Subgroups — C₇×#26025 #13203241

Order 1792.

734 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#2354	C₂	1	1	yes	maximal, characteristic
3	C₇×#2067	C₂	1	2	yes	maximal
4	C₇×#2025	C₂	1	2	yes	maximal
5	C₇×#1989	C₂	1	2	yes	maximal, complemented
6	C₇×#1947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1921	C₂	1	2	yes	maximal, complemented
9	C₇×#1834	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1802	C₂	1	1	yes	maximal, characteristic
11	C₄×C₇×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×#125	C₂²	1	2	yes	—
13	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₇×#117	—	2	1	no	—
15	C₂×C₇×#107	C₂²	1	2	yes	—
16	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₇×#102	C₂²	1	1	yes	characteristic
19	C₂×C₇×#102	C₂²	1	1	yes	characteristic
20	C₂×C₇×#102	C₂²	1	2	yes	—
21	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
22	C₇×#398	—	2	2	no	—
23	C₇×#390	C₂²	1	2	yes	—
24	C₇×#389	—	2	1	no	—
25	C₇×#389	C₂²	1	2	yes	—
26	C₇×#388	—	2	2	no	—
27	C₇×#384	—	2	1	no	—
28	C₇×#384	C₂²	1	1	yes	characteristic
29	C₇×#384	C₂²	1	1	yes	characteristic
30	C₇×#380	—	2	1	no	—
31	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
32	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₇×#340	C₂²	1	1	yes	characteristic
35	C₇×#340	C₂²	1	2	yes	—
36	C₇×#340	C₂²	1	2	yes	—
37	C₇×#340	C₂²	1	2	yes	—
38	C₇×#340	C₂²	1	1	yes	characteristic
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	2	yes	—
41	#26025	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₇	—	2	1	no	—
44	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₇×C₈	C₂³	1	2	yes	—
46	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
47	C₇×#125	—	2	4	no	—
48	C₇×#125	—	4	2	no	—
49	C₄×C₇×D₄	—	2	2	no	—
50	C₄×C₇×D₄	Q₈	1	4	yes	—
51	C₇×#117	—	4	4	no	—
52	C₂×C₇×C₄⋊C₄	—	2	1	no	—
53	C₂×C₇×C₄⋊C₄	—	2	1	no	—
54	C₂×C₇×C₄⋊C₄	—	2	2	no	—
55	C₂×C₇×C₄⋊C₄	—	2	2	no	—
56	C₂×C₇×C₄⋊C₄	—	2	2	no	—
57	C₂×C₇×C₄⋊C₄	—	2	1	no	—
58	C₂×C₇×C₄⋊C₄	—	2	1	no	—
59	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
61	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₄²×C₇	—	2	2	no	—
70	C₂×C₄²×C₇	—	2	1	no	—
71	C₂×C₄²×C₇	C₂³	1	2	yes	—
72	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
73	C₇×#107	—	2	4	no	—
74	C₇×C₄⋊C₈	—	2	2	no	—
75	C₇×C₄⋊C₈	—	4	2	no	—
76	C₇×#102	—	2	2	no	—
77	C₇×#102	—	2	2	no	—
78	C₇×#102	—	4	2	no	—
79	C₄×C₇×C₈	—	2	2	no	—
80	C₇×#95	—	2	2	no	—
81	C₇×#95	—	2	1	no	—
82	C₇×#95	—	2	2	no	—
83	C₇×#95	D₄	1	2	yes	—
84	#2552	C₂×C₇	1	1	yes	characteristic, complemented
85	#2354	C₂×C₇	1	1	yes	characteristic
86	#2067	C₂×C₇	1	2	yes	—
87	#2025	C₂×C₇	1	2	yes	—
88	#1989	C₂×C₇	1	2	yes	complemented
89	#1947	C₂×C₇	1	1	yes	characteristic, complemented
90	#1939	C₂×C₇	1	1	yes	characteristic, complemented
91	#1921	C₂×C₇	1	2	yes	complemented
92	#1834	C₂×C₇	1	1	yes	characteristic, complemented
93	#1802	C₂×C₇	1	1	yes	characteristic
94	C₄×#102	C₂×C₇	1	1	yes	characteristic
