Subgroups — C₇×#24165 #13201381

Order 1792.

1022 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#541	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#479	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2323	C₂	1	1	yes	maximal, characteristic
5	C₇×#2036	C₂	1	1	yes	maximal, characteristic
6	C₇×#2035	C₂	1	1	yes	maximal, characteristic
7	C₇×#2001	C₂	1	1	yes	maximal, characteristic
8	C₇×#2001	C₂	1	1	yes	maximal, characteristic
9	C₇×#1989	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1981	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1798	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
18	C₇×#541	—	2	4	no	—
19	C₇×#541	—	2	4	no	—
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×#126	—	2	1	no	—
22	C₂×C₇×#126	—	2	1	no	—
23	C₂×C₇×#125	—	2	1	no	—
24	C₂×C₇×#125	—	2	1	no	—
25	C₂×C₇×#125	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×#117	C₂²	1	1	yes	characteristic
33	C₇×#479	—	2	4	no	—
34	C₇×#462	—	2	4	no	—
35	C₂×C₇×#107	C₂²	1	1	yes	characteristic
36	C₂×C₇×#106	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₇×#103	C₂²	1	1	yes	characteristic
40	C₂×C₇×#103	C₂²	1	1	yes	characteristic
41	C₂×C₇×#103	C₂²	1	1	yes	characteristic
42	C₂×C₇×#103	C₂²	1	1	yes	characteristic
43	C₂×C₇×#103	C₂²	1	1	yes	characteristic
44	C₂×C₇×#103	C₂²	1	1	yes	characteristic
45	C₂×C₇×#103	C₂²	1	1	yes	characteristic
46	C₂×C₇×#103	C₂²	1	1	yes	characteristic
47	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₇×#391	C₂²	1	1	yes	characteristic
50	C₇×#389	—	2	1	no	—
51	C₇×#389	C₂²	1	1	yes	characteristic
52	C₇×#388	—	2	1	no	—
53	C₇×#388	—	2	1	no	—
54	C₇×#387	—	2	1	no	—
55	C₇×#380	C₂²	1	1	yes	characteristic
56	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₇×#340	C₂²	1	1	yes	characteristic
58	C₇×#340	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	#24165	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
68	C₂×C₇×Q₁₆	—	2	2	no	—
69	C₂×C₇×Q₁₆	—	2	2	no	—
70	C₂×C₇×Q₁₆	—	2	2	no	—
71	C₂×C₇×Q₁₆	—	2	2	no	—
72	C₂×C₇×Q₁₆	—	4	1	no	—
73	C₂×C₇×Q₁₆	—	4	1	no	—
74	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
78	C₇×C₄⋊Q₈	—	2	2	no	—
79	C₇×C₄⋊Q₈	D₄	1	4	yes	—
80	C₇×#126	—	2	8	no	—
81	C₇×#126	—	2	8	no	—
82	C₇×#125	—	2	8	no	—
83	C₇×#125	—	2	8	no	—
84	C₇×#125	—	2	2	no	—
85	C₇×#125	D₄	1	4	yes	—
86	C₇×C₂²⋊Q₈	—	2	2	no	—
87	C₇×C₂²⋊Q₈	—	2	2	no	—
88	C₇×C₂²⋊Q₈	—	2	2	no	—
89	C₇×C₂²⋊Q₈	—	2	2	no	—
90	C₇×C₂²⋊Q₈	—	2	2	no	—
91	C₇×C₂²⋊Q₈	—	2	2	no	—
92	C₄×C₇×Q₈	—	2	2	no	—
93	C₄×C₇×Q₈	—	2	2	no	—
94	C₄×C₇×Q₈	—	2	2	no	—
95	C₄×C₇×Q₈	—	2	2	no	—
96	C₄×C₇×Q₈	—	2	2	no	—
97	C₄×C₇×Q₈	—	2	2	no	—
98	C₇×#117	—	2	2	no	—
99	C₇×#117	—	2	2	no	—
100	C₂×C₇×C₄⋊C₄	—	2	1	no	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	—	2	1	no	—
103	C₂×C₇×C₄⋊C₄	—	2	1	no	—
104	C₂×C₇×C₄⋊C₄	—	2	1	no	—
