₇	—	2	1	no	—
297	C₂²×C₇	—	2	1	no	—
298	C₂²×C₇	—	4	1	no	—
299	C₂²×C₇	—	4	1	no	—
300	C₂²×C₇	—	4	1	no	—
301	C₂²×C₇	—	8	2	no	—
302	C₂²×C₇	—	8	2	no	—
303	C₂²×C₇	—	8	2	no	—
304	C₂²×C₇	#472	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	—	2	1	no	—
310	C₄×C₇	—	4	1	no	—
311	C₄×C₇	—	4	1	no	—
312	C₄×C₇	—	4	1	no	—
313	C₄×C₇	—	8	2	no	—
314	C₄×C₇	C₂×#135	1	1	yes	characteristic
315	C₄×C₇	#575	1	1	yes	characteristic
316	C₄×C₇	#576	1	1	yes	characteristic
317	C₄×C₇	#578	1	1	yes	characteristic
318	#41	—	8	4	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	4	2	no	—
326	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
331	C₂²×C₄	C₇×#41	1	1	yes	characteristic
332	SD₁₆	—	8	2	no	—
333	D₈	—	4	2	no	—
334	D₈	—	4	2	no	—
335	D₈	—	8	2	no	—
336	M₁₆	—	4	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	2	no	—
344	C₂×C₈	—	8	2	no	—
345	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
346	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
347	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
348	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
356	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
357	C₂²⋊C₄	—	2	1	no	—
358	C₂²⋊C₄	—	2	1	no	—
359	C₂²⋊C₄	—	2	1	no	—
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₄²	—	2	1	no	—
365	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
366	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
367	C₄²	C₇×#41	1	1	yes	characteristic
368	C₄²	C₂⁴×C₇	1	1	yes	characteristic
369	C₂×C₇	—	2	2	no	—
370	C₂×C₇	—	8	1	no	—
371	C₂×C₇	—	16	2	no	—
372	C₂×C₇	#3035	1	1	yes	characteristic
373	C₂×C₇	#3061	1	1	yes	characteristic
374	C₂×C₇	C₂×#472	1	1	yes	characteristic
375	C₂³	—	2	1	no	—
376	C₂³	—	4	2	no	—
377	C₂³	C₇×#121	1	1	yes	characteristic
378	Q₈	—	2	1	no	—
379	Q₈	—	2	1	no	—
380	Q₈	—	8	2	no	—
381	D₄	—	2	1	no	—
382	D₄	—	2	1	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	8	2	no	—
389	D₄	—	8	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	8	4	no	—
402	C₂×C₄	C₇×#121	1	1	yes	characteristic
403	C₂×C₄	C₇×#121	1	1	yes	characteristic
404	C₂×C₄	C₇×#121	1	1	yes	characteristic
405	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
407	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
408	C₈	—	2	1	no	—
409	C₈	—	2	1	no	—
410	C₈	—	2	1	no	—
411	C₈	—	4	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	4	2	no	—
414	C₈	—	4	2	no	—
415	C₈	C₇×#135	1	2	yes	—
416	C₇	#19222	1	1	yes	characteristic, direct product factor, Sylow
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	C₇×#472	1	2	yes	—
426	C₂²	C₂×C₇×#121	1	1	yes	characteristic
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	8	2	no	—
435	C₄	C₂×C₇×#135	1	1	yes	characteristic
436	C₄	C₇×#575	1	1	yes	characteristic
437	C₄	C₇×#576	1	1	yes	characteristic
438	C₄	C₇×#578	1	1	yes	characteristic
439	C₂	—	2	2	no	—
440	C₂	—	8	1	no	—
441	C₂	—	16	2	no	—
442	C₂	C₇×#3035	1	1	yes	characteristic
443	C₂	C₇×#3061	1	1	yes	characteristic
444	C₂	C₂×C₇×#472	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×#3247	C₂	semidirect
2. C₇×#3169	C₂	semidirect
3. C₇×#2966	C₂	semidirect
4. C₇×#1698	C₂	semidirect
5. C₇×#1697	C₂	semidirect
6. C₇×#1676	C₂	semidirect
7. C₇×#1675	C₂	semidirect
8. C₇×#1668	C₂	semidirect
9. C₇×#1667	C₂	semidirect
10. C₂×C₇×#335	C₂	semidirect
11. C₇×#1551	C₂	semidirect
47. #19222	C₇	direct (N × H)
103. #3247	C₂×C₇	semidirect
104. #3169	C₂×C₇	semidirect
105. #2966	C₂×C₇	semidirect
106. #1698	C₂×C₇	semidirect
107. #1697	C₂×C₇	semidirect
108. #1676	C₂×C₇	semidirect
109. #1675	C₂×C₇	semidirect
110. #1668	C₂×C₇	semidirect
111. #1667	C₂×C₇	semidirect
112. C₂×#335	C₂×C₇	semidirect
113. #1551	C₂×C₇	semidirect
416. C₇	#19222	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×#3247	2
C₇×#3169	2
C₇×#2966	2
C₇×#1698	2
C₇×#1697	2
C₇×#1676	2
C₇×#1675	2
C₇×#1668	2
C₇×#1667	2
C₂×C₇×#335	2
C₇×#1551	2
#19222	7

Subgroups — C7×#19222 #13196438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19222 #13196438