Finite Group Databasebeta

← C2×#11744566 #14267693

Subgroups — C2×#11744566 #14267693

Order 1792.

60570 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#585C211yesmaximal, characteristic, complemented
2#11744566C2164yesmaximal, direct product factor
3C2×#90620C2112yesmaximal, complemented
4C2×D7×H(5,𝔽2)C2120yesmaximal, complemented
5C2×#90616C2115yesmaximal, complemented
6C22×#6553C2115yesmaximal, complemented
7C7×#585C22132yescomplemented
8C2×C7×2−1+4C2216yescomplemented
9C2×C7×H(5,𝔽2)C22110yescomplemented
10C22×C7×#41C22115yescomplemented
11#90620C221384yescomplemented
12D7×H(5,𝔽2)C221640yescomplemented
13#90616C221480yescomplemented
14C2×#6554C22120yescomplemented
15C2×#6553C22160yescomplemented
16C2×#6553C221120yescomplemented
17C2×#6553C221480yescomplemented
18C2×D7×#41C221120yescomplemented
19C2×#6551C22130yescomplemented
20C22×#1161C22130yescomplemented
21C2×#6548C22190yescomplemented
22C22×D4×D7C22190yescomplemented
23C22×#1157C22145yescomplemented
24C23×D28C22115yescomplemented
25C2×H(7,𝔽2)—71nomaximal, Sylow
26C24×D7C23130yescomplemented
27C7×2−1+4C23196yescomplemented
28C7×H(5,𝔽2)C231160yescomplemented
29C2×C7×#41C23120yescomplemented
30C2×C7×#41C23160yescomplemented
31C2×C7×#41C231240yescomplemented
32C22×C7×Q8C23115yescomplemented
33C22×C7×D4C23145yescomplemented
34C23×C4×C7C23115yescomplemented
35C22×C22⋊D7C23190yescomplemented
36#6554C231320yescomplemented
37#6553C231960yescomplemented
38#6553C2311920yescomplemented
39D7×#41C2311920yescomplemented
40#6551C231480yescomplemented
41C2×#1161C231120yescomplemented
42C2×#1161C231480yescomplemented
43C2×Q8×D7C23140yescomplemented
44#6548C2311440yescomplemented
45C2×#1159C231120yescomplemented
46C2×D4×D7C231360yescomplemented
47C2×D4×D7C2311440yescomplemented
48C2×#1157C23160yescomplemented
49C2×#1157C231180yescomplemented
50C2×#1157C231720yescomplemented
51C22×D28C23145yescomplemented
52C22×D28C23190yescomplemented
53C22×D28C231240yescomplemented
54C22×C4×D7C23190yescomplemented
55C22×Dic14C23115yescomplemented
56H(7,𝔽2)—764no—
57C2×#585—712no—
58C2×#585—715no—
59C2×#585D711yescharacteristic, complemented
60C22×H(5,𝔽2)—720no—
61C22×H(5,𝔽2)—715no—
62C24×C7C24115yes—
63C23×D7—860no—
64C23×D7C24190yes—
65C23×D7C241240yescomplemented
66C7×#41C241480yescomplemented
67C7×#41C241160yescomplemented
68C2×C7×Q8C24120yes—
69C2×C7×Q8C241120yescomplemented
70C2×C7×D4C24160yes—
71C2×C7×D4C241360yescomplemented
72C22×C4×C7C24115yes—
73C22×C4×C7C24145yes—
74C22×C4×C7C241120yescomplemented
75C2×C22⋊D7C241120yes—
76C2×C22⋊D7C241720yescomplemented
77C22×Dic7C24130yes—
78#1161C241960yescomplemented
79Q8×D7C241320yescomplemented
80#1159C241960yescomplemented
81D4×D7C2412880yescomplemented
82#1157C241480yescomplemented
83#1157C2411440yescomplemented
84C2×D28C24110yes—
85C2×D28C24190yes—
86C2×D28C241360yescomplemented
87C2×D28C241720yescomplemented
88C2×C4×D7C241120yes—
89C2×C4×D7C241720yescomplemented
90C2×Dic14C2416yes—
91C2×Dic14C24130yes—
92C2×Dic14C241120yescomplemented
93#585—7384no—
94#585—7480no—
95#585C2×D7132yescomplemented
96C2×2−1+4—720no—
97C2×2−1+4—730no—
98C2×2−1+4C2×D716yescomplemented
99C2×H(5,𝔽2)—7640no—
100C2×H(5,𝔽2)—7120no—