105	C₂×C₇×C₄⋊C₄	—	2	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	D₄	1	1	yes	characteristic
112	C₂×C₇×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
128	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
130	C₇×#107	—	2	2	no	—
131	C₇×#106	—	2	2	no	—
132	C₇×C₄⋊C₈	—	2	2	no	—
133	C₇×C₄⋊C₈	—	2	2	no	—
134	C₇×#103	—	2	2	no	—
135	C₇×#103	—	2	2	no	—
136	C₇×#103	—	2	2	no	—
137	C₇×#103	—	2	2	no	—
138	C₇×#103	—	2	2	no	—
139	C₇×#103	—	2	2	no	—
140	C₇×#103	—	4	1	no	—
141	C₇×#103	—	4	1	no	—
142	C₇×C₂²⋊C₈	—	4	1	no	—
143	C₇×C₂²⋊C₈	—	4	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	C₂×#541	C₂×C₇	1	1	yes	characteristic
150	C₂×#479	C₂×C₇	1	1	yes	characteristic, complemented
151	C₂×#462	C₂×C₇	1	1	yes	characteristic, complemented
152	#2323	C₂×C₇	1	1	yes	characteristic
153	#2036	C₂×C₇	1	1	yes	characteristic
154	#2035	C₂×C₇	1	1	yes	characteristic
155	#2001	C₂×C₇	1	1	yes	characteristic
156	#2001	C₂×C₇	1	1	yes	characteristic
157	#1989	C₂×C₇	1	1	yes	characteristic, complemented
158	#1981	C₂×C₇	1	1	yes	characteristic, complemented
159	#1878	C₂×C₇	1	1	yes	characteristic, complemented
160	#1878	C₂×C₇	1	1	yes	characteristic, complemented
161	#1865	C₂×C₇	1	1	yes	characteristic, complemented
162	#1863	C₂×C₇	1	1	yes	characteristic, complemented
163	#1798	C₂×C₇	1	1	yes	characteristic
164	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
165	C₂×C₇×Q₈	—	2	1	no	—
166	C₂×C₇×Q₈	—	2	1	no	—
167	C₂×C₇×Q₈	—	2	1	no	—
168	C₂×C₇×Q₈	—	2	1	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	C₂×D₄	1	2	yes	—
181	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
182	C₂×C₇×Q₈	#41	1	2	yes	—
183	C₂²×C₄×C₇	—	2	1	no	—
184	C₂²×C₄×C₇	—	2	1	no	—
185	C₂²×C₄×C₇	—	2	1	no	—
186	C₂²×C₄×C₇	—	2	1	no	—
187	C₂²×C₄×C₇	—	2	1	no	—
188	C₂²×C₄×C₇	—	2	1	no	—
189	C₂²×C₄×C₇	—	2	1	no	—
190	C₂²×C₄×C₇	—	2	1	no	—
191	C₂²×C₄×C₇	—	2	1	no	—
192	C₂²×C₄×C₇	—	2	1	no	—
193	C₂²×C₄×C₇	—	2	1	no	—
194	C₂²×C₄×C₇	—	2	1	no	—
195	C₂²×C₄×C₇	—	2	1	no	—
196	C₂²×C₄×C₇	—	2	1	no	—
197	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
203	C₇×Q₁₆	—	4	4	no	—
204	C₇×Q₁₆	—	4	4	no	—
205	C₂×C₇×C₈	—	2	1	no	—
206	C₂×C₇×C₈	—	2	1	no	—
207	C₂×C₇×C₈	—	2	1	no	—
208	C₂×C₇×C₈	—	2	1	no	—
209	C₂×C₇×C₈	—	2	1	no	—
210	C₂×C₇×C₈	—	2	1	no	—
211	C₂×C₇×C₈	—	2	1	no	—
212	C₂×C₇×C₈	—	2	1	no	—
213	C₂×C₇×C₈	—	2	1	no	—
214	C₂×C₇×C₈	—	2	1	no	—
215	C₂×C₇×C₈	—	2	1	no	—
216	C₂×C₇×C₈	—	2	1	no	—
217	C₇×C₄⋊C₄	—	2	4	no	—
218	C₇×C₄⋊C₄	—	2	4	no	—
219	C₇×C₄⋊C₄	—	2	4	no	—
220	C₇×C₄⋊C₄	—	2	4	no	—
221	C₇×C₄⋊C₄	—	2	4	no	—
222	C₇×C₄⋊C₄	—	2	4	no	—
223	C₇×C₄⋊C₄	—	2	4	no	—
224	C₇×C₄⋊C₄	—	2	4	no	—
225	C₇×C₄⋊C₄	—	2	4	no	—
226	C₇×C₄⋊C₄	—	2	2	no	—
227	C₇×C₄⋊C₄	—	2	2	no	—
228	C₇×C₄⋊C₄	—	2	1	no	—
229	C₇×C₄⋊C₄	—	2	1	no	—
230	C₇×C₄⋊C₄	—	2	1	no	—
231	C₇×C₄⋊C₄	—	2	1	no	—
