Subgroups — C₇×#24516 #13201732

Order 1792.

1056 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#450	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2625	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2309	C₂	1	1	yes	maximal, characteristic
5	C₇×#2067	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2065	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1973	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1968	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1936	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1934	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1873	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1854	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1786	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×#117	C₂²	1	1	yes	characteristic
21	C₂×C₇×#117	C₂²	1	1	yes	characteristic
22	C₇×#450	—	2	4	no	—
23	C₇×#433	—	2	4	no	—
24	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₇×#106	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₇×#102	C₂²	1	1	yes	characteristic
31	C₂×C₇×#102	C₂²	1	1	yes	characteristic
32	C₂×C₇×#102	C₂²	1	1	yes	characteristic
33	C₂×C₇×#102	C₂²	1	1	yes	characteristic
34	C₂×C₇×#102	C₂²	1	1	yes	characteristic
35	C₂×C₇×#102	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
40	C₇×#400	—	2	1	no	—
41	C₇×#398	—	2	1	no	—
42	C₇×#397	—	2	1	no	—
43	C₇×#397	—	2	1	no	—
44	C₇×#391	C₂²	1	1	yes	characteristic, complemented
45	C₇×#391	C₂²	1	1	yes	characteristic, complemented
46	C₇×#390	—	2	1	no	—
47	C₇×#390	—	2	1	no	—
48	C₇×#390	C₂²	1	1	yes	characteristic
49	C₇×#390	C₂²	1	1	yes	characteristic
50	C₇×#390	C₂²	1	1	yes	characteristic
51	C₇×#390	C₂²	1	1	yes	characteristic
52	C₇×#389	C₂²	1	1	yes	characteristic, complemented
53	C₇×#389	C₂²	1	1	yes	characteristic, complemented
54	C₇×#380	C₂²	1	1	yes	characteristic
55	C₇×#379	—	2	1	no	—
56	C₇×#379	—	2	1	no	—
57	C₇×#340	C₂²	1	1	yes	characteristic, complemented
58	C₇×#340	C₂²	1	1	yes	characteristic, complemented
59	C₇×#340	C₂²	1	1	yes	characteristic, complemented
60	C₇×#340	C₂²	1	1	yes	characteristic, complemented
61	#24516	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂⁵×C₇	—	2	1	no	—
63	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇×D₄	—	2	2	no	—
65	C₂²×C₇×D₄	—	2	2	no	—
66	C₂²×C₇×D₄	—	2	1	no	—
67	C₂²×C₇×D₄	—	2	2	no	—
68	C₂²×C₇×D₄	—	2	2	no	—
69	C₂²×C₇×D₄	—	4	1	no	—
70	C₂²×C₇×D₄	—	4	1	no	—
71	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
72	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
74	C₂×C₇×SD₁₆	—	2	2	no	—
75	C₂×C₇×SD₁₆	—	2	2	no	—
76	C₂×C₇×SD₁₆	—	2	2	no	—
77	C₂×C₇×SD₁₆	—	2	2	no	—
78	C₂×C₇×SD₁₆	—	4	1	no	—
79	C₂×C₇×SD₁₆	—	4	1	no	—
80	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
84	C₇×C₂²⋊Q₈	—	2	2	no	—
85	C₇×C₂²⋊Q₈	—	2	2	no	—
86	C₇×#117	—	2	2	no	—
