Finite Group Databasebeta

← D7×#3802 #72245738

Subgroups — D7×#3802 #72245738

Order 2016.

998 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 998 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×D7C212yesmaximal, complemented
2#11759635C211yesmaximal, characteristic, complemented
3#11759613C212yesmaximal, complemented
4C7×#3802C211yesmaximal, characteristic, complemented
5C4×D7×C3⋊D3C211yesmaximal, characteristic, complemented
6C3×D7×D12C212yesmaximal, complemented
7#11759432C212yesmaximal, complemented
8#11759431C212yesmaximal, complemented
9D7×#625C212yesmaximal, complemented
10D3×D4×D7—32nomaximal
11C2×(C3⋊D3)⋊D7C2212yescomplemented
12C2×D3×D21C2214yescomplemented
13C2×D32×C7C2212yescomplemented
14C2×D7×C3⋊D3C2211yescharacteristic
15C2×C3×D3×D7C2214yescomplemented
16D32×D7—28no—
17C4×C3⋊D21C2211yescharacteristic, complemented
18C4×C7×C3⋊D3C2211yescharacteristic, complemented
19C3×D84C2212yescomplemented
20C3×C7×D12C2212yescomplemented
21C32×C4×D7C2211yescharacteristic, complemented
22#92695C2212yescomplemented
23#92688C2214yescomplemented
24C7×#625C2212yescomplemented
25#92675C2211yescharacteristic, complemented
26C3⋊D3×Dic7C2211yescharacteristic, complemented
27D7×C3⋊Dic3C2211yescharacteristic, complemented
28C3×#4247C2214yescomplemented
29C22×D3×D7—34no—
30D4×D21—32no—
31D3×C7×D4—32no—
32C3×D4×D7—32no—
33#66694—34no—
34D3×C22⋊D7—34no—
35D7×#67—34no—
36#66681—32no—
37D3×D28—32no—
38D7×D12D312yescomplemented
39C4×D3×D7—32no—
40C4×D3×D7—61no—
41C2×#3802—71nomaximal, Hall
42C2×C3⋊D21C2311yescharacteristic
43C2×C7×C3⋊D3C2311yescharacteristic
44C2×C3×D21C2314yescomplemented
45C2×C3×D3×C7C2314yescomplemented
46C2×C32×D7C2311yescharacteristic
47(C3⋊D3)⋊D7—24no—
48D3×D21—28no—
49D32×C7—24no—
50D7×C3⋊D3D414yescomplemented
51C3×D3×D7—28no—
52C32×C4×C7C2311yescharacteristic, complemented
53C3⋊Dic21C2311yescharacteristic, complemented
54C7×C3⋊Dic3C2311yescharacteristic, complemented
55C32×Dic7C2311yescharacteristic, complemented
56C2×D4×D7—91noHall
57C22×D21—34no—
58C22×D3×C7—34no—
59C22×C3×D7—34no—
60C2×D3×D7—32no—
61C2×D3×D7—34no—
62C2×D3×D7—34no—
63C2×D3×D7—61no—
64C2×D3×D7—616no—
65C2×D3×D7C2×D314yescomplemented
66C3×C7×D4—32no—
67#4268—34no—
68D84C2×D312yescomplemented
69C4×D21—32no—
70C4×D21—61no—
71C7×#67—34no—
72C7×D12C2×D312yescomplemented
73C4×D3×C7—32no—
74C4×D3×C7—61no—
75C3×C22⋊D7—34no—
76C3×D28—32no—
77C3×C4×D7—21no—
78C3×C4×D7C2×D312yescomplemented
79#4247C2×D314yescomplemented
80#4246—34no—
81#4245—34no—
