Subgroups — C₇×#24736 #13201952

Order 1792.

924 conjugacy classes of subgroups.

The subgroup lattice has 690 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
2	C₂×C₇×#464	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2545	C₂	1	1	yes	maximal, characteristic
6	C₇×#2351	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2067	C₂	1	1	yes	maximal, characteristic
9	C₇×#2043	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2042	C₂	1	1	yes	maximal, characteristic
11	C₇×#1958	C₂	1	1	yes	maximal, characteristic
12	C₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1880	C₂	1	1	yes	maximal, characteristic
14	C₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×#124	C₂²	1	1	yes	characteristic
21	C₂×C₇×#124	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×Q₈	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	C₇×#464	—	2	4	no	—
27	C₇×#464	—	2	4	no	—
28	C₇×#462	—	2	4	no	—
29	C₄×C₇×Q₁₆	—	2	4	no	—
30	C₂×C₇×#107	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₄⋊C₈	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×#103	C₂²	1	1	yes	characteristic
41	C₂×C₇×#102	C₂²	1	1	yes	characteristic
42	C₂×C₇×#102	C₂²	1	1	yes	characteristic
43	C₂×C₇×#102	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
45	C₇×#396	—	2	1	no	—
46	C₇×#396	—	2	1	no	—
47	C₇×#391	C₂²	1	1	yes	characteristic
48	C₇×#390	C₂²	1	1	yes	characteristic
49	C₇×#389	—	2	1	no	—
50	C₇×#389	—	2	1	no	—
51	C₇×#389	C₂²	1	1	yes	characteristic
52	C₇×#389	C₂²	1	1	yes	characteristic
53	C₇×#388	—	2	1	no	—
54	C₇×#388	—	2	1	no	—
55	C₇×#382	—	2	1	no	—
56	C₇×#382	C₂²	1	1	yes	characteristic
57	C₄×C₇×C₄⋊C₄	—	2	1	no	—
58	C₄×C₇×C₄⋊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	#24736	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	C₂²×C₇×D₄	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	—	2	2	no	—
73	C₂×C₇×Q₁₆	D₄	1	4	yes	—
74	C₂×C₇×SD₁₆	—	2	2	no	—
75	C₂×C₇×SD₁₆	—	2	2	no	—
76	C₂×C₇×SD₁₆	—	2	2	no	—
77	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
81	C₇×C₄⋊Q₈	—	2	2	no	—
82	C₇×C₄⋊Q₈	—	4	1	no	—
83	C₇×#124	—	2	2	no	—
84	C₇×#124	—	2	2	no	—
85	C₇×#124	—	2	2	no	—
86	C₇×#124	—	4	1	no	—
87	C₄×C₇×Q₈	—	2	2	no	—
88	C₄×C₇×Q₈	—	2	2	no	—
89	C₄×C₇×Q₈	—	2	2	no	—
90	C₄×C₇×Q₈	—	2	2	no	—
91	C₄×C₇×Q₈	—	2	2	no	—
92	C₄×C₇×Q₈	—	4	1	no	—
93	C₄×C₇×Q₈	—	4	1	no	—
94	C₄×C₇×Q₈	D₄	1	4	yes	—
95	C₂×C₇×C₄⋊C₄	—	2	1	no	—
96	C₂×C₇×C₄⋊C₄	—	2	1	no	—
97	C₂×C₇×C₄⋊C₄	—	2	1	no	—
98	C₂×C₇×C₄⋊C₄	—	2	1	no	—
99	C₂×C₇×C₄⋊C₄	—	2	1	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	D₄	1	1	yes	characteristic
104	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₄²×C₇	—	2	1	no	—
116	C₂×C₄²×C₇	—	2	1	no	—
117	C₂×C₄²×C₇	—	2	1	no	—
118	C₂×C₄²×C₇	—	2	1	no	—
119	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
122	C₇×#107	—	2	2	no	—
123	C₇×C₄⋊C₈	—	2	2	no	—
124	C₇×C₄⋊C₈	—	2	2	no	—
125	C₇×C₄⋊C₈	—	2	2	no	—
126	C₇×#103	—	2	2	no	—
127	C₇×#103	—	2	2	no	—
128	C₇×#103	—	2	2	no	—
129	C₇×#103	—	2	2	no	—
130	C₇×#103	—	2	2	no	—
131	C₇×#103	—	2	2	no	—
132	C₇×#103	—	4	1	no	—
133	C₇×#102	—	2	2	no	—
134	C₇×#102	—	2	2	no	—
135	C₇×#102	—	4	1	no	—
136	C₄×C₇×C₈	—	2	2	no	—