232	C₇×C₄⋊C₄	—	2	1	no	—
233	C₇×C₄⋊C₄	—	2	1	no	—
234	C₇×C₄⋊C₄	—	2	1	no	—
235	C₇×C₄⋊C₄	—	4	2	no	—
236	C₇×C₄⋊C₄	—	8	1	no	—
237	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
238	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
239	C₇×C₄⋊C₄	#41	1	2	yes	—
240	C₇×C₂²⋊C₄	—	2	4	no	—
241	C₇×C₂²⋊C₄	—	2	4	no	—
242	C₇×C₂²⋊C₄	—	2	4	no	—
243	C₇×C₂²⋊C₄	—	2	2	no	—
244	C₇×C₂²⋊C₄	—	2	2	no	—
245	C₇×C₂²⋊C₄	—	8	1	no	—
246	C₄²×C₇	—	2	4	no	—
247	C₄²×C₇	—	2	4	no	—
248	C₄²×C₇	—	2	1	no	—
249	C₄²×C₇	—	2	1	no	—
250	C₄²×C₇	—	4	2	no	—
251	C₄²×C₇	—	8	1	no	—
252	C₄²×C₇	C₂×D₄	1	2	yes	—
253	C₄²×C₇	C₂×D₄	1	2	yes	—
254	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
255	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
256	#541	—	2	4	no	—
257	#541	—	2	4	no	—
258	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
259	C₂×#126	—	2	1	no	—
260	C₂×#126	—	2	1	no	—
261	C₂×#125	—	2	1	no	—
262	C₂×#125	—	2	1	no	—
263	C₂×#125	C₂²×C₇	1	1	yes	characteristic
264	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
265	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
266	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
267	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
268	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
269	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
270	C₂×#117	C₂²×C₇	1	1	yes	characteristic
271	#479	—	2	4	no	—
272	#462	—	2	4	no	—
273	C₂×#107	C₂²×C₇	1	1	yes	characteristic
274	C₂×#106	C₂²×C₇	1	1	yes	characteristic
275	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
276	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
277	C₂×#103	C₂²×C₇	1	1	yes	characteristic
278	C₂×#103	C₂²×C₇	1	1	yes	characteristic
279	C₂×#103	C₂²×C₇	1	1	yes	characteristic
280	C₂×#103	C₂²×C₇	1	1	yes	characteristic
281	C₂×#103	C₂²×C₇	1	1	yes	characteristic
282	C₂×#103	C₂²×C₇	1	1	yes	characteristic
283	C₂×#103	C₂²×C₇	1	1	yes	characteristic
284	C₂×#103	C₂²×C₇	1	1	yes	characteristic
285	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
286	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
287	#391	C₂²×C₇	1	1	yes	characteristic
288	#389	—	2	1	no	—
289	#389	C₂²×C₇	1	1	yes	characteristic
290	#388	—	2	1	no	—
291	#388	—	2	1	no	—
292	#387	—	2	1	no	—
293	#380	C₂²×C₇	1	1	yes	characteristic
294	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
295	#340	C₂²×C₇	1	1	yes	characteristic
296	#340	C₂²×C₇	1	1	yes	characteristic
297	#340	C₂²×C₇	1	1	yes	characteristic
298	#340	C₂²×C₇	1	1	yes	characteristic
299	#336	C₂²×C₇	1	1	yes	characteristic
300	#336	C₂²×C₇	1	1	yes	characteristic
301	C₂³×C₇	—	2	1	no	—
302	C₂³×C₇	—	2	1	no	—
303	C₂³×C₇	—	2	1	no	—
304	C₂³×C₇	—	2	1	no	—
305	C₂³×C₇	—	2	1	no	—
306	C₂³×C₇	—	2	1	no	—
307	C₂³×C₇	—	2	1	no	—