87	C₇×#117	—	2	2	no	—
88	C₇×#117	—	4	1	no	—
89	C₇×#117	—	4	1	no	—
90	C₂×C₇×C₄⋊C₄	—	2	1	no	—
91	C₂×C₇×C₄⋊C₄	—	2	1	no	—
92	C₂×C₇×C₄⋊C₄	—	2	1	no	—
93	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
94	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
112	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₇	—	2	1	no	—
114	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
116	C₇×#107	—	4	1	no	—
117	C₇×#106	—	4	1	no	—
118	C₇×C₄⋊C₈	—	2	2	no	—
119	C₇×C₄⋊C₈	—	2	2	no	—
120	C₇×#103	—	4	1	no	—
121	C₇×#103	—	4	1	no	—
122	C₇×#102	—	2	2	no	—
123	C₇×#102	—	2	2	no	—
124	C₇×#102	—	2	2	no	—
125	C₇×#102	—	2	2	no	—
126	C₇×#102	—	4	1	no	—
127	C₇×#102	—	4	1	no	—
128	C₇×C₂²⋊C₈	—	2	2	no	—
129	C₇×C₂²⋊C₈	D₄	1	4	yes	—
130	C₇×#97	—	2	2	no	—
131	C₄×C₇×C₈	—	2	2	no	—
132	C₇×#95	—	2	1	no	—
133	C₇×#95	—	2	1	no	—
134	C₇×#95	—	2	1	no	—
135	C₇×#95	—	2	1	no	—
136	C₇×#95	—	2	1	no	—
137	C₇×#95	—	2	1	no	—
138	C₇×#95	—	2	1	no	—
139	C₂×#450	C₂×C₇	1	1	yes	characteristic
140	C₂×#433	C₂×C₇	1	1	yes	characteristic, complemented
141	#2625	C₂×C₇	1	1	yes	characteristic, complemented
142	#2309	C₂×C₇	1	1	yes	characteristic
143	#2067	C₂×C₇	1	1	yes	characteristic, complemented
144	#2065	C₂×C₇	1	1	yes	characteristic, complemented
145	#2055	C₂×C₇	1	1	yes	characteristic, complemented
146	#2055	C₂×C₇	1	1	yes	characteristic, complemented
147	#1973	C₂×C₇	1	1	yes	characteristic, complemented
148	#1968	C₂×C₇	1	1	yes	characteristic, complemented
149	#1936	C₂×C₇	1	1	yes	characteristic, complemented
150	#1934	C₂×C₇	1	1	yes	characteristic, complemented
151	#1873	C₂×C₇	1	1	yes	characteristic, complemented
152	#1854	C₂×C₇	1	1	yes	characteristic, complemented
153	#1786	C₂×C₇	1	1	yes	characteristic
154	C₂⁴×C₇	—	2	4	no	—
155	C₂⁴×C₇	—	2	1	no	—
156	C₂⁴×C₇	—	2	1	no	—
157	C₂⁴×C₇	—	4	2	no	—
158	C₂⁴×C₇	—	4	2	no	—
159	C₂⁴×C₇	—	8	1	no	—
160	C₂⁴×C₇	—	8	1	no	—
161	C₂⁴×C₇	—	8	1	no	—
162	C₂⁴×C₇	—	8	1	no	—
163	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
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×D₄	—	2	4	no	—
171	C₂×C₇×D₄	—	2	1	no	—
172	C₂×C₇×D₄	—	2	1	no	—
173	C₂×C₇×D₄	—	2	1	no	—
174	C₂×C₇×D₄	—	2	1	no	—
175	C₂×C₇×D₄	—	2	1	no	—
176	C₂×C₇×D₄	—	2	1	no	—
177	C₂×C₇×D₄	—	2	1	no	—
178	C₂×C₇×D₄	—	2	1	no	—
179	C₂×C₇×D₄	—	2	1	no	—
180	C₂×C₇×D₄	—	2	1	no	—
181	C₂×C₇×D₄	—	4	4	no	—
182	C₂×C₇×D₄	—	4	4	no	—
183	C₂×C₇×D₄	—	4	4	no	—
184	C₂×C₇×D₄	—	4	4	no	—
185	C₂×C₇×D₄	—	4	2	no	—
186	C₂×C₇×D₄	—	4	2	no	—
187	C₂×C₇×D₄	#41	1	2	yes	—
188	C₂×C₇×D₄	#41	1	2	yes	—
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	—	2	1	no	—
198	C₂²×C₄×C₇	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₇	#41	1	2	yes	—
206	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
207	C₇×SD₁₆	—	4	4	no	—
208	C₇×SD₁₆	—	4	4	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	C₂×C₇×C₈	—	2	1	no	—