82D21⋊C4—32no—
83D21⋊C4—61no—
84D3×Dic7—32no—
85D3×Dic7—61no—
86Dic3×D7—32no—
87Dic3×D7—61no—
88C22×D32—72no—
89C2×C4×C3⋊D3—71no—
90C2×C3×D12—72no—
91C2×#625—72no—
92#3802—72no—
93#3802—71no—
94#3802—72no—
95#3802—72no—
96#3802D711yescharacteristic, direct product factor
97C2×C32×C7C2411yescharacteristic
98C3⋊D21C2×D412yescomplemented
99C7×C3⋊D3C2×D412yescomplemented
100C3×D21—24no—
101C3×D3×C7—24no—
102C32×D7C2×D412yescomplemented
103C23×D7—92no—
104C2×C7×D4—91no—
105C2×C22⋊D7—92no—
106D4×D7—32no—
107D4×D7—92no—
108D4×D7—92no—
109D4×D7—92no—
110C2×D28—91no—
111C2×C4×D7—91no—
112C2×D3×D4—212no—
113C22×C3×C7—34no—
114C2×D21—32no—
115C2×D21—61no—
116C2×D21—68no—
117C2×D21C22×D314yescomplemented
118C2×D3×C7—32no—
119C2×D3×C7—61no—
120C2×D3×C7—68no—
121C2×D3×C7C22×D314yescomplemented
122C2×C3×D7—21no—
123C2×C3×D7—34no—
124C2×C3×D7—68no—
125C2×C3×D7C22×D312yes—
126D3×D7—28no—
127D3×D7—38no—
128D3×D7—64no—
129D3×D7—68no—
130D3×D7—68no—
131C3×C4×C7—21no—
132C3×C4×C7C22×D312yescomplemented
133Dic21—32no—
134Dic21—61no—
135C3×Dic7—21no—
136C3×Dic7C22×D312yescomplemented
137C7×Dic3—32no—
138C7×Dic3—61no—
139C22×C3⋊D3—71no—
140C22×C3×D3—74no—
141C2×D32—72no—
142C2×D32—74no—
143C2×D32—148no—
144C2×D32C2×D712yescomplemented
145C2×C32×C4—71no—
146C2×C3⋊Dic3—71no—
147C4×C3⋊D3—71no—
148C4×C3⋊D3—71no—
149C4×C3⋊D3—71no—
150C4×C3⋊D3C2×D711yescharacteristic, complemented
151C3×D12—74no—
152C3×D12—72no—
153C3×D12C2×D712yescomplemented
154#625—74no—
155#625—72no—
156#625C2×D712yescomplemented
157C32×C7C22×D411yescharacteristic, complemented, Hall
158C23×C7—92no—
159C22×D7—34no—
160C22×D7—92no—
161C22×D7—94no—
162C22×D7—91no—
163C22×D7—188no—
164C7×D4—32no—
165C7×D4—92no—
166C2×C4×C7—91no—
167C22⋊D7—34no—
168C22⋊D7—94no—
169C2×Dic7—91no—
170D28—32no—
171D28—92no—
172C4×D7—91no—
173C4×D7—91no—
174C4×D7—91no—
175C4×D7D3211yescharacteristic, complemented
176C23×D3—214no—
177C2×C3×D4—212no—
178C2×#67—214no—
179D3×D4—32no—
180D3×D4—212no—
181D3×D4—214no—
182D3×D4—212no—
183D3×D4—214no—
184D3×D4—212no—
185C2×D12—72no—
186C2×C4×D3—212no—
187C2×C4×D3—421no—
188C2×C3×C7—21no—
189C2×C3×C7—64no—
190C2×C3×C7C23×D312yes—
191D21—24no—
192D21—34no—
193D21—62no—
194C3×D7—22no—
195C3×D7—64no—
196C3×D7D3×D414yescomplemented
197D3×C7—24no—
198D3×C7—34no—
199D3×C7—62no—
200C22×C32—71no—
201C2×C3⋊D3—71no—
202C2×C3⋊D3—74no—
203C2×C3⋊D3C22×D711yescharacteristic
204C2×C3×D3—74no—
205C2×C3×D3—148no—
206C2×C3×D3C22×D714yescomplemented
207D32—24no—
208D32—148no—
209D32—144no—
