Subgroups — C₇×#26020 #13203236

Order 1792.

786 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2551	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×#2023	C₂	1	2	yes	maximal
5	C₇×#1988	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×#1918	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×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₇×#117	—	2	1	no	—
16	C₂×C₇×#107	C₂²	1	2	yes	—
17	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₇×#102	C₂²	1	1	yes	characteristic
20	C₂×C₇×#102	C₂²	1	1	yes	characteristic
21	C₂×C₇×#102	C₂²	1	2	yes	—
22	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
23	C₇×#395	—	2	2	no	—
24	C₇×#390	C₂²	1	2	yes	—
25	C₇×#389	—	2	1	no	—
26	C₇×#389	C₂²	1	2	yes	—
27	C₇×#388	—	2	2	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	#26020	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₇×Q₈	—	2	2	no	—
43	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₇	—	2	1	no	—
45	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₇×C₈	C₂³	1	2	yes	—
47	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
48	C₇×C₄⋊Q₈	—	2	4	no	—
49	C₇×C₄⋊Q₈	—	4	2	no	—
50	C₇×C₄⋊Q₈	—	4	4	no	—
51	C₄×C₇×D₄	—	2	2	no	—
52	C₄×C₇×D₄	Q₈	1	4	yes	complemented
53	C₇×#117	—	4	4	no	—
54	C₂×C₇×C₄⋊C₄	—	2	1	no	—
55	C₂×C₇×C₄⋊C₄	—	2	1	no	—
56	C₂×C₇×C₄⋊C₄	—	2	2	no	—
57	C₂×C₇×C₄⋊C₄	—	2	2	no	—
58	C₂×C₇×C₄⋊C₄	—	2	1	no	—
59	C₂×C₇×C₄⋊C₄	—	2	1	no	—
60	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
61	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
62	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₄²×C₇	—	2	2	no	—
71	C₂×C₄²×C₇	—	2	1	no	—
72	C₂×C₄²×C₇	C₂³	1	2	yes	—
73	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
74	C₇×#107	—	2	4	no	—
75	C₇×C₄⋊C₈	—	2	2	no	—
76	C₇×C₄⋊C₈	—	4	2	no	—
77	C₇×#102	—	2	2	no	—
78	C₇×#102	—	2	2	no	—
79	C₇×#102	—	4	2	no	—
80	C₄×C₇×C₈	—	2	2	no	—
81	C₇×#95	—	2	2	no	—
82	C₇×#95	—	2	1	no	—
83	C₇×#95	—	2	2	no	—
84	C₇×#95	D₄	1	2	yes	—
85	#2551	C₂×C₇	1	1	yes	characteristic, complemented
86	#2354	C₂×C₇	1	1	yes	characteristic
87	#2067	C₂×C₇	1	2	yes	—
88	#2023	C₂×C₇	1	2	yes	—
89	#1988	C₂×C₇	1	2	yes	complemented
90	#1947	C₂×C₇	1	1	yes	characteristic, complemented
91	#1939	C₂×C₇	1	1	yes	characteristic, complemented
92	#1918	C₂×C₇	1	2	yes	complemented
93	#1834	C₂×C₇	1	1	yes	characteristic, complemented
94	#1802	C₂×C₇	1	1	yes	characteristic
95	C₄×#102	C₂×C₇	1	1	yes	characteristic
96	C₂⁴×C₇	—	2	1	no	—
97	C₂×C₇×Q₈	—	4	4	no	—
98	C₂×C₇×Q₈	—	4	4	no	—
99	C₂×C₇×Q₈	—	8	2	no	—
100	C₂×C₇×D₄	—	2	1	no	—
101	C₂×C₇×D₄	—	2	1	no	—
102	C₂×C₇×D₄	—	2	1	no	—
103	C₂×C₇×D₄	—	2	1	no	—
104	C₂×C₇×D₄	—	2	1	no	—
105	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
106	C₂²×C₄×C₇	—	2	1	no	—
107	C₂²×C₄×C₇	—	2	1	no	—
108	C₂²×C₄×C₇	—	2	1	no	—
109	C₂²×C₄×C₇	—	2	4	no	—
110	C₂²×C₄×C₇	—	2	2	no	—
