Subgroups — C₇×#22978 #13200194

Order 1792.

870 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#478	C₂	1	1	yes	maximal, characteristic
2	C₇×#2370	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₇×#1992	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1948	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1941	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1920	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1918	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1864	C₂	1	1	yes	maximal, characteristic
11	C₇×#1864	C₂	1	1	yes	maximal, characteristic
12	C₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1762	C₂	1	1	yes	maximal, characteristic
14	C₇×#1762	C₂	1	1	yes	maximal, characteristic
15	C₄×C₇×#102	C₂	1	1	yes	maximal, characteristic
16	C₂×C₇×#125	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
21	C₇×#478	C₄	1	8	yes	complemented
22	C₂×C₇×#107	C₂²	1	1	yes	characteristic
23	C₂×C₇×#106	C₂²	1	1	yes	characteristic
24	C₂×C₇×#106	C₂²	1	1	yes	characteristic
25	C₂×C₇×#106	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×#102	C₂²	1	1	yes	characteristic
28	C₂×C₇×#102	C₂²	1	1	yes	characteristic
29	C₂×C₇×#102	C₂²	1	1	yes	characteristic
30	C₂×C₇×#102	C₂²	1	1	yes	characteristic
31	C₂×C₇×#97	C₂²	1	1	yes	characteristic
32	C₂×C₇×#97	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
34	C₇×#389	—	2	1	no	—
35	C₇×#389	C₂²	1	1	yes	characteristic
36	C₇×#389	C₂²	1	1	yes	characteristic
37	C₇×#389	C₂²	1	1	yes	characteristic
38	C₇×#389	C₂²	1	1	yes	characteristic
39	C₇×#387	—	2	1	no	—
40	C₇×#387	—	2	1	no	—
41	C₇×#385	—	2	1	no	—
42	C₇×#385	—	2	1	no	—
43	C₇×#384	C₂²	1	1	yes	characteristic
44	C₇×#380	—	2	1	no	—
45	C₄×C₇×C₄⋊C₄	—	2	1	no	—
46	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₇×#340	C₂²	1	1	yes	characteristic
51	C₇×#340	C₂²	1	1	yes	characteristic
52	C₇×#340	C₂²	1	1	yes	characteristic
53	C₇×#340	C₂²	1	1	yes	characteristic
54	C₇×#340	C₂²	1	1	yes	characteristic
55	C₇×#340	C₂²	1	1	yes	characteristic
56	C₇×#340	C₂²	1	1	yes	characteristic
57	C₇×#340	C₂²	1	1	yes	characteristic
58	C₇×#336	C₂²	1	1	yes	characteristic
59	C₇×#336	C₂²	1	1	yes	characteristic
60	#22978	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₇	—	2	1	no	—
63	C₂³×C₄×C₇	—	2	1	no	—
64	C₂³×C₄×C₇	—	2	1	no	—
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	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₇×#125	—	2	2	no	—
70	C₇×#125	C₂×C₄	1	4	yes	complemented
71	C₄×C₇×D₄	—	2	2	no	—
72	C₄×C₇×D₄	—	2	2	no	—
73	C₄×C₇×D₄	—	2	2	no	—
74	C₄×C₇×D₄	—	4	1	no	—
75	C₄×C₇×D₄	—	4	1	no	—
76	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
77	C₂×C₇×C₄⋊C₄	—	2	1	no	—
78	C₂×C₇×C₄⋊C₄	—	2	1	no	—
79	C₂×C₇×C₄⋊C₄	—	2	1	no	—
80	C₂×C₇×C₄⋊C₄	—	2	1	no	—
81	C₂×C₇×C₄⋊C₄	—	2	1	no	—
82	C₂×C₇×C₄⋊C₄	—	2	1	no	—
83	C₂×C₇×C₄⋊C₄	—	2	1	no	—
84	C₂×C₇×C₄⋊C₄	—	2	1	no	—
