Subgroups — C₇×#25169 #13202385

Order 1792.

1080 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#451	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#448	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×#441	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2426	C₂	1	1	yes	maximal, characteristic
6	C₇×Q₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2066	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2036	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2034	C₂	1	1	yes	maximal, characteristic
10	C₇×#2015	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1924	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1863	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
17	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₇×#124	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×#121	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
27	C₇×#464	—	2	4	no	—
28	C₇×#451	—	2	4	no	—
29	C₇×#448	—	2	4	no	—
30	C₇×#441	—	2	4	no	—
31	C₂×C₇×#107	C₂²	1	1	yes	characteristic
32	C₂×C₇×#106	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×#103	C₂²	1	1	yes	characteristic
35	C₂×C₇×#103	C₂²	1	1	yes	characteristic
36	C₂×C₇×#103	C₂²	1	1	yes	characteristic
37	C₂×C₇×#103	C₂²	1	1	yes	characteristic
38	C₂×C₇×#103	C₂²	1	1	yes	characteristic
39	C₂×C₇×#103	C₂²	1	1	yes	characteristic
40	C₂×C₇×#102	C₂²	1	1	yes	characteristic
41	C₂×C₇×#102	C₂²	1	1	yes	characteristic
42	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₇×#97	C₂²	1	1	yes	characteristic
45	C₇×#396	—	2	1	no	—
46	C₇×#394	—	2	1	no	—
47	C₇×#391	—	2	1	no	—
48	C₇×#391	—	2	1	no	—
49	C₇×#391	C₂²	1	1	yes	characteristic
50	C₇×#391	C₂²	1	1	yes	characteristic
51	C₇×#390	—	2	1	no	—
52	C₇×#390	C₂²	1	1	yes	characteristic
53	C₇×#389	C₂²	1	1	yes	characteristic
54	C₇×#388	—	2	1	no	—
55	C₇×#380	—	2	1	no	—
56	C₇×#380	C₂²	1	1	yes	characteristic
57	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
58	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
59	C₇×#340	C₂²	1	1	yes	characteristic
60	C₇×#340	C₂²	1	1	yes	characteristic
61	C₇×#336	C₂²	1	1	yes	characteristic
62	C₇×#336	C₂²	1	1	yes	characteristic
63	#25169	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂²×C₇×Q₈	—	2	2	no	—
65	C₂²×C₇×Q₈	—	2	2	no	—
66	C₂²×C₇×Q₈	—	2	1	no	—
67	C₂²×C₇×Q₈	—	2	2	no	—
68	C₂²×C₇×Q₈	—	2	2	no	—
69	C₂²×C₇×Q₈	—	4	1	no	—
70	C₂²×C₇×Q₈	—	4	1	no	—
71	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
73	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
74	C₂²×C₇×D₄	—	2	1	no	—