210C32×C4—71no—
211C32×C4C22×D711yescharacteristic, complemented
212C3⋊Dic3—71no—
213C3⋊Dic3C22×D711yescharacteristic, complemented
214C22×D4—631noSylow
215C22×C7—34no—
216C22×C7—91no—
217C22×C7—184no—
218C2×D7—34no—
219C2×D7—68no—
220C2×D7—91no—
221C2×D7—94no—
222C2×D7—184no—
223C2×D7—188no—
224C2×D7C2×D3211yescharacteristic
225C4×C7—91no—
226C4×C7C2×D3211yescharacteristic, complemented
227Dic7—91no—
228Dic7C2×D3211yescharacteristic, complemented
229C23×C3—214no—
230C22×D3—34no—
231C22×D3—74no—
232C22×D3—214no—
233C22×D3—212no—
234C22×D3—214no—
235C22×D3—214no—
236C22×D3—421no—
237C22×D3—4216no—
238C3×D4—32no—
239C3×D4—214no—
240C3×D4—212no—
241C2×C3×C4—72no—
242C2×C3×C4—141no—
243#67—34no—
244#67—214no—
245#67—214no—
246#67—214no—
247C2×Dic3—212no—
248C2×Dic3—421no—
249D12—74no—
250D12—72no—
251D12D3×D712yescomplemented
252C4×D3—32no—
253C4×D3—61no—
254C4×D3—212no—
255C4×D3—212no—
256C4×D3—212no—
257C4×D3—421no—
258C4×D3—421no—
259C4×D3—421no—
260C3×C7—21no—
261C3×C7C2×D3×D412yescomplemented
262C2×C32—72no—
263C2×C32C23×D711yescharacteristic
264C3⋊D3—72no—
265C3⋊D3D4×D712yescomplemented
266C3×D3—24no—
267C3×D3—144no—
268C24—632no—
269C2×D4—91no—
270C2×D4—212no—
271C2×D4—631no—
272C2×D4—632no—
273C2×D4—632no—
274C2×D4—632no—
275C2×D4—632no—
276C22×C4—631no—
277C2×C7—64no—
278C2×C7—92no—
279C2×C7C22×D3211yescharacteristic
280D7—64no—
281D7—92no—
282D7#380212yesdirect product factor
283C22×C3—34no—
284C22×C3—72no—
285C22×C3—141no—
286C22×C3—214no—
287C22×C3—428no—
288C2×D3—32no—
289C2×D3—61no—
290C2×D3—68no—
291C2×D3—74no—
292C2×D3—148no—
293C2×D3—218no—
294C2×D3—212no—
295C2×D3—424no—
296C2×D3—421no—
297C2×D3—428no—
298C2×D3—428no—
299C2×D3—428no—
300C2×D3C2×D3×D714yescomplemented
301C3×C4—21no—
302C3×C4—72no—
303C3×C4—141no—
304C3×C4C2×D3×D712yescomplemented
305Dic3—32no—
306Dic3—61no—
307Dic3—212no—
308Dic3—421no—
309C32C2×D4×D711yescharacteristic, complemented, Sylow
310C23—92no—
311C23—214no—
312C23—634no—
313C23—631no—
314C23—632no—
315C23—1268no—
316D4—32no—
317D4—92no—
318D4—214no—
319D4—212no—
320D4—632no—
321D4—634no—
322C2×C4—71no—
323C2×C4—91no—
324C2×C4—631no—
325C2×C4—631no—
326C2×C4—631no—
327C2×C4—631no—
328C7C2×#380211yescharacteristic, complemented, Sylow
329C2×C3—21no—
330C2×C3—64no—
331C2×C3—74no—
332C2×C3—142no—
333C2×C3—424no—
334C2×C3C22×D3×D712yes—
335D3—24no—
336D3—34no—
337D3—62no—
338D3—144no—
339D3—214no—
340D3—422no—
341C22—34no—
342C22—71no—
343C22—91no—
344C22—184no—
345C22—214no—
346C22—428no—
347C22—634no—