85	C₂×C₇×C₄⋊C₄	—	4	4	no	—
86	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
88	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₄²×C₇	—	2	1	no	—
99	C₂×C₄²×C₇	—	2	1	no	—
100	C₂×C₄²×C₇	—	2	1	no	—
101	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
104	C₇×#107	C₂×C₄	1	4	yes	complemented
105	C₇×#106	—	4	1	no	—
106	C₇×#106	—	4	1	no	—
107	C₇×#106	C₂×C₄	1	4	yes	complemented
108	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
109	C₇×#102	—	2	2	no	—
110	C₇×#102	C₂×C₄	1	4	yes	—
111	C₇×#102	C₂×C₄	1	4	yes	—
112	C₇×#102	Q₈	1	4	yes	—
113	C₇×#97	—	2	2	no	—
114	C₇×#97	—	4	1	no	—
115	C₄×C₇×C₈	—	4	1	no	—
116	C₇×#95	—	2	1	no	—
117	C₇×#95	—	2	1	no	—
118	C₇×#95	—	2	1	no	—
119	C₇×#95	—	2	1	no	—
120	C₇×#95	—	2	1	no	—
121	C₇×#95	—	2	1	no	—
122	C₇×#95	—	2	1	no	—
123	C₇×#95	D₄	1	1	yes	characteristic
124	C₇×#95	D₄	1	1	yes	characteristic
125	C₂×#478	C₂×C₇	1	1	yes	characteristic
126	#2370	C₂×C₇	1	1	yes	characteristic, complemented
127	D₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic
128	#1992	C₂×C₇	1	1	yes	characteristic, complemented
129	#1948	C₂×C₇	1	1	yes	characteristic, complemented
130	#1943	C₂×C₇	1	1	yes	characteristic, complemented
131	#1941	C₂×C₇	1	1	yes	characteristic, complemented
132	#1920	C₂×C₇	1	1	yes	characteristic, complemented
133	#1918	C₂×C₇	1	1	yes	characteristic, complemented
134	#1864	C₂×C₇	1	1	yes	characteristic
135	#1864	C₂×C₇	1	1	yes	characteristic
136	#1771	C₂×C₇	1	1	yes	characteristic, complemented
137	#1762	C₂×C₇	1	1	yes	characteristic
138	#1762	C₂×C₇	1	1	yes	characteristic
139	C₄×#102	C₂×C₇	1	1	yes	characteristic
140	C₂⁴×C₇	—	2	1	no	—
141	C₂×C₇×D₄	—	2	1	no	—
142	C₂×C₇×D₄	—	2	1	no	—
143	C₂×C₇×D₄	—	2	1	no	—
144	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
145	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
146	C₂×C₇×D₄	#41	1	2	yes	—
147	C₂²×C₄×C₇	—	2	1	no	—
148	C₂²×C₄×C₇	—	2	1	no	—
149	C₂²×C₄×C₇	—	2	1	no	—
150	C₂²×C₄×C₇	—	2	1	no	—
151	C₂²×C₄×C₇	—	2	4	no	—
152	C₂²×C₄×C₇	—	2	1	no	—
153	C₂²×C₄×C₇	—	2	1	no	—
154	C₂²×C₄×C₇	—	2	1	no	—
155	C₂²×C₄×C₇	—	4	2	no	—
156	C₂²×C₄×C₇	—	4	2	no	—
157	C₂²×C₄×C₇	—	4	2	no	—
158	C₂²×C₄×C₇	—	4	2	no	—
159	C₂²×C₄×C₇	—	4	2	no	—
160	C₂²×C₄×C₇	—	4	2	no	—
161	C₂²×C₄×C₇	—	8	1	no	—
162	C₂²×C₄×C₇	—	8	1	no	—
163	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
170	C₂×C₇×C₈	—	2	1	no	—
171	C₂×C₇×C₈	—	2	1	no	—
172	C₂×C₇×C₈	—	2	1	no	—
173	C₂×C₇×C₈	—	2	1	no	—
174	C₂×C₇×C₈	—	2	1	no	—
175	C₂×C₇×C₈	—	2	1	no	—
176	C₂×C₇×C₈	—	2	1	no	—
177	C₂×C₇×C₈	—	2	1	no	—
178	C₂×C₇×C₈	—	2	1	no	—
179	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
180	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
181	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
182	C₇×C₄⋊C₄	—	2	4	no	—
183	C₇×C₄⋊C₄	—	2	4	no	—
184	C₇×C₄⋊C₄	—	2	2	no	—
185	C₇×C₄⋊C₄	—	2	1	no	—
186	C₇×C₄⋊C₄	—	2	1	no	—
187	C₇×C₄⋊C₄	—	2	1	no	—