218	C₂×C₇×C₈	—	2	1	no	—
219	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
220	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
221	C₇×C₄⋊C₄	—	2	2	no	—
222	C₇×C₄⋊C₄	—	2	2	no	—
223	C₇×C₄⋊C₄	—	2	1	no	—
224	C₇×C₄⋊C₄	—	2	1	no	—
225	C₇×C₄⋊C₄	—	2	1	no	—
226	C₇×C₄⋊C₄	—	2	1	no	—
227	C₇×C₄⋊C₄	—	2	1	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	—	4	2	no	—
234	C₇×C₄⋊C₄	—	8	1	no	—
235	C₇×C₄⋊C₄	—	8	1	no	—
236	C₇×C₂²⋊C₄	—	2	2	no	—
237	C₇×C₂²⋊C₄	—	2	2	no	—
238	C₇×C₂²⋊C₄	—	4	2	no	—
239	C₇×C₂²⋊C₄	—	4	2	no	—
240	C₇×C₂²⋊C₄	—	8	1	no	—
241	C₇×C₂²⋊C₄	—	8	1	no	—
242	C₇×C₂²⋊C₄	—	8	1	no	—
243	C₇×C₂²⋊C₄	—	8	1	no	—
244	C₇×C₂²⋊C₄	—	8	1	no	—
245	C₇×C₂²⋊C₄	—	8	1	no	—
246	C₇×C₂²⋊C₄	—	8	1	no	—
247	C₇×C₂²⋊C₄	—	8	1	no	—
248	C₇×C₂²⋊C₄	—	8	1	no	—
249	C₄²×C₇	—	2	1	no	—
250	C₄²×C₇	—	2	1	no	—
251	C₄²×C₇	—	2	1	no	—
252	C₄²×C₇	—	2	1	no	—
253	C₄²×C₇	—	4	2	no	—
254	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
255	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
256	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
257	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
258	C₂×#117	C₂²×C₇	1	1	yes	characteristic
259	C₂×#117	C₂²×C₇	1	1	yes	characteristic
260	#450	—	2	4	no	—
261	#433	—	2	4	no	—
262	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
263	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
264	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
265	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
266	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
267	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
268	C₂×#102	C₂²×C₇	1	1	yes	characteristic
269	C₂×#102	C₂²×C₇	1	1	yes	characteristic
270	C₂×#102	C₂²×C₇	1	1	yes	characteristic
271	C₂×#102	C₂²×C₇	1	1	yes	characteristic
272	C₂×#102	C₂²×C₇	1	1	yes	characteristic
273	C₂×#102	C₂²×C₇	1	1	yes	characteristic
274	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
275	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
276	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
277	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
278	#400	—	2	1	no	—
279	#398	—	2	1	no	—
280	#397	—	2	1	no	—
281	#397	—	2	1	no	—
282	#391	C₂²×C₇	1	1	yes	characteristic, complemented
283	#391	C₂²×C₇	1	1	yes	characteristic, complemented
284	#390	—	2	1	no	—
285	#390	—	2	1	no	—
286	#390	C₂²×C₇	1	1	yes	characteristic
287	#390	C₂²×C₇	1	1	yes	characteristic
288	#390	C₂²×C₇	1	1	yes	characteristic
289	#390	C₂²×C₇	1	1	yes	characteristic
290	#389	C₂²×C₇	1	1	yes	characteristic, complemented
291	#389	C₂²×C₇	1	1	yes	characteristic, complemented
292	#380	C₂²×C₇	1	1	yes	characteristic
293	#379	—	2	1	no	—
294	#379	—	2	1	no	—
295	#340	C₂²×C₇	1	1	yes	characteristic, complemented
296	#340	C₂²×C₇	1	1	yes	characteristic, complemented
297	#340	C₂²×C₇	1	1	yes	characteristic, complemented