137	C₇×#95	—	2	1	no	—
138	C₇×#95	—	2	1	no	—
139	C₇×#95	—	2	1	no	—
140	C₇×#95	—	2	1	no	—
141	C₇×#95	—	2	1	no	—
142	C₇×#95	—	2	1	no	—
143	C₇×#95	D₄	1	1	yes	characteristic
144	C₇×#95	D₄	1	1	yes	characteristic
145	C₂×#464	C₂×C₇	1	1	yes	characteristic
146	C₂×#464	C₂×C₇	1	1	yes	characteristic
147	C₂×#462	C₂×C₇	1	1	yes	characteristic, complemented
148	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
149	#2545	C₂×C₇	1	1	yes	characteristic
150	#2351	C₂×C₇	1	1	yes	characteristic, complemented
151	#2068	C₂×C₇	1	1	yes	characteristic, complemented
152	#2067	C₂×C₇	1	1	yes	characteristic
153	#2043	C₂×C₇	1	1	yes	characteristic, complemented
154	#2042	C₂×C₇	1	1	yes	characteristic
155	#1958	C₂×C₇	1	1	yes	characteristic
156	#1939	C₂×C₇	1	1	yes	characteristic, complemented
157	#1880	C₂×C₇	1	1	yes	characteristic
158	#1878	C₂×C₇	1	1	yes	characteristic, complemented
159	#1805	C₂×C₇	1	1	yes	characteristic, complemented
160	C₂⁴×C₇	—	2	1	no	—
161	C₂×C₇×Q₈	—	2	1	no	—
162	C₂×C₇×Q₈	—	2	1	no	—
163	C₂×C₇×Q₈	—	2	1	no	—
164	C₂×C₇×Q₈	—	2	1	no	—
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	C₂×D₄	1	2	yes	—
176	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
177	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
178	C₂×C₇×Q₈	#41	1	2	yes	—
179	C₂×C₇×D₄	—	2	1	no	—
180	C₂×C₇×D₄	—	2	1	no	—
181	C₂×C₇×D₄	—	2	1	no	—
182	C₂×C₇×D₄	—	2	1	no	—
183	C₂×C₇×D₄	—	2	1	no	—
184	C₂×C₇×D₄	—	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	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
199	C₇×Q₁₆	—	2	8	no	—
200	C₇×Q₁₆	—	4	4	no	—
201	C₇×SD₁₆	—	4	4	no	—
202	C₂×C₇×C₈	—	2	1	no	—
203	C₂×C₇×C₈	—	2	1	no	—
204	C₂×C₇×C₈	—	2	1	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	C₂×D₄	1	2	yes	—
214	C₇×C₄⋊C₄	—	2	4	no	—
215	C₇×C₄⋊C₄	—	2	2	no	—
216	C₇×C₄⋊C₄	—	2	1	no	—
217	C₇×C₄⋊C₄	—	2	1	no	—
218	C₇×C₄⋊C₄	—	2	1	no	—
219	C₇×C₄⋊C₄	—	2	1	no	—
220	C₇×C₄⋊C₄	—	2	1	no	—
221	C₇×C₄⋊C₄	—	2	1	no	—
222	C₇×C₄⋊C₄	—	2	1	no	—
223	C₇×C₄⋊C₄	—	4	1	no	—
224	C₇×C₄⋊C₄	—	4	2	no	—
225	C₇×C₄⋊C₄	—	4	2	no	—
226	C₇×C₄⋊C₄	—	4	2	no	—
227	C₇×C₄⋊C₄	—	4	2	no	—
228	C₇×C₄⋊C₄	—	4	2	no	—
229	C₇×C₄⋊C₄	—	4	2	no	—
230	C₇×C₄⋊C₄	—	4	2	no	—
231	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
232	C₇×C₂²⋊C₄	—	4	2	no	—
233	C₇×C₂²⋊C₄	—	4	2	no	—
234	C₇×C₂²⋊C₄	—	4	2	no	—
235	C₇×C₂²⋊C₄	—	4	2	no	—
236	C₇×C₂²⋊C₄	—	4	2	no	—
237	C₇×C₂²⋊C₄	—	4	2	no	—
238	C₄²×C₇	—	2	4	no	—
239	C₄²×C₇	—	2	1	no	—
240	C₄²×C₇	—	2	1	no	—
241	C₄²×C₇	—	2	1	no	—
242	C₄²×C₇	—	2	1	no	—
243	C₄²×C₇	—	4	2	no	—
244	C₄²×C₇	—	4	2	no	—
245	C₄²×C₇	—	4	2	no	—
246	C₄²×C₇	C₂×D₄	1	2	yes	—
247	C₄²×C₇	#41	1	2	yes	—
248	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
249	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
250	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
251	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
252	C₂×#124	C₂²×C₇	1	1	yes	characteristic
253	C₂×#124	C₂²×C₇	1	1	yes	characteristic
254	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
255	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
256	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