188	C₇×C₄⋊C₄	—	2	1	no	—
189	C₇×C₄⋊C₄	—	2	1	no	—
190	C₇×C₄⋊C₄	—	2	1	no	—
191	C₇×C₄⋊C₄	—	2	1	no	—
192	C₇×C₄⋊C₄	—	2	1	no	—
193	C₇×C₄⋊C₄	—	2	1	no	—
194	C₇×C₄⋊C₄	—	2	1	no	—
195	C₇×C₄⋊C₄	—	4	1	no	—
196	C₇×C₄⋊C₄	—	4	2	no	—
197	C₇×C₄⋊C₄	—	4	2	no	—
198	C₇×C₄⋊C₄	—	4	2	no	—
199	C₇×C₄⋊C₄	—	4	2	no	—
200	C₇×C₄⋊C₄	—	8	1	no	—
201	C₇×C₄⋊C₄	—	8	1	no	—
202	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
203	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
204	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
205	C₇×C₄⋊C₄	C₂×Q₈	1	2	yes	—
206	C₇×C₂²⋊C₄	—	2	4	no	—
207	C₇×C₂²⋊C₄	—	4	2	no	—
208	C₇×C₂²⋊C₄	—	4	2	no	—
209	C₄²×C₇	—	2	1	no	—
210	C₄²×C₇	—	2	1	no	—
211	C₄²×C₇	—	2	1	no	—
212	C₄²×C₇	—	2	1	no	—
213	C₄²×C₇	—	4	2	no	—
214	C₄²×C₇	—	8	1	no	—
215	C₄²×C₇	—	8	1	no	—
216	C₄²×C₇	C₂²×C₄	1	2	yes	—
217	C₄²×C₇	#41	1	2	yes	—
218	C₂×#125	C₂²×C₇	1	1	yes	characteristic
219	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
220	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
222	C₂²×C₄⋊C₄	—	2	1	no	—
223	#478	C₄×C₇	1	8	yes	complemented
224	C₂×#107	C₂²×C₇	1	1	yes	characteristic
225	C₂×#106	C₂²×C₇	1	1	yes	characteristic
226	C₂×#106	C₂²×C₇	1	1	yes	characteristic
227	C₂×#106	C₂²×C₇	1	1	yes	characteristic
228	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
229	C₂×#102	C₂²×C₇	1	1	yes	characteristic
230	C₂×#102	C₂²×C₇	1	1	yes	characteristic
231	C₂×#102	C₂²×C₇	1	1	yes	characteristic
232	C₂×#102	C₂²×C₇	1	1	yes	characteristic
233	C₂×#97	C₂²×C₇	1	1	yes	characteristic
234	C₂×#97	C₂²×C₇	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
236	#389	—	2	1	no	—
237	#389	C₂²×C₇	1	1	yes	characteristic
238	#389	C₂²×C₇	1	1	yes	characteristic
239	#389	C₂²×C₇	1	1	yes	characteristic
240	#389	C₂²×C₇	1	1	yes	characteristic
241	#387	—	2	1	no	—
242	#387	—	2	1	no	—
243	#385	—	2	1	no	—
244	#385	—	2	1	no	—
245	#384	C₂²×C₇	1	1	yes	characteristic
246	#380	—	2	1	no	—
247	C₄×C₄⋊C₄	—	2	1	no	—
248	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
249	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
250	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
251	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
252	#340	C₂²×C₇	1	1	yes	characteristic
253	#340	C₂²×C₇	1	1	yes	characteristic
254	#340	C₂²×C₇	1	1	yes	characteristic
255	#340	C₂²×C₇	1	1	yes	characteristic
256	#340	C₂²×C₇	1	1	yes	characteristic
257	#340	C₂²×C₇	1	1	yes	characteristic
258	#340	C₂²×C₇	1	1	yes	characteristic
259	#340	C₂²×C₇	1	1	yes	characteristic
260	#336	C₂²×C₇	1	1	yes	characteristic
261	#336	C₂²×C₇	1	1	yes	characteristic
262	C₂³×C₇	—	2	2	no	—
263	C₂³×C₇	—	2	2	no	—
264	C₂³×C₇	—	2	2	no	—
265	C₂³×C₇	—	4	1	no	—
266	C₂³×C₇	—	4	1	no	—
267	C₂³×C₇	—	4	1	no	—
268	C₂³×C₇	—	4	1	no	—
269	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
270	C₇×D₄	—	2	2	no	—
271	C₇×D₄	—	2	2	no	—
272	C₇×D₄	—	2	2	no	—