75	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₇	—	2	1	no	—
77	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
78	C₂×C₇×Q₁₆	—	2	2	no	—
79	C₂×C₇×Q₁₆	—	2	2	no	—
80	C₂×C₇×Q₁₆	—	2	2	no	—
81	C₂×C₇×Q₁₆	—	2	2	no	—
82	C₂×C₇×Q₁₆	—	4	1	no	—
83	C₂×C₇×Q₁₆	D₄	1	4	yes	complemented
84	C₂×C₇×SD₁₆	—	2	2	no	—
85	C₂×C₇×SD₁₆	—	2	2	no	—
86	C₂×C₇×SD₁₆	—	2	2	no	—
87	C₂×C₇×SD₁₆	—	2	2	no	—
88	C₂×C₇×SD₁₆	—	2	2	no	—
89	C₂×C₇×SD₁₆	—	4	1	no	—
90	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
91	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
92	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
93	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
94	C₇×#124	—	2	2	no	—
95	C₇×#124	—	4	1	no	—
96	C₇×C₂²⋊Q₈	—	2	2	no	—
97	C₇×C₂²⋊Q₈	—	4	1	no	—
98	C₇×#121	—	2	2	no	—
99	C₇×#121	—	4	1	no	—
100	C₄×C₇×Q₈	—	2	2	no	—
101	C₄×C₇×Q₈	—	2	2	no	—
102	C₄×C₇×Q₈	—	2	2	no	—
103	C₄×C₇×Q₈	—	4	1	no	—
104	C₄×C₇×Q₈	—	4	1	no	—
105	C₄×C₇×Q₈	—	4	1	no	—
106	C₂×C₇×C₄⋊C₄	—	2	1	no	—
107	C₂×C₇×C₄⋊C₄	—	2	1	no	—
108	C₂×C₇×C₄⋊C₄	—	2	1	no	—
109	C₂×C₇×C₄⋊C₄	—	2	1	no	—
110	C₂×C₇×C₄⋊C₄	—	2	1	no	—
111	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
123	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₇	—	2	1	no	—
125	C₂×C₄²×C₇	—	2	1	no	—
126	C₂×C₄²×C₇	—	2	1	no	—
127	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
129	C₇×#107	—	4	1	no	—
130	C₇×#106	—	2	2	no	—
131	C₇×C₄⋊C₈	—	2	2	no	—
132	C₇×#103	—	2	2	no	—
133	C₇×#103	—	2	2	no	—
134	C₇×#103	—	2	2	no	—
135	C₇×#103	—	2	2	no	—
136	C₇×#103	—	2	2	no	—
137	C₇×#103	D₄	1	4	yes	—
138	C₇×#102	—	2	2	no	—
139	C₇×#102	—	4	1	no	—
140	C₇×C₂²⋊C₈	—	2	2	no	—
141	C₇×C₂²⋊C₈	—	2	2	no	—
142	C₇×#97	—	2	2	no	—
143	C₇×#95	—	2	1	no	—
144	C₇×#95	—	2	1	no	—
145	C₇×#95	—	2	1	no	—
146	C₇×#95	—	2	1	no	—
147	C₇×#95	—	2	1	no	—
148	C₇×#95	—	2	1	no	—
149	C₇×#95	D₄	1	1	yes	characteristic
150	C₇×#95	D₄	1	1	yes	characteristic
151	C₂×#464	C₂×C₇	1	1	yes	characteristic, complemented
152	C₂×#451	C₂×C₇	1	1	yes	characteristic, complemented
153	C₂×#448	C₂×C₇	1	1	yes	characteristic
154	C₂×#441	C₂×C₇	1	1	yes	characteristic, complemented
155	#2426	C₂×C₇	1	1	yes	characteristic
156	Q₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
157	#2066	C₂×C₇	1	1	yes	characteristic, complemented
158	#2036	C₂×C₇	1	1	yes	characteristic, complemented
159	#2034	C₂×C₇	1	1	yes	characteristic
160	#2015	C₂×C₇	1	1	yes	characteristic, complemented
161	#1973	C₂×C₇	1	1	yes	characteristic, complemented
162	#1924	C₂×C₇	1	1	yes	characteristic, complemented
163	#1880	C₂×C₇	1	1	yes	characteristic, complemented
