Finite Group Databasebeta

← #11765397

Subgroups — #11765397

Order 1120.

332 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 108 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
1D4×D35C211yesmaximal, characteristic, complemented
2C7×#711C211yesmaximal, characteristic, complemented
3C5×D4×D7C211yesmaximal, characteristic, complemented
4#10587963C212yesmaximal, complemented
5D7×C22⋊D5C212yesmaximal, complemented
6C2×#63306C212yesmaximal, complemented
7#10587952C212yesmaximal, complemented
8D5×D28C211yesmaximal, characteristic, complemented
9#10587946C211yesmaximal, characteristic, complemented
10#10587944C211yesmaximal, characteristic, complemented
11#10587939C211yesmaximal, characteristic, complemented
12C22×D35C2212yescomplemented
13C22×C5×D7C2212yescomplemented
14C2×D5×D7C2212yescomplemented
15C5×C7×D4C2211yescharacteristic, complemented
16C22⋊D35C2212yescomplemented
17D140C2211yescharacteristic, complemented
18C4×D35C2211yescharacteristic, complemented
19C7×C22⋊D5C2212yescomplemented
20C2×C7×Dic5C2212yescomplemented
21C4×C7×D5C2211yescharacteristic, complemented
22C7×Dic10C2211yescharacteristic, complemented
23C5×C22⋊D7C2212yescomplemented
24C5×D28C2211yescharacteristic, complemented
25C4×C5×D7C2211yescharacteristic, complemented
26#63308C2211yescharacteristic, complemented
27#63307C2211yescharacteristic, complemented
28#63306C2212yescomplemented
29#63306C2211yescharacteristic, complemented
30#63306C2212yescomplemented
31#63306C2212yescomplemented
32#63305C2211yescharacteristic, complemented
33#63304C2212yescomplemented
34D7×Dic5C2212yescomplemented
35#6553—51nomaximal, Hall
36#4144—71nomaximal, Hall
37C22×C5×C7C2312yes—
38C2×D35—42no—
39C2×D35C2312yes—
40C2×D35C2311yescharacteristic
41C2×C7×D5C2311yescharacteristic
42C2×C5×D7—42no—
43C2×C5×D7C2312yes—
44C2×C5×D7C2311yescharacteristic
45D5×D7—42no—
46C4×C5×C7C2311yescharacteristic
47Dic35C2311yescharacteristic
48C5×Dic7C2311yescharacteristic
49C7×Dic5C2312yes—
50C7×Dic5C2311yescharacteristic
51C7×#41—51no—
52#1161—51no—
53#1161—51no—
54D4×D7—52no—
55D4×D7—51no—
56D4×D7—52no—
57D4×D7D511yescharacteristic, complemented
58#1157—52no—
59#1157—51no—
60C2×D28—52no—
61C2×D28—51no—
62C2×C5×D4—71no—
63C2×C22⋊D5—72no—
64C2×C22⋊D5—72no—
65#711—72no—
66#711—71no—
67#711D711yescharacteristic, complemented
68D4×D5—71no—
69D4×D5—72no—
70D4×D5—71no—
71#709—71no—
72#709—71no—
73C2×C5×C7—22no—
74C2×C5×C7C2411yescharacteristic
75D35—22no—
76D35—21no—
77C5×D7—22no—
78C5×D7—21no—
79C7×D5—21no—
80C22×D7—52no—
81C22×D7—52no—
82C22×D7C2×D512yescomplemented
83C7×Q8—51no—
84C7×D4—52no—
85C7×D4C2×D511yescharacteristic, complemented
86C2×C4×C7—52no—
87C2×C4×C7—51no—
88C22⋊D7—52no—
89C22⋊D7—51no—
90C22⋊D7—51no—
91C22⋊D7C2×D512yescomplemented
92D28—52no—
93D28—51no—
94D28—52no—
95D28—52no—
96D28—51no—
97D28C2×D511yescharacteristic, complemented
98C4×D7—52no—
99C4×D7—51no—
100C4×D7—52no—
101C4×D7C2×D511yescharacteristic, complemented
102Dic14—51no—
103C23×C5—72no—
104C22×D5—72no—
105C22×D5—72no—
106C5×D4—72no—
107C5×D4—71no—
108C5×D4C2×D711yescharacteristic, complemented
109C2×C4×C5—71no—
110C22⋊D5—72no—
111C22⋊D5—71no—
112C22⋊D5—71no—
113C22⋊D5—72no—
114C22⋊D5—72no—
115C22⋊D5—72no—
116C22⋊D5C2×D712yescomplemented
117C2×Dic5—72no—
118C2×Dic5C2×D712yescomplemented
119D20—71no—
120D20—71no—
121C4×D5—71no—
122C4×D5—72no—
123C4×D5C2×D711yescharacteristic, complemented
124Dic10—71no—
125Dic10C2×D711yescharacteristic, complemented