273	C₇×D₄	C₄×Q₈	1	4	yes	—
274	C₂×C₄×C₇	—	2	1	no	—
275	C₂×C₄×C₇	—	2	1	no	—
276	C₂×C₄×C₇	—	2	1	no	—
277	C₂×C₄×C₇	—	2	1	no	—
278	C₂×C₄×C₇	—	2	1	no	—
279	C₂×C₄×C₇	—	2	1	no	—
280	C₂×C₄×C₇	—	2	2	no	—
281	C₂×C₄×C₇	—	2	2	no	—
282	C₂×C₄×C₇	—	2	2	no	—
283	C₂×C₄×C₇	—	2	1	no	—
284	C₂×C₄×C₇	—	2	1	no	—
285	C₂×C₄×C₇	—	2	1	no	—
286	C₂×C₄×C₇	—	2	2	no	—
287	C₂×C₄×C₇	—	2	1	no	—
288	C₂×C₄×C₇	—	2	1	no	—
289	C₂×C₄×C₇	—	2	1	no	—
290	C₂×C₄×C₇	—	2	1	no	—
291	C₂×C₄×C₇	—	2	1	no	—
292	C₂×C₄×C₇	—	2	1	no	—
293	C₂×C₄×C₇	—	4	8	no	—
294	C₂×C₄×C₇	—	4	1	no	—
295	C₂×C₄×C₇	—	4	1	no	—
296	C₂×C₄×C₇	—	4	1	no	—
297	C₂×C₄×C₇	—	4	1	no	—
298	C₂×C₄×C₇	—	4	1	no	—
299	C₂×C₄×C₇	—	4	1	no	—
300	C₂×C₄×C₇	—	4	1	no	—
301	C₂×C₄×C₇	—	4	1	no	—
302	C₂×C₄×C₇	—	4	1	no	—
303	C₂×C₄×C₇	—	4	1	no	—
304	C₂×C₄×C₇	—	4	1	no	—
305	C₂×C₄×C₇	—	4	1	no	—
306	C₂×C₄×C₇	—	4	1	no	—
307	C₂×C₄×C₇	—	4	1	no	—
308	C₂×C₄×C₇	—	4	1	no	—
309	C₂×C₄×C₇	—	4	1	no	—
310	C₂×C₄×C₇	—	4	1	no	—
311	C₂×C₄×C₇	—	8	4	no	—
312	C₂×C₄×C₇	—	8	4	no	—
313	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
314	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
315	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
316	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
317	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
318	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
319	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
320	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
321	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
322	C₇×C₈	—	2	2	no	—
323	C₇×C₈	—	2	2	no	—
324	C₇×C₈	—	2	2	no	—
325	C₇×C₈	—	4	1	no	—
326	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
327	C₂³×C₄	—	2	1	no	—
328	C₂³×C₄	—	2	1	no	—
329	C₂³×C₄	—	2	1	no	—
330	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
333	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
334	#125	—	2	2	no	—
335	#125	C₂×C₄×C₇	1	4	yes	complemented
336	C₄×D₄	—	2	2	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	4	1	no	—
340	C₄×D₄	—	4	1	no	—
341	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	4	4	no	—
351	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
369	#107	C₂×C₄×C₇	1	4	yes	complemented
370	#106	—	4	1	no	—
371	#106	—	4	1	no	—
372	#106	C₂×C₄×C₇	1	4	yes	complemented
373	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
374	#102	—	2	2	no	—
375	#102	C₂×C₄×C₇	1	4	yes	—
376	#102	C₂×C₄×C₇	1	4	yes	—
377	#102	C₇×Q₈	1	4	yes	—
378	#97	—	2	2	no	—
379	#97	—	4	1	no	—
380	C₄×C₈	—	4	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	#95	—	2	1	no	—
388	#95	C₇×D₄	1	1	yes	characteristic
389	#95	C₇×D₄	1	1	yes	characteristic
390	C₂²×C₇	—	2	4	no	—
391	C₂²×C₇	—	4	2	no	—
392	C₂²×C₇	—	4	2	no	—
393	C₂²×C₇	—	4	2	no	—
394	C₂²×C₇	—	4	2	no	—
395	C₂²×C₇	—	4	2	no	—
396	C₂²×C₇	—	4	2	no	—
397	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