164	#1878	C₂×C₇	1	1	yes	characteristic, complemented
165	#1863	C₂×C₇	1	1	yes	characteristic, complemented
166	C₂⁴×C₇	—	2	1	no	—
167	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
168	C₂×C₇×Q₈	—	2	4	no	—
169	C₂×C₇×Q₈	—	2	1	no	—
170	C₂×C₇×Q₈	—	2	1	no	—
171	C₂×C₇×Q₈	—	2	1	no	—
172	C₂×C₇×Q₈	—	2	1	no	—
173	C₂×C₇×Q₈	—	2	1	no	—
174	C₂×C₇×Q₈	—	2	1	no	—
175	C₂×C₇×Q₈	—	2	1	no	—
176	C₂×C₇×Q₈	—	2	1	no	—
177	C₂×C₇×Q₈	—	2	1	no	—
178	C₂×C₇×Q₈	—	2	1	no	—
179	C₂×C₇×Q₈	—	2	1	no	—
180	C₂×C₇×Q₈	—	2	1	no	—
181	C₂×C₇×Q₈	—	2	1	no	—
182	C₂×C₇×Q₈	—	4	2	no	—
183	C₂×C₇×Q₈	—	4	2	no	—
184	C₂×C₇×Q₈	—	4	4	no	—
185	C₂×C₇×Q₈	—	4	4	no	—
186	C₂×C₇×Q₈	—	4	4	no	—
187	C₂×C₇×Q₈	—	4	4	no	—
188	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
189	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
190	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
191	C₂×C₇×Q₈	#41	1	2	yes	—
192	C₂×C₇×Q₈	#41	1	2	yes	—
193	C₂×C₇×D₄	—	2	1	no	—
194	C₂×C₇×D₄	—	2	1	no	—
195	C₂×C₇×D₄	—	2	1	no	—
196	C₂×C₇×D₄	—	2	1	no	—
197	C₂×C₇×D₄	—	2	1	no	—
198	C₂×C₇×D₄	—	2	1	no	—
199	C₂×C₇×D₄	—	4	2	no	—
200	C₂×C₇×D₄	—	4	2	no	—
201	C₂×C₇×D₄	—	8	1	no	—
202	C₂²×C₄×C₇	—	2	1	no	—
203	C₂²×C₄×C₇	—	2	4	no	—
204	C₂²×C₄×C₇	—	2	1	no	—
205	C₂²×C₄×C₇	—	2	1	no	—
206	C₂²×C₄×C₇	—	2	1	no	—
207	C₂²×C₄×C₇	—	2	1	no	—
208	C₂²×C₄×C₇	—	2	1	no	—
209	C₂²×C₄×C₇	—	2	1	no	—
210	C₂²×C₄×C₇	—	2	1	no	—
211	C₂²×C₄×C₇	—	2	1	no	—
212	C₂²×C₄×C₇	—	2	1	no	—
213	C₂²×C₄×C₇	—	2	1	no	—
214	C₂²×C₄×C₇	—	2	1	no	—
215	C₂²×C₄×C₇	—	2	1	no	—
216	C₂²×C₄×C₇	—	4	2	no	—
217	C₂²×C₄×C₇	—	4	2	no	—
218	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
224	C₇×Q₁₆	—	2	8	no	—
225	C₇×Q₁₆	—	4	4	no	—
226	C₇×SD₁₆	—	4	4	no	—
227	C₇×SD₁₆	—	4	4	no	—
228	C₂×C₇×C₈	—	2	1	no	—
229	C₂×C₇×C₈	—	2	1	no	—
230	C₂×C₇×C₈	—	2	1	no	—
231	C₂×C₇×C₈	—	2	1	no	—
232	C₂×C₇×C₈	—	2	1	no	—
233	C₂×C₇×C₈	—	2	1	no	—
234	C₂×C₇×C₈	—	2	1	no	—
235	C₂×C₇×C₈	—	2	1	no	—
236	C₂×C₇×C₈	—	2	1	no	—
237	C₂×C₇×C₈	—	2	1	no	—
238	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
239	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
240	C₇×C₄⋊C₄	—	2	1	no	—
241	C₇×C₄⋊C₄	—	2	1	no	—
242	C₇×C₄⋊C₄	—	2	1	no	—
243	C₇×C₄⋊C₄	—	2	1	no	—
244	C₇×C₄⋊C₄	—	2	1	no	—
245	C₇×C₄⋊C₄	—	2	1	no	—
246	C₇×C₄⋊C₄	—	2	1	no	—
247	C₇×C₄⋊C₄	—	4	2	no	—
248	C₇×C₄⋊C₄	—	4	2	no	—
249	C₇×C₄⋊C₄	—	4	2	no	—
250	C₇×C₄⋊C₄	—	4	2	no	—
251	C₇×C₄⋊C₄	—	8	1	no	—
252	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
253	C₇×C₂²⋊C₄	—	2	2	no	—
254	C₇×C₂²⋊C₄	—	4	1	no	—
255	C₇×C₂²⋊C₄	—	4	2	no	—
256	C₇×C₂²⋊C₄	—	4	2	no	—
257	C₇×C₂²⋊C₄	—	4	2	no	—