111	C₂²×C₄×C₇	—	2	2	no	—
112	C₂²×C₄×C₇	—	4	2	no	—
113	C₂²×C₄×C₇	—	4	2	no	—
114	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
119	C₂×C₇×C₈	—	2	1	no	—
120	C₂×C₇×C₈	—	2	1	no	—
121	C₂×C₇×C₈	—	2	1	no	—
122	C₂×C₇×C₈	—	2	1	no	—
123	C₂×C₇×C₈	—	2	2	no	—
124	C₂×C₇×C₈	—	2	2	no	—
125	C₂×C₇×C₈	—	2	2	no	—
126	C₂×C₇×C₈	—	2	1	no	—
127	C₂×C₇×C₈	—	2	1	no	—
128	C₇×C₄⋊C₄	—	2	2	no	—
129	C₇×C₄⋊C₄	—	2	1	no	—
130	C₇×C₄⋊C₄	—	2	1	no	—
131	C₇×C₄⋊C₄	—	2	1	no	—
132	C₇×C₄⋊C₄	—	2	2	no	—
133	C₇×C₄⋊C₄	—	2	2	no	—
134	C₇×C₄⋊C₄	—	2	2	no	—
135	C₇×C₄⋊C₄	—	2	2	no	—
136	C₇×C₄⋊C₄	—	4	4	no	—
137	C₇×C₄⋊C₄	—	4	2	no	—
138	C₇×C₄⋊C₄	—	4	4	no	—
139	C₇×C₄⋊C₄	—	4	2	no	—
140	C₇×C₄⋊C₄	—	8	1	no	—
141	C₇×C₄⋊C₄	—	8	1	no	—
142	C₇×C₄⋊C₄	D₈	1	4	yes	—
143	C₇×C₄⋊C₄	C₂×Q₈	1	2	yes	—
144	C₇×C₄⋊C₄	#41	1	2	yes	—
145	C₇×C₄⋊C₄	#41	1	2	yes	—
146	C₇×C₂²⋊C₄	—	2	4	no	—
147	C₇×C₂²⋊C₄	—	4	4	no	—
148	C₇×C₂²⋊C₄	—	8	2	no	—
149	C₄²×C₇	—	2	2	no	—
150	C₄²×C₇	—	2	2	no	—
151	C₄²×C₇	—	4	4	no	—
152	C₄²×C₇	—	4	2	no	—
153	C₄²×C₇	C₂×Q₈	1	2	yes	—
154	C₄²×C₇	#41	1	2	yes	—
155	C₂×C₄⋊Q₈	—	2	1	no	—
156	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
157	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
158	C₂×#117	—	2	1	no	—
159	C₂×#107	C₂²×C₇	1	2	yes	—
160	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
161	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
162	C₂×#102	C₂²×C₇	1	1	yes	characteristic
163	C₂×#102	C₂²×C₇	1	1	yes	characteristic
164	C₂×#102	C₂²×C₇	1	2	yes	—
165	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
166	#395	—	2	2	no	—
167	#390	C₂²×C₇	1	2	yes	—
168	#389	—	2	1	no	—
169	#389	C₂²×C₇	1	2	yes	—
170	#388	—	2	2	no	—
171	#384	C₂²×C₇	1	1	yes	characteristic
172	#384	C₂²×C₇	1	1	yes	characteristic
173	#380	—	2	1	no	—
174	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
175	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
176	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
177	#340	C₂²×C₇	1	2	yes	—
178	#340	C₂²×C₇	1	2	yes	—
179	#340	C₂²×C₇	1	2	yes	—
180	#340	C₂²×C₇	1	1	yes	characteristic
181	#340	C₂²×C₇	1	2	yes	—
182	#340	C₂²×C₇	1	1	yes	characteristic
183	#336	C₂²×C₇	1	2	yes	—
184	C₂³×C₇	—	2	2	no	—
185	C₂³×C₇	—	4	1	no	—
186	C₂³×C₇	—	4	1	no	—
187	C₂³×C₇	—	4	1	no	—
188	C₂³×C₇	—	4	1	no	—
189	C₂³×C₇	—	4	1	no	—
190	C₂³×C₇	—	4	1	no	—
191	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
192	C₇×Q₈	—	8	8	no	—
193	C₇×D₄	—	2	2	no	—
194	C₇×D₄	—	2	2	no	—
195	C₇×D₄	—	4	1	no	—
196	C₇×D₄	—	4	1	no	—
197	C₂×C₄×C₇	—	2	2	no	—
198	C₂×C₄×C₇	—	2	1	no	—
199	C₂×C₄×C₇	—	2	1	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	—	2	2	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	2	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	1	no	—
211	C₂×C₄×C₇	—	4	1	no	—
212	C₂×C₄×C₇	—	4	1	no	—
213	C₂×C₄×C₇	—	4	8	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	—	4	2	no	—