398	C₂²×C₇	#546	1	1	yes	characteristic
399	C₂²×C₇	D₄×Q₈	1	1	yes	characteristic
400	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
401	C₂²×C₇	#575	1	1	yes	characteristic
402	C₂²×C₇	#577	1	1	yes	characteristic
403	C₂²×C₇	#577	1	1	yes	characteristic
404	C₄×C₇	—	2	2	no	—
405	C₄×C₇	—	2	2	no	—
406	C₄×C₇	—	2	2	no	—
407	C₄×C₇	—	4	2	no	—
408	C₄×C₇	—	4	2	no	—
409	C₄×C₇	—	4	2	no	—
410	C₄×C₇	—	4	2	no	—
411	C₄×C₇	—	4	1	no	—
412	C₄×C₇	—	4	1	no	—
413	C₄×C₇	—	4	1	no	—
414	C₄×C₇	—	8	1	no	—
415	C₄×C₇	—	8	1	no	—
416	C₄×C₇	—	8	1	no	—
417	C₄×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
418	C₄×C₇	#520	1	1	yes	characteristic
419	C₄×C₇	#552	1	1	yes	characteristic
420	C₄×C₇	#554	1	1	yes	characteristic
421	C₂⁴	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
426	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
427	C₂×D₄	C₇×#41	1	2	yes	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	4	2	no	—
440	C₂²×C₄	—	4	2	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	8	1	no	—
443	C₂²×C₄	—	8	1	no	—
444	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
446	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
447	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
448	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
449	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
450	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
461	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
462	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	2	no	—
478	C₄⋊C₄	—	4	2	no	—
479	C₄⋊C₄	—	4	2	no	—
480	C₄⋊C₄	—	4	2	no	—
481	C₄⋊C₄	—	8	1	no	—
482	C₄⋊C₄	—	8	1	no	—
483	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
484	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
485	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
486	C₄⋊C₄	C₂×C₇×Q₈	1	2	yes	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	4	2	no	—
489	C₂²⋊C₄	—	4	2	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	4	2	no	—
495	C₄²	—	8	1	no	—
496	C₄²	—	8	1	no	—
497	C₄²	C₂²×C₄×C₇	1	2	yes	—
498	C₄²	C₇×#41	1	2	yes	—
499	C₂×C₇	—	4	4	no	—
500	C₂×C₇	#2360	1	1	yes	characteristic
501	C₂×C₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
502	C₂×C₇	#2952	1	1	yes	characteristic
503	C₂×C₇	#3307	1	1	yes	characteristic
504	C₂×C₇	#3310	1	1	yes	characteristic
505	C₂×C₇	#3384	1	1	yes	characteristic
506	C₂×C₇	#3388	1	1	yes	characteristic
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	4	1	no	—
514	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
515	D₄	—	2	2	no	—
516	D₄	—	2	2	no	—
517	D₄	—	2	2	no	—
518	D₄	C₄×C₇×Q₈	1	4	yes	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	4	8	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	8	4	no	—
557	C₂×C₄	—	8	4	no	—
558	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
559	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