258	C₇×C₂²⋊C₄	—	4	2	no	—
259	C₇×C₂²⋊C₄	—	4	2	no	—
260	C₇×C₂²⋊C₄	—	4	2	no	—
261	C₇×C₂²⋊C₄	—	8	1	no	—
262	C₄²×C₇	—	2	1	no	—
263	C₄²×C₇	—	2	1	no	—
264	C₄²×C₇	—	2	1	no	—
265	C₄²×C₇	—	2	1	no	—
266	C₄²×C₇	—	4	2	no	—
267	C₄²×C₇	—	4	2	no	—
268	C₄²×C₇	—	4	2	no	—
269	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
270	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
271	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
272	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
273	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
274	C₂×#124	C₂²×C₇	1	1	yes	characteristic
275	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
276	C₂×#121	C₂²×C₇	1	1	yes	characteristic
277	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
278	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
279	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
280	#464	—	2	4	no	—
281	#451	—	2	4	no	—
282	#448	—	2	4	no	—
283	#441	—	2	4	no	—
284	C₂×#107	C₂²×C₇	1	1	yes	characteristic
285	C₂×#106	C₂²×C₇	1	1	yes	characteristic
286	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
287	C₂×#103	C₂²×C₇	1	1	yes	characteristic
288	C₂×#103	C₂²×C₇	1	1	yes	characteristic
289	C₂×#103	C₂²×C₇	1	1	yes	characteristic
290	C₂×#103	C₂²×C₇	1	1	yes	characteristic
291	C₂×#103	C₂²×C₇	1	1	yes	characteristic
292	C₂×#103	C₂²×C₇	1	1	yes	characteristic
293	C₂×#102	C₂²×C₇	1	1	yes	characteristic
294	C₂×#102	C₂²×C₇	1	1	yes	characteristic
295	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
296	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
297	C₂×#97	C₂²×C₇	1	1	yes	characteristic
298	#396	—	2	1	no	—
299	#394	—	2	1	no	—
300	#391	—	2	1	no	—
301	#391	—	2	1	no	—
302	#391	C₂²×C₇	1	1	yes	characteristic
303	#391	C₂²×C₇	1	1	yes	characteristic
304	#390	—	2	1	no	—
305	#390	C₂²×C₇	1	1	yes	characteristic
306	#389	C₂²×C₇	1	1	yes	characteristic
307	#388	—	2	1	no	—
308	#380	—	2	1	no	—
309	#380	C₂²×C₇	1	1	yes	characteristic
310	C₄×C₂²⋊C₄	—	2	1	no	—
311	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
312	#340	C₂²×C₇	1	1	yes	characteristic
313	#340	C₂²×C₇	1	1	yes	characteristic
314	#336	C₂²×C₇	1	1	yes	characteristic
315	#336	C₂²×C₇	1	1	yes	characteristic
316	C₂³×C₇	—	2	1	no	—
317	C₂³×C₇	—	2	1	no	—
318	C₂³×C₇	—	2	1	no	—
319	C₂³×C₇	—	2	1	no	—
320	C₂³×C₇	—	2	1	no	—
321	C₂³×C₇	—	2	1	no	—
322	C₂³×C₇	—	4	1	no	—
323	C₂³×C₇	—	4	1	no	—
324	C₂³×C₇	—	4	1	no	—
325	C₂³×C₇	—	4	1	no	—
326	C₂³×C₇	—	4	1	no	—
327	C₂³×C₇	—	4	1	no	—
328	C₂³×C₇	—	4	1	no	—
329	C₂³×C₇	#137	1	2	yes	—
330	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