101C2×H(5,𝔽2)—760no—
102C2×H(5,𝔽2)—7480no—
103C2×H(5,𝔽2)—790no—
104C2×H(5,𝔽2)C2×D7110yescomplemented
105C22×#41—7120no—
106C22×#41—730no—
107C22×#41—745no—
108C22×#41C2×D7115yescomplemented
109C23×D4—790no—
110C23×D4—715no—
111C23×C7—430no—
112C23×C7C25115yes—
113C23×C7C25160yes—
114C22×D7—4180no—
115C22×D7—8240no—
116C22×D7C25120yes—
117C22×D7C251360yes—
118C7×Q8C25180yes—
119C7×D4C251240yes—
120C2×C4×C7C2511yescharacteristic
121C2×C4×C7C25115yes—
122C2×C4×C7C25160yes—
123C2×C4×C7C251180yes—
124C22⋊D7C251480yes—
125C2×Dic7C25112yes—
126C2×Dic7C251120yes—
127D28C25140yes—
128D28C251360yes—
129C4×D7C251480yes—
130Dic14C25124yes—
131Dic14C251120yes—
132C25—730no—
1332−1+4—7320no—
1342−1+4—7480no—
1352−1+4C22×D7196yescomplemented
136H(5,𝔽2)—71920no—
137H(5,𝔽2)—7960no—
138H(5,𝔽2)—71440no—
139H(5,𝔽2)C22×D71160yescomplemented
140C2×#41—71920no—
141C2×#41—7120no—
142C2×#41—7480no—
143C2×#41—7120no—
144C2×#41—7180no—
145C2×#41—760no—
146C2×#41—7720no—
147C2×#41C22×D7160yescomplemented
148C2×#41C22×D7120yescomplemented
149C2×#41C22×D71240yescomplemented
150C22×Q8—740no—
151C22×Q8—715no—
152C22×Q8C22×D7115yescomplemented
153C22×D4—790no—
154C22×D4—7360no—
155C22×D4—71440no—
156C22×D4—790no—
157C22×D4—745no—
158C22×D4—7240no—
159C22×D4C22×D7145yescomplemented
160C23×C4—790no—
161C23×C4C22×D7115yescomplemented
162C22×C7—230no—
163C22×C7—460no—
164C22×C7C26130yes—
165C22×C7C2611yescharacteristic
166C2×D7—240no—
167C2×D7—4360no—
168C2×D7C26140yes—
169C4×C7C2612yes—
170C4×C7C26130yes—
171Dic7C26124yes—
172C24—790no—
173C24—7240no—
174C24—5660no—
175C24C23×D7115yes—
176#41—7960no—
177#41—7960no—
178#41—71440no—
179#41—7480no—
180#41C23×D71480yescomplemented
181#41C23×D71160yescomplemented
182C2×Q8—7320no—
183C2×Q8—730no—
184C2×Q8—76no—
185C2×Q8—7120no—
186C2×Q8C23×D7120yes—
187C2×Q8C23×D71120yescomplemented
188C2×D4—7120no—
189C2×D4—7720no—
190C2×D4—72880no—
191C2×D4—790no—
192C2×D4—710no—
193C2×D4—7720no—
194C2×D4—7360no—
195C2×D4C23×D7160yes—
196C2×D4C23×D71360yescomplemented
197C22×C4—730no—
198C22×C4—7120no—
199C22×C4—7720no—
200C22×C4C23×D7145yes—
201C22×C4C23×D7115yes—
202C22×C4C23×D71120yescomplemented
203C2×C7—230no—
204C2×C7H(7,𝔽2)12yescomplemented
205C2×C7C2711yescharacteristic
206D7—240no—
207C23—430no—
208C23—720no—
209C23—7360no—
210C23—28180no—
211C23—56240no—
212C23C24×D7115yes—
213C23C24×D7160yes—
214Q8—7120no—
215Q8—724no—
216Q8C24×D7180yes—
217D4—7480no—
218D4—7360no—
219D4—740no—
220D4C24×D71240yes—
221C2×C4—7120no—
222C2×C4—712no—
223C2×C4—7480no—
224C2×C4C24×D71180yes—
225C2×C4C24×D7160yes—
226C2×C4C24×D7115yes—
227C2×C4C24×D711yescharacteristic
228C7C2×H(7,𝔽2)11yescharacteristic, complemented, Sylow
229C22—230no—
230C22—460no—
231C22—740no—
232C22—1440no—
233C22—28360no—
234C22C25×D7130yes—
235C22C25×D711yescharacteristic
236C4—724no—
237C4C25×D7130yes—
238C4C25×D712yes—
239C2—230no—
240C2—1440no—
241C2#1174456612yesdirect product factor
242C2C26×D711yescharacteristic
subgroupG/H
centerC22C25×D7
commutator, cosocleC2×C7C27
FrattiniC2C26×D7
FittingC2×C7×#585C2
socleC22×C7C26
hypercenterC2×#585D7
hypocenterC7C2×H(7,𝔽2)
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×#585

