Finite Group Databasebeta

← #11919278

Subgroups — #11919278

Order 1152.

17976 conjugacy classes of subgroups; only the 4701 normal subgroups are shown.

normal subgroups only

This group has 17976 conjugacy classes of subgroups — too many to draw. Only its 4701 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
1C32×#585C211yesmaximal, characteristic, complemented
2#10596760C2112yesmaximal, complemented
3C3⋊D3×H(5,𝔽2)C2120yesmaximal, complemented
4#10596756C2115yesmaximal, complemented
5C2×#64366C2115yesmaximal, complemented
6#87574—34nomaximal
7C32×2−1+4C2216yescomplemented
8C32×H(5,𝔽2)C22110yescomplemented
9C2×C32×#41C22115yescomplemented
10#64367C22120yescomplemented
11#64366C22160yescomplemented
12#64366C221120yescomplemented
13#41×C3⋊D3C221120yescomplemented
14#64364C22130yescomplemented
15C2×#3832C22130yescomplemented
16#64361C22190yescomplemented
17C2×D4×C3⋊D3C22190yescomplemented
18C2×#3828C22145yescomplemented
19C22×C4⋊(C3⋊D3)C22115yescomplemented
20C3×#585D314yescomplemented
21#5968—348no—
22D3×H(5,𝔽2)—380no—
23#5964—360no—
24C2×#1009—360no—
25C23×C3⋊D3C23130yescomplemented
26C32×#41C23160yescomplemented
27C32×#41C23120yescomplemented
28C2×C32×Q8C23115yescomplemented
29C2×C32×D4C23145yescomplemented
30C22×C32×C4C23115yescomplemented
31C2×#638C23190yescomplemented
32#3832C231120yescomplemented
33Q8×C3⋊D3C23140yescomplemented
34#3830C231120yescomplemented
35D4×C3⋊D3C231360yescomplemented
36#3828C23160yescomplemented
37#3828C231180yescomplemented
38C2×C4⋊(C3⋊D3)C23145yescomplemented
39C2×C4⋊(C3⋊D3)C23190yescomplemented
40C2×C4×C3⋊D3C23190yescomplemented
41C2×#634C23115yescomplemented
42H(7,𝔽2)—91noSylow
43C3×2−1+4C2×D3124yescomplemented
44C3×H(5,𝔽2)C2×D3140yescomplemented
45C2×C3×#41C2×D3160yescomplemented
46#1010—380no—
47#1009—3240no—
48#1009—3480no—
49D3×#41—3480no—
50#1007—3120no—
51C2×#239—3120no—
52#1004—3360no—
53C2×D3×D4—3360no—
54C2×#235—3180no—
55C22×D12—360no—
56C23×C32C24115yes—
57C22×C3⋊D3—830no—
58C22×C3⋊D3C24190yes—
59C32×Q8C24120yes—
60C32×D4C24160yes—
61C2×C32×C4C24115yes—
62C2×C32×C4C24145yes—
63#638C241120yes—
64C2×C3⋊Dic3C24130yes—
65C4⋊(C3⋊D3)C24110yes—
66C4⋊(C3⋊D3)C24190yes—
67C4×C3⋊D3C241120yes—
68#634C2416yes—
69#634C24130yes—
70#585—912no—
71#585—915no—
72#585C3⋊D311yescharacteristic, complemented
73C2×H(5,𝔽2)—920no—
74C2×H(5,𝔽2)—915no—
75C23×D3—3120no—
76C3×#41C22×D31240yescomplemented
77C3×#41C22×D3180yescomplemented
78C2×C3×Q8C22×D3160yescomplemented
79C2×C3×D4C22×D31180yescomplemented
80C22×C3×C4C22×D3160yescomplemented
81C2×#67—3360no—
82#239—3480no—
83D3×Q8—3160no—
84#237—3480no—
85D3×D4—31440no—
86#235—3240no—
87#235—3720no—
88C2×D12—3180no—
89C2×D12—3360no—
90C2×C4×D3—3360no—
91C2×Dic6—360no—
92C22×C32—415no—
93C22×C32C25115yes—
94C2×C3⋊D3—490no—
95C2×C3⋊D3C25120yes—
96C32×C4C2511yescharacteristic
97C32×C4C25115yes—
98C3⋊Dic3C25112yes—
992−1+4—920no—
1002−1+4—930no—
1012−1+4C2×C3⋊D316yescomplemented
102H(5,𝔽2)—9120no—
103H(5,𝔽2)—960no—
104H(5,𝔽2)—990no—
105H(5,𝔽2)C2×C3⋊D3110yescomplemented
106C2×#41—9120no—
107C2×#41—930no—
108C2×#41—945no—
109C2×#41C2×C3⋊D3115yescomplemented
110C22×D4—990no—
111C22×D4—915no—
112C23×C3C23×D3160yes—
113C22×D3—3360no—
114C22×D3—24120no—
115C3×Q8C23×D3180yes—
116C3×D4C23×D31240yes—
117C2×C3×C4C23×D3160yes—
118C2×C3×C4C23×D31180yes—
119#67—3480no—
120C2×Dic3—3120no—
121D12—340no—
122D12—3360no—
123C4×D3—3480no—
124Dic6—324no—
125Dic6—3120no—
126C2×C32—215no—
127C2×C32C2611yescharacteristic
128C3⋊D3—220no—
129C24—930no—
130#41—9120no—
131#41—9120no—
132#41—9180no—
133#41—960no—
134#41C22×C3⋊D3160yescomplemented
135#41C22×C3⋊D3120yescomplemented
136C2×Q8—940no—
137C2×Q8—915no—
138C2×Q8C22×C3⋊D3115yescomplemented
139C2×D4—990no—
140C2×D4—9360no—
141C2×D4—990no—
142C2×D4—945no—
143C2×D4C22×C3⋊D3145yescomplemented
144C22×C4—990no—
145C22×C4C22×C3⋊D3115yescomplemented
146C22×C3—460no—
147C22×C3C24×D3160yes—
148C2×D3—380no—
149C2×D3—12360no—
150C3×C4C24×D314yes—
151C3×C4C24×D3160yes—
152Dic3—348no—
153C32H(7,𝔽2)11yescharacteristic, complemented, Sylow
154C23—990no—
155C23—7230no—
156C23C23×C3⋊D3115yes—
157Q8—930no—
158Q8—96no—
159Q8C23×C3⋊D3120yes—
160D4—9120no—
161D4—990no—
162D4—910no—
163D4C23×C3⋊D3160yes—
164C2×C4—930no—
165C2×C4—9120no—
166C2×C4C23×C3⋊D3145yes—
167C2×C4C23×C3⋊D3115yes—
168C2×C3—260no—
169C2×C3C25×D314yes—
170D3—680no—
171C22—415no—
172C22—920no—
173C22—3690no—
174C22C24×C3⋊D3115yes—
175C4—912no—
176C4C24×C3⋊D3115yes—
177C4C24×C3⋊D311yescharacteristic
178C3#8757414yescomplemented
179C2—215no—
180C2—1820no—
181C2C25×C3⋊D311yescharacteristic
subgroupG/H
center, FrattiniC2C25×C3⋊D3
commutator, socle, cosocleC2×C32C26
FittingC32×#585C2
hypercenter#585C3⋊D3
hypocenterC32H(7,𝔽2)
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ #585