298	#340	C₂²×C₇	1	1	yes	characteristic, complemented
299	C₂³×C₇	—	2	1	no	—
300	C₂³×C₇	—	2	1	no	—
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	2	no	—
306	C₂³×C₇	—	2	2	no	—
307	C₂³×C₇	—	4	8	no	—
308	C₂³×C₇	—	4	1	no	—
309	C₂³×C₇	—	4	1	no	—
310	C₂³×C₇	—	4	1	no	—
311	C₂³×C₇	—	4	1	no	—
312	C₂³×C₇	—	4	1	no	—
313	C₂³×C₇	—	4	1	no	—
314	C₂³×C₇	—	4	1	no	—
315	C₂³×C₇	—	4	1	no	—
316	C₂³×C₇	—	4	1	no	—
317	C₂³×C₇	—	4	1	no	—
318	C₂³×C₇	—	4	1	no	—
319	C₂³×C₇	—	4	1	no	—
320	C₂³×C₇	—	8	4	no	—
321	C₂³×C₇	—	8	4	no	—
322	C₂³×C₇	—	8	4	no	—
323	C₂³×C₇	—	8	4	no	—
324	C₂³×C₇	—	8	4	no	—
325	C₂³×C₇	—	8	4	no	—
326	C₂³×C₇	#121	1	2	yes	—
327	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
328	C₇×Q₈	—	4	1	no	—
329	C₇×Q₈	—	4	1	no	—
330	C₇×Q₈	—	4	1	no	—
331	C₇×Q₈	—	4	1	no	—
332	C₇×D₄	—	2	2	no	—
333	C₇×D₄	—	2	2	no	—
334	C₇×D₄	—	2	2	no	—
335	C₇×D₄	—	2	2	no	—
336	C₇×D₄	—	4	8	no	—
337	C₇×D₄	—	4	1	no	—
338	C₇×D₄	—	4	1	no	—
339	C₇×D₄	—	4	1	no	—
340	C₇×D₄	—	4	1	no	—
341	C₂×C₄×C₇	—	2	1	no	—
342	C₂×C₄×C₇	—	2	1	no	—
343	C₂×C₄×C₇	—	2	2	no	—
344	C₂×C₄×C₇	—	2	2	no	—
345	C₂×C₄×C₇	—	2	2	no	—
346	C₂×C₄×C₇	—	2	2	no	—
347	C₂×C₄×C₇	—	2	1	no	—
348	C₂×C₄×C₇	—	2	1	no	—
349	C₂×C₄×C₇	—	2	1	no	—
350	C₂×C₄×C₇	—	2	1	no	—
351	C₂×C₄×C₇	—	2	1	no	—
352	C₂×C₄×C₇	—	2	1	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	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	—	4	1	no	—
363	C₂×C₄×C₇	—	4	1	no	—
364	C₂×C₄×C₇	—	4	1	no	—
365	C₂×C₄×C₇	—	4	1	no	—
366	C₂×C₄×C₇	—	4	1	no	—
367	C₂×C₄×C₇	—	4	1	no	—
368	C₂×C₄×C₇	—	4	1	no	—
369	C₂×C₄×C₇	—	4	1	no	—
370	C₂×C₄×C₇	—	4	1	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	#121	1	2	yes	—
378	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
380	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
381	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
382	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
383	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
384	C₇×C₈	—	2	2	no	—
385	C₇×C₈	—	2	2	no	—
386	C₇×C₈	—	4	1	no	—
387	C₇×C₈	—	4	1	no	—
388	C₂⁵	—	2	1	no	—
389	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
390	C₂²×D₄	—	2	2	no	—
391	C₂²×D₄	—	2	2	no	—
392	C₂²×D₄	—	2	1	no	—
393	C₂²×D₄	—	2	2	no	—
394	C₂²×D₄	—	2	2	no	—
395	C₂²×D₄	—	4	1	no	—
396	C₂²×D₄	—	4	1	no	—
397	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
398	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
399	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
400	C₂×SD₁₆	—	2	2	no	—
401	C₂×SD₁₆	—	2	2	no	—
402	C₂×SD₁₆	—	2	2	no	—
403	C₂×SD₁₆	—	2	2	no	—
404	C₂×SD₁₆	—	4	1	no	—
405	C₂×SD₁₆	—	4	1	no	—
406	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
407	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	—	2	2	no	—
412	#117	—	2	2	no	—
413	#117	—	2	2	no	—
414	#117	—	4	1	no	—