95	C₂⁴×C₇	—	2	1	no	—
96	C₂×C₇×D₄	—	2	1	no	—
97	C₂×C₇×D₄	—	2	1	no	—
98	C₂×C₇×D₄	—	2	1	no	—
99	C₂×C₇×D₄	—	2	1	no	—
100	C₂×C₇×D₄	—	2	1	no	—
101	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₇	—	2	1	no	—
103	C₂²×C₄×C₇	—	2	1	no	—
104	C₂²×C₄×C₇	—	2	1	no	—
105	C₂²×C₄×C₇	—	2	4	no	—
106	C₂²×C₄×C₇	—	2	2	no	—
107	C₂²×C₄×C₇	—	2	2	no	—
108	C₂²×C₄×C₇	—	4	2	no	—
109	C₂²×C₄×C₇	—	4	2	no	—
110	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
115	C₂×C₇×C₈	—	2	1	no	—
116	C₂×C₇×C₈	—	2	1	no	—
117	C₂×C₇×C₈	—	2	1	no	—
118	C₂×C₇×C₈	—	2	1	no	—
119	C₂×C₇×C₈	—	2	2	no	—
120	C₂×C₇×C₈	—	2	2	no	—
121	C₂×C₇×C₈	—	2	2	no	—
122	C₂×C₇×C₈	—	2	1	no	—
123	C₂×C₇×C₈	—	2	1	no	—
124	C₇×C₄⋊C₄	—	2	2	no	—
125	C₇×C₄⋊C₄	—	2	2	no	—
126	C₇×C₄⋊C₄	—	2	1	no	—
127	C₇×C₄⋊C₄	—	2	1	no	—
128	C₇×C₄⋊C₄	—	2	1	no	—
129	C₇×C₄⋊C₄	—	2	2	no	—
130	C₇×C₄⋊C₄	—	2	2	no	—
131	C₇×C₄⋊C₄	—	2	2	no	—
132	C₇×C₄⋊C₄	—	2	2	no	—
133	C₇×C₄⋊C₄	—	4	4	no	—
134	C₇×C₄⋊C₄	—	4	4	no	—
135	C₇×C₄⋊C₄	—	4	2	no	—
136	C₇×C₄⋊C₄	—	4	2	no	—
137	C₇×C₄⋊C₄	—	8	1	no	—
138	C₇×C₄⋊C₄	—	8	1	no	—
139	C₇×C₄⋊C₄	—	8	2	no	—
140	C₇×C₄⋊C₄	C₂×Q₈	1	2	yes	—
141	C₇×C₄⋊C₄	#41	1	2	yes	—
142	C₇×C₄⋊C₄	#41	1	2	yes	—
143	C₇×C₂²⋊C₄	—	2	4	no	—
144	C₇×C₂²⋊C₄	—	4	4	no	—
145	C₇×C₂²⋊C₄	—	8	2	no	—
146	C₄²×C₇	—	2	2	no	—
147	C₄²×C₇	—	2	2	no	—
148	C₄²×C₇	—	4	4	no	—
149	C₄²×C₇	—	4	2	no	—
150	C₄²×C₇	C₂×Q₈	1	2	yes	—
151	C₄²×C₇	#41	1	2	yes	—
152	C₂×#125	C₂²×C₇	1	2	yes	—
153	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
154	C₂×#117	—	2	1	no	—
155	C₂×#107	C₂²×C₇	1	2	yes	—
156	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
157	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
158	C₂×#102	C₂²×C₇	1	1	yes	characteristic
159	C₂×#102	C₂²×C₇	1	1	yes	characteristic
160	C₂×#102	C₂²×C₇	1	2	yes	—
161	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
162	#398	—	2	2	no	—
163	#390	C₂²×C₇	1	2	yes	—
164	#389	—	2	1	no	—
165	#389	C₂²×C₇	1	2	yes	—
166	#388	—	2	2	no	—
167	#384	—	2	1	no	—
168	#384	C₂²×C₇	1	1	yes	characteristic
169	#384	C₂²×C₇	1	1	yes	characteristic
170	#380	—	2	1	no	—
171	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
172	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
173	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
174	#340	C₂²×C₇	1	2	yes	—
175	#340	C₂²×C₇	1	2	yes	—
176	#340	C₂²×C₇	1	2	yes	—
177	#340	C₂²×C₇	1	1	yes	characteristic
178	#340	C₂²×C₇	1	2	yes	—
179	#340	C₂²×C₇	1	1	yes	characteristic
180	#336	C₂²×C₇	1	2	yes	—
181	C₂³×C₇	—	2	2	no	—
182	C₂³×C₇	—	4	1	no	—
183	C₂³×C₇	—	4	1	no	—
184	C₂³×C₇	—	4	1	no	—
185	C₂³×C₇	—	4	1	no	—
186	C₂³×C₇	—	4	1	no	—
187	C₂³×C₇	—	4	1	no	—
188	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
189	C₇×D₄	—	2	2	no	—
190	C₇×D₄	—	2	2	no	—
191	C₇×D₄	—	4	1	no	—
192	C₇×D₄	—	4	1	no	—
193	C₂×C₄×C₇	—	2	1	no	—
194	C₂×C₄×C₇	—	2	1	no	—
195	C₂×C₄×C₇	—	2	2	no	—
196	C₂×C₄×C₇	—	2	2	no	—
197	C₂×C₄×C₇	—	2	2	no	—
198	C₂×C₄×C₇	—	2	2	no	—
199	C₂×C₄×C₇	—	2	2	no	—