218	C₂×C₄×C₇	—	4	2	no	—
219	C₂×C₄×C₇	—	4	2	no	—
220	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
221	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
222	C₂×C₄×C₇	C₂×D₈	1	4	yes	—
223	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
224	C₂×C₄×C₇	#137	1	2	yes	—
225	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
226	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
230	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
231	C₇×C₈	—	4	1	no	—
232	C₇×C₈	—	4	2	no	—
233	C₇×C₈	—	4	1	no	—
234	C₂²×Q₈	—	2	2	no	—
235	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
236	C₂³×C₄	—	2	1	no	—
237	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₇	1	2	yes	—
239	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
240	C₄⋊Q₈	—	2	4	no	—
241	C₄⋊Q₈	—	4	2	no	—
242	C₄⋊Q₈	—	4	4	no	—
243	C₄×D₄	—	2	2	no	—
244	C₄×D₄	C₇×Q₈	1	4	yes	complemented
245	#117	—	4	4	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	C₂³×C₇	1	2	yes	—
265	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
266	#107	—	2	4	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	4	2	no	—
269	#102	—	2	2	no	—
270	#102	—	2	2	no	—
271	#102	—	4	2	no	—
272	C₄×C₈	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	—	2	1	no	—
275	#95	—	2	2	no	—
276	#95	C₇×D₄	1	2	yes	—
277	C₂²×C₇	—	4	2	no	—
278	C₂²×C₇	—	4	2	no	—
279	C₂²×C₇	—	4	2	no	—
280	C₂²×C₇	—	8	1	no	—
281	C₂²×C₇	—	8	1	no	—
282	C₂²×C₇	—	8	1	no	—
283	C₂²×C₇	—	8	1	no	—
284	C₂²×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
285	C₂²×C₇	#546	1	1	yes	characteristic
286	C₂²×C₇	#548	1	1	yes	characteristic
287	C₂²×C₇	C₂²×D₈	1	1	yes	characteristic
288	C₂²×C₇	C₂×#137	1	1	yes	characteristic
289	C₂²×C₇	#577	1	1	yes	characteristic
290	C₂²×C₇	#577	1	1	yes	characteristic
291	C₄×C₇	—	2	2	no	—
292	C₄×C₇	—	2	4	no	—
293	C₄×C₇	—	4	2	no	—
294	C₄×C₇	—	4	2	no	—
295	C₄×C₇	—	4	2	no	—
296	C₄×C₇	—	4	2	no	—
297	C₄×C₇	—	8	2	no	—
298	C₄×C₇	—	8	2	no	—
299	C₄×C₇	#474	1	4	yes	—
300	C₄×C₇	#533	1	1	yes	characteristic
301	C₄×C₇	#544	1	1	yes	characteristic
302	C₄×C₇	#555	1	1	yes	characteristic
303	C₄×C₇	#556	1	1	yes	characteristic
304	C₂⁴	—	2	1	no	—
305	C₂×Q₈	—	4	4	no	—
306	C₂×Q₈	—	4	4	no	—
307	C₂×Q₈	—	8	2	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
323	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
325	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	4	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	8	1	no	—
349	C₄⋊C₄	—	8	1	no	—
350	C₄⋊C₄	C₇×D₈	1	4	yes	—
351	C₄⋊C₄	C₂×C₇×Q₈	1	2	yes	—
352	C₄⋊C₄	C₇×#41	1	2	yes	—
353	C₄⋊C₄	C₇×#41	1	2	yes	—
354	C₂²⋊C₄	—	2	4	no	—
355	C₂²⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	8	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	4	4	no	—
360	C₄²	—	4	2	no	—
361	C₄²	C₂×C₇×Q₈	1	2	yes	—
362	C₄²	C₇×#41	1	2	yes	—