Complements

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

NH ≅ G/Ntype
1. C2×C7×#585C2semidirect
2. #11744566C2direct (N × H)
3. C2×#90620C2semidirect
4. C2×D7×H(5,𝔽2)C2semidirect
5. C2×#90616C2semidirect
6. C22×#6553C2semidirect
7. C7×#585C22semidirect
8. C2×C7×2−1+4C22semidirect
9. C2×C7×H(5,𝔽2)C22semidirect
10. C22×C7×#41C22semidirect
11. #90620C22semidirect
12. D7×H(5,𝔽2)C22semidirect
13. #90616C22semidirect
14. C2×#6554C22semidirect
15. C2×#6553C22semidirect
16. C2×#6553C22semidirect
17. C2×#6553C22semidirect
18. C2×D7×#41C22semidirect
19. C2×#6551C22semidirect
20. C22×#1161C22semidirect
21. C2×#6548C22semidirect
22. C22×D4×D7C22semidirect
23. C22×#1157C22semidirect
24. C23×D28C22semidirect
26. C24×D7C23semidirect
27. C7×2−1+4C23semidirect
28. C7×H(5,𝔽2)C23semidirect
29. C2×C7×#41C23semidirect
30. C2×C7×#41C23semidirect
31. C2×C7×#41C23semidirect
32. C22×C7×Q8C23semidirect
33. C22×C7×D4C23semidirect
34. C23×C4×C7C23semidirect
35. C22×C22⋊D7C23semidirect
36. #6554C23semidirect
37. #6553C23semidirect
38. #6553C23semidirect
39. D7×#41C23semidirect
40. #6551C23semidirect
41. C2×#1161C23semidirect
42. C2×#1161C23semidirect
43. C2×Q8×D7C23semidirect
44. #6548C23semidirect
45. C2×#1159C23semidirect
46. C2×D4×D7C23semidirect
47. C2×D4×D7C23semidirect
48. C2×#1157C23semidirect
49. C2×#1157C23semidirect
50. C2×#1157C23semidirect
51. C22×D28C23semidirect
52. C22×D28C23semidirect
53. C22×D28C23semidirect
54. C22×C4×D7C23semidirect
55. C22×Dic14C23semidirect
59. C2×#585D7semidirect
65. C23×D7C24semidirect
66. C7×#41C24semidirect
67. C7×#41C24semidirect
69. C2×C7×Q8C24semidirect
71. C2×C7×D4C24semidirect
74. C22×C4×C7C24semidirect
76. C2×C22⋊D7C24semidirect
78. #1161C24semidirect
79. Q8×D7C24semidirect
80. #1159C24semidirect
81. D4×D7C24semidirect
82. #1157C24semidirect
83. #1157C24semidirect
86. C2×D28C24semidirect
87. C2×D28C24semidirect
89. C2×C4×D7C24semidirect
92. C2×Dic14C24semidirect
95. #585C2×D7semidirect
98. C2×2−1+4C2×D7semidirect
104. C2×H(5,𝔽2)C2×D7semidirect
108. C22×#41C2×D7semidirect
135. 2−1+4C22×D7semidirect
139. H(5,𝔽2)C22×D7semidirect
147. C2×#41C22×D7semidirect
148. C2×#41C22×D7semidirect
149. C2×#41C22×D7semidirect
152. C22×Q8C22×D7semidirect
159. C22×D4C22×D7semidirect
161. C23×C4C22×D7semidirect
180. #41C23×D7semidirect
181. #41C23×D7semidirect
187. C2×Q8C23×D7semidirect
196. C2×D4C23×D7semidirect
202. C22×C4C23×D7semidirect
204. C2×C7H(7,𝔽2)semidirect
228. C7C2×H(7,𝔽2)semidirect
241. C2#11744566direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5852
#117445662
C2×#906202
C2×D7×H(5,𝔽2)2
C2×#906162
C22×#65532
C2×H(7,𝔽2)7