348C22—631no—
349C22—1268no—
350C22—1264no—
351C4—71no—
352C4—91no—
353C4—631no—
354C4D32×D711yescharacteristic, complemented
355C3—21no—
356C3D3×D4×D712yescomplemented
357C2—64no—
358C2—72no—
359C2—92no—
360C2—424no—
361C2—632no—
362C2C2×D32×D711yescharacteristic
subgroupG/H
center, FrattiniC2C2×D32×D7
commutator, socle, cosocleC2×C32×C7C24
FittingC32×C4×C7C23
hypercenterC4D32×D7
hypocenterC32×C7C22×D4
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×D32×D7C2semidirect
2. #11759635C2semidirect
3. #11759613C2semidirect
4. C7×#3802C2semidirect
5. C4×D7×C3⋊D3C2semidirect
6. C3×D7×D12C2semidirect
7. #11759432C2semidirect
8. #11759431C2semidirect
9. D7×#625C2semidirect
11. C2×(C3⋊D3)⋊D7C22semidirect
12. C2×D3×D21C22semidirect
13. C2×D32×C7C22semidirect
15. C2×C3×D3×D7C22semidirect
17. C4×C3⋊D21C22semidirect
18. C4×C7×C3⋊D3C22semidirect
19. C3×D84C22semidirect
20. C3×C7×D12C22semidirect
21. C32×C4×D7C22semidirect
22. #92695C22semidirect
23. #92688C22semidirect
24. C7×#625C22semidirect
25. #92675C22semidirect
26. C3⋊D3×Dic7C22semidirect
27. D7×C3⋊Dic3C22semidirect
28. C3×#4247C22semidirect
38. D7×D12D3semidirect
44. C2×C3×D21C23semidirect
45. C2×C3×D3×C7C23semidirect
50. D7×C3⋊D3D4semidirect
52. C32×C4×C7C23semidirect
53. C3⋊Dic21C23semidirect
54. C7×C3⋊Dic3C23semidirect
55. C32×Dic7C23semidirect
65. C2×D3×D7C2×D3semidirect
68. D84C2×D3semidirect
72. C7×D12C2×D3semidirect
78. C3×C4×D7C2×D3semidirect
79. #4247C2×D3semidirect
96. #3802D7direct (N × H)
98. C3⋊D21C2×D4semidirect
99. C7×C3⋊D3C2×D4semidirect
102. C32×D7C2×D4semidirect
117. C2×D21C22×D3semidirect
121. C2×D3×C7C22×D3semidirect
132. C3×C4×C7C22×D3semidirect
136. C3×Dic7C22×D3semidirect
144. C2×D32C2×D7semidirect
150. C4×C3⋊D3C2×D7semidirect
153. C3×D12C2×D7semidirect
156. #625C2×D7semidirect
157. C32×C7C22×D4semidirect
175. C4×D7D32semidirect
196. C3×D7D3×D4semidirect
206. C2×C3×D3C22×D7semidirect
211. C32×C4C22×D7semidirect
213. C3⋊Dic3C22×D7semidirect
226. C4×C7C2×D32semidirect
228. Dic7C2×D32semidirect
251. D12D3×D7semidirect
261. C3×C7C2×D3×D4semidirect
265. C3⋊D3D4×D7semidirect
282. D7#3802direct (N × H)
300. C2×D3C2×D3×D7semidirect
304. C3×C4C2×D3×D7semidirect
309. C32C2×D4×D7semidirect
328. C7C2×#3802semidirect
354. C4D32×D7semidirect
356. C3D3×D4×D7semidirect

Maximal subgroups

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

subgroupindex
C2×D32×D72
#117596352
#117596132
C7×#38022
C4×D7×C3⋊D32
C3×D7×D122
#117594322
#117594312
D7×#6252
D3×D4×D73
C2×#38027