331	C₇×Q₈	—	2	2	no	—
332	C₇×Q₈	—	2	2	no	—
333	C₇×Q₈	—	2	2	no	—
334	C₇×Q₈	—	2	2	no	—
335	C₇×Q₈	—	2	2	no	—
336	C₇×Q₈	—	2	2	no	—
337	C₇×Q₈	—	2	2	no	—
338	C₇×Q₈	—	4	8	no	—
339	C₇×Q₈	—	4	1	no	—
340	C₇×Q₈	—	4	1	no	—
341	C₇×Q₈	—	4	1	no	—
342	C₇×Q₈	—	4	1	no	—
343	C₇×Q₈	#121	1	4	yes	—
344	C₇×D₄	—	4	1	no	—
345	C₇×D₄	—	4	1	no	—
346	C₇×D₄	—	4	1	no	—
347	C₇×D₄	—	4	1	no	—
348	C₇×D₄	—	8	4	no	—
349	C₂×C₄×C₇	—	2	2	no	—
350	C₂×C₄×C₇	—	2	2	no	—
351	C₂×C₄×C₇	—	2	2	no	—
352	C₂×C₄×C₇	—	2	2	no	—
353	C₂×C₄×C₇	—	2	1	no	—
354	C₂×C₄×C₇	—	2	1	no	—
355	C₂×C₄×C₇	—	2	1	no	—
356	C₂×C₄×C₇	—	2	1	no	—
357	C₂×C₄×C₇	—	2	1	no	—
358	C₂×C₄×C₇	—	2	2	no	—
359	C₂×C₄×C₇	—	2	2	no	—
360	C₂×C₄×C₇	—	2	1	no	—
361	C₂×C₄×C₇	—	2	1	no	—
362	C₂×C₄×C₇	—	2	1	no	—
363	C₂×C₄×C₇	—	2	1	no	—
364	C₂×C₄×C₇	—	2	1	no	—
365	C₂×C₄×C₇	—	2	1	no	—
366	C₂×C₄×C₇	—	2	1	no	—
367	C₂×C₄×C₇	—	2	1	no	—
368	C₂×C₄×C₇	—	2	1	no	—
369	C₂×C₄×C₇	—	2	1	no	—
370	C₂×C₄×C₇	—	4	8	no	—
371	C₂×C₄×C₇	—	4	1	no	—
372	C₂×C₄×C₇	—	4	1	no	—
373	C₂×C₄×C₇	—	4	1	no	—
374	C₂×C₄×C₇	—	4	1	no	—
375	C₂×C₄×C₇	—	4	1	no	—
376	C₂×C₄×C₇	—	4	1	no	—
377	C₂×C₄×C₇	—	4	1	no	—
378	C₂×C₄×C₇	—	4	1	no	—
379	C₂×C₄×C₇	—	4	1	no	—
380	C₂×C₄×C₇	—	4	1	no	—
381	C₂×C₄×C₇	—	4	1	no	—
382	C₂×C₄×C₇	—	4	1	no	—
383	C₂×C₄×C₇	—	4	1	no	—
384	C₂×C₄×C₇	—	4	1	no	—
385	C₂×C₄×C₇	—	4	1	no	—
386	C₂×C₄×C₇	—	4	1	no	—
387	C₂×C₄×C₇	—	4	1	no	—
388	C₂×C₄×C₇	—	4	1	no	—
389	C₂×C₄×C₇	—	4	1	no	—
390	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
393	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
394	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
395	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
396	C₇×C₈	—	2	2	no	—
397	C₇×C₈	—	2	2	no	—
398	C₇×C₈	—	4	1	no	—
399	C₇×C₈	—	4	1	no	—
400	C₂²×Q₈	—	2	2	no	—
401	C₂²×Q₈	—	2	2	no	—
402	C₂²×Q₈	—	2	1	no	—
403	C₂²×Q₈	—	2	2	no	—
404	C₂²×Q₈	—	2	2	no	—
405	C₂²×Q₈	—	4	1	no	—
406	C₂²×Q₈	—	4	1	no	—
407	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
408	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
409	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
410	C₂²×D₄	—	2	1	no	—
411	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
412	C₂³×C₄	—	2	1	no	—
413	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
414	C₂×Q₁₆	—	2	2	no	—
415	C₂×Q₁₆	—	2	2	no	—
416	C₂×Q₁₆	—	2	2	no	—
417	C₂×Q₁₆	—	2	2	no	—
418	C₂×Q₁₆	—	4	1	no	—
419	C₂×Q₁₆	C₇×D₄	1	4	yes	complemented
420	C₂×SD₁₆	—	2	2	no	—
421	C₂×SD₁₆	—	2	2	no	—
422	C₂×SD₁₆	—	2	2	no	—
423	C₂×SD₁₆	—	2	2	no	—
424	C₂×SD₁₆	—	2	2	no	—
425	C₂×SD₁₆	—	4	1	no	—