200	C₂×C₄×C₇	—	2	2	no	—
201	C₂×C₄×C₇	—	2	2	no	—
202	C₂×C₄×C₇	—	2	2	no	—
203	C₂×C₄×C₇	—	2	2	no	—
204	C₂×C₄×C₇	—	4	1	no	—
205	C₂×C₄×C₇	—	4	1	no	—
206	C₂×C₄×C₇	—	4	1	no	—
207	C₂×C₄×C₇	—	4	1	no	—
208	C₂×C₄×C₇	—	4	1	no	—
209	C₂×C₄×C₇	—	4	1	no	—
210	C₂×C₄×C₇	—	4	8	no	—
211	C₂×C₄×C₇	—	4	2	no	—
212	C₂×C₄×C₇	—	4	2	no	—
213	C₂×C₄×C₇	—	4	2	no	—
214	C₂×C₄×C₇	—	4	2	no	—
215	C₂×C₄×C₇	—	4	2	no	—
216	C₂×C₄×C₇	—	4	2	no	—
217	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
218	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
219	C₂×C₄×C₇	#135	1	2	yes	—
220	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
221	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
222	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
227	C₇×C₈	—	4	1	no	—
228	C₇×C₈	—	4	2	no	—
229	C₇×C₈	—	4	1	no	—
230	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
231	C₂³×C₄	—	2	1	no	—
232	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₇	1	2	yes	—
234	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
235	#125	—	2	4	no	—
236	#125	—	4	2	no	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	C₇×Q₈	1	4	yes	—
239	#117	—	4	4	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂³×C₇	1	2	yes	—
260	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
261	#107	—	2	4	no	—
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	—	4	2	no	—
264	#102	—	2	2	no	—
265	#102	—	2	2	no	—
266	#102	—	4	2	no	—
267	C₄×C₈	—	2	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	1	no	—
270	#95	—	2	2	no	—
271	#95	C₇×D₄	1	2	yes	—
272	C₂²×C₇	—	4	2	no	—
273	C₂²×C₇	—	4	2	no	—
274	C₂²×C₇	—	4	2	no	—
275	C₂²×C₇	—	8	1	no	—
276	C₂²×C₇	—	8	1	no	—
277	C₂²×C₇	—	8	1	no	—
278	C₂²×C₇	—	8	1	no	—
279	C₂²×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
280	C₂²×C₇	#546	1	1	yes	characteristic
281	C₂²×C₇	#548	1	1	yes	characteristic
282	C₂²×C₇	C₂×#135	1	1	yes	characteristic
283	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
284	C₂²×C₇	#576	1	1	yes	characteristic
285	C₂²×C₇	#578	1	1	yes	characteristic
286	C₄×C₇	—	2	2	no	—
287	C₄×C₇	—	4	2	no	—
288	C₄×C₇	—	4	2	no	—
289	C₄×C₇	—	4	2	no	—
290	C₄×C₇	—	4	2	no	—
291	C₄×C₇	—	4	2	no	—
292	C₄×C₇	—	8	2	no	—
293	C₄×C₇	—	8	2	no	—
294	C₄×C₇	#478	1	4	yes	—
295	C₄×C₇	#533	1	1	yes	characteristic
296	C₄×C₇	#544	1	1	yes	characteristic
297	C₄×C₇	#555	1	1	yes	characteristic
298	C₄×C₇	#556	1	1	yes	characteristic
299	C₂⁴	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
315	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
316	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
318	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	8	1	no	—
342	C₄⋊C₄	—	8	1	no	—
343	C₄⋊C₄	—	8	2	no	—
344	C₄⋊C₄	C₂×C₇×Q₈	1	2	yes	—
345	C₄⋊C₄	C₇×#41	1	2	yes	—
346	C₄⋊C₄	C₇×#41	1	2	yes	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	—	4	4	no	—
349	C₂²⋊C₄	—	8	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	4	4	no	—
353	C₄²	—	4	2	no	—