126C5×C7H(5,𝔽2)11yescharacteristic, complemented, Hall
127H(5,𝔽2)—351noSylow
128C22×C7—51no—
129C22×C7C22×D512yes—
130C2×D7—42no—
131C2×D7—51no—
132C2×D7—52no—
133C2×D7—202no—
134C2×D7—202no—
135C2×D7C22×D512yes—
136C2×D7C22×D511yescharacteristic
137C4×C7—51no—
138C4×C7—52no—
139C4×C7C22×D511yescharacteristic
140Dic7—51no—
141Dic7C22×D511yescharacteristic
142C22×C5—72no—
143C22×C5—71no—
144C22×C5—282no—
145C22×C5C22×D712yes—
146C2×D5—72no—
147C2×D5—71no—
148C2×D5—282no—
149C2×D5—282no—
150C2×D5C22×D711yescharacteristic
151C4×C5—71no—
152C4×C5C22×D711yescharacteristic
153Dic5—71no—
154Dic5C22×D711yescharacteristic
155Dic5C22×D712yes—
156#41—51no—
157#41—351no—
158#41—352no—
159#41—351no—
160#41—351no—
161C2×D4—71no—
162C2×D4—351no—
163C2×D4—352no—
164C2×D4—352no—
165C2×D4—352no—
166C2×D4—351no—
167C2×C7—22no—
168C2×C7—101no—
169C2×C7C23×D511yescharacteristic
170D7—21no—
171D7—22no—
172D7—102no—
173D7—101no—
174C2×C5—22no—
175C2×C5—142no—
176C2×C5—141no—
177C2×C5C23×D711yescharacteristic
178D5—21no—
179D5—142no—
180D5—141no—
181C23—72no—
182C23—352no—
183C23—352no—
184Q8—51no—
185Q8—351no—
186D4—52no—
187D4—72no—
188D4—71no—
189D4—351no—
190D4—352no—
191D4—352no—
192D4—352no—
193D4—351no—
194D4—351no—
195D4—352no—
196D4—351no—
197D4D5×D711yescharacteristic, complemented
198C2×C4—52no—
199C2×C4—51no—
200C2×C4—71no—
201C2×C4—352no—
202C2×C4—352no—
203C2×C4—351no—
204C7#414411yescharacteristic, complemented, Sylow
205C5#655311yescharacteristic, complemented, Sylow
206C22—51no—
207C22—71no—
208C22—72no—
209C22—282no—
210C22—352no—
211C22—351no—
212C22—1402no—
213C22—1402no—
214C22C2×D5×D712yes—
215C4—51no—
216C4—52no—
217C4—71no—
218C4—351no—
219C4C2×D5×D711yescharacteristic
220C2—22no—
221C2—101no—
222C2—141no—
223C2—142no—
224C2—701no—
225C2—702no—
226C2C22×D5×D711yescharacteristic
subgroupG/H
center, FrattiniC2C22×D5×D7
commutator, socle, cosocleC2×C5×C7C24
FittingC5×C7×D4C22
hypercenterD4D5×D7
hypocenterC5×C7H(5,𝔽2)
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. D4×D35C2semidirect
2. C7×#711C2semidirect
3. C5×D4×D7C2semidirect
4. #10587963C2semidirect
5. D7×C22⋊D5C2semidirect
6. C2×#63306C2semidirect
7. #10587952C2semidirect
8. D5×D28C2semidirect
9. #10587946C2semidirect
10. #10587944C2semidirect
11. #10587939C2semidirect
12. C22×D35C22semidirect
13. C22×C5×D7C22semidirect
14. C2×D5×D7C22semidirect
15. C5×C7×D4C22semidirect
16. C22⋊D35C22semidirect
17. D140C22semidirect
18. C4×D35C22semidirect
19. C7×C22⋊D5C22semidirect
20. C2×C7×Dic5C22semidirect
21. C4×C7×D5C22semidirect
22. C7×Dic10C22semidirect
23. C5×C22⋊D7C22semidirect
24. C5×D28C22semidirect
25. C4×C5×D7C22semidirect
26. #63308C22semidirect
27. #63307C22semidirect
28. #63306C22semidirect
29. #63306C22semidirect
30. #63306C22semidirect
31. #63306C22semidirect
32. #63305C22semidirect
33. #63304C22semidirect
34. D7×Dic5C22semidirect
57. D4×D7D5semidirect
67. #711D7semidirect
82. C22×D7C2×D5semidirect
85. C7×D4C2×D5semidirect
91. C22⋊D7C2×D5semidirect
97. D28C2×D5semidirect
101. C4×D7C2×D5semidirect
108. C5×D4C2×D7semidirect
116. C22⋊D5C2×D7semidirect
118. C2×Dic5C2×D7semidirect
123. C4×D5C2×D7semidirect
125. Dic10C2×D7semidirect
126. C5×C7H(5,𝔽2)semidirect
197. D4D5×D7semidirect
204. C7#4144semidirect
205. C5#6553semidirect

Maximal subgroups

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

subgroupindex
D4×D352
C7×#7112
C5×D4×D72
#105879632
D7×C22⋊D52
C2×#633062
#105879522
D5×D282
#105879462
#105879442
#105879392
#65535
#41447