257	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
258	#464	—	2	4	no	—
259	#464	—	2	4	no	—
260	#462	—	2	4	no	—
261	C₄×Q₁₆	—	2	4	no	—
262	C₂×#107	C₂²×C₇	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
266	C₂×#103	C₂²×C₇	1	1	yes	characteristic
267	C₂×#103	C₂²×C₇	1	1	yes	characteristic
268	C₂×#103	C₂²×C₇	1	1	yes	characteristic
269	C₂×#103	C₂²×C₇	1	1	yes	characteristic
270	C₂×#103	C₂²×C₇	1	1	yes	characteristic
271	C₂×#103	C₂²×C₇	1	1	yes	characteristic
272	C₂×#103	C₂²×C₇	1	1	yes	characteristic
273	C₂×#102	C₂²×C₇	1	1	yes	characteristic
274	C₂×#102	C₂²×C₇	1	1	yes	characteristic
275	C₂×#102	C₂²×C₇	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
277	#396	—	2	1	no	—
278	#396	—	2	1	no	—
279	#391	C₂²×C₇	1	1	yes	characteristic
280	#390	C₂²×C₇	1	1	yes	characteristic
281	#389	—	2	1	no	—
282	#389	—	2	1	no	—
283	#389	C₂²×C₇	1	1	yes	characteristic
284	#389	C₂²×C₇	1	1	yes	characteristic
285	#388	—	2	1	no	—
286	#388	—	2	1	no	—
287	#382	—	2	1	no	—
288	#382	C₂²×C₇	1	1	yes	characteristic
289	C₄×C₄⋊C₄	—	2	1	no	—
290	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
291	#340	C₂²×C₇	1	1	yes	characteristic
292	#340	C₂²×C₇	1	1	yes	characteristic
293	#336	C₂²×C₇	1	1	yes	characteristic
294	#336	C₂²×C₇	1	1	yes	characteristic
295	C₂³×C₇	—	4	1	no	—
296	C₂³×C₇	—	4	1	no	—
297	C₂³×C₇	—	4	1	no	—
298	C₂³×C₇	—	4	1	no	—
299	C₂³×C₇	—	4	1	no	—
300	C₂³×C₇	—	4	1	no	—
301	C₂³×C₇	—	4	1	no	—
302	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
303	C₇×Q₈	—	2	2	no	—
304	C₇×Q₈	—	2	2	no	—
305	C₇×Q₈	—	2	2	no	—
306	C₇×Q₈	—	2	2	no	—
307	C₇×Q₈	—	2	2	no	—
308	C₇×Q₈	—	4	1	no	—
309	C₇×Q₈	—	4	1	no	—
310	C₇×Q₈	—	4	1	no	—
311	C₇×Q₈	—	4	1	no	—
312	C₇×Q₈	—	4	1	no	—
313	C₇×Q₈	—	4	1	no	—
314	C₇×Q₈	#121	1	4	yes	—
315	C₇×D₄	—	4	1	no	—
316	C₇×D₄	—	4	1	no	—
317	C₇×D₄	—	4	1	no	—
318	C₇×D₄	—	4	1	no	—
319	C₂×C₄×C₇	—	2	2	no	—
320	C₂×C₄×C₇	—	2	1	no	—
321	C₂×C₄×C₇	—	2	2	no	—
322	C₂×C₄×C₇	—	2	2	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	1	no	—
328	C₂×C₄×C₇	—	2	2	no	—
329	C₂×C₄×C₇	—	2	1	no	—
330	C₂×C₄×C₇	—	2	1	no	—
331	C₂×C₄×C₇	—	2	1	no	—
332	C₂×C₄×C₇	—	2	2	no	—
333	C₂×C₄×C₇	—	2	1	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	—	4	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	#121	1	2	yes	—
356	C₂×C₄×C₇	#121	1	2	yes	—
357	C₂×C₄×C₇	#135	1	2	yes	—
358	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
362	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
364	C₇×C₈	—	2	2	no	—
365	C₇×C₈	—	4	1	no	—
366	C₇×C₈	—	4	1	no	—
367	C₇×C₈	—	4	1	no	—
368	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
369	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
370	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
371	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
372	C₂×Q₁₆	—	2	2	no	—
373	C₂×Q₁₆	—	2	2	no	—
374	C₂×Q₁₆	—	2	2	no	—
375	C₂×Q₁₆	—	2	2	no	—
376	C₂×Q₁₆	—	2	2	no	—
377	C₂×Q₁₆	C₇×D₄	1	4	yes	—
378	C₂×SD₁₆	—	2	2	no	—
379	C₂×SD₁₆	—	2	2	no	—
380	C₂×SD₁₆	—	2	2	no	—
381	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
384	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
385	C₄⋊Q₈	—	2	2	no	—
386	C₄⋊Q₈	—	4	1	no	—
387	#124	—	2	2	no	—