415	#117	—	4	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	C₇×D₄	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₇	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×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	1	no	—
437	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
442	#107	—	4	1	no	—
443	#106	—	4	1	no	—
444	C₄⋊C₈	—	2	2	no	—
445	C₄⋊C₈	—	2	2	no	—
446	#103	—	4	1	no	—
447	#103	—	4	1	no	—
448	#102	—	2	2	no	—
449	#102	—	2	2	no	—
450	#102	—	2	2	no	—
451	#102	—	2	2	no	—
452	#102	—	4	1	no	—
453	#102	—	4	1	no	—
454	C₂²⋊C₈	—	2	2	no	—
455	C₂²⋊C₈	C₇×D₄	1	4	yes	—
456	#97	—	2	2	no	—
457	C₄×C₈	—	2	2	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	C₂²×C₇	—	2	2	no	—
466	C₂²×C₇	—	2	2	no	—
467	C₂²×C₇	—	2	2	no	—
468	C₂²×C₇	—	4	1	no	—
469	C₂²×C₇	—	4	1	no	—
470	C₂²×C₇	—	4	1	no	—
471	C₂²×C₇	—	4	1	no	—
472	C₂²×C₇	—	4	2	no	—
473	C₂²×C₇	—	4	2	no	—
474	C₂²×C₇	—	4	2	no	—
475	C₂²×C₇	—	4	2	no	—
476	C₂²×C₇	—	4	2	no	—
477	C₂²×C₇	—	4	2	no	—
478	C₂²×C₇	—	8	16	no	—
479	C₂²×C₇	—	8	1	no	—
480	C₂²×C₇	—	8	1	no	—
481	C₂²×C₇	—	8	1	no	—
482	C₂²×C₇	—	8	1	no	—
483	C₂²×C₇	—	8	1	no	—
484	C₂²×C₇	—	8	1	no	—
485	C₂²×C₇	—	8	1	no	—
486	C₂²×C₇	—	8	1	no	—
487	C₂²×C₇	C₂×#121	1	1	yes	characteristic
488	C₂²×C₇	#525	1	1	yes	characteristic
489	C₂²×C₇	#535	1	1	yes	characteristic
490	C₂²×C₇	#576	1	1	yes	characteristic
491	C₂²×C₇	#577	1	1	yes	characteristic
492	C₂²×C₇	#577	1	1	yes	characteristic
493	C₂²×C₇	#577	1	1	yes	characteristic
494	C₄×C₇	—	2	2	no	—
495	C₄×C₇	—	4	1	no	—
496	C₄×C₇	—	4	1	no	—
497	C₄×C₇	—	4	1	no	—
498	C₄×C₇	—	4	1	no	—
499	C₄×C₇	—	8	1	no	—
500	C₄×C₇	—	8	1	no	—
501	C₄×C₇	—	8	1	no	—
502	C₄×C₇	—	8	1	no	—
503	C₄×C₇	—	8	1	no	—
504	C₄×C₇	—	8	1	no	—
505	C₄×C₇	#546	1	1	yes	characteristic
506	C₄×C₇	#546	1	1	yes	characteristic
507	C₄×C₇	#551	1	1	yes	characteristic
508	C₄×C₇	#551	1	1	yes	characteristic
509	C₂⁴	—	2	4	no	—
510	C₂⁴	—	2	1	no	—
511	C₂⁴	—	2	1	no	—
512	C₂⁴	—	4	2	no	—
513	C₂⁴	—	4	2	no	—
514	C₂⁴	—	8	1	no	—
515	C₂⁴	—	8	1	no	—
516	C₂⁴	—	8	1	no	—
517	C₂⁴	—	8	1	no	—
518	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×D₄	—	2	4	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	4	4	no	—
537	C₂×D₄	—	4	4	no	—
538	C₂×D₄	—	4	4	no	—
539	C₂×D₄	—	4	4	no	—
540	C₂×D₄	—	4	2	no	—
541	C₂×D₄	—	4	2	no	—
542	C₂×D₄	C₇×#41	1	2	yes	—
543	C₂×D₄	C₇×#41	1	2	yes	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
555	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
556	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
557	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
558	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
559	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
560	C₂²×C₄	C₇×#41	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
562	SD₁₆	—	4	4	no	—
563	SD₁₆	—	4	4	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