308	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
309	C₇×Q₈	—	2	2	no	—
310	C₇×Q₈	—	2	2	no	—
311	C₇×Q₈	—	2	2	no	—
312	C₇×Q₈	—	2	2	no	—
313	C₇×Q₈	—	2	2	no	—
314	C₇×Q₈	—	2	2	no	—
315	C₇×Q₈	—	4	1	no	—
316	C₇×Q₈	—	4	1	no	—
317	C₇×Q₈	—	4	1	no	—
318	C₇×Q₈	—	4	1	no	—
319	C₇×Q₈	—	4	1	no	—
320	C₇×Q₈	—	4	1	no	—
321	C₂×C₄×C₇	—	2	1	no	—
322	C₂×C₄×C₇	—	2	1	no	—
323	C₂×C₄×C₇	—	2	1	no	—
324	C₂×C₄×C₇	—	2	1	no	—
325	C₂×C₄×C₇	—	2	1	no	—
326	C₂×C₄×C₇	—	2	1	no	—
327	C₂×C₄×C₇	—	2	2	no	—
328	C₂×C₄×C₇	—	2	2	no	—
329	C₂×C₄×C₇	—	2	2	no	—
330	C₂×C₄×C₇	—	2	2	no	—
331	C₂×C₄×C₇	—	2	1	no	—
332	C₂×C₄×C₇	—	2	2	no	—
333	C₂×C₄×C₇	—	2	2	no	—
334	C₂×C₄×C₇	—	2	1	no	—
335	C₂×C₄×C₇	—	2	1	no	—
336	C₂×C₄×C₇	—	2	1	no	—
337	C₂×C₄×C₇	—	2	1	no	—
338	C₂×C₄×C₇	—	2	1	no	—
339	C₂×C₄×C₇	—	2	1	no	—
340	C₂×C₄×C₇	—	4	1	no	—
341	C₂×C₄×C₇	—	4	1	no	—
342	C₂×C₄×C₇	—	4	1	no	—
343	C₂×C₄×C₇	—	4	1	no	—
344	C₂×C₄×C₇	—	4	1	no	—
345	C₂×C₄×C₇	—	4	1	no	—
346	C₂×C₄×C₇	—	4	1	no	—
347	C₂×C₄×C₇	—	4	1	no	—
348	C₂×C₄×C₇	—	4	1	no	—
349	C₂×C₄×C₇	—	4	1	no	—
350	C₂×C₄×C₇	—	4	1	no	—
351	C₂×C₄×C₇	—	4	1	no	—
352	C₂×C₄×C₇	—	4	1	no	—
353	C₂×C₄×C₇	—	4	1	no	—
354	C₂×C₄×C₇	—	4	1	no	—
355	C₂×C₄×C₇	—	4	1	no	—
356	C₂×C₄×C₇	—	4	1	no	—
357	C₂×C₄×C₇	—	4	1	no	—
358	C₂×C₄×C₇	—	4	1	no	—
359	C₂×C₄×C₇	—	4	1	no	—
360	C₂×C₄×C₇	—	4	1	no	—
361	C₂×C₄×C₇	—	4	1	no	—
362	C₂×C₄×C₇	#120	1	2	yes	—
363	C₂×C₄×C₇	#120	1	2	yes	—
364	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
367	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
368	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
369	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
370	C₇×C₈	—	4	1	no	—
371	C₇×C₈	—	4	1	no	—
372	C₇×C₈	—	4	1	no	—
373	C₇×C₈	—	4	1	no	—
374	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
375	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
376	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
378	C₂×Q₁₆	—	2	2	no	—
379	C₂×Q₁₆	—	2	2	no	—
380	C₂×Q₁₆	—	2	2	no	—
381	C₂×Q₁₆	—	2	2	no	—
382	C₂×Q₁₆	—	4	1	no	—
383	C₂×Q₁₆	—	4	1	no	—
384	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
385	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
386	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
387	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
388	C₄⋊Q₈	—	2	2	no	—
389	C₄⋊Q₈	C₇×D₄	1	4	yes	—
390	#126	—	2	8	no	—
391	#126	—	2	8	no	—
392	#125	—	2	8	no	—
393	#125	—	2	8	no	—
394	#125	—	2	2	no	—
395	#125	C₇×D₄	1	4	yes	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	2	2	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	2	2	no	—
401	C₂²⋊Q₈	—	2	2	no	—
402	C₄×Q₈	—	2	2	no	—
403	C₄×Q₈	—	2	2	no	—
404	C₄×Q₈	—	2	2	no	—
405	C₄×Q₈	—	2	2	no	—
406	C₄×Q₈	—	2	2	no	—
407	C₄×Q₈	—	2	2	no	—
408	#117	—	2	2	no	—
409	#117	—	2	2	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
