Subgroups — C₇×#21548 #13198764

Order 1792.

914 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×#3054	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#443	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2929	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1975	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1946	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1938	C₂	1	2	yes	maximal, complemented
8	C₇×#1897	C₂	1	2	yes	maximal, complemented
9	C₇×#1811	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1772	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1764	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#135	C₂²	1	1	yes	characteristic
13	C₂×C₇×#131	C₂²	1	2	yes	—
14	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
15	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
16	C₇×#525	C₂²	1	2	yes	—
17	C₂×C₇×#117	C₂²	1	1	yes	characteristic
18	C₇×#470	C₄	1	2	yes	complemented
19	C₇×#469	C₄	1	2	yes	complemented
20	C₇×#468	C₄	1	4	yes	complemented
21	C₇×#443	—	2	4	no	—
22	C₇×#435	—	2	4	no	—
23	C₇×C₈×D₄	—	2	4	no	—
24	C₂×C₇×#108	C₂²	1	1	yes	characteristic
25	C₂×C₇×#108	C₂²	1	1	yes	characteristic
26	C₇×#427	C₂²	1	1	yes	characteristic
27	C₇×#424	C₂²	1	2	yes	—
28	C₂×C₇×#104	C₂²	1	2	yes	—
29	C₂×C₇×#104	C₂²	1	2	yes	—
30	C₇×#416	C₂²	1	2	yes	—
31	C₇×#408	C₂²	1	2	yes	—
32	C₇×#407	C₂²	1	2	yes	—
33	C₇×#405	—	2	4	no	—
34	C₇×#405	C₂²	1	2	yes	—
35	C₂×C₇×#97	C₂²	1	1	yes	characteristic
36	C₂×C₇×#97	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
39	C₇×#341	C₂²	1	2	yes	—
40	C₇×#339	C₂²	1	2	yes	—
41	C₇×#339	C₂²	1	2	yes	—
42	#21548	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×C₇×#41	C₂³	1	2	yes	—
44	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
45	C₇×#135	—	2	2	no	—
46	C₇×#135	—	2	2	no	—
47	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
48	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
49	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
50	C₇×#131	—	2	4	no	—
51	C₇×#131	—	2	4	no	—
52	C₂×C₇×M₁₆	—	2	2	no	—
53	C₂×C₇×M₁₆	—	2	2	no	—
54	C₂×C₇×M₁₆	—	2	2	no	—
55	C₂×C₇×M₁₆	C₂×C₄	1	2	yes	—
56	C₂×C₇×M₁₆	C₂×C₄	1	2	yes	—
57	C₂×C₇×M₁₆	C₂³	1	2	yes	—
58	C₂×C₇×M₁₆	C₂³	1	2	yes	—
59	C₂²×C₇×C₈	—	2	2	no	—
60	C₂²×C₇×C₈	—	2	2	no	—
61	C₂²×C₇×C₈	—	2	2	no	—
62	C₂²×C₇×C₈	D₄	1	2	yes	—
63	C₂²×C₇×C₈	D₄	1	2	yes	—
64	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₇×#123	—	2	2	no	—
69	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
70	C₇×#121	C₂×C₄	1	4	yes	—
71	C₇×#120	—	2	2	no	—
72	C₄×C₇×D₄	—	2	4	no	—
73	C₇×#117	—	2	2	no	—
74	C₇×#117	—	2	2	no	—
75	C₇×#117	C₂³	1	2	yes	—
76	C₂×C₇×C₄⋊C₄	—	2	1	no	—
77	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
80	C₇×#108	—	2	2	no	—
81	C₇×#108	—	2	2	no	—
82	C₇×#107	C₂×C₄	1	2	yes	—
83	C₇×#106	C₂×C₄	1	2	yes	—
84	C₇×C₄⋊C₈	—	2	4	no	—
85	C₇×#104	—	2	4	no	—
86	C₇×#104	—	2	4	no	—
87	C₇×#103	C₂×C₄	1	4	yes	—
88	C₇×#102	C₂×C₄	1	4	yes	—
89	C₇×C₂²⋊C₈	—	2	4	no	—
90	C₇×C₂²⋊C₈	—	2	4	no	—
91	C₇×#97	—	2	2	no	—
92	C₇×#97	—	2	2	no	—
93	C₇×#97	—	2	2	no	—
94	C₄×C₇×C₈	—	2	2	no	—
95	C₄×C₇×C₈	—	2	2	no	—
96	C₄×C₇×C₈	D₄	1	4	yes	complemented
97	#3054	C₂×C₇	1	1	yes	characteristic
98	C₂×#443	C₂×C₇	1	1	yes	characteristic, complemented
99	#2929	C₂×C₇	1	2	yes	complemented
100	C₂×#405	C₂×C₇	1	1	yes	characteristic, complemented