575	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	4	2	no	—
589	C₄⋊C₄	—	8	1	no	—
590	C₄⋊C₄	—	8	1	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	4	2	no	—
594	C₂²⋊C₄	—	4	2	no	—
595	C₂²⋊C₄	—	8	1	no	—
596	C₂²⋊C₄	—	8	1	no	—
597	C₂²⋊C₄	—	8	1	no	—
598	C₂²⋊C₄	—	8	1	no	—
599	C₂²⋊C₄	—	8	1	no	—
600	C₂²⋊C₄	—	8	1	no	—
601	C₂²⋊C₄	—	8	1	no	—
602	C₂²⋊C₄	—	8	1	no	—
603	C₂²⋊C₄	—	8	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	2	1	no	—
607	C₄²	—	2	1	no	—
608	C₄²	—	4	2	no	—
609	C₂×C₇	—	4	2	no	—
610	C₂×C₇	—	8	2	no	—
611	C₂×C₇	—	8	2	no	—
612	C₂×C₇	#2411	1	1	yes	characteristic
613	C₂×C₇	#3057	1	1	yes	characteristic
614	C₂×C₇	#3062	1	1	yes	characteristic
615	C₂×C₇	#3118	1	1	yes	characteristic
616	C₂×C₇	#3123	1	1	yes	characteristic
617	C₂×C₇	#3222	1	1	yes	characteristic
618	C₂×C₇	#3224	1	1	yes	characteristic
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	4	8	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	4	1	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	—	4	1	no	—
634	C₂³	—	4	1	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	4	1	no	—
640	C₂³	—	8	4	no	—
641	C₂³	—	8	4	no	—
642	C₂³	—	8	4	no	—
643	C₂³	—	8	4	no	—
644	C₂³	—	8	4	no	—
645	C₂³	—	8	4	no	—
646	C₂³	C₇×#121	1	2	yes	—
647	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
648	Q₈	—	4	1	no	—
649	Q₈	—	4	1	no	—
650	Q₈	—	4	1	no	—
651	Q₈	—	4	1	no	—
652	D₄	—	2	2	no	—
653	D₄	—	2	2	no	—
654	D₄	—	2	2	no	—
655	D₄	—	2	2	no	—
656	D₄	—	4	8	no	—
657	D₄	—	4	1	no	—
658	D₄	—	4	1	no	—
659	D₄	—	4	1	no	—
660	D₄	—	4	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	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	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	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	C₇×#121	1	2	yes	—
698	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
699	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
700	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
701	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
702	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
703	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
704	C₈	—	2	2	no	—
705	C₈	—	2	2	no	—
706	C₈	—	4	1	no	—
707	C₈	—	4	1	no	—
708	C₇	#24516	1	1	yes	characteristic, direct product factor, Sylow
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	1	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	8	16	no	—
723	C₂²	—	8	1	no	—
724	C₂²	—	8	1	no	—
725	C₂²	—	8	1	no	—
726	C₂²	—	8	1	no	—
727	C₂²	—	8	1	no	—
728	C₂²	—	8	1	no	—
729	C₂²	—	8	1	no	—
730	C₂²	—	8	1	no	—
731	C₂²	C₂×C₇×#121	1	1	yes	characteristic
732	C₂²	C₇×#525	1	1	yes	characteristic
733	C₂²	C₇×#535	1	1	yes	characteristic
734	C₂²	C₇×#576	1	1	yes	characteristic
735	C₂²	C₇×#577	1	1	yes	characteristic
736	C₂²	C₇×#577	1	1	yes	characteristic
737	C₂²	C₇×#577	1	1	yes	characteristic