388	#124	—	2	2	no	—
389	#124	—	2	2	no	—
390	#124	—	4	1	no	—
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	—	2	2	no	—
396	C₄×Q₈	—	4	1	no	—
397	C₄×Q₈	—	4	1	no	—
398	C₄×Q₈	C₇×D₄	1	4	yes	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
426	#107	—	2	2	no	—
427	C₄⋊C₈	—	2	2	no	—
428	C₄⋊C₈	—	2	2	no	—
429	C₄⋊C₈	—	2	2	no	—
430	#103	—	2	2	no	—
431	#103	—	2	2	no	—
432	#103	—	2	2	no	—
433	#103	—	2	2	no	—
434	#103	—	2	2	no	—
435	#103	—	2	2	no	—
436	#103	—	4	1	no	—
437	#102	—	2	2	no	—
438	#102	—	2	2	no	—
439	#102	—	4	1	no	—
440	C₄×C₈	—	2	2	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	C₇×D₄	1	1	yes	characteristic
448	#95	C₇×D₄	1	1	yes	characteristic
449	C₂²×C₇	—	8	1	no	—
450	C₂²×C₇	—	8	1	no	—
451	C₂²×C₇	—	8	1	no	—
452	C₂²×C₇	—	8	1	no	—
453	C₂²×C₇	—	8	1	no	—
454	C₂²×C₇	—	8	1	no	—
455	C₂²×C₇	—	8	1	no	—
456	C₂²×C₇	C₂×#121	1	1	yes	characteristic
457	C₂²×C₇	D₄²	1	1	yes	characteristic
458	C₂²×C₇	#548	1	1	yes	characteristic
459	C₂²×C₇	C₂×#135	1	1	yes	characteristic
460	C₂²×C₇	#575	1	1	yes	characteristic
461	C₂²×C₇	#578	1	1	yes	characteristic
462	C₂²×C₇	#578	1	1	yes	characteristic
463	C₄×C₇	—	2	4	no	—
464	C₄×C₇	—	2	2	no	—
465	C₄×C₇	—	2	2	no	—
466	C₄×C₇	—	2	2	no	—
467	C₄×C₇	—	4	2	no	—
468	C₄×C₇	—	4	1	no	—
469	C₄×C₇	—	4	1	no	—
470	C₄×C₇	—	4	1	no	—
471	C₄×C₇	—	4	2	no	—
472	C₄×C₇	—	8	1	no	—
473	C₄×C₇	—	8	1	no	—
474	C₄×C₇	—	8	1	no	—
475	C₄×C₇	—	8	1	no	—
476	C₄×C₇	C₂×#121	1	1	yes	characteristic
477	C₄×C₇	#537	1	1	yes	characteristic
478	C₄×C₇	#547	1	1	yes	characteristic
479	C₄×C₇	#553	1	1	yes	characteristic
480	C₂⁴	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
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	C₂×C₇×D₄	1	2	yes	—
496	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
497	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
498	C₂×Q₈	C₇×#41	1	2	yes	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
513	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
514	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
515	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
516	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
517	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
518	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
519	Q₁₆	—	2	8	no	—
520	Q₁₆	—	4	4	no	—
521	SD₁₆	—	4	4	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	4	1	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	4	2	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	—	4	2	no	—
551	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
552	C₂²⋊C₄	—	4	2	no	—
553	C₂²⋊C₄	—	4	2	no	—
554	C₂²⋊C₄	—	4	2	no	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₄²	—	2	4	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	2	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	4	2	no	—
564	C₄²	—	4	2	no	—
565	C₄²	—	4	2	no	—
566	C₄²	C₂×C₇×D₄	1	2	yes	—
567	C₄²	C₇×#41	1	2	yes	—
568	C₂×C₇	—	16	1	no	—
569	C₂×C₇	#2416	1	1	yes	characteristic
570	C₂×C₇	#3035	1	1	yes	characteristic
571	C₂×C₇	#3044	1	1	yes	characteristic
572	C₂×C₇	#3277	1	1	yes	characteristic
573	C₂×C₇	#3285	1	1	yes	characteristic