440	#107	—	2	2	no	—
441	#106	—	2	2	no	—
442	C₄⋊C₈	—	2	2	no	—
443	C₄⋊C₈	—	2	2	no	—
444	#103	—	2	2	no	—
445	#103	—	2	2	no	—
446	#103	—	2	2	no	—
447	#103	—	2	2	no	—
448	#103	—	2	2	no	—
449	#103	—	2	2	no	—
450	#103	—	4	1	no	—
451	#103	—	4	1	no	—
452	C₂²⋊C₈	—	4	1	no	—
453	C₂²⋊C₈	—	4	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	C₂²×C₇	—	4	1	no	—
460	C₂²×C₇	—	4	1	no	—
461	C₂²×C₇	—	4	1	no	—
462	C₂²×C₇	—	4	1	no	—
463	C₂²×C₇	—	4	1	no	—
464	C₂²×C₇	—	4	1	no	—
465	C₂²×C₇	—	4	1	no	—
466	C₂²×C₇	C₂×#120	1	1	yes	characteristic
467	C₂²×C₇	#525	1	1	yes	characteristic
468	C₂²×C₇	#537	1	1	yes	characteristic
469	C₂²×C₇	#577	1	1	yes	characteristic
470	C₂²×C₇	#578	1	1	yes	characteristic
471	C₂²×C₇	#578	1	1	yes	characteristic
472	C₂²×C₇	#578	1	1	yes	characteristic
473	C₄×C₇	—	2	2	no	—
474	C₄×C₇	—	2	2	no	—
475	C₄×C₇	—	4	2	no	—
476	C₄×C₇	—	4	1	no	—
477	C₄×C₇	—	4	2	no	—
478	C₄×C₇	—	4	2	no	—
479	C₄×C₇	—	4	2	no	—
480	C₄×C₇	—	4	1	no	—
481	C₄×C₇	—	4	2	no	—
482	C₄×C₇	—	4	1	no	—
483	C₄×C₇	—	4	2	no	—
484	C₄×C₇	—	8	1	no	—
485	C₄×C₇	—	8	1	no	—
486	C₄×C₇	#546	1	1	yes	characteristic
487	C₄×C₇	#547	1	1	yes	characteristic
488	C₄×C₇	#548	1	1	yes	characteristic
489	C₄×C₇	#550	1	1	yes	characteristic
490	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
507	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
508	C₂×Q₈	C₇×#41	1	2	yes	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
524	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
525	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
526	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
527	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
529	Q₁₆	—	4	4	no	—
530	Q₁₆	—	4	4	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	2	4	no	—
548	C₄⋊C₄	—	2	4	no	—
549	C₄⋊C₄	—	2	4	no	—
550	C₄⋊C₄	—	2	4	no	—
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	—	2	2	no	—
553	C₄⋊C₄	—	2	2	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	4	2	no	—
562	C₄⋊C₄	—	8	1	no	—
563	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
564	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
565	C₄⋊C₄	C₇×#41	1	2	yes	—
566	C₂²⋊C₄	—	2	4	no	—
567	C₂²⋊C₄	—	2	4	no	—
568	C₂²⋊C₄	—	2	4	no	—
569	C₂²⋊C₄	—	2	2	no	—
570	C₂²⋊C₄	—	2	2	no	—
571	C₂²⋊C₄	—	8	1	no	—
572	C₄²	—	2	4	no	—
573	C₄²	—	2	4	no	—
574	C₄²	—	2	1	no	—
575	C₄²	—	2	1	no	—
576	C₄²	—	4	2	no	—
577	C₄²	—	8	1	no	—
578	C₄²	C₂×C₇×D₄	1	2	yes	—
579	C₄²	C₂×C₇×D₄	1	2	yes	—
580	C₂×C₇	—	8	1	no	—
581	C₂×C₇	#2407	1	1	yes	characteristic
582	C₂×C₇	#3011	1	1	yes	characteristic
583	C₂×C₇	#3013	1	1	yes	characteristic
584	C₂×C₇	#3120	1	1	yes	characteristic
585	C₂×C₇	#3127	1	1	yes	characteristic
586	C₂×C₇	#3258	1	1	yes	characteristic
587	C₂×C₇	#3261	1	1	yes	characteristic