560	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
561	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
562	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
563	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
564	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
565	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
566	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
567	C₈	—	2	2	no	—
568	C₈	—	2	2	no	—
569	C₈	—	2	2	no	—
570	C₈	—	4	1	no	—
571	C₇	#22978	1	1	yes	characteristic, direct product factor, Sylow
572	C₂²	—	2	4	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	4	2	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	2	no	—
579	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
580	C₂²	C₇×#546	1	1	yes	characteristic
581	C₂²	C₇×D₄×Q₈	1	1	yes	characteristic
582	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
583	C₂²	C₇×#575	1	1	yes	characteristic
584	C₂²	C₇×#577	1	1	yes	characteristic
585	C₂²	C₇×#577	1	1	yes	characteristic
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	4	2	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	2	no	—
596	C₄	—	8	1	no	—
597	C₄	—	8	1	no	—
598	C₄	—	8	1	no	—
599	C₄	C₂×C₄×C₇×Q₈	1	1	yes	characteristic
600	C₄	C₇×#520	1	1	yes	characteristic
601	C₄	C₇×#552	1	1	yes	characteristic
602	C₄	C₇×#554	1	1	yes	characteristic
603	C₂	—	4	4	no	—
604	C₂	C₇×#2360	1	1	yes	characteristic
605	C₂	C₄×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
606	C₂	C₇×#2952	1	1	yes	characteristic
607	C₂	C₇×#3307	1	1	yes	characteristic
608	C₂	C₇×#3310	1	1	yes	characteristic
609	C₂	C₇×#3384	1	1	yes	characteristic
610	C₂	C₇×#3388	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂×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
2. C₇×#2370	C₂	semidirect
4. C₇×#1992	C₂	semidirect
5. C₇×#1948	C₂	semidirect
6. C₇×#1943	C₂	semidirect
7. C₇×#1941	C₂	semidirect
8. C₇×#1920	C₂	semidirect
9. C₇×#1918	C₂	semidirect
12. C₇×#1771	C₂	semidirect
21. C₇×#478	C₄	semidirect
60. #22978	C₇	direct (N × H)
70. C₇×#125	C₂×C₄	semidirect
104. C₇×#107	C₂×C₄	semidirect
107. C₇×#106	C₂×C₄	semidirect
108. C₇×C₄⋊C₈	C₂×C₄	semidirect
126. #2370	C₂×C₇	semidirect
128. #1992	C₂×C₇	semidirect
129. #1948	C₂×C₇	semidirect
130. #1943	C₂×C₇	semidirect
131. #1941	C₂×C₇	semidirect
132. #1920	C₂×C₇	semidirect
133. #1918	C₂×C₇	semidirect
136. #1771	C₂×C₇	semidirect
223. #478	C₄×C₇	semidirect
335. #125	C₂×C₄×C₇	semidirect
369. #107	C₂×C₄×C₇	semidirect
372. #106	C₂×C₄×C₇	semidirect
373. C₄⋊C₈	C₂×C₄×C₇	semidirect
571. C₇	#22978	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#478	2
C₇×#2370	2
C₇×D₄×C₄⋊C₄	2
C₇×#1992	2
C₇×#1948	2
C₇×#1943	2
C₇×#1941	2
C₇×#1920	2
C₇×#1918	2
C₇×#1864	2
C₇×#1771	2
C₇×#1762	2
C₄×C₇×#102	2
#22978	7

Subgroups — C7×#22978 #13200194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22978 #13200194