426	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
427	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
428	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
429	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
430	#124	—	2	2	no	—
431	#124	—	4	1	no	—
432	C₂²⋊Q₈	—	2	2	no	—
433	C₂²⋊Q₈	—	4	1	no	—
434	#121	—	2	2	no	—
435	#121	—	4	1	no	—
436	C₄×Q₈	—	2	2	no	—
437	C₄×Q₈	—	2	2	no	—
438	C₄×Q₈	—	2	2	no	—
439	C₄×Q₈	—	4	1	no	—
440	C₄×Q₈	—	4	1	no	—
441	C₄×Q₈	—	4	1	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
459	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
460	C₂×C₄²	—	2	1	no	—
461	C₂×C₄²	—	2	1	no	—
462	C₂×C₄²	—	2	1	no	—
463	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
465	#107	—	4	1	no	—
466	#106	—	2	2	no	—
467	C₄⋊C₈	—	2	2	no	—
468	#103	—	2	2	no	—
469	#103	—	2	2	no	—
470	#103	—	2	2	no	—
471	#103	—	2	2	no	—
472	#103	—	2	2	no	—
473	#103	C₇×D₄	1	4	yes	—
474	#102	—	2	2	no	—
475	#102	—	4	1	no	—
476	C₂²⋊C₈	—	2	2	no	—
477	C₂²⋊C₈	—	2	2	no	—
478	#97	—	2	2	no	—
479	#95	—	2	1	no	—
480	#95	—	2	1	no	—
481	#95	—	2	1	no	—
482	#95	—	2	1	no	—
483	#95	—	2	1	no	—
484	#95	—	2	1	no	—
485	#95	C₇×D₄	1	1	yes	characteristic
486	#95	C₇×D₄	1	1	yes	characteristic
487	C₂²×C₇	—	2	2	no	—
488	C₂²×C₇	—	2	2	no	—
489	C₂²×C₇	—	2	2	no	—
490	C₂²×C₇	—	4	1	no	—
491	C₂²×C₇	—	4	1	no	—
492	C₂²×C₇	—	4	1	no	—
493	C₂²×C₇	—	4	1	no	—
494	C₂²×C₇	—	8	1	no	—
495	C₂²×C₇	—	8	1	no	—
496	C₂²×C₇	—	8	1	no	—
497	C₂²×C₇	—	8	1	no	—
498	C₂²×C₇	—	8	1	no	—
499	C₂²×C₇	—	8	1	no	—
500	C₂²×C₇	—	8	1	no	—
501	C₂²×C₇	#525	1	1	yes	characteristic
502	C₂²×C₇	D₄²	1	1	yes	characteristic
503	C₂²×C₇	D₄²	1	1	yes	characteristic
504	C₂²×C₇	C₂×#137	1	1	yes	characteristic
505	C₂²×C₇	#575	1	1	yes	characteristic
506	C₂²×C₇	#577	1	1	yes	characteristic
507	C₂²×C₇	#578	1	1	yes	characteristic
508	C₄×C₇	—	2	4	no	—
509	C₄×C₇	—	4	1	no	—
510	C₄×C₇	—	4	2	no	—
511	C₄×C₇	—	4	2	no	—
512	C₄×C₇	—	4	1	no	—
513	C₄×C₇	—	4	2	no	—
514	C₄×C₇	—	4	1	no	—
515	C₄×C₇	—	4	1	no	—
516	C₄×C₇	—	4	1	no	—
517	C₄×C₇	—	8	1	no	—
518	C₄×C₇	—	8	1	no	—
519	C₄×C₇	—	8	1	no	—
520	C₄×C₇	C₂×#121	1	1	yes	characteristic
521	C₄×C₇	#538	1	1	yes	characteristic
522	C₄×C₇	#546	1	1	yes	characteristic
523	C₄×C₇	#546	1	1	yes	characteristic
524	C₂⁴	—	2	1	no	—
525	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
526	C₂×Q₈	—	2	4	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	4	2	no	—
541	C₂×Q₈	—	4	2	no	—
542	C₂×Q₈	—	4	4	no	—
543	C₂×Q₈	—	4	4	no	—
544	C₂×Q₈	—	4	4	no	—
545	C₂×Q₈	—	4	4	no	—
546	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