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
596	Q₈	—	2	2	no	—
597	Q₈	—	2	2	no	—
598	Q₈	—	2	2	no	—
599	Q₈	—	2	2	no	—
600	Q₈	—	2	2	no	—
601	Q₈	—	2	2	no	—
602	Q₈	—	4	1	no	—
603	Q₈	—	4	1	no	—
604	Q₈	—	4	1	no	—
605	Q₈	—	4	1	no	—
606	Q₈	—	4	1	no	—
607	Q₈	—	4	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	C₇×#120	1	2	yes	—
650	C₂×C₄	C₇×#120	1	2	yes	—
651	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
652	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
653	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
654	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
655	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
656	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
657	C₈	—	4	1	no	—
658	C₈	—	4	1	no	—
659	C₈	—	4	1	no	—
660	C₈	—	4	1	no	—
661	C₇	#24165	1	1	yes	characteristic, direct product factor, Sylow
662	C₂²	—	4	1	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	C₂×C₇×#120	1	1	yes	characteristic
670	C₂²	C₇×#525	1	1	yes	characteristic
671	C₂²	C₇×#537	1	1	yes	characteristic
672	C₂²	C₇×#577	1	1	yes	characteristic
673	C₂²	C₇×#578	1	1	yes	characteristic
674	C₂²	C₇×#578	1	1	yes	characteristic
675	C₂²	C₇×#578	1	1	yes	characteristic
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	2	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	1	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	2	no	—
687	C₄	—	8	1	no	—
688	C₄	—	8	1	no	—
689	C₄	C₇×#546	1	1	yes	characteristic
690	C₄	C₇×#547	1	1	yes	characteristic
691	C₄	C₇×#548	1	1	yes	characteristic
692	C₄	C₇×#550	1	1	yes	characteristic
693	C₂	—	8	1	no	—
694	C₂	C₇×#2407	1	1	yes	characteristic
695	C₂	C₇×#3011	1	1	yes	characteristic
696	C₂	C₇×#3013	1	1	yes	characteristic
697	C₂	C₇×#3120	1	1	yes	characteristic
698	C₂	C₇×#3127	1	1	yes	characteristic
699	C₂	C₇×#3258	1	1	yes	characteristic
700	C₂	C₇×#3261	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂⁴×C₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#479	C₂	semidirect
3. C₂×C₇×#462	C₂	semidirect
9. C₇×#1989	C₂	semidirect
10. C₇×#1981	C₂	semidirect
11. C₇×#1878	C₂	semidirect
12. C₇×#1878	C₂	semidirect
13. C₇×#1865	C₂	semidirect
14. C₇×#1863	C₂	semidirect
63. #24165	C₇	direct (N × H)
150. C₂×#479	C₂×C₇	semidirect
151. C₂×#462	C₂×C₇	semidirect
157. #1989	C₂×C₇	semidirect
158. #1981	C₂×C₇	semidirect
159. #1878	C₂×C₇	semidirect
160. #1878	C₂×C₇	semidirect
161. #1865	C₂×C₇	semidirect
162. #1863	C₂×C₇	semidirect
661. C₇	#24165	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×#541	2
C₂×C₇×#479	2
C₂×C₇×#462	2
C₇×#2323	2
C₇×#2036	2
C₇×#2035	2
C₇×#2001	2
C₇×#1989	2
C₇×#1981	2
C₇×#1878	2
C₇×#1865	2
C₇×#1863	2
C₇×#1798	2
#24165	7

Subgroups — C7×#24165 #13201381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#24165 #13201381