363	C₂×C₇	—	8	2	no	—
364	C₂×C₇	#2439	1	1	yes	characteristic
365	C₂×C₇	C₂×#474	1	1	yes	characteristic
366	C₂×C₇	#3084	1	1	yes	characteristic
367	C₂×C₇	#3294	1	1	yes	characteristic
368	C₂×C₇	#3329	1	1	yes	characteristic
369	C₂×C₇	#3358	1	1	yes	characteristic
370	C₂×C₇	#3369	1	1	yes	characteristic
371	C₂³	—	2	2	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
379	Q₈	—	8	8	no	—
380	D₄	—	2	2	no	—
381	D₄	—	2	2	no	—
382	D₄	—	4	1	no	—
383	D₄	—	4	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	8	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
408	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
409	C₂×C₄	C₂×C₇×D₈	1	4	yes	—
410	C₂×C₄	C₂×C₇×D₈	1	2	yes	—
411	C₂×C₄	C₇×#137	1	2	yes	—
412	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
413	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
414	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
415	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
416	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
417	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
418	C₈	—	4	1	no	—
419	C₈	—	4	2	no	—
420	C₈	—	4	1	no	—
421	C₇	#26020	1	1	yes	characteristic, direct product factor, Sylow
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
430	C₂²	C₇×#546	1	1	yes	characteristic
431	C₂²	C₇×#548	1	1	yes	characteristic
432	C₂²	C₂²×C₇×D₈	1	1	yes	characteristic
433	C₂²	C₂×C₇×#137	1	1	yes	characteristic
434	C₂²	C₇×#577	1	1	yes	characteristic
435	C₂²	C₇×#577	1	1	yes	characteristic
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	8	2	no	—
443	C₄	—	8	2	no	—
444	C₄	C₇×#474	1	4	yes	—
445	C₄	C₇×#533	1	1	yes	characteristic
446	C₄	C₇×#544	1	1	yes	characteristic
447	C₄	C₇×#555	1	1	yes	characteristic
448	C₄	C₇×#556	1	1	yes	characteristic
449	C₂	—	8	2	no	—
450	C₂	C₇×#2439	1	1	yes	characteristic
451	C₂	C₂×C₇×#474	1	1	yes	characteristic
452	C₂	C₇×#3084	1	1	yes	characteristic
453	C₂	C₇×#3294	1	1	yes	characteristic
454	C₂	C₇×#3329	1	1	yes	characteristic
455	C₂	C₇×#3358	1	1	yes	characteristic
456	C₂	C₇×#3369	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×#2551	C₂	semidirect
5. C₇×#1988	C₂	semidirect
6. C₇×#1947	C₂	semidirect
7. C₇×#1939	C₂	semidirect
8. C₇×#1918	C₂	semidirect
9. C₇×#1834	C₂	semidirect
41. #26020	C₇	direct (N × H)
52. C₄×C₇×D₄	Q₈	semidirect
85. #2551	C₂×C₇	semidirect
89. #1988	C₂×C₇	semidirect
90. #1947	C₂×C₇	semidirect
91. #1939	C₂×C₇	semidirect
92. #1918	C₂×C₇	semidirect
93. #1834	C₂×C₇	semidirect
244. C₄×D₄	C₇×Q₈	semidirect
421. C₇	#26020	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×#2551	2
C₇×#2354	2
C₇×#2067	2
C₇×#2023	2
C₇×#1988	2
C₇×#1947	2
C₇×#1939	2
C₇×#1918	2
C₇×#1834	2
C₇×#1802	2
C₄×C₇×#102	2
#26020	7

Subgroups — C7×#26020 #13203236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#26020 #13203236