547	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
548	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
549	C₂×Q₈	C₇×#41	1	2	yes	—
550	C₂×Q₈	C₇×#41	1	2	yes	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	4	2	no	—
558	C₂×D₄	—	4	2	no	—
559	C₂×D₄	—	8	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	4	2	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
577	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
578	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
579	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
580	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
582	Q₁₆	—	2	8	no	—
583	Q₁₆	—	4	4	no	—
584	SD₁₆	—	4	4	no	—
585	SD₁₆	—	4	4	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
597	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	4	2	no	—
606	C₄⋊C₄	—	4	2	no	—
607	C₄⋊C₄	—	4	2	no	—
608	C₄⋊C₄	—	4	2	no	—
609	C₄⋊C₄	—	8	1	no	—
610	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	4	1	no	—
613	C₂²⋊C₄	—	4	2	no	—
614	C₂²⋊C₄	—	4	2	no	—
615	C₂²⋊C₄	—	4	2	no	—
616	C₂²⋊C₄	—	4	2	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₂²⋊C₄	—	8	1	no	—
620	C₄²	—	2	1	no	—
621	C₄²	—	2	1	no	—
622	C₄²	—	2	1	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	4	2	no	—
625	C₄²	—	4	2	no	—
626	C₄²	—	4	2	no	—
627	C₂×C₇	—	4	2	no	—
628	C₂×C₇	—	16	1	no	—
629	C₂×C₇	#2424	1	1	yes	characteristic
630	C₂×C₇	#3117	1	1	yes	characteristic
631	C₂×C₇	#3121	1	1	yes	characteristic
632	C₂×C₇	#3266	1	1	yes	characteristic
633	C₂×C₇	#3270	1	1	yes	characteristic
634	C₂×C₇	#3271	1	1	yes	characteristic
635	C₂×C₇	#3277	1	1	yes	characteristic
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	C₇×#137	1	2	yes	—
650	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
651	Q₈	—	2	2	no	—
652	Q₈	—	2	2	no	—
653	Q₈	—	2	2	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	2	2	no	—
656	Q₈	—	2	2	no	—
657	Q₈	—	2	2	no	—
658	Q₈	—	4	8	no	—
659	Q₈	—	4	1	no	—
660	Q₈	—	4	1	no	—
661	Q₈	—	4	1	no	—
662	Q₈	—	4	1	no	—
663	Q₈	C₇×#121	1	4	yes	—
664	D₄	—	4	1	no	—
665	D₄	—	4	1	no	—
666	D₄	—	4	1	no	—
667	D₄	—	4	1	no	—
668	D₄	—	8	4	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	4	8	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
711	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
712	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
713	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
714	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
715	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
716	C₈	—	2	2	no	—
717	C₈	—	2	2	no	—