101	#1975	C₂×C₇	1	1	yes	characteristic, complemented
102	#1946	C₂×C₇	1	1	yes	characteristic, complemented
103	#1938	C₂×C₇	1	2	yes	complemented
104	#1897	C₂×C₇	1	2	yes	complemented
105	#1811	C₂×C₇	1	1	yes	characteristic, complemented
106	#1772	C₂×C₇	1	1	yes	characteristic, complemented
107	#1764	C₂×C₇	1	2	yes	complemented
108	C₂⁴×C₇	#41	1	1	yes	characteristic
109	C₇×#41	—	2	2	no	—
110	C₇×#41	—	2	2	no	—
111	C₇×#41	—	2	2	no	—
112	C₇×#41	—	2	2	no	—
113	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
114	C₂×C₇×D₄	—	2	4	no	—
115	C₂×C₇×D₄	—	2	2	no	—
116	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₇	—	2	1	no	—
118	C₂²×C₄×C₇	—	2	1	no	—
119	C₂²×C₄×C₇	—	2	1	no	—
120	C₂²×C₄×C₇	—	2	1	no	—
121	C₂²×C₄×C₇	—	2	1	no	—
122	C₂²×C₄×C₇	—	2	1	no	—
123	C₂²×C₄×C₇	—	2	2	no	—
124	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₇	#41	1	1	yes	characteristic
127	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
128	C₇×Q₁₆	—	2	2	no	—
129	C₇×SD₁₆	—	2	4	no	—
130	C₇×D₈	—	2	2	no	—
131	C₇×M₁₆	—	2	4	no	—
132	C₇×M₁₆	—	2	4	no	—
133	C₇×M₁₆	—	2	2	no	—
134	C₇×M₁₆	—	2	2	no	—
135	C₇×M₁₆	—	2	2	no	—
136	C₇×M₁₆	—	2	2	no	—
137	C₇×M₁₆	—	4	4	no	—
138	C₂×C₇×C₈	—	2	1	no	—
139	C₂×C₇×C₈	—	2	1	no	—
140	C₂×C₇×C₈	—	2	1	no	—
141	C₂×C₇×C₈	—	2	1	no	—
142	C₂×C₇×C₈	—	2	4	no	—
143	C₂×C₇×C₈	—	2	4	no	—
144	C₂×C₇×C₈	—	2	2	no	—
145	C₂×C₇×C₈	—	2	2	no	—
146	C₂×C₇×C₈	—	4	4	no	—
147	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
148	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
151	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
152	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
153	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
154	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₇×C₈	#41	1	2	yes	—
156	C₂×C₇×C₈	#41	1	2	yes	—
157	C₇×C₄⋊C₄	—	2	4	no	—
158	C₇×C₄⋊C₄	—	2	4	no	—
159	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
160	C₇×C₂²⋊C₄	—	2	4	no	—
161	C₇×C₂²⋊C₄	—	2	4	no	—
162	C₇×C₂²⋊C₄	—	2	2	no	—
163	C₇×C₂²⋊C₄	—	2	4	no	—
164	C₄²×C₇	—	2	1	no	—
165	C₄²×C₇	—	2	2	no	—
166	C₄²×C₇	—	2	1	no	—
167	C₄²×C₇	C₂×D₄	1	2	yes	—
168	C₄²×C₇	#41	1	2	yes	—
169	C₂×#135	C₂²×C₇	1	1	yes	characteristic
170	C₂×#131	C₂²×C₇	1	2	yes	—
171	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
172	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
173	#525	C₂²×C₇	1	2	yes	—
174	C₂×#117	C₂²×C₇	1	1	yes	characteristic
175	#470	C₄×C₇	1	2	yes	complemented
176	#469	C₄×C₇	1	2	yes	complemented
177	#468	C₄×C₇	1	4	yes	complemented
178	#443	—	2	4	no	—
179	#435	—	2	4	no	—
180	C₈×D₄	—	2	4	no	—
181	C₂×#108	C₂²×C₇	1	1	yes	characteristic
182	C₂×#108	C₂²×C₇	1	1	yes	characteristic
183	#427	C₂²×C₇	1	1	yes	characteristic
184	#424	C₂²×C₇	1	2	yes	—
185	C₂×#104	C₂²×C₇	1	2	yes	—
186	C₂×#104	C₂²×C₇	1	2	yes	—
187	#416	C₂²×C₇	1	2	yes	—
188	#408	C₂²×C₇	1	2	yes	—
189	#407	C₂²×C₇	1	2	yes	—
190	#405	—	2	4	no	—
191	#405	C₂²×C₇	1	2	yes	—
192	C₂×#97	C₂²×C₇	1	1	yes	characteristic
193	C₂×#97	C₂²×C₇	1	1	yes	characteristic
194	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
195	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
196	#341	C₂²×C₇	1	2	yes	—
197	#339	C₂²×C₇	1	2	yes	—
198	#339	C₂²×C₇	1	2	yes	—
199	C₂³×C₇	—	2	1	no	—
200	C₂³×C₇	—	2	1	no	—
201	C₂³×C₇	—	2	2	no	—
202	C₂³×C₇	—	4	2	no	—
203	C₂³×C₇	C₄×D₄	1	2	yes	—
204	C₂³×C₇	C₂×#41	1	1	yes	characteristic