574	C₂×C₇	#3364	1	1	yes	characteristic
575	C₂×C₇	#3377	1	1	yes	characteristic
576	C₂³	—	4	1	no	—
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	4	1	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
584	Q₈	—	2	2	no	—
585	Q₈	—	2	2	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	2	2	no	—
588	Q₈	—	2	2	no	—
589	Q₈	—	4	1	no	—
590	Q₈	—	4	1	no	—
591	Q₈	—	4	1	no	—
592	Q₈	—	4	1	no	—
593	Q₈	—	4	1	no	—
594	Q₈	—	4	1	no	—
595	Q₈	C₇×#121	1	4	yes	—
596	D₄	—	4	1	no	—
597	D₄	—	4	1	no	—
598	D₄	—	4	1	no	—
599	D₄	—	4	1	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	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	C₇×#121	1	2	yes	—
637	C₂×C₄	C₇×#121	1	2	yes	—
638	C₂×C₄	C₇×#135	1	2	yes	—
639	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
640	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
641	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
642	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
643	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
644	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
645	C₈	—	2	2	no	—
646	C₈	—	4	1	no	—
647	C₈	—	4	1	no	—
648	C₈	—	4	1	no	—
649	C₇	#24736	1	1	yes	characteristic, direct product factor, Sylow
650	C₂²	—	8	1	no	—
651	C₂²	—	8	1	no	—
652	C₂²	—	8	1	no	—
653	C₂²	—	8	1	no	—
654	C₂²	—	8	1	no	—
655	C₂²	—	8	1	no	—
656	C₂²	—	8	1	no	—
657	C₂²	C₂×C₇×#121	1	1	yes	characteristic
658	C₂²	C₇×D₄²	1	1	yes	characteristic
659	C₂²	C₇×#548	1	1	yes	characteristic
660	C₂²	C₂×C₇×#135	1	1	yes	characteristic
661	C₂²	C₇×#575	1	1	yes	characteristic
662	C₂²	C₇×#578	1	1	yes	characteristic
663	C₂²	C₇×#578	1	1	yes	characteristic
664	C₄	—	2	4	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	1	no	—
672	C₄	—	4	2	no	—
673	C₄	—	8	1	no	—
674	C₄	—	8	1	no	—
675	C₄	—	8	1	no	—
676	C₄	—	8	1	no	—
677	C₄	C₂×C₇×#121	1	1	yes	characteristic
678	C₄	C₇×#537	1	1	yes	characteristic
679	C₄	C₇×#547	1	1	yes	characteristic
680	C₄	C₇×#553	1	1	yes	characteristic
681	C₂	—	16	1	no	—
682	C₂	C₇×#2416	1	1	yes	characteristic
683	C₂	C₇×#3035	1	1	yes	characteristic
684	C₂	C₇×#3044	1	1	yes	characteristic
685	C₂	C₇×#3277	1	1	yes	characteristic
686	C₂	C₇×#3285	1	1	yes	characteristic
687	C₂	C₇×#3364	1	1	yes	characteristic
688	C₂	C₇×#3377	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
3. C₂×C₇×#462	C₂	semidirect
4. C₂×C₄×C₇×Q₁₆	C₂	semidirect
6. C₇×#2351	C₂	semidirect
7. C₇×#2068	C₂	semidirect
9. C₇×#2043	C₂	semidirect
12. C₇×#1939	C₂	semidirect
14. C₇×#1878	C₂	semidirect
15. C₇×#1805	C₂	semidirect
63. #24736	C₇	direct (N × H)
147. C₂×#462	C₂×C₇	semidirect
148. C₂×C₄×Q₁₆	C₂×C₇	semidirect
150. #2351	C₂×C₇	semidirect
151. #2068	C₂×C₇	semidirect
153. #2043	C₂×C₇	semidirect
156. #1939	C₂×C₇	semidirect
158. #1878	C₂×C₇	semidirect
159. #1805	C₂×C₇	semidirect
649. C₇	#24736	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×#462	2
C₂×C₄×C₇×Q₁₆	2
C₇×#2545	2
C₇×#2351	2
C₇×#2068	2
C₇×#2067	2
C₇×#2043	2
C₇×#2042	2
C₇×#1958	2
C₇×#1939	2
C₇×#1880	2
C₇×#1878	2
C₇×#1805	2
#24736	7

Subgroups — C7×#24736 #13201952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#24736 #13201952