354	C₄²	C₂×C₇×Q₈	1	2	yes	—
355	C₄²	C₇×#41	1	2	yes	—
356	C₂×C₇	—	8	2	no	—
357	C₂×C₇	#2439	1	1	yes	characteristic
358	C₂×C₇	C₂×#478	1	1	yes	characteristic
359	C₂×C₇	#3083	1	1	yes	characteristic
360	C₂×C₇	#3305	1	1	yes	characteristic
361	C₂×C₇	#3330	1	1	yes	characteristic
362	C₂×C₇	#3364	1	1	yes	characteristic
363	C₂×C₇	#3366	1	1	yes	characteristic
364	C₂³	—	2	2	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
372	D₄	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	4	1	no	—
375	D₄	—	4	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	8	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
401	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
402	C₂×C₄	C₇×#135	1	2	yes	—
403	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
404	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
405	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
406	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
407	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
408	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
409	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
410	C₈	—	4	1	no	—
411	C₈	—	4	2	no	—
412	C₈	—	4	1	no	—
413	C₇	#26025	1	1	yes	characteristic, direct product factor, Sylow
414	C₂²	—	4	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
422	C₂²	C₇×#546	1	1	yes	characteristic
423	C₂²	C₇×#548	1	1	yes	characteristic
424	C₂²	C₂×C₇×#135	1	1	yes	characteristic
425	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
426	C₂²	C₇×#576	1	1	yes	characteristic
427	C₂²	C₇×#578	1	1	yes	characteristic
428	C₄	—	2	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	8	2	no	—
435	C₄	—	8	2	no	—
436	C₄	C₇×#478	1	4	yes	—
437	C₄	C₇×#533	1	1	yes	characteristic
438	C₄	C₇×#544	1	1	yes	characteristic
439	C₄	C₇×#555	1	1	yes	characteristic
440	C₄	C₇×#556	1	1	yes	characteristic
441	C₂	—	8	2	no	—
442	C₂	C₇×#2439	1	1	yes	characteristic
443	C₂	C₂×C₇×#478	1	1	yes	characteristic
444	C₂	C₇×#3083	1	1	yes	characteristic
445	C₂	C₇×#3305	1	1	yes	characteristic
446	C₂	C₇×#3330	1	1	yes	characteristic
447	C₂	C₇×#3364	1	1	yes	characteristic
448	C₂	C₇×#3366	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄×C₇×C₄⋊C₄ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇×#2552	C₂	semidirect
5. C₇×#1989	C₂	semidirect
6. C₇×#1947	C₂	semidirect
7. C₇×#1939	C₂	semidirect
8. C₇×#1921	C₂	semidirect
9. C₇×#1834	C₂	semidirect
41. #26025	C₇	direct (N × H)
84. #2552	C₂×C₇	semidirect
88. #1989	C₂×C₇	semidirect
89. #1947	C₂×C₇	semidirect
90. #1939	C₂×C₇	semidirect
91. #1921	C₂×C₇	semidirect
92. #1834	C₂×C₇	semidirect
413. C₇	#26025	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×#2552	2
C₇×#2354	2
C₇×#2067	2
C₇×#2025	2
C₇×#1989	2
C₇×#1947	2
C₇×#1939	2
C₇×#1921	2
C₇×#1834	2
C₇×#1802	2
C₄×C₇×#102	2
#26025	7

Subgroups — C7×#26025 #13203241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#26025 #13203241