205	C₇×Q₈	—	2	2	no	—
206	C₇×Q₈	—	2	2	no	—
207	C₇×D₄	—	2	2	no	—
208	C₇×D₄	—	2	2	no	—
209	C₇×D₄	—	4	8	no	—
210	C₇×D₄	—	4	2	no	—
211	C₇×D₄	—	4	2	no	—
212	C₂×C₄×C₇	—	2	1	no	—
213	C₂×C₄×C₇	—	2	1	no	—
214	C₂×C₄×C₇	—	2	2	no	—
215	C₂×C₄×C₇	—	2	2	no	—
216	C₂×C₄×C₇	—	2	2	no	—
217	C₂×C₄×C₇	—	2	2	no	—
218	C₂×C₄×C₇	—	2	4	no	—
219	C₂×C₄×C₇	—	2	2	no	—
220	C₂×C₄×C₇	—	2	2	no	—
221	C₂×C₄×C₇	—	2	2	no	—
222	C₂×C₄×C₇	—	4	2	no	—
223	C₂×C₄×C₇	—	4	2	no	—
224	C₂×C₄×C₇	—	4	2	no	—
225	C₂×C₄×C₇	—	4	2	no	—
226	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
233	C₇×C₈	—	2	2	no	—
234	C₇×C₈	—	2	2	no	—
235	C₇×C₈	—	4	2	no	—
236	C₇×C₈	—	4	2	no	—
237	C₇×C₈	C₄×D₄	1	2	yes	—
238	C₇×C₈	C₄×D₄	1	2	yes	—
239	C₇×C₈	#121	1	2	yes	—
240	C₇×C₈	#121	1	2	yes	—
241	C₂×#41	C₂³×C₇	1	2	yes	—
242	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
243	#135	—	2	2	no	—
244	#135	—	2	2	no	—
245	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
246	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
247	C₂×D₈	C₂×C₄×C₇	1	1	yes	characteristic
248	#131	—	2	4	no	—
249	#131	—	2	4	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	C₂×C₄×C₇	1	2	yes	—
254	C₂×M₁₆	C₂×C₄×C₇	1	2	yes	—
255	C₂×M₁₆	C₂³×C₇	1	2	yes	—
256	C₂×M₁₆	C₂³×C₇	1	2	yes	—
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	—	2	2	no	—
259	C₂²×C₈	—	2	2	no	—
260	C₂²×C₈	C₇×D₄	1	2	yes	—
261	C₂²×C₈	C₇×D₄	1	2	yes	—
262	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
266	#123	—	2	2	no	—
267	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
268	#121	C₂×C₄×C₇	1	4	yes	—
269	#120	—	2	2	no	—
270	C₄×D₄	—	2	4	no	—
271	#117	—	2	2	no	—
272	#117	—	2	2	no	—
273	#117	C₂³×C₇	1	2	yes	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
278	#108	—	2	2	no	—
279	#108	—	2	2	no	—
280	#107	C₂×C₄×C₇	1	2	yes	—
281	#106	C₂×C₄×C₇	1	2	yes	—
282	C₄⋊C₈	—	2	4	no	—
283	#104	—	2	4	no	—
284	#104	—	2	4	no	—
285	#103	C₂×C₄×C₇	1	4	yes	—
286	#102	C₂×C₄×C₇	1	4	yes	—
287	C₂²⋊C₈	—	2	4	no	—
288	C₂²⋊C₈	—	2	4	no	—
289	#97	—	2	2	no	—
290	#97	—	2	2	no	—
291	#97	—	2	2	no	—
292	C₄×C₈	—	2	2	no	—
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	C₇×D₄	1	4	yes	complemented
295	C₂²×C₇	—	2	2	no	—
296	C₂²×C₇	—	2	4	no	—
297	C₂²×C₇	—	2	2	no	—
298	C₂²×C₇	—	4	2	no	—
299	C₂²×C₇	—	4	2	no	—
300	C₂²×C₇	—	4	4	no	—
301	C₂²×C₇	—	4	2	no	—
302	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
303	C₂²×C₇	#525	1	1	yes	characteristic
304	C₂²×C₇	#529	1	1	yes	characteristic
305	C₄×C₇	—	2	2	no	—
306	C₄×C₇	—	4	2	no	—
307	C₄×C₇	—	4	2	no	—
308	C₄×C₇	—	4	4	no	—
309	C₄×C₇	—	4	2	no	—
310	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
311	C₄×C₇	C₄×#41	1	1	yes	characteristic
312	C₄×C₇	C₂×#121	1	1	yes	characteristic
313	C₄×C₇	#532	1	1	yes	characteristic
314	C₂⁴	C₇×#41	1	1	yes	characteristic
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
331	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
332	C₂²×C₄	C₇×#41	1	1	yes	characteristic
333	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
334	Q₁₆	—	2	2	no	—
335	SD₁₆	—	2	4	no	—
336	D₈	—	2	2	no	—
337	M₁₆	—	2	4	no	—
338	M₁₆	—	2	4	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	4	4	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	4	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	4	4	no	—
353	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