738	C₄	—	2	2	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	1	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	1	no	—
743	C₄	—	8	1	no	—
744	C₄	—	8	1	no	—
745	C₄	—	8	1	no	—
746	C₄	—	8	1	no	—
747	C₄	—	8	1	no	—
748	C₄	—	8	1	no	—
749	C₄	C₇×#546	1	1	yes	characteristic
750	C₄	C₇×#546	1	1	yes	characteristic
751	C₄	C₇×#551	1	1	yes	characteristic
752	C₄	C₇×#551	1	1	yes	characteristic
753	C₂	—	4	2	no	—
754	C₂	—	8	2	no	—
755	C₂	—	8	2	no	—
756	C₂	C₇×#2411	1	1	yes	characteristic
757	C₂	C₇×#3057	1	1	yes	characteristic
758	C₂	C₇×#3062	1	1	yes	characteristic
759	C₂	C₇×#3118	1	1	yes	characteristic
760	C₂	C₇×#3123	1	1	yes	characteristic
761	C₂	C₇×#3222	1	1	yes	characteristic
762	C₂	C₇×#3224	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂³×C₇×D₄	C₂²
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×#433	C₂	semidirect
3. C₇×#2625	C₂	semidirect
5. C₇×#2067	C₂	semidirect
6. C₇×#2065	C₂	semidirect
7. C₇×#2055	C₂	semidirect
8. C₇×#2055	C₂	semidirect
9. C₇×#1973	C₂	semidirect
10. C₇×#1968	C₂	semidirect
11. C₇×#1936	C₂	semidirect
12. C₇×#1934	C₂	semidirect
13. C₇×#1873	C₂	semidirect
14. C₇×#1854	C₂	semidirect
24. C₂×C₇×#107	C₂²	semidirect
25. C₂×C₇×#106	C₂²	semidirect
26. C₂×C₇×C₄⋊C₈	C₂²	semidirect
27. C₂×C₇×C₄⋊C₈	C₂²	semidirect
28. C₂×C₇×#103	C₂²	semidirect
29. C₂×C₇×#103	C₂²	semidirect
38. C₂×C₇×#97	C₂²	semidirect
39. C₂×C₄×C₇×C₈	C₂²	semidirect
44. C₇×#391	C₂²	semidirect
45. C₇×#391	C₂²	semidirect
52. C₇×#389	C₂²	semidirect
53. C₇×#389	C₂²	semidirect
57. C₇×#340	C₂²	semidirect
58. C₇×#340	C₂²	semidirect
59. C₇×#340	C₂²	semidirect
60. C₇×#340	C₂²	semidirect
61. #24516	C₇	direct (N × H)
140. C₂×#433	C₂×C₇	semidirect
141. #2625	C₂×C₇	semidirect
143. #2067	C₂×C₇	semidirect
144. #2065	C₂×C₇	semidirect
145. #2055	C₂×C₇	semidirect
146. #2055	C₂×C₇	semidirect
147. #1973	C₂×C₇	semidirect
148. #1968	C₂×C₇	semidirect
149. #1936	C₂×C₇	semidirect
150. #1934	C₂×C₇	semidirect
151. #1873	C₂×C₇	semidirect
152. #1854	C₂×C₇	semidirect
262. C₂×#107	C₂²×C₇	semidirect
263. C₂×#106	C₂²×C₇	semidirect
264. C₂×C₄⋊C₈	C₂²×C₇	semidirect
265. C₂×C₄⋊C₈	C₂²×C₇	semidirect
266. C₂×#103	C₂²×C₇	semidirect
267. C₂×#103	C₂²×C₇	semidirect
276. C₂×#97	C₂²×C₇	semidirect
277. C₂×C₄×C₈	C₂²×C₇	semidirect
282. #391	C₂²×C₇	semidirect
283. #391	C₂²×C₇	semidirect
290. #389	C₂²×C₇	semidirect
291. #389	C₂²×C₇	semidirect
295. #340	C₂²×C₇	semidirect
296. #340	C₂²×C₇	semidirect
297. #340	C₂²×C₇	semidirect
298. #340	C₂²×C₇	semidirect
708. C₇	#24516	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×#450	2
C₂×C₇×#433	2
C₇×#2625	2
C₇×#2309	2
C₇×#2067	2
C₇×#2065	2
C₇×#2055	2
C₇×#1973	2
C₇×#1968	2
C₇×#1936	2
C₇×#1934	2
C₇×#1873	2
C₇×#1854	2
C₇×#1786	2
#24516	7

Subgroups — C7×#24516 #13201732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#24516 #13201732