Complements

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

NH ≅ G/Ntype
1. C32×#585C2semidirect
2. #10596760C2semidirect
3. C3⋊D3×H(5,𝔽2)C2semidirect
4. #10596756C2semidirect
5. C2×#64366C2semidirect
7. C32×2−1+4C22semidirect
8. C32×H(5,𝔽2)C22semidirect
9. C2×C32×#41C22semidirect
10. #64367C22semidirect
11. #64366C22semidirect
12. #64366C22semidirect
13. #41×C3⋊D3C22semidirect
14. #64364C22semidirect
15. C2×#3832C22semidirect
16. #64361C22semidirect
17. C2×D4×C3⋊D3C22semidirect
18. C2×#3828C22semidirect
19. C22×C4⋊(C3⋊D3)C22semidirect
20. C3×#585D3semidirect
25. C23×C3⋊D3C23semidirect
26. C32×#41C23semidirect
27. C32×#41C23semidirect
28. C2×C32×Q8C23semidirect
29. C2×C32×D4C23semidirect
30. C22×C32×C4C23semidirect
31. C2×#638C23semidirect
32. #3832C23semidirect
33. Q8×C3⋊D3C23semidirect
34. #3830C23semidirect
35. D4×C3⋊D3C23semidirect
36. #3828C23semidirect
37. #3828C23semidirect
38. C2×C4⋊(C3⋊D3)C23semidirect
39. C2×C4⋊(C3⋊D3)C23semidirect
40. C2×C4×C3⋊D3C23semidirect
41. C2×#634C23semidirect
43. C3×2−1+4C2×D3semidirect
44. C3×H(5,𝔽2)C2×D3semidirect
45. C2×C3×#41C2×D3semidirect
72. #585C3⋊D3semidirect
76. C3×#41C22×D3semidirect
77. C3×#41C22×D3semidirect
78. C2×C3×Q8C22×D3semidirect
79. C2×C3×D4C22×D3semidirect
80. C22×C3×C4C22×D3semidirect
101. 2−1+4C2×C3⋊D3semidirect
105. H(5,𝔽2)C2×C3⋊D3semidirect
109. C2×#41C2×C3⋊D3semidirect
134. #41C22×C3⋊D3semidirect
135. #41C22×C3⋊D3semidirect
138. C2×Q8C22×C3⋊D3semidirect
143. C2×D4C22×C3⋊D3semidirect
145. C22×C4C22×C3⋊D3semidirect
153. C32H(7,𝔽2)semidirect
178. C3#87574semidirect

Maximal subgroups

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

subgroupindex
C32×#5852
#105967602
C3⋊D3×H(5,𝔽2)2
#105967562
C2×#643662
#875743