718	C₈	—	4	1	no	—
719	C₈	—	4	1	no	—
720	C₇	#25169	1	1	yes	characteristic, direct product factor, Sylow
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	8	1	no	—
729	C₂²	—	8	1	no	—
730	C₂²	—	8	1	no	—
731	C₂²	—	8	1	no	—
732	C₂²	—	8	1	no	—
733	C₂²	—	8	1	no	—
734	C₂²	—	8	1	no	—
735	C₂²	C₇×#525	1	1	yes	characteristic
736	C₂²	C₇×D₄²	1	1	yes	characteristic
737	C₂²	C₇×D₄²	1	1	yes	characteristic
738	C₂²	C₂×C₇×#137	1	1	yes	characteristic
739	C₂²	C₇×#575	1	1	yes	characteristic
740	C₂²	C₇×#577	1	1	yes	characteristic
741	C₂²	C₇×#578	1	1	yes	characteristic
742	C₄	—	2	4	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	1	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	1	no	—
749	C₄	—	4	1	no	—
750	C₄	—	4	1	no	—
751	C₄	—	8	1	no	—
752	C₄	—	8	1	no	—
753	C₄	—	8	1	no	—
754	C₄	C₂×C₇×#121	1	1	yes	characteristic
755	C₄	C₇×#538	1	1	yes	characteristic
756	C₄	C₇×#546	1	1	yes	characteristic
757	C₄	C₇×#546	1	1	yes	characteristic
758	C₂	—	4	2	no	—
759	C₂	—	16	1	no	—
760	C₂	C₇×#2424	1	1	yes	characteristic
761	C₂	C₇×#3117	1	1	yes	characteristic
762	C₂	C₇×#3121	1	1	yes	characteristic
763	C₂	C₇×#3266	1	1	yes	characteristic
764	C₂	C₇×#3270	1	1	yes	characteristic
765	C₂	C₇×#3271	1	1	yes	characteristic
766	C₂	C₇×#3277	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂×C₇×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄×C₇×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#464	C₂	semidirect
2. C₂×C₇×#451	C₂	semidirect
4. C₂×C₇×#441	C₂	semidirect
6. C₇×Q₈×C₂²⋊C₄	C₂	semidirect
7. C₇×#2066	C₂	semidirect
8. C₇×#2036	C₂	semidirect
10. C₇×#2015	C₂	semidirect
11. C₇×#1973	C₂	semidirect
12. C₇×#1924	C₂	semidirect
13. C₇×#1880	C₂	semidirect
14. C₇×#1878	C₂	semidirect
15. C₇×#1863	C₂	semidirect
63. #25169	C₇	direct (N × H)
83. C₂×C₇×Q₁₆	D₄	semidirect
151. C₂×#464	C₂×C₇	semidirect
152. C₂×#451	C₂×C₇	semidirect
154. C₂×#441	C₂×C₇	semidirect
156. Q₈×C₂²⋊C₄	C₂×C₇	semidirect
157. #2066	C₂×C₇	semidirect
158. #2036	C₂×C₇	semidirect
160. #2015	C₂×C₇	semidirect
161. #1973	C₂×C₇	semidirect
162. #1924	C₂×C₇	semidirect
163. #1880	C₂×C₇	semidirect
164. #1878	C₂×C₇	semidirect
165. #1863	C₂×C₇	semidirect
419. C₂×Q₁₆	C₇×D₄	semidirect
720. C₇	#25169	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×#464	2
C₂×C₇×#451	2
C₂×C₇×#448	2
C₂×C₇×#441	2
C₇×#2426	2
C₇×Q₈×C₂²⋊C₄	2
C₇×#2066	2
C₇×#2036	2
C₇×#2034	2
C₇×#2015	2
C₇×#1973	2
C₇×#1924	2
C₇×#1880	2
C₇×#1878	2
C₇×#1863	2
#25169	7

Subgroups — C7×#25169 #13202385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#25169 #13202385