354	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
355	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
356	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
357	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
358	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
359	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
360	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
361	C₂×C₈	C₇×#41	1	2	yes	—
362	C₂×C₈	C₇×#41	1	2	yes	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	1	no	—
373	C₄²	C₂×C₇×D₄	1	2	yes	—
374	C₄²	C₇×#41	1	2	yes	—
375	C₂×C₇	—	2	1	no	—
376	C₂×C₇	—	2	1	no	—
377	C₂×C₇	—	4	2	no	—
378	C₂×C₇	—	8	2	no	—
379	C₂×C₇	C₄×#121	1	1	yes	characteristic
380	C₂×C₇	#2955	1	2	yes	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	C₄×C₇×D₄	1	2	yes	—
386	C₂³	C₂×C₇×#41	1	1	yes	characteristic
387	Q₈	—	2	2	no	—
388	Q₈	—	2	2	no	—
389	D₄	—	2	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	8	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
409	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
410	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
412	C₂×C₄	C₂×C₇×#41	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	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	4	2	no	—
419	C₈	C₄×C₇×D₄	1	2	yes	—
420	C₈	C₄×C₇×D₄	1	2	yes	—
421	C₈	C₇×#121	1	2	yes	—
422	C₈	C₇×#121	1	2	yes	—
423	C₇	#21548	1	1	yes	characteristic, direct product factor, Sylow
424	C₂²	—	2	2	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	2	no	—
431	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
432	C₂²	C₇×#525	1	1	yes	characteristic
433	C₂²	C₇×#529	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	4	no	—
438	C₄	—	4	2	no	—
439	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
440	C₄	C₄×C₇×#41	1	1	yes	characteristic
441	C₄	C₂×C₇×#121	1	1	yes	characteristic
442	C₄	C₇×#532	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	4	2	no	—
446	C₂	—	8	2	no	—
447	C₂	C₄×C₇×#121	1	1	yes	characteristic
448	C₂	C₇×#2955	1	2	yes	—

	subgroup	G/H
center	C₂×C₇×C₈	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#3054	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇×C₈ ◁ C₂³×C₇×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#443	C₂	semidirect
3. C₇×#2929	C₂	semidirect
4. C₂×C₇×#405	C₂	semidirect
5. C₇×#1975	C₂	semidirect
6. C₇×#1946	C₂	semidirect
7. C₇×#1938	C₂	semidirect
8. C₇×#1897	C₂	semidirect
9. C₇×#1811	C₂	semidirect
10. C₇×#1772	C₂	semidirect
11. C₇×#1764	C₂	semidirect
18. C₇×#470	C₄	semidirect
19. C₇×#469	C₄	semidirect
20. C₇×#468	C₄	semidirect
42. #21548	C₇	direct (N × H)
96. C₄×C₇×C₈	D₄	semidirect
98. C₂×#443	C₂×C₇	semidirect
99. #2929	C₂×C₇	semidirect
100. C₂×#405	C₂×C₇	semidirect
101. #1975	C₂×C₇	semidirect
102. #1946	C₂×C₇	semidirect
103. #1938	C₂×C₇	semidirect
104. #1897	C₂×C₇	semidirect
105. #1811	C₂×C₇	semidirect
106. #1772	C₂×C₇	semidirect
107. #1764	C₂×C₇	semidirect
175. #470	C₄×C₇	semidirect
176. #469	C₄×C₇	semidirect
177. #468	C₄×C₇	semidirect
294. C₄×C₈	C₇×D₄	semidirect
423. C₇	#21548	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×#3054	2
C₂×C₇×#443	2
C₇×#2929	2
C₂×C₇×#405	2
C₇×#1975	2
C₇×#1946	2
C₇×#1938	2
C₇×#1897	2
C₇×#1811	2
C₇×#1772	2
C₇×#1764	2
#21548	7

Subgroups — C7×#21548 #13198764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21548 #13198764